{"1": {"fulltext": "\u00e2\u0096\u00a0mim\\ni\u00c2\u00a7m\\nill,\\niiiiiiiiiiniiil\\n]m\\\\\\\\\\ni|\\nHi\\nliiiiii", "height": "4390", "width": "2718", "jp2-path": "railroadconstruc00webb_0001.jp2"}, "2": {"fulltext": "", "height": "4270", "width": "2530", "jp2-path": "railroadconstruc00webb_0002.jp2"}, "3": {"fulltext": "", "height": "4270", "width": "2530", "jp2-path": "railroadconstruc00webb_0003.jp2"}, "4": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0004.jp2"}, "5": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0005.jp2"}, "6": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0006.jp2"}, "7": {"fulltext": "RAILROAD CONSTRUCTION.\\nTHEORY AND PRACTICE.\\nA TEXT-BOOK FOB THE USE OF STUDENTS IN\\nCOLLEGES AND TECHNICAL SCHOOLS.\\nBY\\nWALTER LOEIXG WEBB, C.E.,\\nAssociate Membey American Society of Civil Engineers:\\nAssistant Professor of Ciuii Engineering in\\nthe University of Pennsylvania\\netc.\\nFIRST EDITION.\\nFIRST THOUSAND.\\nKEW YORK:\\nJOHN WTLEY SONS.\\nLondon CITAPNfAN fe HALL, Limited.\\n1900.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0007.jp2"}, "8": {"fulltext": "8\u00c2\u00a3C0ND COPY,\\nTWO COPIES RECEIVED,\\nL Ibrary of COR^ret%\\nOffice of tli\u00c2\u00ab\\nAPR 3 1900\\nKe^^Uter of Copyrlfhftk\\n1-^\\n.61540\\nCopyright, 1899,\\nBY\\nWALTER LORING WEBB.\\nROBERT DRUMMOND, PRINTKR, NEW YORE.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0008.jp2"}, "9": {"fulltext": "PREFACE.\\nThe preparation of this book was begun several years ago,\\nwhen much of the subject-matter treated was not to be found in\\nprint, or was scattered through many books and pamphlets, and\\nwas hence unavailable for student use. Portions of the book\\nhave already been printed by the mimeograpli process or have\\nbeen used as lecture-notes, and hence have been subjected to\\nthe retining process of classroom use.\\nThe author would call special attention to the following\\nfeatures\\na. Transition curves the multiform-compound-curve method\\nis used, which has been followed by many railroads in this country\\nthe particular curves here developed have the great advantage of\\nbeino- exceedingly simple, and although the method is not theu-\\nretically exact, it is demonstrable that the differences are so\\nsmall that they may safely be neglected.\\nh. A system of earthwork computations by means of a slide-\\nrule (which accompanies the volume) which enables one to com-\\npute readily the volume of the most complicated earthwork\\nforms with an accuracy only limited by the precision of the\\ncross-sectioning.\\nc. The mass curve in earthwork; the theory and use of\\nthis very valuable process.\\nd. Tables I, II, III, and lY have been computed ah novo.\\nTables I and II were checked (after computation) with other\\ntables, whicli are ofcnerallv considered as standard, and all dis-\\ncrepancies were further examined. They are believed to be\\nperfect.\\nIll", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0009.jp2"}, "10": {"fulltext": "IV PREFACE.\\ne. Tables Y, YI, YII, and IX Lave been borrowed, by per-\\nmission, from Ludlow s Mathematical Tables. It is believed\\nthat five- place tables give as accurate results as actual field prac-\\ntice requires. Tables YIII and X have been compiled to con-\\nform with Ludlow s system.\\nThe author wishes to acknowledge his indebtedness to Mr.\\nChas. A. Sims, civil engineer and railroaJ contractor, for read-\\ning and revising the portions relating to the cost of earthwork.\\nSince the book is written primarily for students of railroad\\nengineering in technical institutions, the author has assumed the\\nusual previous preparation in algebra, geometry, and trio-o-\\nnometry.\\nWalter Loring Webb.\\nUniversity of Pennsylvania,\\nPhiladelphia,\\nJan. 1, 1900.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0010.jp2"}, "11": {"fulltext": "TABLE OF CONTENTS.\\nCHAPTER I.\\nRAILROAD SURVEYS.\\nPAGE\\nReconnoissance 1\\n1. Character of a reconnoissance survey. 2. Selection of a general\\nroute. 3. Valley route. 4. Cross-country route. 5. Mountain route.\\n6. Existing maps. 7. Determination of relative elevations. 8. Hori-\\nzontal measurements, bearings, etc. 9. Importance of a good\\nreconnoissance.\\nPreliminary surveys 8\\n10. Character of survey. 11. Cross-section method. 12. Cross-\\nsectioning. 13. Stadia method. 14. First and second pre-\\nliminary survey.\\nLocation surveys 13\\n15. Paper Location. 16. Surveying methods. 17. Form of\\nNotes.\\nCHAPTER II.\\nALIGNMENT.\\nSimple curves 18\\n18. Designation of curves. 19. Length of a subchord. 20. Length of\\na curve. 21. Elements of a curve. 22. Relation between T, B, and\\n23. Elements of a 1\u00c2\u00b0 curve. 24. Exercises. 25. Curve locjition by\\ndeflections. 26. Instrumental work. 27. Curve location b} two\\ntransits. 28. Curve location by tangential offsets. 29. Curve loca-\\ntion by middle ordinates. 30. Curve location by offsets from the\\nlong chord. 31. Use and value of the above methods. 32. Obstacles\\nto location. 33. Modifications of location. 34. Limitations in loca-\\ntion. 35. Determination of the curvature of existing track. 36.\\nProblems.\\nV", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0011.jp2"}, "12": {"fulltext": "VI TABLE OF CONTENTS,\\nPAGE\\nCompound curves 37\\n37. Nature aud use. 38. Mutual relations of the parts of a com-\\npound curve having two branches. 39. Modifications of location.\\n40. Problems.\\nTransition curves 43\\n41. Superelevation of the outer rail on curves. 42. Practical rules\\nfor superelevation. 43. Transition from level to inclined track.\\n44. Fundamental principle of transition curves. 45. Multiform com-\\npound curves. 46. Required length of spiral. 47. To find the ordi-\\nnates of a l\u00c2\u00b0-per-25-feet spiral. 48. To find the deflections from any\\npoint of the spiral. 49. Connection of spiral with circular curve aud\\nwith tangent. 50. Field-work. 51. To replace a simple curve by a\\ncurve with spirals. 52. Application of transition curves to compound\\ncurves. 53. To replace a compound curve by a curve with spirals.\\nVertical curves 61\\n54. Necessity for their use. 55. Required length. 56. Form of\\ncurve. 57. Numerical example.\\nCHAPTER III.\\nEARTHWORK.\\nForm of excavations and embankments 64\\n58. Usual form of cross-section in cut and fill. 59. Terminal pyra-\\nmids and wedges. 60. Slopes. 61. Compound sections. 62. Width\\nof roadbed. 63. Form of subgrade. 64. Ditches. 65. Effect of\\nsodding the slopes, etc.\\nEarthwork surveys 72\\n66. Relation of actual volume to the numerical result. 67. Pris-\\nmoids. 68. Cross-sectioning. 69. Position of slope-stakes.\\nComputation of volume 76\\n70. Prismoidal formula. 71. Averaging end areas. 72. Middle\\nareas. 73. Two level ground. 74. Level sections. 75. Numerical\\nexample, level sections. 76. Equivalent sections. 77. Equivalent\\nlevel sections. 78. Three-level sections. 79. Computation of prod-\\nucts. 80. Five-level sections. 81. Irregular sections. 82. Volume\\nof an irregular p ismoid. 83. True prismoidal correction for ir-\\nregular prismoids. 84 Numerical example irregular sections\\nvolume, with true prismoidal correction. 85, Volume of irregular\\nprismoid, with approximate prismoidal correction. 80. Illustration\\nof value of approximate rules. 87. Cross-sectioning irregular sections.\\n88. Side-hill w^ork. 89. Borrow-pits. 90. Correction for curvature.\\n91. Eccentricity of the center of gravity. 92. Center of gravity of\\nside-hill sections. 93. Examples of curvature correction. 94. Accu-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0012.jp2"}, "13": {"fulltext": "TABLE OF CONTENTS. vii\\nPAGE\\nracy of earthwork computations. 95. Approximate compulations\\nfrom proliles.\\nFormation of embankments Ill\\n9G. Shrinkage of earthwork. 97. Allowance for shrinkage. 98.\\nMethods of forming embankmeuts.\\nComputation of haul IIG\\n99. Nature of subject. 100. Mass diagram. 101. Properties of\\nthe mass curve. 102. Area of the mass curve. 103. Value of the\\nmass diagram. 104. Changing the grade line. 105. Limit of free\\nhaul.\\nCost of earthwork 136\\n106. General divisions of the subject. 107. Loosening. 108. Load-\\ning. 109. Hauling. 110. Choice of method of haul dependent on\\ndistance. 111. Spreading. 113. Keeping roadways in order. 113.\\nRepairs, wear, depreciation, and interest on cost of plant. 114. Super-\\nintendeuce and incidentals. 115. Contractor s profit. 116. Limit of\\nprofitable haul.\\nBlasting 143\\n117. Explosives. 118. Drilling. 119. Position and direction of\\ndrill-holes. 130. Amount of explosive. 121. Tamping. 133. Ex-\\nploding the charge. 123. Cost. 124. Classification of excavated\\nmaterial. 135. Specifications for earthwork.\\nCHAPTER IV.\\nTRESTLES.\\n126. Extent of use. 137. Trestles vs. embankments. 138. Two\\nprincipal types.\\nPile trestles 155\\n129. Pile bents. 130. Methods of driving piles. 131. Pile-driving\\nformula. 133. Pile-points and pile-shoes. 133. Details of design.\\n134. Cost of pile trestles.\\nFramed trestles 163\\n135, Typical design. 136. Joints. 137. Multiple-story construc-\\ntion. 138. Span. 139. Foundations. 140. Longitudinal bracing.\\n141. Lateral bracing. 143. Abutments.\\nFloor systems 167\\n143. Stringers. 144. Corbels. 145. Guard-rails. 14G. Ties on\\ntrestles. 147. Superelevation of the outer rail on curves. 148. Pro-\\ntection from fire. 149. Timber. 150. Cost of framed timber\\ntrestles.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0013.jp2"}, "14": {"fulltext": "Tiii TABLE OF CONTENTS,\\nPAGE\\nDesign of wooden trestles 174\\n151. Common practice. 152. Required elements of strength. 153.\\nStrength of timber. 154, Loading. 155. Factors of safety. 156.\\nDesign of stringers. 157. Design of posts. 158. Design of caps and\\nsills. 159. Bracing.\\nCHAPTER V.\\nTUNNELS.\\nSurveying\\n160. Surface surveys. 161. Surveying down a shaft. 162. Under-\\nground surveys. 163. Accuracy of tunnel surveying.\\nDesign\\n164. Cross-sections. 165. Grade. 166. Lining. 167. Sljafts.\\n168. Drains.\\nConstruction\\n169. Headings. 170. Enlargement. 171. Distinctive features of\\nvarious methods of construction. 172. Ventilation duriug construc-\\ntion. 173. Excavation for the portals. 174. Tunnels vs. open cuts.\\n175. Cost of tunneling.\\nCHAPTER VI.\\nCULVERTS AND MINOR BRIDGES.\\n176. Definition and object. 177. Elements of the design.\\nArea of the waterway 20o\\n178. Elements involved. 179. Methods of computation of area.\\n180. Empirical formulce. 181. Value of empirical formulse. 182.\\nResults based on observation. 183. Degree of accuracy required.\\nPipe culverts\\n184, Advantages. 185. Construction. 186. Iron-pipe culverts.\\n187. Tile-pipe culverts.\\n910\\nBox culverts\\n188. Wooden box culverts. 189. Stone box culverts. 190. Old-\\nrail culverts.\\nArch culverts 15\\n191. Influence of design on flow. 192. Example of arch-culvert\\ndesign.\\nMinor openings ^1^\\n193. Cattle-guards. 194. Cattle-passes. 195. Standard stringer\\nand I-beam bridges.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0014.jp2"}, "15": {"fulltext": "TABLE OF CONTENTS. IX\\nCHAPTER VII.\\nBALLAST.\\nPAGE\\n196. Purpose and requirements. 197. Materials. 198. Cross-\\nsections. 199. Methods of laying ballast. 200. Cost.\\nCHAPTER VIII.\\nTIES\\nAND OTHER FORMS OF RAIL SUPPORT.\\n201. Various methods of supporting rails. 202. Economics of ties.\\n007\\nWooden ties\\n203. Choice of wood. 204. Durability. 205. Dimensions. 206.\\nSpacing. 207. Specifications. 208. Regulations for laying and\\nrenewing ties. 209. Cost of ties.\\nPreservative processes for wooden ties 232\\n210. General principle. 211. Vulcanizing. 212. Creosoting. 213.\\nBurnettizing. 214. Kyanizing. 215. Wellhouse (or zinc-tannin)\\nprocess. 216. Cost of treating. 217. Economics of treated ties.\\nOQQ\\nMetal ties\\n218. Extent of use. 219. Durability. 220. Form and dimensions\\nof metal cross-ties. 221. Fastenings. 222. Cost. 223. Bowls or\\nplates. 224. Longitudinals.\\nCHAPTER IX.\\nRAILS.\\n225. Early forms. 226. Present standard forms. 227. Weight\\nfor various kinds of traffic. 228. Effect of stiffness on traction. 229.\\nLength of rails. 230. Expansion of rails. 231. Rules for allowing\\nfor temperature. 232. Chemical composition. 233. Testing. 234.\\nRail wear on tangents. 235. Rail wear on curves. 236. Cost of rails.\\nCHAPTER X.\\nra il-fastenings.\\nRail-joints 255\\n237. Theoretical requirements for a perfect joint. 238. Efficiency\\nof the ordinary angle bar. 239. Effect of rail-gap at joints. 240.\\nSupported, suspended, and bridge joints. 241. Failures of rail joints.\\n242. Standard angle-bars. 243. Later designs of rail-joints.\\nTie-plates 260\\n244. Advantages. 245. Elements of the design. 246. Methods of\\nsetting.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0015.jp2"}, "16": {"fulltext": "X TABLE OF CONTENTS.\\nPAGE\\nSpikes 263\\n247. Requirements. 248. Driving. 249. Screws and bolts. 250.\\nWooden spikes.\\nTrack-bolts and nut-locks 266\\n251. Essential requirements. 252. Design of track-bolts. 253.\\nDesign of nut-locks.\\nCHAPTER XI.\\nswitches and crossings.\\nSwitch construction 271\\n254. Essential elements of a switch. 255. Frogs. 256. To find\\nthe frog number. 257. Stub switches, 258. Point switches. 259.\\nSwitch-stauds. 260. Tie-rods. 261. Guard-rails.\\nMathematical design of switches 278\\n262. Design with circular lead rails. 263. Effect of straight frog-\\nrails. 264. Effect of straight point-rails. 265. Combined effect of\\nstraight frog rails and straight point-rails. 266. Comparison of the\\nabove methods. 267. Dimensions for a turnout from the outer side\\nof a curved track. 268. Dimensions for a turnout from the inner\\nside of a curved track. 269. Double turnout from a straight track.\\n270. Two turnouts on the same side. 271. Connecting curve from a\\nstraight track. 272. Connecting curve from a curved track to the\\noutside. 273. Connecting curve from a curved track to the inside.\\n274. Crossover between two parallel straight tracks. 275. Crossover\\nbetween two parallel curved tracks. 276. Practical rules for switch-\\nlaying.\\nCrossings 300\\n277. Two straight tracks. 278. One straight and one curved track.\\n279. Two curved tracks.\\nAppendix. The Adjustments of Instruments 303\\nTables.\\nI. Radii of curves 314\\nII. Tangents and external distances to a 1\u00c2\u00b0 curve. 318\\nIII. Switch leads and distances 321\\nIV. Transition curves 322\\nV. Logarithms of numbers 325\\nVI. Logarithmic sines and tangents of small angles 345\\nVn. Logarithmic sines, cosines, tangents, and cotangents 348\\nVIII. Logarithmic versed sines and external secants 393\\nIX. Natural sines, cosines, tangents and cotangents 439\\nX. Natural versed sines and external secants 444\\nXI. Useful trigonometrical formulae 449\\nIndex 451", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0016.jp2"}, "17": {"fulltext": "RAILROAD CONSTRUCTION.\\nCHAPTER I.\\nRAILROAD SURVEYS.\\nThe proper conduct of railroad surveys presupposes an\\nadequate knowledge of almost the whole subject of railroad\\nengineering, and particularly of some of the complicated ques-\\ntions of Railroad Economics, which are not generally studied\\nexcept at the latter part of a course in railroad engineering, if\\nat all. This chapter will therefore be chiefly devoted to\\nmethods of instrumental work, and the problem of choosing a\\ngeneral route will be considered only as it is influenced by the\\ntopography or by the application of those elementary principles\\nof liailroad Economics which are self-evident or which may be\\naccepted by the student until he has had an opportunity of\\nstudying those principles in detail.\\nRECONNOISSANCE SURVEYS.\\n1. Character of a reconnoissance survey. A reconnoissance\\nsurvey is a very hasty examination of a belt of country to de-\\ntermine which of all possible or suggested routes is the most\\npromising and best worthy of a more detailed survey. It is\\nessentially very rough and rapid. It aims to discover those\\nsalient features which instantly stamp one route as distinctly\\nsuperior to another and so narrow the choice to routes which\\nare so nearly equal in value that a more detailed survey is nec-\\nessary to decide between them.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0017.jp2"}, "18": {"fulltext": "2 BAILBOAD CONSTRVCTION. \u00c2\u00a72.\\n2. Selection of a general route. The general question of\\nrunning a railroad between two towns is usually a financial rather\\nthan an engineering question. Financial considerations usually\\ndetermine that a road must pass through certain more or less\\nimportant towns between its termini. When a railroad runs\\nthrough a thickly settled and very flat country, where, from a\\ntopographical standpoint, the road may be ran by any desired\\nroute tlie rio;ht-of-way agent sometimes has a greater influ-\\nence in locating the road than the engineer. But such modifi-\\ncations of alignment, on account of business considerations, are\\nforeign to the engineer s side of the subject, and it will be here-\\nafter assumed that topography alone determines the location of\\nthe line. The consideration of those larger questions combin-\\ning finance and engineering (such as passing by a town on ac-\\ncount of the necessary introduction of heavy grades hi order to\\nreach it) is likewise ignored.\\n3. Valley route. This is perhaps the simplest problem. If\\nthe two towns to be connected lie in the same valley, it is\\nfrequently only necessary to run a line which shall have a nearly\\nuniform grade. The reconnoissance problem consists largely in\\ndetermining the difference of elevation of the two termini of\\nthis division and the approximate horizontal distance so that the\\nproper grade may be chosen. If there is a large river running\\nthrough the valley, the road will probably remain on one side\\nor the other throughout the whole distance, and both banks\\nshould be examined by the reconnoissance party to determine\\nwhich is preferable. If the river may be easily bridged, both\\nbanks may be alternately used, especially when better alignment\\nis thereby secured. A river valley has usually a steeper slope\\nin the upper part than in the lower part. A uniform grade\\nthroughout the valley will therefore require that the road climbs\\nup the side slopes in the lower part of the valley. In case the\\nrulino- o-rade for tlie whole road is as great as or greater\\nThe ruling grade may liere be loosely defined as the maximum grade\\nwhich is permissible. This definition is not strictly true, as may be seen later\\nwhen studying Railroad Economics, but it may here serve the purpose.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0018.jp2"}, "19": {"fulltext": "5. RAILROAD SURVEYS. 3\\nthan the steepest natural valley slope, more freedom may be\\nused in adopting that alignment which has the least cost\\nregardless of grade. The natural slope of large rivers is almost\\ninvariably so low that grade has no influence in determiniTig the\\nchoice of location. When bridging is necessary, the river\\nbanks should be examined for suitable locations for abutments\\nand piers. If the soil is soft and treacherous much difficultv\\nmay be experienced and the choice of route may be laro;elv\\ndetermined by the difficulty of bridging the river except at\\ncertain favorable places.\\n4. Cross-country route. A cross-country route always has one\\nor more sunnnits to be crossed. The problem becomes more\\ncomplex on account of the greater nundjer of possible solutions\\nand the difficulty of jiroperly weighing the advantages and dis-\\nadvantages of each. The general aim should be to choose the\\nlowest summits and the highest stream crossings, provided that\\nby so doing the grades between these determining points shall\\nbe as low as possible and shall not be greater than the ruling\\ngrade of the road. Xearly all railroads combine cross-country\\nand valley routes to some extent. Usually the steepest natural\\nslopes are to be found on the cross-country routes, and also the\\ngreatest difficulty in securing a low through grade. An approx-\\nimate determination of the ruling grade is usually made during\\nthe reconnoissance. If the ruling grade has been previously\\ndecided on by other considerations, the leading feature of the\\nreconnoissance survey will be the determination of a general\\nroute along which it will be possible to survey a line whose\\nmaximum orrade shall not exceed the rulinir s-rade.\\n5. Mountain route. The streams of a mountainous ree:ion\\nfrequently have a slope exceeding the desired ruling grade. In\\nsuch cases there is no possibility of securing the desired grade\\nby following the streams. The penetration of such a region\\nmay only be accomplished by development accompanied\\nperhaps by tunneling. Development consists in deliber-\\nately increasing the length of the road between two extremes\\nof elevation so that the rate of grade shall be as low as desired.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0019.jp2"}, "20": {"fulltext": "SAILBOAD CONSTBTICTION.\\n\u00c2\u00a75.\\nThe usual method of accomphshing this is to take advantage of\\nsome convenient formation of the ground to introduce some\\nlateral deviation. The methods may be somewhat classified as\\nfollows\\n(a) Running the line up a convenient lateral valley, turning\\na sharp curve and working back up the opposite slope. As\\nshown in Fig. 1, the considerable rise between and was\\nFig. 1.\\nsurmounted by starting off in a very different direction from\\nthe general direction of the road then, when about one-half of\\nthe desired rise had been obtained, the line crossed the valley\\nand continued the climb along the opposite slope, (b) Switch-\\nhack. On the steep side-hill BCD (Fig. 1) a very considerable\\ngain in elevation was accomplished by the switchback CD.\\nThe gain in elevation from B \\\\o D very great. On the\\nother hand, the speed must always be slow there are two com-\\nplete stoppages of the train for each run all trains must run\\nbackward from C to D. (c) Bridge spiral. When a valley is\\nso narrow at some point that a bridge or viaduct of reasonable\\nlength can span the valley at a considerable elevation above the\\nbottom of the valley, a bridge spiral may be desirable. In", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0020.jp2"}, "21": {"fulltext": "6.\\nRAILROAD SURVEYS.\\nb\\nFig. 2 tlie line ascends tlic stream valley past yl, crosses tlie\\nstream at B, works back to the narrow ])lace at C\\\\ and there\\ncrosses itself, having gained perhaps 100 feet in elevation,\\n(d) Tunnel spiral. This is the reverse of the previous plan.\\nV,\\n7//// \\\\\\\\\\\\\\\\V\\\\^.\\n/^/iii\\\\\\\\\\\\\\\\\\nFig. 3.\\nFig. 3\\nIt implies a thin steep ridge, so thin at some place that a tunnel\\nthrough it will not be excessively long. Switchbacks and\\nspirals are sometimes necessary in mountainous countries, but\\nthey should not be considered as normal types of construction.\\nA region must be very difficult if these devices cannot be\\navoided.\\nRack railways and cable roads, although types of mountain\\nrailroad construction, will not be here considered.\\n6. Existing maps. The maps of the U. S. Geological Survey\\nare exceedingly valuable as far as they have been completed.\\nSo far as topographical considerations are concerned, they\\nalmost dispense with the necessity for the reconnoissance and\\nfirst preliminary surveys. Some of the State Survey maps\\nwill give practically the same information. County and town-\\nship maps can often be used for considerable information as to the\\nrelative Jiorizoiital position of governing points, and even some", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0021.jp2"}, "22": {"fulltext": "6 RAILROAD CONSTRVCTION, 7.\\napproximate data regarding eleA^ations may be obtained bj a\\nstudy of the streams. Of course such information will not dis-\\npense with surveys, but will assist in so planning them as to\\nobtain the best information with the least work. AVhen the\\nrelative horizontal positions of points are reliably indicated on a\\nmap, the reconnoissance may be reduced to the determination\\nof the relative elevations of the governing points of the route.\\n7. Determination of relative elevations. A recent description\\nof European methods includes spirit-leveling in the reconnois-\\nsance work. This may be due to the fact that, as indicated\\nabove, previous topographical surveys have rendered unnecessary\\nthe exploratory survey which is required in a new country,\\nand that their reconnoissance really corresponds more nearly to\\nour preliminary.\\nThe perfection to which barometrical methods have been\\nbrought has rendered it possible to determine differences of\\nelevation with sufficient accuracy for reconnoissance purposes\\nby the combined use of a mercurial and an aneroid barometer.\\nThe mercurial barometer should be kept at headquarters, and\\nreadings should be taken on it at such frequent intervals that\\nany fluctuation is noted, and throughout the period that observa-\\ntions with the aneroid are taken in the field. At each observa.\\ntion there should also be recorded the time, the readinsr of the\\nattached thermometer, and the temperature of the external\\nair. For uniformity, the mercurial readings should then be\\nreduced to 32\u00c2\u00b0 F. Before starting out, a reading of the\\naneroid should be taken at headquarters coincident with a read-\\ning of the mercurial. The difference is one value of the correc-\\ntion to the aneroid. As soon as the aneroid is brouo-ht back\\nanother comparison of readings should be made. Even though\\nthere has been considerable rise or fall of pressure in the interval,\\nthe difference in readings (the correction) should be substantially\\nthe same provided the aneroid is a good instrument. The best\\naneroids read directly to of an inch of mercury and may be\\nestimated to yo^qt iiioh which corresponds to about 0.9\\nfoot dift erence of elevation. In the field there should be read,", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0022.jp2"}, "23": {"fulltext": "8. RAILROAD SURVEYS. 7\\nat each point whose elevation is desired, tlie aneroid, the time,\\n-and tlie temperature. These readings, corrected by the mean\\nvahie of the correction between the aneroid and the mercurial,\\nshould then be combined with tlie reading of the mercurial\\n(interpolated if necessary) for the times of the aneroid observa-\\ntions and the difference of elevation obtained. [See the autlior s\\nProblems in the Use and Adjustment of Engineering In-\\nstruments, Prob. 22.] Important points should be observed\\nmore than once if possible. Such duplicate observations will be\\nfound to give surprisingly concordant results even when a\\ngeneral fluctuation of atmospheric pressure so modifies the\\ntabulated readings that an agreement is not at first apparent.\\nYariations of pressure produced by high Avinds, thunder-storms,\\n\u00e2\u0096\u00a0etc., will generally vitiate possible accuracy by this metliod,\\nJ3y headquarters is meant any place wliose elevation above\\na,ny given datum is known and where the mercurial may be\\nplaced and observed while observations within a range of several\\nmiles are made with the aneroid. If necessary the elevation of\\na new headquarters may be determined by the above method,\\nbut there sfiould be if possible several independent observations\\nwhose accordance will give a fair idea of tlieir accuracy.\\nThe above method should be neither sliglited nor used for\\nmore than it is worth. Wlien properly used, the errors are\\ncompensating rather than cumulative. Wlien used, for example,\\nto determine that a pass J^ is 260 feet higlier than a determined\\nbridge crossing at A which is six miles distant, and tliat another\\npass 6^ is 310 feet higher than A and is ten miles distant, the\\nfigures, even with all necessary allowances for inaccuracy, will\\ngive an engineer a good idea as to the choice of route especially\\nas affected by ruling grade. There is no comparison between\\nthe time, and labor involved in obtaining the above information\\nby barometric and by spirit-leveling methods, and ybr recon-\\nnoissance purposes the added accuracy of the spirit-leveling\\nmethod is hardly worth its cost.\\n8. Horizontal measurements, bearings, etc. AVhen there is\\nno map which may be depended on, or when only a skeleton", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0023.jp2"}, "24": {"fulltext": "8 RAILROAD CONSTRUCTION. 9.\\nmap is obtainable, a rapid survey, sufficiently accurate for the\\npurpose, may be made by using a pocket compass for bearings\\nand a telemeter, odometer, or pedometer for distances. The\\ntelemeter [stadia] is more accurate, but it requires a definite clear\\nsight from station to station, which may be difficult through a\\nwooded country. The odometer, which records the revolutions\\nof a wheel of known circumference, may be used even in rough\\nand wooded country, and the results may be depended on to a\\nsmall percentage. The pedometer (or ^^ace -measurer) depends\\nfor its accuracy on the actual movement of the mechanism for\\neach pace and on the uniformity of the pacing. Its results are\\nnecessarily rough and approximate, but it may be used to fill\\nin some intermediate points in a large skeleton map. A hand-\\nlevel is also useful in determining the relative elevation of various\\ntopographical features which may have some bearing on the\\nproper location of the road.\\n9. Importance of a good reconnoissance. The foregoing in-\\nstruments and methods should be considei-ed only as aids in\\nexercising an educated common sense, without which a proper\\nlocation cannot be made. The reconnoissance survey should com-\\nmand the best talent and the greatest experience available.\\nIf the general route is properly chosen, a comparatively low\\norder of engineering skill can fill in a location which will prove\\na paying railroad property but if the general route is so chosen\\nthat the ruling grades are high and the business obtained is small\\nand subject to competition, no amount of perfection in detailed\\nalignment or roadbed construction can make the road a profitable\\ninvestment.\\nPRELIMINAKT SURVEYS.\\n10. Character of survey. A preliminary railroad survey is\\nproperly a topographical survey of a belt of country which has\\nbeen selected during the reconnoissance and within which it is\\nestimated that the located line will lie. The width of this belt\\nwill depend on the character of the country. When a railroad", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0024.jp2"}, "25": {"fulltext": "\u00c2\u00a711\\nRAILROAD SURVEYS.\\n9\\nis to follow a river having very steep banks the choice of loca-\\ntion is sometimes limited at places to a very few feet of width\\nand the belt to be surveyed may I)e correspondingly narrowed.\\nIn very flat coimtry the desired width may be only limited by the\\nability to survey points with sufficient accuracy at a considera])le\\ndistance from w^hat may be called the backbone line of the\\nsurvey.\\n11. Cross-section method. This is the only feasible method\\nin a wooded country, and is employed by many for all kinds\\nof country. The hackbone line is surveyed either by observ-\\ning magnetic bearings with a compass or by carrying forward\\nFig. 4.\\nabsolute azimuths with a transit. The compass method lias\\nthe disadvantages of hmited accuracy and the possibility of", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0025.jp2"}, "26": {"fulltext": "10 RAILROAD CONSTRUCTION. 12.\\nconsiderable local error owing to local attraction. On the other\\nhand there are the advantages of greater simplicity, no necessity\\nfor a back rodman, and tlie fact that the errors are purely\\nlocal and not cumulative, and may be so limited, with care, that\\nthey will cause no vital error in the subsequent location survey.\\nThe transit method is essentially more accurate, but is liable\\nto be more laborious and troublesome. If a large tree is\\nencountered, either it must be cut down or a troublesome opera-\\ntion of offsetting must be used. If the compass is employed\\nunder these circumstances, it need only be set up on the far side\\nof the tree and the former bearing produced. An error in\\nreading a transit azimuth will be carried on throughout the\\nsurvey. An error of only five minutes of arc will cause an off-\\nset of nearly eight feet in a mile. Large azimuth errors may,\\nhowever, be avoided by immediately checking each new azimuth\\nwith a needle reading. It is advisable to obtain true azimuth\\nat the beginning of the survey by an observation on the sun or\\nPolaris, and to check the azimuths every few miles by azimuth\\nobservations. Distances along the backbone line should be\\nmeasured with a chain or steel tape and stakes set every 100\\nfeet. When a course ends at a substation, as is usually the case,\\nthe remaining portion of the 100 feet should be measured along\\nthe next course. The level party should immediately obtain the\\n\u00e2\u0080\u00a2elevations (to the nearest tenth of a foot) of all stations, and also\\nof the lowest points of all streams crossed and even of dry gullies\\n^hicli would require culverts.\\n12. Cross-sectioning. It is usually desirable to obtain con-\\ntours at five-foot intervals. This may readily be done by the\\nuse of a Locke level (w hich should be held on top of a simple\\nfive-foot stick), a tape, and a rod ten feet in length graduated\\nto feet and tenths. The method of use may perhaps be best\\nexplained by an example. Let Fig. 5 represent a section per-\\npendicular to the survey line such a section as would be made\\nby the dotted lines in Fig. 4. C represents the station point.\\nIts elevation as determined by the level is, say, 158.3 above\\ndatum. When the Locke level on its five-foot rod is placed at", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0026.jp2"}, "27": {"fulltext": "\u00c2\u00a712.\\nRAILROAD SURVEYS.\\n11\\nC^ the level has an elevation of 163.3. Therefore when a point\\nis found (as at a) where the level will read 3.3 on the rod, that\\nFig. 5.\\npoint has an elevation of 160.0 and its distance from the center\\ngives the position of the 160-foot contour. Leaving the long\\nrod at that point (rt), carry the level to some point (b) such that\\nthe level will sight at the toj of the rod. h is then on the 165-\\nFiG. 6.\\nfoot contour, and the horizontal distance ah added to the liori-\\nzontal distance ac gives the position of that contour from tlie\\ncenter. The contours on the lower side are found similarly.\\nThe first rod reading will he 8.3, giving the 155-foot contour.\\nPlot the results in a note-book which is ruled in cpiarter-inch\\nsquares, using a scale of 100 feet per inch in both directions.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0027.jp2"}, "28": {"fulltext": "12 BAILROAD CONSTRUCTION. 13.\\nPlot tlie work up the page then when looking ahead along the\\nline, the work is properly oriented. When a contonr crosses\\nthe survey line, the place of crossing may be similarly deter-\\nmined. If the ground flattens out so tliat five-foot contours are\\nvery far apart, the absolute elevations of points at even fifty-\\nfoot distances from the center should be determined. The\\nmethod is exceedingly rapid. Whatever error or inaccuracy\\noccurs is confined in its effect to the oue station where it occurs.\\nThe work being thus plotted in the field, unusually irregular\\ntopography may be plotted with greater certainty and no great\\nerror can occur without detection. It would even be possible\\nby this method to detect a gross error that might have been\\nmade by the level party.\\n13. Stadia method. This method is best adapted to fairly\\nopen country where a shot to any desired point may be\\ntaken without clearing. The haclcbone survey line is the same\\nas in the previous method except that each course is limited to\\nthe practicable length of a stadia sight. The distance between\\nstations should be checked by foresight and backsight also the\\nvertical angle. Azimuths should be checked by the needle.\\nConsidering the vital importance of leveling on a railroad survey\\nit might be considered desirable to run a line of levels over the\\nstadia stations in order that the leveling may be as precise as\\npossible but when it is considered that a preliminary survey is\\na somewhat hasty survey of a route that onay be abandoned, and\\nthat the errors of leveling by the stadia method (which are com-\\npensating) may be so minimized that no proposed route would\\nbe abandoned on account of such small error, and that the effect\\nof such an error may be easily neutralized by a slight change in\\nthe location, it may be seen that excessive care in the leveling\\nof the preliminary survey is hardly justifiable.\\nSince the students taking this work are assumed to be familiar\\nwith the methods of stadia topographical surveys, this j^art of\\nthe subject will not be further elal)orated.\\n14. First and second preliminary surveys. Some engi-\\nneers advocate two preliminary surveys. When this is done,", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0028.jp2"}, "29": {"fulltext": "\u00c2\u00a715. RAILROAD SURVEYS. 13\\nthe first is a very rapid survey, made perhaps witli a compass,\\nand is only a better grade of reconnoissance. Its aim is to\\nrapidly develop the facts which will decide for or against any\\nproposed route, so that if a route is found to be unfavorable\\nanother more or less modified route may be adopted without\\nhaving wasted considerable time in the survey of useless details.\\nBy this time the student should have grasped the fundamental\\nidea that both the reconnoissance and preliminary surveys are\\nnot surveys of li)ies but of areas that their aim is to survey\\nonly those topographical features which would have a deter-\\nmininof influence on anv railroad line which mii^ht be constructed\\nthrough that particular territory, and that the vahie of a locating\\nengineer is largely measured by his ability to recognize those\\ndetermining influences with the least amount of work from his\\n-surveying corps. Frequently too little time is spent on the\\ncomparative study of ]u eliminary lines. A line will be hastily\\ndecided on after very little study it will then be surveyed with\\nminute detail and estimates carefully worked up, and the claims\\nof any other suggested route will then be handicapped, if not\\ndisregarded, owing to an unwillingness to discredit and throw\\naway a large amount of detailed surveying. The cost of two or\\nthree extra preliminary surveys {at critical 2 oints and not over\\nthe whole line) is utterly insignificant compared with the j^rob-\\nable improvement in the operating value of a line located\\nafter such a comparative study of preliminary lines.\\nLOCATION SURVEYS.\\n15. Paper location. When the preliminary survey has\\nbeen plotted to a scale of 200 feet per inch and the contours\\ndrawn in, a study may be made for the location survey. Disre-\\ngarding for the present the effect on location of transition curves,\\nthe alignment may be said to consist of straight lines (or tan-\\ngents and circular curves. The paper location therefore\\nconsists in plotting on the preliminary map a succession of\\nstraight lines which are tangent to the circular curves connect-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0029.jp2"}, "30": {"fulltext": "14 RAILROAD CONSTRUCTION. 15.\\ning tliem. Tlie determining points should first be considered.\\nSuch points are the termini of the road, the lowest practicable\\npoint over a summit, a river-crossing, etc. So far as is possi-\\nble, having due regard to other considerations, the road should\\nbe a surface road, i.e., the cut and fill should be made as\\nsmall as possible. The maximum permissible grade must also\\nhave been determined and duly considered. The method of\\nlocation differs radically according as the lines joining the deter-\\nmining points have a very low grade or have a grade that ap-\\nproaches the maximum permissible. With very low natural\\ngrades it is only necessary to strike a proper balance between\\nthe requirements for easy alignment and the avoidance of exces-\\nsive earthwork. When the grade between two determined\\npoints approaches the maximum, a study of the location may be\\nbegun by finding a strictly surface line which will connect those\\npoints with a line at the given grade. For example, suppose\\nthe required grade is 1.6^ and that the contours are drawn at\\n5-foot intervals. It will require 312 feet of 1.6^ grade to rise\\n5 feet. Set a pair of dividers at 312 feet and step off this in-\\nterval on successive contours. This line will in general be very\\nirregular, but in an easy country it may lie fairly close to the\\nproper location line, and even in difficult country such a surface\\nline will assist greatly in selecting a suitable location. When the\\nlarger part of the Kne will evidently consist of tangents, the tan-\\ngents should be first located and should then be connected by\\nsuitable curves. When the curves predominate, as they gener-\\nally will in mountainous country, and particularly when the line\\nis purposely lengthened in order to reduce the grade, the curves\\nshould be plotted first and the tangents may then be drawn\\nconnecting them. Considering the ease with which such lines\\nmay be drawn on the preliminary map, it is frequently advisable,\\nafter making such a paper location, to begin all over, draw a\\nnew line over some specially difficult section and compare re-\\nsults. Profiles of such lines may be readily drawn by noting their\\nintersection with each contour crossed. Drawing on each profile\\nthe required grade line will furnish an approximate idea of the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0030.jp2"}, "31": {"fulltext": "16. BAILROAD SURVEYS, 15\\ncoTTiparative amount of earthwork required. After deciding on\\nthe paper location, the length of each tangent, the central angle\\n(see 21), and the radius of each curve sliould be measured as\\naccurately as possible. Since a slight error made in such meas-\\nurements, taken from a map with a scale of 200 feet per inch,\\nwould by accumulation cause serious discrepancies between the\\nplotted location and the location as afterward surveyed in the\\nfield, frequent tie lines and angles should be determined between\\nthe ])lotted location line and the preliminary line, and the loca-\\ntion should be altered, as may prove necessary, by changing the\\nlength of a tangent or changing the central angle or radius of a\\ncurve, so that the agreement of the check-points will be suffi-\\nciently close. The errors of an inaccurate preliminary survey\\nmay thus be easily neutralized (see 33). When the pre-\\nliminary line has been properly run, its backbone line will\\nlie very near the location line and will probably cross it at fre-\\nquent intervals, thus rendering it easy to obtain short and nu-\\nmerous tie lines.\\n16. Surveying methods. A transit should be used for align-\\nment, and only precise work is allowable. The transit stations\\nshould be centered with tacks and should be tied to witness-\\nstakes, which should be located outside of the range of the earth-\\nwork, so that they will neither be dug up nor covered up. All\\noriginal property lines lying within the limits of the right of way\\nshould be surveyed with reference to the location line, so that\\nthe right-of-way agent may have a proper basis for settlement.\\nWhen the property lines do not extend far outside of the re-\\nquired right of way they are frequently surveyed completely.\\nThe leveler usually reads the target to the nearest thousandth\\nof a foot on turning-points and bench-marks, but reads to the\\nnearest tenth of a foot for the elevation of the ground at\\nstations. Considering that yif-oir angular value\\nof only 7 seconds at a distance of 300 feet, and that one division\\nof a level-bubble is usually about 30 seconds, it may be seen that\\nit is a useless refinement to read to thousandths unless corre-\\nsponding care is taken in the use of the level. The leveler", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0031.jp2"}, "32": {"fulltext": "16 RAILROAD CONSTRUCTION. 17.\\nshould also locate liis bench-marks outside of the range of\\nearthwork. A knob of rock protruding from the ground affords\\nan excellent mark. A large nail, driven in the roots of a tree,\\nwhich is not to be disturbed, is also a good mark. These marks\\nshould be clearly described in the note-book. The leveler should\\nobtain the elevation of the ground at all station-points also at\\nall sudden breaks in the profile line, determining also the distance\\nof these breaks from the previous even station. This will in-\\nclude the position and elevation of all streams, and even dry\\ngullies, which are crossed.\\nMeasurements should preferably be made with a steel tape,\\ncare being taken on steep ground to insure horizontal measure-\\nments. Stakes are set each 100 feet, and also at the beginning\\nand end of all curves. Transit-points (sometimes called plugs\\nor hubs should be driven flush with the ground, and a\\nwitness- stake, having tlie number of the station, should\\nbe set three feet to the right. For example, tlie witness-stake\\nmight have on one side 137 69.92, and on the other side\\nP C 4\u00c2\u00b0 K, which would signify that the transit hub is 69.92\\nfeet beyond station 137, or 13769.92 feet from the beginning of\\nthe line, and also that it is the point of curve of a 4\u00c2\u00b0-\\ncurve which turns to the right.\\nAlignment. The alignment is evidently a part of the loca-\\ntion survey, but, on account of the magnitude and importance\\nof the subject, it will be treated in a separate chapter.\\n17. Form of Notes. Although the Form of ]N otes cannot be\\nthoroughly understood until after curves are studied, it is nere\\nintroduced as being the most convenient place. The right-hand\\npage should have a sketch showing all roads, streams, and\\nproperty lines crossed with the bearings of those lines. This\\nshould be drawn to a scale of 100 feet per inch the quarter-\\ninch squares which are usually ruled in note-books giving con-\\nvenient 2 5 -foot spaces. This sketch will always be more or less\\ndistorted on curves, since the center line is always shown as\\nstraight regardless of curves. The station points Sta. in\\nfirst column, left-hand page) should be placed opposite to their", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0032.jp2"}, "33": {"fulltext": "\u00c2\u00a717.\\nRAILROAD SURVKYS.\\n17\\nsketched positions, which means that even stations will be\\nrecorded on every fourth line. This allows three intermediate\\nlines for substations, which is ordinarily more than sufficient.\\nThe notes should read up the page, so that the sketch will be\\nproperly oriented when looking ahead along the line. The\\nother columns on the left-hand page will be self-explanatory\\nwhen the subject of curves is understood. If the calculated\\nbearings are based on azimuthal observations, their agreement\\n(or constant diiference) with the needle readings will form a\\nvaluable check oh the curve calculations and the instrumental\\nwork.\\nFORM OF NOTES.\\n[Left-hand papre.] [Right-hand page.]\\nSta.\\n54\\n53\\n0+72.2\\n52\\n51\\nO 50\\n49\\n48\\n0-1-32\\n47\\n46\\nAlign-\\nment\\nVernier\\nP.T.\\nP.O.\\n9\u00c2\u00b0 11\\n7 57\\n6 15\\n4 33\\n2 51\\n1 09\\n0\u00c2\u00b0\\nTang.\\nDefl.\\n18\u00c2\u00b0 22\\nCalc.\\nBearing.\\nN 54\u00c2\u00b0 48 E\\nN 36\u00c2\u00b0 26 E\\nNeedU\\nN 6S\u00c2\u00b0 15 1\\nN 14\u00c2\u00b0 0", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0033.jp2"}, "34": {"fulltext": "CHAPTEK II.\\nALIGNMENT.\\nIn this chapter the alignment of the center line only of a\\npair of rails is considered. When a railroad is crossing a sum-\\nmit in the grade line, altliough the horizontal projection of the\\nalignment may be straight, the vertical projection will consist of\\ntwo sloping lines joined by a cnrve. When a curve is on a\\ngrade, the center line is really a spiral, a curve of double curva-\\nture, although its horizontal projection is a circle. The center\\nline therefore consists of straight lines and curves of single\\nand double curvature. The simplest method of treating them\\nis to consider their horizontal and vertical projections separately.\\nIn treating simple, compound, and transition curves, only the\\nhorizontal projections of those curves will be considered.\\nSIMPLE CURVES.\\n18. Designation of curves. A curve may be designated\\neither by its radius or by the angle\\nsubtended by a chord of unit length.\\nSuch an angle is known as the degree\\nof curve and is indicated by D.\\nSince the curves that are practically\\nused have very long radii, it is gener-\\nally impracticable to make any use of\\nthe actual center, and the curve is\\nlocated without reference to it. If\\nAB in Fig. 7 represents a unit chord\\n((7) of a curve of radius i?, then by the above defini-\\n18", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0034.jp2"}, "35": {"fulltext": "\u00c2\u00a719.\\nALIGNMENT.\\n19\\ntion the angle AOB equals D, Then AO sin ^D iAB\\niO.\\n(1)\\nB\\nor, bj inversion,\\nsin ^J)\\nsin il)\\nC_\\n2E\\n(2)\\nThe unit chord is variously taken throughout the world as\\n100 feet, (S^ feet, and 20 meters. In the United States 100\\nfeet is invariably used as the unit chord length, and throughout\\nthis work it will be so considered. Table I has been computed\\non this basis. It gives the radius, with its logarithm, of all\\ncurves from a 0\u00c2\u00b0 01 curve up to a 10\u00c2\u00b0 curve, varying by single\\nminutes. The sharper curves, which are seldom used, are given\\nwith larger intervals.\\nAn approximate value of i? may be readily found from the\\nfollowing simple rule, which should be memorized\\nB\\n5730\\nIT\\nAlthough such values are not mathematically correct, since jR\\ndoes not strictly vary inversely as D, yet the resulting value is\\nwithin a tentli of one per cent for all\\ncommonly used values of and is suf-\\nficiently close for many purposes, as will\\nbe shown later.\\n19. Length of a sub-chord. Since\\nit is impracticable to measure along a\\ncurved arc, curves are always measured\\nby laying off 100-foot chord lengths.\\nTliis means that the actual arc is always\\na little longer than the chord. It also\\nmeans that a suhchord (a chord shorter than the unit length)\\nwill be a little longer than the ratio of the angles subtended\\nwould call for. The truth of this may be seen without calcu-\\nFiG. 8.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0035.jp2"}, "36": {"fulltext": "20 RAILROAD CONSTRUCTION. 20.\\nlation by noting that two equal subcliords, each subtending the\\nangle j-T), will evidently be slightly longer than 50 feet each.\\nIf c be the length of a subchord subtending the angle d, then,\\nas in Eq. (2),\\nsm 2,ct Q~o)\\nor, by inversion,\\nc=^2B sin ^d (3)\\nd\\nThe no?ninal length of a subchord 100\u00e2\u0080\u0094. For example,,\\na nominal subchord of 40 feet will subtend an angle of -^-^q of\\nD\u00c2\u00b0 its true length will be slightly more than 40 feet, and may\\nbe computed by Eq. 3. The difference between the nominal\\nand true lengths is maximum when the subchord is about 57\\nfeet long, but with the low degrees of curvature ordinarily used\\nthe difference may be neglected. With a 10\u00c2\u00b0 curve and a\\nnominal chord length of 60 feet, the true length is 60.049 feet.\\nVery sharp curves should be laid off with 50-foot or even 25-\\nfoot chords (nominal length). In such cases especially the true\\nlengths of these subcliords should be computed and used instead\\nof the nominal lengths.\\n20. Length of a curve. The length of a curve is always\\nindicated by the quotient of 100/^ D. If the quotient of\\nz/ Z^ is a whole number, the length as thus indicated is the\\ntrue length measured in 100-foot choi d lengths. If it is an\\nodd number or if the curve begins and ends with a subchord\\n(even though A D a whole number), theoretical accuracy\\nrequires that the true subchord lengths shall be used, although\\nthe difference may prove insignificant. The length of the arc\\n(or the mean length of the two rails) is therefore always in\\nexcess of the length as given above. Ordinarily the amount\\nof this excess is of no practical importance. It simply adds an\\ninsignificant amount to the length of rail required.\\nExamjple. Required the nominal and true lengths of a\\n3\u00c2\u00b0 45 curve having a central angle of 17\u00c2\u00b0 25 First reduce", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0036.jp2"}, "37": {"fulltext": "\u00c2\u00a722.\\nALIGNMENT.\\n21\\nthe degrees and minutes to decimals of a degree. (100 X 1T\u00c2\u00b0 25\\n-h 3\u00c2\u00b0 ^5 17^:1.007 3.75 U^AU. The curve has four\\n100-foot chords and a nominal chord of Gir.-l-ll:. The true\\nchord should be 61:. 451. The actual arc is\\n17M:1G7 X\\n7t\\nIbO\\nX E 461:. 527.\\nThe excess is therefore 46-1.527 464.451 0.076 foot.\\n21. Elements of a curve. Considering the line as running\\nfrom A toward I tlie beginning of tlie curve, at A^ is called\\ni\\\\\\\\Q point of curve {PC). The other end of the curve^ at is\\ncalled the point of tangency (PT).\\nThe intersection of the tangents is\\ncalled the vertex {V). The angle\\nmade bj the tangents at T which\\nequals the angle made by the radii to\\nthe extremities of the curve, is called\\nthe central angle [A). A T^and B T\\nthe two equal tangents from tlie vertex\\nto the PC and PT^ are called the\\ntangent distances {T). The chord\\nAB is called the long chord (LC).\\nThe intercept HG from the middle\\nof the long chord to the middle of the arc is called the middle\\nordinate (M). That part of the secant G V from the middle of\\nthe arc to the vertex is called the external distance (E), From\\nthe figure it is very easy to derive the follow^ing frequently used\\nrelations\\nFig. 9.\\nT= R tan J\\nLC\\nM\\n2^ sin i J\\nE\\n(4)\\n(5)\\nR vers ^z/ (6)\\nR exsec ^A (7)\\n22. Relation between T, E, and A. Join A and G in Fig. 9.\\nThe angle VAG iA, since it is measured by one half of the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0037.jp2"}, "38": {"fulltext": "22 RAILROAD CONSTRUCTION. 23.\\narc AG between the secant and tangent. AGO z= 90\u00c2\u00b0 \u00e2\u0080\u0094\\\\A.\\nAY: VG:\\\\miAGV:dn YAG)\\nmiAGY=^ QinAGO cosiz?;\\nT .Ew cos \\\\A sin \\\\A\\nT=Eq,oI\\\\A (8)\\nThe same relation may be obtained by dividing Eq. 4 by Eq. 7,\\nsince tan a exsec a cot \\\\a.\\n23. Elements of a 1^ curve. From Eqs. 1 to 8 it is seen that\\nthe elements of a curve vary directly as R. It is also seen to\\nbe very nearly true that B, varies inversely as D. If the ele-\\nments of a 1\u00c2\u00b0 curve for various central angles are calculated and\\ntabulated, the elements of a curve of Z^\u00c2\u00b0 curvature may be\\napproximately found by dividing by D the corresponding elements\\nof a 1\u00c2\u00b0 curve having the same central angle. For small central\\nangles and low degrees of curvature the errors involved by the\\napproximation are insignificant, and even for larger angles the\\nerrors are so small \\\\h2Xf0r many jpurposes they may be disre-\\ngarded.\\nIn Table II is given the value of the tangent distances,\\nexternal distances, and long chords for a I curve for various\\ncentral angles. The student should familiarize himself with the\\ndegree of approximation involved by solving a large number of\\ncases under various conditions by the exact and approximate\\nmethods, in order that he may know when the approximate\\nmethod is sufficiently exact for the intended purpose. The\\napproximate method also gives a ready check on the exact\\nmethod.\\n24. Exercises, [a) What is the tangent distance of a 4\u00c2\u00b0 20\\ncurve having a central angle of 18\u00c2\u00b0 24\\n{h) Given a 3\u00c2\u00b0 30 curve and a central angle of 16\u00c2\u00b0 20\\nhow far will the curve pass from the vertex [Use Eq. 7.]\\n(c) An 18\u00c2\u00b0 curve is to be laid off using 25-foot (nominal)\\nchord lengths. What is the true length of the subchords", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0038.jp2"}, "39": {"fulltext": "\u00c2\u00a725.\\nALIGNMENT.\\n23\\n{(l) Given two tangents making a central angle of 15\u00c2\u00b0 2^\\nIt is desired to connect these tangents by a curve which shall\\nj^ass 16.2 feet from their intersection. How far down the\\ntangent will the curve begin and what will be its radius (Use\\nEq. S and then use Eq. -i inverted.)\\n25. Curve location by deflections. The ano-le between a\\nsecant and a tangent (or between two secants intersecting on an\\narc) is measured by one half of the intercepted arc. Beginning\\nat the PC {A in Fig. 10), if the first chord is to be a full cliord\\nwe may deflect an angle VAa jP),\\nand the point which is 100 feet from\\n^\u00e2\u0080\u00a21, is a point on the curve. For the\\nnext station, deflect an additional\\nangle hAa ^D) and, with one end\\nof the tape at a, swing the other end\\nuntil the 100-foot point is on the line\\nAh. The points is then on the curve.\\nIf the final chord cjB is a subchord, its\\nadditional deflection {^a) is something\\nless than 4-7 The last deflection\\n{BA Y) is of course It is particularly inqwrtant, when a\\ncurve begins or ends with a subchord and the defiections are\\nodd quantities, that the last additional defiection should be care-\\nfully coni})uted and added to the previous deflection, to check\\nthe mathematical work by the agreement of this last conqnited\\ndeflection with -g-z/.\\nExample. Given a 3\u00c2\u00b0 2-1 curve having a central angle of\\n18\u00c2\u00b0 22 and beginning at sta. -IT 32, to conq^ute the deflections.\\nThe nominal length of curve is 18\u00c2\u00b0 22 3\u00c2\u00b0 24 =18.367\\n3.40 5.402 stations or 540.2 feet. The curve therefore ends\\nat sta. 52 72.2. The deflection for sta. 48 is y^o X K^^ ^^0\\n0.68 X 1\u00c2\u00b0.T 1\u00c2\u00b0.156 r 09 nearly. For each additional\\n100 feet it is 1\u00c2\u00b0 42 additional. The final additional deflection\\nfor the final subchord of 72.2 feet is\\nFig. 10.\\nX K3\u00c2\u00b0 24 1\u00c2\u00b0. 2274\\n100\\n1\u00c2\u00b0 14 nearly.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0039.jp2"}, "40": {"fulltext": "24 RAILROAD CONSTRUCTION. \u00c2\u00a726.\\nThe defections are\\nP. C Sta. 47 32 0\u00c2\u00b0\\n48 0\u00c2\u00b0 1\u00c2\u00b0 09 1\u00c2\u00b0 09\\n49 1\u00c2\u00b0 09 1\u00c2\u00b0 42 2 51\\n50 2\u00c2\u00b0 51 1\u00c2\u00b0 42 r=4\u00c2\u00b0 33\\n51 4\u00c2\u00b0 33 1\u00c2\u00b0 42 ==G\u00c2\u00b0 15\\n52 0\u00c2\u00b0 15 1\u00c2\u00b0 42 7\u00c2\u00b0 57\\nP. T 52 72.2 /7\u00c2\u00b0 57 1\u00c2\u00b0 14^ 9\u00c2\u00b0 11\\nAs a check 9\u00c2\u00b0 11 i(18\u00c2\u00b0 22 (See the Form of Notes\\nin 17.)\\n26. Instrumental work. It is generally impracticable to\\nlocate more than 500 to 600 feet of a curve from one station.\\nObstructions will sometimes require that the transit be moved up\\nevery 200 or 300 feet. There are two methods of setting off\\nthe angles when the transit has been moved up from the PC.\\n(a) The transit may be sighted at the previous transit station\\nwith a reading on the plates equal to the deflection angle from\\nthat station to the station occupied, but with the angle set oif on\\nthe other side of 0\u00c2\u00b0, so that when the telescope is turned to 0\u00c2\u00b0 it\\nwill sight along the tangent at the station occupied. Plunging\\nthe telescope, the forward stations may be set off by deflecting\\nthe proper deflections from the tangent at the station occupied.\\nThis is a very common method and, when the degree of curva-\\nture is an even number of degrees and when the transit is only\\nset at even stations, there is but little objection to it. But the\\ndegree of curvature is sometimes an odd quantity, and the exi-\\ngencies of difiicult location frequently require that substations\\nbe occupied as transit stations. Method {a) will then require\\nthe recalculation of all deflections for each new station occupied.\\nThe mathematical work is largely increased and the probability\\nof error is very greatly increased and not so easily detected.\\nMethod is just as simple as method (a) even for the most\\nsimple cases, and for the more difiicult cases just referred to the\\nsuperiority is very great.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0040.jp2"}, "41": {"fulltext": "\u00c2\u00a726.\\nALIGNMENT.\\n26\\n(b) Calculate the deflection for each station and substation\\nthroughout the curve as though the whole curve were to be lo-\\ncated from the PC. The computations may thus be completed\\nand checked (as above) before beginning the instrumental work.\\nIf it unexpectedly becomes necessary to introduce a substation\\nat any point, its deflection from the P(7may be readily inter-\\npolated. The stations actually set from the PC are located as\\nusual. Rule. When the transit is set on any forward station,\\nbacksight to ANY previous station with the plates set at the deflec-\\ntion angle for the station sighted at. Plunge the telescope and\\nsight at any forward station with the deflection angle originally\\ncomputed for that station. AVlien the plates read the deflection\\nangle for the station occupied, the telescope is sighting along the\\ntangent at that station which is the method of getting the for-\\nward tangent when occupying the PT. Even though the sta-\\ntion occupied is an unexpected substation,\\nwhen the instrument is properly oriented at\\nthat station, the angle reading for any station,\\nforward or back, is that originally computed\\nfor it from the P(7. In diflicult work, where\\nthere are obstructions, a valuable check on\\nthe accuracy may be found by sighting back-\\nward at any visible station and noting whether\\nits deflection agrees with that originally com-\\nputed. As a numerical illustration, assume\\na -t\u00c2\u00b0 curve, with 28\u00c2\u00b0 curvature, with stations\\n0, 2, 4, and T occupied. After setting\\nstations 1 and 2, set up the transit at sta.\\n2 and backsight to sta. with the deflection\\nfor sta. 0, which is 0\u00c2\u00b0. The reading on sta.\\n1 is 2\u00c2\u00b0 when the reading is 4\u00c2\u00b0 the telescope\\nis tangent to the curve, and when sighting\\nat 3 and 4 the deflections will be 6\u00c2\u00b0 and 8\u00c2\u00b0.\\nOccupy 4 sight to 2 with a reading of 4\u00c2\u00b0.\\nis 8\u00c2\u00b0 the telescope is tangent to the curve and, by plunging the\\ntelescope, 5, 6, and 7 may be located with the originally com-\\nFlG. 11.\\nWhen the reading", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0041.jp2"}, "42": {"fulltext": "26\\nRAILROAD CONSTRUCTION.\\n27\\nputed deflections of 10\u00c2\u00b0, 12\u00c2\u00b0, and 14\u00c2\u00b0. When occupying 7\\nbacksight may be taken to any visible station with the plates read\\ning the deflection for that station then when the plates read\\n14\u00c2\u00b0 the telescope will point along the forward tangent.\\nThe location of curves by deflection angles is the normal\\nmethod. A few other methods, to be described, should be con-\\nsidered as exceptional.\\n27. Curve location by two transits. A curve might be located\\nmore or less on a swamp where accurate chaining would be ex-\\nceedingly difficult if not impossible. The long chord AB may\\nbe determined by triangulation or otherwise, and the elements of\\nFig. 13.\\nFig. 13.\\nthe curve computed, including (possibly) subchords at each end.\\nThe deflection from A and B to each point may be computed.\\nA rodman may then be sent (by whatever means) to locate long\\nstakes at points determined by the simultaneous sightings of the\\ntwo transits.\\n28. Curve location by tangential offsets. When a curve is\\nvery flat and no transit is at hand the following method may be", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0042.jp2"}, "43": {"fulltext": "29. ALIGNMENT. 27\\nused Produoe the back tangent as far forward as necessary.\\nCompute the ordinates Oa\\\\ Oh\\\\ Oc\\\\ etc., and the abscissae a a.,\\nh h, c c. etc. If Oa is a full station (100 feet), then\\nOa Oa 100 cosiD, also R sin D;\\n01/ Oa Ara h 100 cos *j9+ 100 cos\\nalso li sin ID L p^\\nOc Oa +a h -\\\\-h c =^100{cos il) +C06 U) co^^I))j\\nalso Ic sin 3D\\netc.\\na a 100 sin ^Z also vers 7\\nh b a: a h h =100 sin ii 100 sin\\nalso J^vers2D; I mq)\\nc c Jj h c c 100(siniZ) sin|Z sinfZ\\nalso I^versoD]\\netc.\\nThe functions Ji fi^, etc., may be more conveniently used\\nwithout logarithms, by adding the several national trigonometrical\\nfunctions and pointing off two decimal places. It may also be\\nnoted that oV (for example) is one half of the long chord\\nfor four stations; also that h h is the middle ordinate for four\\nstations. If the engineer is provided with tables giving the long\\nchords and middle ordinates for various degrees of curvature,\\nthese quantities may be taken (perhaps by interpolation) from\\nsuch tables.\\nIf the curve begins or ends at a substation, the angles and\\nterms will be correspondingly altered. The modifications may\\nbe readily deduced on the same principles as above, and should\\nbe worked out as an exercise by the student.\\n29. Curve location by middle ordinates. Take first the simpler\\ncase when the curve begins at an even station. If we consider\\n(in Fig. 14) the curve produced back to the chord za\\n2 X 100 cos iD, A a 100 cos iZ and A A am .iit\\n100 sin ^D. Set off A A perpendicular to the tangent and\\nA a parallel to the tangent. ^1^1 aa hh cc\\\\ etc.\\n100 sin \\\\D. Set ofi aa per^^endicular to a A. Produce Aa", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0043.jp2"}, "44": {"fulltext": "28\\nBAILROAD COISSTRUCTION.\\n\u00c2\u00a730.\\nuntil a h A a^ thus determining h. Succeeding points of the\\ncurve may thus be determined indefinitely.\\nSuppose the curve begins with a subchord. As before\\nra Am c cos \\\\d and rA am! c sin \\\\d Also sz\\nAn c cos \\\\d and sA zn c sin \\\\d in which\\nFm. 14.\\nFig. 15.\\n(d d D. The points and a being determined on the\\nground, aa may be computed and set off as before and the curve\\ncontinued in full stations. A subchord at the end of the curve\\nmay be located by a similar process.\\n30. Curve location by offsets from the long chord. (Fig. 16.)\\nConsider at once the general case in which the curve commences\\nwith a subchord (curvature, d contains with one or more full\\ncliords (curvature of each, D)^ and ends with a subchord with\\ncurvature d The numerical work consists in computing first\\nAB^ then the various abscissae and ordinates. AB=2B sin ^Zi.\\nAa Aa! c cos ^{J d\\nAh Aa a b d cos \\\\{A-d 00 cos \\\\{A 2d D)\\nAc Aa a b b c c cos i(z/ d 100 cos {{/I 2d D)\\n100cosi(z/-2(f -Z\\nalso\\n-AB-Bc =z2Bs\\\\n^J- c co%^{A d\\nKii)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0044.jp2"}, "45": {"fulltext": "\u00c2\u00a732.\\nALIGNMENT.\\n29\\na a=: a a c sin |(z/ d\\nbb a a mb= c sin 1{J d 100 siu 2d V); j\\nc c bb nb c sin 1{J d 100 siu |(z/ M D) (12)\\n-lOOsin i(J-2(r -Z\\nalso =c s\\\\u\\\\{J d J\\nThe above formulae are considerably simplified when the enrve\\nbegins and ends at even stations. When the curve is very long\\na regular law becomes very apparent in the\\nformation of all terms between the first and last.\\nThere are too few terms in the above equations\\nto show the law.\\n31. Use and value of the above methods. The\\nchief value of the above methods lies in the\\npossibility of doing the work without a transit.\\nThe same principles are sometimes employed,\\neven when a transit is used, when obstacles pre-\\nvent the nse of the normal method (see 32, c).\\nIf the terminal tangents have already been ac-\\ncurately determined, these methods are useful to\\nlocate points of the curve when rigid accuracy\\nis not essential. Track foremen frequently use\\nsuch methods to lay out unimportant sidings,\\nespecially when the engineer and his transit are not at hand.\\nLocation by tangential offsets (or by offsets from the long chord)\\nis to be preferred when the curve is flat (i.e., has a small central\\nangle and there is no obstruction along the tangent, or long\\nchord. Location by middle ordinates may be employed regard-\\nless of the leno;th of the curve, and in cases when both the\\nFig. 16,\\ntangents\\nand the long chord are obstructed. The above\\nmethods are but samples of a large number of similar methods\\nwhich have been devised. The choice of the particular\\nmethod to be adopted nmst be determined by the local con-\\nditions.\\n32. Obstacles to location. In this section will be given only\\na few of the principles involved in this class of problems, with\\nillustrations. The engineer must decide in each case, which is", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0045.jp2"}, "46": {"fulltext": "30\\nJRAILROAD CONSTRUCTION.\\n32.\\ntlie best metliod to use, and it is frequently advisable to devise a\\nspecial solution for some particular case.\\na. When the vertex is inaccessible. As shown in 26, it is\\nnot absolutely essential that the vertex of a curve should be\\nlocated on the ground. But it is xery evident that the angle\\nbetween the terminal tangents is determined with far less prob-\\nable error if it is measured by a single measurement at tlie ver-\\ntex rather than as the result of numerous angle measurements\\nalong the curve, involving several positions of the transit\\nand comparatively short sights. Sometimes the location of the\\ntangents is already determined on the ground (as by hi and am,\\nFig 17), and it is required to join the tangents by a curve of\\ngiven radius. Method. Measure ab and the angles Vba and\\nha V. A is the sum of these angles. The distances h Fand a Y\\nare computable from the above data. Given A and R, the tan-\\nFiG. 18.\\ngent distances are computable, and then Bb and aA are found\\nby subtracting h V and a V from the tangent distances. The\\ncurve may then be run from A, and the work may be checked\\nby noting whether the curve as run ends at previously lo-\\ncated from h.\\nb. When the point of curve (or point of tangency) is inacces-\\nsible. At some distance {As, Fig. IS) an unobstructed line pn", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0046.jp2"}, "47": {"fulltext": "33. ALIGNMENT. 31\\nmay be run parallel with A V. nv jpy As =z Ji vers a.\\nvers (Y As U. ns =j)s It sin\\na.\\nAt which is at a distance jps back from the computed posi-\\ntion of ^i, make an oifset sA to 7 Ilun i)ii parallel to the\\ntano-ent. A tansjent to the curve at n makes an anoxic of with\\nnp. From n the curve is run in as usual.\\nIf the point of tangencj is obstructed, a similar process,\\nsomewhat reversed, may be used. /5 is that portion of A still\\nto be laid off when m is reached, tin tl It sin iriz\\ntB lx =1 B vers ft.\\nc. When the central part of the curve is obstructed. a is\\nthe central angle between two points of the curve between which\\na chord may be run. a may equal any angle, but it is prefer-\\nable that a should be a multiple of Z^, the degree of curve, and\\nthat the points vi and n should be on even stations. m)i\\n2/t sin iot, A point s may be located\\nby an oifset hs from the chord tnn by a T^-^.^\\nsimilar method to that outlined in 30. tjS^^^^-,^\\nThe device of introducin\u00c2\u00a3i^ the dotted ^o^\\ncurve havino; the same radius of cur- \\\\i v^\\nvature as the other, although neither\\nnecessary nor advisable in the case shown\\nin Fig. 19, is sometimes the best method a5^_,\\nof surveying around an obstacle. The\\noifset from any point on the dotted curve\\nto the corresponding point on the true\\ncurve is twice the ordinate to the long chord, as computed\\nin 30.\\n33. Modifications of location. The following methods may\\nbe used in allowing for the discrepancies between the paper\\nlocation based on a more or less rough preliminary survey and\\nthe more accurate instrumental location. (See 15.) They are\\nalso frequently used in locating new parallel tracks and modify-\\ning old tracks.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0047.jp2"}, "48": {"fulltext": "32\\nRAILROAD CONSTRUCTION.\\n33.\\na. To move the forward tangent parallel to itself a distance a?,\\nthe point of curve (^1) remaining fixed. (Fig. 20.)\\nVV -T\\nV h\\nX\\nsinAFF sin\\n(13)\\nAV A V+ VV\\\\\\nThe triano^le BmB is isosceles and Bin B m.\\nR R^ O O^mB^\\nB r\\nX\\nvers BinB vers A\\nR ^R-\\\\-\\nX\\nvers A\\n(U)\\nThe solution is very similar in case the tangent is moved in-\\nward to V^ B^\\\\ IS ote that this method necessarily changes the\\nZ^r-^\\n^-2^^^^\\n^^4-\\n/t^^\\n^^^^^-3:\\n/i\\nr\\n\\\\A\\n/i/j/j\\n0 6 6\\nV\\nV\\nV\\nFig. 20.\\nFig. 21.\\nradius. If the radius is not to be changed, the point of curve\\nmust be altered as follows\\nb. To move the forward tangent parallel to itself a distance x,\\nthe radius being unchanged. (Fig. 21.) In this case the whole", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0048.jp2"}, "49": {"fulltext": "\u00c2\u00a733.\\nALIGNMENT.\\n33\\ncurve is moved bodily a distance 00 A A W BB\\nand moved parallel to the first tangent A V.\\nBB\\nB n\\nX\\nsin iiBB sin A\\nAA\\\\\\n(15)\\nc. To change the direction of the forward tangent at the point\\nof tangency. (Fig. 22.) This problem involves a change in\\nthe central angle and also requires a new radius. An error in the\\ndetermination of the central angle furnishes an occasion for its\\nuse.\\nJ, a, A Vy and B Fare known. a.\\nBs B vers A. Bs R vers A\\nvers A\\nE E\\nvers {A\\nAs E ^m A. A s z= E sin A\\n(16)\\nAA A s As E sin A E sin A. (17)\\nThe above solutions are given to illustrate a large class of\\nproblems which are constantly arising. All of the ordinary\\nFig. 22.\\nFig. 23.\\nproblems can be solved by the application of elementary ge-\\nometry and trigonometry.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0049.jp2"}, "50": {"fulltext": "34 RAILROAD CONSTRUCTION. 34.\\n34. Limitations in location. It may be required to run a\\ncurve that shall join two given tangents and also pass through a\\ngiven point. The point (P, Fig. 23) is assumed to be determined\\nby its distance VP) from the vertex and by the angle A VP\\np.\\nIt is required to determine the radius {E) and the tangent\\ndistance F). A is known.\\nPVG i(180\u00c2\u00b0 J) /5 90\u00c2\u00b0 (iJ\\nPP =2VP sin PVG ^2 VP cos (iJ\\nPSV U. SP YP^\\nsin hA\\nAS VSP X SP VSP{SF PP\\nFP4^r FP-g^ 2 FP cos (iz^\\nsm t^L sm -^n\\n__ Yp i/ sin /g 2 sin yg cos (jz/ jS)\\nsin \\\\A sin ^-z/\\nsni \\\\/i\\nAV^AS^SY\\n=_-^rsin (i// +/i) |/sin /3 2 sin sin i^/ cos (i^ +/i)]. (18)\\nsin ^i^\\nP:= ^FcOtiZl.\\nIn the special case in which P is on the median line F,\\ny5 90\u00c2\u00b0 iJ, and (Jz^ 90\u00c2\u00b0. Eq. (IS) then reduces to\\nVP\\nAV= ^-T^(l cos i J) FP cot iJ,\\nsm 2\\nas mi^ht have been immediately derived from Eq. (8).", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0050.jp2"}, "51": {"fulltext": "35. ALIGNMENT. 35\\n111 case the point P is given by the offset PK and by tlie\\ndistance YK^ the triangle PKV \\\\\\\\\\\\a^\\\\ be readily solved, giving\\nthe distance YP and the angle and the remainder of the\\nsolution will be as above.\\n35. Determination of the curvature of existing track, (a) Vs niy\\na trcuisit. Set up the transit at any point in the center of the\\ntrack. Measure in each direction 100 feet to points also in the\\ncenter of the track. Sight on one point with the plates at 0\u00c2\u00b0.\\nPlunge the telescope and sight at the other point. The angle\\nbetween the chords equals the degree of curvature.\\n(b) Using a tape and string. Stretch a string (say 50 feet\\nlong) between two points on the inside of the head of the outer\\nrail. Measure the ordinate [x) between the middle of the string\\nand the head of the rail. Then\\n_, chord\\ng^ (very nearly) (19)\\nFor, in Fig. 24, since the triangles AGE and ADC are\\nsimilar, AO AE AP PJC or P lAP x. When,\\nas is usual, the arc is very short compared with\\nthe radius, AD -J^-^? very nearly. Making\\nthis sul)stitution we have Eq. (19). With a\\nchord of 50 feet and a 10\u00c2\u00b0 curve, the resulting\\ndifference in x is .0025 of an inch far within\\nthe possible accuracy of such a method. The\\nabove method gives the radius of the inner head\\nof the outer rail. It should be diminished by %g for the radius\\nof the center of the track. With easy curvature, however, this\\nwill not affect the result by more than one or two tenths of one\\nper cent.\\nThe inversion of this formula gives the required middle or-\\ndinate for a rail on a given curve. For example, the middle\\nordinate of a 30-foot rail, bent for a 6\u00c2\u00b0 curve, is\\na; 900 (8 X 955) .118 foot 1.1 inches.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0051.jp2"}, "52": {"fulltext": "36 BAILBOAD CONSTRUCTION. 36.\\nAnother much used rule is to require the foreman to have a\\nstring, knotted at the centre, of such length that the middle or-\\ndinate, measured in inches, equals the degree of curve. To-\\nfind that length, substitute (in eq. (19)) 5730 D for H and\\n2 12 for X. Solving for chords we obtain chord =61.8 feet.\\nThe rule is not theoretically exact, but, considering the uncertain\\nstretching of the string, the error is insignificant. In fact, the\\ndistance usually given is 62 feet, which is close enough for all\\npurposes for which such a method should be used.\\n36. Problems. A systematic method of setting down the\\nsolution of a problem simplifies the work. Logarithms should\\nalways be used, and all the work should be so set down that a\\nrevision of the work to find a supposed error may be readily\\ndone. The value of such systematic work M^ill become more\\napparent as the problems become more complicated. The twa\\nsolutions given below will illustrate such work.\\na. Given a 3\u00c2\u00b0 curve beginning at Sta. 27+60 and running\\nto Sta. 32 -J- 45. Compute the ordinates and offsets used in\\nlocating the curve by tangential offsets.\\nh. With the same data as above, compute the distances to\\nlocate the curve by offsets from the long chord.\\nc. Assume that in Fig. 17 ab is measured as 217.6 feet,,\\nthe angle ah F= 17\u00c2\u00b0 42 and the angle haV 21\u00c2\u00b0 14 Join\\nthe tangents by a 4\u00c2\u00b0 30 curve. Determine hB and aA,\\nd. Assume that in a case similar to Fig. 18 it was noted\\nthat a distance {As) equal to 12 feet would clear the building.\\nAssume that A 38\u00c2\u00b0 20 and that 4\u00c2\u00b0 40 Eequired tiie\\nvalue of a and the position of n. Solution\\nYQY^ a z=z As R ^5=12 log 1.07918\\nR (for 4\u00c2\u00b0 40 curve) log 3.08923\\n0^= 8\u00c2\u00b0 01 log vers a 7.98994\\nm B sin a log sin a 9.14445\\nlog R 3.08923\\n71^ 171.27 log 2.2336^", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0052.jp2"}, "53": {"fulltext": "37. ALIGNMENT. 37\\ne. Assume that the forward tangent of a 3\u00c2\u00b0 2(V curve\\nhavinir a central anii^le of 1G\u00c2\u00b0 50 must be moved 3.62 feet\\ninward^ witliout altering the P. C. Required the cliange in\\nradius.\\nf. Given two tangents making an angle of 36\u00c2\u00b0 18 It is\\nrequired to pass a curve through a point 93.2 feet from the\\nvertex, the line from the vertex to the point making an angle\\nof 42\u00c2\u00b0 21 with the tangent. Required the radius and tangent\\ndistance. Solution: Applying eq. (18), we have\\n2\\n42\u00c2\u00b0 21\\nij 18\u00c2\u00b0 09\\n(ij 60\u00c2\u00b0 30\\n.20667\\nlogsinV 9.656S8 .45382\\n2| 9.81987 .66049\\n9.90993 .81271\\nnat sin 60\u00c2\u00b0 30 .8703\\nlog\\n=z\\n0.30103\\nlog\\nsin\\n9.82844\\nlog\\nsin\\n9.49346\\nlog\\ncos\\n9.69234\\n9.31527\\n1.6836\\nlog= 0.22610\\nYP= 93.2\\n]og= 1.9694i\\n2. 19551\\nlog sin iz/ 9.49346\\ntang. dist. AY 503.56\\nlog= 2.70205\\nlog cot iJ 10.48437\\n7?= 1536.1\\n3.18642\\n1) 3\u00c2\u00b0 44\\nCOMPOUND CURVES.\\n37. Nature and use. Compound curves are formed by a\\nsuccession of two or more simple curves of different curvature.\\nThe curves must have a common tangent at the ])oint of com-\\npound curvature {P.C.C.). In mountainous regions there is\\nfrequently a necessity for compound curves having several\\nchanges of curvature. Such curves may be located separately\\nas a succession of simple curves, *but a combination of two", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0053.jp2"}, "54": {"fulltext": "38\\nRAILROAD CONSTRUCTION.\\n3a\\nsimple curves has special properties wliicli are worth investigat-\\ning and utilizing. In the following demonstrations H^ always\\nrepresents the longer radius and B^ the shorter^ no matter\\nwhich succeeds the other. T^ is the tangent adjacent to the\\ncurve of shorter radius (A*,), and is invariably the shorter tan-\\no-ent. A^ is the central angle of the curve of radius i?j but it\\nmay be greater or less than z/,.\\n38. Mutual relations of the parts of a compound curve havings\\ntwo branches. In .Fig. 25, ^6^ and CB are the two branches of\\nFig 25.\\nthe compound curve having radii of B^ and B^ and central\\nano-les of z/, and z/,. Produce the arc AC to n so that\\nAo{ii A. The chord Cn produced must intersect B. The\\nline ^16 parallel to CO^ will intersect BO^ so that Bs sn\\n(9^(9j 7?^ B^. Draw Am perpendicular to O^n. It will\\nbe parallel to lik.\\nBr S7i vers Bs7i (7?, B,) vers A^\\nm7i AO^ vers A0^7i R^ vers A\\nAk =^AV sin A Vh T, sin A\\nAle J nil mn nli 7/171 -f- Br.\\nT^ sin A^B, vers A-\\\\-{B, B,) vers A^. (20)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0054.jp2"}, "55": {"fulltext": "38. ALIGNMENT. 39\\nSimilarly it may be shown that\\n7; sin A R^ vers A {B, B,) vers A,. (21)\\nThe mutual relations of the elements of compound curves\\nmay be solved by these two equations. For example, assume\\nthe tangents as fixed therefore known) and that a curve of\\ngiven radius Ii^ shall start from a given point at a distance T^\\nfrom the vertex, and that the curve shall continue through a\\ngiven angle Required the other parts of the curve. From\\nEq. (20) we have\\nT, sin J i?i vers A\\ni?, 7?,\\nvers ^2\\nT, sin /I- B^ vers /I\\nIt., li J-. -rr (22)\\nvers -^j\\nT^ may then be obtained from Eq. (21).\\nAs another problem, given the location of the two tangents,\\nwith the two tangent distances (thereby locating the PC and\\nPT)^ and the central angle of each curve required the two\\nradii. Solving Eq. (20) for R^ we have\\nT. sin A R\u00e2\u0080\u009e vers J\u00e2\u0080\u009e\\nvers A vers A^\\nSimilarly from Eq. (21) we may derive\\n_ J!, sin A R^ (vers A vers z/,)\\nvers ^1\\nEquating these, reducing, and solving for R^ we have\\nT, sin A vers z/, T^ sin A (vers A vers z^,)\\nvers A^ vers (vers A \u00e2\u0080\u0094vers ^,)(vers A vers A^\\nAlthouorh the various elements mav be chosen as above with\\nconsiderable freedom, there are limitations. For example, in\\nEq. (22), since R^ is always greater than R^ the term to be\\nadded to R^ must be essentially positive i.e., T^ sin A must be", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0055.jp2"}, "56": {"fulltext": "40\\nRAILROAD CONSTRUCTION.\\n\u00c2\u00a7\u00c2\u00ab^9.\\nVGrs\\ngreater than 7?, vers /I. This means that 7T IL ;r*\\nor that T^ tan |-z/, or that T, is greater than the corre-\\nsponding tangent on a simple curve. Similarly it may be\\nshown that T^ is less than i?, tan or less than the correspond-\\ning tangent on a simj^le curve. E^evertheless T^ is always\\ngreater than T^, In the limiting case when -^i T, T\\nand z/^ ^1-\\n39. Modifications of location. Some of these modifications\\nmay be solved by the methods used for simple curves. For\\nexample\\na. It is desired to move the tangent VB, Fig. 26, parallel to\\nitself to V^B\\\\ Run a new curve from the P. C. O. which shall\\nreach the new tangent at B\\\\ where the chord of the old curve\\nFig. 26.\\nFig. 27.\\nintersects the new tangent. The solution is almost identical with\\nthat in 33, c^.\\nb. Assume that it is desired to change the forward tangent\\n(as above) but to retain the same radius. In Fig. 27\\n(7?2 ^i) cos J, O^n\\n(7?, B,) cos 0:n\\nX O^n O^n {R^ P,)(cos z/^ cos z//).\\nX\\ncos cos Z/^ n __ p (24)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0056.jp2"}, "57": {"fulltext": "\u00c2\u00a739.\\nALIGNMENT.\\n41\\nThe P. C. C. is moved hackward along the sliarper curve an\\nangular distance of z^i\\nIn case the tangent is moved inward rather than outward,\\nthe solution will apply bj transposing A^ and Then we\\nwill have\\ncos\\nA\\ncos p _ p (25)\\nTlie P. C. C. is then moved for-\\nward.\\nc. Assume the same case as (b) ex-\\ncept that the larger radius comes first\\nand that the tangent adjacent to the\\nsmaller radius is moved. In Fisr. 28\\n(i?2 R,) cos J, 0,71\\n(i?, B,) cos zf/ 0;n\\nn^-^\\nFig. 28.\\nX 0/n 0^71 (P, i?,)(cos z// _ cos\\ncos /I/ COS A, p^^_^ (26)\\nThe P. C. C. is moved forward along the easier curve an\\nangular distance of /i^ /l^ A^,\\nIn case the tangent is moved inward, transpose as before and\\nwe have\\ncos Al cos A^\\nX\\np.-pr\\n(27)\\nThe P. C. C. is moved hachioard.\\nd. Assume that the radius of one curve is to be altered witli-\\nout changing either tangent. Assume conditions as in Fig. 29.\\nFor the diagrannnatic solution assume that P, is to be in-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0057.jp2"}, "58": {"fulltext": "42\\nRAILROAD CONSTRUCTION.\\n39.\\ncreased by O^S, Then, since must pass through 0, and ex-\\ntend beyond 0, a distance 0,S, the locus of the new center\\nmust lie on the arc drawn about 0, as center and with OS as\\nradius. The locus of 6*/ is also given\\nby a line O^ j? parallel to F and at a\\ndistance of (equal to S P. CO.)\\nfrom it. The new center is therefore\\nat the intersection 0^\\\\ An arc with\\nradius i?/ will therefore be tangent at\\nJj and tangent to the old curve ^^r^-\\nchiced at new P.C.C. Draw O^n\\nperpendicular to O^B. With 0^ as\\ncenter draw the arc 0,m, and with\\n0^ as center draw the arc 0{in\\nmB m B B,. mn m n\\n\\\\s/U\\nFig. 29.\\n(i?/ B,) vers J/ {B, B,) vers /J,.\\nvers /i: vers J,\\n{It^ It,)\\n(28)\\n0,71= (B,-B,) sin/},\\n0,n ={B:-B,)sm z//.\\nBB 0,n -0,n {B:-B,) sin zJ/- {B~B) sin z^,. (29)\\nThis problem may be further modified by assuming that the\\nradius of the curve is decreased rather than increased, or that the\\nsmaller radius follows the larger. The solution is similar and\\nis suggested as a profitable exercise.\\nIt might also be assumed that, instead of making a given\\nchange in the radius a given change BB is to be made,\\nz?/ and are required. EHminate B^ from Eqs. 28 and 29\\nand solve the resulting equation for z^/. Then determine B^ by\\na suitable inversion of either Eq. 28 or 29.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0058.jp2"}, "59": {"fulltext": "41. ALIGNMENT. 43\\nAs in 32 and 33, the above problems are but a few,\\nalthough perhaps the most common, of the problems tlie\\nengineer may meet with in compound curves. All of tlie\\nordinary problems may be solved by these and simihir\\nmethods.\\n40. Problems, a. Assume that the two tangents of a com-\\npound curve are to be 348 feet and 624 feet, and that\\n22\u00c2\u00b0 16 and 28\u00c2\u00b0 20 Kequired the radii.\\n[Ans. 326.92; 7?, 1574.85.]\\nh. A line crosses a valley by a compound curve which is first\\na 6\u00c2\u00b0 curve for 46\u00c2\u00b0 30 and then a 9\u00c2\u00b0 30 curve for 84\u00c2\u00b0 16 It is\\nafterward decided that the last tangent should be 6 feet farther up\\nthe hill. What are the required changes {Note. The second\\ntangent is evidently moved outward. The solution corresponds\\nto that in the first part of 39, c. The P. C. C. is moved forward\\n16.39 feet. If it is desired to know how far the P. T. is moved\\nin the direction of the tangent (i.e., the projection of JSJ3\\\\ Fig.\\n28, on V B), it may be found by observing that it is equal to\\n7in (7?2 ^,)(sin A, sinz//). In this case it equals 0.65\\nfoot, which is very small because A^ is nearly 90\u00c2\u00b0. The value\\nof z/^ ^^0 is not used, since the solution is independent of\\nthe value of A^. The student should learn to recognize which\\nquantities are mutually related and therefore essential to a solu-\\ntion, and which are independent and non-essential.]\\nTRANSITION CURVES.\\n41. Superelevation of the outer rail on curves. When a mass\\nis moved in a circular path it requires a centripetal force to keep\\nit moving in that path. By the principles of mechanics we\\nknow that this force equals Gv -r- gli^ in which G is the weight,\\nV the velocity in feet per second, g the acceleration of gravity\\nin feet per second in a second, and R the radius of curvature.\\nIf the two rails of a curved track were laid on a level (trans-\\nversely), this centripetal force could only be furnished by the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0059.jp2"}, "60": {"fulltext": "44\\nRAILROAD CONSTRUCTION.\\n41.\\npressure of the wlieel-flanges against tlie rails. As tliis is very\\nobjectionable, the outer rail is elevated so that the reaction of\\nthe rails against the wheels shall contain\\na horizontal component equal to the re-\\ncpiired centripetal force. In Fig. 30, if\\noh represents the reaction, oc will repre-\\nsent the weight G, and ao will represent\\n___^_-l--\u00e2\u0080\u0094 the required centripetal force. From\\nsimilar triangles we may write S7i sm\\nao\\\\oc. Call ^=32.17. Call B\\n5730 Z), which is sufficiently accurate\\nfor this purpose (see 19). Call v= 5280 F-^ 3600, in\\nwhieh T^is the velocity in miles per hour, mn is the distance\\nbetween rail centers, which, for an SO-lb. rail and standard\\ngauge, is 4.916 feet, sin is slightly less than this. As an\\naverage value we may call it 4.900, which is its exact value\\nwhen the superelevation is 4i inches. Calling sn we have\\nFig. 30.\\nsm\\nao\\noc\\ne\\n4.9\\nGv 1\\n4.9 X 5280 F i\\ngR G 32.17 X 3600 X 5730\\n.0000572 F Z\\n(30)\\nIt should be noticed that, according to this formula, the\\nrequired superelevation varies as the sqttare of the velocity,\\nwhich means that a change of velocity of only 10,^ would call\\nfor a change of superelevation of 21^. Since the velocities of\\ntrains over any road are extremely variable, it is impossible to\\nadopt any superelevation which will fit all velocities even\\napproximately. The above fact also shows why any over-\\nrefinement in the calculations is useless and why the above\\napproximations, which are really small, are amply justifiable.\\nFor example, the above formula contains the approximation that\\ni? 5730 -f- Z^. In the extreme case of a 10\u00c2\u00b0 curve the error\\ninvolved would be about Ifo, A change of about i of I fo in", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0060.jp2"}, "61": {"fulltext": "\u00c2\u00a742.\\nALIGNMENT.\\n46\\nthe velocity, or say from 40 to 40.2 miles per hour, would mean\\nas much. The error in e due to tlie assumed constant value\\nof s?n is never more than a very small fraction of Ifc. Tlie\\nrail-laying is not done closer than this. The following tabular\\nform is based on Eq. 30\\nSUPERELEVATION OF THE OUTER RAIL (IN FEET) FOR VARIOUS VELOCI-\\nTIES AND DEGREES OF CURVATURE.\\nVelocity\\nill\\nMiles\\nper\\nHour.\\nDegree of Curve.\\n1\u00c2\u00b0\\no\\n3\u00c2\u00b0\\n.15\\n.27\\n.43\\n4\u00c2\u00b0\\n.20\\n.37\\n5\u00c2\u00b0\\n6\u00c2\u00b0\\n7\u00c2\u00b0\\n8\u00c2\u00b0\\n9\u00c2\u00bb\\n10\u00c2\u00b0\\n30\\n40\\n50\\n60\\n.05\\n.09\\n.14\\n.20\\n.10\\n.18\\n.29\\n.41\\n.26\\n.46\\n.31\\n.36\\n.41\\n.46\\n1.51\\ni .55\\n.86\\n.64\\n.73\\n.82\\n1 .57\\n.82\\n.71\\n1 .62\\n42. Practical rules for superelevation. A much used rule\\nfor superelevation is to elevate one half an inch for each\\ndegree of curvature. The rule is rational in that e in Eq. 30\\nvaries directly as I), The above rule therefore agrees with\\nEq. 30 when Fis about 27 miles per hour. However applica-\\nble the rule may have been in the days of low velocities, the\\nelevation thus computed is too small now.\\nAnother (and better) rule is to elevate for the speed of the\\nfastest trains. This rule is further justified by the fact that a\\nfour-wheeled truck, having two parallel axles, will always tend\\nto run to the outer rail and will require considerable flange\\npressure to guide it along the curve. The effect of an excess of\\nsuperelevation on the slower trains will only be to relieve this\\nflange pressure somewhat. This rule is coupled with the limita-\\ntioirthat the elevation should never exceed a limit of six inches\\n\u00e2\u0080\u0094sometimes eight inches. This limitation implies that locomo-\\ntive engineers must reduce the speed of fast trains around sharp\\ncurves until the speed does not exceed that for which the actual\\nsuperelevation used is suitable. The heavy line in tlie tabular\\nform 41) shows the six-inch limitation.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0061.jp2"}, "62": {"fulltext": "46\\nBAILTtOAD CONSTRUCTION,\\n\u00c2\u00a748.\\nSome roads furnish their track foremen with a Hst of the\\nsuperelevations to be used on each curve in their sections.\\nThis method has the advantage that each location may be\\nseparately studied, and the proper velocity, as affected by local\\nconditions {e.g.^ proximity to a stopping-place for all trains),\\nmay be determined and applied.\\nAnother method is to allow the foremen to determine the\\nsuperelevation for each curve by a simple measurement taken\\nat the curve. The rule is developed as follows By an inversion\\nof Eq. 19 we have\\nX\\nchord 8B (31)\\nPutting X equal to in Eq. 30 and solving for chord,^^ we\\nhave\\nchord .0000572 V DSE\\n2.621 F\\\\\\nchord 1.62 F.\\n(32\\nTo apply the rule, assume that 50 miles per hour is fixed as\\nthe velocity from which the superelevation is to be computed.\\nThen 1.62 F== 1,62 X 50 81 feet, which is the distance given\\nto the trackmen. Stretch a tape (or even a string) with a\\nlength of 81 feet between two points on the inside head of the\\nouter rail or the outer head of the inner rail. The ordinate at\\nthe middle point then equals the superelevation. The values\\nof this chord length for varying velocities are given in the\\naccompanying tabular form.\\nVelocity in miles per hour\\nChord length in feet\\n\u00e2\u0080\u00a220\\n32.4\\n25 30\\n40.5 48.6\\n35\\n56.7\\n40\\n64.8\\n45\\n72.9\\n50\\n81.0\\n55\\n89.1\\n60\\n97.2\\n43. Transition from level to inclined track. On curves the\\ntrack is inclined transversely; on tangents it is level. The\\ntransition from one condition to the other must be made gradu-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0062.jp2"}, "63": {"fulltext": "45. ALIGNMENT.\\n47\\nally. If there is no transition curve, there must be either in-\\nclined track on the tangent or insufficiently inclined track on the\\ncurve or both. Sometimes the full superelevation is continued\\nthrough the total length of the curve and the run- oft\\n(having a length of 100 to 200 feet) is located entirely on the\\ntangents at each end. In other practice it is located partly on\\nthe tangent and partly on the curve. Whatever the method,\\nthe superelevation is correct at only one point of the run-olf.\\nAt all other points it is too great or too small. This (and other\\ncauses) produces objectionable lurches and resistances when\\nentering and leaving curves. The object of transition curves is\\nto obviate these resistances.\\n44. Fundamental principle of transition curves. If a curve\\nhas variable curvature, beginning at the tangent with a curve of\\ninfinite radius, and the curvature gradually sharpens uiitil it\\nequals the curvature of the required simple curve and there\\nbecomes tangent to it, the superelevation of such a transition\\ncurve may begin at zero at the tangent, gradually increase to\\nthe required superelevation for the simple curve, and yet have\\nat every point the superelevation required by the curvature at\\nthat point. Since in Eq. (30) e is directly proportional to\\nthe required curve must be one in which the degree of curve\\nincreases directly as the distance along the curve. The mathe-\\nmatical development of such a curve is quite complicated. It\\nhas, however, been developed, and tables have been computed for\\nits use, by Prof. C. L. Crandall. The following method has\\nthe advantage of great simplicity, while its agreement w^itli the\\ntrue transition curve is as close as need be, as will be shown.\\n45. Multiform compound curves. If the transition curve\\ncommences with a very flat curve and at regular even chord\\nlengths compounds into a curve of sharper curvature until the\\ndesired curvature is reached, the increase in curvature at each\\nchord point being uniform, it is plain that such a curve is a\\nclose approximation to the true spiral, especially since the rails\\nas laid will gradually change their curvature rather than main-\\ntain a uniform curvature throughout each chord loTi\u00c2\u00a3rtli and", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0063.jp2"}, "64": {"fulltext": "48 RAILROAD CONSTRUCTION. 46.\\nthen abruptly change the curvature at the chord points. Such\\na curve, as actually laid^ will be a much closer approximation\\nto the true curve than the multiform compound curve by which\\nit is set out. There will actually be a gradual increase in\\ncurvature which increases directly as the length of the curve.\\n46. Required length of spiral. The required length of spiral\\nevidently depends on the amount of superelevation to be\\ngained, and also depends somewhat on the speed. If the spiral\\nis laid off in 25-foot chord lengths, with the first chord subtend-\\ning a 1\u00c2\u00b0 curve, the second a 2\u00c2\u00b0 curve, etc., the fifth chord will\\nsubtend a 5\u00c2\u00b0 curve, and the increase from this last chord to a\\n6\u00c2\u00b0 curve is the same as the uniform increase of curvature\\nbetween the chords. The same spiral extended would run on\\nto a 12\u00c2\u00b0 curve in (12 1)25 275 feet. The last chord of a\\nspiral should have a smaller degree of curvature than the simple\\ncurve to which it is joined. If the curves are very sharp, such\\nas are used in street work and even in suburban trolley work,\\nan increase in degree of curvature of 1\u00c2\u00b0 per 25 feet will not be\\nsufticiently rapid, as such a rate would require too long curves.\\n2\u00c2\u00b0, 10\u00c2\u00b0, or even 20\u00c2\u00b0 increase per 25 feet may be necessary, but\\nthen the chords should be reduced to 5 feet. Such a rapid rate\\nof increase is justified by the necessary reduction in speed. On\\nthe other hand, very high speed will make a lower rate of\\nincrease desirable, and therefore a spiral whose degree of curva-\\nture increases only 0\u00c2\u00b0 30 per 25 feet may be used. Such a\\nspiral would require a length of 375 feet to run on to an 8\u00c2\u00b0\\ncurve, which is inconveniently long, but it might be used to\\nrun on to a 4\u00c2\u00b0 curve, where its length would be only 175 feet.\\nThree spirals have been developed in Table lY, each with chords\\nof 25 feet, the i*ate of increase in the degree of curvature being\\n0\u00c2\u00b0 30 1\u00c2\u00b0 and 2\u00c2\u00b0 per chord. One of these will be suitable for\\nany curvature found on ordinary steam-railroads.\\n47. To find the ordinates of a l\u00c2\u00b0-per-25-feet spiral. Since the\\nfirst chord subtends a 1\u00c2\u00b0 curve, its central angle is 0\u00c2\u00b0 15 and\\nthe angle aQY (Fig. 31) is 7 30 The tangent at a makes an\\nangle of 15 with VQ. The angle between the chord ha and", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0064.jp2"}, "65": {"fulltext": "\u00c2\u00a748.\\nALIGNMENT.\\n49\\ndie tangent at a is J(30 15 and the angle hah 4(30 15\\n30 Similarly the angle chc i(45 3U 15 OT 3U\\n1\u00c2\u00b0 07 30 and the angle dcd is 2\u00c2\u00b0 0 The ordinate aa\\n25 sin 7 30 and Qa 25 cos 7 30 Qh Qa! aV\\nQa: 4- aV 25 (cos 7 30 cos 30 hb W\\n25 (sin 7 30 sin 30 Similarly the ordinates of c, d,\\netc., may be obtahied.\\nFig. 31.\\nFrG. 32.\\n48. To find the deflections from any point of the spiral.\\naQV=7 30 Tan hQ V hh QV tan cQV cc Qc\\netc. Thus we are enabled to find the deflection angles from\\nthe tangent at Q to any point of the spiral.\\nThe tangent to the curve at c (Fig. 32) makes an angle of\\n1\u00c2\u00b0 30 with Q V, or cm F 1\u00c2\u00b0 30 Qcm cm V cQm. The", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0065.jp2"}, "66": {"fulltext": "50\\nRAILROAD COI^STRUCTION.\\n48.\\nvalue of cQm is known from previous work. The deflection\\nfrom c to Q then becomes known.\\nacm cmV cap ciiiV caq qap, caq is the deflec-\\ntion angle to c from the tangent at a and will have been\\npreviously computed numerically, qaj? 15 acm therefore\\nbecomes known.\\nhcm^iofW 22 30\\nden ioi 60 30\\necn ecd ncd ncd cmV^ tan ecd {ee d d )-r- c e\\\\\\nall of which are known from the previous work.\\nBy this method the deflections from the tangent at any\\nFig. 33.\\npoint of the curve to any other point are determinable. These\\nvalues are compiled in Table lY. The corresponding values\\nof these angles when the increase in the degree of curvature per\\nchord length is 30 and when it is 2\u00c2\u00b0, are also given in\\nTable lY.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0066.jp2"}, "67": {"fulltext": "49. ALIGNMHNT. 51\\n49. Connection of spiral with circular curve and with tangent.\\nSee Fig. 3o. Let A V and I^ V be the tangents to be cunnected\\nbj a D\u00c2\u00b0 curve, having a suitable spiral at each end. If no\\nspirals were to be used, the problem would be solved as in\\nsimple curves giving the curve AMB. Introducing the spiral\\nhas the effect of throwing the curve away from the vertex a\\ndistance MM and reducing the central angle of the D^ curve\\nby 20. Continuing the curve beyond Z and Z \\\\o A and B\\\\\\nwe will have AA BB MM ZK the x ordinate and\\nis therefore known. Call MM m. A N x R vers 0.\\nThen\\nn.^^^, 4 4, X R vers\\nm MM AA (33)\\ncos ^A cos l\\niTJL AA sin l^ (x R vers 0) tan i^.\\nVQ QK- KN-\\\\-NA AV\\nij R sin 7? vers 0) tan \\\\A R tan \\\\A\\ny R sin a; tan 4-^ i^ cos tan \\\\A, (34)\\nWhen A N has already been computed, it may be more con-\\nvenient to write\\nVQ=zy^R (tan ^A sin 0) A N tan ^A. (35)\\nV2r VM+MM\\ni? exsec i^ A r^p. (oo)\\ncos ^A cos\\ni? sin (a? ^^ers 0) tan ^A. (37)\\nExample. To join two tangents making an angle of 34\u00c2\u00b0 :2(\\nby a 5\u00c2\u00b0 40 curve and suitable spirals. Use l\u00c2\u00b0-per-25-feet\\nThe student should at once appreciate the fact of the necessary distor-\\ntion of the figure. The distance MM in Fig. 33 is perhaps 100 times its real\\nproportional value.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0067.jp2"}, "68": {"fulltext": "52\\nRAILROAD CONSTRUCTION.\\n\u00c2\u00a750.\\nspirals with five chords. Then 3\u00c2\u00b0 45^ x 2.999, ^J\\n17\u00c2\u00b0 10 and y 124.942.\\n(Eq. 33)\\nB\\nvers\\n312.471\\nAQ 59.042\\nAF\\n3.00497\\n7.33063\\n2.166\\n0.33560\\nX\\n2.999\\nA N\\n0.833\\ncos ^A\\n9.92064\\n9.98021\\n771\\nMir\\nAA\\n0.872\\n9.94043\\n(Eq.\\n36)\\nR\\n3.00497\\nexsec ^A\\n8.66863\\nV3f\\n47.164\\n1.67365\\non\\n0.872\\n35)\\ny\\n124.942\\nV2r\\nnat.\\n48.036\\n.30891\\n(Eq.\\ntan Jz/\\nnat.\\nsin\\n.06540\\n.24351\\nR\\n9.3865!\\n3.00497\\n246.314\\n[See\\nabove^\\nA N-\\n2.39148\\n9.92064\\ntan ^A\\n9.48984\\nVQ\\n0.257\\nAj}^\\n9.41048\\n371.513\\n(Eq.\\n37)\\nR\\ntan \\\\A\\n3.00497\\n9.48984\\n2.49481\\n50. Field-work. When the spiral is designed during the\\noriginal location, tlie tangent distance VQ should be computed\\nand the point Q located. It is hardly necessary to locate all of\\nthe points of the spiral until the track is to be laid. The\\nextremities should be located, and as there will usually be one\\nand perhaps two full station points on the spiral, these should", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0068.jp2"}, "69": {"fulltext": "51. ALIGNMENT. 53\\nalso be located. Z may be located by setting off QK y and\\nKZ a or else by the tabular deflection for Z from Q and the\\ndistance ZQ, which is the long chord. Setting up the instru-\\nment at Z and sighting back at Q with the proper deflection, the\\ntangent at Z may be found and the circular curve located as\\nusual, its central angle being 20. A snnilar operation will\\nlocate Q from Z\\nTo locate points on the spiral. Set up at Q, with the plates\\nreading 0 when the telescope sights along VQ. Set oft from\\nQ the deflections given in Table IV for the instrument at Q,\\nusino a chord length of 25 feet, the process being like the\\nmethod for simple curves except that the deflections are irregu-\\nlar. If a full station-point occurs within the spiral, interpolate\\nbetween the deflections for the adjacent spiral- points. For ex-\\nample, a spiral begins at Sta. 5G 15. Sta. 57 comes 10 feet\\nbeyond the third spiral point. The deflection for the third point\\nis 35 0 for the fourth it is 56 15 |f of the difference\\n(21 15 is 8 30 the deflection for Sta. 57 is therefore 43 30\\nThis method is not theoretically accurate, but the error is small.\\nArriving at z, the forward alignment may be obtained by sight-\\ning back at Q (or at any other point) with the given deflection\\nfor that point from the station occupied. Then when the plates\\nread 0\u00c2\u00b0 the telescope will be tangent to tlie spiral and to the\\nsucceeding curve. All rear points should be checked from z.\\nIf it is necessary to occupy an intermediate station, use the de-\\nflections given for that station, orienting as just explained for 5,\\nchecking the back points and locating all forward points up to z\\nif possible.\\nAfter the center curve has been located and z is reached, the\\nother spiral must be located but in reverse order, i.e., the sharp\\ncurvature of the spiral is at z and the curvature decreases toward\\nQ\\n51. To replace a simple curve by a curve with spirals. This\\nmay be done by the method of 49, but it involves shifting the\\nwhole track a distance m^ which in the given example equals\\n0.87 foot. Besides this the track is appreciably shortened.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0069.jp2"}, "70": {"fulltext": "54\\nRAILROAD CONSTRUCTION.\\n\u00c2\u00a751.\\nwhich would require rail-cutting. But the track may be kept at\\nj^racticallj the same length and the lateral deviation from the\\nold track may be made very small by slightly sharpening tlie\\ncurvature of the old track, moving the new curve so that it is\\nwholly or partially outside of the old curve, the remainder of it\\nwitli the spirals being inside of the old curve. It is found by\\nexperience that a decrease in radius of from Ifo to 5^ will answer\\no\\nFig. 34.\\nthe purpose. The larger the central angle the less the change.\\nThe solution is as indicated in Fig. 34.\\nO V (9 ir sec 1^\\ncos sec X sec\\nm MM 2fV-M V\\nEex8eci^ -{O V B\\nB exsec J^ B cos sec x sec J^ B (38)\\nAQ QK- KN -\\\\-.\u00c2\u00a5V- YA\\ny\u00e2\u0080\u0094B sin cos x) tan B tan\\n=y\u00e2\u0080\u0094B sin P B cos tan ^A {B x) tan i^. (39)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0070.jp2"}, "71": {"fulltext": "\u00c2\u00a751.\\nALIGNMENT.\\noa\\nThe length of the old curve from Qio Q 2.AQ lOOy\\nThe length of the new curve from Qio Q IL 100 77-^,\\nin Avhich L is the length of each spiral.\\nExample. Suppose the old curve is a Y\u00c2\u00b0 30 curve with a\\ncentral angle of 38\u00c2\u00b0 40 As a trial, compute the relative length\\nof a new 8\u00c2\u00b0 curve with spirals of seven chords. 0=7\u00c2\u00b0 0\\niJ 19\u00c2\u00b0 20 R (for the 7\u00c2\u00b0 30 curve) 76i.-189 jR (for the\\n8\u00c2\u00b0 curve) 716.779; aj 7.628.\\n[Eq. 38]\\n45.687\\nR 716.779\\n[Eq. 89]\\n762.466\\n762.037\\n7n 0.429\\n53. 953\\n8.084\\n762.037\\nR\\nexsec 5 J\\n2.88337\\n8.77642\\n1.65979\\nR\\ncos (p\\nsec iz/\\n2.85538\\n9.99675\\n0.02521\\n2.8773+\\nX\\nsec ^A\\n0.88241\\n0.02521\\n0.90762\\ny 174.722\\n87.353\\n265.543\\nR\\nsin (p\\nR\\ncos (p\\ntan I A\\nR= 764.489\\nx= 7.628\\n2.85538\\n9.08589\\n1.94128\\n2.85538\\n9.99675\\n9.54512\\n249.606\\n2.39725\\n756.861\\ntan ^J\\n2.8790?\\n9.54512\\n2.42413\\n424.328\\n352.896\\n352.896\\nAQ= 71.432", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0071.jp2"}, "72": {"fulltext": "56 RAILROAD CONSTRUCTION. 52.\\nThe length of the old curve from Q to Q is\\n100^ lO^TX^ 515.556\\n2^^=2X71.433= 142.864\\nNew curve 100^-=^ 38.667-14.000\\nJJ o.U\\n2i: 2 X 175 =350.000\\n658.420\\n658.333 658.333\\nDifference iu length 0.087\\nConsidering that this difference may be divided among 22\\njoints (using 30-foot rails) no rail-cutting would be necessary.\\nIf the difference is too large, a slight variation in the value of\\nthe new radius R will reduce the difference as much as neces-\\nsary. A truer comparison of tlie lengths would be found by\\ncomparing the lengths of the arcs.\\n52. Application of transition curves to compound curves.\\nSince compound curves are only employed when the location is\\nlimited by local conditions, the elements of the compound curve\\nshould be determined (as in \u00c2\u00a7\u00c2\u00a738 and 39) regardless of the\\ntransition curves, depending on the fact that the lateral shifting\\nof the curve when transition curves are introduced is very\\nsmall. If the limitations are very close, an estimated allowance\\nmay be made for them.\\nMethods have been devised for inserting transition curves\\nbetween the branches of a compound curve, but the device is\\ncomplicated and usually needless, since when the train is once on\\na curve the wheels press against the outer rail steadily and a\\nchange in curvature will not produce a serious jar even though\\nthe superelevation is temporarily a little more or less than it\\nshould be.\\nIf the easier curve of the compound curve is less than 3\u00c2\u00b0 or\\n4\u00c2\u00b0, there may be no need for a transition curve off from that\\nbranch. This problem then has two cases according as transition\\ncurves are used at both ends or at one end only.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0072.jp2"}, "73": {"fulltext": "\u00c2\u00a752.\\nALIGNMENT.\\n57\\na. With transition curves at loth ends. Adopting the\\nmethod of 49, calling i^, we may compute m, J/ J//.\\nSimilarly, calling A, 4^, we may compute m, 2IMJ. But\\nFig. 35.\\n1// and MJ must be made to coincide. This may be done by\\nmoving the curve Z 3/ and its transition curve parallel to (/V\\na distance M/M,, and the other curve parallel to QV ii distance\\nM M,. In the triangle M, MJf,\\\\ the angle at 31, 00\u00c2\u00b0 J\u00e2\u0080\u009e\\ntlie angle at MJ 90\u00c2\u00b0 and the angle at 21,\\nsin(90\u00c2\u00b0-Z/,) .cos\\nThen M, M, M:M:-^^^^={^^-^^h)^^-\\nsin(90\u00c2\u00b0-^;) OS\\nSimilarly 2f:2f, iZ/^^/Z-^g-Tj\u00e2\u0080\u0094 ^ih71J\\nm", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0073.jp2"}, "74": {"fulltext": "58 BAILROAD CONSTRUCTION, 53.\\nb. With a transition curve on the sharper curve only. Com-\\npute 7?^, MMl as before then move tlie curve Z^Ml parallel\\nto Q V Si distance of\\nJf/Jf, m,5?^^ (41)\\nsm\\nThe simple curve MA is moved parallel to VA a distance of\\n3\u00c2\u00a33\u00c2\u00a3, 971! (42)\\nsm\\nIf /J, and ^5 are both small, M/M^ and IfM^ may be more\\nthan mj, but the lateral deviation of the new curve from the old\\nwill always be less than ^n^.\\n63. To replace a compound curve by a curve with spirals.\\nThe solution is somewhat analogous to that of 51. Compute\\n7n^ for the sharper branch of the curve, placing ^1 in Eq.\\n38. Since 7n^ and m^ for the two branches of the curve must\\nbe identical, a value for must be found which will satisfy\\nthe determined value of 7n^ 7n^. Solving Eq. 38 for B we\\nobtain\\nB vers i^ m cos ^A x\\ncos COS t^\\nSubstituting in this equation the known value of 772/j m^\\nand calling R B^\\\\ 7? i?^, and A^ ^A^ solve for j^,\\nObtain the value oi AQ for each branch of the curve separately\\nby Eq. 39, and compare the lengths of the old and new lines.\\nExample. Assume a compound curve with Z 8\u00c2\u00b0; Z^^ =r 4\u00c2\u00b0\\n36 and 4, 32\u00c2\u00b0. Use l\u00c2\u00b0-per-25-feet spirals 0^ 7\u00c2\u00b0 0\\n02 1\u00c2\u00b0 30 Assume that the sharper curve is sliarpened from\\n8\u00c2\u00b0 0 to 8\u00c2\u00b0 12", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0074.jp2"}, "75": {"fulltext": "\u00c2\u00a753.\\n[Eq. 38]\\nALIGNMENT.\\n169.209\\nRi 699.326\\n868.535\\n857.970\\n9.429\\n[Eq. 43]\\n215.974\\nnat. cos (p .99966\\nnat. cos /1 2 .84805\\ni?, 1424.54 [4\u00c2\u00b01 22\\n[Eq. 39]\\n2/, 174.722\\n85.226\\n504.302\\n679.024\\n600.461\\n515.235\\n600.461\\n^Q, 78.563\\n59\\nexsec 36\u00c2\u00b0\\n2.85538\\n9.37303\\n2.22842\\n11.\\ncos 01\\nsec z/i\\n2.84408\\n9.99075\\n0.09204\\n2.93347\\n3*1\\nsec A I\\n0.88241\\n0.09204\\n0.97445\\nm\\\\\\n867.399\\n1.136\\n217.700\\n1.726\\n^\u00e2\u0080\u00a22\\n867.\\n0.\\n0,\\n1\\n399\\n963\\n.763\\n.726\\nvers 32\u00c2\u00b0\\nm, 1.136\\ncos 32\u00c2\u00b0\\n3.15615\\n9.18175\\n2.33785\\n0.05538\\n9.92842\\n9.98380.\\n2.33440\\n.15161\\n9.1807S\\n3.15307\\nsin 01\\n2.84468\\n9.08589\\n1.93057\\ncos 01\\ntan \\\\AIA, 36\u00c2\u00b0]\\n2.84468\\n9.99675\\n9.86126\\nR, 716.779\\nX, 7.628\\n2 70269\\n709.151\\ntan \\\\A\\n2.85074\\n9.86126\\n2.7120a", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0075.jp2"}, "76": {"fulltext": "60\\n[Eq. 39]\\nRAILROAD CONSTRUCTION.\\n2/a 74.994\\n889.843\\n964.837\\n932.060\\n37 290\\n894.770\\n932.060\\nAQ-.^ 32.777\\nFor the length of the old track we have\\n53.\\nR,\\nsin 02\\n3.15367\\n8.41792\\n1.57159\\nR,\\ncos 0a\\ntan iz/(J2 32\u00c2\u00b0)\\n3.15367\\n9.99985\\n9.79579\\n2.94931\\ni?a 1432.69\\nCCa 0.76\\n1431.93\\ntan iz/\\n3.15592\\n9.79579\\n2.95171\\n100\\n100\\nD,\\n0\\n450.\\n^2\\ni 2\\n100\\n800.\\nAQ,\\n78.563\\nAQ^\\n32.777\\n1361.340\\nFor the length of the new track we have\\n100^i^ 100-J?l= 353.659\\ni\\n8\u00c2\u00b0.20\\n100^i^l^ 10oS.= 758.140\\nA\\n4\u00c2\u00b0. 023\\nSpiral on 8\u00c2\u00b0 12 curve 175.000\\n4\u00c2\u00b0 01 22 75.\\nLength of new track 1361.799\\nold 1361.340\\nExcess in length of new track 0.459 feet.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0076.jp2"}, "77": {"fulltext": "55. ALIGNMENT. 61\\nSince the new track is slightly longer than the old, it shows\\nthat the new track runs too far outside tlie old track at the\\nP.C.C. On the other hand the offset 7n is only 1.186. The\\nmaximum amount by which the new track comes inside of the\\nold track at two points, presumably not far from Z and Z, is\\nvei-y dithcult to determine exactly. Since it is desirable that the\\nmaxinnini offsets (inside and outside) should be made as nearly\\nequal as possible, this feature should not be sacrificed to an effort\\nto make the two lines of precisely equal length so that the rails\\nneed not be cut. Therefore, if it is found that the offsets inside\\nthe old track are nearly equal to m (1.136), the above figures\\nshould stand. Otherwise vi may be diminished (and the above\\nexcess in length of track diminished) by increasing R^ very\\nslightly and making the necessary consequent changes.\\nVERTICAL CURVES.\\n54. Necessity for their use. AYhenever there is a change in\\nthe rate of grade, it is necessary to eliminate the angle that\\nAvould be formed at the point of change and to connect the two\\ngrades by a curve. This is especially necessary at a sag be-\\ntween two grades, since the shock caused by abruptly forcing\\nan upward motion to a rapidly moving heavy train is very\\nsevere both to the track and to the rolling stock.\\n55. Required length. Theoretically the length should de-\\npend on the change in the rate of grade, the greater change\\nrequiring a longer curve. The importance of this was greater\\nin the days when link couplers were in universal use and the\\nslack in a long train was very great. Under such circum-\\nstances, when a train was moving down a heavy grade the cars\\nwould crowd ahead against the engine. Reaching the sag, the\\nengine would begin to pull out, rapidly taking out the slack.\\nSix inches of slack on each car would amount to several feet on\\na long train, and the resulting jerk on the couplers, especially\\nthose near the rear of the train, has frequently resulted in", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0077.jp2"}, "78": {"fulltext": "62 RAILROAD CONSTRUCTION. oQ.\\nbroken couplers or even derailments. A vertical curve will\\npractically eliminate tins danger if the curve is made long\\nenough, but the rapidly increasing adoption of close spring\\ncouplers and air-brakes, even for freight trains, is obviating the\\nnecessity for such very long curves. Two hundred feet may be\\nconsidered sufficiently long for all ordinary changes of grade.\\nFour hundred feet would probably suffice for the greatest\\nchange ever found in practice.\\n56. Form of curve. In Fig. 36 assume that A and C, equi-\\nFiG. 36.\\ndistant from B^ are the extremities of the vertical curve. Bi-\\nsect AG ^i e\\\\ draw Be and bisect it at h. Bisect AB and BC\\nat h and I. The line kl will pass through h. A parabola may\\nbe drawn with its vertex at h which will be tangent to AB and\\nBC 2ii A and B. It may readily be shown from the proper-\\nties of a parabola that if an ordinate be drawn at any point (as\\nat n) we will have\\nsn eh (or JiB) Am Ae\\nAori\\nor sn eri\u00e2\u0080\u0094j~Y (44)\\nSince the elevation of any point along AB or BO is readily\\ndeterminable, the elevation of any point on the curve may be\\ncomputed by adding the correction sn.\\n57. Numerical example. Assume that B is located at Sta.\\n16 20; that the curve is to be 200 feet long; that the grade\\nof AB is 0.8^, and of B0-{- 1.2^; also that the elevation\\nof B above the datum plane is 162.6. Then the elevation of\\nthe various points is as follows: A, 163.4; 0, 163.8; 6,", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0078.jp2"}, "79": {"fulltext": "57. ALIGNMENT. 63\\nJ(163.4 163.8) 163.6; A, |-(168.0 1G2.G) 103.1. Tlien\\neh=^ 0.5. The elevations of the points on the curve are:\\nSta. 15 20, {A) 1G3.4\\n16 163.-1- (.80 X 0.8) (.SO X 0.5) 163.08\\n17 162.6 (.80 X 1.2) (.20 X 0.5) 163.58\\nu 17_|_20, {C) 163.8\\nA theoretical inaccuracy in tlie above method lies in the fact\\nthat eh and all parallel lines are not truly vertical. In the\\nabove case the variation from the vertical is 0\u00c2\u00b0 07^, while tlie\\neffect of this variation on the elevations in this case (as in the\\nmost extreme cases) is absolutely inappreciable. The grades\\nin the figure are necessarily very greatly exaggerated, which\\nincreases the apparent inaccuracy.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0079.jp2"}, "80": {"fulltext": "CHAPTER III,\\nEARTHWORK.\\nFORM OF EXCAVATIONS AN^D EMBANKMENTS.\\n58. Usual form of cross- section in cut or fill. The normal\\nform of cross-section in cut is as sliown^^in Fig. 37, in which\\ne g represents the natural surface of the ground, no matter\\nhow irregular; ab represents the position and width of the re-\\ne\\nquired roadbed ac and hd represent the side slopes which\\nbegin at a and h and which intersect the natural surface at such\\nd\\nFig. 38.\\npoints {g and d^ as will be determined by the required slope\\nangle\\n64", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0080.jp2"}, "81": {"fulltext": "g 00. EARTHWORK. 65\\nThe normal section in iill is as shown in Fig. 38. The points\\nc and d are likewise determined by the intersection of the re-\\nquired side slopes with the natural surface. In case the required\\nroadbed {ah in Fig. 39) intersects the natural surface, both cut\\nFig. 39.\\nand fill are required, and the points c and d are determined as\\nbefore. Is^ ote that and are not necessarily equal. Their\\nj)roper values will be discussed later.\\n59. Terminal pyramids and wedges. Fig. 40 illustrates the\\ngeneral form of cross-sections when there is a transition from\\ncut to fill, a g represents the grade line of the road which\\npasses from cut to fill at d. sdt represents the surface profile.\\nA cross-section taken at the point where either side of the road-\\nbed first cuts the surface (the point m in this case) will usually\\nbe triano-ular if the ground is regular. A similar cross-section\\nshould be taken at o^ where the other side of the roadbed cuts\\nthe surface. In general the earthwork of cut and fill terminates\\nin two pyramids. In Fig. -10 the pyramid vertices are at n\\nand h^ and the bases are Ihrn and opq. The roadbed is generally\\nwider in cut than in fill, and therefore the section Ihm and the\\naltitude In are generally greater than tlie section oj^q and the\\naltitude ^A: When the line of intersection of the roadbed and\\nnatural surface {nodkm) becomes perpendicular to the axis of\\nthe roadbed {ag) the pyramids become wedges whose bases are\\nthe nearest convenient cross- sections.\\n60. Slopes, a. Cuttings. The required slopes for cuttings\\nvary from perpendicular cuts, which may be used in hard rock\\nwhich will not disintegrate by exposure, to a slopeof perhaps", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0081.jp2"}, "82": {"fulltext": "66\\nRAILROAD CONSTRUCTION.\\n60.\\n4 horizontal to 1 vertical in a soft material like quicksand or in\\na clayey soil winch flows easily when saturated. For earthy\\nmaterials a slope of 1 1 is the maximum allowable, and even\\nthis should only be used for firm material not easily affected by\\nFig. 40.\\nsaturation. A slope of IJ horizontal to 1 vertical is a safer\\nslope for average earthwork. It is a frequent blunder that\\nslopes in cuts are made too steep, and it results in excessive work\\nin clearing out from the ditches the material that slides down,\\nat a much higher cost per yard than it would have cost to take\\nit out at first, to say nothing of the danger of accidents from\\npossible landslides.\\nb. Embankments. The slopes of an embankment vary from\\n1 1 to 1.5 1 A rock fill will stand at 1:1, and if some care\\nis taken to form the larger pieces on the outside into a rough\\ndry wall, a much steeper slope can be allowed. This method is\\nsometimes a necessity in steep side-hill work. Earthwork em-\\nbankments generally require a slope of 1 J to 1. If made\\nsteeper at first, it generally results in the edges giving way, re-\\nquiring repairs until the ultimate slope is nearly or quite IJ- 1.\\nThe difficulty of incorporating the added material with the old\\nembankment and preventing its sliding off frequently makes\\nthese repairs disproportionately costly.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0082.jp2"}, "83": {"fulltext": "62. EARTIIWOIiK. 67\\n61. Compound sections. AVlien the cut consists partly of\\nearth and partly of rock, a compound cross-section must be\\nFig. 41.\\nmade. If borings have been made so that tlie contour of the\\nrock surface is accurately known, then the true cross-section may\\nbe determined. The rock and earth should be calculated sepa-\\nrately, and this will require an accurate knowledge of where the\\nrock runs out a difficult matter when it must be deter-\\nmined by boring. During construction the center part of the\\nearth cut would be taken out first and the cut widened until a\\nsufficient width of rock surface had been exposed so that the\\nrock cut would have its proper width and side slopes. Then the\\nearth slopes could be cut down at the proper angle. A berni\\nof about three feet is usually left on the edges of the rock cut as\\na margin of safety against a possible sliding of the earth sloj^es.\\nAfter the work is done, the amount of excavation that has been\\nmade is readily computable, but accurate preliminary estimates\\nare difficult. The area of the cross- section of earth in the figure\\nmust be determined by a method similar to that developed for\\nborrow-pits (see 89).\\n62. Width of roadbed. Owing to the large and often dis-\\nproportionate addition to volume of cut or fill caused by the ad-\\ndition of even one foot to the width of roadbed, there is a\\nnatural tendency to reduce the width until embankments become\\nunsafe and cuts are too narrow for proper drainage. The cost\\nof maintenance of roadbed is so largely dependent on the drain-\\nage of the roadbed that there is true economy in making an", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0083.jp2"}, "84": {"fulltext": "68\\nRAILROAD CONSTRUCTION,\\n\u00c2\u00a763..\\nample allowance for it. The practice of some of the leading\\nrailroads of the country in this respect is given in the following\\ntable, in which are also given some data belonging more properlj\\nto the subject of superstructure.\\nWIDTH OF ROADBED FOR SINGLE AND DOUBLE TRACK-SLOPE RATIOS-\\nDISTANCES BETWEEN TRACK CENTERS.\\nRoad.\\nA., T. Santa Fe.\\nChi., Burl. Quincy\\nChi., Mil. St. Paul.\\nC, C, C. St. Louis\\nIllinois Central.\\nErie\\nLehigh Valley\\nL. S. Michigan So.\\nLouisville Nashv.\\nMichigan Central.\\nN. Y. N. H. H....\\nNorfolk Western...\\nPennsylvania -j\\nUnion Pacific\\nSingle Track.\\nCut.\\nj 28 earth\\n1 2-i rock\\n14 (2 X.5)\\n18 (:i X 6)\\n20 (2 X 4)\\n32.5\\n20 81^\\n14 (2 X3.5)\\n13 (2X4.5)\\n21 2 earth\\n16\\nrock\\n19 2 light traffic\\n27 2 heavy\\n14 -i- (2 X 3.5)\\nFill.\\n20\\n16\\n20 to 24\\n20\\n18\\n20 81^\\n16\\n16\\n17 2\\n19 2\\n19 2\\n16\\nDouble Track.\\nCut.\\n28 (2 X 5)\\n31 (2 X 6)\\n33 (2X4)\\n33 81^\\n27 (2X3.5)\\n33 (8X7.25;\\n33 (2X2.5)\\n30\\n34 2 earth\\n29 rock\\n31 4 +(2 X 4)\\nFill.\\n30\\n33 to 37\\n33\\n33 81^\\n30\\n32\\n33\\n30\\n30 2\\n31 4\\nSlope\\nRatios.\\nCut.\\n1\\nVa\\n1.5\\n1.5\\n1.5\\n1.5\\n1.5\\n1\\n1.5\\n1\\n1.5\\n1.5\\n1 5\\n1.5: 1\\n1 1\\nFill.\\n1.5: 1\\n1.5\\n1.5\\n1.5\\n1.5\\n1.5\\n1.5\\n1.5\\n1.5\\n1.5\\n1.5\\n1.5\\nI\\n1.5: 1\\n1.5 1\\nJ? c\\n.2\u00c2\u00a3E-i\\n14\\n13\\n13\\n13\\n13\\n13\\n13\\n12\\n13\\n13\\n12 2\\n(2 X 5) signifies two ditches each 5 feet wide: the following cases should be interpreted\\nsimilarly.\\nIt may be noted from the above table that the average width\\nfor an eartliworh cut, single track, is about 24.7 feet, with a\\nminimum of 19 feet 2 inches. The widths of fills, single track,\\naverasre over 18 feet, with numerous minimums of 16 feet.\\nThe widths for double track may be found by adding the distance-\\nbetween track centers, which is usually 13 feet.\\n63. Form of subgrade. The stability of the roadbed depends\\nlargely on preventing the ballast and subsoil from becoming\\nsaturated with water. The ballast must be porous so that it\\nwill not retain water, and the subsoil must be so constructed that it\\nwill readily drain off the rain-water that soaks through the ballast.\\nThis is accomplished by giving the subsoil a curved form, convex", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0084.jp2"}, "85": {"fulltext": "64. EARTHWORK. 69\\nupward, or a surface made up of two or three planes, the two\\nouter phines liaviiig a slope of about 1 21 (sometimes more\\nand sometimes less, de23ending on the soil) and the middle plane,\\nif three are used, being level. When a circular form is used,\\na crownini^ of 6 inches in a total width of 17 or 18 feet is iren-\\nerally used. Occasionally the subgrade is made level, especially\\nin rock-cuts, but if the subsoil is previously compressed by\\nrolling, as required on the X. Y. C. cV: H. K. E. E., or if the\\nsubsoil is drained by tile drains laid underneath the ditches, the\\nnecessity for slopes is not so great. Eock cuts are generally\\nrequired to be excavated to one foot below subgrade and then\\ntilled up again to subgrade with the same material, if it is suit-\\nable.\\n64. Ditches. The stability of the track depends upon the\\nstrength and permanence of the roadbed and structures upon\\nwliich it rests whatever will protect them from damage or pre-\\nvent premature decay should be carefully observed. The worst\\nenemy is water, and the further it can be kept away from the\\ntrack, or the sooner it can be diverted from it, the better the\\ntrack will be protected. Cold is damaging only by reason of\\nthe water which it freezes therefore the first and most impor-\\ntant provision for good track is drainage. (Eules of the Eoad\\nDepartment, Illinois Central E. E.)\\nThe form of ditch generally prescribed has a flat bottom V2\\nto 24 wide and with sides having a minimum slo])e, except in\\nrock- work, of 1:1, more generally 1.5 1 and sometimes 2:1.\\nSometimes the ditches are made Y-shaped, which is objection-\\nable unless the slopes are low. The best form is evidently that\\nwhich will cause the greatest flow for a given slope, and this\\nwill evidently be the form in which the ratio of area to wetted\\nperhneter is the largest. The semicircle ful-\\nfills this condition better than any other\\nform, but the nearly vertical sides would be\\ndifiicult to maintain. (See Fig. 42.) A ditch, Fig. 42.\\nwith a flat bottom and such slopes as tlie soil requires, which\\napproximates to the circular form will therefore be the best.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0085.jp2"}, "86": {"fulltext": "70 RAILROAD COJSSTRUCTION. Qb.\\nWhen the flow will probably be large and at times rapid it\\nwill be advisable to pave the ditches with stone, especidly if the\\nsoil is easily washed away. Six-inch tile drains, placed 2^ under\\nthe ditches, are prescribed on some roads. (See Fig. 43.) l^o\\nbetter method could be devised to insure a dry subsoil. The\\nditches through cuts should be led off at the end of the cut so\\nthat the adjacent embankment will not be injured.\\nWherever there is danger that the drainage from the land\\nabove a cut will drain down into the cut, a ditch should be made\\nnear the edge of the cut to intercept this drainage, and this\\nditch should be continued, and paved if necessary, to a point\\nwhere the outflow will be harmless. I^eglect of these simple\\nand inexpensive precautions frequently causes the soil to be\\nloosened on the shoulders of the slopes during the progress of a\\nheavy rain, and results in a landslide which will cost more to\\nrepair than the ditches which would have prevented it for all\\ntime.\\nDitches should be formed along the bases of embankments\\nthey facilitate the drainage of water from the embankment, and\\nmay prevent a costly slip and disintegration of the embankment.\\n65. Effect of sodding the slopes, etc. Engineers are unani-\\nmously in favor of rounding off the shoulders and toes of\\nembankments and slopes, sodding the slopes, paving the ditches,\\nand providing tile drains for subsurface drainage, all to be put\\nin during original construction. (See Fig. 43.) Some of the\\nhighest grade specifications call for the removal of the top layer\\nof vegetable soil from cuts and from under proposed fills to\\nsome convenient place, from which it may be afterwards spread\\non the slopes, thus facilitating the formation of sod from grass-\\nseed. But while engineers favor these measures and their\\neconomic value may be readily demonstrated, it is generally\\nimpossible to obtain the authorization of such specifications\\nfrom railroad directors and 2)i*C)moters. The addition to the\\noriginal cost of the roadbed is considerable, but is by no means\\nas great as the capitalized value of the extra cost of mainte-\\nnance resulting from the usual practice. Fig. 43 is a copy of", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0086.jp2"}, "87": {"fulltext": "^e5.\\nEAHTUWORK.\\n71\\nPROPOSED SECTION OF ROADBED IN EXCAVATION.\\nCUSTOMARY SECTION OF ROADBED ON EMBANKMENT.\\nGRAVELn\\nPROPOSED SECTION OF ROADBED ON EMBANKMENT.\\nGRAVEL,\\nFig. 43.\u00e2\u0080\u0094 VVhittemoke on Railway Excavation and Embankments,\\nTrans. Am. Soc. C. E., Sept. 1894", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0087.jp2"}, "88": {"fulltext": "72 RAILROAD CONSTRUCTION. 66.\\ndesigns presented at a convention of the American Society of\\nCivil Engineers by Mr. D. J. Wliittemore, Past President of\\nthe Society and Chief Engineer of the Chi., Mil. tfe St. Paul\\nR.R. The customary sections represent what is, with some\\nvariations of detail, the practice of many railroads. The pro-\\nposed sections elicited unanimous approval. They should be\\nadopted when not prohibited by financial considerations.\\nEAETHWOKK SURVEYS.\\n66. Relation of actual volume to the numerical result. It\\nshould be realized at the outset that the accuracy of the result\\nof computations of the volume of any given mass of earthwork\\nhas but little relation to the accuracy of the mere numerical\\nwork. The process of obtaining the volume consists of two\\ndistinct parts. In the first place it is assumed that the volume\\nof the earthwork may be represented by a more or less com-\\nplicated geometrical form, and then, secondly, the volume of\\nsuch a geometrical form is computed. A desire for simplicity\\n(or a frank willingness to accept approximate results) will often\\ncause the cross-section men to assume that the volume may be\\nrepresented by a very simple geometrical form which is really\\nonly a very rough approximation to the true volume. In such\\na case, it is only a waste of time to compute the volume with\\nminute numerical accuracy. One of the first lessons to be\\nlearned is that economy of time and effort requires that the\\naccuracy of the numerical work should be kept proportional to\\nthe accuracy of the cross-sectioning work, and also that the\\naccuracy of both should be proportional to the use to be made\\nof the results. The subject is discussed further in 94.\\n67. Prismoids. To compute the volume of earthwork, it is\\nnecessary to assume that it has some geometric form whose vol-\\nume is readily determinable. The general method is to consider\\nTrans. Am. Soc. Civil Eng., Sept. 1894.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0088.jp2"}, "89": {"fulltext": "g 08. EAnrilWORK. 73\\nthe volume as consisting of a series of jprisinoids, which are\\nsolids having parallel plane ends and bounded by surfaces which\\nmay be formed by lines moving continuously along the edges of\\nthe bases. These surfaces may also be considered as the sur-\\nfaces generated by lines moving along the edges joining the cor-\\nresponding points of the bases, these edges being the directrices,\\nand the lines being always parallel to either base, which is a\\nplane director. The surfaces thus developed may or may not\\nbe planes. The volume of such a prismoid is readily determi-\\nnable (as explained in g 70 et seq.), while its definition is so very\\ngeneral that it may be applied to very rough ground. The\\ntwo ])lane ends are sections perpendicular to the axis of the\\nroad. The roadbed and side slopes (also plane) form three of\\nthe side surfaces. The only approximation lies in the degree of\\naccuracy with which the plane (or warped) surfaces coincide with\\nthe actual surface of the ground between these two sections.\\nThis accuracy will depend (a) on the number of points whicli\\nare taken in each cross-section and the accuracy with which the\\nlines joining these points coincide with the actual cross-sections\\n(h) on the skill shown in selecting places for the cross-sections so\\nthat the warped surfaces shall coincide as nearly as possible with\\nthe surface of the ground. In fairly smooth country, cross-\\nsections every 100 feet, placed at the even stations, are suf-\\nficiently accurate, and such a method simplifies the computations\\ngreatly but in rough country cross-sections must be inter-\\npolated as the surface demands. As will be exj^lained later,\\ncarelessness or lack of judgment in cross-sectioning will introduce\\nerrors of such magnitude that all refinements in the computations\\nare utterly wasted.\\n68. Cross-sectioning. The process of cross-sectioning con-\\nsists in determining at any place the intersection by a vertical\\nplane of the prism of earth lying between the roadbed, the side\\nslopes, and the natural surface. The intersection with the road-\\nbed and side slopes gives three straight lines. The intersection\\nwith the natural surface is in general an irregular line. On\\nsmooth regular ground or when approximate results are accc])t-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0089.jp2"}, "90": {"fulltext": "74\\nBAILED AD CONSTRUCTION.\\n68.\\nable this line is assumed to be strais^ht. Accordins: to the irreo^-\\nularitj of the ground and the accuracy desired more and more\\nintermediate points are taken.\\nThe distance {d in Fig. 44) of the roadbed below (or above)\\nthe natural surface at the center is known or determined from\\nFig. 44.\\nthe profile or by the computed establishment of the grade line.\\nThe distances out from the center of all breaks are determined\\nwith a tape. To determine the elevations for a cut, set up a\\nlevel at any convenient point so that the line of sight is higher\\nthan any point of the cross-section, and take a rod reading on\\nthe center point. This rod reading added to d gives the height\\nof the instrument (H. I.) above the roadbed. Subtracting from\\nH. I. tlie rod reading at any break gives the height of that\\npoint above the roadbed (A,, hi, h^, etc.). This is true for all\\ncases in excavation. For fill, the rod reading at center minus\\nd equals the II. I., which may be positive or negative. When\\nnegative, add to the H. I. the rod readings of the inter-\\nmediate points to get their depths below grade when posi-\\ntive, subtract the H. I. from the rod readings.\\nThe heights or depths of these intermediate points above or\\nbelow grade need only be taken to the nearest tenth of a foot,\\nand the distances out from the center will frequenth^ be sufii-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0090.jp2"}, "91": {"fulltext": "69.\\nEAHTUWORK.\\n75\\nciently exact when taken to tlie nearest foot. Tlie roughness of\\nthe surface of farming land or woodland generally renders use-\\nless any attempt to compute the volume with any greater accu-\\nracy than these ligures would im])ly unless the form of the ridges\\nand hollows is especially well delined. The position of the slope-\\nstake points is considered in the next section. Additional dis-\\ncussion regarding cross-sectioning is found in 82.\\n69. Position of slope-stakes. The slope-stakes are set at the\\nintersection of the required side slopes with the natural surface,\\nwhich depends on the center cut or till The distance of\\n1\\ny^-\\n_ rp\\n1\\nSI\\ny\\n1\\n1\\nFig. 45.\\nthe slope-stake from the ceiiter for the lower side is ,r \\\\lj\\ns{d y) for the up-hill side it is x JZ* s{d y\\ns is the slope ratio for the side slopes, the ratio of horizontal\\nto vertical. In the above equation both x and y are unknown.\\nTherefore some position must be found by trial which will sat-\\nisfy the equation. As a preliminary, the value of x for the\\npoint a =z ^h sd, which is the value of x for level cross-\\nsections. In the case of fills on sloping ground the value of x\\non the doiim-Mll side is greater than this; on the up-liill side it\\nis less. The difference in distance is s times the difference of\\nelevation. Take a numerical case corresponding with Fig. 45.\\nThe rod reading on is 2.9 fZ -l.^ therefore the telescope is\\n4.2 2.9 1.3 leloio grade. 1.5 1, Z* K). Hence for\\nthe point a (or for level ground) x Y^ lG-t-1.5x4.2\\n14.3. At a distance out of 14.3 the ground is seen to be about 3\\nfeet lower, which will not only require 1.5x3 45 more, but", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0091.jp2"}, "92": {"fulltext": "70.\\nRAILROAD CONSTRUCTION.\\nenough additional distance so that the added distance shall be\\n1.5 times the additional drop. As a first trial the rod may be\\nheld at 24 feet out and a reading of, say, 8.3 is obtained. 8 3\\n1.3 9.6, the. depth of the point below grade. The point\\non the slope line {n) which has this depth below grade is at a\\ndistance from the center x 8 1.5 X 9.6 22 A. The\\npoint on the surface {s) having that depth is 24 feet out. There-\\nfore the true point (m) is nearer the center. A second trial at\\n20.5 feet out gives a rod reading of, say, 7.1 or a depth of 8.4\\nbelow grade. This corresponds to a distance out of 20.6. Since\\nthe natural soil (especially in farming lands or woods) is generally\\nso rough that a difference of elevation of a tenth or so may be\\nreadily found by slightly varying the location of the rod (even\\nthough the distance from the center is the same), it is useless to\\nattempt too much refinement, and so in a case like the above the\\ncombination of 8.4 below grade and 20.6 out from center may\\nbe taken to indicate the proper position of the slope-stake. This\\nis usually indicated in the form of a fraction, the distance out\\nbeing the denominator and the height above (or below) grade\\nbeing the numerator; the fact of cut or Jill may be indicated by\\nO or F. Ordinarily a second trial will be sufiicient to determine\\nwith sufiicient accuracy the true position of the slope-stake.\\nExperienced men will frequently estimate the required distance\\nout to within a few tenths at the first trial. The left-hand pages\\nof the note-book should have the station number, surface eleva-\\ntion, grade elevation, center cut or fill, and rate of grade. The\\nright-hand pages should be divided in the center and show the\\ndistances out and heights above grade of all points, as is illustrated\\nin 84. The notes should read up .the page, so that when look-\\ning ahead along tlie hue the figures are in their proper relative\\nposition. The fractions farthest from the center line repre-\\nsent the slope-stake points.\\nCOMPUTATION OF VOLUME.\\n70. Prismoidal formula. Let Fig. 46 represent a triangular\\nprismoid. The two triangles forming the ends lie in parallel", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0092.jp2"}, "93": {"fulltext": "70.\\nEARTHWORK.\\n77\\nplanes, but since the angles of one triangle are not equal to the\\ncorresponding angles of the other triangle, at least two of the sur-\\nfaces must be wa7 j)ed. If a section, parallel to the bases, is\\n-6i\u00e2\u0080\u0094\\nFig. 46.\\nmade at any point at a distance x from one end, the area of the\\nsection will evidently be\\ni\\nA, khX 4[j. (^A ,)7ji_/ .)7 J-\\nThe volume of a section of infinitesimal lengtli will be AJx, and\\nthe total volume of the prismoia will be\\n7 X^\\nx y\\nstudents unfamiliar with the Integral Calculus may take for granted the\\nfundamental formula, th^t fdx a, that fxdx l^, and that fx^dx ix-\\nalso that in integrating between the limits of I and (zero) the value of the\\nintegral may be found by simply substituting I for x after integration.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0093.jp2"}, "94": {"fulltext": "8 RAILROAD CONSTRUCTION. 70.\\n^[4^.^. iU^ K) ^\\\\{K K) iKh;]\\n[J, 4^,\u00e2\u0080\u009e ^J, (45)\\nin which and A,,, are the areas respectively of the two\\nbases and of the middle section. IS ote that A^ is not the mean\\nof ^land although it does not necessarily differ very greatly\\nfrom it.\\nThe above proof is absolntely independent of the values, ab-\\nsolute or relative, of 5^ Z h, or h^. For example, h^ may be\\nzero and the second base reduces to a line and the prismoid be-\\ncomes wedge-shaped or l^ and h^ may both vanish, the second\\nbase becoming a point and the prismoid reduces to a pyramid\\nSince every prismoid (as defined in 67) may be reduced to a\\ncombination of triangular prismoids, wedges, and pyramids, and\\nsince the formula is true for any one of them individually, it is\\ntrue for all collectively therefore it may be stated that\\nThe volume of a prismoid equals one sixth of the perpendic-\\ntdar distance hetween the hases multiplied hy the sum of the\\nareas of the two hases plies four times the area of the middle\\nsection.\\nWhile it is always possible to compute the volume of anv\\nprismoid by tlie above method, it becomes an extremely compli-\\ncated and tedious operation to compute the true value of tlie\\nmiddle section if the end sections are complicated in form. It\\nThe student should note that the derivation of equation (45) does not com-\\nplete the proof, but that the statements in the following paragraph are logi-\\ncally necessary for a general proof.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0094.jp2"}, "95": {"fulltext": "72. EAHTUWOKK. 79\\ntherefore becomes a simpler operation to compute volumes by ap-\\nproximate formult 3 and apply, if necessary, a correction. The\\nmost common methods are as follows\\n71. Averaging end areas. The volume of the triangular\\nprismoid (Fig. -iB), computed by averaging end areas, is\\n\u00e2\u0080\u0094[:J^i A, -[-J Subtracting this from the true volume (as\\ngiven in the equation above, Eq. (45) we obtain tlie correction\\nY2^iJ\\\\-h:){K-h,)-]. (46)\\nThi\u00c2\u00ab shows that if either the A s or 5 s are equal, the correc-\\ntion vanishes it also shows that if the bases are roughly similar\\nand h varies roughly with h (which usioally occurs, as will be\\nseen later), the correction will be negative^ which means that the\\nmethod of averaging end areas usually gives too large results.\\n72. Middle areas. Sometimes the middle area is computed\\nand the volume is assumed to be equal to the length times the\\nmiddle area. This will equal X X T Subtract-\\ning this from the true volume, we obtain the correction\\n24(^1 /O (^7)\\nAs l)efore, the form of the correction shows that if either\\nthe A s or s are equal, the correction vanishes; also under the\\nusual conditions, as before, the correction is positive and only\\none-half as large as by averaging end areas. Ordinarily the\\nlabor involved in the above method is no less than that of\\napplying the exact prismoidal formula.\\n73. Two-level ground. When aj)j)roxir)iate computations of\\nearthwork are sufficiently exact the field-work may be materi-\\nally reduced by observing simply the center cut (or fill) and the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0095.jp2"}, "96": {"fulltext": "80\\nRAILROAD CONSTRUCTION.\\n\u00c2\u00a773.\\nnatural slope measured with a clinometer. The area of such\\na section (see Fig. 48) equals\\nN\\nt\u00c2\u00a3^\\n-J\\n_-_(-r^\\n1\\n^-^^^^^^^7\\n\\\\d\\n^^k^^^;==^^^^^^^\\nr\\nFig. 47.\\nFig. 48.\\ni{a-\\\\-d){Xi-\\\\-x,)-\\nab\\n2*\\nBut\\nfrom which\\nSimilarly,\\nSubstituting,\\nsoi tan /3 a d Xj tan or,\\n__\\ntan /J tan a\\na d\\nXj~,\\nArea {a d)\\ntan tan a\\ntan\\n^5\\ntan^ j3 tan^ o 2\\n(48)\\nThe values a^ tan tan are constant for all sections, so\\nthat it requires but little work to find the area of any section.\\nAs this method of cross-sectioning implies considerable approxi-\\nmation, it is generally a useless refinement to attempt to com-\\npute the volume with any greater accuracy than that obtained\\nby averaging end areas. It may be noted that it may be easily\\nproved that the correction to be applied is of the same form as\\nthat found in 71 and equals\\nW {d a)],", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0096.jp2"}, "97": {"fulltext": "74. EARTHWORK. 81\\nwhich reduces to\\nM T/ 7 N t^D 7//V tan Tr I\\nb|L tun- tan* a tan tau a J^ i\\nWhen cZ d the correction vanislies. This shows that\\nwhen the center heights are equal there is no correction\\nregardless of the slope. If the slope is uniform throughout,\\nthe form of the correction is simplified and is invariably nega-\\ntive. Under the usual conditions the correction is negative^\\ni.e., the method generally gives too large results.\\n74. Level sections. AVhen the country is very level or when\\nonly approximate preliminary results are required, it is some-\\ntimes assumed that the cross-sections are level. The method of\\nlevel sections is capable of easy and rapid convputation. The\\narea may be written as\\n{a dp-^- (50)\\n/7777mm77m777mm/J/777777777mm7777777g77mm7m\\nFig. 49.\\n1\\nThis also follows from Eq. (48) when and tan\\n5 here represents the slope ratio, 2. 6., the ratio of the hori-\\nzontal projection of the slope to the vertical. A table is very\\nreadily formed giving the area in square feet of a section of\\ngiven depth and for any given width of roadbed and ratio of\\nside-slopes. The area may also be readily determined (as illus-\\ntrated in the following example) without the use of such a\\ntable; a table of squares will facilitate the work. Assuming", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0097.jp2"}, "98": {"fulltext": "S2 RAILROAD CONSTRUCTION. 75,\\nt-he cross-sections at equal distances Z) apart, tlie total ap-\\nproximate volume for any distance will be\\n2(^ ...^,^_j .4j. (51)\\nThe prismoidal correction may be directly derived from\\nEq. (46) as :^\\\\2{a d )s 2{a d )s][{a d -{a-\\\\- d\\nwhich reduces to\\n-^-^{d -d- r or -^l{d -d (52)\\nThis may also be derived from Eq. (49), since a\\ntan a 0^ and tan 2a h. This correction is always\\nnegative, showing that the method of averaging end areas\\nwhen the sections are level, always gives too large results. The\\nprismoidal correction for any one prismoid is therefore a con-\\nstant times the square of a difference. The squares are always\\npositive whether the differences are positive or negative. The\\ncorrection therefore becomes\\n-I2^a^^ y- (53)\\n75. Numerical example level sections. Given the following\\ncenter heights for the same number of consecutive stations 100\\nfeet apart; width of roadbed 18 feet; slope IJ to 1.\\nThe products in the fifth column may be obtained very\\nreadily and with sufficient accuracy by the use of the slide-rule\\ndescribed in 79. The products should be considered as\\n{a -f d){a -f 6?) -f- In this problem s 1^,- .6667,\\ns\\nTo apply the rule to the first case above, place 6667 on scale jB\\nover 89 on scale A, then opposite 89 on scale B will be found", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0098.jp2"}, "99": {"fulltext": "\u00c2\u00a776\\nEAHTUWOPdv.\\n83\\n118.8 on scale A. The position of the decimal point will\\nbe evident from an approximate mental solution of the prob-\\nlem.\\n1\\nsta.\\nCenter\\nHeiKlit.\\na d\\n(a dV\\n(a d)2s\\n17\\n18\\n19\\n20\\n21\\n22\\n2.9\\n4.7\\n6.8\\n11.7\\n4.2\\n1.6\\n8.9\\n10.7\\n12.8\\n17.7\\n10.2\\n7.6\\n79.21\\n114.49\\n163.84\\n313.29\\n104.04\\n57.76\\n118.81\\n171.741\\n245.76\\n469.93 f\\n156.06 J\\n86.64\\nAreas.\\nX2=^\\n118.81\\nr 343.48\\n491.52\\n939.86\\n1^312.12\\n86.64\\nd d\\n1\\n(d d\\n1.8\\n3.24\\n2.1\\n4.41\\ni 4.9\\n24.01\\ni 7.5\\n56.25\\n2.6\\n6.76\\n2\\n6_XJ8\\n2\\n54\\n1752.43x100\\n2292.43\\n10 X 54 540\\n1752.43\\n94.67\\n2X2\\nCorr.\\n3245 cub. yards approx. vol.\\n100 X 18\\nX 94.67\\n91 cub. yds.\\n12X6X27\\n3245 91 3154 cub. yds. exact volume.\\nThe above demonstration of the correction to be applied to\\nthe approximate volume, found by averaging end areas, is intro-\\nduced mainly to give an idea of the amount of that correction.\\nAbsolutely level sections are practically unknown, and the error\\ninvolved in assuming any given sections as truly level will\\nordinarily be greater than the computed correction. If greater\\naccuracy is required, more points should be obtained in the\\ncross-sectioning, which will generally show that tlie sections\\nare not truly level.\\n76. Equivalent sections. When sections are very irregular\\nthe following method may be used, especially if great accuracy\\nis not required. The sections are plotted to scale and then a\\nuniform slope line is obtained by stretching a thread so that the\\nundulations are averaged and an equivalent section is ol)tained.\\nThe center depth (d) and the slope angle {oi) of tliis line can\\nbe obtained from the drawing, but it is more convenient to\\nmeasure the distances {xi and x^ from the center. The area", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0099.jp2"}, "100": {"fulltext": "84 RAILROAD CONSTRUCTION. 76\\nmay then be obtained, independent of the center depth as\\nfollows Let s the slope ratio of the side slopes cot fi\\n(See Fig. 48.) Then the\\nJL /mS; T~ ^r I T I I OjO\\n(64)\\nThe true volume, according to the prismoidal formula, of a\\nlength of the road measured in this way will be\\nI roo/xj ah foe/ x, x^ xj! 1 ah\\\\ xl xj! ab-^\\n6\\nI ^r\\nah (xl xl x^ V 1 ocl x^\\nIf computed by averaging end areas, the approximate volume\\nwill be\\n(j Xl Xy OjO Xl Xj, O O\\nSubtracting this result from the true volume, we obtain as the\\ncorrection\\nCorrection w-(.^/ ocl){xJ Xr (55)\\nThis shows that if the side distances to either the rip:ht or\\nleft are equal at adjacent stations the correction is zero, and\\nalso that if the difference is small the correction is also small\\nand very probably within the limit of accuracy obtainable by\\nthat method of cross-sectioning. In fact, as has already been\\nshown in the latter part of 75, it will usually be a useless\\nrefinement to compute the prismoidal correction when the\\nmethod of cross-sectioning is as rough and approximate as this\\nmethod generally is.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0100.jp2"}, "101": {"fulltext": "77.\\nEARTHWORK.\\nS^\\n77. Equivalent level sections. These sloping two-level\\nsections are sometimes transformed into level sections of equal\\narea, a\u00c2\u00bbd tli^ volume computed by the method of level sections\\n74). But the true volume of a prismoid with sloping ends does\\nnot agree with tliat of a prismoid with equivalent bases and level\\nends except under special conditions, and wdien this method is\\nused a correction nmst be applied if accuracy is desired, although,\\nas intimated before, the assumption that the sections have uni-\\nform slopes will frequently introduce greater inaccuracies than\\nthat of this method of computation. The following demonstra-\\ntion is therefore given to show the scope and limitations of the\\nerrors involved in this much used method.\\nIn Fig. 50, let d^ be the center height which gives an\\nFig. 50.\\nequivalent level section. The area will equal {a 6?,)V\\nA\\nQC X (to 1)\\nwhich must equal the area given in 76, -r, 5 .-r-.\\ns A 2(1\\n(a-\\\\- d,ys\\nvLitiU\\nI ^r\\nor a d^\\nVxix^\\n(.56)\\nTo obtain d^ directly from notes, given in terras of d and n", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0101.jp2"}, "102": {"fulltext": "86 RAILROAD CONSTRUCTION. \u00c2\u00a777.\\nwe may substitute the values of x^ and x^ given in 73, which\\ngives\\ntan _ a-\\\\- d\\nr tan tan a s tan^\\nThe true volume of the equivalent section may be repre-\\nsented by\\n^/o^;\\nFrom this there should be subtracted the volume of the\\ngrade prism under the roadbed to obtain the volume of the\\ncut that would be actually excavated, but in the following com-\\nparison, as well as in other similar comparisons elsewhere made,\\nthe volume of the grade prism invariably cancels out, and so for\\nthe sake of simplicity it will be disregarded. This expression\\nfor volume may be transposed to\\nf f 1\\nThe true volume of the prismoid with sloj^ing ends is (see\\n76^\\nt^4^)(^^\u00c2\u00b1^)i)+\\n6\\nThe difference of the two volumes\\ni,^,^.\\n(rpf^ f\\\\rY, rp \\\\rY,fry, yrpf ry, f _rp rv, _(}\\\\/r,, ry ry, ry, rp rv.\\nOS\\nV^/^ Vx/ x/y. (58)\\nThis shows that equivalent level sections do not in\\ngeneral give the true volume, there being an exception when", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0102.jp2"}, "103": {"fulltext": "78.\\nEAUTUWOliK.\\n87\\nXi^J x[ Xr This condition is fiillilled when the slo])e is\\nuniforu], i.e., when a tx When this is nearly so the error\\nis evidently not large. On the other hand, if the slopes are in-\\nclined in opposite directions the error may be very considerable,\\nparticularly if the angles of slope are also large.\\n78. Three-level sections. The next method of cross-section-\\nin the order of complexity, and therefore in the order of\\nwmiiijnmih\\nFig. 51.\\naccuracy, is the method of three-level sections. The area of the\\nsection is i{a d){Wr w^) which may be written\\nah\\n\\\\{(i d)w m which vj \\\\0r-\\\\- v\\\\. If the volume is\\ncomputed by averaging end areas, it will equal\\nI\\n-\\\\(a^d )io -al-\\\\-{a cl yD ab\\\\ (59)\\nIf we divide by 27 to reduce to cubic yards, we have, when\\nI 100,\\nYol U{a djw ^ah ^a d ^v ^al.\\nFor the next section\\nYol.\\nTl\\n^(a d yo l\\\\ah f d )io ^ah.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0103.jp2"}, "104": {"fulltext": "S8 RAILROAD CONSTRUCTWI^. 78..\\nFor a partial station length compute as usual and multiply\\nleno^th in feet\\nresult by ilie prismoidal correction mav be\\n100\\nobtained by applying Eq. (46) to each side in turn. For the left\\nside we have\\nr^[(\u00c2\u00ab d {a-\\\\- d ]{w{^ Wi)^ which equals\\n^id d ){iv{ io{).\\nFor the right side we have, similarly,\\nl-{d d ){wj\\nThe total correction therefore equals\\ni^{d d )iw to\\nReduced to cubic yards, and with I 100,\\nPris. Corr. d yw -w (60)\\nWhen this result is compared with that given in Eq. (55)\\nthere is an apparent inconsistency. If two-level ground is con-\\nsidered as but a special case of three-level ground, it would seem\\nas if the same laws should apply. If, in Eq. (55), x/ Xr\\nand x/^ is different from x/, the equation reduces to zero but\\nin this case d would also be different from d and since x/ -f-\\nx/ would io\\\\ and xC x^ w in Eq. (60), V3 %o would\\nnot equal zero and the correction would be some finite quantity\\nand not zero. The explanation lies in the difference in the form\\nand volume of the prismoids, according to the method of the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0104.jp2"}, "105": {"fulltext": "\u00c2\u00a778.\\nEARTHWORK.\\n89\\nformation of tlie warped surfaces. If the surface is supposed to\\nbe generated bj the locus of a Hue moving parallel to the ends\\nas plane directors and along two straight lines lying in the side-\\nslopes, then ,T; will ecpial ^(a?/ a?/ and it will ecpial\\nJ(x/ a?/ but the protile of the center line will not be\\nstraight and t^ will not equal \\\\{(l d On the other\\nhand, if the surfaces be generated by tioo lines moving parallel\\nto the ends as plane directors and along a straight center Hne\\nand straight side lines lying in the slopes, a warped surface will\\nbe generated each side of the center line, which will have uni-\\nform slopes on each side of the center at the two ends and no-\\nwhere else. This shows that when the upper surface of earth-\\nwork is warped (as it generally is), two-level ground should not\\nbe considered as a special case of three-level ground. This dis-\\ncussion, however, is only valuable to explain an apparent incon-\\nsistency and error. The method of two-level ground should\\nonly be nsed when such refinements as are here discussed are of\\nno importance as affecting the accuracy.\\nThe following example is given to illustrate the method of\\nthree-level sections.\\nS,\\nm\\n17\\n18\\n+40\\n19\\n20\\n\u00e2\u0080\u00a2J.\\nC\\nO\\na d\\nw\\nYards.\\nd d\\n-5.5\\n-2.6\\n+4.3\\n+2.7\\nw \u00e2\u0080\u0094w\\n+11.7\\n8.7\\n-13.4\\n-15.1\\nat\\n^6\\n-20\\n3\\n-11\\n-13\\n14.7\\n18.6\\n23.1\\n17.9\\n8.4\\n^(\u00e2\u0096\u00a0^rv\\nc\\n5 3\\n+4\\n+4\\n+5\\n+3\\n3A\\n8.1F\\n10.7^\\n6.4F\\nZ.IF\\n10.6F\\n0.8F\\n7.3\\n12.8\\n15.4\\n11.1\\n8.4\\n31.1\\n42.8\\n51.5\\n38.1\\n23.0\\n210\\n507\\n734\\n392\\n179\\n595\\n448\\n602\\n449\\n+1\\n+3\\n+6\\n+2\\n+1\\n2-, 9\\n1.5.SF\\n8.2\\n3.4F\\n30.7\\n\u00e2\u0080\u00a220.2F\\n37.3\\n14.0F\\n12.1\\n4.8F\\n14.2\\n2AF\\n28.0\\n5.8 F\\n10.1\\n0.2F\\n15.7\\n7.3\\nRoadbed, 14 wide in fill. Approx. Vol, =2094\\nSlope IJ^ to 1. Pris. corr. 47\\n\u00e2\u0096\u00a047\\niT~ ~5~ 4.\\n25^\\n27\\nah 61.\\nTrue Vol. =2047 (disregarding curv. corr).*\\nFor the Derivation of the curvation correction, see 93.\\n+16", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0105.jp2"}, "106": {"fulltext": "90 RAILROAD CONSTRUCTION. 79.\\nIn the first column of yards\\n210 ff(\u00c2\u00ab d)iv f 5 X 7.3 X 31.1\\n507, 734, etc., are found similarly\\n595 210 61 507 61;\\n448 yVo(507 61 734 61);\\n602 -j-Vo( ^34 61 392 61)\\n449 392 61 179 61.\\nFor the prismoidal correction,\\n20 l{{cr fr ){io w |f(2.6 8.1)(42.8 31.1)\\nfK-5-5)(+ii.7).\\nFor the next Hne, 3 -/^o_[|5(_ 2.8)(+ 8.7)], and\\nsimilarly for the rest. The 7^ in the columns of center\\nheights, as well as in the columns of right and left, are\\ninserted to indicate Jill for all those pooints. Cut would be\\nindicated by (7.\\n79. Computation of products. The quantities ~{a-\\\\-d)w\\n25\\nand \u00e2\u0080\u0094ah represent in each case the product of two variable\\nterms and a constant. These products are sometimes obtained\\nfrom tables which are calculated for all ordinary ranges of the\\nvariable terms as arguments. A similar table computed for\\n25\\n(d^ d ){io lo wiir assist similarly in computing the\\nol\\nprismoidal correction. Prof. Charles L. Crandall, of Cornell\\nUniversity, is believed to be the first to prepare such a set of\\ntables, which were first published in 1886 in Tables for the\\nComputation of Railway and Other Earthwork. Another", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0106.jp2"}, "107": {"fulltext": "79. EARTHWORK. 91\\neasy method of obtaining tliese products is by the nse of a slido\\nrule. A slide-rule has been designed by the autlior to accom-\\npany this volume. It is designed particularly for this special\\nwork, although it may be utilized for many other purposes for\\nwhich slide-rules are valuable. To illustrate its use, suppose\\n{ic d) 28.2, and 2^ 62.4; then\\n25, 28.2 X 62.4\\n~\u00e2\u0080\u0094{a -f- a)iv\\n27^ 1.08\\nSet 108 (which, being a constant of frequent use, is specially\\nmarked) on the sliding scale {B) opposite 282 on the other scale\\n(A), and then opposite 624 on scale J] will be found 1629 on\\nscale A, the 162 being read directly and the 9 read by estima-\\ntion. Although strict rules may be followed for pointing off\\nthe final result, it only requires a very simple mental calculation\\nto know that the result must be 1629 rather than 162.9 or\\n16290. For products less than 1000 cubic yards the result\\nmay be read directly from the scale; for products between 1000\\nand 5000 the result may be read directly to the nearest 10\\nyards, and the tenths of a division estimated. Between 5000 and\\n10,000 yards the result may be read directly to the nearest 20\\nyards, and tlie fraction estimated; but prisms of such volume\\nwill never be found as simple triangular prisms at least, an as-\\nsumption that any mass of ground was as regular as this would\\nprobably involve more error than would occur from faulty esti-\\nmation of fractional parts. Facilities for reading as high as\\n10,000 cubic yards would not have been put on the scale ex-\\ncept for tlie necessity of finding such products as |7(^^^-1 X 9.5),\\nfor example. This product would be read off from the same\\npart of the rule as f |(91 X 95). In the first case the ])roduct\\n(80.0) could be read directly to the nearest .2 of a cubic yard,\\nwhich is unnecessarily accurate. In the other case, the jirod-\\nuct (8004) could only be obtained by estimating of a division.\\nThe computation for the prismoidal correction may be made", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0107.jp2"}, "108": {"fulltext": "92 MAILROAD CONSTBUCriON, 80.\\nsimilarly except that the divisor is 3.21 instead of 1.08. For\\nexample, |f(o.5 X 11. T) ^liAliiJ. get the 324 on scale\\nB (also specially marked like 108) opjDOsite 55 on scale A^ and\\nproceed as before.\\n80. Five-level sections. Sometimes the elevations over each\\nedge of the roadbed are observed when cross-sectioning. These\\nare distinctively termed five level sections. If the center,\\nthe slope-stakes, and one intermediate point on each side [not\\nnecessarily over the edge of the roadbed) are observed, it i-s\\ntermed an irregular section. The field-work of cross-section-\\ning five-level sections is no less than for irregular sections with\\none intermediate point; the computations, although capable of\\npeculiar treatment on account of the location of the intermediate\\npoint, are no easier, and in some respects more laborious; the\\ncross-sections obtained will not in general represent the actual\\ncross-sections as truly as when there is perfect freedom in locat-\\ning the intermediate point as it is generally inadvisable or un-\\nnecessary to employ five-level sections throughout the length of\\na road, the change from one method to another adds a possible\\nelement of inaccuracy and loses the advaniage of uniformity of\\nmethod, particularly in the notes and form of computations.\\nOn these accounts the method will not be further developed,\\nexcept to note that this case, as well as any other, may be\\nsolved by dividing the whole prismoid into triangular prismoids,\\ncomputing the volume by averaging end areas, and computing\\nthe prismoidal correction by adding the comjDuted corrections\\nfor each elementary triangular prismoid.\\n81. Irregular sections. In cross-sectioning irregular sec-\\ntions, the distance from the center and the elevation above\\ngrade of every break in the cross-section must be\\nobserved. The area of the irregular section may be obtained\\nby computing the area of the trapezoids ^fi ve^ in Fig. 44) and\\nsubtracting the two external triangles. For Fig. 44 the area\\nwould be", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0108.jp2"}, "109": {"fulltext": "\u00c2\u00a781.\\nhi h\\nEARTHWORK.\\n93\\n{^i yi)\\nh d d +jr jr\\n-y/+\\n^r\\n\\\\yr 2r)\\n-v+i,, _,,_\u00c2\u00bb.(,_ I) -|.(,_ I).\\n^rh\\nFig. 44.\\nExpanding this and collecting terms, of which many will\\ncancel, we obtain\\nArea ^Xiki yi(d hi) x^ yAjr K)\\nJr2M-h)+\\\\(hi K)\\\\. (61)\\nAn examination of this formula will show a perfect regu-\\nlarity in its formation which will enable one to write out a\\nsimilar formula for any section, no matter how irregular or how\\nmany points there are, without any of the preliminary work.\\nThe formula may be expressed in words as follows\\nArea equals one-half the sum of products obtained as folloics\\nthe distance to each slope- stake times the height above grade\\nof the point next inside the slope-stake y\\nthe distance to each intermediate point in turn times the height\\nof the point just inside minus the height of the point just outside\\nfinally^ one-half the width of the roadbed times the sum of\\nthe slope-stake heights.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0109.jp2"}, "110": {"fulltext": "94\\nBAILROAD CONSTRUCTION.\\n82.\\nIf one of the sides is perfectly regular from center to slope-\\nstake, it is easy to show that the rule holds literally good.\\nThe point next inside the slope-stake in this case is the\\ncenter; the intermediate terms for that side vanish. The last\\nterm must always be used. The rule holds good for three -level\\nsections, in which case there are three terms, which may be\\nreduced to two. Since these two terms are both variable quan-\\ntities for each cross-section, the special method, given in 78,\\nin which one term (-^J is a constant for all sections, is pref-\\nerable. In the general method, each intermediate break\\nadds another term.\\n82. Volume of an irregular prismoid. If there is a break at\\none cross-section which is not represented at the next, the ridge\\n(or hollow) implied by that break is supposed to vanish at\\nthe next section. In fact, the volume will not be correctly\\nFig. 52.\\nrepresented unless a cross- section is taken at the point where\\nthe ridge or hollow vanishes or runs out. To obtain\\nthe true prism oidal correction it is necessary to observe on the\\nground the place where a break in an adjacent section, which\\nis not represented in the section being taken, runs out. For\\nexample, in Fig. 52, the break on the left of section A at a", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0110.jp2"}, "111": {"fulltext": "g S3. EARTHWORK. 95\\ndistance of y/ from the center, is observed to run out in section\\nA at a distance of yi from the center. The vohime of the\\nprismoid, computed by the prismoidal fornmkx as in 70, will\\ninvolve the midsection, to obtain the dimension of which will\\nrequire a hiborious computation. A simpler process is to compute\\nthe volume by averaging end areas as in 81 and apply a\\nprismoidal correction. To do this write out an expression for\\neach end area similar to that given in Eq. 61. The sum of\\nthese areas times -r gives the approximate volume. As before,\\n1 -1 1 11 length in feet\\nlor partial station lengths, multiply the result by ^7;?;\\nThere will be no constant subtractive term, f f\u00c2\u00ab^, as in 78.\\nThe true prismoidal correction may be computed, as in 83, or\\nthe following approximate method may be used Consider tlie\\nirregular section to be three-level ground for the purpose of\\ncomputing the correction only. This has the advantage of less\\nlabor in computation than the use of the true prismoidal correc-\\ntion, and although the error involved may be considerable in\\nindividual sections, the error is as likely to be positive as nega-\\ntive, and in the long run the error will not be large and generally\\nwill be much less than would result by the neglect of any\\nprismoidal correction.\\n83. True prismoidal correction for irregular prismoids. As\\nintimated in 82, each cross-section should be assumed to have\\nthe same number of sides as the adjacent cross-section when\\ncomputing the prismoidal correction. This being done, it per-\\nmits the division of the whole prismoid into elementary triangu-\\nlar prismoids, the dimensions of the bases of which being given\\nin each case by a vertical distance above grade line and l)y the\\nhorizontal distance between two adjacent breaks. Tlie summa-\\ntion of the prismoidal corrections for each of the elementary\\ntriangular prismoids will give the true prismoidal correction.\\nAssuming for an example the cross-section of Fig. 44, witli a\\ncross-section of the same number of sides, and witli dimensions", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0111.jp2"}, "112": {"fulltext": "96 RAILROAD CONSTRUCTION. \u00c2\u00a783.\\nsimilarly indicated, for the other end, the prismoidal correction\\nbecomes (see Eq. 46)\\nl4 V\\n)[{xi yi {xi 2/01 {ki ki )[{xi yi (xi yn]\\n(ki ki ){yr y{) {d cV){y{ yi {d! d ){Zr Zr\\n0(2r Zr!) OV -jr )\\\\_{yr Zr (^r s/)l\\n{kr kr )[{yr Zr {yr 2r )l\\n(A;/-V )[(^V -2/r )--(3V -2/r )l (Ar -/^r )[(2;r -yr )-CV-yr\\nExpanding this and collecting terms, of which many will\\ncancel, we obtain\\nPris. Corr. -^^xf -x{\\\\k{ h {yi yi )[{d hi {d Jh\\niXr Xr ){kr kr {yr yr )[{jr hr) {jr h/\\n(Zr -er )[{d -kr )-{d -kr (62)\\nBy comparing this equation with Eq. 61 a remarkable\\ncoincidence in the law of formation may be seen, which enables\\nthis formula to be written by mere inspection and to be applied\\nnumerically with a minim um of labor from the computations for\\nend areas, as will be shown 84) by a numerical example.\\nFor each term in Eq. 61, as, for example, yXjr /^r)? there is\\na correction term in Eq. 62 of the form\\nivr 2//)[ov V) ijr wn\\nEach one of these terms (^z/ 1/r\\\\ (J/ h/), and (J/\\nhas been previously used in finding the end areas and has its\\nplace in the computation sheet. The summation of the products\\nof these differences times a constant gives the total true pris-\\nmoidal correction in cubic yards for the whole prismoid considered.\\nThe constant is the same as that computed in 78, i.e.,", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0112.jp2"}, "113": {"fulltext": "\u00c2\u00a784.\\nEAHTHWORK.\\n97\\n84. Numerical example irregular sections volume^ with true\\nprismoidal correction.\\nSta.\\n19\\n18\\n17\\n43\\n16\\ncut\\nCeiiter-s r\\nfill.\\n0.6c\\n2.3c\\n,6c\\n10.3c\\n6.8c\\nLeft.\\n3.6c\\n1^174\\n4 .2c\\n1573\\n8.2c\\n3l73\\n]2.2c\\n27.3\\n8.9c\\n3274\\n^8.2/ \\\\6.0/\\n6^c\\nsTi\\nl(h2c\\nTtTI\\n|12.3c\\\\\\n\\\\2270/\\n3^2 c\\ny.2\\n8.0c\\n6.1\\n12.6c\\n8.2\\n7.6c\\n12.0\\nRight.\\n0.1c\\n472\\n/1^9cV\\nV3.6/\\n|5^c|\\n\\\\8.0/\\n6.2c\\n775\\n3.2c\\n0.4c\\n9:6\\n1.2c\\nU) 8\\n4.2c\\n1573\\n8.4c\\n2176\\n2.6c\\n12.9\\nKoadbed IS feet wide in cut; slope 1|^ to 1.\\nThe figures in the bracket \\\\-^^-7v j mean that it was noted in\\nthe field that the break, indicated at Sta. 17 as being 17.4 to\\ntlie left, ran out at Sta. 10 42 at 22.0 to the left. By inter-\\npolation between 8.2 and 27.3 the height of this ])oint is\\n!omjputed as 12.3. The quantities in the other l)rackets are\\nobtained similarly. These quantities are only used when the\\ncomputation of the true prismoidal correction is desired. They\\nare not needed in computing the volume by averaging end\\nareas, nor are they used at all if the prismoidal correction is to\\nhe obtained by assuming {fov this jnirpose) the ground to be\\nthree-level ground.\\nlu the tabular form on page 98 the figures within the braces\\nr- are not used in comjniting the volume, but are only\\nused to obtain the differences of widths or heights with which to\\ncompute the true prismoidal correction. It may be noted, as a\\ncheck, that the volume, computed from these figures in the\\nbraces, is the same as that computed from the other figures.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0113.jp2"}, "114": {"fulltext": "98 RAILROAD CONSTRUCTION. \u00c2\u00a784.\\nVOLUME OF IRREGULAR PRISMOID, WITH TRUE PRISMOIDAL CORRECTION.\\nTrue pris. corr.\\nSta.\\nWidth.\\nHeight.\\nVn ^1\\niv w\\nh h\\nYards.\\nJ r22.4\\n12.0\\n7.6\\n158\\n2.1\\n-23\\n16\\n4.1\\n3.2\\n40\\n4.2\\n16\\n9.0\\n11.5\\n96\\nT r27.3\\n8.2\\n12.6\\n319\\n4.9\\n-5.0\\n-7\\n2.0\\n-15\\n-3.8\\n-0.1\\ni 27.3\\n12.3\\n42\\nL-^22.0\\n8.2\\n0.4\\n2.1\\n21. 6-] j^\\n7.5\\n6.2\\n124\\n8.7\\n-3\\n-8\\n1.8\\n13\\n3.4\\n2.4\\n3\\n9.0\\n20.6\\n172\\n378\\n(-5)\\nr21.3\\nL 17.4\\n10.2\\n201\\n6.0\\n2.1\\n-4\\n0.2\\n3\\n4.6\\n0.6\\n1\\n_ 6.1\\n2.6\\n-14\\n2.1\\n0.5\\n17\\n15.3[j^\\n8.0^^\\n5.8\\n6.3\\n0.4\\n1\\n3.4\\n^0.5\\n-1.6\\n15.3]R\\n7 6\\n107\\n9.0\\n12.4\\n103\\n584\\n(-3)\\n-6\\nrl5.3\\n6.8\\n95\\n6.0\\n3.4\\nL\\n8.4\\n1.0\\n,-7\\ni\\n-9.0\\n0.8\\n2\\nu 5.2\\n4.5\\n-22\\n-0.9\\n1.9\\n1\\n18\\n10.8]R\\n10.8^ R\\n3.6 f\\n2.3\\n1.9\\n23\\n-4.5\\n5.3\\n-7\\n1.1\\n9.0\\n5.4\\n45\\n528\\n(-16)\\nL[14.4\\n0.6\\n8\\n14.4\\n2.3\\n-0.9\\n4.5\\n-1\\nL-^ 8.2\\n1.8\\n-0.2\\n0.8\\n19\\n6.0\\n1.7\\n0.8\\n-2.8\\n1\\n4.2\\n0.1\\n1\\n-1.2\\n1.8\\n1\\n0.2\\n1\\n0.6\\n0.9\\n9.0\\n4.0\\n33\\n177\\n(-3)\\nApprox. vol.\\n1667\\n27\\nrrue pris. corr.\\n27\\n1\\nTrue volume\\n1640 ci]\\nbic yards\\nThe figures within each brace (or bracket) constitute a group\\nwliich must be used in connection with a group which has the\\nsame number of points, on the same side of the center, in the\\nnext cross-section, previous or succeeding. In the cohimn of", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0114.jp2"}, "115": {"fulltext": "86.\\nEARTUWORK.\\n99\\nYards under True pris. corr., we have, for example,\\n85. Volume of irregular prismoid, with approximate prismoidal\\ncorrection. It the prismoidal correction is obtained a])proxi-\\nmately, by the method outlined hi 82, the process will be as\\nshown in the tabular form. Kot only is the numerical work\\nconsiderably less than the exact method, but the discrepancy in\\ncubic yards is almost insignilicant.\\nSta.\\nWidtli.\\nHeight.\\nYards.\\nCen.\\nHeight.\\nTotal\\nwidth.\\nd -d\\nto\\nAi)prox.\\npiis. corr.\\n22.4\\n7.6\\n158\\n6.8\\n35.3\\n12.0\\n-2.1\\n23\\n16\\n12 9\\n4.1\\n3.2\\n4.2\\n40\\n16\\n9.0\\n27.3\\n11.5\\n96\\n319\\n10.2\\n48.9\\n12.6\\n-3.4\\n13.6\\n14\\n8.2\\n-2.0\\n15\\n42\\n21.6\\n7.5\\n6.2\\n1.8\\n124\\n13\\n9.0\\n21.3\\n20.6\\n172\\n201\\n378\\n36.6\\n+2.6\\n(-6)\\n10.2\\n7.6\\n12.3\\n10\\n17.4\\n-0.2\\n3\\n17\\n6.1\\n15 3\\n-2.6\\n7.6\\n14\\n107\\n9.0\\n12.4\\n103\\n9o\\n584\\n26.1\\n+5.3\\n(-6)\\n15.3\\n6.8\\n2.3\\n10.5\\n17\\n8.4\\n-1.0\\n7\\n18\\n5.2\\n10.8\\n-4.5\\n2.3\\n22\\n9.0\\n5.4\\n45\\n8\\n528\\n(-17)\\n1\\n14.4\\n0.6\\n0.6\\n24.0\\n+1.7\\n-2.1\\n19\\n9.6\\n0.1\\n1\\n4.2\\n0.2\\n1\\n9.0\\n4.0\\n33\\n177\\n(-1)\\nApprox. volume 1667\\nApprox. pris. corr. 30\\n30\\nCorrected volume 1G37 cubic ards\\n86. Illustration of value of approximate rules. The accom-\\npanying tabulation shows that when the volume of an irregular\\nprismoid is computed by averaging end areas and is corrected\\nby considering the ground as three-level ground {for the j ur\\nu tfa", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0115.jp2"}, "116": {"fulltext": "100\\nRAILROAD CONSTRUCTION.\\n87.\\nposes of the correction only\\\\ the error for tlie different sections\\nis sometimes positive and sometimes negative, and in tins case\\nSections.\\n6\\ns\\n3\\nO\\n0)\\n3\\nU\\nH\\nApprox. vol.\\nby averaging\\nend areas.\\nDifference or\\ntrue pris.\\ncorr.\\nApprox. pris.\\ncorr. on basis\\nof three-level\\nground.\\nError.\\nApprox. vol.,\\ncomputed\\nfrom center\\nand side\\nheights onhj.\\nError.\\n16 16 42\\n16 42. ..17\\n17 18\\n18 19\\n373\\n581\\n174\\n378\\n584\\n528\\n177\\n1667\\n5\\n3\\n16\\n3\\n6\\n6\\n17\\n1\\n1\\n3\\n1\\n2\\n3\\n396\\n577\\n463\\n147\\n23\\n4\\n49\\n27\\n57\\n1640\\n27\\n30\\n15S3\\namounts to only 3 yards in 1640 less than of 1^. If the\\nprismoidal correction had been neglected, the error would have\\nbeen 27 yards nearly li. The approximate results are here\\ntoo large for each section as is usually the case. If points\\nbetween the center and slope stakes are omitted and the volume\\ncomputed as if the ground were three-level ground, the error is\\nquite large in individual sections, but the errors are both posi-\\ntive and negative and therefore compensating.\\n87. Cross-sectioning irregular sections. The prismoids con-\\nsidered have straight lines joining corresponding points in the\\ntwo cross-sections. The center line must be straight between\\ntAvo cross-sections. If a ridge or valley is found lying diago-\\nnally across the roadbed, a cross-section m^icst be interpolated at\\nthe lowest (or highest) point of the profile. Therefore a break\\nat any section cannot be said to run out at the other section on\\nthe opposite side of the center. It must run out on the same\\nside of the center or possibly at the center. Yery frequently\\ncomplicated cross-sectioning may be avoided by computing the\\nvolume, by some special method, of a mound or hollow when\\nthe ground is comparatively regular except for the irregularity\\nreferred to.\\n88. Side-hill work. When the natural slope cuts the roadbed\\nthere is a necessity for both cut and fill at the same cross-section.\\nWhen this occurs the cross-sections of both cut and fill are often\\nso nearly triangular that they may be considered as such without", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0116.jp2"}, "117": {"fulltext": "88.\\nEARTUWORK,\\n101\\ngreat error, and the volumes inaj be computed separately as\\ntriangular prismoids without adopting tlie more elaborate form\\nof computation so necessary for complicated irregular sections.\\nAVhen the ground is too irregular for this the best plan is to\\nfollow the uniform system. In computing the cut, as in Fig. 53,\\nFia. 53.\\nthe left side would be as usual there would be a small center\\ncut and an ordinate of zero at a short distance to the right of the\\ncenter. Then, ignoring the fill and applying Eq. 61 strictly,\\nwe have two terms for the left side, one for the right, and the\\nterm involving \\\\h^ which will be ^lii in this case, since li^ 0,\\nand the equation becomes\\nArea \\\\\\\\xihi -f- yifl ^i) x^d ^Jfhj\\nThe area for fill may also be computed by a strict application\\nFig. 54.\\nof Eq. 61, but for Fig. 54 all distances for the left side are zero\\nand tlie elevation for the first point out is zero, d also must be", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0117.jp2"}, "118": {"fulltext": "102 BAILROAD CONSTRUCTION. 89.\\nconsidered as zero. Following the rule, 81, litexallj, the\\nequation becomes\\nArea(Fin) ^[x^h yr{o K) z,.{o h) iHo A,-)]?\\nwhich reduces to\\n{Note that Xy^ Kj etc., have different significations and\\nvalues in this and in the preceding paragraphs.) The terminal\\npyramids illustrated in Fig. 40 are instances of side-hill work\\nfor very short distances. Since side-hill work always implies\\nhoth cut and fill at the same cross-section, whenever either the\\ncut or fill disappears and the earthwork becomes wholly cut or\\nwholly fill, that point marks the end of the side-hill work,\\nand a cross-section should be taken at this point.\\n89. Borrow-pits. The cross-sections of borrow-pits will vary\\nnot only on account of the undulations of the surface of the\\nJillHlllllllllllUIIIHNIIIillllllllllWlllWllinillllllllliilllllUIIIWIUIIWIIili\\nFig. 55.\\nground, but also on the sides, according to whether they are\\nmade by widening a convenient cut (as illustrated in Fig. 55)\\nor simply by digging a pit. The sides should always be prop-\\nerly sloped and the cutting made cleanly, so as to avoid un-\\nsightly roughness. If the slope ratio on the right-hand side\\n(Fig. 55) is ,9, the area of the triangle is ^sm^. The area of the\\nsection is 2^119 -\\\\-{g-\\\\-h)v-\\\\-{h-\\\\-j)x-^{j-\\\\-li )y-\\\\-{k-\\\\-m)z smj\\nIf all the horizontal measurements were referred to one side as\\nan origin, a formula similar to Eq. 61 could readily be devel-\\noped, but little or no advantage would be gained on account of\\nany simplicity of computation. Since the exact volume of the\\n\u00e2\u0082\u00acarth borrowed is frequently necessary, the prismoidal correc-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0118.jp2"}, "119": {"fulltext": "90. EARTHWORK. 103\\ntiou sliould be computed and since such a section as Yi r. 55\\ndoes not even approximate to a three-level section, thj method\\nsuggested in 82 cannot be employed. It will then be neces-\\nsary to employ the exact method, 83, by dividing the volume\\ninto triangular prismoids and taking the summation of their\\ncorrections, found according to the general method of 71.\\n90. Correction for curvature. The volume of a solid, iren-\\nerated by revolving a plane area about an axis lying in the\\nplane but outside of the area, equals the product of the given\\narea times the length of the path of the center of gravity of the\\narea. If the centers of gravity of all cross-sections lie in the\\ncenter of the road, where the length of the road is measured,\\nthere is absolutely no necessary correction for curvature. If all\\nthe cross- sections in any given length were exactly the same\\nand therefore had the same eccentricity, the correction for\\ncurvature would be very readily computed according to the\\nabove principle. But when both the areas and the eccentrici-\\nties vary from point to point, as is generally the case, a theo-\\nretically exact solution is quite complex, both in its derivation\\nand application. Suppose, for simplicity, a curved section of\\nthe road, of uniform cross-sections and w^ith the center of o-rav-\\nity of every cross-section at the same distance e from the center\\nline of the road. The length of the path of the center of\\ngravity will be to the length of the center line as R \u00c2\u00b1e\\\\ R.\\nTherefore we have True vol. nominal vol. B e R.\\nTi \u00c2\u00b1e\\nTrue vol. lA 73 for a volume of uniform area and\\neccentricity. For any other area and eccentricity we have,\\nR e\\nsimilarly, True vol. IA This shows that the eifect\\nof curvature is the same as increasing (or diminishing) tlie area\\nby a quantity depending on the area and eccentricity, the\\nincreased (or diminished) area being found by nuiltiplying the\\n.1 1 R e\\nactual area by the ratio This being independent of the\\nvalue of Z, it is true for infinitesimal lengths. If the eccen-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0119.jp2"}, "120": {"fulltext": "104 RAILROAD CONSTRUCTION. 91.\\ntricity is assumed to vary uniformly between two sections, the\\nequivalent area of a cross- section located midway between the\\ntwo end cross-sections would be A^- There-\\nfore the volume of a solid which, when straight, would be\\n4 ^^m would then become\\nTrue vol. ^_^X^ e )+4.A,^[R\u00c2\u00b1 ^-^^)+A \\\\B e )j.\\nSubtracting the nominal volume (the true volume when the\\nprismoid is straight), the\\nr 1\\nCorrectio7i -^\\\\_{A ^A,^)e (2^\u00e2\u0080\u009e, A y j, (63)\\nAnother demonstration of the same result is given by Prof.\\nC. L. Crandall in his Tables for the Computation of Rail-\\nway and other Earthwork, in which is obtained by calculus\\nmethods the summation of elementary volumes having variable\\nareas with variable eccentricities. The exact application of\\nEq. (63) requires that A^^ be known, which requires laborious\\ncomputations, but no error worth considering is involved if the\\nequation is written approximately\\nCurv. GOVT. ^{A e A e (64)\\nwhich is the equation generally used. The approximation con-\\nsists in assuming that the difference between A and A,^^ equals\\nthe difference between A^^ and A but with opposite sign.\\nThe error due to the approximation is always utterly insig-\\nniiicant.\\n91. Eccentricity of the center of gravity. The determina-\\ntion of the true positions of the centers of gravity of a long\\nseries of irregular cross-sections would be a very laborious\\noperation, but fortunately it is generally sufficiently accurate to", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0120.jp2"}, "121": {"fulltext": "91. EARTHWORK. 105\\nconsider the cross-sections as three-level ground, or, fur side-hill\\nwork, to be triangular, /br the purpose of this correction. The\\nmmihii\\\\iimh\\\\ mw.\\nFig. 56.\\neccentricity of the cross-section of Fig. 56 (including the grade\\ntriangle) may be written\\n{a^d)xiXi {a-\\\\-d)x^.Xy\\n2 3 2 3 _ 1^ Xi x; _ 1\\n(a^d)x, (^5 r 3 xi X, 3\\n2 2\\nThe side toward x^. being considered positive in the above\\ndemonstration, if x^, Xi^ e would be negative, i.e., the center\\nof gravity would be on the left side. Therefore, for three-level\\nground, the correction for curvature (see Eq. 64) may be\\nwritten\\nCorrection ^[A (x/ cc/) A {x/ x/\\nSince the approximate volume of the prismoid is\\n^{A A I A \\\\a r F\\nin which V^ and V represent the number of cubic yards\\ncorresponding to the area at each station, we may write\\nCorr. in cuh. yds. V\\\\xj .t/)+ F", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0121.jp2"}, "122": {"fulltext": "106 RAILROAD CONSTRUCTION. 91.\\nIt should be noted that the value of derived in Eq. 65, is\\nthe eccentricity of the whole area including the triangle under\\nthe roadbed. The eccentricity of the true area is greater than\\nthis and equals\\ntrue area -f- i^t^^\\ntrue area\\ne X e,.\\nThe required quantity {A e of Eq. 64) equals true area X ^n\\nwhich equals {true area ^ah) X e. Since the value of e is very\\nsimple, while the value of e^ would, in general, be a complex\\nquantity, it is easier to use the simple value of Eq. Q^ and add\\n^ah to the area. Therefore, in the case of three-level ground\\nthe subtractive term ^^ah 78) should not be subtracted in\\ncomputing this correction. For irregular ground, when com-\\nputed by the method given in 81 and 82, which does not\\ninvolve the grade triangle, a term f ^5 must be added at every\\nstation when computing the quantities V and V for Eq. QQ.\\nIt should be noted that the factor 1 Sic, which is\\nconstant for the length of the curve, may be computed with all\\nnecessary accuracy and without resorting to tables by remember-\\ning that\\ndeojree of curve\\nSince it is useless to attempt the computation of railroad\\nearthwork closer than the nearest cubic yard, it will frequently\\nbe possible to write out all curvature corrections by a simple\\nmental process upon a mere inspection of the computation sheet.\\nEq. QQ shows that the correction for each station is of the form\\nP 3i? is generally a large quantity for a 6\u00c2\u00b0 curve\\nSic\\nit is 2865. {xi x^) is generally small. It may frequently be\\nseen by inspection that the product Y{Xi x,) is roughly twice\\nor three times 3^, or perhaps less than half of 3^, so that the\\ncorrective term for that station may be written 2, 3, or cul)ic\\nyards, the fraction being disregarded. For much larger absolute", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0122.jp2"}, "123": {"fulltext": "\u00c2\u00a792. EARIHWORK. 1()7\\namounts the correction must be computed with a correspondingly\\ncloser percentage of accuracy.\\nThe algebraic sign of the curvature correction is best deter-\\nmined by noting that the center of gravity of the cross-section is\\non the riglit or left side of tlie center according as x,. is greater\\nor less than xi^ and that the correction is positive if the center of\\ngravity is on the outside of the cur\\\\ e, and iiegative if on the\\ninside.\\nIt is frequently found that Xi is uniformly greater (or uni-\\nformly less) than x,. throughout the length of the curve. Then\\nthe curvature correction for each station is uniformly positive or\\nnegative. But in irregular ground the center of gravity is apt\\nto be irregularly on the outside or on the inside of the curve,\\nand the curvature correction will be correspondingly positive or\\nnegative. If the curve is to the right, the correction will be\\npositive or negative according as {xi x,.) is positive or negative\\nif the curve is to the left, the correction ill be positive or nega-\\ntive according as {Xy xi) is positive or negative. Therefore\\nwhen computing curves to the 7 ight use the form {xi x, in\\nEqs. 66 and Q^ wdien computing curves to the left use the form\\n{x^ x^ in these equations the algebraic sign of the correction\\nwill then be strictly in accordance with the results thus obtained.\\n92. Center of gravity of side-hill sections. In computing the\\nFi(.. 57.\\ncorrection for side-hill work the cross section would be treated\\nas trianirular unless the error involved would evidentlv be too", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0123.jp2"}, "124": {"fulltext": "108\\nRAILROAD CONSTRUCTION.\\n92,\\ngreat to be disregarded. Tlie center of gravity of the triangle\\nlies on the line joining the vertex with the middle of the base\\nand at of the length of this line from the base. It is therefore\\nequal to the distance from the center to the foot of this line plus\\nof its horizontal projection. Therefore\\ne\\n2 2 \\\\2\\n1 r\\nXl\\n2 ~2 \\\\2+^\\n\u00e2\u0080\u00a2JCy\\nXl\\nt-O V\\n4 2\\nh Xl\\n3\\n3\\nXy\\n3\\n{xi-x,)j.\\n12+6\\nn\\n(67)\\nBj the same process as that used in 91 the correction equation\\nmay be written\\nCorr. in cub. yds. .IPf^I a-/)) ^2\\n(68)\\nIt should be noted that since the grade triangle is not used in\\nthis computation the volume of the grade prism is 7wt involved\\nin computing the quantities V and V\\nThe eccentricities of cross-sections in side-hill work are\\nnever zero, and are frequently quite large. The total volume\\nis generally quite small. It follows that the correction for\\ncurvature is generally a vastly larger proportion of the total\\nvolume than in ordinary three-level or irregular sections.\\nIf the triangle is wholly to one side of the center, Eq. 67\\ncan still be used. For example, to compute the eccentricity of\\nthe triangle of fill, Fig. 57, denote the two distances to the\\nslope-stakes by y,. and yi (note the minus sign). Applying\\nEq. 67 literally (noting that must here be considered as nega-\\ntive in order to make the notation consistent) we obtain\\n1\\ne\\n3\\n2/^- Vr)]", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0124.jp2"}, "125": {"fulltext": "94. EABTIlWOliK. 109\\nwhich reduces to\\nin n\\n-^[j yi f/ j\\nAs the algebraic signs tend to create confusion in tliese\\nforinula3, it is more simple to remember that for a triangle\\nlying on hoth sides of the center e is always numerically c(|ual\\nlYh n\\nto {xi x^) and for a triangle entirely on one side, e is\\n-j- the numerical su/n of the two dis-\\nnumerically equal to\\n3 L2\\ntances out]. The algebraic sign of e is readily determinable as\\nin 91.\\n93. Example of curvature correction. Assume that the fill in\\n78 occurred on a 6\u00c2\u00b0 curve to the ri(/ht. ^-jj The\\nquantities 210, 507, etc., represent the quantities V\\\\ V\\netc., since they include in each case the 61 cubic yards due to\\nthe grade prism. Then\\nV(xi Xr) 210(22.9 8.2) _ 3101.7 _\\n3i? 2865 2865\\nThe sign is plus since the center of gravity of the cross-sec-\\ntion is on the left side of the center and the road curves to the\\nright, thus making the true volume larger. For Sta. 18 the\\ncorrection, computed similarly, is -f- 3, and the correction for\\nthe whole section is 1 -f- 3 4. For Sta. 18 40 the cor-\\nrection is computed as 6 yards. Therefore, for the 40 feet, the\\ncorrection is y\\\\%-(3 6) 3.6, which is called 4. Computing\\nthe others similarly we obtain a total correction of 16 cubic\\nyards.\\n94. Accuracy of earthwork computations. The preceding\\nmethods give the precise vohc7ne (except where approximations\\nare distinctly admitted) of the prismoids which are sujij^osed to\\nrepresent the volume of the earthwork. To appreciate the\\naccuracy necessary in cross-sectioning to obtain a given accuracy", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0125.jp2"}, "126": {"fulltext": "110 JiAIfAlO AD CONSTRUCTION. \u00c2\u00a794.\\nin volume, consider that a fifteen-foot length of the cross-section,\\nwhich is assumed to be straight, really sags 0.1 foot, so that the\\ncross-section is in error by a triangle 15 feet wide and 0.1 foot\\nhigh. This sag 0.1 foot high would hardly be detected by the\\neye, but in a length of 100 feet in each direction it would make\\nan error of volume of 1.4 cubic yards in each of the two pris-\\nmoids, assuming that the sections at the other ends were perfect.\\nIf the cross-sections at both ends of a prismoid were in error by\\nthis same amount, the volume of that prismoid would be in error\\nby 2.8 cubic yards if the errors of area were both plus or both\\nminus. If one were plus and one minus, the errors would\\nneutralize each other, and it is the compensating character of\\nthese errors which permits any confidence in the results as\\nobtained by the usual methods of cross-sectioning. It demon-\\nstrates the utter futility of attempting any closer accuracy than\\nthe nearest cubic yard. It will thus be seen that if an error\\nreally exists at any cross-section it involves the prismoids on\\nhoth sides of the section, even though all the other cross-sections\\nare perfect. As a further illustration, suppose that cross-sec-\\ntions were taken by the method of slope angle and center depth\\n73), and that a cross-section, assumed as uniform, sags 0.4\\nfoot in a width of 20 feet. Assume an equal error (of same\\nsign) at the other end of a 100-foot section. The error of\\nvolume for that one prismoid is 38 cubic yards.\\nThe computations further assume that the warped surface,\\npassing through the end sections, coincides with the surface of\\nthe ground. Suppose that the cross-sectioning had been done\\nwith mathematical perfection and, to assume a simple case,\\nsuppose a sag of 0.5 foot between the sections, which causes an\\nerror equal to the volume of a pyramid having a base of 20 feet\\n(in each cross-section) times 100 feet (between the cross-sections)\\nand a height of 0.5 foot. The volume of this pyramid is\\ni(20 X 100) X 0.5 z= 333 cub. ft. 12 cub. yds. And yet\\nthis sag or hump of 6 inches would generally be utterly un-\\nnoticed, or at least disregarded.\\nWhen the ground is very rough and broken it is sometimes", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0126.jp2"}, "127": {"fulltext": "\u00c2\u00a796. eartuwohk. Ill\\npractically impossible, even with tVeqiient oross-sections, to\\nlocate warped surfaces which will closely coincides with all the\\nsudden irregularities of the ground. In such cases the compu-\\ntations are necessarily more or less approximate and dependence\\nmust be placed on the compensating character of the errors.\\n95. Approximate computations from profiles. As a means\\nof comparing the relative amounts of earthwork on two or\\nmore proposed routes which have been surveyed by preliminary\\nsurveys, it will usually be sufficiently accurate to com})are the\\nareas of cutting (assuming that the cut and till are approximately\\nbalanced) as shown by the several profiles. The errors involved\\nmay be large in individual cases and for certain small sections,\\nbut fortunately the errors (in comparing two lines) will be\\nlargely compensated. The errors are nmch larger on side-hill\\nwork than when the cross-sections are comparatively level.\\nThe errors become large when the depth of cut or fill is very\\ngreat. If the lines compared have the same general character\\nas to the slope of the cross-sections, the proportion of side-liill\\nwork, and the average depth of cut or iill, the error involved in\\nconsidering their relative volumes of cutting to be as the relative\\nareas of cutting on the profiles (obtained perhaps by a planim-\\neter) will probably be small. If the volume in each case is\\ncomputed by assuming the sections as level^ with a depth espial\\nto the center cut, the error involved will depend only on the\\namount of side-hill work and the degree of the slope. if these\\nfeatures are about the same on the two lines compared, the error\\ninvolved is still less.\\nFORMATION OF EMUANKMKNTS.\\n96. Shrinkage of earthwork. The evidence on this subject\\nas to the amount of shrinkage is very conflicting, a fact which\\nis probably due to the following causes\\n1. The various kinds of earthy material act very differently\\nas respects shrinkage. There has been l)ut little uniforniity in\\nthe classification of earths in the tests and experiments tliat\\nhave been made.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0127.jp2"}, "128": {"fulltext": "112 RAILROAD CONSTRUCTION. 96.\\n2. Yery much depends on tlie method of forming an em-\\nbankment (as will be shown later). Different reports have been\\nbased on different methods often without mention of the\\nmethod.\\n3. An embankment requires considerable time to shrink to\\nits final volume, and therefore much depends on the time\\nelapsed between construction and the measurement of what is\\nsupposed to be the settled volume.\\nP. J. Fljnn quotes some experiments {Eng. News^ May 1,\\n1886) made in India in which pits were dug, having volumes of\\n400 to 600 cubic feet. The material, when piled into an em-\\nbankment, measured largely in excess of the original measure-\\nment as is the universal experience. The pits were refilled\\nwith the same material. As the rains, very heavy in India,\\nsettled the material in the pits, more was added to keep the pits\\nfull. Even after the rainy season was over, there was in every\\ncase material in excess. This would seem to indicate a per-\\nmanent expansion^ although it is possible that the observations\\nwere not continued for a sufficient time to determine the final\\nsettled volume.\\nOn the contrary, notes made by Mr. Elwood Morris many\\nyears ago on the behavior of embankments of several thousand\\ncubic yards, formed in layers by carts and scrapers, one winter\\nintervening between commencement and completion, showed in\\neach case a permanent contraction averaging about 10^.\\nAll authorities agree that rockwork expands permanently\\nwhen formed into an embankment, but the percentages of\\nexpansion given by different authorities differ even more than\\nwith earth varying from 8 to 90^. Of course this very large\\nranore in the coefficient is due to differences in the character of\\nthe rock. The softer the rock and the closer its similarity to\\nearth, the less will be its expansion. On account of the conflict-\\ning statements made, and particularly on account of the influence\\nof methods of work, but little confidence can be felt in any\\ngiven coefficient, especially when given to a fraction of a per", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0128.jp2"}, "129": {"fulltext": "97. EARTHWORK. 113\\ncent, but the consensus of American practice seems to avera -e\\nabout as follows\\nPermanent contraction of earth about 10^\\nexpansion of rock 40 to GO^\\nThese values for rock should be materially reduced, according\\nto judgment, when the rock is soft and liable to disintegrate.\\nThe hardest rocks, loosely piled, may occasionally give even\\nhigher results. The following is given by several authors as\\nthe permanent contraction of several grades of earth\\nGravel or sand about 8^\\nClay lOfo\\nLoam 12^\\nLoose vegetable surface soil 15^\\nIt may be noticed from the above table that the harder and\\ncleaner the material the less is the contraction. Perfectly clean\\ngravel or sand would not probably change volume appreciably.\\nThe above coefficients of shrinkage and expansion may be used\\nto form the following convenient table.\\nMaterial.\\nTo make 1000 cubic\\nyards of embankment\\nwill require\\n1000 cubic yards measured\\nin excavation will make\\nGravel or sand\\nClav\\n1087 cubic yards\\n1111\\n1136\\n1176\\n714\\n625\\nmeasured in excavation\\n920 cubic yards\\n900\\n880\\n8.50\\n1400\\n1600\\nof embaukmeut.\\nLoam\\nLoose vegetable soil\\nRock, larg(, pieces\\nsmall\\n97. Allowance for shrinkage. On account of the initial\\nexpansion and subsequent contraction of earth, it becomes\\nnecessary to form embankments higher than their required\\nultimate form in order to allow for the subsequent shrinkage.\\nAs the shrinkage appears to be all vertical (practically), the\\nembankment must be formed as shown in Fi 2:. .58. Tlic effect", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0129.jp2"}, "130": {"fulltext": "114\\nRAILROAD CONSTRUCTION.\\n97.\\nof shrinkage should not be confounded with that of sUpping of\\nthe sides, which is especially apt to occur if the embankment is\\nsubjected to heavy rains very soon after being formed, and also\\nwhen the embankments are originally steep. It is often difficult\\nFig. 58.\\nto form an embankment at a slope of 1 1 which will not slip\\nmore or less before it hardens.\\nVery high embankments shrink a greater percentage than\\nlower ones. Various rules giving the relation between shrink-\\nage and height have been suggested, but they vary as badly as\\nthe suggested coefficients of contraction, probably for the same\\ncauses. As the fact is unquestionable, however, the extra\\nheight of the embankment must be varied somewhat as in Fig.\\n59, which represents a longitudinal section of an embankment.\\nFig. 59.\\nAs considerable time generally elapses between the completion\\nof the embankment and the actual riinnincr of trains, the o^rade\\nad will generally be nearly flattened down to its ultimate form\\nbefore traffic commences, but such grades are occasionally objec-\\ntionable if added to what is already a ruling grade. With some\\nkinds of soil the time required for complete settlement may be\\nas much as two or three years, but, even in such cases, it is", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0130.jp2"}, "131": {"fulltext": "98. EARTHWORK. 115\\nprobable that one-half of the settlement will take place during\\nthe first six months. The engineer should therefore require\\nthe contractor to make all fills about 8 to 15^ (accordin*^ to\\nthe material) higher than the profiles call for, in order that\\nsubsequent shrinkage may not reduce it to less than the re-\\nquired volume.\\n98. Methods of forming embankments. When the method is\\nnot otherwise ol jectionable, a high embankment can be formed\\nvery cheaply (assuming that carts or wheelbarrows are used) by\\ndumjiing over the. end and building to the full height (or even\\nhigher, to allow for shrinkage) as the embankment proceeds.\\nThis allows more time for shrinkage, saves nearly all the cost of\\nspreading (see Item 4, 111), and reduces the cost of roadways\\n(Item 5). Of course this method is especially applicable when\\nthe material comes from a place as liigh as or higher than grade,\\nso that no up-hill hauling is required.\\nAnother method is to spread it in layers two or three feet\\nthick (see Fig. GO), which are made concave upwards to avoid\\nlimiHUUiiimmmimiiimmuiiniv\\nFig. 60.\\npossible sliding on each other. Spreading in layers has the\\nadvantage of partially ramming each layer, so that the subse-\\nquent shrinkage is very small. Sometimes small trendies are\\ndug along the lines of the toes of the embankment. This will\\nfrequently prevent the sliding of a large mass of the embank-\\nment, which will then require extensive and costly repairs, to\\nsay nothing of possible accidents if the sliding occurs after the\\nroad is in operation. Incidentally these trenches will be of\\nvalue in draining the subsoil. AVhen circumstances require an\\nembankment on a hillside, it is advisable to cut out steps to\\nprevent a possible sliding of the whole embankment. Merely", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0131.jp2"}, "132": {"fulltext": "116 RAILROAD CONSTRUCTION. 99.\\nploughing the side-hill will often be a cheajDer and sufficiently\\neffective method.\\nFig. 61.\\nOccasionally the formation of a very high and lono- embank-\\nment may be most easily and cheaply accomplished by building\\na trestle to grade and opening the road. Earth can then be\\nprocured where most convenient, perhaps several miles away,\\nloaded on cars with a steam-shovel, hauled by the trainload, and\\ndumped from the cars with a patent unloader. On such a large\\nscale, the cost per yard would be very much less than by ordi-\\nnary methods enough less sometimes to more than pay for the\\ntemporary trestle, besides allowing the road to be opened for\\ntraffic very much earlier, which is often a matter of prime\\nfinancial importance. It may also obviate the necessity for\\nextensive borrow-pits in the immediate neighborhood of the\\nheavy fill and also utilize material which would otherwise be\\nwasted.\\nCOMPUTATION OF HAUL.\\n99. Nature of subject. As will be shown later when analyz-\\ning the cost of earthwork, the most variable item of cost is that\\ndepending on the distance hauled. As it is manifestly imprac-\\nticable to calculate the exact distance to which every individual\\ncartload of earth has been moved, it becomes necessary to devise\\na means which will give at least an equivalent of the haulao-e of\\nall the earth moved. Evidently the average haul for any mass\\nof earth moved is equal to the distance from the center of 2:rav-\\nity of the excavation to the center of gravity of the embank-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0132.jp2"}, "133": {"fulltext": "\u00c2\u00a7100.\\nEARTHWORK.\\n117\\nmerit formed by the excavated material. As a rongli approxi-\\nmation the center of gravity of a cut (or fill) may sometimes be\\nconsidered to coincide with the center of gravity of that part of\\ntlie profile representing it, but the error is frequently very large.\\nThe center of gravity may be determined by various methods,\\nbut the method of the mass diagram accomplishes the same\\nultimate purpose (the determination of the haul) with all-suffi-\\ncient accuracy and also furnishes other valuable information.\\n100. Mass diagram. In Fig. 62 let A R G represent\\na profile and grade line drawn to the usual scales. Assume A\\nFig. 63.\u00e2\u0080\u0094 Mass Diagram.\\nto be a point past which no earthwork will be hauled. Above\\nevery station point in the profile draw an ordinate which\\nwill represent the algebraic sum of the cubic yards of cut and\\nfill (calling cut and fill from the point A to the point\\nconsidered. In doing this shrinkage must be allowed for by\\nconsidering how much embankment would actually be made by\\nso many cubic yards of excavation of such material. For\\nexample, it will be found that 1000 cubic yards of sand or\\ngravel, measured in place (see 97), will make about 920 cubic\\nyards of embankment; therefore all cuttings in sand or gravel\\nshould be discounted in about this proportion. Excavations in\\nrock should be increased in the proper ratio. In short, all ex-\\ncavations should be valued according to the amount of settled\\nembankment that could be made from them. The computations\\nmay be made systematically as shown in the tabular form. Place", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0133.jp2"}, "134": {"fulltext": "118\\nRAILROAD CONSTRUCTION.\\n101.\\nin the first column a list of the stations; in the second column,\\nthe number of cubic yards of cut or fill between each station\\nand the preceding station in the third and fourth columns, the\\nkind of material and the proper shrinkage factor; in the fifth\\ncolumn, a repetition of the quantities in cubic yards, except that\\nthe excavations are diminished (or increased, in the case of rock)\\nto the number of cubic yards of settled embankment which may\\nbe made from tliem. In the sixth column, place the algehraic\\nsum of the quantities in the fifth column (calling cuts and\\nfills from the starting-point to the station considered. These\\nalgebraic sums at each station will be the ordinates, drawn to\\nsome scale, of the mass curve. The scale to be used will depend\\nsomewhat on whether the work is heavy or light, but for ordi-\\nnary cases a scale of 5000 cubic yards per inch may be used.\\nDrawing these ordinates to scale, a curve A^ B^ G may be\\nobtained by joining the extremities of the ordinates.\\nSta.\\nYards{-*\\nMaterial.\\nShrinkage\\nfactor.\\nYards, reduced\\nfor shrinkage.\\nOrdinate in\\nmass curve.\\n46 +70\\n47\\n48\\n60\\n49\\n50\\n51\\n32\\n30\\n53\\n70\\n54\\n42\\n55\\n56\\n57\\n175\\n1788\\n2341\\n2198\\n1292\\n693\\n-2414\\n2526\\n-2243\\n1954\\n-2006\\n-2077\\n-1828\\n710\\n462\\n195\\n1792\\n614\\n143\\n906\\n-1985\\n-1721\\n112\\n177\\n180\\n52\\n71\\n276\\n1242\\n1302\\nClayey soil\\n10 per ceut\\n-10\\n-10\\n175\\n1613\\n553\\n143\\n906\\n-1985\\n-1721\\n112\\n283\\n289\\n52\\n71\\n249\\n1118\\n1172\\nHard rock\\n1\\n+60 per cent\\n+60\\nClayey soil\\ni i It\\n1\\n10 percent\\n-10\\n-10\\n101. Properties of the mass curve.\\n1. The curve will be rising while over cuts and falling\\nwhile over fills.\\n2. A tangent to the curve will be horizontal (as at B^ 7), E^\\nF^ and G) when passing from cut to fill or from fill to cut.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0134.jp2"}, "135": {"fulltext": "101. EARTHWORK. 119\\n3. Wlieii the curve is helow the zero line it shows that\\nmaterial must be drawn backward (to the left) and vice versa^\\nwhen the curve is above the zero line it shows that material\\nmust be drawn ybri^arc? (to the right).\\n4. When the curve crosses the zero line (as at A and 6 it\\nshows (in this instance) that the cut between A and B will just\\nprovide the materinl required for the fill between^ and 6^ and\\nthat no material should be hauled past C\\\\ or, in general, past\\nany intersection of the mass curve and the zero line.\\n5. If any horizontal line be drawn (as ah)^ it indicates that\\nthe cut and fill between a and b will just balance.\\n6. When the center of gravity of a given volume of\\nmaterial is to be moved a given distance, it makes no difference\\n(at least theoretically) how far each individual load may be\\nhauled or how any individual load may be disposed of. The\\nsummation of the products of each load times the distance\\nhauled will be a constant, whatever the method, and will equal\\nthe total volume times the movement of the center of gravity.\\nThe a/verage haul, which is the movement of the center of\\ngravity, will therefore equal the summation of these products\\ndivided by the total volume. If we draw two horizontal ])ar-\\nallel lines at an infinitesimal distance dx a})art, as at the\\nsmall increment of cut dx at a will fill the corresponding incre-\\nment of fill at b\\\\ and this material must be hauled the distance\\nab. Therefore the product of ab and dx, which is the product\\nof distance times volume, is represented by the area of the\\ninfinitesimal rectangle at ab, and the total area ABC represents\\nthe summation of volume times distance for all the earth move-\\nment between A and C This sunnnation of ])roducts divided\\nby the total volume gives the average haul.\\n7. The horizontal line, tangent at E and cutting the curve\\nat e,f, and g, shows that the cut and fill between e and E will\\njust balance, and that a possible method of hauling (whether\\ndesirable or not) would be to M orrow earth for the fill\\nbetween C and e use the material between D and K foi- the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0135.jp2"}, "136": {"fulltext": "1^0 RAILROAD CONSTRUCTION. 101.\\nfill between e and I)\\\\ and similarly balance cut and fill between\\nE andy^ and also between y^ and g\\n8. Similarly the horizontal line hldw, may be drawn cuttino-\\nthe curve, which will show another possiUe method of hauling.\\nAccording to this plan, the fill between C and h would be\\nmade by borrowing the cut and fill between h and h would\\nbalance; also that between Jc and V and between V and m\\nSince the area ehDkE represents the measure of haul for tlie\\nearth between e and E\\\\ and the other areas measure the corre-\\nsponding hauls similarly, it is evident that the sum of the areas\\neliDhE and ElFmf^ which is the measure of haul of all the\\nmaterial between e and/ is largely in excess of the sum of\\nthe areas IWk^ hEl^ and IFm^ plus the somewhat uncertain\\nmeasures of haul due to borrowing material for e h and wastino-\\nthe material between m and/ Therefore to make the meas-\\nure of haul a minimum a line should be drawn which will\\nmake the sum of the areas between it and the mass curve a\\nminimum. Of course this is not necessarily the cheapest plan,\\nas it implies more or less borrowing and wasting of material,\\nwhich may cost more than the amount saved in haul. The\\ncomparison of the two methods is quite simple, however. Since\\nthe amount of fill between e and li is represented by the differ-\\nence of the ordinates at e and A, and similarly for m and/ it\\nfollows that the amount to be borrowed between e and li will\\nexactly equal the amount wasted between in and By the\\nfirst of the above methods the haul is excessive, but is definitely\\nknown from the mass diagram, and all of the material is util-\\nized by the second method the haul is reduced to about one-\\nhalf, but there is a known quantity in cubic yards wasted at one\\nplace and the same quantity borrowed at another. The leno th\\nof haul necessary for the borrowed material would need to be\\nascertained also the haul necessary to w^aste the other material\\nat a place where it would be unobjectionable. Frequently this\\nis best done by widening an embankment beyond its necessary\\nwidth. The computation of the relative cost of the above\\nmethods will be discussed later 116).", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0136.jp2"}, "137": {"fulltext": "102. EARTHWORK. 121\\n9. Suppose that it were deemed best, after drawing the mass\\ncurve, to introduce a trestle between s and v tlms savin an\\namount in fill equal to tv. If such Lad been tlie original desi ni\\nthe mass curve would have been a straight horizontal line\\nbetween s and i and would continue as a curve which would be\\nat all points a distance tv above the curve vFmzfGg. If the\\nline Ef is to be used as a zero line, its intersection with the new\\ncurve at x will show that the material between E and z will\\njust balance if the trestle is used, and that the amount of liaul\\nwill be measured by the area between the line Ex and the broken\\nline Estx. The same computed result may. be obtained without\\ndrawing the auxiliary curve txn by drawing the horizontal\\nline zy at a distance xz {j=^ tv) below Ex. The amount of the\\nhaul can then be obtained by adding the triangular area between\\nEs and the horizontal line Ex, the rectangle between st and Ex^\\nand the irregular area between vFz and y z (which last is\\nevidently equal to the area between tx and E x). The dis-\\nposal of the material at the right of z would then be governed\\nby the indications of the profile and mass diagram wdiicli would\\nbe found at the right of g In fact it is difficult to decide with\\nthe best of judgment as to the proper disposal of material with-\\nout having a mass diagram extending to a considerable distance\\neach side of that part of the road under immediate considera-\\ntion\\n102. Area of the mass curve. The area may be computed\\nmost readily by means of a planimeter, -which is capable with\\nreasonable care of measuring such areas with as great accuracy\\nas is necessary for this work. If no such instrument is obtain-\\nable, the area may be obtained by an application of Simpson s\\nrule. The ordinates will usually be spaced 100 feet apart.\\nSelect an even number of such spaces, leaving, if necessary, one\\nor more triangles or trapezoids at the ends for separate and\\nindependent computation. Let y^ y,x ^^e the ordinates, i.e.,\\nthe number of cubic yards at each station of the mass curve., or\\nthe figures of column six referred to in 100. Let the\\nuniform distance between ordinates 100 feet) be called 1, i.e.,", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0137.jp2"}, "138": {"fulltext": "122 RAILROAD COISSTRUCTION, 103.\\none station. Then tlie units of the resulting area will be cubic\\nyards hauled one station. Then the\\nArea ^[y, ^{y, ^3 y^^^ _ ^p _|_ ^^y^ 2/4 y^,^_^^) y^l (70)\\nWhen an ordinate occurs at a substation, tlie best plan is to\\nignore it at first and calculate the area as above. Then, if the\\ndifference involved is too great to be neglected, calculate the\\narea of the triangle having the extremity of the ordinate at the\\nsubstation as an apex, and the extremities of the ordinates at the\\nadjacent stations as the ends of the base. This may be done by\\nfinding the ordinate at the substation tliat would be a propor-\\ntional between the ordinates at the adjacent full stations. Sub-\\ntract this from the real ordinate (or vice versa) and multiply the\\ndifference by i X 1. An inspection will often show that the\\ncorrection thus obtained would be too small to be worthy of con-\\nsideration. If there is more than one substation between two\\nfull stations, the corrective area will consist of two triangles and\\none or more trapezoids which may be similarly computed, if\\nnecessary.\\nWhen the zero line (Fig. 62) is shifted to eE^ the drop from\\nAC (produced) to E is known in the same units, cubic yards.\\nThis constant may be subtracted from the numbers column\\n4, 100) representing the ordinates, and will thus give, with-\\nout any scaling from the diagram, the exact value of the modi-\\nfied ordinate?.\\n103. Value of the mass diagram. The great value of the mass\\ndiagram lies in the readiness with which different plans for the\\ndisposal of material may be examined and compared. When\\nthe mass curve is once drawn, it will generally require only a\\nshifting of the horizontal line to show the disposal of the material\\nby any proposed method. The mass diagram also shows the\\nextreme length of haul that will be required by any proposed\\nmethod of disposal of material. This brings into consideration\\nthe limit of profitable haul, which will be fully discussed in\\n116. For the present it may be said that with each method\\nof carrying material there is some limit beyond which the expense", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0138.jp2"}, "139": {"fulltext": "104. EARTHWORK. 123\\nof hauling will exceed the loss resulting from borrowing and\\nwasting. With wheelbarrows and scrapers the limit of profit-\\nable haul is comparatively short, with carts and tram-cars it is\\nmuch longer, while with locomotives and cars it may be several\\nmiles. If, in Fig. 62, eE ov ^J^ exceeds the limit of profitable\\nhaul, it shows at once that some such line as hklm should be\\ndrawn and the material disposed of accordingly.\\n104. Changing the grade line. The formation of the mass\\ncurve and the resulting plans as to the disposal of material are\\nbased on the mutual relations of the grade line and the surface\\nprofile and the amounts of cut and fill which are thereby im-\\nplied. If the grade line is altered, every cross-section is\\naltered, the amount of cut and fill is altered, and the mass\\ncurve is also changed. At the farther limit of the actual\\nchange of the grade line the revised mass curve will have (in\\ngeneral) a different ordinate from the previous ordinate at that\\npoint. From that point on, the revised mass curve will be par-\\nallel to its former position, and the revised curve may be treated\\nsimilarly to the case previously mentioned in which a trestle was\\nintroduced. Since it involves tedious calculations to determine\\naccurately how much the volume of earthwork is altered by a\\nchange in grade line, especially through irregular country, the\\neffect on the mass curve of a change in the grade line cannot\\ntherefore be readily determined except in an approximate way.\\nliaising the grade line will evidently increase the fills and\\ndiminish the cuts, and vice versa. Therefore if the mass curve\\nindicated, for example, either an excessiv^ely long haul or the\\nnecessity for borrowing material (implying a fill) and wasting\\nmaterial farther on (implying a cut), it would be possible to\\ndiminish the fill (and hence the amount of material to l)e bor-\\nrowed) by lowering the grade line near that place, and diminish\\nthe cut (and hence the amount of material to be wav ^ted) by\\nraising the grade line at or near the ])lace farther on. Whether\\nthe advantage thus gained would compensate \u00c2\u00abfor the possibly\\ninjurious effect of these changes on the grade line would require\\npatient investigation. But the method outlined shows how the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0139.jp2"}, "140": {"fulltext": "124\\nItAILROAD CONSTRUCTION.\\n105.\\nmass curve might be used to indicate a possible change in -rade\\nline which might be demonstrated to be profitable.\\n105. Limit of free haul. It is sometimes specified in con-\\ntracts for earthwork that all material shall be entitled to free\\nhaul up to some specified limit, say 500 or 1000 feet, and that\\nall material drawn farther than that shall be entitled to an\\nallowance on the excess of distance. It is manifestly imprac-\\nticable to measure the excess for each load, as much so as to\\nmeasure the actual haul of each load. The mass diagram also\\nsolves this problem very readily. Let Fig. 63 represent a pro-\\nFig. G3.\\nfile and mass diagram of about 2000 feet of road, and suppose\\nthat 800 feet is taken as the limit of free haul. Find two\\npoints, a and h, in the mass curve which are on the same hori-\\nzontal Une and which are 800 feet apart. Project these points\\ndown to a and V. Then the cut and fill between a and h will\\njust balance, and the cut between A and a will be needed for\\nthe fill between h and C. In the mass curve, the area between\\nthe horizontal line ah and the curve aBh represents the haula-e\\nof the material between a and V which is all free. The reel-\\nangle ahnn represents the haulage of the material in the cut\\nA a across the 800 feet from a to h\\\\ This is also free. The\\nsum of the two areas Aam and hiC represents the haulage\\nentitled to an allowance, since it is the summation of the products\\nof cubic yards times the excess of distance hauled.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0140.jp2"}, "141": {"fulltext": "105. EARTUWORK. 125\\nIf tlie amount of cut and lill was synnnetrical about the\\npoint B\\\\ the mass curve would be a symmetrical curve about the\\nvertical line through /i, and the two limiting lines of free haul\\nwould be placed symmetrically about B and B h\\\\ o-eneral\\nthere is no such symmetry, and frequently the difference is con-\\nsiderable. The area ciBhnm will be materially chano-ed accord-\\ning as the two vertical lines am and hi, always 800 feet apart,\\nare shifted to the right or left. It is easy to show^ that the area\\naBhnm is a maximuni when ah is horizontal. The minimum\\nvalue would be obtained either when 7)i reached A or n reached\\nC, depending on the exact form of the curve. Since the posi-\\ntion for the minimum value is manifestly unfair, the best dehnite\\nvalue obtainable is the maximum, which must be obtained as\\nabove described. Since aBhim, is made maximum, the re-\\nmainder of the area, which is the allow^ance for overhaul, be-\\ncomes a minhnum. The areas Aam and ICn may be obtained\\nas in 102. If the whole area AaBhCA has been previously\\ncomputed, it may be more convenient to compute the area\\naBhnm and subtract it from the total area.\\nSince the intersections of the mass curve and the zero line\\nmark limits past wdiich no material is drawm, it follows that\\nthere will be no allowance for overhaul except where the dis-\\ntance between consecutive intersections of the zero line and mass\\ncurve exceeds the limit of free haul.\\nFrequently all allowances for overhaul are disregarded the\\nprofiles, estimates of quantities, and the required disposal of ma-\\nterial are shown to bidding contractors, and they must tlien make\\ntheir own allowances and bid accordingly. This method luis\\nthe advantage of avoiding possible disputes as to the amount of\\nthe overhaul allow^ance, and is popular with railroad companies on\\nthis account. On the other hand the facility with which differ-\\nent plans for the disposal of material may be studied and com-\\npared by the mass-curve method facilitates the adoption of the\\nmost economical plan, and the elimination of uncertaintv will\\nfrequently lead to a safe reduction of the bid, and so the method\\nis valuable to both the railroad company and the contractor.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0141.jp2"}, "142": {"fulltext": "126 RAILROAD CONSTRUCTION, 106.\\nELEMENTS OF THE COST OF EARTHWORK.\\n(The following analysis of the cost of earthwork follows the\\ngeneral method given in the well-known papers published bj\\nEllwood Morris, C.E., in the Journal of the Franklin Institute\\nin September and October, 1841. l^umerous corroborative\\ndata have been obtained from various other- sources, and also\\nfigures on methods not then in vogue.)\\n106. General divisions of the subject. The variations in the\\ncost of earthwork are caused by the greatly varying conditions\\nunder which the work is done, chief among which is character\\nof material, method of carriage, and length of haul. Any gen-\\neral system of computation must therefore differentiate the total\\ncost into such elementary items that all differences due to varia-\\ntions in conditions may be allowed for. The variations due to\\ncharacter of material will be allowed for by an estimate on loose\\nlight sandy soil, and also an estimate on the heaviest soils, such\\nas stiff clay and hard-pan. These represent the extremes (ex-\\ncluding rock, which will be treated separately), and the cost of\\nintermediate grades must be estimated by interpolating between\\nthe extreme values. The general divisions of the subject will\\nbe:*\\n1. Loosening.\\n2. Loading.\\n3. Hauling.\\n4. Spreading.\\n5. Keeping roadways in order.\\n6. Kepairs, wear, depreciation, and interest on cost of plant.\\n7. Superintendence and incidentals.\\n8. Contractor s profit.\\nBy making the estimates on the basis of $1 per day for the\\ncost of common labor, it is a simple matter to revise the esti-\\nmates according to the local price of labor by multiplying the\\nfinal estimate of cost by the price of labor in dollars per day.\\nTrautwine.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0142.jp2"}, "143": {"fulltext": "107. EAHTIIWORK. \\\\2ll\\n107. Item 1. Loosening, (a) Ploughs. Very liglit sandy\\nsoils can frequently be shovelled without any previous loosenin*\\nbut It is generally economical, even with very light material, to\\nuse a plough. Morris quotes, as the results of experiments,\\nthat a three-horse plough would loosen from 250 to 800 cubic\\nyards of earth per day, which at a valuation of So per day\\nwould make the cost per yard vary from 2 cents to O.G cent.\\nTrautwine estimates the cost on the basis of two men handlino-\\na two-horse plough at a total cost of $3.87 per day, beino- ,^l\\neach for the men, 75 c. for each horse, and an allowance of 37 c.\\nfor the plough, harness, etc. From 200 to 600 cubic yards is\\nestimated as a fair day s work, which makes a cost of 1.9 c. to\\n0.65 c. per yard, which is substantially the same estimate as\\nabove. Extremely heavy soils have sometimes been loosened\\nby means of special ploughs operated by traction-engines.\\n(b) Picks. When picks are used for loosening the earth, as\\nis frequently necessary and as is often done when plou^hino-\\nwould perhaps be really cheaper, an estimate for a fair day s\\nwork is from 14 to 60 cubic yards, the 14 yards being the esti-\\nmate for stiff clay or cemented gravel, and the 60 yards the esti-\\nmate for the lightest soil that would require loosening. At 81\\nper day this means about 7 c. to 1.7 c. per cubic yard, which is\\nabout three times the cost of ploughing. Five feet of the face\\nis estimated f as the least width along the face of a bank that\\nshould be allowed to enable each laborer to work with freedom\\nand hence economically.\\n(c) Blasting. Although some of the softer shaly rocks may\\nbe loosened with a pick for about 15 to 20 c. per yard, yet rock\\nin general, frozen earth, and sometimes even compact clay is\\nmost economically loosened by blasting. The subject of blast-\\ning will be taken up later, \u00c2\u00a7g 117-123.\\n(d) Steam-shovels. The items of loosening and loading merge\\ntogether with this method, which will therefore be treated in\\nthe next section.\\nTrautwine. f Hurst.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0143.jp2"}, "144": {"fulltext": "128 RAILROAD CONSTRUCTION. 108.\\n108. Item 2. Loading, (a) Hand-shovelling. Much depends\\non proper management, so that the shovellers need not wait\\nunduly either for material or carts. With the best of manage-\\nment considerable time is thus lost, and yet the intervals of rest\\nneed not be considered as entirely lost, as it enables the men to\\nwork, while actually loading, at a rate which it would be physi-\\ncally impossible for them to maintain for ten hours. Seven\\nshovellers are sometimes allowed for each cart otherwise there\\nshould be five, two on each side and one in the rear. Economy\\nrequires that the number of loads per cart per day should be\\nmade as large as possible, and it is therefore wise to employ as\\nmany shovellers as can work without mutual interference and\\nwithout wasting time in waiting for material or carts. The\\nfigures obtainable for the cost of this item are unsatisfactory on\\naccount of their large disagreements. The following are quoted\\nas the number of cubic yards that can be loaded into a cart by\\nan average laborer in a working day of ten hours, the lower\\nestimate referring to heavy soils, and the higher to light sandy\\nsoils 10 to 14 cubic yards (Morris), 12 to 17 cubic yards (Has-\\nkoll), 18 to 22 cubic yards (Hurst), IT to 24 cubic yards (Traut-\\nwine), 16 to 48 cubic yards (Ancelin). As these estimates are\\ngenerally claimed to be based on actual experience, the discre-\\npancies are probably due to difierences of management. If the\\naverage of 15 to 25 cubic yards be accepted, it means, on the\\nbasis of $1 per day, 6.7 c. to 4c. per cubic yard. These esti-\\nmates apply only to earth. Bockworic costs more, not only\\nbecause it is harder to handle, but because a cubic yard of solid\\nrock, measured in place, occupies about 1.8 cubic yards when\\nbroken up, while a cubic yard of earth will occupy about 1.2\\ncubic yards. Eockwork will therefore require about 50^ more\\nloads to haul a given volume, measured in place, than will the\\nsame nominal volume of earthwork. The above authorities give\\nestimates for loading rock varying from 6.9 c. to 10 c. per cubic\\nyard. The above estimates apply only to the loading of carts\\nor cars with shovels or by hand (loading masses of roek). The", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0144.jp2"}, "145": {"fulltext": "108. EARTHWORK. 120\\ncost of loading wheelbarrows and the cost of scraper work will\\nbe treated under the item of hauling.\\n(b) Steam-shovels.- AVhenever the magnitude of the work\\nwill warrant it there is- great economy in the use of steam-shovels.\\nThese have a bucket or dipper on the end of a long\\nbeam, the bucket having a capacity varying from to 2^ cubic\\n3 ards. Steam-shovels handle all kinds of material from the\\nsoftest earth to shale rock, earthy material containing large\\nboulders, tree-stumps, etc. The capacity of the lai-ger sizes is\\nabout 3000 cubic- yards in 10 hours. They perform all the\\nwork of loosening and loading. Their economical working\\nrequires that the material shall be hauled away as fast as it can\\nbe loaded, wdiich usually means that cars on a track, hauled by\\nhorses or mules, or still better by a locomotive, shall be used.\\nThe expenses for a steam-shovel, costing about $5000, will\\naverage about $1000 per month. Of this the engineer will get\\n$100 the fireman $50 the cranesman 890 repairs perhaps\\n\u00c2\u00a7250 to 8300; coal, from 15 to 25 tons, cost very variable on\\naccount of expensive hauling; water, a very uncertain amount,\\nsometimes costing 8100 per month; about five laborers and a\\nforeman, the laborers getting 81.25 per day and the foreman\\n82.50 per day, which will amount to 8227.50 per month.\\nThis gang of laborers is employed in shifting the shovel when\\nnecessary, taking up and relaying tracks foi* the cars, shifting\\nloaded and unloaded cars, etc. In shovelling through a deep\\ncut, the shovel is operated so as to undermine the upper parts\\nof the cut, which then fall down within reach of the shovel, thus\\nincreasing the amount of material handled for each new position\\nof the shovel. If the material is too tough to fall down by its\\nown weight, it is sometimes found economical to employ a gang\\nof men to loosen it or even blast it rather than shift tlie shovel\\nso frequently. Non-condensing engines of 50 horse-power use\\nso much water that the cost of water-supply becomes a serious\\nFor a thorough treatment of the capabilities, cost, and raanacrPTnent of\\n;team-shovels the reader is referred to Steam-shovels and Steam-shovel\\nWork, by E. A. Hermann. D. Van Nostrand Co., New York.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0145.jp2"}, "146": {"fulltext": "130 RAILROAD CONSTRUCTION. 109.\\nmatter if water is not readily obtainable. The lack of water\\nfacilities will often justify the construction of a pipe line from\\nsome distant source and the installation of a steam-pump.\\nHence the seemingly large estimate of $100 per month for\\nwater-supply, although under favorable circumstances the cost\\nmay almost vanish. The larger steam-shovels wdll consume\\nnearly a ton of coal per day of 10 hours. The expense of haul-\\ning this coal from the nearest railroad or canal to the location of\\nthe cut is often a very serious item of expense and may easily\\ndouble the cost per ton. Some steam-shovels have been con-\\nstructed to be operated by electricity obtained from a plant\\nperhaps several miles away. Such a method is especially\\nadvantageous when fuel and water are difficult to obtain.\\n109. Item 3. Hauling. The cost of hauling depends on the\\nnumber of round trips per day that can be made by each vehicle\\nemployed. As the cost of each vehicle is practically the same\\nAvhether it makes many trips or few, it becomes important that\\ntlie number of trips should be made a maximum, and to that\\nend there should be as little delay as possible in loading and un-\\nloading. Therefore devices for facilitating the passage of the\\nvehicles have a real money value.\\n(a) Carts. The average speed of a horse hauling a two-\\nwheeled cart has been found to be 200 feet per minute, a little\\nslower when hauling the load and a little faster when returning\\nempty. This figure has been repeatedly verified. It means an\\nallowance of one minute for each 100 feet (or station of\\nlead the lead being the distance the earth is hauled. The\\ntime lost in loading, dumping, waiting to load, etc., has been\\nfound to average 4 minutes per load. Representing the num-\\nber of stations (100 feet) of lead by 5, the number of loads\\nhandled in 10 hours (600 minutes) would be 600 {s-\\\\- 1). The\\nnumber of loads per cubic yard, measured in the bank, is differ-\\nentiated by Morris into three classes, viz.\\n3 loads per cubic yard in descending hauling\\n3^ level hauling and\\n4 ascending hauling.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0146.jp2"}, "147": {"fulltext": "\u00c2\u00a7109. EARTUWORK. 131\\nAttempts have been made to estimate the effect of the grade\\nof the roadway by a theoretical consideration of its rate, and of\\nthe comparative strength of a horse on a level and on various\\ngrades. While such computations are always practicable on a\\nrailway (even on a temporary construction track), the traction on\\na temporary earth roadway is always very large and so very\\nvariable that any refinements are useless. On railroad earth-\\nwork the hauling is generally nearly level or it is descending\\nforming embankments on low ground with material from cuts in\\nhigh ground. The only common exception occurs when an\\nembankment is formed from borrow-pits on low ground. One\\nmethod of allowing for ascending grade is to add to the hori-\\nzontal distance 14 times the difference of elevation for work\\nwith carts and 24 times the difference of elevation for work\\nwith wheelbarrows, and use that as the lead. For example,\\nusing carts, if the lead is 300 feet and there is a difference of\\nelevation of 20 feet, the lead would be considered equivalent to\\n300 (14 X 20) 580 feet on a level.\\nTrautwine assumes the average load for all classes of work\\nto be cubic yard, which figure is justified by large experience.\\nUsing one figure for all classes of work simplifies the calculations\\nand gives the number of cubic yards carried per day of 10 hours\\nequal to r^ tt. Dividino: the cost of a cart per dav by the\\n^3(^ 4) ir J\\nnumber of cubic yards carried gives the cost of hauling per\\nyard. In computing the cost of a cart per day, Trautwine\\nrefers to the practice of having one driver manage four carts,\\nthus making a charge of 25 c. per day for each cart for the\\ndriver. 75 c. is allowed for the horse, which is supposed to be\\nthe total cost, including that for Sundays and rainy days. 25 c.\\nmore is allowed for the cart, harness, repairs, etc., thus making\\na total cost of $1.25 per day. Some contractors employ a\\ngreater number of drivers and expect each to assist in loading.\\nThere is found to be no saving in total cost per yard, while the\\nehances of loafing are perhaps greater. Morris instances five\\nactual cases in which the cost of the cart (reduced to the basis of", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0147.jp2"}, "148": {"fulltext": "132 RAILROAD CONSTRUCTION. 109.\\n$1 per day for labor) varied from $1.37 to $1.48. The items\\nof these costs were not given.\\nSince the time required for loading loose rock is greater than\\nfor earthwork, less loads will be hauled per day. The time\\nallowance for loading, etc., is estimated by Trautwine as 6\\nminutes instead of 4 as for earth. Considering the great ex-\\npansion of rock when broken up (see 97), one cubic yard of\\nsolid rock, measured in place, w^ould furnish the equivalent of\\nfive loads of earthwork of J cubic yard. Therefore, on the\\nbasis of five loads per cubic yard, the number of cubic yards\\nhandled per day per cart would be\\nr. 125 X ^(s 6)\\n(Jost per yard m cents (71)\\n(b) Wagons. For longer leads (i.e., from J- to f of a mile)\\nwagons drawn by two horses have been found most economical.\\nThe wagons have bottoms of loose thick narrow boards and are\\nunloaded very easily and quickly by lifting the individual boards\\nand breaking up the continuity of the bottom, thus depositing\\nthe load directly underneath the wagon. The capacity is about\\none cubic yard. The cost may be estimated on the same prin-\\nciples as that for carts.\\n(c) Wheelbarrows. According to Trautwine, the speed of\\nmoving wheelbarrows may be considered the same as for carts,\\n200 feet per minute the time spent in loading and dumping is\\nli minutes, and in addition about Jg- of the time is wasted in\\nshort rests, adjusting the wheeling plants, etc. On the basis of\\n$1 per day for labor, an allowance of 5 c. for the barrow, and 14\\nloads per cubic yard, the cost of hauling per cubic yard (com-\\nputed on the same principles as above) will be\\n105 X 14(^ 1.25)\\n600 X 0.9", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0148.jp2"}, "149": {"fulltext": "109. EARTHWORK. 138\\nFor rockwork the number of loads per cubic yard is estimated\\nas 24, and the time spent in loading, etc., estimated at l.G min-\\nutes instead of 1.25 minutes, which makes the estimate\\n105x24(5 1.6)\\nCost per cubic yard 3)\\n(d) Scrapers. Scrapers, or scoops, are especially useful in\\ncanal work, and also for railroad work when a low embankment\\nis to be formed from borrow-pits at the sides, when the distance\\ndoes not exceed 100 feet, nor the vertical height 15 feet. The\\nslope should not exceed 1.5 to 1 Under these conditions scraper\\nwork is cheaper than any other method. Scooping may be done\\nall in one direction, in which case two half -turns are made for\\neach load moved or it may be done in both directions (from\\nboth sides on to a bank, or, in canal work, from the center to\\neach bank), in w^hich case one load is hauled to each half -turn.\\nThe capacity of the scoops (the drag variety) is JL cubic\\nyard the time lost in loading, unloading, and all other ways\\nper load (except in turning) will average minute the time lost\\nin each half-turn (semi-circle) is J minute the speed of tlie\\nhorses may be estimated as 70 feet of lead per minute, the lead\\nbeing here considered as the stem of the vertical and horizontal\\ndistances, and the estimate including: the time of o-oino- and re-\\nturning. If a represents the sum of the horizontal and vertical\\ndistances, the number of cubic yards handled per day of 10\\nhours by side- scooping will be\\n600\\nr. 4200\\nFor double-scooping the formula becomes\\n600\\nVto\\nA -1 1-1 4200\\n0.1 rt which equals\\nCondensed from Journ. Franklin Inst., Oct. 1841, by Morris.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0149.jp2"}, "150": {"fulltext": "134 RAILROAD CONSTRUCTION. 109.\\nDividing the cost of a scraper per day (estimated at 82.75) by\\nthe number of yards handled per day gives the average cost per\\nvard.\\nExcept in very loose sandy soil it is best to plough the earth\\nfirst, whicli will cost about 1 c. per yard. (See 107.) Drag-\\nscrapers are now made chiefly of steel, and their capacity is more\\nnearly 0.15 cubic yard. AVheeled scrapers, having a capacitv\\nof about 0.5 cubic yard, are frequently used with even greater\\neconomy and for greater distances, as they are cheaper than\\ncarts up to 250 or 300 feet of lead. Both drag- and wheel-\\nscrapers are best operated in gangs of perhaps 10, using extra\\nor snap teams to help load, and a few extra men to help in\\nloading and unloading. The average cost of one scraper per\\nday may thus be easily calculated and the average number of\\ncubic yards handled per day computed as above, from which\\nthe cost per yard may be estimated.\\n(e) Cars and horses. The items of cost by this method are\\n{a) charge for horses employed, ijb) charge for men employed\\nstrictly in hauling, (c) charge for shifting rails when necessary,\\n(rZ) repairs, depreciation, and interest on cost of cars and track.\\nPart of this cost should strictly be classified under items 5 and\\n6, mentioned in 106, but it is perhaps more convenient to\\nestimate them as follows.\\nThe traction of a car on rails is so very small and constant\\nthat grade resistance constitutes a very large part of the total\\nresistance if the grade is I fc or more. For all ordinary grades\\nit is sufiiciently accurate to say that the grade resistance is to\\nthe gross weight as the rise is to the distance. If the distance\\nis supposed to be measured along the slope, the proportion is\\nstrictly true; i.e., on a Ifo grade the grade resistance is 1 lb.\\nper 100 of weight or 20 lbs. per ton. If the resistance on a\\nlevel at the usual velocity is yi^-, a grade of 1 120 (0.83^) will\\nexactly double it. If the material is hauled down a grade of\\n1 120, the cars will run by gravity after bein^ started. TJie\\nwork of hauling will then consist practically of hauling the\\nempty cars up the grade. The grade resistance depends only", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0150.jp2"}, "151": {"fulltext": "109. EARTinVORK. 135\\non the rate of grade and the weight, but the tractive resistance\\nwill be (J r eater per ton of lo eight for the unloaded than for the\\nloaded cars. The tractive power of a horse is less on a grade\\nthan on a level, not only because the horse raises his own weight\\nin addition to the load, but is anatomically less capable of\\npulling on a grade than on a level. In general it will be pos-\\nsible to plan the work so that loaded cars need not be hauled up\\na erade, unless an embankment is to be formed from a low\\nborrow-pit, in which case another method would probably be\\nadvisable. These computations are chietly utilized in designing\\nthe method of work the proportion of horses to cars. An\\nexample may be quoted from English practice (Hurst), in w^hich\\nthe cars had a capacity of 3J- cubic yards, weighing 30 cwt.\\nempty. Two horses took live wagons f of a mile on a level\\nrailroad and made 15 journeys per day of 10 hours, i.e., they\\nhandled 250 yards per day. In addition to those on the\\nstraight road, another horse ^vas employed to make up the\\ntrain of loaded wagons. With a short lead the straight-road\\nhorses were employed for this purpose. In the above example\\nthe number of men required to handle these cars, shift the\\ntracks, etc., is not given, and so the exact cost of the above\\nwork cannot be analyzed. It may be noticed that the two\\nhorses travelled 22J miles per day, drawing in one direction a\\nload, including the weight of the cars, of about 57,300 lbs. or\\n28.65 net tons. Allowing yi^- as the necessary tractive force,\\nit would require a pull of 477.5 lbs., or 239 lbs. for each horse.\\nWith a velocity of 220 feet per minute this would amount to\\nhorse-power per horse, exerted for only a short time, how-\\never, and allowing considerable time for rest and for drawing\\nonly the empty cars. The cars generally used in this country\\nhave a capacity of IJ cubic yards and cost about $65 apiece.\\nBesides the shovellers and dumping-gang, several men and a\\nforeman will be required to keep the track in order and to make\\nthe constant shifts that are necessary. Two trains are generally\\nused, one of which is loaded while the other is run to the\\ndump. Some passing-place is necessary, but this is generally", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0151.jp2"}, "152": {"fulltext": "136 RAILROAD CONSTRUCTION. 109,\\nprovided by having a switch at the cut and running the trains\\non each track alternately. This insures a train of cars always\\nat the cut to keep tlie shovellers employed. The cost of haul-\\ning per cubic yard can only be computed when the number of\\nlaborers, cars, and horses employed are known, and these will\\ndepend on the lead, on the character of the excavation, on the\\ngrade, if any, etc., and must be so proportioned that the shovel-\\nlers need not wait for cars to fill, nor the dumping-gang for\\nmaterial to handle, nor the horses and drivers for cars to haul.\\nMuch*skill is necessary to keep a large force in smooth running\\norder.\\n(f Cars and locomotives. 30-lb. rails are the lightest that\\nshould be used for this work, and 35- or 40-lb. rails are better.\\nOne or two narrow-gauge locomotives (depending on the length\\nof haul), costing abont $2500 each, will be necessary to handle\\ntwo trains of about 15 cars each, the cars having a .capacity of\\nabout 2 cubic yards and costing about 8100 each. Some cars\\ncan be obtained as low as $70. A force of about five men and\\na foreman will be required to shift the tracks. The track-\\nshifters, except the foreman, may be common laborers. The\\ndumping-gang will require about seven men. Even when the\\nmaterial is all taken down grade the grades may be too steep for\\nthe safe hauling of loaded cars down the grade, or for hauling\\nempty cars up the grade. Under such circumstances temporary\\ntrestles are necessary to reduce the grade. ^Yhen these are\\nused, the uprights and bracing are left in the embankment\\nonly the stringers being removed. This is largely a necessity,\\nbut is partially compensated by the fact that the trestle forms a\\ncore to the embankment which prevents lateral shifting during\\nsettlement. The average speed of the trains may be taken as\\n10 miles per hour or 5 miles of lead per hour. The time lost\\nin loading and unloading is estimated (Trautwine) as 9 minutes\\nor .15 of an hour. The number of trips per day of 10 hours\\n^.jj 10_ 50\\n1^ (miles of lead) .15 (miles of lead) .75*\\ncourse this quotient Tnust be a whole number. Knowing the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0152.jp2"}, "153": {"fulltext": "g 1 10. EARTUWOIiK. 137\\niiuinber of trains and their capacity, the total number of cubic\\nyards handled is known, which, divided into the total daily cost\\nof the trains, will give the cost of hauling per yard. The daily\\ncost of a train will include\\n(a) Wages of engineer, who frequently iires his own engine\\n(h) Fuel, about J to 1 ton of bitumnious coal, depending on\\nwork done;\\n(c) Water, a very variable item, fi-equently costing $3 to \u00c2\u00a75\\nper day\\n{(I) Repairs, variable, frequently at rate of 50 to 60^ per\\nyear\\n(e) Interest on cost and depreciation, 16 to 40;^.\\nTo these must be added, to obtain the total cost of the haul,\\n(f) Wages of the gang employed in sliifting track.\\n110. Choice of method of haul dependent on distance.\\nIn light side-hill work in which material need not be moved\\nmore than 12 or 15 feet, i.e., moved laterally across the road-\\nbed, the earth may be moved most chea})ly by mere shovelling.\\nBeyond 12 feet scrapers are more economical. At about 100\\nfeet drag-scrapers and wheelbarrows are equally economical.\\nBetween 100 and 200 feet wheelbarrows are generally cheaper\\nthan either, c arts or drag-scrapers, but wheeled scrapers are\\nalways cheaper than wheelbarrows. Beyond 500 feet two-\\nwheeled carts become the most economical up to about 1700\\nfeet then four-wheeled wagons become more economical u]) to\\n3500 feet-. Beyond this cars on rails, drawn by horses or by\\nlocomotives, become cheaper. The economy of cars on rails\\nbecomes evident for distances as small as 300 feet provided the\\nvolume of the excavation w^ill justify the outlay. Locomotives\\nwill always be cheaper than horses and mules providing the\\nwork to be done is of sufhcient magnitude to justify the jnir-\\nchase of the necessary plant and risk the loss in selling the plant\\nultimately as second-hand equipment, or keeping the plant on\\nhand and idle for an indefinite ])eriod waiting for other work.\\nHorses will not be economical for distances much over a mile.\\nFor greater distances locomotives are more economical, but the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0153.jp2"}, "154": {"fulltext": "138 RAILROAD CONSTRUCTION. \u00c2\u00a7111.\\nquestion of limit of profitable haul 116) must be closely\\nstudied, as the circumstances are certainly not common when it\\nis advisable to haul material much over a mile.\\n111. Item 4. Spreading. The cost of spreading varies with\\nthe method employed in dumping the load. When the earth is\\ntipped over the edge of an embankment there is little if any\\nnecessary work. Trautwine allows about J c. per cubic yard\\nfor keeping the dumping-places clear and in order. This would\\nrepresent the wages of one man at $1 ]3er day attending to the\\nunloading of 1200 two- wheeled carts each carrying J cubic yard.\\n1200 carts in 10 hours would mean an average of two per\\nminute, which implies more rapid and efficient work than may be\\ndepended on. The allowance is probably too small. AYhen the\\nmaterial is dumped in layers some levelling is required, for\\nwhich Trautwine allows 50 to 100 cubic yards as a fair day s\\nwork, costing from 1 to 2 cents per cubic yard. The cost of\\nspreading will not ordinarily exceed this and is frequently noth-\\ning all depending on the method of unloading. It should be\\nnoted that Mr. Morris s examples and computations (Jour. Frank-\\nlin Inst., Sept. 181:1) disregard altogether any special charge\\nfor this item.\\n112. Item 5. Keeping Roadways in order. This feature\\nis important as a measure of true economy, whatever the system\\nof transportation, but it is often neglected. A petty saving in\\nsuch matters will cost many times as much in increased labor in\\nhaulino: and loss of time. With some methods of haul the cost\\nis best combined with that of other items.\\n(a) Wheelbarrows. Wheelbarrows should generally be run\\non planks laid on the ground. The adjusting and shifting of\\nthese planks is done by the wheelers, and the time for it is allowed\\nfor in the 10^ allowance for short rests, adjusting the wheel-\\ning plank, etc. The actual cost of the planks must be added,\\nbut it would evidently be a very small addition per cubic yard\\nin a large contract. When the wheelbarrows are run on planks\\nplaced on horses or on trestles the cost is very appreciable\\nbut the method is frequently used with great economy. The", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0154.jp2"}, "155": {"fulltext": "114. EARTHWORK. 139\\nvariations in tlie requirements render any general estimate of\\nSLich cost impracticable.\\n(b) Carts and wagons. The cost of keeping roadways in\\norder for carts and Avagons is sometimes estimated merely as so\\nmncli per cubic yard, but it is evidently a function of the lead.\\nThe work consists in draining off puddles, filling up ruts, pick-\\ning up loose stones that may have fallen off the loads, and in\\ngeneral doing everything that will reduce the traction as much\\nas possible. Temporary inclines, built to avoid excessive grade\\nat some one point, are often measures of true economy. Traut-\\nwine suggests ^l c. per cubic yard per 100 feet of lead for earth-\\nwork and y2_. c. for rockwork, as an estimate for this item when\\ncarts are used.\\n(c) Cars. AVhen cars are used a sliifting-gang, consisting\\nof a foreman and several men (say five), are constantly employed\\nin shifting the track so that the material may be loaded and un-\\nloaded where it is desired. The averao^e cost of this item mav\\nbe estimated by dividing the total daily cost of this gang by the\\nnumber of cubic yards handled in one day.\\n113. Item 6. Repairs, Wear, Depreciation, and Interest\\nON Cost of Plant. Tlie amount of this item evidently depends\\nupon the character of the soil the harder the soil the worse the\\nwear and depreciation. The interest on cost depends on the\\ncurrent borrowing: value of monev. The estimate for this item\\nhas already been included in the allowances for horses, carts,\\nploughs, harness, wheelbarrows, steam-shovels, etc. Trautwine\\nestimates J c. per cul)ic yard for picks and shovels. Deprecia-\\ntion is generally a large percentage of the cost of earth-working\\ntools, the life of all being limited to a few years, and of many\\ntools to a few months.\\n114. Item 7. Superintendence and Incidentals. The inci-\\ndentals include water-carriers, trimming cuts to grade, digging\\nthe side ditches, trimming up the sides of borrow-pits to prevent\\ntheir becoming unsightly, etc. These last operations yield but\\nlittle earth and cost far more than the price paid per cubic yard.\\nMorris allows 1 c. per cubic yard for this item Trautwine", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0155.jp2"}, "156": {"fulltext": "140 BAILROAD CONSTRUCTION. 115.\\nallows If to 2 c. for it; while others combine items 6 and 7\\nand call them 5^ of the total cost, which method has the merit\\nof making the cost of items 6 and 7 a function of the character\\nof soil and length of lead.\\n115. Items. Contractor s Profit. This is usually estimated\\nat from 6 to 15^, according to the sharpness of the competition\\nand the possible uncertainty as to true cost owing to unfavorable\\ncircumstances. The contractor s real profit may vary considerably\\nfrom this. He often pays clerks, boards and lodges the laborers\\nin shanties built for the purpose, or keeps a supply-store, and\\nhas various other items both of profit and expense. His profit\\nis largely dependent on skill in so handUng the men that all can\\nAvork effectively without interference or delays in w^aiting for\\nothers. An unusual season of bad weather will often affect the\\ncost very seriously. It is a common occurrence to find that two\\ncontractors may be working on the same kind of material and\\nunder precisely similar conditions and at the same price, and yet\\none may be making money and the other losing it all on ac-\\ncount of difference of management.\\n116. Limit of profitable haul. As intimated in 103 and\\n110, there is with every method of haul a limit of distance be-\\nyond w^liich the expense for excessive hauling will exceed the\\nloss resulting from borrowing and wasting. Tliis distance is\\nsomewhat dependent on local conditions, thus requiring an inde-\\npendent solution for each particular case, but the general prin-\\nciples involved will be about as follows Assume that it has been\\ndetermined, as in Fig. 62, that the cut and fill will exactly bal-\\nance between two points, as between e and a?, assuming that, as\\nindicated in 101 (9), a trestle has been introduced between s\\nand t^ thus altering the mass curve to Estxn Since there\\nis a balance between A and (7 the material for the fill between\\nC and must be obtained either by borrowing in the im-\\nmediate neighborhood or by transportation from the excavation\\nbetween z and n If cut and fill have been approximately\\nbalanced in the selection of grade line, as is ordinarily done,\\nborrowing material for the fill C e implies a wastage of material", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0156.jp2"}, "157": {"fulltext": "^116. EARTHWORK. 141\\nat the cut z n To compare the two methods, we may place\\nagainst the phiii of borrowing and wasting, {a) cost, if any, of\\n\u00c2\u00abxtra right of way that may be needed from whicli to obtain\\nearth for the fill C e (h) cost of loosening, loading, hauling\\na distance equal to that between the centers of gravity of the\\nborrow-pit and of the fill, and the other expenses incidental to\\nborrowing J/ cubic yards for the fill C e (c) cost of loosening,\\nloading, hauling a distance equal to that between the centers\\nof gravity of the cut z ?i and of the spoil-bank, and the other\\nexpenses incidental to wasting J/ cubic yards at the cut z 7i\\n(d) cost, if any, of land needed for the spoil-bank. The cost of\\nthe other plan will be the cost of loosening, loading, hauling (tlie\\nhauling being represented by the trapezoidal figure Gexn)^ and\\nthe other expenses incidental to making the fill C e with the\\nmaterial from the cut z n\\\\ the amount of material being J/ cubic\\nyards, which is represented in the figure by the vertical ordi-\\nnate from e to the line Cn. The difference between these costs\\nwill be the cost, if any, of land for borrow-pit and spoil-bank\\nplus the cost of loosening, loading, etc. (except hauling and\\nroadways) of M cubic yards, minus the difference in cost of the\\nexcessive haul from Ce to xn and the comparatively short hauls\\nfrom borrow-pit and to spoil- bank.\\nAs an illustration, taking some of the estimates previously\\ngiven for operating with average material, the cost of all items,\\nexcept hauling and roadways, would be about as follows\\nloosening, with plough, 1.2 c, loading 5.0 c, spreading 1.5 c.,\\nwear, depreciation, etc., .25 c, superintendence, etc., 1.5 c.\\ntotal 8.95 c. Suppose that the haul for both borrowing and\\nwasting averages 100 feet or 1 station. Then the cost of haul\\nper yard, using carts, would be 109, a) [125 X 3(1 -j- 4)] h-\\n600 3.125 c. The cost of roadways would be about 0.1 c.\\nper yard, making a total of 3.225 c. per cubic yard. Assume\\nM 10000 cubic yards and the area Ce,rn ISOOOO yards-\\nstations or the equivalent of 10000 yards hauled 1800 feet.\\nThis haul would cost [125 X 3(18 600 13.75 c. per\\ncubic yard. The cost of roadways will be 1.^ X .1 or 1.8 c,", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0157.jp2"}, "158": {"fulltext": "142\\nRAILROAD CONSTRUCTION.\\n117.\\nmaking a total of 15.55 c. for hauling and roadways. The\\ndifference of cost of hauling and roadways will be 15.55\\n(2 X 3.225) 9.10 c. per yard or 8910 for the 10000 yards.\\nOifsetting this is the cost of loosening, etc., 10000 yards, at\\n8.95 c, costing $895. These figures may be better compared\\nas follows\\nLong Haul.\\nf Loosening, etc., 10000 yards,\\nHauling, 10000\\n8.95 c.\\n15.55 c.\\nI\\n895.\\n1555.\\n$2450.\\nBORROWIXG\\nAND Wasting.\\nc. 1895.\\nc. 895.\\ni\\nLoosening, etc., 10000 yards (borrowed), 8.95\\n10000 (wasted). 8.95\\nHauling, etc., 10000 (borroAved), 3.225 c. 322.50\\n10000 (wasted), 3.225 c. 322.50\\n$2485.00\\nThese costs are practically balanced, but no allowance has\\nbeen made for right of way. If any considerable amount had\\nto be paid for that, it would decide this particular case in favor\\nof the long haul. This shows that under these conditions 1800\\nfeet is a^out the limit of profitable haul, the land costing nothing\\nextra.\\nBLASTING.\\n117. Explosives. The effect of blasting is due to the ex-\\ntremely rapid expansion of a gas which is developed by the\\ndecomposition of a very small amount of solid m.atter. Blasting\\ncompounds may be divided into two general classes, (a) slow-\\nburning and (h) detonating. Gunpowder is a type of the slow-\\nburning compounds. These are generally ignited by heat the\\nignition proceeds from grain to grain the heat and pressure\\nproduced are comparatively low. Xitro-glycerine is a type of\\nthe detonating compounds. They are exploded by a sliock\\nwhich instantaneoicsly explodes the whole mass. The heat and\\npressure developed are far in excess of tliat produced by the\\nexplosion of poAvder. IN^itro-glycerine is so easily exploded\\nthat it is very da^ngerous to handle. It was discovered that if\\nthe nitro-glycerine was absorbed by a sjjongy material like infu-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0158.jp2"}, "159": {"fulltext": "117. EARTHWORK. 143\\nserial earth, it was miicli less liable to explode, while its power\\nwhen actually exploded was practically equal to ihat of the\\namount of pure nitro-glycerine contained in the dynamite, which\\nis the name given to the mixture of nitro-glycerine and infusorial\\nearth. Xitro-glycerine is expensive; many other explosive\\nchemical compounds which properly belong to the slow-burning\\nclass are comparatively cheap. It has been conclusively demon-\\nstrated that a mixture of nitro-glycerine and some of the cheaper\\nchemicals has a greater explosive force than the sum of the\\nstrengths of the component parts when exploded separately.\\nAVhatever the reason, the fact seems established. The reason is\\npossibly that the explosion of the nitro-glycerine is sufficiently\\npowerful to produce a detonation of the other chemicals, which\\nis impossible to produce by ordinary means, and that this explo-\\nsion caused by detonation is more powerful than an ordinary\\nexplosion. The majority of the explosive compounds and\\npowders on the market are of this character a mixture of\\n20 to 60 per cent, of nitro-glycerine with variable proportions\\nof one or more of a great variety of explosive chemicals.\\nThe choice of the explosive depends on the character of the\\nrock. A hard brittle rock is most effectively blasted by a\\ndetonating compound. The rapidity with which the full force\\nof the explosive is developed has a shattering effect on a brittle\\nsubstance. On the contrary, some of the softer tougher rocks\\nand indurated clays are but little affected by dynamite. The\\nresult is but little more than an enlargement of the blast-hole.\\nQuarrying must generally be done with blasting-powder, as the\\nquicker explosives are too shattering. Although the results\\nobtained by various experimenters are very variable, it may be\\nsaid that pure nitro-glycerine is eight times as powerful as black\\npowder, dynamite (75^ nitro-glycerine) six times, and gun-cotton\\nfour to six times as powerful. For open work where time is not\\nparticularly valuable, black powder is by far the cheapest, but\\nin tunnel-headings, whose progress determines the progress of\\nthe whole work, dynamite is so much more effective and so\\nexpedites the work that its use becomes economical.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0159.jp2"}, "160": {"fulltext": "144\\nRAILROAD CONSTRUCTION.\\n\u00c2\u00a7118.\\n118. Drilling. Altliougli many very com^^licated forms of\\ndrill-bars liave been devised, tlie best form (with slight modifi-\\ncations to suit circumstances) is as shown in Fig. 64, (a) and (b).\\ni^O\\nFig. r)4.\\nThe width should flare at the bottom {a) about 15 to 30^. For\\nhard rock the curve of the edge should be somewhat flatter and\\nfor soft rock somewhat more curved than shown, Fig. 64, (ct).\\nSometimes the angle of the two faces is varied from that given.\\nFig. 64, (5), and occasionally tlie edge is purposely blunted so\\nas to give a crushing rather than a cutting effect. The di ills\\nAvill require sharpening for each 6 to 18 inches deptli of hole,\\nand will require a new edge to be worked every 2 to 4 days.\\nFor drilling vertical holes the churn-drill is the most econom-\\nical. The drill-bar is of iron, about 6 to 8 feet long, 1 J in\\ndiameter, weighs about 25 to 30 lbs., and is shod with a piece\\nof steel welded on. The bar is lifted a few inches between each\\nblow, turned partially around, and allowed to fall, the impact\\ndoing the work. From 5 to 15 feet of holes, depending on the\\ncharacter of the rock, is a fair day s work 10 hours. In very\\nsoft rocks even more tlian this may be done. This method is\\ninapplicable for inclined holes or even for vertical holes in con-\\nfined places, such as tunnel-headings. For such places the only\\npractical hand method is to use hammers. This may be done\\nby light drills and light hammers (one-man work), or by heavier\\ndrills held by one man and struck by one or two men with\\nheavy hammers. The conclusion of an exhaustive investigation\\nas to the relative economy of light or heavy hammers is that the\\nlight-hammer method is more economical for the softer rocks,\\nthe heavy-hammer method is more economical for the harder", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0160.jp2"}, "161": {"fulltext": "\u00c2\u00a7119.\\nEARTHWORK.\\n145\\nrucks, but that tlie liglit-liaiiuncr method is always more ex-\\npeditious and hence to be preferred when time is important.\\nThe subject of macliine rock-drills is too vast to be treated\\nhere. The method is only practicable when the amount of\\nwork to be done is large, and especially when time is valuable.\\nThe machines are generally operated by compressed air for tun-\\nnel-work, thus doing the additional service of supplying fresh\\nair to the tunnel-headings wdiere it is most needed. The cost\\nper foot of hole drilled is quite variable, but is usually some-\\nwhat less than that of hand-drilling sometimes but a small\\nfraction of it.\\n119. Position and direction of drill-holes. As the cost of\\ndrilling holes is the largest single item in the total cost of blast-\\ning, it is necessary that skill and judgment should be used in so\\nlocating the holes that the blasts will be most effective. The\\ngreatest effect of a blast will evidently be in the direction of the\\nline of least resistance. In a strictly homogeneous material\\nthis will be the shortest line from the center of the explosive to\\nthe surface. The variations in homogeneity on account of\\nlaminations and scams require that each case shall be judo-ed\\naccording to experience. In open-pit blasting it is generallv\\neasy to obtain two and sometimes three exposed faces to the\\nrock, making it a simple matter to drill holes so that a blast will\\ndo effective work. When a solid face of rock must be broken\\ninto, as in a tunnel-heading, the\\nwork is necessarily ineffectual and\\nexpensive. A conical or wedge-\\nshaped mass will first be blown out\\nby simultaneous blasts in the holes\\nmarked 1, Fig. %b\\\\ blasts in the\\nholes marked 2 and 3 will then com-\\nplete the cross-section of the head-\\ning. A great saving in cost may\\noften be secured by skilfully taking\\nadvantage of seams, breaks, and irregularities. When the work\\nis economically done there is but little noise or throwing of rock,\\ndrill holes i.n tunne^l heading\\nFig. 65.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0161.jp2"}, "162": {"fulltext": "146 BAILROAD CONSTRUCTION. 120.\\na covering of old timbers and branches of trees generally sufficing\\nto confine the smaller pieces which would otherwise fly up.\\n120. Amount of explosive. The amount of explosive required\\nvaries as the cube of the line of least resistance. The best\\nresults are obtained when the line of least resistance is f of the\\ndepth of the hole also when the powder fills about i of the\\nhole. For average rock the amount of j)owder required is as\\nfollows\\nLine of least resistance.\\nWeight of powder\\n2 ft.\\n4 ft.\\n2 lbs.\\n6 ft.\\n8 ft.\\n16 lbs.\\nStrict compliance with all of the above conditions would re-\\nquire that the diameter of the hole should vary for every case.\\nWhile this is impracticable, there should evidently be some\\nvariation in the size of the hole, depending on the work to be\\ndone. For example, a V hole, drilled 2 8 deep, with its\\nline of least resistance 2 and loaded with J lb. of powder,\\nwould be filled to a depth of which is nearly i of the\\ndepth. A Z hole, drilled 8 deep, with its line of least resist-\\nance 6 and loaded with Gf lbs. of powder, would be filled ta\\na depth of over 28 which is also nearly of the depth. One\\npound of blasting-powder will occupy about 28 cubic inches.\\nQuarrying necessitates the use of nuuierous and sometimes\\nrepeated hght charges of powder, as a heavy blast or a powerful\\nexplosive like dynamite is apt to shatter the rock. This\\nrequires more powder to the cubic yard than blasting for mere\\nexcavation, which may usually be done by the use of J to i lb.\\nof powder per cubic yard of easy open blasting. On account\\nof the great resistance offered by rock when blasted in headings\\nin tunnels, the powder used per cubic yard will run up to 2, 4\\nand even 6 lbs. per cubic yard. As before stated, nitro-\\nglycerine is about eight times (and dynamite about six times) as\\npowerful as the same weight of powder.\\n121. Tamping. Blasting-powder and the slow-burnino- ex-\\nplosives require thorough tamping. Clay is probably the best^", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0162.jp2"}, "163": {"fulltext": "123 EARTUWOUK. 147\\nbut sand and fine powdered rock are also used. AVooden plugs,\\ninverted expansiv^e cones, etc., are periodically reinvented by\\nenthusiastic inventors, only to be discarded for the simpler\\nmethods. Owing to the extreme rapidity of the development\\nof the force of a nitro-glycerine or dynamite explosion, tamping\\nis not 60 essential with these explosives, although it unquestion-\\nably adds to their effectiveness. Blasting under water has been\\neffectively accomplished by merely pouring nitro-glycerine into\\nthe drilled holes through a tube and then exploding the charge\\nwithout any taniping except that furnished by the superincum-\\nbent water. It has been found that air-spaces about a charge\\nmake a material reduction in the effectiveness of the explosion.\\nIt is therefore necessary to carefully ram the explosive into a\\nsolid mass. Of course the liquid nitro-glycerine needs no ram-\\nming, but dynamite should be rammed with a wooden rammer.\\nIron should be carefully avoided in ramming gunpowder. A\\ncopper bar is generally used.\\n122. Exploding the charge. Black powder is generally ex-\\nploded by means of a fuse which is essentially a cord in which\\nthere is a thin vein of gunpowder, the cord being protected by\\ntar, extra linings of hemp, cotton, or even gutta-percha. The\\nfuse is inserted into the middle of the charge, and the tamping\\ncarefully packed around it so that it will not be injured. To\\nproduce the detonation required to explode nitro-glycerine and\\ndynamite, there must be an initial explosion of some easily\\nignited explosive. This is generally accomplished by means of\\neaps containing fulminating-powder wdiicli are exploded by\\nelectricity. The electricity (in one class of caps) heats a very\\nfine platinum wire to redness, thereby igniting the sensitive\\npowder, or (in another class) a spark is caused to jump through\\nthe powder between the ends of two wires suitably separated.\\nDyKamite can also be exploded by using a small cartridge of\\ngunpowder which is itself exploded by an ordinary fuse.\\n123. Cost. Trautwine estimates the cost of blasting (for\\nmere excavation) as averaging 45 cents per cubic yard, falling\\nas low as 30 cents for easy but hrittle rock, and running up to", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0163.jp2"}, "164": {"fulltext": "148 BAILROAD CONSTRUCTION. 124.\\n60 cents and even $i when the cutting is shallow, the rock\\nespecially tough, and the strata unfavorably placed. Soft tough\\nrock frequently requires more powder than harder brittle\\nrock.\\n124. Classification of excavated material. The classification of\\nexcavated material is a fruitful source of dispute between con-\\ntractors and railroad companies, owing mainly to the fact that\\nthe variation between the softest earth and the hardest rock is\\nso gradual that it is very difficult to describe distinctions between\\ndifferent classifications which are unmistakable and indisputable.\\nThe classification frequently used is {a) earth, (J)) loose rock, and\\n(c) solid rock. As blasting is frequently used to loosen loose\\nrock and even earth (if it is frozen), the fact that blasting\\nis employed cannot be used as a criterion, especially as this\\nwould (if allowed) lead to unnecessary blasting for the sake of\\nclassifying material as rock.\\nEarth. This includes clay, sand, gravel, loam, decomposed\\nrock and slate, boulders or loose stones not greater than 1 cubic\\nfoot (3 cubic feet, P. R. R.), and sometimes even hard-pan.\\nIn general it will signify material which can be loosened by a\\nplough with two horses, or with which one picker can keep one\\nshoveller busy.\\nLoose rock. This includes boulders and loose stones of more\\nthan one cubic foot and less than one cubic yard stratified rock,\\nnot more than six inches thick, separated by a stratum of clay\\nalso all material (not classified as earth) which may be loosened\\nby pick or bar and which can be quarried without blasting,\\nalthough blasting may occasionally be resorted to.\\nSolid rock includes all rock found in masses of over one cubic\\nyard which cannot be removed except by blasting.\\nIt is generally specified that the engineer of the railroad\\ncompany shall be the judge of the classification of the material,\\nbut frequently an appeal is taken from his decisions to the courts.\\n125. Specifications for earthwork. The following specifica-\\ntions, issued by the Norfolk and Western R. R., represent the\\naverage requirements. It should be remembered that very strict", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0164.jp2"}, "165": {"fulltext": "125. EARTHWORK. 149\\nspecifications invariably increase the cost of the work, and fre-\\nquently add to the cost more than is gained by improved quality\\nof work.\\n1. The grading will be estimated and paid for by the cubic\\nyard, and will include clearing and grubbing, and all open ex-\\ncavations, channels, and embankments required for the forma-\\ntion of the roadbed, and for turnouts and sidings; cutting all\\nditches or drains about or contiguous to the road; digging the\\nfoundation-pits of all culverts, bridges, or walls reconstructing\\nturnpikes or common roads in cases where they are destroyed or\\ninterfered with changing the course or channel of streams and\\nall other excavations or embankments connected with or incident\\nto the construction of said Railroad.\\n2. All grading, except where otherwise specified, whether\\nfor cuts or fills, will be measured in the excavations and will be\\nclassified under the following heads, viz. Solid Rock, Loose\\nRock, Hard-pan, and Earth.\\nSolid Rock shall include all rock occurring in masses Avhich,\\nin the judgment of the said Engineer Maintenance of AVay, may\\nbe best removed by blasting.\\nLoose Rock shall include all kinds of shale, soapstone, and\\nother rock Avhich, in the judgment of the said Engineer Main-\\ntenance of Way, can be removed by pick and bar, and is soft\\nand loose enough to be removed without blasting, although\\nblasting may be occasionally resorted to also, detached stone of\\nless than one (1) cubic yard and more than one (1) cubic foot.\\nHard-pan shall consist of tough indurated clay or cemented\\ngravel, which requires blasting or other equally expensive\\nmeans for its removal, or which cannot be ploughed with less\\nthan four horses and a railroad plough, or which requires two\\npickers to a shoveller, the said Engineer Maintenance of Way\\nto be the judge of these conditions.\\nEarth shall include all material of an earthy nature, of\\nwhatever name or character, not unquestionably loose rock or\\nhard-pan as above defined.\\nPowder. The use of powder in cuts will not be considered", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0165.jp2"}, "166": {"fulltext": "150 RAILROAD CONSTRVCTION, 125\\niis a reason for any other classification than earth, unless the\\nmaterial in the cut is clearly other than earth under the above\\nspecifications.\\n3. Earth, o^ravel, and other materials taken from the exca-\\nvations, except when otherwise directed by the said Engineer\\nMaintenance of Way or his assistant, shall be deposited in the\\nadjacent embankment; the cost of removing and depositing\\nwhich, when the. distance necessary to be hauled is not niore\\nthan sixteen hundred (1600) feet, shall be included in the price\\npaid for the excavation.\\n4. ExTEA Haul will be estimated and paid for as follows\\nw^henever material from excavations is necessarily hauled a\\ngreater distance than sixteen hundred (1600) feet, there shall be\\npaid in addition to the price of excavation the price of extra\\nhaul per 100 feet, or part thereof, after the first 1600 feet; the\\nnecessary haul to be determined in each case by the said Engi-\\nneer Maintenance of AVay or his assistant, from tlie profile and\\n3ross- sections, and the estimates to be in accordance therewith.\\n5. All embankments shall be made in layers of such thick-\\nness and carried on in such manner as the said Eno^ineer Mainte-\\nnance of Way or his assistant may prescribe, the stone and\\nheavy materials being placed in slopes and top. And in com-\\npleting the fills to the proper grade such additional heights and\\nfulness of slope shall be given them, to provide for their settle-\\nment, as the said Engineer Maintenance of Way, or his assistant,\\nmay direct. Embankments about masonry shall be built at\\nsuch times and in such manner and of such materials as the said\\nEngineer Maintenance of Way or his assistant may direct.\\n6. In procuring materials for embankments from without\\nthe line of the road, and in wasting materials from cuttings, the\\nplace and manner of doing it shall in each case be indicated by\\nthe Engineer Maintenance of Way or his assistant; and care\\nmust be taken to injure or disfigure the land as little as possible.\\nBorrow-pits and spoil-banks must be left by the Contractor in\\nregular and sightly shape.\\n7. The lands of the said Railroad Company shall be cleared", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0166.jp2"}, "167": {"fulltext": "125. EARTHWORK. lol\\nto the extent required by the said Engineer ^laintenance of\\nAVay, or his assistant, of all trees, Inrushes, logs, and other\\nperishable materials, which shall be destroyed by burning or\\ndeposited in heaps as the said Engineer Maintenance of Way,\\nor his assistant, may direct. Lai ge trees must be cut not more\\nthan two and one-half (2 J) feet from the ground, and under\\nembankments less than four (4) feet high they shall be cut close\\nto the o:round. All small trees and bushes shall be cut close to\\nthe ground.\\n8. Clearing shall be estimated and paid for by the acre or\\nfraction of an acre.\\n9. All stumps, roots, logs, and other obstructions shall be\\ngrubbed out, and removed from all places where embankments\\noccur less than two (2) feet in height also, from all places\\nwhere excavations occur and from such other places as the said\\nEngineer Maintenance of Way or his assistant may direct.\\n10. Grnbbing shall be estimated and j^aid for by the acre or\\nfraction of an acre.\\n11. Contractors, when directed by the said Engineer Main-\\ntenance of Way or his assistant in charge of the work, will\\ndeposit on the side of the road, or at such convenient points as\\nmay be designated, any stone, rock, or other materials that they\\nmay excavate; and all materials excavated and deposited as\\nabove, together with all timber removed from the line of the\\nroad, will be considered the property of the Kailroad Company,\\nand the Contractors upon the respective sections will be respon-\\nsible for its safe-keeping until removed by said Railroad Com-\\npany, or nntil their work is finished.\\n12. Contractors will be accountable for the maintenance\\nof safe and convenient places wherever public or private roads\\nare in any way interfered with by them during the progi*ess of\\nthe work. They will also be responsible for fences thrown\\ndown, and for gates and bars left open, and for all damages\\noccasioned thereby.\\n18. Temporary bridges and trestles, erected to facilitate the\\nprogress of the work, in case of delays at masonry structures", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0167.jp2"}, "168": {"fulltext": "152 RAILROAD CONSTRUCTION. 125.\\nfrom any cause, or for other reasons, will be at the expense of\\nthe Contractor.\\nItt. The line of road or the gradients niaj be changed in.\\nany manner, and at any time, if tlie said Engineer Maintenance\\nof Way or his assistant shall consider such a change necessary\\nor expedient but no claim for an increase in prices of excava-\\ntion or embankment on the part of the Contractor will be allowed\\nor considered unless made in writing before the work on that\\npart of the section where the alteration has been made shall have\\nbeen commenced. The said Engineer Maintenance of Way or\\nhis assistant may also, on the conditions last recited, increase or\\ndiminish the length of any section for the purpose of more\\nnearly equalizing or balancing the excavations and embankments,\\nor for any other reason.\\n15. The roadbed will be graded as directed by the said En-\\ngineer Maintenance of Way or his assistant, and in conformity\\nwith such breadths, depths, and slopes of cutting and filling as\\nhe may prescribe from time to time, and no part of the work\\nwill be finally accepted until it is properly completed and dressed\\no\u00c2\u00a3E at the required grade.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0168.jp2"}, "169": {"fulltext": "CHAPTER lY.\\nTRESTLES.\\n126. Extent of use. Trestles constitute from 1 to Sfo of the\\nlength of the average raih-oad. It was esthnated in 1889 that\\nthere was then about 2400 miles of single-track railway trestle\\nin the United States, divided among 150,000 structures and\\nestimated to cost about $75,000,000. The annual charire for\\nmaintenance, estimated at of the cost, therefore amounted to\\nabout $9,500,000 and necessitated the annual use of perhaps\\n300,000,000 ft. B.M. of timber. The corresponding figures at\\nthe present time must be somewhat in excess of this. The\\nmagnitude of this use, which is causing the rapid disappearance\\nof forests, has resulted in endeavors to limit the use of timber\\nfor this purpose. Trestles may be considered as justifiable under\\nthe following conditions\\na. Permanent trestles.\\n1. Those of extreme height then called viaducts and fre-\\nquently constructed of iron or steel, as the Kinzua viaduct, 302\\nft. high.\\n2. Those across waterways e.g.^ that across Lake Pontchar-\\ntrain, near IS ew Orleans, 22 miles long.\\n3. Those across swamps of soft deep mud, or across a river-\\nbottom, liable to occasional overflow.\\nh. Temporary trestles.\\n1. To open the road for traffic as quickly as possible often\\na reason of great financial importance.\\n2. To quickly replace a more elaborate structure, destroyed\\n153", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0169.jp2"}, "170": {"fulltext": "154 RAILROAD CONSTRUCTION. 127.\\nby accident, on a road already in operation, so that the inter-\\nruption to traffic shall be a minimum.\\n3. To form an earth embankment with earth brought from\\na distant point by the train-load, when such a measure would\\ncost less than to borrow earth in the immediate neighborhood.\\n4. To bridge an opening temporarily and thus allow time to\\nlearn the regimen of a stream in order to better proportion the\\nsize of the waterway and also to facilitate bringing suitable stone\\nfor masonry from a distance. In a new country there is always\\nthe double danger of eitlier bnilding a culvert too small, requir-\\ning expensive reconstruction, perhaps after a disastrous washout,\\nor else wasting money by constructing the culvei t unnecessarily\\nlarge. Much masonry has been built of a very poor quality of\\nstone because it could be conveniently obtained and because good\\nstone was unobtainable except at a prohibitive cost for transpor-\\ntation. Opening the road for traffic by the nse of temporary\\ntrestles obviates both of these difficulties.\\n127. Trestles vs. embankments. Low embankments are very\\nmuch cheaper than low trestles both in first cost and mainte-\\nnance. Yery high embankments are yqyj expensive to construct,\\nbut cost comparatively little to maintain. A trestle of equal\\nheight may cost much less to construct, but will be expensive to\\nmaintain perhaps -J of its cost per year. To determine the\\nheight beyond which it will be cheaper to maintain a trestle\\nrather than build an embankment, it will be necessary to allow\\nfor the cost of maintenance. The height will also depend on\\nthe relative cost of timber, labor, and earthwork. At the pres-\\nent average values, it will be found that for less heights than\\n25 feet i\\\\\\\\e first cost of an embankment will generally be less\\nthan that of a trestle; this implies that a permanent trestle\\nshould never be constructed with a height less than 25 feet\\nexcept for the reasons given in 126. The height at which a\\npermanent trestle is certainly cheaper than earthwork is more\\nuncertain. A high grade line joining two hills will invariably\\nimply at least a culvert if an embankment is used. If the\\nculvert is built of masonry, the cost of the embankment will be", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0170.jp2"}, "171": {"fulltext": "129. TRESTLES. 155\\nso increased that the lieiglit at wliicli a trestle becomes economi-\\ncal will be materially reduced. The cost of an embankment\\nincreases much more rai^idlv than the heiu lit with very liitrh\\nembankments more nearly as the square of the height while\\nthe cost of trestles does not increase as rapidly as the height.\\nAlthough local circumstances may modify the application of any\\nset rules, it is probably seldom that it will be cheaper to build\\nan embankment 40 or 50 feet high than to permanently maintain\\na wooden trestle of that height. A steel viaduct would proba-\\nbly be the best, solution of such a case. These are frequently\\nused for permanent structures, especially when very high. The\\ncost of maintenance is nuich less than that of wood, which\\nmakes the use of iron or steel preferable for permanent trestles\\nunless wood is abnormally cheap. Neither the cost nor the con-\\nstruction of iron or steel trestles will be considered in this chapter.\\n128. Two principal types. There are two- principal types of\\nwooden trestles pile trestles and framed trestles. The great\\nobjection to pile trestles is the rapid rotting of the portion of\\nthe pile which is underground, and the difficulty of renewal.\\nThe maximum height of pile trestles is about 30 feet, and even this\\nheight is seldom reached. Framed trestles have been constructed\\nto a height of considerably over 100 feet. They are frequently\\nbuilt in such a manner that any injured piece may be readily\\ntaken out and renewed without interfering with traffic. Trestles\\nconsist of two parts the supports called bents, and the\\nstringers and floor system. As the stringers and floor system\\nare the same for both pile and framed trestles, the bents are\\nall that need be considered separately.\\nPILE TRESTLES.\\n129. Pile bents. A pile bent consists generally of four })iles\\ndriven into the ground deep enough to afford not only sufficient\\nvertical resistance but also lateral resistance. On top of these\\npiles is placed a horizontal cap. The caps are fastened to\\nthe tops of the piles by methods illustrated in Fig. 66. The", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0171.jp2"}, "172": {"fulltext": "156\\nRAILROAD CONSTRUCTION.\\n\u00c2\u00a7129.\\nmethod of fastening shown in each case should not be considered\\nas applicable only to the particular tyj)e of j)ile bent used to illus-\\ntrate it. Fig. {a and d) illustrates a mortise- joint with a hard-\\nFiG. 66.\\nwood pin about 1^ in diameter. The hole for the pin should\\nbe bored separately tlirough the cap and the mortise, and\\nthe hole through the cap should be at a slightly higher\\nlevel than that through the mortise, so that the cap will be\\ndrawn down tight when the j)in is driven. Occasionally an\\niron dowel (an iron pin about 1| in diameter and about 6\\nlong) is inserted partly in the cap and partly in the pile. The\\nuse of drift-bolts, shown in Fig. Q^ (h), is cheaj^er in first cost, but\\nrenders repairs and renewals very troublesome and expensive.\\nSplit caps, shown in Fig. 66 (r), are formed by bolting two\\nhalf-size strips on each side of a tenon on top of the pile.\\nRepairs are very easily and cheaply made without interference\\nwith the ti-affic and without injuring other pieces of the bent.\\nThe smaller pieces are more easily obtainable in a sound con-\\ndition the decay of one does not affect the other, and the first\\ncost is but little if any greater than the method of using a single\\npiece. For further discussion, see 186.\\nFor very light trafific and for a height of about 5 feet three\\nvertical piles will sufiice, as shown in Fig. 66 (a). Up to a height\\nof 8 or 10 feet four piles may be used without eway-bracino;, as\\nin Fig. 66 (5), if the piles have a good bearing. For heights\\ngreater than 10 feet sway-bracing is generally necessary. The\\noutside piles are frequently driven with a batter varying from\\n1 12 to 1 4.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0172.jp2"}, "173": {"fulltext": "180. TRESTLES. 157\\nPiles are made, if possible, from timber obtained in the\\nvicinity of the work.- Durability is tlie great requisite rather\\nthan strength, for almost any timber is strong enough (except\\nas noted below) and will be suitable if it will resist rapid decay.\\nThe following list is quoted as being in the order of preference\\non account of durability\\n1. Red cedar\\n2. Red cypress\\n3. Pitch-pine\\n4. Yellow pine\\n5. Wliile piue\\n6. Redwood\\n7. Elm\\n8. Spruce\\n9. White ouk\\n10. Post-oak\\n11. Red oak\\n12. Black oak\\n13. Hemlock\\n14. Tamarac\\nRed-cedar piles are said to have an average life of 27 years\\nwith a possil)le. maximum of 50 years, but the timber is rather\\nweak, and if exposed in a river to flowing ice or driftwood is\\napt to be injured. Under these circumstances oak is prefer-\\nable, although its life may be only 13 to 18 years.\\n130. Methods of driving piles. The following are the prin-\\ncipal methods of driving piles\\na. A hammer weighing 2000 to 3000 lbs. or more, sliding\\nin guides, is drawn up by horse- power or a portable engine, and\\nallowed to id^W. freely.\\nh. The same as above except that the hammer does not fall\\nfreely, but drags the rope and revolving drum as it falls and is\\nthus quite materially retarded. The mechanism is a little more\\nsimple, but is less effective, and is sometimes made deliberately\\ndeceptive by a contractor by retarding the blow, in order to\\napparently indicate the requisite resistance on the part of\\nthe pile.\\nThe above methods have tlie advantage that the mechanism\\nis cheap and can be transported into a new country with com-\\nparative ease, but the work done is somewhat ineffective and\\ncostly compared with some of the more elaborate methods\\ngiven below.\\nc. Gunjpowder pile-drivers^ which automatically explode a\\ncartridge every time the hammer falls. The explosion not only\\nforces the pile down, but throws up the hammer for the next\\nblow. For a given height of fall the effect is therefore doubled.\\nIt has been shown by experience, however, tliat when it is at-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0173.jp2"}, "174": {"fulltext": "158 RAILROAD CONSTRUCTION. 130,\\ntempted to use such a pile-driver rapidly the meclianism be-\\ncomes so heated that the cartridges explode prematurely, and the\\nmethod has therefore been abandoned.\\nd. Steam pile-drivers, in which the hammer is operated\\ndirectly by steam. The hammer falls freely a height of about\\n40 inches and is raised again by steam. The effectiveness is\\nlargely due to the rapidity of the blows, which does not allow\\ntime between the blows for the ground to settle around the pile\\nand increase the resistance, which does happen w^hen the blows\\nare infrequent. The hammer-cylinder weighs 5500 lbs., and\\nwith 60 to 75 lbs. of steam gives 75 to 80 blows per minute.\\nWith 11 blows a large unpointed pile was driven 35 feet into a\\nhard clay bottom in half a minute. Such a driver would cost\\nabout $800.\\nThe above four methods are those usual for dry earth.\\nIn very soft wet or sandy soils, where an unlimited supply of\\nwater is available, the water-jet is sometimes employed. A pipe\\nis fastened along the side of the pile and extends to the pile-\\npoint. If water is forced through the pipe, it loosens the sand\\naround the point and, rising along the sides, decreases the side\\nresistance so that the pile sinks by its own weight, aided perhaps\\nby extra weights loaded on. This loading may be accomplished\\nby connecting the top of the pile and the pile-driver by a block\\nand tackle so that a portion of the weight of the pile-driver is\\ncontinually thrown on the pile.\\nExcessive driving frequently fractures the pile below the\\nsurface and thereby greatly weakens its bearing power. To\\nprevent excessive brooming of \\\\\\\\\\\\q top of the\\npile, owing to the action of the hammer, the top\\nshould be protected by an iron ring fitted to the top\\nof the pile. The brooming not only renders the\\ndriving ineffective and hence uneconomical, but\\nvitiates the value of any test of the bearing power\\nof the pile by noting the sinking due to a given\\nFig. 67. weight falling a given distance. If the ])ile is so\\nsoft that brooming is unavoidable, the top should be adzed of[", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0174.jp2"}, "175": {"fulltext": "131. TRESTLES. I59\\nfrequently, and especially should it be done just before the linal\\nblows which are to test its bearing-power.\\nIn a new country judgment and experience will be required\\nto decide intelligently whether to employ a simple drop-hanmier\\nmachine, operated by horse-power and easily transported but\\nuneconomical in oi)eration, or a more complicated machine\\nworking cheaply and effectively after being transported at\\ngreater expense.\\n131. Pile-driving formulae. If R the resistance of a pile,\\nand s the set of the pile during the last blow, iv the weight of\\nthe pile-hammer, and h the fall during the last blow, tl^en we\\nmay state the approximate relation that 7?^ w/i, or A*\\ns\\nThis is the basic principle of all rational formulae, but the\\nmaximum weight which a pile will sustain after it has been\\ndriven some time is by no means equal to the resistance of the\\npile during the last blow. There are also many other modi-\\nfying elements which have been variously allowed for in the\\nmany proposed formulre. The formuh^ range from the extreme\\nof empirical simplicity to very complicated attempts to allow\\nproperly for all modifying causes. As the simplest rule,\\nspecifications sometimes require that the piles shall be driven\\nuntil the pile will not sink more than 5 inches under five\\nconsecutive blows of a 2000 11)., hammer falling 25 feet.\\nThe Engineering News formula gives the safe load as\\n2w;A\\n^-^pj, m which i^ weight of hammer, fall feet,\\ns set of pile in inc/tes under the last blow. This formula is\\nderived from the above basic formula by calling the safe load\\nof the final resistance, and by adding (arbitrarily) 1 to the final\\nset (s) as a conq^ensation for the extra resistance caused by the\\nsetthng of earth around the pile between each blow. This\\nformula is used only for ordinary hammer-driving. When the\\npiles are driven by a steam pile-driver the formula becomes\\nEngineering Neics, Nov. IT, 1892.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0175.jp2"}, "176": {"fulltext": "160\\nRAILROAD CONSTRUCTION.\\n\u00c2\u00a7132.\\nsafe load\\n2iuh\\nFoi tlie gunpowder pile-driver, since\\n5 0.1*\\nthe explosion of the cartridge drives the pile in with the same\\nforce with w^hich it throws the hammer upward, the effect is\\ntivice that of the fall of the hammer, and the formula becomes\\nsafe load In these last two formulae the constant\\ns 0.1\\nin the denominator is changed from .9 1 to 5+0.1. The\\nconstant (1.0 or 0.1) is supposed to allow, as before stated, for the\\neffect of the extra resistance caused by the earth settling around the\\npile between each blow. The more rapid the blows tlie less the\\nopportunity to settle and the less the proper value of the constant.\\nThe above formulae have been given on account of their\\nsimplicity and their practical agreement with experience. Many\\nother formulae have been j)roposed, the majority of which are\\nmore complicated and attempt to take into account the weight of\\nthe pile, resistance of the guides, etc. While these elements,\\nas well as many others, have their influence, their effect is so\\novershadowed by the indeterminable effect of other elements as,\\nfor example, the effect of the settlement of earth around the pile\\nbetween blows that it is useless to attempt to employ anything\\nbut a purely empirical formula.\\n132. Pile-points and pile-shoes. Piles are generally sharpened\\nto a blunt point. If the pile is liable to strike boulders, sunken\\nlogs, or other obstructions which are liable to turn the point, it\\nis necessary to protect the point by some\\nform of shoe. Several forms in cast iron\\nhave been used, also a wrought-iron shoe,\\nhaving four straps radiating from the\\napex, the straps being nailed on to the pile,\\nas shown in Fig. %S (h). The cast-iron\\nform show^n in Fig. 68 {a) has a base cast\\naround a drift-bolt. The recess on the top\\nof the base receives the bottom of the pile\\nand prevents a tendency to split the bottom\\nof the pile or to force the shoe off laterally.\\nFicx. 68.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0176.jp2"}, "177": {"fulltext": "134. TRESTLES. 161\\n133. Details of design. Xo theoretical calculations of the\\nstrength of pile bents need be attempted on account of the ex-\\ntreme complication of the theoretical strains, the uncertainty as\\nto the real strength of the timber used, the variability of that\\nstrength with time, and the insigniiicance of the economy that\\nwould be possible even if exact sizes could be computed. The\\npiles are generally required to be not less than 10 or 12 in\\ndiameter at the large end. The P. E. E. requires that they shall\\nbe not less than 14 and 7 inches in diameter at butt and small\\nend respectively, exclusive of bark, which must be removed.\\nThe removal of the bark is generally required in good work.\\nSoft durahle woods, such as are mentioned in 129, are best\\nfor the piles, but the caps are generally made of oak or yellow\\npine. The caps are generally 14 feet long (for single track)\\nwith a cross-section 12 X 12 or 12 X 14 Split caps\\nwould.consist of two pieces Q X 12 The sway-braces, never\\nused for less heights than 6 are made of 3 X 12 timber, and\\nare spiked on with f spikes 8 long. The floor system will be\\nthe same as that descri])ed later for framed trestles.\\n134. Cost of pile trestles. The cost, per linear foot, of piling\\ndepends on the method of driving, the scarcity of suitable tim-\\nber, the price of labor, the length of the piles, and the amount\\nof shifting of the pile-driver required. The cost of soft-wood\\npiles varies from 8 to 15 c. per lineal foot, and the cost of oak\\npiles varies from 10 to 30 c. per foot according to the length,\\nthe longer piles costing more per foot. The cost of driving will\\naverage about $2.50 per j^ile, or 7.5 to 10 c. per lineal foot.\\nSince the cost of shifting the pile-driver is quite an item in tlie\\ntotal cost, the cost of driving a long pile would be less per foot\\nthan for a short pile, but on the other hand the cost of the pile\\nis greate^^ per foot, which tends to make the total cost per\\nfoot constant. Specifications generally say that the piling will\\nbe paid for per lineal foot of piling left in the worl. The wast-\\nage of the tops of piles sawed off is always something, and is\\nfrequently very large. Sometimes a small amount per foot of\\npiling sawed off is allowed the contractor as compensation for", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0177.jp2"}, "178": {"fulltext": "162\\nBAILROAD CONSTRUCTION.\\n\u00c2\u00a7135.\\nliis loss. This reduces the contractor s risk and possibly reduces\\nhis bid by an equal or greater amount than the extra amount\\nactually paid him.\\nFRAMED TRESTLES.\\n135. Typical Design. A typical design for a framed trestle\\nbent is given in Fig. 69. This represents, with slight variations\\nof detail, the plan according to which a large part of the framed\\nFig. 69.\\ntrestle bents of the country have been built i.e., of those less\\nthan 20 or 30 feet in height, not requiring multiple-story\\nconstruction.\\n136. Joints, (a) The mortise-and-tenon joint is illustrated in\\nFig. 69 and also in Fig. %Q (a). The tenon should be about\\n3 thick, 8 wide, and 5^ long. The mortise should be cut\\na little deeper than the tenon. Drip-holes from the mortise\\nto the outside will assist in draining off water that\\nmay accumulate in the joint and thus prevent the\\nrapid decay that would otherwise ensue. These\\njoints are very troublesome if a single post decays\\nand requires renewal. It is generally required that\\nFig. 70. the mortise and tenon should be thoroughly daubed\\nwith paint before putting them together. This will tend to\\nr\\\\M\\nm\\nm\\nHOLE", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0178.jp2"}, "179": {"fulltext": "137.\\nTRESTLES.\\n163\\nmake the joint watei -tiglit and prevent decay from the ac-\\ncumulation and retention of water in the joint.\\n(b) The plaster joint. This joint is made by bolting and\\nspiking a 3 X 12 plank on both\\nsides of the joint. The cap and\\nsill should be notched to receive\\nthe posts. Repairs are greatly\\nfacilitated by the use of these\\njoints. This method has been\\nused by the Delaware and Hud-\\nson Canal Co. [R. R.].\\n(c) Iron plates. An iron plate of the form shown in Fig. 72\\n(b) is bent and used as shown in Fig. 72 {a). Bolts passing through\\nthe bolt-holes shown secure the\\nplates to the timbers and make a\\nstrong joint which may be readily\\nloosened for repairs. By slight\\nc modifications in the design the\\nmethod may be used for inclined\\nFig. 71.\\n.:::i:/i\\n^^^1\\na\\nPt\\ni\\n(a)\\n-J\\nc posts and complicated joints.\\nFtg 72.\\n(d) Split caps and sills. These\\nare described in 129. Their\\nadvantages apply with even greater force to framed trestles.\\n(e) Dowels and drift-bolts. These joints facilitate cheap and\\nrapid construction, but renewals and repairs are very difficult, it\\nbeing almost impossible to extract a drift-bolt which has been\\ndriven its full length without splitting open the pieces contain-\\ning it. Notwithstanding this objection they are extensively\\nused, especially for temporary work which is not expected to\\nbe used long enough to need repairs.\\n137. Multiple-story construction. Single-story framed trestle\\nbents are used for heights up to 18 or 20 feet and excejitionally\\nup to 30 feet. For greater heights some such construction\\nas is illustrated in a skeleton design in Fig. 73 is used. By\\nusing split sills between each story and separate vertical and\\nbatter posts in each story, any piece may readily be removed and", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0179.jp2"}, "180": {"fulltext": "164\\nRAILROAD CONSTRUCTION.\\n138.\\nrenewed if necessary. The height of these stories varies, in\\ndifferent designs, from 15 to 25 and\\neven 30 feet. In some designs tlie\\nstructure of each storj is independent\\nof the stories above and below. This\\ngreatly facilitates both the original con-\\nstruction and subsequent repairs. In\\nother designs the verticals and batter-\\nposts are made continuous through two\\nconsecutive stories. The structure is\\nsomewhat stiffer, but is much more diffi-\\ncult to repair.\\nSince the bents of any trestle are\\nusually of variable height and those\\nFig. 73. heights are not always an even multiple\\nof the uniform height desired for the stories, it becomes\\nnecessary to make the upper stories of unifoi-m height and let\\nFig. 74.\\nthe odd amount go to the lowest story, as shown in Figs. 73\\nand 74.\\n138. Span. The shorter the span the greater the number\\nof trestle bents; the longer the span the greater the required\\nstrength of the stringers supporting the floor. Economy de-\\nmands the adoption of a span that shall make the sum of these\\nrequirements a minimum. The liigher the trestle the greater\\nthe cost of each bent, and the greater the span that would be\\njustifiable. Nearly all trestles have bents of variable height,\\nbut the advantage of employing uniform standard sizes is so\\ngreat that many roads use the same span and sizes of timber not\\nonly for the panels of any given trestle, but also for all trestles", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0180.jp2"}, "181": {"fulltext": "\u00c2\u00a7139\\nTRESTLES.\\n165\\nregardless of height. The spans generally used vary from 10\\nto 16 feet. The Norfolk and Western E. K. uses a span of\\n12 Q for all single-story trestles, and a span of 25 for\\nall multiple-story trestles. The stringers are the same in both\\ncases, but wheu the span is 25 feet, knee- braces are run\\nFig. 75.\\nfrom the sill of the lirst story below to near the middle of each\\nset of stringers. These knee-braces are connected at the top by\\na straining-beam on which the stringers rest, thus support-\\ning the stringer in the center and virtually reducing the span\\nabout one-half.\\n139. Foundations, (a) Piles. Piles are frequently used as a\\nfoundation, as in Fig. 76, particularly in soft ground, and also\\nfor temporary structures. These\\nfoundations are cheap, quickly con-\\nstructed, and are particularly valuable\\nwhen it is financially necessary to open\\n(^Va\\n^fAJ\\nSILL\\ntne road tor tratlic as soon as possible ^^m^^M^m^mm^^\\nand with the least expenditure of U U\\nmoney; but there is the disadvantage Fig. 76.\\nof inevitable decay within a few years unless the piles are chemi-\\ncally treated, as will be discussed later. Chemical treatment,\\nhowever, increases the cost so that such a foundation would\\noften cost more tlian a foundation of stone. A pile should be\\ndriven under each post as shown in Fig. 76.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0181.jp2"}, "182": {"fulltext": "166\\nRAILROAD CONSTRUCTION.\\n\u00c2\u00a7140.\\n(b) Mud-sills. Fig. 77\\nn w/ n\\nillustrates the use of mud-sills as\\nbuilt bj the Louisville and Nash-\\nville E. K. Eight blocks 12 X 12\\nX 6 are used under each bent.\\nWhen the ground is very soft, two\\nadditional timbers (12 X 12 X\\nlength of bent- sill), as shown by the\\ndotted lines, are placed underneath.\\nFig. 77. The number required evidently de-\\npends on the nature of the ground.\\n(c) Stone foundations. Stone foundations are the best and\\nthe most expensive. For very high trestles the JS orfolk and\\nWestern R.R. employs foundations as shown in Fig. 78, the\\nSILL 0!^ TRESTLE\\nr\\nL\\n-i\\n-J\\n1 SILL 1\\ni-\\n-J\\n^13 8 13\\nFig. 78.\\nwalls being 4 feet thick. When the height of the trestle is 72\\nfeet or less (the plans requiring for 72 in height a foundation-\\nwall 39 6 long) the foundation is made continuous. The sill\\nof the trestle should rest on several short lengths of 3 X 12\\nplank, laid transverse to the sill on top of the wall.\\n140. Longitudinal bracing. This is required to give the\\nstructure longitudinal stiifness and also to reduce the columnar\\nlength of the posts. This bracing generally consists of hori-\\nzontal waling-strips and diagonal braces. Sometimes the\\nbraces are placed wholly on the outside posts unless the trestle\\nis very high. For single-story trestles the P. R. R. employs\\nthe laced system, i.e., a line of posts joining the cap of one\\nbent with the sill of the next, and the sill of that bent with the\\ncap of the next. Some plans employ braces forming an X in\\nalternate panels. Connecting these braces in the center more\\nthan doubles their columnar strength. Diagonal braces, when\\nbolted to posts, should be fastened to them as near the ends of", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0182.jp2"}, "183": {"fulltext": "143.\\nTI^ESTLES.\\n1G7\\nthe posts as possible. The sizes employed vary largely, depend-\\ning on the clear length and on whether they are expected to act\\nby tension or compression. 3 X 12 planks are often used\\nwhen the design would require tensile strength only, and\\nS X S posts are often used when compression may be\\nexpected.\\n141. Lateral bracing. Several of the more recent designs of\\ntrestles employ diagonal lateral bracing between the caps of\\nadjacent bents. It adds greatly to the stiffness of the trestle\\nand better maintains its alignment. 6 X 6 posts, formincr\\nan X and connected at the center, will answer the purpose.\\n142. Abutments. When suitable stone for masonry is at\\nhand and a suitable subsoil for a foundation is obtainable without\\ntoo much excavation, a masonry abutment will be the best.\\nSuch an abutment would probably be used when masonry\\nfootings for trestle bents were employed 139, c).\\nAnother method is to construct a crib of 10 x 12\\ntimber, laid horizontally, drift-bolted together, securely braced\\nand embedded into the ground. Except for temporary con-\\nstruction such a method is generally objectionable on account of\\nrapid decay.\\nAnother method, used most commonly for pile trestles, and\\nfor framed trestles having pile\\nfoundations 139, a\\\\ is to use a\\npile bent at such a place that the\\nnatural surface on the up-hill side\\nis not far below the cap, and the\\nthrust of the material, filled in to\\nbring the surface to grade, is insig-\\nnificant. 3 X 12 planks are placed Fig. 79.\\nbehind the piles, cap, and stringers to retain the filled material.\\nFLOOR SYSTEMS.\\n143. stringers. The general practice is to use two, three,\\nand even four stringers under each rail. Sometimes a strin rer", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0183.jp2"}, "184": {"fulltext": "168\\nRAILBOAD CONSTRUCTION.\\n\u00c2\u00a7144\\nis placed under eacli guard-rail. Generally the stringers are\\nmade of two panel lengths and laid so that the joints alternate.\\nA few roads use stringers of only one panel length, but this\\npractice is strongly condemned by many engineers. The\\nstringers should be separated to allow a circulation of air around\\nthem and prevent the decay which would occur if they were\\nplaced close together. This is sometimes done by means of 2\\nplanks, 6 to 8 long, which are placed over each trestle bent.\\nSeveral bolts, passing through all the stringers forming a group\\nand through the separators, bind them all into one solid con-\\nstruction. Cast-iron spools or washers, varying from 4z to\\nin length (or thickness), are sometimes strung on each bolt so\\nas to separate the stringers. Sometimes washers are used\\nbetween the separating planks and the stringers, the object of\\nthe separating planks then being to bind the stringers, especially\\nabutting stringers, and increase their stiffness.\\nThe most common size for stringers is 8 X 16 The\\nPennsylvania Railroad varies the width, depth, and number of\\nstringers under each rail according to the clear span. It may\\nbe noticed that, assuming a uniform load per running foot, both\\nClear span.\\nNo. of pieces\\nunder each rail.\\nWidth.\\nDepth.\\n10 feet\\n12\\n14\\n16\\n2\\n2\\n2\\n3\\n8 iuches\\n8\\n10\\n8\\n15 inches\\n16\\n17\\n17\\nthe pressure per square inch at the ends of the stringers (the\\ncaps having a width of 12 and also the stress due to trans-\\nverse strain are kept approximately constant for the variable gros:*\\nload on these varying spans.\\n144. Corbels. A corbel (in trestle-work) is a stick of timber\\n(perhaps two placed side by side), about 3 to 6 long, placed\\nunderneath and along the stringers and resting on the cap.\\nThere are strong prejudices for and against their use, and a", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0184.jp2"}, "185": {"fulltext": "S 145.\\nTRESTLES.\\n169\\ncorresponding diversity in practice. They are bolted to tlie\\nstriijgers and thus stilten the joint. They certainly reduce the\\nobjectionable crushing of the libers at each end of the stringer,\\nbut if the corbel is no wider than the stringers, as is generally\\nthe case, the area of pressure between the corbels and the cap is\\nFig. 80.\\nno greater and the pressure per square inch on the cap is no less\\nthan the pressure on the cap if no corbels were used. If the\\ncorbels and cap are made of hard wood, as is recommended by\\nsome, the danger of crushing is lessened, but the extra cost and\\nthe frequent scarcity of hard wood, and also the extra cost and\\nlabor of using, corbels, may often neutralize the advantages\\nobtained by their use.\\n145. Guard-rails. These are frequently made of b X 8\\nstuff, notched 1 for each tie. The sizes vary up to S X 8\\nand the depth of notch from f to 1^ They are generally\\nbolted to every third or fourth tie. It is frequently specified\\nthat they shall be made of oak, white pine, or yellow pine. The\\njoints are made over a tie, by halving each piece, as illustrated\\nin Fig. 81. The joints on opposite sides of the trestle should be\\nFicx. 81.\\nstaggered. Some roads fasten every tie to the guard-rail,\\nusing a bolt, a spike, or a lag-screw.\\nGuard-rails were originally used with the idea of preventing\\nthe wheels of a derailed truck from running off the ends of the\\nties. But it has been found that an outer guard-rail alone (with-\\nout an inner guard-rail) becomes an actual element of danger,\\nsince it lias frequently happened that a derailed wheel has cauglit", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0185.jp2"}, "186": {"fulltext": "170 RAILROAD CONSTRUCTION. 147.\\non the outer guard-rail, thus causing the truck to slew around\\nand so produce a dangerous accident. The true function of the\\n\u00e2\u0080\u00a2outside guard-rail is thus changed to that of a tie-spacer, which\\nkeeps the ties from spreading when a derailment occurs. The\\ninside guard-rail generally consists of an ordinary steel rail\\nspiked about 10 inches inside of the running rail. These inner\\nguard-rails should be bent inward to a point in the center of the\\n-track about 50 feet from the end of the bridge or trestle. If\\nthe inner guard-rails are placed with a clear space of 10 inches\\ninside the running rail, the outer guard-rails should be at least\\nQ 10 a]3art. They are generally much farther apart than this.\\n146. Ties on trestles. If a car is derailed on a bridge or\\ntrestle, the heavily loaded wheels are apt to force their way be-\\ntween the ties by displacing them unless the ties are closely\\nspaced and fastened. The clear space between ties is generally\\nequal to or less than their width. Occasionally it is a little more\\nthan their width. Q X 8 ties, spaced 14: to 16 from cen-\\nter to center, are most frequently used. The length varies from\\n9 to 12 for single track. They are generally notched deep\\non the under side where they rest on the stringers. Oak ties\\nare generally required even when cheaper ties are used on the\\nother sections of the road. Usually every third or fourth tie is\\nbolted to the stringers. When stringers are placed underneath\\nthe guard-rails, bolts are run from the top of the guard-rail to\\nthe under side of the stringer. The guard-rails thus hold down\\nthe whole system of ties, and no direct fastening of the ties to\\nthe stringers is needed.\\n147. Superelevation of the outer rail on curves. The location\\nof curves on trestles should be avoided if possible, especially\\nwhen the trestle is high. Serious additional strains are in-\\ntroduced especially when the curvature is sharp or the\\nspeed high. Since such curves are sometimes practically un-\\navoidable, it is necessary to design the trestle accordingly.\\nIf a train is stopped on a curved trestle, the action of the train on\\nthe trestle is evidently vertical. If the train is moving with a\\n\u00c2\u00a9onsiderable velocity, the resultant of the weight and the cen-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0186.jp2"}, "187": {"fulltext": "\u00c2\u00a7147.\\nTRESTLES.\\n171\\ntrifuixal action is a force somewhat inclined from tlie vertical.\\nBoth of these conditions may be expected to exist at times. If\\nthe axis of the system of posts is vertical (as illustrated in\\nmethods a, Z d, and e), any lateral force, such as would be\\nproduced by a moving train, will tend to rack the trestle bent.\\nIf the stringers are set vertically, a centrifugal force likewise\\ntends to tip them sidewise. If the axis of the system of posts\\n(or of the stringers) is inclined so as to coincide w^ith the j^ressure\\nof the train on the trestle when the train is moving at its normal\\nvelocity, there is no tendency to rack the trestle when the train\\nis moving at that velocity, but there will be a tendency to rack\\nthe trestle or twist the stringers when the train is stationary.\\nSince a moving train is usually the normal condition of affairs,\\nas well as the condition which produces the maximum stress, an\\ninclined axis is evidently preferable from a theoretical stand-\\npoint but whatever design is adopted, the trestle should evi-\\ndently be sufficiently cross-braced for either a moving or a\\nstationary load, and any proposed design must be studied as to\\nthe effect of hoth of these conditions. Some of the various\\nmethods of securing the requisite superelevation may be described\\nas follows\\n(a) Framing the outer posts longer than the inner posts, so\\nthat the cap is inclined at the proper angle axis of posts verti-\\ncal. (Fig. 82.) The method requires\\nmore work in framing the trestle,\\nbut simplifies subsequent track-laying\\nand maintenance, unless it should be\\nfound that the superelevation adopted\\nis unsuitable, in which case it could be\\ncorrected by one of the other methods\\ngiven below. The stringers tend to\\ntwist when the train is stationary. Fia. 8?\\n(b) Notching the cap so that the stringers are at a different\\nelevation. (Fig. 83.) This weakens the cap and requires that\\nall ties shall be notched to a bevelled surface to fit the striuircrs.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0187.jp2"}, "188": {"fulltext": "172\\nRAILROAD CONSTRUCTION.\\n147.\\n\u00e2\u0096\u00a0which also weakens the ties. A centrifugal force will tend to\\ntwist the stringers and rack the trestle,\\n(c) Placing wedges underneath the\\nties at each stringer. These wedges are\\nfastened witli two bolts. Two or more\\nwedges will be required for each tie.\\nThe additional number of pieces re-\\nquired for a long curve wiJl be im-\\nU mense, and the work of inspection and\\nFi 83. keeping the nuts tight will greatly in-\\ncrease the cost of maintenance.\\n(d) Placing a wedge under the outer rail at each tie. This\\nrequires but one extra piece per tie. There is no need of a\\nwedge under the inner tie in order to make the rail normal to\\nthe tread. The resulting inward inchnatiori is substantially that\\nproduced by some forms of rail-chairs or tie-plates. The spikes\\n(a little longer than usual) are driven through the wedge into\\nthe tie. Sometimes lag-screws are used instead of spikes.\\nIf experience proves that the superelevation is too much or too\\nlittle, it may be changed by this method with less work than by\\nany other.\\n(e) Corbels of different heights. When corbels are used (see\\n144) the required inclination of the floor system may be ob-\\ntained by varying the depth of the corbels.\\n(f Tipping the whole trestle.\\nThis is done by placing the\\ntrestle on an inclined founda-\\ntion. If very much inclined,\\nthe trestle bent must be secured\\nagainst the possibility of slip-\\nping sidewise, for the slope\\nwould be considerable with a\\nsharp curve, and the vibration\\nof a moving train would reduce Fig. 84.\\nthe coeflicient of friction to a comparatively small quantity.\\n(g) Fra^ming the outer posts longer. This case is identical", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0188.jp2"}, "189": {"fulltext": "149. TRESTLES. 173\\nwith case {a) except that the axis of the system of posts is\\ninchiied, as in case but the sill is horizontal.\\nThe above-described plans will suggest a great variety of\\nmethods which are possible and which dili er from the above\\nonly in minor details.\\n148. Protection from fire. Trestles are peculiarly subject to\\niire, from passing locomotives, which may not only destroy the\\ntrestle, but perhaps cause a terrible disaster. This danger is\\nsometimes reduced by placing a strip of galvanized iron along\\nthe top of each set of stringers and also along the tops of the\\ncaps. Still greater protection was given on a long trestle on the\\nLouisville and Nashville R. R. by making a solid flooring of\\ntimber, covered with a layer of ballast on which the ties and\\nrails were laid as usual.\\nBarrels of water should be provided and kept near all trestles,\\nand on very long trestles barrels of water should be placed every\\ntwo or three hundred feet along its length. A place for the bar-\\nrels may be provided by using a few ties which have an extra\\nlength of about four feet, thus forming a small platform, which\\nshould be surrounded by a railing. The track-walkers should be\\nheld accountable for the maintenance of a supply of water in\\nthese barrels, renewals being frequently necessary on account of\\nevaporation. Such platforms should also be provided as refuge-\\nbays for track- walkers and trackmen working on the trestle. On\\nvery long trestles such a platform is sometimes provided with\\nsufiicient capacity for a hand-car.\\n149. Timber. Any strong durable timber may be used when\\nthe choice is limited, but oak, pine, or cypress are preferred\\nwhen obtainable. When all of these are readily obtainable,\\nthe various parts of the trestle will be constructed of different\\nkinds of wood the stringers of long-leaf pine, the posts and\\nbraces of pine or red cypress, and the caps, sills, and corbels (if\\nused) of white oak. The use of oak (or a similar hard wood)\\nfor caps, sills, and corbels is desirable because of its greater\\nstrength in resisting crushing across the grain, which is the\\ncritical test for these parts. There is no physiological basis to", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0189.jp2"}, "190": {"fulltext": "174 EAILROAD CONSTRUCTION, 151.\\nthe objection, sometimes made, that different species of timber,\\nin contact with each other, will rot quicker than if only one\\nkind of timber is used. When a very extensive trestle is to be\\nbuilt at a place where suitable growing timber is at hand but\\nthere is no convenient sawmill, it will pay to transport a port-\\nable sawmill and engine and cut up the timber as desired.\\n150. Cost of framed timber trestles. The cost varies widely\\non account of the great variation in the cost of timber. When\\na railroad is first penetrating a new and undeveloped region, the\\ncost of timber is frequently small, and when it is obtainable from\\nthe company s right-of-way the only expense is felling and\\nsawing. The work per M., B. M., is small, considering that a\\nsingle stick 12 X 12 X 25 contains 300 feet, B. M., and\\nthat sometimes a few hours work, worth less than $1, will\\nfinish all the work required on it. Smaller pieces will of course\\nrequire more work per foot, B. M. Long-leaf pine can be pur-\\nchased from the mills at from \u00c2\u00a78 to $12 per M. feet, B. M.,\\naccording to the dimensions. To this must be added the freight\\nand labor of erection. The cartage from the nearest railroad to\\nthe trestle may often be a considerable item. Wrought iron\\nwill cost about 3 c. per pound and cast iron 2 c, although the\\nprices are often lower than these. The amount of iron used\\ndepends on the detailed design, but, as an average, will amount\\nto $1.50 to $2 per 1000 feet, B. M., of timber. Alarge part of\\nthe trestling of the country has been built at a contract price of\\nabout $30 per 1000 feet, B. M., erected. While the cost will\\nfrequently rise to $10 and even $50 when timber is scarce, it\\nwill drop to $13 (cost quoted) when timber is cheap.\\nDESIGN OF WOODEN TRESTLES.\\n161. Common practice. A great deal of trestling has been\\nconstructed without any rational design except that custom and\\nexperience have shown that certain sizes and designs are probahly\\nsafe. This method has resulted occasionally in failures but\\nmore frequently in a very large waste of timber. Many railroads", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0190.jp2"}, "191": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0191.jp2"}, "192": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0192.jp2"}, "193": {"fulltext": "152. TRESTLES. 175\\nemploy a uniform size for all posts, caps, and sills, and a\\nuniform size for stringers, all regardless of the height or span of\\nthe trestle. For repair work there are practical reasons favoring\\nthis. To attempt to run a large lot of sizes would be more\\nwasteful in the end than to maintain a few stock sizes only.\\nLumber can be bought more cheaply by giving a general order\\nfor the run of the mill for the season, or a cargo lot,\\nspecifying approximate percentages of standard stringer size, of\\n12 X 12-inch stuff, 10 X 10-inch stuff, etc., and a liberal pro-\\nportion of 3- or tt-inch plank, all lengths thrown in. The 12 x 12-\\ninch stuff, etc., is ordered all lengths, from a certain specified\\nlength up. In case of a wreck, washout, burn-out, or sudden\\ncall for a trestle to be completed in a stated time, it is much\\nmore economical and practical to order a certain number of\\ncarloads of trestle stuff to the ground and there to select piece\\nafter piece as fast as needed, dependent only upon the length of\\nstick required. When there is time to make the necessary sur-\\nveys of the ground and calculations of strength, and to wait for a\\nspecial bill of timber to be cut and delivered, the use of differ-\\nent sizes for posts in a structure would be warranted to a certain\\nextent. For new construction, when there is generally\\nsufficient time to design and order the proper sizes, such waste-\\nfulness is less excusable, and under any conditions it is both\\nsafer and more economical to prepare standard designs which\\ncan be made applicable to varying conditions and which will at\\nthe same time utilize as much of the strength of the timber as\\ncan be depended on. In the following sections will be given\\nthe elements of the preparation of such standard designs, which\\nwill utilize uniform sizes with as little waste of timber as possible.\\nIt is not to be understood that special designs should be made\\nfor each individual trestle.\\n152. Required elements of strength. The stringers of\\ntrestles are subject to transverse strains, to crushing across the\\ngrain at the ends, and to shearing along the neutral axis. The\\nFrom Economical Desif^nini; of Timber Trestle Bridges.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0193.jp2"}, "194": {"fulltext": "176 RAILROAD CONSTRUCTION 153.\\nstrength of tlie timber must therefore be computed for all these\\nkinds of stress. Caps and sills will fail, if at all, by crushing\\nacross the grain although subject to other forms of stress, these\\ncould hardly cause failure in the sizes usually employed. There\\nis an apparent exception to this if piles are improperly driven\\nand an uneven settlement subsequently occurs, it may have the\\neffect of transferring practically all of the weight to two or three\\npiles, while the cajy is subjected to a severe transverse strain\\nwhich may cause its failure. Since such action is caused gener-\\nally by avoidable errors of construction it may be considered as\\nabnormal, and since such a failure will generally occur by a\\ngradual settlement, all danger may be avoided by reasonable\\ncare in inspection. Posts must be tested for their columnar\\nstrength. These parts form the bulk of the trestle and are the\\nparts which can be definitely designed from known stresses.\\nThe stresses in the bracing are more indefinite, depending on\\nindeterminate forces, since the inclined posts take up an un-\\nknown proportion of the lateral stresses, and the design of the\\nbracing may be left to what experience has shown to be safe,\\nwithout involving any large waste of timber.\\n153. Strength of timber. Until recently tests of the strength\\nof timber have generally been made by testing small, selected,\\nwell-seasoned sticks of clear stuff, free from knots or imper-\\nfections. Such tests would give results so much higher than\\nthe vaguely known strength of large unseasoned commercial\\ntimber that very large factors of safety were recommended\\nfactors so large as to detract from any confidence in the whole\\ntheoretical design. Recently the U. S. Government has been\\nmaking a thoroughly scientific test of the strength of full-size\\ntimber under various conditions as to seasoning, etc. The work\\nhas been so extensive and thorough as to render possible the\\neconomical designing of timber structures.\\nOne important result of the investigation is the determina-\\ntion of the great influence of the moisture in the timber and\\nthe law of its effect on the strength. It has been also shown\\nthat timber soaked with water has substantially the same", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0194.jp2"}, "195": {"fulltext": "153.\\nTRESTLES.\\n177\\nstrength as green timber, even tliough tlic timber had once been\\nthoroughly seasoned. Since trestles are exposed to the weather\\nthey should be designed on the basis of using green timber.\\nIt has been shown that the strength of green timber is very\\nregularly about 55 to 60^ of the strength of timber in which\\nthe moisture is 12^ of the dry weight, l^fo being the proportion\\nof moisture usually found in timber that is protected from the\\nweather but not heated, as, e.g., the timber in a barn. Since\\nthe moduli of rupture have all been reduced to this standard of\\nmoisture (12^), if we take one-eighth of the ruj^ture values, it\\nstill allows a factor of safety of about fixQ^ even on green timber.\\nModuli of rupture for various timbers. [\\\\2% moisture.]\\n(Coudeused from U. S. Forestry Circular, No. 15.)\\nNo.\\n9\\n10\\n11\\n12\\n13\\n14\\n15\\n16\\n19\\n20\\n21\\n27\\n28\\n29\\n30\\nSpecies.\\nLong-leaf pine..\\nCuban\\nShort-leaf\\nLoblollv\\nWhite\\nRed\\nSpruce\\nBald cypress\\nWhite cedar\\nDouglas spruce,\\nWhite oak\\nOvercup\\nPost\\nCow\\nRed\\nTexan\\nWillow\\nSpanish\\nSliagbark hickory\\nPignut\\nWhite elm\\nCedar\\nWhite ash\\nWeight\\nper\\ncubic\\nfoot.\\n38\\n39\\n32\\n33\\n24\\n31\\n39\\n29\\n23\\n32\\n50\\n46\\n50\\n46\\n45\\n46\\n45\\n46\\n51\\n56\\n34\\n46\\n39\\nCross-bending.\\nUltimate\\nStrength.\\n12 600\\n13 600\\n10100\\n11300\\n7 900\\n9100\\n10000\\n7900\\n6 300\\n7 900\\n13100\\n11300\\n12 300\\n11500\\n11400\\n13100\\n10400\\n12 000\\n16 000\\n18 700\\n10 300\\n13 500\\n10 800\\nModulus of\\nElasticity.\\n2 070 ono\\n2 370 000\\n1 680 000\\n2 050 000\\n1 390 000\\n1 620 000\\n1 640 000\\n1 290 000\\n910 000\\n1 680 000\\n2 090 000\\n1 620 000\\n2 080 000\\n1 610 000\\n1 970000\\n1860 000\\n17^0 000\\n19 50000\\n2 390 000\\n2 730 000\\n1540 000\\n1700000\\n1640000\\nCrush-\\ning end\\nwise.\\n8000\\n8700\\n6500\\n7400\\n5400\\n6700\\n7300\\n6000\\n5200\\n5700\\n8500\\n7800\\n7100\\n7400\\n7300\\n8100\\n7200\\n7700\\n9500\\n10900\\n6500\\n8000\\n7200\\nCrush-\\nShear-\\ning\\ning\\nacross\\nalong\\ngram.\\ngram.\\n1180\\n700\\n1220\\n700\\n960\\n700\\n1150\\n700\\n700\\n400\\n1000\\n500\\n1200\\n800\\n800\\n500\\n700\\n400\\n800\\n500\\n2200\\n1000\\n1900\\n1000\\n3000\\n1100\\n1900\\n900\\n2300\\n1100\\n2000\\n900\\n1600\\n900\\n1800\\n900\\n2700\\n1100\\n8200\\n1200\\n1200\\n800\\n2100\\n1800\\n1900\\n1100", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0195.jp2"}, "196": {"fulltext": "178\\nRAILROAD CONSTRUCTION.\\n\u00c2\u00a7153.\\nQ\\nH\\ntf\\nH O\\n0*0\\na\\nCQ\\nO\\nH\\nO\\no\\nO\\noi\\noa 5\\nJ\\n^9\\n51 H\\n03\\nO\\nz\\niz;\\nO\\nO\\nJ\\n3\\n1\\nfa\\nK o\\nSB\\n03\\ncc\\nW\\nc\\n2 M\\n5\\n0)\\no o o\\no o o\\nO O\\no\\no\\no\\no o o o\\niO o o o\\no o oo\\no o o o\\no\\no\\no o oo\\no o o o\\noo\\no o\\n3 b\\no \u00c2\u00abs\\no o o o o o o\\no o o o o o o\\no o o o o o o\\no o o o o O o\\nlO O lO o o o o\\nIC O 00 t^- CO O CD\\noooooooo\\n\u00e2\u0080\u00a2oooooooo\\nloooooooo\\n\u00e2\u0096\u00a0oooooooo\\noo\u00c2\u00bbciooo\u00c2\u00bbco\\nt- CO -Tt^ CO O CO o\\nC a;\\nr /I\\nH\\noooooooo\\noooooooo\\nOt-OJT-iOOOQOi\\noooooooo\\noooooo\u00c2\u00bbco\\nQOi coaoxaoc-GO\\n2-3\\nu\\noooo\\nO O lO o\\nO C^ CO CO\\no o o\\n\u00e2\u0080\u00a2coo\\nCVJ Oi Ci\\no o o o o o\\no lt o o i.t o\\nCQ 1-1 Oi (M 07 W\\noooo o o o o o o o o o o o o\\noooo o o o o o o o o o o o o\\nC5 t- O CO GO oo GO O O CO 00 GO X) O OD 00\\nfe\\nM\\na\\nc\\nt^\\nc3\\no\\nW)\\nd\\n5d\\noooo\\nOOOO\\nrf 1\u00e2\u0080\u0094 I CO O\\nooo\\no o\\n01 CQ CQ\\no\\no\\nCQ\\no o\\no o\\nO CQ\\nooo\\nO O \u00c2\u00abD\\nCQ\\nOO -o\\noooooooooooooooo\\noooooooooooooooo\\nOi CQCQO0i0500OO00C0C00005t-\\na", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0196.jp2"}, "197": {"fulltext": "\u00c2\u00a7154.\\nTRESTLES. 179\\nOn page 177 there are quoted the vahies taken from the U. S.\\nGovernment reports on the strength of timber, the tests probably\\nbeino- the most thorough and reliable that were ever made.\\nOn page 178 are given the average safe allowable work-\\nin o- unit stresses in pounds per square inch, as recommended\\nb^^the committee on Strength of Bridge and Trestle Timbers,\\nthe work being done under the auspices of the Association of\\nEailway Superintendents of Bridges and Buildings. The report\\nwas presented at their fifth annual convention, held in New\\nOrleans, in October, 1895.\\n154. Loading. As shown in 138, the span of trestles is\\nalways small, is generally 14 feet, and is never greater than IS\\nexcept when supported by knee-braces. The greatest load that\\nwill ever come on any one span will be the concentrated loading\\nof the drivers of a consolidation locomotive. With spans of 14\\nfeet or less it is impossible for even the four pairs of drivers to\\nbe on the same span at once. The weight of the rails, ties, and\\nguard-rails should be added to obtain the total load on the string-\\ners, and the weight of these, plus the weight of the stringers,\\nshould be added to obtain the pressure on the caps or corbels.\\nThis dead load is almost insignificant compared with the live\\nload and may be included with it. The weight of rails, ties,\\netc., may be estimated at 200 pounds per foot To obtain\\nthe weight on the caps the weight of the stringers must be\\nadded, which depends on the design and on the weight per cubic\\nfoot of the wood employed. But as the weight of the stringers\\nis comparatively small, a considerable percentage of variation\\nin wei^ -ht will have but an insignificant effect on the result.\\nDisreo-ardinfi- all refinements as to actual dimensions, the ordi-\\nnary maximum loading for standard gauge railroads may be\\ntaken as that due to four pairs of driving-axles, spaced 5 0\\napart and giving a pressure of 25,000 pounds per axle. This\\nshould be increased to 40,000 pounds per axle (same spacing)\\nfor the heaviest trafiic. On the basis of 25,000 pounds per\\naxle the following results have been computed", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0197.jp2"}, "198": {"fulltext": "180\\nRAILBOAD CONSTRUCTION\\n155.\\nSTRESSES ON VARIOUS SPANS DUE TO MOVING LOADS OF 25,000 POUNDS,\\nSPACED 5 0 APART.\\nSpan in feet.\\nMax. mom.\u00e2\u0080\u0094\\nft. lbs.\\nMax. shear.\\nMax load on\\none cap.\\n10\\n12\\n14\\n16\\n18\\n65 000\\n103 600\\n142 400\\n181 400\\n220 600\\n38 500\\n45 000\\n49 600\\n54 725\\n60100\\n52100\\n62 700\\n74 200\\n85 700\\n97 900\\nAlthough the dead load does not vary in proportion to the\\nlive load, jet, considering the very small influence of the dead\\nload, there will be no appreciable error in assuming the corre-\\nsponding values, for a load of 40,000 lbs. per axle, to be |o ^f\\nthose given in the above tabulation.\\n155. Factors of safety. The most valuable result of the gov-\\nernment tests is the knowledge that under given moisture condi-\\ntions the strength of various species of sound timber is not the\\nvariable uncertain quantity it was once supposed to be, but that\\nits strength can be relied on to a comparatively close percentage.\\nThis confidence in values permits the employment of lower fac-\\ntors of safety than have heretofore been permissible. Stresses,\\nwhich when excessive would result in immediate destruction,\\nsuch as cross- breaking and columnar stresses, should be allowed\\na higher factor of safety say 6 or 8 for green timber. Other\\nstresses, such as crushing across the grain and shearing along the\\nneutral axis, which will be apparent to inspection before it is\\ndangerous, may be allowed lower factors say 3 to 5.\\n156. Design of stringers. The strength of rectangular beams\\nof equal width varies as the square of the depth therefore deep\\nbeams are the strongest. On the other hand, when any cross-\\nsectional dimension of timber much exceeds 12 the cost is\\nmuch higher per M., B.M., audit is correspondingly difi^cult to\\nobtain thoroughly sound sticks, free from wind-shakes, etc.\\nWind-shakes especially affect the shearing strength. Also, if\\nthe required transverse strength is obtained by using high nar-\\nrow stringers, the area of pressure between the stringers and the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0198.jp2"}, "199": {"fulltext": "156. TRESTLES, 181\\ncap niaj become so small as to induce crushing across the grain.\\nThis is a very common defect in trestle design. As already in-\\ndicated in 138, the span should vary roughly with the average\\nhei^ ht of the trestle, the longer spans being employed when the\\ntrestle bents are very high, although it is usual to employ the\\nsame span throughout any one trestle.\\nTo illustrate, if we select a span of l-i feet, the load on one\\ncap will be 74,200 lbs. If the stringers and cap are made of\\nlong-leaf yellow pine, which require the closely determined value\\nof 1180 lbs. per square inch to produce a crushing amounting\\nto ^fo of the height on timber with 12^ moisture, we may use\\n200 lbs. per square inch as a safe pressure even for green tim-\\nber; this will require 371 square inches of surface. If the cap\\nis 12^ wide, this will require a width of 31 inches, or say 2\\nstringers under each rail, each 8 inches wide. For rectangular\\nbeams\\nMoment ^R hh\\\\\\nUsing for 11 the safe value 1575 lbs. per square inch, we have\\n142400 X 12 i X 1575 X 32 X h\\\\\\nfrom which h 15^ 9. If desired, the width may be increased\\nto 9 and the depth correspondingly reduced, which will give\\nsimilarly h 14 8, or say 15 This show^s that two beams,\\n9 X 15 under each rail will stand the transverse bending and\\nhave more than enough area for crushing.\\nThe shear per square inch will equal\\n3 total shear 3 49600\\nzrz 138 lbs. per so. inch,\\n2 cross section 2 4 X 9 X lo\\nwhich is a safe value, although it should preferably be less.\\nHence the above combination of dimensions will answer.\\nThe deflection should be computed to see if it exceeds the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0199.jp2"}, "200": {"fulltext": "182 RAILROAD CONSTRUCTION, 157.\\nsomewhat arbitrary standard of gi^ of the span. The deflection\\nfor tiniforni loading is\\nA\\nZ^WE\\nin which I length in inches\\nIF total load, assumed as uniform\\nE modulus of elasticity, given as 2,070,000 lbs.\\nper sq. in. for long-leaf pine, 12^ dry, and assumed to be\\n1,200,000 for green timber. Then\\n_ 5 X 72800 X 168\\n32 X 36 X 15 X 1200000\\n^^X168 =0 .84,\\nso that the calculated deflection is well within the limit. Of\\ncourse the loading is not strictly uniform, but even with a lib-\\neral allowance the deflection is still safe.\\nFor the heaviest practice (40000 lbs. per axle) these stringer\\ndimensions must be correspondingly increased.\\n157. Design of posts. Four posts are generally used for\\nsingle-track work. The inner posts are usually braced by the\\ncross-braces, so that their columnar strength is largely increased\\nbut as they are apt to get more than their share of work, the ad-\\nvantage is compensated and they should be treated as unsupported\\ncolumns for the total distance between cap and sill in simple\\nbents, or for the height of stories in multiple-story construction.\\nThe caps and sills are assumed to have a width of 12 It\\nfacilitates the application of bracing to have the columns of the\\nsame width and vary the other dimension as required.\\nUnfortunately the experimental work of the U. S. Govern-\\nment on timber testing has not yet progressed far enough to\\nestablish unquestionably a general relation between the strength\\nof lono- columns and the crushing: streno^th of short blocks. The", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0200.jp2"}, "201": {"fulltext": "157. TRESTLES. 183\\nfollowing formula has been suggested, but it cannot be consid-\\nered as established\\nf -F X \u00c2\u00bb^r. in which\\nJ 700 15c c\\nf allowable working stress per sq. in. for long columns;\\nji^== short blocks;\\nI\\nI length of column in inches\\nd least cross-sectional dimension in inches.\\nEnough work has been done to give great reliability to the two\\nfollowing formulae for white pine and yellow pine, quoted from\\nJohnson s Materials of Construction, p. 684\\n1 fiy\\nWorking load per sq. in. 1000 ^[jj long-leaf pine;\\n=p 600 ^(y-j white pine;\\nin which I length of column in inches, and\\nh least cross-sectional dimension in inches.\\nThe frequent practice is to use 12 X 12 posts for all tres-\\ntles. If we substitute in the above formula 20 240 and\\nh 12 we have p 1000 i(\\\\V-) ^^0 lbs.\\n900 X 1-11: 129600 lbs., the loorking load for each post.\\nThis is more than the total load on one trestle bent and il-\\nlustrates the usual great waste of timber. Making the post\\n8 X 12 and calculating similarly, we have p T75, and\\nthe working load per column is 775 X 06 74400 l])s. As\\nconsiderable must be allowed for weathering, which destroys\\nthe strength of the outer layers of the wood, and also for the\\ndynamic effect of the live load, 8 X 12 may not be too great,", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0201.jp2"}, "202": {"fulltext": "184 BAILROAD CONSTRUCTION, 158.\\nbut it is certainly a safe dimension. 12 X 6 would possibly\\nprove amply safe in practice. One method of allowing for\\nweathering is to disregard the outer half-inch on all sides of the\\npost, i.e., to calculate the strength of a post one inch smaller in\\neach dimension than the post actually employed. On this basis\\nan 8 X 12 X 20 post, computed as a 7 X 11 post, would\\nhave a safe columnar strength of 706 lbs. per square inch. With\\nan area of 77 square inches, this gives a working load of 54362\\nlbs. for each post^ or 217148 lbs. for the four posts. Consider-\\ning that 74200 lbs. is the maximum load on one cap (14 feet\\nspan), the great excess of strength is apparent.\\n158. Design of caps and sills. The stresses in caps and sills\\nare very indefinite, except as to crushing across the grain. As\\nthe stringers are placed almost directly over the inner posts, and\\nas the sills are supported just under the posts, the transverse\\nstresses are almost insignificant. In the above case four posts\\nhave an area of 4 X 12 X 8 384 sq. in. The total load,\\n74200 lbs., will then give a pressure of 193 pounds per square\\ninch, which is within the allowable limit. This one feature\\nmight require the use of 8 X 12 posts rather than 6 X 12\\nposts, for the smaller posts, although probably strong enough as\\nposts, would produce an objectionably high pressure.\\n159. Bracing. Although some idea of the stresses in the\\nbracing could be found from certain assumptions as to wind-\\npressure, etc. yet it would probably not be found wise to de-\\ncrease, for the sake of economy, the dimensions which practice\\nhas shown to be sufiicient for the work. The economy that\\nwould be possible would be too insignificant to justify any risk.\\nTherefore the usual dimensions, given in 139 and 140, should\\nbe employed.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0202.jp2"}, "203": {"fulltext": "CHAPTEE Y.\\nTUNNELS.\\nSURVEYING.\\n160. Surface surveys. As tunnels are always dug from each\\nend and frequently from one or more intermediate shafts, it is\\nnecessary that an accurate surface survey should be made\\nbetween the two ends. As the natural surface in a locality\\nwhere a tunnel is necessary is almost invariably very steep and\\nrough, it requires the employment of unusually refined methods\\nof work to avoid inaccuracies. It is usual to run a line on the\\nsurface that will be at every point vertically over the center line\\nof the tunnel. Tunnels are generally made straight unless\\ncurves are absolutely necessary, as curves add greatly to the\\ncost. Fig. 85 represents roughly a longitudinal section of the\\n^^-IQOOD H* 7000 t-- CUWJ TyJO- ^000^ j -5000\u00e2\u0080\u0094\\nFig. 85 \u00e2\u0080\u0094Sketch of Section of the Hoosac Tunnel.\\nHoosac Tunnel. Permanent stations were located at ^i, B^ C^\\nE^ and F^ and stone houses were built at A^ B, C^ and 7\\nThese were located with ordinary field transits at first, and then\\nall the points were placed as nearly as possible in one vertical\\nplane by repeated trials and minute corrections, using a verv\\nlarge specially constructed transit. The stations 7 and F weva\\nnecessary because E and A were invisible from (7 niid\\n185", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0203.jp2"}, "204": {"fulltext": "186 RAILROAD CONSTRUCTION. 160.\\nThe alignment at A and having been determined with great\\naccuracy, the true ahgnment was easily carried into the tunnel.\\nThe relative elevations of A and E were determined with\\ngreat accuracy. Steep slopes render necessary many settings\\nof the level per unit of horizontal distance and require that the\\nwork be unusually accurate to obtain even fair accuracy per\\nunit of distance. The levels are usually re-run many times\\nuntil the probable error is a very small quantity.\\nThe exact horizontal distance between the two ends of the\\ntunnel must also be known, especially if the tunnel is on a\\ngrade. The usual steep slopes and rough topography likewise\\nrender accurate horizontal measurements very difficult. Fre-\\nquently when the slope is steep the measurement is best\\nobtained by measuring along the slope and allowing for grade.\\nThis may be very accurately done by employing two tripods\\n(level or transit tripods serve the purpose very well), setting\\nthem up slightly less than one tape-length apart and measuring\\niDetween horizontal needles set in wooden blocks inserted in the\\ntop of each tripod. The elevation of each needle is also\\nobserved. The true horizontal distance between two successive\\npositions of the needles then equals the square root of the\\ndifference of the squares of the inclined distance and the differ-\\nence of elevation. Such measurements will probably be more\\naccurate than those made by attempting to hold the tape\\nhorizontal and plumbing down with plumb-bobs, because (1)\\nit is practically difficult to hold both ends of the tape truly\\nhorizontal; (2) on steep slopes it is impossible to hold the down-\\nMil end of a 100-foot tape (or even a 25-foot length) on a level\\nwith the other end, and the great increase in the number of\\napplications of the unit of measurement very greatly increases\\nthe probable error of the whole measurement (3) the vibrations\\nof a plumb-bob introduce a large probability of error in trans-\\nferring the measurement from the elevated end of the tape to\\nthe ground, and the increased number of such applications of\\nthe unit of measurement still further increases the probable\\nerror.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0204.jp2"}, "205": {"fulltext": "161. TUNNELS. 187\\nc\\n161. Surveying down a shaft. If a shaft is sunk, as at S^\\nFig. 85, and it is desired to dig out the tunnel in both directions\\nfrom the foot of the shaft so as to meet tlie headings from the\\noutside, it is necessary to know, when at the bottom of the\\nshaft, the elevation, alignment, and horizontal distance from\\neach end of the tunnel.\\nThe elevation is generally carried down a shaft by means of\\na steel tape. This method involves the least number of ai)pli-\\ncations of the unit of measurement and greatly increases the\\naccuracy of the final result.\\nThe horizontal distance from each end may be easily trans-\\nferred down the shaft by means of a plumb-bob, using sonVe of\\nthe precautions described in the next paragraph. 1\\nTo transfer the alignment from the surface to the bottom of\\na shaft requires the highest skill because the shaft is always\\nsmall, and to produce a line perhaps several thousand feet long\\nin a direction given by two points 6 or 8 feet apart requires\\nthat the two points must be determined with extreme accuracy..\\nThe eminently successful method adopted in the Hoosac Tunnel\\nwill be briefly described Two beams were securely fastened\\nacross the top of the shaft (1030 feet deep), tlie beams being:\\nplaged transversely to tlie direction of the tunnel and as far\\napart as possible and yet allow plumb-lines, hung from the\\nintersection of each beam with the tunnel center line, to swing\\nfreely at the bottom of the shaft. These intersections of the\\nbeams with the center line were determined by averaging the\\nresults of a large number of careful observations for alio-nment.\\nTwo fine parallel wires, spaced about J^ apart, were then\\nstretched between the beams so that the center line of the\\ntunnel bisected at all points the space between the wires.\\nPlumb-bobs, weighing 15 pounds, were suspended by fine wires\\nbeside each cross-beam, the wires passing between the two\\nparallel alignment wures and bisecting the space. The plumb-\\nbobs were allowed to swing in pails of water at the. bottom.\\nDrafts of air up the shaft required the construction of boxes\\nsurrounding the wires. Even these precautions did not suffice", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0205.jp2"}, "206": {"fulltext": "188 RAILROAD CONSTRUCTION. 162.\\nto absolutely prevent vibration of the wire at the bottom\\nthrough a very small arc. The mean point of these vibrations\\nin each case was then located on a rigid cross-beam suitably\\nplaced at the bottom of the shaft and at about the level of the\\nroof of the tunnel. Short plumb-lines were then suspended\\nfrom these points whenever desired a transit was set (by trial)\\nso that its line of collimation passed through both plumb lines\\nand tlie line at the bottom could thus be prolonged.\\n162. Underground surveys. Survey marks are frequently\\nplaced on the timbering, but they are apt to prove unreliable on\\naccount of the shifting of the timbering due to settlement of the\\nsurrounding material. They should never be placed at the bottom\\nof the tunnel on account of the danger of being disturbed or\\ncovered up. Frequently holes are drilled in the roof and filled\\nwith wooden plugs in which a hook is screwed exactly on line.\\nAlthough this is probably the safest method, even these plugs are\\nnot always undisturbed, as the material, unless very hard, will\\noften settle slightly as the excavation proceeds. When a tunnel\\nis perfectly straight and not too long, alignment-points may be\\ngiven as frequently as desired from permanent stations located\\noutside the tunnel where they are not liable to disturbance.\\nThis has been accomplished by running the alignment through\\nthe upper part of the cross-section, at\\none side of the center, where it is out of\\nthe way of the piles of masonry material,\\ndebris, etc., which are so apt to choke\\nup the lower part of the cross-section.\\nThe position of this line relative to the\\ncross-section being fixed, the alignment\\nof any required point of the cross-section\\nis readily found by means of a light frame\\nor template with a fixed target located\\nwhere this line would intersect the frame\\nFjG. 86. when properly placed. A level -bubble\\non tlie frame will assist in setting the frame in its proper position.\\nIn all tunnel surveying the cross-wires must be illuminated", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0206.jp2"}, "207": {"fulltext": "163. TUNNELS. 189\\nby a lantern, and the object sighted at must also be illuminated.\\nA powerful dark-lantern with the opening covered with (jroxind\\nglass has been found useful. This may be used to illuminate a\\nplumb-bob string or a very fine rod, or to place behind a brass\\nplate having a narrow slit in it, the axis of the slit and plate\\nbeing coincident with the plumb-bob string by which it is hung.\\nOn account of the interference to the surveying caused by\\nthe work of construction and also by the smoke and dust in the\\nair resulting from the blasting, it is generally necessary to make\\nthe surveys at times when construction is tenq^orarily sus-\\npended.\\n163. Accuracy of tunnel surveying. Apart from the very\\nnatural desire to do surveying which shall check well, there is\\nan important financial side to accurate tunnel surveying. If\\nthe survev lines do not meet as desired when the headino^s come\\ntogether, it may be found necessary, if the error is of appreciable\\nsize, to introduce a slight curve, perhaps even a reversed curve,\\ninto the alignment, and it is even conceivable that the tunnel\\nsection would need to be enlarged somewhat to allow for these\\ncurves. The cost of these changes and the perpetual annoyance\\ndue to an enforced and undesirable alteration of the original\\ndesign will justify a considerable increase in the expenses of the\\nsurvey. Considering that the cost of surveys is usually but a\\nsmall fraction of the total cost of the work, an increase of 10 or\\neven 20^ in the cost of the surveys will mean an insignificant\\naddition to the total cost and frequently, if not generally, it will\\nresult in a saving of many times the increased cost. The\\naccuracy actually attained in two noted American tunnels is\\ngiven as follows The Musconetcong tunnel is about 5000 feet\\nlong, bored through a mountain -100 feet high. The error of\\nalignment at the meeting of the headings was O .Oi, error of\\nlevels O .Olo, error of distance 0 .52. The Hoosac tunnel is\\nover 25,000 feet long. The heading from the east end met the\\nheading from the central shaft at a point 11271 feet from the\\neast end and 15G3 feet from the shaft. The error in align-\\nment was y\\\\ of an inch, that of levels a few hundredths,", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0207.jp2"}, "208": {"fulltext": "190 RAILROAD CONSTRUCTION. 164.\\nerror of distance trifling. Tlie alignment, corrected at the\\nshaft, was carried on through and met the heading from the west\\nend at a point 10138 feet from the west end and 2056 feet from\\nthe shaft. Here the error of alignment was and that of\\nlevels 0.134 ft.\\nDESIGN.\\n164. Cross-sections, l^early all tunnels have cross-sections\\npeculiar to themselves all varying at least in the details. The\\ngeneral form of a great many tunnels is that of a rectangle sur-\\nmounted by a semi-circle or semi-ellipse. In very soft material\\nan inverted arch is necessary along the bottom. In such cases\\nthe sides will generally be arched instead of vertical. The sides\\nare frequently battered. With very long tunnels, several forms\\nof cross-section will often be used in the same tunnel, owing to\\ndifferences in the material encountered. In solid rock, which\\nw^ill not disintegrate upon exposure, no lining is required, and\\nthe cross-section will be the irregular section left by the blasting,\\nthe only requirement being that no rock shall be left within the\\nrequired cross-sectional figure. Farther on, in the same tunnel,\\nwhen passing through some very soft treacherous material, it\\nmay be necessary to put in a full arch lining top, sides, and bot-\\ntom which will be nearly circular in cross-section. For an\\nillustration of this see Figs. 87 and 88.\\nThe width of tunnels varies as greatly as the designs. Single-\\ntrack tunnels generally have a width of 15 to 16 feet. Occa-\\nsionally they have been built 14 feet wide, and even less, and\\nalso up to 18 feet, especially when on curves. 24 to 26 feet is\\nthe most common width for double track. Many double- track\\ntunnels are only 22 feet wide, and some are 28 feet wide. The\\nheights are generally 19 feet for single track and 20 to 22 feet\\nfor double track. The variations from these figures are con-\\nsiderable. The lower limits depend on the cross-section of the\\nrolling stock, with an indefinite allowance for clearance and ven-\\ntilation. Cross-sections which coincide too closely with what is", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0208.jp2"}, "209": {"fulltext": "164.\\nTUNNELS.\\n191\\nFig. 87.\u00e2\u0080\u0094 Housac Tunnel. Section through Solid Rock.\\nFig. 88.\u00e2\u0080\u0094 Hoosac Tunnel Section through Soft Ground,", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0209.jp2"}, "210": {"fulltext": "192\\nRAILROAD CONSTRUCTION.\\n165.\\nabsolutely required for clearance are objectionable, because any\\nslight settlement of the lining which would otherwise be harm-\\nless would then become troublesome and even dangerous. Figs.\\n87, 88, and 89 show some typical cross-sections.\\nFig. 89. St. Cloud Tunnel.\\n165. Grade. A grade of at least 0.2^ is needed for drainage.\\nIf the tunnel is at the summit of two grades, the tunnel grade\\nshould be practically level, with an allowance for drainage, the\\nactual summit being perhaps in the center so as to drain both\\nways. When the tunnel forms part of a long ascending grade,\\nit is advisable to reduce the grade through the tunnel unless the\\ntunnel is very short. The additional atmospheric resistance and\\nthe decreased adhesion of the driver wheels on the damp rails in\\na tunnel will cause an engine to work very hard and still more\\nrapidly vitiate the atmosphere until the accumulation of poison-\\nous gases becomes a source of actual danger to the engineer and\\nfireman of the locomotive and of extreme discomfort to the\\npassengers. If the nominal ruling grade of the road were\\nmaintained through a tunnel, the maximum resistance would be\\nDrinker s Tunneling.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0210.jp2"}, "211": {"fulltext": "PLATE 11.\\nTuN^ El.-TIMBERI^G\u00e2\u0080\u0094 English System (6*).\\nTUNNEL-TIMBERTXG\u00e2\u0080\u0094 ENGTJSn SYSTEM (6).\\n{To face page 192.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0211.jp2"}, "212": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0212.jp2"}, "213": {"fulltext": "PLATE III.\\n\u00e2\u0096\u00a0///\u00e2\u0096\u00a0//\u00e2\u0096\u00a0/r. Mi i)j i:/M ir ii//.i//, ///f,/j -^^i .w ;^y: y/ -y//fr/M/ ,r, y, ///i- ^y^v/fif^y^\\nTUJS2HiiL-TIMJ3EKlIS G\u00e2\u0080\u0094 ENGLISH SYSTEM {c).\\nTuNNEL-TTMBERiKG\u00e2\u0080\u0094 English System {d),\\n{To face page 192.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0213.jp2"}, "214": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0214.jp2"}, "215": {"fulltext": "167. TUNNELS. 193\\nfound in the tunnel. This would probably cause trains to stall\\nthere, which would be objectionable and perhaps dangerous.\\n166. Lining. It is a characteristic of many kinds of rock\\nand of all earthy material that, although they may be self-sus-\\ntaining when first exposed to the atmosphere, they rapidly dis-\\nintegrate and require that the top and perhaps the sides and\\neven the bottom shall be lined to prevent caving in. In this\\ncountry, when timber is cheap, it is occasionally framed as an\\narch and used as the permanent lining, but masonry is always\\nto be preferred.- Frequently the cross-section is made extra\\nlarge so that a masonry lining may subsequently be placed inside\\nthe wooden lining and thus postpone a large expense until the\\nroad is better able to pay for the work. In very soft unstable\\nmaterial, like quicksand, an arch of cut stone voussoirs may be\\nnecessary to withstand the pressure. A good quality of brick is\\noccasionally used for lining, as they are easily handled and make\\ngood masonry if the pressure is not excessive. Only the best\\nof cement mortar should be used, economy in this feature being\\nthe worst of folly. Of course the excavation must include the\\noutside line of the lining. Any excavation which is made out-\\nside of this line (by the fall of earth or loose rock or by exces-\\nsive blasting) must be refilled with stone well packed in. Occa-\\nsionally it is necessary to fill these spaces with concrete. Of\\ncourse it is not necessary that the lining be uniform throughout\\nthe tunnel.\\n167. Shafts. Shafts are variously made with square, rectan-\\ngular, elliptical, and circular cross-sections. The rectangular\\ncross-section, with the longer axis parallel with the tunnel, is\\nmost usually employed. Generally the shaft is directly over the\\ncenter of the tunnel, but that always implies a complicated con-\\nnection between the linings of the tunnel and shaft, provided\\nsuch linings are necessary. It is easier to sink a shaft near to\\none side of the tunnel and make an opening through the nearly\\nvertical side of the tunnel. Such a method was employed in the\\nChurch Hill Tunnel, illustrated in Fig. 90. Fig. 91 f shows\\nDrinker s Tunneling.\\nf Rziha, Lebrbuch der Gesammteu Tunnelbaukunsi.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0215.jp2"}, "216": {"fulltext": "194\\nRAILROAD CONSTRUCTION,\\n167.\\na cross-section for a large main sliaft. Many shafts have been\\nbuilt with the idea of being left open permanently for ventila-\\ntion and have therefore been elaborately Uned with masonry.\\nFig. 90.\u00e2\u0080\u0094 Connection with Shaft, Church Hill Tunnel.\\nFig. 91. Cross-section, Large Main Shaft.\\nThe general consensus of opinion now appears to be that shafts\\nare worse than useless for ventilation that the quick passage of\\na train through the tunnel is the most effective ventilator and\\nthat shafts only tend to produce cross-currents and are ineffective\\nto clear the air. In consequence, many of these elaborately\\nlined shafts have been permanently closed, and the more recent", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0216.jp2"}, "217": {"fulltext": "PLATE IV\\nTuNNEL-TiMBEKiNG\u00e2\u0080\u0094 French System (a).\\nTuNN^:L-TIMREHI^\u00e2\u0080\u00a2G-FKE^XII System\\n(To face page 194.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0217.jp2"}, "218": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0218.jp2"}, "219": {"fulltext": "PLATE y.\\nTunnel timbeking\u00e2\u0080\u0094 Belgian Sy tem (a).\\nMi\\nTunnel-timbeking\u00e2\u0080\u0094 Belglvn System (6).\\n{To face page 194.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0219.jp2"}, "220": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0220.jp2"}, "221": {"fulltext": "169. TUNNELS. 195\\npractice is to close up a shaft as soon as the tunnel is completed.\\nShafts always form drainage-wells for the material they pass\\nthrough, and sometimes to such an extent that it is a serious\\nmatter to dispose of the water that collects at the bottom,\\nrequiring the construction of large and expensive drains.\\n168. Drains. A tunnel will almost invariably strike veins of\\nwater which will promptly begin to drain into the tunnel and\\nnot only cause considerable trouble and expense during construc-\\ntion, but necessitate the provision of permanent drains for its\\nperpetual disposal. These drains nmst frequently be so large as\\nto appreciably increase the required cross- section of the tunnel.\\nGenerally a small open gutter on each side will suffice for this\\npurpose, but in double-track tunnels a large covered drain is\\noften built between the tracks. It is sometimes necessary to\\nthoroughly grout the outside of the lining so that water will not\\nforce its way through the masonry and perhaps injure it, but\\nmay freely drain down the sides and pass through openings in\\nthe side walls near their base into the gutters.\\nCONSTRUCTION.\\n169. Headings. The methods of all tunnel excavation de-\\npend on the general principle that all earthy material, except\\nthe softest of liquid mud and quicksand, will be self-sustaining\\nover a greater or less area and for a greater or less time after\\nexcavation is made, and the work consists in excavating some\\nmaterial and immediately propping up the exposed surface by\\ntimbering and poling-boards. The excavation of the cross-sec-\\ntion begins with cutting out a heading, which is a small\\nhorizontal drift whose breast is constantly kept 15 feet or\\nmore in advance of the full cross-sectional excavation. In solid\\nself-sustaining rock, which will not decompose upon exposure\\nto air, it becomes simply a matter of excavating the rock with\\nthe least possible expenditure of time and energy. In soft\\nground the heading must be heavily timbered, and as the heading\\nis gradually enlarged the timbering must be gradually extended", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0221.jp2"}, "222": {"fulltext": "196\\nRAILROAD CONSTRUCTION,\\n170.\\nand perhaps replaced, according to some regular system, so that\\nwhen the full cross-section has been excavated it is supported\\nby such timbering as is intended for it. The heading is some-\\ntimes made on the center line near the top with other plans,\\non the center line near the bottom and\\nsometimes two simultaneous headings are run\\nin the two low^er corners. Headings near the\\nbottom serve the purpose of draining the\\nmaterial above it and facilitating the excava-\\ntion. The simplest case of heading timber-\\ning is that shown in Fig. 92, in which cross-\\ntimbers are placed at intervals just under the\\nroof, set in notches cut in the side walls and\\nsupporting poling-boards which sustain what-\\never pressure may come on them. Cross-timbers near the bottom\\nsupport a flooring on which vehicles for transporting material\\nmay be run and under which the drainage may freely escape.\\nAs the necessity for timbering becomes greater, side timbers and\\neven bottom timbers must be added, these timbers supporting\\npoHng-boards, and even the breast of the heading must be pro-\\ntected by boards suitably braced, as shown in Fig. 93. The\\nFig. 93.\\nFk;} 93 TiMBEEixa FOK Tunnel Heading.\\nsupporting timbers are framed into collars in such a manner that\\nadded pressure only increases their rigidity.\\n170. Enlargement. Enlargement is accomplished by remov-\\ning the poling-boards, one at a time, excavating a greater or less", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0222.jp2"}, "223": {"fulltext": "PLATE VI.\\n7^^ j -4\\nTunnel timeeiung\u00e2\u0080\u0094 German System (a).\\nr.,Xir\\\\\\n\u00e2\u0080\u00a2^v/ ^ii\\nci\\nv^\\n::-^^:^-.;^J^.i\u00e2\u0080\u00a2\\n^^^Ifv^\\nTuNNEL-TiMBET? TNG\u00e2\u0080\u0094 German Sys iem (6).\\n{To face page 196.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0223.jp2"}, "224": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0224.jp2"}, "225": {"fulltext": "PLATE VII.\\npr-T^^i^\\nTunnel-timbering German System [c).\\nJmiW^r^\\nTunnel-timbering\u00e2\u0080\u0094 German System {d)\\n{To face page 1%", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0225.jp2"}, "226": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0226.jp2"}, "227": {"fulltext": "\u00c2\u00a7171.\\nTUNNELS.\\n197\\namount of material, and immediately supporting the exposed\\nmaterial with poling-boards suitably braced. (See Figs. 93 and\\n94.) This work being systematically done, space is therel)y\\nFig. 94.\\nobtained in which the framing for the full cross- section may be\\ngradually introduced. The framing is constructed with a cross-\\nsection so large that the masonry lining may be constructed\\nwithin it.\\n171. Distinctive features of various methods of construction.\\nThere are six general systems, known as the English, German,\\nBelgian, French, Austrian, and American. They are so named\\nfrom the origin of the methods, although their use is not confined\\nto the countries named. Fig. 95 shows by numbers (1 to 5)\\nthe order of the excavation within the cross-sections. The Eriir-\\nlish, Austrian, and American systems are alike in excavating the\\nentire cross-section before beginning the construction of the\\nmasonry lining. The German method leaves a solid core (5)\\nuntil practically the whole of the lining is complete. This has\\nthe disadvantage of extremely cramped quarters for work, poor\\nventilation, etc. The Belgian and French methods agree in\\nexcavating the upper part of the section, building the arch at\\nonce, and supporting it temporarily until the side walls are\\nbuilt. The Belgian method then takes out the core (3), removes\\nvery short sections of the sides (4), immediately underpinning\\nthe arch with short sections of the side walls and thus gradually\\nconstructing the whole side wall. The French method digs out\\nthe sides (3), supporting the arch temporarily with timbers and", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0227.jp2"}, "228": {"fulltext": "198\\nRAILROAD CONSTRUCTION.\\n171.\\ntlien replacing the timbers with masonry the core (4) is taken\\nout last. The French method has the same disadvantage as the\\nGerman working in a cramped space. The Belgian and French\\nsystems have the disadvantage that the arch, supported tempo-\\nrarily on timber, is very apt to be strained and cracked by the\\nslight settlement that so frequently occurs in soft material. The\\nEnglish, Austrian, and American methods differ mainly in the\\nf\\n^1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\n1\\nfx\\n4\\n3\\n-4--\\n4\\n5\\n1\\n5\\nENGLISH\\nAUSTRIAN\\nAMERICAN\\ngerman belgian french\\nFig. 95. Order of Working by the Various Systems.\\ndesign of the timbering. The English support the roof by lines\\nof very heavy longitudinal timbers which are supported at com-\\nparatively wide intervals by a heavy framework occupying the\\nwhole cross-section. The Austrian system uses such frequent\\ncross-frames of timber- work that poling-boards will suffice to\\nsupport the material between the frames. The American sys-\\ntem agrees with the Austrian in using frequent cross-frames\\nsupporting poling-boards, but differs from it in that the cross-\\nframes consist simply of arches of 3 to 15 wooden voussoirs,\\nthe voussoirs being blocks of 12 X 12 timber about 2 to 8 feet\\nlong and cut with joints normal to the arch. These, arches are\\nput together on a centering which is removed as soon as the arch", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0228.jp2"}, "229": {"fulltext": "PLATE VIII.\\nTUNNEL-TIMBEIIING AUSTRIAN SYSTEM (a).\\nTUNNEL-TlMliEKlNG AUSTRIAN JSYSTEM (6).\\nTuNNET,-TiMBERiNG\u00e2\u0080\u0094 Austrian System (rt).\\n{To face page 198.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0229.jp2"}, "230": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0230.jp2"}, "231": {"fulltext": "PLATE IX.\\nMM^\\n.0\\nTuNNEL-TiMiifiiiiNa\u00e2\u0080\u0094 Austrian System [d).\\nv. J^^\\nTunnel-timbering Austrian System {e).\\n(To face page 198.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0231.jp2"}, "232": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0232.jp2"}, "233": {"fulltext": "PLATE X.\\nTunnel-timbering\u00e2\u0080\u0094 AusTiaAN System\\nV V vi.-^^:::^^\\nTunnel-timbering Austrian System {g).\\n(To face page 198", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0233.jp2"}, "234": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0234.jp2"}, "235": {"fulltext": "g 173. TUNNELS. 199\\nis keyed up and thus immediately opens up the full cross-section,\\nso that the center core (4) may be immediately dug out and the\\nmasonry constructed in a large open space. The American sys-\\ntem has been used successfully in very soft ground, but its ad-\\nvantages are greater in loose rock, when it is much cheaper than\\nthe other methods which employ more timber. Fig. 90 illus-\\ntrates the use of the American system. The iigure shows the\\nwooden arch in place. The masonry arch may be placed when\\nconvenient, since it is possible to lay the track and commence\\ntraffic as soon as the wooden arch is in place. Plates II to XIV\\nillustrate the methods of excavating and timbering by these\\nvarious systems.\\n172. Ventilation during construction. Tunnels of any great\\nlength must be artificially ventilated during construction. If\\nthe excavated material is rock so that blasting is necessary, the\\nneed for ventilation becomes still more imperative. The inven-\\ntion of compressed-air drills simultaneously solved two difficul-\\nties. It introduced a motive power which is unobjectionable in\\nits application (as gas would be), and it also furnished at the same\\ntime a supply of just what is needed pure air. If no blasting\\nis done (and sometimes even when there is blasting), air must be\\nsupplied by direct pumping. The cooling effect of the sudden\\nexpansion of compressed air only reduces the otherwise objection-\\nably high temperature sometimes found in tunnels. Since pure\\nair is being continually pumped in, the foul air is thereby forced\\nout.\\n173. Excavation for the portals. Under normal conditions\\nthere is always a greater or less amount of open cut preceding\\nand following a tunnel. Since all tunnel methods depend (to\\nsome slight degree at least) on the capacity of the exposed ma-\\nterial to act as an arch, there is implied a considerable thickness\\nof material above the tunnel. This thickness is reduced to\\nnearly zero over the tunnel portals and therefore requires special\\ntreatment, particularly when the material is very soft. Fig. 90\\nKziba, Lehrbucli der Qersammten Tunnelbaukunst.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0235.jp2"}, "236": {"fulltext": "200\\nBAILROAD CONSTRUCTION,\\n174.\\nillustrates one method of breaking into the ground at a portal.\\nThe loose stones are piled on the framing to give stability to the\\nframing by their weight and also to retain the earth on the\\nslope above. Another method is to sink a temporary shaft to\\nthe tunnel near the portal immediately enlarge to the full size\\nand build the masonry lining then work back to the portal.\\nFig. 96.\u00e2\u0080\u0094 Timbering for Tunnel Portal.\\nThis method is more costly, but is preferable in very treacherous\\nground, it being less liable to cause landslides of the surface\\nmaterial.\\n174. Tunnels vs. open cuts. In cases in which an open cut\\nrather than a tunnel is a possibility the ultimate consideration\\nis generally that of first cost combined with other financial con-\\nsiderations and annual maintenance charges directly or indirectly\\nconnected with it. Even when an open cut may be constructed at\\nthe same cost as a tunnel (or perhaps a little cheaper) the tunnel\\nmay be preferable under the following conditions\\n1 When the soil indicates that the open cut would be liable\\nto landslides.\\n2. When the open cut would be subject to excessive snow-\\ndrifts or avalanches.\\n3. When land is especially costly or it is desired to run under\\nexisting costly or valuable buildings or monuments. When run-\\nning through cities, tunnels are sometimes constructed as open\\ncuts and then arched over.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0236.jp2"}, "237": {"fulltext": "PLATE XL\\n/yYZ.\\nPERMANENT TIMBERING OF HEADING.\\nj- _\\nt r\\nPncENixviLLE Tunnel. P. S. V. R.R.\\n{To face page 200.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0237.jp2"}, "238": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0238.jp2"}, "239": {"fulltext": "PLATE XIL\\nPhcenixville Tunnel, P. S. V. R.R.\\n{To face page dO.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0239.jp2"}, "240": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0240.jp2"}, "241": {"fulltext": "PLATE XIII.\\nPhcenixville Tunnel. P. S. V. R.R.\\n{To face page 2^0.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0241.jp2"}, "242": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0242.jp2"}, "243": {"fulltext": "PLx\\\\TE XIV.\\nElevatio:^ of Purtai.,\\nLongitudinal Section of Portal.\\nPnoENixviLLE Tunnel. P. S. V. R.R.\\niTo face page 2^", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0243.jp2"}, "244": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0244.jp2"}, "245": {"fulltext": "\u00c2\u00a7175.\\nTUN2iELS.\\n201\\nThese cases apply to tunnels vs. open cuts when the ahgn-\\nment is fixed by other considerations than the mere topography.\\nThe broader question of excavating tunnels to avoid excessive\\ngrades or to save distance or curvature, and siniihir problems,\\nare hardly susceptible of general analysis except as questions of\\nrailway economics and must be treated individually.\\n175. Cost of tunneling. Tlie cost of any construction wdiicli\\ninvolves such uncertainties as tunneling is very varinble. It de-\\npends on the material encountered, the amount and kind of tim-\\nbering required, on the size of the cross- section, on the price of\\nlabor, and especially on the reconstruction that may be necessary\\non account of mishaps.\\nHeadings generally cost $4 to $5 per cubic yard for excava-\\ntion, while the remainder of the cross-section in the same tunnel\\nmay cost about half as much. The average cost of a large number\\nof tunnels in this country may be seen from the following table\\nMaterial.\\nCost per cubic yard.\\nCost per\\nlineal foot.\\nExcavation.\\nMasonry.\\nSingle.\\nDouble.\\nSingle.\\nDouble.\\nSingle.\\nDouble.\\nHard rock\\nLoose rock.\\nSoft ground.\\n$5.89\\n3.12\\n3.62\\n$5.45\\n3.48\\n4.64\\n$12.00\\n9.07\\n15.00\\n8.25\\n10.41\\n10.50\\n69.76\\n80.61\\n135.31\\n$142.82\\n119.26\\n174.42\\nA considerable variation from these figures may be found in\\nindividual cases, due sometimes to unusual skill (or the lack of\\nit) in prosecuting the work, but the figures will generally be\\nsufficiently accurate for preliminary estimates or for the compari-\\nson of two proposed routes.\\nFigures derived from Drinker s Tunneling.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0245.jp2"}, "246": {"fulltext": "CHAPTEK YI.\\nCULVERTS AND MINOR BRIDGES.\\n176. Definition and object. Although a variable percentage\\nof the rain falling on any section of country soaks into the\\nground and does not immediately reappear, yet a very large\\npercentage flows over the surface, always seeking and following\\nthe lowest channels. The roadbed of a railroad is constantly\\nintersecting these channels, which frequently are normally drv.\\nIn order to prevent injury to railroad embankments by the im-\\npounding of such rainfall, it is necessary to construct waterways\\nthrough the embankment through which such rainflow may\\nfreely pass. Such waterways, called culverts, are also appli-\\ncable for the bridging of very small although perennial streams,\\nand therefore in this work the term culvert will be applied to\\nall water-channels passing through a railroad embankment which\\nare not of sufficient magnitude to require a special structural\\ndesign, such as is necessary for a large masonry arch or a truss\\nbridge.\\n177. Elements of the design. A well-designed culvert must\\nafford such free passage to the water that it will not back up\\nover the adjoining land nor cause any injury to the embankment\\nor culvert. The ability of the culvert to discharge freely all the\\nwater that comes to it evidently depends chiefly on the area of\\nthe waterway, but also on the form, length, slope, and materials\\nof construction of the culvert and the nature of the approach\\nand outfall. When the embankment is very low and the amount\\nof water to be discharged very great, it sometimes becomes\\nnecessary to allow the water to discharge under a head, i.e.,\\n202", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0246.jp2"}, "247": {"fulltext": "178. CULVERTS AND MINOR BRIDGES. 203\\nwith the surface of the water above the top of the culvert.\\nSafety then requires a much stronger construction than would\\notherwise be necessary to avoid injury to the culvert or embank-\\nment by wasliing. The necessity for such construction should\\nbe avoided if possible.\\nAREA OF THE WATERWAY.\\n178. Elements involved. The determination of the required\\narea of the waterway involves such a nmltiplicity of indeter-\\nminate elements that any close determination of its value from\\npurely theoretical considerations is a practical impossibility.\\nThe principal elements involved are:\\na. Rainfall. The real test of the culvert is its capacity to\\ndischarge without injury the flow resulting from the extraordi-\\nnary rainfalls and cloud bursts that may occur once in many\\nyears. Therefore, while a knowledge of the average annual\\nrainfall is of very little value, a record of the maximum rainfall\\nduring heavy storms for a long term of years may give a relative\\nidea of the maximum demand on the culvert.\\nb. Area of watershed. This signifies the total area of country\\ndraining into the channel considered. When the drainage\\narea is very small it is sometimes included within the area\\nsurveyed by the preliminary survey. When larger it is fre-\\nquently possible to obtain its area from other maps with a per-\\ncentage of accuracy sufficient for the purpose. Sometimes a\\nspecial survey for the purpose is considered justifiable.\\nc. Character of soil and vegetation. This has a large in-\\nfluence on the rapidity with which the rainflow from a given\\narea will reach the culvert. If the soil is hard and impermeable\\nand the vegetation scant, a heavy rain will run off suddenly,\\ntaxing the capacity of the culvert for a short time, while a\\nspongy soil and dense vegetation will retard the flow, making it\\nmore nearly uniform and the maximum flow at any one time\\nmuch less.\\nd. Shape and slope of watershed. If the watershed is very\\nlong and narrow (other things being equal), the water from the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0247.jp2"}, "248": {"fulltext": "204 RAILROAD COJSSTRUCTION. 179.\\nremoter parts will require so mucli longer time to reach the\\n;ulvert that the flow will be comparatively uniform, especially\\nwhen the sloj)e of the whole watershed is very low. When the\\nslope of the remoter portions is quite steep it may result in the\\nnearly simultaneous arrival of a storm-flow from all parts of the\\nwatershed, thus taxing the capacity of the culvert.\\ne. Effect of design of culvert. The principles of hydraulics\\nshow that the slope of the culvert, its length, the form of the\\ncross-section, the nature of the surface, and the form of the\\napproach and discharge all have a considerable influence on the\\narea of cross-section required to discharge a given volume of\\nwater in a given time, but unfortunately the combined\\nhydraulic efi^ect of these various details is still a very uncertain\\nquantity.\\n179. Methods of computation of area. There are three pos-\\nsible methods of computation.\\n(a) Theoretical. As shown above it is a practical impossi-\\nbilitv to estimate correctlv the combined eftect of the ^reat mul-\\ntiplicity of elements which influence the final result. The nearest\\napproach to it is to estimate by the use of empirical formulae\\nthe amount of water which will be presented at the upper end\\nof the culvert in a given time and then to compute, from the\\nprinciples of hydraulics, the rate of flow through a culvert of\\ngiven construction, but (as shown in 178, e) such methods are\\nstill very unreliable, owing to lack of experimental knowledge.\\nThis method has apparently greater scientific accuracy than other\\nmethods, but a little study will show that the elements of un-\\ncertainty are as great and the final result no more reliable. The\\nmethod is most reliable for streams of uniform flow, but it is\\nunder these conditions that method (c) is most useful. The\\ntheoretical method will not therefore be considered further.\\n(b) Empirical. As illustrated in 180, some formulae make\\nthe area of waterway a function of the drainage area, the for-\\nmula being afl ected by a coeflicient the value of which is esti-\\nmated between limits according to the judgment. Assuming\\nthat the formulae are sound, their use only narrows the limits of", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0248.jp2"}, "249": {"fulltext": "180. CULVERTS AND MINOR BRIDGES. 205\\nerror, the final determination depending on experience and judg-\\nment.\\n(c) From observation. This method, considered by far the\\nbest for permanent work, consists in observing the high -water\\nmarks on contracted channel-openings which are on the same\\nstream and as near as possible to the proposed culvert. If the\\ncountry is new and there are no such openings, the wisest plan\\nis to bridge the opening by a temporary structure in wood which\\nhas an ample waterway (see 126, J, 4) and carefully observe\\nall high- water marks on that opening during the 6 to 10 years\\nwhich is ordinarily the minimum life of such a structure. As\\nshown later, such observations may be utilized for a close com-\\nputation of the required waterway. Method (b) may be utilized\\nfor an approximate calculation for the required area for the tem-\\nporary structure, using a value which is intentionally excessive,\\nso that a permanent structure of sufficient capacity may subse-\\nquently be constructed within the temporary structure.\\n180. Empirical formulae. Two of the best known empirical\\nformulae for area of the waterway are the following\\n(a) Myer s formula:\\nArea of waterway in square feet C X V^drainage area in acres,\\nwhere 6^ is a coefficient varying from 1 for flat country to 4 for\\nmountainous country and rocky ground. As an illustration, if\\nthe drainage area is 100 acres, the waterway area should be from\\n10 to 40 square feet, according to the value of the coefficient\\nchosen. It should be noted that this formula does not reo^ard\\nthe great variations in rainfall in various parts of the world nor\\nthe design of the culvert, and also that the final result depends\\nlargely on the choice of the coefficient.\\n(b) Talbot s formula:\\nArea of waterway in square feet C X V(drainage area in acres)\\nFor steep and rocky ground O varies from to 1. For rolling\\nagricultural country subject to floods at times of melting snow,\\nand with the length of the valley three or four times its width,\\nis about J; and if the stream is longer in proportion to the area,\\ndecrease 0. In districts not affected by accumulated snow, and", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0249.jp2"}, "250": {"fulltext": "206 RAILROAD CONSTRUCTION, 181.\\nwhere the length of the valley is several times the width, 1 or i\\nor even less, may be used. C should be increased for steep side\\nslopes, especially if the upper part of- the valley has a much\\ngreater fall than the channel at the culvert. As an illustration,\\nif the drainage area is 100 acres the area of waterway should be\\nCx 31.6. The area should then vary from 5 to 31 square\\nfeet, according to the character of the country. Like the\\nprevious estimate, the result depends on the choice of a coef-\\nficient and disregards local variations in rainfall, except as they\\nmay be arbitrarily allowed for in choosing the coefficient.\\n181. Value of empirical formulse. The fact that these for-\\nmulae, as well as many others of similar nature that have been\\nsuggested, depend so largely upon the choice of the coefficient\\nshows that they are valuable more as a guide to the judgment\\nthan as a working rule, as Prof. Talbot exphcitly declares in\\ncommenting on his own formula. In short, they are chiefly valu-\\nable in indicating a probable maximum and minimum between\\nwhich the true result probably lies.\\n182. Results based on Observation. As already indicated in\\n179, observation of the stream in question gives the most\\nreliable results. If the country is new and no records of the\\nflow of the stream during heavy storms has been taken, even\\nthe life of a temporary wooden structure may not be lono-\\nenough to include one of the unusually severe storms which\\nmust be allowed for, but there will usually be some high-water\\nmark which will indicate how much opening will be required.\\nThe following quotation illustrates this: A tidal estuary may\\ngenerally be safely narrowed considerably from the extreme\\nwater lines if stone revetments are used to protect the\\nbank from wash. Above the true estuary, where the stream\\ncuts through the marsh, we generally find nearly vertical banks,\\nand we are safe if the faces of abutments are placed even with\\nthe banks. In level sections of the country, where the current\\nis sluggish, it is usually safe to encroach somewhat on the\\n*Prof. A. N. Talbot, Selected Papers of the Civil Engineers Club of\\nthe Univ. of Illinois.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0250.jp2"}, "251": {"fulltext": "183. CULVERTS AND MINOR BRIDGES. 207\\ngeneral width of the stream, but in rapid streams among the\\nhills the width that the stream has cut for itself through the\\nsoil should not be lessened, and in ravines carrying mountain\\ntorrents the openings must be left very much larger than the\\nordinary appearance of the banks of the stream would seem to\\nmake necessary.\\nAs an illustration of an observation of a storm-flow throuo^h\\na temporary trestle, the following is quoted: Having the\\nflood height and velocity, it is an easy matter to determine the\\nvolume of water to be taken care of. I have one ten-bent pile\\ntrestle 135 feet long and 24 feet high over a spring branch that\\nordinarily runs about six cubic inches per second. Last sum-\\nmer during one of our heavy rainstorms (four inches in less\\nthan three hours) I visited this place and found by float observa-\\ntions the surface velocity at the highest stage to be 1.9 feet per\\nsecond. I made a high- water mark, and after the flood- water\\nreceded found the width of stream to be 12 feet and an averao^e\\ndepth of 2} feet. This, with a surface velocity of 1.9 feet i)er\\nsecond, would give approximately a discharge of 50 cubic feet,\\nor 375 gallons, per second. Having this information it is easy\\nto determine size of opening required. f\\n183. Degree of accuracy required. The advantages result-\\ning from the use of standard designs for culverts (as well as\\nother structures) have led to the adoption of a comparatively\\nsmall number of designs. The practical use made of a compu-\\ntation of required waterway area is to determine which one of\\nseveral standard designs will most nearly fulflll the require-\\nments. For example, if a 24-incli iron pipe, having an area of\\n3.14 square feet, is considered to be a little small, the next size\\n(30-inch) would be adopted but a 30-inch pipe has an area of\\n4.92 square feet, which is ^Q% larger. A siniihir result, except\\nthat the percentage of difference might not be quite so marked,\\nJ. P. Snow, Boston Maine Railway. From Report to Association of\\nRailway Superintendents of Bridges and Buildings. 1897.\\nf A. J. Kelley, Kansas City Belt Railway. From Report to Association\\nof Railway Superintendents of Bridges and Buildings. 1807.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0251.jp2"}, "252": {"fulltext": "S08 RAILROAD CONSTRUCTION, 184.\\nwill be found by comparing the areas of consecutive standard\\ndesigns for stone box culverts.\\nThe advisability of designing a culvert to withstand any\\nstorm-flow that may ever occur is considered doubtful. Several\\nyears ago a record-breaking storm in New England carried\\naway a very large number of bridges, etc., hitherto supposed to\\nbe safe. It was not afterward considered that the design of\\nthose bridges was faulty, because the extra cost of constructing\\nbridges capable of withstanding such a flood, added to interest\\nfor a long period of years, would be enormously greater than\\nthe cost of repairing the damages of such a storm once or twice\\nin a century. Of course the element of danger has some\\nweight, but not enough to justify a great additional expendi-\\nture, for common prudence would prompt unusual precautions\\nduring or immediately after such an extraordinary storm.\\nPIPE CULVERTS.\\n184. Advantages. Pipe culverts, made of cast iron or\\nearthenware, are very durable, readily constructed, moderately\\ncheap, will pass a larger volume of water in proportion to the\\narea than many other designs on account of the smoothness of\\nthe surface, and (when using iron pipe) may be used very close\\nto the track w^hen a low opening of large capacity is required.\\nAnother advantage lies in the ease with which they may be in-\\nserted through a somewhat larger opening that has been tem-\\nporarily lined with wood, without disturbing the roadbed or\\ntrack.\\n185. Construction. Permanency requires that the founda-\\ntion shall be firm and secure against being washed out. To\\naccomplish this, the soil of the trench should be hollowed out to\\nfit the lower half of the pipe, making suitable recesses for the\\nbells. In very soft treacherous soil a foundation -block of con-\\ncrete is sometimes placed under each joint, or even throughout\\nthe whole length. When pipes are laid through a sHghtly\\nlarger timber culvert great care should be taken that the pipes\\nare properly supported, so that there will be no settling nor", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0252.jp2"}, "253": {"fulltext": "186. CUL VERTS AND MINOR BRIDGES. 209\\ndevelopment of unusual strains when tlie timber finally decays\\nand gives way. To prevent the washing away of material\\naround the pipe tlie ends should be protected by a bulkhead.\\nThis is best constructed of masonry (see Fig. 97), although wood\\nis sometimes used for cheap and minor constructions. The joints\\nshould be calked, especially when the culvert is liable to run\\nfull or when the outflow is impeded and the culvert is liable to\\nbe partly or wholly tilled during freezing weather. The cost of\\na calking of clay or even hydraulic cement is insignificant com-\\nl)ared with the value of the additional safety afforded. When\\nthe grade of the pipe is perfectly uniform, a very low rate of\\ngrade will suffice to drain a pipe culvert, but since some uneven-\\nness of grade is inevitable through uneven settlement or im-\\n2)erfect construction, a grade of 1 in 20 should preferably be\\nrequired, although much less is often used. The length of a\\npipe culvert is approximately determined as follows\\nLength 25 {dejjth of embankment to top of pipe) {width of roadbed)^\\nin which s is the slope ratio (horizontal to vertical) of the banks.\\nIn ])ractice an even number of lengths will be used which will\\nmost nearly agree with this formula.\\n186. Iron-pipe culverts. Simple cast-iron pipes are used in\\nsizes from 12 to 48 diameter. These are usually made in\\nlengths of 12 feet w^th a few lengths of 6 feet, so that any\\nrequired length may be more nearly obtained. The lightest\\npipes made are sufficiently strong for the purpose, and even those\\nwdiicli would be rejected because of incapacity to withstand pres-\\nsure may be utilized for this work. In Fig. 97 are shown the\\nstandard plans used on the C. C. C. St. L. Ry., which may\\nbe considered as typical plans.\\nPipes formed of cast-iron segments liave been used up to 12\\nfeet diameter. The shell is then made comparatively thin, but\\nis stiffened by ribs and flanges on the outside. The segments\\nbreak joints and are bolted together through the flanges. The\\njoints are made tight by the use of a tarred rope, together with\\nneat cement.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0253.jp2"}, "254": {"fulltext": "210\\nRAILROAD CONSTRUCTION,\\n\u00c2\u00a7186.\\n5=\\nk\\nc\\n3\\nt\\n4-\\n^0\\nnvhIl J\\nt\\ni\\\\\\nss\\n31 X\\nDM\\nt\\nf\\nr", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0254.jp2"}, "255": {"fulltext": "\u00c2\u00a7187.\\nCULVERTS AND MINOR BRIDGES.\\n211\\n187. Tile-pipe culverts. The pipes used for tliis purpose\\nvary from 12 to 24 in diameter. When a larger capacity\\nis required two or more pipes may be laid side by side, but in\\nsuch a case another design might be preferable. It is frequently\\nspecified that double-strength or extra-heavy pipe shall\\nbe used, evidently with the idea that the stresses on a culvert-\\npipe are greater than on a sewer-pipe. But it has been con-\\nclusively demonstrated that, no matter how deep the embankment,\\nthe pressure cannot exceed a somewhat uncertain maximum,\\nalso that the greatest danger consists in placing the pipe so near\\nthe ties that shocks may be directly transferred to the pipe with-\\nout the cusliioning effect of the earth and ballast. When the\\npipes are well bedded in clear earth and there is a sufficient\\ndepth of earth over them to avoid direct impact (at least three\\nfeet) the ordinary sewer-pipe will be sufficiently strong.\\nDouble-strength pipe is frequently less perfectly burned, and\\nup-str\u00c2\u00a3am_e id. down-stream end. down-stream end. three pipes.\\nFig. 98.\u00e2\u0080\u0094 Standard Vitrified-pipe Culvert. Plant System. (1891.)\\nthe supposed extra strength is not therefore obtained. In Fig.\\n98 are shown the standard plans for vitrified- pipe culverts as used\\non the Plant system. Tile pipe is much clieaper than iron\\npipe, but is made in much shorter lengths and requires nmch\\nmore work in laying and especially to obtain a uniform grade.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0255.jp2"}, "256": {"fulltext": "212\\nRAILROAD CONSTRUCTION.\\n\u00c2\u00a7188.\\nBOX CULVERTS.\\n188. Wooden box culverts. This form serves the purpose of\\na cheap temporary construction which allows the use of a bal-\\nlasted roadbed. As in all temporary constructions, the area\\nshould be made considerably larger than the calculated area\\n179-182), not only for safety but also in order that, if the\\nsmaller area is demonstrated to be sufficiently large, the per-\\nmanent construction (probably pipe) may be placed inside with-\\nout disturbing the embankment. All designs agree in using\\nheavy timbers (12 X 12 10 X 12 or 8 X 12 for the\\nside walls, cross-timbers for the roof, every fifth or sixth timber\\nbeing notched down so as to take up the thrust of the side walls,\\nand planks for the flooring. Fig. 99 shows some of the standard\\ndesigns as used by the C, M. tfe St. P. Ry.\\nFig. 99.\u00e2\u0080\u0094 Standard Timber Box Culvert. C, M. St. P. Ry. (Feb. 1889.\\n189. Stone box culverts. In localities where a good quality\\nof stone is cheap, stone box culverts are the cheapest form of\\npermanent construction for culverts of medium capacity, but\\ntheir use is decreasing owing to the frequent difficulty in obtain-\\ning really suitable stone within a reasonable distance of the\\nculvert. The clear span of the cover-stones varies from 2 to 4\\nfeet. The required thickness of the cover-stones is sometimes\\ncalculated by the theory of transverse strains on the basis of cer-\\ntain assumptions of loading as a function of the height of the\\nembankment and the unit strength of the stone used. Such a\\nmethod is simply another illustration of a class of calculations", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0256.jp2"}, "257": {"fulltext": "190. CULVERTS AND MINOR BRIDGES. 213\\nwliicli look very precise and beautiful, but which are worse than\\nuseless (because misleading) on account of the hopeless uncertainty\\nas to the true value of certain quantities which must be used in\\nthe computations. In the first place the true value of the unit\\ntensile strength of stone is such an uncertain and variable\\nquantity that calculations based on any assumed value for it are\\nof small reliability. In the second place the weight of the prism\\nof earth lying directly above the stone, plus an allowance for live\\nload, is by no means a measure of the load on the stone nor of\\nthe forces that. tend to fracture it. All earthwork will tend to\\nform an arch above any cavity and thus relieve an imcertain and\\nprobably variable proportion of the pressure that might other-\\nwise exist. The higher the embankment the less the propor-\\ntionate loading, until at some uncertain height an increase in\\nheight will not increase the load on the cover-stones. The effect\\nof frost is likewise large, but uncertain and not computable. The\\nusual practice is therefore to make the thickness such as experi-\\nence has shown to be safe with a good quality of stone, i.e.,\\nabout 10 or 12 inches for 2 feet span and up to 16 or 18 inches\\nfor 4 feet span. The side walls should be carried down deep\\nenough to prevent their being undermined by scour or heaved\\nby frost. The use of cement mortar is also an important feature\\nof first-class work, especially when there is a rapid scouring cur-\\nrent or a liability that the culvert will run under a head. In\\nFig. 100 are shown standard plans for single and double stone box\\nculverts as used on the IS^orfolk and Western R.R.\\n190. Old-rail culverts. It sometimes happens (although very\\nrarely) that it is necessary to bring the grade line within 3 or 4\\nfeet of the bottom of a stream and yet allosv an area of 10 or 12\\nsquare feet. A single large pipe of sufficient area could not be\\nused in this case. The use of several smaller pipes side by side\\nwould be both expensive and inefficient. For similar reasons\\nneither wooden nor stone box culverts could be used. In sucli\\ncases, as well as in many others where the head-room is not so\\nlimited, the plan illustrated in Fig. 101 is a very satisfactory\\nsolution of the problem. The old rails, having a length of 8 or", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0257.jp2"}, "258": {"fulltext": "214\\nRAILROAD CONSTRUCTION.\\n190.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0258.jp2"}, "259": {"fulltext": "191.\\nCULVERTS AND MINOR BRIDGES.\\n215\\n9 feet, are laid close togetlier across a G-foot opeiiing. Some-\\ntimes the rails are held together by long bolts passing through\\nthe webs of the rails. In the plan shown the rails are confined\\n[TnTTTT TTTTTTr TTr.TTTT,TT;TT TTTrTTTTTTTrTr 7?1\\n^fe\\nFig. 101.\u00e2\u0080\u0094 Standard Old-rail Culvert. N. W. R.R. (1895.)\\nby low end walls on each abutment. This plan requires only 15\\ninches between the base of the rail and the top of the culvert\\nchannel. It also gives a continuous ballasted roadbed.\\nARCH CULVERTS.\\n191. Influence of design on flow. The variations in the\\ndesign of arch culverts have a very marked influence on the\\ncost and efficiency. To combine the least cost with the great-\\nest efficiency, due weight should be given to the following\\nelements (a) the amount of masonry, (h) the simplicity of\\nthe constructive work, {c) the design of the wing walls, {d\\nthe design of the junction of the wing walls with the barrel\\nLI\\n(a)\\nFio. 102. Types of Culverts.\\nand faces of the arch, and {e) the safety and permanency of the\\nconstruction. These elements are more or less antagonistic to\\neach other, and the defects of most designs are due to a lack of\\nproper proportion in the design of these opposing interests. The\\nsimplest construction (satisfying elements 1 and e) is the straight", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0259.jp2"}, "260": {"fulltext": "216 RAILROAD CONSTRUCTION. 192.\\nbarrel arch between two parallel vertical head walls, as sketched\\nin Fig. 102, a. From a hydraulic standpoint the design is poor,\\nas the water eddies around the corners, causing a great resistance\\nwhich decreases the flow. Fig. 102, 5, shows a much better de-\\nsign in many respects, but much depends on the details of the\\ndesign as indicated in elements {h) and (c/). As a general thing\\na good hydraulic design requires complicated and expensive\\nmasonry construction, i.e., elements (b) and {d) are opposed.\\nDesign 102, is sometimes inapplicable because the water is\\nliable to work in behind the masonry during floods and perhaps\\ncause scour. This design uses less masonry than {a) or (h).\\n192. Example of arch culvert design. In Plate XY is shown\\nthe design for an 8-foot arch culvert according to the standard\\nof the ISTorfolk and Western R.R. Note that the plan uses\\nthe flaring wing walls (Fig. 102, h) on the up-stream side\\n(thus protecting the abutments from scour) and straight wing\\nwalls (similar to Fig. 102, c) on the down-stream end. This\\neconomizes masonry and also simplifies the constructive work.\\nNote also the simplicity of the junction of the wing walls with\\nthe barrel of the arch, there being no re-entrant angles below\\nthe springing line of the arch. The design here shown is but\\none of a set of designs for arches varying in span from 6 to 30\\nMINOR OPENINGS.\\n193. Cattle-guards, (a) Pit guards. Cattle-guards will be\\nconsidered under the head of minor openings, since the old-\\nfashioned plan of pit guards, which are even now defended and\\npreferred by some railroad men, requires a break in the con-\\ntinuity of the roadbed. A pit about three feet deep, five feet\\nlong, and as wide as the width of the roadbed, is w^alled up with\\nstone (sometimes with wood), and the rails are supported on heavy\\ntimbers laid longitudinally with the rails. The break in the\\ncontinuity of the roadbed produces a disturbance in the elastic\\nwave running through the I ails, the effect of which is noticeable\\nat high velocities. The greatest objection, however, lies in the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0260.jp2"}, "261": {"fulltext": "--41^2--\\nX", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0261.jp2"}, "262": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0262.jp2"}, "263": {"fulltext": "193.\\nCULVERTS AND MINOR BRIDGES.\\n217\\ndangerous consequences of a derailment or a failure of the tim-\\nbers owing to unobserved decay or destruction by fire caused\\nperhaps by sparks and cinders from passing locomotives. The\\nvery insignificance of the structure often leads to careless in-\\n.t i:; o 1\\n12 X Vl\\\\ l.i 8\\nm^.\\n12 10-\\n-Cil2\\nFig. 103.\u00e2\u0080\u0094 Pit Cattle-guahds. P. R.R.\\nspection. But if a single pair of wheels gets off the rails and\\ndrops into the pit, a costly wreck is inevitable. The (once)\\nstandard design for such a structure on the Pennsylvania E.R.\\nis shown in Fig. 103.\\n(b) Surface cattle-guards. These are fastened on top of the\\nties; the continuity of the roadbed is absolutely unbroken and\\nthus is avoided much of the danger of a bad wreck owing to a\\npossible derailment. The device consists essentially of overlay-\\ning the ties (both inside and outside the rails) with a surface on\\nwhich cattle w411 not walk. The multitudinous designs for such\\na surface are variously effective in this respect. An objection,\\nwhich is often urged indiscriminately against all such designs, is\\nthe liability that a brake-chain which may happen to be drag-\\nging may catch in the rough bars which are used. The bars\\nare sometimes home-made, of wood, as shown in Fig. 104.\\nIron, or steel bars are made as shown in Fig. 105. The\\ngeneral construction is the same as for the wooden bars. The", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0263.jp2"}, "264": {"fulltext": "218\\nMAILROAD CONSTRUCTION.\\n194.\\nmetal bars have far greater dnrabilitv, and it is claimed that they\\nare more effective in discouraging cattle from attempting to\\ncross.\\nFig. 104.\u00e2\u0080\u0094 Cattle-guard with Wooden Slats.\\nFig. 105.\u00e2\u0080\u0094 Merrill- Stevexs Steel Cattle-guard.\\n194. Cattle-passes. Frequently when a railroad crosses a\\nfarm on an embankment, cutting the farm into two parts, the\\nrailroad company is obliged to agree to make a passageway\\nthrough the embankment sufficient for the passage of cattle and\\nperhaps even farm-was^ons. If the embankment is hi^h enousrh\\nso that a stone arch is practicable, the initial cost is the only\\ngreat objection to such a construction but if an open wooden\\nstructure is necessary, all the objections against the old-fashioned\\ncattle-guarda apply witli equal force here. The avoidance of a\\ngrade crossing which would otherwise be necessary is one of the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0264.jp2"}, "265": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0265.jp2"}, "266": {"fulltext": "PLATE XVL\\niH BOLT EVERY THIRD TIE.\\n-N,, O-\\nSTANDARD I-BRIDGES-14-FT. SPAN.\\nNORFOLK AND WESTERN R.R.\\n(1891.)\\nTYPES OF PLATE GIRDER BRIDGES.\\nC. M. St.P. RY.\\n(Dec. 1895.)\\nTYPE GIRDER\\n25 FEET AND UNDER,\\n(To face page 219.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0266.jp2"}, "267": {"fulltext": "195. CULVERTS AND MINOR BHTDGE8. 219\\ngreat compensations for the expense of the construction and\\nmaintenance of these structures. The construction is sometimes\\nmade by placing two pile trestle bents about 6 to 8 feet apart,\\nsupporting the rails by stringers in the usual way, the special\\nfeature of this construction being that the embankments are\\nfilled in behind the trestle bents, and the thrust of the embank-\\nments is mutually taken up through the stringers, which are\\nnotched at the ends or otherwise constructed so that they may\\ntake up such a thrust. The designs for old-rail culverts and\\narch culverts are also utilized for cattle-passes when suitable and\\nconvenient, as well as the designs illustrated in the following\\nsection.\\n195. Standard stringer and I-beam bridges. The advantages\\nof standard designs apply even to the covering of short spans\\nwith wooden stringers or with I beams especially since\\nthe methods do not require much vertical space between the\\nrails and the upper side of the clear opening, a feature which is\\noften of prime importance. These designs are chiefly used for\\nculverts or cattle-passes and for crossing over highways pro-\\nviding such a narrow opening would be tolerated. The plans\\nall imply stone abutments, or at least abutments of sufficient\\nstability to withstand all thrust of the embankments. Some of\\nthe designs are illustrated in Plate XVI. The preparation of\\nthese standard desii^ns should be attacked bv the same oreneral\\nmethods as already illustrated in 156. When computing the\\nrequired transverse strength, due allowance should be made for\\nlateral bracing, which should be amply provided for. Xote\\nparticularly the methods of bracing illustrated in Plate XYI.\\nThe designs calling for iron (or steel) stringers may be classed\\nas permanent constructions, which are cheap, sate, easily in-\\nspected and maintained and therefore a desirable method of\\nconstruction.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0267.jp2"}, "268": {"fulltext": "CHAPTER YII.\\nBALLAST.\\n196. Purpose and requirements. The object of the ballast\\nis to transfer the applied load over a large surface to hold the\\ntimber work in place horizontally to carry off the rain-water\\nfrom the superstructure and to prevent freezing up in winter\\nto afford means of keeping the ties truly up to the grade line\\nand to give elasticity to the roadbed. This extremely con-\\ndensed statement is a description of an ideally perfect ballast.\\nThe value of any given kind of ballast is proportional to the\\nextent to which it fulfills these requirements. The ideally per-\\nfect ballast is not necessarily the most economical ballast for all\\nroads. Light traffic generally justifies something cheaper, but\\na very common error is to use a very cheap ballast when a small\\nadditional expenditure would procure a much better ballast\\nwhich would be much more economical in the long run.\\n197. Materials. The materials most commonly employed are\\ngravel and broken stone. Burnt clay, cinders, shells, and small\\ncoal are occasionally used as ballast when they are especially\\ncheap and convenient or when better kinds are especially expen-\\nsive. Although it is hardly correct to speak of the natural soil\\nas ballast, yet many miles of cheap railways are ballasted\\nwith the natural soil, which is then called mud ballast.\\nMud ballast. When the natural soil is gravelly so that rain\\nwill drain through it quickly, it will make a fair roadbed for\\nlight traffic, but for heavy traffic, and for the greater part of the\\nlength of most roads, the natural soil is a very poor material for\\nballast for, no matter how suitable the soil might be along\\n220", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0268.jp2"}, "269": {"fulltext": "197. BALLAST. 221\\nlimited sections of the road, it would practically never liappen\\nthat the soil would be uniformly good throughout the whole\\nlength of the road. Considering that a heavy rain will in one\\nday spoil the results of weeks of patient surfacing with mud\\nballast, it is seldom economical to use mud if there is a\\ngravel-bed or other source of ballast anywhere on the line of\\nthe road.\\nCinders. Tlie advantages consist in the excellent facilities\\nfor drainage, ease of handling, and cheapness after the road is\\nin operation. One disadvantage is excessive dust in dry weather.\\nCinders are considered preferable to gravel in yards.\\nSlag. When slag is readily obtainable it furnishes an ex-\\ncellent ballast, free from dust and perfect in drainage qualities.\\nSome kinds of slag are objectionable on account of their delete-\\nrious chemical effect on the ties and spikes especially on\\nmetallic ties.\\nShells, small coal, etc. These comparatively inferior kinds\\nof ballast are used for light traffic when they are especially cheap\\nand convenient. They are extremely dusty in dry weather,\\nbreak up into very fine dust, and are but little better than mud.\\nGravel. This is the most common form of ballast which\\nmay be called good ballast. In 1885, the Roadmasters Associa-\\ntion of America voted in favor of gravel ballast as against rock\\nballast. Although not so stated, this action was perhaps due to\\na conviction of its real economy for the average railroad of this\\ncountry, which may be called a light traffic road. Gravel\\nshould preferably be screened over a screen having a mesh,\\nso as to screen out all dirt and the finest stones. Generally a\\nrailroad will be able to find at some point along its line a\\ngravel-pit affording a suitable supply. This may be dug out\\nwith a steam-shovel, screened if necessary, and sent out over\\nthe line by the train-load at a comparatively small cost.\\nRock or broken stone. Ruck ballast is generally specified to\\nbe such as will pass through a (or 2 ring. Although pref-\\nerably broken by hand, machine-broken stone is much cheaper.\\nIt is most easily handled with forks. This also has the effect of", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0269.jp2"}, "270": {"fulltext": "222 RAILROAD CONSTRUCTION. 198.\\nscreening out tlie dirt and fine chips which would interfere with\\neliectual drainage. Rock ballast is more expensive in first cost,\\nand also more troublesome to handle, than any other kind, but\\nunder heavy trafiic will keep in surface better and will require\\nless work for maintenance after the ties have become thoroughly\\nbedded. For roads with very light traffic, running few trains,\\nat comparatively low velocities, the advantages of rock ballast\\nover other kinds are not so pronounced. For such roads rock\\nballast is an expensive luxury. The amount of trafi^ic which\\nwill justify the use of rock ballast will depend on the cost of\\nobtaining ballast of the various kinds.\\n198. Cross-sections. A depth of 12 under the tie is gener-\\nally required on the best roads, but for light trafiic this is some-\\ntimes reduced to Q and even less. The width is generally 1 to\\n2 feet less than the wddth of the roadbed proper excluding\\nditches. If the ballast has an average width of 10 feet (12 feet\\nat bottom and 8 feet at top) and an average depth of 15 inches\\n(including that placed between the ties), it will require 2144\\ncubic yards per mile of track. The P. R.R. estimates 2500\\ncubic yards of gravel and 2800 cubic yards of stone ballast per\\nmile of single track. On account of the requirements of drain-\\nage the best form of cross-section depends on the kind of ballast\\nused.\\nMud ballast. Since the great objection to mud ballast lies in\\nits liability to become soft by soaking up the rain that falls, it\\nbecomes necessary that it should be drained as quickly and\\nreadily as its nature will permit. Fig. 106 shows a typical\\nFig. OP.\u00e2\u0080\u0094 Mud Ballast.\\ncross-section for mud ballast. It should be crowned 2 above\\nthe top of the tie at the center, thence sloped so as to leave a\\nslight clearance under the rail between the ties, thence sloping\\ndown to the bottom of the tie at each end and continuing to", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0270.jp2"}, "271": {"fulltext": "\u00c2\u00a7199.\\nBALLAST.\\n223\\nslope down to the ditcli (in cut), wliicli should be 18 or 20 be-\\nlow the bottom of the tie.\\nGravel, cinders, slag, etc. The subgrade is crowned 6 or\\n8 in the center, as shown in Fig. 107. The ballast is crowned\\nFig. 107.\u00e2\u0080\u0094 Gravel Ballast.\\nto the top of the tie in the center, but is sloped down to the\\nbottom of the tie at each end. This is necessary (and more\\nespecially so with mud ballast) to prevent a possible accumula-\\ntion and settlement of water at the ends of the tie, which would\\nreadily soak into the end fibers and produce decay.\\nBroken stone. Stone ballast is shouldered out beyond the\\nends of the ties so as to aiford greater lateral binding. The\\nspace betAveen the ties is filled up level with the tops. The\\nFig. 108.\u00e2\u0080\u0094 Broken Stone Bali^ast.\\nperfect drainage of stone ballast permits this to be done w^ithout\\nany danger of causing decay of the ties by the accumulation and\\nretention of water.\\n199. Methods of laying ballast. The cheapest method of\\nlaying ballast on new roads is to lay ties and rails directly on\\nthe prepared subgrade and run a construction train over the\\ntrack to distribute the ballast. Then the track is lifted up until\\nsufficient ballast is worked under the ties and the track is prop-\\nerly surfaced. This method, although cheap, is apt to injure\\nthe rails by causing bends and kinks, due to the passage of\\nloaded construction trains when the ties are very unevenly and\\nroughly supported, and the method is therefore condemned and\\nprohibited in some specifications. The best method is to draw", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0271.jp2"}, "272": {"fulltext": "224 RAILROAD CONSTRUCTION, 200.\\nill carts (or on a contractor s temporary track) the ballast that is\\nrequired under the level of the hottoin of the ties. Spread this\\nballast carefully to the required surface. Then lay the ties and\\nrails, which will then have a very fair surface and uniform sup-\\nport. A construction train can then be run on the rails and\\ndistribute sufficient additional ballast to pack around and between\\nthe ties and make the required cross-section.\\nThe necessity for constructing some lines at an absolute\\nminimum of cost and of opening them for traffic as soon as pos-\\nsible has often led to the policy of starting traffic when there is\\nlittle or no ballast perhaps nothing more than a mere tamping\\nof the natural soil under the ties. When this is done ballast\\nmay subsequently be drawn where required by the train-load on\\nflat cars and unloaded at a minimum of cost by means of a\\nplough. The plough has the same width as the cars and is\\nguided either by a ridge along the center of each car or by short\\nposts set up at the sides of the cars. It is drawn from one end\\nof the train to the other by means of a cable. The cable is\\nsometimes operated by means of a small hoisting-engine carried\\non a car at one end of the train. Sometimes the locomotive is\\ndetached temporarily from the train and is run ahead with the\\ncable attached to it.\\n200. Cost. The cost of ballast in the trade is quite a variable\\nitem for different roads, since it depends (a) on the first cost of\\nthe material as it comes to the road, (h) on the distance from\\nthe source of supply to the place where it is used, and {c) on\\nthe method of handling. The first cost of cinder or slag is\\nfrequently insignificant. A gravel-pit may cost nothing except\\nthe price of a little additional land beyond the usual limits of the\\nright of way. Broken stone will usually cost $1 or more per\\ncubic yard. If suitable stone is obtainable on the company s\\nland, the cost of blasting and breaking should be somewhat less\\nthan this. The cost of loading the ballast on to trains will be\\nsmall (per cubic yard) if it is handled with steam-shovels as in\\nthe case of gravel taken from a gravehpit. Hand-shovelling\\nwill cost more. The cost of hauling will depend on the distance", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0272.jp2"}, "273": {"fulltext": "200 BALLAST, 225\\nhauled, and also, to a considerable extent, on the limitations on\\nthe operation of the train due to the necessity of keeping out of\\nthe way of regular trains. There is often a needless waste in\\nthis way. The mud train is considered a pariah and entitled\\nto no rights whatever, regardless of the large daily cost of such\\na train and of the necessary gang of men. The cost of broken\\nstone ballast m the track is estimated at $1.25 per cubic yard.\\nThe cost of gravel ballast is estimated at 60 c. per cubic yard\\nin the track. The cost of placing and tamping gravel ballast is\\nestimated at 20 c. to 24 c. per cubic yard, for cinders 12 c. to\\n15 c. per cubic yard. The cost of loading gravel on cars, usintr\\na steam-shovel, is estimated at 6 c. to 10 c. per cubic yard.^\\nReport Roadmasters Association, 1885.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0273.jp2"}, "274": {"fulltext": "CHAPTER YIII.\\nTIES,\\nAND OTHER FORMS OF RAIL SUPPORT.\\n201. Various methods of supporting rails. It is necessary\\nthat the rails shall be sufficiently supported and braced, so that\\nthe gauge shall be kept constant and that the rails shall not be\\nsubjected to excessive transverse stress. It is also preferable\\nthat the rail support shall be neither rigid (as if on solid rock)\\nnor too yielding, but shall have a uniform elasticity throughout.\\nThese requirements are more or less fulfilled by the following\\nmethods.\\n(a) Longitudinals. Supporting the rails throughout their\\nentire length. This method is very seldom used in this country\\nexcept occasionally on bridges and in terminals when the\\nlongitudinals are supported on cross- ties. In 224: will be\\ndescribed a system of rails, used to some extent in Europe,\\nhaving such broad bases that they are self-supporting on the\\nballast and are only connected by tie-rods to maintain the\\ngauge.\\n(b) Cast-iron bowls or pots. These are castings resem-\\nbling large inverted bowls or pots, having suitable chairs on\\ntop for holding and supporting the rails, and tied together\\nwith tie-rods. They will be described more fully later 223).\\n(b) Cross-ties of metal or wood. These will be discussed in\\nthe following sections.\\n202. Economics of ties. The true cost of ties depends on the\\nrelative total cost of maintenance for long periods of time. The\\nfirst cost of the ties delivered to the road is but one item in the\\n226", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0274.jp2"}, "275": {"fulltext": "203. TIES. 227\\neconomics of tlie question. Clieap ties require fre(|uent renew-\\nals, whicli cost for the lahor of each renewal practically the\\nsame whether the tie is of oak or hemlock. Clieap ties make a\\npoor roadbed which will require more track labor to keep even\\nin tolerable condition. The roadbed will require to be disturbed\\nso frequently on account of renewals that the ties never get an\\nopportunity to get settled and to form a smooth roadbed for any\\nlength of time. Irregularity in width, thickness, or length of\\nties is especially detrimental in causing the ballast to act\\nand wear unevenly. The life of ties has thus a more or less\\ndirect influence on the life of the rails, on the wear of rollinof\\nstock, and on the speed of trains. _/ These last items are not so\\nreadily reducible to dollars and cents, but when it can be shown\\nthat the total cost, for a long period of time, of several renewals\\nof cheap ties, with all the extra track labor involved, is as great as\\nor greater than that of a few renewals of durable ties, then there\\nis no question as to the real economy. In the following dis-\\ncussions of the mei-its of untreated ties (either cheap or costly),\\nchemically treated ties, or metal ties, the true question is there-\\nfore of the ultimate cost of maintaining any particular kind of\\nties for an indefinite period, the cost including the flrst cost of\\nthe ties, the labor of placing them and maintaining them to\\nsurface, and the somewhat uncertain (but not therefore non-\\nexistent) effect of frequent renewals on repairs of rolling stock,\\non possible speed, etc.\\nWOODEN TIES.\\n203. Choice of wood. This naturally depends, for any partic-\\nular section of country, on the supply of wood wliicli is most\\nreadily available. The woods most commonly used, especially\\nin this country, are oak and pine, oak being the most durable\\nand generally the most expensive. Kedwood is used very ex-\\ntensively in California and proves to be extremely durable, so\\nfar as decay is concerned, but it is very soft and is much injured\\nby rail-cutting. This defect is being partly remedied by the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0275.jp2"}, "276": {"fulltext": "228 RAILROAD CONSTRUCTION. 204.\\nuse of tie-plates, as will be explained later. Cedar, chestnut,\\nliemlock, and tamarack are frequently used in this country, In\\ntropical countries very durable ties are frequently obtained from\\nthe hard woods peculiar to those countries. According to a re-\\ncent bulletin of tlie U. S. Department of Agriculture the pro-\\nportions of the various kinds used in the United States are about\\nas follows\\nOak 60^\\nPine 20\\nCedar 6\\nChestnut 5j\\nHemlock and Tama-\\nrack 3\\nRedwood 3\\nCypress 2%\\nVarious 1\\nTotal 100^\\n204. Durability. The durability of ties depends on the cli-\\nmate the drainage of the ballast the volume, weight, and\\nspeed of the traffic the curvature, if any the use of tie-plates\\nthe time of year of cutting the timber the age of the timber\\nand the degree of its seasoning before placing in the track the\\nnature of the soil in which the timber was grown; and, chiefly,\\non the species of wood employed. The variability in these\\nitems will account for the discrepancies in the reports on the life\\nof various woods used for ties.\\nWhite oak is credited with a life of 5 to 12 years, depending\\nprincipally on the traffic. Is is both hard and durable, the\\nhardness enabling it to withstand the cutting tendency of the\\nrail-flanges, and the durability enabling it to resist decay. Pine\\nand redwood resist decay very well, but are so soft that they are\\nbadly cut by the rail-flanges and do not hold the spikes very\\nwell, necessitating frequent respiking. Since the spikes must\\nbe driven within certain very limited areas on the face of each\\ntie, it does not require many spike-holes to spike-kill the\\ntie. On sharp curves, especially with heavy traffic, the vdieel-\\nflange pressure produces a side pressure on the rail tending to\\noverturn it, which tendency is resisted by the spike, aided some-\\ntimes by rail-braces. Whenever the pressure becomes too great\\nthe spike will yield somewhat and will be slightly withdrawn.\\nThe resistance is then somewhat less and the spike is soon so loose\\nthat it must be redriven in a new hole. If this occurs very", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0276.jp2"}, "277": {"fulltext": "\u00c2\u00a7206. TIES. 229\\noften, the tie may need to be replaced long before any decay has\\nset in. When the traffic is v^ery light, the wood very durable,\\nand the climate favorable ties have been known to last 25 years.\\n205. Dimensions. The usual dimensions for the best roads\\n(standard gauge) are 8 to 8 6 long, 6 to 7 thick, and 8 to\\n10 wide on top and bottom (if they are hewed) or 8 to 9\\nwide if they are sawed. For cheap roads and light traffic the\\nlength is shortened sometimes to 7 and the cross-section also re-\\nduced. On the other hand a very few roads use ties 9 long.\\nTwo objections are urged against sawed ties first, that the\\ngrain is torn by the saw, leaving a woolly surface which induces\\ndecay and secondly, that, since timber is not perfectly straight-\\ngrained, some of the fibers are cut obliquely, exposing their ends,\\nwhich are thus liable to decay. The use of a planer-saw ob-\\nviates the first difficulty. Chemical treatment of ties obviates\\nboth of these difficulties. Sawed ties are more convenient to\\nhandle, are a necessity on bridges and trestles, and it is even,\\nclahned, although against connnonly received opinion, that\\nactual trial has demonstrated that they are more durable than\\nhewed ties.\\n206. Spacing. The spacing is usually 14 to 16 ties to a 30-\\nfoot rail. This number is sometimes reduced to 12 and even\\n10, and on the other hand occasionally increased to 18 or 20 by\\nemploying narrower ties. There is no economy in reducing the\\nnumber of ties very nuich, since for any required stiffness of\\ntrack it is more economical to increase the number of supports than\\nto increase the weight of the rail. The decreasinir cost of rails\\nand the increasing cost of ties have materially changed the rela-\\ntion between number of ties and weight of rail to produce a\\ngiven stiffness at minimum cost, but many roads have found it\\neconomical to employ a large number of ties rather than increase\\nthe weight of the rail. On the other hand there is a practical\\nlimit to the number that may be employed, on account of the\\nnecessary space between the ties that is required for proper\\ntamping. This width is ordinarily about twice the width of the\\ntie. At this rate, with light ties 6 wide and with 12^ clear", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0277.jp2"}, "278": {"fulltext": "230 RAILROAD CONSTRUCTION. 207.\\nspace, there would be 20 ties per 30-foot rail, or 3520 per mile.\\nThe smaller ties can generally be bought much cheaper (propor-\\ntionately) than the larger sizes, and hence the economy.\\nTrack instructions to foremen generally require that the\\nspacing of ties shall 7iot be uniform along the lengtli of any\\nrail. Since the joint is generally the weakest part of the rail\\nstructure, the joint requires more support than the center of the\\nrail. Therefore the ties are placed with but 8 or 10 clear\\nspace between them at the joints, this applying to 3 or 4 ties at\\neach joint the remaining ties, required for each rail length, are\\nequally spaced along the remaining distance.\\n207. Specifications. The specifications for ties are apt to\\ninclude the items of size, kind of wood, and method of con-\\nstruction, besides other minor directions about time of cutting,\\nseasoning, delivery, quality of timber, etc.\\n(a) Size. The particular size or sizes required will be some-\\nwhat as indicated in 205.\\n(b) Kind of wood. When the kind or kinds of wood are spe-\\ncified, the most suitable kinds that are available in that section\\nof country are usually required.\\n(c) Method of construction. It is generally specified that the\\nties shall be hewed on two sides; that the two faces thus made\\nshall be parallel planes and that the bark shall be removed. It\\nis sometimes required that the ends shall be sawed off square\\nthat the timber shall be cut in the w^inter (when the sap is down)\\nand that the ties shall be seasoned for six months. These last\\nspecifications are not required or lived up to as much as their\\nimportance deserves. It is sometimes required that the ties shall\\nbe delivered on the right of way, neatly piled in rows, the alter-\\nnate rows at right angles, piled if possible on ground not lower\\nthan the rails and at least seven feet away from them, the lower\\nrow of ties resting on two ties which are themselves supported\\nso as to be clear of the ground.\\n(d) Q,uality of timber. The usual specifications for sound\\ntimber are required, except that they are not so rigid as for a\\nbetter class of timber work. The ties must be sound, reason-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0278.jp2"}, "279": {"fulltext": "208. TIES. 231\\nably straight-grained, and not very crooked one test being that\\na hne joining the center of one end with the center of the middle\\nshall not pass outside of the other end. Splits or shakes, espe-\\nciallj if severe, should cause rejection.\\nSpecifications sometimes require that the ties shall be cut\\nfrom single trees, making what is known as pole ties and\\ndefinitely condemnino: those which ____\u00e2\u0080\u009e _____\\nare cut or split from larger trunks, 1\\ngiving two slab ties or four 3,,,,,,. quartert,.\\nquarter ties for each cross- Fig. 109.\u00e2\u0080\u0094 Methods of cutting\\nsection, as is illustrated in Fig. Ties.\\n109. Even if pole ties are better, their exclusive use means the\\nrapid destruction of forests of young trees.\\n208. Regulations for laying and renewing ties. The regula-\\ntions issued by railroad companies to their track foremen will\\ngenerally include the following, in addition to directions regard-\\ning dimensions, spacing, and specifications given in 20t1:-207.\\nWhen hewn ties of somewhat variable size are used, as is fre-\\nquently the case, the largest and best are to be selected for use\\nas joint ties. If the upper surface of a tie is found to be warped\\n(contrary to the usual specifications) so that one or both rails do\\nnot get a full bearing across the wdiole width of the tie, it must\\nbe adzed to a true surface along its whole length and not merely\\nnotched for a rail-seat. AYhen respiking is necessary and spikes\\nhave been pulled out, the holes should be immediately plutrged\\nwith wooden spikes, which are supplied to the foremen for\\nthat express purpose, so as to fill up the holes and prevent the\\ndecay which would otherwise take place when the hole becomes\\nfilled wdth rain-water. Ties sliould always be laid at right angles\\nto the rails and never obliquely. Minute regulations to prevent\\npremature rejection and renewal of ties are frequently made. It\\nis generally required that the requisitions for renewals shall be\\nmade by the actual count of the individual ties to be renewed\\ninstead of l)y any wholesale estimates. It is unwise to have ties\\nof widely variable size, hardness, or durability adjacent to each", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0279.jp2"}, "280": {"fulltext": "232 BAILROAB CONSTRUCTION. 209.\\nother in the track, for the uniform elasticity, so necessary for\\nsmooth riding, will be unobtainable under those circumstances.\\n209. Cost of ties. When railroads can obtain ties cut by\\nfarmers from woodlands in the immediate neighborhood, the\\nprice will frequently be as low as 20 c. for the smaller sizes,\\nrunning up to 50 c. for the larger sizes and better qualities, espe-\\ncially when the timber is not very plentiful. Sometimes if a\\nrailroad cannot procure suitable ties from its immediate neigh-\\nborhood, it will find that adjacent railroads control all adjacent\\nsources of supply for their own use and that ties can only be\\nprocured from a considerable distance, with a considerable added\\ncost for transportation. First-class oak ties cost about 75 to 80 c.\\nand frequently much more. Hemlock ties can generally be\\nobtained for 35 c. or less.\\nPKESERVATIVE PROCESSES FOR WOODEN TIES.\\n210. General principle. Wood has a fibrous cellular struc-\\nture, the cells being filled with sap or air. The woody fiber is\\nbut little subject to decay unless the sap undergoes fermentation.\\nPreservative processes generally aim at removing as much of the\\nw^ater and sap as possible and filling up the pores of the wood\\nwith an antiseptic compound. The most common methods (ex-\\ncept one) all agree in this general process and only differ in the\\nmethod employed to get rid of the sap and in the antiseptic\\nchemical with which the fibers are filled. One valuable feature\\nof these processes lies in the fact that the softer cheaper woods\\n(such as hemlock and pine) are more readily treated than are the\\nharder woods and yet will produce practically as good a tie as a\\ntreated hard-wood tie and a very much better tie than an un-\\ntreated hard -wood tie. The various processes will be briefly\\ndescribed, taking up first the process which is fundamentally\\ndifferent from the others, viz., vulcanizing.\\n211. Vulcanizing. The process consists in heating the timber\\nto a temperature of 300\u00c2\u00b0 to 500\u00c2\u00b0 F. in a cylinder, the air being\\nunder a pressure of 100 to 175 lbs. per square inch. By this\\nprocess the albumen in the sap is coagulated, the water evap-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0280.jp2"}, "281": {"fulltext": "21-2. TIES. 233\\norated, and the pores are partially closed by the coagulation of\\nthe albumen. It is claimed that the heat sterilizes the wood and\\nproduces chemical changes in the wood which give it an antisep-\\ntic character. It has been very extensively used on the elevated\\nlines of New York City, and it is claimed to give perfect satis-\\nfaction. The treatment has cost that road 25 c. ])cr tie.\\n212. Creosoting. This process consists in impregnating the\\nwood with toood-creosote or with dead oil of coal-tar. Wood-\\ncreosote is one of the products of the destructive distillation of\\nwood usually long-leaf pine. Dead oil of cocd-tar is a prod-\\nuct of the distillation of coal-tar at a temperature between 480\u00c2\u00b0\\nand 760\u00c2\u00b0 F. It would require about 35 to 50 pounds of creo-\\nsote to completely till the pores of a cubic foot of w^ood. But\\nit would be impossible to force such an amount into the wood,\\nnor is it necessary or desirable. About 10 pounds per cubic\\nfoot, or about 35 pounds per tie, is all that is necessary. For\\npiling placed in salt water about 18 to 20 pounds per cubic foot\\nis used, and the timber is then perfectly protected against the\\nravages of the teredo navcdis. To do the work, long cylinders,\\nwhich may be opened at the ends, are necessary. Usually the\\ntimbers are run in and out on iron carriaii:es runninof on rails\\nfastened to braces on the inside of the cylinder. AVhen the load\\nhas been run in, the ends of the cylinder are fastened on. The\\nwater and air in the pores of the wood are first drawn out by\\nsubjecting the wood alternately to steam-pressure and to the\\naction of a vacuum-pump. This is continued for several hours.\\nThen, after one of the vacuum 23eriods, the cylinder is filled\\nwith creosote oil at a temperature of about 170\u00c2\u00b0 F. The pumps\\nare kept at work until the pressure is about 80 to 100 pounds\\nper square inch, and is maintained at this pressure from one to\\ntwo hours according to the size of the timber. The oil is then\\nwithdrawn, the cylinders opened, the train pulled out and an-\\nother load made up in 40 to 60 minutes. The average time re-\\nquired for treating a load is about 18 or 20 hours, the absorption\\nabout 10 or 11 pounds of oil per cubic foot, and the cost (1894)\\nfrom $12.50 to 814.50 per thousand feet B. M.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0281.jp2"}, "282": {"fulltext": "234 RAILROAD CONSTRUCTION. \u00c2\u00a7213.\\n213. Burnettizing (chloride -of -zinc process). This process is\\nvery similar to the creosotiiig process except that the chemical is\\nchloride of zinc, and that tlie chemical is not heated before use.\\nThe preliminary treatment of the wood to alternate vacuum and\\npressure is not continued for quite so long a period as in the\\ncreosoting process. Care must be taken, in using this process,\\nthat the ties are of as uniform quality as possible, for seasoned\\nties will absorb much more zinc chloride than unseasoned (in the\\nsame time), and the product will lack uniformity unless the sea-\\nsoning is uniform. The A., T. S. Fe K.R. has works of its\\nown at which ties are treated by this process at a cost of about\\n25 c. per tie. The Southern Pacific R.R. also has works for\\nburnettizing ties at a cost of 9.5 to 12 c. per tie. The zinc-\\nchloride solution used in these works contains only 1.7^ of zinc\\nchloride instead of over 3^ as used in the Santa Fe works, which\\nperhaps accounts partially for the great difference in cost per tie.\\nOne great objection to burnettized ties is the fact that the chem-\\nical is somewhat easily washed out, when the wood again be-\\ncomes subject to decay. Another objection, which is more\\nforcible with respect to timber subject to great stresses, as in\\ntrestles, than to ties, is the fact that when the solution of zinc\\nchloride is made strong (over 3^) the timber is made very brittle\\nand its strength is reduced. The reduction in strength has been\\nshown by tests to amount to J to of the ultimate strength,\\nand that the elastic limit has been reduced by about\\n214. Kyanizing (bichloride-of-mercury or corrosive-sublimate\\nprocess) This is a process of steeping. It requires a much\\nlonger time than the previously described processes, but does not\\nrequire such an expensive plant. Wooden tanks of sufficient\\nsize for the timber are all that is necessary. The corrosive subli-\\nmate is first made into a concentrated solution of one part of\\nchemical to six parts of hot water. When used in the tanks this\\nsolution is weakened to 1 part in 100 or 150. The wood will\\nabsorb about 5 to 6.5 pounds of the bichloride per 100 cubic\\nfeet, or about one pound for each 4 to ties. The timber is\\nallowed to soak in the tanks for several days, the general rule", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0282.jp2"}, "283": {"fulltext": "215. TIES. 235\\nbeing about one day for each inch of least thickness and one day\\nover wliich means seven days for six-inch ties, or thirteen (to\\nfifteen) days for 1 2 timber (least dimension). The process is\\nsomewhat objectionable on account of the chemical being such a\\nvirulent poison, workmen sometimes being sickened by the fumes\\narising from the tanks. On the Baden railway (Germany)\\nkyanized ties last 20 to 30 years. On this railway the wood is\\nalways air-dried for two weeks after impregnation and before\\nbeing used, which is thought to have an important effect on its\\ndurability. The solubility of the chemical and the liability of\\nthe chemical washing out and leaving the wood unprotected is\\nan element of weakness in the method.\\n215. Wellhouse (or zinc-tannin) process. The last two\\nmethods described (as well as some others employing siinilar\\nchemicals) are open to the objection that since the wood is im-\\npregnated with an aqueous solution, it is liable to be washed out\\nvery rapidly if the wood is placed under water, and will even\\ndisappear, although more slowly, under the action of moisture\\nand rain. Several processes have been proposed or patented to\\nprevent this. Many of them belong to one class, of which the\\nWellhouse process is a sample. By these processes the timber\\nis successively subjected to the action of two chemicals, each\\nindividually soluble in water, and hence readily impregnating\\nthe timber, but the chemicals when brought in contact form in-\\nsoluble compounds which cannot be washed out of the w^ood-\\ncells. By the Wellhouse process, the wood is first impregnated\\nwith a solution of chloride of zinc and glue, and is then subjected\\nto a bath of tannin under pressure. The glue and tannin com-\\nbine to form an insoluble leathery compound in the cells, wliich\\nwill prevent the zinc chloride from being washed out. It is\\nbeing used by the A., T. k S. Fe E,.R., their works being\\nlocated at Las Yegas, New Mexico, and also by the Union\\nPacific E.B. at their works at Laramie, Wyo. In 1897 Mr.\\nM. Meade, a resident engineer on the A., T. tfe S. Fe, exhibited\\nto the Road masters Association of America a piece of a tie treated\\nby this process which had been taken from the tracks after", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0283.jp2"}, "284": {"fulltext": "236 RAILROAD CONSTRUCTION. 216.\\nnearly 13 years service. Tlie tie was selected at random, was\\ntaken out for the sole purpose of having a specimen, and Avas\\nstiii in sound condition and capable of serving many years longer.\\nThe cost of the treatment was then quoted as 13 c. per tie.\\nIt was claimed that the treatment trebled the life of the tie\\nbesides adding to its spike-holding power.\\n216. Cost of treating. The cost of treating ties by the vari-\\nous methods has been estimated as follows assuming that\\nthe plant was of sufficient papacity to do the work economi-\\ncally creosoting, 25 c. per tie; vulcanizing, 25 c. per tie;\\nburnettizing (chloride of zinc), 8.25 c. per tie kyanizing\\n(steeping in corrosive sublimate), 14.6 c. per tie; Wellhouse\\nprocess (chloride of zinc and tannin), 11.25 c. per tie. These\\nestimates are only for the net cost at the works and do not\\ninclude the cost of hauling the ties to and from the works, which\\nmay mean 5 to 10 c. per tie. Some of these processes have\\nbeen installed on cars which are transported over the road and\\noperated where most convenient.\\n217. Economics of treated ties. The fact that treated ties are\\nnot universally adopted is due to the argument that the added\\nlife of the tie is not worth the extra cost. If ties can be bought\\nfor 25 c, and cost 25 c. for treatment, and the treatment\\nonlv doubles their life, there is apparently but little gained\\nexcept the work of placing the extra tie in the track, which is\\nmore or less offset by the interest on 25 c. for the life of the\\nuntreated tie, and the larger initial outlay makes a stronger im-\\npression on the mind than the computed ultimate economy.\\nBut when ties cost 75 c. and treatment costs only 25 c,\\nor perhaps less, then the economy is more apparent and un-\\nquestionable. But this analysis may be made more closely.\\nAs shown in 202, the disturbance of the roadbed on account\\nof frequent renewals of untreated ties is a disadvantage which\\nwould justify an appreciable expenditure to avoid, although it is\\n*Bull. No. 9, U. S. Dept. of Agric, Div. of Forestry. App. No. 1, hj\\nHenry Flad.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0284.jp2"}, "285": {"fulltext": "217. TIKS. 237\\nvery difficult to closely estiuicate its true value. The annual cost\\nof a system of ties may be considered as the sum of {a) the\\ninterest on the first cost, {h) the annual sinking fund that would\\nbuy a new tie at the end of its life, and (c) the average annual\\ncost of maintenance for the life of the tie, which includes the\\ncost of laying and the considerable amount of subsequent tamp-\\ninoj that must be done until the tie is fairlv settled in the road-\\nbed, beside the regular trackwork on the tie, which is practically\\nconstant. This last item is difficult to compute, but it is easy to\\nsee that, since the cost of laying the tie and the subsequent\\ntamping to obtain proper settlement is the same for all ties (of\\nsimilar form), the average annual charge on the longer-lived tie\\nwould be much less. In the following comparison item {e) is\\ndisregarded, simply remembering that the advantage is with the\\nlonger-lived tie.\\nUntreated tie.\\nOriginal cost 40 cents\\nLife (assumed at) 7 years\\nTreated tie.\\n65 cents\\n14 years\\nItem {a) interest on first cost 4^ 1.6 cents\\n[Jj) sinking fund 4^ 5.1\\n(c (considered here as offsetted)\\n2.6 cents\\n3.6\\nAverage annual cost (except item {c)) 6.7 cents 6.2 cents\\nOn this basis treated ties will cost 0.5 cent less per annum\\nhesides the advantage of item (c) and the still more indefinite\\nad van tastes resultinor from smoother runnino^ of trains, less wear\\nand tear on rolling stock, etc., due to less disturbance of the\\nroadbed.\\nIn Europe, where wood is expensive, untreated ties are\\nseldom used, as the treatment is always considered to be worth\\nmore than it costs. The rapid destruction of the forests of tim-\\nber in this country is having the effect of increasing the price, so\\nthat it will not be long before treated ties (or metal ties) will be\\neconomical for a large majority of the railroads of the country.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0285.jp2"}, "286": {"fulltext": "22S RAILROAD CONSTRUCTION. 218.\\nMETAL TIES.\\n218. Extent of use. In 1894 there were nearly 35000 miles\\nof metal track in various parts of the world. Of this total,\\nthere were 3645 miles of longitudinals (see 224), found ex-\\nclusively in Europe, nearly all of it being in Germany. There\\nwere over 12000 miles of bowls and plates (see 223), found\\nalmost entirely in British India and in the Argentine Republic.\\nThe remainder, over 18000 miles, was laid with metal cross-ties\\nof various designs. There were over 8000 miles of metal cross-\\nties in Germany alone, about 1500 miles in the rest of Europe\\nover 6000 miles in British India, nearly 1000 miles in the rest\\nof Asia, and about 1500 miles more in various other parts of the\\nworld. Several railroads in this country have tried various de-\\nsigns of these ties, but their use has never passed the experi-\\nmental stage. These 35000 miles represent about 9^ of the\\ntotal railroad mileage of the world nearly 400000 miles. They\\nrepresent about 17.6^ of the total railroad mileage, exclusive of\\nthe United States and Canada, where they are not used at all\\nexcept experimentally. In the four years from 1890 to 1894 the\\nuse of metal track increased from less than 25000 miles to neai-ly\\n35000 miles. This increase was practically equal to the total in-\\ncrease in railroad mileage during that time, exclusive of the in-\\ncrease in the United States and Canada. This indicates a laro-e\\ngrowth in the percentage of metal track to total mileage, and\\ntherefore an increased appreciation of the advantages to be de-\\nrived from their use.\\n219. Durability. The durability of metal track is still far\\nfrom being a settled question, due largely to the fact that the\\nbest form for such track is not yet determined, and that a large\\npart of the apparent failures in metal track have been evidently\\ndue to defective design. Those in favor of them estimate the\\nlife as from 30 to 50 years. The opponents place it as not more\\nthan 20 years, or perhaps as long as the best of wooden ties.\\nBulletin No. 9, U. S. Dept. of Agriculture, Div. of Forestry.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0286.jp2"}, "287": {"fulltext": "220. TIES. 239\\nUnlike the wooden tie, however, whicli deteriorates as mueh\\nwith time as with usage, the life of a metal tie is more largely a\\nfunction of the trafhc. The life of a well-designed metal tie has\\nbeen estimated at 150000 to 200000 trains; for 20 trains per\\nday, or say 6000 per year, this would mean from 25 to 33 years.\\n20 trains per day on a single track is a much larger number than\\nwill be found on the majority of railroads. Metal ties are found\\nto be subject to rust, especially when in damp localities, such as\\ntunnels; but on the other hand it is in such confined localities,\\nwhere renewals are troublesome, that it is especially desirable to\\nemploy the best and longest-liv^ed ties. Faint, tar, etc., have\\nbeen tried as a protection against rust, but the efficacy of such\\nprotection is as yet uncertain, the conditions preventing any re-\\nnewal of the protection such as may be done by repainting a\\nbridge, for example. Failures in metal cross-ties have been\\nlargely due to cracks which begin at a corner of one of the square\\nholes which are generally punched through the tie, the holes\\nbeing. made for the bolts by whicli the rails are fastened to the\\ntie. The holes are generally punched because it is cheaper.\\nHeaming the holes after punching is thought to be a safeguard\\nagainst this frequent cause of failure. Another method is to\\nround the corners of the square punch with a radius of about\\n1- If a crack has already started, the spread of the crack may\\nbe prevented by drilling a small hole at the end of it.\\n220. Form and dimensions of metal cross-ties. Since stability\\nin the ballast is an essential quality for a tie, this must be accom-\\nplished either by turning down the end of the tie or by having\\nsome form of lug extending downward from one or more points\\nof the tie. The ties are sometimes depressed in the center (see\\nFlate XYII, IS Y. C. H. R. R.R. tie) to allow for a thick\\ncovering of ballast on top in order to increase its stability in the\\nballast. This form requires that the ties should be sufficiently\\nwell tamped to prevent a tendency to bend out straight, thus\\nwidening the gauge. Many designs of ties are objection-\\nable because they cannot be ])laced in the track without\\ndisturbing adjacent ties. The failure of many metal cross-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0287.jp2"}, "288": {"fulltext": "240 RAILROAD CONSTRUCTION. 221.\\nties, otherwise of good design, may be ascribed to too light\\nweight. Those weighing nmch less than 100 pounds have\\nproved too light. From 100 to 130 pounds weight is being used\\nsatisfactorily on German railroads. Tlie general outside dimen-\\nsions are about the same as for wooden ties, except as to thick-\\nness. The metal is generally from J to f thick. They are,\\nof course, only made of wrought iron or steel, cast iron being\\nused only for bowls or plates (see 213). The details\\nof construction of some of the most commonly used ties may be\\nseen by a study of Plate XVII.\\n221. Fastenings. The devices for fastening the rails to the\\nties should be such that the gauge may be widened if desired on\\ncurves, also that the gauge can be made true regardless of slight\\ninaccuracies in the manufacture of the ties, and also that shims\\nmay be placed under the rail if necessary during cold weather\\nwhen the tie is frozen into the ballast and cannot be easily\\ndisturbed. Some methods of fastening require that the base of\\nthe rail be placed against a lug which is riveted to the tie or\\nwhich forms a part of it. This has the advantage of reducing\\nthe number of pieces, but is apt to have one or more of the\\ndisadvantao^es named above. Metal kevs or wooden wedges are\\nO tJ CD\\nsometimes used, but the majority of designs employ some form\\nof bolted clamp. The form adopted for the experimental ties\\nused by the :N Y. C. H. R. E.R. (see Plate XYII) is especially\\ningenious in the method used to vary the gauge or allow for\\ninaccuracies of manufacture. Plate XYII shows some of the\\nmethods of fastening adopted on the principal types of ties.\\n222. Cost. The cost of metal cross-ties in Germany averages\\nabout 1.6 c. per pound or about $1.60 for a 100-lb. tie. The\\nties manufactured for the IST. Y. C. H. P. P.P. in 1892\\nweighed about 100 lbs. and cost $2.50 per tie, but if they had\\nbeen made in larger quantities and with the j^resent price of\\nsteel the cost would possibly have been much lower. The\\nitem of freight from the place of manufacture to the place where\\nused is no inconsiderable item of cost with some roads. Metal\\njross-ties have been used by some street railroads in this country.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0288.jp2"}, "289": {"fulltext": "PLATE XVIL\\nMetal Ties.\\n{Tofacfipnge2A(\\\\", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0289.jp2"}, "290": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0290.jp2"}, "291": {"fulltext": "224. TIES. 241\\nThose used on the Terre Haute Street Kailway weigli GO pounds\\nand cost about 06 c. for the tie, or 74 c. per tie with tlie\\nfastenings.\\n223. Bowls or plates. As mentioned before, over 12000\\nmiles of railway, chiefly in British India and in the Argentine\\nRepublic, are laid with this form of track. It consists essentially\\n\u00e2\u0096\u00a0of large cast-iron inverted bowls laid at intervals under each\\nrail and opposite each other, the opposite bowls being tied\\ntogether with tie-rods. A suitable chair is riveted or bolted on\\nto the top of each bowl so as to properly hold the rail. Being\\nmade of cast iron, they are not so subject to corrosion as steel\\nor wrought iron. They have the advantage that when old and\\nworn out their scrap value is from 60 to 80^ of their initial\\ncost, while the scrap value of a steel or wrought-iron tie is\\npractically nothing. Failure generally occurs from breakage,\\nthe failures from this cause in India being about 0.4 per cent\\nper annum. They weigh about 250 lbs. apiece and are there-\\nfore quite expensive in first cost and transportation charges.\\nThere are miles of them in India which have already lasted\\n25 years and are still in a serviceable condition. Some illustra-\\ntions of this form of tie are show^n in Plate XYII.\\n224. Longitudinals. This form, the use of which is con-\\nflned almost exclusively to Germany, is being gradually replaced\\non many lines by metal cross- ties. The system generally con-\\nsists of a compound rail of several parts, the u])per bearing rail\\nLeing very light and supported throughout its length by other\\nrails, which are suitably tied together with tie-rods so as to\\nmaintain the proper gauge, and which have a sufficiently broad\\nAltliou^li the discussion of longitudinals might be considered to belong\\nmore properly to the subject of Rails, yet the essential idea of all designs\\nmust necessarily be the support of a rail-head on which the rolling stork may\\nrun, and therefore this form, unused in this country, will be briefly described\\nhere.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0291.jp2"}, "292": {"fulltext": "242 RAILROAD construction; 224.\\nbase to be properly supported in the ballast. One great objection\\nto this method of construction is the difficulty of obtaining\\nproper drainage especially on grades, the drainage having a\\ntendency to follow along the lines of the rails.\\nThe construction is much more complicated on\\nsharp curves and at frogs and switches. An-\\n%zzzzzzz2zzi, other fundamentally different form of longi-\\nFiG. 110. tudinal is the Haarman compound self -bear-\\ning rail, having a base 12 wide and a height of 8 the\\nalternate sections breaking joints so as to form a practically\\ncontinuous rail.\\nSome of the other forms of longitudinals are illustrated in\\nPlate XYII.\\nFor a very complete discussion of the subject of metal ties,\\nsee the Report on the Substitution of Metal for AYood in\\nRailroad Ties by E. E. Russell Tratman, it being Bulletin\\n1^0. 4, Forestry Division of the U. S. Dept. of Agriculture.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0292.jp2"}, "293": {"fulltext": "CHAPTER IX.\\nRAILS.\\n225. Early forms. The first rails ever laid were wooden\\nstringers wliich were used on very short tram-roads around coal-\\nmines. As the necessity for a more durable rail increased,\\nowing chiefly to the invention of the locomotive as a motive\\npower, there were invented successively the cast-iron fish-\\nbelly rail and various forms of wrought-iron strap rails which\\nfinally developed into the T rail used in this country and the\\ndouble-lieaded rail, supported by chairs, used so extensively in\\nEngland. The cast-iron rails were cast in lengths of about 3\\nfeet and were supported in iron chairs which were sometimes\\nset upon stone piers. A great deal of the first railroad track\\nof this country was laid with longitudinal stringers of wood\\nplaced upon cross-ties, the inner edge of the stringers being\\nCAMDEN AMBOY. STEPHENSON. PEAR.\\n1832. 1338.\\nREYNOLDS\u00e2\u0080\u0094 1767.\\nFig. 111.\u00e2\u0080\u0094 Early Forms of Rails.\\nprotected by wrought-iron straps. The bridge rails were\\nfirst rolled in this country in 1844. The pear section was\\n243", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0293.jp2"}, "294": {"fulltext": "244 RAILROAD CONSTRUCTION. 226.\\nan approach to the present form, but was very defective on\\naccount of the difficulty of designing a good form of joint. The;\\nStevens section was designed in 1830 by CoL Robert L.\\nStevens, Chief Engineer of the Camden and Amboy Railroad\\nalthough quite defective in its proportions, according to the:\\npresent knowledge of the requirements, it is essentially the pres-\\nent form. In 1836, Charles Yignoles invented essentially the\\nsame form in England this form is therefore known throughout\\nEngland and Europe as the Yignoles rail.\\n226. Present standard forms. The larger part of modern\\nrailroad track is laid with rails which are either T rails or\\nthe double-headed or bull-headed rails which are carried in\\nchairs. The double-headed rail was designed with a symmetri-\\ncal form with the idea that after one head had been worn out\\nby traffic the rail could be reversed, and that its life would be\\npractically doubled. Experience has shown that the wear of the\\nrail in the chairs is very great so much so that when one head\\nhas been w^orn out by traffic the whole rail is generally useless..\\nIf the rail is turned over, the worn places, caused by the chairs,\\nmake a rough track and the rail appears to be more brittle and\\nsubject to fracture, possibly due to the crystallization that may\\nhave occurred during the previous usage and to the reversal of\\nstresses in the fibers. Whatever the explanation, experience has\\ndemonstrated the fact. The bull-headed rail has the lower\\nhead only large enough to properly hold\\nthe wooden keys with which the rail is.\\nsecured to the chairs (see Fig. 112) and\\nfurnish the necessary strength. The use\\nFiQ.112.\u00e2\u0080\u0094 Bull-headed of these rails requires the use of two cast-\\nRail and Chair. ^j^^.^.^ ^^^j^ ^i^-j^^^j ^j^^^\\nsuch track is better for heavy and fast traffic, but it is more\\nexpensive to build and maintain. It is the standard form of\\ntrack in England and some parts of Europe.\\nUntil a few years ago there was a very great multiplicity\\nin the designs of T rails as used in this country, nearly\\nevery prominent railroad having its own special design, which", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0294.jp2"}, "295": {"fulltext": "^226.\\nHAILS.\\n245\\nperhaps differed from that of some otlier road by only a very\\niiiiiiute and insignilicant detail, but which nevertheless wonld\\nrequire a complete new set of rolls for rolling. This certainly\\nmust haye had a yery appreciable effect on the cost of rails. In\\nl^i93, the American Society of Ciyil Engineers, after a very\\nexhaustive investigation of the subject, extending over several\\nyears, having obtained the opinions of tlie best experts of the\\ncountry, adopted a series of sections wliich have been very ex-\\ntensively adopted by the railroads of this country. Instead of\\nhaving the rail sections for yarious weights to be geometrically\\nsimilar figures, certain dimensions are made constant, regardless\\nof the weight. It was decided that the metal should be dis-\\ntributed through the section in the proportions of head 42^,\\nweb 21^, and flange 37^. The top of the head should have a\\nradius of 12 the top corner radius of head should be f-^ the\\nFig. 113.\u00e2\u0080\u0094 Am. See. C. E. Standard Rail Section.\\nlower corner radius of head should be the corners of the\\nflanges, radius; side radius of web, 12 top and bottom\\nradii of web corners, J and angles with the horizontal of the\\nunder side of the head and the top of the flange, 13\u00c2\u00b0. The\\nsides of the head are vertical.\\nThe height of the rail and the width of the base {C) are\\nalways made equal to each other.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0295.jp2"}, "296": {"fulltext": "246\\nRAILHOAD CONSTRUCTION.\\n227.\\nWeight per Yard.\\n40\\n45\\n50\\n55\\n60\\n65\\n70\\n75\\n80\\n85\\n90\\n95\\n100\\nA\\nB\\nC D\\nE\\nF\\nG\\n1 7//\\n5\\ng\\nHI\\n2\\n27\\n6\u00c2\u00ab\\nOil\\n\u00e2\u0080\u00a2^TB\\n21\\n32\\nli-s\\nOl//\\n4x^B\\n23\\n3Z\\nOil\\n\u00e2\u0096\u00a0*B4\\n111\\n\u00e2\u0096\u00a01B4\\nii\\nII\\nU 2\\n2M\\n4/e\\n2iV\\n11\\n41\\n2y\\n241\\n1 7\\n32\\n4B\\n\u00c2\u00a71\\n211\\nHI\\n2h\\n35\\n64\\n5\\n7\\n8\\n2f\\n2t^b\\nII\\n2|\\nIff\\nOS//\\n5|\\n59\\n2||\\nHi\\n2H\\n15\\niB\\n963\\nHi\\n2|\\nT^B\\n5|\\nHI\\nThe chief features of disagreement among railroad men\\nrelate to the radius of the upper corner of the head and the\\nslope of the side of the head. The radius (y^g O adopted for\\nthe upper corner (constant for all weights) is a little more\\nthan is advocated by those in favor of sharp corners\\nwho often use a radius of J On the other hand it is\\nmuch less than is advocated by those who consider that it\\nshould be nearly equal to (or even greater than) the larger\\nradius universally adopted for the corner of\\nthe wheel-flange. The discussion turns on\\nthe relative rapidity of rail wear and the wear\\nof the wheel-flanws as affected bv the relation\\nof the form of the wheel-tread to that of the\\nrail. It is argued that sharp rail corners wear\\nthe wheel-flanges so as to produce sharp\\nflanges, which are liable to cause derailment\\nFig 114 Rela- switches and also to require that the tires\\nTioN OF Rail to of enfi^ine-drivers must be more frequently\\nWhEEL-TKEAD. X xi J- A 1\\nturned down to their true lorm. On the\\nother hand it is generally believed that rail wear is much less\\nrapid while the area of contact between the rail and wheel-flange\\nis small, and that when the rail has worn down, as it invariably\\ndoes, to nearly the same form as the wheel-flange, the rail wears\\naway very quickly.\\n227. Weight for various kinds of traffic. The heaviest rails\\nin regular use weigh 100 lbs. per yard, and even these are only\\nused on some of the heaviest traflic sections of such roads as the\\nN. Y. Central, the Pennsvlvaiiia, the Y., N. H. H., and", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0296.jp2"}, "297": {"fulltext": "228. HAILS. 247\\na few others. Probably the larger part of the mileage of the\\ni0untrj is laid with 60- to 75-lb. rails cunsidering the fact that\\nthe larger part of the mileage consists of comparatively\\nlio-ht-tratiic roads and mav exclude all the heavy truuk lines.\\nYery light-traffic roads are sometimes laid with 5G-lb. rails.\\nKoads with fairly heavy traffic generally use 75- to 85-lb. rails,\\nespecially when grades are heavy and there is much and sharp\\ncurvature. The tendency on all roads is toward an increase in\\nthe weight, rendered necessary on account of the increase in the\\nweight and capacity of rolling stock, and due also to the fact that\\nthe price of rails has been so reduced that it is both better and\\ncheaper to obtain a more solid and durable track by increasing\\nthe weight of the rail rather than by attempting to support a\\nweak rail by an excessive nuinber of ties or by excessive track\\nlabor in tamping. It should be remembered that in buying rails\\nthe mere weight is, in one sense, of no importance. The im-\\nportant thing to consider is the strength and the stiffness. If\\nwe assume that all weights of rails have similar cross-sections\\n(which is nearly although not exactly true), then, since for beams\\nof similar cross-sections the strength varies as the citbe of the\\nhomologous dimensions and the stiffness as the fourth 2^ower\\\\\\nwdiile the area (and therefore the weight per unit of length)\\nonly varies as the square^ it follows that the stiffness varies as\\nthe square of the weight, and the strength as the f power of the\\nweight. Since for ordinary variations of weight the price er\\nton is the same, adding (say) 10^ to the weight (and cost) adds\\n21^ to the stiffness and over 15 fo to the strength. As another\\nillustration, using an 80-lb. rail instead of a 75-11). rail adds only\\ni^%% to the cost, but adds about 14^ to the stiffness and neai-ly\\nto the strength. This shows wdiy heavier rails are mure\\neconomical and are being adopted even wdien they are not abso-\\nlutely needed on account of heavier rolling stock. The stiffness,\\nstrength, and consequent durability are increased in a much\\ngreater ratio than the cost.\\n228. Effect of stiffness on traction. A very important but\\ngenerally unconsidered feature of a stiff rail is its effect on trac-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0297.jp2"}, "298": {"fulltext": "248 RAILROAD CONSTRUCTION. 229.\\ntive force. An extreme illustration of this principle is seen\\nwhen a vehicle is drawn over a soft sandj road. The constant\\ncompression of the sand in front of the wheel has virtually the\\nsame effect on traction as drawing the wheel up a grade whose\\nsteepness depends on the radius of the wheel and the depth of\\nthe rut. On the other hand, if a wheel, made of perfectly\\nelastic material, is rolled over a surface which, while supported\\nwith absolute rigidity, is also perfectly elastic, there would be a\\nforward component, caused by the expanding of the compressed\\nmetal just behind the center of contact, which would just bal-\\nance the backward component. If the rail was supported\\nthroughout its length by an absolutely rigid support, the high\\nelasticity of the wheel-tires and rails would reduce this form of\\nresistance to an insignificant quantity, but the ballast and even\\nthe ties are comparatively inelastic. When a weak rail yields,\\nthe ballast is more or less compressed or displaced, and even\\nthough the elasticity of the rail brings it back to nearly its\\nformer place, the work done in compressing an inelastic material\\nis wholly lost. The effect of this on the fuel account is certainly\\nvery considerable and yet is frequently entirely overlooked. It\\nis practically impossible to compute the saving in tractive power,\\nand therefore in cost of fuel, resulting from a given increase in\\nthe weight and stiffness of the rail, since the yielding of the rail\\nis so dependent on the spacing of the ties, the tamping, etc. But\\nit is not difficult to perceive in a general way that such an econ-\\nomy is possible and that it should not be neglected in considering\\nthe value of stiffness in rails.\\n229. Length of rails. The standard length of rails with most\\nrailroads is 30 feet. In recent years many roads have been try-\\ning 45-foot and even 60-foot rails. The argument in favor of\\nlonger rails is chiefly that of the reduction in track-joints, which\\nare costly to construct and to maintain and are a fruitful source\\nof accidents. Mr. Morrison of the Lehigh Yalley R.R.^ de-\\nclares that, as a result of extensive experience with 45-foot rails\\nReport, Roadrnasters Association, 1895.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0298.jp2"}, "299": {"fulltext": "230. RAILS. 249\\non that road, he finds that they are much less expensive to\\nhandle, and that, being so long, they can be laid around sharp\\ncurves without being curved in a machine, as is necessary with\\nthe shorter rails. The great objection to longer rails lies in the\\ndifficnltv in allowing for the expansion, which will require, in\\nthe coldest weather, an opening at the joint of nearly for a\\n60-foot rail. The Pennsylvania K.R. and the Norfolk and\\nWestern R.R. each have a considerable mileage laid with GO-foot\\nrails.\\n230. Expansion of rails. Steel expands at the rate of .0000065\\nof its length per degree Fahrenheit. The extreme range of tem-\\nperature to which any rail will be subjected will be about 160\u00c2\u00b0,\\nor say from 20\u00c2\u00b0 F. to 140\u00c2\u00b0 F. With the above coefficient\\nand a rail length of 60 feet the expansion would be 0.0624 foot,\\nor about J inch. But it is doubtful Avhether there would ever\\nbe such a range of motion even if there were such a range of\\ntemperature. Mr. A. Torrey, chief engineer of the Mich.\\nCent. R.E., experimented with a section over 500 feet long,\\nwhich, although not a single rail, was made continuous by\\nrio-id splicing, and he found that there was no appreciable addi-\\ntional contraction of the rail at any temperature below ^0 F.\\nThe reason is not clear, but i\\\\iQ fact is undeniable.\\nThe heavy girder rails, used by the street railroads of the\\ncountry, are bonded together with perfectly tight rigid joints\\nwliich do not permit expansion. If the rails are laid at a tem-\\nperature of 60\u00c2\u00b0 F. and the temperature sinks to 0\u00c2\u00b0, the rails\\nhave a tendency to contract .00039 of their length. If this\\ntendency is resisted by the friction of the pavement in which the\\nrails are buried, it only results in a tension amounting to .00039\\nof the modulus of elasticity, or say 10920 pounds per square\\ninch, assuming 28 000 000 as the modulus of elasticity. This\\nstress is not dangerous and may be permitted. If the tempera-\\nture rises to 120\u00c2\u00b0 F., a tendency to expansion and buckling will\\ntake place, which will be resisted as before by the pavement,\\nand a compression of 10920 pounds per square inch will be in-\\nduced, which will likewise be harmless. The range of tempera-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0299.jp2"}, "300": {"fulltext": "250\\nRAILROAD CONSTRUCTION.\\n231\\nture of rails which are buried in pavement is much less than\\nwhen thej are entirely above the ground and will probably\\nnever reach the above extremes. Eails supported on ties which\\nare only held in place by ballast must be allowed to expand and con-\\ntract almost freely, as the ballast cannot be depended on to resist\\nthe distortion induced by any considerable range of temperature,\\nespecially on curves.\\n231. Rules for allowing for temperature. Track regulations\\ngenerally require that the track foremen shall use iron {not\\nwooden) shims for placing between the ends of the rails while\\nsplicing them. The thickness of these shims should vary with\\nthe temperature. Some roads use such approximate rules as the\\nfollowing The proper thickness for coldest weather is of an\\ninch during spring and fall use i of an inch, and in the very\\nhottest weather of an inch should be allowed. This is on\\nthe basis of a 30-foot rail. When a more accurate adjustment\\nthan this is desired, it may be done by assuming some veiy high\\ntemperature (120\u00c2\u00b0 to 150\u00c2\u00b0 F.) as a maximum, when the joints\\nshould be tight; tlien compute in tabular form the spacing for\\neach temperature, varying by 20\u00c2\u00b0, allowing 0 .01:68 (almost\\nexactly -f-^ for each 20\u00c2\u00b0 change. Such a tabular form would\\nbe about as follows (rail length 30 feet)\\nTemperature\\n150\u00c2\u00b0\\n180\u00c2\u00b0\\n110\u00c2\u00b0\\n90\u00c2\u00b0\\n70\u00c2\u00b0\\n50\u00c2\u00b0\\n30\u00c2\u00b0\\n10\u00c2\u00b0\\n10\u00c2\u00b0\\n30\u00c2\u00b0\\nRail opening.\\n3\\n6T\\nJL\\n3 2\\n9\\n6\u00c2\u00a5\\n3\\nT6\\n15\\n64\\n9\\n32\\n21\\n64\\n3\\n8\\n2 7\\nOne practical difficulty in the way of great refinement in this\\nwork is the determination of the real temperature of the rail\\nwhen it is laid. A rail lying in the hot sun has a very nnich\\nMgher temperature than the air. The temperature of the rail\\ncannot be obtained even by exposing a thermometer directly to\\nthe sun, although such a result might be the best that is easily\\nobtainable. On a cloudy or rainy day the rail has practically\\nthe same temperature as the air therefore on such days there\\nneed be no such trouble.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0300.jp2"}, "301": {"fulltext": "2 62. KAILS. 251\\n232. Chemical composition. About OS to 99.5,^ of the com-\\nposition of steel rails is iron, but the value of the rail, as a rail,\\nis almost wholly dependent upon the large number of other\\nchemical elements which are, or may be, present in very small\\namounts. The manager of a steel- rail mill once declared that\\ntheir aim was to produce rails having in them\\nCarbon 0.32 to O.\u00c2\u00b1yjyo\\nSilicon 0.04 to 0.06^\\nPhosphorus 0.09 to 0.105^\\nMano-anese 1.00 to 1.50^\\nThe analysis of 32 specimens of rails on the Chic, Mil.\\nSt. Paul K.R. showed variations as follows:\\nCarbon 0.211 to 0.52^\\nSilicon 0.013 to 0.256^\\nPhosphorus 0.055 to 0.181^\\nManganese 0.35 to 1.63^\\nThese quantities have the same general relative proportions\\nas the rail- mill standard given above, the diiferences lying;\\nmainly in the broadening of the limits. Increasing the percent-\\nage of carbon by even a few hundredths of one per cent makes-\\nthe rail harder, but likewise more brittle. If a track is well\\nballasted and not subject to heaving by frost, a harder and more;\\nbrittle rail may be used without excessive danger of breakage,,\\nand such a rail will wear much lon^rer than a softer toiiirher\\nrail, although the softer tougher rail may be the better rail for\\na road having a less perfect roadbed.\\nA small but objectionable percentage of sulphur is some-\\ntimes found in rails, and very delicate analysis will often show\\nthe presence, in very minute quantities, of several other\\nchemical elements. The use of a very small quantity of nickel\\nor aluminum has often been suggested as a means of ])roducing\\na more durable rail. The added cost and the uncertaintv of", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0301.jp2"}, "302": {"fulltext": "252 RAILROAD CONSTRUCTION. 233.\\nthe amount of advantage to be gained has hitherto prevented\\nthe practical nse or manufacture of such rails.\\n233. Testing. Cliemical and mechanical testing are both\\nnecessary for a thorough determination of the value of a rail.\\nThe chemical testing has for its main object the determination\\nof those minute quantities of chemical elements which have such\\na marked influence on the rail for good or bad. The mechanical\\ntesting consists of the usual tests for elastic limit, ultimate\\nstrength, and elongation at rupture, detennined from pieces cut\\nout of tlie rail, besides a drop test. The drop test consists\\nin dropping a weight of 2000 lbs. from a height of 16 to 20\\nfeet on to the center of a rail which is supported on abutm.ents\\nplaced three or four feet apart. The number of blows required\\nto produce rupture or to produce a permanent set of specified\\nmagnitude gives a measure of the strength and toughness of\\nthe rail.\\n234. Rail wear on tangents. When the wheel loads on a rail\\nare abnormally heavy, and particularly when the rail has but\\nlittle carbon and is unusually soft, the concentrated pressure on\\nthe rail is frequently greater than the elastic\\nlimit, and the metal flows so that the head,\\nalthough greatly abraded, will spread somewhat\\noutside of its original lines, as shown in Fig.\\n115. The rail wear that occurs on tangents is\\nFig. 115. almost exclusively on top. Statistics show that\\nthe rate of rail wear on tangents decreases as the rails are more\\nW Orn. Tests of a large number of rails on tangents have shown\\na rail wear averaging nearly one pound per yard per 10 000 000\\ntons of trafiic. There is about 33 pounds of metal in one yard\\nof the head of an 80 -lb. rail. As an extreme value this may be\\nworn down one-half, thus giving a tonnage of 165 000 000 tons\\nfor the life of the rail. Other estimates bring the tonnage\\ndown to 125 000 000 tons. Since the locomotive is considered\\nto be responsible for one half (and possibly more) of the damage\\ndone to the rail, it is found that the rate of wear on roads with\\nshorter trains is more rapid in proportion to the tonnage, and it", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0302.jp2"}, "303": {"fulltext": "23o. BAILS. 25-3\\nis therefore thought that the life of a rail should be expressed in\\nterms of the number of trains. This has been estimated at\\n300 000 to 500 000 trains.\\n235. Rail wear on curves. On curves the maximum rail wear\\noccurs on the inner side of the head of the outer rail, irivinir a\\nworn form somewhat as shown in Fig. 116. The dotted line\\nshows the nature and progress of the rail wear\\non the inner rail of a curve. Since the pressure\\non the outer rail is somewhat lateral rather than\\nvertical, the flow does not take place to the\\nsame extent, if at all, on the outside, and what-\\never flow would take place on the inside is Fig. 116.\\nimmediately worn off by the wheel-flange. Unlike the wear on\\ntangents, the wear on curves is at a greater rate as the rail\\nbecomes more worn.\\nThe inside rail on curves wears chiefly on top, the same as\\non a tangent, except that the wear is much greater owing to the\\nlongitudinal slipping of the wheels on the rail, and the lateral\\nslipping that must occur when a rigid four-wheeled truck is\\nguided around a curve. The outside rail is subjected to a\\ngreater or less proportion of the longitudinal slipping, likewise\\nto the lateral slipping, and, worst of all, to the grinding action\\nof the flange of the wheel, which grinds off the side of the\\nhead.\\nThe results of some very elaborate tests, made by Mr.\\nA. M. Wellington, on the Atlantic and Great Western R.R., on\\nthe wear of rails, seem to show that the I ail wear on curves\\nmay be expressed by tlie formula: Total wear of rails on a el\\ndegree curve in pounds per yard per 10 000 000 tons duty\\n1 O.OScP. It is not pretended that this fornmla is\\nstrictly correct even in theory, but several theoretical consider-\\nations indicate that it may be nearly so. According to this\\nformula the average rail wear on a 6\u00c2\u00b0 curve will be about twice\\nthe rail wear on a tangent. While this is approximately true,\\nthe various causes modifying the rate of rail wear (length of\\ntrains, age and quality of rails, etc.) will result in numerous and", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0303.jp2"}, "304": {"fulltext": "254 RAILUOAD COIslSTRUCTION. 236.\\nlarge variations from tlie above formula, which should only be\\ntaken as indicating an a^^proximate law.\\n236. Cost of rails. In 1873 the cost of steel rails was about\\n$120 per ton, and the cost of iron rails about $70 per ton.\\nAlthough the steel rails were at once recognized as superior to\\niron rails on account of more uniform wear, they were an\\nexpensive luxury. The manufacture of steel rails by the Ues-\\nsemer process created a revolution in prices, and they have\\nsteadily dropped in price until, during the last few years, steel\\nrails have been manufactured and sold for $22 per ton. At\\nsuch prices there is no longer any demand for iron rails, since\\nthe cost of manufacturing them is substantially the same as that\\nof steel rails, while their durability is unquestionably inferior to\\nthat of steel rails.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0304.jp2"}, "305": {"fulltext": "CHAPTEE X.\\nRAIL- FASTENINGS.\\nRAIL-JOINTS.\\n237. Theoretical requirements for a perfect joint. A perfect\\nrail- joint is one that has the same strength and stifness no more\\nand ho less as the rails which it joins, and which will not\\ninterfere with the regular and uniform spacing of ties. It\\nshould also be reasonably cheap both in first cost and in cost of\\nmaintenance. Since the action of heavy loads on an elastic rail\\nis to cause a wave of translation in front of each wheel, any\\nchange in the stiffness or elasticity of the rail structure will\\ncause more or less of a shock, which must be taken up and\\nresisted by the joint. The greater the change in stiffness the\\ngreater the shock, and the greater the destructive action of the\\nshock. The perfect rail- joint must keep both rail ends trulv in\\nline both laterally and vertically, so that the flange or tread of\\nthe wheel need not jump or change its direction of motion sud-\\ndenly in passing from one rail to the other. A consideration of\\nall the above requirements will show that only a perfect weldino\\nof rail-ends would produce a joint of uniform strength and stiff-\\nness which would give a uniform elastic wave ahead of each\\nwheel. As welding is impracticable for ordinary railroad work\\n(see 230), some other contrivance is necessary which will\\napproacli this ideal as closely as may be.\\n238. Efficiency of the ordinary angle-bar. Throughout the\\nmiddle portion of a rail the rail acts as a continuous girder. If\\nwe consider for simplicity that the ties are unyielding, the deflec-\\ntion of such a continuous girder between the ties will be but\\n255", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0305.jp2"}, "306": {"fulltext": "256 RAILROAD CON STRUCTIO:sr. 239.\\none-fourtli of tlie deflection that would be found if the rail were\\ncut half-way between the ties and an equal concentrated load\\nwere divided equally between the two unconnected ends. The\\nmaximum stress for the continuous girder would be but one-half\\nof that in the cantilevers. Joining these ends with rail-joints\\nwill give the ordinary suspended joint. In order to main\\ntain uniform strength and stiffness the angle-bars must supply\\nthe deficiency. These theoretical relations are modified to an\\nunknown extent by the unknown and variable yielding of the ties.\\nFrom some experiments made by the Association of Engineers\\nof Maintenance of Way of the P. R.K.^ the following deduc-\\ntions were made\\n1. The capacity of a suspended joint is greater than that\\nof a supported joint whether supported on one or three\\nties. (See 240.)\\n2. That (with the particular patterns tested) the angle-bars\\nalone can carry only 53 to 56/^ of a concentrated load placed\\non a joint.\\n3. That the capacity of the whole joint (angle-bars and rail)\\nis only 52.4:^ of the strength of the unbroken rail.\\n4. That the ineffectiveness of the angle-bar is due chiefly to\\na deficiency in compressive resistance.\\nAlthough it has been universally recognized that the angle-\\nbar is not a perfect form of joint, its simplicity, cheapness, and\\nreliability have caused its almost universal adoption. Within a\\nvery few years other forms (to be described later) have been\\nadopted on trial sections and have been more and more extended,\\nuntil their present use is very large. The present time (1900) is\\nevidently a transition period, and it is quite probable tliat within a\\nvery few years the now common angle-plate will be as unknown\\nin standard practice as the old-fashioned fish-plate is at the\\npresent time.\\n239. Eifect of rail gap at joints. It has been found that the\\njar at a joint is due almost entirely to the deflection of the joint\\nRoadmasters Association of America Reports for 1897.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0306.jp2"}, "307": {"fulltext": "240. RAIL-FASTENINQS. 257\\nand scarcely at all to the small gap required for expansion.\\nThis gap causes a drop equal to the versed sine of the arc hav-\\ning a chord equal to the gap and a radius equal to the radius of\\nthe wheel. Taking the extreme case (for a 30-foot rail) of a f\\ngap and a 33 freight-car wheel, the drop is about yijVtt\\norder to test how much the jarring at a joint is due to a gap be-\\ntween the rails, the experiment was tried of cutting shallow\\nnotches in the top of an otherwise solid rail and running a loco-\\nmotive and an inspection car over them. The resulting jarring\\nwas practically imperceptible and not comparable to the jar pro-\\nduced at joints. Xotwithstanding this fact, many plans have\\nbeen tried for avoiding this gap. The most of these plans con-\\nsist essentially of some form of compound rail, the sections\\nbreaking joints. (Of course the design of the compound rail\\nhas also several other objects in view.) In Fig. 117 are shown a\\nFig. 117.\u00e2\u0080\u0094 CoMrouxD Ratl Section^s.\\nfew of the very many designs which have been proposed. These\\ndesigns have invariably been abandoned after triaL Another\\nplan, which has been extensively tried on the Lehigh Yalley\\nU.K., is the use of mitered joints. The advantages gained by\\ntheir use are as yet doubtful, while the added expense is unques-\\ntionable. The Eoadmasters Association of America in 1S95\\nadopted a resolution recommending mitered joints for double\\ntrack, l)ut their use does not seem to be growinir.\\n240. Supported, suspended, and bridge joints. In a\\nsupported joint the ends of the rails are on a tie. If the angle-\\nplates are short, the joint is entirely supported on one tie if\\nvery long, it may be possible to place three ties under one angle-\\nbar and thus the joint is virtually supported on three ties rather\\nthan one. In a suspended joint the ends of the rails are midway\\nbetween two ties and the joint is supported by the two. There", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0307.jp2"}, "308": {"fulltext": "258 RAILROAD CONSTRUCTION. 241.\\nhave always been advocates of both methods, but suspended joints\\nare more generally used than supported joints. The opponents of\\nthree-tie joints claim that either the middle tie will be too\\nstrongly tamped, thus making it a supported joint, or that, if\\nthe middle tie is weakest, the joint becomes a very long (and\\ntherefore weak) suspended joint between the outer joint-ties, or\\nthat possibly one of the outer joint-ties gives way, thus breaking\\nthe angle-plate at the joint. Another objection which is urged\\nis that unless the bars are very long (say tti inches, as used on\\nthe Mich. Cent. E.K.) the ties are too close for proper tamp-\\ning. The best answer to these objections is the successful use\\nof these joints on several heavy-traffic roads.\\nBridge -joints are similar to suspended joints in that the\\njoint is supported on two ties, but there is the important differ-\\nence that the bridge- joint supports the rail from underneath and\\nthere is no transverse stress in the rail, whereas the supported\\njoint requires the combined transverse strength of both angle-\\nbars and rail. A serious objection to bridge- joints lies in the\\nfact of their considerable thickness between the rail base and the\\ntie. When joints are placed staggered rather than oppo-\\nsite (as is now the invariable standard practice), the ties sup-\\nporting a bridge-joint must either be notched down, thus\\nw^eakening the tie and promoting decay at the cut, or else the\\ntie must be laid on a slope and the joint and tlie opposite rail\\ndo not get a fair bearing.\\n241. Failures of rail-joints. It has been observed on double-\\ntrack roads that the maximum rail wear occurs a few inches be-\\nyond the rail gap at the joint in the direction of the traffic. On\\nsingle-track roads the maximum rail wear is found a few inches\\neach side of the joint rather than at the extreme ends of the rail,\\nthus showing that the rail end deflects down under the wheel\\nuntil (with fast trains especially) the wheel actually jumps the\\nspace and strikes the rail a few inches beyond the joint, the\\nimpact producing excessive wear. This action, which is called the\\ndrop, is apt to cause the first tie beyond the joint to become\\ndepi essed, and unless this tie is carefully watched and main-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0308.jp2"}, "309": {"fulltext": "242.\\nRAIL-FA STEISINOb.\\n259\\ntained at its proper level, the stresses in the aiigle-l)ar may\\nactually become rev^ersed and the bar may break at the tu]). The\\nangle-bars of a suspended joint are normally in coinpression at\\nthe top. The mere reversal of the stresses would cause the bars\\nFig. 118. Eh-ect of Wheel Drop (Exaggerated).\\nto give way with a less stress than if the stress were always the\\nsame in kind. A supported joint, and especially a three-tie\\njoint (see 240), is apt to be broken in the same manner.\\n242. Standard angle-bars.\u00e2\u0080\u0094 An angle-bar must be so made\\nas to closely fit the rails. The great multiplicity in the designs\\nof rails (referred to in Chapter IX) results in nearly as great\\nvariety in the detailed dimensions of the angle-bars. The sec-\\ntions here illustrated must be considered only as types of the\\nvariable forms necessary for each different shape of rail. The\\nabsolutely essential features required for a fit are (1) the angles\\nFig. 119.\u00e2\u0080\u0094 Standard Angle-bar\u00e2\u0080\u0094 80-lb. Rail. M. C. R.R.\\nof the upper and lower surfaces of the bar where they fit against\\nthe rail, and (2) the height of the bar. The bolt-holes in the", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0309.jp2"}, "310": {"fulltext": "260 RAILROAD CONSTRUCTION. 243.\\nbar and rail must also correspond. The holes in the angle-plates\\nare elongated or made oval, so that the track-bolts, which are\\nmade of corresponding shape immediately mider the head, will\\nnot be turned by jarring or vibration. The holes in the rails\\nare made of larger diameter (by about than the bolts, so as\\nto allow the rail to expand with temperature.\\n243. Later designs of rail-joints. In Plate XYIII are shown\\nvarious designs which are competing for adoption. The most\\nj)rominent of these (judging from the discussion in the conven-\\ntion of the Roadmasters Association of America in 1897) are\\nthe Continuous and the Weber. Each of them has been\\nvery extensively adopted, and where used are universally pre-\\nferred to angle-plates. [N^early all the later designs embody\\nmore or less directly the principle of the bridge- joint, i.e., sup-\\nport the rail from underneath. An experience of several years\\nwill be required to demonstrate which form of joint best satis-\\nfies the somewhat opposed requirements of minimum cost (])oth\\ninitial and for maintenance) and minimum wear of rails and\\nrolling stock.\\nTIE-PLATES.\\n244. Advantages. (a) As already indicated in 204, the\\nlife of a soft-wood tie is very much reduced by rail-cutting\\nand spike-killing, such ties frequently requiring renewal\\nlong before any serious decay has set in. It has been practi-\\ncally demonstrated that the rail-cutting is not due to the\\nmere pressure of the rail on the tie, even with a maximum\\nload on the rail, but is due to the impact resulting from\\nvibration and to the lono^itudinal workino of the rail. It has\\nbeen proved that this rail-cutting is practically prevented by\\nthe use of tie-plates. (h) On curves there is a tendency to\\noverturn the outer rail due to the lateral pressure on the side of\\nthe head. This produces a concentrated pressure of the outer\\nedge of the base on the tie which produces rail-cutting and also\\ndraws the inner spikes. Formerly the only method of guarding", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0310.jp2"}, "311": {"fulltext": "PLATE XVIII.\\nWEIR BOLTED STIFF FROG.\\nr7?ff; \u00c2\u00aby^yw. y.^\\\\t\\nSECTION THROUGH C-D. SECTION THROUGH A-B.\\nELLIOT PLATE RIVETED FROG.\\nSECTION THROUGH PLATE AT POINT.\\nKail Joints and Frogs.\\nSECTION THROtIGH SPRING-HOUSING.\\n{To face page 260.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0311.jp2"}, "312": {"fulltext": "", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0312.jp2"}, "313": {"fulltext": "245.\\nRAIL-FASTENiyGS.\\n201\\nas ainst this was bv the use of rail -braces, one pattern of\\nwhich is shown in Fig. 12U.\\nBut it has been found that tie-\\nFiG. 120.\\nplates serve the purpose even better, and rail-braces have been\\nabandoned where tie-plates are used, {c) Driving spikes through\\nholes in the plate enables the spikes on each side of the rail to\\nmutually support each other, no matter in which (lateral) direc-\\ntion the rail may tend to move, and this probably accounts in\\nlarge measure for the added stability obtained by the use of tie-\\nplates, id) The wear in spikes, called necking, caused by\\nthe vertical vibration of the rail against them, is very greatly\\nreduced, {e) The cost is very small compared with the value\\nof the added life of the tie, the large reduction in the work of\\ntrack maintenance, and the smoother running on the better track\\nwhich is obtained. It has been estimated that by the use of\\ntie-plates the life of hard-wood ties is increased from one to\\nthree years, and the life of soft-wood ties is increased from three\\nto six years. From the very nature of the case, the value of\\ntie-plates is greater when they are used to protect soft ties.\\n245. Elements of the design. The earliest forms of tie-plates\\nwere llat on the bottom, but it was soon found that they would\\nwork loose, allow sand and dirt to o^et between the rail and the\\nplate and also between the plate and the tie, which would cause\\nexcessive wear. Such plates are also apt to produce an objec-\\ntionable rattle. Another fault of the earlier designs was the use\\nof plates so thin that they would buckle. The latest designs\\nhave flanges or teetli formed on the lower surface which\\npenetrate the tie about f to If Opinion is still divided on\\nthe question of whether these teeth should run with the grain", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0313.jp2"}, "314": {"fulltext": "262 BAILBOAD CONSTRUCTION. 246.\\nor across the grain. If the flanges run with the grain, they\\ngenerally extend the whole length of the tie-plate as in the\\nWolhaupter design. If the grain is to be cut crosswise, several\\nteeth about 1 wide will be used as in the Goldie design.\\nWOLHAUPTER\\nFig. 121. Tie-plates.\\nIt is a very important feature that the spike-holes shou/d be\\nso punched that the spikes will fit closely to the base of tlie rail.\\nOtherwise a lateral motion of the rail will be permitted which\\nwill defeat one of the main objects of the use of the plate.\\nAnother unsettled detail is the use of shoulders on the\\nupi^er surface. On the one hand it is claimed that tlie use of\\nshoulders relieves the spikes of side pressure from the rail and\\nprevents necking. On the other hand it is claimed that if\\nthe plain plate is once properly set with new spikes (at least\\nAvith spikes not already necked) the spikes will not neck appre-\\nciably, and that, as the shouldered plates cost more, the additional\\nexpenditure is unnecessary.\\nThe above designs should be studied with reference to the\\nmanner in which they fulfill the requirements which have been\\nalready stated. As in the case of rail-joints, the best forms of\\ntie-plates are of comparatively recent design, and experience\\nwith them is still insufticient to determine beyond all question\\nwhich designs are the best.\\n246. Methods of setting. A very important detail in the\\nprocess of setting the tie-plates on the ties is that the flanges or\\nteeth should penetrate the tie as far as desired when the plates\\nare flrst put in position. It requires considerable force to press\\nthe teeth into a tie. In a few cases trackmen have depended on\\nthe easy process of waiting for passing trains to force the teeth", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0314.jp2"}, "315": {"fulltext": "\u00c2\u00a7247.\\nRAIL-FASTENINGS.\\n263\\ndown. Until tlie teeth arc down the spikes cannot l)e driven\\nhome, and this apparently clieap and easy process resiiks in loose\\nspikes and rails. If the trackmen neglect even temporarily to\\ntighten these spikes, it will become impossible to make them\\ntight ultimately. The })lates are generally pomided into place\\nwith a 10- to 16-pound sledge-hanmier. A very good method\\nwas adopted once during the construction of a bridge when a\\npile-driver was at hand. The bridge-ties were placed nnder the\\npile-hammer. The plates, accurately set to gauge, were then\\nforced in by a blow from the 8000-lb. hammer falling 2 or 3\\nfeet.\\nSPIKES.\\n247. Requirements. The rails must be held to the ties by a\\nfastening wdiich will not only give sufHcient resistance, but which\\nwill retain its capacity for resistance. It must also be cheap\\nand easily applied. The ordinary track-spike fulfills the last\\nrequirements, but has comparatively small resisting power, com-\\npared with screws or bolts. Worse than all, the tendency to^\\nvertical vibration in the rail produces a series of upward pulls on\\nthe spike that soon loosens it. When motion has once beo-nn\\nthe capacity for resistance is greatly reduced, and but little more\\nvibration is required to pull the spike out\\nso much that redriving is necessary.\\nDriving the spike to place again in the\\nsame hole is of small value except as a\\nvery temporary expedient, as its holding\\npower is then very small. Redriving the\\nspikes in new holes very soon spike-kills\\nthe tie. Many plans have been devised to\\nincrease the holding power of spikes, such\\nas making them jagged, twisting the spike,\\nswelling the spike at about the center of its\\nlength, etc. But it has been easily demon-\\nstrated that the fibers of the wood are gen- ^22.\\nerally so crushed and torn by driving such spikes that their\\nholding power is less than that of the plain spike.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0315.jp2"}, "316": {"fulltext": "264\\nRAILROAD CONSTRUCTION.\\n248.\\nThe ordinary spike (see Fig. 122) is made with a square\\ncross-section which is uniform through the middle of\\nits length, the lower If tapering down to a chisel\\nedge, the upper part swelling out to the head. The\\nGoldie spike (see Fig. 123) aims to improve this form\\nby reducing to a minimum the destruction of the\\nfibers. To this end, the sides are made smooth^ the\\nedges are clean-cut, and the point, instead of being\\nchisel-shaped, is ground down to a pyramidal form.\\nSuch fiber- cutting as occurs is thus accomplished\\nwithout much crushing, and the fibers are thus\\npressed away from the spike and slightly downward.\\nAny tendency to draw the spike will therefore cause\\nFig. 123. the fibers to press still harder on the spike and thus\\nincrease the resistance.\\n248. Driving. The holding power of a spike depends largely\\non how it is driven. If the blows are eccentric and irregular\\nin direction, the hole will be somewhat\\nenlarged and the holding power largely\\ndecreased. The spikes on each side of\\nthe rail in any one tie should not be\\ndirectly opposite, but should be staggered.\\nPlacing them directly opposite will tend\\nto split the tie, or at least decrease the\\nholding power of the spikes. The direc-\\ntion of staggering should be reversed in\\nthe tAvo pairs of spikes in any one tie ^24. Spike-driving.\\n(see Fig. 124). This will tend to prevent any twisting of the tie\\nin the ballast, which would otherwise loosen the rail from the tie.\\n249. Screws and bolts. The use of these abroad is very ex-\\ntensive, but their use in this country has not passed the experi-\\nmental stage. The screws are wood -screws (see Fig. 125),\\nhaving large square heads, which are screwed down with a\\ntrack- wrench. Holes, having the same diameter as the hase of\\nthe screw-threads, should first be bored into the tie, at exactly\\nthe right position and at the proper angle with the vertical.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0316.jp2"}, "317": {"fulltext": "\u00c2\u00a7249.\\nRAIL-FASTENINGS.\\n265\\nA liirlit wooden frame is soinetiiiies used to niido the aiicer at\\nthe proper angle. Sometimes the large head of the screw bears\\ndirectly against the base of the rail, as with the ordinary\\nspike. Other designs employ a plate, made to tit the\\nrail on one side, bearing on the tie on the other side, and\\nthrough which the screw passes. These screws cost\\nmuch more than spikes and require more work to put\\nin place, but their holding power is much greater\\nand the work of track maintenance is very nmcb\\nless. Screw-bolts, passing entirely through the tie,\\nliavinir the head at the bottom of the tie and the nut on Fig 125.\\nthe upper side, are also used abroad. These are quite difficult\\nto replace, requiring that the ballast be dug out beneath the tie,\\nbut on the other hand the occasions for replacing such a bolt\\nare comparatively rare, as their durability is very great. The\\n^1\\ni\\nF\\n1\\n^-J\\nill\\nFig. 126.\\nuse of screws or bolts increases the life of the tie by the avoid-\\nance of spike-killing. It is capable of demonstration tliat\\nthe reduced cost of maintenance and the resulting improvement\\nin track would much more than repay the added cost of screws\\nand bolts, but it seems impossible to induce railroad directors to\\nauthorize a large and immediate additional expenditure to make\\nan annual saving whose value, although unquestionably consider-\\nable, cannot be exactly computed.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0317.jp2"}, "318": {"fulltext": "266\\nRAILROAD CONSTRUCTION.\\n250.\\n250. Wooden spikes. Among the regulations for track-\\nlajing given in 208, mention was made of wooden spikes,\\nor plugs, wliicli are used to fill up the holes wlien spikes are\\nwithdrawn. The value of the policy of filling up these holes is\\nunquestionable, since the expense is insignificant compared with\\nthe loss due to the quick and certain decay of the tie if these\\nholes are allowed to fill with water and remain so. But the\\nmethod of making these plugs is variable. On some roads they\\nare hand-made by the trackmen out of otherwise useless\\nscraps of lumber, the work being done at odd\\nmoments. This policy, while apparently cheap, is\\nnot necessarily so, for the hand-made plugs are ir-\\nreofular in size and therefore more or less inefticient.\\ngang\\nIS\\na track\\nthey may spend\\nwhich could be\\nSince the holes\\nIt is also quite probable that if\\nrequired to make their own plugs,\\ntime on these very cheap articles\\nmore profitably employed otherwise,\\nmade by the spikes are larger at the top than they are\\nnear the bottom, the plugs should not be of uniform\\ncross section but should be slightly wedge-shaped.\\nThe Goldie tie-plug (see Fig. 127) has been de-\\nsigned to fill these requirements. Being machine-\\nmade, they are uniform in size they are of a shape\\nwhich will best fit the hole they can be furnished of any desired\\nwood, and at a cost which makes it a wasteful economy to at-\\ntempt to cut them by hand.\\nFig. 127.\\nTRACK-BOLTS AND NUT-LOCKS.\\n251. Essential requirements. The track-bolts must have\\nsufticient strength and must be screwed up tight enough to hold\\nthe angle-plates against the rail with sufficient force to develop\\nthe full transverse strength of the angle-bars. On the other\\nhand the bolts should not be screwed so tight that slipping may\\nnot take place when the rail expands or contracts with temperature.\\nIt would be impossible to screw the bolts tight enough to prevent", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0318.jp2"}, "319": {"fulltext": "252. liAIL-FA8TENINGS. 267\\nslipping chiring the contraction due to a considerable fall of\\ntemperature on a straight track, but when the track is curved,\\nor when expansion takes place, it is conceivable that the resist-\\nance of the ties in the ballast to lateral motion may be less than\\nthe resistance at the joint. A test to determine this resistance\\nwas made by Mr. A. Torrey, chief engineer of the Mich. Cent.\\nR.R., using 80-lb. rails and ordinary angle-bars, the bolts being\\nscrewed up as usual. It required a force of about 31000 to\\n35000 lbs. to start the joint, which would be equivalent to the\\nstress induced by a change of temperature of about 22\u00c2\u00b0. Bnt\\nif the central angle of any given curve is small, a comparatively\\nsmall lateral component will be sufficient to resist a compression\\nof even 35000 lbs. in the rails. Therefore there Avill ordinarily\\nbe no trouble about having the joints screwed too tight. The\\nvibration caused by the passage of a train reduces the resistance\\nto slipping. This vibration also facilitates an objectionable\\nfeature, viz., loosening of the nuts of the track-bolts. The bolt\\nis readily prevented from turning by giving it a form wdiich is\\nnot circular innnediately under the head and making corre-\\nsponding holes in the angle-plate. Square holes would answer\\nthe purpose, except that the square corners in the holes in the\\nangle-plates would increase the danger of fracture of the plates.\\nTherefore the holes (and also the bolts, under the head) are\\nmade of an oval form, or perhaps a square form with rounded\\ncorners, avoiding angles in the outline.\\nThe nut-locks should be simple and cheap, should have a life\\nat least as long as the bolt, should be effective, and should not\\nlose their effectiveness with age. IFany of the designs that\\nhave been tried have been failures in one or more of these\\nparticulars, as will ])e described in detail below.\\n252. Design of track-bolts. In Fig. 128 is shown a common\\ndesign of track-bolt. In its general form this represents\\ndie bolt used on nearly all roads, being used not only\\nwith the common angle-plates, but also with many of the im-\\nproved designs of rail- joints. The variations are chiefly a\\ngeneral increase in size to correspond with the increased", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0319.jp2"}, "320": {"fulltext": "268\\nRAILROAD CONSTRUCTION.\\n253.\\nFig. 128 \u00e2\u0080\u0094Track-bolt.\\nweight of rails, besides variations in detail dimensions wliicli\\nare frequently unimportant. The diameter is usually f to\\ny 1 bolts are sometimes used for\\nthe heaviest sections of rails. As\\nto length, the bolts should not ex-\\ntend more than -J outside of the\\nnut when it is screwed up. If it\\nextends farther than this, it is liable\\nto be broken olf by a possible derail-\\nment at that point. The lengths used\\nvary from 3i^ which may be used\\nf^ with 60 lbs. rails, to 5 which is\\nrequired with 100-lb. rails. The\\nlength required depends somewliat on\\nthe type of nut- lock used.\\n253. Design of nut-locks. The designs for nut-locks may be\\ndivided into three classes {a) those depending entirely on an\\nelastic washer which absorbs the vibration which might other-\\nwise induce turning; (Ij) those which jam the threads of the\\nbolt and nut so that, when screwed up, the frictional resistance\\nis too great to be overcome by vibration {c) the positive\\nnut-locks those which mechanically hold the nut from turning.\\nSome of the designs combine these principles to some extent.\\nThe vulcanized fiber nut-lock is an example of the first\\nclass. It consists essentially of a rubber washer which is pro-\\ntected by an iron ring. When first placed this lock is effective,\\nbut the rubber soon hardens and loses its elasticity and it is then\\nineffective and worthless. Another illustration of class {a) is\\nthe use of wooden blocks, generally of 1 to \u00e2\u0096\u00a02 oak, which\\nextend the entire length of the angle- bar, a single piece forming\\nthe washer for the four or six bolts of a joint. This form is\\ncheap, but the wood soon shrinks, loses its elasticity, or decays so\\nthat it soon becomes worthless, and it requires constant adjust-\\nment to keep it in even tolerable condition. The Yerona\\nnut-lock is another illustration of class {a) which also combines\\nsome of the positive elements of class {c). It is made of", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0320.jp2"}, "321": {"fulltext": "\u00c2\u00a7258.\\nRAIL- FASTE^^INGS.\\n269\\ntempered steel and, as shown in Fig. 129, is warped aiid lias\\nsharp edges or points. The warped form furnishes the element\\nof elastic pressure when the nut is screwed up. The steel\\nbeino- harder than the iron of the angle-bar or of the nut, it\\nbites into them, owing to the great pressure that must exist\\nVERONA\\nNATIONAL^\\nJONES\\nexcelsior--\\nFig. 129.\u00e2\u0080\u0094 Types of Nut-locks.\\nTvhen the washer is squeezed nearly flat, and thus prevents any\\nhackward movement, although forward movement (or tighten-\\ning the bolt) is not interfered with. The National nut-lock\\nis a type of the second class {h), in which, like the Harvey\\nnut-lock, the nut and lock are combined in one piece. With\\nsix-bolt ande-bars and 30-foot rails, this means a saving of 2112\\npieces on each mile of single track. The National nuts are\\nopen on one side. The hole is drilled and the thread is cut\\nsliijhtly smaller than the bolt, so that when the nut is sci ewed", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0321.jp2"}, "322": {"fulltext": "270 BAILROAD CONSTRUCTION. 253.\\nup it is forced slightly open and therefore presses on the threads\\nof the bolt with such force that vibration cannot jar it loose.\\nUnlike the j^ational nut, the Harvey nut is solid, but\\nthe form of the thread is progressively varied so that the thread\\npinches the thread of the bolt and the friction al resistance to\\nturning is too great to be affected by vibration.\\nThe Jones nut-lock, belonging to class is a type of\\na nut-lock that does not depend on elasticity or jamming of\\nscrew-threads. It is made of a thin flexible plate, the square\\npart of which is so large that it will not turn after being placed\\non the bolt. After the nut is screwed up, the thin plate is bent\\nover so that the re-entrant angle of the plate engages the corner\\nof the nut and thus mechanically prevents any turning. The\\nmetal is supposed to be sufficiently tough to endure without\\nfracture as many bondings of the plate as will ever be desired.\\nJS^ut-locks of class (d) are not in common use.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0322.jp2"}, "323": {"fulltext": "CHAPTEK XI.\\nSWITCHES AND CROSSINGS.\\nSWITCH CONSTRUCTION.\\n254. Essential elements of a switch. Flanges of some sort are\\na necessity to prevent car-wheels from running olf from the rails\\non which they may be moving. But the lianges, although a\\nnecessity, are also a source of complication in that they require\\nsome special mechanism which will, when desired, guide the\\nwlieels out from the controlling inHuence of the main-line rails.\\nThis must either he done by raising the wheels high enough\\nso that the flanges may pass over the rails, or by breaking the\\ncontinuity of the rails in such a way that channels or flange\\nspaces are formed through the rails. An oi-dinary stub switch\\nbreaks the continuity of the main-line rails in three places, two\\nof them at the switch- block and one at the frog. The Wharton\\nswitch avoids two of these breaks by so placing inclined planes\\nthat the wheels, rolling on their flanges, will surmount these\\ninclines until they are a little higher than the rails. Then the\\nwheels on the side toward which the switch runs are guided\\nover and across the main rail on that side. This rise being ac-\\ncomplished in a short distance, it becomes impracticable to\\noperate these switches except at slow speeds, as any sudden\\nchange in the path of the center of gravity of a car causes very\\ndestructive jars both to the switch and to the rolling stock. The\\nother general method makes a break in one main rail (or both)\\nat the switch-block. In both methods the wheels are led to one\\nside l)y means of the lead rails, and Anally one line of wheels\\npasses through the main rail on that side by means of a frog.\\nThere are some designs by which even this break in the main\\nrail is avoided, the wheels being led on. er the main rail by means\\n271", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0323.jp2"}, "324": {"fulltext": "212 RAILROAD CONSTRUCTION. 255.\\n\u00e2\u0096\u00a0of a sliort movahle rail wliicli is on occasion placed across the\\nmain rail, but such designs have not come into general use.\\n255. Frogs. Frogs are provided with two channel- ways or\\nflange spaces through which the flanges of the wheels move.\\nEach channel cuts out a parallelogram from the tread area.\\nSince the wheel-tread is always wider than the rail, the wing-\\nrails will support the wheel not only across the space cut out by\\na\\n:::i\\nFig. 130. Diagrammatic Design of Frog.\\nthe channel, but also until the tread has passed the point of the\\nfrog and can obtain a broad area of contact on the tongue of the\\nfrog. This is the theoretical idea, but it is very imperfectly\\nrealized. The wing rails are sometimes subjected to excessive\\nwear owing to hollow treads on the wheels owing also to\\nthe frog being so flexible that the point ducks when the\\nwheel approaches it. On the other hand the sharp point of the\\nfrog will sometimes cause destructive wear on the tread of the\\nwheel. Therefore the tons^ue of the froo; is not carried out to\\nthe sharp theoretical point, but is purposely somewhat blunted.\\nBut the break which these channels make in the continuity of\\nthe tread area becomes extremely obje ;tionable at high speeds,\\nbeing mutually destructive to the rolling stock and to the frog.\\nThe jarring has been materially reduced by the device of\\nspring frogs to be described later. Frogs were originally\\nmade of cast iron then of cast iron with wearing parts of cast\\nsteel, which were fitted into suitable notches in the cast iron.\\nThis form proved extremely heavy and devoid of that elasticity\\nof track which is necessary for the safety of rolling stock\\nand track at high speeds. The present universal practice is to\\nbuild the frog up of pieces of rails which are cut or bent as re-\\nquired. These pieces of rails (at least four) are sometimes", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0324.jp2"}, "325": {"fulltext": "256. SWrrCRES AND CROSSINGS 273\\nassembled by riveting tbein to a iiat plate, but tbis inetliod is\\nnow but little used, except for very ligbt work. Tbe usual\\npractice is now cbietiy divided between bolted and keyed\\nfrogs. In eacli case tbe space between tbe rails, except a sutH-\\ncicnt liange-way, is tilled witb a cast-iron tiller and tbe wbole\\nassemblage of parts is suitably bolted or clamped togetber, as is\\nillustrated in Plate XVIII. Tbe operation of a spring-rail frog\\nis evident from tbe ligure. Since a siding is usually o[)erated at\\nslow speed, wliile tbe main track may be operated at fast speed,\\na spring- rail frog will be so set tbat tbe tread is continuous for\\ntbe main track and broken for tbe sidinii-. Tliis also means tbat\\ntbe spi ing rail will only be moved by trains moving at a (pre-\\nsumably) slow speed on to tbe siding. For tbe fast trains on tbe\\nmain line sucli a frog is substantially a fixed frog and lias a\\ntread wbicb is practically continuous.\\n256. To find the frog number. Tbe frog number (71) equals\\ntbe ratio of tbe distance of any point on tbe tongue of tbe frog\\nfrom tbe tbeoretical point of tbe frog divided by tbe widtb of\\ntbe tongue at tbat point, i.e. he ah (Fig. 130). Tbis\\nvalue may be directly measured by applying any convenient\\nunit of measure (even a knife, a sbort pencil, etc.) to some\\npoint of tbe tongue wliere tbe widtb just equals tbe unit of\\nmeasure, and tlien noting bow many times tbe unit of measure\\nis contained in tbe distance from tbat place to tbe tbeoretical\\npoint. But since c, tbe tbeoretical point, is not so readily\\ndeterminable witb exactitude, it being tbe imaginary inter-\\nsection of tbe gauge lines, it may be more accurate to measure\\nde^ ab^ and lis tben n^ tbe frog number, hs -4- {ah -j- de).\\nIf tbe frog angle be called 7^, tben\\nn he H- ah hs {ah de) cot ^F 1\\ni.e.. cot \\\\F 2n.\\n257. Stub switches. Tbe use of these, although once nearly\\nuniversal, has been practically abandoned as turnouts from\\n7)iain track except for the poorest and cheapest roads. In some\\nStates, their use on main track is prohibited by law. Tliey", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0325.jp2"}, "326": {"fulltext": "274\\nBAILKOAD CONSTRUCTION.\\n257.\\nhave the sole merit of cheapness with adaptabihty to the cir-\\ncumstances of very light traffic operated at slow speed when a\\nconsiderable element of danger may be tolerated for the sake of\\neconomy. The rails from to (see Fig. ISl are not fastened\\nFig. 131.\u00e2\u0080\u0094 Stub Switch.\\nto the ties they are fastened to each other by tie-rods which\\nkeep them at the proper gauge at and back of B they are\\nsecurely spiked to the ties, and at A they are kept in place by\\nthe connecting bar ((7) fastened to the switch-stand. One great\\nobjection to the switch is that, in its usual form, when operated\\nas a trailing switch, a derailment is inevitable if the switch is\\nmisplaced. The very least damage resulting from such a derail-\\nment must include the bending or breaking of the tie-rods of the\\nswitch-rail. Several devices have been invented to obviate this\\nobjection, some of wdiich succeed very well mechanically,\\nalthough their added cost precludes any economy in the total\\ncost of the switch. Another objection to the switch is the\\nlooseness of construction which makes the switches objectionable\\nat high speeds. The gap of the rails at the head-block is always\\nconsiderable, and is sometimes as much as two inches. A\\nThe student sliould at once appreciate tliat in Fig. 131, as well as in\\nnearly all the remaining figures in this chapter, it becomes necessary to use\\nexcessively large frog angles, short radii, and a very wide gauge in order to\\nillustrate the desired principles with figures which are sufficiently small for\\nthe page. In fact, the proportions used in the figures are such that serious\\nmechanical difficulties would be encountered if they were used. These\\ndifficulties are here ignored because they can he neglected in the proportions\\nused in practice.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0326.jp2"}, "327": {"fulltext": "258.\\nSWITCHES AND CROSSINGS.\\n275\\ndriving-wheel with a load of 12000 to 20000 pounds, jumping\\nthis gap with any considerable velocity, will do innnense damage\\nto the farther rail end, besides producing such a stress in the\\nconstruction that a breakage is rendered quite likely, and such a\\nbreakage might have very serious consequences.\\n258. Point switches. The essential principle of a point\\nswitch is illustrated in Fig. 132. As is shown, one main rail\\nand also cue of the switch-rails is unbroken and inmiovable.\\nFig. 132. Point Switch.\\nThe other main rail (from A to F) and the corresponding\\nportion of the other lead rail are snbstantially the same as in a\\nstub switch. A portion of the main rail {AB) and an equal\\nlength of the opposite lead rail (usually 15 to 2-1 feet long) are\\nfastened together by tie-rods. The end at A is jointed as usual\\nand the other end is pointed, both sides being trimmed down\\nso that the feather edge at B includes the web of the rail. In\\norder to retain in it as much strength as pos-\\nsible, tlie point-rail is raised so that it rests\\non the base of the stock- rail, one side of the\\nl)ase of the point-rail being entirely cut away.\\nAs may be seen in Fig. 133, although the\\ninfluence of the point of the rail in moving\\nthe wheel-flange away from the stock-rail is\\nreally zero at that point, yet the rail has all\\nthe strength of the web and about one-half\\nthat of the base a very fair angle-iron.\\nThe planing runs back in straight lines, until at about six or\\nseven feet back fromx the point the full width of the head is\\nFig. 133.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0327.jp2"}, "328": {"fulltext": "276\\nRAILROAD CONSTRUCTION.\\n259.\\nobtained. The full width of the base will only be obtained at\\nabout 13 feet from the point. An 80-lb. rail is 5 inclies\\nFig. 134.\u00e2\u0080\u0094 Ground Lever foe Throwing a Switch.\\nwide at the base. Allowing I more for a spike between\\nthe rails, this gives ^l as the minimum width between rail\\ncenters at the joint. The minimum angle of\\nthe switch-point (using a 15-foot point rail)\\nis therefore tlie angle w^iose tangent is\\n5.75\\n-.g yr -.9 -03914, which is the tangent of\\n1\u00c2\u00b0 50 Switch-rails are sometimes used with\\na length of 24 feet, which reduces the angle\\nof the switch- point to 1\u00c2\u00b0 09\\n259. Switch-stands. The simplest and\\ncheapest form is the ground lever, wdiich\\nhas no target. The radius of the circle de-\\nscribed by the connecting-rod pin is precisely\\none-half the throw. From the nature of the\\nmotion the device is practically self-locking in\\neither position, padlocks being only used to\\nprevent malicious tampering. The numerous\\ndesigns of upright stands are always combined\\nwith targets, one design of which is illustrated\\nin Fig. 135. When the road is ecpiipped\\nwith interlocking signals, the switch-throw\\nmeclianisra forms a part of the design.\\n260. Tie-rods. These are fastened to tlie\\nwebs of the rails by means of lugs which are bolted on, there", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0328.jp2"}, "329": {"fulltext": "261. SWITCHES AND CROSSINGS. 217\\nbeing usually a hinge-joint between the rod and the lug. Four\\nsuch tie-rods are generally necessary. The hrst rod is some-\\ntimes made without hinges, which gives additional stiffness to\\nthe comparatively w^eak rail-points. The old fashioned tie- rod,\\nIiaving jaws litting the base of the rail, was almost universally\\nused in the days of stub switches. One great inconvenience\\nin their use lies in the fact that they must be slipped on, one by\\none, over the free ends of the switch-rails. Somethnes the\\nhigs are fastened to the rail-webs bv rivets instead of bolts.\\niR\\n^K:\\ni\\n33 d^\\nFig, 186. FouMS of Tie-kods.\\n261. Guard-rails. As shown in Figs. 131 and 132, guard-\\nrails are used on both the main and switch tracks opposite the\\nfrog-point. Their function is not only to prevent the possibil-\\nity of the wheel-flanges passing on the wrong side of the frog-\\npoint, but also to save the side of the frog-tongue from exces-\\nsive wear. The necessity for their use may be realized by\\nnoting the very apparent wear usually found on the side of the\\nhead of the guard-rail. The flange- way space between the\\nheads of the guard-rail and wheel-rail therefore becomes a\\ndefinite quantity and should equal about two inches. Since this\\nis less than the space between the heads of ordinary (say\\n80-pound) rails when placed base to base, to say nothing of the\\nf necessary for spikes, it becomes necessary to cut the flange\\nof the guard-rail. The length of the rail is made from 10 to\\n15 feet, the ends being bent as shown in Fig. 132, so as to", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0329.jp2"}, "330": {"fulltext": "278\\nRAILROAD CONSTRUCTION.\\n\u00c2\u00a72t)2.\\nprevent the possibility of the end of the rail being struck by a.\\nwheel -flange.\\nMATHEMATICAL DESIGN OF SWITCHES.\\nIn all of the following demonstrations regarding switches,\\nturnouts, and crossovers, the lines are assumed to represent the\\ngauge-lines i.e., the lines of the inside of the head of the\\nrails.\\n262. Design with circular lead-rails. The sim^^lest method\\nis to consider that the lead -rails curve\\nout from the main track -rails by arcs\\nof circles which are tangent to the main\\nrails and which extend to the frog-jDoint\\nF. The simple curve from D to F\\nof such radius that ^g) vers 7^= g^\\nin which F the frog angle, g\\ngauge, Z the lead (^F), and\\nr the radius of tne center of the\\nFig. 137. switch rails.\\nig\\n9\\nvers I^\\nAlso BF-^ BD cotiF BD g; BF=Z.\\n(74)\\nAlso\\nZ\\nZ\\nQT\\ng cot ^F\\nsin F;\\n2r sin \\\\F.\\n(75)\\n(76)\\n(77)\\nThese formulae involve the angle F. As shown in Table III,\\nthe angles {F) are always odd quantities, and their trigononietric\\nfunctions are somewhat troublesome to obtain closely with\\nordinary tables. The formulae may be simplified by substitut-\\ning the frog -number n^ from the relation that n =z cot \\\\F.\\nSince\\n\\\\g L cot F and r ^g L cosec F^\\nr", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0330.jp2"}, "331": {"fulltext": "262. SWITCHES AND CROSSINGS. 279\\nthen r \\\\L (cot F cosec F)\\n^g cot h,F io^oi FA;- co^^ec 7^\\ni^ *-^t^ i-^^5 since (cot a cosec ol) cot ^^-\u00c2\u00bbr\\n2^/^^ (78)\\nAlso L 2g?i, (TD)\\nfrom which r ?i X (80)\\nThese extremely simple relations may obviate altogether the\\nnecessity for tables, since they involve only the frog-nnmber and\\nthe gauge. On account of the great simplicity of these rules,\\nthey are frequently used as they are, regardless of the fact that\\nthe curve is never a uniform simple curve from switch-block to\\nfrog. In the first place there is a considerable length of the\\ngauge-line within the frog, which is straight unless it is pur-\\nposely curved to the proper curve while being manufactured,\\nwhich is seldom if ever done except for the very large-angled\\nfrogs used for street-railway work, etc. It is also doubtful\\nwhether the switch-rails (^xl, Fig. 131) are bent to the com-\\nputed curve when the rails are set for the switch. The switch-\\nrails of point switches are straight, thus introducing a stretch of\\nstraio;ht track which is about one-fifth of the total leno-th of the\\nlead-rails. The effect of these modifications on the length and\\nradius of the lead-rails Avill be developed and discussed in the\\nnext four sections.\\nThe throw (t) of a stub switch depends on the weight of the\\nrail, or rather on the width of its base. The throw nuist be at\\nleast f more than that width. The head-block should there-\\nfore be placed at such a distance from the heel of the switch {B)\\nthat the versed sine of the arc equals the throw. These points\\n7nvst be opposite on the two rails, but the points on the two rails\\nwhere these relations are exactly true will not be opposite.\\nTherefore, instead of considering either of the two radii (r -j- iff}\\nand {r ig), the mean radius r is used. Then (see Fig. 137)\\nvers KOQ t i\\\\", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0331.jp2"}, "332": {"fulltext": "280 RAILROAD CONSTRUCTION.\\nand the length of the switch- rails is\\nQK r sin KOQ.\\n\u00c2\u00a7263.\\n(81)\\nThese relations develop another disadvantage in the use of a\\nstub switch. The required value of BG, using a Xo. 10 frog\\nand SO-pound rail, is 30.1 feet slightly more than a full rail\\nleno:th. It would be unsafe to leave so much of the track un-\\nspiked from the ties. AYliether this is obviated by spiking down\\na portion of the switch-rails (virtually shortening the lead) or by\\nmoving the switch-block nearer the heel of the switch (shorten-\\ning the switch- rails), but still maintaining the required throw,\\nthe theoretical accuracy of the curve is hopelessly lost.\\n263. Effect of straight frog-rails. A. portion of the ends of\\nthe rails of a frog are free and may be bent to conform to the\\nswitch-rail curve, but there is a con-\\nsiderable portion which is fitted to the\\ncast-iron filler, and this portion is always\\nstraight. Call the length of this straight\\nportion back from the frog-point f\\nFII, Fig. 138). Then Ve have\\ni^ -/sill F) vers F\\nFig. 138.\\nvers\\n9\\nvers F\\n^-/cotii^\\n-2\\n(82)\\nBF= L {g -/sin F) cot 17^+/ cos F\\n2gn y* sin F cot iF-\\\\-f cos F\\n^^gn -/(I cos F) cos F\\n^-gn-f.\\nSince r ig (Z \u00e2\u0080\u0094f sec F) cot F^ and\\nr -\\\\-^g {L f cos F) cosec i%\\n(83)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0332.jp2"}, "333": {"fulltext": "264.\\nSWITCHES AND CROSSINGS\\n281\\nr iZ (cot jF-\\\\- cosec i^) if sec F QOt F \\\\f cos F cosec i\\n2 i^ gill J\\nr Z?i i/ cot \\\\F\\nLn fn. Then from (S3)\\nr 2^71^ 2f?i\\n(8i)\\n264. Effect of straight point-rails. The point switches,\\nnow so generally used, have straight switcli-rails. This requires\\nan angle in the aHgnnient rather than turning off by a tangential\\ncurve. The angle is, however, very small (between 1\u00c2\u00b0 and 2\u00c2\u00b0),\\nand the disadvantages of this angle are small compared with the\\nvery great advantages of the device.\\n.^\\\\v-\\n?-a\\no\\nMN /C\\na\\n-a\\nFM=\\nFig. 139.\\ng h\\nig\\nsmi{F+ a)\\nFiV\\n2 sin i(F a)\\ng k\\n2 sin i{F a) sin i{F\\ng\\ncos a cos F\\n-a)\\n(85)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0333.jp2"}, "334": {"fulltext": "282\\nBAILBOAD CONSTRUCTION.\\n\u00c2\u00a7265.\\nBF=L=: FM cos i(i^+ a) DJSr\\n{g- I cot i{F-\\\\- a) D^\\\\\\n(86)\\n265. Combined effect of straight frog-rails and straight point-\\nrails. It becomes necessary in this case to find a curve which\\nshall be tangent to both the point-rail and the frog-rail. The\\ncurve therefore begins at M, its tangent making an angle of (x\\n(nsiiallj 1\u00c2\u00b0 50 with the main rail, and runs to H. The central\\n1\\nFH=/\\nVMDN=a:\\nP_^ VHMR=M(F-n:)\\na\\nFig. 140.\\nangle of the curve is therefore {F a). The angle of the chord\\nJIM with the main rails is therefore\\ni{F^a)+a=.UF+a);\\n_ g f sin F k\\nsinU-^+a)\\n^-r 29 sin^(i^- a)\\ng f sin F h\\n2 sin ^X^ a) sin ^{F a)\\ng f m\\\\ F h\\ncos a cos F\\nST 2r sin ^{F a).\\n(87)\\n(88)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0334.jp2"}, "335": {"fulltext": "\u00c2\u00a7266.\\nSWITCHES AND CROSSINGS.\\n283\\nBF L lUL cos \\\\{F cos 7 DN\\n=z{g f sin F k) cot i{F a) cos 7^^+ D^\\\\ (SO)\\nIt may be more simple, if ^fj) lias already been com-\\nputed, to write\\nZ 2(/ i(/) sin i{F- a) cos U^+a) +/cos F+ DJV\\n4-^)(sin F sin cos Z DJS (90)\\n266. Comparison of the above methods. Computing values\\nfor r and Z by tlie various methods, on the uniform basis of a\\nIs^o. 9 frog, standard gauged sy\\\\f= 3 37, k 5i 0 .479,\\nDy =15 0 and 1\u00c2\u00b0 50 we may tabulate the compara-\\ntive results\\nSimple circle\\nCurved frog r.\\nCurved s\\\\vitch-r.\\n263.\\nStraitrht frop:-r.\\nCurved switch-r.\\n204.\\nCurved frop:-r.\\nStraight switch-r.\\n265.\\nStraight frog-r.\\nStraight switch r.\\nr\\nDeg. of curve\\nL\\n762.75\\n7 31\\n84.75\\n702.00\\n8\u00c2\u00b0 10\\n81.37\\n747.48\\n7\u00c2\u00b0 40\\n74.00\\n681.16\\n8\u00c2\u00b0 25\\n72.13\\nThis shows that the effect of using straight frog-rails and\\nstraight switch-rails is to sharpen the curve and shorten the lead\\nin each case separately, and that the combined effect is still\\ngreater. The effect of the straight switch -rails is especially\\nmarked in reducing the length of lead, and therefore Eq. 78 to\\n80, although having the advantage of extreme simplicity, can-\\nnot be used for point-switches without material error. The\\neffect of the straio-ht froo^-rail is less, and since it can be mate-\\nrially reduced by bending the free end of the frog- rails, the in-\\nfluence of this feature is frequently ignored, the frog-rails are\\nassumed to be curved and Eq. 85 and 86 are used. (Soe 276\\nfor a further discussion of this point.)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0335.jp2"}, "336": {"fulltext": "284\\nRAILROAD CONSTRUCTION.\\n267.\\n267. Dimensions for a turnout from the outer side of a curved\\ntrack. In this demonstration the switch-rails will be considered\\nas uniformly circular from the switch-points to the frog-point.\\nFig. 141.\\nIn the triangle FCD (Fig. 141) we have\\n{FC+ CD) (FC- CD) tan i{FDC+DFC) tan i(FDC-DFC)\\nbut i{_FDC+ DFC) 90\u00c2\u00b0 \\\\d\\nand \\\\{FDC DFC) iF.\\nAlso FG+ CD 2E and FC CD g;\\n2B:g: cot tan iF\\ncot ^F: tan\\ntan ^6\\n(91)\\nAlso OF FC: sin 6 sin but cp {F 6)\\\\\\nthen r -X- -ka M -X- ^a^-. r-^^- (92)\\n(93)\\n^7^ L 2{R ^g) sin i^.\\nIf the curvature of the main track is very sharp or the frog\\nangle unusually small, i^may be less than 6-^ in which case the\\ncenter will be on the same side of the main track as C, Eq.\\n92 will become (by calling r r and changing the signs)\\n(r \\\\g) \\\\g)\\nsin B\\nsin\\n{6-F)-\\n(94)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0336.jp2"}, "337": {"fulltext": "\u00c2\u00a7267.\\nSWITCHES AND CROSSINGS.\\n285\\nIf we call d the degree of curve corresponding to the radius\\nr, and D the degree of curve corresponding to the radius i?, also\\nd the degree of curve of a turnout from a straight track (the\\nfrog angle F being the same), it may be shown that d d D\\n(very nearly). To illustrate we will take three cases, a number\\n6 frog (very blunt), a number 9 frog (very commonly used), and\\na number 12 frog (unusually sharp). Suppose 2 4\u00c2\u00b0 0 also\\nZ) 10\u00c2\u00b0 0 g Si Ir .TOS.\\nD-.\\n4\u00c2\u00b0.\\nFrog:\\nnumber.\\nL for\\nstraight track.\\nd D\\nError.\\nL\\n6\\n12\u00c2\u00b0\\n54 20\\n12 57 52\\n0 03 32\\n56.57\\n56.50\\n9\\ni 3\\n30 27\\n3 31 04\\n37\\n84.85\\n84.75\\n12\\n13 33\\n13 36\\n03\\n112.72\\n113.00\\nD\\n10\u00c2\u00b0\\nFrog:\\nnumber.\\ni for\\nstraight track.\\nd\\nd D\\nError.\\nL\\n6\\n6\u00c2\u00b0\\n53 24\\n6\u00c2\u00b0 57 52\\n0\u00c2\u00b0 04 28\\n56.66\\n56.50\\n9\\n2\\n27 54\\n2 28 56\\n01 02\\n84.86\\n84.75\\n12\\n5\\n44 26\\n5 40 24\\n01 58\\n112.91\\n113.00\\nA brief study of the above tabular form will show that the\\nerror involved in the use of the approximate rule for ordinary\\ncurves (-1\u00c2\u00b0 or less) and for the usual frogs (about Xo. 9) is really\\ninsignificant, and that, even for sharper curves (10\u00c2\u00b0 or more),\\nor for very blunt frogs, the error would never cause damage,\\nconsidering the lower probable speed. In the most unfavorable\\ncase noted above the change in radius is about Ifc. On account\\nof the closeness of the approximation the method is frequently\\nused. The remarkable agreement of the computed values of Z\\nwith the corresponding values for a straight main track (the lead", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0337.jp2"}, "338": {"fulltext": "286\\nRAILROAD CONSTRUCTION.\\n268.\\nrails circular tlirougliout) shows that the error is insignificant in\\nusing the more easily computed values.\\n268. Dimensions for a turnout from the inner side of a curved\\ntrack. (Lead rails circular throughout.) From Fig. 142 we\\nhave\\nDC+FC\\\\DC -FC::i^ni{DFC+FI)C) i^n^{DFC- FDC)]\\nbut k{DFC+ FDC) 90\u00c2\u00b0 ^6\\nand\\n^(DFC FDC) \\\\F\\n2i?:^: :cot 1(9: tan ^F\\ncot ^F: tan |-6\\ntan 16\\ngn\\nR\\n(95)\\nOF:FC:\\\\du e ,^in{F+6).\\nir J,) (i? ^,)g^^^^.\\nZ BF 2{R ig) sin id.\\n(96)\\n(97)\\nAs in 267, it may be readily shown that the degree of the\\nturnout (d) is nearly the sum of the degree of the main track\\n(7 and the degree (d of a turnout from a straight track when\\nthe frog angle is the same. The discrepancy in this case is", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0338.jp2"}, "339": {"fulltext": "260.\\nSWITCHES AND CROSSINGS.\\n287\\nsomewhat greater tlian in the other, especially when the curva-\\nture of the main track is sharp. If the frog angle is also laro-e,\\nthe curvature of the turnout is excessively sharp. If the fro r\\nangle is very small, the liability to derailment is great. Turn^\\nouts to the inside of a curved track should therefore be avoided,\\nunless the curvature of the main track is small.\\n269. Double turnout from a straight track. In Fig. 143 the\\nfrogs Fi and F, are generally made ecpuil. Then, if^ there are\\nFig. 143.\\nuniform curves from B to F, and from B to i^,, the required\\nvalue of F,n is obtained from\\nvers hF^. /qo\\\\\\n2-^ m\\nr being found from Eq. 78, in which n is the froo- number\\nof Fi or F,.\\n3IF\u00e2\u0080\u009e, 7 tan ^F.\\nm\\nbut since n\u00e2\u0080\u009e, cot ^F,\\n2-*- \u00c2\u00bbl 5\\nMK,\\nr\\n2n,\\n(99)\\nSince vers F,\\n_ 9\\n(r igy\\nvers IF\u00e2\u0080\u009e\\nvers Fi\\n(100)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0339.jp2"}, "340": {"fulltext": "288 RAILROAD CONSTRUCTION. 269.\\nAlso, since {C,F,) {MF^nY we have\\nr rg l(f 7^\\\\\\nSimplifying and substituting r ^gn we have\\n2/^ V\\n^nm\\na 5\\n/t ,jj5\\nn*\\n2n i\\n1\\nDropping the i, which is always insignificant in comparison\\nwith 27i we have\\n-2 X .707 (approx.). (101)\\nFrogs are usually made with angles corresponding to integral\\nvalues of /i, or sometimes in half sizes, e.g. 6, 6|-, 7, 7^, etc.\\nIf No. 8^ frogs are used for Fi and F^ the exact frog number\\nfor i^^ is 6.01. This is so nearly 6 that a ]^o. 6 frog may be\\nused without sensible inaccuracy. Numbers 7 and 10 are a\\nless perfect combination. If sharp frogs must be used, Sj- and\\n12 form a very good combination.\\nIf it becomes necessary to use other frogs because the right\\ncombination is unobtainable, it may be done by compounding\\nthe curve at the middle frog. Fi and F^ should be greater\\nthan ^F,y^. If equal to J7^\u00e2\u0080\u009e, the rails would be straight from\\nthe middle frog to the outer frogs. In Fig. 144, 6^ Fi~ iF,n^\\nDrawing the chord FiF^,\\nKF,F\u00e2\u0080\u009e F,-i( F,-iF, iF\u00e2\u0080\u009e i{F, iF\u00e2\u0080\u009e)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0340.jp2"}, "341": {"fulltext": "\u00c2\u00a7270.\\nSWITCHES A^D CliOSSINQS.\\n289\\ni^.i^...\\nKF,.\\n9\\nI-*- m\\nin KFiK, 2 sin i{Fi iF,,)\\nsin\\n0^02)\\nKFi KF,,, cot KFiF\u00e2\u0080\u009e, \\\\(j cot \\\\{F, W.:) (103)\\n{r. 4^)\\nF,F.\\nl-*- rn\\n2 sin i^\\n4 sin iCi- ii^\u00e2\u0080\u009e,) sin i(JP, ^F,,)\\n^9\\nCOS ^Fm COS i^i\\n(104)\\nFig. 144.\\nIf three frogs, all different, miist be used, the largest may be\\nselected as F^n the radius of the lead rails may be found by an\\ninversion of Eq. 98; F,n may be located in the center of the\\ntracks by Eq. 99 then each of the smaller frogs may be located\\nby separate applications of Eq. 102 or 103, the radius being\\ndetermined by Eq. 104.\\n270. Two turnouts on the same side. In Fig. 145, let\\n0, bisect 0,D. Then {r, \\\\g) ^{r, -f- ^g) also, 0,0, 0,F,\\nand Fr F^,\\nvers\\nF\\nni\\n(105)\\n^F\u00e2\u0080\u009e, {9\\\\ i^)sin F\u00e2\u0080\u009e, (106)\\nIt may readily be shown that the relative values of F^, Fiy\\nand F,n are almost identical with those given in 269 as may", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0341.jp2"}, "342": {"fulltext": "290\\nRAILROAD CONSTRUCTION.\\n\u00c2\u00a7271.\\nbe apparent when it is considered that the middle switch may\\nbe regarded simply as a curved main track, and that, as\\nFig. 145.\\ndeveloped in 267, the dimensions of turnouts are nearly the,\\nsame whether the main track is straight or slightly curved.\\n271. Connecting curve from a straight track. The con-\\nnecting curve is the track lying\\nbetween the frog and the side\\ntrack where it becomes parallel\\nto the main track (FS in Fig.\\n146 or 147). Call d the distance\\nbetween track centers. The angle\\nFO,R F (see Fig. 146). Call\\nt the radius of the connecting\\ncurve. Then\\nd g _\\nFm. 146.\\n\u00c2\u00a5j)\\nvers F\\n(107)\\nFR (r ig) sin F. (108)\\nIf it is considered that the distance FI^ consumes too much\\ntrack room, it may be shortened by the method indicated in\\nFig. 151.\\n272. Connecting curve from a curved track to the outside.\\nWhen the main track is curved, the required quantities are the\\nradius r of the connecting curve from Fto S, Fig. 147, and its\\nlength or central angle. In the triangle CSF\\nOS+CF: CS-OF:: tstn i{OFS-i- CSF) tmi{CFS -CSF);", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0342.jp2"}, "343": {"fulltext": "\u00c2\u00a7273.\\nSWITCHES AND CROSSINGS.\\n291\\nbut 1{CFS+ CSF) 90 and, since the triangle 0,SF\\nis isosceles, i{CFS CSF) iF;\\no-o 27?+6Z 6? cot tan ^i^\\ncot ^F tan ^ip\\n1 _\\nFig. 147.\\nFrom the triangle OO^F we may derive\\nr ig J2 ig sin tp sin (i^\\nsin i/j\\nAlso\\nir^3.2(r-i^)sini(i^+^).\\n(109)\\n(110)\\n(111)\\n273. Connecting curve from a curved track to the inside.\\nAs above, it may readily be deduced from the triangle CFS (see\\nFig. 148) that\\n{2B d) {d g) cot i^p tan iF,\\nand finally that\\n2n(d a)\\ntan i.p ^^j^l\\n(112)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0343.jp2"}, "344": {"fulltext": "292 RAILROAD CONSTRUCTION.\\nSimilarly we may derive (as in Eq. 110)\\n273.\\nAlso\\nFS 2{r kg) sin 4(i^\\n(113)\\n(114)\\nFig. 148.\\nTwo other cases are possible, {a) r may increase until it\\nbecomes infinite (see Fig. 149), then\\nF ziz tp. In such a case we may\\nwrite, by substituting in Eq. 112,\\n2R-d^^n\\\\d-g),\\n(115)\\nFig. 149.\\nThis equation shows the value of\\ni?, which renders this case possible\\nwith the given values of n^ c/, and\\ng. (b) ip may be greater than F.\\nAs before (see Fig. 150)\\n2^ i 6? cot -J^ tan Ji^;\\n2n{cl g)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0344.jp2"}, "345": {"fulltext": "274. SWITCHES AND CROSSINGS.\\nthe same as Eq. 112, but\\nrJ^ig^{R -ig)\\nsin tp\\nsin {ip F)\\n293\\n(116)\\nFig. 150.\\n274. Crossover between two parallel straight tracks. (See\\nFig. 151.) The turnouts are as usual. The crossover track may\\nbe straight, as shown by the full\\nlines, or it may be a reversed\\ncurve, as shown by the dotted\\nlines. The reversed curve short-\\nens the total length of track re-\\nquired, but is somewhat objection-\\nable. The first method requires\\nthat both frogs must be equal.\\nThe second method permits un-\\nequal frogs, although equal frogs\\nare preferable. The length of\\nstraiglit crossover track is F^ T.\\nF^T sin F,+gcosF, d-g\\nF,T= ^.^^-g cot F,.\\nsm J^.\\n(117)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0345.jp2"}, "346": {"fulltext": "294 RAILROAD CONSTRUCTION. 274.\\nThe total distance along the track may be derived as follows\\nDV= 2DF, F,Y= 2DF, XT- XF,-,\\nXY= {d g) cot F, XF, g-T-smF,;\\nDV 2I)F, {d-g) cot F,-^^^. (118)\\nIf a reversed curve with equal frogs is used, we have\\nvers 6\\nd\\nalso\\n2^, (119)\\nDQ 2/ sin 0. (120)\\nFig. 152.\\nIf the frogs are unequal, we will have (see Fig. 152)\\nr, vers 6 r^ vers 6 d\\\\\\nvers 6\\nd\\nalso the distance along the track\\nB^N {r, n) sin 6.\\n(121)\\n(122)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0346.jp2"}, "347": {"fulltext": "275.\\nSWITCHES AND CROSSINGS.\\n295\\n275. Crossover between two parallel curved tracks, (a) Using\\na straight connecting curve. This solution has limitations. If\\none frog (i^,) is chosen, i becomes determined, being a function\\nof i^j. If F^ is less than some limit, depending on the width\\nFtg. 153.\\n{d) between the parallel tracks, this solution becomes impossible.\\nIn Fig. 153 assume i^, as known. Then F^H g sec F,. In\\nthe triangle TIOF^ we have\\nsin HF,0 sin F,HO HO F,0\\nsin FJIO cos F, HF,0 90\u00c2\u00b0 F,\\nsin IIF.O cos F^.\\nJIO I^ id ig sec Fr, F,0 7? \\\\g\\\\\\n7^ T^ ^d ig g sec F,\\ncos F, cos F, f^ (123)\\nPi hd ig", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0347.jp2"}, "348": {"fulltext": "296\\nRAILROAD CONSTRUCTION,\\n\u00c2\u00a7275.\\nKnowing i^,, /9, is determinable from Eq. 91. Fig. 153 shows\\nthe case where 0^ is greater than F^. Fig. 154 shows the case\\nwhere it is less. The demonstration of Eq. 123 is applicable to\\nFig. 154.\\nboth figures. The relative position of the frogs F^ and F^ may\\nbe determined as follows, the solution being applicable to both\\nFigs. 153 and 154:\\nHOF, 180\u00c2\u00b0 (90\u00c2\u00b0 F) (90\u00c2\u00b0 F,) F, F,.\\nThen\\nGF, 2{R ^d-\\\\g)^mi{F,-F:). (124)\\nSince F^ comes out any angle, its value will not be in general\\nthat of an even frog number, and it will therefore need to be\\nmade to order.\\n(b) Continuing the switch-rail curves until they meet as a\\nreversed curve. In this case F^ and F^ may be chosen at pleasure\\n(within limitations), and they will of course be of regular sizes\\nand equal or unequal as desired. F^ and F^ being known, 0^\\nand 0^ are computed by Eq. 95 and 91. In the triangle 00^0^\\n(see Fig. 155)\\n2{S-00,){S^ 00,)\\n^ers rp oo:zroo^\\nin which\\nS=i{00, 00,+ 0,0,);", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0348.jp2"}, "349": {"fulltext": "275. SWITCHES AjS^D crossings.\\nbut Or\\\\ J2+hJ j\\\\.\\n297\\nS Ot\\\\ ^.B r, n id r, id;\\n^-00, B -B-id r, r^ id;\\nFig. 155.\\nvers ip\\nsin 0(\\\\0,\\nd(r, 7\\\\ id)\\n{R idTYr M ^id ^^y\\n00, B id-r,\\ns,n^,^=sm^^-^-p^; (126)\\ni^+ 0,0,0; (127)\\n2{/2 id i(/) sin J(-A ^J. (128)", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0349.jp2"}, "350": {"fulltext": "298\\nRAILROAD CONSTRUCTION.\\n276.\\nAlthougli tlie above method introduces a reversed curve, yet\\nit uses up less track than the first method and permits the use of\\nordinary frogs rather than those having some special angle which\\nmust be made to order.\\n276. Practical rules for switch-laying. A consideration of\\nthe previous sections will show that the formulae are compara-\\ntively simple when the lead rails are assumed as circular that\\nthey become complicated, even for turnouts from a straight\\nmain track, when the effect of straight frog and point rails is\\nallowed for, and that they become hopelessly complicated when\\nalio wins; for this effect on turnouts from a curved main track.\\nIt is also shown 267) that the length of the lead is practically\\ni r\\nMN=fc\\nFH=/\\nVhmr^v:; (F-a)\\nFig. 140.\\nthe same whether the main track is straight or is curved with\\nsuch curves as are commonly used, and that the degree of curve\\nof the lead rails from a curved main track may be found with\\nclose approximation by mere addition or subtraction. From\\nthis it may be assumed that, if the length of lead (Z) and the\\nradius of the lead rails (r) are computed from Eq. 87 and 90 for\\nvarious fros: ans^les, the same leads mav be used for curved main\\ntrack also, that the degree of curve of the lead rails may be\\nfound by addition or subtraction, as indicated in 267, and that\\nthe approximations involved will not be of practical detriment.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0350.jp2"}, "351": {"fulltext": "\u00c2\u00a7276.\\nSWITCHES AJSD CROSSINGS.\\n299\\nIn accordance with this pkm Table III has been computed from\\nEq. 87, 88, and 90. The leads there given may be used for all\\nmain tracks straight or curved. The table gives the degree of\\ncurve of the lead rails for straight main track; for a turnout to\\nthe inside, add the degree of curve of the main track for a\\nturnout to the outside, suhtract it.\\nIf the position of the switch-block is definitely determined,\\nthen the rails must be cut accordingly but when some freedom\\nis allowable (wdiich never need exceed 15 feet and may require\\nbut a few inches), one rail-cutting may be avoided. Mark on\\nthe rails at B, F, and D measure off the length of the switch-\\nrails DN\\\\ offset \\\\(j -f li from N for the point S.\\nThe point H may be located (temporarily) by meas-\\nuring along the rail a distance i^7/ and then\\nswinging out a distance of ii (n being the frog\\nnumber). HT \\\\(j and is measured at right\\nangles to FII. Points for track centers between S\\nand T may be laid off by a transit or by the use of a\\nstring and tape. Substituting in Eq. 31 the value\\nof R and of chord 8T), w^e may compute x\\ndh). Locate the middle point d and the quarter\\npoints a and c Then a a and c c each equal\\nthree-fourths of dl. Theoretically this gives a parabola rather\\nthan a circle, but the difference for all practical cases is too\\nsmall for measurement.\\nExample. Given a main track on a 1\u00c2\u00b0 curve a turnout to\\nthe outside, using a number 9 frog; gauge 8i 8 87*\\nh hi DY 15 0 and a 1\u00c2\u00b0 50 Then for a straight\\ntrack r would equal 681.16 [d 8\u00c2\u00b0 25 For this curved\\ntrack d will be nearly (8\u00c2\u00b0 25 4\u00c2\u00b0) 4 25 or r will be\\n1207.6. Z for the straight track would be 72.20; but since\\nthe lead is slightly increased (see 2(w) when the turnout is on\\nthe outside of a curve, Z may hei-e l)e called 72.5. Z7/ f\\n3 .37;/-- ii 3.37--9=0 .375=4 .5. 7/, T, and\\nmay be located as described above. ST may be measured on the\\nground, or it may be computed from Eq. 88, giviuir the value\\n\u00c2\u00abh-\\nFiG. 156.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0351.jp2"}, "352": {"fulltext": "300\\nRAILROAD CONSTRUCTION.\\n217.\\nof 53.80 feet for straiglit track. Since it is slightly more for a\\nturnout to the outside of a curve, it may be called 54.0. Then\\n(54. oy\\n8 X 1297.6 ^-21\\nfoot.\\nCROSSINGS.\\n277. Two straight tracks. When two straight tracks cross\\neach other, four frogs are necessary, the angles of two of them\\nbeing supplementary to the angles of the other. Since such\\ncrossings are sometimes operated at high speeds, they should be\\nSECTION ON A-B\\nSrCTION^ON OD\\nFm. 157.\u00e2\u0080\u0094 Crossing,\\nvery strongly constructed, and the angles should preferably be\\n90\u00c2\u00b0 or as near that as possible. The frogs will not in o-eneral\\nbe stock frogs of an even number, especially if the angles\\nare large, but must be made to order with the required angles\\nas measured. In Fig. 157 are shown the details of such a cross-\\ning. Note the fillers, bolts, and guard-rails.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0352.jp2"}, "353": {"fulltext": "\u00c2\u00a7279.\\nSWITCHES AND CIIOSSINGS.\\n301\\n278. One straight and one curved track. Structurally the\\ncrossino: is about the same as above, but the froir aiiirles are\\nall unequal. In Fig. 158, 7? is known,\\nand the angle J/, made by the center\\nlines of the tracks at their point of inter-\\nsection, is also known.\\nJ/ XCM. SC n COS M.\\nR cos J/+ \\\\(j\\nCOS i^,=\\n7?-\\ni^\\no. .1 1 7^ ^C0SJ/+^^\\nSimilarly cos r Trv~y\\nR cos M\u00e2\u0080\u0094 \\\\(j\\nR cos 2f\u00e2\u0080\u0094 ^g\\ncos F,=z p\u00e2\u0080\u0094z;,\\n^(129)\\nFig. 158.\\n279. Two curved tracks. The four frogs are unequal, and\\nthe angle of each must be computed. The radii if, and 7?, are\\n:i--\\nFig. 159.\\nknown also the angle M. r, 7\\\\ r, and 7\\\\ are therefore\\nknown by adding or subtracting ^g, but the lines are so indi-", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0353.jp2"}, "354": {"fulltext": "302\\nRAILROAD CONSTRUCTION.\\n279.\\nTrn 7 t^e angle\\nMC^C C[, and the line 0,0, c. Then\\nand\\nKC, 6^) 90\u00c2\u00b0 -J- Jf\\ntan iiC C) cot iM^^^^\\nC, and C, then become known and\\nsm 6,\\nIn the triangle F, (7. C. call K\u00c2\u00ab r,) s, then\\nvers i^. ?^^^=i^XfL^Zi)\\nSimilarly vers i^, n)(.?, ^j\\nvers i^. ^i^^^ll^k^n) (130)\\nl 3\\nvers i^, ?(fi_ZLZ?)lfi^^\\nIn the above equations", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0354.jp2"}, "355": {"fulltext": "APPENDIX.\\nTHE ADJUSTMENTS OP INSTRUMENTS.\\nThe accuracy of instrumental work may be vitiated by any\\none of a large number of inaccuracies in the geometrical rela-\\ntions of the parts of the instruments. Some of these relations\\nare so apt to be altered by ordinary usage of the instrument that\\nthe makers have provided adjusting-screws so that the inaccura-\\ncies may be readily corrected. There are other possible defects,\\nwhich, however, will seldom be found to exist, provided the\\ninstrument was properly made and has never been subjected to\\ntreatment sufficiently rough to distort it. Such defects, when\\nfound, can only be corrected by a competent instrument maker\\nor repairer.\\nA WARNING is necessary to those who would test the accuracy\\nof instruments, and especially to those whose experience in such\\nwork is small. Lack of skill in handlintr an instrument will\\noften indicate an apparent error of adjustment when tlie real\\nerror is very different or perhaps non-existent. It is always a\\nsafe plan wlien testing an adjustment to note the amount of the\\napparent error; then, beginning anew, make another independ-\\nent determination of the amount of tlie error. When two or\\n\\\\noYe perfectly independent determinations of such an error are\\nmade it will generally be found that they differ by an appreciable\\namount. The differences may be due in variable measure to\\ncareless inaccurate manipulation and to instrumental defects\\nwhich are wholly independent of the particular test being made.\\nSuch careful determinations of the amounts of the errors are\\ngenerally advisable in view of the next paragraph.\\n303", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0355.jp2"}, "356": {"fulltext": "304 THE ADJUSTMENTS OF INSTRUMENTS.\\nDo NOT DISTURB THE ADJUSTING -SCREWS ANY MORE THAN\\nNECESSARY. Altliougli metals are apparently rigid, tliey are\\nreally elastic and yielding. If some parts of a complicated\\nmechanism, which is held together largely by friction, are sub-\\njected to greater internal stresses than other parts of the mech-\\nanism, the jarring resulting from handling will frequently cause\\na slight readjustment in the parts which will tend to more nearly\\nequalize the internal stresses. Such action frequently occurs\\nwith the adjusting mechanism of instruments. One screw may\\nbe strained more than others. The friction of parts may pre-\\nvent the opposing screw from mimediately taking up an equal\\nstress. Perhaps the adjustment appears perfect under these\\nconditions. Jarring diminishes the friction between the j)arts,\\nand the unequal stresses tend to equalize. A motion takes place\\nwhich, although microscopically minute, is sufficient to indicate\\nan error of adjustment. A readjustment, made by unskillful\\nhands, may not make the final adjustment any more perfect.\\nThe frequent shifting of adjusting-screws wears them badly,\\nand when the screws are worn it is still more difficult to keep\\nthem from moving enough to vitiate the adjustments. It is\\ntherefore preferable in many cases to refrain from disturbing the\\nadjusting-screws, especially as the accuracy of the work done is\\nnot necessarily affected by errors of adjustment, as may be illus-\\ntrated\\n{a) Certain operations are absolutely unaffected by certain\\n-errors of adjustment.\\n{J)) Certain operations are so slightly affected by certain small\\nerrors of adjustment that their effect may properly be neglected.\\n(c) Certain errors of adjustment may be readily allowed for\\nand neutralized so that no error results from the use of the un-\\nadjusted instrument. Illustrations of all these cases will be\\ngiven under their proper heads.\\nAD.JUSTMENTS OF THE TRANSIT.\\n1. To have the jplate-huhhles m the centei of the tiibes when\\nthe axis is vertical. Clamp the upper plate and, with the lower", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0356.jp2"}, "357": {"fulltext": "THE ADJUSTMENTS OF INSTRUMENTS. 305\\nclamp loose, swing the instruineiit so that the plate-bubbles are\\nparallel to the lines of opposite leveling-screws. Level up until\\nboth bubbles are central. Swing the instrument 180\u00c2\u00b0. If the\\nbubbles again settle at the center, the adjustment is perfect. If\\neither bubble does not settle in the center, move the leveling-\\nscrews until the bubble is half-icaij back to the center. Then,\\nbefore touching the adjusting-screws, note carefully the position\\nof the bubbles and observe whether the bubbles always settle at\\nthe same place in the tube, no matter to what position the in-\\nstrument may be rotated. When the instrument is so leveled,\\nthe axis is truly vertical and the discrepancies between this con-\\nstant position of the bubbles and the centers of the tubes measure\\nthe errors of adjustment. By means of the adjusting-screws\\nbring each bubble to the center of the tube. If this is done so\\nskillfully that the true level of the instrument is not disturbed,\\nthe bubbles should settle in the center for all positions of the\\ninstrument. Under unskillful hands, two or more such trials\\nmay be necessary.\\nWhen the plates are not horizontal, the measured angle is greater than\\nthe true horizontal angle by the difference between the measured ancle\\n^nd its projection on a horizontal plane. When this angle of inclination\\nis small, the difference is insignificant. Therefore when the plate-bubbles\\nare very nearly in adjustment, the error of measurement of horizontal\\nangles may be far within the lowest unit of measurement used. A smaJl\\n\u00e2\u0082\u00acrror of adjustment of the plate-bubble J9e7pm(izm?ar to the telescope will\\naffect the horizontal angles by only a small proportion of the error, which\\nwill be perhaps imperceptible. Vertical angles will be affected by the\\nsame insignificant amount. A small error of adjustment of the plate-\\nbubble iMrallel to the telescope will affect horizontal angles very slightly,\\nbut will affect vertical angles by the full amount of the error.\\nAll error due to unadjusted plate-bubbles may be avoided by noting in\\nwhat positions in the tubes the bubbles will remain fixed for all positions\\nof azimuth and then keeping the bubbles adjusted to these positions, for\\nthe axis is then truly vertical. It will often save time to work in this way\\ntemporarily rather than to stop to make the adjustments. This should\\nespecially be done when accurate vertical angles are required.\\nWhen the bubbles are truly adjusted, they should remain stationary,\\nregardless of whether the telescope is revolved with the upper plate loose\\nand the lower plate clamped or whether the whole instrument is revolved,\\nthe plates being clamped together. If there is any appreciable difference,", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0357.jp2"}, "358": {"fulltext": "306 THE ADJUSTMENTS OF INSTRUMENTS.\\nit shows that the two vertical axes or centers of the plates are not con-\\ncentric. This may be due to cheap and faulty construction or to the exces-\\nsive wear that may be sometimes observed in an old instrument originally\\nwell made. In either case it can only be corrected by a maker.\\n2 To make the revolving axis of the telescoi: e jyerpendicular\\nto the vertical axis of the instrument. This is best tested by\\nusing a long plumb-line, so placed that the telescope must be\\n]3ointed upward at an angle of about 45\u00c2\u00b0 to sight at the top of\\nthe plumb-line and downward about the same amount, if pos-\\nsible, to sight at the lower end. The vertical axis of the transit\\nmust be made truly vertical. Sight at the upper part of the\\nline, clamping the horizontal plates. Swing the telescope down\\nand see if the cross- wire a T^ain bisects the cord. If so, the\\nadjustment is i^rohaljly perfect (a conceivable exception will be\\nnoted later) if not, raise or lower one end of the axis by means\\nof the adjusting-screws, placed at the top of one of the stan-\\ndards, until the cross-wire will bisect the cord both at top and\\nbottom. The plumb-bob may be steadied, if necessary, by\\nhanging it in a pail of water. As many telescopes cannot be\\nfocused on an object nearer than 6 or 8 feet from the telescope,\\nthis method requires a long plumb-line swung from a high point,\\nwhich may be inconvenient.\\nAnother method is to set up the instrument about 10 feet\\nfrom a high wall. After leveling, sight at some convenient\\nmark high up on tlie wall. Swing the telescope down and make\\na mark (when working alone some convenient natural mark may\\ngenerally be found) low down on the wall. Plunge the telescope\\nand revolve the instrument about its vertical axis and ao^ain sisrht\\nat the upper mark. Swing down to the lower mark. If the\\nwire again bisects it, the adjustment is perfect. If not, fix a\\npoint half-way between the two positions of the lower mark.\\nThe plane of this point, the upper point, and the center of the\\ninstrument is truly vertical. Adjust the axis to tliese upper and\\nlower points as when using the plumb-line.\\n3. To inake the line of collimation jperpendicular to the\\nrevolving axis of the telescope AYitli the instrument level and", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0358.jp2"}, "359": {"fulltext": "THE ADJUSTMENTS OF INSTRUMENTS. 307\\nthe telescope nearly horizontal point at some well-defined point\\nat a distance of 200 feet or more. Plunge the telescope and\\nestablish a point in the opposite direction. Turn the whole\\ninstrument about the vertical axis until it again points at the\\nfirst mark. Again plunge to direct position (i.e., with the\\nlevel-tube under the telescope). If the vertical cross- wire again\\npoints at the second mark, the adjustment is perfect. If not,\\nthe error is one-fourth of the distance between the two positions\\nof the second mark. Loosen the capstan-screw on one side of\\nthe telescope and tighten it on the other side until the vertical\\nwire is set at the one-fourth mark. Turn the whole instrument\\nby means of the tangent screw until the vertical wire is midway\\nbetween the two positions of the second mark. Plunge the\\ntelescope. If the adjusting has been skillfully done, the cross-\\nwire should come exactly to the first mark. As an erecting\\neyepiece reinverts an image already inverted, the ring carrying\\nthe cross-wires must be moved in the same direction as the\\napparent error in order to correct that error.\\nThe necessity for the third adjustment lies principally in the practice\\nof producing a line by plunging the telescope, but when this is required to\\nbe done with great accuracy it is always better to obtain the forward point\\nby reversion (as described above for making the test) and take the mean\\nof the two forward points. Horizontal and vertical angles are practically\\nunaffected by small errors of this adjustment, unless, in the case of\\nhorizontal angles, the vertical angles to the points observed are very\\ndifferent.\\nUnnecessary motion of the adjusting-screws may sometimes be avoided\\nby carefully establishing the forward point on line by repeated reversions\\nof the instrument, and thus determining by repeated trials the exact\\namount of the error. Diffei^ences in the amount of error determined\\nwould be evidence of inaccuracy in manipulating the instrument, and\\nwould show that an adjustment based on the first trial would xwohahJy\\nprove unsatisfactory.\\nThe 2d and 3d adjustments are mutually dependent. If either adjust-\\nment is badly out, the other adjustment cannot be made except as\\nfollows\\n{a) The second adjustment can be made regardless of the third when\\nthe lines to the high point and the low point make equal angles with the\\nhorizontal.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0359.jp2"}, "360": {"fulltext": "308 TEE ADJUSTMENTS OF INSTRUMENTS.\\n(b) The third adjustment can be made regardless of the second when\\nthe front and rear points are on a level with the instrument.\\nWhen both of these requirements are nearly fulfilled, and especially\\nwhen the error of either adjustment is small, no trouble will be found in\\nperfecting either adjustment on account of a small error in the other\\nadjustment.\\nIf the test for the second adjustment is made by means of the plumb-\\nline and the vertical cross-wire intersects the line at all points as the tele-\\nscope is raised or lowered, it not only demonstrates at once the accuracy\\nof that adjustment, but also shows that the third adjustment is either\\nperfect or has so small an error that it does not affect the second.\\n4. To have the hulible of the telescope-level in the center of\\nthe tube ivhen the line of colUmation is horizontal. The line of\\ncollimation should coincide with the optical axis of the telescope.\\nIf the object-glass and eyepiece have been properly centered,\\nthe previous adjustment will have brought the vertical cross-\\nwire to the center of the field of view. The horizontal cross-\\nwire should also be brought to the center of the field of view,\\nand the bubble should be adjusted to it.\\na. Peg method. Set up the transit at one end of a nearly\\nlevel stretch of about 300 feet. Clamp the telescope with its\\nbubble in the center. Drive a stake vertically under the eye-\\npiece of the transit, and another about 300 feet away. Observe\\nthe height of the center of the eyepiece (the telescope being\\nlevel) above the stake (calUng it a) observe the reading of the\\nrod when held on the other stake (calling it J) take the instru-\\nment to the other stake and set it up so that the eyepiece is ver-\\ntically over the stake, observing the height, c take a reading on\\nthe first stake, calling it d. If this adjustment is perfect, then\\na d h G^\\nor {a d) (b c) 0.\\nCall (a-d) Q) c) 2m,\\nWhen m is positive, the line points downward;\\n??i negative, upward.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0360.jp2"}, "361": {"fulltext": "THE ADJUSTMENTS OF INSTRUMENTS. 309\\nTo adjust: if the line points up^ sight the horizontal cross-\\nwire (by moving the vertical tangent screw) at a point which is\\nra lower, then adjust the bubble so that it is in the center.\\nBy taking several independent values for b, c, and c?, a mean value\\nfor m is obtained, which is more reliable and which may save much un-\\nnecessary working of the adjusting-screws.\\nh. Using an auxiliary level. When a carefully adjusted\\nlevel is at hand, this adjustment may sometimes be more easily\\nmade by setting up the transit and level, so that their lines of\\ncollimation are as nearly as possible at the same height. If a\\npoint may be found which is half a mile or more away and\\nwhich is on the horizontal cross- wire of the level, the horizontal\\ncross- wire of the transit may be pointed directly at it, and the\\nbubble adjusted accordingly. Any slight difference in the\\nheights of the lines of collimation of the transit and level (say\\nmay almost be disregarded at a distance of mile or more, or,\\nif the difference of level w^ould have an appreciable effect, even\\nthis may be practically eliminated by making an estimated allow-\\nance when sighting at the distant point. Or, if a distant point\\nis not available, a level-rod with target may be used at a dis-\\ntance of (say) 300 feet, making allowance for the carefully de-\\ntermined difference of elevation of the two lines of collimation.\\n5. Zero of vertical circle. When the line of collimation is\\ntruly horizontal and the vertical axis is truly vertical, the read-\\ning of the vertical circle should be 0\u00c2\u00b0. If the arc is adjustable,\\nit should be brought to 0\u00c2\u00b0. If it is not adjustable, the index\\nerror should be observed, so that it may be applied to all read-\\nings of vertical angles.\\nADJUSTMENTS OF THE WYE LEVEL.\\n1. To make the line of collimation coincide with the center\\nof the rings. Point the intersection of the cross-wires at some\\nwell-defined point which is at a considerable distance. The in-\\nstrument need not be level, which allows much greater liberty\\nin choosing a convenient point. The vertical axis should be", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0361.jp2"}, "362": {"fulltext": "310 THE ADJUSTMENTS OF INSTRUMENTS.\\nclarajDed, and the clips over the wyes should be loosened and raised.\\nRotate the telescope in the wyes. The intersection of the cross-\\nwires should be continually on the point. If it is not, it requires\\nadjustment. Rotate tlie telescope 180\u00c2\u00b0 and adjust one-lialf of\\nthe error by means of the capstan-headed screws that move the\\ncross- wire ring. It should be remembered that, with an erect-\\ning telescope, on account of the inversion of the image, tlie ring\\nshould be moved in the direction of the ajpjparent error. Adjust\\nthe other half o:t the error witli the leveling-screws. Then ro-\\ntate the telescope 90\u00c2\u00b0 from its usual position, sight accurately at\\nthe point, and then rotate 180\u00c2\u00b0 from that position and adjust\\nany error as before. It may require several trials, but it is\\nnecessary to adjust the ring until the intersection of the cross-\\nwires will remain on the point for any position of rotation.\\nIf such a test is made on a very distant point and again on a point only\\n10 or 15 feet from the instrument, the adjustment may be found correct\\nfor one point and incorrect for the other. This indicates that the object-\\nslide is improperly centered. Usually this defect can only be corrected by\\nan instrument-maker. If the difference is very small it may be ignored,\\nbut the adjustment should then be made on a point which is at about the\\nmean distance for usual practice say 150 feet.\\nIf the whole image appears to shift as the telescope is rotated, it indi-\\ncates that the eyepiece is improperly adjusted. This defect is likewise\\nusually corrected only by the maker. It does not interfere with instru-\\nmental accuracy, but it usually causes the intersection of the cross- wires to\\nbe eccentric with the held of view.\\n2. To make the axis of the level tube parallel to the line of\\ncollimation. Raise the clips as far as possible. Swing tlie level\\nso that it is parallel to a pair of opposite leveling-screws and\\nclamp it. Bring the bubble to the middle of the tube by means\\nof the leveling-screws. Take the telescope out of the wyes and\\nreplace it end for end, using extreme care that the wyes are not\\njarred by the action. If the bubble does not come to the center,\\ncorrect one-half of the error by the vertical adjuHting-screws at\\none end of the bubble. Correct the other half by the leveling-\\nscrews. Test the work by again changing liie telescope end for\\nend in the wyes.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0362.jp2"}, "363": {"fulltext": "THE ADJUSTMENTS OF INSTRUMENTS. 311\\nCare should be taken wliile making this adjustment to see\\nthat the level-tube is vertically under the telescope. With the\\nbubble in the center of the tube, rotate the telescope in the wyes\\nfor a considerable angle each side of the vertical. If the first\\nhalf of the adjustment has been made and the bubble moves, it\\nshows that the axis of the wyes and the axis of the level-tube\\nare not in the same vertical plane although both have been made\\nhorizontal. By moving one end of the level-tube sidewise by\\nmeans of the horizontal screws at one end of the tube, the two\\naxes may be brought into the same plane. As this adjustment\\nis liable to disturb the other, both should be alternately tested\\nuntil both requirements are complied with.\\nBy these methods the axis of the bubble is made parallel to\\nthe axis of the wyes and as this has been made parallel to the\\nlines of collimation by means of the previous adjustment, the\\naxis of the bubble is therefore parallel to the line of collimation.\\n3. To make the line of collimation jyerpendicular to tliever-\\ntical axis. Level up so that the instrument is approximately level\\nover both sets of leveling-screws. Then, after leveling carefully\\nover one pair of screws, revolve the telescope 180\u00c2\u00b0. If it is not\\nlevel, adjust half of the error by means of the capstan-headed\\nscrew under one of the wyes, and the other half by the leveling-\\nscrews. Reverse ao;ain as a test.\\nWhen the first two adjustments have been accurately made, good level-\\ning may always be done by bringing the bubble to the center by means of\\nthe leveling-screws, at every sight if necessary, even if the third adjust-\\nment is not made. Of course this third adjustment shoukl be made as a\\nmatter of convenience, so that the line of collimation may be always level\\nno matter in what direction it may bo pointed, but it is not necessary to\\nstop work to make this adjustment every time it is found to be defective.\\nADJUST^IENTS OF THE DUMPY LEVEL.\\n1. To make the axis of the level-tuhe perpendicular to the\\nvertical axis. Level up so that the instrument is approximately\\nlevel over both sets of leveling-screws. Then, after leveling\\ncarefully over one pair of screws, revolve the telescope 180\u00c2\u00b0. If", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0363.jp2"}, "364": {"fulltext": "312 THE ADJUSTMENTS OF INSTRUMENTS.\\nit is not level, adjust one-half of tlie error bj means of the\\nadjusting- screws at one end of the bubble, and the other half\\nbj means of the leveling-screws. Eeverse again as a test.\\n2. To laa ke the line of collbnation jyerpendicular to the ver-\\ntical axis. The method of adjustment is identical with tliat for\\nthe transit (No. 4, p. 308) except that the cross-wire must be\\nadjusted to agree with the level-bubble rather tlian vice versa as\\nis the case with the corresponding adjustment of the transit\\ni.e., with the level-bubble in the center, raise or lower the\\nhorizontal cross-wire until it points at the mark known to be on\\na level with the center of the instrument.\\nIf the instrument has been w^ell made and has not been dis-\\ntorted by rough usage, the cross-wires will intersect at the\\ncenter of the field of view when adjusted as described. If they\\ndo not, it indicates an error which ordinarily can only be cor-\\nrected by an instrument-maker. The error may be due to any\\none of several causes, which are\\n{a) faulty centering of object-slide\\n{b) faulty centering of eyepiece\\ndistortion of instrument so that the geometric axis of\\nthe telescope is not perpendicular to the vertical axis. If the\\nerror is only just j)erceptible, it will not probably cause any\\nerror in the work.", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0364.jp2"}, "365": {"fulltext": "EXPLANATORY NOTE ON THE USE OF THE TABLES.\\nThe logarithms here given are five-place, but the last\\nfigure sometimes has a special mark over it (e.g., g) which in-\\ndicates that one-half a unit in the last place should be added.\\nFor example\\nthe value\\n.69586\\n.69586\\nincludes all values between\\n.6958575000 and .6958624999\\n.6958635000 and .6958674999\\nThe maximum error in any one value therefore does not ex-\\nceed one-quarter of a fifth-place unit.\\nAYlien adding or subtracting such logarithms allow a half-unit\\nfor such a sign. For example:\\n.69586 .69586 .69586\\n.10841 .10841 .1084!\\n.12947 .12947 .12947\\n.93374 .93375 .93375\\nAll other logarithmic operations are performed as usual and\\nare supposed to be understood by the student.\\n313", "height": "4210", "width": "2410", "jp2-path": "railroadconstruc00webb_0365.jp2"}, "366": {"fulltext": "TABLE I.\u00e2\u0080\u0094 RADII OF CURVES.\\nDeg.\\n0\u00c2\u00b0\\n10\\n2\u00c2\u00b0\\n1\\nDeg.\\nMill.\\nKadias.\\nLog It\\nRadius.\\nLog R\\nRadius. Log R\\nRadius.\\nLogiJ 1\\nMin.\\no\\nI\\n2\\n3\\n4\\n5\\nCO\\n343775\\n171887\\n1 14592\\n85944\\n68755\\n00\\n5.53627\\n5.23524\\n5-05915\\n4-93421\\n4.83730\\n5729.6\\n5635-7\\n5544-8\\n5456.8\\n5371.6\\n5288.9\\n3.75813\\n\u00e2\u0080\u00a275095\\n.74389\\n.73694\\n.73010\\n.72336\\n2864.9\\n2841.3\\n2818.0\\n2795.1\\n2772.5\\n2750.4\\n3-\\n45711\\n45351\\n44993\\n44639\\n44287\\n43939\\n1910. I\\n1899.5\\n1889. I\\n1878.8\\n1868.6\\n1858.5\\n3.\\n28105\\n27864\\n27625\\n27387\\n27151\\n26915\\nI\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n9\\nlO\\n57296\\n491 II\\n42972\\n38197\\n34377\\n4.75812\\n.69117\\n.633I8\\n.58203\\n.53627\\n5208.8\\n5131.0\\n5055.6\\n4982.3\\n491 1. 2\\n3.71673\\n.71026\\n.70377\\n.69743\\n.691I8\\n2728.5\\n2707.0\\n2685.9\\n2665.1\\n2644 6\\n3-\\n43593\\n43249\\n42909\\n42571\\n42235\\n1848.5\\n1838.6\\n1828.8\\n1819.I\\n1809.6\\n3-\\n26681\\n26448\\n26217\\n25985\\n25757\\n6\\n7\\n8\\n9\\n10\\nII\\n12\\n13\\n14\\n15\\n31252\\n28648\\n26444\\n24555\\n229[8\\n4.49488\\n.45709\\n.42233\\n.39014\\n.3601 8\\n4842.0\\n4774.7\\n4709.3\\n4645.7\\n4583-8\\n3.68502\\n.67895\\n.67296\\n.66705\\n.66122\\n2624.4\\n2604.5\\n2584-9\\n2565.6\\n2546.6\\n3\\n41903\\n41572\\n41245\\n40919\\n40597\\n1800. I\\n1790.7\\n1781.5\\n1772.3\\n1763.2\\n3\\n25529\\n25303\\n25077\\n24853\\n24629\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21486\\n20222\\n19099\\n18093\\nI7I89\\n4.33215\\n.30582\\n.28100\\n.25752\\n.23524\\n4523-4\\n4464.7\\n4407 5\\n4351.7\\n4297 3\\n3.65547\\n.64979\\n.64419\\n.63865\\n.63319\\n2527.9\\n2509.5\\n2491.3\\n2473-4\\n2455.7\\n3\\n.40276\\n.39958\\n.39642\\n.39329\\n39017\\n1754.2\\n1745-3\\n1736.5\\n1727.8\\n1719.1\\n3\\n24407\\n24185\\n23967\\n23748\\n23530\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n16370\\n15626\\n14947\\n14324\\n13751\\n4.2140^\\n.19385\\n.17454\\nI 5606\\n.13833\\n4244.2\\n4192.5\\n4142.0\\n4092.7\\n4044.5\\n3.62780\\n.62247\\n.61726\\n.61206\\n.60685\\n2438.3\\n2421 1\\n2404 2\\n2387.5\\n2371.0\\n3\\n38708\\n.38401\\n38097\\n.37794\\n37494\\n1710.6\\n1 702 1\\n1693.7\\n1685.4\\n1677.2\\n3\\n23314\\n23098\\n22884\\n.22676\\n22458\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n13222\\n12732\\n12278\\nII854\\n1 1459\\n4.12130\\n.10491\\n.08911\\n.07387\\n.05915\\n3997.5\\n3951-5\\n3906 6\\n3862.7\\n3819.8\\n3.60178\\n.59676\\n.59186\\n.58689\\n58204\\n2354.8\\n2338.8\\n2323.0\\n2307.4\\n2292 .0\\n3\\n37195\\n.36899\\n36604\\n.36312\\n3602 1\\n1 669 I\\n1661.0\\n1653.0\\n1645. I\\n1637.3\\n3\\n22247\\n,22037\\n.2182^\\n.21619\\n21412\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n1 1090\\n10743\\nI04I7\\nlOIII\\n9822.2\\n4.04491\\n.03112\\n.01776\\n4.00479\\n3.99221\\n3777.9\\n3736.8\\n3696 6\\n3657.3\\n3618.8\\n3.57724\\n.57250\\n56786\\n.56316\\n.55856\\n2276.8\\n2261 .9\\n2247 I\\n2232.5\\n2218. I\\n3\\n.35733\\n.35446\\n.35162\\n.34879\\n.34598\\n1629.5\\n1621.8\\n1614.2\\n1606.7\\n1599.2\\n3\\n2 1 206\\n.21006\\n.20795\\n.20593\\n20396\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n9549-3\\n9291-3\\n9046 7\\n8814.8\\n8594.4\\n3.97997\\n.9680^\\n.95649\\n-94521\\n.93421\\n3581. I\\n3544.2\\n3508.0\\n3472.6\\n3437.9\\n3.5540T\\n.54951\\n54506\\n54065\\n.53629\\n2203.9\\n2189.8\\n2176.0\\n2162.3\\n2148.8\\n3\\n-34318\\n.34041\\n-33765\\n.33491\\n.33219\\n1591.8\\n1584.5\\n1577.2\\n1570.0\\n1562.9\\n3\\n.20189\\n.19988\\n.19789\\n.19596\\n-19392\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n8384.8\\n8185.2\\n7994-8\\n7813. I\\n7639-5\\n3.92349\\n.91302\\n.90281\\n.89282\\n-88306\\n3403.8\\n3370.5\\n3337-7\\n3305.7\\n3274.2\\n3-53197\\n.52769\\n.52345\\n.51925\\n.51510\\n2135-4\\n2122.3\\n2109.2\\n2096.4\\n2083.7\\n3\\n.32949\\n.32680\\n.32412\\n.32147\\n.31883\\n1555.8\\n1548.8\\n1541.9\\n1535.0\\n1528.2\\n3\\n.19195\\n.18999\\n.18804\\n.18616\\n.18417\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n7473-4\\n7314.4\\n7162.0\\n7015.9\\n6875.6\\n3-87352\\n.86418\\n-85503\\n84608\\n.83731\\n3243-3\\n3213.0\\n3183.2\\n3154.0\\n3125.4\\n3.51098\\n.50691\\n.50287\\n.49886\\n.49490\\n2071 I\\n2058.7\\n2046 5\\n2034.4\\n2022.4\\n3\\n.31621\\n.31360\\n.31101\\n30843\\n.30587\\n1521.4\\n1514.7\\n1 508 1\\n1501.5\\nM95-0\\n3\\n18224\\n18032\\n.17842\\n.17652\\n.17462\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n6740.7\\n6611 1\\n6486.4\\n6366.3\\n6250.5\\n3.82871\\n.82027\\n8 1 200\\n.80388\\n.79591\\n3097 2\\n3069 6\\n3042.4\\n3015.7\\n2989-5\\n3.49097\\n.48707\\n.48321\\n.47939\\n.47559\\n2010.6\\n1998.9\\n1987.3\\n1975-9\\n1964.6\\n3\\n.30332\\n.30079\\n.2982^\\n29577\\n29328\\n1488.5\\n1482.1\\n1475-7\\n1469.4\\n1463.2\\n3\\n-17274\\n.17087\\n1 6900\\n.16714\\n.16529\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n6138.9\\n603 1 2\\n5927.2\\n5826.8\\n5729.6\\n3.78809\\n78046\\n.77285\\n.76542\\n.75813\\n2963.7\\n2938.4\\n2913.5\\n2889.0\\n2864.9\\n3.47183\\n.46811\\n.46441\\n.46075\\n-45711\\n1953.5\\n1942.4\\n1931.5\\n1920.7\\n1910. I\\n3\\n29081\\n28835\\n28590\\n28347\\n28105\\n1457-0\\n1450.8\\n1444.7\\n1438.7\\n1432.7\\n3\\n-16344\\n16161\\n.15978\\n.15796\\n15615\\n56\\n57\\n58\\n59\\n60\\n314", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0366.jp2"}, "367": {"fulltext": "TABLE I.\u00e2\u0080\u0094 RADII OF CURVES.\\nDeg.\\n4\u00c2\u00b0 1\\n5\\n1\\n1\\nDeg.\\nMill.\\nliadiiis.\\nLOK It\\nKiidiuN. Loff It\\nItadiuN.\\nLog Jt\\nBud i 118.\\nLo\u00c2\u00bb? Jt\\n2.91329\\n.91226\\n.91123\\n.91021\\n.909 1 8\\n908 1 6\\nMill.\\nO\\nI\\n2\\nJ\\n4\\n5\\n1432.7\\n1426.7\\n1420.8\\n1415.0\\n1409.2\\n1403 -5\\n3-15615\\n1 5434\\n.15255\\n.15076\\n.14897\\n.14720\\n1146.3\\nII42.5\\n1138.7\\n1134.9\\nII3I .2\\nII27.5\\n3.05929\\n.05784\\n.05640\\n.05497\\n.05354\\n.05211\\n955-37\\n952.72\\n950.09\\n947.48\\n944.88\\n942.29\\n2.98017\\n.97896\\n.97776\\n.97657\\n.97537\\n.97418\\n819.02\\n817.08\\n815.14\\n813.22\\n811 .30\\n809 40\\n807 50\\n805.61\\n803.73\\n801.86\\n8co 00\\n1\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n9\\nlO\\n1397.8\\n1392.1\\n1386.5\\n1380.9\\n1375-4\\n3-14543\\n.14367\\n.14191\\n.14017\\n.13843\\n1123.8\\n11 20 2\\n1 116. 5\\n1 112.9\\n1109.3\\n3.05069\\n.04928\\n.04787\\n04646\\n.04506\\n939.72\\n937.16\\n934.62\\n932.09\\n929-57\\n2.97300\\n.97181\\n.97063\\n.96945\\n.96828\\n2 907 1 4\\n906 1 2\\n.90511\\n904 I\\n.90309\\n6\\n7\\n8\\n9\\n10\\n1 1\\n12\\n13\\n14\\n15\\n1369.9\\n1364-5\\nI359-I\\n1353-8\\n1348.4\\n1343-2\\n1338.0\\n1332.8\\n1327.6\\n1322.5\\n3 1 3669\\n.13497\\n.13325\\n.13154\\n.12983\\n1105.8\\nI 102. 2\\n1098.7\\n1095.2\\n1091.7\\n3.04366\\n.04227\\n.04088\\n.03949\\n.03811\\n927.07\\n924.58\\n922. 10\\n919.64\\n917.19\\n2 967 1 1\\n.96594\\n.96478\\n.96361\\n.96246\\n798.14\\n796.30\\n794.46\\n792.63\\n790.81\\n2.90208\\n90 1 07\\n9000\\n.8990?\\n89807\\n1 1\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n3.12813\\n1 2644\\n.12475\\n.12307\\n1 2 1 40\\n1088.3\\n1084.8\\n1081 .4\\n1078.1\\n1074.7\\n3.03674\\n.03537\\n.03400\\n.03264\\n.03128\\n914-75\\n912.33\\n909.92\\n907.52\\n905-13\\n2 96 1 36\\n.96015\\n.95900\\n.95785\\n.95671\\n789.00\\n787.20\\n785.41\\n783.62\\n781.84\\n2.89708\\n89608\\n.89509\\n.89416\\n.89312\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n1317-5\\n1312.4\\n1307-4\\n1302.5\\n1297.6\\n3.11974\\n.11808\\n.11642\\n.11477\\n.11313\\n1071.3\\n1068.0\\n1064.7\\n1061 .4\\n1058.2\\n3.02992\\n.02857\\n.02723\\n.02589\\n.02455\\n902 76\\n900 40\\n898.05\\n895-71\\n893-39\\n2.95557\\n.95443\\n.95330\\n.95217\\n.95104\\n780.07\\n778.31\\n776.55\\n774.81\\n773.07\\n2.89213\\n.89115\\n.89017\\n.88919\\n.8882T\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n1292.7\\n1287.9\\n1283. 1\\n1278.3\\n1273.6\\n3.11150\\n.10987\\n.10825\\n10663\\n10502\\n1054.9\\n1051.7\\n1048.5\\n1045-3\\n1042. 1\\n3.02322\\n.02189\\n.02056\\n.01924\\n.01792\\n891.08\\n888.78\\n886.49\\n884.21\\n881.95\\n2.94991\\n.94879\\n.94767\\n.94655\\n.94544\\n771.34\\n769.61\\n767.90\\n766. 19\\n764.49\\n2.88724\\n.88627\\n.88536\\n.88433\\n.88337\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n1268.9\\n1264.2\\n1259.6\\n1255.0\\n1250.4\\n3.10341\\n.10182\\n.10022\\n.09864\\n.09703\\n1039.0\\n1035-9\\n1032.8\\n1029.7\\n1026.6\\n3.01661\\n.01536\\n1 400\\n.01270\\n1 1 40\\n879.69\\n877-45\\n875.22\\n873.00\\n870.80\\n2.94433\\n.94322\\n.94212\\n.9410T\\n.93991\\n762.80\\n761. 1 1\\n759-43\\n757.76\\n756. 10\\n2.88241\\n.88145\\n.88049\\n.87953\\n.87858\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n1245.9\\n1241.4\\n1236.9\\n1232.5\\n1228.1\\n3.09548\\n.09391\\n.09234\\n.09079\\n.08923\\n1023.5\\n1020.5\\n1017.5\\nIOI4.5\\n101 I 5\\n3.01016\\n.00882\\n.00753\\n.00625\\n.00497\\n868.60\\n866.41\\n864.24\\n862.07\\n859.92\\n2.93882\\n.93772\\n.93663\\n.93554\\n93446\\n754.44\\n752.80\\n751.16\\n749.52\\n747.89\\n2.87762\\n.87668\\n.87573\\n.87478\\n.87384\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n1223.7\\n1219.4\\n1215.1\\n1210.8\\n1206.6\\n3.08769\\n.08614\\n.08461\\n.08308\\n.08155\\n1008.6\\n1005.6\\n1002.7\\n999-76\\n996.87\\n3.00370\\n.00242\\n3 00 1 1 6\\n2 99989\\n.99863\\n857-78\\n855.65\\n853-53\\n851.42\\n849-32\\n2.93337\\n.93229\\n.93122\\n.93014\\n.92907\\n746.27\\n744.66\\n743.06\\n741.46\\n739.86\\n2.87290\\n.87196\\n.87102\\n.87008\\n869 1 5\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n1202.4\\n1198.2\\n1194.0\\n1189.9\\n1185.8\\n3.08003\\n.07852\\n.07701\\n.07550\\n.07406\\n993-99\\n991-13\\n988.28\\n985-45\\n982.64\\n2.99738\\n.99613\\n.99488\\n.99363\\n.99239\\n847-23\\n845-15\\n843.08\\n841 .02\\n838.97\\n2.92800\\n.92693\\n.92587\\n.92486\\n.92374\\n738.28\\n736.70\\n735-13\\n733-56\\n732.01\\n2.86822\\n.86729\\n.86636\\n.86544\\n.86451\\n2.86359\\n.86267\\n.86175\\n.86084\\n.85992\\n2.85901\\n.85816\\n.85719\\n.S5629\\n.85538\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n1181 .7\\nII77-7\\n1173.6\\n1169.7\\n1165.7\\n3.07251\\n.07102\\n.06954\\n.06806\\n.06658\\n979 84\\n977.06\\n974-29\\n971-54\\n968.81\\n2.99115\\n.98992\\n.98869\\n.98746\\n.98624\\n836.93\\n834.90\\n832.89\\n830.88\\n828.88\\n2.92269\\n.92163\\n.92058\\n.91953\\n.91849\\n730.45\\n728.91\\n727.37\\n725.84\\n724.31\\n51\\n52\\n53\\n54\\n55\\n1161.8\\n1157.9\\n1154.0\\nII 50. I\\n1146.3\\n3.0651 T\\n.06365\\n.06219\\n.06074\\n1 .05929\\n966 09\\n963-39\\n960 70\\n958.03\\n955-37\\n2.9850T\\n.98380\\n.98258\\n.98137\\n.98017\\n826.89\\n824.91\\n822.93\\n820.97\\n819.02\\n2.91744\\n9 1 646\\n.91536\\n.91433\\n.91329\\n722.79\\n721.28\\n719.77\\n718.27\\n716.78\\n56\\n57\\n58\\n59\\n60\\n315", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0367.jp2"}, "368": {"fulltext": "TABLE I.\u00e2\u0080\u0094 RADII OF CURVES.\\nDeg.\\nis\\n9\\n1\\n1 1\\nl\u00c2\u00bbeg.\\nMill.\\nRadius.\\nLos J\u00c2\u00ab\\nRadius.\\nLogr a\\nRadius.\\nLog K\\nKauiu.s.\\nL\u00c2\u00ab i. 1\\\\\\n3Iin.\\no\\n716.78\\n2.85538\\n637.27\\n2 80432\\n573.69\\n2.75867\\n521.67\\n2.71739\\nI\\n715.29\\n.85448\\n636. 10\\n.80352\\n572.73\\n.75795\\n520.88\\n.71674\\nI\\n2\\n713.81\\n.85358\\n634.93\\n.80272\\n571.78\\n.75723\\n520. 10\\n.71608\\n2\\n3\\n712.34\\n.85268\\n633.76\\n.80192\\n570.84\\n.75651\\n519.32\\n.71543\\n3\\n4\\n710.87\\n.85178\\n632.60\\n.80113\\n569.90\\n.75579\\n518.54\\n.71478\\n4\\n5\\n6\\n709.40\\n.85089\\n631.44\\n80033\\n568.96\\n.75508\\n517.76\\n.71413\\n5\\n707.95\\n2.85000\\n630.29\\n2.79954\\n568.02\\n2.75436\\n516.99\\n2.71348\\n6\\n7\\n706.49\\n.84911\\n629. 14\\n.79874\\n567.09\\n.75365\\n516.21\\n.71283\\n7\\n8\\n705.05\\n.84822\\n627.99\\n.79795\\n566.16\\n.75293\\n515.44\\n.71218\\n8\\n9\\n703.61\\n.84733\\n626.85\\n.79716\\n565-23\\n7 ^222\\n514.68\\n\u00e2\u0080\u00a27II53\\n9\\nlO\\n702. 17\\n.84644\\n625.71\\n.79637\\n564.31\\n.75151\\n513.91\\n.71088\\n2.71024\\n10\\nII\\n700.75\\n2.84556\\n624.58\\n2.79558\\n563.38\\n2.75086\\n513.15\\nII\\n12\\n699.33\\n.84468\\n623.45\\n.79480\\n562.47\\n.75009\\n512.38\\n.70959\\n12\\n1.3\\n697.91\\n.84380\\n622.32\\n.79401\\n561.55\\n\u00e2\u0080\u00a274939\\n511.63\\n.70895\\n13\\n14\\n696.50\\n.84292\\n621 .20\\n.79323\\n560.64\\n.74868\\n510.87\\n.70831\\n14\\n15\\ni6\\n695.09\\n84204\\n620.09\\n.79245\\n559.73\\n.74798\\n510. II\\n.70767\\n15\\n693.70\\n2.84117\\n618.97\\n2.79167\\n558.82\\n2.74727\\n509.36\\n2.70702\\n16\\n17\\n692.30\\n84029\\n617.87\\n.79089\\n557.92\\n.74657\\n508.61\\n.70638\\n17\\ni8\\n690.91\\n.83942\\n616.76\\n.79011\\n557.02\\n.74587\\n507.86\\n\u00e2\u0080\u00a270575\\n18\\n19\\n689.53\\n.83855\\n615.66\\n.78934\\n556.12\\n\u00e2\u0080\u00a274517\\n507. 12\\n.70511\\n19\\n20\\n688.16\\n.83768\\n614.56\\n.78856\\n555-23\\n74447\\nC06.38\\n.7044/\\n20\\n21\\n686.78\\n2.83682\\n613.47\\n2.78779\\n554.34\\n2.74377\\n305.64\\n2.70383\\n21\\n22\\n685.42\\n\u00e2\u0080\u00a283595\\n612.38\\n.78702\\n553-45\\n.74307\\n504.90\\n.70320\\n22\\n23\\n684.06\\n.83509\\n611.30\\n.78625\\n552.56\\n.74238\\n504. 16\\n.70257\\n23\\n24\\n682.70\\n.83423\\n610.21\\n.78548\\n551.68\\n.74168\\n503.42\\n.70193\\n24\\n25\\n26\\n681.35\\n.83337\\n609 1 4\\n.7847T\\n550.80\\n.74099\\n502 69\\n.70130\\n25\\n680.01\\n2.83251\\n608 06\\n2.78395\\n549.92\\n2.74030\\n501 .96\\n2.70067\\n26\\n27\\n678.67\\n.83166\\n606 99\\n.78318\\n549.05\\n.73961\\n501 .23\\n70004\\n27\\n28\\n677.34\\n.83086\\n605.93\\n.78242\\n548.17\\n.73892\\n500.51\\n.69941\\n28\\n29\\n676.01\\n.82995\\n604.86\\n.78165\\n547.30\\n.73823\\n499.78\\n.69878\\n29\\n30\\n674.69\\n.82910\\n603 80\\n.78089\\n546.44\\n\u00e2\u0080\u00a273754\\n499 06\\n.69815\\n30\\n31\\n^n-zi\\n2.8282^\\n602.75\\n2.78013\\n545.57\\n2.73685\\n498 34\\n2.69752\\n31\\n32\\n672.06\\n.82746\\n601 .70\\n\u00e2\u0080\u00a277938\\n544.71\\n.73617\\n497.62\\n69690\\n32\\n33\\n670.75\\n.82656\\n600.65\\n.77862\\n543.86\\n.73548\\n496.91\\n.69627\\n33\\n34\\n669.45\\n.8257T\\n599.61\\n.77786\\n543.00\\n.73480\\n496.19\\n.69565\\n34\\n35\\n668.15\\n.82487\\n598.57\\n.77711\\n542.15\\n.73412\\n495.48\\n.69503\\n35\\n36\\n666.86\\n2.82403\\n597-53\\n2.77636\\n541.30\\n2.73343\\n494.77\\n2 69446\\n36\\n37\\n665.57\\n.82319\\n596.50\\n.77561\\n540.45\\n.73275\\n494.07\\n\u00e2\u0080\u00a269378\\n37\\n3\u00c2\u00ab\\n664.29\\n.82235\\n595-47\\n.77486\\n539.61\\n.7320^\\n493.36\\n.69316\\n38\\n39\\n663.01\\n.82152\\n594.44\\n.77411\\n538.76\\n.73140\\n492.66\\n.69254\\n39\\n40\\n661 .74\\n.82068\\n593-42\\n.77336\\n537.92\\n.73072\\n491.96\\n.69192\\n40\\n41\\n660.47\\n2.81985\\n592.40\\n2.7726T\\n537.09\\n2.73004\\n491 .26\\n2.69131\\n41\\n42\\n659.21\\n.81902\\n591.38\\n.77187\\n536.25\\n.72937\\n490.56\\n69069\\n42\\n43\\n657.95\\n.81819\\n590.37\\n.77112\\n535.42\\n.72869\\n489.86\\n69007\\n43\\n4+\\n656.69\\n.81736\\n589.36\\n.77038\\n534.59\\n.72802\\n489.17\\n.68946\\n44\\n45\\n655.45\\n.81653\\n588.36\\n.76964\\n533.77\\n.72735\\n488.48\\n.68884\\n45\\n46\\n654.20\\n2.81571\\n587.36\\n2.76890\\n532.94\\n2.72668\\n487.79\\n2.68823\\n46\\n47\\n652.96\\n.81489\\n586.36\\n.76816\\n532.12\\n.72601\\n487.10\\n.68762\\n47\\n48\\n651.73\\n.81406\\n585-36\\n.76742\\n531.30\\n.72534\\n486.42\\n.68701\\n48\\n49\\n650. 50\\n.81324\\n584-37\\n.76669\\n530.49\\n.72467\\n485.73\\n.68640\\n49\\n50\\n649.27\\n.81243\\n583-38\\n.76595\\n529.67\\n.72401\\n485.05\\n.68579\\n2.68518\\n50\\n51\\n648.05\\n2.8116]\\n582.40\\n2.76522\\n528.86\\n2.72334\\n484-37\\n51\\n52\\n646.84\\n.81079\\n581.42\\n76449\\n528.05\\n.72267\\n483.69\\n.68457\\n52\\n53\\n645.63\\n80998\\n580.44\\n.76376\\n527.25\\n.72201\\n483.02\\n.68396\\n53\\n54\\n644.42\\n.80917\\n579-47\\n.76303\\n526.44\\n.72135\\n482.34\\n.68335\\n54\\n55\\n643.22\\n.80836\\n578.49\\n.76230\\n525.64\\n.72069\\n481.67\\n.68275\\n55\\n56\\n642.02\\n2.80755\\n577.53\\n2.76157\\n524.84\\n2.72003\\n48 1 00\\n2.68214\\n56\\n57\\n640.83\\n.80674\\n576.56\\n.76084\\n524.05\\n.71937\\n480.33\\n.68154\\n57\\n5\u00c2\u00ab\\n639.64\\n.80593\\n575-60\\n.76012\\n523.25\\n.71871\\n479.67\\n.68094\\n58\\n59\\n638.45\\n.80513\\n574-64\\n.75939\\n522.46\\n.71805\\n479.00\\n.68033\\n59\\n60\\n637.27\\n.80432\\n573-69\\n.75867\\n521.67\\n.71739\\n478.34\\n.67973\\n60 1\\n316", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0368.jp2"}, "369": {"fulltext": "TABLE I.\u00e2\u0080\u0094 RADII OF CURVES.\\nKndius. i Log li\\n4\\n6\\n8\\nlO\\n12\\ni6\\n_i8_\\n20\\n22\\n24\\n26\\n28\\n30\\n32\\n34\\n36\\n40\\n42\\n44\\n46\\n_48_\\n50\\n52\\n54\\n56\\n58\\n4\\n6\\n8\\n10\\n12\\n14\\n16\\n18\\n20\\n22\\n24\\n26\\n28\\n30\\n32\\n34\\n36\\n-.8\\n478.34 2\\n477.02\\n47571\\n474-40\\n473- ^o _\\n471.81 2\\n470.53\\n469.25\\n467 98\\n466.72\\n.67973\\n.67853\\n.67734\\n.67614\\n\u00e2\u0096\u00a067495\\n.67376\\n.67258\\n.67146\\n.67022\\n.6690:;\\n465.46\\n464.21\\n462 97\\n461.73\\n!;o\\n460\\n.66788\\n.66671\\n.66555\\n66439\\n\u00e2\u0080\u00a266323\\nl\u00c2\u00bbeff. 1 Radius. Lo\u00c2\u00ab? It\\nu\\n10\\n12\\n14\\n16\\n20\\n22\\n24\\n26\\n459.28 2\\n458.06 I\\n456.85\\n45565\\n454-45\\n453^26 2\\n.66207\\n.66092\\n.65977\\n.65863\\n.65748\\n30\\n32\\n34\\n36\\n38\\n452.07\\n450.89\\n449-72\\n448 56\\n447 40\\n446.24\\n445.09\\n443^95\\n442.81 _\\n441 .68 \\\\2.\\n440.56\\n439-44\\n438.331\\n437-22 ;_\\n436.12;2\\n435-02(\\n433^93 I\\n432 \u00e2\u0080\u00a284!\\n431^76\\n430.69 2\\n429.62\\n428.561\\n427.50\\n426.44\\n.65634\\n.65521\\n.65407\\n.65294\\n.6518T\\n,65069\\n.64957\\n,64845\\n.64733\\n.64622\\n,64511\\n64400\\n.64290\\n.64180\\n64070\\n40\\n42\\n44\\n46\\n48\\n410.28 2\\n409.31 I\\n408 34\\n407 38 j\\n406.42\\n.61307\\n.61205\\n.61 102\\n6 I 000\\n60898\\n405-47\\n404-53\\n403.58\\n402.65\\n401.71\\nDeg.\\n16^\\n400.78 2\\n399.86\\n398.941\\n398.02\\n397\\n1 1\\n60796\\n60694\\n\u00e2\u0080\u00a260593\\n.60492\\n\u00e2\u0080\u00a260391\\n.60291\\n60 1 96\\n60096\\n59990\\n.59891\\n5\\n10\\n15\\n20\\n25\\nKadi us. Log It\\n359.26 2.55541\\n35742 .55317\\n50\\n52\\n54\\n56\\n58\\n15\\n396. 20\\n395-30\\n394^40\\n393 50\\n392.61\\n391 .72 I2\\n390.84\\n389.96\\n389.08\\n388.21\\n387^34 2\\n386.48\\n385.62\\n384 77\\n383^91\\n63966\\n63851\\n63742\\n63633\\n,63524\\n.63416\\n.63308\\n.63201\\n\u00e2\u0096\u00a063093\\n.62986\\n10\\n12\\n14\\n16\\n18\\n20\\n22\\n24\\n26\\n28\\n40\\n42\\n44\\n46\\n48\\n5--\\n54\\n56\\n58\\n425.40\\n424^35\\n423-32\\n422.28\\n421 .26\\n420.23\\n419.22\\n418.20\\n417.19\\n416. 19\\n.62879\\n.62773\\n.62665\\n.62566\\n.62454\\n32\\n34\\n36\\n38\\n415.19\\n414.20\\n413.21\\n412.23\\n411.25\\n.62349\\n.62243\\n.62138\\n.62034\\n.61929\\n14^ 1 410.28 2\\n61825\\n,61721\\n,61617\\n.61514\\n.61416\\n61307\\n40\\n42\\n44\\n46\\n48\\n50\\n52\\n54\\n56\\n58\\n30\\n35\\n40\\n4 5\\n50\\n55\\n355-59\\n353-77 1\\n351-98\\n35021\\n348.45\\n346.71\\n344-99\\n343-29\\n341 .60\\n339-93\\nDeg. HailiuH. Log Jt\\n21\\n17\\n-55094\\n.54872\\n54652\\n54432\\n2.54214\\n-53997\\n-53786\\n\u00e2\u0080\u00a253565\\n-5335\\n-53138\\n338.27 2.52927\\n336.64 .52716\\n52506\\n52297\\n52090\\n51883\\n10\\n20\\n30\\n40\\n50\\n2.51677\\n.51472\\n.51269\\n5 1 066\\n50864\\n50663\\n319.62 2. 50464\\n318.16 .50265\\n50067\\n.49869\\n\u00e2\u0080\u00a249673\\n\u00e2\u0080\u00a249478\\n383.06 2\\n382.22 1\\n381.38\\n380.54\\n379.71\\n378.88 2\\n378^05\\n377-23\\n376-41\\n375.60\\n374^79\\n373-98\\n373-17\\n372.37\\n371-57\\n370.78\\n369.99\\n369.20\\n368.42\\n3 67^64 i_\\n366.86 2\\n366.09 I\\n365^31\\n364^55\\n363^78\\n22\u00c2\u00b0\\n10\\n20\\n30\\n40\\ni\u00c2\u00a3\\n2.-{\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n274^37\\n272.23\\n270. 13\\n268.06\\n26^6 02\\n264 02\\n262 04\\n260 I o\\n258.18\\n256.29\\n254-43\\n252.60\\n.49284\\n49096\\n.48898\\n.48706\\n515\\n\u00e2\u0080\u00a248325\\n302.94 2.48136\\n.47948\\n.47766\\n-47573\\n-47388\\n-47203\\n250\\n79\\n249\\n01\\n247\\n26\\n245\\n53\\n243\\n82\\n242\\n14\\n24\u00c2\u00b0\\n10\\n20\\n30\\n40\\n25\u00c2\u00b0\\n30\\n2\u00c2\u00ab\u00c2\u00b0\\n30\\n2?\\n30\\n28\u00c2\u00b0\\n30\\n2D\u00c2\u00b0\\n30\\n:}0\u00c2\u00b0\\n^o\\n81\\n32\\nU\\ni5\\n56911\\n,56819\\n.56726\\n56634\\n,56542\\n56450\\n56358\\n56266\\n,56175\\n56084\\nl(i\\n363-02\\n362. 26\\n361.51\\n360.76\\n360.01\\n55993\\n55902\\n55812\\n55721\\n5563\\n359-26 2.5554T\\n2.47018\\n-46835\\n.46652\\n4647 1\\n.46289\\n46 1 09\\n5\\n10\\n15\\n20\\n25\\n30\\n35\\n40\\n45\\n50\\n55\\n21\\n287.94\\n286.76\\n285.58\\n284.42\\n283.27\\n282. 12\\n280.99\\n279.86\\n278.75\\n277.64\\n276.54\\n275-45\\n274-37\\n2-45930\\n\u00e2\u0080\u00a245751\\n\u00e2\u0080\u00a245573\\n-45396\\n.45219\\n-45044\\nMy\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n2 44869\\n.44694\\n.44521\\n\u00e2\u0080\u00a244348\\n.4417^\\n44004\\n2.438\\njj\\n4(J\\n47\\n48\\n40\\n52\\n54\\n5(i\\n58\\n(io\\n240\\n238\\n49\\n85\\n237\\n235\\n234\\n24\\n65\\n08\\nO T 2\\nS4\\n2-43833\\n\u00e2\u0096\u00a043494\\n\u00e2\u0080\u00a243157\\n\u00e2\u0080\u00a242823\\n.42492\\n.42163\\n2.41837\\n\u00e2\u0080\u00a241513\\n.41192\\n\u00e2\u0080\u00a240873\\n\u00e2\u0080\u00a240557\\n\u00e2\u0080\u00a240243\\n2 \u00e2\u0096\u00a039931\\n.39622\\n393 5\\n.39016\\n\u00e2\u0080\u00a238707\\n3840 7\\n2.38109\\n\u00e2\u0080\u00a237813\\n.37519\\n.37227\\n.36937\\n36649\\n231 .01\\n226.55\\n222 27\\n218. 15\\n2.36363\\n\u00e2\u0080\u00a235517\\n34688\\n-33875\\n214. 18\\n210.36\\n206.68\\n203.13\\n2.33078\\n\u00e2\u0080\u00a232296\\n-31529\\n\u00e2\u0096\u00a0307/6\\n99.70\\n96-38\\n93-19\\n90.09\\n30037\\n29316\\n-28597\\n27896\\n87. 10\\n81 .40\\n76.05\\n71 .02\\n66.28\\n61 .80\\n57-58\\n53-58\\n49-79\\n46.19\\n42.77\\n39-52\\n36-43\\n33-47\\n^o 66\\n27 97\\n25-39\\n22.93\\n20.57\\n18.31\\n14.06\\n10.13\\n06. 50\\n03^13\\n00.00\\n27207\\n25863\\n24563\\n23303\\n22083\\n20899\\n19749\\n18633\\n17547\\n16492\\n2 1 5464\\n-14464\\n.13489\\n.12539\\n\u00e2\u0080\u00a211613\\n2. 10709\\n.09827\\n.08965\\n.08124\\n317", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0369.jp2"}, "370": {"fulltext": "TABLE II.\u00e2\u0080\u0094\\nTANGENTS. EXTERNAL DISTANCES, AND LONG CHORDS\\nFOR M\\n1\u00c2\u00b0 CURVE.\\n1\\nA\\nTaiigeut\\nExt.Dist. LoiigCh d\\nA\\nTaii:;eiit\\nExt.Dist.\\nLoiigCh d\\nA\\nTansreut\\nExt.Dist.\\nLoiigCh d\\nV\\nT.\\ni;.\\nxc.\\nT.\\n-K.\\nLC.\\nT.\\nE.\\nLC.\\n50.00\\n0.218\\nI 00 00\\n11\u00c2\u00b0\\n551.70\\n26 500\\n1098.3\\n21\u00c2\u00b0\\n1061 .9\\n97.58\\n2088.3\\nlo\\n58.34\\n0.297\\n116.67\\n10\\n560. 11\\n27.313\\nIII4.9\\n10\\n1070.6\\n99-15\\n2104.7\\n20\\n66.67\\n0.388\\n133-33\\n20\\n568.53\\n28. 137\\nII3I-5\\n20\\n1079.2\\n100.75\\n2121 1\\n30\\n75.01\\n0.491\\n1 50 00\\n30\\n576.95\\n28.974\\nI 1 48 1\\n30\\n1087.8\\n102.35\\n2137.4\\n40\\n83.34\\n0.606\\n166.66\\n40\\n585.36\\n29.824\\nI164.7\\n40\\n1 096 4\\n103.97\\n2153.8\\n50\\n91.68\\n0.733\\n183.33\\n50\\n593-79\\n30.686\\nI181.2\\n50\\n1105. I\\n105.60\\n2170.2\\n2\u00c2\u00b0\\n100.01\\n0.873\\n199.99\\n12=\\n602.21\\n31.561\\nI 197.8\\n22\u00c2\u00b0\\n1113.7\\n107.24\\n2186.5\\n10\\n108.35\\n1 .024\\n216.66\\n10\\n610.64\\n32.447\\n1214.4\\n10\\n1122.4\\n1 08 90\\n2202.9\\n20\\n116.68\\n1.188\\n233-32\\n20\\n619.07\\n33-347\\n1231 .0\\n20\\nII3I.O\\n110.57\\n2219.2\\n30\\n125.02\\n1.364\\n249.98\\n30\\n627.50\\n34-259\\n1247.5\\n30\\nII39-7\\n112.25\\n2235.6\\n40\\n133.36\\n1.552\\n266.65\\n40\\n635-93\\n35-183\\n1264. I\\n40\\n1148.4\\n113-95\\n2251 .9\\n50\\n141.70\\n1.752\\n283.31\\n50\\n644-37\\n36.120\\n1280.7\\n50\\n1157.0\\n115.66\\n2268.3\\n3\u00c2\u00b0\\nI 50 04\\n1.964\\n299.97\\n13\u00c2\u00b0\\n652.81\\n37.069\\n1297.2\\n23\u00c2\u00b0\\n1165.7\\n117.38\\n2284.6\\n10\\n158.38\\n2.188\\n316.63\\n10\\n661 .25\\n38.031\\nI313-8\\n10\\n1174.4\\n119. 12\\n2301 .0\\n20\\n166.72\\n2.425! 333-29i\\n20\\n669.70\\n39 006\\n1330.3\\n20\\n1183.1\\n120.87\\n2317.3\\n30\\n175.06\\n2.674\\n349-95\\n30\\n678.15\\n39-993\\n1346.9\\n30\\n1191.8\\n122.63\\n2333-6\\n40\\n183.40\\n2.934\\n366 6 1\\n40\\n686.60\\n40.992\\n1363-4\\n40\\n1 200 5\\n124.41\\n2349.9\\n50\\n191-74\\n3.207\\n383-27\\n50\\n695.06\\n42 004\\n1380.0\\n50\\nI 209 2\\n126. 20\\n2366.2\\n4\u00c2\u00b0\\n200 08\\n3-492\\n399-92\\nir\\n703.51\\n43-029\\n1396.5\\n24\u00c2\u00b0\\n1217.9 128.00\\n2382.5\\n10\\n208.43\\n3.790\\n416.58\\n10\\n711.97\\n44.066\\n1413-I\\n10\\n1226.6\\n129.82\\n2398.8\\n20\\n216.77\\n4.099\\n433-24\\n20\\n720.44\\n45.116\\n1429.6\\n20\\n1235-3\\n131.65\\n2415.1\\n30\\n225.12\\n4.421\\n449.89\\n30\\n728.90\\n46.178\\n1446.2\\n30\\n1244.0\\n133.50\\n2431.4\\n40\\n233-47\\n4.755\\n466.54\\n40\\n737-37\\n47.253\\n1462.7\\n40\\n1252.8\\n135-36\\n2447.7\\n50\\n5\u00c2\u00b0\\n241 .81\\n5. 100\\n483.20\\n50\\n745-85\\n48.341\\n1479-2\\n50\\n1261.5\\n137-23\\n2464\\n250.16\\n5.459 499-85\\n15\u00c2\u00b0\\n754-32\\n49.441\\n1495-7\\n25\u00c2\u00b0\\n1270.2\\n139.11\\n2480.2\\n10\\n258.51\\n5.829 516.50\\n10\\n762.80\\n50.554\\n1512.3\\n10\\n1279.0\\n141 .01\\n2496-5\\n20\\n266.86\\n6. 211 533-15\\n20\\n771.29\\n51.679\\n1528.8\\n20\\n1287.7\\n142.93\\n2512.8\\n30\\n275.21\\n6.606 549.80\\n30\\n779-77\\n52.818\\n1545-3\\n30\\n1296.5\\n144.85\\n2529.0\\n40\\n283.57\\n7.013 566.44\\n40\\n788.26\\n53-969\\n1561.8\\n40\\n1305-3\\n146.79\\n2545-31\\n50\\n6\u00c2\u00b0\\n291 .92\\n7.432 583-09\\n50\\n796.75\\n55-132\\n1578.3\\n50\\n1314.0\\n148.75\\n2561.5\\n300.28\\n7.863 599-73\\n10\u00c2\u00b0\\n805.25\\n56.309\\n1594.8\\n20\u00c2\u00b0\\n1322.8\\n150.71\\n2577.8\\n10\\n308 64\\n8.307 616.38\\n10\\n813.75\\n57-498\\n1611.3\\n10\\n1331.6\\n152.69\\n2594.0\\n20\\n316.99\\n8.762\\n633.02\\n20\\n822.25\\n58-699\\n1627.8\\n20\\n1340.4\\n154.69\\n2610.3\\n30\\n325.35\\n9-230\\n649 66\\n30\\n830.76\\n59-914\\n1644.3\\n30\\n1349-2\\n156.70\\n2626.5\\n40\\n333.71\\n9.710\\n666 30\\n40\\n839.27\\n61 141\\n1660.8\\n40\\n1358.0 158.72\\n2642.7\\n50\\n342.08\\n10.202\\n682.94\\n50\\n847-78\\n62.381\\n1677.3\\n50\\n1366.8 160.76\\n2658.9\\n7\u00c2\u00b0\\n350.44\\n10.707\\n699-57\\n17\u00c2\u00b0\\n856.30\\n63-634\\n1693.8\\n27\u00c2\u00b0\\n1375-6\\n162.81\\n2675.11\\n10\\n358.81\\n11.224\\n716.21\\n10\\n864.82\\n64 900\\n1710.3\\n10\\n1384-4\\n164.87\\n2691.3\\n20\\n367.17\\n11-753\\n732-84\\n20\\n873-35\\n66.178\\n1726.8\\n20\\n1393.2\\n166.95\\n2707.5!\\n30\\n375.54\\n12.294\\n749-47\\n30\\n881.88\\n67.470\\n1743-2\\n30\\n1402.0\\n1 69 04\\n2723.7\\n40\\n383.91\\n12.847\\n766. 10\\n40\\n890.41\\n68.774\\n1759.7\\n40\\n1410.9\\n171.15\\n2739-9\\n50\\n392.28\\n13-413\\n782.73\\n50\\n898.95\\n70.091\\n1776.2\\n50\\n1419.7\\n173-27\\n2756.1\\n8\u00c2\u00b0\\n400 66\\n13.991\\n799-36\\n18\u00c2\u00b0\\n907.49\\n71.421\\n1792.6\\n28\u00c2\u00b0\\n1428.6\\n175-41\\n2772.3\\n10\\n409.03\\n14.582\\n815.99\\n10\\n916.03\\n72.764\\n1809.1\\n10\\n1437.4\\n177-55\\n2788.4\\n20\\n417.41\\n15.184\\n832.61\\n20\\n924.58\\n74.119\\n1825.5\\n-20\\n1446.3\\n179.72\\n2804.6\\n30\\n425.79\\n15-799\\n849-23\\n30\\n933-13\\nZ5-488\\n1842.0\\n30\\n1455. I\\n181.89\\n2820.7\\n40\\n434.17\\n16.426\\n865.85\\n40\\n941.69\\n76.869\\n1858.4\\n40\\n1464.0\\n184.08\\n2836.9\\n50\\n442.55\\n1 7 066\\n882.47\\n50\\n950.25\\n78.264\\n1874.9\\n50\\n1472.9\\n186.29\\n2853.0\\n0\u00c2\u00b0\\n450.93\\n17.717\\n899 09\\n19\u00c2\u00b0\\n958.81\\n79.671\\n1891.3\\n29\u00c2\u00b0\\n1481.8\\n188.51\\n2S69.2\\n10\\n459-32\\n18.381\\n915.70\\n10\\n967-38\\n81 .092\\n1907.8\\n10\\n1490.7\\n190.74\\n2885.31\\n20\\n467.71\\n19.058\\n932.31\\n20\\n975.96\\n82.525\\n1924.2\\n20\\n1499.6\\n192.99\\n2901 .4\\n30\\n476.10\\n19.746\\n948.92\\n30\\n984-53\\n83.972\\n1 940 6\\n30\\n1508.5\\n195.25\\n2917.6\\n40\\n484.49\\n20.447\\n965-53\\n40\\n993.12\\n85-431\\n1957.1\\n40\\n1517.4\\n197-53\\n2933-7\\n50\\n492.88\\n21 161\\n982 14\\n50\\n20\u00c2\u00b0\\nI 00 I .70\\n86 904\\n1973-5\\n50\\n1526.3\\n199.82\\n2949.8\\n10\u00c2\u00b0\\n501 .28\\n21.886\\n998.74\\n1010.29\\n88.389\\n1989.9\\n30\u00c2\u00b0\\n1535.3\\n202. 12\\n2965.9\\n10\\n509.68\\n22.624\\nio^5-35\\n10\\n1018.89\\n89.888\\n2006 3\\n10\\n1544.2\\n204.44\\n2982.0\\n20\\n518.08\\n23-375\\n1031.95\\n20\\n1027.49\\n91-399\\n2022.7\\n20\\n1553-I\\n206 J7\\n2998. 1\\n30\\n526.48\\n24.138\\n1048.54\\n30\\n1036.09\\n92.924\\n2039.1\\n30\\n1562. I\\n209 1 2\\n3014.2\\n40\\n534.89\\n24.913\\n1065. 14\\n40\\n1044.70\\n94.462\\n2055.5\\n40\\n1571.0\\n211 .48\\n3030.2\\n50\\n543.29\\n25.700\\n1081.73\\n50\\n2V\\n1053-31\\n96.013\\n2071 .9\\n50\\n1580.0\\n213.86\\n3046.3\\n11\u00c2\u00b0\\n551-70\\n26 500\\n1098.33\\n1061.93\\n97-577\\n2088.3\\n31\u00c2\u00b0\\nT589.0\\n216.25 3062.4 1\\n318", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0370.jp2"}, "371": {"fulltext": "TABLE II.\u00e2\u0080\u0094 TANGENTS, EXTERNAL DISTANCES, AND LONG CHORDS FOR A\\n1\u00c2\u00b0 CURVE.\\nA Taiii^ent\\nKxt.Dist.\\nLoiitfCh il\\nA\\nTan ire lit\\nKxt.Dist. LoiiirCh (1\\nA\\nTaiiireiit\\nKxt.nist.\\nLonirChd\\nT.\\ni\\n1 Lt.\\nT.\\nLt.\\nT.\\nA\\nJ. 1\\n31\\n1 1589.0\\n216.25\\n3062.4\\n41\\n2142.2\\n387.38 4013.1\\n51\u00c2\u00b0\\n2732.9\\n618.39\\n4933 4|\\nlo i 1598.0\\n218.66\\n3078.4\\n10\\n2151.7\\n390.71 4028.7\\n10\\n2743.1\\n622.81\\n4948\\n4\\n20\\n1 606 9\\n221 .08\\n3094.5\\n20\\n2161 .2\\n394.06: 4044-3\\n20\\n2753.4\\n627 24\\n4963\\n4\\n30\\n1615.9\\n223.51\\n3110.5\\n30\\n2170.8\\n397-43; 4059 -9\\n30\\n2763.7\\n631 .69\\n4978\\n4\\n40\\n1624.9\\n225.96\\n3126.6\\n40\\n2180.3\\n400.82\\n4075-5\\n40\\n2773.9\\n636.16\\n4993\\n4\\n50\\n1633.9\\n228.42\\n3142.6\\n50\\n2189.9\\n404.22\\n4091 I\\n50\\n2784.2\\n640 66\\n5008\\nj4\\n4\\n32\\n1643.0\\n230.90\\n3158.6\\n42^\\n2199.4\\n407.64\\n4106.6\\n52\u00c2\u00b0\\n2794.5\\n645.17\\n5023\\n10\\n1652.0\\n233.39\\n3174.6\\n10\\n2209.0\\n411.07\\n4122. 2\\n10\\n2804.9\\n649.70\\nS038\\n4\\n20\\n1661 .0\\n235.90\\n3 1 90 6\\n20\\n2218.6\\n414.52\\n4137-7\\n20\\n2815.2\\n654.25\\nS053\\n4\\n30\\n1670.0\\n238.43\\n3206.6\\n30\\n2228. I\\n417.99\\n4153-3\\n30\\n2825.6\\n658.83\\n5068\\n40\\n1679.1\\n240 96\\n3222.6\\n40\\n2237.7\\n421 .48\\n4108.8\\n40\\n2835.9\\n663.42\\n5083\\n3\\n50\\n1688. I\\n243.52\\n3238.6\\n50\\n2247.3\\n424.98 4184.3\\n50\\n2846.3\\n668.03\\n5098\\n2\\n33\u00c2\u00b0\\n1697.2\\n246.08\\n3254.6\\n43\u00c2\u00b0\\n2257.0\\n428. 50 4199.8\\n53\u00c2\u00b0\\n2856.7\\n672.66\\n5113\\nI\\n10\\nI 706 3\\n248.66\\n3270.6\\n10\\n2266.6\\n432.04 42153\\n10\\n2867.1\\n677.32\\n5128\\n20\\nI715.3\\n251 .26\\n3286.6\\n20\\n2276.2\\n435-59 4230.8\\n20\\n2877.5\\n681 .99\\n5142\\n9\\n30\\n1724.4\\n253.87\\n3302.5\\n30\\n2285.9\\n439-16; 4246.3\\n30\\n2S88.O\\n686.68\\n5157\\n8\\n40\\n1733.5\\n256.50\\n3318.5\\n40\\n2295.6\\n442.75 4261.8\\n40\\n2898.4\\n69 I 40\\n5172\\n7\\n50\\n1742.6\\n259.14\\n3334.4\\n50\\n2305.2\\n446.35 4277.3\\n50\\n2908.9\\n696 1 3\\n5187\\n6\\n34\u00c2\u00b0\\n1751.7\\n261 .80\\n3350.4\\n44^\\n2314-9\\n449.98 4292.7\\n54\\n2919.4\\n700.89\\n5202\\n4\\n10\\n1760.8\\n264.47\\n3366.3\\n10\\n2324.6\\n453.62 4308.2\\n10\\n2929.9\\n705.66\\n5217\\n3\\n20\\n1770.0\\n267. 16\\n3382.2\\n20\\n2334.3\\n457-27 43236\\n20\\n2940.4\\n710.46\\n5232\\nI\\n30\\n1779. I\\n269.86\\n3398.2\\n30\\n2344.1\\n460.95 4339-0\\n30\\n2951 .0\\n715.28\\n5246\\n9\\n40\\n1788.2\\n272.58\\n3414.1\\n40\\n2353.8\\n464.64! 4354-5\\n40\\n2961.5\\n720. II\\n5261\\n7\\n50\\n1797.4\\n275.31\\n3430.0\\n50\\n2363.5\\n468.35 4369-9\\n50\\n2972. I\\n2982.7\\n724.97\\n5276\\n5\\n35\\n1806.6\\n278.05\\n3445-9\\n45\u00c2\u00b0\\n2373-3\\n472.08 4385-3\\n55\u00c2\u00b0\\n729.85\\n5291\\n10\\n1815.7\\n280.82\\n3461.8\\n10\\n2383-1\\n475.82\\n4400.7\\n10\\n2993.3\\n734.76\\n5306\\nI\\n20\\n1824.9\\n283.60\\n3477.7\\n20\\n2392.8\\n479.59\\n4416.1\\n20\\n3003.9\\n739.68\\n5320\\n9\\n30\\n1834. I\\n286.39\\n3493-5\\n30\\n2402 6\\n483.37\\n4431-4\\n30\\n3014.5\\n744.62\\n5335\\n6\\n40\\n1843.3\\n289.20\\n3509-4\\n40\\n2412.4\\n487.16\\n4446 8\\n40\\n3025.2\\n749.59\\n5350\\n4\\n50\\n30\u00c2\u00b0\\n1852.5\\n1861.7\\n292 .02\\n3525-3\\n50\\n4(i\u00c2\u00b0\\n2422.3\\n490 98\\n4462 2\\n50\\n3035-8\\n754-57\\n5365\\nI\\n294.86\\n3541. I\\n2432 I\\n494.82 4477.5\\n5(r\\n3046.5\\n759.58\\n5379\\n8\\n10\\n1870.9\\n297.72\\n3557.0\\n10\\n2441.9\\n498.67 4492.8\\n10\\n3057.2\\n764.61\\n5,394\\nS\\n20 1880. I\\n300.59\\n3572.8\\n20\\n2451.8\\n502.54 4508.2\\n20\\n3067 9\\n769.66\\n5409\\n2\\n30\\n1889.4\\n303.47\\n3588.6\\n30\\n2461 .7\\n506.42 4523- 5\\n30\\n3078.7\\n774-73\\n5423\\n.9\\n40\\n1898.6\\n306.37\\n3604.5\\n40\\n2471.5\\n510.33 4538.8\\n40\\n3089.4\\n779.83\\n5438\\n.6\\n50\\n1907.9\\n309.29\\n3620.3\\n50\\n2481 .4\\n514.25 4554-1\\n50\\n3100.2\\n784.94! 5453\\n3\\n37\u00c2\u00b0\\nI917.I\\n312.22\\n3636. I\\n17\u00c2\u00b0\\n2491.3\\n518.20 4569.4\\n57\\n3110.9\\n790.08 5467\\n9\\n10\\n1926.4\\n315-17\\n3651.9\\n10\\n2501 .2\\n522.16 4584.7\\n10\\n3121.7\\n795-241 5482\\nS\\n20\\n1935.7\\n318.13\\n3667.7\\n20\\n2511 .2\\n526.13 4599-9\\n20\\n3132.6\\n800.42\\n5497\\n2\\n30\\n1945.0\\n321. II\\n3683.5\\n30\\n2521 1\\n530.13 4615.2\\n30\\n3143-4\\n805.62\\n5511\\n8\\n40\\n1954.3\\n324.11\\n3699.3\\n40\\n2531.1\\n534.15 4630.4\\n40\\n3154-2\\n810.85\\n5526\\n-4\\n50 1963.6\\n327.12\\n3715.0\\n50\\n2541.0\\n538.18 46457\\n50\\n3165.1\\n816. 10\\n5541\\n38\\n1972.9\\n330.15\\n3730.8\\n48\u00c2\u00b0\\n2551.0\\n542.23 4660.9\\n58\\n3176.0\\n821.37\\n5555\\n6\\n10\\n1982.2\\n333.19\\n3746.5\\n10\\n2561 .0\\n546.30\\n4676. I\\n10\\n3186.9\\n826.66\\nSS70\\n2\\n20\\nI99I.5\\n336.25\\n3762.3\\n20\\n2571.0\\n550.39 4691.3\\n20\\n3197.8\\n831.98\\n5584\\n7\\n30\\n2000 9\\n339.32\\n3778.0\\n30\\n2581 .0\\n554.50 4706.5\\n30\\n3208.8\\nS37.31\\n5599\\n3\\n40\\n2010.2\\n342.41\\n3793-8\\n40\\n2591.1\\n558.63 4721.7\\n40\\n3219.7\\n842.67\\n5613\\n8\\n50 2019.6\\n345.52\\n3809.5\\n50\\n4y\u00c2\u00b0\\n2601 I\\n562.77, 4736.9\\n50\\n3230.7\\n848.06\\n5628\\n3\\n8\\n39\u00c2\u00b0 1 2029.0\\n348.64\\n3825.2\\n2611 .2\\n566.94 4752.1\\n51)\u00c2\u00b0\\n3241-7\\n853.46 5642\\n10 2038.4\\n351.78\\n3840.9\\n10\\n2621 .2\\n571.12 4767.3\\n10\\n3252.7\\n858.89, 5657\\n3\\n20\\n2047 8\\n354.94\\n3856.6\\n20\\n2631.3\\n575.32 4782.4\\n20\\n3263.7\\n\u00c2\u00a364.34; 5671\\n8\\n30\\n2057.2\\n358.11\\n3872.3\\n30\\n2641,4\\n579.54\\n4797-5\\n30\\n3274-8\\n869.82; 5686\\n3\\n40\\n2066 6\\n361 .29\\n3888.0\\n40\\n2651.5\\n583.78\\n4812.7\\n40\\n3285.8\\n875.32 5700\\n8\\n50 2076.0\\n364.50\\n3903 6\\n50\\n2661.6\\n588.04\\n592.32\\n4827.8\\n50\\n3296.9\\n880.84 1 5715\\n2\\n7\\n40\\n2085.4\\n367.72\\n3919-3\\n50\u00c2\u00b0\\n2671.8\\n4842.9\\n0\\n3308.0\\n886.38; 5729\\n10\\n2094.9\\n370.95\\n3935-0\\n10\\n2681.9\\n596.62\\n4858.0\\n10\\n3319-1\\n891.95 5744\\nI\\n20\\n2104.3\\n374.20\\n3950.6\\n20\\n2692. I\\n600.93\\n4873-1\\n20\\n3330.3\\n897.54 5758\\n5\\n30\\n2113.8\\n377.47\\n3966.3\\n30\\n2702.3\\n605.27\\n4888.2\\n30\\n3341-4\\n903. 15 1 5772\\n9\\n40\\n2123.3\\n380.76\\n3981.9\\n40\\n2712. 5\\n609.62 1\\n4903 2\\n40\\n3352.6\\n908.79; 5787\\n50\\n2132.7\\n384.06\\n3997 5\\n50\\n51\u00c2\u00b0\\n2722.7\\n6 1 4 00\\n4918.3\\n3363-81 914-45,\\n5801\\n7\\n41\u00c2\u00b0 2142.2\\n387.38\\n4013. I\\n2732.9\\n_6 8.39i\\n4933.4\\n\u00c2\u00abr 1\\n3375 -oi\\n920. 14 1\\n5816.\\n319", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0371.jp2"}, "372": {"fulltext": "TABLE II.\u00e2\u0080\u0094 TANGENTS, EXTERNAL DISTANCES, AND LONG CHORDS FOR A\\n1\u00c2\u00b0 CURVE.\\nA\\n61\u00c2\u00b0\\nID\\n20\\n30\\n40\\n50\\nTangent\\nT.\\nExt.Dist.\\nLongCh d\\nA\\n71\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\nTangent\\nT.\\nExt.Dist.\\nLongCird\\nLC.\\nA\\n1 Tangent\\nExt.Dist.\\nE.\\nLongCh d\\nLC.\\n3375-0\\n3386.3\\n3397.5\\n3408 8\\n3420.1\\n3431.4\\n920. 14\\n925-85\\n931-58\\n937.34\\n943.12\\n948.92\\n5816.0\\n5830.4\\n5844-7\\n5859.1\\n5873-4\\n5887.7\\n4086 9\\n4099.5\\n4II2.I\\n4124.8\\n4137-4\\n4150. I\\n1 308 2\\n1315-5\\n1322.9\\n1330-3\\n1337-7\\n1345- I\\n6654.4\\n6668.0\\n6681.6\\n6695 I\\n6708 6\\n6722. I\\n81\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n4893 6\\n4908\\n4922 5\\n4937-0\\n4951-5\\n4966 1\\n1805.3\\n1814.7\\n1824. I\\n1833-6\\n1843. I\\n1852.6\\n7442 2\\n7454-9\\n7467 5\\n7480.2\\n7492 8\\n7505-4\\n62\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n68\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n3442.7\\n3454.1\\n3465.4\\n3476.8\\n3488 2\\n3499-7\\n954.75\\n960 60\\n966.48\\n972.39\\n978.31\\n984.27\\n5902.0\\n5916.3\\n5930-5\\n5944.8\\n5959-0\\n5973-3\\n72=\\n10\\n20\\n30\\n40\\n50\\n4162.8\\n4175-6\\n4188.4\\n4201 .2\\n4214.0\\n4226.8\\n1352.6\\n1360. I\\n1367.6\\n1375-2\\n1382.8\\n1390-4\\n6735.6\\n6749.1\\n6762.5\\n6776.0\\n6789-4\\n6802 8\\n82\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n4980.7\\n4995-4\\n5010.0\\n5024.8\\n5039-5\\n5054-3\\n1862.2\\n1871.8\\n1881.5\\n189I .2\\n1 900 9\\nI9IO.7\\n7518.0\\n7530.5\\n7543-1\\n7555-6\\n7568.2\\n7580.7\\n3511.1\\n3522.6\\n3534-1\\n3545-6\\n3557-2\\n3568.7\\n990.24\\n996.24\\n1002.3\\n1008.3\\nIOI4.4\\n1020.5\\n5987-5\\n6001 .7\\n6015.9\\n6030\\n6044 2\\n6058.4\\n73\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n4239-7\\n4252.6\\n4265.6\\n4278.5\\n4291.5\\n4304-6\\n1398.0\\n1405 7\\ni4i3-5\\n1421 .2\\n1429.0\\n1436.8\\n6816.3\\n6829.6\\n6843\\n6856.4\\n6869.7\\n6883.1\\n83\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n5069 2\\n5084.0\\n5099-0\\n5113-9\\n5128.9\\n5143-9\\n1920. 5\\n1930-4\\n1940.3\\n1950-3\\nI 960 2\\n1970.3\\n7593-2\\n7605.6\\n7618.1\\n7630.5\\n7643.0\\n7655-4\\n64\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n3580.3\\n3591-9\\n3603.5\\n3615-1\\n3626.8\\n3638.5\\n1026.6\\n1032.8\\n1039.0\\n1045.2\\nI051.4\\n1057.7\\n6072. 5\\n6086.6\\n6100.7\\n6114.8\\n6128.9\\n6143.0\\n74\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n75\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n4317-6\\n4330-7\\n4343-8\\n4356.9\\n4370.1\\n4383-3\\n4396.5\\n4409.8\\n4423 I\\n4436.4\\n4449-7\\n4463 1\\n1444.6\\n1452.5\\n1460.4\\n1468.4\\n1476.4\\n1484.4\\n6896.4\\n6909.7\\n6923.0\\n6936 2\\n6949-5\\n6962 8\\n84\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n5159.0\\n5174-1\\n5189.3\\n5204.4\\n5219.7\\n5234-9\\n1980.4\\n1990.5\\n2000 6\\n2010. 8\\n2021 I\\n2031.4\\n7667.8\\n7680.1\\n7692.5\\n7704-9\\n7717.2\\n7729-5\\n65\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n66\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n3650.2\\n3661 .9\\n3673.7\\n3685.4\\n3697 2\\n3709.0\\n3720.9\\n673^.7\\n3744.6\\n3756.5\\n3768.5\\n3780.4\\n1063.9\\n1070.2\\n1076.6\\n1082.9\\n1089.3\\n1095.7\\n1 102. 2\\nIIO8.6\\nIII5.I\\nII2I.7\\nII28.2\\n1134.8\\n6157. I\\n6171 I\\n6185.2\\n6199.2\\n6213.2\\n6227.2\\n1492-4\\n1500.5\\n1508.6\\n1516.7\\n1524.9\\n1533-1\\n6976.0\\n6989.2\\n7002 4\\n7015.6\\n7028.8\\n7041.9\\n85\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n5250-3\\n5265.6\\n5281.0\\n5296.4\\n5311-9\\n5327-4\\n2041.7\\n2052. I\\n2062 5\\n2073.0\\n2083.5\\n2094 I\\n7741-8\\n7754-1\\n7766.3\\n7778.6\\n7790.8\\n7803.0\\n6241 .2\\n6255.2\\n6269. I\\n6283.1\\n6297.0\\n6310.9\\n76\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n4476.5\\n4489.9\\n4503 -4\\n4516.9\\n4530.4\\n4544-0\\n1541.4\\n1549-7\\n1558.0\\n1566.3\\n1574-7\\n1583. I\\n7055\\n7068 2\\n7081.3\\n7094-4\\n7107.5\\n7120.5\\n86\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n5343-0\\n5358-6\\n5374-2\\n5389-9\\n5405-6\\n5421.4\\n2 1 04 7\\n2115.3\\n2126.0\\n2136.7\\n2147.5\\n2158.4\\n7815.2\\n7827.4\\n7839.6\\n7851.7\\n7863.8\\n7876.0\\n67\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n68\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n6d\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n3792.4\\n3804.4\\n3816.4\\n3828.4\\n3840.5\\n3852.6\\nII4I.4\\nII48.O\\n1154.7\\nII61 .3\\nII68.I\\nri74.8\\n6324.8\\n6338.7\\n6352.6\\n6366.4\\n6380.3\\n6394-1\\n77\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n4557-6\\n4571.2\\n4584-8\\n4598-5\\n4612.2\\n4626\\n1591.6\\n1 600 1\\n1608.6\\n1617. I\\n1625.7\\n1634.4\\n7133-6\\n7146.6\\n7159-6\\n7172.6\\n7185.6\\n7198.6\\n87\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n5437-2\\n5453-1\\n5469.0\\n5484-9\\n5500.9\\n5517-0\\n2169. 2\\n2180.2\\n2191 I\\n2202.2\\n2213.2\\n2224.3\\n7888.1\\n7900.1\\n7912.2\\n7924.3\\n7936.3\\n7948 3\\n3864.7\\n3876.8\\n3889.0\\n3901 .2\\n3913.4\\n3925.6\\n1181.6\\n1188.4\\n1195.2\\n1202.0\\n1208.9\\n1215.8\\n1222.7\\n1229.7\\n1236.7\\n1243-7\\n1250.8\\n1257.9\\n6408\\n6421.8\\n6435-6\\n6449.4\\n6463 1\\n6476 9\\n78\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n4639.8\\n4653-6\\n4667.4\\n4681.3\\n4695 2\\n4709.2\\n1 643\\n1651.7\\n1 660 5\\n1669.2\\n1678. 1\\n1686.9\\n7211 .6\\n7224.5\\n7237-4\\n7250.4\\n7263.3\\n7276.1\\n88\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n5533-1\\n5549-2\\n5565-4\\n5581-6\\n5597-8\\n5614.2\\n2235-5\\n2246.7\\n2258.0\\n2269.3\\n2280.6\\n2292.0\\n7960.3\\n7972.3\\n7984.2\\n7996.2\\n8008.1\\n8020\\n3937.9\\n3950.2\\n3962.5\\n3974.8\\n3987.2\\n3999-5\\n6490 6\\n6504-4\\n6518. I\\n6531.8\\n6545-5\\n6559.1\\n7D\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n4723.2\\n4737-2\\n4751-2\\n4765.3\\n4779-4\\n4793-6\\n1695.8\\n1704.7\\n1713-7\\n1722.7\\n1731-7\\n1740.8\\n7289.0\\n7301.9\\n7314.7\\n7327.5\\n7340.3\\n7353-1\\n89\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n5630.5\\n5646.9\\n5663.4\\n5679-9\\n5696.4\\n57130\\n2303.5\\n2315.0\\n2326.6\\n2338.2\\n2349-8\\n2361.5\\n8031 .9\\n8043 8\\n8055-7\\n8067.5\\nS079.3\\n8091 .2\\n70=:\\n10\\n20\\n30\\n40\\n50\\n4011.9}\\n4024.4\\n4036.8\\n4049-3\\n4061.8\\n4074.4\\n1265.0\\n1272. I\\n1279-3\\n1286.5\\n1293.7\\n1300.9\\n6572.8\\n6586.4\\n6600 I\\n6613.7\\n6627.3\\n6640 9\\n80\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n4808 7\\n4822.0\\n4836.2\\n4850.5\\n4864.8\\n4879.2\\n1749-9\\n1759-0\\n1768.2\\n1777-4\\n1796.0\\n7365-9\\n7378.7\\n7391-4\\n7404-1\\n7416.8\\n7429-5\\nJ)0\u00c2\u00b0\\n10\\n20\\n30\\n40\\n50\\n5729-7\\n5746.3\\n5763-1\\n5779-9\\n5796-7\\n5813.6\\n2373.3\\n2385.1\\n2397.0\\n2408 9\\n2420.9\\n2432.9\\n8103.0\\n8114.7\\n8126.5\\n8138.2\\n8150.0\\n8161.7\\n71\u00c2\u00b0\\n4086 9\\n1308.2\\n6654.4\\n\u00c2\u00a71\u00c2\u00b0 1\\n4893.61\\n1805.3\\n7442 2\\nt)i\u00c2\u00b0\\n5830.5\\n2444.9\\n8173-4I\\n320", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0372.jp2"}, "373": {"fulltext": "TABLE III.\u00e2\u0080\u0094 SWITCH LEADS AND DISTANCES.\\nLEAD-RAILS CIRCULAR THROUGHOUT; GAUGE 4 S| See \u00c2\u00a7262.\\nFrog\\nNumber\\n4\\n4-5\\n5\\n5.5\\n6\\n6.5\\n7\\n7-5\\n8\\nS.5\\n9\\n9-5\\n10\\n10.5\\nII\\nII. 5\\n12\\nFrog Angle (F)\\n14\\n12 40\\nII\\n15 00\\n59\\n10 23\\n9 31\\n25 16\\n20\\n38\\n47\\n10\\n51\\n16\\n37 41\\n09 10\\n43 59\\n21 35\\n01 32\\n43 29\\n27 09\\n12 18\\n58 45\\n46 19\\nLead (L)\\n(Eq. 79).\\n37-67\\n42 -37\\n47.08\\n51.79\\n56.50\\n61.21\\n65.92\\n70.62\\n75-33\\n80.04\\n84-75\\n89.46\\n94.17\\n98.87\\n103.58\\n108.29\\n113.00\\nChord (QT)\\n(Eq- 77)-\\n37-38\\n42. 12\\n46.85\\n51-58\\n56.30\\n61.03\\n65-75\\n70.47\\n75.19\\n79.90\\n84.62\\n89.33\\n94-05\\n98.76\\n103.47\\n108.19\\n112.90\\nRadius of Lead\\nRails (r, Eq.7S).\\n150.67\\n190.69\\n23542\\n2S4.S5\\n339.00\\n397. S5\\n461.42\\n529.69\\n602.67\\n680.36\\n762.75\\n849-85\\n941.67\\n1038. 19\\n1139.42\\n1245.36\\n1356.00\\nLog r.\\n2.I780I\\n.2S032\\n\u00e2\u0080\u00a2371S3\\n.45462\\n.53020\\n\u00e2\u0080\u00a259972\\n6640 3\\n.72402\\n.78007\\n-83273\\n.8S238\\n.92934\\n2.97389\\n3.01627\\n05668\\n.09529\\n3.13226\\nDegree of\\nCurve\\n38 46\\n30 24\\n24 32\\n20 13\\n16 58\\n14 26\\n12 26\\n10 50\\n9 31\\n8 26\\n7 31\\nFrog\\nNumber\\n7.5\\n8\\n8.5\\n9\\n45\\n05\\n32\\n02\\n36\\n14\\n9\\n10\\n10\\nII\\nII\\n12\\nTURNOUTS WITH STRAIGHT POINT-RAILS AND STRAIGHT FROG-RAILS GAUGE 4 8^ See 265.\\nFrog\\nNumber\\nin).\\n4\\n4-5\\n5\\n5.5\\n6\\n6-5\\n7\\n7-5\\n8\\n8.5\\n9\\n9.5\\n10\\n10.5\\nII\\nII-5\\n12\\nSwitch\\nPointAngle\\n(a).\\n40\\n40\\n45\\n45\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\nLength of\\nSwitch\\nPoint\\n7-5\\n7.5\\n10.\\n10. o\\n15.0\\n15.0\\n15-0\\n15\\n15\\n15\\n15-0\\n15\\n15\\n15.0\\n15.0\\n15-0\\n15.0\\nLength of\\nStraight\\nFrog-rail\\n(7\\n1.50\\n1.69\\n1.87\\n2.06\\n2.25\\n2.44\\n2.62\\n2. Si\\n3.00\\n3.19\\n3-37\\n3-56\\n3- 75\\n3-94\\n4.12\\n4-31\\n4.50\\nLead (L)\\n(Eq. 90).\\n32.20\\n34.29\\n41.85\\n44-16\\n56.00\\n58.84\\n61.65\\n64.36\\n67.04\\n69.60\\n72.20\\n74.70\\n77.04\\n79.51\\n81.82\\n84.09\\n86.16\\nChord\\n(ST)\\n(Eq. 88).\\n23.09\\n25-03\\n29. ss\\n32.03\\n38.66\\n41.34\\n43.98\\n46.50\\n48. 99\\n51. 38\\n53.80\\n56.11\\n58.28\\n60.57\\n62.69\\n64.78\\n66.67\\nRadius of\\nLead-\\nrails\\n(r.Eq.87).\\n125.21\\n159.25\\n197-65\\n240.44\\n2S8.09\\n340.19\\n397-65\\n460.00\\n527.91\\n600 94\\n6S1.16\\n767.11\\n85S.14\\n959-00\\n1065.52\\nII80. 16\\n1299.93\\nLog\\n09764\\n20208\\n2958(3\\n38100\\n45953\\n53172\\n59950\\n66276\\n72256\\n77883\\n83325\\n8S4S6\\n93356\\n98182\\n02756\\n07194\\n11392\\nDegree of\\nCurve\\n47\\n05\\n36\\n36\\n29\\n22\\n24\\n00\\n19\\n59\\n16\\n54\\n14\\n27\\n12\\n29\\n10\\n52\\n9\\n33\\n8\\n25\\n7\\n28\\n6\\n41\\n5\\n59\\n5\\n23\\n4\\n51\\n4\\n24\\nFrog\\nNumber\\n4\\n4-5\\n5\\n5.5\\n6\\n6.5\\n7\\n7-5\\n8\\n8.5\\n9\\n9-5\\n10\\n10.5\\nII\\nII-5\\n12\\nTRIGONOMETRICAL FUNCTIONS OF THE FROG ANGLES (F).\\nFrog\\nNumber FrogAngle (F).\\n4\\n4-5\\n5\\n5.5\\n6\\n6.5\\n7\\n7.\\n8\\nS.\\n9\\n9-\\n10\\n10.\\nII\\nII\\n12\\n5\\n14\\n12\\nII\\n10\\n9\\n8\\n8\\n7\\n7\\n6\\n6\\n6\\n5\\n5\\n5\\n4\\n4\\n15\\n40\\n25\\n23\\n31\\n47\\n10\\n37\\n09\\n43\\n21\\n01\\n43\\n27\\n12\\n58\\n46\\n00\\n49\\n16\\n20\\n38\\n51\\n16\\n41\\n10\\n59\\n35\\n32\\n29\\n09\\n18\\n45\\n19\\nNat. sin F. Na\\nt. COSi^.\\n.24615\\n96923\\n\u00e2\u0080\u00a221951 j\\n97561\\n.19802\\n98020\\n.1S033\\n9S360\\n.16552\\n98621\\n-15294\\n98S23\\n.14213\\n98985\\n\u00e2\u0080\u00a213274\\n99II5\\n.12452\\n99222\\n.11724\\n99310\\n.11077\\n993S5\\n.10497\\n99448\\n\u00e2\u0080\u00a209975\\n99501\\n.09502\\n99548\\n.09072\\n995S8\\n.08679\\n99623\\n\u00e2\u0080\u00a208319\\n99653\\nLog sin F.\\n9.39120\\n\u00e2\u0080\u00a234145\\n29670\\n.25606\\n.21884\\n\u00e2\u0080\u00a218453\\n.1526s\\n1230I\\n.09522\\n.06909\\n.04442\\n9.02107\\n8. 9989 I\\n.97781\\n\u00e2\u0080\u00a295770\\n.93S4S\\n8. 92007\\n321\\nLog cos F.\\n1.98642\\n.98927\\n\u00e2\u0080\u00a29913I\\n.992S2\\n\u00e2\u0080\u00a299397\\n.99486\\n\u00e2\u0080\u00a299557\\n.99614\\n9966(3\\n99699\\n\u00e2\u0080\u00a299732\\n\u00e2\u0080\u00a299759\\n.997S3\\n.99803\\n.99S20\\n.99S36\\n1.9SS49\\nLog cot F.\\n10.59522\\n.647S2\\n.69461\\n-73675\\n.77513\\n.81033\\n.8428s\\n\u00e2\u0080\u00a287313\\n\u00e2\u0080\u00a29013s\\n.92790\\n.9528C3\\n.97652\\nIO.99S92\\n11.02021\\n.04050\\n.05987\\nII.07S42\\nLog vers .F.\\n8.48811\\n.38721\\n.29670\\n.21467\\n13966\\n\u00e2\u0080\u00a20705s\\nS. 0065 5\\n7.94691\\n.8911(3\\n.83S64\\n.78915\\n.74232\\n.6978S\\n\u00e2\u0080\u00a265560\\n.6152S\\n.57676\\n7.539S6\\nFrog\\nNumber\\n4\\n4.5\\n5\\n5-\\n6\\n6.\\n7\\n7\\n8\\n8.\\n9\\n9-\\n10\\n10.\\nII\\nII\\n12\\n5", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0373.jp2"}, "374": {"fulltext": "TABLE IV.\u00e2\u0080\u0094 ELEMENTS OF TRANSITION CURVES.\\n1\\n0\\nd\\nLO\\nt^\\nCl\\nLO\\nIn\\nCO\\nM\\nCO\\nM\\nCO\\nO O 0\\\\ ^-r\\\\ xj-\\\\ \\\\0 O\\nN\\nCO\\n5i\\nO O 0\\\\ On CO VO ro\\nO O CN a\\\\ ON ON On\\noo\\ntN\\nIN\\nNO\\n00\\nn\\nLO\\nCO\\nCO\\nVO\\nCO\\ntN\\nCO\\nlA 6 C On\\nON\\nOn\\nC) LO t\\\\ On f^ t^\\nOn\\nn\\nN\\nCNl\\nCO\\nCO\\nCO\\nM Cl\\ni-O\\nCO\\nCO\\nIN\\ntN\\n00\\nLO\\nc^\\nLO\\nLO\\nt\\\\\\nCO\\nLO\\nLO\\nC\\nCO\\nIN\\ntoo 0 f^\\nCi\\nNO\\nH\\nvO vO oo CO O r^\\nNO\\nS\\nCO\\no\\nCl\\nCO\\nCO\\nCO\\nri vO\\nLTl\\nO\\nic\\nOn\\nri\\no\\nLn On ro LO\\nt^\\nOO\\nq\\nCO\\nCO\\nCO\\nCl\\nCl\\nd 1\u00e2\u0080\u0094\\nod d\\\\ d\\\\ d\\\\ 6 6 6\\nd\\nd\\n1\\nLO\\ntN\\nCl\\nLO r^\\nQ\\nLO\\nCl\\nX\\nCO\\nLO\\nCO\\nt^\\nLO\\nNO\\nCO CO\\nCO\\nCl\\nON\\nLO\\nCI\\nd LO\\nCO\\nCO\\n^N. vo n oo o r^\\n_\\nM\\nON\\nCI\\nCI\\nn\\nCl\\nh-i\\nH\\nrj m CO o oo\\nO to oo -n 00\\nNO\\nON\\nOO\\nLO\\nIN\\n1\\n1\\nb\\nIN\\nLO\\nCJ\\nIN LO\\nCl\\nLO\\nd d d d cj fo\\nLO\\nJN\\nd\\nLO\\nCO\\nCO H-\\nLO\\nC\\nl\\nLO\\nCO\\n00\\nCO\\n1\u00e2\u0080\u0094 c\\nw\\nNO\\n10 Cl\\nCO\\nVO\\nCO\\n-e-\\n(00 CO On 1- (n\\nLO t^ oo vo On r^\\n(04\\nM\\nLO\\nIn\\na\\n3\\n1-1\\n\u00c2\u00b0(N\\nM\\nX\\nUN n;^\\n_C\\nVO O M vo 00 O O\\nCO\\nM\\nNO\\nt^ ro m i^ M rj t^\\nCO\\nOO\\nLO\\nr^\\nCI\\nLO\\nr-^\\nLO\\nCl\\nIn\\nm CO On CO t^ o\\nNO\\n00\\nm\\nLO\\nHH\\nCO\\n1\u00e2\u0080\u0094 1\\nCl\\nlt\\\\\\nO\\nrt vr^ vA ^O O t^ t^\\nIN.\\nIN.\\ntN\\nc\\nN^\\nNO\\n1\u00e2\u0080\u0094\\nCO\\nCl\\nNO\\nLO\\nCO\\nft\\n-a\\n5.\\n3\\no\\n(J\\nCO\\nCl\\nCl\\nLO\\nCl\\nLO\\nX\\nOn (On (vO On vo\\nO C^ON0O r^ -r\\\\H-^\\nO OnOnOOnOnOnoo\\n(Q NO\\nOn CO\\ntN NO\\n*Lo\\nCJ\\nLO\\n8\\nCO\\nLO\\n8\\nCO\\nCl\\nLO\\nLO\\ntN\\nw\\nO On On On On On On\\nON\\nOn\\no\\\\\\no\\nO On On 0\\\\ On On On\\nOn\\nON\\nON\\n4i\\nOP\\no\\na\\nL*:\\nLO\\nLO\\nCO\\n00\\nCl\\nVO\\nCO\\nCO\\nLO\\nd d\\\\ On On On d\\\\ On\\nOn\\nOn\\nd\\\\\\nM\\n10\\n0)\\nM\\nW\\nrt\\nVi\\nLO\\nIN\\nLO Cl\\nIn\\nLO\\nn\\n-e-\\n(CO (0 (M O r\\\\\\nO\\n0\\nLO\\nCl\\nCO\\nw\\nLO\\nr^ ON On t^ oo oo NO\\nNO\\nCO\\nc\\nc\\ns\\n00 LO vo oo O -o\\nCO\\nX\\nCO -1 w CO NO CO\\nON\\nOn\\nIN\\nft\\nNO\\n00\\nCO\\nLO\\nCO On\\nCl\\nCO\\nVO\\nVO\\ntc\\nCO oo CO NO t^\\nCO\\n0\\\\\\no\\nrt\\nCO\\nCl\\n-H CO\\nCl\\nLO\\nCl\\no\\n00\\nco\\nOn\\nb\\no\\no\\nV\\nS\\no\\nn\\n0\\nIN\\nLO\\nn LO\\nIN\\nCJ\\nLO\\nCO\\nCO\\nl-l\\nvo hm\\nCO\\nCl\\n\u00e2\u0096\u00a0e-\\nM\\nX\\nOn (r^ (On\\n3^ 2^ On On On oo 00\\nC C On JN On ON ON\\nOn\\nNO\\nOn\\nLO\\nON\\nCO\\nC)\\nON\\nc\\n.2\\nu\\nCO\\ntn\\nC^\\n8\\nLO\\nCO LO\\nCO\\nIN\\nCO\\nCO\\nCO\\ncS\\nO O On ON On On On\\nOn\\nON\\nOn\\nK,\\nH-\\nCl\\nCl\\nQ\\nIn\\nLO\\nc^\\nIN\\nLO\\nCl\\nIn\\n^1\\nco\\nCO\\nIN\\n00\\nCO\\nLO\\nCO\\ntN\\nCO\\nLO\\n-e-\\nI\u00e2\u0080\u0094\\nM\\nLO\\n5-\\nCO\\nss\\n(N (vn oo t^ CO (0\\no\\nIN\\nX\\nr NO CO n LTi\\nO O c) CO t- NO\\nCO\\nIn\\nOO\\nOn\\nOn\\nM\\nCl\\nCl\\n-i\\nq q q q q q o\\nq\\nq\\nV\\nCJ\\nLO\\nt\\\\\\nCl\\nLO\\nIn\\nw\\nco\\nCO\\nLO\\nNO\\nCO\\nc\\nCO\\nCl\\nOn\\nCO\\nLO\\nCO\\nCl\\n4^\\ni\\nCl\\nt-\\nCO\\no o o o o o o\\no\\no\\nO\\ntc\\nCO CO O O CO CO O\\no\\nCO\\nCO\\nSi\\nK, D VO iJ-\u00c2\u00bb C) t~^ O\\no\\nIN\\nM\\n1\u00e2\u0080\u0094 1\\nc\\nM\\nt^-^\\nM\\nn Lo CO CO\\nCO\\nCO\\nLO\\nb\\nLO\\nc\\nIN\\nLO Cl\\ntN\\nLO\\nM\\nCO\\nLO\\nCO\\nTt-\\nCl\\nz\\nO O O i-i -I ci CO\\nLO\\nNO\\nG?\\nu\\nb\\nCO\\nt^\\nCO\\nVO\\nLO\\nLO\\n00\\nCl\\nLO\\nCO\\nLO\\nCl\\nCl\\n-4^\\nt/j\\ns\\n-t C^ ro vo t^\\nCO\\nOn\\no\\np\\n*-Cj\\n\u00e2\u0096\u00a055\\nrt\\nfH\\n^1\\ncc\\nrj^\\nLt C\\nb\u00c2\u00bb 0(0\\na\\n322", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0374.jp2"}, "375": {"fulltext": "TABLE IV.\u00e2\u0080\u0094 ELEMENTS OF TRANSITION CURVES.\\ns\\nas 0\\\\ o\\\\ o\\\\ oo r^rt-o\\nn r^ On c~\u00c2\u00bb Tf t^ C\\\\ r\\nH^ \u00e2\u0096\u00baH -I c^ cs\\nvO^O M ro^ \u00c2\u00bb-nr -oo O\\nr^-\u00c2\u00b1DO M \\\\D oo O CO\\ni-r^mroooooor-^ri fO\\n-c n\\n0 -t CO (ro ro CO rO\\nvOcoco i-nvo r~^cocovO f^\\nONON CAfOOOO O C) t1-\\ntJ- lA \\\\d o t^ r^ i^ 00* CO CO\\n-e-\\niO\\\\\\n(vO\\ni-r\\nCXD\\nrv, (t^\\n\\\\-r\\\\\\nri\\nr^\\nt^\\n0\\\\\\nOn\\nCO\\niJ-\\nO\\nr\\\\\\nNO\\nur\\nro\\ns\\nV\\nON\\nOS\\nOn\\nON\\nOn CO\\nNO\\n-t-\\nr^\\nON\\nON\\nC7n\\nOn\\nON ON\\nON\\nCA\\nON\\nCO\\nif)\\nON\\nON\\nOn\\nON\\nON ON\\nON\\nON\\nON\\nUN\\ne\\nON\\nON\\nON\\nON\\nON On\\nON\\nON\\nON\\nON\\n(D\\nrj CO\\no\\nrn\\nfON\\nro\\nm\\no\\nCO On\\nOn no\\nNO\\nCO\\nro\\nri\\no\\nON vO\\nr-^ On\\nLO\\nLO\\nO\\nNO\\nm\\nro\\n\u00c2\u00bbM\\nNO\\nCO\\nOn\\nON\\nr^\\nVO\\nNO\\nCO\\nON\\no\\nM\\nm\\nt^OOCOCOCOCO OnOnOnOn\\nON 0 0 CO CO OJ^ t^ CO (r\\nONONONr^i-nn j^O\\nOnOnOnOnOnOncoco r\\\\\\nO OnOnOnOnOnOnOnCnOn\\n(CO n NO i- (CO r^\\n\u00e2\u0080\u0094frONO rO -iNO \u00c2\u00ab-/^r^\\nO NO ON r i/^ On f\\nOOOOOO- -rJ\\ni-r\u00c2\u00bbw-iO O Lou-iO O i-nvn\\n\u00e2\u0080\u00a2+rom^\u00e2\u0080\u0094 00\u00c2\u00ab-t\\nO O ^l rO ^r^CN\u00c2\u00ab rO\\nM cO ^h^^NO t ^co OnO\\nC3\\nI\\nCi\\nOC\\nC\\nCO\\n*1\\no^\\nCI lo On M l^ Q i-* O o O\\nNO CO r^ O ro n NO ^i O\\nn -rt O ro ro ro ri I O\\nCO CO r^ t x NO\\nro r I O\\nCO -t- O CO\\nr-^ CO i NO n\\n\u00e2\u0096\u00a0-I -rt ro LO\\nto\\nrn o\\no\\nyr\\\\ O\\no\\nrv NO NO Tf c n\\nr O Lo\\nCO\\n00 ri\\nO -o\\nO\\ni/~i ro\\nO u^\\nCO\\nr\\\\ NO\\nu-iioT^- ^fOri\\n8\\n8\\nO\\nO\\n8\\nO -o\\nCO Th\\nr^ CO\\nO\\nO O\\nO CO\\nO NO r^\\nro O CO\\nV? 8\\nro\\nO r)\\nrf Tt CO CO N\\nlo O\\nro\\no\\n8\\nO ir^ O\\nO -r CO\\nO ro n\\no o\\n8\\nO CO\\nCI O CO\\nO\\nro\\nCl NO\\nO ci\\nCO CO M CI M\\nO \u00c2\u00bbJ~i O -o\\nro O\\nM oo O NO\\nLO Tj- l-O LO\\nO CJ CO\\nO Lo O\\nCO O\\nc) CO O\\nC) O\\nir-i\\no\\nCO\\no\\no\\nCO\\nc\\no\\nO\\nlr^ O N O\\ni- CO O\\nCO r^ NO O\\nro ci ci ro\\nLO o\\nCO\\nCO t^ VO\\nro\\nO O\\nO u-i\\nro -rj-\\nO io O ro\\nO ro -t\\nr\\\\ CO\\nro\\nNO CI ro\\nO iJ^i lo\\nO ci Cl CO\\no\\nlO\\no\\nCO\\n8\\nLO\\no\\no\\nD\\no\\no\\ni-r\\\\ O\\n-t CO\\nro C\\nO -i-\\nS 8\\nuo oo\\n\u00e2\u0080\u00a2rt CJ\\nNO CO r\\\\\\nci O O\\nO NH \u00c2\u00ab-l C CO \u00c2\u00abJ^\\n8\\no\\no\\nNO\\nVO\\no\\no\\no\\no\\nO\\no\\nO tr\\\\\\nro -1-\\nri CO\\nCl -t\\no\\nO NO\\nCl\\nO w-i CO\\nro N\\nr^ ro -f\\nro C)\\nGO cico-t-LO\\no\\nCO\\n8\\nO\\n8\\n\u00c2\u00b0o\\nCO\\niT 8\\nCO f^\\nCO VO\\nNO O\\nCl O\\nvi-i O CO vr-i\\nTt CO LO\\nCO Cl -t\\nro Cl O\\nOOO fO-t\\nO o\\nro -t\\nr-^ CO\\nO\\nO vn\\nO\\n\\\\r\\\\ VO\\nro -o\\nO\\nro -f\\nCl ro\\nCl\\nO CO NO oo\\nO H- Cl CO\\nO t^ oo\\nro 1-0\\nOOOO^^\\n^1 W It C t- X Ct O\\n323", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0375.jp2"}, "376": {"fulltext": "TABLE IV.\u00e2\u0080\u0094 ELEMENTS OF TRANSITION CURVES.\\n*l-n\\nfS\\n(S NO\\nC)\\nfs\\nCO\\nCO\\n55\\nO OS r^\\nO ON On On\\nNO\\nOn O\\nw-i On\\nd- CO\\nOn\\nNO\\nr^ CO\\nCO o\\nLO\\nLO\\nXI\\nCO\\nLO\\ns-\\nLO C)\\nLTl\\nCO\\nLTi CN On\\nOn CO\\nr^\\nTt-\\nr^\\nir%\\nrj-\\nn\\nh.\\nOn\\nt^ Tf\\nM\\nM r^ On\\nr)\\n1? J^\\nOn\\n0\\nn\\nU-l\\nON\\nLO\\nCO\\n\\\\_r\\\\\\nCO\\nLO\\nCO\\nCO\\nun\\nt\\n1\\nr^\\n(\u00e2\u0096\u00a0xt- (O CO CO\\n(n\\nOn (T^\\nr^\\nr^ CO\\nCO\\nCO\\nCO\\nM\\nn\\nCO\\nH\\nrv\u00c2\u00bb t-^ oo NO\\nNO\\nr^ O\\nCO 00 1\\nrv. NO fo\\nr^\\nLO n\\nr^ NO\\nCO\\n1\u00e2\u0080\u00941\\nON 00\\nM\\nr)\\nNJ\\nm CO CO\\nr-^\\nOn OO\\noo\\n1\u00e2\u0080\u00941\\n\u00e2\u0080\u00a2-1\\n1\u00e2\u0080\u0094 1\\nd\\\\ 6\\\\ 6 6\\nd\\nON I-.\\nd\\nCO\\nI\\nuo\\nQO\\nl-O\\nCO\\nCO\\n10\\nCO\\nn\\nLO\\nCO\\nCO\\nCO\\nCO\\n10\\nCO\\nOn 1^ t-^ i-H\\nM\\nCO CO\\nOn\\np r^\\n0\\\\ 00\\nrv.\\nLO\\nCO\\nn\\nn\\nO n t^\\nON\\nO O\\nOn\\nVO\\n1\u00e2\u0080\u0094 1\\n\u00e2\u0080\u00941\\nS\\nd 6 CO\\nON\\nOn M\\nOn lo\\nq\\nr^ CO\\nd\\nj^\\ni\\nN\\nCO\\nto\\nuo\\nT^\\nM\\nCO\\nCO\\nCO\\nCO\\nb\u00c2\u00bb\\n8\\nOn\\nri\\nLO\\nNO\\nCO\\n8\\nn\\nrl- NO\\n-6-\\nB\\n3\\n00\\nrv.\\nNO 00 t^ On (M\\nNO 00 00 m rj\\nOn rj\\nOO CO\\n(ON\\nNO\\nO (CO\\nLO O\\n1/)\\nO NO O\\nOO CO CO CO\\nCO\\nCO C)\\nOn\\nCO\\nNO\\nCO\\noo LO\\nCO O\\nCO\\nCO\\n8\\nCO\\n8\\n8\\nCO\\n8\\nCO\\nLo NO rC. t\\ntv.\\noo oo\\noo\\noo On\\nc\\nH^\\nu\\nn\\nr^\\n10\\nM\\nLo r~^\\nn\\nJ3\\n-a\\nNO\\nNO\\nLO\\nCO\\nCO\\n1- CO\\ntn\\nLO\\ncS\\n\u00e2\u0096\u00a05.\\nO\\n(00 Lo o\\nOn OO CO\\nOn On On OO\\nNO\\n(no (O\\nNO On\\nD NO\\n(0\\noo\\n(NH CO\\nNO ON\\n3\\ny\\nu\\n^0\\nCO\\n8\\nCO\\n8\\n8\\nCO\\nCO\\nV\\nOn On On On\\nOn\\n7n CO\\nt^\\nNO\\nas\\nO\\n1^\\nOn On On On\\nON\\nON On\\nON\\nON On\\nc\\n10\\nIn\\nr^\\nM\\nITN\\nt-^\\nN\\nOn\\nCf\\\\ On CTn On\\nd\\\\\\nOn d\\\\\\nOn\\nOn d\\\\\\n0)\\n0\\na\\nM\\nn\\n1-1\\nCO\\n~i\\nu^\\nLO\\nCO\\nr\\nt\u00e2\u0080\u0094\\nCO Tl- NO\\n00\\n^0\\nc\\nun\\n00\\n-6-\\nrf n O On\\no\\n(CO (fv.\\noo\\n(O\\nc\\nCO\\nCO\\nCO\\nCO\\nw^\\n_\\nOO On OO M\\nr^\\nNO NO\\nOn\\nCO\\nu\\n1\\no\\nV\\nin\\nO r^ CO\\na\\\\ rt- r On\\nLO\\nO CO\\nNO CO\\nC CO\\nON\\noo\\n00 NO\\nLr \\\\0\\nbe\\nB\\nCO\\n8\\nUO\\nCO\\nc^\\no\\nl Oo OO CO\\nOn\\nd\\\\ On\\nCfv\\nds dv\\nV\\nN\\ne\\nCO\\nc^\\nM\\ni^ VO\\nt^\\n0\\nNO\\nu\\nCO\\nCO\\nCO LO\\nn\\n-0-\\nc\\nCO\\nd\\nN\\n\\\\-r\\\\\\nt^\\nVO\\nM On\\nt^\\ns\\n(On (NO no rJ\\nt-^\\n(N CO\\n(O\\nOn O\\nLO\\nn\\nTt\\nn\\nLO M\\no\\nOn On OO NO\\nN^\\nCO O\\nCO r^\\nOn ON ON On\\nOn CO r\\\\\\n\\\\^r\\\\\\nn oo\\n\u00c2\u00abJ\\nOn On On On\\nOn\\n0\\\\ JN\\nOn\\nOn oo\\nc\\nM\\nHH\\nM\\nri\\nCO\\nNO\\n00\\neS\\n(U\\nQ\\n0\\n00 Tj-\\nli^\\n8\\nei\\nro\\nLO\\nCO\\nCO\\nLO C)\\nON\\n\u00e2\u0080\u00a2e-\\nir\\\\\\nCO\\nCO\\nTf\\nLO\\nN- t:^\\nn\\nM\\n(t^ M (CO (i-\u00c2\u00ab\\nO-O\\n(N On\\nO\\nt^ (r^\\nS\\nCO NO M r^\\nO n Lo 00\\nO n\\nCO OO\\nOn\\nn 1-1\\noo nO\\n\u00c2\u00b0o\\nr\\nCO\\nlJ- NO\\n00\\no q q q\\ni-c n\\nCO\\nCO ^t\\nOn NO\\n00\\nrv\\nCO\\nl-O\\nCO\\n10\\nON\\nn Lo\\nON\\nCO\\nuo\\nLO\\nLO\\nn\\ns\\n^O o o\\nCO CO O O\\no\\nCO\\nO O\\nCO O\\nO\\nO\\nO O\\nCO CO\\nK4\\nM\\nCO\\nir\\\\ \\\\o\\nCO\\nsr\\nO l-l CO LO\\nt^\\nO OO\\nn r^\\n00\\nCO LO\\n\u00e2\u0096\u00a0LTt\\nt\u00e2\u0080\u0094 1 HH\\nci n\\nCO\\nCO\\nM\\nW)\\nCO\\nCO\\n0\u00c2\u00bb\\n0\\nu-v\\nt^\\nn\\n10\\nt^\\nOn f^\\nNO\\nc\\nCO\\nLO\\nCO\\nrf NO\\nCO\\nOn\\nM\\nN CO rt\\nir\\\\\\nNO t^\\n00\\nON O\\nc\\n0\u00c2\u00bb\\nH\\nCI\\nW\\nTj^\\n10\\nt X\\na\\nrt\\n1H\\n324", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0376.jp2"}, "377": {"fulltext": "TABLE v.\u00e2\u0080\u0094 LOGARITHMS OF NUMBERS.\\nN.\\n1\\n1 12 1 :5\\n4 5 a 1\\n7 S 1\\n1*. P. 1\\n100\\nlOI\\nI02\\n00 000\\n432\\n860\\n043\\n087\\n130\\n173 216\\n260\\n303\\n775\\n*i99\\n389\\n817\\n^241\\n^7\\n475\\n902\\n518\\n945\\n561\\n987\\nC04\\n*o3o\\n646 689\\n^072 *ii4\\n732\\n*i57\\n43\\n4.5\\n43\\n4.3\\n42\\n4.2\\n41\\n41\\n103\\n104\\n01 283\\n703\\n326\\n745\\n368\\n787\\n410\\n828\\n452\\n870\\n494\\n911\\n53t\\n953\\n578\\n994\\n619\\n^036\\n661\\n*o77\\n2 8.7\\n3 130\\n8.6\\n12.9\\n8.4\\n12.6\\nrA\\n8.3\\n13 3\\nifi A 1\\n105\\n02 119\\n160\\n201\\n243\\n284\\n325\\n3^6\\n407\\n448\\n489\\n4 \u00c2\u00bb74\\n5 21.7\\n17.2\\n21. s\\n21.0\\n20.5\\n106\\n530\\n571\\n612\\n653\\n694\\n735\\n775\\n816\\n857\\n898\\n6 26. 1\\n25.8\\n25-2\\n24.6,\\n107\\n108\\n938\\n03 342\\n979\\n382\\n^019\\n422\\n*o6o\\n463\\n^100\\n503\\n*i4i\\n543\\n*i8i\\n583\\n*22I\\n623\\n*262\\n663\\n*302\\n703\\n7 304\\n834.8\\n(^i3y-i\\n30.1\\n34-4\\n38.7\\n29.4\\n33.6\\n37.8\\n28.7\\n32.8\\n36-\u00c2\u00bb\\n109\\n110\\nIII\\n112\\n742\\n04 139\\n782\\n822\\n862\\n901\\n941\\n981\\n*026\\n*o6o\\n*ioo\\n178\\n218\\n257\\n297\\n33^^\\n375\\n415\\n454\\n493\\n883\\n^269\\n532\\n922\\n57?\\n960\\n616\\n999\\n649\\n*o38\\n688\\n*o76\\n727\\n^115\\n766\\n*i54\\n805\\n*I92\\n844\\n*23I\\n40\\nI 4.0\\n40\\n4.0\\n39\\n3-9\\n38\\n3.8I\\n113\\n05 308\\n346\\n384\\n423\\n461\\n499\\n538\\n576\\n614\\n652\\n2 8.1\\n3 12. i\\n8.0\\n12.0\\n7.8\\n11.7\\n7.6\\nII. 4\\n114\\n690\\n728\\n765\\n804\\n842\\n880\\n9^8\\n956\\n994\\n*032\\nir, 6\\nIt;. 2\\n115\\n06 070\\n107\\n145\\n183\\n220\\n258\\n296\\n333\\n371\\n408\\n5 20.2\\n20.0\\n9-5\\n19.0\\n116\\n446\\n483\\n520-\\n558\\n595\\n632\\n670\\n707\\n744\\n781\\n624.3\\n24.0\\n23.4\\n33.8\\n117\\n818\\n855\\n893\\n930\\n967\\n*oo4\\n*04o\\n*o77\\n*i 14\\n*i5i\\n728.3\\n832.4\\n28.0\\n32.0\\n27 -3\\n31.2\\n36.6\\n30-4\\n118\\n07 188\\n225\\n261\\n298\\n335\\n372\\n408\\n445\\n481\\n518\\n9 36.4\\n36.0\\n351\\n34.2\\n119\\n120\\n121\\n554\\n591\\n627\\n664\\n700\\n737\\n773\\n809\\n*i76\\n529\\n845\\n882\\n3f 77 76\\n918\\n954\\n990\\n*026\\n386\\n*o62\\n*098\\n*i34\\n*206\\n564\\n*242\\n08 278\\n314\\n350\\n422\\n457\\n493\\n606\\n122\\n636\\n671\\n707\\n742\\n778\\n813\\n849\\n884\\n920\\n955\\nI 3-7\\n3-7\\n3.6 ^.i;|\\n123\\n124\\n995\\n09 342\\n*026\\n377\\n*o6i\\n412\\n*o96\\n447\\n*i3i\\n482\\n*i66\\n517\\n*202\\n552\\n237\\n586\\n*272\\n621\\n*307\\n656\\n2 7-5\\n3 II. 2\\n7-4\\n11. 1\\n7.2\\n10.8\\n7.0\\n10.5\\nI2S\\n691\\n725\\n760\\n795\\n830\\n864\\n899\\n933\\n968\\n*002\\n4 150\\n5 18.7\\n14.8\\n18.5\\n14.4\\n18.0\\n14.0\\n17-5\\n126\\n10 037\\n071\\n106\\n140\\n174\\n209\\n243\\n277\\n312\\n346\\n6 22.5\\n22.2\\n21.6\\n21.0\\n127\\n380\\n414\\n448\\n483\\n517\\n551\\n585\\n619\\n^53\\n687\\n7 26.2\\n8 ^0.0\\n25.9\\n2Q.6\\n25.2\\n?a 8\\n24-5\\n28.0\\n128\\n721\\n755\\n789\\n822\\n^56\\n890\\n924\\n958\\n991\\n*025\\n9 33-7\\n33-3\\n324\\n31-5\\n129\\n130\\n131\\n132\\n133\\nII 059\\n092\\n126\\n160\\n193\\n227\\n260\\n294\\n327\\n361\\n394\\n427\\n461\\n494\\n528\\n561\\n594\\n627\\n661\\n694\\n727\\n12 057\\n385\\n760\\n096\\n418\\n793\\n123\\n450\\n826\\n156\\n483\\n859\\n189\\n515\\n892\\n221\\n548\\n925\\n254\\n580\\n958\\n287\\n613\\n991\\n320\\n645\\n*024\\n352\\n678\\n34\\n1 3-4\\n2 6.9\\n34\\n3-4\\n6.8\\n33\\n3-3\\n6.6\\n32\\n3-3\\n6.4\\n134\\n7x5\\n743\\n775\\n807\\n840\\n872\\n904\\n937\\n969\\n*OOI\\n3 10.3\\n10.2\\n9.9\\n9.6\\n135\\n13 033\\n065\\n097\\n130\\n162\\n194\\n226\\n258\\n290\\n322\\n4 138\\n5 172\\n13.6\\n17.0\\n13.2\\n16. s\\n12.8\\n16.0\\n136\\n354\\n386\\n417\\n449\\n481\\n513\\n545\\n577\\n608\\n640\\n6 20.7\\n20.4\\n19.8\\n19.2\\n137\\n138\\n672\\n988\\n703\\n*oi9\\n735\\n*o5i\\n767\\n*o82\\n798\\n*ii3\\n830\\n*i45\\n862\\n*i76\\n893\\n*207\\n925\\n*239\\n956\\n^270\\n7 24.1\\n827.6\\n931.5\\n23.8\\n27.2\\n30.6\\n23.1\\n26.4\\n29.7\\n22.4\\n25.6\\n28.8\\n139\\n110\\n141\\n14 301\\n332\\n364\\n395\\n426\\n457\\n767\\n*o75\\n488\\n519\\n550\\n582\\n31 ^0 20\\n613\\n644\\n675\\n706\\n736\\n798\\n*io6\\n829\\n866 891 1\\n922\\n952\\n983\\n*oi4\\n*o45\\n*i37\\n*i67\\n^198\\n142\\n15 229\\n259\\n290\\n320\\n351\\n381\\n412\\n442\\n473\\n503\\n1 3.1\\n3.1\\n30\\n3.9\\n143\\n144\\n533\\n836\\n564\\n866\\n594\\n896\\n624\\n926\\n655\\n956\\n685\\n987\\n715\\n*oi7\\n745\\n*o47\\n770\\n*o77\\n806\\n*io7\\n2 6.3\\n3 9-4\\n4 12.6\\n5 \u00c2\u00ab5-7\\n6.2\\n9-3\\n6.0\\n9.0\\n5.8\\n8.7\\nTT\\n14s\\n16 137\\n165\\n196\\n226\\n256\\n286\\n316\\n346\\n376\\n405\\n12.4\\n15-5\\n15.0\\n14-5\\n146\\n435\\n465\\n494\\n524\\n554\\n584\\n613\\n643\\n672\\n702\\n6 18.9\\n18.6\\n18.0\\n17-4\\n147\\n731\\n761\\n791\\n820\\n849\\n879\\n908\\n938\\n967\\n997\\n7 22.0\\n8 25.2\\n21.7\\n74 R\\n31.\\n24.0\\n20.3\\n23.3\\n148\\n17 026\\n055\\n085\\n114\\n143\\nT72\\n202\\n231\\n266\\n289\\n928.3\\n27.9\\n27.0\\na6.i\\nT49\\n150\\n318\\n609\\n348\\n377\\n406\\n435\\n464\\n493\\n522\\n551\\n580\\n638\\n667\\n696\\n725\\n753\\n782\\n811\\n840\\n869\\nN.\\n1 1 2\\n3 4\\n5\\n1 6 1 7\\n8\\n9\\nP.P.\\n325", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0377.jp2"}, "378": {"fulltext": "TABLE v.\u00e2\u0080\u0094 LOGARITHMS OF NUMBERS.\\nN.\\n150\\n151\\n152\\n153\\n154\\n155\\n156\\n157\\n158\\n159\\n160\\n161\\n162\\n163\\n164\\n165\\n166\\n167\\n168\\n169\\n170\\n171\\n172\\n173\\n174\\n175\\n176\\n177\\n178\\n179\\n180\\n181\\n182\\n183\\n184\\n185\\n186\\n187\\n188\\n189\\n190\\n191\\n192\\n193\\n194\\n195\\n196\\n197\\n198\\n199\\n200\\nN.\\nO\\n17 609\\n897\\n18 184\\n469\\n752\\n19 \u00c2\u00b033\\n312\\n590\\n865\\n20 139\\n2\\n412\\n682\\n951\\n21 219\\n484\\n748\\n22 on\\n271\\n53T\\n788\\n23 045\\n299\\n553\\n804\\n24 055\\n304\\n551\\n797\\n25 042\\n285\\n527\\n768\\n26 007\\n245\\n482\\n717\\n951\\n27 184\\n416\\n646\\n875\\n28 103\\n330\\n555\\n780\\n29 003\\n225\\n446\\n666\\n885.\\n3Q 103\\nO\\n638\\n926\\n213\\n497\\n780\\n061\\n340\\n617\\n893\\n167\\n439\\n709\\n978\\n245\\n511\\n774\\n037\\n297\\n557\\n814\\n070\\n667\\n955\\n241\\n526\\n808\\n089\\n368\\n645\\n926\\n194\\n792\\n031\\n269\\n505\\n740\\n974\\n207\\n439\\n669\\n898\\n466\\n736\\n126\\n352\\n578\\n802\\n025\\n248\\n468\\n688\\n907\\n124\\n350\\n603\\n855\\n105\\n353\\n600\\n846\\n091\\n334\\n575\\n816\\n055\\n292\\n529\\n764\\n998\\n230\\n462\\n692\\n921\\n696\\n984\\n270\\n554\\n836\\n117\\n396\\n673\\n948\\n221\\n493\\n763\\n012\\n298\\n582\\n864\\n145\\n423\\n700\\n975\\n249\\n520\\n790\\n\u00e2\u0080\u00a2032 f^o58\\n149\\n375\\n600\\n825\\n048\\n270\\n490\\n710\\n929\\n146\\n298\\n564\\n827\\n089\\n349\\n608\\n865\\n121\\n375\\n628\\n880\\n129\\n378\\n625\\n871\\n115\\n358\\n599\\n325\\n590\\n853\\n115\\n375\\n634\\n891\\n147\\n401\\n653\\n905\\n154\\n403\\n650\\n895\\n139\\n382\\n840\\n078\\n316\\n552\\n787\\n021\\n254\\n485\\n715\\n944\\n171\\n398\\n623\\n847\\n070\\n292\\n512\\n732\\n950\\n168\\n623\\n863\\n102\\n340\\n576\\n811\\n044\\n277\\n508\\n738\\n966\\n194\\n426\\n645\\n869\\n092\\n3M\\n534\\n754\\n972\\n190\\n753\\n041\\n327\\n611\\n893\\n173\\n451\\n728\\n^003\\n276\\n6\\n782\\n811\\n547\\n817\\n085\\n352\\n616\\n880\\n141\\n401\\n660\\n917\\n070\\n355\\n639\\n921\\n201\\n479\\n755\\n^030\\n303\\n574\\n172\\n426\\n679\\n930\\n179\\n427\\n674\\n920\\n164\\n406\\n647\\n007\\n126\\n599\\n834\\n*o68\\n300\\n531\\n761\\n989\\n844\\n112\\n378\\n643\\n906\\n167\\n427\\n686\\n942\\n098\\n384\\n667\\n949\\n229\\n507\\n783\\n057\\n33^\\n8\\n9\\n840\\n601\\n198\\n451\\n704\\n955\\n204\\n452\\n699\\n944\\n188\\n430\\n672\\n911\\n150\\n387\\n623\\n858\\n091\\n323\\n554\\n784\\n012\\n239\\n465\\n696\\n914\\n137\\n358\\n578\\n798\\n*oi6\\n233\\n6\\n871\\n139\\n405\\n669\\n932\\n193\\n453\\n711\\n968\\nl27\\n412\\n695\\n977\\n256\\n534\\n8i5\\n*o85\\n357\\n869\\n*i56\\n446\\n724\\n*oo5\\n284\\n562\\n838\\n112\\n385\\n628\\n223\\n477\\n729\\n980\\n229\\n477\\n723\\n968\\n212\\n455\\n696\\n898\\n^165\\n43 J\\n695\\n958\\n219\\n479\\n737\\n994\\n249\\n502\\n754\\n005\\n254\\n502\\n748\\n993\\n237\\n479\\n935\\n174\\n411\\n646\\n881\\n114\\n346\\n577\\n806\\n\u00e2\u0080\u00a2035\\n262\\n488\\n713\\n936\\n159\\n380\\n6o5\\n820\\n*o38\\n254\\n720\\n959\\n197\\n434\\n670\\n904\\n137\\n369\\n600\\n829\\n058\\n285\\n510\\n735\\n959\\n181\\n402\\n622\\n841\\n059\\n276\\n8\\n^5\\n924\\n^^192\\n458\\n722\\n984\\n245\\n505\\n763\\n^019\\nP. P.\\n274\\n527\\n779\\n030\\n279\\n526\\n773\\n017\\n261\\n503\\n744\\n983\\n221\\n458\\n693\\n928\\n*i6i\\n392\\n623\\n_85l\\n*o8o\\n307\\n533\\n758\\n981\\n203\\n424\\n644\\n863\\n\u00c2\u00bbo8i\\n298\\n9\\n29 28 27\\nI\\n2.9\\n2.8\\n2.\\n.2\\n\u00e2\u0096\u00a03\\n5-8\\n8.7\\n5.6\\n8.4\\n5-\\n8.\\n\u00e2\u0096\u00a04\\n11.6\\nT1.2\\n10.\\n\u00e2\u0080\u00a25\\n.6\\nM-5\\n17.4\\n14.0\\n16.8\\n13-\\n16.\\n\u00e2\u0080\u00a27\\n20.3\\nig.6\\n18.\\n.8\\n23.2\\n22.4\\n21.\\n\u00e2\u0080\u00a29\\n26.1\\n25.2\\n24.\\n2\u00c2\u00a7 26\\nI\\n2-6\\n.2\\n5-3\\n\u00e2\u0080\u00a23\\n7-9\\n\u00e2\u0080\u00a24\\nS\\nTO. 6\\n13.2\\n.6\\n15-9\\n\u00e2\u0096\u00a07\\n18.5\\n.8\\n21.2\\n\u00e2\u0080\u00a29\\n23-8\\n2.6\\n5-2\\n7.8\\n10.4\\n13.0\\n15-6\\n20.8\\n234\\n2S 25 24\\nI\\n2.5\\n2. K\\n.2\\n5-1\\n50\\n\u00e2\u0080\u00a23\\n7-6\\n7-5\\n\u00e2\u0080\u00a24\\n10.2\\nTO.O\\n\u00e2\u0080\u00a25\\n12.7\\n12.5\\n.6\\n15-3\\n150\\n\u00e2\u0096\u00a07\\n17-8\\n17-5\\n.8\\n20.4\\n20.0\\n\u00e2\u0080\u00a29\\n22.9\\n22.5\\n2.4\\n4.8\\n7.2\\n9.6\\n12.0\\n14.4\\n16.8\\n19. a\\n21 .6\\nI\\n2-3\\n.2\\n\u00e2\u0080\u00a23\\n4-7\\n7.0\\n4\\n9-4\\n\u00e2\u0080\u00a25\\n.6\\nII. 7\\n14. 1\\n\u00e2\u0080\u00a27\\n.8\\n\u00e2\u0080\u00a29\\n16.4\\n18.8\\n21. 1\\n23 23\\n2-3\\n4.6\\n6.9\\n9.2\\n11-5\\n13-8\\n16. 1\\n18.4\\n20.7\\n22 22 21\\n2.1\\n4-3\\n6.4\\n8.6\\nTO. 7\\n12.9\\n15.0\\n17.2\\n19-3\\n.1\\n2.2\\n2.2\\n.2\\n\u00e2\u0080\u00a23\\n6.7\\n4.4\\n6.6\\n\u00e2\u0080\u00a24\\n9.0\\n8.8\\n\u00e2\u0080\u00a2s\\nII. 2\\nII.\\n.6\\n13-5\\n13.2\\n\u00e2\u0080\u00a27\\n.8\\n15-7\\n18.0\\n15-4\\n17.6\\n\u00e2\u0080\u00a29\\n20.2\\n19.8\\nP. p.\\n326", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0378.jp2"}, "379": {"fulltext": "TABLE V.-\\n\u00e2\u0080\u0094LOG\\nARITinL^\\n)F XI\\nMHERS.\\nTn.\\n1\\n2\\n3 4\\n5\\n7 S\\nr. p. 1\\n200\\n30 103\\n124\\n146\\n168 190\\n211\\n233\\n254\\n276\\n298\\nj 20I\\n319\\n341\\n3^3\\n384\\n406\\n427\\n449\\n470\\n492\\n513\\nI\\n2 2\\n2 I\\n202\\n535\\n556\\n578\\n599\\n621\\n642\\n664\\n685\\n707\\n728\\n4-4\\n4.2\\n203\\n749\\n771\\n792\\n813 835\\n856\\n878\\n899\\n920\\n941\\n3\\n6.6\\n6.3\\n204\\n963\\n984\\n\u00e2\u0099\u00a6005\\n*o27 *o48\\n^069\\n*og6\\n*II2\\n^^^33\\n*i54\\nR R\\nR 1\\n205\\n31 175\\n196\\n217\\n239\\n260\\n281\\n302\\n323\\n344\\n365\\n\u00e2\u0080\u00a24\\n.5\\nII .0\\n0.4\\n10.5\\n206\\n386\\n408\\n429\\n450\\n471\\n492\\n513\\n534\\n555\\n576\\n.6\\n13.2\\n12.6\\n207\\n597\\n618\\n639\\n660\\n681\\n702\\n722\\n743\\n764\\n785\\n208\\n806\\n827\\n848\\n869\\n890\\n910\\n931\\n952\\n973\\n994\\n\u00e2\u0080\u00a27\\n.8\\n154\\n17.6\\n14.7\\n16.8\\n209\\n210\\n32 014\\n222\\n035\\n056\\n077\\n097\\n118\\n139\\n160\\n186\\n387\\n201\\n407\\n\u00e2\u0080\u00a29\\n19. s\\n18.9\\n242\\n263\\n284\\n304\\n325\\n346\\n3^6\\n35 -1\\n211\\n428\\n449\\n469\\n490\\n510\\n531\\n551\\n572\\n592\\n613\\n20\\n^KJ\\n212\\n^33\\n654\\n674\\n695\\n715\\n736\\n756\\n776\\n797\\n817\\n.2\\n4. 1\\n4.0\\n213\\n838\\n858\\n878\\n899\\n919\\n940\\n960\\n980 1*001\\n*02I\\n\u00e2\u0080\u00a23\\n6.1\\n6.0\\n214\\n33 041\\n061\\n082\\n102\\n122\\n142\\n163\\n183 j 203\\n223\\n8.0\\n10. t\\n215\\n244\\n264\\n284\\n304\\n324\\n344\\n365\\n385 405\\n425\\n4\\n\u00e2\u0080\u00a25\\n.6\\n0.2\\n10. 2\\n216\\n44!\\n465\\n485\\n505\\n525\\n546\\n566\\n586 606\\n626\\n12.3\\n12.0\\n217\\n646\\n666\\n6S6\\n706\\n726\\n746\\n766\\n786 806\\n825\\nL\\n218\\n845\\n865\\n885\\n905\\n925\\n945\\n965\\n985 *oo4 *024\\n\u00e2\u0080\u00a2V\\n8\\n14-3\\n16.4.\\n14.0\\n16.0\\n219\\n220\\n221\\n34 044\\n064\\n084\\n104\\n123\\nM3\\n163\\n183 203 222\\n\u00e2\u0080\u00a29\\n1S.4\\n18.0\\n242\\n439\\n262\\n281\\n301 1 321\\n341\\n366\\n380 400 I 419\\n19 19\\n459\\n478\\n498\\n5^8\\n537\\n557 j 576\\n596 615\\n222\\n^35\\n655\\n674\\n694\\n713\\n733\\n752 I 772\\n791 i 811\\nI\\n2\\n1.9\\n3-9\\n5-8\\n1.9\\n3.8\\n5-7\\n223\\n830\\n850\\n869\\n889\\n908\\n928\\n947 1 9^6 986\\n*oo5\\n\u00e2\u0080\u00a23\\n224\\n35 025\\n044\\n063\\n083\\n102\\n121\\n141 166 179\\n199\\n225\\n218\\n237\\n257\\n276\\n29!\\n3 4\\n334\\n353 372\\n391\\n\u00e2\u0080\u00a24\\n7.8\\n9-7\\nII. 7\\n7.6\\n9-5\\nII. 4\\n226\\n411\\n430\\n449\\n468\\n487\\nS ^7\\n526\\n545\\n564\\n583\\n5\\n.6\\n227\\n602\\n621\\n641\\n660\\n679\\n698\\n717\\n736\\n755 774\\n228\\n793\\n812\\n83?\\n850\\n869\\n88h\\n907\\n926\\n945 9^4\\n\u00e2\u0080\u00a2V\\n.8\\n\u00e2\u0080\u00a29\\n13-6\\n15-6\\n17-5\\n13-3\\n229\\n230\\n231\\n983\\n*002\\n^021\\n*o4o\\n*o59\\n*o78\\n*o97 1*116 1*135 ;*i54\\n15-2\\n17. 1\\n36 173\\n191\\n216\\n229\\n248\\n267\\n286 1 305\\n323 342\\n1\\n361\\n380\\n399\\n417\\n436\\n455\\n474\\n492\\n511\\n530\\n18\\n10\\n232\\n549\\n567\\n586\\n605\\n623\\n642\\n661\\n679\\n698\\n717\\nI\\n2\\n1-8\\n3-7\\n5-5\\n1 .8\\n3-6\\n5-4 1\\n233\\n735\\n754\\n773\\n791\\n810\\n828\\n847\\n866\\n884\\n903\\n3\\n|234\\n921\\n940\\n958\\n977\\n996\\n*oi4\\n*o33\\n*o5i\\n*o7o\\n*o88\\n1 235\\n37 107\\n125\\n143\\n162\\n186\\n199\\n217\\n236\\n254 1 273\\n\u00e2\u0080\u00a24\\n7-4\\n9.2\\nII .1\\n7.2\\n9.0\\n10.8\\nI236\\n291\\n309\\n328\\n346\\n364\\n383\\n401\\n420\\n438\\n456\\n5\\n.6\\n237\\n475\\n493\\n511\\n530\\n548\\n5^6\\n584 603\\n621\\n639\\n238\\n657\\n676\\n694\\n712\\n730\\n749\\n767 785\\n803\\n821\\n\u00e2\u0080\u00a27\\n.8\\n\u00e2\u0080\u00a29\\n12.(3\\n14.8\\n16.6\\n12.6\\n1239\\n240\\n241\\n840\\n858\\n876\\n894\\n912\\n930\\nIII\\n948 i 967\\n985 1*003\\n14.4\\n16.2\\n38 021\\n039\\n057\\n075\\n093\\n129 147\\n165 183\\n201\\n219\\n237\\n255\\n273\\n291\\n309\\n327\\n345\\n3^3\\n17\\n1 242\\n38i\\n399\\n417\\n435\\n453\\n471\\n489\\n507\\n525\\n543\\nI\\n1-7\\n3-5\\n5-2\\n1.7\\n^\u00e2\u0080\u00a24\\n5-1\\n243\\n566\\n578\\n596\\n614\\n632\\n650\\n667 685\\n703\\n721\\n\u00e2\u0080\u00a23\\n244\\n739\\n757\\n774\\n792\\n810\\n828\\n845 863\\n881\\n899\\n|245\\n1 246\\n9^6\\n39 093\\n934\\nIII\\n952\\n129\\n970\\n146\\n987\\n164\\n*oo5\\n181\\n*023\\n199\\n*046\\n217\\n*o58\\n234\\n*o76\\n252\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n7.0\\n8.7\\n10.5\\n6.8\\n8.5 1\\n10.2\\n1247\\n269\\n287\\n305\\n322\\n340\\n357\\n375\\n392\\n410\\n427\\nI248\\n445\\n462\\n480\\n497 515\\n532\\n550\\n567\\n585\\n602\\n.7\\n.8\\n\u00e2\u0080\u00a29\\n12.2\\nII. 9\\n13.6\\n249\\n250\\n620\\n637\\n655\\n672 689\\n707\\n724\\n742\\n759\\n776\\n14 -O\\n157\\n794\\n811\\n828\\n846 863\\n881\\n898\\n915\\n933\\n950\\ni N.\\n1\\n1\\n2\\n3 4\\n5 7 1 8 1 9\\nP. P. 1\\n327", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0379.jp2"}, "380": {"fulltext": "TABLE V.-\\n-LOGARITHMS\\n3F NUMBERS.\\n1 N.\\n250\\n251\\n1 2\\n3 4\\n5\\n6\\n7 1 8\\np. p.\\n39 794\\n811\\n828\\n846\\n863\\n881\\n898\\n915\\n933\\n950\\n967\\n984\\n*002\\n*oi9\\n*o36\\n*o54\\n*o7i\\n*o88\\n*io5\\n*I23\\n252\\n40 140\\n157\\n174\\n191\\n209\\n226\\n243\\n266\\n277\\n295\\n1\\n253\\n312\\n329\\n346\\nz^i\\n380\\n398\\n415\\n432\\n449\\n466\\nif\\n17\\n254\\n483\\n500\\n517\\n534\\n551\\n569\\n586\\n603\\n620\\n637\\nI\\n1-7\\n1.7\\n255\\n654\\n671\\n688\\n705\\n722\\n739\\n756\\n773\\n790\\n807\\n.3\\n3-5\\n5.2\\n3-4\\n5.1 1\\n255\\n824\\n841\\n858\\n875\\n892\\n908\\n925\\n942\\n959\\n976\\n257\\n993\\n*OIO\\n^027\\n*044\\n*o6i\\n*o77\\n*094\\n*iii\\n*I28\\n145\\n\u00e2\u0080\u00a24\\n7.0\\nR\\n6.8\\n8.5\\n10.2\\n25\u00c2\u00ab\\n41 162\\n179\\n195\\n212\\n229\\n246\\n263\\n279\\n296\\n3^3\\n\u00e2\u0080\u00a25\\n.6\\n0.7\\n10.5\\n259\\n260\\n261\\n32,^\\n346\\n3^3\\n380\\n397\\n413\\n430\\n447\\n464\\n631\\n480\\n647\\n\u00e2\u0080\u00a27\\n.8\\n12.2\\n14.0\\n15.7\\nII. 9\\n13.6\\n15.\\n497\\n664\\n514\\n536\\n547\\n564\\n581\\n597\\n614\\n680\\n697\\n714\\n730\\n747\\n764\\n780\\n797\\n8n\\n262\\n830\\n846\\n863\\n880\\n896\\n913\\n929\\n946\\n962\\n979\\n263\\n995\\n*OI2\\n\u00e2\u0080\u00a2^023\\n*o45\\n*o6i\\n^078\\n^094\\n*iii\\n*I27\\n*i44\\n264\\n42 160\\n177\\n193\\n209\\n226\\n242\\n259\\n275\\n292\\n308\\n5\\n265\\n324\\n341\\n357\\n373\\n390\\n406\\n423\\n439\\n455\\n472\\n16\\n10\\n266\\n488\\n504\\n521\\n537\\n553\\n569\\n586\\n602\\n613\\n635\\n.1\\n1-6\\n3-3\\n4.9\\n1.6\\n267\\n651\\n667\\n6^%\\n700\\n716\\n732\\n748\\n765\\n781\\n797\\n\u00e2\u0096\u00a03\\n4.8\\n268\\n813\\n829\\n846\\n862\\n878\\n894\\n910\\n927\\n943\\n959\\n269\\n270\\n271\\n975\\n991\\n^^007\\n*o23 *o4o\\n^056\\n^072\\n*o88\\n*io4\\n*I26\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n6.6\\n8.2\\n9.9\\n6.4\\n8.0\\n9.6\\n43 ^36\\n152\\n168\\n184\\n200\\n216\\n233\\n249\\n265\\n281\\n297\\n3^Z\\n329\\n345\\n361\\n377\\n393\\n409\\n425\\n441\\n272\\n457\\n473\\n489\\n505\\n520\\n536\\n552\\n568\\n584\\n600\\n8\\nII-5\\n13.2\\n14-8\\n11 .2\\n12 8\\n273\\n6ig\\n632\\n648\\n664\\n680\\n695\\n711\\n727\\n743\\n759\\n\u00e2\u0080\u00a29\\n14.4\\n274\\n775\\n791\\n8og\\n822\\n^Z^^\\n854\\n870\\nSS6\\n901\\n917\\ni\\n275\\n933\\n949\\n965\\n980\\n996\\n*OI2\\n*028\\n*043\\n*oS9\\n*o7s\\n1 276\\n44091\\n105\\n122\\n138\\n154\\n169\\n185\\n201\\n216\\n232\\n277\\n248\\n263\\n279\\n295\\n310\\n326\\n342\\n357\\n373\\n38Q\\niS\\n15\\ni\\n278\\n404\\n420\\n435\\n451\\n467\\n482\\n498\\n513\\n529\\n545\\n2\\n1-5\\n3-1\\n4-6\\n6.2\\n7-7\\n1-5\\n3-0\\n4-5\\n6.0\\n7-5\\n279\\n280\\n281\\n560\\n576\\n591\\n607\\n622\\n638\\n653\\n669\\n685\\n700\\n.3\\n.4\\ni\\n716\\n870\\n731\\n747\\n762\\n778\\n793\\n809\\n824\\n839\\n855\\n*oo9\\n886\\n901\\n917\\n932\\n948\\n963\\n978\\n994\\n282\\n45 025\\n040\\n055\\n071\\n085\\n102\\n117\\n132\\n148\\n163\\n.6\\n9-3\\n9.0\\n283\\n178\\n194\\n209\\n224\\n240\\n255\\n270\\n286\\n301\\n3^6\\n284\\n332\\n347\\n362\\n377\\n393\\n408\\n423\\n438\\n454\\n469\\n.7\\n.8\\n10. 8\\n12.4\\n10.5 1\\n12.0\\n2\u00c2\u00ab5\\n484\\n499\\n515\\n530\\n545\\n560\\n576\\n591\\n606\\n621\\n\u00e2\u0080\u00a29\\n13-9\\n13-5\\n286\\n^2 6\\n652\\n667\\n682\\n697\\n712\\n727\\n743\\n758\\n773\\n287\\n788\\n803\\n818\\n^ZZ\\n848\\n864\\n879\\n894\\n909\\n924\\n288\\n939\\n954\\n969\\n984\\n999\\n*oi4\\n*029\\n*044\\n*o59\\n*o75\\n289\\n290\\n291\\n46 090\\n105\\n120\\n135\\n150\\n165\\n180\\n195\\n210\\n225\\nI\\n.2\\n\u00e2\u0080\u00a23\\n14\\n1.4\\n4-3\\n^4\\n1-4\\n2.8\\n4.2\\n240\\n255\\n269\\n284\\n299\\n314\\n329\\n344\\n359\\n374\\n389\\n404\\n419\\n434\\n449\\n464\\n479\\n493\\n508\\n523\\n292\\n538\\n553\\n568\\n583\\n597\\n612\\n627\\n642\\n657\\n672\\n.4\\n5.8\\n7.2\\n5.6\\n7.0\\n293\\n687\\n701\\n716\\n731\\n746\\n761\\n775\\n790\\n805\\n820\\n294\\n834\\n849\\n864\\n879\\n894\\n908\\n923\\n938\\n952\\n967\\n.6\\n8.7\\n8.4\\n295\\n982\\n997\\n^OII\\n^025\\n^41\\n*o55\\n*o75\\n*o85\\n*IOO\\n*ii4\\n.7\\n.8\\nICt T\\nn R\\n296\\n47 129\\n144\\n158\\n173\\n188\\n202\\n217\\n232\\n246\\n261\\nII. 6\\n9.0\\nII. 2\\n297\\n275\\n290\\n305\\n319\\n334\\n348\\n3^3\\n378\\n392\\n407\\n\u00e2\u0080\u00a29\\n13.0\\n12.6\\n298\\n421\\n436\\n451\\n465\\n480\\n494\\n509\\n523\\n538\\n552\\n299\\n300\\nN.\\n567\\n58I\\n596\\n610\\n625\\n639 654\\n66s\\n683\\n697\\n712\\n726\\n741\\n755\\n770\\n784 799\\n813\\n828\\n842\\n1\\n2\\n3\\n4\\n5 1 6\\n7\\n8 9\\nP. P.\\n328", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0380.jp2"}, "381": {"fulltext": "TABLE v.\u00e2\u0080\u0094 T.OGARITTIMS OF yUMT^FRq.\\n300\\n301\\n1\\n2\\n3\\n4\\n5\\n7\\n8\\nJ)\\nr. i\u00c2\u00bb. 1\\n47 712\\n726\\n741\\n755\\n770\\n784\\n799\\n813\\n828\\n842\\n856\\n871\\n885\\n900\\n914\\n928\\n943\\n957\\n972\\n986\\n302\\n48 000\\n015\\n029\\n044\\n058\\n072\\n087\\n101\\n11?\\n130\\n3 3\\n144\\n158\\n173\\n187\\n201\\n216\\n230\\n244\\n259\\n273\\n304\\n287\\n301\\n316\\n33^\\n344\\n358\\n0/0\\n387\\n401\\n415\\n30s\\n430\\n444\\n458\\n472\\n487\\n50i\\n515\\n529\\n543\\nSS8\\n306\\n572\\n586\\n606\\n614\\n629\\n^43\\n657\\n671\\n685\\n699\\nf\\n307\\n714\\n728\\n742\\n756\\n770\\n784\\n798\\n812\\n827\\n841\\n2\\n1 .4\\n2.9\\n1 .4\\n2.S\\n308\\n855\\n869\\n^^3\\n897\\n911\\n925\\n939\\n953\\n967\\n982\\n\u00e2\u0080\u00a23\\n4-3\\n4.2\\n309\\n310\\n311\\n996 OIO\\n*024\\n*o38\\n*052\\n=^^066\\n*o8o\\n*o94\\n*io8\\n*I22\\n\u00e2\u0080\u00a24\\n5\\n.6\\n5.S\\n7.2\\n8.7\\n5.6\\n7.0\\n8.4\\n49 136 i 150\\n164\\n178\\n192\\n206\\n220\\n234\\n248\\n262\\n276\\n290\\n304\\n318\\n332\\n346\\n359\\n373\\n387\\n401\\n312\\n415\\n429\\n443\\n457\\n471\\n485\\n499\\n513\\n526\\n540\\n\u00e2\u0080\u00a27\\n.8\\n9.8\\nII. 2 1\\n3^3\\n554\\n5^8\\n582\\n596\\n610\\n624\\n^37\\n65 J\\n665\\n679\\nII. 6\\n314\\n693\\n707\\n720\\n734\\n748\\n762\\n776\\n789\\n803\\n817\\n\u00e2\u0080\u00a29\\n13.0\\n12.6\\n315\\n831\\n845\\n858\\n872\\n886\\n900\\n913\\n927\\n941\\n955\\n316\\n9^8\\n982\\n996\\n*OIO\\n=^023\\n*o37\\n*o5i\\n*o65\\n*078\\n*092\\n317\\n50 106\\n119\\n^33\\n147\\n160\\n174\\n188\\n201\\n215\\n229\\n31S\\n242\\n256\\n270\\n283\\n297\\n311\\n324\\n33^\\n352\\n365\\n319\\n320\\n321\\n379\\n515\\n392\\n406\\n420\\n433\\n569\\n447\\n466\\n474\\n488\\nsoil\\nt5 to\\n528\\n542\\n555\\n583\\n596\\n610\\n623 1 637\\n650\\n664\\n677\\n691\\n704\\n718\\n731\\n745\\n758 772\\nI\\n-0\\n1-3\\n2.7\\n1\\n1-3\\n2.6\\n322\\n785\\n799\\n812\\n826\\n839\\n853\\n866\\n880\\n893\\n907\\n.2\\n323\\n920\\n933\\n947\\n960\\n974\\n987\\n*OOI\\n*oi4\\n*02 7\\n*04i\\n\u00e2\u0080\u00a23\\n4.0\\n3-9\\n324\\n51 054\\n068\\n081\\n094\\n108\\n121\\n135\\n148\\n161\\n175\\n\u00e2\u0080\u00a24\\n5.4\\n6.7\\n5-2\\n6.5\\n325\\n188\\n201\\n215\\n228\\n242\\n255\\n268\\n282\\n295\\n308\\n326\\n322\\n335\\n348\\n361\\n375\\n388\\n401\\n415\\n428\\n441\\n.6\\n8.1\\n7.8\\n327\\n455\\n468\\n481\\n494\\n508\\n521\\n534\\n547\\n561\\n574\\n\u00e2\u0080\u00a27\\n.8\\n9-4\\n10.8\\nr T\\n328\\n587\\n6o5\\n614\\n627\\n640\\n653\\n667\\n680\\n693\\n706\\ny .1\\n10.4\\n329\\n330\\n33^\\n719\\n733\\n746\\n759\\n772\\n904\\n785\\n798\\n812\\n825\\n838\\n\u00e2\u0080\u00a29\\n12. i\\nII. 7\\n851\\n983\\n864\\n877\\n891\\n917\\n930\\n943\\n956\\n969\\n996\\n*oo9\\n*022\\n*o35\\n*o48\\n*o6i\\n*o74\\n*o87\\n*ioo\\n332\\n52 114\\n127\\n140\\n153\\n166\\n179\\n192\\n205\\n218\\n231\\n244\\n257\\n270\\n283\\n296\\n309\\n322\\n335\\n348\\n361\\n334\\n374\\n387\\n400\\n413\\n426\\n439\\n452\\n465\\n478\\n491\\n335\\n504\\n517\\n530\\n543\\n556\\n569\\n582\\n595\\n608\\n621\\nr S 1\\n33^\\n634\\n647\\n660\\n672\\n685\\n^98\\n711\\n724\\n737\\n750\\nI 2\\nI 2\\n337\\n763\\n776\\n789\\n801\\n814\\n827\\n840\\n853\\n866\\n879\\n2\\n2.5\\n2.4\\n338\\n891\\n904\\n917\\n930\\n943\\n956\\n9^8\\n981\\n994\\n*oo7\\n.3\\n3.7\\n3.6\\n339\\n53 020\\n033\\n045\\n058\\n071\\n084\\n097\\n109\\n122\\n135\\n/I R\\n340\\n341\\n148\\ni65\\n173\\n186\\n199\\n211\\n224\\n237\\n250\\n377\\n262\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n5\\n6.2\\n7.5\\n4.0\\n6.0\\n7.2\\n275\\n288\\n301\\n313\\n326\\n339\\n352\\n364\\n390\\n342\\n402\\n415\\n428\\n440\\n453\\n466\\n478\\n491\\n504\\n516\\n7\\nS.7\\n10.\\n8.4\\n9.6\\n343\\n529\\n542\\n554\\n567\\n580\\n592\\n605\\n618\\n630\\n643\\n.8\\n344\\n656\\n66s\\n681\\n693\\n706\\n719\\n731\\n744\\n756\\n76(3\\n\u00e2\u0080\u00a29\\nII. 2\\n10.8 j\\n345\\n782\\n794\\n807\\n819\\n832\\n845\\n857\\n870\\n882\\n895\\n346\\n907\\n920\\n932\\n945\\n958\\n970\\n983\\n995\\n*oo8\\n*020\\n347\\n54033\\n045\\n058\\n076\\n083\\n095\\n108\\n120\\n^33\\n14!\\n348\\n158\\n170\\n183\\n195\\n208\\n220\\n232\\n245\\n257\\n270\\n349\\n350\\n282\\n295\\n307\\n320\\n332\\n344\\n357\\n369\\n3S2\\n394\\n407\\n419\\n431\\n444\\n456\\n469\\n481\\n493\\n506\\n5^S\\nN.\\n1\\n2\\n1 3\\n4\\n1\\n7 1 8\\n9\\nP.P.\\n329", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0381.jp2"}, "382": {"fulltext": "TABLE v.-\\n-LOGARITHMS\\n3F NUMBERS.\\n1 N.\\n1\\n2 j 3\\n4\\n5 6\\n7 8 9 1\\nP.\\nP.\\n350\\n351\\n54 407\\n419\\n431\\n444.\\n456\\n469\\n481\\n493\\n506\\n518\\nI\\n12\\n1 2\\n530\\n543\\n555\\n568\\n580\\n592\\n605\\n617\\n629\\n642\\n\\\\352\\n654\\n666\\n679\\n691\\n703\\n716\\n728\\n740\\n753\\n765\\n.2\\n2.5\\n353\\n777\\n790\\n802\\n814\\n826\\n839\\n851\\n863\\n876\\n888\\n\u00e2\u0080\u00a23\\n3-7\\n1354\\n900\\n912\\n925\\n937\\n949\\n961\\n974\\n986\\n998\\n*oi6\\n.J.\\nK .0\\ni355\\n55 023\\n035\\n047\\n059\\n071\\n084\\n096\\n108\\n120\\n133\\n.5\\n6.2\\n1356\\n145\\n157\\n169\\n181\\n194\\n206\\n218\\n230\\n242\\n254\\n.6\\n7.5\\n1357\\n267\\n279\\n291\\n303\\n315\\n327\\n340\\n352\\n364\\n376\\n.7\\n.8\\n8.7\\n10.\\n1358\\n3H\\n400\\n412\\n424\\n437\\n449\\n461\\n473\\n485\\n497\\n359\\n360\\n1361\\n509\\n630\\n750\\n521\\n533\\n545\\n558\\n570\\n696\\n582\\n594\\n606\\n618\\n\u00e2\u0080\u00a29\\nII. 2\\n12\\nI 2\\n642\\n654\\n775\\n666\\n678\\n702\\n714\\n726\\n738\\n762\\n787\\n799\\n811\\n823\\n835\\n847\\n859\\n3^2\\n871\\n883\\n895\\n907\\n919\\n931\\n943\\n955\\n966\\n978\\n2\\n2.4\\n\\\\3^3\\n990\\n*002\\n*oi4\\n^025\\n^038\\n*o56\\n^062\\n*o74\\n*o86\\n^098\\n\u00e2\u0080\u00a23\\n3.6\\n364\\n56 no\\n122\\n134\\n146\\n158\\n170\\n181\\n193\\n205\\n217\\n4.8\\n6.0\\n365\\n229\\n241\\n253\\n265\\n277\\n288\\n306\\n312\\n324\\n33^\\n\u00e2\u0080\u00a24\\n.5\\n366\\n348\\n360\\n372\\n383\\n395\\n407\\n419\\n431\\n443\\n455\\n.6\\n7.2\\n367\\n465\\n478\\n490\\n502\\n514\\n525\\n537\\n549\\n561\\n573\\n8.4\\n9.6\\n10.8\\nII\\n368\\n585\\n596\\n6o\u00c2\u00a7\\n620\\n632\\n643\\n655\\n667\\n679\\n691\\n\u00e2\u0080\u00a27\\n.8\\n369\\n370\\n371\\n702\\n714\\n726\\n738\\n749\\n761\\n879\\n773\\n785\\n796\\n808\\n\u00e2\u0080\u00a29\\n820\\n832\\n843 855\\n867\\n984\\n896 1 902\\n914\\n925\\n937\\n949\\n961\\n972\\n996\\n*oo7\\n*oi9\\n*o3i\\n^042\\n372\\n57 054\\n066\\n077\\n089\\nlOI\\n112\\n124\\n136\\n147\\n159\\n.2\\n2.3\\nI373\\n171\\n182\\n194\\n206\\n217\\n229\\n240\\n252\\n264\\n275\\n\u00e2\u0080\u00a23\\n3-4\\n374\\n287\\n299\\n310\\n322\\n333\\n345\\n357\\n3^S\\n380\\n391\\n4-6\\n7\\nJ375\\n403\\n414\\n426\\n438\\n449\\n461\\n472\\n484\\n495\\n507\\n\u00e2\u0080\u00a24\\n376\\n519\\n530\\n542\\n553\\n565\\n576\\n588\\n599\\n611\\n622\\n.6\\n6.9\\n377\\n634\\n645\\n657\\n668\\n680\\n691\\n703\\n714\\n726\\n737\\n8.0\\n9.2\\n10.3\\nII\\n378\\n749\\n760\\n772\\n783\\n795\\n806\\n818\\n829\\n841\\n852\\n\u00e2\u0080\u00a27\\n8\\n379\\n380\\n381\\n864\\n875\\n887\\n898\\n909\\n921\\n932\\n944\\n955\\n967\\n\u00e2\u0080\u00a29\\n978\\n990\\n*OOI\\n*OI2 *024\\n*o35\\n149\\n*o47\\n*o58\\n069\\n*o8i\\n58 092\\n104\\n115\\n126\\n138\\n161\\n172\\n183\\n195\\n382\\n206\\n217\\n229\\n240\\n252\\n263\\n274\\n286\\n297\\n3^S\\n.2\\n2.2\\n3^3\\n320\\n33^\\n342\\n354\\n365\\n376\\n388\\n399\\n410\\n422\\n\u00e2\u0080\u00a23\\n3-3\\n384\\n433\\n444\\n455\\n467\\n478\\n489\\n501\\njI2\\n523\\n535\\n385\\n546\\n557\\n568\\n580\\n591\\n602\\n613\\n625\\n636\\n647\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n4.4\\n5.5\\n6.6\\n386\\n658\\n670\\n681\\n692\\n703\\n715\\n726\\n737\\n748\\n760\\n387\\n771\\n782\\n793\\n804\\n816\\n827\\n838\\n849\\n861\\n872\\n388\\n883\\n894\\n905.\\n916\\n928\\n939\\n950\\n961\\n972\\n984\\n\u00e2\u0080\u00a27\\nQ\\n7-7\\n8.8\\n9 9\\n10\\n389\\n1390\\n391\\n995\\n59 106\\n*oo6\\n*oi7\\n*028\\n*o39\\n*o5o\\n162\\n*o62\\n*o73\\n184\\n^084\\n*o95\\n\u00e2\u0080\u00a29\\n117\\n128\\n140\\n^51\\n173\\n195\\n206\\n217\\n229\\n240\\n251\\n262\\n273\\n284\\n295\\n3^6\\n317\\n392\\n328\\n339\\n35^\\n362\\n373\\n384\\n395\\n406\\n417\\n428\\nI\\nI.O\\n1393\\n439\\n450\\n461\\n472\\n483\\n494\\n505\\n5I6\\n527\\n53S\\n.3\\n3.1\\n394\\n549\\n560\\n571\\n582\\n593\\n604\\n615\\n626\\n637\\n648\\n395\\n659\\n670\\n681\\n692\\n703\\n714\\n725\\n736\\n747\\n758\\n\u00e2\u0080\u00a24\\n4.2\\n396\\n769\\n786\\n791\\n802\\n813\\n824\\n835\\n846\\n857\\n868\\n\u00e2\u0080\u00a25\\n.6\\n5-2\\n6.3\\n397\\n879\\n890\\n901\\n912\\n923\\n933\\n944\\n955\\n9^6\\n^977\\n398\\n988\\n999\\n*OIO\\n*02I\\n*032\\n*o43\\n*o53\\n*o64\\n*o75\\n*o86\\n.7\\n7-3\\n8.4\\n9.4\\n399\\n400\\n60 097\\n206\\n108\\n119\\n130\\n141\\n151\\n162\\n173\\n184\\n195\\n.8\\n.9\\n217\\n227\\n238\\n249\\n260\\n271\\n282\\n293\\n3^3\\n1\\n2\\n3\\n4\\n5 6\\n7\\n8 9 1\\nP.\\nP.\\n330", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0382.jp2"}, "383": {"fulltext": "TABLE V.-\\n-LOGARITHMS\\n)F NUMHERS.\\nIn.\\n400\\n401\\n1\\n21314\\n5 e\\n7 1 8\\nI*\\nV.\\n60 206\\n217\\n1 227 1 238\\n249\\n260\\n271\\n379\\n282\\n293\\n401\\n412\\n314\\n325\\n1 zz(^\\n347\\n357\\nz^l\\n390\\n402\\n422\\n433\\n444\\n455\\n466\\n476\\n487\\n498\\n509\\n519\\n403\\n530\\n541\\n552\\n563\\n573\\n584\\n595\\n606\\n616\\n627\\nII\\n,404\\n638\\n649\\n659\\n670\\n681\\n692\\n702\\n713\\n724\\n735\\nI\\n.2\\nI I\\n2.2\\n405\\n745\\n756\\n767\\n777\\n788\\n799\\n810\\n826\\nH^\\n842\\n\u00e2\u0080\u00a23\\n3-3\\n406\\n852\\n863\\n874\\n884\\n895\\n906\\n916\\n927\\n938\\n949\\n407\\n959\\n970\\n981\\n991\\n*00 2\\n*oi3\\n*023\\n*o34\\n*044\\n*o55\\n.4\\n.5\\n4.4\\n5-5\\n408\\n61 066\\n076\\n087\\n098\\nI08\\n119\\n130\\n140\\n151\\n161\\n.6\\n6.6\\n409\\n410\\n411\\n172\\n183\\n193\\n204\\n215\\n225\\n331\\n236\\n342\\n246\\n352\\n257\\n268\\n.7\\n.8\\n\u00e2\u0080\u00a29\\n7.7\\nS.8\\n9.9\\n278 289\\n299 1 310\\n326\\nTi^Z\\n373\\n384 1 394\\n405\\n416\\n426\\n437\\n447\\n458\\n468\\n479\\n412\\n489\\n500\\n511\\n521\\n532\\n542\\n553\\n563\\n574\\n584\\n413\\n595\\n605\\n616\\n625\\n637\\n647\\n658\\n668\\n679\\n689\\n414\\n700\\n710\\n721\\n731\\n742\\n752\\n763\\n773\\n784\\n794\\n415\\n805\\n8 5\\n825\\n%l6 846\\n857\\n867\\n878\\n888\\n899\\n416\\n909\\nQ20\\n930\\n940\\n951\\n961\\n972\\n982\\n993 *oo3\\n.2\\n2. 1\\n[417\\n62 013 024\\n034\\n045\\n^y:i\\n065\\n076\\n086\\n097\\n107\\n\u00e2\u0080\u00a23\\n3-1\\n418\\n117\\n128\\n^zl\\n149\\n159\\n169\\n180\\n190\\n200\\n211\\n419\\n420\\n421\\n221\\n325\\n428\\n232\\n242\\n252\\n263\\n3^6\\n469\\n273\\n376\\n480\\n283\\n294\\n304\\n314\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n\u00e2\u0080\u00a27\\n.8\\n4.2\\n5-2\\n6.3\\n7-3\\n8.4\\n335\\n345\\n356\\n459\\n387\\n397\\n407 418\\n438\\n449\\n490\\n506\\n510 521\\n422\\n531\\n541\\n552\\n562\\n572\\n582\\n593\\n603\\n6^s\\n624\\n423\\n634\\n644\\n654\\n665\\n675\\n685\\n695\\n706\\n716\\n726\\n.9\\n9.4\\n424\\n736\\n747\\n757\\n767\\n777\\n7S8\\n798\\n808\\n818\\n828\\n425\\n839\\n849\\n859\\n869\\n879\\n890\\n900\\n910\\n926\\n931\\n426\\n941\\n951\\n961\\n971\\n981\\n992\\n*002\\n*OI2\\n*022\\n*032\\n427\\n63 043\\n053\\n063\\n073\\n083\\n093\\n104\\n114\\n124\\n134\\n10\\n428\\n144\\n154\\n164\\n175\\n185\\n195\\n205\\n215\\n225\\n235\\nI\\n.2\\nI.O\\n2.0\\n429\\n430\\n431\\n245\\n347\\n256\\n266\\n276\\n286\\n387\\n296\\n3O6\\n3I6\\n326\\n336\\n\u00e2\u0080\u00a23\\n\u00e2\u0080\u00a24\\n.5\\n3-0\\n4.0\\n5-0\\n357\\n367 1 377\\n397 407\\n417\\n427\\n437\\n447\\n458\\n468\\n478\\n488\\n498\\n508\\n518\\n528\\n538\\n432\\n548\\n558\\n5^8\\n578\\n588\\n598 608\\n618\\n628\\n639\\n.6\\n6.0\\n433\\n649\\n659\\n669\\n679\\n689\\n699 709\\n719\\n729\\n739\\n434\\n749\\n759\\n769\\n779\\n789\\n799\\n809\\n819\\n829\\n839\\n\u00e2\u0080\u00a27\\n.8\\n7.0\\n8.0\\n435\\n849\\n859\\n869\\n879\\n889\\n899\\n909\\n919\\n928\\n938\\n\u00e2\u0080\u00a29\\n9.0\\n436\\n948\\n958\\n9^^8\\n978\\n988\\n998\\n\u00e2\u0096\u00a0^^oog\\n*oi8\\n*028\\n^038\\n437\\n64 048\\n058\\n068\\n078\\n088\\n09S\\n107\\n117\\n127\\n137\\n43^\\n147\\n157\\n167\\n177\\n187\\n197\\n207\\n217\\n226\\n236\\n439\\n440\\n441\\n246\\n256\\n266\\n276\\n286\\n296\\n394\\n306\\n315\\n325\\n335\\n.1\\n.2\\n.3\\n9\\n0.9 J\\n^\u00e2\u0080\u00a29\\n2-8\\n345\\n444\\n355\\n453\\n365\\n375\\n384\\n404\\n414\\n424\\n434\\n463\\n473\\n483\\n493\\n503\\n512\\n522\\n532\\n442\\n542\\n552\\n562\\n571\\n58i\\n591\\n601\\n611\\n621\\n636\\n443\\n640\\n650\\n660\\n670\\n679\\n689\\n699\\n709\\n7I8\\n728\\n\u00e2\u0080\u00a24\\n.5\\n.6\\n3-s\\n4-7\\n5.7\\n444\\n738\\n748\\n758\\n767\\n777\\n787\\n797\\n806\\n8I6\\n826\\n445\\n836\\n846\\n855\\n865\\n875\\n885 894\\n904\\n914\\n923\\n446\\n933\\n943\\n953\\n962\\n972\\n982\\n992\\n*OOI\\n*oii\\n*02I\\n.7\\n.8\\n6.6\\n7.6\\n447\\n65 031\\n040\\n050\\n060\\n069\\n079\\n089\\n098\\n108\\n118\\n\u00e2\u0080\u00a29\\n8.5 1\\n448\\n128\\n137\\n147\\n157\\n166\\n176\\n186\\n195\\n205\\n215\\n449\\n450\\n224\\n234\\n244\\n253\\n263\\n273\\n282\\n292\\n302\\n311\\n321\\n7^7\\n1 340\\n350 360\\n3^^9 379\\n389\\n398\\n408\\ni\\n1\\n1 2 1 3 1 4\\nr is\\n7 1 8\\nV\\nP.\\n331", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0383.jp2"}, "384": {"fulltext": "TABLE V.-\\n-LOGARITHMS\\nOF NUMBERS.\\n4\\nI~x7\\n450\\n451\\n1 1 j 2\\n3\\n4\\n5\\n6\\n7\\n8\\nP\\n.P.\\n65 321\\n33^\\n340\\n350\\n360\\n369\\n379\\n389\\n398\\n408\\n417\\n427\\n437\\n446\\n456\\n466\\n475\\n485\\n494\\n504\\n452\\n514\\n523\\n533\\n542\\n552\\n562\\n571\\n581\\n590\\n600\\n453\\n610\\n619\\n629\\n^38\\n648\\n657\\n667\\n677\\n686\\n696\\n10\\n454\\n705\\n715\\n724\\n734\\n744\\n753\\n763\\n772\\n782\\n791\\n.2\\n2.0\\n|455\\n801\\n810\\n820\\n830\\n839\\n849\\n858\\n868\\n877\\n887\\n.3\\n3-0\\n456\\n896\\n906\\n9^5\\n925\\n934\\n944\\n953\\n963\\n972\\n982\\n457\\n991\\n*OOI\\n*oi3\\n*020\\n^029\\n*o39\\n*o48\\n^058\\n*o67\\n*o77\\n\u00e2\u0080\u00a24\\n.5\\n4.0\\n5.0\\n45\\n66 085\\n096\\n105\\n115\\n124\\n134\\n143\\n153\\n162\\n172\\n.6\\n6.0\\n459\\n460\\n461\\n181\\n190\\n200\\n209\\n219\\n228\\n238\\n247\\n257\\n266\\n\u00e2\u0080\u00a27\\n.8\\n\u00e2\u0080\u00a29\\n7.0\\n8.0\\n9.0\\n276\\n285\\n294\\n304\\n313\\n323\\n332\\n342\\n351 1 3^0\\n370\\n379\\n389\\n398\\n408\\n417\\n426\\n436\\n445\\n455\\n462\\n464\\n473\\n483\\n492\\n502\\n511\\n520\\n530\\n539\\n548\\n463\\n558\\n567\\n577\\n586\\n595\\n605\\n614\\n623\\n^33\\n642\\n464\\n652\\n661\\n673\\n680\\n689\\n698\\n708\\n7x7\\n726\\n736\\na\\n465\\n745\\n754\\n764\\n773\\n782\\n792\\n801\\n816\\n820\\n829\\n9\\n466\\n838\\n84S\\n857\\nS6e\\n876\\n885\\n894\\n904\\n913\\n922\\n.1\\n.2\\n0.9\\n1.9\\n2.8\\n467\\n931\\n941\\n950\\n959\\n969\\n978\\n987\\n996\\n*oo6\\n*oi5\\n.3\\n468\\n67 024\\n034\\n043\\n052\\n061\\n071\\n080\\n089\\n099\\n108\\n469\\n470\\n471\\n117\\n126\\n136\\n228\\n145\\n154\\n163\\n173\\n182\\n191\\n200\\n4\\n.5\\n.6\\n\u00e2\u0080\u00a27\\n.8\\n3.8\\n4.7\\n5.7\\n210\\n302\\n219\\n237\\n246\\n256\\n265\\n274\\n283\\n293\\n311\\n320\\n329\\n339\\n348\\n357\\n3(^6\\n376\\n385\\n472\\n394\\n403\\n412\\n422\\n431\\n440\\n449\\n458\\n467\\n477\\n0.5\\n7.6\\n473\\n486\\n495\\n504\\n513\\n523\\n532\\n541\\n550\\n559\\n5^8\\n\u00e2\u0080\u00a29\\n8.5\\n474\\n578\\n587\\n596\\n605\\n614\\n623\\n^33\\n642\\n651\\n660\\n475\\n669\\n^78\\n687\\n697\\n706\\n715\\n724\\n733\\n742\\n75 J\\n476\\n760\\n770\\n779\\n788\\n797\\n806\\n815\\n824\\n^33\\n842\\n477\\n852\\n861\\n870\\n879\\n8SS\\n897\\n906\\n915\\n924\\n933\\n9\\n478\\n943\\n952\\n961\\n970\\n979\\n988\\n997\\n*oo6\\n*oi5\\n*024\\n.1\\n2\\n0.9\\nI 8\\n479\\n480\\n481\\n68 033 042\\n051\\n060\\n070\\n166\\n079\\n088\\n097\\n106\\n115\\n\u00e2\u0080\u00a23\\n.4\\n1;\\n2.7\\n3.6\\n4.\\n124\\n^33\\n142\\n151\\n169\\n259\\n178\\n187\\n196\\n205\\n214\\n223\\n232\\n241\\n250\\n268\\n277\\n286\\n295\\n482\\n304\\n3^3\\n322\\n331\\n340\\n349\\n358\\n367\\n376\\n385\\n.6\\n5.4\\n483\\n394\\n403\\n412\\n421\\n430\\n439\\n448\\n457\\n4^6\\n475\\n484\\n484 493\\n502\\n511\\n520\\n529\\n538\\n547\\n556\\n565\\n\u00e2\u0080\u00a27\\n.8\\n6.3\\n7 2\\n485\\n574 583\\n592\\n601\\n610\\n61Q\\n628\\n637\\n646\\n654\\n\u00e2\u0080\u00a29\\n8.1\\n480\\n663 672\\n681\\n690\\n699\\n708\\n717\\n726\\n735\\n744\\n487\\n753 762\\n770\\n779\\n788\\n797\\n806\\n815\\n824\\n^33\\n488\\n842\\n851\\n860\\nS6s\\n877\\n886\\n895\\n904\\n913\\n922\\n489\\n490\\n491\\n931\\n940\\n948\\n957\\n966\\n975\\n984\\n993\\n*002\\n*oi5\\n.1\\n.2\\n\u00e2\u0080\u00a23\\n8\\no.S\\n1-7\\n2.5\\n69 019 02g\\n037\\n046\\n055\\n064\\n073\\n081\\n090\\n099\\n108\\n117\\n126\\n134\\n143\\n152\\n161\\n170\\n179\\n187\\n492\\n196\\n205\\n214\\n223\\n232\\n240\\n249\\n258\\n267\\n276\\n493\\n284\\n293\\n302\\n311\\n320\\n328\\n337\\n346\\n355\\n364\\n.4\\n.5\\n3-4\\na. 2\\n494\\n372\\n38^^\\n390\\n399\\n408\\n41 6\\n425\\n434\\n443\\n451\\n.6\\n5-1\\n495\\n460\\n469\\n478\\n487\\n495\\n504\\n513\\n522\\n530\\n539\\n496\\n548\\n557\\n565\\n574\\n583\\n592\\n600\\n609\\n618\\n627\\n.7\\n8\\n5.9\\n6 A\\n497\\n635\\n644\\n653\\n662\\n670\\n679\\n688\\n697\\n705\\n714\\n\u00e2\u0080\u00a29\\n7.6\\n498\\n723\\n731\\n740\\n749\\n758\\n766\\n775\\n784\\n792\\n801\\n499\\n500\\nN.\\n810\\n819\\n827\\n836\\n845\\n853\\n862\\n871\\n879\\n888\\n897\\n905\\n914\\n923\\n931\\n946\\n949\\n958\\n966\\n975\\n1\\n2\\n3\\n4\\n5 6\\n7\\n8\\n9\\nP.\\nP.\\n332", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0384.jp2"}, "385": {"fulltext": "TABLE V.-\\n-LOGARITHMS OF NUMBERS.\\n500\\n1\\n\u00e2\u0080\u00a2.i\\n4\\n7 S 1)\\np\\nP.\\n69 897\\n984\\n905\\n914\\n923\\n931\\n946\\n*027\\n949\\n*o36\\n958 9^6\\n975\\n*o6i\\n992\\n*OOI\\n*OIO\\n*oi8\\n*o44 *o53\\n502\\n70 070\\n079\\n087\\n096\\n105\\n113\\n122\\n131\\n139\\n148\\n9\\n0.0\\n5^3\\n157\\n165\\n174\\n182\\n191\\n200\\n208\\n217\\n226\\n234\\nI\\n504\\n243\\n251\\n260\\n269\\n277\\n286\\n294\\n303\\n312\\n326\\n.2\\n1.8\\n505\\n329\\n337\\n346\\n355\\n3(^3\\n372\\n386\\n389\\n398\\n406\\n\u00e2\u0080\u00a23\\n2.7\\n506\\n415\\n423\\n432\\n441\\n449\\n458\\n4^6\\n475\\n483\\n492\\n\u00e2\u0080\u00a24\\n5\\n3.6\\n4-5\\n507\\n501\\n509\\n518\\n526\\n535\\n543\\n552\\n566\\n569\\n578\\n508\\n586\\n595\\n603\\n612\\n626\\n629\\n637\\n646\\n654\\n663\\n.6\\n5-4\\n509\\n510\\n511\\n672\\n6Sd\\n689\\n697\\n706\\n791\\n714\\n723\\n731\\n740\\n748\\n833\\n9J8\\n\u00e2\u0080\u00a27\\n.8\\n\u00e2\u0080\u00a29\\n6.3\\n7-2\\nS.I\\n757\\n765\\n774\\n782\\n799\\n884\\n808\\n816\\n825\\n842\\n856\\n859\\n867\\n876\\n893\\n901\\n910\\n512\\n927\\n935\\n944\\n952\\n961\\n969\\n978\\n986\\n995\\n*oo3\\n5^3\\n71 oil\\n020\\n028\\n037\\n045\\n054\\n062\\n071\\n079\\n088\\n514\\n096\\n105\\n113\\n121\\n130\\n138\\n147\\n155\\n164\\n172\\n515\\n186\\n189\\n197\\n206\\n214\\n223\\n231\\n239\\n248\\n256\\n8\\n516\\n265\\n273\\n282\\n290\\n298\\n307\\n315\\n324\\n332\\n340\\nI\\n.2\\n0.8\\nI -7\\n517\\n349\\n357\\n366\\n374\\n382\\n391\\n399\\n408\\n416\\n424\\n\u00e2\u0080\u00a23\\n2.5\\n5^^\\n433\\n441\\n449\\n458\\n465\\n475\\n483\\n491\\n500\\n508\\n519\\n520\\n521\\n516\\n600\\n525\\n533\\n542\\n550\\n633\\n558\\n567\\n575\\n583\\n592\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n3.4\\n4.2\\n5.1\\n608\\n617\\n625\\n642\\n656\\n659 667\\n675\\n684\\n692\\n700\\n709\\n717\\n725\\n734\\n742\\n750\\n758\\n522\\n767\\n775\\n783\\n792\\n806\\n808\\n817\\n825\\n833\\n842\\n\u00e2\u0080\u00a27\\n.8\\n5-9\\n6.8\\n523\\n850\\n858\\n867\\n875\\n883\\n891\\n900\\n908\\n916\\n925\\n\u00e2\u0080\u00a29\\n7-6\\n524\\n933\\n941\\n949\\n958\\n9^6\\n974\\n983\\n991\\n999\\n*oo7\\n525\\n72 016\\n024\\n032\\n040\\n049\\n057\\n065\\n074\\n082\\n090\\n526\\n098\\n107\\n115\\n123\\n131\\n140\\n148\\n156\\n164\\n173\\n527\\n181\\n189\\n197\\n206\\n214\\n222\\n230\\n238\\n247\\n255\\n8\\n528\\n263\\n271\\n280\\n288\\n296\\n304\\n312\\n321\\n329\\n337\\n.1\\no.S\\nI 6\\n529\\n530\\nr53i\\n345\\n354\\n362\\n370\\n378\\n386\\n395\\n403\\n411\\n419\\n\u00e2\u0080\u00a23\\n\u00e2\u0080\u00a24\\n2.4\\n3-2\\n4..0\\n427\\n436\\n444\\n452\\n466\\n4^8\\n55Q\\n476\\n558\\n485\\n493\\n501\\n509\\n517\\n526\\n534\\n542\\n566\\n575\\n583\\n532\\n591\\n599\\n607\\n615\\n624\\n632\\n640\\n648\\n658\\n664\\n.6\\n4.8\\n533\\n672\\n68i\\n689\\n697\\n705\\n713\\n721\\n729\\n738\\n746\\n534\\n754\\n762\\n770\\n778\\n785\\n795\\n803\\n811\\n819\\n827\\n\u00e2\u0080\u00a27\\n8\\n5-6\\n6.4\\n7.2\\n535\\n835\\n843\\n851\\n859\\n868\\n876\\n884\\n892\\n900\\n908\\n\u00e2\u0096\u00a09\\n53^\\n916\\n924\\n932\\n941\\n949\\n957\\n965\\n973\\n981\\n989\\n537\\n997\\n*oo5\\n*oi3\\n*02i\\n*o3o\\n*o3S\\n*o46\\n*o54\\n*o62\\n*o7o\\n538\\n73 078\\n085\\n094\\n102\\n1 10\\n118\\n126\\n134\\n143\\n151\\n539\\n540\\n541\\n159\\n239\\n3^9\\n167\\n175\\n183\\n191\\n199\\n279\\n207\\n287\\n368\\n215\\n223\\n231\\nI\\n_ 2\\n.3\\n1\\n0.7\\n1-5\\n2.2\\n247\\n255\\n263\\n344\\n271\\n295\\n303\\n311\\n328\\n336\\n352\\n360\\n376\\n384\\n392\\n542\\n400\\n408\\n416\\n424\\n432\\n440\\n448\\n456\\n464\\n472\\n543\\n480\\n488\\n496\\n504\\n512\\n520\\n528\\n536\\n544\\n552\\n\u00e2\u0080\u00a24\\n3-0\\n544\\n560\\n568\\n576\\n584\\n592\\n600\\n608\\n615\\n623\\n631\\n\u00e2\u0080\u00a25\\n.0\\n3-7\\n4-5\\n545\\n639\\n647\\n655\\n663\\n671\\n679\\n687\\n695\\n703\\n711\\n546\\n719\\n727\\n735\\n743\\n75^\\n759\\n767\\n775\\n783\\n791\\n\u00e2\u0080\u00a27\\n.8\\n\u00e2\u0080\u00a29\\n^.2\\n6.0\\n6.7\\n547\\n798\\n806\\n814\\n822\\n830\\n838\\n846\\n854\\n862\\n870\\n548\\n878\\n886\\n894\\n902\\n909\\n917\\n925 933\\n941 949\\n549\\n550\\n1 X.\\n957\\n965\\n973\\n981\\n989\\n997\\n075\\n*004 *OI2\\n*026\\n1*028\\n107\\n74 036\\n044\\n052\\n060\\n068\\n083 091 1 099\\n1\\n2\\n1 3\\n1 4\\n5\\nC, 7 S\\nP\\nP.\\n333", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0385.jp2"}, "386": {"fulltext": "TABLE V.-\\n-LOGARITHMS OF NUMBERS.\\n650\\n551\\n1 1\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n9\\nP^\\nP.\\n74 036\\nn5\\n044\\n052\\n060\\n068\\n075\\n083\\n091\\n099\\n178\\n107\\n186\\n123\\n131\\n139\\n146\\n154\\n1O2\\n170\\n55-\\n194\\n202\\n209\\n217\\n225\\n233\\n241\\n249\\n257\\n264\\n553\\n272\\n280\\n288\\n296\\n304\\n312\\n319\\n327\\n335\\n343\\n554\\n351\\n359\\nS ^G\\n374\\n3S2\\n390\\n398\\n406\\n413\\n421\\n55^\\n5S(^\\n429\\n437\\n445\\n453\\n466\\n463\\n476\\n484\\n492\\n499\\n507\\n515\\n523\\n531\\n538\\n546\\n554\\n562\\n570\\n577\\n8\\n557\\n585\\n593\\n601\\n609\\n616\\n624\\n62,2\\n640\\n648\\n655\\n.1\\n0.8\\nT 6\\n55S\\n663\\n671\\n679\\n687\\n694\\n702\\n710\\n718\\n725\\n733\\n.3\\n2.4\\n559\\n741\\n819\\n896\\n749\\n756\\n764\\n772\\n850\\n780\\n788\\n795\\n803\\n811\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n3-2\\n4.0\\n4.8\\n560\\n826\\n834\\n842\\n857\\n865\\n873\\n881\\n888\\n5^1\\n904\\n912\\n919\\n927\\n935\\n942\\n950\\n958\\n966\\n562\\n973\\n981\\n989\\n997\\n\u00e2\u0080\u00a2004\\n*OI2\\n*020\\n*027\\n*o3,S\\n*o43\\n5^3\\n75 051\\n058\\n065\\n074\\n081\\n089\\n097\\n105\\n112\\n120\\n\u00e2\u0080\u00a27\\n5-6\\nfi A\\n565\\n566\\n128\\n135\\n143\\n151\\n158\\n166\\n174\\n182\\n189\\n197\\n\u00e2\u0080\u00a29\\nD.4\\n7.2\\n205\\n212\\n220\\n228\\n235\\n243\\n251\\n258\\n266\\n274\\n281\\n289\\n297\\n304\\n312\\n320\\n327\\n335\\n343\\n350\\n5^7\\n568\\n569\\n670\\n571\\n358\\n366\\n*T -7\\nJ/3\\n38i\\n389\\n396\\n404\\n412\\n419\\n427\\n435\\n442\\n450\\n458\\n465\\n473\\n4S0\\n488\\n496\\n503\\n511\\n5^9\\n525\\n534\\n541\\n549\\n557\\n564\\n572\\n580\\n1\\n587\\n595\\n602\\n6 10\\n618\\n625\\n633\\n641\\n648 656\\n663\\n671\\n679\\n6-6\\n694\\n701\\n709\\n717\\n724\\n732\\n!57-^\\n739\\n747\\n755\\n762\\n770\\nM\\nill\\n785\\n7Q2\\n800\\n808\\nI\\n0.7\\n1-5\\n2.2\\n573\\n815\\n823\\n830\\n838\\n846\\n853\\n861\\n868\\n876\\n883\\n3\\n574\\n891\\n899\\n906\\n914\\n921\\n929\\n936\\n944\\n9Si\\n959\\n575\\n967\\n974\\n982\\n989\\n997\\n004\\n*OI2\\n^019\\n*027\\n*o34\\n\u00e2\u0080\u00a24\\n3-9\\n570\\n76 042\\n050\\n057\\n065\\n072\\noSo\\n087\\n095\\n102\\nno\\n\u00e2\u0080\u00a25\\n.6\\n3-7\\n4.5\\n577\\n117\\n125\\n132\\n140\\n147\\n155\\n162\\n170\\n178\\n185\\n57S\\n193\\n200\\n208\\n2^5\\n223\\n230\\n238\\n245\\n253\\n260\\n\u00e2\u0080\u00a27\\n.8\\n\u00e2\u0080\u00a29\\n5-2\\n6.0\\n6.7\\n579\\n680\\n581\\n268\\n275\\n283\\n290\\n298\\n305\\n380\\n313\\n387\\n320\\n328\\n335\\n343\\n350\\n358\\n365\\n372\\n395\\n470\\n4c 2\\n410\\n417\\n425\\n432\\n440\\n447\\n455\\n462\\n477\\n485\\n582\\n492\\n500\\n507\\n514\\n522\\n529\\n537\\n544\\n552\\n559\\n5^3\\n567\\n574\\n582\\n589\\n596\\n604\\n6ii\\n619\\n626\\n634\\n^5H\\n641\\n648\\n656\\n663\\n671\\n678\\n686\\n693\\n700\\n708\\n|5^5\\n715\\n723\\n730\\n738\\n745\\n752\\n760\\n767\\n775\\n782\\n5S0\\n790\\n797\\n804\\n812\\n819\\n827\\n534\\n841\\n849\\n856\\n7\\ni5\u00c2\u00ab7\\n864\\n871\\n878\\nSS6\\n893\\n901\\n908\\n9LS\\n923\\n930\\nI\\n0.7\\n588\\n589\\n590\\n591\\n937\\n945\\n952\\n960\\n967\\n974\\n982\\n989\\n997\\n004\\n.3\\n1.4\\n2.1\\n77 on\\n019\\n026\\n^33\\n041\\n114\\n048\\n055\\n129\\n063\\n070\\n078\\n151\\n225\\n.4\\n\u00e2\u0080\u00a25\\n.6\\n2.8\\n3-5\\n4.2\\n085\\n158\\n092\\n100\\n107\\n122\\n195\\n136\\n210\\n144\\n166\\n173\\n181\\n188\\n2C3\\n217\\n592\\n232\\n239\\n247\\n254\\n261\\n269\\n276\\n283\\n2QI\\n298\\n593\\n305\\n313\\n320\\n327\\n335\\n342\\n349\\n3S6\\n364\\n371\\n\u00e2\u0080\u00a27\\ns\\n4-9\\n6\\n594\\n378\\n386\\n393\\n400\\n408\\n415\\n422\\n430\\n437\\n444\\n.9\\n6.3\\n|595\\n451\\n459\\n465\\n473\\n481\\n488\\n495\\nS^3\\n510\\n517\\n59t\\n524\\n532\\n539\\n546\\n554\\n561\\nS^d\\n575\\n583\\n590\\n1597\\n597\\n604\\n612\\n619\\n626\\n634\\n641\\n648\\n6SS\\n667,\\n!598\\n670\\n677\\n684\\n692\\n699\\n706\\n713\\n721\\n728\\n735\\nj599\\n600\\nN.\\n742\\n750\\n757\\n764\\n771\\n779\\n786\\n793\\n8o5\\n808\\n815\\n822\\n829\\n837\\n844\\n851\\n858\\nS66\\n873\\n880\\n1\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n9\\nP,\\np-\\n334", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0386.jp2"}, "387": {"fulltext": "TABLE V.-\\n-LOGARITHMS\\n3F NUMBERS.\\nN.\\n1\\n.ad\\n1 3 1 4\\nn a 7\\nS 1)\\nP\\nP.\\n600\\n6oi\\n602\\n603\\n77 ^15\\n887\\n959\\n78 031\\n822\\n829\\n1 ^37\\n844\\n85 i\\n858\\n866\\n873\\n8S0\\n894\\n1 967\\n039\\n902\\n974\\n046\\n909\\n981\\n053\\n9^6\\n988\\n060\\n923\\n995\\n067\\n931\\n*oo3\\n075\\n938\\n*OIO\\n082\\n945\\n*oi7\\n089\\n952\\n*024\\n096\\n604\\n605\\n606\\n103\\n175\\n247\\n1 1 1\\n182\\n254\\n118\\n190\\n261\\n125\\n197\\n269\\n132\\n204\\n276\\n139\\n211\\n283\\n147\\n218\\n290\\n154\\n226\\n297\\n161\\n233\\n304\\n168\\n240\\n311\\n1\\n607\\n608\\n609\\n319\\n390\\n461\\ni 3^^\\n397\\n469\\n333\\n404\\n476\\n340\\n412\\n483\\n347\\n419\\n490\\n354\\n426\\n568\\n362\\n433\\n504\\n369\\n446\\n511\\n376\\n447\\n518\\n383\\n454\\n526\\n.1\\n.2\\n\u00e2\u0080\u00a23\\n\u00e2\u0080\u00a24\\n.5\\n.6\\n\u00e2\u0096\u00a07\\n8\\n0.7\\n1-5\\n2.2\\n3.0\\n3-7\\n4.5\\n5.2\\n6\\n610\\n533\\n604\\n675\\n746\\n540\\n1 547\\n554\\nJ6i\\n632\\n703\\n774\\n575\\n583\\n590\\n597\\n611\\n612\\n613\\n61 1\\n682\\n753\\n618\\n689\\n760\\n625\\n696\\n767\\n639\\n716\\n781\\n646\\n717\\n788\\n654\\n725\\n795\\n661\\n732\\n802\\n668\\n739\\n8jo\\n614\\n615\\n616\\n817\\n887\\n958\\n824\\n894\\n965\\n831\\n901\\n972\\n838\\n908\\n979\\n845\\n915\\n986\\n852\\n923\\n993\\n859\\n930\\n*ooo\\n866\\n937\\n*oo7\\n873\\n944\\n*oi4\\n886\\n951\\n*02I\\n.9\\n6.7\\n617\\n618\\n619\\n79 028\\n099\\n169\\n035\\n106\\n176\\n042\\n113\\n183\\n049\\n120\\n190\\n260\\n056\\n127\\n197\\n267\\n063\\n134\\n204\\n076\\n141\\n211\\n078\\n148\\n218\\n085\\n155\\n225\\n092\\n162\\n232\\n.1\\n.2\\n\u00e2\u0080\u00a23\\n7\\n0.7\\n1.4\\n2.1\\n620\\n239\\n309\\n379\\n449\\n246\\n253\\n274\\n281\\n288\\n295\\n302\\n621\\n622\\n623\\n316\\n386\\n456\\n323\\n393\\n462\\n330\\n400\\n469\\n337\\n407\\n476\\n344\\n414\\n483\\n351\\n421\\n490\\n358\\n428\\n497\\n365\\n435\\n504\\n372\\n442\\n511\\n624\\n625\\n626\\n518\\n588\\n657\\n595\\n664\\n532\\n602\\n671\\n539\\n609\\n678\\n546\\n6r6\\n685\\n553\\n622\\n692\\n560\\n629\\n699\\n567\\n^36\\n706\\n574\\n643\\n713\\n581\\n656\\n720\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n2.8\\n3-5\\n4.2\\n627\\n628\\n629\\n727\\n796\\n865\\n733\\n803\\n872\\n740\\n810\\n879\\n74?\\n8i\u00c2\u00a7\\nS86\\n754\\n823\\n892\\n761\\n830\\n_89i_\\n968\\n768\\n837\\n9O6\\n775\\n844\\n913\\n782\\n85 f\\n920\\n789\\n858\\n927\\n\u00e2\u0080\u00a27\\n.8\\n\u00e2\u0080\u00a29\\n4.9\\n5-6\\n6.3\\n680\\n934\\n941\\n948\\n954\\n961\\n975\\n982\\n989\\n058\\n126\\n195\\n996\\n065\\n^33\\n202\\n631\\n632\\n^33\\n80 003\\n071\\n140\\n010\\n078\\n147\\n016\\n085\\n154\\n023\\n092\\ni6i\\n036\\n099\\n168\\n037\\n106\\n174\\n044\\n113\\niSi\\n051\\n120\\n188\\n634\\n635\\n636\\n209\\n277\\n345\\n216\\n284\\n352\\n222\\n291\\n359\\n229\\n298\\n366\\n236\\n304\\n373\\n243\\n311\\n380\\n250\\n3^8\\n386\\n257\\n325\\n393\\n263\\n332\\n406\\n270\\n339\\n407\\n6\\n637\\n639\\n414\\n482\\n550\\n618\\n686\\n753\\n821\\n421\\n489\\n557\\n427\\n495\\n563\\n434\\n502\\n570\\n441\\n509\\n577\\n448\\n516\\n584\\n455\\n523\\n591\\n461\\n529\\n597\\n468\\n536\\n604\\n672\\n475\\n543\\n611\\n679\\n746\\n814\\n882\\n.1\\n.2\\n\u00e2\u0080\u00a23\\n.4\\n\u00e2\u0080\u00a25\\n.6\\n\u00e2\u0080\u00a27\\n8\\n0.6\\n1-3\\n1.9\\n.6\\n3-2\\n3-9\\n4-5\\n5-2\\n5-S\\n640\\n625\\n631\\n638\\n645\\n652\\n658\\n665\\n641\\n642\\n643\\n692\\n760\\nS2S\\n699\\n767\\n834\\n706\\n774\\n841\\n713\\n780\\n848\\n719\\n787\\n855\\n726\\n794\\n86:\\n733\\n801\\n868\\n740\\n807\\n875\\n644\\n645\\n646\\n888\\n956\\n81 023\\n895\\n962\\n030\\n902\\n969\\n^36\\n909\\n976\\n043\\n915\\n983\\n050\\n922\\n989\\n057\\n929\\n996\\n063\\n936\\n*oo3\\n076\\n942\\n*OIO\\n077\\n949\\n*oi6\\n083\\n\u00e2\u0080\u00a29\\n647\\n648\\n649\\n090\\n157\\n224\\n097\\n164\\n231\\n104\\n171\\n238\\nno\\n177\\n244\\n117\\n184\\n251\\n124\\n191\\n258\\n135\\n197\\n264\\n137\\n204\\n27!\\n144\\n211\\n278\\n345\\n151\\n218\\n284\\n351\\n650\\n291\\n298\\n304\\n311\\n3^8\\n324 33^\\n338\\nN.\\n1 1\\n2\\n3\\n4\\n5 1\\n7 8 i 9 1\\nP.\\nP.\\n335", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0387.jp2"}, "388": {"fulltext": "TABLE v.\u00e2\u0080\u0094 LOGARITHMS OF NUMBERS.\\nN.\\n1\\n2\\n3\\n4\\n5\\n6\\n7 1 8\\n9\\nP.P.\\n650\\n|65i\\n81 291\\n298\\n304\\n311\\n318\\n324\\n33^\\n33^\\n345\\n351\\n358\\n365\\n371\\n378\\n3^5\\n391\\n398\\n405\\n411\\n418\\n652\\n425\\n431\\n438\\n444\\n451\\n458\\n464\\n471\\n478\\n484\\n5S\\n491\\n498\\n504\\n511\\n518\\n524\\n531\\n538\\n544\\n551\\n654\\n558\\n564\\n571\\n577\\n584\\n591\\n597\\n604\\n611\\n617\\n655\\n624\\n631\\n637\\n644\\n650\\n657\\n664\\n676\\n677\\n684\\nj\\n656\\n696\\n697\\n703\\n710\\n717\\n723\\n730\\n736\\n743\\n750\\n7\\n657\\n756\\n763\\n770\\n776\\n783\\n789\\n796\\n803\\n809\\n816\\n.1\\n0.7 1\\n658\\n822\\n829\\n836\\n842\\n849\\n855\\n862\\n869\\n875\\n882\\n1.4\\n2. 1\\n659\\n660\\n661\\n888\\n895\\n901\\n908\\n915\\n921\\n928\\n934\\n941\\n948\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n2.8\\n3.5\\n4.2\\n954\\n961\\n967\\n974\\n986\\n987\\n994\\n*oo6\\n*oo7\\n*oi3\\n82 020\\n^^6.\\n^33\\n040\\n046\\n053\\n059\\n066\\n072\\n079\\n662\\n086\\n092\\n099\\n105\\n112\\n118\\n125\\n131\\n^3^\\n145\\n663\\n151\\n158\\n164\\n171\\n177\\n184\\n190\\n197\\n203\\n210\\n\u00e2\u0080\u00a27\\n4.9\\n664\\n217\\n223\\n230\\n236\\n243\\n249\\n256\\n262\\n269\\n275\\n\u00e2\u0080\u00a29\\n5 0\\n6.3\\n665\\n282\\n288\\n295\\n302\\n308\\n3^5\\n321\\n328\\n334\\n341\\n666\\n347\\n354\\n360\\n367\\n373\\n380\\n386\\n393\\n399\\n406\\n667\\n412\\n419\\n425\\n432\\n438\\n445\\n451\\n458\\n464\\n471\\n668\\n477\\n484\\n490\\n497\\n5^3\\n510\\n516\\n523\\n529\\n53\\n1 669\\n670\\n,671\\n542\\n549\\n555\\n562\\n568\\n575\\n581\\n588\\n594\\n601\\n9\\n607\\n614\\n620\\n627\\n^33\\n640\\n646\\n653\\n659\\n666\\n672\\n678\\n685\\n691\\n698\\n704\\n711\\n717\\n724\\n730\\nA 2\\n672\\n737\\n743\\n750\\n756\\n763\\n769\\n775\\n782\\n788\\n795\\n.2\\n0-6\\n1 .3\\n673\\n801\\n808\\n814\\n821\\n827\\n834\\n840\\n846\\n853\\n859\\n\u00e2\u0080\u00a23\\n1.9\\n674\\n866\\n872\\n879\\n885\\n892\\n898\\n904\\n911\\n917\\n924\\n2.6\\n3-2\\n3.9\\n675\\n930\\n937\\n943\\n949\\n956\\n962\\n969\\n975\\n982\\n988\\n\u00e2\u0080\u00a24\\n676\\n994\\n*OOI\\n*oo7\\n*oi4\\n*020\\n*027\\n*o33\\n*o39\\n*046\\n*052\\n.6\\n677\\n83 059\\n065\\n071\\n078\\n084\\n091\\n097\\n103\\nno\\n116\\n678\\n123\\n129\\n136\\n142\\n148\\n155\\n161\\n168\\n174\\n180\\n\u00e2\u0080\u00a27\\ns\\n4-5\\n5-2\\n5-8\\n679\\n680\\nj68i\\n187\\n251\\n193\\n200\\n206\\n212\\n219\\n225\\n231\\n238\\n244\\n\u00e2\u0080\u00a29\\n257\\n263\\n270\\n276\\n283\\n289\\n295\\n302\\n308\\n314\\n321\\n327\\n334\\n340\\n346\\n353\\n359\\n365\\n372\\n682\\n378\\n385\\n391\\n397\\n404\\n410\\n416\\n4.23\\n429\\n435\\nI683\\n442\\n448\\n455\\n461\\n467\\n474\\n480\\n486\\n493\\n499\\n684\\n50^\\n512\\n518\\n524\\n531\\n537\\n543\\n550\\n556\\n562\\n685\\n569\\n575\\n581\\nS88\\n594\\n6o5\\n607\\n613\\n619\\n626\\nA\\n6S6\\n632\\n^38\\n645\\n651\\n657\\n664\\n676\\n676\\n683\\n689\\nJ\\n6\\ni687\\n695\\n702\\n708\\n714\\n721\\n727\\n733\\n740\\n746\\n752\\n.2\\n1.2\\n68S\\n759\\n765\\n771\\n778\\n784\\n790\\n796\\n803\\n809\\n815\\n\u00e2\u0080\u00a23\\n1.8\\n689\\n690\\n691\\n822\\n885\\n828\\n834\\n841\\n847\\n853\\n859\\n866\\n872\\n878\\n.4\\n5\\n.6\\n2.4\\n3-0\\n3.6\\n891\\n897\\n904\\n910\\n916\\n922\\n929\\n935\\n941\\n948\\n954\\n960\\n966\\n973\\n979\\n985\\n992\\n998\\n*oo4\\n692\\n84 010\\n017\\n023\\n029\\n035\\n042\\n048\\n054\\n061\\n067\\n\u00e2\u0080\u00a27\\n.8\\n4.2\\n4.8\\n693\\n073\\n079\\n086\\n092\\n098\\n104\\nIII\\n117\\n123\\n129\\n694\\n136\\n142\\n148\\n154\\n161\\n167\\n179\\n186\\n192\\n\u00e2\u0080\u00a29\\n5.4\\n695\\n198\\n204\\n211\\n217\\n223\\n229\\n236\\n242\\n248\\n254\\n696\\n261\\n267\\n273\\n279\\n286\\n292\\n298\\n304\\n311\\n317\\n697\\n323\\n329\\n335\\n342\\n348\\n354\\n360\\n367\\n373\\n379\\n698\\n385\\n392\\n398\\n404\\n410\\n416\\n423\\n429\\n435\\n441\\n699\\n700\\n447\\n510\\n454\\n460\\n465\\n472\\n479\\n485\\n491\\n553\\n497\\n5^3\\n516\\n522\\n528\\n534\\n541\\n547\\n559 i\\n565\\nL\\nN.\\n1\\n2\\n3\\n4\\n5\\n6 7\\n8 9 P. P, 1\\n336", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0388.jp2"}, "389": {"fulltext": "TABLE V.-\\n-LOGARITHMS OF NUMBERS.\\n700\\n701\\n1 12\\ni\\n4\\n5\\n7\\ns\\nP.\\n84 510\\n572\\n516\\n522\\n528\\n534\\n541\\n547\\n553\\n559\\n565\\n578\\n584\\n590\\n596\\n603\\n609\\n615\\n621\\n627\\n702\\nl\\n640\\n646\\n652\\n658\\n664\\n671\\n677\\n683\\n689\\n,703\\n695\\n701\\n708\\n714\\n720\\n726\\n732\\n739\\n745\\n751\\n704\\n757\\n763\\n769\\n776\\n782\\n788\\n794\\n806\\n806\\n813\\n705\\n819\\n825\\n831\\n837\\n843\\n849\\n856\\n862\\n868\\n874\\n706\\n880\\n886\\n893\\n899\\n905\\n911\\n917\\n923\\n929\\n936\\n6\\n707\\n942\\n948\\n954\\n960\\n9^6\\n972\\n979\\n985\\n991\\n997\\nI\\n.2\\n0.6\\n1 .3\\n708\\n85 003\\n009\\n015\\n021\\n028\\n034\\n040\\n046\\n052\\n05 8\\n\u00e2\u0080\u00a23\\n1.(3\\n1709\\n710\\n711\\n064\\n070\\n077\\n083\\n089\\n095\\n156\\n217\\nlOI\\n162\\n107\\n163\\n113\\n119\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n2.6\\n3-2\\n3.9\\n126\\n132\\n138\\n144\\n150\\n174\\n181\\n187\\n193\\n199\\n205\\n211\\n223\\n229\\n236\\n242\\n712\\n248\\n254\\n260\\n265\\n272\\n278\\n284\\n290\\n297\\n303\\n713\\n309\\n315\\n321\\n327\\nZZ2\\n339\\n345\\n351\\n357\\nZ^?\\n\u00e2\u0080\u00a27\\n.8\\n4-5\\n5-2 1\\n714\\n370\\n376\\n382\\n388\\n394\\n400\\n406\\n412\\n418\\n424\\n\u00e2\u0080\u00a29\\n5-8\\n715\\n430\\n436\\n443\\n449\\n455\\n461\\n467\\n473\\n479\\n485\\n716\\n491\\n497\\n503\\n509\\n515\\n521\\n527\\n533\\n540\\n546\\n717\\n552\\n558\\n564\\n570\\n576\\n582\\n588\\n594\\n600\\n606\\n718\\n612\\n618\\n624\\n635\\n^36\\n642\\n648\\n655\\n661\\n667\\n719\\n720\\n721\\n673\\n679\\n685\\n691\\n697\\n703\\n709\\n715\\n721\\n727\\n6\\nn f\\\\\\n733\\n739\\n745\\n751\\n757\\n763\\n769\\n775\\n781\\n787\\n793\\n799\\n805\\n8ii\\n817\\n823\\n829\\n835\\n841\\n847\\n722\\n853\\n859\\n865\\n872\\n878\\n884\\n890\\n896\\n902\\n908\\n.2\\nI .2\\n1723\\n914\\n920\\n926\\n932\\n938\\n944\\n95Q\\n956\\n962\\n968\\n\u00e2\u0080\u00a23\\nI. 8\\n724\\n974\\n980\\n986\\n992\\n998\\n*oo4\\n*OTO\\n*oi6\\n*022\\n*028\\ni725\\n86034\\n040\\n046\\n052\\n058\\n063\\n069\\n075\\n081\\n087\\n\u00e2\u0080\u00a24\\n2.4\\n3.0\\n1726\\n093\\n099\\n105\\nIII\\n117\\n123\\n129\\n135\\n141\\n147\\n.6\\n3.6\\nJ727\\n153\\n159\\n165\\n171\\n177\\n183\\n189\\n195\\n201\\n207\\n728\\n213\\n219\\n225\\n231\\n237\\n243\\n249\\n255\\n261\\n267\\n\u00e2\u0080\u00a27\\n.8\\n4.2\\n4.8 1\\n729\\n730\\n731\\n273\\n332\\n391\\n278\\n284\\n290\\n296\\n302\\n3O8\\n314\\n320\\n326\\n9\\n5.4\\n338\\n397\\n344\\n350\\n356\\n362\\n368\\n374\\n380\\n386\\n403\\n409\\n415\\n421\\n427\\n433\\n439\\n445\\n732\\n451\\n457\\n463\\n469\\n475\\n481\\n486\\n492\\n498\\n504\\n733\\n510\\nS ^G\\n522\\n528\\n534\\n540\\n546\\n552\\n558\\n563\\n|734\\n569\\n575\\n58I\\n587\\n593\\n599\\n605\\n611\\n617\\n623\\n735\\n623\\n634\\n640\\n646\\n652\\n658\\n664\\n670\\n676\\n682\\n5\\n736\\n688\\n693\\n699\\n705\\n711\\n717\\n723\\n729\\n735\\n741\\n737\\n746\\n752\\n758\\n764\\n770\\n776\\n782\\n788\\n794\\n800\\nI\\n.2\\n0.5\\nI I\\n738\\n805\\n8ii\\n817\\n823\\n829\\n835\\n841\\n847\\n852\\n858\\n\u00e2\u0080\u00a23\\n1-6\\n,739\\n740\\n741\\n864\\n923\\n982\\n870\\n929\\n987\\n876\\n882\\n888\\n894\\n899\\n905\\n911\\n917\\n976\\n*o34\\n.4\\n5\\n.6\\n2.2\\n2.7\\n3-3\\n935\\n941\\n946\\n952\\n*OII\\n958\\n964\\n970\\n993\\n999\\n*oo5\\n*oi7\\n*023\\n*028\\n742\\n87 040\\n046\\n052\\n058\\n064\\n069\\n075\\no8i\\n087\\n093\\n743\\n099\\n104\\nno\\n116\\n122\\n128\\n134\\n140\\n145\\n151\\n\u00e2\u0080\u00a27\\n.8\\n3-8\\n4.4\\n744\\n157\\n163\\n169\\n175\\n180\\n1 86\\n192\\n198\\n204\\n210\\n\u00e2\u0080\u00a29\\n4.9\\n745\\n215\\n221\\n227\\n233\\n239\\n245\\n250\\n256\\n262\\n268\\n746\\n274\\n279\\n285\\n291\\n297\\nZ^3\\n309\\n314\\n320.\\n326\\n747\\n332\\n338\\n343\\n349\\n355\\n361\\n367\\n372\\n378\\n384\\n748\\n390\\n396\\n402\\n407\\n413\\n419\\n425\\n431\\n436\\n442\\n749\\n750\\n448\\n454\\n460\\n465\\n471\\n529\\n477\\n483\\n489\\n546\\n494\\n500\\n5:s8\\n506\\n512\\n517\\n523\\n535\\n541\\n552\\n1 2\\n3\\n4\\n5\\nG\\n7\\n8\\nJ)\\nP.\\nP.\\n337", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0389.jp2"}, "390": {"fulltext": "TABLE V.-\\n-LOGARITHMS OF NUMBERS.\\nN.\\n1 1\\n2\\n3 1 4\\n5 1\\n6\\n7\\n8\\n9\\nP.\\nP.\\n750\\n1751\\n87 ^06 512\\n517\\n523\\n529\\n535\\n541\\n546\\n552\\n558\\n1\\n564\\n570\\n575\\n58i\\n587\\n593\\n598\\n604\\n610\\n616\\n752\\n622\\n627\\n^33\\n639\\n645\\n650\\n656\\n662\\n668\\n673\\n;753\\n679\\n685\\n691\\n697\\n702\\n708\\n714\\n720\\n725\\n731\\n!754\\n737\\n743\\n748\\n754\\n760\\n766\\n771\\n777\\n783\\n789\\n755\\n794\\n800\\n806\\n812\\n817\\n823\\n829\\n835\\n840\\n846\\n75t\u00c2\u00bb\\n852\\n858\\n863\\n869\\n875\\n881\\n886\\n892\\n898\\n904\\n6\\n757\\n909 915\\n921\\n927\\n932\\n938\\n944\\n949\\n955\\n961\\n.1\\n2\\n0.6\\nI 2\\nI75S\\n967\\n972\\n978\\n984\\n990\\n995\\n*ooi\\n^007\\n*OI2\\n*oi8\\n.3\\ni. s\\n1759\\ni760\\n761\\n88 024\\n030\\n035\\n041\\n047\\n1 04\\n053\\n058\\n064\\n070\\n075\\n133\\n\u00e2\u0080\u00a24\\n.5\\n.6\\n2.4\\n3.0\\n3.6\\n081\\n087\\n093\\n098\\nno\\n115\\n121\\n178\\n127\\n138\\n144\\n150\\n155\\n161\\n167\\n172\\n184\\n190\\n762\\n195\\n201\\n207\\n212\\n218\\n224\\n229\\n235\\n241\\n247\\n\\\\7^3\\n252\\n258\\n264\\n269\\n275\\n281\\n286\\n292\\n298\\n303\\n\u00e2\u0096\u00a07\\n4.2\\n4.8\\n5-4\\n1764\\n309\\n315\\n320\\n3^6\\n332\\n337\\n343\\n349\\n355\\n366\\n\u00e2\u0080\u00a29\\ni7t^5\\n366\\n372\\n377\\n383\\n389\\n394\\n400\\n406\\n411\\n417\\n766\\n423\\n428\\n434\\n440\\n445\\n451\\n457\\n462\\n468\\n474\\n7^7\\n479\\n485\\n491\\n496\\n502\\n508\\n513\\n519\\n525\\n530\\nI708\\n536\\n542\\n547\\n553\\n558\\n564\\n570\\n575\\n58i\\n587\\n(709\\n770\\n1771\\n592\\n598\\n604\\n609\\n615\\n671\\n621\\n626\\n632\\n638\\n643\\ns\\n649\\n654\\n660\\n666\\n677\\n683\\n688\\n694\\n700\\n705\\n711\\n716\\n722\\n728\\n733\\n739\\n745\\n750\\n756\\ni772\\n761\\n767\\n773\\n778\\n784\\n790\\n795\\n801\\n806\\n812\\n.1\\n0-5\\n773\\n818\\n823\\n829\\n835\\n846\\n846\\n851\\n857\\n863\\nS6s\\n.3\\n1 I\\n1-6\\n774\\n874\\n879\\n885\\n891\\n896\\n902\\n907\\n913\\n919\\n924\\n!775\\n930\\n936\\n941\\n947\\n952\\n958\\n964\\n969\\n975\\n980\\n\u00e2\u0080\u00a24\\n2,2\\n|77^\\n986\\n992\\n997\\n*oo3\\n*oo8\\n*oi4\\n*oi9\\n*025\\n*o3i\\n*o36\\n\u00e2\u0080\u00a25\\n.6\\n2.7\\n3-3\\n|777\\n89 042\\n047\\n053\\n059\\n064\\n070\\n075\\n081\\n087\\n092\\n778\\n098\\n103\\n109\\n114\\n120\\n126\\n131\\n137\\n142\\n148\\n.7\\n3-8\\n779\\n1780\\n1781\\n153\\n159\\n165\\n170\\n176\\n181\\n187\\n193\\n248\\n198\\n204\\n\u00e2\u0080\u00a29\\n4-4 i\\n4.9\\n209 215\\n226\\n226\\n231\\n237\\n243\\n254\\n259\\n265\\n276\\n276\\n282\\n287\\n293\\n298\\n304\\n309\\n315\\n1782\\n320\\n326\\n332\\n337\\n343\\n348\\n354\\n359\\n365\\n370\\n|7\u00c2\u00ab3\\n376\\n38i\\n387\\n393\\n398\\n404\\n409\\n415\\n420\\n426\\n1784\\n431\\n437\\n4J2\\n448\\n454\\n459\\n465\\n470\\n476\\n481\\n^785\\n487\\n492\\n498\\n503\\n509\\n514\\n520\\n525\\n531\\n536\\n786\\n542\\n548\\n553\\n559\\n564\\n570\\n575\\n581\\n586\\n592\\n5\\n787\\n597\\n603\\n60s\\n614\\n619\\n625\\n630\\n636\\n641\\n647\\n.1\\n0.5\\n788\\n652\\n658\\n66s\\n669\\n674\\n680\\n685\\n691\\n696\\n702\\n.3\\n1-5\\n789\\n790\\n791\\n707\\n7^3\\n718\\n724\\n729\\n735\\n740\\n746\\n751\\n757\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n1\\n2.0\\n2.5\\n3-0\\n762\\n768\\n773\\n779\\n784\\n790\\n795\\n801\\n806\\n812\\n867\\n817\\n823\\n828\\n834\\n839\\n845\\n856\\n856\\n861\\n792\\n872\\n878\\n883\\n889\\n894\\n900\\n905\\n911\\n916\\n922\\n793\\n927\\n933\\n938\\n943\\n949\\n954\\n960\\n965\\n971\\n976\\n.7\\n.8\\n\u00e2\u0080\u00a29\\n3-5\\n794\\n982\\n987\\n993\\n998\\n*oo4\\n*oo9\\n*o,5\\n*020\\n*026\\n*o3i\\n4.0\\n4-5\\n795\\n90 036\\n042\\n047\\n053\\n058\\n064\\n069\\n075\\n080\\n086\\n796\\n091\\n097\\n102\\n107\\n113\\n118\\n124\\n129\\n135\\n140\\n797\\n146\\n151\\n156\\n162\\n167\\n173\\n178\\n184\\n189\\n195\\n798\\n200\\n205\\n211\\n216\\n222\\n227\\n233\\n238\\n244\\n249\\n799\\n800\\n254\\n260\\n265\\n271\\n276\\n282\\n287\\n292\\n298\\n3^3\\n309\\n314\\n320\\n325\\n330\\n33^\\n341\\n347\\n352\\n358\\n1 N.\\n1\\n2\\n3 1 4\\n5\\n6\\n7\\n8\\n9\\nP\\n.P.\\n1\\n338", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0390.jp2"}, "391": {"fulltext": "TABLE V.-\\n-LOGARITHMS OF NUMBERS.\\n1800\\n8oi\\n1\\n2\\n3\\n4\\n5 7\\nS\\n9\\nP. P.\\n90 309\\n314\\n320\\n325\\n330\\n336\\n341\\n347\\n352\\n358\\n363\\n3^8\\n374\\n379\\n385\\n390\\n396\\n401\\n406\\n412\\n802\\n417\\n423\\n428\\n433\\n439\\n444\\n450\\n455\\n466\\n466\\n803\\n471\\n477\\n482\\n488\\n493\\n498\\n504\\n509\\n515\\n520\\n804\\n525\\n531\\n536\\n542\\n547\\n552\\n558\\n563\\n569\\n574\\n805\\n579\\n585\\n590\\n596\\n601\\n6og\\n612\\n617\\n622\\n628\\n;8o6\\n633\\n639\\n644\\n649\\n655\\n666\\n666\\n671\\n^76\\n682\\n807\\n687\\n692\\n698\\n703\\n709\\n714\\n719\\n725\\n730\\n736\\n808\\n741\\n746\\n752\\n757\\n762\\n768\\n773\\n778\\n784\\n789\\n809\\n810\\n811\\n795\\n800\\n805\\n811\\n816\\n821\\n827\\n832\\n838\\n891\\n843\\na\\n848\\n854\\n859\\n864\\n870\\n875\\n886\\n886\\n896\\n902\\n907\\n913\\n918\\n923\\n929\\n934\\n939\\n945\\n950\\nb\\n812\\n955\\n961\\n9^6\\n971\\n977\\n982\\n987\\n993\\n998\\n*oo3\\nI\\n.2\\n0. 3\\nI.I\\n\u00c2\u00abi3\\n91 009\\n014\\n019\\n025\\n030\\n036\\n041\\n046\\n052\\n057\\n\u00e2\u0080\u00a23\\n1-6\\n814\\n062\\n068\\n073\\n078\\n084\\n089\\n094\\n100\\n105\\n1 16\\n815\\n116\\n121\\n126\\n131\\n137\\n142\\n147\\n153\\n158\\n163\\n\u00e2\u0080\u00a24\\n.6\\n2 2\\n2. 7\\n816\\n169\\n174\\n179\\n185\\n190\\n195\\n201\\n206\\n211\\n217\\n3-3\\n817\\n222\\n227\\n233\\n238\\n243\\n249\\n254\\n259\\n264\\n270\\n818\\n275\\n280\\n286\\n291\\n296\\n302\\n307\\n312\\n318\\n323\\n\u00e2\u0080\u00a27\\n8\\n3-8\\n4-4\\n4.Q\\n819\\n820\\n821\\n328\\n381\\n333\\n339\\n344\\n349\\n402\\n355\\n360\\n365\\n418\\n471\\n371\\n376\\n\u00e2\u0080\u00a29\\n3H\\n392\\n397\\n408\\n413\\n423\\n429\\n434\\n439\\n445\\n450\\n455\\n461\\n466\\n476\\n482\\n1822\\n487\\n492\\n497\\n503\\n508\\n513\\n519\\n524\\n529\\n534\\n823\\n540\\n545\\n550\\n556\\n561\\n5^6\\n571\\n577\\n582\\n587\\n824\\n592\\n598\\n603\\n608\\n614\\n619\\n624\\n629\\n635\\n640\\n1825\\n645\\n655\\n656\\n661\\n666\\n671\\n677\\n682\\n687\\n692\\n826\\n698\\n703\\n708\\n714\\n719\\n724\\n729\\n735\\n740\\n745\\n827\\n750\\n756\\n761\\n766\\n771\\n777\\n782\\n787\\n792\\n798\\n828\\n803\\n808\\n813\\n819\\n824\\n829\\n834\\n839\\n84s\\n8so\\n829\\n830\\n831\\n855\\n908\\n960\\n860\\nS66\\n871\\n876\\n881\\n887\\n892\\n897\\n902\\nf\\n913\\n918\\n923\\n928\\n934\\n939\\n944\\n949\\n955\\n965\\n976\\n976\\n981\\n986\\n991\\n996\\n*002\\n*oo7\\nI\\n0.5\\nI.O\\n832\\n92 012\\n017\\n023\\n028\\n033\\n038\\n043\\n049\\n054\\n059\\n.2\\n833\\n064\\n069\\n075\\n080\\n085\\n090\\n096\\nlOI\\n106\\nIII\\n.3\\n1-5\\n834\\n116\\n122\\n127\\n132\\n137\\n142\\n148\\n153\\n158\\n163\\n835\\n168\\n174\\n179\\n184\\n189\\n194\\n200\\n205\\n210\\n215\\n\u00e2\u0080\u00a24\\n.5\\n2.5\\n836\\n220\\n226\\n231\\n236\\n241\\n246\\n252\\n257\\n262\\n267\\n.6\\n30\\n837\\n272\\n277\\n283\\n288\\n293\\n298\\n3^3\\n309\\n314\\n319\\n838\\n324\\n329\\n335\\n340\\n345\\n350\\n355\\n366\\n366\\n37^\\n\u00e2\u0080\u00a27\\n.8\\n3-5\\n4.0\\n839\\ni840\\n1841\\n376\\n381\\n386\\n391\\n397\\n402\\n407\\n412\\n417\\n423\\n474\\n\u00e2\u0080\u00a29\\n4.5\\n428\\n433\\n438\\n490\\n443\\n448\\n500\\n454\\n459\\n464\\n515\\n469\\ni\\n479\\n485\\n495\\n505\\n510\\n521\\n526\\nI842\\n531\\n536\\n541\\n546\\n552\\n557\\n562\\n567\\n572\\n577\\n843\\n583\\n588\\n593\\n598\\n603\\n608\\n613\\n619\\n624\\n629\\n844\\n634\\n639\\n644\\n649\\n655\\n660\\n665\\n670\\n675\\n686\\n1845\\n685\\n691\\n696\\n701\\n706\\n711\\n716\\n721\\n727\\n732\\n846\\n737\\n742\\n747\\n752\\n757\\n762\\n768\\n773\\n778\\n783\\n847\\n788\\n793\\n798\\n803\\n809\\n814\\n819\\n824\\n829\\n834\\n1848\\n839\\n844\\n850\\n855\\n860\\n865\\n876\\n875\\n886\\n885\\n849\\n850\\n891\\n942\\n896\\n947\\n901\\n906\\n911\\n9^6\\n921\\n926\\n977\\n931\\n982\\n937\\n988\\n952\\n957\\n962\\n967\\n972\\n1\\n1\\n2\\n3 4\\n5\\nG\\n7\\n8\\nP. P.\\n339", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0391.jp2"}, "392": {"fulltext": "TABLE V.-\\n-LOGARITHMS OF NUMBERS.\\n850\\n851\\n1\\n2\\n3\\n4 5 1 6 1 7 i\\n8 9 1\\nP.\\nP. 1\\n92 942\\n947\\n952\\n957\\n962\\n967\\n972\\n977\\n982\\n988\\n993\\n998\\n*oo3\\n*oo8\\n*oi3\\n*oi8\\n*023\\n*028\\n*o34\\n*o39\\n852\\n93 044\\n049\\n054\\n059\\n064\\n069\\n074\\n079\\n084\\n090\\n853\\n095\\n100\\n105\\nno\\n115\\n120\\n125\\n130\\n135\\n140\\n854\\n146\\n151\\n156\\n161\\n166\\n171\\n176\\n181\\n186\\n191\\n855\\n196\\n201\\n207\\n212\\n217\\n222\\n227\\n232\\n237\\n242\\n1\\n856\\n247\\n252\\n257\\n262\\n267\\n272\\n278\\n283\\n288\\n293\\ns\\n857\\n298\\n303\\n308\\n313\\n318\\n323\\n328\\n333\\n338\\n343\\n.1\\n2\\n0.5\\nI I\\n858\\n348\\n354\\n359\\n364\\n369\\n374\\n379\\n384\\n389\\n394\\n.3\\n1.6\\n859\\n860\\n861\\n399\\n404\\n409\\n414\\n419\\n424\\n429\\n434\\n439\\n445\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n2.2\\n2.7\\n3.3\\n450\\n455\\n460\\n465\\n470\\n475\\n480\\n485\\n490\\n495\\n506\\n505\\n510\\n515\\n526\\n525\\n530\\n535\\n540\\n545\\n862\\n550\\n556\\n561\\n566\\n571\\n576\\n581\\n586\\n591\\n596\\n863\\n601\\n606\\n611\\n616\\n621\\n626\\n631\\n636\\n641\\n646\\n\u00e2\u0080\u00a27\\n3-8\\n864\\n65J\\n656\\n661\\n66s\\n671\\n676\\n681\\n686\\n691\\n696\\n\u00e2\u0080\u00a29\\n4.4\\n4.9\\n865\\n701\\n706\\n711\\n716\\n721\\n726\\n731\\n736\\n742\\n747\\n866\\n752\\n757\\n762\\n767\\n772\\n777\\n782\\n787\\n792\\n797\\n867\\n802\\n807\\n812\\n817\\n822\\n827\\n832\\n837\\n842\\n847\\n868\\n852\\n857\\n862\\n867\\n872\\n877\\n882\\n887\\n892\\n897\\n869\\n870\\n871\\n902\\n907\\n912\\n917\\n922\\n927\\n932\\n937\\n942\\n947\\n5\\n952\\n94 002\\n957 962 1 967\\n972\\n977\\n982\\n987\\n992\\n997\\n007 012\\n017\\n022\\n025\\n031\\n^36\\n041\\n046\\n872\\n051\\n056\\n061\\n065\\n071\\n076\\n081\\n086\\n091\\n096\\n.1\\n2\\n0.5\\nI\\n873\\nlOI\\n105\\nIII\\n116\\n121\\n126\\n131\\n136\\n141\\n146\\n.3\\n1.5\\n874\\n151\\n156\\n161\\n166\\n171\\n176\\n181\\n186\\n191\\n196\\n875\\n201\\n206\\n210\\n215\\n226\\n225\\n236\\n235\\n246\\n245\\n.4\\n2.0\\n876\\n250\\n255\\n260\\n265\\n270\\n275\\n280\\n285\\n290\\n295\\n\u00e2\u0080\u00a25\\n.6\\n2.5\\n3.0\\n877\\n300\\n305\\n310\\n315\\n320\\n324\\n329\\n334\\n339\\n344\\n878\\n349\\n354\\n359\\n364\\n369\\n374\\n379\\n384\\n389\\n394\\n7\\n3-5\\n879\\n880\\n881\\n399\\n404\\n409\\n413\\n418\\n468\\n423\\n428\\n433\\n438\\n443\\n.0\\n\u00e2\u0080\u00a29\\n4.0\\n4.5\\n448 4S3\\n458 i 463\\n473\\n478\\n483\\n487\\n492\\n497\\n502\\n507\\n512\\n517\\n522\\n527\\n532\\n537\\n542\\n882\\n547\\n552\\n556\\n56i\\n566\\n571\\n576\\n58i\\n586\\n591\\nI883\\n596\\n601\\n606\\n611\\n615\\n626\\n625\\n636\\n635\\n646\\n|884\\n645\\n650\\n655\\n660\\n665\\n670\\n674\\n679\\n684\\n689\\n885\\n694\\n699\\n704\\n709\\n714\\n719\\n724\\n728\\n733\\n738\\n886\\n743\\n748\\n753\\n758\\n763\\n768\\n773\\n777\\n782\\n787\\n4\\n887\\n792\\n797\\n802\\n807\\n812\\n817\\n821\\n826\\n83I\\n836\\n.1\\n0.4\\n888\\n841\\n846\\n851\\n856\\n861\\n865\\n870\\n875\\n886\\n885\\n.3\\nU.9\\n1-3\\n889\\n890\\n891\\n890\\n895\\n900\\n905\\n909\\n914\\n919\\n924\\n929\\n934\\n.4\\n.6\\n1.8\\n2.2\\n2.7\\n939\\n944\\n949\\n1 953\\n958\\n963\\n968\\n973\\n978\\n983\\n988\\n992\\n997 j*002\\n*oo7\\n*OI2\\n*oi7\\n*022\\n*026\\n031\\n892\\n95 036\\n041\\n046\\n051\\n056\\n061\\n065\\n070\\n075\\no85\\n893\\n085\\n090\\n095\\n099\\n104\\n109\\n114\\n119\\n124\\n129\\n.7\\ng\\n3-1\\n3.6\\n4.6\\n894\\n134\\n138\\n143\\n148\\n153\\n158\\n163\\n167\\n172\\n177\\n\u00e2\u0080\u00a29\\n895\\n182\\n187\\n192\\n197\\n201\\n206\\n211\\n216\\n221\\n226\\n896\\n231\\n235\\n240\\n245\\n250\\n255\\n260\\n264\\n269\\n274\\n897\\n279\\n284\\n289\\n294\\n298\\n3 3\\n308\\n3^3\\n318\\n323\\n898\\n327\\n332\\n337\\n342\\n347\\n352 356\\n361\\n366\\n371\\n899\\n900\\n376\\n381\\n385\\n390\\n395\\n400 405\\n410\\n414\\n419\\n424\\n429\\n434\\n438\\n443\\n448 1 453\\n458\\n463\\n467\\n1\\n2\\n3\\n4\\n5 6\\n7 8\\n9\\nP\\nP.\\n340", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0392.jp2"}, "393": {"fulltext": "TABLE v.\u00e2\u0080\u0094 LOGARITHMS OF NUMHERS.\\n900\\n901\\n1\\n12\\n3\\n4\\n(i\\n7\\nS\\nl\\\\ l\u00c2\u00bb.\\n95 424\\n472\\n429\\n434\\n438\\n443\\n492\\n448\\n453\\n458\\n4^J3\\n467\\n516\\n477\\n482\\n487\\n496\\n501\\n506\\n511\\n902\\n520\\n525\\n530\\n535\\n540\\n544\\n549\\n554\\n559\\n564\\n903\\n569\\n573\\n578\\n5 ^^3\\n588\\n593\\n597\\n602\\n607\\n612\\n904\\n617\\n621\\n626\\n63?\\n636\\n641\\n^M5\\n650\\n655\\n660\\n905\\n665\\n669\\n674\\n679\\n684\\n689\\n^93\\n^98\\n703\\n708\\n906\\n713\\n717\\n722\\n727\\n732\\n737\\n741\\n746\\n751\\n756\\n907\\n760\\n765\\n770\\n775\\n780\\n784\\n789\\n794\\n799\\n804\\n908\\n808\\n813\\n8i8\\n823\\n827\\n832\\n837\\n842\\n847\\n851\\n909\\n910\\n911\\n^56\\n861\\n866\\n870\\n875\\n923\\n880\\n885\\n890\\n894\\n942\\n899\\n904\\n952\\n_9\u00c2\u00b09_\\n956\\n9^3\\n918\\n928\\n933\\n986\\n937\\n947\\n961\\n966\\n971\\n975\\n985\\n990\\n994\\n5 1\\n912\\n999\\n*oo4\\n^009\\n*oi4\\n*oi8\\n^023\\n*028\\n*^33\\n*o37\\n*042\\n.1\\n0.5\\n913\\n96 047\\n052\\n056\\n061\\n066\\n071\\n075\\n086\\n085\\n090\\n.3\\n1-5\\n914\\n094\\n099\\n104\\n109\\n113\\n1^8\\n123\\n128\\n132\\n137\\n915\\n142\\n147\\n151\\n156\\n161\\n166\\n170\\n175\\n180\\n185\\n\u00e2\u0080\u00a24\\n2.0\\n916\\n189\\n194\\n199\\n204\\n208\\n213\\n218\\n222\\n227\\n232\\n\u00e2\u0080\u00a25\\n.6\\n2-5\\n3-0\\n917\\n237\\n241\\n246\\n251\\n256\\n260\\n265\\n270\\n275\\n279\\n918\\n284\\n289\\n293\\n298\\n303\\n308\\n312\\n317\\n322\\n327\\n\u00e2\u0080\u00a27\\n.8\\nQ\\n3-5\\n919\\n920\\n921\\n331\\n336\\n341\\n345\\n350\\n355\\n360\\n364\\n369\\n374\\n4.0\\n.1 c.\\n379 3^\\n388\\n393\\n397\\n402\\n407\\n412\\n416\\n421\\n426\\n430\\n435\\n440\\n445\\n449\\n454\\n459\\n463\\n4^8\\n922\\n473\\n478\\n482\\n487\\n492\\n496\\n501\\n506\\n511\\n515\\n923\\n520\\n525\\n529\\n534\\n539\\n543\\n548\\n553\\n558\\n562\\n924\\n567\\n572\\n576\\n58i\\n586\\n590\\n595\\n600\\n605\\n609\\n925\\n614\\n619\\n623\\n628\\n^33\\n637\\n642\\n647\\n651\\n656\\n926\\n661\\n666\\n670\\n675\\n680\\n684\\n689\\n694\\n^^98\\n703\\n927\\n708\\n712\\n717\\n722\\n726\\n731\\n736\\n741\\n745\\n750\\n928\\n755\\n759\\n764\\n769\\n773\\n778\\n783\\n787\\n792\\n797\\n929\\n930\\n931\\n801\\n806\\n811\\n815\\n820\\n825\\n829\\n834\\n839\\n843\\n^48\\nS95\\n853\\n857\\n862\\n867\\n871\\n876\\n881\\n885\\n896\\n899\\n904\\n909\\n913\\n918\\n923\\n927\\n932\\n937\\n4\\n932\\n941\\n946\\n951\\n955\\n960\\n965\\n969\\n974\\n979\\n983\\nI\\n0.4\\n933\\n^88\\n993\\n997\\n^^002\\n*oo7\\n*OII\\n*oi6\\n*020\\n*025\\n^030\\n\u00e2\u0080\u00a23\\nu 9\\n1.3\\n934\\n97 034\\n039\\n044\\n048\\n053\\n058\\n062\\n067\\n072\\n076\\n935\\n081\\n086\\n090\\n095\\n099\\n104\\n109\\n113\\n118\\n123\\n.4\\n1.8\\n936\\n127\\n132\\n137\\n141\\n146\\n151\\n155\\n160\\n164\\n169\\n\u00e2\u0080\u00a25\\n.6\\n2.7\\n937\\ni74\\n178\\n183\\n188\\n192\\n197\\n202\\n206\\n21 1\\n215\\n93\u00c2\u00ab\\n220\\n225\\n229\\n234\\n239\\n243\\n248\\n252\\n257\\n262\\n\u00e2\u0080\u00a27\\n.8\\n9\\n31\\na. 6\\n939\\n940\\n941\\n265\\n3^3\\n271\\n317\\n276\\n280\\n285\\n289\\n33^\\n294\\n340\\n299\\n345\\n303\\n308\\n322\\n328\\n33\\n377\\n349\\n396\\n354\\n359\\n3^3\\n368\\n373\\n382\\n386\\n391\\n406\\n942\\n405\\n409\\n414\\n419\\n423\\n428\\n432\\n437\\n442\\n446\\n943\\n451\\n456\\n460\\n465\\n469\\n474\\n479\\n483\\n488\\n492\\n944\\n497\\n502\\n506\\n511\\n515\\n520\\n525\\n529\\n534\\n538\\n945\\n543\\n548\\n552\\n557\\n561\\n566\\n570\\n575\\n580\\n584\\n946\\n589\\n593\\n598\\n603\\n607\\n61 2\\n616\\n621\\n626\\n630\\n947\\n635\\n639\\n644\\n649\\n653\\n658\\n662\\n667\\n671\\n676\\n948\\n681\\n685\\n690\\n694\\n699\\n703\\n708\\n713\\n717\\n722\\n949\\n950\\n725\\n772\\n731\\n736\\n740\\n745\\n749\\n754\\n758\\n763\\n768\\n777\\n781\\n786\\n790\\n795\\n800\\n804\\n809\\n813\\nN.\\n1\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\nP. P.\\n341", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0393.jp2"}, "394": {"fulltext": "TABLE\\nv.\u00e2\u0080\u0094 LOGARITHMS OF\\nNUMBERS\\nN.\\n1\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n9\\nP.P.\\n950\\n97 772\\n818\\n777\\n822\\n781\\n786\\n796\\n795\\n800\\n804\\n809\\n^^3\\n951\\n827\\n83 J\\n836\\n841\\n845\\n850\\n854\\n859\\n952\\nS63\\n868\\n873\\n877\\n882\\n886\\n891\\n895\\n900\\n904\\n953\\n909\\n914\\n918\\n923\\n927\\n932\\n936\\n941\\n945\\n950\\n954\\n955\\n959\\n964\\n968\\n973\\n977\\n982\\n986\\n991\\n996\\n1 955\\n98 000\\n005\\n009\\n014\\noig\\n023\\n027\\n032\\n036\\n041\\n5\\n956\\n046\\n050\\n055\\n059\\n064\\n068\\n073\\n077\\n082\\n086\\n.1\\n0.5\\n957\\n091\\n095\\n100\\n105\\n109\\n114\\n118\\n123\\n127\\n132\\n.2\\nI.O\\n958\\n136\\n141\\n145\\n150\\n154\\n159\\n163\\n168\\n173\\n177\\n\u00e2\u0080\u00a23\\n1-5\\n959\\n960\\n961\\n182\\n227\\n272\\n186\\n191\\n195\\n200\\n204\\n209\\n213\\n218\\n222\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n2.0\\n2.5\\n3-0\\n231\\n236\\n246\\n245\\n249\\n254\\n259\\n263\\n268\\n277\\n281\\n286\\n296\\n295\\n299\\n304\\n308\\n313\\n962\\n317\\n322\\n326\\n33^\\n335\\n340\\n344\\n349\\n353\\n358\\n7\\n3-5\\n1 963\\n362\\n367\\n371\\n376\\n380\\n385\\n389\\n394\\n398\\n403\\n.8\\n4.0\\n964\\n407\\n412\\n416\\n421\\n425\\n430\\n434\\n439\\n443\\n448\\n\u00e2\u0080\u00a29\\n4-5\\n965\\n452\\n457\\n461\\n466\\n470\\n475\\n479\\n484\\n488\\n493\\n966\\n497\\n502\\n506\\n511\\n515\\n520\\n524\\n529\\n533\\n538\\n967\\n545\\n547\\n551\\n556\\n560\\n565\\n569\\n574\\n578\\n583\\n968\\n587\\n592\\n596\\n601\\n605\\n610\\n614\\n619\\n623\\n628\\n969\\n970\\n971\\n632\\n677\\n722\\n637\\n641\\n646\\n650\\n655\\n659\\n663\\n668\\n672\\n4\\n681\\n686\\n696\\n695\\n699\\n704\\n708\\n713\\n717\\n726\\n731\\n735\\n740\\n744\\n749\\n753\\n757\\n762\\n.1\\n0.4\\n972\\n766\\n771\\n775\\n780\\n784\\n789\\n793\\n798\\n802\\n807\\n.2\\n0.9\\n973\\n8ii\\n815\\n820\\n824\\n829\\n^33\\n838\\n842\\n847\\n85?\\n\u00e2\u0080\u00a23\\n1-3\\n974\\n856\\n860\\n865\\n869\\n873\\n878\\n882\\n887\\n891\\n896\\n\u00e2\u0080\u00a24\\n1.8\\n975\\n900\\n905\\n909\\n914\\n918\\n922\\n927\\n931\\n936\\n940\\n\u00e2\u0080\u00a25\\n.6\\n2.2\\n976\\n945\\n949\\n954\\n958\\n963\\n967\\n971\\n976\\n980\\n985\\n2.7\\n977\\n989\\n994\\n998\\n*oo3\\n*oo7\\n*OII\\n*oi6\\n*020\\n*025\\n*029\\n7\\n3-1\\n978\\n99 034\\n038\\n043\\n047\\n051\\n056\\n060\\n065\\n069\\n074\\n.8\\n3.6\\ni 979\\n980\\n1 981\\n078\\n082\\n087\\n091\\n096\\n100\\n105\\n109\\n113\\n118\\n9\\n4.0\\n122\\n127\\n131\\n136\\n146\\n145\\n149\\n153\\n158\\n162\\n167\\n171\\n176\\n180\\n184\\n189\\n193\\n198\\n202\\n206\\n982\\n211\\n215\\n220\\n224\\n229\\n233\\n237\\n242\\n246\\n251\\n983\\n255\\n260\\n264\\n263\\n273\\n277\\n282\\n286\\n290\\n295\\n984\\n299\\n304\\n308\\n312\\n317\\n321\\n326\\n330\\n335\\n339\\n985\\n343\\n348\\n352\\n357\\n361\\n365\\n370\\n374\\n379\\n383\\n4\\n986\\n387\\n392\\n396\\n401\\n405\\n409\\n414\\n418\\n423\\n427\\n.1\\n0.4\\ni 987\\n431\\n436\\n440\\n445\\n449\\n453\\n458\\n462\\n467\\n471\\n.2\\n0.8\\n1 988\\n475\\n480\\n484\\n489\\n493\\n497\\n502\\n506\\n511\\n515\\n\u00e2\u0080\u00a23\\n1 .2\\n989\\n990\\n991\\n519\\n563\\n607\\n524\\n528\\n533\\n537\\n541\\n54^\\n550\\n554\\n559\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n1.6\\n2.0\\n2.4\\n568\\n572\\n576\\n581\\n585\\n590\\n594\\n598\\n603\\n611\\n616\\n626\\n625\\n629\\n^33\\n638\\n642\\n647\\n992\\n651\\n655\\n660\\n664\\n668\\n673\\n677\\n682\\n686\\n696\\n\u00e2\u0080\u00a27\\n2.8\\n993\\n695\\n699\\n703\\n708\\n712\\n717\\n721\\n725\\n730\\n734\\n.8\\n3.2\\n3.6\\n994\\n738\\n743\\n747\\n751\\n756\\n760\\n765\\n769\\n773\\n778\\n\u00e2\u0080\u00a29\\ni 995\\n782\\n786\\n791\\n795\\n800\\n804\\n808\\n813\\n817\\n821\\n996\\n826\\n836\\n834\\n839\\n843\\n847\\n852\\n856\\n861\\n865\\n997\\n869\\n874\\n878\\n882\\n887\\n891\\n895\\n900\\n904\\n908\\n998\\n913\\n917\\n922\\n926\\n93^\\n935\\n939\\n943\\n948\\n952\\n999\\n1000\\n956\\n00 000\\n961\\n965\\n969\\n974\\n978\\n982\\n987\\n991\\n995\\n004\\noog\\n013\\n017\\n021\\n026\\n030\\n034\\n039\\n1\\n1\\n2\\n3\\n4\\n5\\nG\\n7\\n8\\n9 P. P. 1\\n342", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0394.jp2"}, "395": {"fulltext": "TABLE\\nv.\u00e2\u0080\u0094 LOGARITHMS OF\\nNUMBERS\\nN.\\n1\\n2 1 3 1 4\\n5 1 6\\n7 8 1)\\nP. P\\n1000\\nOI\\n000 000\\n434\\n043\\n087 1 136\\nJ 73\\n607\\n217 266\\n304\\n347\\n390\\n477\\n521\\n564\\n651\\n694\\n737\\n781\\n824\\n02\\n867\\n911\\n954\\n997\\n*o4i\\n*o84\\n*I27\\n*i7i\\n^214\\n*257\\n03\\n001 301\\n344\\n387\\n431\\n474\\n517\\n566\\n604\\n647\\n696\\n04\\n733\\n777\\n820\\n863\\n906\\n950\\n993\\n*036\\n*o79\\n*I23\\n^5\\n002 166\\n209\\n252\\n295\\n339\\n382\\n425\\n468\\n511\\n555\\nc6\\n59S\\n641\\n684\\n727\\n770\\n814\\n857\\n900\\n943\\n9^ ^6\\n07\\n003 029\\n072\\n115\\n159\\n202\\n245\\n288\\n331\\n374\\n417\\n47\\n43\\noS\\n466\\n503\\n545\\n590\\n^33\\n676\\n719\\n762\\n805\\n848\\n.1\\n4-3\\n4-3\\n09\\n1010\\n1 1\\n891\\n934\\n977\\n*026\\n^063\\n493\\n*io6\\n536\\n*i49\\n579\\n*I92\\n622\\n*235\\n665\\n*278\\n.2\\n\u00e2\u0080\u00a23\\n\u00e2\u0080\u00a24\\n5\\n.6\\n8.7\\n13.6\\n174\\n21.7\\n26. 1\\n8.6\\n12.9 1\\n17.2\\n25.8 I\\n004 321\\n751\\n364\\n407\\n450\\n708\\n794\\n837\\n880\\n923\\n966\\n*oo9\\n*o5i\\n*094\\n*i37\\n12\\n005 186\\n223\\n265\\n309\\n352\\n395\\n438\\n481\\n523 566\\n13\\n609\\n652\\n695\\n738\\n781\\n824\\n866\\n909\\n952 995\\n\u00e2\u0080\u00a27\\n.8\\n30 -4\\n34.8\\n30.1\\n34-4\\n14\\n006 038\\n081\\n123 165\\n209\\n252\\n295\\n337\\n386 423\\n\u00e2\u0080\u00a29\\n39- 1\\n38.7\\n15\\na66\\n509\\n551 i 594\\n637\\n680\\n722\\n765\\n808 851\\n16\\n893\\n936\\n979 i*02 2\\n^064\\n*io7\\n*i5o\\n*i93\\n*235\\n*278\\n17\\n007 321\\n3^3\\n4O6\\n449\\n491\\n534\\n577\\n620\\n662\\n705\\n18\\n748\\n790\\nS33 875\\n918\\n961\\n*oo3\\n*o46\\n*o89 131\\n19\\n1020\\n21\\n008 174\\n600\\n009 025\\n217\\n642\\noog\\n259 302\\n344\\n770\\n196\\n387\\n813\\n430\\n472\\n515 557\\n685\\n728\\n153\\n855\\n898\\n946 9S3\\nIII\\n238\\n281 323\\n366 1 408\\n22\\n451\\n493\\n536\\n578\\n621\\n663\\n706 748\\n790 i 833\\n42\\n42\\n23\\n875\\n918\\n966\\n*oo3\\n*045\\n*o88\\n*i36\\n*I72\\n215\\n*257\\n.2\\n4-^\\n8.5\\n4.2\\n8.4\\n24\\n010 300\\n342\\n385\\n427\\n469\\n512\\n554\\n1 596\\n639\\n681\\n\u00e2\u0096\u00a03\\n12.7\\n12.6\\n25\\n724\\n766\\n808\\n851\\n893\\n935\\n978\\n*026\\n*o62\\n*io5\\n\u00e2\u0096\u00a04\\n17.0\\n21 .2\\n16.8\\n21 .0\\n26\\non 147\\n189\\n232\\n274\\n316\\n359\\n401\\n443\\n486\\n528\\n.6\\n25-5\\n25.2\\n27\\n570\\n612\\n655\\n697\\n739\\n782\\n824\\n866\\n908\\n951\\n\u00e2\u0080\u00a27\\n29-7\\n29.4\\n28\\n993\\n*o35\\n*o77\\n*I20\\n*l62\\n*204\\n*246\\n*288\\n*33^\\n*373\\n.8\\n\u00e2\u0080\u00a29\\n340\\n38.2\\n33-6\\n37-8\\n29\\n1030\\n31\\n012 415\\n837\\n457\\n500\\n542\\n584\\n625\\n^048\\n668\\n710\\n753\\n795\\n879\\n921\\n963 i*oo6\\n*OQO\\n511\\n*I32\\n174\\n216\\n637\\n013 258\\n301\\n343\\n385\\n427\\n469\\n553\\n595\\n32\\n679\\n722\\n764\\n806\\n848\\n890\\n932\\n974\\n*oi6\\n*o58\\n33\\n014 100\\n142\\n184\\n225\\n263\\n310\\n352\\n394\\n436\\n478\\n34\\n526\\n562\\n604\\n648\\n688\\n730\\n772\\n814\\n856\\n898\\ni 35\\n940\\n982\\n*024\\n*o66\\n*io8\\n*i50\\n*I92\\n*234\\n*276\\n*3i8\\n1 3\\n015 360\\n401\\n443\\n485\\n527\\n569\\n611\\n653\\n695\\n737\\n0S\\nAl\\n41\\n37\\n779\\n820\\n862\\n904\\n946\\n988\\n^030\\n*072\\n*TI3\\n155\\n.1\\n41\\n4.1\\n9, 1\\n3^\\n016 197\\n239\\n281\\n323\\n364\\n406\\n448\\n490\\n532\\n573\\n\u00e2\u0096\u00a03\\n12.4\\n12.3\\n39\\n1010\\n41\\n615\\n017 033\\n450\\n657\\n699\\n741\\n782\\n824\\n866\\n908\\n950\\n991\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n.6\\n16.6\\n20.7\\n24.9\\n16.4\\n20.5\\n24.6\\n075\\n492\\n117\\n534\\n158\\n206\\n242\\n284\\n325\\n742\\n367\\n409\\n826\\n576\\n617\\n659\\n701\\n784\\n42\\n867\\n909\\n95 J\\n992\\n*034\\n*o76\\n*ii7\\n*i59\\n*20I\\n^242\\n.8\\n33-2\\n2fc.7\\n?2.8\\n43\\n01 S 284\\n326\\n367\\n409\\n451\\n492\\n534\\n575\\n617\\n659\\n\u00e2\u0080\u00a2y\\n37-3\\n36.9\\n1 44\\n706\\n742\\n783\\n825\\n867\\n908\\n950\\n991\\n*os3\\n*o74\\n45\\n019 116\\n158\\n199\\n241\\n282\\n324\\n365\\n407\\n448\\n490\\n1 46\\n531\\n573\\n614\\n656\\n697\\n739\\n786\\n822\\n863\\n905\\n47\\n946\\n988\\n*029\\n*o7i\\n*II2\\n*i54\\n*i95\\n*237\\n*278\\n*320\\n48\\n020 361\\n402\\n444\\n485\\n527\\n5^8\\n610\\n651\\n692\\n734\\n49\\n1050\\n775\\n021 189\\n817\\n236\\n1\\n858\\n899\\n941\\n982\\n396\\n*024\\n437\\n*o65 *i06\\n\u00e2\u0099\u00a6148\\n272\\n2\\n3^3 354\\n478 520 561\\nN.\\n3 1 4\\nr 7 8 5)\\nP. P\\n343", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0395.jp2"}, "396": {"fulltext": "TABLE\\nv.\u00e2\u0080\u0094 LOGARITHMS OF\\nNUMBERS\\ni\\n1\\n2\\n3\\n4\\n5 6 7 I 8\\n9\\nP.P.\\n1050\\n51\\n021 189\\n602\\n230\\n272\\n313\\n3^)4\\n396\\n437\\n478\\n892\\n520\\n561\\n644\\n685\\n726\\n16?,\\n809\\n856\\n933\\n974\\n52\\n022 015\\n057\\n098\\n139\\n181\\n222\\n263\\n304\\n346\\n387\\n41\\n53\\n423\\n469\\n511\\n552\\n593\\n634\\n676\\n717\\n758\\n799\\n.1\\n4.1\\n8 -i\\n54\\n840\\n882\\n923\\n964\\n*oo5\\n*o46\\n*o88\\n*I29\\n*i7o\\n*2II\\n\u00e2\u0080\u00a23\\n12.4\\n55\\n023 252\\n293\\nzzs\\n376\\n417\\n458\\n499\\n540\\n58i\\n623\\n\u00e2\u0080\u00a24\\n16.6\\n56\\n664\\n705\\n746\\n787\\n828\\n869\\n910\\n951\\n993\\n*o34\\n\u00e2\u0080\u00a25\\n.6\\n20.7\\n24.9\\n57\\n024 075\\n116\\n157\\n198\\n239\\n280\\n321\\n362\\n403\\n444\\n5^\\n485\\n526\\n568\\n609\\n650\\n691\\n732\\n773\\n814\\n855\\n.8\\n33-2\\n59\\n1060\\n61\\n896\\n025 306\\n715\\n937\\n978\\n*oi9\\n*o6o\\n*IOI\\n^142\\n*i83\\n*224\\n*265\\n\u00e2\u0080\u00a29\\n37.3\\n347\\n388\\n429\\n469\\n5TO\\n551\\n592\\n^3%\\n674\\n*o83\\n1\\n756\\n797\\n^Z^\\n879\\n920\\n961\\n*002\\n^042\\n1 62\\n026 124\\n165\\n205\\n247\\n288\\n329\\n370\\n410\\n451\\n492\\n.41 1\\n63\\n533\\n574\\n615\\n656\\n696\\n737\\n778\\n819\\n860\\n901\\n.1\\n.2\\n4.1\\n8.2\\n64\\n941\\n982\\n*023\\n*o64\\n*io5\\n*i45\\n*i86\\n*227\\n*268\\n*309\\n\u00e2\u0080\u00a23\\n12.3\\n65\\n027 349\\n390\\n431\\n472\\n512\\n553\\n594\\n635\\n675\\n7^6\\n.4\\n16.4\\n66\\n757\\n798\\n^z^^\\n879\\n920\\n961\\n*OOI\\n*042\\n*o83\\n*I23\\n.6\\n24.6\\n1 67\\n028 164\\n205\\n246\\n285\\n327\\n368\\n408\\n449\\n490\\n530\\n\u00e2\u0080\u00a27\\n28.7\\n1 68\\n571\\n612\\n652\\n693\\n734\\n774\\n815\\n856\\n896\\n937\\n.8\\nQ\\n32.8\\n26. Q\\n69\\n1070\\n1 71\\n977\\n029 384\\n789\\n*oi8\\n*o59\\n*099\\n^140\\n*i8i\\n*22I\\n^262\\n*302\\n*343\\nJ\\n424\\n465\\n505\\n546\\n586\\n627\\n668\\n708\\n749\\n830\\n870\\n911\\n951\\n992\\n*032\\n*o73\\n*ii4\\n*i54\\n72\\n030 195\\n235\\n276\\n2 ^6\\n357\\n397\\n438\\n478\\n519\\n559\\n.1\\n4.0\\n73\\n599\\n040\\n680\\n721\\n761\\n802\\n842\\n883\\n923\\n964\\n.2\\n.\u00e2\u0080\u00a21\\n8.1\\n12. 1\\n74\\n031 004\\n044\\n085\\nI2g\\n166\\n205\\n247\\n287\\n327\\n368\\n75\\n408\\n449\\n489\\n529\\n570\\n610\\n651\\n691\\n73?\\n772\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a25\\n20.2\\n76\\n812\\n852\\n893\\n933\\n973\\n*oi4\\n*o54\\n*094\\n^ZS\\n*i75\\n.6\\n24-3\\n77\\n032 215\\n256\\n296\\n3Z6\\n377\\n417\\n457\\n498\\n538\\n578\\n\u00e2\u0080\u00a27\\n.8\\n28.3\\n^2.4\\n78\\n619\\n659\\n699\\n739\\n780\\n820\\n866\\n900\\n941\\n981\\n\u00e2\u0080\u00a29\\n36.4\\n1 79\\n1080\\n81\\n033 021\\n424\\n825\\n061\\n102\\n142\\n182\\n222\\n263\\n303\\n343\\n383\\nAr\\\\\\n464\\n504\\n544\\n584\\n625\\n665\\n705\\n745\\n785\\n866\\n906\\n946\\n986\\n*025\\n*o66\\n*io7\\n147\\n187\\n82\\n034 227\\n267\\n307\\n347\\n388\\n428\\n468\\n508\\n548\\n588\\n.1\\n4.0\\n1 ^2\\n623\\n668\\n708\\n748\\n789\\n829\\n869\\n909\\n949 989\\n.2\\n.3\\n8.0\\n12.0\\n84\\n035 029\\n069\\n109\\n149\\n189\\n229\\n269\\n309\\n349\\n3S9\\n.4\\n16.0\\n1 85\\n429\\n470\\n510\\n550\\n590\\n630\\n670\\n710\\n750\\n790\\n\u00e2\u0080\u00a2S\\n20.0\\n86\\n830\\n870\\n910\\n950\\n990\\n^029\\n^069\\n*i09\\n*i49\\n*i89\\n.6\\n24.0\\n87\\n036 229\\n269\\n309\\n349\\n389\\n429\\n469\\n509\\n549\\n589\\n\u00e2\u0080\u00a27\\n.8\\n28.0\\n32.0\\n88\\n629\\n669\\n708\\n748\\n788\\n828\\n868\\n908\\n948\\n988\\n.9\\n36.0\\n89\\n1090\\n91\\n037 028\\n068\\n107\\n147\\n187\\n227\\n267\\n307\\n705\\n347\\n386\\n!^0 I\\n425\\n825\\n465\\n506\\n546\\n586\\n625\\n665\\n745 785\\n864\\n904\\n944\\n984\\n*023\\n^063\\n*io3\\n143\\n183\\n92\\n038 222\\n262\\n302\\n342\\n38J\\n421\\n461\\n501\\n540\\n580\\n.1\\n3.\u00c2\u00a7\\n92,\\n620\\n660\\n699\\n739\\n779\\n819\\n858\\n898\\n938\\n977\\n.2\\n.3\\n7-9\\n11-8\\n94\\n039 017\\n057\\n096\\n^ze\\n176\\n216\\n255\\n295\\n/I\\n374\\n\u00e2\u0080\u00a24\\n15-8\\n95\\n414\\n454\\n493\\n533\\n572\\n612\\n652\\n691\\n73 i\\n771\\n\u00e2\u0080\u00a25\\n19.7\\n96\\n810\\n850\\n890\\n929\\n969\\n*oo8\\n^048\\n*o88\\n*I27\\n*i67\\n23-/\\n97\\n040 205\\n246\\n286\\n325\\n365\\n404\\n444\\n483\\n523\\n5^3\\n\u00e2\u0080\u00a27\\n.8\\n27-6\\n31-6\\n98\\n602\\n642\\n681\\n721\\n766\\n800\\n839\\n879\\n918\\n958\\n\u00e2\u0080\u00a29\\n35-5 1\\n99\\n1100\\n997\\n041 392\\n*o37\\n*o76\\n*ii6\\n*i55\\n*i95\\n*234\\n*274\\n^Z^l 353\\n432\\n471\\n511\\n550\\n590\\n629\\n669\\n708 748\\nN.\\n1\\n2\\n3\\n4\\n5\\n6\\n7\\n8 9\\nP.P.\\n344", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0396.jp2"}, "397": {"fulltext": "VI.\u00e2\u0080\u0094 LOGARITHMIC SINES AND TANGENTS OF SMALL ANGLES.\\nlog sin ip log (p S.\\n0\u00c2\u00b0\\nlog\\nlog sin (p S 1\\nlog tan 04- 7 II\\nlog tan (p log T.\\nlog (p\\nS\\n4.685 57\\nT\\nLo^. Sin.\\nS\\nT\\nLoJT. Tan.\\no\\n57\\n00\\n5.31442\\n42\\n00 t\\n60\\nI\\n57\\n57\\n6.46 372\\n42\\n42\\n6.46 372\\n120\\n2\\nsf\\n57\\n.76475\\n42\\n42\\n.76475\\n180\\n3\\nSi\\nSi\\n.94 084\\n42\\n42\\n.94 084\\n240\\n4\\nSi\\nSi\\n7.06 578\\n7.16 269\\n42\\n42\\n7.06 578\\n7.16 269\\n300\\n5\\n4.685 Si\\n57\\n5.31442\\n42\\n360\\n6\\nSi\\nSi\\n.24187\\n42\\n42\\n.24188\\n420\\n7\\n57\\nSi\\n.30 882\\n42\\n42\\n.30882\\n480\\n8\\nSi\\n57\\n.36681\\n42\\n42\\n.36681\\n540\\n600\\n9\\n10\\nSi\\nSi\\n.41 797\\n42\\n42\\n.41 797\\n4.685 si\\nSi\\n7.46 372\\n5.31442\\n42\\n7.46 372\\n660\\nII\\n57\\nSi\\n.50512\\n42\\n42\\n.50512\\n720\\n12\\nSi\\nSi\\n.54 290\\n42\\n42\\n.54291\\n780\\n13\\nSi\\n57\\n57 767\\n42\\n42\\n57 767\\n840\\n14\\nSi\\n57\\n.60985\\n42\\n42\\n.60 985\\n900\\n15\\n4.685 57\\n58\\n7.63 981\\n5.31442\\n42\\n7.63 982\\n960\\n16\\nSi\\n58\\n.66 784\\n42\\n42\\n.66 785\\n1020\\n17\\n57\\n58\\n.6941^\\n42\\n42\\n.69418 1\\n1080\\n18\\n57\\n58\\n.71 899\\n42\\n42\\n.71 900 1\\n1 140\\n19\\n57\\n4.685 57\\n58\\n_ ^.74.248\\n42\\n42\\n.74 248\\n1200\\n20\\n58\\n7.76475\\n5.31443\\n42\\n7.76476\\n1260\\n21\\n57\\n58\\n.78 594\\n43\\n42\\n.78 595\\n1320\\n22\\n57\\n58\\n.80614\\n43\\n42\\n.80615\\n1380\\n23\\n57\\n58\\n.82 545\\n43\\n42\\n.82 546\\n1440\\n24\\n57\\n58\\n\u00e2\u0080\u00a284 393\\n43\\n42\\n\u00e2\u0080\u00a284 394\\n1500\\n25\\n4.685 57\\n58\\n7.86 166\\n5.31443\\n41\\n7.86 167\\n1560\\n26\\n57\\n58\\n.87 869\\n43\\n41\\n.87871\\n1620\\n27\\n57\\n58\\n.89 508\\n43\\n41\\n.89 510\\n1680\\n28\\n57\\n58\\n.91 088\\n43\\n41\\n.91 089\\n1740\\n29\\n57\\n58\\n.92 612\\n43\\n41\\n.92613\\n1800\\n30\\n4.685 57\\n58\\n7.94 084\\n5.31443\\n41\\n7.94 086\\ni860\\n31\\n57\\n58\\n\u00e2\u0080\u00a295 508\\n43\\n41\\n.95510\\n1920\\n32\\n57\\n58\\n.96 887\\n43\\n41\\n.96 889\\n1980\\n33\\n57\\n59\\n.98 223\\n43\\n41\\n.98 225\\n2040\\n34\\n57\\n59\\n.99 520\\n43\\n41\\n\u00e2\u0080\u00a299 522\\n2100\\n35\\n4.685 56\\n59\\n8.00 778\\n5.31443\\n41\\n8.00781\\n2160\\n36\\n56\\n59\\n.02 002\\n43\\n41\\n.02 004\\n2220\\n37\\n56\\n59\\n.03 192\\n43\\n4J\\n.03 194\\n2280\\n38\\n56\\n59\\n.04 350\\n43\\n40\\n\u00e2\u0080\u00a204352\\n2340\\n39\\n56\\n4.685 56\\n59\\n.05 478\\n43\\n40\\n.05481\\n2400\\n40\\n59\\n8.06 577\\n5.31443\\n46\\n8.06 580\\n2460\\n41\\n56\\nS9\\n.07 650\\n43\\n40\\n.07 653\\n2520\\n42\\n56\\n59\\n.08 695\\n43\\n40\\n.08 699\\n2580\\n43\\n56\\n60\\n.09718\\n43\\n40\\n.09721\\n2640\\n44\\n56\\n60\\n.10716\\n43\\n40\\n.10720\\n2700\\n45\\n4.685 56\\n60\\n8. 1 1 692\\n5.31444\\n40\\n8. 1 1 696\\n2760\\n46\\n56\\n60\\n.12647\\n44\\n40\\n.12 651\\n2820\\n47\\n56\\n60\\n.13581\\n44\\n40\\n.13585\\n2880\\n48\\n56\\n60\\n.14495\\n44\\n39\\n.14499\\n^940\\n49\\n56\\n60\\n.15390\\n44\\n39\\n\u00e2\u0080\u00a215395\\n3000\\n50\\n4.685 56\\n60\\n8.16268\\n5.31444\\n39\\n8.16272\\n3060\\n51\\n56\\n60\\n.17 128\\n44\\n39\\n17 133\\n3120\\n52\\n56\\n61\\n.17971\\n44\\n39\\n17 976\\n3180\\n53\\n56\\n61\\n.18798\\n44\\n39\\n.18803\\n3240\\n54\\n55\\n61\\n.19610\\n44\\n39\\n.19615\\n3300\\n55\\n4.685 Si\\n61\\n8.20 407\\n5-3H44\\n39\\n8.20412\\n3360\\n56\\nSi\\n61\\n.21 189\\n44\\n38\\n.21 195\\n3420\\n57\\n55\\n61\\n.21958\\n44\\n38\\n.21 964\\n3480\\nS\u00c2\u00ab\\n55\\n61\\n.22713\\n44\\n38\\n.22719\\n3540\\n_ 59_\\nsi\\n62\\n.23 45J\\n44\\n38\\nJ ^23 462 _\\n345", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0397.jp2"}, "398": {"fulltext": "TABLE\\nVI.\u00e2\u0080\u0094 LOGARITHMIC SINES AND TANGENTS OF\\nSMALL ANGLES.!\\nlog sin if) =z log 0 S. 10 log (p log sin -f- 5 1\\nlog tan cp log P log P log tan 7\\nr\\nS\\nT\\nLog. Sin.\\nS\\nT\\nLog. Tan.\\n3600\\n3660\\n3720\\n3780\\n3840\\nI\\n2\\n3\\n4\\n4.685 55\\n55\\n55\\n55\\n55\\n62\\n62\\n62\\n62\\n62\\n8.24185\\n.24 903\\n.25 609\\n.26 304\\n.26 988\\n5-31444\\n45\\n45\\n45\\n45\\n38\\n38\\n38\\n37\\n37\\n8.24 192\\n.24910\\n.25616\\n.26 31?\\n-26 99\u00c2\u00a7\\n3900\\n3960\\n4020\\n4080\\n4140\\n5\\n6\\n7\\n8\\n9\\n4.685 55\\n55\\n54\\n54\\n54\\n62\\n63\\n63\\n63\\n63\\n8.27 661\\n.28 324\\n.28 97 f\\n.29 626\\n.30254\\n5-31445\\n45\\n45\\n45\\n45\\n37\\n37\\n37\\n37\\n36\\n8.27 669\\n.28 332\\n.28985\\n.29629\\n.30 263\\n4200\\n4260\\n4320\\n4380\\n4440\\n10\\nII\\n12\\nJ3\\n14\\n4.685 54\\n54\\n54\\n54\\n54\\n63\\n63\\n64\\n64\\n64\\n8.30 879\\n.31495\\n.32 102\\n.32 701\\n\u00e2\u0080\u00a233 292\\n5-31445\\n45\\n45\\n46\\n46\\n36\\n36\\n36\\n36\\n36\\n8.30 888\\n.31 504\\n.32 112\\n.32711\\n.33 302\\n4500\\n4560\\n1 4620\\n4680\\n4740\\n15\\n16\\n17\\n18\\n19\\n4.685 54\\n54\\n54\\n54\\n53\\n64\\n64\\n65\\n65\\n65\\n8.33875\\n.34450\\n.35018\\n\u00e2\u0096\u00a035 578\\n.36131\\n5.31446\\n46\\n46\\n46\\n46\\n35\\n35\\n35\\n35\\n35\\n8.33 885\\n.34461\\n.35029\\n\u00e2\u0080\u00a235 589\\n.36 143\\n4800\\n4860\\n4920\\n4980\\n5040\\n20\\n21\\n22\\n23\\n24\\n4-685 53\\n53\\n53\\n53\\n53\\n6$\\n65\\n65\\n66\\n66\\n8.36677\\n.37217\\n.37750\\n.38 276\\n.38 796\\n5.31446\\n46\\n46\\n46\\n47\\n34\\n34\\n34\\n34\\n34\\n8.36689\\n.37 229\\n.37 762\\n.38 289\\n.38 809\\n5100\\n5160\\n5220\\n5280\\n5340\\n25\\n26\\n27\\n28\\n29\\n4.685 53\\n53\\n53\\n52\\n52\\n66\\n66\\n67\\n67\\n67\\n8.39310\\n.39818\\n.40 320\\n.40816\\n\u00e2\u0080\u00a241 307\\n5-31447\\n47\\n47\\n4?\\n4f\\n33\\n33\\n33\\n33\\n33\\n8.39 323\\n.39 831\\n\u00e2\u0080\u00a240 334\\n.40 836\\n.41 321\\n5.400\\n5460\\n5520\\n5580\\n5640\\n30\\n31\\n32\\n33\\n34\\n4.685 52\\n52\\n52\\n52\\n52\\n67\\n67\\n68\\n68\\n68\\n8.41 792\\n.42 271\\n.42 746\\n.43215\\n.43 680\\n5-3144^\\n4l\\n48\\n48\\n32\\n32\\n32\\n32\\n31\\n8.41 807\\n.42 287\\n.42 762\\n.43 231\\n.43 696\\n5700\\n5760\\n5820\\n5880\\n5940\\n35\\n36\\n37\\n38\\n39\\n4.685 52\\n52\\n51\\n51\\n51\\n68\\n69\\n69\\n69\\n69\\n8.44139\\n.44 594\\n.45 044\\n.45 489\\n\u00e2\u0080\u00a245 930\\n5.31448\\n48\\n48\\n48\\n48\\n31\\n31\\n31\\n30\\n30\\n8.44 1 56\\n.44611\\n.45 061\\n.45 507\\n.45 948\\ni 6000\\n6060\\n6120\\n6180\\n6240\\n40\\n41\\n42\\n43\\n44\\n4.685 51\\n51\\n51\\n51\\n51\\n69\\n70\\n70\\n76\\n70\\n8.46 366\\n.46 798\\n.47 226\\n.47 650\\n.48 069\\n5.31448\\n49\\n49\\n49\\n49\\n30\\n30\\n30\\n29\\n29\\n8.46 385\\n.46817\\n\u00e2\u0080\u00a247 245\\n.47 669\\n.48 089\\n6300\\n6360\\n6420\\n6480\\n6540\\n45\\n46\\n47\\n48\\n49\\n4.685 56\\n50\\n50\\n55\\n50\\n71\\n71\\n71\\n72\\n72\\n8.48 485\\n.48 896\\n.49 304\\n.49 70S\\n.50 108\\n5-31449\\n49\\n49\\n49\\n50\\n29\\n28\\n28\\n28\\n28\\n8.48 505\\n.48917\\n\u00e2\u0080\u00a249325\\n.49 729\\n.50 130\\n6600\\n6660\\n6720\\n6780\\n6840\\n50\\n51\\n52\\n53\\n54\\n4.685 50\\nSO\\n50\\n49\\n49\\n72\\n72\\n73\\n73\\n73\\n8.50 504\\n\u00e2\u0080\u00a250897\\n.51 286\\n.51 672\\n.52055\\n5-31450\\n50\\n50\\n55\\n53\\n2?\\n2j\\n27\\n27\\n26\\n8.50 526\\n.50920\\n.51 310\\n.51 696\\n.52079\\n6900\\n6960\\n7020\\n7080\\n7140\\n55\\n56\\n57\\n58\\n59\\n4.685 49\\n49\\n49\\n49\\n49\\n73\\n74\\n74\\n74\\n75\\n8.52434\\n.52 810\\n.53183\\n\u00e2\u0080\u00a253552\\n.53918\\n5-31450\\n51\\n51\\n51\\n51\\n26\\n26\\n25\\n25\\n25\\n8.52458\\n.52835\\n.53 208\\n-53578\\n\u00e2\u0080\u00a253 944\\n346", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0398.jp2"}, "399": {"fulltext": "TABLE VI.\u00e2\u0080\u0094 LOGARITHMIC SINES AND TANGENTS OF SMALL ANGLES.\\nlog sin\\n:/j log (p -f S.\\n2\u00c2\u00b0\\nlog lug\\nsin ip-\\\\- S\\nlog tan\\np log p r.\\nlog 0 log\\ntan 04- 7\\nS\\nT\\nLo^. Sill.\\nS\\nT\\nLojr. Tan.\\n7200\\n4.685 48\\n75\\n8.54282\\n5-3\u00c2\u00ab4 5i\\n25\\n8-54 308\\n1 7260\\nI\\n48\\n75\\n.54642\\n51\\n24\\n.54669\\n7320\\n2\\n48\\n75\\n\u00e2\u0080\u00a254 999\\n51\\n24\\n\u00e2\u0080\u00a255027\\n7380\\n3\\n48\\n76\\n.55354\\n52\\n24\\n.55381\\n1 7440\\n4\\n48\\n76\\n\u00e2\u0080\u00a255705\\n52\\n23\\n\u00e2\u0080\u00a255 733\\n8.56083\\n7500\\n5\\n4.68548\\n76\\n8.56054\\n5.31452\\n23\\n7560\\n6\\n48\\n77\\n.56 400\\n52\\n23\\n.56429\\n7620\\n7\\n47\\n77\\n56743\\n52\\n22\\n\u00e2\u0080\u00a256772\\n7680\\n8\\n47\\n77\\n57083\\n52\\n22\\n\u00e2\u0080\u00a257 113 1\\n7740\\n9\\n47\\n78\\n.57421\\n52\\n22\\n\u00e2\u0080\u00a257452 i\\n7800\\n10\\n4.685 47\\n78\\n8^57 756\\n5-3U53\\n22\\n8.57 787\\n7860\\n1 1\\n47\\n78\\n.58 089\\n53\\n21\\n.58 121\\n7920\\n12\\n47\\n79\\n.58419\\n53\\n21\\n-58 45t\\n7980\\n13\\n46\\n79\\n\u00e2\u0080\u00a258 747\\n53\\n21\\n-58779\\n8040\\n8100\\n14\\n46\\n79\\n.59072\\n53\\n26\\n.59105\\n15\\n4.685 46\\n80\\n8.59395\\n5-31453\\n20\\n8-59 428\\n8160\\n16\\n46\\n80\\n\u00e2\u0080\u00a259715\\n54\\n20\\n-59 749\\n8220\\n17\\n46\\n86\\n.60 033\\n54\\n19\\n.60 067\\n1 8280\\n18\\n46\\n81\\n.60 349\\n54\\n19\\n.60 384\\n8340\\n19\\n45\\n81\\n.60 662\\n54\\n19\\n18\\n.60 698 1\\n8.61 009 1\\n1 8400\\n20\\n4.68545\\n81\\n8.60 973\\n5.31454\\n1 8460\\n21\\n45\\n82\\n.61 282\\n54\\n18\\n.61 319\\n8520\\n22\\n45\\n82\\n.61 589\\n55\\n18\\n.61 626\\n8580\\n23\\n45\\n82\\n.61 893\\n55\\nI?\\n.61 931\\n8640\\n24\\n45\\n83\\n.62 196\\n55\\n17\\n\u00e2\u0080\u00a262 234\\n8700\\n25\\n4.68544\\n83\\n8.62 496\\n5-31455\\n16\\n8.62 535\\n8760\\n26\\n44\\n83\\n\u00e2\u0080\u00a262 795\\n55\\n16\\n.62 834\\n8820\\n27\\n44\\n84\\n.63 091\\n55\\n16\\n\u00e2\u0080\u00a263 131\\n8880\\n28\\n44\\n84\\n\u00e2\u0080\u00a263 385\\n56\\nj5\\n\u00e2\u0080\u00a263425\\n8940\\n29\\n44\\n84\\n\u00e2\u0080\u00a263 677\\n56\\n15\\n\u00e2\u0080\u00a263 7 18\\n9000\\n30\\n4.68543\\n85\\n8.63 968\\n5-314 56\\n15\\n8..64 009\\n9060\\n31\\n43\\n8^\\n.64256\\n56\\n14\\n.64 298\\n9120\\n32\\n43\\n86\\n\u00e2\u0080\u00a264 543\\n56\\n14\\n.64 585\\n9180\\n33\\n43\\n86\\n.64 827\\n57\\n14\\n.64 870\\n9240\\n34\\n43\\n86\\n.65 1 10\\n57\\n13\\n\u00e2\u0080\u00a265153\\n9300\\n35\\n4.68543\\n87\\n8.65 391\\n5-3H57\\n13\\n8.65 435\\n9360\\n36\\n42\\n87\\n.65 670\\n57\\n12\\n.65715\\n9420\\n37\\n42\\n87\\n\u00e2\u0080\u00a265 947\\n57\\n12\\n\u00e2\u0096\u00a0^S 993\\n9480\\n33\\n42\\n88\\n.66 223\\n58\\n12\\n.66 269\\n9540\\n9600\\n39\\n42\\n88\\n.66 497\\n58\\nII\\n.66 543\\n40\\n4.685 42\\n89\\n8.66 769\\n5-31458\\nII\\n8.66816\\n9660\\n41\\n41\\n89\\n.67 039\\n58\\n10\\n.67 0S7\\n9720\\n42\\n41\\n89\\n.67 308\\n58\\n10\\n\u00e2\u0080\u00a267 356\\n9780\\n43\\n41\\n90\\n.67575\\n59\\n10\\n.67 624\\n9840\\n44\\n41\\n90\\n.67 845\\n59\\n09\\n.67 890\\n9900\\n45\\n4.685 41\\n91\\n8.68 104\\n5^31459\\n09\\n8.68 I 54\\n9960\\n46\\n40\\n91\\n.68 366\\n59\\n08\\n.68417\\n10020\\n47\\n40\\n91\\n.68 627\\n59\\n08\\n.68 678\\n10080\\n48\\n40\\n92\\n.68 886\\n60\\n08\\n.68 938\\n10140\\n49\\n40\\n92\\n.69144\\n60\\nof\\n\u00e2\u0080\u00a269 96\\n10200\\n50\\n4.685 40\\n93\\n8.69 400\\n5.31460\\n07\\n8.69453\\n10260\\n51\\n39\\n93\\n.69654\\n60\\n06\\n.69 708\\n10320\\n52\\n39\\n93\\n.69 907\\n66\\n06\\n.69 96\\n10380\\n53\\n39\\n94\\n.70159\\n61\\n06\\n.70214\\n10440\\n54\\n39\\n94\\n.70 409\\n61\\n05\\n.70 464\\n10500\\n55\\n4.685 38\\n95\\n8.70657\\n5.31461\\n05\\n8.70714\\n10560\\n56\\n38\\n95\\n.70905\\n61\\n04\\n.70 962\\n10620\\n57\\n38\\n96\\n.71 150\\n61\\n04\\n.71 208\\n10680\\n58\\n38\\n96\\n.71 395\\n62\\n03\\n\u00e2\u0080\u00a271 453\\n10740\\n59\\n38\\n97\\n\u00e2\u0080\u00a271638\\n62\\n03\\n.71697\\n347", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0399.jp2"}, "400": {"fulltext": "TABLE VIL\u00e2\u0080\u0094 LOGARITHMIC\\nSINES, COSINES,\\nTANGENTS, AND COTANGENTS\\nLog. Sin.\\nD\\nLog. Tan.\\nCom. D.\\nLog. Cot.\\nLog. Cos.\\n00\\n00\\n-i- 00\\n0.00000\\nGO\\nI\\n6.46 372\\n6.46 372\\n3-5362^\\n0.00000\\n59\\n2\\ne j6Ail\\n17609\\n6.76475\\n17609\\n3.23 524\\n0.00000\\n58\\n3\\n6.94084\\n6.94084\\n3-05915\\n0.00000\\n57\\n4\\n7.06 578\\n12494\\n9691\\n7918\\n6695\\n7.06 578\\n12494\\n9691\\n2.93421\\n0.00000\\n56\\n5\\n7.16 269\\n7.16 269\\n2.83736\\n0.00 000\\n55\\n6\\n7.24 1 8f\\n7.24188\\n791 8\\n2.75 812\\n0.00000\\n54\\n7\\n7.30882\\n7.30882\\n6094\\n2.69 11^\\n0.00000\\n53\\n8\\n7.36681\\n5799\\n7.36681\\n5799\\n2.63 3I8\\n0.00000\\n52\\n9\\n7.41 797\\n5 5\\n4575\\n7.41 797\\n5 5\\n4575\\n4139\\n2.58 203\\n0.00000\\n51\\n10\\n7.46 372\\n7.46372\\n2.5362^\\n0.00 000\\n50\\nII\\n7.50512\\n3778\\n7.50512\\n2.49488\\n0.00000\\n49\\n12\\n7.54290\\n7.54291\\n2.45 709\\n9.99999\\n48\\n13\\n7.57767\\n3476\\n7.57767\\n3476\\n2.42 233\\n9.99999\\n47\\n14\\n7.60985\\n3218\\n2996\\n2803\\n2633\\n7.60985\\n3218\\n2996\\n2803\\n2.39014\\n9.99999\\n4.6\\n15\\n7.63981\\n7.63982\\n2,36018\\n9.99999\\n45\\ni6\\n7.66784:\\n7.66 785\\n2.33215\\n9.99999\\n44\\n17\\n7.6941^\\n7.69418\\n2633\\n2.30 582\\n9.99999\\n43\\ni8\\n7.71 899\\n7.71 900\\n2482\\n2.28 099\\n9.99999\\n42\\n19\\n7.74248\\n2348\\n2227\\n2119\\n7.74248\\n2348\\n2227\\n2.25751\\n9.99999\\n41\\n20\\n7.76475\\n7.76476\\n2.23 524\\n9.99999\\n40\\n21\\nT.^Z 594\\nI l^ 595\\n2.21 405\\n9.99999\\n39\\n22\\n7.80614\\n7.80615\\n2.19384\\n9.99999\\n38\\n23\\n7.82545\\n1930\\n7.82 546\\n1930\\n2.17454\\n9.99999\\n37\\n24\\n7.84393\\n1843\\n1772\\n7-84394\\n1848\\n1773\\n2.15 605\\n9.99999\\n36\\n25\\n7.86 166\\n7.86 16^\\n2.13832\\n9.99999\\n35\\n26\\n7.87869\\n1703\\n1639\\n7.87871\\n1703\\n1639\\n2.12 129\\n9.99999\\n34\\n27\\n7.89 508\\n7.89510\\n2.10490\\n9-99 998\\n33\\n28\\n7.91 088\\n1579\\n7.91 089\\n1579\\n2.08 916\\n9-99 998\\n32\\n29\\n7.92 612\\n1524\\n7.92613\\n1524\\n2.07 386\\n9-99 998\\n31\\n30\\n7.94084\\n1472\\n7.94086\\n1472\\n1424\\n2.05 914\\n9-99 998\\n30\\n3i\\n7.95 508\\n7.95510\\n2.04 490\\n9.99998\\n29\\n32\\n7.96 887\\n1379\\n7.96 8S9\\n1379\\n2.03 III\\n9-99998\\n28\\n33\\n7.98 223\\n1336\\n7.98225\\n1336\\n2.01 774\\n9.99998\\n27\\n34\\n7.99 520\\n1296\\n7.99 522\\n1296\\n2.00478\\n9.99998\\n26\\n1 35\\n8.00 778\\n1253\\n1223\\n1 190\\n1158\\n1128\\n1099\\n1072\\n8.00781\\n\u00e2\u0096\u00a01^59\\n1223\\niigo\\n1158\\n1.99 219\\n9.9999?\\n25\\ni 36\\n37\\n8.02 002\\n8.03 192\\n8.02 004:\\n8.03 191\\n1.97995\\n1.96 805\\n9.9999?\\n9.99997\\n24\\n23\\n38\\n8.04 350\\n8.04 352\\n1.95 647\\n9.99997\\n22\\n39\\n8.05 478\\n8.05481\\n1123\\n1099\\n1072\\n1.94 519\\n9.99997\\n21\\n40\\n8.06 577\\n8.06 580\\n1-93 419\\n9-99 997\\n20\\n41\\n8.07 650\\n8.07653\\n1.92 347\\n9.99997\\n19\\n42\\n8.08 696\\n8.08 699\\n1. 91 300\\n9-99 997\\n18\\n43\\n8.09 718\\n998\\n976\\n8.09721\\n1.90278\\n9-99 996\\n17\\n1 44\\n8.10716\\n8.10720\\n999\\n976\\n1.89 279\\n9-99 996\\n16\\n45\\n8. 1 1 692\\n8. 1 1 696\\n1.88303\\n9-99 996\\n15\\n46\\n8.12647\\n8.12651\\n954\\n1.87 349\\n9.99996\\n14\\n47\\n8.13 581\\n934\\n8.13585\\n934\\n1.86 415\\n9.99996\\n13\\n48\\n8.14495\\n914\\n895\\n877\\n860\\n8.14499\\n914\\n1.85 506\\n9.99996\\n12\\n49\\n8.15396\\n8.15395\\n895\\n877\\n860\\n1.84605\\n1.8372?\\n9-99 995\\nII\\n50\\n8.16268\\n8.16272\\n9.99995\\n10\\n51\\n8.17 128\\n843\\n8.17 133\\n843\\n827\\n1.82867\\n9-99 995\\n9\\n52\\n8.17 971\\n8.17 976\\n1.82023\\n9-99 995\\n8\\n53\\n8.18798\\n811\\n797\\n782\\n768\\n8.18803\\n1. 81 igg\\n9-99 995\\n7\\n54\\n8.19610\\n8.19615\\n797\\n783\\n763\\n1.80384\\n9-99 994\\n6\\n55\\n56\\n8.20407\\n8.21 189\\n8.20412\\n8.21 195\\n1.79587\\n1.78804\\n9-99 994\\n9-99 994\\n5\\n4\\n57\\n8.21 958\\n8.21 964\\n1.78036\\n9.99994\\n3\\n58\\n8.22 713\\n755\\n8.22 719\\n755\\n1.77 286\\n9.99994\\n2\\n59\\n8.23455\\n8.24185\\n742\\n730\\n8.23462\\n742\\n730\\n1.76538\\n9-99 993\\nI\\n60\\n8.24 192\\n1.75808\\n9-99 993\\n1\\nLog. Cos.\\nD\\nLog. Cot.\\nCom. D.\\nLog. Tau.\\nLog. Sin.\\n89^\\n348", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0400.jp2"}, "401": {"fulltext": "TABLE VII. LOGARITHMIC SIXES, COSINES, TANGENTS, AND COTANGENTS.\\n1\\nTiOK. sin.\\n8.24 18S\\nI\\n8. 24 903\\no\\n8.25 609\\n3\\n8.26 304\\n4\\n8.26988\\n5\\n8.27 661\\n6\\n8.28324\\n7\\n8.28977\\n8\\n8.29620\\n9\\n8.30254\\n10\\n8.30879\\n1 II\\n8.31495\\n12\\n8.32 102\\n13\\n8.32 701\\n14\\n8.33292\\n15\\n8.33 87S\\ni6\\n8.34450\\n17\\n8.35018\\ni8\\n8-35 578\\n19\\n8.36 1 31\\n20\\n8.36677\\n21\\nS.37 2r7\\n22\\n8.37750\\n23\\n8.38276\\n24\\n8.38796\\n25\\n8.39310\\n26\\n8.39818\\n27\\n8.40320\\n28\\n8.40816\\n29\\n8.41 307\\n30\\n8.41 792\\n31\\n8.42 271\\n32\\n8.42 746\\n33\\n843215\\n34\\n8.43 680\\n35\\n8.44 139\\n36\\n8.44 594\\n37\\n8.45 044\\n38\\n8.45489\\n39\\n8.45930\\n40\\n8.46 365\\n41\\n8.46798\\n42\\n8.47 226\\n43\\n8.47 650\\n44\\n8.48069\\n45\\n8.48485\\n46\\n8.48 896\\n47\\n8.49 304\\n48\\n8.49 708\\n49\\n8.50 108\\n1 50\\n8. 50 504\\n1 51\\n8.50897\\n52\\n8.51286\\n53\\n8.51 672\\n54\\n8.52055\\n1 55\\n8.52434\\n56\\n8.52810\\n57\\n8.53183\\n58\\n8.53552\\n59\\n8-53918\\nGO\\n8.542S2\\nLot;. Cos.\\nD\\n718\\n706\\n694\\n684\\n673\\n663\\n653\\n643\\n634\\n625\\n616\\n607\\n599\\n591\\n583\\n575\\n567\\n560\\n553\\n546\\n539\\n533\\n526\\n520\\n514\\n503\\n502\\n496\\n491\\n485\\n479\\n474\\n469\\n464\\n459\\n454\\n450\\n44S\\n440\\n436\\n432\\n428\\n423\\n419\\n415\\n411\\n407\\n404\\n400\\n396\\n393\\n389\\n386\\n382\\n379\\n375\\n373\\n369\\n366\\n363\\nI\\nLoir, Tan.\\nCom, I).\\n8.24 192\\n8.24910\\n8.25 6I6\\n8.26 311\\n8.26 99^\\n8.27 669\\n8.28 332\\n8,28985\\n8.29 629\\n8.30263\\n8,30888\\n8.31 504\\n8.32 112\\n8.32711\\n8.33302\\n8,33885\\n8,34461\\n8.35029\\n8.35 589\\n8.36 143\\n8.36 689\\n8.37 229\\n8.37 762\\n8.38289\\n8.38809\\n8.39323\\n8.39831\\n8.40334\\n8.40830\\n8.41 321\\n8.41 807\\n8.42 287\\n8.42 762\\n8.43231\\n8.43 696\\n8.44 156\\n8.44 611\\n8.45061\\n8.45 507\\n8.45 948\\n8.46 385\\n8,46817\\n8.47 245\\n8.47 669\\n8.48089\\n8.48 505\\n8.48917\\n8.49325\\n8.49729\\n8,50130\\n8-50526\\n8.50 920\\n8.51 310\\n8,51 696\\n8,52079\\n875^2 458~\\n8.52835\\n8.53208\\n8.53578\\n8.53944\\n8-54 308\\nLos:. Cot.\\n718\\n706\\n695\\n6S4\\n673\\n663\\n653\\n643\\n634\\n625\\n616\\n607\\n599\\n591\\n583\\n575\\n568\\n560\\n553\\n546\\n539\\n533\\n527\\n520\\n514\\n50S\\n502\\n496\\n491\\n4S5\\n480\\n475\\n469\\n464\\n460\\n455\\n450\\n445\\n441\\n437\\n432\\n428\\n424\\n419\\n416\\n412\\n408\\n404\\n400\\n396\\n393\\n390\\n386\\n383\\n379\\n376\\n373\\n370\\n366\\n364\\nCom, l\u00c2\u00bb.\\nI-oir. Cut.\\nLoir. Cos.\\n1,75 808\\n9-99 993\\n1.75090\\n9-99 993\\n1.74383\\n9-99 993\\n1.73 688\\n9.99992\\n1.73004\\n9.99992\\n1.72 331\\n9.99992\\n1. 71 667\\n9.99992\\n1. 71 014\\n9.99992\\n1.70 371\\n9.99991\\n1.69736\\n9.99991\\n1.69 III\\n9.99991\\n1.68495\\n9.99990\\n1.67888\\n9.99990\\n1.67288\\n9.99990\\n1.66697\\n9.99990\\n1.66 1 14\\n9.99989\\n1.65 539\\n9-99989\\n1,64971\\n9.99989\\n1. 64410\\n9.99989\\n1.63857\\n9.99988\\n1.63 310\\n9.99988\\n1.62 771\\n9.99988\\n1,62 238\\n9.99987\\n1,61 711\\n9.99 9S7\\n1. 61 191\\n9.99987\\n1,60676\\n9.99986\\n1,60 168\\n9,99986\\n1.59666\\n9.99986\\n1.59 169\\n9.99986\\n1.58678\\n9.99985\\n1.58 193\\n9.99985\\n1. 57713\\n9-99985\\n1.57238\\n9.99984\\n1,56768\\n9-99984\\n1,56304\\n9.99984\\n1,55844\\n9.99983\\n1-55389\\n9.99983\\n1-54 938\\n9.99982\\n1-54 493\\n9.99982\\n1.54052\\n9.99982\\n1. 53615\\n9.9998!\\n1-53183\\n9.99981\\n1-52754\\n9.99981\\n1.52330\\n9.99980\\n1. 51 911\\n9,99980\\n9-99 979\\n1. 51 495\\n1. 5 1 083\\n9-99 979\\n1.50675\\n9-99 979\\n1.50270\\n9-99 978\\n1.49870\\n9.99978\\n1-49 473\\n9.99978\\n1,49080\\n9.99977\\n1,48690\\n9-99 977\\n1.48 304\\n9-99 976\\n1,47921\\n9.99976\\n1,47541\\n9-99 975\\n1,47 165\\n9-99 973\\n1,46792\\n9-99 975\\n1,46422\\n9-99 974\\n1,46055\\n1.45 691\\n9-99 974\\n9.99973\\nLoir, I jin.\\nLoir. Sin.\\nss\\n349", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0401.jp2"}, "402": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n2\\nLog. Sin.\\nD\\nLog. Tan.\\nCom. D. L\\nog. Cot.\\nLog. Cos.\\n8.54 282\\n360\\n8.543O8\\n\u00e2\u0096\u00a0^(m\\n45691\\n9-99 973\\n60\\nI\\n8.54642\\n8.54669\\n45331\\n9\\n99 973\\n59\\n2\\n8.54999\\n357\\n8.55027\\n358 J\\n44 973\\n9\\n99972\\n58\\n3\\n8-55 354\\n354\\n8.55381\\n354 J\\n44618\\n9\\n99972\\n57\\n4\\n8-55 705\\n8.56054\\n351\\n348\\n8-55 733\\n8.56083\\n352 J\\n44266\\n9\\n99971\\n56\\n5\\n349 J\\n346 J\\n43917\\n9\\n99971\\n55\\n6\\n8. 56 400\\n8.56429\\n43571\\n9\\n99971\\n54\\n7\\n8.56743\\n343\\n8.56772\\n343 I\\n4322^\\n9\\n99970\\n53\\n8\\n8.57083\\n340\\n8.57 113\\n341 I\\n42886\\n9\\n99970\\n52\\n9\\n8. 57 421\\n338\\n335\\n8.57452\\n338 I\\n42 548\\n9\\n99969\\n51\\n10\\n8.57 756\\n^\u00e2\u0080\u00a2Sll^l\\n335\\n.42 212\\n9\\n\u00e2\u0080\u00a299969\\n50\\nII\\n8.58089\\n332\\n8.58 121\\n333 J\\n41879\\n9\\n99968\\n49\\n12\\n8.58419\\n330\\n8.58451\\n330 I\\n41 548\\n9\\n99 968\\n48\\n13\\n8.58747\\n327\\n8.58779\\n328 J\\n41 220\\n9\\n99967\\n47\\n14\\n8.59072\\n325\\n323\\n8.59105\\n8.59428\\n325 I\\n40895\\n9\\n99967\\n46\\n15\\n8-59 395\\n323 J\\n40571\\n9\\n99966\\n45 i\\ni6\\n8.59715\\n320\\n8.59749\\n40251\\n9\\n99966\\n44 i\\n7\\n8.60033\\n3^3\\n8.60067\\n318 I\\n39932\\n9\\n99965\\n43\\ni8\\n8.60349\\n310\\n8.60384\\n316 I\\n.39616\\n9\\n99965\\n42 1\\n19\\n8.60662\\n313\\n311\\n8.60698\\n314 I\\n39302\\n9\\n99 964\\n41\\n20\\n8.60973\\n8.61 009\\n6^ J\\n38990\\n9\\n99964\\n40\\n1\\n8.61 282\\n309\\n8.61 319\\n309 J\\n38681\\n9\\n99963\\n39\\n22\\n8.61 589\\n306\\n8.61 626\\n307 I\\n38374\\n9\\n99963\\n38\\n23\\n8.61 893\\n304\\n8.61 931\\n3C5 I\\n38068\\n9\\n99962\\n37\\n1 24\\n8.62 196\\n302\\n300\\n8.62 234\\n303 I\\n37765\\n9\\n99962\\n1 25\\n8.62 496\\n8.62 535\\n300\\n37465\\n9\\n99.961\\n35\\ni 26\\n8.62795\\n298\\n8.62 834\\n299 I\\n37 166\\n9\\n99961\\n34 1\\nV\\n8.63 091\\n296\\n8-63 131\\n297 I\\n36869\\n9\\n99960\\n33\\n28\\n8-6338!\\n294\\n8.63425\\n294 J\\n36574\\n9\\n99 959\\n32\\n29\\n8.63677\\n292\\n290\\n8.63 718\\n293 I\\n36281\\n9\\n99 959\\n31 1\\n1 30\\n8.63968\\n8.64009\\n291\\n35990\\n9\\n99 958\\n30\\n31\\n8.64256\\n283\\n8.64 298\\n283 J\\n35702\\n9\\n99958\\n29\\n32\\n8.64 543\\n285\\n8.64585\\n287\\n35414\\n9\\n99 957\\n28 1\\n33\\n8.64827\\n284\\n8.64870\\n285 I\\n35 129\\n9\\n99 957\\n27 i\\n34\\n8.65 no\\n282\\n281\\n8.65153\\n283 I\\n34846\\n9\\n99 956\\n26\\n35\\n8.65 391\\n8.65435\\n2S1\\n34565\\n9\\n99956\\n25\\n36\\n8.65670\\n279\\n8.65715\\n280\\n34285\\n9\\n9995!\\n24\\n37\\n8.65 94f\\n277\\n8.65 993\\n278 J\\n34007\\n9\\n99 954\\n23\\n38\\n8.66223\\n275\\n8.66 269\\n276 J\\n33731\\n9\\n99 954\\n22\\n1 39\\n8.66497\\n274\\n272\\n8.66 543\\n274 I\\n33 456\\n9\\n99 953\\n21\\n1 40\\n8.66 769\\n8.66816\\n33184\\n9\\n99 953\\n20\\n41\\n8.67 039\\n26\u00c2\u00a7\\n8.67087\\n271\\n32913\\n9\\n99952\\n19\\n42\\n8.67 308\\n8.67 356\\n32643\\n9\\n99952\\n18\\n43\\n8-67575\\n8.67624\\n32376\\n9\\n99951\\n17\\n44\\n8.67 840\\n265\\n264\\n8.67 890\\n266\\n32 no\\n9\\n99950\\n16\\n1 45\\n8.68 104\\n8.68 154\\n262\\n31845\\n9\\n99950\\n15\\n46\\n8.68 366\\n8.68417\\n31 583\\n9\\n99 949\\n14\\n47\\n8.68627\\n8.68 678\\n31 321\\n9\\n99 948\\n13\\n48\\n8.68 886\\n259\\n8.68938\\n259 J\\n31 062\\n9\\n99948\\n12\\n1 49\\n8.69 144\\n257\\n256\\n8.69 196\\n258 I\\n30803\\n9\\n99 947\\nII\\n50\\n8.69400\\n8.69453\\n256\\n30547\\n9\\n99 947\\n10\\n51\\n8.69654\\n254\\n8.69708\\n255 J\\n30 292\\n9\\n99 946\\n9\\n52\\n8.69907\\n253\\n8.69 961\\n253 J\\n30038\\n9\\n99 945\\n8\\n53\\n8.70159\\n251\\n8.70214\\n29786\\n9\\n99 945\\n7\\n54\\n8. 70 409\\n250\\n248\\n8.70464\\n250\\n29 53?\\n9\\n99 944\\n6\\n55\\n8.7065^\\n8.70714\\n249\\n248\\n29286\\n9\\n99 943\\n5 1\\n56\\n8.70905\\n247\\n8.70962\\n29038\\n9\\n99 943\\n4\\n57\\n8.71 150\\n245\\n8.71 208\\n246\\n28 791\\n9\\n99942\\n3 1\\n58\\n8.71 395\\n244\\n8.71453\\n245 J\\n28546\\n9\\n99942\\n2\\n57\\n8.71 638\\n243\\n241\\n8.71 697\\n243 J\\n28303\\n9\\n99941\\nI i\\n60\\n8.71 880\\n8.71 939\\n242\\n28060\\n9-\\n99940\\n1\\nLog. Cos.\\nD\\nLog. Cot.\\nCom. D. Lc\\n)g. Tan.\\nLog. Sin. j\\n1\\n87\\n350", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0402.jp2"}, "403": {"fulltext": "TABLE VII. LOGARITHMIC SINES, COSIXES, TANGENTS, AND C0TAN(;ENTS\\n10\\nII\\n12\\n13\\n14\\n25\\n26\\n27\\n28\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\noO\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLog. Sin.\\n8.71 880\\n8.72 120\\n8.72359\\n8.72597\\n8.72833\\n8.73069\\n8.73 302\\n8-73 533\\n^\u00e2\u0096\u00a073 766\\n8.73997\\n8.74 226\\n8-74453\\n8.74680\\n8.74905\\n8.75 129\\n8-75 353\\n8-75 574\\n8-75 795\\n8.76015\\n8.76233\\n8.76451\\n8.7666;\\n8.76883\\n8.77097\\n8.77310\\n8.77 522\\n8.77 733\\n8.77943\\n8.78 152\\n8.78360\\n8.78 567\\n8.78773\\n8.78978\\n8.79183\\n8.79386\\n8.79588\\n8.79789\\n8.79989\\n8.80189\\n8.80387\\n8.80585\\n8.80782\\n8.80977\\n8.81 172\\n8.81 366\\n8.81 560\\n8.81 752\\n8.81 943\\n8.82 134\\n8.82324\\n8.82 513\\n8.82 701\\n8.82888\\n8.83075\\n8.83260\\n^-83445\\n8.83629\\n8.83813\\n8.83995\\n8.8417;\\n8-84 358\\nLog. Cos.\\n240\\n239\\n237\\n236\\n235\\n233\\n233\\n231\\n230\\n229\\n227\\n226\\n225\\n224\\n223\\n221\\n221\\n219\\n2I\u00c2\u00a7\\n217\\n215\\n215\\n214\\n213\\n212\\n211\\n210\\n209\\n208\\n207\\n206\\n205\\n204\\n203\\n202\\n201\\n200\\n199\\n198\\n197\\n197\\n195\\n195\\n194\\n193\\n192\\n191\\n191\\n187\\n186\\n185\\n185\\n184\\n183\\n182\\n182\\n181\\nd.\\nLoy. Tan.\\n8-71 939\\n8.72186\\n8.72420\\n8.72 659\\n8.72896\\n8.73 131\\n8-73366\\n8-73 599\\n8.73831\\n8.74062\\n8.74 292\\n8.74 520\\n8-74748\\n8.74974\\n8.75 199\\n8.75422\\n8.7564$\\n8.75867\\n8.76087\\n8.76 306\\n8.76524\\n8.76741\\n8.76958\\n8.77 172\\n8.77386\\n8.77 599\\n8.77 811\\n8.78022\\n8.78232\\n8.78441\\n8.78648\\n8.7885$\\n8.79061\\n8.79 266\\n8.79470\\n8.79673\\n8.79875\\n8.80075\\n8.80275\\n8.80476\\n8.80674\\n8.80871\\n8.81 068\\n8.81 264\\n8.81 459\\n8.81 653\\n8.81 846\\n8.82038\\n8.82 230\\n8.82 420\\n8.82616\\n8.82 799\\n8.82987\\n8.83175\\n8.83 361\\n8.83547\\n8.83732\\n8.83 916\\n8.84 100\\n8.84282\\n8.84464\\nLog. Cot.\\nc. d.\\n241\\n240\\n2J8\\n237\\n235\\n235\\n233\\n232\\n231\\n229\\n228\\n227\\n226\\n225\\n223\\n223\\n221\\n220\\n219\\n218\\n217\\n216\\n214\\n214\\n213\\n212\\n210\\n210\\n209\\n207\\n207\\n206\\n204\\n204\\n203\\n202\\n201\\n200\\n199\\n198\\n197\\n197\\n195\\n195\\n194\\n193\\n192\\n191\\n190\\n190\\n187\\n186\\n185\\n185\\n184\\n183\\n182\\n182\\n3\u00c2\u00b0\\nLotf. Cot.\\n1.28 066\\n1.27 819\\n1.27 579\\n1.27 341\\n1.27 104\\n1.26868\\n1.26633\\n1 26 400\\n1.26 168\\n1.25937\\n1.25 708\\n1.25479\\n1.25 252\\n1.25 026\\n1.24 801\\n1.24577\\n1.24 35-?\\n1-24133\\n1-23913\\n\u00e2\u0080\u00a23 693\\nI.\\n1-23475\\n1.23258\\n1.23 042\\n1.22 82;\\n1.22 613\\n1.22 400\\n1.22 188\\n1. 21 978\\n1. 2 1 768\\n1. 21 559\\n1. 21 351\\n1. 21 144\\n1.20 938\\n1.20734\\n1.20 530\\n1.20 327\\n1.20 125\\n1. 19923\\n1. 19 723\\n1. 19 524\\n1. 19 326\\n1. 19 128\\n1. 18 931\\n1. 18736\\n1. 18 541\\n1. 18 347\\n1. 18 154\\n1. 17 961\\n1. 17 770\\n1. 17 579\\n1-17389\\n1. 17 201\\n1. 17 012\\n1. 16825\\n1. 16 638\\n1. 16453\\n1. 16 268\\n1. 16083\\n1 1 5 900\\n1.1571;\\n^\u00e2\u0080\u00a215535\\nc. (1. Log. Tan.\\nLoe. Cos.\\n9.99940\\n9.99940\\n9-99 939\\n9-99 938\\n9.99938\\n9.99937\\n9-99 936\\n9-99 935\\n9-99 935\\n9-99 93-+\\n9-99 933\\n9-99 933\\n9-99932\\n9-99 931\\n9-99931\\n9.99930\\n9-99929\\n9.99928\\n9.99928\\n9-99927\\n9-99926\\n9.99925\\n9-99925\\n9-99924\\n9.99923\\n9.99922\\n9.99922\\n9.99921\\n9.99926\\n9.99919\\n9.99919\\n9.99918\\n9.9991;\\n9-99 916\\n9.99916\\n9.99915\\n9.99914\\n9-99913\\n9.99912\\n9.99912\\n9.99 911\\n9.99910\\n9-99 909\\n9-99 908\\n9.99907\\n9.99907\\n9.99906\\n9-99905\\n9.99904\\n9.99903\\n9.99902\\n9.99902\\n9.99901\\n9.99900\\n9-99899\\n9.99898\\n9.99897\\n9.99895\\n9.99896\\n9-99895\\n9-99894\\nLug. Sin, i\\n50\\n49\\n48\\n47\\n_46^\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n_3i\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n9\\n8\\n7\\n6\\nr. r.\\n330\\n320\\n310\\n6\\n330\\n32.0\\n31\\n7\\n38.5\\n37-3\\n36.1\\n8\\n44.0\\n42-6\\n41 3\\n9\\n49-5\\n48.0\\n46.5\\n10\\n55 -o\\n53-3\\nS O\\n20\\n110.\\n106.6\\nJ03-3\\n30\\n165.0\\n160.0\\n1550\\n40\\n220.0\\n213.3\\n206. A\\n50\\n275.0\\n266.6\\n258.3\\n290\\n280\\n270\\n6\\n29.0\\n28.0\\n27.0\\n7\\n8\\n33-8\\n38.6\\n32-6\\n37-3\\n360\\n9\\n10\\n43 S\\n48.3\\n42.0\\n46.6\\n40.5\\n450\\n20\\n96.6\\n93-3\\n90.0\\n30\\n40\\n145.0\\n193-3\\n140.0\\n186.^\\n135-0\\n180.0\\n5\\n241.6\\n233 -3\\n225.0\\n300\\n30.0\\n350\\n40.0\\n45.0\\n50.0\\n100.0\\n150.0\\n200.0\\n250.0\\n260\\n26.0\\n30-3\\n34-6\\n39 o\\n43-3\\n86.6\\n130.0\\n173-3\\n216.6\\n250\\n240\\n230\\n220\\n6\\n25.0\\n24.0\\n23.0\\n22.0\\n7\\n29\\nI\\n28.0\\n26\\n25\\n6\\n8\\n33\\n3\\n32.0\\n30\\n6\\n29\\n3\\n9\\n37\\n5\\n36.0\\n34\\n5\\n33\\n10\\n41\\n6\\n40.0\\n38\\n3\\n36\\nft\\n20\\n83\\n3\\n80.0\\n76\\n6\\n73\\n3\\n30\\n12s\\n120.0\\nIIS\\nno\\n40\\n166\\n6\\n160.0\\n153\\n3\\n146\\n6\\n50\\n208\\n3\\n200.0\\n191\\n6\\nX83\\n3\\n210\\n200\\n190\\n180\\n6\\n21 .0\\n20.0\\n19.0\\n18.0\\n7\\n24-5\\n23-3\\n22.1\\n21 .0\\n8\\n28.0\\n26.6\\n25-3\\n24.0\\n9\\n31-5\\n30.0\\n28.5\\n27.0\\n10\\n35-0\\n33-3\\n31-6\\n30.0\\n20\\n70.0\\n66.6\\n63-3\\n60.0\\n30\\n105.0\\n100.0\\n05.0\\n90.0\\n40\\n140.0\\n1.33-3\\n126.6\\n120.0\\n50\\n175-0\\n166.6\\n158-3\\n150.0\\n6\\n9\\n0.9\\n9\\n0.9\\n8\\n0.8\\n7\\n0.7\\n6\\n0.6\\n7\\n8\\ni.i\\n1.2\\n1.0\\n1.2\\n0.9\\n1.0\\n0.8\\n0.9\\n0.7\\n0.8\\n9\\n1.4\\n1-3\\n1.2\\n1 .0\\n0.9\\n10\\n1.6\\n1-5\\n1-3\\n1.1\\n1.0\\n20\\n31\\n3-0\\n2-6\\n2-3\\n2.0\\n30\\n40\\n50\\n4-7\\n6-3\\n7-9\\n4 5\\n6.0\\n7 5\\n4.0\\n6-6\\n3-5\\n5-8\\n30\\n4.0\\n5-0\\n0.5\\n0.6\\no 6\\n0.7\\n2-5\\n3|\\n4-1\\n4\\n4\\n3\\n2\\nI\\n6\\n0.4\\n0.4\\n0.5\\n0.2\\n0.1\\n7\\no.,S\\n0.4\\n0.3\\n0.2\\n0.1\\n8\\n0.6\\n0.5\\n0.4\\n0.2\\nI\\n9\\n0.6\\n0.4\\n0.3\\n0.1\\n10\\n0.7\\n0-^\\nO..S\\n0.3\\n0.1\\n20\\n1-5\\n\u00e2\u0096\u00a03\\nI.O\\n0.6\\n03\\n30\\n2.2\\n2.0\\n-5\\n1.0\\n0-5\\n40\\n3?\\n^\u00e2\u0080\u00a26\\n2.0\\n0$\\n5 J\\n3-7\\n3-3\\n2-5\\n1-6\\n0-8\\n0-3\\n0.4\\nv. r\\n351", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0403.jp2"}, "404": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES/COSINES, TANGENTS, AND COTANGENTS.\\n4\u00c2\u00b0\\n10\\nII\\n12\\ni6\\n17\\ni8\\n19\\n20\\n21\\n24\\nLoir. Niii.\\n^\u00e2\u0080\u00a2^4 358\\n8.84 538\\n8.84 718\\n8.84897\\n8.85075\\n8.85 252\\n8.85 429\\n8.85605\\n8.85780\\n8.85954\\n8.86128\\n8. 86 301\\n8.86474\\n8.86645\\n8.86 816\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n8.86987\\n8.87156\\n8.87325\\n8.87494\\n8.87661\\n8.87828\\n8.87995\\n8.88 160\\n8.88326\\n8.88490\\n8.88654\\n8.8881^\\n8.88980\\n8.89 142\\n8.893 03\\n8.89464\\n8.89624\\n8.89784\\n8.89943\\n8.90 1 01\\n8.90 259\\n8.90417\\n8.90573\\n8.90729\\n8.90885\\n8.91 040\\n8.91 195\\n8.91 349\\n8.91 502\\n8.91655\\n8.91 807\\n8.91 959\\n8.92 no\\n8.92 261\\n8.92 411\\n8.92 561\\n8.92 710\\n8.92858\\n8.93007\\n8.93154\\n8.93 301\\n8.93448\\n8.93 594\\n8.93 740\\n8.93885\\n5.94029\\nLog. \u00e2\u0082\u00acos.\\nd.\\n78\\n7S\\n77\\n76\\n76\\n75\\n74\\n74\\n73\\n72\\n71\\n71\\n70\\n69\\n69\\n68\\n67\\n67\\n66\\n65\\n^5\\n64\\n63\\n63\\n62\\n62\\n61\\n61\\n60\\n59\\n59\\n58\\n58\\n57\\n56\\n56\\n56\\n55\\n54\\n54\\n53\\n53\\n52\\n51\\n51\\n50\\n50\\n50\\n49\\n48\\n48\\n47\\n47\\n46\\n46\\n46\\n45\\n44\\nLog. Tan.\\n8.84464\\n8.84645\\n8.84826\\n8.85005\\n8.85 184\\n8.85363\\n8.85 540\\n8.85717\\n8.85893\\n8.86068\\n8.86243\\n8.8641^\\n8.86596\\n8.86763\\n8.86935\\n8.87 I06\\n8.87277\\n8.87447\\n8.87616\\n8.87785\\n8.87953\\n8.88 120\\n8.88287\\n8.88453\\n8.88 618\\n8.88783\\n8.88 94^\\n8.89 III\\n8.89274\\n8.89436\\n8.89598\\n8.89759\\n8.89 926\\n8.90086\\n8.90 240\\n8-90398\\n8.90557\\n8.90714:\\n8.90872\\n8.91 028\\n8.91 184\\n8.91 340\\n8.91 495\\n8.91 649\\n8.91 803\\n8.91 957\\n8.92 109\\n8.92 262\\n8.92413\\n8.92 565\\n8.92715\\n8.92866\\n8.93015\\n8.93 164\\n8-93313\\n8.93461\\n8.93 609\\n893756\\n8.93903\\n8.94049\\n8.94195\\nc. d.\\nLog. Cot.\\n79\\n79\\n78\\n77\\n76\\n76\\n75\\n75\\n74\\n73\\n72\\n72\\n71\\n70\\n70\\n69\\nLog. Cot.\\nI-I5 535\\n1. 15 354\\n1. 15 174\\n1. 14 994\\n1.14815\\n1. 14637\\n1. 14459\\n1. 14283\\n1. 14 107\\n1-13931\\nI-I3756\\n1. 13 582\\n1.13409\\n1. 13237\\n1. 13065\\n1. 12 893\\n1. 12 723\\nI.I2 553\\n1. 12 384\\n1. 12 215\\n1 1 2 047\\nI. II 880\\nI. II 713\\n1. 1 1 547\\nI. II 381\\nI. II 216\\nI. II 052\\n1. 10 889\\n1. 10726\\n1. 10 563\\n1. 10 401\\n1. 10 246\\n1. 10 079\\n1.09 919\\n1.09 760\\nc. d.\\n1.09 601\\n1.09443\\n1.09285\\n1.09 128\\n1.08 971\\n1.08 815\\n1.08660\\n1.08 505\\n1.08356\\n1.08 196\\n1.08 043\\n1.07 896\\n1.07 738\\n1.07 586\\n1.07435\\n1.07 284\\n1.07 134\\n1.06 984\\n1.06 835\\n1.06686\\n1.06 538\\n1.06 396\\n1.06 243\\n1.06097\\nI-05 950\\n1.05 805\\nLog. Tan.\\n85\\nLog. Cos.\\n9.99894\\n9.99893\\n9.99892\\n9-99891\\n9.99896\\n9.99 889\\n9.99888\\n9.99888\\n9.99887\\n9.99886\\n9.99885\\n9.99884\\n9.99883\\n9.99 882\\n9.99881\\n9.99886\\n9.99879\\n9.99878\\n9.9987^\\n9-99876\\n9.99875\\n9.99874\\n9.99874\\n9-99873\\n9.99872\\n9.99871\\n9.99 870\\n9.99869\\n9.99868\\n9-99867\\n9.99 866\\n9.99 865\\n9.99 864\\n9.99863\\n9.99 862\\n9.99 861\\n9.99 860\\n9-99859\\n9-99858\\n9.99857\\n9.99856\\n9-99855\\n9-99853\\n9.99852\\n9-99851\\n9.99856\\n9.99849\\n9.99848\\n9-99847\\n9-99846\\n9.99845\\n9.99844\\n9.99843\\n9.99842\\n9.99841\\n9.99840\\n9.99839\\n9-99837\\n9-99836\\n9-99835\\n9.99834\\nLog. Sin.\\n60\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\nlo\\n9\\n8\\n7\\n6\\np. P.\\nx8i\\n180\\n178\\n176\\n6\\n18. 1\\n18.0\\n17.8\\n17.6\\n7\\n21. 1\\n21.0\\n20\\n7\\n20.5\\n8\\n24.1\\n24.0\\n23\\n7\\n234\\n9\\n27.1\\n27.0\\n26\\n7\\n26. 4\\n10\\n30.1\\n30.0\\n29\\n6\\n29-3\\n20\\n60.3\\n60.0\\n59\\n3\\n58.6\\n30\\n90-5\\n90.0\\n89\\n88.0\\n40\\n120.6\\n120.0\\n118\\n6\\n117-3\\n50\\n150-8\\n150.0\\n148\\n3\\n146.6 1\\n174\\n172\\n170\\n6\\n17.4\\n17.2\\n17.0\\n7\\n20.3\\n20.0\\n19-8\\nb\\n23. 2\\n22.9\\n22-6\\n9\\n26.1\\n25.\\n25. s\\n10\\n29.0\\n28.6\\n28.3\\n20\\n58.0\\n57-3\\n.56.6\\n30\\n87.0\\n86.0\\n85.0\\n40\\n116.\\n114. 6\\n3-3\\n50\\n145-0\\n143-3\\n141. 6\\n6\\n166\\n16.6\\n164\\n16.4\\n162\\n16.2\\n7\\n8\\n19-3\\n22.1\\n19.1\\n21-8\\n18.9\\n21.6\\n9\\n24.9\\n24.6\\n24-3\\n10\\n27-6\\n27-3\\n27.0\\n20\\n30\\n55-3\\n83.0\\n54-6\\n82.0\\n54-0\\n81.0\\n40\\n50\\nno. 6\\n138.3\\n109.3\\n136.6\\n108 .0\\n135-0\\n158\\ni.S6\\nI.S4\\n6\\n15-8\\n15.6\\n15-4\\n7\\n18.4\\n18.2\\n17.9\\n8\\n21.0\\n20.8\\n20.5\\n9\\n23-7\\n23-4\\n23-1\\n10\\n26.3\\n20.\\n25-6\\n20\\n52.6\\n52.0\\n51-3\\n30\\n79.0\\n78.0\\n77.0\\n40\\n105 -3\\n104.0\\n102.6\\n50\\n131-6\\nT30.0\\n128.3\\n168\\n16.8\\n19.6\\n22.4\\n25.2\\n28.0\\nce.o\\n84.0\\n112.0\\n140.0\\n160\\n16.0\\n18.6\\n21.3\\n24.0\\n26 6\\n53-3\\n80.0\\n106.6\\n133-3\\n15.2\\n17.7\\n20.2\\n22.8\\n25-3\\n50.6\\n76.0\\n101.3\\n126.6\\n146\\n145\\n1^\\nI\\nI\\n6\\nT4.6\\n14-5\\n0.1\\n0. 1\\n7\\n17.0\\n16\\nQ\\n0.2\\n0. 1\\n8\\n19 4\\n19\\n3\\n2\\n0.1\\n9\\n21.9\\n21\\n7\\n0.2\\n0.1\\n10\\n24-3\\n24\\nI\\n0.2\\n0.1\\n20\\n48.6\\n48\\n3\\n05\\n0-3\\n30\\n73.0\\n72\\n5\\n0.7\\no-s\\n40\\n50\\n97-3\\n121. 6\\n96\\n120\\n6\\n8\\nx.o\\n1.2\\n\u00c2\u00b0-6\\n0-8\\nP. p\\n150\\n149\\n148\\n147 1\\n6\\n15.0\\n14.9\\n14.8\\n14.7\\n7\\n17-5\\n17\\n4\\n17\\n2\\n17.1\\n8\\n20.0\\n19\\n8\\n19\\n7\\n19.6\\n9\\n22.5\\n22\\n3\\n22\\n3\\n22.0\\n10\\n25.0\\n24\\n8\\n24\\n6\\n24-5\\n20\\n50.0\\n49\\n6\\n49\\n3\\n49.0\\n30\\n75-0\\n74\\n5\\n74\\n73-5\\n40\\n100.0\\n99\\n3\\n98\\n6\\n98.0\\n50\\n125.0\\n124\\n1\\n123\\n3\\n122.5\\n0.0\\n0.0\\n352", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0404.jp2"}, "405": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGEN IS, AND C()TAN(iENTS.\\n10\\nII\\n12\\n13\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\nLot?. Sip. I d.\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n00\\n8.94029\\n8.94174\\n8.94317\\n8.94460\\n8.94603\\n8.94745\\n8.94887\\n8.95028\\n8.95 169\\n8.95310\\n8.95450\\n8.95 589\\n8.95728\\n8.95867\\n8.96 005\\n8.96 143\\n8.96280\\n8.96417\\n8-96553\\n8.96689\\n8.96825\\n8.96960\\n8.9709^\\n8.97 229\\n8.97 363\\n8.97496\\n8.97 629\\n8.97 762\\n8.97894\\n8.98026\\n8.Q8 ii;7\\n8.98288\\n8.98419\\n8.98 549\\n8.98679\\n8.98 808\\n8.98937\\n8.99066\\n8.99194\\n8.99322\\n8.99449\\n8.99 577\\n8.99703\\n8.99830\\n8.99956\\n9.00081\\n9.00 207\\n9.00 332\\n9.00456\\n9.00 580\\n9.00704\\n9.00828\\n9.00951\\n9.01 073\\n9.01 196\\n9.01 318\\n9.01 440\\n9.01 561\\n9.01 682\\n9.01 803\\n9.QI 923\\nLog. Cos.\\n144\\n143\\n143\\n143\\n142\\n142\\n141\\n141\\n140\\n140\\n139\\n139\\n138\\n138\\n138\\n137\\n137\\n136\\n136\\n135\\n135\\n134\\n\u00c2\u00bb34\\n134\\n133\\n133\\n132\\n132\\n132\\n131\\n131\\n130\\n130\\n130\\n129\\n129\\n12\u00c2\u00a7\\nI2g\\n127\\n127\\n127\\n126\\n126\\n126\\n125\\n125\\n125\\n124\\n124\\n124\\n123\\n123\\n122\\n122\\n122\\n122\\n121\\n121\\n120\\n126\\nLog. Tan. c. d. Log. t.\\n8.94 195\\n8.94346\\n8.94485\\n8.94629\\n8.94773\\n8.94917\\n8.95059\\n8.95 202\\n8.95 344\\n8.95485\\n8.95626\\n8.95767\\n8.95 90^\\n8.9604^\\n8.96 i8g\\n8.96325\\n8.96464\\n8.96602\\n8.96739\\n8.96876\\n8.97 013\\n8.97 149\\n8.97 285\\n8.97421\\n8.97 556\\n8.97 690\\n8.97 825\\n8.97 958\\n8.98 092\\n8.98225\\n8.98357\\n8.98490\\n8.98621\\n8.98753\\n8.98884\\n8.9901$\\n8.99 145\\n8.\\n99275\\n8.\\n99404\\n8.\\n99 533\\n8.\\n99662\\n8.\\n99791\\n8.\\n99919\\n9\\n00046\\n9\\n00 174\\n9\\n00 306\\n9\\n00427\\n9\\n00553\\n9\\n00679\\n9\\n00804\\n9\\n00 930\\n9.01 054\\n9.01 179\\n9.01 303\\n9.01 427\\n9.01 550\\n9.01 673\\n9.01 796\\n9.01 9I8\\n9. 02 046\\n9.02 162\\nLog. Cot.\\n145\\n144\\n144\\n144\\nM3\\n142\\n142\\n142\\n141\\n141\\n141\\n140\\n140\\n139\\n139\\n138\\n138\\n137\\n137\\n137\\n136\\n136\\n135\\n135\\n134\\n134\\n133\\n133\\n133\\n132\\n132\\n131\\n131\\n131\\n131\\n130\\n130\\n129\\n129\\n129\\nI2g\\n128\\n127\\n127\\n126\\n126\\n126\\n125\\n125\\n125\\n124\\n124\\n124\\n124\\n123\\n723\\n123\\n122\\n122\\n121\\ncTJT\\n1.05 803\\n1.05659\\n1.05 515\\n1.05 370\\n1.05226\\n1.05 083\\n1.04946\\n1.04 798\\n1.04 656\\n1.04 514\\n1.04373\\n1.04 232\\n1.04092\\n1.03952\\nj_^03_8_i^\\n1.03674\\n1.03 536\\n1.03398\\n1.03 266\\n1.03 123\\n1.02 986\\n1.02 856\\n1.02 714\\n1.02 579\\n1.02 444\\n1.02 309\\n1.02 175\\n1.02 041\\n1. 01 908\\n1. 01 775\\nLour. Cos.\\n1. 01 642\\n1. 01 510\\n1. 01 378\\n1. 01 247\\n1. 01 116\\n1.00985\\n1.00855\\n1. 00 725\\n1.00595\\n1.00466\\n1.00337\\n1. 00 209\\n1 00 08 1\\n0.99953\\n0.99 826\\n0.99699\\n0.99 573\\n0.99 446\\n0.99321\\n0.99195\\n0.99070\\n0.98945\\n0.98821\\n0.98 697\\n0.98 573\\n0.98 450\\n0.98327\\n0.98 204\\n0.98 081\\n0.97959\\n0.97 838\\nJiOg. Tan.\\nS4t\\n9.99834\\n9-99833\\n9.99832\\n9.99831\\n9.99830\\n9.99829\\n9.99827\\n9.99826\\n9-99825\\n9.99824\\n9.99823\\n9.99 822\\n9.99 821\\n9.99819\\n9.99 81 8\\n9.99817\\n9-99816\\n9.99815\\n9.99814\\n9-99 Si 3\\n9.99 81 1\\n9.99 816\\n9.99809\\n9.99 808\\n9.99807\\n9.99805\\n9-99804\\n9.99803\\n9.99 802\\n9.99801\\n9.99799\\n9-99 798\\n9.99797\\n9.99796\\n9-99 794\\n9-99 793\\n9.99 792\\n9.99791\\n9-99789\\n9-99788\\n9.99787\\n9.99786\\n9.99784\\n9-99783\\n9-99782\\n9.99781\\n9.99779\\n9-99 778\\n9.99777\\n9.99776\\n9-99 774\\n9-99 773\\n9.99772\\n9.99776\\n9.99769\\n9.99768\\n9.99766\\n9.99765\\n9.99764\\n9.99763\\n9-99761\\nLog. Sin.\\n00\\n59\\n58\\n57\\nJi\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n35\\n34\\n33\\n32\\n31\\nI I\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\n1 1\\nTo\\n9\\n8\\n7\\n6\\n140 139 138 137\\n14.0\\n13.9\\n13.8\\n13-7\\n16. s\\n16.2\\n16. 1\\n16.0,\\n18.6\\n18.5\\n18.4\\n18.2,\\n21 .0\\n20.8\\n20.7\\n20.5\\n23-3\\n23.1\\n23.0\\n22.8\\n46.6\\n46.3\\n46.0\\n45-6\\n70.0\\n69-5\\n69.0\\n68.5\\n93-3\\n92.$\\n92.0\\n9 -3\\n116. 6\\ni 5-8\\n115.\\n114.1\\n3-5\\n13-4\\n13\\n3\\n\u00c2\u00bb5 7\\n15-6\\n15\\n5\\n18.0\\n17-8\\n17\\n7\\n20.2\\n20. 1\\n19\\n9\\n22.5\\n22.3\\n22\\n1\\n45.0\\n675\\n90.0\\n44-6\\n67.0\\n89.3\\n44\\n66\\n88\\n3\\n5\\n112.5\\nIII. 6\\n110\\n8\\n145\\n144\\n143\\n142\\n141\\n6\\n14-5\\n14.4\\n14.3\\n14.2\\n14 I\\n7\\n16.9\\n16.8\\n16.7\\n16 .S\\n16.4\\n8\\n19-3\\n19.2\\n19.0\\n18.9\\n18.8\\n9\\n21.7\\n21.6\\n21.4\\n21.3\\n31. I\\n10\\n24.1\\n24.0\\n23\\n23-6\\n23-5\\n20\\n48-3\\n48.0\\n47-6\\n47-3\\n47.0\\n30\\n72 5\\n72.0\\n71 5\\n71.0\\n70.5\\n40\\n9 6\\n96.0\\n95-3\\n94-^\\n94.0\\n50\\n120.8\\n120.0\\n119. 1\\n118.3\\nH7-5\\n136\\n13.6\\no; 15-8\\n18. 1\\n20.4\\n22.^\\n45-3\\n68.0\\n90-6\\nl 3-3\\n135 134 133 132\\n13.2\\n15-4\\n17.6\\n19.8\\n22.0\\n44.0\\n66.0\\n131\\n130\\n129\\n128\\n6\\n13-1\\n13.0\\n12.9\\n12.8\\n7\\n153\\n151\\n15.0\\n14 9\\n8\\n17-4\\n173\\n17.2\\n17.0\\n9\\n19-$\\n19.5\\n193\\n19.2\\n10\\n21.\\n21.6\\n2t-5\\n21-3\\n20\\n43-6\\n43-3\\n43\\n42.6\\n30\\n6s.,S\\n65.0\\n64.5\\n64.0\\n40\\n87.3\\n86.^\\n86.0\\n85.3\\n50\\n109.1\\n108.3\\n107-5\\n106.6\\n127\\n126\\n125\\n124\\n123\\n12.7\\n12.6\\n12.5\\n12.4\\n12.3\\n14.8\\n14-7\\n14.6\\n14.4\\n14-3\\n16.9\\n16.8\\n16.6\\n16.5\\n16.4\\n19.0\\n18.9\\n18 7\\n18.5\\n18.4\\n21.1\\n21.0\\n20.\\n20.^\\n20.5\\n42.3\\n42.0\\n41 6\\n41-3\\n41.0\\n63. s\\n63.0\\n62.5\\n62.0\\n6t.5\\n84-6\\n84.0\\n83.3\\n82. 6\\n82.0\\n105-8\\n105.0\\n104.1\\n103.3\\n102.5\\n122\\n12.2\\n14.2\\n16.2\\n.8.3\\n20.3\\n40.6\\n61 .0\\n81.3\\nlOI.fi\\n121\\n12. 1\\n14.1\\ni6.i\\n18.1\\n20. T\\n40.3\\n6a. s\\n80.^\\n100. 8\\n120 I\\no.i\\n0.2\\n0.2\\n12.0\\n\u00e2\u0080\u00a24\\n16.0\\n18.0\\n20\\n40\\n60\\n80\\n100. o\\nO. 2\\n0-5\\n0.7\\nI O\\n0.0\\n0.0\\n0.1\\n0.1\\n0.1\\no.i\\no 3\\n0.4\\n0-3\\no-S\\no\\n0-8\\nP. P.\\n353", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0405.jp2"}, "406": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC\\nSINES, COSINES, TANGENTS, AND COTANGENTS.\\n10\\nII\\n12\\n14\\n15\\n16\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n^5\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLo^. Sin.\\n9.01 923\\n9.02 043\\n9,02 163\\n9.02 282\\n9.02 40T\\n9.02 520\\n9.02638\\n9.02 756\\n9.02 874\\n9.02 992\\n9.03 109\\n9.03 22^\\n9-03 342\\n9.03458\\n9-03 574\\n9.03689\\n9.03 805\\n9.03919\\n9.04034\\n9.04 148\\n9.04 262\\n9.04376\\n9.04489\\n9.04 602\\n9.04715\\n9.04 828\\n9.04 940\\n9.05 052\\n9.05 163\\n9.05275\\n9.05 386\\n905496\\n9.05 607\\n9.05717\\n9.05 827\\n9-05 936\\n9.06046\\n9.06155\\n9.06 264\\n9.06 372\\n9.06480\\n9.06 588\\n9.06 696\\n9.06 803\\n9.06 910\\n9.07 017\\n9.07 124\\n9.07 230\\n9-07 336\\n9.07 442\\n9.07 548\\n9.07653\\n9-07 758\\n9.07 863\\n9.07 96^\\n9.08 072\\n9.08 176\\n9.08 279\\n9.08 383\\n9.08485\\n9.08 589\\nLog. Cos.\\n(1.\\n120\\n119\\n119\\n119\\n119\\n118\\n118\\n118\\n117\\n117\\n6\\n6\\n116\\n116\\n115\\n115\\n114\\n114\\n114\\n114\\n3\\n113\\n113\\n113\\n112\\n112\\nIII\\nIII\\nno\\nlog\\n109\\n109\\n109\\nio\u00c2\u00a7\\n108\\n108\\n107\\n107\\n107\\n107\\nlog\\nlog\\n106\\n106\\n105\\n105\\n105\\n104\\n104\\n104\\n104\\n103\\n103\\n103\\n103\\n(1.\\nLost. Tan.\\n9.02 162\\n9.02 283\\n9.02 404\\n9.02 525^\\n9.02 645\\n9.02 765\\n9.02885\\n9.03 004\\n9.03 123\\n9.03 242\\n9.03 361\\n9-03 479\\n9-03 597\\n9.03714\\n9.03 831\\n9-03 948\\n9.04065\\n9.04 18T\\n9.04 297\\n9.04413\\n9.04 528\\n9.04643\\n9.04758\\n9.04 872\\n9.04987\\n9.05 lOI\\n9.05 214\\n9.05 32^\\n9.05 446\\n9-05 553\\nc. d.\\n9.05 666\\n9.05778\\n9.05 890\\n9.06001\\n9.06 113\\n9.06 224\\n9-o6 335\\n9.06445\\n9.06555\\n9.06 665\\n9.06775\\n9.06 884\\n9.06 994\\n9.07 102\\n9.07 211\\n9.07319\\n9.07 428\\n9-07 53^\\n9.07 643\\n9.07 756\\n9.07857\\n9.07 964\\n9.08 071\\n9.08 177\\n9.08 283\\n9.08 389\\n9.08 494\\n9.08 600\\n9.08 705\\n9.08 810\\n9.08 914\\n121\\n121\\n120\\n120\\n120\\n119\\n119\\n119\\n119\\n8\\n118\\n118\\n117\\n117\\n117\\n6\\n116\\n115\\n114\\n114\\n114\\n114\\n113\\n3\\n3\\n3\\n112\\n112\\n112\\nIII\\nIII\\nIII\\nIII\\nno\\nno\\nno\\n109\\n109\\n109\\nlog\\n109\\n108\\nlog\\n107\\n107\\n107\\n107\\n107\\nlog\\nlog\\n106\\n105\\n105\\n105\\n105\\n105\\n104\\nLog. Cot.\\n0.97 838\\n0.97 7I6\\n0.97595\\n0.97475\\n0.97 354\\n0.97234\\n0.97 115\\n0.96995\\n0.96876\\n0.96757\\n0.96639\\n0.96 521\\n0.96403\\n0.96 285\\n0.96 168\\n0.96 051\\n0-95 935\\n0.95 818\\n0.95 702\\n0.95 587\\n0.95471\\n0.95 356\\n0.95 242\\n0.95 127\\n0.95013\\n0.94899\\n0.94785\\n0,94672\\n0.94559\\n0.94 446\\n0.94 334\\n0.94 222\\n0.94 no\\n0-93 998\\n0.93887\\nLost. Cos.\\n9.99761\\n9.99760\\n9-99 759\\n9-99 757\\n9.99756\\n99 754\\n99 753\\n99752\\n99756\\n99 749\\n9.99748\\n9-99 746\\n9-99 745\\n9-99 744\\n9.99742\\n9.99741\\n9-99 739\\n9-99 738\\n9-99 737\\n9-99 735\\n9-99 734\\n9.99732\\n9-99731\\n9-99730\\n9-99 728\\n9.99727\\n9.99725\\n9.99724\\n9.99723\\n9.99721\\n0.93776\\n0.93 665\\n0.93 554\\n0.93444\\n0.93334\\n0.93 225\\n0.93 115\\n0.93 006\\n0.92 897\\n0.92788\\n0.92 686\\n0.92 572\\n0.92 464\\n0.92357\\n0.92 249\\n0.92 142\\n0.92035\\n0.91 929\\n0.91 822\\n0.91 716\\n0.91 611\\n0.91 505\\n0.91 400\\n0.91 295\\n0.91 190\\n0.91 085\\nLog. Cot*- I c. (1. i Log. Tan.\\n83\\n9.99720\\n9-99 718\\n9.99717\\n9-99715\\n9.99714\\n9.99712\\n9-99 71 1\\n9.99710\\n9-99 708\\n9-99707\\n9.99705\\n9.99 704\\n9-99702\\n9.99701\\n9.99699\\n9.99698\\n9.99696\\n9.99695\\n9-99693\\n9.99692\\n9.99696\\n9.99689\\n9.99687\\n9.99 686\\n9.99684\\n9.99683\\n9.99 681\\n9.99679\\n9.99678\\n999676\\n9-99675\\nLog. Sin.\\n00\\n59\\n58\\n57\\nJi\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n\u00e2\u0096\u00a0^i\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\np. p.\\n121 121 120 119 118\\n6\\n12. 1\\n12.1\\n12.0\\nII. 9\\n7\\n8\\n14.2\\n16.2\\n14.1\\n16. i\\n14.0\\n16.0\\n139\\n15-8\\n9\\n18.2\\n18. i\\n18.0\\n17-8\\n10\\n20.2\\n20. 1\\n20.0\\n19-8\\n20\\n30\\n40\\n40-5\\n60.7\\n81.0\\n40-3\\n60.5\\n80. g\\n40.0\\n60.0\\n80.0\\n39-6\\n59-5\\n79-3\\n50\\n101.2\\n100.\\n100.\\n99.1\\nII\\n7\\n117\\n116\\n6\\nn 7\\nII. 7\\n11.6\\n7\\n13\\n7\\n13-6\\n13-5\\n8\\n15\\n6\\n15-6\\n15-4\\n9\\n17\\n6\\nJ7-5\\n17.4\\n10\\n19\\n6\\n19-5\\n19-3\\n20\\n39\\nI\\n39 -o\\n.38.6\\n30\\n5\u00c2\u00ab\\n7\\n5\u00c2\u00ab-.5\\n58.0\\n40\\n7\u00c2\u00bb\\n3\\n78.0\\n77-3\\n50\\n97\\n9\\n97-5\\n96. g\\n13-7\\n15-7\\n17.7\\n19-6\\n39-3\\n590\\n78. g\\n5\\n\u00e2\u0080\u00a25\\n134\\n15-3\\n17.2\\n19. 1\\n38.3\\n57-5\\n76-6\\n95-8\\n114\\n114\\n113\\n112\\nII\\n6\\n11.4\\nII. 4\\n\u00e2\u0080\u00a23\\nII. 2\\nII.\\n7\\n13-3\\n13-3\\n13.2\\n13.0\\n12.\\nb\\n15.2\\n15.2\\n15.0\\n14.9\\n14.\\n9\\n17.2\\n17. 1\\n16.9\\n16.8\\n16.\\n10\\n19. 1\\n19.0\\n18. H\\n18. g\\n18\\n20\\n38.1\\n38.0\\n37-6\\n37-3\\n37\\n30\\n57-2\\n57-0\\nst -s\\n56.0\\n55\\n40\\n76-3\\n76.0\\n75-3\\n74-6\\n74\\n50\\n95-4\\n95 -o\\n94-1\\n93-3\\n92\\nIIO\\nIIO\\n109\\n6\\nn.o\\nn.o\\n10.9 1\\n7\\n12.9\\n12.8\\n12\\n7\\n8\\n14.7\\n14 6\\n14\\n5\\n9\\n16.6\\n16. s\\n16\\n3\\n10\\n18.4\\n18.3\\n18\\nI\\n20\\n36.8\\n36-6\\n36\\n3\\n30\\n55-2\\n55-0\\n54\\n5\\n40\\n73-6\\n73-3\\n72 6 1\\n50\\n92.1\\n91-6\\n90\\n8 1\\n10^\\n107\\n106\\n105\\n6\\n10.7\\n10.7\\n10.6\\n10.5\\n7\\n12. 5\\n12.5\\n12.3\\n12.2\\n8\\n14-3\\n14.2\\n14. 1\\n14.0\\n9\\n16. 1\\n16\\n15-9\\n15-7\\n10\\n17.9\\n17-8\\n17 6\\n17-5\\n20\\n35-8\\n35-6\\n35-3\\n35-0\\n30\\n53-7\\n53-5\\n53-0\\n52.5\\n40\\n71-6\\n71-3\\n70-6\\n70.0\\n50\\n89.6\\n89.1\\n88.3\\n87-5\\n103\\n103\\n2\\nI\\n6\\n10.3\\n10.3\\n0.2\\n0.1\\n7\\n12\\nI\\n12\\n0.2\\n0.2\\n8\\n13\\n8\\n13\\n7\\n0.2\\n0.2\\n9\\n15\\n5\\n15\\n4\\n0.3\\n0.2\\n10\\n17\\n2\\n17\\nI\\n0-3\\n0.2\\n20\\n34\\n5\\n34\\n3\\n0.6\\n0.5\\n30\\n40\\n50\\n51\\n69\\n86\\n7\\n2\\n51\\n68\\n85\\n5\\n6\\n8\\nI.O\\n1-3\\n1-6\\n0.7\\nI\\n1.2\\n108\\n10.8\\n12.6\\n14.4\\n16.2\\n18.0\\n36.0\\n540\\n72.0\\n90 o\\n104\\n10.4\\n12. I\\n13-8\\n15-6\\n17-3\\n34-g\\n52.0\\n69.3\\n86-6\\nI\\n0.1\\n0.1\\no.i\\no. I\\n0.1\\n0-3\\n0-5\\no.^\\nP. P.\\n354", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0406.jp2"}, "407": {"fulltext": "TABLE VII. -LOGARITHMIC SINES. COSINES, TANGENTS, AND COTANGENTS.\\n10\\nII\\n12\\n14\\ni5\\n16\\n18\\n19\\n20\\n21\\n24\\n26\\n27\\n28\\n^9\\n30\\n31\\n32\\n33\\n34\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nGO\\nLog. Sin. I d.\\n9.08 589\\n9.08 692\\n9.08 794\\n9.08 897\\n9.08 999\\n9.09 lOI\\n9.09 202\\n9.09 303\\n9.09404\\n909 50!\\n9.09 606\\n9.09 706\\n9.09 806\\n9 09 906\\n9 10006\\n9. 10 lO^\\n9. 10 205\\n9. 10 303\\n9. 10 402\\n9. 10 501\\n9.10599\\n9. 10 697\\n9.10795\\n9. 10 892\\n9. 10 990\\n91\\n9-1\\n91\\n9.1\\n91\\n9.1\\n9.1\\n91\\n91\\n9-1\\n087\\n184\\n281\\n37f\\n473\\n570\\n665\\n761\\n856\\n952\\n9. 1 2 047\\n9. 12 14T\\n9. 12 236\\n9.12 330\\n9.12425\\n9 12 518\\n9. 12 612\\n9. 1 2 706\\n9.12 799\\n9. 12 892\\n12985\\n13078\\n13 175\\n13 263\\n13 355\\n9- 1 3 447\\n9 13 538\\n9.13636\\n9.13 721\\n9-13 813\\n9- 1 3 903\\n9- 1 3 994\\n9.14085\\n9- 14 17!\\n9 14265\\n9 14355\\nLog. Cos.\\n99\\n99\\n99\\n98\\n99\\n98\\n98\\n98\\n97\\n97\\n97\\n97\\n96\\n97\\n96\\n96\\n96\\n95\\n96\\n95\\n9S\\n95\\n94\\n94\\n94\\n94\\n93\\n94\\n93\\n93\\n93\\n93\\n92\\n92\\n92\\n92\\n92\\n91\\n92\\n91\\n91\\n90\\n91\\n90\\n90\\n90\\n90\\ndT\\nLog. Tail. I c. d.\\n9.08 914\\n9.090I8\\n9.09 123\\n9.09 226\\n9- 09 330\\n9-09 433\\n909536\\n9.09 639\\n9.09 742\\n9.09 844\\n9.09 947\\n9.10048\\n9.10 150\\n9,10 252\\n9 10353\\n9.10454\\n9- 10 555\\n9. JO 655\\n9.10756\\n9.10 856\\n9. 10 956\\n9. 1 1 055\\n9.11 155\\n9 II 254\\n9ir 353\\n9. 1 1 452\\n9. 1 1 553\\n9. 1 1 649\\n9. 1 1 747\\n9. II 845\\n11 943\\n12 040\\n12 137\\n12 235\\n12 331\\n9.12428\\n9.12 525\\n9. 12 621\\n9. 12 717\\n9.12 813\\n9. 1 2 908\\n9. 1 3 004\\n9. 1 3 099\\n9-13 194\\n9.13289\\n9-13384\\n9-13 478\\n9.13 572\\n9.13665\\n9. 1 3 766\\n9- 13 854\\n9- 1 3 947\\n9. 14 041\\n9-14134\\n9. 14 227\\n9.14319\\n9.14412\\n9.14504\\n9-14 596\\n9-14688\\n9. 14 786\\nLost. Cot.\\n104\\n104\\n103\\n103\\n103\\n103\\n103\\n102\\n102\\n102\\nloi\\n102\\nlOI\\n101\\nlOI\\nlOI\\n100\\n100\\n100\\nlOO\\n99\\n99\\n99\\n99\\n98\\n98\\n98\\n97\\n97\\n97\\n96\\n97\\n96\\n96\\n96\\n96\\n95\\n95\\n95\\n95\\n95\\n94\\n94\\n94\\n94\\n94\\n93\\n93\\n93\\n93\\n93\\n92\\n92\\n92\\n92\\n92\\n92\\nc. d.\\nLot Cot.\\n0.91 085\\n0.90 98!\\n0.90 877\\n0.90773\\n0.90 670\\n0.90 566\\n0.90463\\n0.90 360\\n0.90 258\\n0.90 155\\n0.90053\\n0.89 95T\\n0.89 849\\n0.89 748\\n0.89 647\\n0.89 546\\n0.89445\\n0.89344\\n0.89 244\\n0.89 144\\n0.89 044\\n0.88 944\\n0.88845\\n0.88745\\n0.8 8646\\n0.88 548\\n0.88 449\\n0.88 351\\n0.88 253\\n0.88 155\\n0.88057\\n0.87 959\\n0.87 862\\n0.87 765\\n0.87 668\\n0.87 571\\n0.87475\\n0.87 379\\n0.87 283\\n0.87 187\\n0.87 091\\n0.86 996\\no. 86 906\\n0.86805\\n0.86 716\\n0.86616\\n0.86 521\\n0.86 427\\n0.86333\\n0.86 239\\n0.86 146\\n0.86 052\\n0.85 959\\n0.85 866\\n0.85773\\n0.85 686\\n0.85 588\\n0.85495\\n0.85403\\n0.85 31T\\n85 219\\n\\\\AMi. r.-iii.\\n\\\\Mii. C(\u00c2\u00bbS.\\n9.99675\\n9-99673\\n9.99672\\n9.99676\\n9.99669\\n9.99667\\n9.99665\\n9.99664\\n9.99 662\\n9.99661\\n9-99~65\u00c2\u00a7^\\n9.99658\\n9.99656\\n9.99654\\n9-99653\\n9-99651\\n9.99650\\n9.99648\\n999646\\n9-99645\\n9-99643\\n9-99641\\n9.99640\\n9-99638\\n9-99637\\n9-99635\\n9-99633\\n9.99632\\n9.99630\\n9.99628\\n9.99627\\n9.99625\\n9.99623\\n9.99622\\n9.99 620\\n9.99 6Tf\\n9.99617\\n9-99615\\n9.99613\\n9.99 6 iT\\n9.99 610\\n9-99608\\n9.99606\\n9.99605\\n9-99603\\n9.99 60T\\n9.99 600\\n9-99598\\n9-99 596\\n9-99 594\\n9-99 593\\n9-99 591\\n9-99 589\\n9-99 587\\n9-99 586\\n9.99 584\\n9.99582\\n9.99586\\n9-99 579\\n9 99 577\\n9 99 5/5\\nLoir. Sin.\\n0\\n59\\n58\\n57\\n_56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\nTo\\n9\\n8\\n7\\n6\\n20\\n30\\n40\\n50\\nI I\\n104 103 102 lOI\\n10.4\\n10.3\\n10.2\\n10. 1\\n12 I\\n12.0\\n11.9\\n11.8\\n13-8\\n^3-7\\n13-6\\n13-4\\n15 6\\nI5-4\\n5 3\\n5-1\\n173\\n17.1\\n17.0\\n16 I\\n34-6\\n34-3\\n34\\n33-6\\n52.0\\n693\\n86.6\\n5 -5\\n68.6\\n85-8\\n510\\n68.0\\n85.0\\n50- 5\\n^7-3\\n84.!\\n100\\n100\\n99\\n6\\n10.\\n10.\\n9-9 i\\n7\\nII. 7\\nII. g\\n\u00e2\u0096\u00a05\\n8\\n13-4\\n3-3\\n13.2\\n9\\n10\\n151\\n16.7\\n15.0\\n16.6\\n14-8\\n16.5\\n20\\n33-5\\n33-3\\n33-0\\n30\\n40\\n50\\n50.2\\n67.0\\n83-7\\n50.0\\n66.6\\n83.3\\n49-5\\n66.0\\n82.5\\n98\\n9.8\\nII. 4\\n13.0\\n14.7\\n16.3\\n32-6\\n49.0\\n65.3\\nSi. 6\\n97\\n97\\n96\\n95\\n6\\n9-7\\n9-7\\n9.6\\n9-5\\n7\\nII. 4\\nII. 3\\nII. 2\\n11 1\\n8\\n130\\n12.9\\n12.8\\n12.6\\n9\\n14.6\\n145\\n14.4\\n14\\n2\\n10\\n16.2\\n16. i\\n16.0\\n15\\n20\\n325\\n32 -3\\n32.0\\n31\\n6\\n30\\n48.7\\n48.5\\n48.0\\n47\\n5\\n40\\n65.0\\n64.6\\n64.0\\n63\\n3\\n50\\n81.2\\n80.8\\n80.0\\n79\\nI\\n91\\n91\\n90\\n2\\n6\\n9.1\\n9.1\\n9.0\\n0.2\\n7\\n10.7\\n10.6\\n10.5\\n0.2\\nU\\n12.2\\n12. 1\\n12.0\\n0.2\\n9\\n13-7\\ni3-\u00c2\u00a7\\n3-5\\n0.3\\n10\\n15.2\\n15.1\\nI5-0\\n3\\n20\\n30.5\\n30. 3\\n30.0\\n0.6\\n30\\n45-7\\n45-5\\n45.0\\nI.O\\n40\\n50\\n61 .0\\n76.2\\n60.^\\n75-8\\n60.0\\n75\\n\u00e2\u0096\u00a02\\n\u00c2\u00bb-6\\n0.5\\n0.7\\n94\\n94\\n93\\n92\\n6\\n9.4\\n9-4\\n9-3\\n9.2\\n7\\nII.\\n10.9\\n10\\nR\\n10.7\\n8\\n12.6\\n12-3\\n12\\n4\\n12.2\\n9\\n14.2\\n14.1\\n13\\n9\\n13-8\\n10\\n5-7\\ni5-$\\n15\\n5\\n5-3\\n20\\n3 -5\\n31-3\\n3\\n30 6\\n30\\n47 2\\n47.0\\n46\\nS\\n46.0\\n40\\n63.0\\n62. A\\n62\\n61. 1\\n50\\n78.7\\n78-3\\n77\\n5\\n76.1\\nr. I\\n8*e\u00c2\u00b0\\n355", "height": "4287", "width": "2573", "jp2-path": "railroadconstruc00webb_0407.jp2"}, "408": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS. AND COTANGENTS.\\n8\u00c2\u00b0\\nLog. hill d. Log. Tan.\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n9-H355\\n9.14445\\n9-14 535\\n9. 14 624\\n9-14713\\n9. 14 802\\n9.14891\\n9.14 980\\n9.15068\\n915 157\\n9.15245\\n9-15 333\\n9. 15 421\\n9-15 508\\n9-15595\\n9.15683\\n9.15770\\n9.15857\\n9-15 943\\n9. 16 030\\n9.16 116\\n9.16 202\\n9.16 283\\n9.16374\\n9. 1 6 460\\n9.16545\\n9.16 630\\n9.16 716\\n9.16 801\\n9.16885\\n9.16 970\\n9.17054\\n9.17 139\\n9.17 223\\n9.17307\\n9.17 391\\n9 17474\\n9.17558\\n9-17641\\n9.17724\\n9.17 807\\n9.17 890\\n9.17972\\n9.18055\\n9.18 137\\n9. 18 219\\n9.18 301\\n9.18383\\n9.18465\\n9.18 546\\n9.18628\\n9. 1 8 709\\n9. 1 8 790\\n9.18 871\\n9.18 952\\n9. 19032\\n9.19113\\n9.19 193\\n9 19273\\n9-19353\\n9-19433\\nLog. Cos.\\n90\\n89\\n89\\n89\\n89\\n89\\n88\\n88\\n88\\n88\\n87\\nS?\\n87\\n87\\n87\\n86\\n86\\n86\\n86\\n86\\n86\\n85\\n85\\n85\\n85\\n85\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n83\\n83\\n83\\n83\\n83\\n83\\n82\\n82\\n82\\n82\\n82\\n82\\n81\\n81\\n81\\n81\\n81\\n80\\n81\\n80\\n86\\n80\\n80\\n80\\n79\\n9.14 780\\n9.14872\\n9.14963\\n9.15054\\n9.15 145\\n9-15236\\n9.15327\\n9-15417\\n9.15 507\\n9.15 598\\n9.15687\\n9-1577?\\n9.15867\\n9-15 956\\n9.16045\\nc. d.\\n16 134\\n16 223\\n16 312\\n16 401\\n16 489\\n9 16577\\n9.16665\\n9.16753\\n9. 16 841\\n9.16928\\n17015\\n17 103\\n17 190\\n17276\\n17363\\n9-\\n9-\\n9-\\n9-\\n9:\\n9.17450\\n9.17 536\\n9.17 622\\n9.17708\\n9 17794\\n9 17880\\n9.17965\\n9. 18 051\\n9.18 136\\n9. 18 221\\n9. 1 8 306\\n9.18 390\\n9-18475\\n9.18559\\n9. 1 8 644\\n9-\\n18728\\n9.\\n18812\\n9-\\n18896\\n9-\\n18979\\n9-\\n19063\\n9-\\n19 146\\n9-\\n19 229\\n9-\\n19312\\n9-\\n19395\\n9-\\n19478\\n9-\\n19 566\\n9-\\n19643\\n9-\\n19725\\n9-\\n1980^\\n9-\\n19889\\n9. 19 971\\n91\\n91\\n91\\n91\\n91\\n96\\n96\\n90\\n90\\n89\\n90\\n89\\n89\\n89\\n89\\n89\\n89\\n88\\n87\\n88\\n87\\nS7\\n87\\n87\\n86\\n87\\n86\\n86\\n86\\n86\\n85\\n86\\n85\\n85\\n85\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n83\\n83\\n83\\n83\\n83\\n83\\n82\\n82\\n82\\n82\\n82\\n82\\n82\\nLog Cot. I c. d.\\ntiog. Cot.\\n0.85 219\\n0.85 128\\n0.85037\\n0.84945\\n0.84854\\n0.84763\\n0.84673\\n0.84582\\n0.84492\\n0.84 402\\n0.84 312\\n0.84 222\\n0.84 133\\no. 84 043\\n0-83954\\n0.83865\\n0.83776\\n0.83687\\n0-83 599\\n0.83 511\\n0.83 422\\n0.83334\\n0.83 247\\n0.83 159\\n0.83 071\\n0.82 984\\n0.82 897\\n0.82 810\\n0.82 723\\n0.82636\\n0.82 550\\n0.82 464\\n0.82 377\\n0.82 291\\n0.82 206\\n0.82 120\\n0.82 034\\n0.81 949\\n0.81 864\\n0.81 779\\n0.81 694\\n0.81 609\\n0.81 525\\n0.81 446\\n0.81 356\\n0.81 272\\n0.81 188\\n0.81 104\\n0.81 026\\n0.80937\\n0.80 854\\n0.80 770\\n0.80687\\no. 80 604\\n0.80 522\\n0.80439\\n0.80357\\n0.80 274\\n0.80 192\\n0.80 II 6\\n0.80 023\\nJiOg. Tan.\\n81\\nLog. Cos.\\n9-99 575\\n9-99 ^7%\\n9.99 371\\n9.99 570\\n9-99 568\\n9.99 566\\n9-99564\\n9-99563\\n9.99561\\n9-99 559\\n9-99 55?\\n9-99 555\\n9-99 553\\n9.99552\\n9.99550\\n9-99 548\\n9-99 546\\n9-99 544\\n9-99 542\\n9.99541\\n9-99 539\\n9-99 537\\n9-99 535\\n9-99 533\\n9-99 531\\n9-99 529\\n9.99528\\n9.99526\\n9-99 524\\n9.99522\\n9.99520\\n9-99 518\\n9-99 516\\n9.99514\\n9.99512\\n9-99 511\\n9-99 509\\n9-99 507\\n9-99 505\\n9-99 503\\n9-99 501\\n9.99499\\n9-99 497\\n9.99495\\n9-99 493\\n9.99491\\n9.99489\\n9.99487\\n9.99485\\n9.99484\\n9.99482\\n9-99480\\n9.99478\\n9-99476\\n9-99 474\\n9.99472\\n9.99470\\n9-99468\\n9.99466\\n9.99464\\n9.9946:\\nLog. Sin.\\n60\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\nTo\\n9\\np. p.\\n91\\n91\\n90\\n89\\n6\\n9.1\\n9-1\\n9-0\\n8.9\\n7\\n10.7\\n10.6\\n10.5\\n10.4\\n8\\n12.2\\n12.T\\n12.0\\nII. 8\\n9\\n13.7\\n13-6\\n13-5\\n13-3\\n10\\n15.2\\n1 5. 1\\n15.0\\n14-8\\n20\\n30.5\\n30.3\\n30.0\\n29.6\\n30\\n45-7\\n45-5\\n45.0\\n44-5\\n40\\n61.0\\n60.6\\n60.0\\n^9\\n50\\n76.2\\n75-8\\n75.0\\n74-1\\n88\\n88\\n87\\n6\\n8.8\\n8.8\\n8.7\\n7\\n10. s\\n10.2\\n10. 1\\n8\\n11.8\\nII.?\\nII. 6\\n9\\n13-3\\n1.3-2\\n13.0\\n10\\n14-7\\n14-6\\n14.5\\n20\\n29.5\\n29-3\\n29.0\\n30\\n44-2\\n44-0\\n43-5\\n40\\n59.0\\n58-6\\n58.0\\n50\\n73-1\\n73-3\\n72.5\\n85\\n85\\n84\\n6\\n8.5\\n8.5\\n8.4\\n7\\nlO.O\\n9-9\\n9.8\\n8\\n11.4\\n1 1-3\\nII. 2\\n9\\n12.8\\n12.?\\n12.6\\n10\\n14.2\\n14. 1\\n14.0\\n20\\n28.5\\n28.3\\n28.0\\n30\\n42.?\\n42.5\\n42.0\\n40\\n57.0\\n56-6\\n56.0\\n50\\n71.2\\n70.8\\n70.0\\n82\\n82\\n81\\n6\\n8.2\\n8.2\\n8.1\\n7\\n9.6\\n9.5\\n9.4\\n8\\nII.\\n10.9\\n10.8\\n9\\n12.4\\n12.3\\nI2\u00e2\u0080\u009eI\\n10\\n13-7\\n13-6\\n13-5\\n20\\n27.5\\n27-3\\n27.0\\n30\\n41.2\\n41.0\\n40.5\\n40\\n55.0\\n54 6\\n54.0\\n50\\n68.^\\n68.3\\n67.5\\n86\\n8.6\\n10.6\\nII. 4\\n12.9\\n14-3\\n28.6\\n43-0\\n57-3\\n71.6\\n83\\n8.3\\n9-7\\nII. o\\n12.4\\n13-8\\n27-6\\n41.5\\n55-3\\n69.1\\n80\\n8.0\\n9-3\\n10.6\\n12.0\\n13-3\\n26.6\\n40.0\\n53-3\\n66.6\\n10\\n20\\n30\\n40\\n50\\n79\\n7-9\\n9-3\\n10.6\\nII. 9\\n13.2\\n26.5\\n39-?\\n53.0\\n66.2\\n2\\n0.2\\n0.2\\n0.2\\n0.3\\n0-3\\n0.6\\ni.o\\n1-3\\n1-6\\nI\\no. I\\n0.2\\n0.2\\n0.2\\n0.2\\n0.5\\no.?\\n1.0\\n1.2\\nP.P.\\ni\\n356", "height": "4287", "width": "2598", "jp2-path": "railroadconstruc00webb_0408.jp2"}, "409": {"fulltext": "TAP LE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANCiENTS.\\n9\u00c2\u00b0\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\nL nf. Sin.\\nd.\\n^9 433\\n19513\\n19592\\n19672\\n19751\\n19 830\\n19909\\n19988\\n20065\\n20 145\\n20 22\\n20 301\\n20379\\n20457\\n20 533\\n20 613\\n20690\\n20 768\\n20845\\n20 922\\n20 999\\n21 076\\n21 152\\n21 229\\n21 303\\n21 382\\n21 458\\n21 534\\n21 6oq\\n21 685\\n761\\n836\\n911\\n987\\n062\\n136\\n211\\n286\\n360\\n435\\n509\\n583\\n657\\n731\\n805\\n878\\n952\\n025\\n098\\n17T\\n244\\n317\\n390\\n462\\n535\\n607\\n679\\n751\\n823\\n89S\\n9.23967\\n80\\n79\\n79\\n79\\n79\\n79\\n79\\n78\\n78\\n78\\n78\\n78\\n7S\\n78\\n77\\n77\\n71\\n77\\n77\\n77\\n77\\n76\\n76\\n76\\n76\\n76\\n^6\\n71\\n76\\n75\\n75\\n75\\n7l\\n75\\n74\\n75\\n74\\n7-+\\n74\\n74\\n74\\n74\\n73\\n74\\n73\\n73\\n73\\n73\\n73\\n73\\n72\\n73\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n71\\nLo?. Tan. 0. d. I Loir. df.\\nLog. Cos.\\nd.\\nI9971\\n20053\\n20 134\\n20 216\\n.20 297\\n.20 378\\n20459\\n20 540\\n20 626\\n20 701\\n20 781\\n20862\\n20942\\n022\\n102\\n181\\n261\\n340\\n420\\n499\\n578\\n657\\n73?\\n814\\n892\\n21 971\\n22 049\\n22 127\\n22 205\\n22 283\\n22 366\\n22 438\\n22.515\\n22 593\\n22 670\\n22747\\n22 824\\n22 900\\n22 977\\n23054\\n23 130\\n23 206\\n23 282\\n23 358\\n23434\\n23 510\\n23586\\n23 661\\n23737\\n23 812\\n23 887\\n23 962\\n24037\\n24 112\\n24 185\\n24 261\\n24335\\n24409\\n24484\\n24558\\n24632\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n86\\n81\\n80\\n86\\n80\\n80\\n80\\n79\\n79\\n79\\n79\\n79\\n79\\n79\\n78\\n78\\n7^\\n78\\n7^\\n78\\n78\\n7^\\n71\\n71\\n71\\n71\\n77\\n77\\n77\\n76\\n77\\n76\\n76\\n76\\n76\\n76\\n76\\n7^\\n7%\\n71\\n7l\\n75\\n75\\n75\\n75\\n75\\n74\\n74\\n74\\n74\\n74\\n74\\n74\\n0.80 02J^\\n0.79947\\n0.79865\\n0.79784\\n0.79703\\n0.79 622\\n0.79541\\n0.79 460\\n0.79379\\n0.79298\\n0.79213\\n0.79 138\\n0.79058\\n0.78978\\n0.78898\\n0.78 ^l^\\n0.78739\\n0.78 659\\n0.78 580\\n0.78 501\\n0.78 422\\n0.78 343\\n0.78 264\\n0.78 186\\n0.78 107\\n0.78 029\\n0.77 951\\n0.77 873\\n0.77 795\\n0.77 717\\n0.77 639\\n0.77 562\\n0.77 484\\n0.77 407\\n0-77 330\\n0.77 253\\n0.77 176\\n0.77099\\n0.77 022\\no. 76 946\\n0.76 870\\n0.76 793\\n0.76 71^\\n0.76641\\n0.76 565\\n0.76 489\\n0.76414\\n0.76338\\n0.76 263\\n0.76 188\\n0.76 113\\n0.76 038\\n0.75963\\n0.75888\\n0.75813\\n0-75 739\\n0.75 664\\n0.75 596\\n0.75 516\\n0.75442\\n0.75 368\\noer. Cot. c. d. Lojf. Tiin.\\nidtf. Cos.\\n99 462\\n99 460\\n99458\\n99456\\n99 454\\n99452\\n99450\\n99448\\n99 446\\n99 444\\n99442\\n99440\\n99:437\\n99 435\\n99 433\\n99431\\n99429\\n99427\\n99425\\n99423\\n99421\\n99419\\n99417\\n99415\\n9 9413\\n99 41 1\\n99408\\n99406\\n99404\\n99 402\\n99 400\\n99398\\n99 396\\n99 394\\n99392\\n99389\\n99387\\n99385\\n99 383\\n99381\\n99 379\\n99 377\\n99 374\\n99372\\n99370\\n99 368\\n99 366\\n99364\\n99361\\n99 359\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9-99 335\\n99 357\\n99 355\\n99 353\\n99350\\n99 348\\n99346\\n99 344\\n99 342\\n99 339\\n99 33?\\nL(\u00c2\u00bb r. Sin.\\n0\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\nJ6\\n45\\n44\\n43\\n42\\n41\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n9\\n8\\n7\\n6\\nI r\\n81\\n81\\n80\\n6\\n8.1\\n8.1\\n8.0\\n7\\n8\\n9-5\\n10.8\\n9-4\\n10.8\\n9 3\\n10.6\\n9\\n12.2\\n12.1\\n12. ol\\n10\\n20\\n13.6\\n27.1\\n135\\n27.0\\n13.3I\\n26.6 i\\n30\\n40.7\\n40.5\\n40.0\\n40\\n50\\n54-3\\n67.9\\n54.0\\n67.5\\n53-3\\n66.6\\n79\\n7-9\\n9.2\\n10.\\nII. 8\\nI3-J\\n26.3\\n39-5\\n52.6\\n65-8\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n78\\n7-8\\n9- 1\\n10.4\\nII. 8\\n131\\n26. T\\n39-2\\n52.3\\n65.4\\n78\\n7-8\\n9.1\\n10.4\\nII. 7\\n13.0\\n26.0\\n390\\n52.0\\n65.0\\n77\\n7-7\\n9.0\\n10.2\\nII. 5\\n12.8\\n25-6\\n38.5\\n51.3\\n64. T\\n76\\n8\\n9\\n10\\n20\\n30\\n40\\n7\\n8\\n6\\n9\\n10\\n2\\n1 1\\n5\\n12\\n7i\\n25\\n38\\n5!\\n2\\n51\\n63\\n1.\\n76\\n7.6\\n8.8\\n10. T\\nII. 4\\n12.6\\n25-3\\n38.0\\n50.6\\n63- 3\\n75\\n7-5;\\n8.^1\\n10. o!\\n1 1.2\\n12.5\\n25.0\\n37-5\\n74\\n7-4\\n8.6\\n98\\n1 1. 1\\n12.3\\n24-6\\n37-0\\n73\\n73\\n6\\n7-3\\n7-3,\\n7\\n8.6\\n8.5!\\n8\\n9.8\\n9-7\\n9\\nII.\\n10.9\\n10\\n12.2\\n12. T\\n20\\n24.5\\n24-3\\n30\\n36.7\\n36.5\\n40\\n49.0\\n48.6\\n50\\n61.2\\n60.8\\n50.0 49.3\\n62.5 61.6\\n72\\n7.2\\n8.4\\n9.6\\n10.8\\n12.0\\n24.0\\n36.0\\n48.0\\n60.0\\nn\\n71\\n5\\n2\\n6\\n7-1\\n71\\n0.2\\n0.2\\n7\\n8. .3\\n8.3\\n03\\n0.2\\n8\\n9.5\\n9.4\\n0.3\\n0.2\\n9\\n10.7\\n106\\n0.4\\n0.3\\n10\\nII. 9\\nII. 8\\n0.4\\n03\\n20\\n23-8\\n23-6\\n0.8\\n0.6\\n30\\n35.7\\n35-5\\n1.2\\nI.O\\n40\\n47-6\\n47.3\\n\u00e2\u0080\u00a26\\n1-3\\n50\\n59.6\\n59.1\\n2.1\\n1-6\\nr. i*.\\n80\\n357", "height": "4287", "width": "2598", "jp2-path": "railroadconstruc00webb_0409.jp2"}, "410": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n10\u00c2\u00b0\\nLog. Sin. d.\\n9.23967\\n9.24 038\\n9.24 1 10\\n9.24 181\\n9.24 252\\n9-24323\\n9.24394\\n9.24465\\n9.24536\\n9.24 607\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n9.24677\\n9.24748\\n9.24818\\n9.24888\\n9-24 958\\n9.25 028\\n9.25 098\\n9.25 167\\n9.25237\\n9 25 306\\n20\\n21\\n22\\n23\\n24\\n26\\n27\\n28\\n2Q\\n9.25 376\\n9.25443\\n9.25514\\n9-25 583\\n9 25652\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n9.25 721\\n9.25790\\n925858\\n9.25927\\n9-25 995\\n9.26 063\\n9 26 13T\\n9 26 199\\n9.26 267\\n9-26335\\n9. 26 402\\n9.26470\\n9.26 537\\n9. 26 605\\n9.26 672\\n9.26739\\n9.26 805\\n9-26873\\n9 26 940\\n9.27 007\\n9.27073\\n9.27 140\\n9-27205\\n9.27 272\\n9-27 339\\n9.27405\\n9.27471\\n9-27 536\\n9.27 602\\n9.27668\\n9-27 733\\n9-27 799\\n9.27 S64\\n9-27 929\\n9.27995\\n9.28 060\\nLog. Cos.\\n71\\n7t\\n71\\n71\\n71\\n71\\n71\\n71\\n70\\n70\\n70\\n70\\n76\\n70\\n69\\n70\\n69\\n70\\n69\\n69\\n69\\n69\\n69\\n69\\n6q\\n6\u00c2\u00a7\\n68\\n68\\n68\\n68\\n68\\n67\\n^1\\n68\\n67\\n67\\n67\\n(^1\\n67\\n^1\\n66\\n67\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n65\\n66\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\nLog. Tan.\\n9.24632\\n9.24705\\n9.24779\\n9.24853\\n9.24925\\n9.25 000\\n9.25073\\n9.25 146\\n9.25 219\\n9.25 292\\n9.25 365\\n9-25437\\n9.25 510\\n9.25 582\\n9.25654\\nd.\\n9-25 727\\n9-25799\\n9.25871\\n9.25 943\\n9.26 014\\n9. 26 085\\n9.26 158\\n9.26 229\\n9. 26 300\\n9 26 371\\n9-26443\\n9.26514\\n9.26 584\\n9.26 655\\n9.26 726\\n9.26 795\\n9.26 867\\n9.26 93f\\n9.27 007\\n9.27 078\\n9.27 148\\n9.27 218\\n9.27 287\\n9-27 357\\n9.27427\\n9.27495\\n9.27 566\\n9-27635\\n9.27704\\n9-27 773\\n9.27 842\\n9.27 91T\\n9.27 9S0\\n9. 28 049\\n9.28 117\\n9.28 186\\n9.28254\\n9.28 322\\n9.28 390\\n9 28459\\n9.28 527\\n9.28 594\\n9.28 662\\n9.28 730\\n9.28 79f\\n9.28865\\nLog. Cot.\\njc^d^\\n73\\n74\\n73\\n73\\n73\\n11\\n73\\n7j\\n7Z\\n73\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n71\\n72\\n71\\n71\\n7?\\nn\\n71\\n71\\n70\\n71\\n70\\n70\\n70\\n70\\n70\\n70\\n70\\n70\\n69\\n70\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n68\\n69\\n68\\n68\\n6Z\\n68\\n68\\n68\\n68\\n67\\n6Z\\n^7\\nLog. Cot.\\n0.75 368\\n0.75294\\n0.75 220\\n0.75 147\\n0.75073\\n0.75 000\\n0.74927\\n0.74854\\n0.74781\\n0.74708\\n0.74635\\n0.74 562\\n0.74490\\n0.74417\\n0.7434!\\n0.74273\\n0.74 201\\n0.74 129\\n0.74057\\n0.73985\\n0-73913\\n0.73 842\\n0.73 771\\n0.73 699\\n0.73628\\n0.73 557\\n0.73486\\n0.73415\\n0.73344\\n0.73274\\n0.73 203\\n0.73 J33\\n0.73 062\\n0.72 992\\n0.72 922\\n0.72 852\\n0.72 782\\n0.72 712\\n0.72 642\\n0.72 573\\n0.72 503\\n0.72434\\n0.72 365\\n0.72 295\\n0.72 225\\n0.72 157\\n0.72 088\\n0.72 020\\n0.71 951\\n0.71 882\\n0.71 814\\n0.71 746\\n0.71 677\\n0.71 609\\n0.71 541\\n0.71 473\\n0.71 405\\n0.71 337\\n0.71 270\\n0.71 202\\n0.71 135\\nc. d. I Log. Tan.\\nLog. Cos.\\n9-99 335\\n9-99 333\\n9-99330\\n9-99 328\\n9.99326\\n9.99324\\n9.99321\\n9-99319\\n9-99317\\n9-99315\\n9.99312\\n9.99316\\n9.99308\\n9.99 306\\n9-99303\\n9.99301\\n9.99299\\n9.99295\\n9.99294\\n9.99292\\n9.99290\\n9.99287\\n9.99285\\n9.99283\\n9.99 280\\n9.99278\\n9-99276\\n9.99273\\n9.99271\\n9.99269\\n9.99265\\n9.99264\\n9.99 262\\n9.99259\\n9.99257\\n9.99255\\n9.99252\\n9.99250\\n9.99248\\n9.99245\\n9.99243\\n9.99 246\\n9.99238\\n9.99236\\n9-99233\\n9.99231\\n9.99228\\n9.99225\\n9.99224\\n9.99 221\\n9-99219\\n9-99 216\\n9-99214\\n9.99 212\\n9.99209\\n9.99207\\n9.99204\\n9 99 202\\n9-99 199\\n9-99 197\\n9 99 194\\n00\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n\u00e2\u0080\u00a234\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\np. p.\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\nLog. Sin.\\n74\\n6\\n7.4\\n7\\n8.6\\n8\\n98\\n9\\nII. I\\n10\\n12.3\\n20\\n24 6\\n30\\n37.0\\n40\\n49-3\\n50\\n61.6\\n73\\n7-1\\n8.6\\n9.8\\nII. o\\n12.2\\n24.5\\n36.7\\n49.0\\n61.2\\n73\\n7.3\\n5\\n7\\n9\\nI\\n3\\n5\\n6\\n9\\n10\\n12\\n24\\n36\\n48\\n60\\n72\\n72\\n7\\nI\\n7\\n6\\n7.2\\n7.2\\n7-1\\n7.\\n7\\n8.4\\n8.4\\n8\\n3\\n8.\\n8\\n9-6\\n9.6\\n9\\nI\\n9-\\n9\\n10.9\\n10.8\\n10\\n7\\n10.\\n10\\n12. 1\\n12.0\\nII\\n9\\nII.\\n20\\n24.1\\n24.0\\n23\\n8\\n23-\\n30\\n36.2\\n36.0\\n35\\n7\\n35-\\n40\\n48.3\\n48.0\\n47\\n6\\n47.\\n50\\n60.4\\n60.0\\n59\\n6\\n59-\\n6\\n7.6\\n7-0\\n6.9 j\\n7\\n8.2\\n8.1\\n8.1\\n8\\n9-4\\n9-3\\n9.2\\n9\\n10.6\\n10.5\\n10.4\\n10\\n11.^\\n11.6\\n11.6\\n20\\n23.5\\n23.3\\n23.T\\n30\\n35-2\\n35-0\\n34-7\\n40\\n47.0\\n46.5\\n46.3;\\n50\\n58.^\\n58.3\\n57-91\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n70\\n7-\\n8.\\n9.,\\n0.1\\nI.\\n,5.:\\n7-\\n8.\\n68\\n6.8\\n8.0\\n9.1\\n10.3\\nII. 4\\n22.8\\n34.2\\n45-6\\n57.1\\n68\\n70\\n7-\\n8.\\n9-\\no.\\ni.(\\n3-\\n5-\\n.6.,\\n8.,\\n68\\n6.S\\n7-9\\n9.6\\n10.2\\n11-3\\n22-6\\n34-0\\n45-3\\n56.6\\n66\\ne\\n7\\nc\\nc\\nc\\n,c\\nc\\nc\\n2\\n69\\n6.C\\n8.]\\n9.:\\no.z\\nI.(\\n53.1\\n14-^\\n.6.1\\n\\\\7-l\\n6^\\n6.^\\n7-9\\n9.0\\n10. 1\\n11. 2\\n22.5\\n33-^\\n45.0\\nc6.2\\n6S\\n6\\n7\\n8\\n6.6\\n7.1\\n8.8\\n6.6\\n7-7\\n8.8\\n6.5\\n7-6\\n8.^\\n6.\\n7-\\n8.\\n9\\n10\\nlO.O\\n11. 1\\n9.9\\nII.\\n9.8\\n10.9\\n9.\\n10.\\n20\\n22.1\\n22.0\\n21.8\\n21.\\n30\\n40\\n50\\n33-2\\n44- S\\n55-4\\n33-0\\n44-0\\n55.0\\n32-^\\n43-6\\n54.6\\n32.\\n43.\\n54-\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n2\\n3\\n3\\n4\\n4\\n8\\nI\\n2\\n1\\n6\\n2.\\nI\\n2\\n0.2\\n0,2\\n0.2\\n0.3\\n0.3\\n0.6\\nI.O\\n1-3\\n1-6\\n6\\n5\\n3\\nI\\n69\\n6.9\\n8.6\\n9.2\\n10.3\\nII. 5\\n23.0\\n34-5\\n46.0\\n57-5\\n67\\n6.7\\n7.Z\\n8.9\\n10.6\\nII. I\\n22.3\\n33-5\\n44-6\\n55-8\\n65\\n5\\n6\\n6\\n7\\n8\\n6\\n5\\n3\\nI\\nP. P.\\n79\\n358", "height": "4287", "width": "2598", "jp2-path": "railroadconstruc00webb_0410.jp2"}, "411": {"fulltext": "T\\\\HLE VII. LOGARITHMIC SINES, COSINES. TANGENTS. AND COTANGENTS.\\n11\u00c2\u00b0\\n10\\n1 1\\n12\\n14\\n15\\ni6\\n17\\n19\\n20\\n21\\n-J\\n^4\\n26\\n-7\\n28\\n-9\\nao\\n34\\nJ3\\n36\\n37\\n38\\n39\\n10\\n41\\n42\\n43\\n44\\n-15\\n46\\n47\\n4S\\n49\\n0\\n51\\n52\\n34\\n55\\n56\\nS7\\n58\\n0\\nLotf. sill.\\n\u00e2\u0080\u00a2I.\\n28 060\\n28 125\\n28 189\\n28254\\n28 319\\n28383\\n28448\\n28 512\\n28576\\n28641\\n703\\n769\\n832\\n896\\n960\\n29\\n29\\n29\\n29\\n29\\n087\\n156\\n213\\n277\\n29340\\n29403\\n29 466\\n29528\\n29591\\n29654\\n29716\\n29779\\n29841\\n29903\\n29963\\n30027\\n33089\\n30 151\\n30213\\n30275\\n30336\\n30398\\n30459\\no ;2o\\n30582\\n30643\\n30704\\n30765\\n30 826\\n30886\\n30947\\n31 008\\n068\\n129\\n189\\n249\\n309\\n370\\n429\\n489\\n549\\n609\\n669\\n728\\nLost. Cos.\\n65\\n64\\n65\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n63\\n64\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n62\\n63\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n61\\n62\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n60\\n6r\\n60\\n65\\n60\\n60\\n60\\n60\\n60\\n59\\n60\\n60\\n59\\n60\\n59\\n59\\nd7\\nLoff. Tiiii. c. (1. 1 Loir. int. Lotr. Cos\\n28 865\\n28932\\n29 000\\n29 067\\n29 134\\n29 201\\n29 268\\n29 jj:)\\n29401\\n29468\\n29535\\n29 601\\n29 667\\n29734\\n29 800\\n29866\\n29932\\n29998\\n30064\\n30 129\\n30195\\n30 260\\n30326\\n30391\\n30456\\n30 522\\n30587\\n30652\\n30717\\n30781\\n30846\\n30 91 1\\n30975\\n040\\n104\\n168\\n232\\n297\\n361\\n424\\n488\\n552\\n616\\n679\\n743\\n806\\n869\\n933\\n996\\n32059\\n-32 I 22\\n32185\\n32 248\\n32310\\n32 373\\n32436\\n32498\\n32 566\\n32 623\\n32 68g\\n9-3274^\\nLoir. Cot.\\n67\\n67\\n67\\n67\\n67\\n66\\n67\\n66\\n67\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n64\\n65\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n63\\n64\\n64\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n62\\n63\\n62\\n62\\n62\\n62\\n62\\n62\\n77T\\n71 135\\n71 067\\n71 000\\n70933\\n70 866\\n70798\\n70732\\n70 665\\n70 598\\n70531\\n70465\\n70398\\n70332\\n70 266\\n70 200\\n70134\\n70068\\n70 002\\n69936\\n69 870\\n69 805\\n69739\\n69674\\n69 608\\n69 543\\n69478\\n69413\\n69348\\n69 283\\n69 218\\n69 153\\n69 089\\n69 024\\n68960\\n68896\\n68831\\n68767\\n68703\\n68639\\n68575\\n68 511\\n68447\\n68384\\n68 326\\n68257\\n68 193\\n68 136\\n,68067\\n.68 004\\n\u00e2\u0080\u00a267 941\\n.67 878\\n67815\\n67752\\n67689\\n67 626\\n.67 564\\n.67 501\\n67 439\\n\u00e2\u0080\u00a267 377\\n67 314\\n67 252\\notr. Tan.\\n9-99\\n9.99\\n9-99\\n9.99\\n9.99\\n9.99098\\n9 99 096\\n9.99093\\n9.99091\\n9.99088\\n9.99085\\n9-99083\\n9.99086\\n9.99077\\n9.99075\\n9.99072\\n9-99069\\n9.99067\\n9.99064\\n9.99062\\n9.99059\\n9.99056\\n9.99054\\n9.99051\\n9-99 04 8\\n9.99046\\n999043\\n9.99046\\nI,ou sin.\\n1 1\\n21\\n20\\n19\\n18\\n17\\n16\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n6g\\n6\\n6.6\\n7\\n8\\n7-f\\n8.8\\n9\\nlO.O\\n10\\nII. I\\n20\\n22.1\\n30\\n33-2\\n40\\n44-3\\n50\\n55-4\\n64\\n6\\n6.4\\n7\\n8\\n7-5\\n8.6\\n9\\n9-7\\n10\\n10.7\\n20\\n21.5\\n30\\n32.2\\n40\\n43-0\\n30\\n53-7\\n62\\n6\\n6.2\\n7\\n8\\n7-3\\n8.3\\n9\\n94\\n10\\n10.4\\n20\\n20.8\\n30\\n31.2\\n40\\n41.6\\n50\\n52.1\\n67\\n7-9\\n9.0\\n10.1 i\\n11. 2\\n22.\\n337\\n45-0\\n56.2\\n66\\n6.6\\n7-7\\n8.8\\n67\\n6.7\\n7.8\\n8.9\\nlo.o\\nII. T\\n22.3\\n33-5\\n44.6\\n55-8\\n65\\n6\\n9.9\\nII. o\\n22.0\\n330\\n44.0\\n55.0\\n64\\n6\\n4\\n6.3\\n7\\n4\\n7-4\\n8\\n5\\n8.4\\n9\\n6\\n9-5\\n10\\n6\\n10.6\\n21\\n3\\n21. 1\\n32\\n31-7\\n42\\n6\\n42.3\\n53\\nJ\\n52.9\\n62\\n6.2\\n7.2\\n8.2\\n9.3\\n10.3\\n20.6\\n31.0\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n41\\n51\\n66\\n6.6\\n7.6\\n8.6\\n9.1\\n10. 1\\n20. T\\n30.2\\n40.3\\n50.4\\n3\\n9\\n10\\n21\\n32\\n43\\n54\\n63\\n6.;\\n7-\\n8..\\n9-:\\no.(\\nI.\\nI.!\\n2.\\n2.(\\n61\\n6.1\\n7.2\\n8.2\\n9-2\\n10.2\\n20.5\\n30- 7\\n41.0\\n51.2\\n60\\n6.0\\n7.0\\n8.0\\n9.0\\n1 0.0\\n20.0\\n30.0\\n40.0\\n50.0\\n2\\n65\\n6.5\\n7\\n8\\n9\\n10\\n21\\n32\\n43\\n54.\\n63\\n6.3\\n7.3\\n8.4\\n9-4\\n10.5\\n21.0\\n31-5\\n42.0\\n52.5\\n61\\n6.1\\n7-1\\n8.T\\n9.1\\n10. 1\\n20.3\\n30.5\\n40.6\\n50-8\\n59\\n5-9\\n9\\n9\\n9\\n9\\n8\\n7\\n6\\n6\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n0-3\\n0.2\\n0.3\\n0.3\\n0.4\\n0-3\\n0.4\\n0.4\\n0.5\\n0.4\\nI.O\\n0.8\\n1-5\\n1.2\\n2.0\\n1-6\\n2.5\\n2.1\\n0.2\\n0.2\\n0.2\\n03\\n0.3\\n0-6\\n1.0\\n1-3\\n1-6\\nv. I\\n78\\n359", "height": "4287", "width": "2598", "jp2-path": "railroadconstruc00webb_0411.jp2"}, "412": {"fulltext": "TABLE VII.\u00e2\u0080\u0094\\nLOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS\\n12\u00c2\u00b0\\n10\\nII\\n12\\n13\\n14\\nliOic. Sin.\\n9.31 788\\n9-31 847\\n9 3 1 906\\n9.31 966\\n9.32025\\n9.32084\\n9-32 143\\n9.32 202\\n9.32 260\\n9-32 319\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n9-32378\\n9-32 436\\n9-32495\\n9-32553\\n9.32611\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n9.32670\\n9.32 728\\n9.32 7^6\\n9.32844\\n9.32 902\\n9.32 960\\n9-33017\\n9-3307?\\n9-33 133\\n9-33 190\\n9-33248\\n9-33 305\\n9-33 362\\n9-33419\\n9-33 476\\n35\\n36\\n37\\n3S\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nGO\\n9-33 533\\n9-33590\\n9-3364?\\n9-33704\\n9-33761\\n9-3381?\\n9-33874\\n933930\\n9-33 9S7\\n9- 34 043\\n9.34099\\n9.34156\\n9.34212\\n9.34268\\n9-34324\\n9-34 379\\n9-34 435\\n9-34 491\\n9-34 547\\n9. 34 602\\n9.34658\\n9-34713\\n9-34768\\n9.34824\\n9-34879\\n9-34 934\\n9-34989\\n9-35044\\n9-35099\\n9-35 154\\n9.35 209\\nLog.jCos,\\nd.\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n58\\n59\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n57\\n58\\n57\\n57\\n5?\\n57\\n57\\n57\\n57\\n57\\n57\\n57\\n57\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\nSi\\n56\\n5?\\n56\\nSi\\n5?\\n5?\\n55\\n55\\n55\\n55\\n55\\n55\\n54\\n55\\n55\\nLog. Tail.\\n9-32747\\n9,32 809\\n9.32871\\n9-32933\\n9-32995\\n9-33057\\n9-33 118\\n9.33 186\\n9-33242\\n9-33303\\nc. d.\\n9-33364\\n9-33426\\n9-33487\\n9-33548\\n9.33609\\n9.33670\\n9-33731\\n9-33792\\n9-33852\\n9-33913\\n9-33 974\\n9-34034\\n9-34095\\n9-34155\\n9-34215\\n9-34275\\n9-34336\\n9-34396\\n9-34456\\n9-34515\\n9-34 575\\n9-34635\\n9-34695\\n9-34 754\\n9.34814\\n9-34873\\n9-34 933\\n9. 34 992\\n9-35051\\n9-35 I TO\\n9-35 169\\n9-35 228\\n9.35287\\n9-35 346\\n9-35405\\n9-35464\\n9-35 522\\n9-35 581\\n9.35640\\n9-35698\\n9-35 756\\n9-35815\\n9.35873\\n9.35931\\n9-35989\\n9.3604?\\n9.36 105\\n9.36163\\n9.36 221\\n9-36278\\nd.\\n9-36336\\n62\\n62\\n62\\n62\\n61\\n61\\n62\\n61\\n61\\n61\\n6i\\n61\\n61\\n6i\\n60\\n61\\n61\\n66\\n61\\n60\\n60\\n66\\n60\\n66\\n60\\n60\\n60\\n60\\n59\\n60\\n60\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n58\\n58\\n59\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n5f\\n58\\n5?\\n58\\nLog. Cot.\\n0.67 252\\n0.67 196\\n0.67 128\\no. 67 065\\no. 67 004\\n0.66 943\\n0.66 881\\n0.66 819\\n0.66758\\n0.66 695\\n0.66 635\\n0.66 574\\n0.66 513\\n0.66 452\\n0.66 396\\n0.66 330\\n0.66 269\\n0.66 208\\n0.66 147\\n0.66085\\n0.66 026\\n0.65 965\\n0.65 905\\n0.65 845\\n0.65 784\\n0.65 724\\n0.65 664\\n0.65 604\\n0.65 544\\n0.65 484\\n0,65 424\\n0.65364\\n0.65 305\\n0.65 245\\n0.65 186\\n0.65 125\\n0.65 067\\n0.65 008\\n0.64948\\n0.64889\\n0.64 836\\n0.64 771\\no. 64 7 1 2\\n0.64 653\\n0.64 594\\n0.64536\\n0.6447?\\n0.64418\\no. 64 360\\n0.64 302\\n0.64243\\n0.64 185\\n0.64 127\\no. 64 068\\n0.64016\\n0.63952\\n0.63894\\n0.63 837\\n0.63 779\\n0.63 721\\n0.63.663\\niO g. Cot, le d. I Log. Tan.\\nLog. Cos.\\n9.99040\\n9-99038\\n9-99035\\n9.99032\\n9.99029\\n9-99027\\n9.99024\\n9.99021\\n9.99019\\n9.99016\\n999013\\n9.99 016\\n9. 99 008\\n9.99005\\n9.99 002\\n9.98999\\n9.98997\\n9.98994\\n9.98991\\n9.98988\\n9.98986\\n9-98983\\n9.98 986\\n9-9897?\\n9.98975\\n9.98972\\n9.98969\\n9.98965\\n9-98963\\n9.98 961\\n9.98958\\n9.98955\\n9.98952\\n9-98949\\n9-98947\\n9.98944\\n9-98 941\\n998938\\n9-98935\\n9-98933\\n9.98930\\n9.98 927\\n9-98924\\n9.98 921\\n9.98 9I8\\n9-98915\\n9.98913\\n9.98 910\\n9.98907\\n9.98904\\n9.98 901\\n9.98898\\n9-98895\\n9.98 892\\n9.98 890\\n9.98887\\n9.98884\\n9.98881\\n9.98878\\n9-98875\\n9.98 872\\nLog. Sin.\\n00\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\nP. P.\\n62\\n61\\n61\\n6\\n6.2\\n6.T\\n6.1\\nI\\n7.2\\n8.2\\n7.2\\n8.2\\n7-1\\n8.1\\n9\\n10\\n9.3\\n10.3\\n9.2\\n10.2\\n9-1\\n10. 1\\n20\\n30\\n40\\n50\\n20.6\\n31.0\\n41-3\\n51-0\\n20.5\\n30.7\\n41.0\\n51.2\\n20.3\\n30.5\\n40.6\\n50.8\\n66\\n60\\n59\\n59\\n6\\n6.6\\n6.0\\n5 9\\n5-9\\n7\\n7.6\\n7.0\\n6.9\\n6.9;\\n8\\n8.6\\n8.0\\n7.9\\n7-8\\n9\\n9.1\\n9.0\\n8.9\\n8-8\\n10\\n10. 1\\n10.0\\n9.9\\n9-8\\n20\\n20.1\\n20.0\\n19-8\\n19-6\\n30\\n30.2\\n30.0\\n29.7\\n29.5\\n40\\n40.3\\n40.0\\n39-6\\n39.3\\n50\\n50.4 1\\n50.0\\n49-6\\n49.1\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n58\\n5-8\\n6.8\\n9-?\\n19-5\\n29.2\\n39-0\\n48.?\\n58\\n5-8\\n6.?\\n7-?\\n^.7\\n9-6\\n19-3\\n29.0\\n38.6\\n48.3\\nSi\\n5-?\\n6.7\\n7-6\\n8.6\\n9.6\\n19.1\\n28.?\\n38.3\\n47-9\\n57\\n5-7\\n6.6\\n7.6\\n8.5\\n9-5\\n19.0\\n28.5\\n38.0\\n47.5\\n5S\\n56\\n5S\\n55\\n6\\n7\\n5-6\\n6.6\\n5-6\\n6.5\\n5-5\\n6.5\\n5-5\\n6.4\\n8\\n9\\n7.5\\n8-5\\n7.4\\n8.4\\n7-4\\n8.3\\n7-3\\n8.2\\n10\\n20\\n9-4\\n18.8\\n9-3\\n18.6\\n9-2\\n18.5\\n9-1\\n18.3\\n30\\n28.2\\n28.0\\n27.?\\n27.5\\n40\\n50\\n37.6\\n47.1\\n37.3\\n46.6\\n37-0\\n46.2\\n36.6\\n45-8\\n54\\n3\\n6\\nS-4\\n0.3\\n7\\n6. .3\\n0.3\\n8\\n7.2\\n0.4\\n9\\n8.2\\n0.4\\n10\\n9-1\\n0-5\\n20\\n18. 1\\nI.O\\n30\\n27.2\\n1-5\\n40\\n36.3\\n2.0\\n50\\n45-4\\n2.5\\n2\\n0.2\\n0.3\\n0.3\\n0.4\\n0.4\\n0.8\\n1.2\\n1-6\\n2.1\\np. p\\n77\\n360", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0412.jp2"}, "413": {"fulltext": "TABLE VII. LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS,\\n13\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\niO:;. Sill.\\n(I.\\n9.35 209\\n9-35 263\\n9-35 318\\n9-35 372\\n9-35427\\n9-35481\\n9-35 536\\n9-35 590\\n9-35 644\\n9-35698\\n9-35 752\\n9-35805\\n9.35 865\\n9-35914\\n9.35968\\n9.36 021\\n9.36075\\n9.36 123\\n9.36 182\\n9-36235\\n20\\n9.36 289\\n21\\n9-36342\\n22\\n9-36393\\n23\\n9-36448\\n24\\n9.3650?\\n9- 36 554\\n9. 36 607\\n9. 36 660\\n9 36713\\n9-36766\\n9-36818\\n9.36 871\\n9-36923\\n9-36976\\n9-37 028\\n9.37081\\n9-37 133\\n9-37 185\\n9-3723^\\n9.37 289\\n9-37341\\n9 37 393\\n9-37 445\\n9-37 497\\n9-37 548\\n9. 37 600\\n9-37652\\n9-37703\\n9.37755\\n9-37 806\\n9-37857\\n9.37909\\n9.37960\\n9.3801T\\n9.38 062\\n9.38 113\\n9.38 164\\n9.38215\\n9.38 266\\n9-38317\\n9-38367\\n54\\n5-4\\n5-4\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n53\\n54\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n52\\n53\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n51\\n52\\n51\\n52\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n50\\n51\\n51\\n50\\nIan.\\n(1.\\n(\u00c2\u00bbt.\\n9-36336\\n936394\\n9.36451\\n9.36509\\n9-36566\\n9.36623\\n9. 36 68 1\\n9-36738\\n9-36795\\n9.36852\\n9.36909\\n9. 36 965\\n9.37023\\n9.37080\\n9-37 136\\n9-37 193\\n9.37 250\\n9-37 306\\n9- 37 363\\n9.37419\\nLog. Cos. I (1.\\n9-37 475\\n9-37 532\\n9.37 588\\n9-37644\\n9-37 700\\n9-37 756\\n9.37 812\\n9-37868\\n9-37924\\n9-37 979\\n9-38035\\n9.38091\\n9-38 146\\n9.38 202\\n9-38257\\n9-38313\\n9-38368\\n9-38423\\n9-38478\\n9-38 533\\n9-38 589\\n9- 38 644\\n9-38698\\n9-38753\\n9-38 808\\n9.38863\\n9.38 918\\n9-38972\\n9.39027\\n9.39081\\n9-39 136\\n9.39 190\\n9- 39 244\\n9-39299\\n9-39 353\\n9-39407\\n9-39461\\n9-39 5i\u00c2\u00a7\\n9-39569\\n9-39623\\n9-39677\\nLog. Cot.\\n57\\n57\\n57\\n57\\n57\\n57\\n57\\n57\\n57\\n57\\n57\\n56\\n57\\n56\\n57\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\nSi\\n56\\n56\\n5^^\\n56\\n5S\\nSi\\n55\\nSi\\nSi\\n55\\n55\\n55\\n55\\nD\\n55\\n54\\n55\\n55\\n54\\n55\\n54\\n5^\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n53\\n0.63 663\\n0.63 606\\n0.63 548\\n0.63491\\n063433\\n0-63 376\\n0.63319\\n0.63 262\\n0.63 204\\n0.63 147\\n0.63 096\\n0.63033\\n0.62 977\\n0.62 920\\n0.62 863\\n0.62 806\\n0.62 730\\n0.62 693\\n0.62 637\\n0.62 580\\nl.dU Cos.\\n0.62 524\\n0.62 468\\n0.62 412\\n0.62 356\\n0.62 299\\n0.62 243\\n0.62 188\\n0.62 132\\n0.62 076\\n0.62 020\\n06\\n0.6\\n0.6\\n0.6\\n0.6\\n0.6\\n0.6\\n0.6\\n0.6\\n0.6\\nc. d.\\n0.6\\n0.6\\n0.6\\n0.6\\n0.6\\n0.6\\n0.6\\n0.6\\n964\\n909\\n853\\n798\\n742\\n687\\n632\\n576\\n521\\n466\\n411\\n356\\n301\\n246\\n191\\n137\\n082\\n7\\n0.60973\\n0.60 913\\n0.60 8 64\\n0.60 809\\n0.60 755\\n0.60 701\\n0.60 647\\n0.60 592\\n0-60 538\\n0.60 484\\n0.60 430\\n0-60375\\n0.60 323\\nLog. Tan.\\n9.98 872\\n9. 98 869\\n9.98865\\n9-98863\\n9.98 860\\n9.98 858\\n9.98855\\n9.98852\\n9.98849\\n9.98 840\\n9-98843\\n9.98 840\\n9-98837\\n9.98834\\n9.98831\\n9.98 828\\n9.98 825\\n9.98822\\n9.98 819\\n9.98815\\n9.98813\\n9.98 816\\n9.98 S07\\n9.98 804\\n9.98 80T\\n9-98798\\n9.98795\\n9.98792\\n9-98789\\n9.98 786\\n9-98783\\n9.98 780\\n9-98777\\n9-98774\\n9.98771\\n9.98768\\n9-98765\\n9.98 762\\n9.98759\\n9-98755\\n9.98752\\n9.98749\\n9.98745\\n9-98743\\n9.98 746\\n998737\\n9-98734\\n9.98731\\n9.98728\\n9-98725\\n9.98 72T\\n9-98718\\n9.98/ 15\\n9.98 712\\n9-98 709\\n9.98 706\\n9-98 703\\n9.98 700\\n9.98695\\n9.98693\\n9.98 696\\n40\\n39\\n3^\\n37\\nI\\n-3\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n_i6\\n15\\n14\\n13\\n12\\n1 1\\nTo\\n9\\n8\\n7\\nLoer. Sin.\\n6\\n7\\n8\\n9\\nloj\\n20 i\\n30\\n401\\n50 I\\n57\\nS-7\\n6.7\\n7-6\\n8.6\\n9.6\\n19.T\\n28.^\\n38.3\\n47-9\\n57\\n5-7\\n6\\n7\\n8\\n9\\n19\\n28\\n38\\n47\\n56\\n5-^\\n6.\\n7-\\n18\\n28\\n37\\n47\\n\u00e2\u0080\u00a20\\n.6\\n3-\\n6.\\n\u00e2\u0080\u00a25\\n\u00e2\u0080\u00a25\\n7-\\n8.\\n\u00e2\u0080\u00a24\\n9-\\n\u00e2\u0080\u00a28\\n18.\\n28.\\n\u00e2\u0080\u00a26\\n.1\\n37-\\n46.\\n55\\n55\\n54\\n6\\n5-5\\n5-5\\n5--+\\n7\\n6.5\\n6\\n4\\n6.3\\n8\\n7.4\\n7\\n3\\n7.2\\n9\\n8.3\\n8\\n2\\n8.2\\n10\\n9.2\\n9\\nI\\n9-1\\n20\\n18.5\\n18\\n3\\n18.1\\n30\\n27-7\\n27\\n5\\noy n\\n40\\n37.0\\n36\\n6\\n36.3\\n50\\n46.2\\n45\\n8\\n45-4\\n56\\n6\\n54\\n5-4\\n6.3\\n7-2\\n8.1\\n9.0\\n18.0\\n27.0\\n36.0\\n45.0\\n53\\n53\\n52\\n52 1\\n6\\n7\\n5-3\\n6.2\\n5-3\\n6.2\\n5-2\\n6.1\\n5-2\\n6.6\\n8\\n7.1\\n7.0\\n7.0\\n6.9\\n9\\n10\\n8.0\\n8.9\\n7-9\\n8-8\\n7-9\\n^-7\\n7.8\\n8.6\\n20\\n30\\n17.8\\n26. f\\n17-6\\n26.5\\n17.5\\n26.2\\n26.0\\n40\\n35.6\\n35-3\\n35.0\\n34-6\\n50\\n44.6\\n44.1\\n43-7\\n43.3\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n51\\n5.1\\n6.0\\n6-8\\n7-7\\n8.6\\n17.1\\n25. f\\n34-3\\n42.9\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n3\\n0.3\\n0.4\\n0.4\\n0.5\\n0.6\\nI.I\\ni.f\\n2.3\\n2.9\\n51\\n5-1\\n5-9\\n6.8\\n7-6\\n8-5\\n17.0\\n25-5\\n34.0\\n42.5\\n0-3\\n0.3\\n0.4\\n0.4\\n0.5\\ni.o\\n1.5\\n2.0\\n2.5\\n50\\n5.0\\n5\\n6\\n7\\n8\\n16\\n25\\n33\\n42\\n2\\n0.2\\n0.3\\n0.3\\n0.4\\n0.4\\n0.8\\n1.2\\n1-6\\n2.1\\n1 1\\n76\u00c2\u00b0\\n361", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0413.jp2"}, "414": {"fulltext": "TABLE Vli.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n14\u00c2\u00b0\\n_9_\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\nJi\\n55\\n56\\n57\\n58\\n59\\n60\\nLog. Sill. d.\\n9-3836?\\n9.38418\\n9-38468\\n9.38519\\n9.38569\\n9.38 620\\n9.38670\\n9.38 726\\n9.38771\\n9.38821\\n9.38871\\n9.38 921\\n9.38971\\n9.39 021\\n9.39071\\n9.39 120\\n9.39176\\n9.39 220\\n9.39269\\n9-39319\\n9-39368\\n9.39418\\n9-3946?\\n9-39515\\n9.39566\\n9.39615\\n9.39664\\n9-39713\\n9.39762\\n9-39 81 1\\n9. 39 860\\n9.39909\\n9-39 95?\\n9.40006\\n9.40055\\n9.40 103\\n9.40152\\n9. 40 200\\n9.40249\\n9.40 297\\n9-40345\\n9-40394\\n9.40442\\n9.40490\\n9.40 538\\n9.40 586\\n9.40634\\n9.40682\\n9.40 730\\n9.4077?\\n9.40 825\\n9.40873\\n9.40 920\\n9.40968\\n9.41015\\n9.41 063\\n9.41 116\\n9.41 158\\n9.41 205\\n9.41 252\\n9.41 299\\nLog. Cos. d.\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n49\\n50\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n48\\n48\\n49\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n47\\n48\\n4?\\n4?\\n4?\\n4?\\n4?\\n4?\\n4?\\n47\\n4?\\n47\\nLog. Tau.\\n9-39677\\n9-39 731\\n9-39784\\n9-39838\\n9.39892\\n9-39 945\\n9-39 999\\n9.40052\\n9.40 106\\n9.40159\\n9. 40 2 1 2\\n9.40 265\\n9-40 318\\n9.40372\\n9-40425\\n9.40478\\n9.40531\\n9.40 583\\n9-40636\\n9.40 689\\n9.40742\\n9.40794\\n9.40847\\n9.40899\\n9.40952\\n9.4\\n9-4\\n9-4\\n9-4\\n9-4\\n9-4\\n9-4\\n9.4\\n9-4\\n9-4\\n9-4\\n9.4\\n9-4\\n9-4\\n9.4\\n9.4\\n9-4\\n9.4\\n9.4\\n9.4\\n004\\n057\\n109\\n161\\n213\\n266\\n318\\n370\\n422\\n474\\n525\\n57?\\n629\\n681\\n732\\n784\\n836\\n887\\n938\\n990\\n9.42041\\n9.42 092\\n9-42 144\\n9-42 195\\n9-42 246\\n9.42 29?\\n9-42 348\\n9.42 399\\n9.42450\\n9.42 501\\n9.42 552\\n9.42 602\\n9.42653\\n9-42 704\\n9.42 754\\n9.42 805\\nLoe. Cot.\\nc. d. I Log. Cot.\\n54\\n53\\n54\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n52\\n53\\n52\\n53\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n51\\n52\\n52\\n51\\n51\\n51\\n52\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n50\\n51\\n50\\n51\\n53\\n50\\n50\\nc. d.\\n0.60 323\\n0.60 269\\n0.60 21 5\\n0.60 1 61\\n0.60 108\\n0.60054\\n0.60001\\no. 59 94?\\n0.59894\\n0.59 841\\n0.5978?\\n0.59734\\nO.5968T\\n0.59 628\\n0.59575\\n0.59 522\\n0.59469\\n0.59 4I6\\n0.59363\\n0-5931 I\\n0.59258\\n0.59 205\\n0.59153\\n0.59 100\\no. 59 048\\n0.58995\\n0.58943\\n0.58891\\n0.58838\\n0.58786\\n0.58734\\n0.58682\\n0.58 630\\n9.58578\\n0.58 526\\n0.58474\\n0.58 422\\n0.58 370\\n0.58319\\n0.58 26?\\n0.58 216\\n0.58 164\\n0.58 112\\no. 58 061\\nO.58CIO\\n0.57 958\\n0.5790?\\n0.57856\\n0.57805\\n0.57753\\n0.57 702\\n0.57651\\n0.57 606\\n0.57549\\no. 57 499\\n0.57448\\n0.5739?\\n0.57 346\\n0.57 296\\no 57245\\no S7 195\\nLog. Tan.\\nLog. Cos.\\n9.98 696\\n9.9868?\\n9.98684\\n9.98681\\n9.98678\\n9.98674\\n9.98 67T\\n9.98668\\n9.98 665\\n9.98 662\\n9-98658\\n9.98655\\n9.98 652\\n9.98649\\n9. 98 646\\n9.98 642\\n9.98639\\n9-98636\\n9.98633\\n9-98630\\n9.98626\\n9-98623\\n9.98 620\\n9.98 617\\n9.98613\\n9.98 616\\n9.98 607\\n9.98 604\\n9.98 606\\n9.98 59?\\n9.98 594\\n9.98 591\\n9.98 58?\\n9.98 584\\n9.98 581\\n9.98 578\\n9.98 574\\n9.98571\\n9.98 568\\n9.98 564\\n9.98 561\\n9.98558\\n9.98 554\\n9.98551\\n9.98 548\\n9.98 544\\n9.98 541\\n9.98 538\\n9-98 534\\n9.98 531\\n9.98 528\\n9.98 524\\n9.98 521\\n9.98518\\n9.98 514\\n9.98511\\n9.98 508\\n9.98 504\\n9.98 501\\n9.98498\\n9-98494\\nLog. Sin.\\nd.\\n00\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\np. P.\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n54\\n53\\n5.4\\n5-3\\n6.3\\n6.2\\n7.2\\n7.1\\n8.1\\n8.0\\n9.0\\n8.9\\n18.0\\n17.8\\n27.0\\n26.?\\n36.0\\n35-6\\n45-0\\n44.6\\n53\\n5.3\\n6.2\\n7.0\\n7-9\\n8.8\\n17-6\\n26.5\\n35-3\\n44.1\\n52\\n52\\n51\\n51\\n6\\n5.2\\n5.2\\n5.1\\n5.\\n7\\n6.1\\n6.6\\n6.0\\n5-\\n8\\n7.0\\n6.9\\n6.8\\n6.\\n9\\n7.9\\n7.8\\n7-7\\n7-\\n10\\n8.?\\n8.6\\n8.6\\n8.\\n20\\n17.5\\n17.3\\n17.!\\n17.\\n30\\n26.2\\n26.0\\n25-?\\n25.\\n40\\n35.0\\n34.6\\n34.3\\n34.\\n50\\n43-?\\n43.3\\n42.9\\n42.\\n56\\nSO\\n49\\n49\\n6\\n5.S\\n5.0\\n4.9\\n4-\\n7\\n5-9\\n5-8\\n5.8\\n5-\\n8\\n6.7\\n6.6\\n6.6\\n6.\\n9\\n7.6\\n7.5\\n7.4\\n7-\\n10\\n8.4\\n8.. 3\\n8.2\\n8.\\n20\\n16.8\\n16.6\\n16.5\\n16.\\n30\\n25.2\\n25.0\\n24.?\\n24.\\n40\\n33.6\\n33-3\\n33.0:32.\\n50\\n42.1\\n41-6\\n41.2\\n40.\\n48\\n48\\nAl\\n47\\n6\\n4-8\\n4.8\\n4-?\\n4-\\n7\\n5-6\\n5.6\\n5-5\\n5-\\n8\\n6.4\\n6.4\\n6.3\\n6.\\n9\\n7.3\\n7.2\\n7.1\\n7.\\n10\\n8.1\\n8.0\\n7.9\\n7.\\n20\\n16. 1\\n16.0\\n15.8\\n15.\\n30\\n24.2\\n24.0\\n23-?\\n23.\\n40\\n32.3\\n32.0\\n31.6\\n31.\\n50\\n40.4\\n40.0\\n39.6\\n39.\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n3\\n0.3\\n0.4\\n0.4\\n0.5\\n0.6\\nI.I\\nI.?\\n2.3\\n2.9\\n3\\n0.3\\n0.3\\n0.4\\n0.4\\n0.5\\ni.o\\n1.5\\n2.0\\n2.5\\np. P.\\n75*\\n362", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0414.jp2"}, "415": {"fulltext": "TABLE VII. L()GARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n15\u00c2\u00b0\\n10\\nII\\n12\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n^3\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\nLotf. Sill.\\n9-4\\n9.4\\n9.4\\n9.4\\n9-4\\n9.4\\n9-4\\n9.4\\n9-4\\n9.4\\n9 4\\n9-4\\n9.4\\n9.4\\n9.4\\n299\\n346\\n394\\n441\\n488\\n534\\n581\\n628\\n675\\n721\\n768\\n815\\n861\\n908\\n954\\n9.42 000\\n9.42 047\\n9.42093\\n9.42 139\\n9.42 185\\n9.42 232\\n9.42 278\\n9.42 324\\n9.42 369\\n9.42415\\n9.42 461\\n9.42 507\\n9-42 553\\n9-42 598\\n9.42644\\n9.42 690\\n9-42735\\n9.42781\\n9.42825\\n9.42 871\\n9.42917\\n9.42 962\\n9.4300^\\n9.43052\\n9.43098\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nGO\\n9-43 143\\n9.43 188\\n943233\\n9.43278\\n9-43322\\n9-43 367\\n9.43412\\n9-43 457\\n9-43 501\\n9-43 546\\n9.43 591\\n943635\\n9.43680\\n9-43724\\n9-43 768\\n9-43813\\n9-43857\\n9-43 901\\n9-43 945\\n9-43989\\n9-44034\\nLog. Cos.\\n47\\n47\\n47\\n47\\n46\\n47\\n47\\n46\\n46\\n47\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n45\\n46\\n46\\n46\\n45\\n45\\n46\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n44\\n45\\n44\\n45\\n44\\n4-+\\n45\\n44\\n44\\n44\\n4-1\\n44\\n44\\n4-1\\n44\\n44\\n44\\nLou Tnii. c. d.\\n9.42 805\\n9.42 856\\n9.42 906\\n9-42956\\n9.43007\\n9-43057\\n9 43 107\\n9-43 157\\n9.43 208\\n9.43258\\n9-43308\\n943358\\n9-43408\\n9-43458\\n9-43 508\\n9-43 557\\n9.43607\\n9-43657\\n9-43 706\\n9-43 756\\n9-43 806\\n943855\\n9-43 905\\n9-43 954\\n9-44003\\n9-44053\\n9.44 102\\n9-44 151\\n9.44 200\\n9-44249\\n9.44299\\n9-44 348\\n9-44 397\\n9.44446\\n9-44 494\\n9-44 543\\n9-44 592\\n9.44641\\n9.44690\\n9-44 738\\n944787\\n9.44835\\n9.44884\\n9-44932\\n9.44981\\n9.45029\\n9.4507^\\n9.45 126\\n9.45 174\\n9.45 222\\n9.45 270\\n9-45 318\\n9-45 367\\n9.45415\\n9:_45J:^\\n9.45 515\\n9-45 558\\n9-45 606\\n9.45654\\n9-45 702\\n9-45 749\\nLog. Cot.\\n51\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n49\\n50\\n49\\n49\\n50\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n48\\n49\\n49\\n48\\n49\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n47\\n48\\n48\\n^1\\n48\\n47\\nLoe. Col.\\n0.57 195\\n0.57 144\\n0.57094\\n0.57043\\no. 56 993\\no. 56 942\\n0.56 892\\no. 56 842\\n0.56 792\\no. 56 742\\n0.56 692\\no. 56 642\\n0.56 592\\n0.56 542\\no. 56 492\\n0.56442\\no. 56 392\\n0.56 343\\n0.56 293\\no. 56 243\\n0.56 194\\n0.56 144\\n0.56095\\n0.56 04^\\n0.55996\\n0.55947\\n0.55898\\n0.55848\\n0.55799\\n0.55 750\\n0.55701\\n0.55652\\n0.55 603\\n0.55 554\\n0.55 505\\n0.55 456\\n0.5540^\\n0.55359\\n0.55310\\n0.55 261\\nliOir. Cos.\\n0.55 213\\n0.55 164\\n0.55 116\\n0.55 067\\n0.55019\\n0.54970\\n0.54 922\\n0.54874\\n0.54 825\\n0.5477?\\n0.54729\\no. 5468T\\n0.54633\\n0.54585\\n0.54537\\no. 54 489\\n0.54441\\n0.54393\\n0.54346\\no 54 298\\n0.54256\\n9-98494\\n9.98491\\n9-98487\\n9.98484\\n9. 98 481\\n9-9847?\\n9.98 474\\n9-98470\\n9.98467\\n9.98464\\n9. 98 466\\n9-98457\\n9-98453\\n9.98 450\\n9-98446\\n9-98443\\n9-98439\\n9-98436\\n9-98433\\n9.98 429\\n9.98 426\\n9.98 422\\n9.98419\\n9.98415\\n9.98 412\\n9.98 408\\n9.98405\\n9.98 401\\n9-98 398\\n9-98 394\\n9.98 391\\n9-98 387\\n9.98 384\\n9.98 386\\n9.98 377\\n998373\\n9-98370\\n9.98365\\n9-98363\\n9-98 359\\n9.98356\\n9.98352\\n9-98348\\n9-98345\\n9-98 341\\nc. (1. I Lotr. Tan.\\n9-98 338\\n9-98334\\n9-98331\\n9.98 32^\\n9.98 324\\n9.98 320\\n9-98 3I6\\n9-98313\\n9-98309\\n9-98 306\\n9.98 302\\n9.98298\\n9-98295\\n9.98 29T\\n9.98288\\n9-98 284\\nLoir. Sin.\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\nr. I\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\n1 1\\n10\\n9\\n8\\n7\\n6\\n50\\n5\\nD\\n6\\n5.6\\n5.0\\n7\\n5-9\\n5\\n8\\n8\\n6.?\\n6\\n6\\n9\\n7.6\\n7\\n5\\n10\\n8.4\\n8\\n3\\n20\\n16.8\\n16\\n6\\n30\\n25.2\\n25\\n40\\n33-6\\n33\\n3\\n50\\n42.1\\n41\\n6\\n6\\n7\\n81\\n9!\\n10,\\n49\\n4.9\\n5-8\\n6.6\\n7-4\\n8.2\\n20 16.5\\n30,24.?\\n4033-0\\n5041.2\\n47\\n4.?\\n5\\n6\\n9\\n10\\n20 15\\n3o|23\\n4031\\n50:39\\n49\\n4-9\\n5\\n6\\n5\\nT\\n16.3\\n24.5\\n32.6\\n40\\n47\\n4-7\\n48\\n4\\n5\\n48\\n4-8\\n5-6\\n6.4\\n7.2\\n8.0\\n16.0\\n24.0\\n32.0\\n40.0\\n7\\n7\\n15\\n?|23\\n631\\n6|39\\n46\\n4-6\\n5\\n23\\n31\\nTI38\\n46\\n4.6\\n5-3\\n6.T\\n6.9\\n7-6\\n15-3\\n2123.0\\n030.6\\n?!38.3\\n6\\n7\\n8\\n9\\n10\\n20\\n45\\n4.5\\n5-3\\n6.6\\n6.8\\n7.6\\n15.1\\n30 22.^\\n40 30. 3\\n50:37.9\\n10\\n20\\n45\\n4-5\\n5-2\\n6.0\\n6.?\\n7.5\\n15.0\\n22. 5\\n44\\n4-4\\n5\\n30.0 29\\n37.5I37\\n40\\n50\\n0.4\\n0.3\\n0.4\\n0.4\\n0.5\\n0.4\\n0.6\\no.S\\n0.6\\n0.6\\n1-3\\ni.i\\n2.0\\nI-?\\n2-6\\n2-3\\n3.3\\n2.9\\n9\\n7\\n4\\n8\\n2 22\\n6*29\\nM36\\n3\\n0.3\\n0.3\\n0.4\\n0.4\\n0.5\\ni.o\\n1-5\\n2.0\\n2-5\\n44\\n4-4\\n5\\n5\\n6\\n7\\n74\u00c2\u00b0\\n563", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0415.jp2"}, "416": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS\\n16\u00c2\u00b0\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nGO\\nhog. Si:i.\\n9-44034\\n9-44078\\n9.44122\\n9.44 166\\n9.44209\\n(1.\\n9-44253\\n9.44 297\\n944341\\n9-44384\\n9-44 428\\n9.44472\\n9-44515\\n9-44 559\\n9.44602\\n9.44646\\n9.44689\\n9-44732\\n9.44776\\n9.44819\\n9.44 862\\n9-44 905\\n9-44 948\\n9.44991\\n9-45 034\\n9.45077\\n9.45 120\\n9.45 163\\n9.45 206\\n9.45 249\\n9.45 291\\n9-45 334\\n9-45 377\\n9.45419\\n9.45462\\n9-45 504\\n9-45 547\\n9.45 589\\n9-45631\\n9.45 674\\n9.45716\\n9-45 758\\n9.45 800\\n9-45 842\\n9.45 885\\n9.45927\\n9-45 969\\n9.46 on\\n9.46052\\n9.46094\\n9-46 136\\n9.46 178\\n9.46 220\\n9.46 261\\n9-46 303\\n9-46 345\\n9.46 385\\n9.46 428\\n9.46469\\n9.46 511\\n9.46552\\n9-46 593\\nLo?. Cos.\\n44\\n44\\n44\\n43\\n44\\n44\\n43\\n43\\n44\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n42\\n43\\n43\\n42\\n42\\n43\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n41\\n42\\n42\\n41\\n42\\n41\\n41\\n42\\n41\\n41\\n41\\n41\\n41\\n41\\nd.\\nLost. Tan. c. d.\\n9-45 749\\n9-45 797\\n9-45 845\\n9.45 892\\n9.45 940\\n9.45 98^\\n9.46035\\n9.46082\\n9.46 129\\n9.46 177\\n9.46 224\\n9.46 271\\n9-46318\\n9.46 366\\n9.46413\\n9. 46 460\\n9.46 507\\n9.46 554\\n9.46 601\\n9.46647\\n9.46 694\\n9.46 741\\n9.46788\\n9.46834\\n9.46881\\n9.46 928\\n9.46974\\n9.47 021\\n9.47 067\\n9.47 114\\n9.47 166\\n9 47 207\\n9.47253\\n9-47 299\\n9 47 345\\n9-47 392\\n9.47 438\\n9.47 484\\n9-47 530\\n9-47 576\\n9.47 622\\n9-47 668\\n947714\\n9.47 760\\n9.47 806\\n9-47851\\n9.47 897\\n9-47 943\\n9.47 989\\n9.48034\\n9.48 080\\n9.48 125\\n9.48 171\\n9.48 216\\n9.48 262\\n9-48 307\\n948353\\n9.48 398\\n9-48443\\n9-48488\\n9-48 534\\nhog. Cot.\\n48\\n47\\n47\\n4?\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n46\\n47\\n47\\n46\\n46\\n47\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n45\\n46\\n46\\n45\\n46\\n45\\n46\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\nc. d.\\nLog. Cot.\\n54256\\n54202\\n155\\n107\\n060\\n54\\n54\\n54\\n0.54012\\n0.53965\\n0.53917\\n0.53876\\n0.53823\\n0.53776\\n0.53728\\n0.53681\\n0.53634\\n0.53 587\\n0.53\\n0.53\\n0.53\\n0.53\\n0.53\\n540\\n493\\n446\\n399\\n352\\n0.53\\n0.53\\n0.53\\n0.53\\n0.53\\n0.53\\n0.53\\n0.52\\n0.52\\n0.52\\n305\\n258\\n212\\n165\\niii\\n072\\n025\\n979\\n932\\n886\\n0.52\\n0.52\\n0.52\\n0.52\\n0.52\\n839\\n793\\n747\\n706\\n654\\n0.52\\n0.52\\n0.52\\n0.52\\n0.52\\n608\\n562\\n516\\n469\\n423\\n0.52\\n0.52\\n0.52\\n0.52\\n0.52\\n377\\n33?\\n286\\n240\\n194\\n0.52\\n0.52\\n0.52\\n0.52\\no.5t\\n0.51\\n0.51\\n0.51\\n0.51\\n0.51\\n148\\n102\\n057\\n01 1\\n96|_\\n920\\n874\\n829\\n783\\n738\\n0.51\\n0.51\\n0.51\\n0.51\\n0.51\\n692\\n647\\n602\\n556\\n511\\n0.51 466\\nhog. Tan. I\\nLoar. Cos.\\n9.98 284\\n9.98 286\\n9.98277\\n9.98273\\n9.98 269\\n9.98 266\\n9.98 262\\n9.98258\\n9.98255\\n9.98 251\\n9.98 247\\n9-98 244\\n9.98 246\\n9.98236\\n9-98233\\n9.98 229\\n9.98 22^\\n9.98 222\\n9-98218\\n9.98 214\\n9.98 211\\n9.98 207\\n9.98203\\n9.98 200\\n9.98\\n9.98\\n9.98\\n9.98\\n9.98\\n9-98\\n9.98\\n9.98\\n9.98\\n9.98\\n9-98\\n9.98\\n9.98\\n9.98\\n9.98\\n9.98\\n9.98\\n9.98\\n9.98\\n9.98\\n9.98\\n9.98\\n9-98\\n9.98\\n9.98\\n9.98\\n96\\n92\\n85\\n81\\n77\\n73\\n70\\n66\\n62\\n58\\n55\\n51\\n47\\n43\\n40\\n36\\n32\\n28\\n24\\n21\\n17\\n13\\n09\\n05\\n02\\n9.98 098\\n9.98094\\n9.98 096\\n9.98086\\n9.98 082\\n9.98079\\n9.98075\\n9.98 071\\n9.98 o6f\\n9.98063\\n9-98059\\nliOir. Sin.\\n3\\n3\\n3\\n4\\n3\\n3\\n4\\n3\\n3\\n4\\n3\\n3\\n4\\n3\\n3\\n4\\n3\\n3\\n4\\n3\\n4\\n3\\n3\\n4\\n3\\n4\\n3\\n4\\n3\\n4\\n3\\n4\\n3\\n4\\n3\\n4\\n3\\n4\\n3\\n4\\n3\\n4\\n4\\n3\\n4\\n3\\n4\\n4\\n3\\n4\\n4\\n3\\n4\\n4\\n3\\n4\\n4\\n3\\n4\\n4\\n(iT\\n00\\n59\\n58\\n57\\n5^\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\nV. V.\\n48\\n4^\\n6\\n4.8\\nA- 7\\n7\\n5.6\\n5.5\\n8\\n6.4\\n6.3\\n9\\n7.2\\n7-1\\n10\\n8.0\\n7-9\\n20\\n16.0\\n15-8\\n30\\n24.0\\n23-7\\n40\\n32.0\\n31-6\\n50\\n40.0\\n39.6\\n46\\n46\\n4S\\n6\\n4-6\\n4.6\\n4-5\\n7\\n5-4\\n5-3\\n5-3\\n8\\n6.2\\n6.T\\n6.6\\n9\\n7.0\\n6.9\\n6.8\\n10\\n7-9\\n7-6\\n7.6\\n20\\n15-5\\n15-3\\n15.1\\n30\\n23.2\\n23.0\\n22.7\\n40\\n31.0\\n30.6\\n30.3\\n50\\n38.^\\n38.3\\n37.9\\n44\\n43\\n43\\n6\\n4.4\\n4.3\\n4.\\n7\\n8\\n9\\n5-1\\n5-8\\n6.6\\n5-1\\n5-8\\n6.5\\n5-\\n5-\\n6.\\n10\\n7-3\\n7.2\\n7-\\n20\\n14-6\\n14.5\\n14.\\n30\\n22.0\\n21. f\\n21.\\n40\\n50\\n29-3\\n36.6\\n29.0\\n36.2\\n28.\\n35-\\n47\\n4-7\\n5-5\\n6.2\\n7.6\\n7-8\\n15-6\\n23-5\\n31-3\\n39-1\\n45\\n4.5\\n5.2\\n6.0\\n7.5\\n15.0\\n22.5\\n30.0\\n37.5\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n4\\n04\\n0.4\\n0.5\\n0.6\\n0.6\\n1-3\\n2.0\\n2-6\\n3-3\\nP. I\\n3\\n0.3\\n0.4\\n0.4\\n0.5\\n0.6\\ni.i\\ni- 7\\n2.3\\n2.9\\n42\\n42\\n41\\n41\\n6\\n4.2\\n4.2\\n4.1\\n4.1\\n7\\n8\\n9\\n4.9\\n5-6\\n6.4\\n4-9\\n5.6\\n6.3\\n4.8\\n5-5\\n6.2\\n4.8\\n5-4\\n6.T\\n10\\n7-1\\n7.0\\n6.9\\n6.8\\n20\\n14. 1\\n14.0\\n13-8\\n13-6\\n30\\n40\\n21.2\\n28.3\\n21.0\\n28.0\\n20.^\\n27.6\\n20.5\\n27-3\\n50\\n35-4\\n35-0\\n34-6\\n34-1\\n364", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0416.jp2"}, "417": {"fulltext": "TAHLE VII. LOGARITHMIC SINES, COSINES, TANGENTS, AND CO lAN(iEXTS.\\n17\\n4\\n5\\n6\\n7\\n8\\n9\\n10\\nII\\n12\\n13\\nU\\n15\\ni6\\n17\\ni8\\n19\\n20\\n\u00e2\u0080\u00a221\\n22\\n23\\n24\\n25\\n26\\n28\\n30\\n31\\n32\\njj\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n55\\n56\\n57\\n58\\n59\\n(;o\\nLotf. Sill.\\n(I.\\n9-46 593\\n9.46635\\n9.46676\\n9.46717\\n9-46758\\n9.46799\\n9.46 840\\n9.46881\\n9.46 922\\n9- 46 963\\n9.47004\\n9.47 04^\\n9.47086\\n9.47 127\\n9.47 168\\n9.47 208\\n9.47 249\\n9.47 290\\n9-47 330\\n9 47 371\\n9.47 41 1\\n9.47452\\n9.47492\\n9-47 532\\n9-47 573\\n9.47613\\n9-47653\\n9.47694\\n9-47 734\\n9 47 774\\n9.47814\\n9.47 854\\n9.47 894\\n9-47 934\\n9-47 974\\n9.48 014\\n9.48054\\n9.48093\\n948 133\\n9- 48 173\\n948213\\n9.48252\\n9.48 292\\n948 331\\n9.48371\\n9.48 410\\n9.48450\\n9.48 489\\n9.48 529\\n9.48 568\\n9.48 607\\n9.48646\\n9,48686\\n9.48725\\n9.48 764\\n9.48 803\\n9.48 842\\n9.48 881\\n9.48 920\\n9.48959\\n9.48998\\nLoe. Cos.\\n41\\n4i\\n41\\n41\\n41\\n41\\n41\\n4f\\n\u00e2\u0080\u00a241\\n41\\n41\\n40\\n41\\n40\\n40\\n41\\n40\\n40\\n40\\n46\\n40\\n40\\n40\\n40\\n40\\n46\\n40\\n43\\n40\\n4^\\n40\\n40\\n40\\n40\\n40\\n39\\n40\\n39\\n40\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n29\\n39\\n38\\nLoif. Tan.\\n9-48 534\\n9.48 579\\n9.48 624\\n9.48 669\\n9.48714\\n9.48759\\n9.48 804\\n9.48 849\\n9.48 894\\n948939\\n9.48984\\n9.49028\\n9-49073\\n9.49 118\\n9.49 162\\n9.49 207\\n9-49252\\n9.49296\\n9-49 341\\n949385\\n9-49430\\n9-49 474\\n9-49 518\\n9-49 563\\n9.49607\\n9-49651\\n9.49695\\n9.49 740\\n9.49784\\n9.49 828\\n9.49872\\n9.49 916\\n9.49960\\n9. 50 004\\n9. 50 048\\n9. 50 092\\n9.50136\\n9.50179\\n9.50223\\n9.50 267\\n9.50 31 1\\n9-50354\\n9.50398\\n9.50442\\n9.50485\\n0. d.\\niOir. Cot.\\n9.50529\\n9-50572\\n9.50616\\n9.50659\\n9.50702\\nd.\\n9. 50 746\\n9.50789\\n9.50832\\n9.50876\\n9.50919\\n9. 50 962\\n9.51005\\n9.51 048\\n9.51 091\\n95^ 134\\n9.51 i7f\\n45\\n45\\n45\\n45\\n45\\n45\\n44\\n45\\n45\\n45\\n44\\n45\\n44\\n44\\n45\\n44\\n44\\n44\\n4^\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n4T\\n41-\\n43\\n44\\n44\\n44\\n43\\n44\\n43\\n44\\n43\\n43\\n44\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n.43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n51 46O\\n51 421\\n51 376\\n51 330\\n51 285\\n51 240\\n51 195\\n51 151\\n51 106\\n51 061\\n51 016\\n50971\\n50926\\n50 882\\n5083?\\n50792\\n50748\\n50703\\n50659\\n50614\\n50570\\n50525\\n50481\\n50437\\n5039 2_\\n50 348\\n50304\\n50 260\\n50 216\\n50 172\\n50 128\\n50083\\n50039\\n49996\\n49_952^\\n49 908\\n49 864\\n49 826\\n49 776\\n49 733\\nIjOU Cos.\\n49 689\\n49 645\\n49602\\n49558\\n49 5 U\\n49 47 1\\n49427\\n49384\\n49340\\n49297\\n49254\\n49 216\\n49167\\n49 124\\n49 081\\n49038\\n48994\\n48 951\\n48908\\n48 865\\n48 822\\n9.98059\\n9.98 056\\n9. 98 052\\n9.98 048\\n9.98044\\n9. 98 040\\n9.98036\\n9.98032\\n9.98:028\\n9.98024\\n9.98 02 1\\n9.98 017\\n9.98013\\n9.98 009\\n9.98005\\n9.98 001\\n9-97 997\\n9-97 993\\n9.97989\\n9.97985\\n9.97981\\n9.97 977\\n9-97 973\\n9.97969\\n9-97966-\\n9.97962\\n9.97958\\n9-97 954\\n9.97950\\n9.97946\\n9-97 942\\n9-97938\\n9-97 934\\n997930\\n9.97926\\nivOi;. Cot. I i. I liOi;. Tan.\\n9.97922\\n9.97918\\n9.97914\\n9.97910\\n9.97906\\n9.97902\\n9-97898\\n9.97894\\n9-97 890\\n9.97886\\n9.97 881\\n9.97 Syf\\n9-97873\\n9-97 869\\n9.97865\\n9.97 861\\n9.97857\\n9-97853\\n9-97849\\n9.97845\\n9.97841\\n9-97837\\n9-97833\\n9.97829\\n9.97824\\n9.97 820\\nLoL Sin.\\n3\\n4\\n4\\n4\\n3\\n4\\n4\\n4\\n4\\n3\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n3\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\u00c2\u00bb0\\n59\\n58\\n57\\n55\\n54\\n53\\n52\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n_3l\\n35\\n34\\n32\\nJL\\n30\\n29\\n28\\n27\\n26,\\nr. 1\\n24.\\n21\\n20\\n19\\n18\\n17\\n16\\n6\\n4.5\\n4.5\\n4-\\n7\\n5.3\\n5.2\\n5-\\n8\\n6.6\\n6.0\\n5.\\n9\\n6.8\\n6.f\\n6.\\n10\\n7.6\\n7-5\\n7-\\n20\\n15. 1\\n15.0\\n14.\\n30\\n22.7\\n22.5\\n22.\\n40\\n30.3\\n30.0\\n29.\\n50\\n37-9\\n37-5\\n37-\\n4S 45 44 44\\n4 4-4\\n2 5.1\\n9 5-8\\n7, 6.6\\n4 7-3\\n8 4-6\\n2 22.0\\n6 29-3\\n1:36.6\\n43\\n4-3\\n5-0\\n5-^\\n6.4\\n7.1\\n14.3\\n21.5\\n28.6\\n35-8\\n43\\n6\\n4-3\\n7\\n5-\\n8\\nS-8\\n9\\n6.5\\n10\\n7.2\\n20\\n14.5\\n30\\n21.^\\n40\\n29.0\\n50\\n36.2\\n4\\n4\\n6\\n0.4\\n0.4\\n7\\n0.5\\n0.4\\n8\\n0.6\\n0.5\\n9\\n0.7\\n0.6\\n10\\n0.7\\n0.6\\n20\\n1.5\\n1-3\\n30\\n2. 2\\n2.0\\n40\\n3.0\\n2.6\\n50\\n3.7\\n3-3\\n3\\n0.3\\n0.4\\n0.4\\n0.5\\n0.6\\ni.T\\ni.f\\n2.3\\n2.9\\n1 I\\n41\\n41\\n40\\n40\\n6\\n4.1\\n4.1\\n4.0\\n4.0\\n7\\n4-8\\n4.8\\n4-7\\n4-\u00c2\u00ab6\\n8\\n5-5\\n5.4\\n5-4\\n\u00e2\u0080\u00a25-3\\n9\\n6.2\\n6.T\\n6.1\\n^.0\\n10\\n6.9\\n6.8\\n6.^\\n\u00e2\u0080\u00a26.6\\n20\\n13-8\\n13-6\\n13-5\\n13-3\\n30\\n20.^\\n20.5\\n20.2\\n20.0\\n40\\n27-6\\n27-3\\n27.0\\n26.6\\n50\\n34-6\\n34-1\\n33-7\\n33-3\\n39\\n39\\n38\\n6\\n3-9\\n3-9\\n3-8\\n7\\n8\\n4.6\\n5-2\\n4-5\\n5-2\\n4-5\\n5-1\\n9\\nlO\\n5-9\\n6.6\\n5 8\\n6.5\\n5-\u00c2\u00ab\\n6.4\\n20\\n13.1\\n13.0.\\n12.8\\n30\\n40\\n19.7\\n26.3\\n195\\n26.0\\n19.2\\n25-6\\n50\\n32-9\\n32.5\\n32.1\\n4 -w\\n3^-5", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0417.jp2"}, "418": {"fulltext": "TABLE VIL\\nLog. Sin.\\n-LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS\\n18\u00c2\u00b0\\n10\\nII\\n12\\nl6\\n17\\ni8\\n19\\n9.48 998\\n9-49 0-37\\n9.49076\\n9.49 114\\n9-49 153\\n9.49192\\n9.49231\\n9.49269\\n949308\\n9-49 346\\n20\\n21\\n22\\n23\\n_24_\\n25\\n26\\n27\\n28\\n29\\n80\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\nil\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n00\\n949385\\n9-49423\\n9.49462\\n9.49 500\\n9-49 539\\n9 49 577\\n9.49615\\n9-49653\\n9.49692\\n9-49730\\n9.49760\\n9.49805\\n9.49 844\\n9.49882\\n949920\\n9 49 958\\n9 49 996\\n9.50034\\n9.50072\\n9.50 no\\n9.50147\\n9.50185\\n9.50223\\n9.50 265\\n9. 50 293\\n9-50336\\n9-50373\\n9. 50 41 1\\n9- 50 448\\n9. ;o 486\\n9-5o 52j\\n9.50561\\n9.50598\\n9.50635\\n9. 50 672\\n9.50710\\n9-50747\\n9-50784\\n9.50 821\\n9.50858\\n9.50895\\n9.50932\\n9. 50 969\\n9.51 006\\n9-51043\\n9. 5 1 080\\n9.51 117\\n9.51 154\\n9.51 190\\n9.51 22^\\n9.51 264\\nLoff. Cos.\\n(1. I liOe:. Tan.\\n39\\n39\\n38\\n39\\n38\\n39\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\nj\\n3^\\n3^\\n38\\n38\\n38\\n38\\n3^\\n38\\n38\\n37\\n38\\n38\\n37\\n38\\n37\\n37\\n38\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n36\\n37\\n36\\n37\\n36\\n(I.\\n9.f,i 177\\n9.51 226\\n9.51 263\\n9-51 306\\n9-51 349\\n9.51 392\\n9-51435\\n9-51477\\n9.51 520\\n9.51 563\\n9.51 605\\n9.51 648\\n9.51 691\\n9-51 733\\n9.51 776\\n9.51 818\\n9.51 861\\n9.51 903\\n9.51 946\\n9.51 988\\n9.52 030\\n9.52073\\n9.52 115\\n9.52 157\\n9 52 199\\n9.52241\\n9.52284\\n9.52 326\\n9.52 368\\n9.52410\\n9.52452\\n9.52494\\n9.52536\\n9.52578\\n9.52 619\\n9.52 661\\n9.52703\\n9-52745\\n9.52787\\n9-52828\\n9.52870\\n9.52 912\\n9 52953\\n9.52995\\n9 53036\\n9.53078\\n9-53 119\\n9.53 161\\n9.53 202\\n9-53244\\n9.53285\\n9-53 326\\n9- 53 368\\n9-53409\\n9-53450\\n9-53491\\n9-53 533\\n9-53 574\\n9-53615\\n9.53656\\n9-53697\\nC. (I.\\n43\\n43\\n43\\n43\\n42\\n43\\n42\\n43\\n42\\n42\\n43\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n41\\n42\\n42\\n41\\n42\\n41\\n41\\n42\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\nLos?. Cot.\\n0.48822\\n0.48 779\\n0.48 736\\n0.48 693\\n0.48 656\\n0.48 608\\n0.48 565\\n0.48 522\\n0.48 479\\n0-48437\\n0.48 394\\n0.48 351\\n0.48 309\\n0.48 265\\n0.48 224\\n0.48 181\\n0.48 139\\n0.48 096\\n0.48 054\\n0.48 012\\n0.47 969\\n0.47 927\\n0.47 885\\n0.47 842\\n0.47 806\\n0-47 758\\n0.47 716\\n0.47 674\\n0,47 632\\n0.47 590\\n0.47 548\\n0.47 506\\n0.47 464\\n0.47 422\\n0.47 386\\n0-47 338\\n0.47 296\\n0.47 255\\n0.47 213\\n0.47 1 71\\n0.47 130\\n0.47 088\\n0.47 046\\n0.47 005\\n0.46 963\\n0.46 922\\n0.46 886\\n0.46 839\\n0.4679?\\n0.46 756\\n0.46 714\\n0.46673\\n0.46 632\\n0.46 591\\n0.46 549\\nLot?. Cot. I c. d.\\n0.46 5O8\\n0.46 467\\n0.46426\\n0.46 385\\n0-46 344\\n0-46 303\\nLog^. Tan.\\nLos. Cos.\\n9.97 826\\n9-97816\\n9.97 812\\n9.97 808\\n9.97 804\\n9.97 800\\n9-97796\\n9-97792\\n9.97787\\n9-97783\\n9-97 779\\n9-97 775\\n9.97771\\n9.97 767\\n9.97 763\\n9-97 758\\n9-97 754\\n9-97750\\n9-97746\\n9-97742\\n9-97 73?\\n9-97 733\\n9.97729\\n9.97725\\n9-97721\\n9-97 716\\n9.97712\\n9-97 708\\n9.97704\\n9-97 700\\n9.97695\\n9.97691\\n9-97687\\n9.97 683\\n9-97678\\n9.97674\\n9.97670\\n9.97 666\\n9.97 661\\n9.9765^\\n9-97653\\n9.97649\\n9.97644\\n9.97646\\n9.97636\\n9.97632\\n9-97 62f\\n9.97623\\n9.97619\\n9.97614\\n9.97 616\\n9.97 606\\n9.97 601\\n9-97 59?\\n9-97 593\\n9-97 588\\n9.97584\\n9.97580\\n9.97 575\\n9-97 571\\n9-97 567\\nLog. Sin.\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\ndT\\nGO\\n59\\n58\\n57\\n56\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n19\\n18\\n17\\n16\\np. p.\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\n43\\n42\\n6\\n4-3\\n4.2\\n7\\n8\\n9\\n5.0\\n5.?\\n6.4\\n4.9\\n5-6\\n6.4\\n10\\n7-1\\n7-1\\n20\\n14-3\\n14.1\\n30\\n21. s\\n21.2\\n40\\n28.6\\n28.3\\n50\\n35-8\\n354\\n42\\n4.2\\n4-9\\n5.6\\n6.3\\n7.0\\n14.0\\n21.0\\n28.0\\n35-0\\n41\\n6\\n4-1\\n7\\n4-8\\n8\\n5-5\\n9\\n6.2\\n10\\n6.9\\n20\\n13-8\\n30\\n20.7\\n40\\n27-6\\n50\\n34-6\\n41\\n4.1\\n4-8\\n5-4\\n6.1\\n6.8\\n13-6\\n20.5\\n27-3\\n34-1\\n39\\n38\\n6\\n3-9\\n3-8\\n7\\n4-5\\n4-5\\n8\\n5.2\\n5-1\\n9\\n58\\n5.8\\n10\\n6.5\\n6.4\\n20\\n13.0\\n12.8\\n30\\n195\\n19.2\\n40\\n26.0-\\n25-6\\n50\\n32.5\\n32.1\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n31\\n3.?\\n4.4\\n5.0\\n5.6\\n6.2\\n12.5\\n18.^\\n25.0\\n31.2\\n37\\n3-7\\n4.3\\n4.9\\n5-5\\n6.1\\n12.3\\n18.5\\n24.6\\n30.8\\n38\\n3-8\\n4.4\\n5.6\\n5-7\\n6.3\\n12.6\\n19.0\\n25.3\\n31-6\\n36\\n3-6\\n4.2\\n4-8\\n5-5\\n6.1\\n12. T\\n18.2\\n24-3\\n30.4\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n4\\n0.4\\n0.5\\n0.6\\n0.7\\no.?\\n1-5\\n2.2\\n3-0\\n3-?\\n4\\n04\\n0.4\\no.S\\n0.6\\n0.6\\n1-3\\n2.0\\n2.6\\n3-3\\nP. p.\\n366", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0418.jp2"}, "419": {"fulltext": "TABLE VII. -LOGARITHMIC SINES. COSINES. TANGENTS, AND COTANGENTS\\n19\\n10\\nII\\n12\\n13\\n1\u00c2\u00b1\\n15\\ni6\\n17\\ni8\\n19\\n20\\n2;\\n22\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n4\u00c2\u00a3\\n45\\n46\\n47\\n^8\\n49\\nr o\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n0\\nLo:;. Sill.\\n9-\\n9-\\n9\\n9.\\n9:\\n9-\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n264\\n301\\n337\\n374\\n416\\n447\\n483\\n520\\n556\\n593\\n629\\n665\\n702\\n738\\n774\\n816\\n847\\n883\\n919\\n955\\n51 991\\n52 027\\n52 063\\n52099\\n52 135\\n52 170\\n52206\\n52242\\n52278\\n52314\\n52349\\n52385\\n52421\\n52456\\n52492\\n5252?\\n52563\\n52598\\n52634\\n52 669\\n52704\\n52740\\n52775\\n52 810\\n52846\\n52881\\n52 916\\n52951\\n52986\\n53021\\n53056\\n53091\\n53 126\\n5316T\\n53 196\\n53231\\n53 266\\n53301\\n53 335\\n53370\\n9-53405\\nLog. Cos.\\n37\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n3l\\n36\\n35\\n3l\\n36\\n35\\n35\\n35\\n35\\nJD\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n3:)\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n34\\n35\\n35\\n34\\n35\\n34\\nog. Tail. I c. (I. I Log. Cot.\\n53697\\n53738\\n53 779\\n53 S20\\n53861\\n53902\\n53 943\\n53983\\n54024\\n54065\\n54 106\\n54147\\n54187\\n54228\\n54269\\n54309\\n54350\\n54390\\n54431\\n54471\\n54512\\n54552\\n54 593\\n54633\\n54673\\n54714\\n54 754\\n54 794\\n54834\\n54874\\n54915\\n54 955\\n54 995\\n55035\\n55075\\n55115\\n55 155\\n55 195\\n55235\\n55275\\n55315\\n55 355\\n55 394\\n55 434\\n55 474\\n55 514\\n55 553\\n55 593\\n55633\\n55672\\n55712\\n55751\\n55791\\n55831\\n55870\\n55909\\n55 949\\n55988\\n56028\\n5606^\\n56 106\\nLOK. Cot.\\n41\\n41\\n41\\n41\\n41\\n41\\n40\\n41\\n41\\n46\\n41\\n40\\n40\\n41\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n46\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n39\\n40\\n40\\n40\\n40\\n40\\n39\\n40\\n39\\n40\\n39\\n40\\n39\\n39\\n39\\n39\\n40\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n0.46 303\\n0.46 262\\n0.46 221\\n0.46 180\\n0.46 139\\n0.46 098\\n0.46057\\n0.46 015\\n0.45975\\n0.45 934\\n0.45 894\\n0.45 853\\n0.45 812\\n0.45 772\\n0.45731\\n0.45 690\\n0.45 650\\n0.45 609\\n0.45 569\\no 45 528\\n0.45 488\\n0.45 447\\n0.45 407\\n0.45 367\\n0.45 326\\n0.45 286\\n0.45 246\\n0.45 205\\n0.45 165\\n0.45 125\\n0.45 085\\n0.45045\\n0.45 005\\n0.44965\\n0.44925\\n0.44884\\n0.44845\\n0.44 805\\n0.44 765\\n0.44725\\n0.44 685\\n0.44645\\n0.44 60 5\\n0.44 565\\n0.44 526\\n0.44486\\n0.44 446\\n0.44406\\n0.44 367\\n0.44327\\n0,44 288\\n0.44 248\\n0.44 208\\n0.44 169\\n0.44 129\\n0.44090\\n0.44 051\\n0.44 01 T\\n0.43 972\\n0.43 932\\n0.43893\\nLoir. Tan.\\nLoir. Cos.\\n9.97 567\\n9.97 562\\n9.97 558\\n9-97 554\\n9-97 549\\n9-97 545\\n9-97 541\\n9-97 536\\n9-97 532\\n9.97 527\\n9-97 523\\n9.97 519\\n9.97514\\n9.97 510\\n9.97 505\\n9.97 501\\n9-97 497\\n9-97492\\n9.97488\\n997483\\n9-97 479\\n9-97 475\\n9.97476\\n9.97466\\n9-97461\\n9-97 457\\n9.97452\\n9.97448\\n9-97 443\\n9-97 439\\n9-97 434\\n9-97430\\n9-97425\\n9.97421\\n9-97 416\\n9-97412\\n9.97407\\n9-97403\\n9-97 398\\n9-97 394\\n9-97 389\\n9-97385\\n9-97 380\\n9-97376\\n9-97371\\n9-97 367\\n9-97 362\\n9-97358\\n9-97 353\\n9-97 349\\n9-97 344\\n9-97 340\\n9-97 335\\n9-97330\\n9-97 326\\n9-97321\\n9-97317\\n9.97312\\n9-97 308\\n9-97303\\n9 97 298\\nLoif. Sin.\\nl.\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\u00e2\u0080\u00a24\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n5\\n4\\n4\\n4\\n4\\n4\\n4\\n5\\n4\\n00\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n_5i\\nr o\\n49\\n48\\n47\\n^6^\\n45\\n44\\n43\\n42\\n41\\n24\\n21\\n20\\n9\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\n1 1\\n1(7\\n9\\n8\\n7\\n6\\n5\\n4\\n3\\nr. I\\n41\\n40\\n40\\n6\\n41\\n4.6 4.0 1\\n7\\n4.8\\n4-7\\n46\\n8\\n5-4\\n5-4\\n5-3\\n9\\n6.1\\n6.1\\n6.0\\n10\\n6.8\\n6.f\\n6.6\\n20\\n\u00e2\u0096\u00a03-6\\n3-5\\n13-3\\n30\\n20.5\\n20.2\\n20.0\\n40\\n27.3\\n27.0\\n26.6\\n50\\n34-1\\n33-i^\\n33-3\\n39\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n3.9\\n3-\\n4.6\\n4-\\n5-2\\n5-\\n5.9\\n5-\\n6.6\\n6.\\n13-1\\n13-\\n19-7\\n19-\\n26.3\\n26.\\n32.9\\n32-\\n39\\n9\\n37\\n36\\n6\\n3-7\\n3-6\\n7\\n4-3\\n4-2\\n8\\n4.9\\n4.8\\n9\\n5-5\\n5-5\\n10\\n6.T\\n6.1\\n20\\n12.3\\n12. 1\\n30\\n18.5\\n18.2\\n40\\n24-6\\n24-3\\n50\\n30.8\\n30.4\\n36\\n3-6\\n4.2\\n4-8\\n5-4\\n6.0\\n12.0\\n18.0\\n24.0\\n^o.o\\n35 35 34\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\nJ 5\\n3-5\\n3-\\n4\\nI\\n4.1\\n4-\\n4\\n7\\n4-6\\n4-\\n5\\n3\\n5.2\\n5-\\n5\\n9\\n5-8\\n5-\\nII\\n8\\nII. 6\\n1 1.\\n17\\n7\\n17-5\\n17-\\n23\\n6\\n23-3\\n23-\\n29\\n6\\n29.1\\n28.\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n5\\n0.5\\n0.6\\n0.6\\no. 7\\n0.8\\n1-6\\n2-5\\n3-3\\n4.1\\n4\\n0.4\\n0.5\\n0.6\\n0.7\\no.f\\n1.5\\n3-f\\n4\\n0.4\\n0.4\\n0.5\\n0.6\\n0.6\\n1-3\\n2.0\\n2.6\\n3-3\\nO\\n3( 1", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0419.jp2"}, "420": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n-7 1\\n-T\\n25\\n26\\n27\\n28\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\ni 57\\n58\\n59\\n60\\nLost. Mil\\n53 405\\n53440\\n53 474\\n53509\\n53 544\\n53 578\\n53613\\n53647\\n53682\\n53716\\n53750\\n53785\\n53819\\n53854\\n53888\\n53922\\n53 956\\n53990\\n54025\\n54059\\n54093\\n54127\\n5416T\\n9 54195\\n9 54229\\n9.54263\\n9.54297\\n9-54331\\n9-54365\\n9-54 398\\n9-54 432\\n9- 54 466\\n9- 54 500\\n9-54 534\\n9-54567\\n9.54601\\n9-54634\\n9.54668\\n9.54702\\n9-54 73?\\n9.54769\\n9. 54 802\\n9-54836\\n9.54869\\n9 54 902\\n9-54936\\n9.54969\\n9.55002\\n9- 55 036\\n9-55069\\n9-55 102\\n9-55 135\\n9-55 168\\n9.55 202\\n9-55 235\\n9-55\\n268\\n9.55301\\n9-55 334\\n9-55367\\n9-55400\\n9-55 433\\nLoff. Cos.\\nd.\\n35\\n34\\n34\\n35\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n3-4\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n33\\n34\\n34\\n34\\n33\\n34\\n34\\n33\\n34\\n33\\n33\\n33\\n34\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\nLos. Tail.\\n9.56 IO6\\n9.56 146\\n9.56 185\\n9.56 224\\n9.56263\\n9-56303\\n9.56342\\n9-56381\\n9.56420\\n9.56459\\n9.56498\\n9-56537\\n9-56576\\n9.56615\\n9.56654\\n56693\\n56732\\n56771\\n56810\\n56848\\n9.56 887\\n9.56 926\\n9.56965\\n9-57003\\n9-57042\\n9.57081\\n9.57 119\\n9.57 158\\n9-57 196\\n9-57235\\n9-57274\\n9.57 312\\n9-57350\\n9-57389\\n9-57427\\n9.57466\\n9-57 504\\n9-57 542\\n9.57581\\n9.57619\\n9-57657\\n9.57696\\n9-57 734\\n9-57772\\n9.57810\\n9-37848\\n9-57886\\n9.57925\\n9-57963\\n9.58 001\\n9.58039\\n9-58077\\n9.58 115\\n9-58153\\n9.58 196\\n9.58 228\\n9.58266\\n9-58304\\n9.58342\\n9-58380\\n9-58417\\nLost. Cot.\\nc, (1.\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n38\\n39\\n39\\n39\\n39\\n38\\n39\\n38\\n39\\n38\\n38\\n39\\n38\\n38\\n38\\n38\\n39\\n38\\n38-\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n37-\\n38\\n38\\n38\\n37\\n38\\n37\\nLog. Cot.\\n0.43 893\\n0.43 854\\n0.43815\\n0.43775\\n0.43 736\\n0.43 697\\n0.43658\\n0.43619\\n0.43 580\\n0.43 540\\n0.43 501\\n0.43 462\\n0.43423\\n0.43 384\\n0.43 346\\n0.43 307\\n0,43 268\\n0.43 229\\n0.43 190\\n0.43 151\\n0.43 1 12\\n0.43074\\n0.4303 s\\n0.42 996\\n0.42 958\\n0.42 919\\n0.42 880\\n0.42 842\\n0.42 803\\n0.42 765\\n0.42 726\\n0.42 687\\n0.42 649\\n0.42 611\\n0.42 572\\n0.42 534\\n0.42 495\\n0.42457\\n0.42 419\\n0.42 380\\n0.42 342\\n0.42 304\\n0.42 266\\n0.42 227\\n0.42 189\\n0.42 151\\n0.42 113\\n0.42075\\n0.42037\\n0.41 999\\n0.41 961\\n0.41 923\\n0.41 885\\n0.41 847\\n0.41 809\\n0.41 771\\n0.41 733\\n0.41 6gl\\n0.41 658\\n0.41 620\\n0.41 582\\nc. (I. I Loi?. Tan.\\nLoir. Cos.\\n9.97 298\\n9.97 294\\n9.97 289\\n9-97 285\\n9.97 280\\n9-97275\\n9.97271\\n9.97 266\\n9.97 261\\n9.97257\\n9.97 252\\n9.97 248\\n9-97 243\\n9-97238\\n9-97 234\\n9-97 229\\n9.97 224\\n9.97 220\\n9.97215\\n9.97 210\\n9.97 206\\n9.97 201\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9-97\\n9.97097\\n9.97092\\n59\\n54\\n49\\n44\\n40\\n35\\n30\\n25\\n21\\n16\\nII\\n06\\n02\\n9.97087\\n9.97 082\\n9.97078\\n9.97073\\n9.97068\\n9.97063\\n9-97058\\n9.97054\\n9.97049\\n9.97044\\n9-97039\\n9-97034\\n9.97029\\n9-97025\\n9.97 020\\n9-97015\\nLost. Sin.\\n4\\n4\\n4\\n5\\n4\\n4\\n4\\n5\\n4\\n4\\n4\\n5\\n4\\n4\\n5\\n4\\n4\\n5\\n4\\n4\\n5\\n4\\n5\\n4\\n4\\n5\\n4\\n5\\n4\\n4\\n5\\n4\\n5\\n4\\n5\\n4\\n5\\n4\\n5\\n4\\n5\\n4\\n5\\n5\\n4\\n5\\n4\\n5\\n4\\n5\\n5\\n4\\n5\\n5\\n4\\n5\\n5\\n4\\n5\\n5\\n60\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n^i\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\nV_\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\np. P.\\n39\\n3S\\n6\\n7\\n8\\n3.9\\n4.6\\n5-2\\n3-\\n4.\\n5-\\n9\\n10\\n5-9\\n6.6\\n5-\\n6.\\n20\\n13-1\\n13-\\n30\\n40\\n19.7\\n26.3\\n19.\\n26.\\n50\\n32.9\\n32-\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n38\\n3-8\\n4-5\\n5-1\\n5-8\\n6.4\\n12.8\\n19.2\\n25-6\\n32,1\\n38\\n3-8\\n4.4\\n5.6\\n5-7\\n6.3\\n12.6\\n19.0\\n25-3\\n31-6\\n27\\n3-7\\n4\\n5\\n5\\n6\\n12\\n18\\n25\\n31\\n35\\n34\\n6\\n3-5\\n3-4\\n7\\n4.1\\n4.0\\n8\\n4-6\\n4.6\\n9\\n5-2\\n5.2\\n10\\n5-8\\n5-7\\n20\\nII. 6\\n11-5\\n30\\n17-5\\n17.2\\n40\\n23-3\\n23.0\\n50\\n29.1\\n28.?\\n34\\n3-4\\n3-9\\n4-5\\n5-1\\n5-6\\nII-3\\n17.0\\n22.6\\n28.3\\n6\\n3-3\\n3-\\n7\\n3-9\\n3.\\n8\\n4-4\\n4-\\n9\\n5-0\\n4-\\n10\\n5.6\\n5-\\n20\\nII. I\\nII.\\n30\\n16.7\\n16.\\n40\\n22.3\\n22.\\n50\\n27.9\\n27-\\n23 22\\n4\\n0.4\\n0.5\\n0.6\\n0.7\\n0.7\\n1-5\\n2.2\\n3-0\\n3-7\\n5\\n6\\n0.5\\n7\\n0.6,\\n8\\n0.6!\\n9\\n0.7\\n10\\n0.8\\n20\\n1-6\\n30\\n40\\n2-5\\n3-3\\n50\\n4.1\\np. p.\\nG9\\n368", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0420.jp2"}, "421": {"fulltext": "LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n2\\\\\\n10\\nII\\n12\\n14\\n15\\n16\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n26\\n27\\n28\\n29\\n80\\n31\\n32\\n33\\n34\\nJ3\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\nLocr. Sill.\\n9-55 433\\n9.55466\\n9-55 498\\n9-55 531\\n9-55 564\\n9-55 597\\n9.55630\\n9.55662\\n9.5569^\\n9.55728\\n9.55760\\n9-55 793\\n9.55826\\n9-55^58\\n9.55891\\n(1.\\n9-55923\\n9-55956\\n9-55 9S8\\n9.56 020\\n9.56053\\n9. 56085\\n9.56 118\\n9.56 150\\n9.56 182\\n9.56214\\n9.56247\\n9.56279\\n9.56311\\n9-56343\\n9-56375\\n9- 56 407\\n9-56439\\n9.56471\\n9.56503\\n9-56533\\n9.56567\\n9-56599\\n9.56631\\n9.56663\\n9.56695\\n9.56727\\n9-56758\\n9. 56 790\\n9.56 822\\n9.56854\\n50\\n51\\n52.\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n9.56885\\n9.56917\\n9- 56 949\\n9 56 980\\n9.57012\\n9- 57 043\\n9.57075\\n9-57 106\\n9-57 138\\n9-57 169\\n9.57 201\\n9.57232\\n9-57263\\n9.57295\\n9-57 326\\n9-57 357\\nlj(\u00c2\u00bbff. Cos.\\n33\\n32\\njj\\n33\\n32\\n33\\n32\\n33\\n32\\n32\\n32\\n33\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n31\\n32\\n32\\n31\\n32\\n31\\n32\\n3f\\n31\\n32\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\nLost. Tan. 0. d. I Loe. Cot.\\n9.58417\\n9.58455\\n9- 58 493\\n9-58531\\n9.58568\\n9.58 606\\n9.58644\\n9.58681\\n9.58719\\n9-58756\\n9.58794\\n9-58831\\n9.58869\\n9-58906\\n9 58 944\\n9.58 981\\n9.59019\\n9.59056\\n9- 59 093\\n9-59 131\\n9.59 168\\n9-59205\\n9.59242\\n9.59 280\\n9.59317\\n9-5935\\n9-59391\\n9.59428\\n9.59465\\n9.59502\\n9.59540\\n9-59 577\\n9.59614\\n9.59651\\n9.59688\\n9-59724\\n9-59761\\n9-59 798\\n9-59833\\n9.59872\\n9. 59 909\\n9- 59 946\\n9.59982\\n9.60019\\n9 60056\\n9.60093\\n9.60 129\\n9.60 165\\n9.60 203\\n9.60239\\nd.\\n9.60 276\\n9.60 312\\n9-60349\\n9.60 386\\n9.60422\\n9-60459\\n9.60495\\n9.60 531\\n9.60 568\\n9.60 604\\n9. 60 64 1\\n38\\n3?\\n38\\n37\\n3f\\n38\\n37\\n3f\\n37\\n37\\n37\\n3?\\n37\\n3?\\n3?\\n3l\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n36\\n37\\n37\\n37\\n36\\n37\\n37\\n36\\n37\\n36\\n37\\n36\\n37\\n36\\n36\\n36\\n36\\n37\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n0.41 582\\n0.41 544\\n0.41 507\\n0.41 469\\n0.41 43?\\n0.41 394\\n0.41 356\\n0.41 318\\n0.41 281\\n0.41 243\\n0.41 206\\n0.41 163\\n0.41 131\\n0.41 093\\n0.41 056\\n0.41 oig\\n0.40 981\\n0.40 944\\n0.40 906\\n0.40 869\\n0.40 832\\n0.40 794\\n0.40757\\n0.40 720\\n0.40 683\\n0.40 646\\n0.40 608\\n0.40 571\\n0.40 534\\n0.40 497\\n0.40 460\\n0.40423\\n0.40 386\\n0.40 349\\n0.40 312\\nl,nir. OS.\\n0.40 275\\n0.40 238\\n0.40 201\\n0.40 164\\n0.40 128\\n0.40 091\\n0.40 054\\n0.40017\\n0.39 980\\n0.39944\\no. 39 907\\n0.39876\\n0-39833\\n0.39797\\n0.39766\\n0.39724\\n0.3968^\\n0.39650\\n0.39614\\n0.3957?\\n0.39541\\n0.39 504\\n0.39468\\n0.39432\\n0.39395\\n9.97015\\n9.97 016\\n9.97005\\n9.97 000\\n9.96995\\n9.96991\\n9.96 986\\n9.96 981\\n9.96976\\n9-96971\\n9-96966\\n9.96 961\\n9-96956\\n9-96952\\n9-96947\\n9-96942\\n9-96937\\n9.96932\\n9-96927\\n9.96 922\\n9.96917\\n9.96 912\\n9-96907\\n9. 96 902\\n9-9689?\\n9.96 892\\n9.9688?\\n9.96882\\n9.96877\\n9.96873\\n9.96868\\n9.96 863\\n9.96858\\n9.96853\\n9.96848\\n9.96843\\n9.96838\\n9-96833\\n9.96828\\n9.96823\\n9.96 818\\n9.96 813\\n9.96808\\n9.96 802\\n9.96797\\n9-96792\\n9.96787\\n9.96 782\\n9-9677?\\n9.96772\\n9-96 767\\n9.96 762\\n9-9675?\\n9.96752\\n9.96747\\no- 39 359\\nCot. c. d. liOtr. In 11.\\n9 96 742\\n9-96737\\n9.96732\\n9.96727\\n9.96 721\\n9.96 7 16\\n4\\n5\\n5\\n5\\n4\\n5\\n5\\n5\\n4\\n5\\n5\\n5\\n4\\n5\\n5\\n5\\n5\\n5\\n4\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n4\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\nI\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n35\\n34\\n33\\n32\\n31\\nI I\\n30\\n29\\n28\\n27\\n26\\nl,ou sin.\\n25\\n24\\n23\\n22\\n21\\n20\\n9\\n18\\n17\\n16\\n38\\n37\\n37\\n6\\n3-8\\n3-?\\n3-7\\n7\\n4.4\\n4-4\\n4\\n3\\n8\\nS.o\\n5.0\\n4\\n9\\n9\\nS-7\\n5.6\\n5\\n10\\n6. .3\\n6.2\\n6\\nI\\n20\\n12.6\\n12.5\\n12\\n3\\n30\\n19.0\\n18.?\\n18\\n5\\n40\\n25-3\\n25.0\\n24\\n6\\n50\\n31-6\\n31.2\\n30\\n8\\n36\\n36\\n6\\n3-6\\n3-6\\n7\\n4.2\\n4-2\\n8\\n4.8\\n4.8\\n9\\n5-5\\n5-4\\n10\\n6.1\\n6.0\\n20\\n12. T\\n12.0\\n30\\n18.2\\n18.0\\n40\\n24-3\\n24.0\\n50\\n30.4\\n30.0\\n33 32 32\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n3-3\\n3-2\\n3-2\\n3\\n8\\n3\\n8\\n3-?\\n4\\n4\\n4\\n3\\n4.2\\n4\\n9\\n4\\n9\\n4.8\\n5\\n5\\n5\\n4\\n5-3\\nII\\n10\\n8\\n10.6\\n16\\n5\\n16\\n2\\n16.0\\n22\\n21\\n6\\n21.3\\n27\\n5\\n27\\nI\\n26.6\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n31 31\\n3-1\\n3-6\\n4.1\\n4.6\\n5-1\\n10.3\\n15-5\\n20.6\\n25 8\\n3\\nT\\n3\\n7\\n4\\n2\\n4\\n5\\n7\\n2\\n10\\n5\\n15\\n21\\n26\\nT\\n0.5\\n0.6\\n0.5\\n0.6\\n0.?\\n0.6\\n0.8\\n0.7\\n0.9\\n0.8\\n1-8\\n2.?\\n3-6\\n4-6\\n1-6\\n2-5\\n3-3\\n4.1\\n4\\n0.4\\n0.5\\n0.6\\n0.7\\n0.7\\n\u00e2\u0080\u00a25\\n2\\n30\\n3-?\\n1 I\\nG8^\\n3 -^y", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0421.jp2"}, "422": {"fulltext": "TABLE VII.-LOGARITHMIC SINES, COSINES. TANGENTS. AND COTANGENT^\\n23\u00c2\u00b0\\nLog. Siu.\\n9-57 35^\\n9-57389\\n9.57420\\n9-57 451\\n9-57482\\n9-57513\\n9-57 544\\n9-57576\\n9.57607\\n9.57638\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n9.57669\\n9.57700\\n9-57731\\n9.57762\\n9.57792\\n9-57823\\n9-57854\\n9.5788$\\n9-57916\\n9-57 947\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n-31\\n35\\n36\\n37\\n38\\n39\\n9-57 977\\n9-58008\\n9.58039\\n9.58070\\n9.58 TOO\\n9-58 131\\n9.58 162\\n9.58192\\n9.58223\\n9-58253\\n9.58284\\n9-58314\\n9-58345\\n9-5837$\\n9.58 406\\n9.58436\\n9.58465\\n9.58497\\n9.58527\\n9-58557\\n40 9.58587\\n41 9.58618\\n42 9.58648\\n43 9-58678\\n9-58708\\n50\\n51\\n52\\n53\\n54\\n9-58738\\n9.58769\\n9.58799\\n9.58 829\\n9.58859\\n9.58889\\n9.58919\\n9- 58 949\\n9-58979\\n9.59009\\n9-59038\\n9- 59 068\\n9- 59 098\\n9.59128\\n9-59158\\n9-59 188\\nLog. Cos.\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n30\\n31\\n31\\n31\\n30\\n31\\n30\\n31\\n30\\n31\\n30\\n30\\n31\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n29\\n30\\n30\\n29\\n30\\n30\\nd. Log. Tail. c. 1\\n9.60 641\\n9.60677\\n9.60713\\n9.60 750\\n9.60 785\\n9.60 822\\n9.60 859\\n9.60 895\\n9-60931\\n9.60 967\\n9.61 003\\n9.61 039\\n9.61 076\\n9.61 112\\n9.61 148\\n9.61 184\\n9.61 220\\n9.61 256\\n9.61 292\\n9.61 328\\n9-6i 364\\n9.61 400\\n9.61 436\\n9.61 472\\n9.61 507\\n9.61 543\\n9-61 579\\n9.61 615\\n9.61 651\\n9.61 685\\n9.61 722\\n9.61 758\\n9.61 794\\n9.61 829\\n9 61 865\\n9.61 901\\n9.61 936\\n9.61 972\\n9. 62 007\\n9-62043\\n9.62078\\n9.62 114\\n9.62 149\\n9.62 185\\n9.62 220\\n9.62 256\\n9.62 291\\n9.62 327\\n9.62 362\\n9-62 39^\\n9-62433\\n9.62468\\n9.62 503\\n9-62 539\\n9-62 574\\n9.62 609\\n9.62 644\\n9.62 679\\n9.62 715\\n9.62 750\\n9.62 785\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n3!\\n36\\n36\\n3\u00c2\u00a7\\n36\\n35\\n36\\n3l\\n36\\n35\\n35\\n36\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\nLog. Cot.\\n0-39359\\n0.39322\\n0.39285\\n0.39250\\n0.39213\\n0.39 177\\n0.39 141\\n0.39 105\\n0.39069\\n0.39032\\n0.38995\\no. 38 966\\n0.38924\\n0.38888\\n0.38852\\n0.38816\\n0.38 780\\n0.38744\\n0.38 708\\n0.38 672\\n0.38636\\n0.38 600\\n0.38 564\\n0.38 528\\n0.38492\\n0-38456\\n0.38 420\\n0.38385\\n0.38349\\n0.38 313\\n0.3827^\\n0.38 242\\n0.38 206\\n0.38 170\\n0.38 135\\n0.38099\\n0.38 063\\n0.38028\\n0.37 992\\n0.37 957\\n0.37 921\\n0.37 S86\\n0.37 850\\n0.37815\\n0.37779\\n0-37 744\\n0.37 708\\n0.37673\\n0.3763^\\n0.37 602\\n0-37 567\\n0.37 531\\n0-37 496\\n0.37461\\n0.37426\\nLog. Cot. led.\\n0.37390\\n0.37355\\n0.37326\\n0.37 28 5\\n0.37250\\nLog. Cos.\\no- 37 215\\nLog. Tan.\\n9.96715\\n9.96 711\\n9.96705\\n9.96 701\\n9.96 696\\n9.96 691\\n9.96686\\n9.96681\\n9-9667$\\n9.96 676\\n9.96665\\n9.96660\\n9.96655\\n9.96 650\\n9-96644\\n9.96639\\n9.96634\\n9.96 629\\n9.96 624\\n9.96 619\\n9.96 613\\n9-96608\\n9. 96 603\\n9.96598\\n9.96593\\n9-96 587\\n9.96 582\\n9.96577\\n9-96572\\n9-96 567\\n9.96 561\\n9-96556\\n9.96551\\n9.96546\\n9-96 540\\n9-96 535\\n9-96 530\\n9.96525\\n9.96519\\n9.96514\\n9.96 509\\n9-96 503\\n9.96498\\n9-96493\\n9.96488\\n9.96482\\n9-96477\\n9.96472\\n9.96465\\n9.96461\\n9.96456\\n9-96450\\n9-96445\\n9.96440\\n9-96434\\n9-96429\\n9-96424\\n9-96418\\n9.96413\\n9. 96 408\\n9.96 402\\nLog. 8111.\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\nd.\\n60\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n_3i\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\nTo\\n9\\n8\\n7\\n6\\n5\\n4\\n3\\n2\\nI\\n~0~\\nP. p.\\n36\\n6\\n3-6\\n7\\n4.2\\n8\\n4.8\\n9\\n5-5\\n10\\n6.1\\n20\\n12. 1\\n30\\n18.2\\n40\\n24-3\\n50\\n30.4\\n3S\\n6\\n3-5\\n7\\n4.1\\n8\\n4.?\\n9\\n5-3\\n10\\n5-9\\n20\\n11.8\\n30\\n17-7\\n40\\n23-6\\n50\\n29.6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n3i\\n3-1\\n3-7\\n4.2\\n4-7\\n5.2\\n10.5\\n15-^\\n21.0\\n26.2\\n30\\n30\\n6\\n3-0\\n3-0\\n7\\n3-5\\n3.5\\n8\\n4-0\\n4.0\\n9\\n4.6\\n4-5\\n10\\n5-1\\n5.0\\n20\\n10. 1\\nlO.O\\n30\\n15.2\\n15.0\\n40\\n20.3\\n20.0\\n50\\n25.4\\n25.0\\n36\\n3-6\\n4.2\\n4.8\\n5-4\\n6.0\\n12.0\\n18.0\\n24.0\\n30.0\\n35\\n3.5\\n4-1\\n4-6\\n5.2\\n5-8\\nII. 6\\n17.5\\n23-3\\n29.1\\n31\\n3-1\\n3-6\\n4-1\\n4.6\\n5-1\\n10.3\\n15.5\\n20.6\\n25-8\\n29\\n2.9\\n3-4\\n3-9\\n4.4\\n4-9\\n9-8\\n14.^\\n19-6\\n24.6\\nB\\n5\\n6\\n0.5\\n0-5\\n7\\n0.5\\n0.6\\n8\\n0.7\\n0.6\\n9\\n0.8\\n0.7\\n10\\n0.9\\n0.8\\n20\\n1-8\\n1-6\\n30\\n2.7\\n2.5\\n40\\n3-6\\n3-3\\n50\\n4-6\\n4.1\\np. p.\\n67\\n370", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0422.jp2"}, "423": {"fulltext": "TAl^LE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES,\\nCOSINES,\\n2:v\\nTANGENTS, AND COTANGENTS.\\n10\\nII\\n12\\n13\\n14\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLog. Sill. I d.\\n15\\n9-59\\n16\\n9-59\\n17\\n9-59\\n18\\n9.59\\n19\\n9.59\\n9-59\\n9-59\\n9-59\\n9-59\\n9-59\\n188\\n21^\\n247\\n277\\n306\\n9-59\\n9-59\\n9-59\\n9-59\\n9-59\\n336\\n366\\n39^\\n425\\n454\\n9-59\\n9-59\\n9-59\\n9-59\\n9-59\\n484\\n513\\n543\\n572\\n602\\n631\\n661\\n696\\n719\\n749\\n9-59\\n9-59\\n9-59\\n9-59\\n9-59\\n778\\n807\\nS37\\n866\\n895\\n9-59\\n9.59\\n9-59\\n9.60\\n9.60\\n924\\n953\\n982\\n012\\n041\\n9.60\\n9.60\\n9.60\\n9.60\\n9.60\\n070\\n099\\n128\\n157\\n186\\n9.60\\n9.60\\n9.60\\n9.60\\n9.60\\n215\\n244\\n273\\n301\\n330\\n9.60\\n9.60\\n9.60\\n9.60\\n9.60\\n359\\n388\\n417\\n445\\n474\\n9.60\\n9.60\\n9.60\\n9.60\\n9.60\\n503\\n532\\n560\\n589\\n618\\n9.60\\n9.60\\n9.60\\n9.60\\n9.60\\n646\\n675\\n703\\n732\\n766\\n9.60\\n9.60\\n9.60\\n9.60\\n9.60\\n789\\n817\\n846\\n874\\n903\\n9-60931\\nLog. Cos.\\n29\\n30\\n29\\n29\\n30\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n28\\n29\\n29\\n28\\n29\\n28\\n29\\n28\\n29\\n28\\n28\\n29\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\nd.\\nLou. Tan.\\n9.62 785\\n9.62 820\\n9.62855\\n9.62 890\\n9.62 925\\n9.62 966\\n9.62995\\n9.63030\\n9.63065\\n9.63 106\\n963 135\\n9.63 170\\n9.63 205\\n9.63 240\\n9.63275\\n9.63310\\n9-63344\\n9-63379\\n9.63414\\n9-63449\\n9.63484\\n9-63 5I8\\n9-63553\\n9.63 588\\n9.63 622\\n9-63657\\n9.63 692\\n9-63726\\n9.63761\\n9-63795\\n9.63830\\n9.63 864\\n9.63899\\n9-63933\\n9-63 968\\n9. 64 002\\n9.64037\\n9.64071\\n9.64 106\\n9.64 140\\n9.64 174\\n9.64 209\\n9.64 243\\n9.64 277\\n9.64312\\n9-64 346\\n9.64 380\\n9.64415\\n9.64449\\n9-64483\\n9-6451?\\n9.64551\\n9.64585\\n9.64620\\n9.64654\\nc. d.\\n9.64688\\n9.64 722\\n9.64756\\n9.64790\\n9.64 824\\n9.64 85\u00c2\u00a7\\nLoir. Cot. led.\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n34\\n35\\n35\\n3I\\n35\\n35\\n34\\n35\\n34\\n34\\n35\\n3-+\\n34\\n35\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n3^\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\nLog. Cot.\\n0.37 215\\n0.37 179\\n0.37 144\\n0.37 109\\n0.37074\\n0.37039\\n0.37004\\no. 36 969\\n0.36934\\n0.36899\\no. 36 864\\n0.36 829\\n0.36794\\n0.36 760\\n0.36725\\n0.36 690\\n0.36655\\n0.36 626\\n0.36585\\n0.36 551\\n0.36 516\\n0.36481\\n0.36447\\n0.36 412\\n0.36 377\\n0.36 343\\n0.36308\\n0.36273\\n0.36239\\no. 36 204\\n0.36 170\\n0.36 135\\n0.36 lOI\\no. 36 065\\n0.36 032\\no- 3 5 997\\n03 5 963\\n0-35928\\n0.35894\\n0-35859\\n0.35825\\n0.35791\\n0.35 756\\n0.35 722\\n0.35688\\n0-35653\\n0.35619\\n0.35585\\n0.35551\\n0-35 517\\n0.35482\\n0.35 448\\n0.35414\\n0.35 380\\n0.35 346\\n0.35 312\\n0.35 278\\n0.35244\\n0.35 209\\n0-35 i7l\\n0.35 141\\nLoir. Tsui.\\nLocr. Cos.\\n96 402\\n96 397\\n96 392\\n96386\\n96381\\n96375\\n96370\\n96365\\n96359\\n96354\\n96 349\\n96343\\n96338\\n96332\\n96327\\n96 321\\n96316\\n96 31 1\\n9630I\\n96 300\\n96 294\\n96 289\\n96 283\\n96278\\n96 272\\n96 267\\n96 261\\n96 256\\n96 251\\n96245\\n96 240\\n96234\\n96 229\\n96 223\\n96 218\\n96 212\\n96 205\\n96 201\\n96\\n96\\n96\\n96\\n96\\n96\\n96\\n96\\n96\\n96\\n96\\n96\\n96\\n96\\n96\\n96\\n96\\n95\\n90\\n84\\n79\\n73\\n68\\n62\\n57\\n51\\n46\\n40\\n34\\n29\\n23\\n18\\n12\\n06\\n96 lOI\\n96095\\n96 090\\n96 084\\n96078\\n9-96073\\nLost. Sin.\\n\u00c2\u00ab0\\n59\\n58\\n57\\n56\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\nI 1\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n3S\\n3.5\\n4.1\\n4-7\\n5-3\\n5-9\\nII. 8\\n23-6\\n29.6\\n35\\n3\\n4\\n4\\n5\\n5\\n1 1\\n17\\n23\\n29\\n34\\n34\\n3-4\\n3.4\\n4.0\\n4.6\\n3\\n4\\n9\\n5\\n5.2\\n5\\n5\\nI\\n6\\nII. 5\\n1 1\\n3\\n17.2\\n17\\n23-0\\n28.7\\n22\\n28\\n6\\n3\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n30\\n3-0\\n3.5\\n4.0\\n4-5\\n5.0\\nlo.o\\n15.0\\n20.0\\n25.0\\n29\\n29\\n28\\n6\\n2.9\\n2.9\\n2.\\n7\\n3-4\\n3-4\\n3-\\n8\\n3-9\\n3-8\\n3-\\n9\\n4.4\\n4-3\\n4-\\n10\\n4.9\\n4-8\\n4-\\n20\\n9-8\\n9-6\\n9-\\n30\\n14-7\\n14.5\\n14.\\n40\\n19-6\\n19-3\\n19.\\n50\\n24.6\\n24.1\\n23-\\n6\\n6\\n0.6\\n5\\n0-5\\n7\\n8\\n0.7\\n0.8\\n0.6\\n9\\n10\\n0.9\\nI.O\\n0.8\\n0.9\\n20\\n2.0\\n1-8\\n30\\n40\\n50\\n3-0\\n4.0\\n5.0\\n2.?\\n3-6\\n4.6\\n5\\n0.5\\n0.6\\n0.6\\no.?\\n0.8\\n1-6\\n2.5\\n3-3\\n4.1\\nr. r\\n66\\n371", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0423.jp2"}, "424": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n24\u00c2\u00b0\\n29\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLoff. Sin.\\n9.60931\\n9.60959\\n9.60988\\nd.\\n772\\n800\\n828\\n856\\n883\\n911\\n938\\n966\\n994\\n9.62 021\\n9.62 049\\n9.62075\\n9.62 104\\n9.62 13T\\n9.62 158\\n9.62 186\\n9.62 213\\n9.62 241\\n9.62 268\\n9.62 295\\n9.62323\\n9.62 350\\n9.62 yj^\\n9.62 404\\n9.62432\\n9.62459\\n9.62486\\n9.62 513\\n9.62 540\\n9.62 56^\\n9 62 595\\nLog. Cos.\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n27\\n28\\n28\\n28\\n27\\n28\\n27\\n28\\n2^\\n28\\n2f\\n28\\n27\\n2^\\n2^\\n27\\n28\\n27\\n27\\n2?\\n27\\n2f\\n27\\n2f\\nif\\n27\\n27\\n2^\\n27\\n27\\n27\\n27\\n2^\\n27\\nIf\\n27\\n27\\n27\\n2?\\nLos, i an. C. d. Log. Cot.\\n9.64858\\n9.64 892\\n9.64926\\n9.64 960\\n9-64994\\n9.65 028\\n9.65 062\\n9.65 096\\n9.65 129\\n9-65 163\\n9.65 197\\n9.65 231\\n9.65 265\\n9.65 299\\n9-65 332\\n9-65 366\\n9.65 400\\n9-65433\\n9.65467\\n9-65 501\\n9-65 535\\n9.65 568\\n9.65 602\\n9.65635\\n9.65 669\\n9.65703\\n9-65 736\\n9-65 770\\n9.65 803\\n9-65 837\\n9.65 870\\n9-65 904\\n965 937\\n9.65971\\n9. 66 004\\n9.66037\\n9.66071\\n9.66 104\\n9.66 13^\\n9.66 171\\n9.66 204\\n9.66 23^\\n9.66 271\\n9. 66 304\\n96633^\\n9.66370\\n9.66404\\n9.66437\\n9.66 470\\n9- 66 503\\n9.66\\n9.66\\n9.66\\n536\\n570\\n603\\n9.66 636\\n9.66669\\n9.66 702\\n9.66735\\n9.66768\\n9.66 801\\n9.66 834\\n9^86f\\nLog. Cot. c. d.\\n34\\n34\\n33\\n34\\n34\\n34\\n34\\n33\\n34\\n34\\n33\\n34\\n34\\n33\\n34\\n33\\n33\\n34\\n33\\n34\\n33\\n33\\n33\\n33\\n34\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n0.35 141\\n0.35 107\\n0-35073\\n0.35 040\\n0.35 006\\n0.34972\\n0.34938\\n0.34904\\n0,34 ]0\\n0.34836\\no. 34 802\\n0.34769\\n0.34735\\n0.34701\\n0.3466^\\n0.34633\\no. 34 600\\n0.34566\\n0.34532\\n0.34499\\n0.34465\\n0.34431\\n0.34398\\n0.34364\\n0.34331\\n0.34297\\n0.34263\\n0.34230\\n0.34196\\n0.34 163\\n0.34 129\\n0.34096\\no. 34 062\\n0.34029\\n0.33996\\n0.33 962\\n0.33929\\n0-3389?\\n0.33862\\n0.33829\\n0.33795\\n0.33762\\n0.33729\\n0.33696\\n0.33 662\\nLog. Cos.\\n0.33629\\n0.33 596\\n0.33 563\\n0.33529\\no. 33 496\\n0.33463\\n0.33430\\n0.33397\\n0.33364\\n0.33331\\n0.33 298\\n0.33265\\n0.33232\\n0.33 198\\n0.33 i6g\\n0.33 J 32\\nLog. Tan.\\n9.96073\\n9. 96 067\\n9.96062\\n9.96056\\n9.96050\\n9.96045\\n9-96039\\n9.96033\\n9.96 028\\n9.96 022\\n9-96016\\n9.96 01 1\\n9.96005\\n9-95 999\\n9.95994\\n9.95988\\n9.95982\\n9-95 977\\n9.95971\\n9.95965\\n9-95 959\\n9-95 954\\n9-95 948\\n9.95942\\n9-95 937\\n9-95931\\n9-95925\\n9.95919\\n9.95914\\n9.95908\\n9-95 902\\n9.95 896\\n9.95891\\n9.95885\\n9-95 879\\n9-95 873\\n9.95867\\n9.95 862\\n9-95 856\\n9.95850\\n9.95 844\\n9-95838\\n9-95833\\n9-95 827\\n9-95821\\nd.\\n9.95815\\n9.95809\\n9.95 804\\n9.95798\\n9.95 792\\n9-95786\\n9.95786\\n9-95 774\\n9-95 768\\n9-95 763\\n9-95 757\\n9-95 751\\n9-95 745\\n9-95 739\\n9-95 733\\n9-95 72^\\nLog. Sin.\\n6\\n6\\n5\\n6\\n6\\nI\\n6\\n6\\n6\\nI\\n6\\n6\\n6\\nI\\n6\\n6\\ndT\\nGO\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\noO\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\nP. p.\\n34\\n33\\n33\\n6\\n3.4\\n3-3\\n3-\\n7\\n3-9\\n3\\n9\\n3-\\n8\\n4-5\\n4\\n4\\n4-\\n9\\n5-1\\n5\\n4-\\n10\\n5-6\\n5\\n6\\n5-\\n20\\nII-3\\nII\\nI\\nII.\\n30\\n17.0\\n16\\n1\\n16.\\n40\\n22.6\\n22\\n3\\n22.\\n50\\n28.3\\n27.9\\n27.\\n28 28\\n3-2\\n3-^\\n4.2\\n4-6\\n9-\\n14.\\n18.\\n23-\\n6\\n2.8\\n7\\n3-3\\n8\\n3.8\\n9\\n4-3\\n10\\n4.7\\n20\\n9.5\\n30\\n14.2\\n40\\n19.0\\n50\\n23-/\\n2f\\n6\\n2.f\\n7\\n3-2\\n8\\n3-6\\n9\\n4.1\\n10\\n4.6\\n20\\n9.1\\n30\\n13-7\\n40\\n18.3\\n50\\n22.9\\n27\\n2.7\\n3-1\\n3.6\\n4.6\\n4-5\\n9.0\\n13-5\\n18.0\\n22.5\\n6\\n6\\n0.6\\n7\\n8\\n0.7\\n0.8\\n9\\n10\\n0.9\\nI.O\\n20\\n2.0\\n30\\n40\\n50\\n3-0\\n4.0\\n5.0\\n0.5\\n0.6\\n0.1\\n0.8\\n0.9\\n1-8\\n2.^\\n3-6\\n4.6\\nP. p.\\n65\\n372", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0424.jp2"}, "425": {"fulltext": "TABLE VII.\\nLOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n25\\nI\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n9\\n10\\nII\\n12\\n13\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\nao\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49_\\noO\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nGO\\nliOir. sill.\\n9.62 595\\n9.62 622\\n9.62 649\\n9.62 676\\n9.62 703\\n9.62 730\\n9.62757\\n9.62 784\\n9.62 81 I\\n9.62838\\n9.62864\\n9.62 89T\\n9.62 9I8\\n9.6294^\\n9.62 972\\n9.62999\\n9.63025\\n9.63 052\\n9.63079\\n9.63 106\\n9.63 132\\n9.63159\\n9.63 186\\n9.63 212\\n9.63239\\n9.63 266\\n9.63 292\\n9-63319\\n9-63 34 5\\n9.63372\\n9-63 398\\n9.63425\\n9.63451\\n9.63478\\n9.63 504\\n9.63 530\\n9-63557\\n9-63 583\\n9.63609\\n9 63 636\\n9.63 662\\n9.63688\\n9.63715\\n9.63 741\\n9.63767\\n9-63793\\n9.63819\\n9.63 846\\n9.63 872\\n9.63898\\n9.63 924\\n9.63956\\n9-63976\\n9.64002\\n9.64028\\n9.64054\\n9.64086\\n9.64 106\\n9.64 132\\n9-64 158\\n9.64 184\\nLog. Cos. J d.\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n26\\n27\\n27\\n27\\n26\\n27\\n^6\\n27\\n26\\n27\\n26\\n27\\n26\\n26\\n26\\n27\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n25\\nLog. Tan. I c d. I Lot?. Cot\\n9.66867\\n9. 66 900\\n9-66933\\n9.66 966\\n9.66999\\n9.67032\\n9.67 065\\n9-6709?\\n9-67 130\\n9-67 163\\n9.67 196\\n9.67 229\\n9.67 262\\n967294\\n9.67 327\\n9.67 360\\n9-67393\\n9-67425\\n9-67458\\n9.67 491\\n9.67 523\\n9-67 556\\n9.67 589\\n9.67 621\\n9.67654\\n9.67 687\\n9.67719\\n9.67752\\n9.67784\\n9.67 817\\n9.67849\\n9.67 882\\n9.67 914\\n9-67947\\n9.67979\\n9.68 012\\n9.68 044\\n9.68 077\\n9.68 109\\n9.68 14T\\n9.68 174\\n9.68 205\\n9-68 238\\n9.68 271\\n9-68 303\\n9-68 335\\n9.68 368\\n9. 68 400\\n9.68432\\n9.68 464\\n9-68497\\n9.68 529\\n9.68 561\\n9-68 593\\n9.68625\\n9.6865^\\n9.68 690\\n9.68 722\\n9-68754\\n9.68786\\n9.68818\\n32\\n33\\n33\\n33\\n33\\n33\\n32\\n33\\n33\\n33\\n32\\n33\\n32\\n33\\n32\\n33\\n32\\n33\\n32\\n32\\n33\\n32\\n32\\n33\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\nLog. Cot. I c. (1.\\n0.33 132\\n0.33 100\\n0.33067\\n0-33034\\n0.33001\\n0.32 968\\n0-32935\\n0.32 902\\n0.32 869\\n0.32836\\n0.32 803\\n0.32 771\\n0.32738\\n0.32 705\\n0.32 672\\n0.32 640\\n0.32 607\\n0.32 574\\n0.32 54T\\n0.32 509\\n0.32476\\n0.32443\\n0.32 41 I\\n0.32 378\\n0.32 345\\n0.32 313\\n0.32 286\\n0.32 248\\n0.32 215\\n0.32 183\\n0.32 150\\n0.32 118\\n0.32 085\\n0.32053\\n0.32 026\\n0.3\\n03\\n0.3\\n0.3\\n0.3\\n0-3\\n0.3\\n0.3\\n3\\n0.3\\n0.3\\n0.3\\n0.3\\n0.3\\n0.3\\n0.3\\n0.3\\n0-3\\n0.3\\n0.3\\n988\\n955\\n923\\n891\\n858\\n826\\n793\\n761\\n729\\n6%\\n66if\\n632\\n600\\n56?\\n535\\n503\\n471\\n439\\n406\\n374\\n342\\n310\\n278\\n246\\n214\\nT82\\nLog. Tan.\\nLocr. Cos.\\n(1.\\n9.95 727\\n9.95721\\n9.95716\\n9.95710\\n9.95704\\n9.95698\\n9.95692\\n9.95 686\\n9.95 686\\n9.95674\\n9.95668\\n9.95 662\\n9-95656\\n9.95656\\n9-95644\\n9-95 638\\n9.95632\\n9.95627\\n9.95 621\\n9.95615\\n9.95609\\n9.95 603\\n9-95 597\\n9-95 591\\n9-95 585\\n9-95 579\\n9-95 573\\n9.95 567\\n9.95 561\\n9-95 555\\n9-95 549\\n9-95 543\\n9-95 537\\n9-95 530\\n9-95 524\\n9 95 518\\n9.95512\\n9-95 506\\n9 95 506\\n9-95 494\\n9-95488\\n9.95482\\n9.95476\\n9.95 470\\n9.95464\\n9-95458\\n9.95452\\n9-95 445\\n9-95 439\\n9-95 433\\n9.95427\\n9.95421\\n9.95415\\n9-95409\\n9-95403\\n9-95 397\\n9-95 390\\n9.95 384\\n9-95 378\\n9-95 372\\n9-95 366\\nLog. Sin. I\\n(iO\\n59\\n58\\n57\\n56\\n30\\n29\\n23\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n^9\\n18\\n17\\n_i6\\nIS\\n14\\n13\\n12\\nII\\n9\\n8\\n7\\n6\\np. I*.\\n27\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n18\\n22.\\n33\\n32\\n32\\n6\\n3-3\\n3-2\\n3-2\\n7\\n3-8\\n3-8\\n3-^\\n8\\n4.4\\n4-3\\n4.2\\n9\\n4-9\\n4.9\\n4-8\\n10\\n5-5\\n5-4\\n5-3\\n20\\nII.\\n10.8\\n10.6\\n30\\n16.5\\n16.2\\n16.0\\n40\\n22.0\\n21.6\\n21.3\\n50\\n27.5\\n27.1\\n26.6\\n2S\\n26\\n25\\n6\\n2.6\\n2.6\\n2.\\n7\\n8\\n3\\n3\\nI\\n3\\n3\\n4\\n3-\\n3-\\n9\\n4\\n3\\n9\\n3-\\n10\\n20\\n4\\n8\\n4\\n8\\n4\\n8\\n3\\n6\\n4-\\n8.\\n30\\n13\\n2\\n13\\n12.\\n40\\n17\\n6\\n17\\n3\\n17.\\n50\\n22\\nI\\n21\\n6\\n21.\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n8 6 5\\n0.5\\n0.6\\n0.7\\n0.8\\n0.9\\n1-8\\n2.f\\n3-6\\n4-6\\n0.6\\n0.6\\n0.7\\n0.7\\n0.8\\n0.8\\nI.O\\n0.9\\n1. 1\\n1.0\\n2.1\\n2.0\\n3-2\\n3-0\\n4-3\\n4.0\\n5-4\\n5.0 i\\nP. 1\\nG4\\n373", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0425.jp2"}, "426": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS\\n26\u00c2\u00b0\\n10\\nII\\n12\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nGO\\nLo^. Sill. d.\\n64 184\\n64 210\\n64236\\n64 262\\n64 287\\n64313\\n64339\\n64365\\n64391\\n644I6\\n64442\\n64468\\n64493\\n64519\\n64545\\n64576\\n64596\\n64622\\n6464^\\n64673\\n64698\\n64724\\n64749\\n64775\\n64 800\\n64826\\n64851\\n64876\\n64902\\n64927\\n64952\\n64978\\n65 003\\n65028\\n65054\\n65079\\n65 104\\n65 129\\n65 155\\n65 180\\n65 205\\n65 230\\n6525.^\\n65 286\\n65305\\n65331\\n65356\\n65381\\n65 406\\n65431\\n65456\\n65481\\n65 506\\n65530\\n65555\\n65 586\\n65605\\n65 630\\n65655\\n65 680\\n9^65704\\n26\\n26\\n26\\n25\\n26\\n26\\n25\\n26\\n25\\n26\\n25\\n25\\n26\\n25\\n25\\n25\\n26\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n24\\n25\\n25\\n25\\n24\\n25\\n25\\n24\\nLog. Cos. i d.\\nLoff. Tan. c. d\\n69615\\n69647\\n69678\\n69 716\\n69742\\n68818\\n68850\\n68882\\n68 914:\\n68946\\n68978\\n69016\\n69042\\n69074\\n69 106\\n69138\\n69 170\\n69 202\\n69234\\n69 265\\n69 297\\n69329\\n69 361\\n69393\\n69425\\n69456\\n69488\\n69 520\\n69552\\n69583\\n69773\\n69805\\n69837\\n69868\\n69 900\\n69931\\n69 963\\n69994\\n70026\\n70058\\n70089\\n70 121\\n70152\\n70183\\n70215\\n70246\\n70278\\n70309\\n70341\\n70372\\n70403\\n70435\\n70466\\n70497\\n70529\\n70 566\\n70591\\n70623\\n70654\\n70685\\n70716\\nLog. Cot.\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n31\\n32\\n32\\n32\\n32\\n32\\n31\\n32\\n32\\n31\\n32\\n32\\n31\\n32\\n31\\n32\\n31\\n32\\n31\\n31\\n32\\n31\\n31\\n32\\n31\\n31\\n31\\n31\\n31\\n31\\n32\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\nTTd.\\nLog. Cot.\\n0.31 182\\n0.31 150\\n0.31 11^\\n0.31085\\n0.31053\\n0.31 021\\n0.30989\\n0.3095?\\n0.30 926\\n0.30894\\n0.30 862\\n0.30830\\n0.30798\\n0.30 766\\n0.30734\\no. 30 702\\n0.30 676\\n0.30639\\no. 30 607\\n0.30575\\n0.30543\\n0.30 511\\n0.30480\\no. 30 448\\n0.30 4I6\\n0.30384\\n0.30353\\n0.30321\\n0.30 289\\n0.30 258\\n0.30226\\n0.30194\\n0.30163\\n0.30 1 31\\n0.30 100\\n0.30068\\n0.30037\\n0.30005\\n0.29973\\n0.29 942\\n0.29 910\\n0.29 879\\no. 29 847\\n0.29 8 16\\n0,29 785\\n0.29753\\n0.29 722\\no. 29 696\\n0.29 659\\n0.29 628\\n0.29596\\n0.29 565\\n0.29533\\n0.29 502\\n0.29471\\nLog. Cos.\\n0.29439\\nO.29408\\n0.29377\\n0.29346\\n0.29314\\n0.29 283\\nLog. Tan.\\n95366\\n95360\\n95 353\\n95 34?\\n95341\\n95 335\\n95329\\n95323\\n95316\\n95310\\n95304\\n95298\\n95292\\n95285\\n95279\\n95273\\n95267\\n95 266\\n95254\\n95248\\n95242\\n95235\\n95229\\n95223\\n95 217\\n95 210\\n95204\\n95\\n95\\n95\\n95\\n95\\n95\\n95\\n95\\n95\\n95\\n95\\n95\\n95\\n98\\n91\\n85\\n79\\n73\\n66\\n60\\n54\\n47\\n41\\n35\\n28\\n22\\n16\\n09\\n03\\n95097\\n95090\\n95084\\n95078\\n95071\\n95065\\n95058\\n95052\\n95046\\n95039\\n95033\\n95026\\n95 020\\n95014\\n9500?\\n95 001\\n94 994\\n9-94988\\nLog. Sin.\\nd.\\n00\\n59\\n58\\n57\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\np. p.\\n32\\n6\\n3-2\\n7\\n3.8\\n8\\n4-3\\n9\\n4.9\\n10\\n5.4\\n20\\n10.8\\n30\\n16.2\\n40\\n21.6\\n50\\n27.1\\n32\\n3-2\\n3-7\\n4.2\\n4.8\\n5-3\\n10.6\\n16.0\\n21.3\\n26. s\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n31\\n3-1\\n3-7\\n4.2\\n4-7\\n5.2\\n10.5\\nI5-?\\n21.0\\n26.2\\n31\\n3-1\\n3\\n4\\n4\\n5\\n10\\n15\\n20\\n25\\n26\\n25\\n6\\n2.6\\n2.5\\n7\\n3-0\\n3-0\\n8\\n3-4\\n3-4\\n9\\n3-9\\n3-8\\n10\\n4.3\\n4.2\\n20\\n8.6\\n8.5\\n30\\n13.0\\ni2.^\\n40\\n17-3\\n17.0\\n50\\n21.6\\n21.2\\n24\\n6\\n2.4\\n0.6\\n7\\n2-8\\n0.7\\n8\\n3-2\\n0.8\\n9\\n37\\ni.o\\n10\\n4.1\\nI.I\\n20\\n8.T\\n2.1\\n30\\n12.2\\n3-2\\n40\\n16.3\\n4-3\\n50\\n20.4\\n5-4\\n25\\n2.5\\n2.9\\n3-3\\n3-?\\n4.1\\n8.3\\n12.5\\n16.6\\n20.8\\n6\\n0.6\\n0.7\\n0.8\\n0.9\\n1.0\\n2.0\\n3.0\\n4.0\\n5.0\\nP. P.\\no\\n374", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0426.jp2"}, "427": {"fulltext": "TABLE VII.\\nLOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\nLo;?. Sin.\\n9.65 704\\n9.65729\\n965754\\n9.65779\\n9-65 80 3\\n9.65828\\n9.65853\\n9.65 878\\n9.65 902\\n9.65927\\n9.65 95T\\n9-65 976\\n9.66001\\n9.6602^\\n9.66 050\\n9.66074\\n9. 66 099\\n9.66 123\\n9.66 1 48\\n9.66 172\\n9 66 197\\n9.66 221\\n9.66 246\\n9.66 276\\n9.66 294\\n9.66 319\\n9-66343\\n9.66 367\\n9.66 392\\n9.66416\\n9. 66 440\\n9.66 465\\n9.66489\\n9.66513\\n9.66 537\\n9.66 561\\n9.66 586\\n9.66 610\\n9.66634\\nQ 66 658\\n9.66682\\n9-66705\\n9.66 730\\n9.66754\\n9.66778\\n9.66 802\\n9.66 825\\n9.66 850\\n9.66874\\n9.66898\\n9.66 922\\n9.66946\\n9.66 976\\n9-66994\\n9 67 018\\n(1.\\n9.67 042\\n9.67 066\\n9.67089\\n9.67 1 13\\n9-67 137\\n9.67 161\\nLog. Cos. I (1.\\n25\\n24\\n25\\n24\\n25\\n24\\n25\\n24\\n24\\n24\\n25\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n23\\n24\\n24\\n24\\n23\\n24\\n23\\n24\\nliOff. Tan. c. d. 1 Lot?, lot.\\n70716\\n70748\\n70779\\n70810\\n70 841\\n70872\\n70903\\n70935\\n70 966\\n70997\\n028\\n059\\n090\\n121\\n152\\n183\\n214\\n24^\\n276\\n307\\n338\\n369\\n400\\n431\\n462\\n493\\n524\\n555\\n586\\n617\\n647\\n678\\n709\\n740\\n771\\n80 f\\n832\\n863\\n894\\n925\\n955\\n986\\n72 017\\n72047\\n72 078\\n72 109\\n72 139\\n72 170\\n72 201\\n72231\\n72 262\\n72 2G2\\n72323\\n72354\\n72384\\n72415\\n7244?\\n72476\\n72 5O6\\n72 537\\n9-72 567\\nLot, Cot.\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\no\\n^I\\n31\\n31\\n31\\n30\\n31\\n31\\n31\\n30\\n31\\n31\\n30\\n31\\n30\\n31\\n31\\n33\\n31\\n33\\n30\\n31\\n30\\n31\\n30\\n30\\n30\\n31\\n30\\n30\\n30\\n30\\n31\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n0.29 283\\n0.29 252\\n0.29 221\\n0.29 190\\n0.29 158\\n0.29 127\\no. 29 096\\n0.29065\\n0.29034\\no. 29 003\\n0.28 972\\n0.28 946\\n0.28 909\\n0.28 878\\n0.28847\\n0.28 815\\n0.2878^\\n0.28754\\n0.28 723\\n0.28 692\\n0.28 661\\n0.28 636\\n0.28 599\\n0.28 568\\n0.28537\\n0.28 505\\n0.28 476\\n0.28 445\\n0.28 414\\n0.28383\\n0.28 352\\n0.28 321\\n0.28 290\\n0.28 260\\n0.28 229\\n0.28 198\\n0.28 167\\n0.28 136\\n0.28 106\\n0.28 075\\no. 28 044\\n0.28 014\\n0.27983\\n0.27 952\\n0.27 921\\n0.27 891\\n0.27 860\\n0.27 830\\n0.27799\\n0.27 768\\n0.27 738\\n0.27707\\n0.27 677\\n0.27 646\\n0.27 615\\n0.27 585\\n0.27 554\\n0.27 524\\n0.27493\\n0.27 463\\n0-27432\\nc. (1. I Log. Tun.\\nLot;. Co.s.\\n94988\\n94981\\n94 975\\n94969\\n94962\\n94956\\n94 949\\n94 943\\n94 936\\n94930\\n94923\\n94917\\n94910\\n94904\\n9489?\\n94891\\n94884\\n94878\\n94871\\n94865\\n94858\\n94852\\n94845\\n94839\\n94832\\n94825\\n94819\\n94812\\n94806\\n94 799\\n94 793\\n94786\\n94 779\\n94 773\\n94766\\n94760\\n94 753\\n94 746\\n94740\\n94733\\n94727\\n94720\\n94713\\n94707\\n94706\\n94693\\n94687\\n94680\\n94674\\n94667\\n94 660\\n94654\\n94647\\n94 646\\n94633\\n94627\\n94 620\\n94613\\n94 607\\n94 600\\n9-94 593\\nLoir. Sin.\\n00\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n3\\n30\\n29\\n28\\n27\\n26\\n24\\n23\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\n1 1\\nTo\\n9\\n8\\n7\\n6\\nr. i\\\\\\n3\\nI\\n3\\nI\\n6\\n3-1\\n3-1\\n7\\n3\\n7\\n3\\n6\\n8\\n4\\n4\\nI\\n9\\n4\\n7\\n4\\n6\\n10\\n5\\n-7\\n5\\nI\\n20\\n10\\n5\\n10\\n3\\n30\\n15\\n1\\n15\\n5\\n40\\n21\\n20\\n6\\n50\\n26\\n2\\n25\\n8\\n25\\n6\\n2.\\n7\\n2.\\n8\\nJ-\\n9\\n3-\\n10\\n4-\\n20\\n8.\\n30\\n12.\\n40\\n16.\\n50\\n20.\\n30\\n3-3\\n4.6\\n4-6\\n5-1\\n10. r\\n15.2\\n20.3\\n25.4\\n24\\n24\\n2j\\n6\\n2.4\\n2.4\\n2.\\n7\\n8\\n9\\n2\\n3\\n8\\n2\\n7\\n2.8\\n3-2\\n3-6\\n2.\\n3-\\n10\\n20\\n4\\n8\\nI\\nI\\n8.0\\n3-\\n7-\\n30\\n12\\n2\\n12.0\\n11.\\n40\\n16\\n3\\n16.0\\n15-\\n50\\n20\\n4\\n20.0\\n19.\\n6\\n7\\n8\\n9\\n10\\n20\\n3^\\n40\\n50\\nI\\n0.7\\n0.6\\n0.6\\n0.8\\n0.9\\n0.7\\no-S\\n0.7\\no.S\\nI.O\\n1.0\\n0.9\\ni.T\\n1. 1\\n1.0\\n2.3\\n3-5\\n4.6\\n2.1\\n3-2\\n4-3\\n2.0\\n3-0\\n4.0\\n5-8\\n5-4\\n5.0\\n63\\n375", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0427.jp2"}, "428": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n28\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\nI\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLos. Siu.\\n9.67 161\\n9.67 184\\n9.67 208\\n9.67 232\\n9.67 256\\n9.67279\\n9.67 303\\n9.67 327\\n9.67356\\n9-67 374\\n9.67 397\\n9.67421\\n9.67445\\n9.67468\\n9.67492\\n9.67515\\n9-67 539\\n9.67 562\\n9.67 586\\n9.67 609\\n967633\\n9.67 656\\n9.67679\\n9.67703\\n9.67 726\\n9.67 750\\n9.67773\\n9-67 796\\n9.67 819\\n9.67 843\\n9.67 866\\n9.67889\\n9.67913\\n9.67936\\n9.67959\\n9.67 982\\n9.68005\\n9.68 029\\n9.68 052\\n9.68075\\n9.68098\\n9.68 12T\\n9.68 144\\n9.68 167\\n9.68 190\\n9.68 213\\n9.68236\\n9 68 259\\n9.68282\\n9.68305\\n9.68328\\n9.68351\\n9.68374\\n9.68 397\\n9.68 420\\n9.68443\\n9.68466\\n9.68488\\n9.68 51T\\n9-68 534\\n9-68 557\\nLog. Cos.\\nd.\\n23\\n24\\n23\\n24\\n23\\n23\\n24\\n23\\n23\\n23\\n24\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n22\\n23\\n23\\n23\\n22\\n23\\n23\\n22\\ndT\\nLoff. Tail. c. d\\n9.7256;\\n9.72 598\\n9.72628\\n9.72659\\n9.72 689\\n9.72719\\n9.72750\\n9.72 780\\n9.72 811\\n9.72841\\n9.72 871\\n9.72 902\\n9.72932\\n9.72 962\\n9.72993\\n9.73023\\n9-73053\\n9.73084\\n9-73 114\\n9-73 144\\n9-73 ^74\\n9.73205\\n9-73235\\n9.73265\\n9-73295\\n9.73 325\\n973356\\n9-73386\\n9.73416\\n9-73 446\\n9-73 476\\n9-73 506\\n9-73 536\\n9-73567\\n9-73 597\\n9.73627\\n9-73657\\n9-73687\\n9-73717\\n9-73 747\\n9-73777\\n9.73807\\n9-73837\\n9.73867\\n9-73897\\n9.73927\\n9.73957\\n9-73987\\n9.74017\\n9.74047\\n9- 74076\\n9.74 106\\n9-74 136\\n9.74 166\\n9.74 196\\n9.74 226\\n9-74256\\n9.74 286\\n9-74315\\n9-74 34g\\n9-74 375\\nLog. Cot.\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n29\\n30\\n30\\n30\\n29\\n30\\n30\\n30\\n29\\n30\\n29\\nLog. Cot.\\n0.27432\\n0.27 402\\n0.27371\\n0.27341\\n0.27 311\\n0.27 286\\n0.27 250\\n0.27 219\\n0.27 189\\n0.27 159\\n0.27 128\\n0.27098\\n0.27067\\n0.2703;\\n0.27 007\\n0.26976\\n0.26946\\n0.26 916\\n0.26886\\n0.26855\\n0.26 825\\n0.26 795\\n0.26 765\\n0.26734\\no. 26 704\\n0.26674\\no. 26 644\\n0.26 614\\n0.26 584\\n0.26553\\n0.26 523\\n0.26493\\n0.26463\\n0.26433\\n0.26 403\\n0.26373\\n0.26343\\n0.26313\\n0.26 283\\n0.26 253\\n0,26 223\\n0.26 193\\n0.26 163\\n0.26 133\\n0.26 103\\n0.26 073\\no. 26 043\\n0.26 013\\n0.25 983\\n0.25953\\n0.25923\\n0.25893\\n0.25 863\\n0.25 833\\n0.25 804\\n0.25774\\n0.25744\\n0.25 714\\n0.25 684\\n0-25654\\n0.25 625\\nc. d. i Log. Tan.\\nLos. Cos.\\n9.94 593\\n9.94587\\n9.94580\\n9.94 573\\n9.94 566\\n9.94560\\n9 94 553\\n9-94 546\\n9-94 539\\n9-94 533\\n9.94 526\\n9.94519\\n9.94512\\n9.94 506\\n9-94 499\\n9.94492\\n9-94485\\n9-94 478\\n9-94472\\n9-94465\\n9-94458\\n9-94451\\n9-94 444\\n9-94 437\\n9-94 431\\n9.94424\\n9.94417\\n9.94416\\n9-94403\\n9-94 396\\n994390\\n9-94383\\n9-94376\\n9-94369\\n9.94 362\\n9-94 355\\n9-94 348\\n9-94 341\\n9-94 335\\n9.94328\\n9.94321\\n994314\\n9-94307\\n9.94306\\n9-94295\\n9.94286\\n9.94279\\n9.94272\\n9.94265\\n9-94258\\n9.94251\\n9-94 245\\n9.94238\\n9.94231\\n9.94224\\n9.94217\\n9.94 210\\n9-94203\\n9.94 196\\n9-94 189\\n9.94 182\\nLog. Siu.\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n3^-\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\nP. P.\\n30 30 29\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n24\\n2.4\\n2.8\\n3-2\\n3-6\\n4.0\\n8.0\\n12.0\\n16.0\\n20.0\\n6\\n3.0\\n3-0\\n-7\\n7\\n3-5\\n3-5\\n3-\\n8\\n4.0\\n4.0\\n3-\\n9\\n4-6\\n4-5\\n4-\\n10\\n5-1\\n5.0\\n4-\\n20\\n10. 1\\nlo.o\\n9-\\n30\\n15.2\\n15.0\\n14.\\n40\\n20.3\\n20.0\\n19.\\n50\\n25.4\\n25.0\\n24.\\n23\\n23\\n6\\n2-3\\n2.3\\n7\\n2.7\\n2.7\\n8\\n3-1\\n3-0\\n9\\n3-5\\n3-4\\n10\\n3-9\\n3-8\\n20\\n7-8\\n7-6\\n30\\nII. 7\\nII. 5\\n40\\n15-6\\n15-3\\n50\\n19.6\\n19. 1\\n22\\n2.2\\n2.6\\n3-0\\n3-4\\n3-?\\n7.5\\nII. 2\\n15.0\\n18.7\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n7\\n0.7\\n0.8\\n0.9\\n1.6\\ni-i\\n2.3\\n3-5\\n4-6\\n5-8\\n0.6\\n0.7\\n0.8\\ni.o\\nI.I\\n2.t\\n3-2\\n4.3\\n5-4\\nP. P.\\nGl\\n376", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0428.jp2"}, "429": {"fulltext": "TABLE VII.\\nLOGARITHMIC SINES, COSINES, TANGENTS, AND CO TANGENTS,\\n2\\\\y\\nI\\n2\\n4\\n5\\n6\\n7\\n8\\n9\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n-3\\n26\\n27\\n28\\n29\\n;io\\n3^\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n00\\nliOc:. Sin.\\n9.68557\\n9.68 580\\n9.68 602\\n9.68625\\n9.68648\\n9.68671\\n9.68 693\\n9-68716\\n9.68739\\n9.68 76T\\nd.\\n9.68 784\\n9.68807\\n9.68 829\\n9.68852\\n9.68 874\\n9.68897\\n9.68 920\\n9.68 942\\n9.68 965\\n9.68 987\\n9.69 010\\n9.69 032\\n9.69055\\n9.69077\\n9.69099\\n9.69 122\\n9.69 144\\n9.69 167\\n9.69 189\\n9.69 211\\n9.69 234\\n9.69 256\\n9.69278\\n9.69 301\\n9.69323\\n9 69 34^\\n9.69367\\n9.69390\\n9.69412\\n9-69434\\n9-69 456\\n9.69478\\n9.69 506\\n9.69523\\n9.69 545\\n9-69 567\\n9-69 589\\n9.69 61T\\n9.69633\\n9.69655\\n9.69677\\n9.69699\\n9.69 721\\n9-69743\\n9.69765\\n9-69787\\n9.69 809\\n9.69 831\\n9.69853\\n9-69875\\n9-69897\\nLog. Cos.\\n23\\n22\\n-3\\n22\\n23\\n23\\n23\\n22\\n22\\n22\\n22\\n22\\n23\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n21\\n22\\n22\\ndT\\nLos. Tan. led.\\n9-74 375\\n9.74405\\n9-74 435\\n9.74464\\n9-74 49-1\\n9.74524\\n9.74554\\n9-74583\\n9.74613\\n9- 74 643\\n9.74672\\n9.74702\\n974732\\n9.74761\\n9.74791\\n9.74821\\n9-74850\\n9. 74 880\\n9.74909\\n9-74 939\\n9-74969\\n9-74 998\\n9.75 028\\n9.75057\\n9.75087\\n9-75 116\\n9.75 146\\n9-75 17^\\n9.75205\\n9-75 234\\n9.75 264\\n975293\\n975323\\n9-75352\\n9.75382\\n9.75 411\\n9.75441\\n9.75470\\n9-75 499\\n9.75 529\\n9-75 558\\n9.75 588\\n9.75617\\n9.75 646\\n9.75676\\n9.75705\\n9-75 734\\n9-75764\\n9-75 793\\n9.75 822\\n9.75851\\n9.75881\\n9.75910\\n9-75 939\\n9.75968\\n9-75998\\n9.76027\\n9.76056\\n9.76085\\n976 115\\n9.76 144\\n30\\n30\\n29\\n30\\n29\\n30\\n29\\n29\\n30\\n29\\n30\\n29\\n29\\n30\\n29\\n29\\n29\\n29\\n30\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\nLog. Cot. I c. d.\\nLo\u00c2\u00ab?. Cot.\\nl-(u:. Cos.\\nd.\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n1\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n1\\n7\\n7\\n7\\n1\\n7\\n7\\n1\\n7\\n0.25625\\n9.94 182\\n()0\\n0.25 595\\n9.94175\\n59\\n0.25 565\\n9.94 168\\n58\\n0-25 53^\\n9.94 161\\n57\\n0.25505\\n9.94154\\n56\\n0.25476\\n9.94 147\\n55\\n0.25 446\\n9.94 140\\n54\\n0.25 416\\n9-94133\\n53\\n0.25387\\n9.94126\\n52\\n0.25357\\n0.25 327\\n9-94 118\\n51\\n50\\n9.94111\\n0.25 297\\n9.94 104\\n49\\n0.25 268\\n9-9409?\\n48\\n0.25 238\\n9-94090\\n47\\n0.25 208\\n9.94083\\n9- 94076\\n46\\n45\\n0.25 179\\n0.25 149\\n9.94069\\n44\\n0.25 120\\n9.94062\\n43\\n0.25 090\\n9.94055\\n42\\n0. 2 5 060\\n9.94048\\n41\\n0.25 031\\n9-94041\\n40\\n0.25 001\\n9-94034\\n39\\n0.24972\\n9-94026\\n3a\\n0.24 942\\n9.94019\\n37\\n0.24913\\n9.94012\\n36\\n35\\n0.24883\\n9.94005\\n0.24854\\n9.93998\\n34\\n0.24 824\\n9.93991\\n33\\n0.24795\\n9-93984\\n32\\n0.24 765\\n9-93 977\\n3\u00c2\u00bb\\n0.24736\\n9.93969\\nao\\n0.24 706\\n9.93 962\\n29\\n0.24677\\n9-93 955\\n28\\n0. 24 64^\\n9-93948\\n27\\n0.24 618\\n9-93941\\n7\\n26\\n25\\n0.24588\\n9-93 934\\n0.24559\\n9.93926\\n7\\n7\\n1\\n7\\n7\\n1\\n7\\n7\\n7\\n1\\n7\\n1\\n7\\n7\\n1\\n7\\n1\\n1\\n7\\n1\\n7\\n1\\n24\\n0.24529\\n9-93919\\n23\\n0.24 500\\n9.93912\\n22\\n0.24471\\n9-93905\\n21\\n0.24441\\n9.93898\\n20\\n0.24 412\\n9.93891\\nJ9\\n0.24383\\n9-93883\\n18\\n0.24353\\n9-93876\\n17\\n0.24324\\n9.93 869\\n9.93 862\\ni\u00c2\u00ab\\n0.24 295\\n15\\n0.24 265\\n9-93854\\n14\\n0.24 236\\n9-9384?\\n13\\n0.24 207\\n9.93840\\n12\\n0.2417^\\n9-93833\\n11\\n10\\n9\\n0.24 148\\n0.24 119\\n9.93 826\\n9-93 818\\n0. 24 090\\n9-93811\\n8\\n0. 24 066\\n9.93 804\\n7\\n0.24031\\n0.24002\\n9-93 796\\n6\\n993789\\n5\\n0.23973\\n9.93782\\n4\\n0.23943\\n9-93 775\\n3\\n0.23914\\n9.93767\\n2\\n0.23885\\n9-93766\\n7\\n1\\nd.\\nI\\n0.23 856\\n9-93 753\\nLoff. Tun.\\n!.(!g. sill.\\nr. I*\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n30\\n3.0\\n3.5\\n4.0\\n4.5\\n5.0\\nlo.o\\n15.0\\n20.0\\n25.0\\n29\\n2.9\\n3-4\\n3-9\\n4 4\\n4.9\\n9.8\\n14.?\\n19.6\\n24.6\\n23\\n6\\n2-3\\n7\\n2\\n7\\n8\\n3\\n9\\n3\\n4\\n10\\n3\\n8\\n20\\n7\\n6\\n30\\n1 1\\n5\\n40\\n15\\n3\\n50\\n19\\nI\\n22\\n22\\n6\\n2.2\\n2.2\\n7\\n2.6\\n2.5\\n8\\n3.0\\n2.9\\n9\\n3-4\\n3-3\\n10\\n3-7\\n3-6\\n20\\n7.5\\n7.3\\n30\\nII. 2\\nII.\\n40\\n15.0\\n14-6\\n50\\n18.7\\n18.3\\n29\\n2.9\\n3\\n3\\n4\\n4\\n9\\n14\\n19\\n24\\n21\\n2.T\\n2.5\\n2-8\\n3.2\\n3.6\\n7-1\\n10.?\\n14-3\\n17.9\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n1\\n0.1\\n0.9\\ni.o\\n1. 1\\n1.2\\n2.5\\n3-?\\n5.0\\n6.2\\n7\\n0.7\\n0.8\\n0.9\\n1.6\\ni.i\\n2-3\\n3-5\\n4-6\\n5.8\\np. P.\\nGO\\n377", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0429.jp2"}, "430": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n19\\n26\\n27\\n28\\n29\\nao\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n42\\n43\\n44\\n55\\n56\\n57\\n58\\n59\\n0\\n30\\n20\\n9\\n21\\n9\\n22\\n9\\n23\\n9\\n24\\n9\\nLost. sin.\\n69897\\n69919\\n69 940\\n69 962\\n69 984\\n70006\\n70028\\n70050\\n70071\\n70093\\n70 115\\n70137\\n70158\\n70 180\\n70 202\\n70 223\\n70245\\n70 267\\n70288\\n70310\\n70331\\n70353\\n70375\\n70396\\n70418\\n70439\\n70461\\n70482\\n70504\\n70525\\n70547\\n70568\\n70590\\n70 61 1\\n70 632\\n70654\\n70675\\n70696\\n70718\\n70739\\n70 760\\n70782\\n70803\\n70 824\\n70846\\n70867\\n70888\\n70 909\\n70930\\n70 952\\n70973\\n70994\\n7101I\\n71036\\n71 05^\\n71 078\\n71099\\n71 121\\n71 142\\n71 163\\n71 184\\nhog. Cos.\\nd.\\n22\\n21\\n22\\n22\\n21\\n22\\n22\\n21\\n22\\n21\\n22\\n21\\n21\\n22\\n21\\n21\\n22\\n21\\n21\\n21\\n22\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n(IT\\nLoir. Tan.\\n76 144\\n76 173\\ny6 202\\n76 231\\n76 266\\n76 289\\n76319\\n76348\\n76377\\n76406\\n76435\\n76464\\n76493\\n76 522\\n76551\\n76580\\n76 609\\n76638\\n76667\\n76696\\n76725\\n76754\\n76783\\n76812\\n76 841\\n76 870\\n76899\\n76 928\\n76957\\n76986\\n77015\\n77043\\n77 072\\n77 lOI\\n77 130\\n77 159\\n77 188\\n77217\\n77245\\n77274\\n77303\\n77332\\n77361\\n77389\\n77418\\n77 447\\n77476\\n77 504\\n77 533\\n77 562\\n77 591\\n77619\\n77648\\n77677\\n77705\\n77 734\\n77763\\n77791\\n77 820\\n77849\\n77 87^\\nLog. Cot.\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n28\\n29\\n29\\n29\\n29\\n28\\n29\\n29\\n29\\n28\\n29\\n29\\n28\\n29\\n29\\n28\\n29\\n28\\n29\\n28\\n29\\n28\\n29\\n28\\n29\\n28\\n28\\n29-\\n28\\n28\\n29\\n28\\n28\\n29\\n28\\nliOg. Cot.\\n0.23 856\\n0.23 827\\n0.23797\\n0.23768\\n0.23739\\n0.23 710\\n0.23 681\\n0.23 652\\n0.23 623\\n0.23 594\\n0.23 565\\n0.23 535\\n0.23 506\\n0.23477\\n0.23 448\\n0.23419\\n0.23 396\\n0.23 361\\n0.23332\\n0.23303\\n0.23 274\\n0.23245\\n0.23 216\\n0.23 18^\\n0.23 158\\n0.23 129\\n0.23 lOI\\n0.23 072\\n0.23043\\n0.23 014\\n0.22 985\\n0.22 956\\n0.22 92^\\n0.22 898\\n0.22 869\\n0.22 841\\n0.22 812\\n0.22 783\\n0.22 754\\n0.22 725\\n0.22 696\\n0.22 668\\n0.22 639\\n0.22 616\\n0.22 581\\n0.22553\\n0.22 524\\n0.22 495\\n0.22 466\\n0.22 438\\n0.22 409\\n0.22 386\\n0.22 352\\n0.22 323\\n0.22 294\\n0.22 266\\n0.22 237\\n0.22 208\\n0.22 180\\n0.22 151\\n0.22 122\\nLog. Tail.\\nLos:. Cos.\\n9-93 753\\n93746\\n93 738\\n93731\\n93724\\n93716\\n93709\\n93 702\\n93694\\n93687\\n93680\\n93 672\\n93665\\n95658\\n93656\\n93643\\n93635\\n93628\\n93621\\n93613\\n93606\\n93 599\\n93591\\n93584\\n93 576\\n93569\\n93562\\n93 554\\n93 547\\n93 539\\n93532\\n93524\\n93517\\n93509\\n93502\\n93 495\\n93487\\n93480\\n93472\\n93465\\n93 457\\n93450\\n93442\\n93 435\\n93427\\n93420\\n93412\\n93405\\n93 39?\\n93390\\n93382\\n93 374\\n93367\\n93 359\\n93352\\n93 344\\n93 337\\n93329\\n93321\\n93314\\n9-93 306\\nLog. Sill.\\nd.\\n00\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\np. p.\\n22\\n21\\n6\\n2.2\\n2.T\\n7\\n2.5\\n2.5\\n8\\n2.9\\n2.8\\n9\\n3-3\\n3-2\\n10\\n3-6\\n3-6\\n20\\n7-3\\n7.1\\n30\\nII.\\n10.7\\n40\\n14-6\\n14.3\\n50\\n18.3\\n17.9\\n21\\n2.1\\n2.4\\n2.8\\n3-1\\n3-5\\n7.0\\n10.5\\n14.0\\ni7 S\\n8\\n1\\n6\\n0.8\\nO.J\\n7\\n8\\n0.9\\n1.6\\n0.9\\nI.O\\n9\\n10\\n1.2\\nI-.3\\nI.I\\n1.2\\n20\\n2-6\\n2.5\\n30\\n4.0\\nZ-1\\n40\\n50\\n5.3\\n6.6\\n5.0\\n6.2\\n7\\n0.7\\n0.8\\n0.9\\n1.6\\nI.I\\n2.3\\n3-5\\n4--6\\n5.8\\n29\\n29\\n28\\n6\\n2.9\\n2.9\\n2.8\\n7\\n3-4\\n3.4\\n3-3\\n8\\n3-9\\n3-8\\n3-8\\n9\\n4.4\\n4.3\\n4-3\\n10\\n4.9\\n4-8\\nA-1\\n20\\n9-8\\n9-6\\n9-5\\n30\\n14-7\\n14.5\\n14.2\\n40\\n19-6\\n19-3\\n19.0\\n50\\n24.6\\n24.1\\n23.^\\np. p.\\n59\\n378", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0430.jp2"}, "431": {"fulltext": "TABLE VII. LOGARITHMIC SINES. COSINES, TANGENTS, AND COTANGENTS.\\ni o\\nO 1\\n5\\n6\\n7\\n8\\n9\\n10\\nII\\n12\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\noO\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n-59_\\n00\\nliOsr. Sill.\\nd.\\n9-7\\n9-7\\n9-7\\n9-7\\n9.7\\n9.7\\n9-7\\n9.7\\n9-7\\n9-7\\n9.7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9.7\\n9-7\\n9-7\\n9-7\\n9-7\\n9.7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n9-7\\n184\\n205\\n226\\n247\\n268\\n289\\n310\\n331\\n351\\n372\\n393\\n414\\n435\\n456\\n477\\n498\\n518\\n539\\n560\\n581\\n601\\n622\\n643\\n664\\n684\\n705\\n726\\n746\\n767\\n788\\n808\\n829\\n849\\n870\\n891\\n911\\n932\\n952\\n973\\n993\\n9.72 014\\n9.72034\\n9.72055\\n9.72075\\n9.72 096\\n9.72 116\\n9-72 136\\n9.72 157\\n9.72 177\\n9.72 198\\n9.72 218\\n9.72 238\\n9.72259\\n9.72279\\n9.72299\\n9.72319\\n9.72340\\n9.72360\\n9.72380\\n9.72 400\\n9.72 421\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n20\\n21\\n21\\n21\\n20\\n21\\n21\\n21\\n20\\n21\\n20\\n21\\n26\\n21\\n20.\\n21\\n26\\n21\\n20\\n26\\n21\\n20\\n26\\n20\\n26\\n21\\n20\\n20\\n20\\n26\\n26\\n20\\n20\\n20\\n26\\n20\\n20\\n20\\n20\\n26\\n26\\n26\\n20\\n26\\n20\\n20\\n26\\n20\\n26\\n20\\n20\\n20\\n20\\nI,otr. Tail. c. d.\\n-otr. Cot.\\n9.77^77\\n9.77906\\n9-77 934\\n9-77963\\n9.77992\\n9.78 020\\n9.78049\\n9.78077\\n9.78 106\\n9-78 134\\n9.78 163\\n9.78 19T\\n9.78 220\\n9.78 248\\n9-78277\\nLog. Cos. i iU\\n9.78305\\n9-78334\\n9.78362\\n9.78391\\n9.78419\\n9.78448\\n9-78476\\n9.78505\\n9-78533\\n9.78561\\n9.78590\\n9-78618\\n9.78647\\n9-78675\\n9.78703\\n9.78732\\n9.78 760\\n9.78788\\n9.78817\\n9.78845\\n9.78873\\n9.78 902\\n9.78930\\n9-78958\\n9.78987\\n9.79015\\n9-79043\\n9.79071\\n9.79 100\\n9.79 128\\n9-79156\\n9-79 184\\n9.79213\\n9.79241\\n9.79269\\n9.79297\\n9-79325\\n9-79 354\\n9.79382\\n9.79410\\n9-79 438\\n9.79465\\n9.79494\\n9-79522\\n9-79551\\n9.79 579\\n28\\n28\\n28\\n29\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\nO. 22 I 22\\n0.22 094\\n0.22 065\\n0.22 037\\n0.22 008\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0,2\\n0.2\\n02\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n0.2\\n979\\n951\\n922\\n894\\n865\\n837\\n808\\n780\\n751\\n723\\n694\\n666\\n637\\n609\\n586\\n552\\n523\\n495\\n467\\n438\\n410\\n381\\n353\\n325\\n296\\n268\\n239\\n211\\n183\\n154\\n126\\n098\\n070\\n041\\n013\\n0.20 985\\n0.20 956\\n0.20 928\\no. 20 900\\n0.20 872\\n0.20 843\\no. 20 8 1 5\\n0.20 787\\n0.20 759\\n0.20 731\\n0.20 702\\n0.20 674\\no. 20 646\\n0.20618\\n0.20 590\\n0.20 561\\n0.20533\\n0.20 505\\n0.20477\\no. 20 449\\n0.20 421\\nl.oir. Cos\\nliO^. C \u00c2\u00bbt. c. \u00c2\u00ab1. I, otr. Tiin.\\n93 306\\n93 299\\n93291\\n93 284\\n93276\\n93268\\n93 261\\n93253\\n93245\\n93238\\n93230\\n93 223\\n93215\\n93207\\n93 200\\n93 192\\n93 184\\n93 ^77\\n93 169\\n93 161\\n93 153\\n93 146\\n93 138\\n93 30\\n93 123\\n93 115\\n93 107\\n93 100\\n93 092\\n93084\\n93076\\n93069\\n93 061\\n93053\\n93045\\n93038\\n93030\\n93 022\\n93014\\n93 006\\n92 999\\n92991\\n92983\\n92975\\n9296?\\n92 960\\n92952\\n92944\\n92936\\n92928\\n92 920\\n92913\\n92905\\n92 897\\n92889\\n92 881\\n92873\\n92865\\n92858\\n92 850\\n92 842\\n9\\n9\\n9\\n9\\n9_\\nLoJT. sill.\\nl.\\nGO\\n59\\n58\\n57\\nJi\\n55\\n54\\n53\\n52\\niO\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n30\\n29\\n28\\n27\\n26\\n24\\n23\\n22\\n21\\n20\\n9\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\n1 1\\n10\\n9\\n8\\n7\\n6\\nV. V\\nw29\\n28\\n6\\n2.9\\n2-8\\n7\\n3-4\\n3-3\\n8\\n3-8\\n3-8\\n9\\n4-3\\n4-3\\n10\\n4-8\\n4-7\\n20\\n9-6\\n9-5\\n30\\n14.5\\n14.2\\n40\\n19.3\\n19.0\\n50\\n24.1\\n23.7\\n28\\n2.8\\n3-2\\n3-^\\n4.2\\n4^\\n9-3\\n14.0\\n18.6\\n23-3\\n21\\n26\\n6\\n2.1\\n2.C\\n7\\n2.4\\n2.4\\n8\\n2.8\\n2.?\\n9\\n3-1\\n3-1\\n10\\n3-5\\n3-4\\n20\\n7.0\\n6-8\\n30\\n10.5\\n10.2\\n40\\n14.0\\n13-6\\n50\\n17.5\\n17.1\\n20\\n2.0\\n2-3\\n2.6\\n3-0\\n3-3\\n6.6\\nlO.O\\n13-3\\n16.6\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n8\\n0.8\\n0.9\\n1.6\\n1.2\\n1-3\\n2-6\\n4-0\\n5-3\\n6.6\\no.f\\n0.9\\ni.o\\n1. 1\\n1.2\\n2.5\\n3-7\\n5.0\\n6.2\\nI I\\n58\\n379", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0431.jp2"}, "432": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS\\n32\u00c2\u00b0\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLo^. ISiii.\\n72 421\\n72441\\n72 46T\\n72 481\\n72 501\\n72 522\\n72542\\n72 562\\n72 582\\n72 602\\n72 622\\n72 642\\n72 662\\n72682\\n72 702\\n72 723\\n72743\\n72 763\\n72783\\n72 802\\n72 822\\n72 842\\n72862\\n72882\\n72 902\\n72 922\\n72942\\n72 962\\n72 982\\n73 002\\n73021\\n73041\\n73061\\n73081\\n73 loi\\n73 120\\n73140\\n73 160\\n73 180\\n73199\\n73219\\n73239\\n73258\\n73278\\n73298\\n73317\\n73 33^\\n73 357\\n9 73 376\\n9 73 396\\n73415\\n73 435\\n73 455\\n73 474\\n73 494\\n73513\\n73 533\\n73552\\n73 572\\n73 59^\\n9-73611\\nd.\\n20\\n20\\n20\\n20\\n26\\n20\\n20\\n26\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n19\\n20\\n20\\n20\\n20\\n20\\n20\\n19\\n20\\n20\\n20\\n19\\n20\\n20\\n19\\n20\\n19\\n20\\n19\\n20\\n19\\n20\\n19\\n19\\n20\\n19\\n19\\n20\\n19\\n19\\n19\\n19\\n20\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\nLo^. Tan. c. d\\n9-79 579\\n9.79607\\n9-79635\\n9.79663\\n9.7969!\\n9.79719\\n9-79 747\\n9-79 775\\n9.79803\\n9-79831\\n9.79859\\n9.79887\\n9.79915\\n9.79943\\n9.79971\\n9.79999\\n9.80027\\n9.80055\\n9.80083\\n9. 80 1 1 1\\n9.80 139\\n9.8016^\\n9.80 195\\n9 80 223\\n9.80251\\n9.80279\\n9. 80 307\\n9.80335\\n9-80363\\n9.80391\\n9-80418\\n9.80446\\n9.80474\\n9.80 502\\n9-80 530\\n9.80558\\n9.80 586\\n9.80 613\\n9.80 641\\n9.80 669\\n9.80697\\n9.80725\\n9.80 752\\n9.80786\\n9. 80 803\\n9.80836\\n9.80864\\n9.80 891\\n9.80 919\\n9.80947\\n9.80975\\n9.8\\n9.8\\n9.8\\n9.8\\n9-\\n9. J\\n9-\\n9.i\\n9.i\\n002\\n030\\n058\\n085\\n113\\n141\\n168\\n196\\n224\\nJsl\\nJiOg. Cot.\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n2?\\n28\\n28\\n28\\n28\\n2?\\n28\\n28\\n28\\n27\\n28\\n28\\n2f\\n28\\n28\\n2f\\n28\\n2?\\n28\\n28\\n2f\\n28\\n2f\\n28\\n27\\n28\\n27\\n2?\\n28-\\n2f\\n28\\n2?\\n29\\n28\\n2f\\n2f\\ncTJr\\nLog. Cot.\\no. 20 42 1\\n0.20393\\n0.20 365\\n0.20337\\n0.20308\\n0.20 286\\n0.20 252\\n0.20 224\\n0.20 195\\n0.20 168\\n0.20 140\\nO. 20 112\\no. 20 084\\n0.20 055\\n0.20 028\\no. 20 000\\n0,19 972\\n0.19944\\nO.I99I6\\n0.19\\no.\\n9866\\n9832\\n9 804\\n9 776\\n9 748\\n9721\\n9693\\n9665\\n9637\\n9 609\\n9 581\\n9 553\\n9525\\n9 49^\\n9470\\n9442\\n9414\\n9386\\n9 358\\n9330\\n9303\\n9275\\n924^\\n9219\\n9 191\\n9164\\n9136\\n9 log\\n9 086\\n9053\\n9025\\n899?\\n8970\\n8 942\\n8914\\n8 886\\n8859\\n8 831\\n8803\\n8 776\\n8748\\nLot?. Tail.\\nLog. Cos.\\n9.92 842\\n9.92834\\n9.92826\\n9.92 818\\n9.92 816\\n9.92 802\\n9.92794\\n9.92786\\n9.92 778\\n9.92771\\n9.92763\\n9.92755\\n9-92747\\n9-92739\\n9.92731\\n9.92723\\n992715\\n9.92707\\n9.92699\\n9.92 691\\n9.92 683\\n9.92675\\n9.92 667\\n9.92659\\n9.92 651\\n9 92 643\\n9.92635\\n9.92 627\\n9.92 619\\n9.92 611\\n9.92 603\\n9.92595\\n9-92 587\\n9-92579\\n9-92 570\\n9.92 562\\n9.92554\\n9-92 546\\n9-92 538\\n9-92 530\\n9.92 522\\n9.92514\\n9.92 506\\n9.92498\\n9.92489\\n9.92 481\\n9-92473\\n9.92465\\n9.92457\\n9-92449\\n9.92441\\n9-92433\\n9.92424\\n9.92 416\\n9-92 408\\n9.92 400\\n9.92392\\n9-92383\\n9-92375\\n9-92 367\\n9-92359\\nLog. Sin.\\nd.\\n00\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\np. p.\\n28\\n28\\n6\\n2.8\\n2.8\\n7\\n3-3\\n3-2\\n8\\n3-8\\n3-f\\n9\\n4-3\\n4.2\\n10\\n4-7\\n4-6\\n20\\n9-5\\n9-3\\n30\\n14.2\\n14.0\\n40\\n19.0\\n18.6\\n50\\n23-7\\n23-3\\n20\\n20\\n6\\n2.6\\n2.0\\n7\\n8\\n2.4\\n2.f\\n2.3\\n2-6\\n9\\n3.1\\n3-0\\n10\\n20\\n3-4\\n6.8\\n3-3\\n6.6\\n30\\n10.2\\nlO.O\\n40\\n50\\n13-6\\n17. 1\\n13-3\\n16.5\\n8\\n8\\n6\\n0.8\\n0.8\\n7\\nI.O\\n0.9\\n8\\nI.I\\n1.0\\n9\\n1-3\\n1.2\\n10\\n1-4\\n1-3\\n20\\n2-8\\n2-6\\n30\\n4.i2\\n4.0\\n40\\n5-6\\n5-3\\n50\\n7.1\\n6.6\\n2f\\n2.1\\n3-2\\n3-6\\n4.1\\n4-6\\n9.1\\n13-^\\n18.3\\n22.9\\n19\\n1.9\\n2-3\\n2.6\\n2.9\\n3-2\\n6.5\\n9-1\\n13.0\\n16.2\\n7\\n0.1\\n0.9\\n1.0\\nI.I\\n1.2\\n2-5\\n3-^\\n5.0\\n6.2\\nP. p.\\n^T\\n380", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0432.jp2"}, "433": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES,\\n\u00e2\u0080\u00a2ANGENTS, AND COTANGENTS.\\n10\\n1 1\\n2\\n13\\n14\\n15\\n16\\n17\\niS\\n22-\\n20\\n21\\n24\\n25\\n26\\n27\\n28\\n29\\n31\\n32\\n33\\n_34_\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n60\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n(10\\nLoff. Sin.\\n9.73 611\\n9.73 630\\n9.73650\\n73 669\\n73688\\n73708\\n73727\\n73 746\\n73766\\n73785\\n73805\\n73824\\n73843\\n73 862\\n73882\\n73901\\n73 926\\n73940\\n73 959\\n73 978\\n73 99?\\n740^6\\n74036\\n74055\\n74074\\n74093\\n74 112\\n74 131\\n74151\\n74 170\\n74189\\n74 208\\n74227\\n74246\\n74265\\n74284\\n74303\\n74322\\n74341\\n74360\\n74 379\\n74398\\n74417\\n74436\\n74455\\n74 474\\n74 493\\n74 51 1\\n74530\\n74 549\\n74568\\n74587\\n74606\\n74625\\n74643\\n74 662\\n74681\\n74700\\n74718\\n74 737\\n74756\\nLog. Cos.\\nliOt;. Tun.\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9^\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n251\\n279\\n307\\n334\\n362\\n390\\n417\\n445\\n473\\n500\\n528\\n555\\n583\\n610\\n638\\n666\\n693\\n.721\\n748\\n776\\n803\\n831\\n858\\n886\\n913\\n941\\n968\\n996\\n9.82 023\\n9.82 051\\n9.82078\\n9.82 105\\n9.82 133\\n9.82 166\\n9.82 188\\n9.82 215\\n9.82243\\n9.82 276\\n9.82 29^\\n9.82 325\\n9.82352\\n9.82 380\\n9.82 407\\n9.82434\\n9.82 462\\n9.82 489\\n9-82516\\n9.82 544\\n9 82 571\\n9.82 598\\nc. (I. Loir. Cot.\\n9.82 626\\n9.82 653\\n9.82686\\n9.82708\\n9.82735\\n9.82 762\\n9 82 789\\n9.82817\\n9.82 844\\n9.8 2871\\n9 82 898\\nliOj;. Cot.\\n2f\\n2?\\n28\\n2?\\n2?\\n2?\\n28\\n27\\n2f\\n27\\n2f\\n2f\\n2?\\n28\\n2?\\n2f\\n2l\\n2l\\n2l\\n2l\\n2l\\n21\\n2f\\n2j\\n2j\\n2j\\n2j\\n2l\\n2l\\n27\\n2l\\n2l\\n2l\\n2j\\n2j\\n2l\\n27\\n2l\\n2l\\n2j\\n27\\n2l\\n27\\n27\\n27\\n2l\\n27\\n27\\n2j\\n27\\n2l\\n2l\\n27\\n2l\\n27\\n2l\\n27\\n2l\\n27\\n0.18748\\n0.18 720\\n0.18 693\\no.i8 66|\\n0.1863^\\nLoir. Cos.\\no. 1 8 6 1 o\\n0.18 582\\n0.18555\\n0.18 527\\no. 1 8 499\\n0.18 472\\no. 1 8 444\\n0.18417\\n0.18389\\no. 18 362\\n0.18334\\nO.I8306\\n0.18 279\\n0.18 251\\no. 18 224\\n0.18 196\\n0.18 169\\n0.18 I4T\\n0,18 114\\no. 1 8 o8a\\n0.18 059\\n0.18 031\\no. 1 8 004\\n0.17 976\\n0.17949\\n0.17 921\\n0.17 894\\n0.17 867\\n0.17 839\\no. 1 7 8 1 2\\n0.17784\\n0.17757\\n0.17 729\\n0.17 702\\n0.17675\\n0.17 647\\n0.17 620\\n0.17 593\\n0.17565\\n0.17 538\\n17 510\\n17483\\n17456\\n17428\\n1 7 401\\n0.17 374\\n0.17347\\n0.17 319\\no. 17 292\\n0.17 265\\n0.1723?\\no. 1 7 216\\n0.17 183\\n0.17 156\\n0.17 128\\no. 17 loT\\nc. (1. I Loir. Tan.\\n992359\\n9.92351\\n9.92342\\n9-92334\\n9.92 326\\n9.92318\\n9.92 310\\n9.92 301\\n9-92293\\n9.92 285\\n9.92 277\\n9.92 268\\n9.92 266\\n9.92 252\\n9.92 244\\n9.92235\\n9.92 227\\n9.92 219\\n9.92 216\\n9.92 202\\n9.92\\n9.92\\n9.92\\n9.92\\n9-92\\n9.92\\n9.92\\n9.92\\n9.92\\n9.92\\n94\\n85\\n7f\\n69\\n66\\n52\\n44\\n35\\n2?\\n19\\n10\\n02\\n9.92\\n9.92\\n9.92094\\n9.92 085\\n9.92077\\n9.92 069\\n9.92 066\\n9.92 052\\n9.92043\\n9-92035\\n9.92 027\\n9.92 018\\n9.92 010\\n9.92 001\\n9-91 993\\n9-9\\n9.9\\n99\\n9-9\\n9.9\\n9.9\\n9-9\\n9.9\\n9-9\\n9.9\\n9-9\\n9.9\\n9-9\\n9 9\\n9.9\\n984\\n976\\n967\\n959\\n951\\n942\\n934\\n925\\n917\\n908\\n900\\n891\\n883\\n874\\n866\\n9 91 857\\nLoir. sin.\\n0\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n24\\n23\\n22\\n21\\n10\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\n1 1\\n9\\n8\\n7\\n6\\nr.\\n28\\n21\\n6\\n2.8\\n2.1\\n7\\n3-2\\n3.2\\n8\\n3-?\\n3-6\\n9\\n4.2\\n4.1\\n10\\n4-6\\n4.6\\n20\\n9-3\\n9.1\\n30\\n14.0\\n13-7\\n40\\n18.6\\n18.3\\n50\\n23-3\\n22.9\\n27\\n2.7\\n3-1\\n3-6\\n4.6\\n4-5\\n9.0\\n13-5\\n18.0\\n22.5\\n19\\n19\\n6\\n1.9\\n1.9\\n7\\n2-3\\n2.2\\n8\\n2.6\\n2.5\\n9\\n2.9\\n2-8\\n10\\n3-2\\n3-1\\n20\\n6.5\\n6.3\\n30\\n9-?\\n9.5\\n40\\n13.0\\n12.6\\n50\\nli5.2\\n15.8\\n18\\n1-8\\n2.1\\n2.4\\n2.8\\n3-1\\n6.T\\n9.2\\n12.3\\n15.4\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\nSO\\n8\\n0.8\\ni.o\\nI.I\\n1.3\\n1-4\\n2-8\\n4-2\\n5-6\\n7-1\\n8\\n0.8\\n0.9\\n1.6\\n1.2\\n1-3\\n2.6\\n4.0\\n5-3\\n6.6\\nr. I\\n5(j\\n3*1", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0433.jp2"}, "434": {"fulltext": "iAiiLl. V 11. -LOGARITHMIC SiNES, COSINES, TANGENTS, AND COTANGENTS\\n34\\n24\\nLog. Sill.\\n9-74756\\n9-74 775\\n9 74 793\\n9.74812\\n9.74831\\n9.74849\\n9.74868\\n9-74887\\n9.7490?\\n9.74924\\n9-74 943\\n9.74961\\n9.74980\\n9-74 998\\n9.75017\\n9-75036\\n9-75054\\n9.75073\\n9.75091\\n9-75 no\\n9-75 128\\n9-75 147\\n9.75 165\\n9.75 184\\n9.75 202\\n9.75 221\\n9-75239\\n9-75 257\\n9.75276\\n9-75 294\\n9-75313\\n9-75331\\n9-75 349\\n975368\\n9-75386\\n9-75404\\n9-75423\\n9-75441\\n9-75 459\\n9-75478\\n9-75496\\n9-75 54\\n9-75 532\\n9-75551\\n9.75569\\n9-75587\\n9.75605\\n9.75623\\n9-75642\\n9.75 660\\n9-75678\\n9-75695\\n9-75714\\n9-75 732\\n9-75750\\n9-75769\\n975787\\n9.75805\\n9-75823\\n9-75841\\n975859\\nliOf?. Cos.\\n(1.\\n19\\n18\\n19\\n18\\n18\\n19\\n18\\n19\\n18\\n18\\n18\\n18\\n18\\n19\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\nIS\\nLog. Tan, c. d. I Log. Cot.\\n9.82898\\n9.82 926\\n9-82953\\n9.82 980\\n9.83007\\n9-83035\\n9.83 062\\n9.83 089\\n9-83 116\\n9-83 143\\n9.83 171\\n9.83198\\n9.83 225\\n9-83252\\n9-83279\\n9-83307\\n9-83334\\n9-83361\\n9.83388\\n9.83415\\n9.83442\\n9.83469\\n9-83496\\n9-83524\\n9-83551\\n9.83578\\n9.83 605\\n9-83632\\n9-83659\\n9-83686\\n9-83713\\n9.83740\\n9.83767\\n9-83794\\n9.83821\\n9-83848\\n9.83875\\n9.83 902\\n9-83929\\n9.83957\\n9.83984\\n9.84 01 1\\n9-84038\\n9.84065\\n9.84091\\n9.84 118\\n9-84 Hi\\n9.84 172\\n9.84199\\n9-84225\\n9.84253\\n9.84 286\\n9-84 307\\n9-84334\\n9-84361\\n9-84388\\n9.84415\\n9-84442\\n9.84469\\n9.84496\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n2f\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n2f\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n2?\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n26\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n26\\n27\\n27\\n27\\n27\\n27\\n26\\nLog. Cot. I 0. d.\\n9.84 522\\n0.17 lOI\\n0.17074\\n0.17 047\\n0.17 019\\no. 16 992\\n0.16 965\\n0.16938\\n0.16 916\\n0.16883\\n0.16 855\\n0.16 829\\n0.16 802\\n0.16774\\n0.16 747\\no. 16 720\\no. 16 693\\n0.16 666\\no. 16 639\\n0.16 612\\n0.16 584\\n0.16557\\n0.16 536\\n0.16 503\\n0.16 476\\no. 1 6 449\\n0.16422\\no. 16 395\\n0.16368\\n0.16 346\\no. 16 313\\n0.16 285\\no, 16 259\\no. 16 232\\n0.16 205\\n0-16 178\\n0,16 151\\n0.16 124\\no. 16 097\\no. 16076\\no. 16 043\\nO.I60I6\\no. 1 5 989\\no. 1 5 962\\n0-15935\\no. 1 5 908\\n0.15 881\\n0.15854\\n0.15 827\\no. 1 5 800\\n0.15773\\n0.1 5 746\\n0.15719\\no. 1 5 692\\n0.15 665\\n0-1563 9\\n0.15 612\\n0.15 585\\n0.15 558\\n0.15 531\\n0.15504\\nLog. Cos.\\n9.91 857\\n9.91 849\\n9.91 846\\n9.91 832\\n9.91 823\\n9.91 814\\n9.91 806\\n9.91 79^\\n9.91 789\\n9.91 786\\n9.91 772\\n9.91 763\\n9-91 755\\n9.91 746\\n9-91 737\\n9.91 729\\n9.91 720\\n9.91 712\\n9.91 703\\n9.91 694\\n9.91 686\\n9.91 677\\n9.91 668\\n9.91 660\\n9.91 651\\n9.91 642\\n9.91 634\\n9.91 625\\n9.91 616\\n9.91 608\\n9.91 599\\n9.91 590\\n9.91 582\\n9-91 573\\n9.91 564\\n9.91 556\\n9-91 547\\n9 91 538\\n9.91 529\\n9.91 521\\n9.91 512\\n9.91 503\\n9.91 495\\n9.91 486\\n9.91 477\\n9.91468\\n9.91 460\\n9-91451\\n9.91 442\\n9.91433\\n9.91424\\n9.91 416\\n9.91407\\n9.91 398\\n991 389\\n9.91 386\\n9.91 372\\n9-91 363\\n9-91 354\\n9-9t 345\\n0.15 47f 9-91336\\nLog. Tan. Log. Sin.\\nP. P.\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n2f\\n2.7\\n3-2\\n3-6\\n4.1\\n4.6\\n9.1\\n13-?\\n18.3\\n22.9\\n27\\n2.7\\n3-1\\n3-6\\n4.6\\n4-5\\n9.0\\n13-5\\n18.0\\n22.5\\n19\\n18\\n6\\n1-9\\n1.8\\n7\\n2.2\\n2.1\\n8\\n2.5\\n2.4\\n9\\n2.8\\n2.8\\n10\\n3-1\\n.3.1\\n20\\n6.3\\n6.1\\n30\\n9-5\\n9.2\\n40\\n12.6\\n12.3\\n50\\n15-8\\n15.4\\nI\\n9\\n10\\n20\\n30\\n40\\n50\\n9\\n0.9\\n1.6\\n1.2\\n1-3\\n1-5\\n3-0\\n4-5\\n6.0\\n7.5\\n26\\n2-6\\n3-1\\n3-S\\n4.0\\n4.4\\n8.8\\n13.2\\n17-6\\n22.1\\n18\\n1.8\\n2.1\\n2.4\\n2.7\\n30\\n6.0\\n9.0\\n12.0\\n15.0\\n8\\n0.8\\no\\nI\\n3\\n4\\nP. P.\\nai\\n382", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0434.jp2"}, "435": {"fulltext": "TABLE VII.-LOGARITHMIC SINES. COSINES. TANGENTS. AND COTANGENTS\\n;}5\\nLop. Sill.\\n9-75^59\\n9-75877\\n9.75895\\n9-75913\\n9-75 931\\n9-75 949\\n9.75967\\n9.75985\\n9.76003\\n9.76021\\n9.76039\\n9.76057\\n9.76075\\n9.76092\\ng. jd no\\n19\\n9.76 128\\n9.76146\\n9.76 164\\n9.76 182\\n9. j6 200\\n9.76 21^\\n9.76235\\n9.76253\\n9.76 271\\n9.76 289\\n9-76306\\n9.76324\\n9.76342\\n9.76 360\\n9-7637?\\n9-76395\\n9.76413\\n9.76431\\n9-76443\\n9.76466\\n9-76484\\n9.76 501\\n9.76519\\n9-76536\\n976554\\n9.76572\\n9765S9\\n9.76607\\n9 76 624\\n9.76 642\\n9.76 660\\n9.76677\\n9.76695\\n9.76 712\\n9.76730\\n9-76747\\n9.76765\\n9.76 782\\n9.76 800\\n9.76 8if\\n9-76835\\n9.76 852\\n9.76 869\\n9.76887\\n9.76904\\n9.76 922\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\nIf\\n18\\n18\\niS\\nIf\\n18\\n18\\nIf\\n18\\n18\\nIf\\n18\\nIf\\n18\\nIf\\n18\\nIf\\n18\\nIf\\n18\\nIf\\nIf\\n18\\nIf\\nIf\\nIf\\n18\\nIf\\nIf\\nIf\\n17\\n18\\n17\\nIf\\nIf\\nIf\\nIf\\nIf\\nIf\\nIf\\nIf\\nIf\\nIf\\n17\\nIf\\nIf\\nIf\\nIf\\nfiOe. Tiin. r. d.\\n9 84522\\n9-84549\\n9-84576\\n9. 84 603\\n9.84630\\n9.84657\\n9.84684\\n9.84 71 1\\n984 73f\\n9.84764\\n9.8479!\\n9.84818\\n9.84845\\n9.84871\\n9.84898\\n9.84925\\n9.84952\\n9.84979\\n9.85 005\\n9-85032\\n9.85059\\n9.85 086\\n9-85 113\\n985 139\\n9.85 166\\n9.85 193\\n9.85 220\\n9.85246\\n9.85273\\n9.85 300\\n9.85327\\n985353\\n9.85 380\\n9.85407\\n9-85433\\n9.85 466\\n9-85487\\n9-85513\\n9.85 540\\n9-85567\\n594\\n9.85\\n9.85 620\\n9.85647\\n9-85673\\n9.85 700\\n9.85727\\n9-85753\\n9.85780\\n9.85 807\\n9.85833\\n9.85 860\\n9.85887\\n9.85913\\n9.85940\\n9.85966\\nLog. Cos. I d.\\n985993\\n9.86 020\\n9.86046\\n9.86073\\n9. 86 099\\n9.86 126\\n27\\n27\\n27\\n26\\n27\\n27\\n27\\n26\\n27\\n27\\n26\\n27\\n26\\n27\\n27\\n26\\n27\\n26\\n27\\n27\\n26\\n27\\n26\\n27\\n26\\n27\\n26\\n27\\n26\\n27\\n26\\n26\\n27\\n26\\n27\\n26\\n26\\n27\\n2S\\n27\\n26\\n26\\n26\\n27\\n2S\\n26\\n27\\n26\\n2S\\n26\\n27\\n26\\n26\\n26\\n26\\n27\\n26\\n26\\n26\\n26\\nLotr. Cot.\\no-i5 47f\\n0.15456\\n0.15423\\n0-15 396\\no. 1 5 370\\n0-15343\\nO.I53I6\\no. 15 289\\no. 15 262\\n0.15235\\n0.15 208\\n0.15 182\\n0.15 155\\n0.15 128\\n0.15 loT\\no. 1 5 074\\no. 1 5 048\\no 1 5 02 1\\no. 14 994\\no. 14 967\\nLoir. Cos.\\n9-9 336\\n9.91 327\\n9.91 318\\n9.91 310\\n9.91 301\\n9.91 292\\n9.91 283\\n9.91 274\\n9.91 265\\n9-91 256\\n9-91 24f\\n9.91 239\\n9.91 230\\n9.91 221\\n9.91 212\\n9.91 203\\n9.91 194\\no. 1 4 940\\n0.14 914\\n0.14887\\n0.14 866\\n0.14833\\n9.91\\n9-91\\n9.91\\n185\\n176\\n167\\n0.14807\\n0.14 780\\n0-14753\\n0.14726\\no. 14700\\no. 14 673\\n0.14646\\no. 14620\\n0.14593\\n0.14566\\n9.91\\n9.91\\n9.91\\n9.91\\n9.91\\n158\\n149\\n146\\n131\\n122\\n9.91 113\\n9.91 104\\n9-91 095\\n9.91086\\n9.91 077\\n0.14539\\n0.14513\\n0.14486\\n0.14459\\n0-14 433\\no. 1 4 406\\n0.14379\\no- 14 353\\n0.14326\\no. 14 299\\n9.91 068\\n9.91 059\\n9.91 056\\n9.91 041\\n9.91 032\\n9.91 023\\n9.91 014\\n9.91 005\\n9.90996\\n9.90987\\n0.14 273\\no. 14 246\\n0.14 219\\n0.14 193\\n0.14 166\\n0.14 140\\n0.14 113\\no. 14 086\\no. 1 4 060\\n0.14033\\n9.90978\\n990969\\n9. 90 960\\n9.90951\\n9.90942\\n990933\\n9.90923\\n9.90914\\n9.90905\\n9-90896\\nLog. Cot. I c. (1.\\no. 14007\\no. 1 3 980\\n0.13953\\n0.13927\\no. 13 906\\nLog. Tan.\\n9.90887\\n9.90878\\n9. 90 869\\n9. 90 860\\n9.90 856\\n9.90 841\\n9-90832\\n9-90823\\n9.90814\\n9.90 805\\n9.90796\\n9\\n9\\n8\\n9\\n9\\n8\\n9\\n9\\n9\\n9\\n8\\n9\\n9\\n9\\n9\\n9\\n8\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\nLog. Sill.\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\n1 1\\nTo\\n9\\n8\\n7\\n_6\\n5\\n4\\n1*. i\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n27\\n2.7\\n3-1\\n3-6\\n4.6\\n4-5\\n9-0\\n13 5\\n18.0\\n22.5\\n28\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n18\\n1.8\\n2.1\\n2.4\\n2.7\\n30\\n6.0\\n9-0\\n12.0\\n15.0\\nIf\\ni-f\\n2.6\\n2-3\\n2.6\\n2.9\\n5.8\\nir.6\\n14.6\\n17\\n1-7\\n2.0\\n2.2\\n2.5\\n2-8\\n5.6\\n8.5\\nII-3\\n14. 1\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n9\\n0.9\\n1. 1\\n1.2\\n1.4\\n1.6\\n3-1\\n4.f\\n40 6.3\\n9\\n0.9\\n1.6\\n1.2\\n1-3\\n1-5\\n3-0\\n4-5\\n8\\n0.8\\ni.o\\nI.I\\n13\\n1-4\\n2.8\\n4.2\\n6.0 5.6\\n5oj7-9l7.5l7.i\\nV\\n54\\n383", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0435.jp2"}, "436": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n10\\nII\\n12\\n14\\n15\\n16\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n9.76 922\\n9.76939\\n9-76950\\n9.76974\\n9.76991\\nLog. Sill. I (I.\\n17\\n17\\nIf\\nIf\\n17\\nif\\n17\\nIf\\nIf\\n17\\nIf\\n9.77 008\\n9.77 026\\n9-77043\\n9.77 066\\n9.77078\\n9.77095\\n9.77 112\\n9.77 130\\n9.77 147\\n9.77 164\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n9.77 181\\n9-77 198\\n9.77 216\\n9-77233\\n9.77250\\n9.77 267\\n9-77284\\n9.77302\\n9-77319\\n9-77336\\n9-77 353\\n9-77370\\n9-77387\\n9.77404\\n9.77421\\n9-77 439\\n9-77456\\n9-77 473\\n9.77490\\n9-77 507\\n9-77 524\\n9-77 541\\n9-77558\\n9-77 575\\n9-77 592\\n9-77 609\\n9.77 626\\n9-77643\\n9.77 660\\n9-77 ^77\\n9-77693\\n977710\\n9-77 72f\\n9-77 744\\n9.77761\\n9-77778\\n9-77 795\\n9.77812\\n9.77828\\n9-77845\\n9.77 862\\n9-77879\\n9.77896\\n9-77913\\n9.77929\\n9-77 946\\nLog. Cos.\\n17\\n17\\nIf\\n17\\nIf\\n17\\n17\\nIf\\n17\\n17\\nIf\\n17\\n17\\n17\\n17\\nIf\\n17\\n17\\n17\\n17\\nLog. Tan.\\n9.86 126\\n9.86 152\\n9.86 179\\n9.86 206\\n9.86 232\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n17\\n16\\n17\\n17\\n17\\n17\\n16\\n17\\n17\\n16\\n17\\n17\\n16\\n17\\n17\\n16\\n17\\n9.86 259\\n9.86285\\n9.86 312\\n9-86338\\n9-86365\\n9.86 391\\n9.86418\\n9.86444\\n9.86471\\n9-86497\\n(1.\\n86524\\n.86550\\n.86577\\n.86603\\n86630\\n9\\n.86656\\n9.86683\\n9.86709\\n9.86 736\\n9.86762\\n9-86788\\n9.86815\\n9.86841\\n9.86868\\n9.86894\\n9.86 921\\n9.86 94f\\n9-86973\\n9. 87 000\\n9 -87026\\n9.87053\\n9.87079\\n9.87 105\\n9.87 132\\nQ-87 158\\n1.87 185\\n9\\nII\\n9.872\\n9.87237\\n9.87 264\\n9.87 290\\n:56\\nc. d.\\n9-87 3I6\\n987343\\n9.87369\\n9-87395\\n9.87422\\n9^448\\n9.87474\\n9.87501\\n9-87 52f\\n9-87553\\n9.87 580\\n9.87 606\\n9.87 632\\n9-87659\\n9.87685\\n9-87 711\\nLog. Cot.\\nLog. Cot.\\n26\\n26\\n27\\n26\\n26\\n2\u00c2\u00a7\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n2\u00c2\u00a7\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n2S\\n26\\n26\\n26\\n26\\n26\\n26\\n2\u00c2\u00a7\\n26\\n26\\n26\\n26\\ncTd^\\n0.13874\\n0.1384^\\n0.13 821\\n0.13794\\no.i3 76f\\n0.13 741\\nO.I37I4\\n0.13688\\n0.13 661\\n0.13635\\n9-90796\\n9.90786\\n9-90 77f\\n9.90 768\\n9.90759\\no. 1 3 608\\n0.13 582\\n0.13555\\n0.13529\\no. 1 3 502\\n0.13476\\n0.13449\\n0.13423\\n0.13396\\n0.13 370\\n0.13343\\nO.I33I7\\n0.13 290\\n0.13 264\\n0.13237\\n9.90750\\n9-90740\\n990731\\n9.90 722\\n9.90713\\n9.90703\\n9-90694\\n9.90685\\n9.90676\\n9.90666\\n9.9065^\\n9. 90 648\\n9.90639\\n9.90 629\\n9. 90 620\\n0.13 211\\n0.13 185\\n0.13 158\\n0.13 132\\n0.13 105\\n0.13079\\n0.13 052\\n0.13026\\no. 1 3 000\\n0.12973\\no. 1 2 947\\nO. I 2 920\\n0.12 894\\n0.12868\\n0.12 841\\nO. 12 815\\n0.12 789\\nO. 12 762\\n0.12 736\\nO. I 2 709\\n0.12 683\\n0.12 657\\nO. 1 2 636\\n0. 1 2 604\\n0.12 578\\n9.9061 1\\n9. 90 602\\n9.90592\\n9.90583\\n9-90 574\\n9.90 564\\n9-90 555\\n9.90 546\\n990 536\\n9.90 527\\n9.90 518\\n9-90 508\\n9-90499\\n9-90490\\n9.90 486\\n9.90471\\n9.90 461\\n9.90452\\n9-90443\\n9-90433\\n0.12 551\\n0.12 525\\n0.12 499\\n0.12 472\\n0.1 2 446\\n0.12 420\\n0.12 393\\no. 12 36f\\n0.12 341\\n0.12315\\n9.90424\\n9.90414\\n9-90405\\n9.90396\\n9-90386\\n9.90377\\n9-90 36f\\n9.90358\\n9-90348\\n9-90339\\n9-90330\\n9-90 320\\n9.90 311\\n9-90301\\n9.90 292\\no. 12 288\\nLog. Tan.\\n9.90 282\\n9-90 273\\n9.90 263\\n9.90254\\n9.90244\\n990235\\nLog. Sin.\\nLog. Cos. I d.\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\nd.\\n00\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\np. P.\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n27 28\\n2.7\\n2.6\\n3-1\\n3-1\\n3-6\\n3-5\\n4.0\\n4.0\\n4-5\\n4-4\\n9.0\\n8.8\\n13-5\\n13-2\\n18.0\\n17-6\\n22.\\n22.1\\n26\\n2.6\\n3-0\\n3-4\\n3-9\\n4-3\\n8.6\\n13.0\\n17.3\\n21.\\nIf 17\\nI.f\\n1.7\\n2.0\\n2.0\\n2-3\\n2.2\\n2.6\\n2.5\\n2.9\\n2.8\\n5-8\\n5-6\\n8.7\\n8.5\\nII. 6\\nII. J\\n14.6\\n14.1\\n18\\n1.6\\n1-9\\n2.2\\n2.5\\n2.f\\n5-5\\n8.2\\nII. o\\ni3-f\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n9\\n0.9\\nI.I\\n1.2\\n1.4\\n1.6\\n3-1\\n4-7\\n6.3\\n7-9\\n9\\n0.9\\ni.o\\n1.2\\n1-3\\n1-5\\n3-0\\n4-5\\n6.0\\n7.5\\nP. P.\\n53\u00c2\u00b0\\n3^4", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0436.jp2"}, "437": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\nLoer. sill.\\n9\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\nJ3\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nm\\n9-77 946\\n9.77963\\n9.77980\\n9-77 996\\n9.78013\\n9.78030\\n9.78046\\n9 78063\\n9.78080\\n9.78097\\n9.78 113\\n9.78 130\\n9.78 147\\n9.78 163\\n9.78 180\\n9.78 196\\n9.78213\\n9.78 230\\n9.78246\\n9.78263\\n9.78 279\\n9.78 296\\n9.78 312\\n9.78329\\n9.78346\\n9.78 362\\n9-78379\\n9-7839?\\n9.78412\\n9.78428\\n9.78444\\n9.78461\\n9-78 47f\\n9.78494\\n9.78510\\n9.78 527\\n9-78 543\\n978559\\n9.78576\\n9-78 592\\n9.78 609\\n9.78625\\n9.78 641\\n9.78658\\n9.78674\\n9.78 696\\n9.78707\\n9.78723\\n9-78739\\n9-78755\\n9.78772\\n9-78788\\n9.78 804\\n9.78821\\n9.78837\\n9.78853\\n9.78869\\n9.78885\\n9.78 902\\n9.78918\\n9- 78 934\\nliOtr. (;os. I\\nliOer. Tan. r. \u00c2\u00abl.\\n9-87711\\n9-8773?\\n9.87764\\n9.87796\\n9-87 816\\n9-87843\\n9.87869\\n9.87895\\n9.87 921\\n9-87948\\n9.87974\\n9.88 000\\n9.88 026\\n9.88053\\n9.88 079\\n9.88 105\\n988 I3T\\n9.88157\\n9.88 184\\n9.88 210\\n9.88236\\n9.88262\\n9.88288\\n9.88315\\n9.88341\\n9.88 367\\n9.88393\\n9.88 419\\n9-88445\\n9.88472\\n9.88498\\n9.88 524\\n9.88556\\n9-88 576\\n9.88602\\n9.88629\\n9.88655\\n9.88681\\n9.88707\\n988733\\n9.88759\\n9 88785\\n9.88 81T\\n9.88838\\n9.8 8864\\n9. 88 890\\n9.88916\\n9.88942\\n9.88968\\n9-88 994\\n9.89 026\\n9.89046\\n9.89 072\\n9.89098\\n9.89 124\\n9.89 156\\n9-89 ^11\\n9.89203\\n9.89 229\\n9-89255\\n9.89 281\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n2S\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\nl.op. Cot.\\no.\\nIjOu. (!()t. c. d. I Loir. Tan\\n2288\\n2 262\\n2 236\\n2 209\\n2183\\n2 157\\n2 131\\n2 104\\n2 078\\n2 052\\n2 026\\n999\\n973\\n947\\n921\\n895\\n868\\n842\\n816\\n790\\n763\\nIZl\\n711\\n685\\n659\\n371\\n345\\n319\\n293\\n266\\n240\\n214\\n188\\n162\\n136\\n1 10\\n084\\n058\\n032\\n005\\n0979\\n0953\\n092^\\no 90T\\n0875\\no 849\\no 823\\n0797\\n0771\\n0745\\n07 9\\nDtf. Con. I d.\\n90235\\n90 225\\n90 216\\n90 206\\n90196\\n90 187\\n90177\\n90 168\\n90158\\n90 149\\n90 139\\n90 130\\n90 120\\n90 116\\n90 lOI\\n90091\\n90082\\n90072\\n90062\\n90053\\n90 043\\n90033\\n90024\\n90014\\n90004\\n89995\\n89985\\n89975\\n89966\\n89 956\\n89946\\n89937\\n89927\\n8991?\\n89908\\n89898\\n89888\\n89878\\n89869\\n89859\\n89 849\\n89839\\n89 830\\n89820\\n89816\\n89791\\n89781\\n89771\\n89761\\n89751\\n89742\\n89 732\\n89722\\n89712\\n89702\\n89692\\n89683\\n89673\\n89663\\n989653\\n9\\n9\\n9\\n10\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n10\\n9\\n9\\n9\\n9\\nlO\\n9\\n9\\n9\\n10\\n9\\n9\\n10\\n9\\n9\\n10\\n9\\n9\\n10\\n9\\n9\\n10\\n9\\n10\\n9\\n10\\n9\\n10\\n9\\n10\\n9\\n10\\n9\\n10\\n9\\n10\\n10\\n9\\n10\\n9\\n10\\n10\\n9\\n10\\n10\\n9\\n10\\n10\\n10\\nLot;. Sill.\\n0\\n59\\n58\\n57\\n55\\n54\\n53\\n52\\n51\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\nr.\\n2\u00c2\u00a7 26\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n2-6\\n2\\n3-1\\n3\\n3-5\\n3-\\n4.0\\n3-\\n4.4\\n4-\\n8.8\\n8.\\n13.2\\n13-\\n17-6\\n17-\\n22.1\\n21.\\n17\\n18\\n6\\n1-7\\n1-6\\n7\\n2.0\\n1.9\\n8\\n2.2\\n2.2\\n9\\n2-5\\n2-5\\n10\\n2-8\\n2-y\\n20\\n5-6\\n5-5\\n30\\n8.5\\n8.2\\n40\\n11-3\\nII.\\n50\\n14.1\\n13.7\\n16\\n1.6\\n1-8\\n2.1\\n2.4\\n2-6\\n5-3\\n8.0\\n10.6\\n13-3\\n10\\n6\\nI.O\\n7\\nI.I\\n8\\n1-3\\n9\\n1-5\\n10\\n1-6\\n20\\n3-3\\n30\\n5.0\\n40\\n6 6\\n50\\n8-3\\n9\\n0.9\\n1. 1\\n1.2\\n1.4\\n1.6\\n3-1\\n4-?\\n6.3\\n7.9\\n5:^\\n385", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0437.jp2"}, "438": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n88^\\n10\\nII\\n12\\n14\\n15\\n16\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n60\\nLo^. Sin.\\n9-78934\\n9.78 950\\n9.78965\\n9.78 982\\n9.78 999\\n9.79015\\n9.79031\\n9.79047\\n9.79063\\n9.79079\\n9.79095\\n9.79 III\\n9.79 12^\\n9-79 143\\n9.79 159\\n9.79175\\n9.79 191\\n9.7920^\\n9.79223\\n9.79239\\n9-79255\\n9.79271\\n9.79287\\n9-79303\\n9 79319\\n9-79 33^\\n979351\\n979367\\n979383\\n9-79 399\\n9.79415\\n9-79431\\n9-79 446\\n9.79462\\n9-79 478\\n9-79 494\\n9.79510\\n9.79526\\n9-79541\\n9-79 557\\n9-79 573\\n9-79589\\n9.79605\\n9.79 620\\n9-79635\\n9.79652\\n9.79668\\n9.79683\\n9 79 699\\n979715\\n9.79730\\n9-79 746\\n9.79762\\n9.79777\\n9-79 793\\n9.79809\\n979824\\n9.79840\\n9.79856\\n9.79871\\n9-79887\\nLog.J^os^\\nd.\\nLoff. Tan.\\n9.89 281\\n9.89307\\n9-89333\\n9-89359\\n9.89385\\n9.89 411\\n9-89437\\n9.89463\\n9.89489\\n9.89515\\n9-89 541\\n9.89 567\\n9-89 593\\n9.89 619\\n9.89645\\n9.89 671\\n9.89697\\n9.89723\\n9-89749\\n9.89775\\n9.89 801\\n9.89827\\n9.89853\\n9.89879\\n9.89905\\n9.89931\\n9-89957\\n9.89 982\\n9.90008\\n9.90034\\n9.90066\\n9.90085\\n9. 90 112\\n990 138\\n9.90 164\\n9.90 190\\n9.90 216\\n9.90 242\\n9 90 268\\n9.90294\\n9.90319\\n9-9c\u00c2\u00bb 345\\n9.90371\\n9.9039;\\n9.90423\\n9.90449\\n990475\\n9.90 501\\n9.90 525\\n9:90552\\n990578\\n9. 90 604\\n9.90630\\n9.90656\\n9.90 682\\n9.9070;\\n9-90733\\n9.90759\\n9.90785\\n9.90 81 1\\n9.90837\\nLog. Cot.\\nc. d.\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n25\\n26\\n26\\n26\\n26\\n26\\n26\\n2$\\n26\\n26\\n26\\n26\\n26\\n25\\n26\\n26\\n26\\n25\\n26\\n26\\n26\\n25\\n26\\n26\\n26\\n2?\\n26\\n26\\n2?\\n26\\n26\\n26\\n25\\n26\\nc. d.\\nLog. Cot.\\n0719\\n0693\\n0667\\n0641\\n0615\\n0589\\n0563\\n0537\\no 511\\n0485\\n0459\\n0433\\n0407\\n0381\\n0355\\n0329\\n0303\\no 277\\no 251\\no 225\\no 199\\no 173\\n0147\\nO 121\\n0095\\no 069\\n0043\\no 01;\\n0.09 991\\n0.09 965\\n0.09939\\n0.09913\\n0.09 887\\n0.09 861\\n0.09 836\\n0.09 810\\n0.09 784\\n0.09 758\\n0.09 732\\n0.09 706\\n0.09 686\\n0.09 654\\n0.09 623\\n0.09 602\\n0.09 577\\n0.09551\\n0.09 525\\n0.09 499\\no 09 473\\n0.09 44;\\n0.09 421\\n0.09 395\\n0.09 370\\n0.09 344\\n0.09 318\\n0.09 292\\n0.09 265\\n0.09 246\\n0.09 214\\n0.09 189\\n0.09 163\\nLog. Tan.\\nLos. Cos.\\n9.89653\\n9.89643\\n9-89633\\n9.89623\\n9.89613\\n9.89 604\\n9-89594\\n9-89584\\n9.89574\\n9.89564\\n9.89554\\n9-89544\\n9-89534\\n9.89524\\n9.89514\\n9.89 504\\n9-89494\\n9.89484\\n9.89474\\n9.89464\\n9-89454\\n9-89444\\n9-89434\\n9.89424\\n9.89414\\n9.89404\\n9.89394\\n9-89384\\n989374\\n9.89364\\n9-89354\\n9.89344\\n9-89334\\n9.89324\\n9.89314\\n9.89304\\n9.89294\\n9.89 284\\n9-89274\\n9.89 264\\n9.89253\\n9-89243\\n9-89233\\n9.89223\\n9.89213\\n9.89 203\\n9.89193\\n9.89 182\\n9.89 172\\n9.89 162\\n9.89152\\n9.89 142\\n9.89132\\n9.89 I2T\\n9 89 1 1 1\\n9.89 lOI\\n9.89091\\n9.89081\\n9.89076\\n9.89066\\n9.89 056\\nLog. Sin.\\nd.\\nGO\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\nV\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\np. P.\\n26\\n2S\\n6\\n2.6\\n2.5 s\\n7\\n3-0\\n3.0\\n8\\n3-4\\n3-4\\n9\\n3-9\\n3-8\\n10\\n4-3\\n4.2\\n20\\n8.6\\n8-5\\n30\\n13.0\\n12.; i\\n40\\n17.3\\n17.0\\n50\\n21.6\\n21.2 1\\n16\\n16\\n6\\n1-6\\n1.6\\n7\\n1.9\\n1-8\\n8\\n2.2\\n2. 1\\n9\\n2-5\\n2.4\\n10\\n2.7\\n2-6\\n20\\n5-5\\n5-3\\n30\\n8.2\\n8.0\\n40\\nII.\\n10.6\\n50\\n13-y\\n13-3\\n15\\n1.8\\n2.6\\n2-3\\n26\\n5-1\\n1-1\\ni,o-3\\n12.9\\n10\\n10\\n6\\n1.6\\nI.O\\n7\\n1.2\\nI.I\\n8\\n1-4\\nI-.3\\n9\\n1.6\\ni.S\\n10\\n1.7\\n1-6\\n20\\n3-5\\n3-3\\n30\\n5-2\\n5.0\\n40\\n7-0\\n6.5\\n50\\n8.;\\n8.3\\n9\\n0.9\\nI.I\\n1.2\\n1.4\\n1.6\\n3-1\\n^\u00e2\u0080\u00a21\\n6.3\\n7.9\\np. p\\n51\u00c2\u00b0\\n386", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0438.jp2"}, "439": {"fulltext": "TABLE VII. LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n10\\n1 1\\n12\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n80\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n43\\n50\\n51\\n52\\n53\\n54\\nLojf. Sill. I (1. Loi?. Tan.\\n55\\n56\\n57\\n58\\n59\\n60\\n9.79887\\n9.79903\\n9-79918\\n9-79 934\\n9-79 949\\n9.79965\\n9.79980\\n9.79996\\n9.8001T\\n9.80027\\n9.80042\\n9.80058\\n9.80073\\n9.80089\\n9.80 104\\n9.80 120\\n9.80135\\n9. 80 1 5 1\\n9.80 165\\n9 80 182\\n9.80 197\\n9. 80 2 1 3\\n9.80228\\n9.80243\\n9.80 259\\n9.80 274\\n9.80 289\\n9.80305\\n9.80 320\\n9-80335\\n980351\\n9.80366\\n9.80381\\n9.80397\\n9 80412\\n9 80427\\n9.80443\\n9.80458\\n9 80473\\n9 8048Q\\n9.80 504\\n9.80 519\\n9.80534\\n9-80549\\ng.8o 564\\n9.80 580\\n9.80595\\n9. 80 610\\n9. 80 62 1\\n9. 80 646\\n9.80655\\n9.80671\\n9.80686\\n9.80 701\\n9-80 716\\n9-80731\\n9.80746\\n9.80 761\\n9-80776\\n9.80791\\n80 806\\n16\\n15\\n15\\n15\\n15\\n15\\nIS\\n15\\niS\\n15\\n15\\n15\\nil\\nil\\n15\\nIS\\niS\\niS\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\niS\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\nIS\\n15\\n15\\nIS\\n15\\nIS\\n15\\n15\\n15\\nIS\\n15\\n15\\nIS\\n15\\n15\\n15\\n15\\n15\\n15\\njiOg. Cos i 1.\\n90837\\n90863\\n90 8S3\\n90914\\n90940\\n90 966\\n90 992\\n01^\\n043\\n069\\n095\\n121\\ni4o\\n172\\n198\\n224\\n250\\n27S\\n301\\n327\\n353\\n378\\n404:\\n430\\n456\\n481\\n507\\n533\\n559\\n584\\n616\\n636\\n662\\n68^\\n713\\n739\\n765\\n790\\n816\\n842\\n867\\n893\\n919\\n945\\n970\\n996\\n92 022\\n92 04f\\n92073\\n92 099\\n92 124\\n92 150\\n92 176\\n92 201\\n92 22^\\n92253\\n92 278\\n92304\\n92 330\\n9235S\\n92 381\\n26\\n2S\\n26\\n25\\n26\\n26\\n2S\\n26\\n26\\n2S\\n26\\n2S\\n26\\n2S\\n26\\n26\\n2S\\n26\\n2S\\n26\\n2S\\n26\\n2S\\n26\\n2S\\n26\\n2S\\n26\\n2S\\n26\\n2S\\n26\\n2S\\n26\\n2S\\n26\\n2S\\n26\\n25\\n2S\\n26\\n2S\\n26\\n2S\\n2S\\n26\\n2S\\n26\\n2S\\n2S\\n26\\n2S\\n2S\\n26\\n2S\\n2S\\n26\\n2S\\n2S\\n26\\nL(\u00c2\u00abr. Cot-\\n0.09 163\\n0.09 137\\n0.09 1 1 T\\n0.09085\\n0.09 060\\n0.09034\\n0.09008\\n0.08 982\\n0.08956\\n0.08 930\\n0.08 905\\n0.08 879\\n0.08853\\n0.08827\\n0.08 802\\n0.08 776\\n0.08 750\\n0.08 724\\n0.08 693\\n0.08 673\\n0.08 647\\n0.08 621\\n0.08 595\\n0.08 570\\n0.08 544\\n0.08 518\\n0.08 492\\n0.08 467\\n0.08 441\\n0.08 415\\n0.08 389\\n0.08 364\\n0.08 338\\n0.08 312\\n0.08 286\\n0.08 261\\n0.08 235\\n0.08 209\\n0.08 183\\n0.08 158\\n0.08 132\\n0.08 106\\n0.08 081\\n0.08 055\\n0.08 029\\n0.08 004\\n0.07 978\\n0.07 952\\n0.07 926\\n0.07 901\\n0.07 875\\n0.07 849\\n0.07 824\\n0.07 798\\n0.07 772\\n0.07 747\\n0.07 721\\n0.07 695\\n0.07 670\\n0.07 644\\no. 07 6 1 8\\nliOp. Cot. 1 c. \u00c2\u00ab1. I liO^. Tan.\\nLour. Cos.\\n(I.\\n89056\\n89040\\n89030\\n89019\\n89009\\n88 999\\n88989\\n88978\\n88968\\n88958\\n88947\\n88937\\n88927\\n88917\\n88906\\n88 896\\n88 886\\n88875\\n88865\\n88855\\n88844\\n88834\\n88823\\n88813\\n88803\\n88792\\n88782\\n88772\\n88761\\n88751\\n88746\\n88730\\n88720\\n88 709\\n88699\\n88 688\\n88678\\n88667\\n88657\\n88646\\n88636\\n88625\\n88615\\n88604\\n88594\\n88 583\\n88573\\n88562\\n88 552\\n88 541\\n88531\\n88 526\\n88 510\\n88 499\\n88489\\n9-88 478\\n9.88467\\n9.88457\\n9.88446\\n9-88 436\\n9.88425\\nliOi?. Sill.\\n10\\n10\\n10\\n10\\n16\\n10\\n16\\n16\\n10\\ni5\\n10\\n10\\n10\\n16\\n16\\n10\\n16\\n16\\n10\\ni5\\n16\\n16\\n10\\n16\\n16\\n16\\n10\\n16\\n16\\n10\\n10\\n10\\n16\\n16\\n16\\n16\\n16\\ni5\\n16\\n10\\n16\\n16\\n10\\n10\\n16\\ni5\\n16\\n16\\n10\\ni5\\n10\\n10\\n10\\ni5\\n10\\nI r\\n16\\n16\\n10\\n10\\n50\\n49\\n48\\n47\\nj^\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n19\\n18\\n17\\n16\\n14\\n13\\n12\\n1 1\\nlo\\n9\\n8\\n7\\n6\\n1 r.\\n26 2S\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n2.6\\n2.S\\n3-0\\n3-0\\n3-4\\n3-9\\n3-4\\n3-8\\n4-3\\n8.6\\n4-2\\n8-5\\n13.0\\n12.5^\\n17.3\\n21.5\\n17.0\\n21.2\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\nSO\\n16\\n1.6\\n1-8\\n2.1\\n2.4\\n2-6\\n5-3\\n8.0\\n10.6\\n13-3\\nIS\\ni-S\\n1.8\\n2.6\\n2.3\\n2.6\\n5-1\\n7-f\\n10.3\\n12.9\\n15\\n1-5\\nI-?\\n2.0\\n2.2\\n2-5\\n5-0\\n7.5\\n1 0.0\\n12.5\\nII\\n10\\nI\\n6\\nI.I\\n1.6\\n7\\n1-3\\n1.2\\n8\\n1.4\\n1.4\\n9\\n1-6\\n1.6\\n10\\n1-8\\n1-7\\n20\\n3.6\\n3-5\\n3-\\n30\\n5-5\\n5-2\\n5-\\n40\\n7-. 3\\n7-0\\n6.\\n50\\n9.1\\n8.?\\n8.\\n.0\\n.1\\n\u00e2\u0096\u00a03\\n.5\\n\u00e2\u0080\u00a26\\n\u00e2\u0096\u00a03\\n.0\\n-6\\n\u00e2\u0080\u00a23\\np. I\\n50\\n337", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0439.jp2"}, "440": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n40\u00c2\u00b0\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\nLoe. Sill.\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n(JO\\n9.80805\\n9.80822\\n9.80837\\n9.80852\\n9.80867\\n9.80882\\n9.80897\\n9.80 912\\n9.80927\\n9.80942\\n9.80957\\n9,80972\\n9.80987\\nooT\\n016\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\nao\\n9.8\\n31\\n9.8\\n32\\n9.8\\n33\\n9.8\\n34\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9^\\n9.8\\n031\\n046\\n061\\n076\\n091\\n106\\n121\\n136\\n150\\n165\\n186\\n195\\n210\\n225\\n239\\n254\\n269\\n284\\n299\\n313\\n328\\n343\\n358\\n372\\n387\\n402\\n416\\n431\\n446\\n460\\n475\\n490\\n504\\n519\\n534\\n548\\n563\\n578\\n592\\n607\\n621\\n636\\n650\\n665\\n680\\n694\\nLog. Cos.\\n(1.\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\n15\\n14\\n15\\n15\\n15\\n15\\n15\\n14\\n15\\n15\\n15\\n14\\n15\\n15\\n14\\n15\\n15\\n14\\n15\\n14\\n15\\n15\\n15\\n14\\n15\\n14\\n14\\n15\\n14\\n15\\n14\\n14\\n15\\n14\\n14\\n15\\n14\\n1$\\n14\\n15\\n14\\n14^\\n14^\\n14\\n15\\n14\\nLop. Tan.\\n9.92 38T\\n9.92407\\n9.92432\\n9-92 458\\n9.92484\\n9.92 509\\n9-92 535\\n9.92 561\\n9.92 585\\n9.92 612\\n9.92638\\n9.92663\\n9.92 689\\n9.92714\\n9.92 746\\n9.92 766\\n9.92 791\\n9.92 817\\n9.92 842\\n9.92 868\\n9.92894\\n9.92919\\n9.92945\\n9.92971\\n9.92996\\nC. (1.\\n9.93022\\n9-9304?\\n993073\\n9-93 098\\n9.93 124\\n9.93 150\\n9-93 175\\n9.93 201\\n9.93225\\n9.93 252\\n9-93 278\\n9-93 303\\n993329\\n9-93 354\\n9-93380\\n9-93405\\n9-93 431\\n9-93 456\\n9.93 482\\n9-93 508\\n9-93 533\\n9-93 559\\n9-93 584\\n9.93610\\n9-93635\\n9.93661\\n9-93685\\n9.93712\\n9-93 73?\\n9-93763\\n9-93788\\n9.93814\\n9.93 840\\n9.93 865\\n9-93891\\n9-93 9^6\\nLog. Cot.\\n25\\n25\\n26\\n25\\n25\\n25\\n26\\n25\\n25\\n26\\n25\\n25\\n25\\n26\\n25\\n25\\n25\\n25\\n26\\n25\\n25\\n25\\n26\\n25\\n25\\n25\\n25\\n25\\n26\\n25\\n25\\n25\\n25\\n25\\n26\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n26\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n26\\n25\\n25\\n25\\ncTdT\\nLog. Cot.\\n0.07 618\\n0.07 593\\n0.07 567\\n0.07 54T\\n0.07 516\\n0.07 490\\n0.07 465\\n0.07 439\\n0.07 413\\n0.07 388\\nLog. Cos.\\n9.88425\\n9.88415\\n9.88404\\n9-88393\\n9-88383\\n(1.\\n9.88372\\n9.88 36T\\n9.88351\\n9.88346\\n9.88 329\\n0.07 362\\n0.07 336\\n0.07 311\\n0.07 285\\n0.07 259\\n0.07 234\\n0.07 208\\n0.07 183\\n0.07 15^\\n0.07 1 31\\n0.07 106\\n0.07 086\\n0.07 055\\n0.07 029\\n0.07 003\\n0.06 978\\n0.06 952\\n0.06 927\\n0.06 901\\n0.06 875\\n0.06 850\\n0.06 824\\n0.06 799\\n0.06 773\\n0.06 748\\n0.06 722\\n0.06 695\\n0.06 671\\n0.06 645\\n0.06 620\\n0.06 594\\n0.06 569\\n0.06 543\\n0.06 518\\n0.06 492\\n0.06 465\\n0.06 441\\n0.06415\\n0.06 390\\n0.06 364\\n9.88319\\n9-88308\\n9.8829^\\n9.88 287\\n988275\\n9.88265\\n9.88255\\n9.88 244\\n9-88233\\n9.88223\\n9.88 212\\n9.88 201\\n9.88 196\\n9.88 180\\n9.88 169\\n158\\n147\\n137\\n126\\n115\\n9.88 104\\n9. 88 094\\n9.88083\\n9.88072\\n9.88 061\\n9.88050\\n9.88039\\n9.88029\\n9.88018\\n9.88007\\n9.87995\\n9.87985\\n9-87974\\n9.87963\\n9-87953\\n0.06 339\\n0.06 313\\n0.06 288\\n0.06 262\\n0.06 237\\n0.06 21 T\\n0.06 186\\n0.06 160\\n0.06 134\\n0.06 109\\n0.06083\\nLog. Tan.\\n9.87942\\n9.87931\\n9.87 920\\n9.87909\\n9.87898\\n9.8788?\\n9-87876\\n9.87865\\n9-87854\\n9.87844\\n9-87833\\n9.87 822\\n9.87 811\\n9.87 800\\n987789\\n9-87778\\nliOg. Sin.\\n10\\nII\\n16\\n16\\n16\\nII\\n10\\n16\\nII\\nid\\n16\\n1 1\\n16\\n16\\n1 1\\n16\\nid\\nII\\n16\\n1 1\\n16\\nII\\n16\\nII\\n16\\nII\\n16\\nII\\n16\\nII\\nid\\nII\\nII\\n16\\nII\\nII\\n16\\nII\\nII\\n16\\nII\\nII\\nII\\n16\\nII\\nII\\nII\\n16\\nII\\nII\\nII\\nII\\nII\\n16\\nII\\nII\\nII\\nII\\nII\\nII\\nGO\\n59\\n58\\n57\\n56\\np. p\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n12\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\nTo\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\n1 1\\n10\\n9\\n8\\n7\\n6\\n26 2$\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n2.6\\n2.5\\n30\\n3-0\\n3-4\\n3-4\\n3-9\\n4-3\\n8.6\\n3-8\\n4.2\\n8.5\\n13.0\\n12.^\\n17-3\\n21.6\\n17.0\\n21.2\\n15\\nS5\\n6\\n1-5\\n1-5\\n7\\n1.8\\nI.?\\n8\\n2.0\\n2.0\\n9\\n2.3\\n2.2\\n10\\n2.6\\n2.5\\n20\\n5-1\\n5.0\\n30\\n7.?\\n7.5\\n40\\n10.3\\nlO.O\\n50\\n12.9\\n12.5\\n14\\n1.4\\n1-7\\n1.9\\n2.2\\n2.4\\n4-8\\n7.2\\n9-6\\n12. 1\\nII\\n10\\n6\\nI.I\\nI.O\\n7\\n1-3\\n1.2\\n8\\n1.4\\n1.4\\n9\\n1-6\\n1.6\\n10\\n1-8\\n1-7\\n20\\n36\\n3.5\\n30\\n5-5\\n5-2\\n40\\n7-3\\n7-0\\n50\\n9.1\\n8.?\\nP. p.\\n49\\n388", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0440.jp2"}, "441": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES. COSINES, TANGENTS, AND COTANGENTS.\\n11\\n5\\n6\\n7\\n8\\n9\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\nLotr. sill.\\n25\\n26\\n27\\n28\\n29\\nao\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n43\\n44\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n9.8\\n694\\n709\\n723\\n738\\n752\\n767\\n781\\n796\\n810\\n824\\n839\\n853\\n868\\n882\\n897\\n911\\n925\\n940\\n954\\nq6o\\n983\\n997\\n9.82 012\\n9.82 025\\n9.82 040\\n9.82055\\n9.82 069\\n9.82 083\\n9.82 098\\n9 82 112\\n9.82 126\\n9.82 146\\n982 155\\n9.82 169\\n9.82183\\n9.82 197\\n9.82 212\\n9.82 226\\n9.82 246\\n9.82 2U\\n9.82 269\\n9.82283\\n9.82 297\\n9-82311\\n9.8232^\\n45\\n46\\n47\\n48\\n49\\no\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nm\\n9-82339\\n9.82354\\n9.82368\\n9.82 382\\n9-82 396\\n9.82 410\\n9.82424\\n9.82438\\n9.82452\\n9.82467\\n9.82 481\\n9.82495\\n9.82 509\\n9.82 523\\n9-82537\\n9-82 551\\nLot?. Cos. \u00c2\u00bbK\\nliOur. Tan. c. \u00c2\u00abl\\n9939I6\\n9 93942\\n9.93967\\n9-93 993\\n9.94018\\n9.94044\\n9.94069\\n9.94095\\n9.94 120\\n9.94146\\n9-94171\\n9.94 197\\n9.94 222\\n9.94248\\n9-94273\\n9-94299\\n9.94324\\n9.94350\\n9-94 375\\n9.94400\\n9.94426\\n9.94451\\n9-94 477\\n9.94502\\n9-94528\\n9-94 553\\n9-94 579\\n9.94604\\n9.94630\\n9-94655\\n9.94681\\n9-94 706\\n9-94732\\n9-94 757\\n9-94782\\n9. 94 808\\n9-94833\\n9-94859\\n9.94884\\n9.94910\\n9-94 935\\n9.94961\\n9.94986\\n9.95011\\n9-95037\\n9.95 062\\n9.95 o83\\n9-95 113\\n9-95 139\\n9.95 164\\n9.95 189\\n9-95 215\\n9.95 240\\n9.95 266\\n9-95291\\n9-95 316\\n9-95 342\\n9-95367\\n9-95 393\\n9-95 418\\n9-95 443\\nliOtr. ot. c. (I.\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n2S\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n2^\\n25\\n25\\n2?\\n25\\n25\\n25\\n25\\n25\\n25\\nlA.ir. Cot.\\nLou Cos. (1.\\n0.06 083\\n9-87778\\n0.06 058\\n9\\n87 767\\n59\\n0.06 032\\n9\\n87756\\n58\\n0.06 007\\n9\\n87745\\n57\\n0.05 981\\n9\\n87734\\n56\\n55\\n0.05 956\\n9\\n87723\\n0.05 930\\n9\\n87712\\n54\\n0.05 905\\n9\\n87701\\n53\\n0.05 879\\n9\\n87 690\\n52\\n0.05 854\\n9\\n87679\\n51\\noO\\n0.05 828\\n9\\n87668\\n0.05 803\\n9\\n87657\\n49\\n0.05 777\\n9\\n87645\\n48\\n0.05752\\n9\\n87634\\n47\\n0.05 726\\n9\\n87623\\n46\\n0.05 701\\n9\\n87612\\n45\\n0.05 67I\\n9\\n87 601\\n44\\n0.05 650\\n9\\n87 590\\n43\\n0.05 625\\n9\\n87579\\n42\\n0.05 599\\n9\\n87 568\\n41\\n0.05 574\\n9\\n87557\\n40\\n0.05 548\\n9\\n87546\\n39\\n0.05 523\\n9\\n87535\\n1\\n38\\n0.05 497\\n9\\n87523\\n37\\n0.05 472\\n9\\n87512\\n36\\n0.05 446\\n9\\n87 501\\n35\\n0.05 421\\n9\\n87490\\n34\\n0.05 395\\n9\\n87479\\n33\\n0.05 370\\n9\\n87468\\n32\\n0.05 344\\n9\\n87457\\n31\\n0.05 319\\n9\\n87445\\n30\\n0.05 293\\n9\\n87434\\n29\\n0.05 268\\n9\\n87423\\n28\\n0.05 243\\n9\\n87412\\n27\\n0.05 217\\n9\\n87 401\\nj^\\n26\\n0.05 192\\n9\\n87389\\n25\\n0.05 166\\n9\\n87 378\\n24\\n0.05 141\\n9\\n87367\\n23\\n0.05 III\\n9\\n87356\\n22\\n0.05 090\\n9\\n87345\\n21\\n0.05 064\\n9\\n87333\\n20\\n0.05 039\\n9\\n87322\\n19\\n0.05 014\\n9\\n8731^\\n18\\n0.04 988\\n9\\n87300\\n17\\n0.04 963\\n9\\n.87 2(88\\nj|\\n16\\n0.04 937\\n9\\n.87277\\n15\\n0,04 912\\n9\\n87266\\n14\\n0.04 886\\n9\\n87254\\n13\\n0.04 861\\n9\\n87243\\n12\\n0.04 836\\n9\\n87232\\nII\\n10\\n0.04 816\\n9\\n87 221\\n0.04785\\n9\\n.87 209\\n9\\n0.04759\\n9\\n87 198\\n8\\n0.04734\\n9\\n87187\\n7\\n0.04 708\\n9\\n87175\\n6\\n5\\n0.04683\\n9\\n87164\\n0.04658\\n9\\n87153\\n4\\n0.04632\\n9\\n87 141\\n3\\n0.04607\\n9\\n87 130\\nT\\n0.04 581\\n9\\n87 118\\nI\\n0.04 556\\n9\\n87 107\\n\\\\a)S. Tan.\\n1\\nour. Sin.\\n(1.\\nt\\nV. V\\n2S 25\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n2\\n5\\n3\\n2.\\n3\\n4\\n3-\\n3\\n8\\n3-\\n4\\n2\\n4-\\n8\\n5\\n8.\\n12\\n1\\n12.\\n17\\n16.\\n21\\n2\\n20.\\n14\\n6\\n1.4\\n7\\n1.7\\n8\\n1-9\\n9\\n2.2\\n10\\n2.4\\n20\\n4-8\\n30\\n7-2\\n40\\n9.6\\n50\\n12. 1\\n14\\n1-4\\n1.6\\n1-8\\n2.1\\n2-3\\n4-6\\n7-0\\n9-3\\nII. 6\\nII\\nI\\n6\\nI.I\\n7\\n1-3\\n8\\n1-5\\n9\\n1-7\\n10\\n1.9\\n20\\n3-8\\n3-\\n30\\n5-7\\n5-\\n40\\n7-6\\n7-\\n50\\n9-6\\n9-\\nI V\\n48\\n3\u00c2\u00bb9", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0441.jp2"}, "442": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n42\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n(io\\nLoff. Siu.\\n82551\\n82565\\n82 579\\n82593\\n82 607\\n82621\\n82635\\n82649\\n82663\\n82 677\\n82691\\n82 705\\n82 719\\n82733\\n82746\\n82 766\\n82774\\n82788\\n82802\\n82816\\n82830\\n82844\\n82858\\n8287T\\n82885\\n82899\\n82 913\\n82 927\\n82 940\\n82954\\n82968\\n82982\\n82 996\\n83009\\n83023\\n83037\\n83051\\n83 064\\n83078\\n83092\\n83 106\\n83 !I9\\n83 133\\n83 147\\n83 166\\n83 174\\n83 188\\n83 201\\n83215\\n83229\\n83 242\\n83256\\n83 269\\n83283\\n83297\\n,10\\n83\\n83324\\n83337\\n83351\\n83365\\n83 378\\nLog. Cos. (1.\\nLofr. Tan. c. 1. I Loer. Cot.\\n9-95 443\\n9.95 469\\n9.95494\\n9.95 520\\n9-95 54^\\n9-95 571\\n9.95 596\\n9.95 621\\n9.95647\\n9.95672\\n9.95697\\n9.95723\\n9-95 748\\n9-95 774\\n9-95 799\\n9.95 824\\n9-95850\\n9-95873\\n9.95901\\n9.95 926\\n95951\\n95 977\\n96 002\\n96027\\n96053\\n9.96078\\n9.96 104\\n9.96 129\\n9.96154\\n9.96 180\\n9.96 205\\n9.96230\\n9.96 256\\n9.96 281\\n996306\\n9-96332\\n9-96357\\n9-96383\\n9. 96 408\\n9-96433\\n9-96459\\n9.96484\\n9-96 509\\n9-96535\\n9.96 560\\n9-96 58S\\n9.96 611\\n9.96636\\n9.96 661\\n9.96687\\n9.96 712\\n9.96737\\n9.96763\\n9-96788\\n9-96813\\n9.96839\\n9.96 864\\n9.96889\\n9.96915\\n9.96 940\\n9-9696!\\nLot, Cot. c. d\\n25\\n25\\n2l\\nA\\n25\\n25\\n2!\\n25\\n2S\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n2^\\n25\\n25\\n25\\n25\\n25\\n2?\\n2S\\n25\\n25\\n2?\\n2?\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n2!\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n2?\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n0.04 556\\n0.04531\\n0.04 505\\n0.04 480\\n0.04454\\n0.04429\\n0.04404\\n0.04 378\\n0.04353\\n0.04327\\n0.04 302\\n0.04 277\\n0.04 251\\n0.04 226\\n0.04 206\\n0.04175\\n0.04 I 50\\n0.04 124\\no. 04 099\\n0.04074\\n0.04048\\n0.04 023\\n0.03 997\\n0.03 972\\n0.03 947\\nLoe. Cos.\\n0.03 921\\n0.03 896\\n0.03 871\\n0.03 84!\\n0.03 820\\n0.03 795\\n0.03 769\\n0.03 744\\n0.03 718\\n0.03693\\n0.03 668\\n0.03 642\\n0.03 617\\n0.03 592\\n0.03 565\\n0.03 541\\n0.03 516\\n0.03496\\n0.03465\\n0.03 440\\n0.03414\\n0.03 389\\n0.03 364\\n0-03 338\\n0.03313\\n0.03 28^\\n0.03 262\\n0.03 237\\n0.03 21 T\\n0.03 186\\n0.03 161\\n0.03 135\\n0.03 1 16\\n0.03 085\\n0.03059\\n0-03034\\nLog. Tan.\\n9.87 107\\n9.87 096\\n9.87 084\\n9-87073\\n9.87 062\\n9.87 056\\n9.87039\\n9.87 027\\n9.87 016\\n9.87 004\\n9-86993\\n9.86982\\n9.86 976\\n9.86959\\n9-86947\\n9-86936\\n9.86 924\\n9-86913\\n9.86 90T\\n9.86890\\n9-86 878\\n9.86867\\n9.86855\\n9.86 844\\n9.86832\\n9.86821\\n9.86809\\n9.86798\\n9.86786\\n9-867 74\\n9.86 763\\n9.86751\\n9.86 740\\n9.86728\\n986 716\\n9.86 705\\n9.86 693\\n9.86682\\n9.86 676\\n9-86658\\n9.86647\\n9.86 63I\\n9.86 623\\n9.86612\\n9. 86 606\\n86588\\n86577\\n86565\\n86553\\n86542\\n9.86 530\\n9-86 518\\n9.86 507\\n9.86495\\n9.86483\\n9.86471\\n9. 86 460\\n9.86448\\n9.86436\\n9.86424\\n9.86412\\nLos. Sin.\\n00\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n.5\\n4\\n3\\n2\\nI\\np. P.\\n25\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n2.S\\n2.\\n3-0\\n2.\\n3-4\\n3-\\n3-8\\n3-\\n4.2\\n4-\\n8.5\\n8.\\n12.7\\n12.\\n17.0\\n16.\\n21.2\\n20.\\n25\\n5\\n9\\n3\\n7\\nI\\n3\\n5\\n6\\n14\\n6\\n1.4\\n7\\n1-6\\n8\\n1.8\\n9\\n2.1\\n10\\n2-3\\n20\\n4-6\\n30\\n7.0\\n40\\n9-3\\n50\\nII. 6\\n13\\n1-3\\n1.6\\n1.8\\n2.0\\n2.2\\n4-5\\n6.7\\n9.0\\nII. 2\\n12\\nII\\nI]\\n6\\n1.2\\nI.I\\n7\\n1.4\\n1.3\\n8\\n1.6\\n1.5\\n9\\n1.8\\n1.7\\n10\\n2.0\\n1.9\\n20\\n4.0\\n3-8\\n3-\\n30\\n6.0\\n5-7\\n5-\\n40\\n8.0\\n7-6\\n7.\\n50\\nlO.O\\n9.6\\n9-\\np. p.\\n47\\n390", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0442.jp2"}, "443": {"fulltext": "TABLE VIL\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n43\u00c2\u00b0\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLofj. Sin. (1.\\n83378\\n83392\\n83405\\n83419\\n83432\\n83446\\n83459\\n83473\\n83486\\n83500\\n83513\\n83527\\n83540\\n83554\\n83567\\n83585\\n83594\\n83607\\n83621\\n83634\\n83647\\n83661\\n83674\\n83688\\n83701\\n83714\\n83728\\n83741\\n83754\\n83768\\n83781\\n83794\\n83808\\n83821\\n83834\\n83847\\n83861\\n83874\\n83887\\n83900\\n83914\\n83927\\n83940\\n83953\\n83967\\n83980\\n83993\\n84005\\n84019\\n84033\\n84046\\n84059\\n84072\\n8408I\\n84098\\n84 III\\n84 124\\n84138\\n84 151\\n84 164\\n84177\\nLog. Cos. (I.\\nLoff. Tnii. c. (1\\n9.96965\\n9.96991\\n9.97 016\\n9-97041\\n9.97067\\n9.97092\\n9.97 117\\n9-97 143\\n9.97 168\\n9-97 193\\n9.97219\\n9.97 244\\n9.97 269\\n9.97 295\\n9.97320\\n9-97 345\\n9-97 370\\n9.97396\\n9-97421\\n9-97 446\\n9.97472\\n9-97 497\\n9-97 522\\n9 97 548\\n9-97 573\\n9-97 598\\n9.97624\\n9.97649\\n9-97 674\\n9-97699\\n9.97725\\n9.97 750\\n9-97 775\\n9.97 801\\n9.97 826\\n9-97 851\\n9-97 877\\n9-97902\\n9.9792^\\n9.97952\\n9-97 978\\n9.98 003\\n9.98028\\n9-98054\\n9.98079\\n9.98 104\\n9.98 129\\n9.98155\\n9.98 186\\n9.98 205\\n9-98231\\n9.98 256\\n9.98 281\\n9-98 306\\n9-98 332\\n9-98 357\\n9.98 382\\n9.98 408\\n998433\\n9-984 58\\n9-98483\\nLop. Cot.\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\nLop. Cot.\\n0.03034\\n0.03 009\\n0.02 984\\n0.02 958\\n0.02933\\n0.02 908\\n0.02 882\\n0.02 857\\n0.02 832\\n0.02 806\\n0.02 781\\n0.02 756\\n0.02 736\\n0.02 705\\n0.02 680\\n0.02 654\\n0.02 629\\n0,02 604\\n0.02 578\\n0.02 553\\n0.02 528\\n0.02 502\\n0.02 47^\\n0.02 452\\n0.02 427\\n0.02 401\\n0.02 376\\n0.02 351\\n0.02 325\\n0.02 306\\n0.02 275\\n0.02 249\\n0.02 224\\n0.02 199\\n0.02 174\\n0.02 148\\n0.02 123\\n0.02 098\\n0.02 072\\n0.02 04^\\n0.02 022\\n0.0 1 996\\no.oi 971\\n0.0 1 946\\n0.01 921\\n0.01 895\\n0.01 876\\n0.01 845\\n0.01 819\\n0.01 794\\n0.01 769\\n0.01 744\\n0.01 718\\n0.01 693\\n0.01 668\\n0.01 642\\n0.01 61^\\n0.01 592\\n0.01 567\\n0.01 541\\no-oi 5 16\\nLor. Tan.\\nLoe. Cos.\\n9.86354\\n9.86342\\n9.86330\\n9-86318\\n9- 8630 6\\n9.86 294\\n9.86282\\n9.86 271\\n9.86 259\\n9.86 247\\n86412\\n86 401\\n86389\\n8637?\\n86365\\n86235\\n86 223\\n86 21 1\\n86 199\\n86187\\n86 176\\n86164\\n86 152\\n86 140\\n86128\\n86 116\\n86 104\\n86092\\n86080\\n86068\\n86056\\n86044\\n9.86032\\n9.86 020\\n86 008\\n85996\\n85984\\n85972\\n85 960\\n85948\\n85936\\n85924\\n85 912\\n85 900\\n85887\\n85875\\n85863\\n85851\\n85839\\n85827\\n85815\\n85803\\n85791\\n85 778\\n85766\\n85754\\n85742\\n85730\\n85718\\n85705\\n985693\\nLot;. Sin.\\n(io\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n31\\n30\\n29\\n28\\n27\\n26\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\nI V.\\n2S\\n25\\n6\\n2-5\\n2.5\\n7\\n3-0\\n2.9\\n8\\n3-4\\n3.3\\n9\\n3-8\\n3.^\\n10\\n4.2\\n4.1\\n20\\n8.5\\n8.3\\n30\\n12. f\\n12.5\\n40\\n17.0\\n16.6\\n50\\n21.2\\n20.8\\n13\\n13\\n6\\n1-3\\n1.3\\n7\\n1.6\\n1.5\\n8\\n1.8\\ni.^\\n9\\n2.0\\n1.9\\n10\\n2.2\\n2.1\\n20\\n4-5\\n4.3\\n30\\n6.7\\n6.5\\n40\\n9.0\\n8.S\\n50\\nII. 2\\nI0.8\\n12\\n12\\nII\\n6\\n1.2\\n1.2\\nI.I\\n7\\n1-4\\n1.4\\n1-3\\n8\\n1-6\\n1.6\\n1-5\\n9\\n1-9\\n1.8\\n1-7\\n10\\n2.1\\n2.0\\n1-9\\n20\\n4.T\\n4.0\\n3-8\\n30\\n6.2\\n6.0\\nS-7\\n40\\n8.3\\n8.0\\n7-6\\n50\\n10.4\\nlO.Q\\n9.6\\n1 F.\\n46\\n391", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0443.jp2"}, "444": {"fulltext": "TABLE VII.\u00e2\u0080\u0094 LOGARITHMIC SINES, COSINES, TANGENTS, AND COTANGENTS.\\n44\u00c2\u00b0\\n10\\nII\\n12\\n14\\n15\\ni6\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLog. Sin.\\n9.84177\\n9.84 190\\n9.84 203\\n9.84 216\\n9.84229\\n9.84 242\\n9.84255\\n9.84268\\n9.84281\\n9.84294\\n9.84307\\n9.84320\\n9-84333\\n9-84 346\\n9-84359\\n9.84372\\n9-84385\\n9-84398\\n9.84411\\n9.84424\\n9-84437\\n9.84450\\n9.84463\\n9.84476\\n9.84489\\n9.84502\\n9.84514\\n9.84 52f\\n9.84540\\n9-84553\\n9.84 566\\n9-84579\\n9-84592\\n9. 84 604\\n9.8461^\\n9. 84 630\\n9.84643\\n9.84656\\n9.84669\\n9.84681\\nd.\\n9.84694\\n9.84707\\n9.84720\\n9.84732\\n9.84745\\n9.84758\\n9-84771\\n9-84783\\n9-84796\\n9.84809\\n9.84822\\n9-84834\\n9.84847\\n9.84860\\n9.84872\\n9.84885\\n9.84898\\n9.84 916\\n9.84923\\n9-84936\\n9-84948\\nLo g. Cos.\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n12\\n13\\n13\\n13\\n13\\n13\\n12\\n13\\n13\\n13\\n12\\n13\\n13\\n12\\n13\\n13\\n12\\n13\\n13\\n12\\n13\\n12\\n13\\n12\\n13\\n12\\n13\\n12\\n13\\n12\\n13\\n12\\n12\\n13\\n12\\n12\\n13\\n12\\n12\\n13\\n12\\nLog. Tan.\\n9.98483\\n9.98 509\\n9-98 534\\n9-98 559\\n9.98 585\\n9.98 610\\n9.98635\\n9. 98 666\\n9.98686\\n9.98 711\\n9-98736\\n9.98 762\\n9-98787\\n9.98 812\\n9.98837\\n9.98863\\n9.98888\\n9.98913\\n9-98 938\\n9.98964\\n9.98989\\n9.99014\\n9.99040\\n9.99065\\n9.99096\\n9-99115\\n9.99 141\\n9.99 166\\n9.99 1 91\\n9-99 216\\n9.99242\\n9.99267\\n9.99292\\n9.99318\\n9-99 343\\n9-99368\\n9-99 393\\n9.99419\\n9-99 444\\n9.99469\\n9.99494\\n9-99 520\\n9-99 545\\n9.99570\\n9-99 59?\\n9.99 621\\n9.99646\\n9.99671\\n9.99697\\n9.99722\\n9-99 74^\\n9-99772\\n9.99798\\n9-99823\\n9-99848\\nc. d.\\n9-99873\\n9-99899\\n9.99924\\n9-99 949\\n9-99 974\\n0.00000\\n2S\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n2\u00c2\u00a7\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\nLog. Cot.\\no.oi 516\\no.oi 491\\nO.OI 465\\nO.OI 446\\nO.OI 415\\nO.OI 390\\nO.OI 364\\nO.OI 339\\nO.OI 314\\nO.OI 289\\nO.OI 263\\nO.OI 238\\nO.OI 213\\nO.OI 18^\\nO.OI 162\\nO.OI 137\\nO.OI 112\\nO.OI 086\\nO.OI 061\\nO.OI 036\\nO.OI 010\\n0.00 985\\n0.00 960\\n0.00 935\\n0.00 909\\n0.00 884\\n0.00 859\\n0.00 834\\n0.00 808\\n0.00 783\\n0.00758\\n0.00733\\n0.00 70^\\n0.00 682\\n0.00 657\\n0.00 631\\n0.00 606\\n0.00 581\\n0.00 556\\n0.00 536\\nLog. Co t, led.\\n0.00 505\\n0.00 480\\n0.00455\\n0.00429\\n0.00404\\n0.00 379\\n0.00353\\n0.00 328\\n0.00 303\\n0.00 278\\n0.00 252\\n0.00 227\\n0.00 202\\n0.00 177\\n0.00 151\\n0.00 126\\n0.00 lOI\\n0.00076\\n0.00056\\n0.00025\\no. 00 000\\nLo g. Ta n.\\nLog. Cos.\\n9.85693\\n9.85681\\n9.85 669\\n9.85657\\n9.85644\\n9.85 632\\n9.85 620\\n9.85608\\n9-85 595\\n9-85 583\\n9.85571\\n9.85559\\n9-85 546\\n9-85 534\\n9.85 522\\n9-85 509\\n9-8549^\\n9.85485\\n9-85472\\n9.85 466\\n9.85448\\n9-85435\\n9.85423\\n9.85411\\n9-85 398\\n9.85 386\\n9-85374\\n9.85361\\n9-85349\\n9-85336\\n9.85 324\\n9.85312\\n9-85299\\n9.85 287\\n9-85 274\\n9,85 262\\n9-85 249\\n9.85 237\\n9.85 224\\n9.85 212\\nd.\\n9.85 199\\n9-85 187\\n9.85 174\\n9.85 162\\n9.85 149\\n9-85 137\\n9.85 124\\n9.85 112\\n9.85099\\n9.85087\\n9.85074\\n9.85 062\\n9.85049\\n9.85037\\n9.85 024\\n9.85 Oil\\n9.84999\\n9.84986\\n9.84974\\n9.84961\\n9-84948\\nLog. aiu.\\nd.\\nGO\\n59\\n58\\n57\\n56\\n55\\n54\\n53\\n52\\n51\\n50\\n49\\n48\\n47\\n46\\n45\\n44\\n43\\n42\\n41\\n40\\n39\\n38\\n37\\n36\\n25\\n24\\n23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nII\\n10\\n9\\n8\\n7\\n6\\nP. P.\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n2S 25\\n2-5\\n2.\\n3-0\\n2.\\n3-4\\n3-8\\n3.\\n3-\\n4.2\\n8.5\\n4-\\n8.\\nI2.f\\n12.\\n17.0\\n16.\\n21.2\\n20.\\n12\\n1.2\\n1-4\\n1-6\\n1-9\\n2.1\\n4.1\\n6.2\\n8-3\\n10.4\\n13\\n13\\n6\\n1-3\\n1.3\\n7\\n1.6\\ni.S\\n8\\n1.8\\ni-f\\n9\\n2.0\\n1.9\\n10\\n2.2\\n2.1\\n20\\n4.5\\n4.3\\n30\\n6-^\\n6.5\\n40\\n9.0\\n8.6\\n50\\nII. 2\\n10.8\\n12\\n1.2\\n1.4\\n1.6\\n1.8\\n2.0\\n4.0\\n6.0\\n8.0\\nlO.O\\np. p.\\n45\\n392", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0444.jp2"}, "445": {"fulltext": "TABLE VIII.\\nLOGARITHMIC VERSED SINES AND EXTERNAL\\nSECANTS.", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0445.jp2"}, "446": {"fulltext": "TABLE VIII. \u00e2\u0080\u0094LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n0\u00c2\u00b0 1\u00c2\u00b0\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\nLos. Vers.\\n2\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\ni9.\\n60\\nCO\\n2.62642\\n3.22848\\n3.58066\\n3-83054\\n4.02436\\n.18272\\n.31662\\n.43260\\n53490\\n4.62642\\n,70920\\n.78478\\n.85431\\n.91-\\n4.97860\\n5.03466\\n.08732\\n\u00e2\u0080\u00a213696\\n\u00e2\u0080\u00a218393\\n5.22848\\n27086\\n\u00e2\u0080\u00a231126\\n34987\\n.38684\\n5.42230\\n\u00e2\u0080\u00a245636\\n.48915\\n.52073\\n.55121\\n5 58066\\n.60914\\n.63672\\n66344\\n\u00e2\u0080\u00a268937\\n5^7i455\\n.73902\\n.76282\\n\u00e2\u0080\u00a278598\\n.80854\\n5-83053\\n\u00e2\u0080\u00a285198\\n.87291\\n\u00e2\u0080\u00a289335\\n.91332\\n5.93284\\n\u00e2\u0080\u00a295193\\n.97061\\n5.98890\\n6 00680\\n6.02435\\n.04155\\n.05842\\n\u00e2\u0080\u00a207496\\n.09120\\n6. 10714\\n12279\\n.13816\\n.15327\\n.16811\\n6.18271\\nLog. Vers.\\nLoe. Exsec.\\n60206\\n352I8\\n24987\\n19382\\n15836\\n13389\\nI I 598\\n10230\\n915T\\n8278\\n7558\\n6953\\n6437\\n5992\\n5605\\n5266\\n4964\\n4696\\n4455\\n4238\\n4046\\n3861\\n3697\\n3545\\n3406\\n3278\\n3158\\n3048\\n2944\\n2848\\n2757\\n2672\\n2593\\n2518\\n2447\\n2379\\n23 6\\n2256\\n2199\\n2145\\n2093\\n2044\\n1996\\n1952\\n1909\\n1868\\n1829\\n1790\\n1755\\n1720\\n1654\\n1623\\n1594\\n1565\\n1537\\n1511\\n1484\\n1460\\nJ)\\n00\\n2,62642\\n3.22848\\n3.58066\\n3-83054\\n4^02436\\n18272\\n,31662\\n,43260\\n\u00e2\u0080\u00a253491\\n4.62642\\n.70921\\n.78478\\n\u00e2\u0080\u00a285431\\n.91868\\n4.97861\\n5^03466\\n.08732\\n\u00e2\u0080\u00a213697\\n\u00e2\u0080\u00a218393\\n5.22849\\n.27087\\n.31127\\n34988\\n.38685\\n\u00e2\u0096\u00a05.42231\\n\u00e2\u0080\u00a245638\\n.48916\\n\u00e2\u0080\u00a252075\\n\u00e2\u0080\u00a255123\\n58068\\n.60916\\n\u00e2\u0080\u00a263674\\n\u00e2\u0080\u00a266346\\n68940\\n5^71457\\n.73904\\n.76284\\n.78601\\n.8085^\\n5-83056\\n.85201\\n.87295\\n.89338\\n-91335\\n5-93288\\n\u00e2\u0080\u00a295197\\n.97065\\n5.98894\\n6.00685\\n6 02440\\n.04160\\n.05847\\n.07501\\n.09125\\nn\\n6. 10719\\n12284\\n13822\\n.15333\\n.16818\\n6.18278\\nLos. Exsec.\\nLog. Vers.\\nJ\u00c2\u00bb\\n60206\\n35218\\n2498?\\n19382\\n15836\\n13389\\n1 1 598\\n10236\\n9151\\n8279\\n7557\\n6952\\n6437\\n5993\\n5605\\n5266\\n4964\\n4696\\n4456\\n4238\\n4046\\n386T\\n3697\\n3545\\n3407\\n3278\\n31591\\n3048\\n2945\\n2848\\n2758\\n2672\\n2593\\n251?\\n2447\\n2380\\n2316\\n2256\\n2199\\n2145\\n2093\\n2043\\n1997\\n1952\\n1909\\n1829\\nI79I\\n1755\\n1720\\n1687\\n1654\\n1623\\n1594\\n1565\\n1537\\nI5II\\n1485\\n1460\\n7\\n6,18271\\n.19707\\n.211 19\\n.22509\\n.23877\\n6.25223\\n.26549\\n.27856\\n.29142\\n.30416\\n6. 31666\\n,32892\\n.34107\\n\u00e2\u0080\u00a235305\\n.36487\\n6.37653\\n38803\\n39938\\n,41059\\n.42165\\n43258\\n.44337\\n.45403\\n.46455\\n47496\\n6.48524\\n.49539\\n.50544\\n\u00e2\u0080\u00a251536\\n.52518\\n6.53488\\n54448\\n.55397\\n\u00e2\u0080\u00a256336\\n.57265\\n6.58184\\n59093\\n59993\\n.60884\\n.61766\\n6.62639\\n.63503\\n\u00e2\u0080\u00a264359\\n.65206\\n.66045\\n6.66876\\n,67700\\n.68515\\n.69323\\n.70124\\n6.70917\\n.71703\\n.72482\\n.73254\\n.74019\\n6.7477^\\n.75529\\n.76275\\n.77014\\n.777 aJ\\n6.78474\\nLoir. Vers.\\nLog. Exsec.\\n1435\\nI412\\n1389\\n1368\\n1346\\n1326\\n1306\\n1286\\n1268\\n1250\\n1232\\n1214\\n1 1 98\\n1182\\n1 166\\n1 1 50\\n1135\\n1121\\n1 106\\n1093\\nI078\\n1066\\n1052\\n1046\\n1028\\n1015\\n1004\\n992\\n981\\n970\\n960\\n949\\n939\\n929\\n919\\n909\\n900\\n891\\n882\\n872\\n864\\n855\\n84^\\n839\\n831\\n823\\n815\\n806\\n793\\n786\\n779\\n772\\n765\\n758\\n752\\n745\\n739\\n733\\n726\\n6.18278\\n.19714\\n.21126\\n.225I6\\n.23884\\n6.2523T\\n.2655^\\n.27864\\n,29151\\n\u00e2\u0080\u00a230419\\n6.31669\\n,32901\\n-34II6\\n\u00e2\u0080\u00a235315\\n36497\\n6.37663\\n.38814\\n39949\\n.41076\\n.42177\\n6.43270\\n\u00e2\u0080\u00a244349\\n\u00e2\u0080\u00a245415\\n\u00e2\u0080\u00a246468\\n\u00e2\u0080\u00a247509\\n48537\\n49553\\n\u00e2\u0096\u00a050557\\n\u00e2\u0096\u00a051550\\n\u00e2\u0096\u00a052532\\n6^53503\\n54463\\n\u00e2\u0080\u00a255413\\n\u00e2\u0080\u00a256352\\n\u00e2\u0080\u00a257281\\n58201\\n.59116\\n.60011\\n60902\\n.61784\\n6.62657\\n,63522\\n.64378\\n.65226\\n.66065\\n6.66897\\n,67726\\n\u00e2\u0096\u00a068536\\n\u00e2\u0080\u00a269345\\n.70145\\n6.70939\\n.71725\\n.72505\\n.7327^\\n74043\\n6.74802\\n\u00e2\u0080\u00a275554\\n76306\\n77040\\n.7777%\\n6.78506\\nI, Off. Kxst C\\n2)\\n1436\\nI412\\n1390\\n1368\\n1347\\n1326\\nI3O6\\n1287\\nI26g\\n1250\\n1232\\nI215\\nII98\\n1182\\n1 166\\n1151\\n1135\\n1121\\n1106\\n1093\\n1079\\n1066\\n1053\\n1046\\n1028\\n1016\\n1004\\n993\\n982\\n976\\n960\\n950\\n939\\n929\\n919\\n909\\n906\\n891\\n882\\n873\\n864\\n856\\n848\\n839\\n83I\\n823\\n816\\n808\\n806\\n794\\n786\\n779\\n772\\n765\\n759\\n752\\n746\\n739\\n733\\n727\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n4S\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n394", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0446.jp2"}, "447": {"fulltext": "TABLE VIII.-\\n-LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n2\u00c2\u00b0 :r\\n5\\n6\\n7\\n8\\n9\\n10\\nII\\n12\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n0\\nLou:. A ers.\\n78474\\n79195\\n79909\\n8061 8\\n81322\\n82019\\n,82711\\n,83398\\n84079\\n\u00e2\u0080\u00a284755\\n85425\\n86091\\n8675t\\n,87407\\n,88057\\n88703\\n89344\\n89980\\n90612\\n91239\\n91862\\n,92480\\n93093\\n93703\\n94308\\n94909\\n95506\\n96099\\n,96688\\n,97272\\n\u00e2\u0080\u00a297853\\n\u00e2\u0080\u00a298430\\n99004\\n\u00e2\u0080\u00a299573\\n\u00e2\u0080\u00a200139\\n.00701\\n.01259\\n.01814\\n.02366\\n.02914\\n03458\\n.03999\\n.04537\\n.05071\\n.05603\\n06 1 30\\n.06655\\n.07177\\n.07695\\n.0821 1\\n\u00e2\u0080\u00a208723\\n.09232\\n\u00e2\u0080\u00a209739\\n10242\\n10743\\n1 1240\\n11735\\n1 222^\\n12716\\n13203\\n13687\\n7_\\nIjOsj. \u00c2\u00bbrs.\\n721\\n71-+\\n709\\n703\\n697\\n692\\n686\\n681\\n676\\n670\\n665\\n666\\n655\\n656\\n646\\n641\\n636\\n631\\n627\\n622\\n618\\n613\\n609\\n605\\n601\\n597\\n592\\n589\\n58-+\\n581\\n577\\n573\\n569\\n565\\n562\\n558\\n555\\n551\\n548\\n544\\n541\\n537\\n534\\n531\\n527\\n525\\n521\\n518\\n515\\n512\\n509\\n506\\n503\\n506\\n497\\n495\\n492\\n489\\n486\\n484\\nIjO!?. Kxsec\\nT\\n6.78500\\n.79221\\n79937\\n80645\\n.81350\\n6.82048\\n.82740\\n.83427\\n.84109\\n\u00e2\u0080\u00a284785\\n6.85457\\n.86123\\n.86783\\n\u00e2\u0080\u00a287439\\n88096\\n6.88737\\n\u00e2\u0080\u00a289378\\n.90015\\n.90647\\n.91275\\n6.91898\\n.92516\\n\u00e2\u0080\u00a293131\\n\u00e2\u0080\u00a293741\\n94346\\n6 94948\\n\u00e2\u0080\u00a295545\\n.96139\\n.96728\\n\u00e2\u0080\u00a2973J3\\n6.97895\\n.98472\\n\u00e2\u0080\u00a299046\\n6.99616\\n7.00182\\n7.00745\\n.01304\\n.01860\\n.02412\\n.02966\\n7.03505\\n.04047\\n\u00e2\u0080\u00a204585\\n.05126\\n.05652\\n7 06 1 86\\n06706\\n.07228\\n\u00e2\u0096\u00a00774?\\n.08263\\n7.08776\\n.09286\\n\u00e2\u0080\u00a209793\\n10297\\nI0798\\n1 1297\\n1 1792\\n12285\\n12775\\n13262\\n7 Loif. Vers.\\n7 1 3746\\n721\\n715\\n709\\n703\\n698\\n692\\n687\\n682\\n676\\n671\\n666\\n666\\n656\\n651\\n646\\n641\\n636\\n632\\n628\\n623\\n61 8\\n614\\n610\\n605\\n601\\n597\\n593\\n589\\n585\\n581\\n577\\n574\\n570\\n566\\n563\\n559\\n555\\n552\\n548\\n545\\n541\\n538\\n535\\n531\\n528\\n525\\nr 2\\n519\\n516\\n513\\n509\\n507\\n503\\n501\\n498\\n495\\n493\\n490\\n487\\n484\\nKxser.\\ni\\n7\\n13687\\n14168\\n14646\\n15122\\n15595\\n16066\\n16534\\n17000\\n17463\\n17923\\n18382\\n18837\\n19291\\n19742\\n201 91\\n20637\\n21081\\n21523\\n21963\\n22406\\n22836\\n23269\\n23700\\n24129\\n24555\\n24980\\n25402\\n25823\\n2624T\\n26658\\n27072\\n27485\\n27895\\n28304\\n287 II\\n29116\\n29518\\n29919\\n30319\\n307 1 6\\n31112\\n31505\\n3189^\\n32288\\n32676\\n33063\\n33448\\n33831\\n34213\\n34593\\n34971\\n35348\\n35723\\n36097\\n36468\\n36839\\n37207\\n37574\\n37940\\n38304\\n38667\\n481\\n478\\n475\\n473\\n470\\n468\\n466\\n463\\n466\\n458\\n455\\n453\\n451\\n448\\n446\\n444\\n442\\n440\\n437\\n435\\n433\\n431\\n429\\n426\\n424\\n422\\n426\\n418\\n4 6\\n414\\n412\\n416\\n409\\n406\\n405\\n402\\n401\\n399\\n397\\n395\\n393\\n392\\n390\\n388\\n386\\n385\\n383\\n382\\n380\\n378\\n377\\n375\\n373\\n371\\n370\\n368\\n367\\n366\\n364\\n^62\\nl,(n:. K\\\\s c\\nliOer. Vers.\\n7\\n13746\\n14228\\n14707\\n15183\\n15657\\n1 61 29\\n16598\\n17064\\n17528\\n17989\\n18448\\n18905\\n19359\\n1 98 II\\n20260\\n2070^\\n21 152\\n21595\\n22035\\n22473\\n22909\\n23343\\n23775\\n24204\\n24632\\n25057\\n25486\\n25902\\n26321\\n26738\\n27153\\n27567\\n27978\\n28387\\n28795\\n29200\\n29604\\n30006\\n30406\\n30804\\n3 1 201\\n31595\\n31988\\n32379\\n32768\\n33 56\\n33542\\n33926\\n34309\\n34689\\n35069\\n35446\\n35822\\n36196\\n36569_\\n36940\\n373 0\\n37678\\n38044\\n38409\\nIt\\n38773\\n481\\n479\\n476\\n474\\n471\\n469\\n466\\n464\\n46 1\\n459\\n456\\n454\\n452\\n449\\n447\\n445\\n442\\n446\\n438\\n436\\n434\\n431\\n429\\n427\\n425\\n423\\n421\\n419\\n41^\\n415\\n413\\n411\\n409\\n407\\n405\\n404\\n402\\n400\\n398\\n396\\n394\\n393\\n391\\n389\\n388\\n385\\n38-;\\n382\\n386\\n379\\n377\\n376\\n374\\n37\\n569\\n368\\n366\\n365\\n363\\nliOe. Kxscr.\\n395", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0447.jp2"}, "448": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n4\u00c2\u00b0 5\u00c2\u00b0\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\nLof?. Vers.\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n7.38667\\n39028\\n\u00e2\u0080\u00a239387\\n.39745\\n.40102\\n7.40457\\n.40810\\n.41163\\n.41513\\n.41863\\nD Loff. Exsec. 2\\n.4221 I\\n\u00e2\u0080\u00a24255^\\n.42903\\n.43246\\n.43589\\n7.43930\\n.44270\\n.44608\\n.44946\\n.45281\\n7.45616\\n.4594-9\\n.46281\\n466 1 2\\n.46941\\n7.47270\\n.47597\\n.47922\\n.48247\\n.48570\\n7.48892\\n.49213\\n.49533\\n.49852\\n.50169\\n7. 5048 S\\n50800\\n.51114\\n.51427\\n.51739\\n7\\n52050\\n52359\\n5266^\\n.52975\\n.53281\\n7.53586\\n53890\\n.54193\\n54495\\n54796\\n60\\n7.55096\\n.55395\\n.55692\\n.55989\\n.5628^\\n7.56580\\n.56873\\n.57166\\n\u00e2\u0080\u00a257458\\n57749\\n7.58039\\n361\\n359\\n358\\n356\\n355\\n353\\n352\\n350\\n349\\n348\\n346\\n345\\n343\\n342\\n341\\n339\\n338\\n337\\n335\\n334\\n332\\n330\\n329\\n328\\n327\\n325\\n324\\n323\\n322\\n321\\n320\\n318\\n3^7\\n316\\n315\\n314\\n313\\n311\\n311\\n309\\n308\\n30^\\n306\\n305\\n304\\n303\\n302\\n300\\n300\\n299\\n29?\\n297\\n295\\n295\\n293\\n293\\n292\\n290\\n290\\nLo:r. Vers.\\n7-38773\\n\u00e2\u0080\u00a239134\\n.39495\\n.39854\\n402 1 1\\n7.4056;\\n.40922\\n.41275\\n.41627\\n.41977\\n7.42326\\n.42673\\n.43019\\n.43364\\n.43708\\n7.44050\\n.44390\\n.44730\\n.45068\\n.4540=;\\n7.457401\\n.46075\\n.4640^ i\\n.46739 i\\n.47070 i\\n7.47399\\n.47727\\n.48054\\n.48379\\n.48703\\n7.49026\\n.49348\\n49669\\n.49989\\n.5030;\\n7 50624\\n50941\\n.51256\\n.51569\\n.51882\\n7.52194\\n.52504\\n.52814\\n.53122\\n.53429\\n7.53735\\n.54041\\n54345\\n54648\\n.54950\\n7\\nn\\n.55251\\n.55550\\n.55849\\n.5614^\\n56444\\n7.56740\\n\u00e2\u0080\u00a257035\\n\u00e2\u0080\u00a257329\\n.57621\\n\u00e2\u0080\u00a257913\\n7.58204\\n361\\n366\\n359\\n35^\\n356\\n354\\n353\\n352\\n350\\n349\\n34^\\n346\\n345\\n343\\n342\\n340\\n339\\n338\\n337\\n335\\n334\\n332\\n332\\n330\\n329\\n328\\n327\\n325\\n324\\n323\\n322\\n321\\n319\\n318\\n317\\n316\\n315\\n313\\n313\\n311\\n316\\n309\\n308\\n307\\n306\\n305\\n304\\n303\\n302\\n301\\n299\\n299\\n298\\n296\\n296\\n295\\n294\\n292\\n292\\n291\\nLog. Vers.\\n7\\nLos;. Kxsec\\n7\\n7\\n58039\\n58328\\n58615\\n58902\\n59188\\n59473\\n59758\\n60041\\n60323\\n60604\\n60885\\n61 164\\n61443\\n61721\\n61998\\n62274\\n62549\\n62823\\n63096\\n63369\\n63641\\n63911\\n6418T\\n64451\\n64719\\n64986\\n65253\\n65519\\n65784\\n66048\\n6631 1\\n66574\\n66836\\n67097\\n6735^\\n67617\\n67875\\n68133\\n68396\\n68647\\nD Loff. Exsec. I 2\\n68902\\n6915;\\n6941 1\\n69665\\n6991;\\n70169\\n70421\\n70671\\n70921\\n71 170\\n714I8\\n71666\\n71913\\n72159\\n72404\\n72649\\n72893\\n73137\\n73379\\n73621\\n73863\\nLo!. Vers.\\n289\\n287\\n287\\n286\\n285\\n284\\n283\\n282\\n281\\n286\\n279\\n279\\n27?\\n277\\n276\\n275\\n274\\n273\\n272\\n272\\n276\\n270\\n269\\n268\\n26^\\n266\\n266\\n265\\n264\\n263\\n263\\n26T\\n261\\n266\\n259\\n258\\n258\\n257\\n256\\n255\\n255\\n254\\n253\\n252\\n252\\n251\\n250\\n250\\n249\\n248\\n24^\\n247\\n246\\n245\\n245\\n244\\n243\\n242\\n242\\n241\\n7.\\n58204\\n58494\\n58783\\n59071\\n59358\\n59645\\n59930\\n,60214\\n60498\\n.60786\\n7.\\n7\\n61062\\n61342\\n61622\\n6190T\\n62179\\n.62456\\n.62733\\n63008\\n.63282\\n.63556\\n63829\\n,64101\\n,64372\\n64643\\n.64912\\n,65181\\n.65449\\n.65716\\n.65982\\n.6624^\\n.66512\\n.66776\\n.67039\\n.67301\\n,67562\\n,67823\\n,68083\\n,68342\\n,68601\\n,68858\\n,69115\\n,69371\\n,69627\\n.69881\\n.70135\\n70388\\n,70641\\n70893\\n,71144\\n71394\\n71644\\n,71892\\n,72141\\n\u00e2\u0080\u00a272388\\n.72635\\n,72881\\n.73126\\n.73371\\n.73615\\n\u00e2\u0080\u00a273859\\n7-74iot\\nLour. Kxsec\\n290\\n289\\n288\\n287\\n286\\n285\\n284\\n283\\n282\\n281\\n286\\n280\\n279\\n278\\n277\\n276\\n275\\n274\\n274\\n273\\n272\\n271\\n276\\n269\\n269\\n268\\n267\\n266\\n265\\n264\\n264\\n263\\n262\\n261\\n261\\n260\\n259\\n258\\n25;\\n257\\n256\\n255\\n254\\n254\\n253\\n252\\n252\\n251\\n250\\n250\\n248\\n248\\n24?\\n246\\n246\\n245\\n245\\n244\\n243\\n242\\nI\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n_9L\\n10\\nII\\n12\\n13\\n14\\np. P.\\n15\\n]6\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n6\\n360\\n36.0\\n35.0\\n7\\n8\\n42.0\\n48.0\\n40.8\\n46.6\\n9\\n10\\n54-0\\n60.0\\n51.5\\n58., S\\n20\\n120.0\\n116. 6\\n30\\n180.0\\n175-0\\n40\\n240.0\\n233.3\\n50\\n300.0\\n291.6\\nGO\\n330\\n33^o\\n38.5\\n44.0\\n49.5\\n55-0\\nIIO.O\\n165.0\\n220.0\\n275.0\\n270\\n27.0\\n31-5\\n36.0\\n40-5\\n45.0\\ngo.o\\n135-0\\n180.0\\n225.0\\n320\\n32.0\\n37-3\\n42-6\\n48.0\\n53.3\\n106.6\\n160.0\\n213.3\\n266.6\\n!6\\n30.3\\n34-6\\n39-0\\n43.3\\n8^.-6\\n130.0\\n173.3\\n216.6\\n340\\n34-0\\n39-6\\n45-3\\n51.0\\n56.6\\n3-3\\n170.0\\n226.6\\n283.3\\n310\\n31.0\\n36.!\\n41-3\\n46-5\\n51-6\\n103.3\\n155-0\\n206.6\\n258.3\\n300 290 280\\n6\\n30.0\\n29.0\\n7\\n35.0\\n33-8\\n8\\n40.0\\n38-6\\n9\\n45 -o\\n43.5\\n10\\n50.0\\n48.3\\n20\\n100.0\\n96.6\\n30\\n150.0\\n145.0\\n40\\n200.0\\n193-3\\n50\\n250.0\\n241.6\\n28.\\n32-6\\n37-3\\n42.0\\n46.6\\n93-3\\n140.\\n1 6.6\\n233 .3\\n260 250\\n240\\n230\\n6\\n24.0\\n23.0\\n7\\n28 .0\\n26.8\\n8\\n32.0\\n30.6\\n9\\n36.0\\n34.5\\n10\\n40.0\\n38.3\\n20\\n80.0\\n76-6\\n30\\n120.0\\n115.0\\n40\\n160.0\\n153-3\\n50\\n200.0\\n191-6\\n210\\n200\\n6\\n21.0\\n20.0\\n7\\n8\\n24-5\\n28.0\\n23.3\\n26.6\\n9\\n31-5\\n30.0\\n10\\n20\\n35.0\\n70.0\\n33-3\\n66.6\\n30\\n105.0\\n100.0\\n40\\n50\\n140.0\\n175.0\\n133-3\\n166.6\\n25-\\n29.\\n33-3\\n37-5\\n41-6\\n83-3\\n125.0\\n166.6\\n208.3\\n220\\n22.0\\n25-6\\n29-3\\n33-0\\n36.6\\n73-3\\nIIO.O\\n146.6\\n^83.3\\n190\\n19.\\n25\\n28,\\n31\\n63\\n95\\n126\\nI t*.\\n396", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0448.jp2"}, "449": {"fulltext": "TABLE VIII. \u00e2\u0080\u0094LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\nG\\n7\u00c2\u00b0\\n10\\n1 1\\n12\\n14\\n15\\ni6\\n1 8\\n19\\n20\\n21\\n2 2\\n23\\nii_\\n23\\n26\\n27\\n28\\n29\\n30\\n3i\\n32\\n33\\n34\\n35\\n36\\n37\\ni 38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n4B\\n49\\n50\\n54\\n56\\n57\\n5S\\n59\\n0\\nLoir. Vers. I J\\n7\\n74104\\n74344\\n74583\\n74822\\n75060\\n75297\\n75534\\n75770\\n76006\\n76246\\n76475\\n76708\\n76941\\n77173\\n77405\\n77636\\n77867\\n78097\\n78326\\n78554\\n78783\\n79010\\n79237\\n79463\\n79689 I\\n79914!\\n80F38\\nS0362\\n805S6\\n80808\\n81031\\n81252\\n81473\\n81694\\n81914\\n82133\\n82352\\n82570\\n82788\\n83005\\n83222\\n83438\\n83653\\n83868\\n84083\\n84297\\n84516\\n84723\\n84933\\n85147\\n85359\\n85570\\n85780\\n85990\\n86199\\n86408\\n86616\\n86824\\n87031\\n87238\\nLou Vers.\\n241\\n240\\n239\\n239\\n238\\n237\\n236\\n236\\n235\\n234\\n234\\n233\\n233\\n231\\n236\\n230\\n229\\n2 7\\n227\\n226\\n22 S\\n225\\n224\\n22 1\\n223\\n221\\n221\\n226\\n220\\n219\\n219\\n218\\n217\\n217\\n217\\n216\\n215\\n215\\n214\\n214\\n213\\n213\\n212\\n212\\n211\\n21 I\\n210\\n210\\n209\\n209\\n208\\n208\\n207\\n206\\nIt\\nLocr. Kxsec.I I\\n74101\\n74343\\n74585\\n74826\\n75066\\n75305\\n75544\\n75782\\n76019\\n76256\\n76492\\n76728\\n76963\\n77197\\n77431\\n77664\\n77S97\\n78128\\n78360\\n78596\\n78826\\n79050\\n79279\\n79507\\n79735\\n79962\\n80188\\n80414\\n80639\\n80864\\n81088\\n81312\\n8i53d\\n81758\\n81980\\n82201\\n82422\\n82642\\n82862\\n83081\\n83300\\n83518\\n83735\\n83952\\n84169\\n84385\\n84606\\n84815\\n85030\\n85243\\n85457\\n85670\\n85882\\n86094\\n86305\\n86516\\n86726\\n86936\\n87146\\n87354\\n87563\\nliOir. Kxser.\\n242\\n24?\\n241\\n240\\n239\\n239\\n238\\n237\\n237\\n236\\n235\\n235\\n234\\n233\\n233\\n232\\n231\\n231\\n230\\n230\\n229\\n229\\n228\\n228\\n227\\n226\\n226\\n225\\n225\\n224\\n224\\n223\\n222\\n222\\n221\\n226\\nI 219\\nI 219\\n219\\n218\\n217\\n217\\n3,6\\n216\\n215\\n215\\n214\\nI 213\\nI\\ni 213\\n3\\n212\\n21T\\n211\\n21 1\\n210\\n210\\n209\\n208\\n208\\n7\\nLocr. Vers. J Lok- Kxse(\\n7.87238\\n87444\\n87650\\n87855\\n88060\\n88264\\n88468\\n88672\\n88875\\n8907 f\\n89279\\n89481\\n89682\\n89882\\n90082\\n90282\\n9048 T\\n90680\\n90878\\n91076\\n91273\\n91476\\n91667\\n91863\\n9205^\\n92253\\n92448\\n92642\\n92836\\n9 1029\\nQ-3 2 22\\n93415\\n93607\\n93799\\n93990\\n94181\\n94371\\n94561\\n94751\\n94940\\n95129\\n95317\\n95505\\n95693\\n95880\\n96066\\n96253\\n96439\\n96624\\n96809\\n96994\\n97178\\n97362\\n97546\\n97729\\n97912\\n98094\\n98276\\n98458\\n98639\\n7 .08820\\nlAta. Vt rs.\\n200\\n205\\n205\\n204\\n204\\n204\\n203\\n203\\n202\\n202\\n20 f\\n201\\n206\\n200\\n99\\n99\\n98\\n98\\n97\\n97\\n97\\n96\\n96\\n95\\n95\\n95\\n94\\n94\\n93\\n93\\n92\\n92\\n91\\n91\\n90\\n96\\n90\\n89\\n89\\n89\\n88\\n87\\n88\\n87\\n86\\n86\\n86\\n85\\n85\\n84\\n84\\n84\\n83\\n83\\n83\\n82\\n82\\n82\\n81\\n81\\n87563\\n87771\\n87978\\n88185\\n88391\\n88597\\n88803\\n89008\\n8921 2\\n894 1 6\\n89620\\n89823\\n90025\\n90228\\n90429\\n90636\\n90831\\n91032\\n91231\\n91431\\nIt\\n91630\\n91828\\n92027\\n92224\\n9242T\\n926 1 8\\n92815\\n93016\\n93206\\n93401\\n93596\\n93790\\n93984\\n94177\\n94370\\n94562\\n94754\\n94946\\n9513?\\n95328\\n95519\\n95709\\n95898\\n96088\\n96276\\n96465\\n96653\\n96841\\n97028\\n97215\\n97401\\n9758?\\n97773\\n97958\\n98143\\n9832?\\n98512\\n98695\\n98879\\n99062\\n90244\\nI.Ki;. Ixsic.\\n208\\n207\\n207\\n206\\n206\\n205\\n205\\n204\\n204\\n203\\n203\\n202\\n202\\n201\\n201\\n201\\n2C6\\n99\\n99\\n99\\n98\\n98\\n97\\n97\\n97\\n96\\n95\\n95\\n95\\n95\\n94\\n94\\n93\\n93\\n92\\n92\\n92\\n91\\n91\\n96\\n90\\n89\\n89\\n88\\n88\\n88\\n88\\n87\\n87\\n86\\n86\\n85\\n85\\n84\\n84\\n84\\n83\\n83\\n83\\n82\\n5\\n6\\n7\\n8\\n9\\n10\\n1 1\\n12\\n13\\n14\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\nr. I*\\nJ5\\n36\\n57\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n_49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\ni\\n(iO\\n180\\n9\\n9\\n6\\niS\\no.y\\n0.\\n7\\n21 .0\\nI .1\\n8\\n24.0\\nI .2\\n9\\n27\\n1.4\\n10\\n30.0\\n1 6\\n20\\n00.0\\n3-1\\n30\\nQO.O\\n4-7\\n4-\\n40\\nI30.0\\n6.3\\n6.\\n50\\n150.0\\n7 9\\n7\\n30\\n40\\n5\\n8\\n8\\n0-8\\n0.8 1\\nI\\n9\\nI\\nI\\nI\\nI\\n3\\nI\\n2\\nI\\n4\\nI\\n3\\n2\\n2\\n6\\n4\\n2\\n4\\n5\\nfi\\n,s 3 1\\n7\\n1\\n6\\n6 1\\n7\\n6\\n6\\n0.7\\n\u00c2\u00b0f 1\\n7\\n8\\n7\\n8\\n9\\n8\\n9\\nI\\n1\\n10\\nI\\nI\\n1\\n1\\n20\\n2\\n3\\n2\\nI\\n3\\n3\\n5\\n3\\n2\\n40\\n4\\n6\\n4\\n3\\n50\\n5\\n8\\n5\\n4\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\no 7\\n09\\n0.6\\n0.7\\n0.8\\n0.9\\n1 .0\\n2.0\\n3-0\\n4.0\\n5-0\\n4\\n3\\n6\\n4\\n0-3\\n0.\\n7\\n4\\n4\\n8\\n5\\n4\\n0.\\n9\\n6\\n5\\n0.\\n10\\n6\\n6\\n0.\\n20\\nI\\n3\\nI\\nI\\nI\\n3 3\\n2\\nI\\n7\\nI\\n4\u00c2\u00b0\\n2\\n6\\n2\\n3\\n2.\\n50\\n3\\n3\\n2\\n9\\n2.\\n2\\n2\\n6\\n0.2\\n0.2\\n7\\n8\\n3\\n3\\n0.2\\n2\\n9\\n4\\n0.3\\n0.\\n10\\n20\\n4\\n0-3\\n0-6\\n30\\n40\\nI\\nI\\n2\\n6\\nI.O\\n\u00e2\u0080\u00a23\\n0.\\nI.\\n50\\n2\\nI\\n1-6\\n1\\nI\\n5\\n4\\n6\\nt--5\\n0.5\\n0.4\\n7\\n\u00c2\u00b0-6\\n6\\n5\\n8\\n7\\nb\\n9\\n0.8\\n7\\n7\\n10\\n0.9\\n7\\n20\\nI\\n6\\nI\\n5\\n30\\n2.7\\n2\\n5\\n2\\n2\\n40\\n3-6\\n3\\n3\\n50\\n4.t\\n4\\nI\\n3\\n7\\n397", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0449.jp2"}, "450": {"fulltext": "TABLE VIII. \u00e2\u0080\u0094LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n8\u00c2\u00b0 9\\n10\\nII\\n12\\n14\\n15\\n16\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\nao\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\nLog. Vers.\\n98820\\n99000\\n99186\\n99360\\n99539\\n\u00e2\u0080\u00a299718\\n,99897\\n0007 5\\n,00253\\n,00431\\n00608\\n.00784\\n0096 r\\n,01137\\n,01313\\nT Lost. Exsec.\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n.01488\\n.01663\\n,01838\\n.02012\\n.02186\\n\u00e2\u0080\u00a202359\\n\u00e2\u0080\u00a202533\\n,02706\\n.02878\\n,030^6\\n,03222\\n\u00e2\u0080\u00a203394\\n\u00e2\u0096\u00a003565\\n\u00e2\u0080\u00a203736\\n03906\\n.04076\\n,04246\\n.04416\\n\u00e2\u0080\u00a204585\\n\u00e2\u0080\u00a204754\\n,04922\\n,05090\\n\u00e2\u0096\u00a005258\\n.05426\\n\u00e2\u0080\u00a205593\\nm\\n,05760\\n\u00e2\u0080\u00a205926\\n\u00e2\u0096\u00a006093\\n.06259\\n.06424\\n,06589\\n,06754\\n.06919\\n07083\\n.07247\\n.07411\\n.07575\\n.07738\\n.07906\\n.08063\\n.08225\\n,08387\\n.08549\\n.08710\\n,08871\\n0Q03 1\\nIjosr. Vers.\\n86\\n80\\n79\\n79\\n79\\n78\\n78\\n77\\n78\\n77\\n76\\n76\\n76\\n76\\n75\\n75\\n75\\n74\\n74\\n73\\n73\\n73\\n72\\n72\\n72\\n71\\n71\\n71\\n70\\n70\\n70\\n69\\n69\\n69\\n68\\n68\\n68\\n67\\n67\\n7\\n66\\n66\\n66\\n65\\n65\\n65\\n65\\n64\\n64\\n64\\n63\\n63\\n62\\n62\\n62\\n61\\n62\\n61\\n61\\n66\\n7\\n99244\\n99427\\n99609\\n99796\\n99971\\n.00152\\n\u00e2\u0096\u00a000332\\n,00512\\n00692\\n,00871\\n.01050\\n.01229\\n,01407\\n\u00e2\u0096\u00a001585\\n,01763\\n.01940\\n.021 17\\n.02293\\n,02469\\n,0264.!;\\nz\\n,02820\\n,02995\\n,03176\\n.03345\\n03519\\n,03692\\n,03866 I\\n,04039 1\\n,04212\\n04384 I\\n1)\\n\u00c2\u00abi\\n81\\n86\\n86\\n80\\n80\\n79\\n79\\n78\\n7^\\n78\\n77\\n77\\n77\\n76\\n76\\n75\\n75\\n75\\n75\\n74\\n74\\n73\\n73\\n73\\n73\\n72\\n72\\n71\\n71\\n71\\n70\\n70\\n70\\n70\\n69\\n69\\n69\\n68\\n68\\n68\\n67\\n67\\n67\\n66\\n66\\n66\\n65\\n65\\n65\\n64\\n64\\n64\\n63\\n64\\n63\\n63\\n62\\n8.09569\\n\u00e2\u0080\u00a2045 56\\n,04728 I\\n.04899 j\\n.05076 I\\n.05241 i\\n,05411\\n,05581\\n,05751\\n,05921\\n06090\\n,06259\\n,06427\\n\u00e2\u0096\u00a006595\\n.06763\\n.06931\\n,07098\\n.07265\\n.07431\\n.07598\\n.07764\\n.07929\\n,08095\\n,08260\\n,08424\\n,08589\\n.08753\\n,08917\\n0908 I\\n,09244\\n09407\\nLoff. Vers.\\n8. 0903 T\\n.09192\\n.09352\\n,09512\\n,09671\\n09836\\n09989\\n0148\\n0306\\n0464\\n0622\\n0779\\n0936\\n1093\\n1250\\n1406\\n1562\\n1718\\n1873\\n2029\\n2184\\n2338\\n2492\\n2647\\n2806\\n2954\\n3107\\n3266\\n34^3\\n3565\\nT Los. Kxsec.\\n3717\\n3869\\n4021\\n4172\\n4323\\n4474\\n4625\\n4775\\n4925\\n5075\\n5225\\n5374\\n5523\\n5672\\n5826\\n59^8\\n6116\\n6264\\n6412\\n6559\\n6706\\n6852\\n6999\\n7145\\n729T\\n7437\\n7582\\n7728\\n7873\\n8017\\n8162\\n66\\n60\\neo\\n59\\n59\\n59\\n58\\n58\\n58\\n57\\n57\\n57\\n57\\n56\\n56\\n56\\n55\\n55\\n55\\n55\\n54\\n54\\n54\\n53\\n53\\n53\\n53\\n52\\n52\\n52\\n52\\n51\\n51\\n51\\n51\\n50\\n50\\n50\\n49\\n50\\n49\\n49\\n49\\n48\\n48\\n48\\n48\\n47\\n47\\n47\\n46\\n46\\n46\\n46\\n45\\n45\\n45\\n45\\n44\\n44\\nliOjr. Vers.\\nI\\n8\\n8\\n09569\\n09732\\n09894\\n0056\\n0217\\n0378\\n0539\\n0700\\n0866\\n1026\\n1 186\\n1340\\n1499\\n1658\\n1816\\n1975\\n2133\\n2291\\n2448\\n2605\\nD\\n2762\\n2919\\n3075\\n3232\\n338?\\n3543\\n3698\\n3854\\n4008\\n4163\\n4317\\n4471\\n4625\\n4778\\n4932\\n5085\\n523^\\n5390\\n5542\\n5694\\n5846\\n5997\\n6148\\n6299\\n6450\\n6606\\n6750\\n6906\\n7050\\n7199\\n7349\\n7497\\n7646\\n7795\\n7943\\n8091\\n8238\\n8386\\n8533\\n8686\\n8827\\n62\\n62\\n62\\n61\\n61\\n61\\n66\\n66\\n60\\n60\\n59\\n59\\n59\\n58\\n58\\n58\\n58\\n57\\n57\\n57\\n57\\n56\\n56\\n55\\n56\\n55\\n55\\n54\\n54\\n54\\n54\\n53\\n53\\n53\\n53\\n52\\n52\\n52\\n52\\n52\\n51\\n51\\n51\\n50\\n56\\n50\\n50\\n49\\n49\\n49\\n48\\n49\\n48\\n48\\n48\\n4?\\n47\\na1\\n47\\n46\\np. P\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49_\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n(JO\\nliOff. Kxseo. I\\n180\\n170\\n6\\n18.0\\n17.0\\n7\\n21.0\\n19-8\\n8\\n24.0\\n22-6\\n9\\n27.0\\n2.S-5\\n10\\n30.0\\n28.3\\n20\\n60.0\\n5^-6\\n30\\n90.0\\n8=i.o\\n40\\n120.0\\ni 3-3\\n50\\n150.0\\n141.6\\n20\\n30\\n40\\n50\\n30\\n40\\n50\\n40\\n5\\n40\\n50\\n40\\n50\\n160\\n16 .0\\n18.6\\n21.3\\n24.0\\n26.6\\n53-\\n80.0\\nic6.6\\n133-\\n150 140\\n14.0\\n21.0\\n23-3\\n46.6\\n70.0\\n93-3\\n116. 6\\n15\\n17\\n5\\n20\\n22\\n5\\n25\\n50\\n75\\n100\\n.0\\n125\\n.0\\n0.9 0.9 o\\n1.1 1.0 I\\n1.2 1.2 1\\n1.4 1.3 I\\n1 .6 1.5 I\\n3-1 3-0 2\\n4-7 4-5 4\\n6.3 6.0 5\\n7-9 7-5 7\\n7\\no 7\\n0.9\\n0.6\\ns\\nC\\n05\\n0.6\\n0.\\n7\\n0.\\n0.8\\nc.g\\n1-8\\nI\\n2.7\\n3-6\\n4.6\\n3-\\n4\\nP. p\\n398", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0450.jp2"}, "451": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n10 11\\n6\\n7\\n8\\n9\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n26\\n27\\n29\\n80\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\nLojf. Vers. 1 J Lop. Kxsec.\\n8. 18162\\n.18306\\n.18456\\n.18594\\n.1S738\\n8\\n.18881\\n19024\\n.19167\\n.19309\\n.1945^\\n8.19594\\n.19736\\n.19878\\n.20019\\n.20166\\n8.20301\\n20442\\n.20582\\n.20723\\n.20861\\n8. 21003\\n.21142\\n.21282\\n.21421\\n2 560\\n8.2169^\\n.21837\\n.2197^\\n.221 13\\n.22251\\n8.22389\\n.22526\\n.22663\\n.22800\\n.22937\\n8.23073\\n.23209\\n.23346\\n.23481\\n.23617\\n8.23752\\n.23888\\n.24023\\n.24158\\n24292\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n8.24425\\n.24561\\n.24695\\n.24828\\n24962\\n25095\\n25228\\n25361\\n25494\\n,25627\\n(iO\\n8.25759\\n.25891\\n.26023\\n.26155\\n.26285\\n8.2641^\\nLotf. Vers. I J\\n144\\n144\\n144\\n143\\nU3\\n143\\n142\\n142\\n142\\n142\\n142\\n142\\n141\\n141\\n141\\n146\\n146\\n146\\n140\\n140\\n139\\n139\\n139\\n139\\n138\\n38\\n138\\n138\\n137\\n138\\n137\\n137\\n136\\n137\\n136\\n136\\n136\\n13^\\n136\\n135\\n135\\n135\\n135\\n134\\n134\\n134\\n134\\n133\\n133\\n133\\n133\\n133\\n132\\n133\\n132\\n132\\n132\\n132\\n131\\n131\\n8. 18827\\n.18973\\n.19120\\n1 9266\\n.19411\\n8.19557\\n.19702\\n.19847\\n.19992\\n.20137\\n8.20281\\n.20425\\n20569\\n.20713\\n.20857\\n8.21 000\\n.21143\\n.21286\\n.21428\\n.21571\\n8.21713\\n.21855\\n.21995\\n.22138\\n22279\\n8.22420\\n.22561\\n.22701\\n.22842\\n.22982\\n8.23122\\n.23262\\n.23401\\n.23540\\n.23679\\n8.23818\\n.23957\\n.24095\\n.24234\\n.24372\\n8.24509\\n24647\\n.24784\\n.24922\\n.25059\\n8.25195\\n\u00e2\u0080\u00a225332\\n.25468\\n.25604\\n.25746\\n8.25876\\n.26012\\n.2614^\\n.26282\\n.26417\\n8.26552\\n26685\\n.26821\\n.26955\\n.27089\\n8. 27223\\niOp. Kxsec.\\n146\\n146\\n146\\n145\\n145\\n45\\n145\\n145\\n144\\n144\\n144\\n144\\n144\\n143\\n143\\n143\\n143\\n142\\n142\\n142\\n142\\n141\\n141\\n141\\n141\\n146\\n146\\n146\\n140\\n140\\n140\\n139\\n139\\n139\\n139\\n138\\n138\\n138\\n138\\n137\\n138\\n137\\n137\\n137\\n136\\n136\\n136\\n136\\n136\\n136\\n135\\n135\\n135\\n135\\n134\\nI 134\\n134\\n134\\n,134\\n134\\nIt\\nLoff. Vers.\\nJt\\n8.26417\\n\u00e2\u0080\u00a226548\\n.26679\\n.26816\\n.26941\\n8.27071\\n.27201\\n\u00e2\u0080\u00a227331\\n.27461\\n.27596\\n8.27719\\n.27849\\n.27977\\n.28105\\n.28235\\n8.28363\\n.28491 j\\n.28619\\n28747\\n.28S75\\n8.29002\\n.29129\\n\u00e2\u0096\u00a029^56\\n.29383\\n.29510\\n8.29635\\n,29763\\n.29889\\n.30015\\n.30146\\n8,\\n30266\\n3039\\n305 1 6\\n30642\\n30765\\n3089 1\\n.31015\\n.31140\\n.31264\\n.31388\\n8.3151T\\n.3 635\\n.31758\\n.31882\\n.32005\\n8.32128\\n.32256\\n\u00e2\u0080\u00a232373\\n\u00e2\u0080\u00a232495\\n.32617\\n8.32739\\n.32861\\n\u00e2\u0080\u00a232983\\n\u00e2\u0080\u00a233104\\n\u00e2\u0080\u00a233225\\n8.33347\\n33468\\n\u00e2\u0080\u00a233588\\n33709\\n\u00e2\u0080\u00a233829\\n8.33930\\nliOir. Vers.\\n131\\n131\\n131\\n136\\n130\\n130\\n130\\n130\\n129\\n129\\n129\\n128\\nI 29\\n28\\n128\\n128\\n128\\n128\\n127\\n2^\\n127\\n127\\n127\\n126\\n126\\n126\\n126\\n126\\n125\\n125\\n125\\n125\\n125\\n124\\n124\\n124\\n124\\n124\\n124\\n123\\n124\\n23\\n123\\n123\\n123\\n122\\n122\\nI\\n122\\n122\\n122\\nI2T\\nI2T\\n121\\n121\\n121\\n126\\n126\\n126\\n126\\nKxser.\\nn\\n8.27223\\n\u00e2\u0080\u00a227356!\\n.27490\\n.27623\\n.27756\\n8.27889\\n.28021\\n.28153\\n.28286\\n.28418\\n8.28550\\n.28681\\n.28813\\n28944\\n.29075\\n8 29206\\n\u00e2\u0080\u00a229336\\n29467\\n\u00e2\u0080\u00a229597\\n29727\\n8\\n.29857\\n29987\\n.30117\\n.30245\\n.30375\\n8 30504\\n\u00e2\u0080\u00a230633\\n.30762\\n.30896\\n.31019\\n8\\n3 47\\n.31275\\n.31402\\n\u00e2\u0080\u00a231530\\n.31657\\n8.32418\\n\u00e2\u0080\u00a23254-+\\n.32676\\n\u00e2\u0080\u00a232796\\n.32922\\n8.31785\\n.31912\\n.32039\\n.32165\\n.32292\\n8.33047\\n\u00e2\u0080\u00a233173\\n\u00e2\u0080\u00a233298\\n\u00e2\u0080\u00a233423\\n\u00e2\u0080\u00a233547\\n8.33675\\n\u00e2\u0080\u00a233797\\n\u00e2\u0080\u00a233921\\n.34045\\n.34169\\n8.34293\\n.34417\\n\u00e2\u0080\u00a234540\\n34663\\n.34785\\n33\\n33\\n33\\n33\\nj-\\n32\\n30\\n29\\n29\\n29\\n29\\n29\\n28\\n28\\n28\\n28\\n28\\n27\\n27\\n27\\n27\\n27\\n27\\n26\\n26\\n26\\n26\\n26\\n26\\n25\\n25\\n25\\n25\\n25\\n24\\n25\\n24\\n24\\n24\\n23\\n24\\n24\\n3\\n_4\\n5\\n6\\n7\\n8\\n9\\n10\\n1 1\\nI 2\\n13\\ni4\\n15\\n16\\n17\\n18\\n19\\nr. 1\\n8 3490\\nl.nir. Kxsnr.\\nJ\\nJO\\n21\\n25\\n26\\n27\\n28\\n29\\n60\\n3\\n32\\n33\\n1^\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n40\\n47\\n48\\n49\\no\\n5\\n52\\n53\\n55\\n56\\n57\\n58\\n59\\n0\\n6\\n13\\n7\\nS\\n15.1\\nJ7.5\\n9\\n19.5\\n10\\n21.^\\n20\\n30\\n40\\n50\\n43-3\\n65.0\\n86.^\\n108.3\\n40\\n50\\n40\\n50\\n20\\n30\\n40\\n50\\n03\\n\u00c2\u00a9\u00e2\u0080\u00a23\\n0.4\\n0,4\\n0.5\\ni.o\\n2.0\\n2-5\\n120\\n12 .0\\n14 .0\\n16.0\\n18.0\\n20.0\\n40.0\\n60 o\\n80.0\\n100. o\\n3\\n0-3\\n0.4\\n0.4\\n0.5\\n0.6\\n1 .1\\n2\\n0.2\\n0.3\\n0.3\\n0.4\\n0.4\\no.\u00c2\u00a7\\n1.2\\n2\\n0.\\n0.2\\n0.\\n2\\n0.\\n3\\n0.\\n3\\n0.\\n6\\n0.\\nI\\n0.\\nI\\n3\\nI\\nI\\n6\\nI\\n03\\n0.4\\nI*. V.\\n399", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0451.jp2"}, "452": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS,\\n13\u00c2\u00b0 13\u00c2\u00b0\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\ni8\\n19\\n20\\n21\\n22\\n23\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLos. Vers.\\n33950\\n34070\\n34190\\n34309\\n34429\\n34549\\n34668\\n34787\\n34906\\n35025\\n35143\\n35262\\n35386\\n35498\\n35616\\n35734\\n35852\\n35969\\n36086\\n36204\\n36321\\n3643?\\n36554\\n36671\\n36787\\n36903\\n37019\\n37135\\n37251\\n37366\\n37482\\n3759^\\n37712\\n3782^\\n37942\\n38057\\n38171\\n382S6\\n38400\\n38514\\n38628\\n38741\\n38855\\n38969\\n39082\\n39195\\n39308\\n39421\\n39534\\n39646\\n39758\\n39871\\n39983\\n40095\\n40207\\nD\\n40318\\n40430\\n40541\\n40652\\n40764\\n8.40875\\nLour. Vers, i I)\\n20\\n20\\n19\\n20\\n9\\n9\\n9\\n9\\n9\\nLojf. Exsec. 2\\n8\\n34909\\n35032\\n35155\\n35277\\n35399\\n35522\\n35644\\n35765\\n35887\\n36009\\n36130\\n36251\\n36372\\n36493\\n36614\\n36734\\n36855\\n36975\\n37095\\n37215\\n37931\\n38050\\n38169\\n38287\\n38406\\n38524\\n38642\\n38760\\n38878\\n38995\\n39113\\n39230\\n39347\\n39464\\n3958T\\n39698\\n39814\\n39931\\n4004^\\n40163\\n40279\\n40395\\n405 II\\n40626\\n40742\\n40857\\n40972\\n4108^\\n41202\\n41317\\n37335\\n37454\\n37574\\n37693\\n37812\\n41431\\n41546\\n41666\\n41774\\n41888\\n42002\\njOfj. Kxsec.\\n23\\n22\\n22\\n22\\n22\\n22\\n21\\n22\\n21\\n21\\n21\\n21\\n26\\n21\\n26\\n26\\n20\\n20\\n20\\n20\\n9\\n9\\n9\\n9\\n9\\n8\\n9\\n8\\n8\\n8\\nJ\\n1\\n7\\n7\\n7\\n7\\n6\\n6\\n6\\n6\\n6\\n6\\n6\\n5\\n5\\n5\\n5\\n5\\n5\\n5\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\nIF\\nLog. Vers. It |Loif. Exsec.\\n40875\\n40985\\n41096\\n412O6\\n41317\\n41427\\n4153^\\n4164^\\n41757\\n41867\\n41976\\n42086\\n42195\\n42304\\n42413\\n42522\\n42636\\n42739\\n4284^\\n42956\\n43064\\n43172\\n43280\\n43388\\n43495\\n43603\\n43710\\n43817\\n43924\\n44031\\n44138\\n44245\\n44351\\n44458\\n44564\\n44670\\n44776\\n44882\\n44988\\n45093\\n45 99\\n45304\\n45409\\n45514\\n45619\\n45724\\n45829\\n45934\\n46038\\n46142\\n46247\\n46351\\n46455\\n46558\\n46662\\n46766\\n46869\\n46972\\n47076\\n47179\\n47282\\nLotf. Vers.\\n10\\n16\\n16\\n16\\n16\\n10\\n10\\n09\\n10\\n09\\n09\\n09\\n09\\n09\\n09\\n08\\n09\\n08\\n08\\n08\\n08\\n08\\n08\\n07\\n07\\n07\\n07\\n07\\n07\\n06\\n07\\n06\\n06\\n06\\n06\\n06\\n05\\n06\\n05\\n05\\n05\\n05\\n05\\n05\\n05\\n04\\n05\\n04\\n04\\n04\\n04\\n04\\n03\\n04\\n03\\n03\\n03\\n03\\n03\\n03\\n77\\n42002\\n42 II 6\\n42229\\n42343\\n42456\\n42569\\n42682\\n42795\\n42908\\n43021\\n43133\\n43246\\n43358\\n43470\\n43582\\n43694\\n43805\\n43917\\n44028\\n44 39\\n44251\\n44362\\n44473\\n44583\\n44694\\n44804\\n44915\\n45025\\n45135\\n45245\\n45355\\n45465\\n45574\\n45684\\n45793\\n45902\\n4601 T\\n46126\\n46229\\n46338\\n46446\\n46555\\n46663\\n46771\\n46879\\n46987\\n47095\\n47203\\n47316\\n47417\\n47525\\n47632\\n47739\\n47846\\n47953\\n48060\\n48166\\n48273\\n48379\\n48485\\n8.48591\\nLosj. Exsec.\\nD\\n13\\n13\\n13\\n13\\n13\\n13\\n3\\n13\\n12\\n12\\n12\\n12\\n12\\n12\\n12\\ni\\nI\\nI\\nI\\nI\\nI\\nI\\n16\\n16\\n16\\n16\\n10\\n16\\n09\\n10\\n10\\n09\\n09\\n09\\n09\\n09\\n09\\n08\\n09\\n08\\n08\\n08\\n08\\n08\\n08\\n07\\n08\\n07\\n07\\n07\\n07\\n07\\n07\\n06\\n07\\n05\\n06\\n06\\n06\\n06\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n55\\n56\\n57\\n58\\n59\\n(50\\nP. P\\n120\\n119\\n6\\n12,0\\nII. 9\\n7\\n8\\n9\\n14.0\\n16.0\\n18.0\\n139\\n15.8\\n17-8\\n10\\n20.0\\n19-8\\n20\\n30\\n40\\n40.0\\n60.0\\n80.0\\n39-6\\n59-5\\n79-3\\n50\\n100.\\n99.1\\n117\\nII. 7\\n13-6\\n15.6\\n175\\n19-5\\n39 o\\n58.5\\n78.0\\n97.5\\n13-5\\n15-4\\n17.4\\n9-3\\n38.6\\n58 o\\n77-3\\n96.6\\n118\\n116 115\\nII-5\\n13.4\\n^5-3\\n17.2\\niQ.i\\n38.3\\n57-5\\n76.6\\n95.8\\nII\\n4\\n113\\n11:\\n6\\n11.4\\n\u00e2\u0080\u00a23\\nII.\\n7\\n13\\n3\\n13.2\\n13-\\n8\\nTS\\n2\\n15.0\\n14-\\n9\\n17\\nI\\n16.3\\n16.\\n10\\n19\\n18.8\\n18.\\n20\\n38\\n37-6\\n37\\n30\\n57\\n5 j-5\\n5b.\\n40\\n76\\n75.3\\n74-\\n50\\n95\\n94.1\\n93-\\nIII\\nIIO\\n6\\n11 .1\\n11.\\n7\\n12.9\\n12.8\\n8\\n14.8\\n14-6\\n9\\n16.6\\n16.5\\n10\\n18.5\\n18.3\\n20\\n37-0\\n36-6\\n30\\n55-5\\n55-0\\n40\\n74.0\\n73-3\\nSO\\n92-5\\n91-6\\n109\\n14-5\\n16.3\\n18.1\\n36.3\\n54-5\\n72-6\\n90.8\\n6\\n108\\n10.8\\n107\\n10.7\\n7\\n12.6\\n12-5\\n8\\n9\\n14.4\\n16.2\\n14.2\\n16.0\\n10\\n20\\n18.0\\n36.0\\n17-8\\n35-6\\n30\\n54\\n53-5\\n40\\n50\\n72.0\\n90.0\\n89.1\\n106\\n10.6\\n105\\n104\\n6\\n10.5\\n10.4 1\\n7\\n12.2\\n12\\nI\\n8\\n14.0\\n13\\n8\\n9\\n5-7\\n13\\nfi\\n10\\n17-5\\n17\\n3\\n20\\n35 -o\\n34\\n6\\n33\\n52.5\\n52\\n40\\n70.0\\ntq\\n3\\n50\\n87.5\\n86\\n6\\n0.0\\n0.0\\n0.0\\nO.I\\nO.I\\nO. I\\n0.2\\n0-3\\n0.4\\nP. l*\\n400", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0452.jp2"}, "453": {"fulltext": "TABLE VIII. \u00e2\u0080\u0094LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n14\u00c2\u00b0 15\\n10\\n1 1\\n12\\nJ3\\nU\\n15\\ni6\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n80\\n31\\n32\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n00\\nLoir. V\u00c2\u00ab rs.\\nI)\\n8.47282\\n47384\\n47487\\n47590\\n47692\\n8\\n47795\\n47897\\n47999\\n48 1 01\\n48203\\n48304\\n48406\\n48507\\n48609\\n48716\\n4881 1\\n48912\\n49013\\n491 14\\n49215\\n49315\\n494 Id\\n49516\\n49616\\n49716\\n49816\\n49916\\n50015\\n501 1 5\\n50215\\n50314\\n50413\\n50512\\n5061 1\\n50710\\n50809\\n50908\\n51006\\n51105\\n51203\\n5 1 301\\n51399\\n51497\\n51595\\n51693\\n51791\\n51888\\n519.S6\\n52083\\n52180\\n52277\\n52374\\n52471\\n52568\\n52665\\n52761\\n52858\\n52954\\n53050\\n53146\\n53242\\n02\\n03\\n02\\n02\\n02\\n02\\n02\\n02\\n02\\n01\\n01\\n01\\n01\\n01\\n01\\n01\\n01\\nCO\\n01\\n06\\n00\\n00\\n00\\n00\\n00\\n00\\n99\\n100\\n99\\n99\\n99\\n99\\n99\\n99\\n98\\n99\\n98\\n98\\n98\\n98\\n98\\n98\\n98\\n97\\n98\\n97\\n97\\n97\\n97\\n97\\n97\\n97\\n96\\n97\\n96\\n96\\n96\\n96\\n96\\n96\\nLoir. KxN\u00c2\u00abM\\nLoir. Vers.\\n8\\n48591\\n48697\\n48803\\n48909\\n49014\\n49120\\n49225\\n49331\\n49436\\n4954\\n49646\\n49750\\n49855\\n49960\\n50064\\n50168\\n50273\\n50377\\n50481\\n50585\\n50688\\n50792\\n50896\\n50999\\n51 102\\n51205\\n51309\\n51412\\n51514\\n51617\\n51720\\n51822\\n51925\\n52027\\n52129\\n52231\\n52333\\n52435\\n52537\\n52638\\n52740\\n5284T\\n52943\\n53044\\n53 45\\n53246\\n53347\\n53448\\n53548\\n53649\\n53749\\n53850\\n53950\\n54050\\n54150\\n54250\\n54350\\n54449\\n54549\\n54649\\n54748\\nKxser.\\n06\\n06\\n05\\n05\\n05\\n05\\n05\\n05\\n05\\n05\\n04\\n05\\n04\\n04\\n04\\n04\\n04\\n04\\n04\\n03\\n04\\n03\\n03\\n03\\n03\\n03\\n03\\n02\\n03\\n02\\n02\\n02\\n02\\n02\\n02\\n02\\n02\\noT\\n01\\n01\\n01\\nof\\n01\\n01\\n01\\n01\\n01\\n00\\n06\\n06\\n06\\n00\\n00\\n00\\n00\\n00\\n99\\n100\\n99\\n99\\nLoir. Vers.\\n8\\n8\\n53242\\n5^ o\\njjj8\\n53434\\n53530\\n53625\\n53721\\n53816\\n53911\\n54007\\n54102\\n54197\\n54291\\n54386\\n54481\\n54575\\n54670\\n54764\\n54858\\n54952\\n55046\\n55140\\n55234\\n55328\\n55421\\n55515\\n55608\\n55701\\n55795\\n55888\\n55981\\n56074\\n56166\\n56259\\n56352\\n56444\\n56536\\n56629\\n56721\\n56813\\n56905\\n56997\\n57089\\n57186\\n57272\\n57363\\n57455\\n57546\\n57637\\n57728\\n57819\\n57910\\n58001\\n58092\\n58182\\n58273\\n58363\\n58453\\n58544\\n58634\\n58724\\n;88i4\\n96\\n95\\n96\\n95\\n95\\n95\\n95\\n95\\n95\\n95\\n94\\n95\\n94\\n94\\n94\\n94\\n94\\n94\\n94\\n94\\n93\\n94\\n93\\n93\\n93\\n93\\n93\\n93\\n93\\n93\\n92\\n92\\n93\\n92\\n92\\n92\\n92\\n92\\n92\\n92\\n92\\n91\\n91\\n91\\n91\\n91\\n91\\n91\\n91\\n91\\n96\\n91\\n90\\n96\\n90\\n90\\n96\\n90\\n90\\n90\\nLojr. Vers.\\n8\\nLmr\\n55736\\n55834\\n55933\\n56031\\n56129\\n56226\\n56324\\n56422\\n56519\\n56617\\n56714\\n56812\\n56909\\n57006\\n57103\\n57200\\n57296\\n57393\\n57490\\n57586\\n57682\\n57779\\n57875\\n57971\\nc;8o67\\n58163\\n58259\\n58354\\n58450\\n58546\\n58641\\n58736\\n58832\\n58927\\n59022\\n59117\\n592 1 T\\n59306\\n59401\\n5949^\\n59590\\n59684\\n59779\\n59873\\n59967\\n60061\\n60)55\\n60249\\n60342\\n60436\\n60 5 30\\n99\\n99\\n99\\n99\\n99\\n99\\n98\\n98\\n98\\n98\\n98\\n98\\n98\\n98\\n97\\n98\\n97\\n97\\n97\\n97\\n97\\n97\\n97\\n97\\n97\\n96\\n97\\n96\\n96\\n96\\n96\\n96\\n96\\n96\\n95\\n90\\n95\\n96\\n95\\n95\\n95\\n95\\n95\\n95\\n95\\n94\\n95\\n94\\n94\\n94\\n94\\n94\\n94\\n94\\n94\\n94\\n94\\n93\\n94\\n93\\n10\\n1 1\\nI 2\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\ni9\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\nV. V\\n103\\n10.3\\n68.6\\n102\\n10\\nlOI\\nII\\n9\\n11.8\\n13\\n6\\n13.4\\n15\\n3\\n15.:\\n17\\n.6.fi\\n34\\n33-6\\n5\u00c2\u00bb\\n50-5\\n68\\n67. H\\n85\\n84.1\\n100\\n99\\n6\\n1 0.0\\n9.9\\n7\\nII. 6\\n\u00e2\u0080\u00a25\\n8\\n3-3\\n13.2\\n9\\n10\\n15-0\\n16.6\\n14.8\\n16.5\\n20\\n33-3\\n33-0\\n30\\n40\\n50.0\\n66.6\\n4Q-5\\n66.0\\n50\\n83.3\\n82.5\\n98\\n9.S\\n1 1. 4\\n13.0\\n14.7\\n,6.5\\n3\u00c2\u00ab.6\\n49.0\\n65.3\\n8:. 6\\n6\\n9\\n9\\n7\\n7\\n96\\n9.6\\n95\\n9-5\\n7\\nII\\n3\\nII. 2\\n11. 1\\n8\\n12\\n9\\n12.8\\n12.6\\n9\\n10\\n14\\n16\\ni\\n14.4\\n16.0\\n14.2\\n\u00c2\u00bb5-8\\n20\\n30\\n40\\n32\\n48\\n64\\n3\\n5\\n32.0\\n48.0\\n64.0\\n3\u00c2\u00ab-6\\n47 -5\\n633\\n50\\n80\\n8\\n80.0\\n79.1\\n94\\n93\\nb\\n9.4\\n9-i 1\\n7\\n10.9\\n10.8\\n8\\n12.5\\n12.4\\n9\\n14. 1\\n\u00c2\u00ab3-9\\n10\\n5-0\\n15-5\\n20\\n31-3\\n31.0\\n30\\n47.0\\n46.5\\n40\\n62.6\\n62.0\\n50\\n78.3\\n77.5\\n92\\nQ.2\\n10.7\\n12.2\\n13.8\\nJ5 3\\n30-6\\n46.0\\n61.3\\n76.6\\n91\\n90\\n6\\n9-1\\n9.0\\n7\\n10.6\\n10.5\\n8\\n12. I\\n13.0\\n9\\n3-6\\n\u00c2\u00bb3o\\n10\\nJ5-I\\n5\\n20\\n30-3\\n30.0\\n^0\\n45-5\\n45.0\\n40\\n60.^\\n60.0\\n50\\n75-8\\n75.0\\n0.11\\n06\\n0.0\\nO. I\\nO.I\\no.i\\no.a\\no 3\\n0.4\\n^!^s(\\nI\\n401", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0453.jp2"}, "454": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n16\\n11\u00c2\u00b0\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n29\\n80\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\nLoa:. Vers.\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n(io\\n8.58814\\n58904\\n58993\\n59083\\n59173\\nz\\n8\\n59262\\n59351\\n59441\\n59530\\n59619\\n59708\\n59797\\n59886\\n59974\\n60063\\n60152\\n60246\\n60328\\n60417\\n60505\\n60593\\n60681\\n60769\\n60857\\n60944\\n61032\\n61119\\n61207\\n61294\\n6138T\\n61469\\n61556\\n61643\\n61730\\n61816\\n61903\\n61990\\n62076\\n62163\\n62249\\n62336\\n62422\\n62508\\n62594\\n62680\\n62766\\n62852\\n62937\\n63023\\n63108\\n63194\\n63279\\n63364\\n63449\\n63534\\n63619\\n63704\\n63789\\n63874\\n63959\\n8 64043\\nLost. Veix. 7\\n90\\n89\\n90\\n89\\n89\\n89\\n89\\n89\\n89\\n89\\n88\\n89\\n8S\\n88\\n87\\nSf\\n87\\n87\\n87\\n87\\n87\\n87\\n86\\n87\\n86\\n86\\n86\\n86\\n86\\n86\\n86\\n86\\n86\\n85\\n85\\n85\\n85\\n85\\n85\\n85\\n85\\n84\\n85\\n84\\nLoff. Kxsec\\n8.60530\\n.60623\\n.607 16\\n.60810\\n60903\\n8.60996\\n.61089\\n.61182\\n.61275\\n.61368\\n8.61466\\n\u00e2\u0080\u00a261553\\n.61645\\n.61738\\n.61830\\n8.61922\\n.62014\\n.621O6\\n.62198\\n.62296\\n8.62382\\n.62474\\n.62565\\n.62657\\n.62748\\nn\\ni. 62840\\n.62931\\n.63022\\n.63113\\n.63204\\n8.63295\\n.63386\\n.63477\\n.63567\\n.63658\\n8.63748\\n.63839\\n.63929\\n.64019\\n.64109\\n8.64199\\n.64289\\n\u00e2\u0080\u00a264379\\n64469\\n.64559\\n8 64649\\n\u00e2\u0080\u00a264738\\n.64828\\n.6491^\\n.65006\\n8.65096\\n.65185\\n.65274\\n\u00e2\u0080\u00a265363\\n.65452\\n8.65541\\n.65629\\n.65718\\n.65807\\n\u00e2\u0080\u00a265895\\n8.65984\\n93\\n93\\n93\\n93\\n93\\n93\\n93\\n92\\n93\\n92\\n92\\n92\\n92\\n92\\n92\\n92\\n92\\n92\\n92\\n91\\n92\\n91\\n91\\n91\\n9^\\n91\\n91\\n91\\n91\\n96\\n91\\n91\\n96\\n90\\n90\\n96\\n90\\n90\\n90\\n90\\n90\\n90\\n90\\n89\\n90\\n89\\n89\\n89\\n89\\n89\\n89\\n89\\n89\\n89\\n89\\n88\\n88\\n89\\n88\\n88\\nKxsec. I J)\\nLog\\n8.\\nVers.\\n64043\\n64128\\n64212\\n64296\\n64381\\n,64465\\n,64549\\n64633\\n,64717\\n,64801\\n,64884\\n64968\\n,65052\\n.65135\\n.652I8\\n,65302\\n.65385\\n.65468\\n,65551\\n\u00e2\u0080\u00a265634\\n,65717\\n,65806\\n,65883\\n,65965\\n66048\\n.66131\\n.66213\\n.66295\\n.66378\\n66460\\n.66542\\n.66624\\n,66706\\n,66788\\n,66870\\n,66951\\n67033\\n,67115\\n\u00e2\u0080\u00a267196\\n,67277\\n67359\\n.67446\\n.67521\\n.67602\\n\u00e2\u0080\u00a267683\\n,67764\\n,67845\\n67926\\n68007\\n,6808^\\n,68168\\n.68248\\n.68329\\n68409\\n,68489\\n8.68569\\n.68650\\n.68730\\n.68810\\n.68889\\n8.68969\\nLoir. AVrs.\\nn\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n83\\n83\\n84\\n83\\n83\\n83\\n83\\n83\\n83\\n83\\n83\\n83\\n82\\n82\\n83\\n82\\n82\\n81\\n81\\n82\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n86\\n81\\n86\\n86\\n86\\n86\\n86\\n80\\n80\\n86\\n80\\n80\\n79\\n80\\ntT\\nLost. Kxsec.\\n8.\\n65984\\n66072\\n66166\\n66248\\n66336\\n,66425\\n,66512\\n66606\\n.66688\\n.66776\\n8.\\n66863\\n66951\\n67039\\n67126\\n67213\\n8.\\n01\\n67j\\n67388\\n67475\\n67562\\n67649\\n,67736\\n,67822\\n,67909\\n.67996\\n,68082\\n,68169\\n,68255\\n,68341\\n,68428\\n.68514\\n68600\\n.68686\\n.68772\\n,68858\\n68944\\n.69029\\n.69115\\n.69201\\n,69286\\n.69372\\n69457\\n69542\\n,6962^\\n,69712\\n,69798\\n69883\\n6996^\\n70052\\n,7013^\\n,70222\\n70306\\n70391\\n70475\\n,70560\\n70644\\n8.70728\\n.70813\\n70897\\n.70981\\n.71065\\n8.71149\\niOjr. Kxspc.\\ni\u00c2\u00bb\\n88\\n88\\n88\\n8?\\n88\\n88\\n87\\n8?\\n88\\nS?\\n87\\n8?\\n8f\\n87\\n87\\n87\\n87\\n87\\n86\\n87\\n86\\n86\\n86\\n86\\n86\\n86\\n86\\n86\\n86\\n85\\n86\\n86\\n85\\n86\\n85\\n85\\n85\\n85\\n85\\n85\\n85\\n85\\n85\\n84\\n85\\n85\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n77\\np. P.\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nCO\\n93\\n92\\n6\\n9-3\\n9.2\\n7\\n10. 8\\n10.7\\n8\\n12.4\\nt2.2\\n9\\n13-9\\n13-8\\n10\\n15-5\\n15.3\\n20\\n31.0\\n30.6\\n^0\\n46.5\\n46.0\\n40\\n62.0\\n61.3\\n50\\nn-s\\n76.6\\n90\\n89\\n6\\n9.0\\n8.9\\n7\\n10.5\\n10.4\\n8\\n12.0\\nII. 8\\n9\\n13^5\\n13-3\\n10\\n15.0\\n14-8\\n20\\n30.0,\\n29^6\\n30\\n450\\n44-5\\n40\\n60.0\\n59-3\\n50\\n75-0\\n74.1\\n87\\n86\\n6\\n8.7\\n8.6\\n7\\n10. 1\\n10.\\n8\\nII. 6\\nII. 4\\n9\\n13.0\\n12.9\\n10\\n14-5\\n14.3\\n20\\n29.0\\n28.6\\n30\\n43-5\\n43^o\\n40\\n58.0\\n57-3\\n50\\nT^ l\\n71-6\\n84\\n83\\n6\\n8.4\\n8.3\\n7\\n9.8\\n9-7\\n8\\nII. 2\\n1 1.O\\n9\\n12.6\\n12.4\\n10\\n14.0\\n13.8\\n20\\n28.0\\n27.6\\n30\\n42.0\\n41.5\\n40\\n56.0\\n55.3\\n50\\n70.0\\n69.1\\n81\\n80\\n6\\n8.1\\n8.0\\n7\\n8\\n9.4\\n10.8\\n9-3\\n10.6\\n9\\n12.1\\n12.0\\n10\\n20\\n13-5\\n27\\n133\\n26.6\\n3 3\\n40\\n50\\n40-5\\n54-0\\n67.5\\n40.0\\n53-3\\n66.6\\n7\\n8\\n0.0\\n0.0\\n9\\n10\\nI\\n0.1\\n20\\n0.1\\n30\\n40\\n50\\n0.2\\n0-3\\n0.4\\n91\\n9-\\n10. 1\\n12.\\n13-1\\n15-\\nZ\u00c2\u00b0\\n45-\\n60.\\n75-8\\n88\\nII. 7\\n13.2\\n14-6\\n29-3\\n44.0\\n58.6\\n73-\\n85\\n8.S\\n9.9\\n\u00e2\u0080\u00a2I\\n12.7\\n14.\\n28.3\\n42.5\\n56.6\\n70.8\\n82\\n8.2\\n9-5\\n10.9\\n12.3\\n13-6\\n27.\\n41.\\n54-6\\n68.3\\n79\\n7-9\\n9-\\n10.5\\nII\\n26.3\\n39-5\\n52 6\\n65^8\\nP. P\\n402", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0454.jp2"}, "455": {"fulltext": "Table viil\u00e2\u0080\u0094 logarithmic versed sines and external secants.\\n18\\n19\\n10\\n1 1\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n10\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nLoff. Vers, i 2\\n8.68969\\n.69049\\n.69129\\n.6920^\\n.69288\\n8.69367\\n.69446\\n.69526\\n,69605\\n.69684\\n8.69763\\n.69842\\n.69921\\n70000\\n70079\\n8.70157\\n.70236\\n.70314\\n.70393\\n.70471\\n8,70550\\n.70628\\n.707O6\\n.70784\\n70862\\n8 70946\\n.71018\\n.71096\\n.71174\\n.71251\\n71329\\n71406\\n,71484\\n,71561\\n,71639\\n71716\\n.71793\\n.71876\\n\u00e2\u0096\u00a071947\\n.72024\\n8.7210T\\n.72178\\n.72255\\n.72331\\n.72408\\n8.72485\\n.72561\\n,72637\\n.72714\\n,72796\\nGO\\n8.72866\\n.72942\\n.73018\\n\u00e2\u0080\u00a273094\\n,73176\\n8.73246\\n.73322\\n\u00e2\u0080\u00a273398\\n\u00e2\u0080\u00a273473\\n\u00e2\u0080\u00a273549\\n8.73625\\nLog. Vers\\n79\\n80\\n79\\n79\\n79\\n79\\n79\\n79\\n79\\n79\\n79\\n79\\n7^\\n79\\n78\\n78\\n78\\n78\\n78\\n7^\\n78\\n78\\n78\\n78\\n78\\n78\\n77\\n78\\n77\\n71\\n7l\\n77\\n77\\n77\\n77\\n77\\n77\\n77\\n77\\n77\\n7l\\n77\\n76\\n77\\n7l\\n76\\n76\\n76\\n76\\n76\\n76\\n76\\n76\\n76\\n76\\n76\\n7%\\n71\\n76\\n7%\\nLog. Kxsec.\\n.71149\\n.71232\\n.713I6\\n7 1 400\\n,71484\\nJ*\\n8.71567\\n,71651\\n.71734\\n,71817\\n7 1 90 1\\n8,71984\\n.72067\\n.72150\\n.72233\\n.72316\\n8.72399\\n.72481\\n.72564\\n.72647\\n.72729\\n8.72812\\n.72894\\n.72977\\n\u00e2\u0080\u00a273059\\n.73141\\n8.73223\\n.73306\\n.73388\\n.73470\\n.73551\\n8.73633\\n\u00e2\u0080\u00a273715\\n.73797\\n.73878\\n.73960\\n74041\\n.74123\\n74204\\n,74286\\n.74367\\n8.74448\\n.74529\\n.74616\\n.74691\\n.74772\\n8.74853\\n.74934\\n.75014\\n.75095\\n.75175\\n8.75256\\n\u00e2\u0080\u00a275336\\n\u00e2\u0080\u00a275417\\n.7549?\\n\u00e2\u0080\u00a275577\\n8.75658\\n\u00e2\u0080\u00a275738\\n.75818\\n.75898\\n\u00e2\u0080\u00a275978\\n8.76058\\nJ IliOSf. Kxsec\\n83\\n84\\n83\\n84\\n83\\n83\\n83\\n83\\n83\\n83\\n83\\n83\\n83\\n83\\n83\\n82\\n83\\n82\\n82\\n82\\n82\\n82\\n82\\n82\\n82\\n82\\n81\\n82\\n82\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n86\\n81\\n81\\n86\\n86\\n86\\n86\\n86\\n86\\n86\\n80\\n86\\n80\\n80\\n80\\n80\\n80\\nLog.\\n8\\n7\\n73^23\\n73700\\n73775\\n73851\\n73926\\n74001\\n74076\\n74151\\n74226\\n7430T\\n74376\\n74451\\n74526\\n74606\\n74675\\n74749\\n74824\\n74898\\n74973\\n75047\\n75121\\n75195\\n75269\\n75343\\n75417\\n75491\\n75565\\n75639\\n75712\\n75786\\n75860\\n75933\\n76006\\n76080\\n76153\\n76226\\n76300\\n76373\\n76446\\n76519\\n76592\\n76664\\n7673?\\n76810\\n76883\\n76955\\n77028\\n77106\\n77^72\\n772AS\\n771 ^7\\n77390\\n77462\\n77534\\n77606\\n77678\\n77750\\n77822\\n77893\\n77965\\n78037\\n75\\n75\\n75\\n75\\n75\\n75\\n75\\n75\\n75\\n75\\n74\\n75\\n74\\n7-1\\n74\\n71\\n74\\n7l\\n74\\n74\\n74\\n74\\n74\\n74\\n74\\n73\\n73\\n73\\n73\\n74\\n73\\n74\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\n72\\n73\\n72\\n73\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n71\\n72\\n71\\nLog. KxKec.\\nLog. Vers.\\n76058\\n76137\\n76217\\n76297\\n76376\\n76456\\n76536\\n76615\\n76694\\n76774\\n76853\\n76932\\n7701T\\n77096\\n77169\\n48\\n.2?\\n77\\n77?\\n77406\\n77485\\n77563\\n77642\\n77799\\n77^77\\n77956\\nIt\\n78034\\n78112\\n78191\\n78269\\n78347\\n78425\\n78503\\n78581\\n78659\\n7873S\\n78814\\n78892\\n78969\\n79047\\n79124\\n79202\\n79279\\n79357\\n79434\\n79511\\n79588\\n79665\\n79742\\n79819\\n79896\\n79973\\n80050\\n80126\\n80203\\n80280\\n80356\\n80433\\n80509\\n80586\\nS0662\\n8.80738\\n79\\n80\\n79\\n79\\n80\\n79\\n79\\n79\\n79\\n79\\n79\\n79\\n79\\n79\\n79\\n79\\n78\\n79\\n78\\n78\\n78\\n79\\n78\\n78\\n78\\n78\\n78\\n78\\n78\\n78\\n78\\n78\\n78\\n71\\n78\\n7l\\n7l\\n71\\n7l\\n7l\\n7l\\n7l\\n77\\n77\\n7l\\n77\\n77\\n77\\n77\\n76\\n77\\n76\\n77\\n76\\n76\\n76\\n76\\n76\\n76\\n76\\nliOir. Kxser.l i\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n32\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\nP. 1*.\\n84\\n83\\n6\\n84\\n8.j\\n7\\n9\\n8\\n9-7\\n8\\nII\\n2\\n11.\\n9\\n12\\n6\\n12.4\\n10\\n4\\n13-8\\n20\\n28\\n27 6\\n30\\n42\\n4^ 5\\n40\\n56\\n55-3\\n50\\n70\\n69.1\\n81\\n80\\n6\\n8.1\\n8.0\\n7\\n8\\n9.4\\n10.8\\n9^3\\n10.6\\n9\\n12 I\\n12.0\\n10\\n3.5\\ni3^3\\n20\\n27.0\\n26.6\\n30\\n40.5\\n40.0\\n40\\n50\\n54.0\\n67.5\\n53 3\\n66.6\\n78\\n77\\n6\\n7.8\\n7.7\\n7\\n9.1\\n9.0\\n8\\n10.4\\n10.2\\n9\\nII. 7\\n\u00e2\u0080\u00a25\\n10\\n13.0\\n12.\\n20\\n26.0\\n25-6\\n30\\n39.0\\n38.5\\n40\\n52 .0\\n5 -3\\n50\\n65.0\\n64.1\\n75\\n74\\n6\\n7.5\\n7^4\\n7\\n8.7\\n8.6\\n8\\n10.0\\n9-8\\n9\\nII. 2\\nII .1\\n10\\n12.5\\n12 3\\n20\\n25.0\\n24-6\\n30\\n37.5\\n37.0\\n40\\n50.0\\n49.3\\n50\\n62.5\\n61.6\\n72 71\\n7.2\\n7.\u00c2\u00ab\\n8.4\\n8.3\\n9.6\\n9.4\\n10.8\\nJO. 6\\n12.0\\n8\\n24.0\\n23^\\n36.0\\n3S^5\\n48.0\\n*7-3\\n60.0\\n59.1\\n82\\n8.2 j\\n9-5\\n10. y\\n12.3\\n\u00c2\u00bb3.6\\n27^3\\n41 .0\\n54.6\\n68.3\\n79\\n7.9\\n9.2\\n10 5\\n13.1\\n26.3\\n39-5\\n52.6\\n65-3\\n76\\n7.6\\nII. 4\\nia.\u00c2\u00a7\\n25.3\\n38.0\\n63.3\\n73\\n7^3\\n8.5\\n9-7\\n10.9\\n12.\\n24.\\n36.\\n48.6\\n60.8\\n0.3\\n0.4\\nr. i\\n403", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0455.jp2"}, "456": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n20\u00c2\u00b0 21\u00c2\u00b0\\nLog. Vers.\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n8.78037\\n.78108\\n.78180\\n.78251\\n.78323\\n8.78394\\n.78466\\n.78537\\n78608\\n.78679\\n8.78753\\n.78821\\n.78892\\n.78963\\n\u00e2\u0080\u00a279034\\n8,\\n79105\\n79175\\n79246\\n79317\\n79387\\njy Log. Exsec. X\\n79458\\n79528\\n79598\\n79669\\n79739\\n79809\\n,79879\\n\u00e2\u0080\u00a279949\\n.80019\\n80089\\n80159\\n.80229\\n80299\\n80369\\n80438\\n80508\\n8057^\\n80647\\n.807 16\\n80786\\n.80855\\n80924\\n.80993\\n.81063\\n.81132\\n0\\n81201\\n.81270\\n\u00e2\u0096\u00a081339\\n8 1 407\\n\u00e2\u0080\u00a281476\\n81545\\n.81614\\n,81682\\n.81751\\n,81819\\n8.81888\\n\u00e2\u0080\u00a281956\\n.82025\\n.82093\\n.82161\\n8.82229\\nLog. Vers.\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n70\\n71\\n70\\n71\\n70\\n70\\n70\\n70\\n70\\n70\\n70\\n70\\n70\\n70\\n70\\n70\\n70\\n70\\n69\\n70\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n68\\n69\\n68\\n69\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n8\\n.80738\\n.80814\\n.80891\\n80967\\n\u00e2\u0080\u00a281043\\n8.81119\\n.81195\\n.81271\\n.81346\\n.81422\\n8.81498\\n.81573\\n.81649\\n.81725\\n.81806\\n8.81876\\n.81951\\n.82025\\n.82102\\n.82177\\n82252\\n82327\\n82402\\n8247^\\n82552\\n.82627\\n.82702\\n.82776\\n.82851\\n.82926\\n83006\\n.83075\\n.83149\\n\u00e2\u0080\u00a283224\\n.83298\\n\u00e2\u0080\u00a283373\\n\u00e2\u0080\u00a283447\\n.83521\\n.83595\\n.83670\\n.83744\\n.83818\\n.83892\\n.83966\\n84039\\n8.84113\\n.84187\\n.84261\\n.84334\\n84408\\n.84481\\n.84555\\n.84628\\n84702\\n\u00e2\u0080\u00a284775\\n8.84848\\n.84922\\n.84995\\n.85068\\n.8514^\\n8.85214\\nLog. Kxsec.\\n76\\n76\\n76\\n76\\n76\\n76\\n76\\n75\\n76\\n75\\n75\\n76\\n75\\n75\\n75\\n75\\n75\\n75\\n75\\n75\\n75\\n75\\n75\\n74\\n75\\n75\\n74\\n75\\n74\\n74\\n74\\n74\\n74\\n74\\n74\\n74\\n74\\n74\\n74\\n74\\n74\\n74\\n74\\n73\\n74\\n73\\n74\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\nLog. Vers.\\n82229\\n.8229^\\n,82366\\n.82434\\n.82502\\n82569\\n8263^\\n82705\\n82773\\n82841\\n829O8\\n,82976\\n83043\\n,83111\\n83178\\n83246\\n83313\\n83386\\n8344^\\n83515\\n,83582\\n,83649\\n,83716\\n.83783\\n83850\\n839I6\\n.83983\\n.84050\\n.84117\\n.84183\\nD Loe. Exsec.\\n84250\\n843I6\\n.84383\\n84449\\n.84515\\n84582\\n84648\\n,84714\\n84786\\n,84846\\n,84912\\n84978\\n.85044\\n.85116\\n.85176\\n85242\\n85308\\n85373\\n85439\\n85505\\n85570\\n85626\\n85701\\n85766\\n85832\\n8.85897\\n.85962\\n.8602^\\n86092\\n.86158\\n8.86223\\nJ) Lost. Vers.\\n68\\n68\\n68\\n68\\n6?\\n68\\n68\\n6?\\n68\\n67\\n6J\\n6?\\n6^\\n6?\\n6J\\n67\\n6J\\n67\\n6J\\n67\\n67\\n67\\n67\\n67\\n66\\n67\\n66\\n67\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n65\\n66\\n65\\n65\\n66\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n8.\\n85214\\n8528^\\n85366\\n85433\\n85506\\n85579\\n85651\\n85724\\n85797\\n85869\\n,85942\\n86014\\n86087\\n,86159\\n,86231\\n86304\\n86376\\n86448\\n86526\\n86592\\n86664\\n86736\\n86808\\n,86886\\n86952\\n87024\\n87095\\n,8716^\\n.87239\\n,87316\\n87382\\n87453\\n87525\\n87596\\n87668\\n87739\\n,87816\\n.87881\\n\u00e2\u0096\u00a087953\\n88024\\nz\\n88095\\n88166\\n88237\\n,88308\\n.88378\\n88449\\n88526\\n,88591\\n,88661\\n,88732\\n88803\\n,88873\\n88944\\n89014\\n,89085\\n8.89155\\n.89225\\n.89295\\n.89366\\n.89436\\n8.89506\\nt) Log. Exsec.\\n73\\n73\\n72\\n73\\n73\\n72\\n73\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n71\\n72\\n71\\n72\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n71\\n76\\n71\\n71\\n76\\n70\\n71\\n76\\n76\\n70\\n76\\n76\\n70\\n76\\n70\\n76\\n70\\n70\\nn\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\nr. p.\\n50\\n51\\n52\\n53\\n55\\n56\\n57\\n58\\ni9^\\n60\\n76 75 74\\n6\\n7.6\\n7.5\\n7\\n\u00c2\u00ab-8\\n8.7\\n10. 1\\n10.0\\n9\\n11.4\\n11.2\\n10\\n12 6\\n12.5\\n20\\n25-3\\n25.0\\n30\\n38.0\\n37.5\\n40\\n50.6\\n50.0\\n50\\n63.3\\n62.5\\n20\\n30\\n40\\n50\\n7.4\\n12.3\\n24.6\\n37-0\\n49-3\\n61.5\\n73\\n72\\n6\\n7\\n8\\n7.3\\n8.5\\n9.7\\n7.2\\n8.4\\n9.6\\n9\\n10.9\\n10.8\\n10\\n12.1\\n12.0\\n20\\n30\\n40\\n50\\n24-3\\n36.5\\n48.6\\n60.\\n24.0\\n36.0\\n48.0\\n60.0\\n6\\n7\\n70\\n7.0\\n8.1\\n69\\n6.9\\n8.5\\n8\\n9.3\\n9.2\\n9\\n10.5\\n10.3\\n10\\nII. 6\\nII. 5\\n20\\n233\\n23.0\\n30\\n40\\n50\\n35-0\\n4C.6\\n58.3\\n34.5\\n46.0\\n57-5\\n71\\n7.1\\n8.3\\n9.4\\n10. 6\\nII.\\n23.6\\n35-5\\n47.3\\n59-\\n68\\n6.8\\n7-9\\n9.0\\nIO-2\\n22.6\\n34-0\\n45-3\\n56-6\\n6\\n67\\n6.7\\n66\\n6.6\\n6\u00c2\u00ab\\n6.\\n7\\n8\\n7.8\\n8.9\\n7.7\\n8.8\\n7-\\n8.\\n9\\n10.\\n9.9\\n9.\\n10\\nII .1\\nII.\\n10\\n20\\n22.3\\n22.0\\n21.\\n30\\n33-5\\n33.0\\n32\\n40\\n44.6\\n44.0\\n43\\n50\\n55.8\\n55.0\\n54-\\nP. p\\n404", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0456.jp2"}, "457": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n22\u00c2\u00b0 2:r\\n10\\n1 1\\n12\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n-5\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n34\\nJ3\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n4S\\n49\\n50\\n51\\n52\\n53\\n54\\nLoj?. Vers. J*\\n8.S6223\\n.86287\\n.86352\\n.86417\\n.86482\\n8.86547\\n.86612\\n.86676\\n.86741\\n.86805\\n8.86870\\n.86934\\n86999\\n.87063;\\n.87127 I\\n8.87192\\n.87256\\n.87326\\n.87384\\n87448\\n8.87512\\n\u00e2\u0080\u00a287576\\n.87640\\n.87704\\n.87768\\n8.87832\\n.87895\\n.87959\\n.88023\\n88085\\n8.88150\\n.88213\\n.88277\\n.88340\\n88404\\n8.88467\\n.88536\\n.88593\\n.88656\\n.88720\\n8.88783\\n.88846\\n.88909\\n.88971\\n89034\\n8 89097\\n.89160\\n\u00e2\u0080\u00a289223\\n.89285\\n\u00e2\u0080\u00a289348\\n8.8941 1\\n\u00e2\u0080\u00a289473\\n.89536\\n.89598\\n89666\\n55\\n56\\n57\\n58\\n59\\n0\\n8.89723\\n\u00e2\u0080\u00a289785\\n\u00e2\u0080\u00a289847\\n.89910\\n\u00e2\u0080\u00a289972\\n8 90Q34\\nIjOj;. Vers. I 7\\n64\\n65\\n65\\n65\\n64\\n65\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n63\\n64\\n63\\n64\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n65\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n62\\n63\\n63\\n62\\n63\\n62\\n62\\n63\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\nKxsec I\\n8\\n89506\\n89576\\n89646\\n897 16\\n89786\\n89856\\n89926\\n89995\\n90065\\n90135\\n90205 I\\n90274 I\\n90344\\n90413\\n90483 I\\n90552\\n90622\\n90691\\n90766\\n90830\\n90899\\n90968\\n91037\\n91106\\n91175\\n91244\\n91313\\n91382\\n91451\\n91520\\n91588\\n91657\\n91726\\n91794\\n91863\\n91932\\n92006\\n92063\\n92137\\n92205\\n92274\\n92342\\n92416\\n92478\\n92546\\n92615\\n92683\\n92751\\n92819\\n92887\\n92955\\n93022\\n93096\\n93158\\n93226\\n93361\\n93429\\n93496\\n93564\\n8.93631\\niOS. Kxsec.\\n70\\n70\\n70\\n69\\n70\\n70\\n69\\n70\\n69\\n70\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n68\\n69\\n69\\n68\\n69\\n68\\n68\\n68\\n69\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n67\\n68\\n67\\n68\\n67\\n68\\n67\\n67\\n67\\n67\\n77\\nLotf. Vers.\\nJ\\n8 90034\\n90096\\n901 58\\n90220\\n90282\\n90344\\n90406\\n90467\\n90529\\n90591\\n90652\\n90714\\n90776\\n90837\\n90899\\n90966\\n91021\\n91083\\n91144\\n91205\\n91267\\n91328\\n91389\\n91450\\n91511\\n91572\\n91633\\n91694\\n91755\\n91815\\n91876\\n91937\\n91997\\n92058\\n921 19\\n92179\\n92240\\n92306\\n92361\\n92421\\n92487\\n92542\\n92602\\n92662\\n92722\\n92782\\n92842\\n92902\\n92962\\n93022\\n93082\\n93142\\n93202\\n93261\\n93321\\n93381\\n93440\\n93506\\n93560\\n93619\\n8.93679\\nlidsr. Vers.\\n62\\n62\\n62\\n62\\n62\\n62\\n61\\n62\\n61\\n61\\n62\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n6r\\n61\\n66\\n61\\n66\\n66\\n61\\n66\\n66\\n66\\n66\\n66\\n60\\n66\\n66\\n60\\n60\\n66\\n60\\n60\\n60\\n60\\n60\\n60\\n59\\n60\\n59\\n60\\n59\\n59\\n60\\n59\\n59\\n59\\nLoir. Kxsec.\\n7\\n8\\n8\\n93631\\n93699\\n93766\\n93833\\n93901\\n93968\\n94035\\n94102\\n94170\\n94237\\n94304\\n94371\\n94438\\n94505\\n94572\\n94638\\n94705\\n94772\\n94839\\n94905\\n94972\\n95039\\n95105\\n95172\\n95238\\n95305\\n95371\\n9543?\\n95504\\n95570\\n95636\\n95703\\n95769\\n95835\\n95901\\n95967\\n96033\\n96099\\n96165\\n96231\\n96297\\n96362\\n96423\\n96494\\n96560\\n96625\\n96691\\n96757\\n96822\\n96888\\n96953\\n97013\\n97084\\n97149\\n97214\\n97280\\n97345\\n97410\\n97475\\n97540\\n()76o\\njOir. Kxsec.\\n67\\n67\\n67\\n67\\n67\\n67\\n67\\n67\\n67\\n67\\n67\\n67\\n67\\n67\\n66\\n67\\n66\\n67\\n66\\n66\\n67\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n66\\n65\\n66\\n65\\n66\\n65\\n65\\n66\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n65\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\ni9\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\nsQ\\nCO\\n70\\n69\\n6\\n70\\n0.9\\n7\\n8\\nI\\n8.0\\n8\\n9\\n3\\n9.2\\n9\\n10\\n5\\n10.3\\n10\\nII\\nf\\n11. 5\\n20\\n23\\n3\\n23.0\\n.1\u00c2\u00b0\\n35\\n34-5\\n40\\n46\\nfi\\n46.0\\n50\\n5B\\n3\\n57-5\\n68\\n6.8\\n7.9\\n9.0\\n10.2\\nIt. 3\\n22.6\\n34.0\\n45-3\\n56.0\\n67\\n66\\n6\\n6.7\\n0.6\\n7\\n7.8\\n7.7\\n8\\n8.9\\n8.8\\n9\\n10.0\\n9.9\\n10\\nII. I\\nII.\\n20\\n22 3\\n22.0\\n30\\n33.5\\n33.0\\n40\\n44-6\\n44.0\\n50\\n55. 8\\n55.0\\n65\\n6.5\\n7.6\\n9.7\\n10.\\n21.6\\n32.5\\n43-3\\n54.1\\n64\\n63\\n62\\n6\\n6.4\\n6.3\\n6.\\n7\\n7.4\\n7-3\\n7-\\n8\\n8.5\\n8.4\\n8.\\n9\\n9.6\\n9.4\\n9-\\n10\\n10 6\\n10.5\\n10\\n\u00e2\u0096\u00a020\\n1-3\\n21.0\\n20.\\n30\\n32.0\\n31.5\\n3\u00c2\u00bb\\n40\\n42.6\\n42.0\\n41.\\n50\\n53.3\\n52.5\\n5\\n6\\n60\\n6\\n6.1\\n6.0\\n7\\n8\\n7\\n8\\nI\\nI\\n7.0\\n8.0\\n9\\n9\\nI\\n9.0\\n10\\n10\\nI\\n10.\\n30\\n20\\n3\\n20.0\\n30\\n30\\n5\\n30.0\\n40\\n40 6\\n40.0\\n50\\n50\\n8\\n50.0\\n59\\n5-9\\n6.9\\nH\\n9.\u00c2\u00a7\\n\u00c2\u00bb9 6\\n29.5\\n39.3\\n49. i\\n5\\n6\\n0.0\\n7\\n8\\n9\\nI\\n10\\nt\\n20\\nI\\n30\\n2\\n40\\n3\\n50\\n4\\nI I\\n405", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0457.jp2"}, "458": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n24\u00c2\u00b0 25\u00c2\u00b0\\n10\\n1 1\\n12\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nLos;. Vers.\\n8\\n00\\n93679\\n93738\\n93797\\n93857\\n93916\\nD iLoff. Exsec\\n93975\\n94034\\n94094\\n94153\\n94212\\n94271\\n94330\\n94389\\n94448\\n94506\\n94565\\n94624\\n94683\\n94742\\n94800\\n94859\\n94917\\n94976\\n95034\\n95093\\n95151\\n95210\\n95268\\n95326\\n95384\\n95443\\n95501\\n95559\\n95617\\n9567?\\n95733\\n95791\\n95849\\n95907\\n95965\\n96023\\n96086\\n96138\\n96196\\n96253\\n9631 1\\n96368\\n96426\\n96483\\n96541\\n96598\\n96656\\n96713\\n96776\\n9682^\\n96885\\n96942\\n96999\\n97056\\n97113\\n97170\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n58\\n59\\n59\\n58\\n59\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n57\\n58\\n58\\n58\\nSf\\nSJ\\n58\\n57\\n5f\\n57\\n57\\n5f\\n57\\n57\\n57\\n57\\n57\\n57\\n5?\\n57\\n57\\nSi\\n57\\n57\\n8.97606\\n.97671\\n.97736\\n.97801\\n\u00e2\u0080\u00a297865\\n97930\\n\u00e2\u0080\u00a297995\\n98060\\n.98125\\n.98190\\nI)\\n8.98254\\n.98319\\n.98383\\n.98513\\n8.98577\\n.98642\\n.98706\\n.98776\\n\u00e2\u0080\u00a298835\\n8.98899\\n.98963\\n.99028\\n.99092\\n\u00e2\u0080\u00a299156\\n.99220\\n.99284\\n\u00e2\u0096\u00a099348\\n.99412\\n\u00e2\u0080\u00a299476\\n99540\\n.99604\\n.99668\\n.99732\\n.99796\\n8.99860\\n.99923\\n8.99987\\n9.00051\\n.001 14\\n9.OJ178\\n00242\\n.00305\\n,00369\\n.00432\\n9-00495\\n.00559\\n.00622\\n.00686\\n.00749\\nLog. Vers. 1 I) Log. Kxsec. J\\n9 008 I 2\\n.00875\\n.00938\\n.01002\\n.01065\\n9.01 128\\n.01191\\n.01254\\n.01317\\n.01380\\n9.01443\\n65\\n65\\n65\\n64\\n65\\n65\\n64\\n65\\n65\\n64\\n64\\n64\\n65\\n64\\n64\\nI 64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n64\\n63\\n64\\n63\\n64\\n63\\n63\\n64\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\nLog. Vers.\\n8.97176\\n9722^\\n97284\\n97341\\n97398\\n8\\nI) Log. Exsec. 2\\n97455\\n97511\\n97568\\n97625\\n9768T\\n97738\\n97795\\n97851\\n97908\\n97964\\n98026\\n98077\\n98133\\n98190\\n98246\\n98302\\n98358\\n98414\\n98470\\n98527\\n98583\\n98639\\n98695\\n98750\\n98806\\n98802\\n989 1 8\\n98974\\n99030\\n99085\\n99141\\n99197\\n99252\\n99308\\n99363\\n99419\\n99474\\n99529\\n99585\\n99646\\n99695\\n99751\\n99806\\n99861\\n999 1 6\\n99971\\n00025\\n00081\\n00136\\n00 1 91\\n00246\\n00301\\n00356\\n0041 1\\n00466\\n9.00520\\nLost. V\u00c2\u00ab\u00c2\u00bbrs.\\n57\\n56\\n57\\n57\\n57\\n56\\n57\\n56\\n56\\n56\\n57\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n55\\n56\\n56\\n56\\n55\\n56\\n55\\n55\\n56\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n54\\n55\\n54\\n01443\\n01505\\n01568\\n01631\\n01694\\nOI756\\n01819\\n01882\\n01944\\n02007\\n02070\\n02132\\n02195\\n02257\\n02319\\n02382\\n02444\\n02506\\n02569\\n02631\\n02693\\n02755\\n0281^\\n02880\\n02942\\n03004\\n03066\\n03128\\n03190\\n03252\\n03313\\n03375\\n03437\\n03499\\n03561\\n03622\\n03684\\n03746\\n03807\\n03869\\n03930\\n03992\\n04053\\n041 1 5\\n04176\\n04238\\n04299\\n04366\\n0442 T\\n04483\\n04544\\n04605\\n04666\\n04727\\n04788\\n04850\\n0491 1\\n04972\\n05033\\n\u00c2\u00a3i\u00c2\u00b093\\n05154\\n62\\n63\\n62\\n63\\n62\\n63\\n62\\n62\\n63\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n61\\n62\\n62\\n61\\n62\\n61\\n61\\n62\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n6t\\n61\\n61\\n61\\n61\\n66\\n61\\nLoir. Exsec. I\\n5\\n6\\n7\\n8\\n9\\n10\\nII\\n12\\n13\\n14\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n00\\ni\u00c2\u00bb. p.\\n65 64 63\\n6\\n6.5\\n6.4\\n7\\n7.6\\n7-4\\n8\\n8-6\\n8^5\\n9\\n9-7\\n9.6\\n10\\nIO-8\\n10.6\\n2?\\n21-6\\n21.3\\n30\\n32-5\\n32.0\\n40\\n43-3\\n42.6\\n50\\n54-1\\n53 3\\n40\\n50\\n56\\n55\\n6\\n5-6\\n5^5\\n7\\n6^5\\n6.4\\n8\\n7-4\\n7^3\\n9\\n8.4\\n8.2\\n10\\n9-3\\n9.1\\n20\\ni\u00c2\u00ab.6\\n18.3\\n30\\n28.0\\n27^5\\n40\\n37-3\\n36^6\\n50\\n46.6\\n45-8\\n8.4\\n9.4\\n10.5\\n21 .0\\n3i^5\\n42.0\\n52.5\\n62 61 60\\n6.\\n7.0\\n8.0\\n9^\\n10.0\\n20.0\\n30.0\\n40.0\\n50-\\n59\\n58\\n6\\n5^9\\n5.8\\n7\\n6.9\\n6.7\\n8\\n7-8\\n7-7\\n9\\n8-8\\n8.7\\nlO\\n9^8\\n9-6\\n20\\n19-6\\n19-3\\n30\\n29^5\\n29.0\\n40\\n39-3\\n38.6\\n50\\n49.1\\n48.3\\n57\\n5-7\\n6.6\\n7.6\\n8.5\\n9-5\\n19\\n28\\n38\\n47-5\\n54\\n5.4\\n6.\\n7-\\n8.\\n9-\\n18.\\n97.\\n36.0\\n45-\\nP. P.\\n406", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0458.jp2"}, "459": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n^G\\n27\\nliOK. VlMV\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n18\\n10\\n20\\n21\\n22\\n^3\\n^4\\n-3\\n26\\n27\\n28\\n29\\n;{o\\n31\\n32\\n33\\n34\\n35\\n56\\n37\\n38\\n30\\n4tl\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n9.00520\\n.00575\\n.00630\\n.00684\\n.00739\\n9.00794\\n.00848\\n.00903\\n.00957\\n.0101 T\\n9.0\\n.0\\n.0\\n.0\\n.0\\n9.0\\n.0\\n.0\\n.0\\n.0\\n9.0\\n.0\\n.0\\n.0\\n.0\\n9.0\\n.0\\n.0\\n066\\n120\\n174\\n229\\n28^,\\n337\\n391\\n44 3\\n499\\nt)05\\n662\\n715\\n769\\n823\\n877\\n93\\n985\\n.02038\\n.02092\\n9.02146\\n.02199\\n.02253\\n.02307\\n.02360\\n9.02414\\n.02467\\n.02521\\n.02574\\n.02627\\n9.02681\\n.02734\\n.02787\\n.02840\\n.02894\\n9.02947\\n.03000\\n.03053\\n03 1 o5\\n.03159\\n51\\n54\\n35\\n56\\n57\\n58\\n59\\n00\\n9.03212\\n.03265\\n.03318\\n\u00e2\u0080\u00a203371\\n\u00e2\u0080\u00a203423\\n9 -03476\\n.03529\\n.03582\\n\u00e2\u0080\u00a203634\\n\u00e2\u0080\u00a203^87\\n9-03740\\nliOa:. Vers. I\\n55\\n54\\n5-+\\n54\\n55\\n54\\n54\\n54\\n54\\n54\\n5-i\\n54\\n54\\n34\\n54\\n54\\n5\\n54\\n54\\n54\\n54\\n53\\n54\\n54\\n54\\n53\\n54\\n53\\n54\\n53\\n53\\n54\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n52\\n53\\n53\\n52\\n52\\n53\\n52\\nliOir. Kxsec\\n9.03154\\n\u00e2\u0080\u00a2O521S\\n\u00e2\u0080\u00a205276\\n.05337\\n\u00e2\u0080\u00a205398\\n9^05458\\n.05519\\n.05580\\n.05640\\n.05701\\n9.05762\\n.05822\\n.05883\\n\u00e2\u0080\u00a205943\\n06004\\n9 06064\\n06 1 24\\n.06185\\n.0624^\\n.06305\\n9.06366\\n.06426\\n.06485\\n.06546\\n06605\\n9 06667\\n.06727\\n.06787\\n.06847\\n.06907\\n9.06967\\n.07027\\n.07087\\n\u00e2\u0080\u00a207146\\n.07205\\n9.07265\\n.07326\\n.07386\\n074-L^\\n.07505\\n9.07565\\n.07624\\n.07684\\n.07743\\n.07803\\n9.07863\\n.07922\\n.07981\\n0804 I\\n08 1 00\\n9 08 1 60\\n.08219\\n\u00e2\u0080\u00a208278\\n\u00e2\u0080\u00a208338\\n\u00e2\u0080\u00a208397\\n9.08455\\n.0851I\\n.08574\\n.08634\\n08693\\n9.08752\\nMH. Kxspc.\\n61\\n61\\n66\\n61\\n60\\n61\\n66\\n66\\n66\\n61\\n66\\n66\\n66\\n66\\n66\\n60\\n60\\n,60\\n60\\n66\\n60\\n66\\n60\\n60\\n60\\n60\\n60\\n60\\n60\\n60\\n60\\n60\\n59\\n60\\n60\\n59\\n60\\n59\\n60\\n59\\n59\\n59\\n59\\n60\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\nI am:. V\u00c2\u00abms.\\n9.03740\\n.03792\\n.03845\\n.03898\\n.03950\\n,04002\\n04055\\n.04107\\n,04160\\n,0421 2\\n9.04264\\n.04317\\n.04369\\n.O442T\\n\u00e2\u0080\u00a204473\\n9.0452^\\n.04577\\n.04630\\n.04682\\n.04734\\n9.04786\\n\u00e2\u0080\u00a204837\\n.04889\\n.04941\\n\u00e2\u0080\u00a204993\\n9.05045\\n.05097\\n\u00e2\u0080\u00a205148\\n.05206\\n.05252\\n9^05303\\n\u00e2\u0080\u00a20535^\\n.05407\\n\u00e2\u0080\u00a205458\\n.05510\\n905561\\n.05613\\n.05664\\n.05715\\n.05767\\n9-05818\\n.05869\\n.05921\\n.05972\\n.06023\\n9.06074\\n06 1 2 5\\n.06175\\n.06227\\n.06279\\n9.06330\\n.06386\\n.06431\\n.06482\\n-06533\\n9.06584\\n.06635\\n.06686\\n.06735\\n.0678^\\n9.06838\\nliOif. Vers.\\n52\\n52\\n53\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n51\\n52\\n52\\n52\\n51\\n52\\n51\\n52\\n52\\n51\\n52\\n51\\n51\\n51\\n51\\n51\\n5\\n51\\n51\\n5J\\n51\\n51\\n5\\n51\\n51\\n51\\n51\\n51\\n51\\n5\\n50\\n51\\n51\\n51\\n51\\n50\\n5\\n50\\n5\\n50\\n1.0\\nl. \\\\^t\\n08752 I\\n0881 I\\n08870\\n08929\\n08988\\n09047\\n09106\\n09164\\n09223\\n09282\\n09341\\n09400\\n094 5 8\\n09517\\n09576\\n09634\\n09693\\n09752\\n09816\\n09869\\n09927\\n09986\\n0044\\n0102\\n0161\\n0219\\n0278\\n0336\\n039-+\\n0452\\n051 1\\n0569\\n0627\\n0685\\n0743\\n080T\\n0859\\n0917\\n097^\\n033\\n091\\n149\\n207\\n265\\n323\\n386\\n438\\n496\\n554\\n61T\\n669\\n727\\n784\\n842\\n899\\n95^\\n2015\\n2072\\n2129\\n2 1 87\\n2244\\nK\\\\s\u00c2\u00ab r.\\n59\\n59\\n59\\n59\\n59\\n59\\n58\\n59\\n59\\n58\\n59\\n58\\n59\\n58\\n58\\n58\\n59\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n57\\n58\\n58\\n57\\n58\\n58\\n57\\n57\\n58\\n57\\n57\\n5/\\n57\\n58\\n3/\\n57\\n57\\n57\\n57\\n77\\n4\\n5\\n6\\n7\\n8\\n9\\n10\\n1 1\\n12\\nJ\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n^_\\n;jo\\n31\\n32\\njj\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n45\\n46\\n47\\n48\\n50\\n5\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nr. 1\\n6\\n6\\n6\\nI\\n60\\n6.0 1\\n7\\n8\\n7\\n8\\n7.0\\n8.0\\n9\\n10\\n9\\nlO\\n9.0 1\\n10.\\n20\\n20\\n.3\\n20.0\\n30\\nno\\n50\\n30\\n40\\n50\\n5\\n8\\n30\\n40.0\\n50.0\\n59\\n5-9\\n6.9\\n7-8\\n8.8\\n9-8\\n9-\u00c2\u00a7\\n29.5\\n39.3\\n49.1\\n58 57\\n6\\n5-8\\n7\\n6.7\\n8\\n7-7\\n9\\n8-7\\n10\\n9-6\\n20\\n19.3\\n30\\n29.0\\n40\\n3S.6\\n50\\n48.3\\n5-7\\n6.6\\n7.6\\n8.5\\n9^5\\n19.0\\n28.5\\n38.0\\n47^5\\n55\\n.54\\n6\\n5-5\\n5^4\\n7\\n6.4\\n6.3\\n8\\n7-3\\n7.2\\n9\\n8.2\\n8.1\\n10\\n9^1\\n9.0\\n20\\n18.3\\n18.0\\n30\\n27.5\\n27.0\\n40\\n36.^\\n36.0\\n50\\n45^8\\n45.0\\n53\\n52\\n6\\n5^3\\n5.2\\n7\\n6.2\\n6.0\\n8\\n7.0\\n6.9\\n9\\n7-9\\n7.8\\n10\\n8^8\\n8-6\\n20\\n7-6\\n17.3\\n30\\n26.5\\n26.0\\n40\\n35^3\\n34. 6\\n50\\n44.1\\n43.3\\n51\\n6\\n5.1\\n0.6\\n7\\n5.9\\n0.5\\n8\\n6.8\\n0.0\\n9\\n7.6\\no.x\\n10\\n8.5\\nO.T\\nao\\n17.0\\nO.I\\n30\\n25.8\\n0.2\\n40\\n34.0\\n03\\n50\\n42.=;\\n0.4\\nI p\\n407", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0459.jp2"}, "460": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n28\u00c2\u00b0 29\u00c2\u00b0\\nLog. Vers. I)\\n9.06838\\nI\\n.06888\\n2\\n.06939\\n3\\n06996\\n4\\n07040\\n5\\n9.07091\\n6\\n.07141\\n7\\n.07192\\n8\\n.07242\\n9\\n.07293\\n10\\n9 -07 343\\nII\\n.97393\\n12\\n.07444\\n13\\n.07494\\n14\\n\u00e2\u0096\u00a007544\\n15\\n9.07594\\ni6\\n.07644\\n17\\n.07695\\ni8\\n.07745\\n19\\n.0779^\\n20\\n9.07845\\n21\\n.07895\\n22\\n.07945\\n23\\n.07995\\n24\\n.08045\\n25\\n9.08095\\n26\\n.08145\\n27\\n.08195\\n28\\n.08244\\n29\\n.08294\\n30\\n9-Oii344\\n31\\n.08394\\n32\\n.08443\\n33\\n.08493\\n34\\n\u00e2\u0080\u00a208543\\n35\\n9.08592\\n36\\n.08642\\n37\\n.08691\\n3\u00c2\u00ab\\n.08741\\n39\\n.08790\\n40\\n9.08840\\n41\\n.08889\\n42\\n.08939\\n43\\n.08988\\n44\\n.090^^7\\n45\\n9.09087\\n46\\n.09136\\n47\\n.09185\\n48\\n.09234\\n49\\n.09284\\n50\\n9.09333\\n51\\n.09382\\n52\\n.09431\\n53\\n09480\\n54\\n.09529\\n55\\n9-09578\\n56\\n.0962^\\n57\\n\u00e2\u0080\u00a209676\\n5^\\n.09725\\n59\\n.09774\\n60\\n9.09823\\nliOSj. Vers.\\n50\\n51\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n49\\n50\\n49\\n50\\n49\\n49\\n50\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n48\\n49\\n49\\nLoar. Kxsec. Z\\n7\\n2244\\n2302\\n2359\\n24 1 6\\n2474\\n2531\\n2588\\n2645\\n2703\\n2760\\n2817\\n2874\\n293T\\n2988\\n3045\\n3102\\n3159\\n3216\\n3273\\n33 ^o\\n33^7\\n3444\\n3500\\n3557\\n3614\\n3671\\n3727\\n3784\\n3841\\n3897\\n3954\\n401 1\\n4067\\n4124\\n4180\\n42J7\\n4293\\n4350\\n4406\\n4462\\n45^9\\n457?\\n4631\\n4688\\n4744\\n4800\\n4856\\n4913\\n4969\\n5025\\n5081\\n513?\\n5193\\n5249\\n5305\\n5361\\n541^\\n5473\\n5529\\n5585\\n5641\\nSi\\n57\\nSi\\n57\\nSi\\n57\\n57\\n57\\n57\\n57\\n57\\n57\\n57\\n57\\n57\\n57\\n56\\n57\\n57\\n57\\n56\\n57\\n56\\n57\\n56\\n57\\n56\\n56\\n57\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n55\\n56\\nLoff. Vers.\\n9.09823\\n09872\\n09926\\n09969\\n0018\\nf Off. Exsec. D Lost. Vers.\\n0067\\n01 ll\\n0164\\n0213\\nO26T\\n0310\\n0358\\n0407\\n0455\\n0504\\n0552\\n0601\\n0649\\n069^\\n0746\\n0794\\n0842\\n0896\\n0939\\n0987\\n035\\n083\\n131\\n179\\n227\\n-D Los. Exsec.\\n323\\n371\\n419\\n467\\n515\\n562\\n616\\n658\\n706\\n754\\n801\\n849\\n897\\n944\\n992\\n2039\\n2087\\n2134\\n2182\\n2229\\n2277\\n2324\\n2371\\n2419\\n2466\\n2513\\n2566\\n2608\\n2655\\n2702\\n49\\n48\\n49\\n48\\n49\\n48\\n48\\n49\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\nAl\\n48\\n48\\n47\\n48\\n48\\n47\\n48\\n47\\nAl\\n48\\n47\\nAl\\nAl\\n47\\n47\\n47\\nAl\\nAl\\n47\\n47\\n47\\n47\\nAl\\n47\\nAl\\n47\\n47\\nn\\nJ)\\n5641\\n5697\\n5752\\n5808\\n5864\\n5920\\n5975\\n6031\\n6087\\n6142\\n6198\\n6254\\n6309\\n6365\\n6426\\n6476\\n6531\\n6587\\n6642\\n6698\\n6753\\n6808\\n6864\\n6919\\n6974\\n7029\\n7085\\n7140\\n7195\\n7256\\n7305\\n7361\\n7416\\n7471\\n7526\\n7581\\n7636\\n7691\\n7746\\n78or\\n7856\\n7916\\n7965\\n8026\\n8075\\n8130\\n8185\\n8239\\n8294\\n8349\\n8403\\n8458\\n8513\\n856^\\n8622\\n8676\\n8731\\n8786\\n8846\\n8894\\n8949\\n56\\nSi\\n56\\n55\\n56\\nSi\\n56\\nSi\\n55\\n56\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n54\\n55\\n55\\n54\\n55\\n55\\n54\\n55\\n54\\n54\\n55\\n54\\n54\\n54\\n54\\n54\\n55\\n54\\n54\\n54\\nTiOii. Exseo. Jt\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\np. p.\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n(JO\\n5l 57 58\\n54\\n5.4\\n6.3\\n7.2\\n8.1\\n9.0\\n18.0\\n27.0\\n36.0\\n45.0\\n51 50\\n54\\n6\\n5.4\\n7\\n6.3\\n8\\n7.2\\n9\\n8.2\\n10\\n9.1\\n20\\n18.\\n30\\n27.2\\n40\\n36.3\\n50\\n45-4\\n5-7\\n6.7\\n5-7\\n6.6\\n6.0\\n7-6\\n8.6\\n7.6\\n8.5\\n7-5\\n8.5\\n9.6\\n9-5\\n9.4\\n10. 1\\n19.0\\n18.8\\n28.7\\n=8.5\\n28.2\\n38.3\\n38.0\\n37-6\\n47.9\\n47-5\\n47.1\\n56\\n55\\n6\\n5-6\\n5-5 1\\n7\\n6.5\\n6\\n5\\n8\\n7-4\\n7\\n4\\n9\\n8.4\\n8\\n3\\n10\\n9.3\\n9\\n2\\n20\\n18.6\\n18\\n5\\n30\\n28.0\\n27\\n7\\n40\\n37-3\\n37\\n50\\n46.6\\n46\\n2\\n9.1\\n27.\\n36.\\n45-\\n5-1\\n5-0\\n5-\\n5-9\\n6.8\\n5-9\\n6.7\\n5-\\n6.\\n7.6\\n8.5\\n17.0\\n7.6\\n8.4\\n16.8\\n7-\\n8.\\n16\\n25.5\\n25.2\\n25-\\n340\\n42.5\\n33-6\\n42.1\\n33\\n41.\\n49\\n49\\nAl\\n6\\n4.9\\n4.9\\n4\\n7\\n8\\n5.8\\n6.6\\n5-7\\n6.5\\n5-\\n6.\\n9\\n10\\n7-4\\n8.2\\n7-3\\n8i\\n7-\\n8\\n20\\n16.5\\n16.3\\n16.\\n30\\n24.7\\n24-5\\n24.\\n40\\n33.0\\n32-6\\n32-\\n50\\n41.2\\n40.3\\n40.\\n48\\n4f\\n6\\n4.8\\n4-7\\n7\\n5-6\\n5 5\\n8\\n6.4\\n6-3\\n9\\n7.2\\n7.1\\n10\\n8.0\\n7-9\\n20\\n16.0\\n15-8\\n30\\n24.0\\n23.7\\n40\\n32.0\\n31-6\\n50\\n40.0\\n39-6\\n7-\\n15-\\n23.\\n31-\\n39-\\nP. P\\n40a", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0460.jp2"}, "461": {"fulltext": "TABLF VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n30\u00c2\u00b0 31\u00c2\u00b0\\nLoc Vers.\\nI)\\n2702\\n2749\\n2796\\n2843\\n2896\\n2937\\n2984\\n3031\\n3078\\n3172\\n3219\\n3266\\n3313\\n33^9\\n3406\\n3453\\n3500\\n3546\\n3593\\n3(^39\\n3686\\n3733\\n3779\\n3826\\n3872\\n3919\\n3965\\n401 1\\n4058\\n4104\\n4151\\n4197\\n4243\\n428g\\n433(3\\n4382\\n4428\\n4474\\n45^0\\n45%\\n4612\\n4658\\n4704\\n4750\\n4796\\n4842\\n4888\\n4934\\n4980\\n5026\\n5071\\n5117\\n5163\\n5209\\n5254\\n5306\\n5346\\n5391\\n5437\\n1483\\nLos;. Vers.\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n46\\n47\\n47\\n46\\n47\\n46\\n47\\n46\\n46\\n46\\n47\\n46\\n4i,\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n45\\n46\\n45\\n46\\n46\\n45\\n45\\n46\\n45\\n45\\n45\\n46\\niOJT. Kxsec.\\nJ\\n9 ^949\\n19003\\n19058\\n191 12\\n19167\\nn\\n19221\\n19275\\n19329\\n19384\\n19438\\n19492\\n19546\\n1 960 1\\n19655\\n19709\\n19763\\n1 9817\\n1 987 1\\n19925\\n1997^^\\n20033\\n20087\\n20141\\n20195\\n20249\\n20^0\\nj^j\\n20357\\n204 r I\\n20465\\n20518\\n20572\\n20626\\n20680\\n20733\\n20787\\n20841\\n20894\\n20948\\n21002\\n210;\\n21 109\\n21162 I\\n21216\\n21269\\n21323\\n21376}\\n21430 1\\n21483;\\n21537\\n21 596\\n21643\\n21697\\n21750\\n21803\\n21857\\n21910\\n21963\\n22015\\n22070\\n22123\\n22176\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n53\\n54\\n54\\n54\\n53\\n54\\n53\\n54\\n53\\n54\\n53\\n53\\n54\\n53\\n52\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\nLoar. Vei!\\nn I.\\nI 0K. Kxsec. J I Loii. Vers\\nQ\\n54^^; 3\\n5528\\n5574\\n5619\\n5665\\n5710\\n5755\\n5801\\n5846\\n589T\\n5937\\n5982\\n6027\\n6073\\n6118\\n6163\\n6208\\n6253\\n6298\\n6343\\n6388\\n6434\\n6479\\n6523\\n6568\\n6613\\n6658\\n6703\\n6748\\n6793\\n6838\\n6882\\n692^\\n6972\\n7017\\n7061\\n7106\\n7151\\n7195\\n7240\\n7284\\n7329\\n7373\\n7418\\n7462\\n7507\\n7551\\n7596\\n7640\\n7684\\n7729\\n7773\\n7817\\n786T\\n7906\\n7950\\n7994\\n8038\\n8082\\n8i26\\n8170\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n44\\n45\\n45\\n45\\n45\\n45\\n44\\n45\\n44\\n45\\n44\\n45\\n44\\n44\\n45\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\nK\\\\\\n22170\\n2222Q\\n22282\\n22335\\n22388\\n22441\\n22494\\n22547\\n22606\\n22653\\n227O6\\n22759\\n22812\\n22865\\n22918\\n22971\\n23024\\n23076\\n23129\\n23182\\n23235\\n23287\\n23340\\n23393\\n23446\\n23498 I\\n23551\\n23603\\n23656 i\\n23709\\n23761\\n23814\\n23866\\n23919\\n23971\\n24024\\n24076\\n24128\\n24181\\n24233\\n24285\\n24338\\n24396\\n24442\\n24495\\n24547\\n24599\\n24651\\n24704\\n24756\\n24808\\n24860\\n24912\\n24964\\n25016\\n25068\\n25126\\n25172\\n25224\\n2 527(3\\n25328\\nL tir. Kxsec.\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n52\\n53\\n53\\n52\\n53\\n52\\n53\\n52\\n53\\n52\\n53\\n52\\n52\\n52\\n52\\n53\\n52\\n52\\n52\\n52\\n52\\n53\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\njt\\n4\\n5\\n6\\n7\\n8\\n_9\\n10\\n1 1\\nI 2\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\nI\\n54 54 53\\n5-4\\n63\\n5-4\\n6.3\\n7-2\\n8.2\\n7.2\\n8.1\\n9.1\\n18.1\\n90\\n18\\n27.2\\n36.3\\n27.0\\n36.0\\n45-4\\n45.\\n5 3\\n0.2\\n7-\\n8\\n8.9\\n17 8\\n26.7\\n35-6\\n44.6\\nS3\\n52\\n6\\n7\\n5-3\\n6.2\\n5-2\\n8\\n7.0\\n7.0\\n9\\n10\\n7-9\\n8-8\\n7-9\\n8.7\\n20\\n30\\n17-6\\n26.5\\n7-5\\na6.2\\n40\\n35-3\\n35 -o\\n50\\n441\\n43-7\\n52\\n5-2\\n6.5\\n6.9\\n7.8\\n86\\n17-3\\n26.0\\n47\\n47\\n6\\n4-7\\n4-7\\n7\\n5-5\\n5-5\\n8\\n6.3\\n6.2\\n9\\n71\\n7.0\\n10\\n7-9\\n7-8\\n20\\n5-8\\n15-6\\n30\\n23.7\\n23 -5\\n40\\n31-6\\n31-3\\n50\\n39-6\\n39- 1\\n46\\n4-6\\n5-4\\n6.2\\n7.0\\n7-7\\n^5-5\\n23-\\n31 .0\\n38.7\\n46 4S 45\\n6\\n4.6\\n4-5\\n7\\n5-3\\n5-3\\n8\\n6.1\\n6.6\\n9\\n6.9\\n6.8\\n10\\n7-\u00c2\u00a7\\n7.6\\n20\\n\u00c2\u00bb5-3\\n15. 1\\n30\\n23.0\\n22.7\\n40\\n3?-6\\n30.3\\n50\\n38.3\\n37.9\\n4\\n5\\n6.\\n6.\\n7\\n15\\n22.5\\n30.\\n37-\\n20\\n30\\n40\\n50\\n44\\n4-4\\n5-2\\n5-9\\n6.7\\n7-4\\ni4-\u00c2\u00a7\\n22.2\\n29-6\\n37.1\\n44\\n4-4\\n5-\u00c2\u00ab\\n5-8\\n6.6\\n7-3\\n14-6\\n22.0\\n29-3\\n36.6\\nv. r.\\n409", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0461.jp2"}, "462": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANT!\\n33\u00c2\u00b0 33\u00c2\u00b0\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\nLos. A ers. 1 Lofr. Exsee\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n(io\\n8170\\n8214\\n8258\\n8302\\n8346\\n8390\\n8434\\n8478\\n8522\\n8566\\n8610\\n8654\\n8697\\n874t\\n878s\\n8829\\n8872\\n8916\\n8959\\n9003\\n9047\\n9090\\n9134\\n9177\\n9221\\n9264\\n9308\\n9351\\n9395\\n9438\\n9481\\n9525\\n9568\\n961 T\\n9654\\n9698\\n9741\\n9784\\n9827\\n9870\\n9914\\n9957\\n20000\\n20043\\n20086\\n20129\\n20172\\n20215\\n20258\\n2030[\\n20343\\n20385\\n20429\\n20472\\n20515\\n20558\\n20600\\n20643\\n20686\\n20728\\n9.20771\\nLog. Vers.\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n43\\n44\\n44\\n43\\n44\\n43\\n44\\n43\\n43\\n43\\n44\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n42\\n43\\n43\\n43\\n42\\n43\\n42\\n43\\n43\\n42\\n43\\n2\\n25328\\n25386\\n25432\\n25484\\n25536\\n25588\\n25640\\n25692\\n25743\\n25793\\n25847\\n25899\\n25950\\n26002\\n26054\\n26105\\n26157\\n26209\\n26260\\n26312\\nJ)\\nLog. V\u00c2\u00ab^rs. 1}\\n26364\\n26415\\n26467\\n265I8\\n26570\\n26621\\n26673\\n26724\\n26776\\n26827\\n26878\\n26930\\n2698T\\n27032\\n27084\\n27135\\n27185\\n27238\\n27289\\n27340\\n27391\\n27443\\n27494\\n27545\\n27596\\n27647\\n27698\\n27749\\n27800\\n27852\\n27903\\n27954\\n28005\\n28056\\n28107\\n28157\\n28208\\n28259\\n28316\\n2836T\\n28412\\nLog. Exsec.\\n52\\n52\\n52\\n51\\n52\\n52\\n52\\n51\\n52\\n51\\n52\\n51\\n52\\n51\\n51\\n52\\n51\\n51\\n51\\n52\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n50\\n51\\n51\\n51\\n51\\n50\\n7\\n9.20771\\n20814\\n20855\\n20899\\n20942\\n20984\\n027\\n069\\n112\\n154\\n196\\n239\\n281\\n324\\n-.66\\n408\\n451\\n493\\n535\\n577\\n620\\n662\\n704\\n746\\n788\\n836\\n872\\n914\\n956\\n998\\n22040\\n22082\\n22124\\n22165\\n22208\\n22250\\n22292\\n22334\\n22376\\n2241^\\n22459\\n22501\\n22543\\n22584\\n22626\\n22668\\n22709\\n22751\\n22792\\n22834\\n22875\\n22917\\n22959\\n23006\\n23042\\n23083\\n23124\\n23166\\n2320^\\n23248\\n9.23290\\nLog. Vers.\\n42\\n42\\n42\\n43\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\nZI2\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n41\\n42\\n42\\n41\\n42\\n41\\n42\\n41\\n41\\n42\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\nILoi\\n9\\nExsec.\\nI)\\n28412\\n28463\\n28514\\n28564\\n28615\\n28665\\n28717\\n28768\\n28818\\n28869\\n28920\\n28976\\n29021\\n29072\\n29122\\n29173\\n29223\\n29274\\n29324\\n29375\\n29426\\n29476\\n29527\\n29577\\n29627\\n29678\\n29728\\n29779\\n29829\\n29879\\n29930\\n29986\\n30036\\n30081\\n30131\\n3018T\\n3023T\\n30282\\n30332\\n30382\\nI)\\n30432\\n30482\\n30533\\n30583\\n30633\\n30683\\n30733\\n30783\\n30833\\n30883\\n30933\\n30983\\n31033\\n31083\\n3fT33\\n31183\\n31233\\n31283\\n31333\\n31383\\n31432\\n51\\n51\\n50\\n51\\n51\\n50\\n51\\n50\\n50\\n51\\n50\\n50\\n51\\n56\\n51\\n50\\n50\\n50\\n51\\n50\\n50\\n56\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n49\\n50\\n50\\n50\\n50\\n49\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22,\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\nil\\n55\\n56\\n57\\n58\\n59\\nLog. Exseo.l 7\\nGO\\np. p.\\n52\\n51\\n6\\n5-2\\n5-1\\n7\\n6.0\\n6.0\\n8\\n6.9\\n6-8\\n9\\n7.8\\n7-7\\n10\\n8.6\\n8.6\\n20\\n17-3\\n17. 1\\n30\\n26.0\\n25-7\\n40\\n34.6\\n34-3\\n50\\n43.3\\n42.9\\n6\\n50\\n5-0\\n50\\n5-0\\n7\\n8\\n5-9\\n6.7\\n5-8\\n6.6\\n9\\n10\\n20\\n7.6\\n8.4\\n16.8\\n7-5\\n16.6\\n30\\n25.2\\n25.0\\n40\\n33-6\\n33-3\\n50\\n42.1\\n41-6\\n6\\n44\\n4.4\\n43\\n4-3\\n7\\n8\\n9\\n5-1\\n5-8\\n6.6\\n51\\n5-8\\n6.5\\n10\\n7-3\\n7.2\\n20\\nM.6\\n14-5\\n30\\n22.0\\n21.7\\n40\\n50\\n29-3\\n36.6\\n29.0\\n36.2\\n6\\n42\\n4.2\\n42\\n4.2\\n7\\n8\\n9\\n4.9\\n5-6\\n6.4\\n4.9\\n5-6\\n6.3\\n10\\n7-1\\n7.0\\n20\\n14.1\\n14.0\\n30\\n40\\n21 .2\\n28.3\\n21.0\\n28.0\\n50\\n35-4\\n35-0\\n6\\n41\\n4.1\\n7\\n8\\n4.S\\n5-4\\n9\\n10\\n6.1\\n6.8\\n20\\nJ3-6\\n30\\n20.5\\n40\\n27-3\\n50\\n34-1\\nP. p.\\n410", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0462.jp2"}, "463": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n34\u00c2\u00b0 85\u00c2\u00b0\\nVers.\\n7\\n23290\\n23331\\n23372\\n23414\\n23455\\n23496\\n23537\\n23579\\n23620\\n23661\\n23702\\n23743\\n237^4\\n2382^\\n23866\\n23907\\n23948\\n23989\\n24036\\n24071\\n24112\\n24153\\n24194\\n24235\\n24275\\n243 1 6\\n24357\\n24398\\n24438\\n24479\\n24520\\n24561\\n2460 T\\n24642\\n24682\\n24723\\n24764\\n24804\\n24845\\n24885\\n24926\\n24966\\n25007\\n25047\\n25087\\n25128\\n25168\\n25209\\n25249\\n25289\\n25329\\n25370\\n25410\\n25450\\n25496\\n25531\\n25571\\n25611\\n25651\\n2569T\\n9-25731\\nLost. Vers.\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n41\\n40\\n41\\n41\\n41\\n46\\n41\\n46\\n41\\n46\\n41\\n40\\n41\\n46\\n46\\n46\\n41\\n46\\n46\\n40\\n40\\n40\\n40\\n46\\n40\\n40\\n46\\n46\\n40\\n40\\n40\\n40\\n46\\n40\\n46\\n40\\n46\\n40\\n40\\n40\\n40\\n40\\n77\\nli );r. Kxsec\\nn\\n432\\n482\\n532\\n582\\n6^2\\n681\\n731\\n781\\n83\\n886\\n930\\n980\\n32029\\n32079\\n32129\\n32178\\n32228\\n32277\\n32327\\n32377\\n32426\\n32476\\n32525\\n32575\\n32624\\n32673\\n32723\\n32772\\n32822\\n32871\\n32920\\n32970\\n33019\\n33069\\n33118\\n33167\\n33216\\n33266\\n33315\\n33364\\n33413\\n33463\\n33512\\n33561\\n33616\\n33659\\n33708\\n33758\\n33807\\n33856\\n33905\\n33954\\n34003\\n34052\\n34101\\n34150\\n34199\\n34248\\n34297\\n34346\\n34395\\n50\\n50\\n49\\n50\\n49\\n50\\n49\\n50\\n49\\n50\\n49\\n49\\n49\\n50\\n49\\n49\\n49\\n49\\n50\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\nLost. Kxspo.\\nLour. Vers.\\n25731\\n25771\\n2581I\\n25851\\n25891\\n25931\\n25971\\n2601 T\\n26051\\n26091\\n261 31\\n26171\\n26216\\n26256\\n26296\\n26330\\n26370\\n26409\\n26449\\n26489\\n26528\\n2656^\\n26608\\n2664^\\n26687\\n26725\\n26765\\n26806\\n26845\\n26885\\n26924\\n26964\\n27003\\n27042\\n27082\\n27121\\n27161\\n27200\\n27239\\n27278\\n27318\\n27357\\n27396\\n2743S\\n27475\\n27514\\n27553\\n27592\\n27631\\n27676\\n27709\\n27749\\n27788\\n27827\\n27866\\n27905\\n27944\\n27982\\n28021\\n28066\\n28099\\nLost. Vers.\\nn\\n40\\n40\\n40\\n40\\n40\\n40\\n40\\n39\\n40\\n40\\n40\\n39\\n40\\n40\\n39\\n40\\n39\\n40\\n39\\n39\\n40\\n39\\n39\\n39\\n39\\n40\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n39\\n38\\n39\\n39\\n39\\nIT\\n\\\\A\u00c2\u00bbi. K.Vht C.\\nIt\\n34395\\n34444\\n34492\\n3454\\n34590\\n34639\\n34688\\n34737\\n34785\\n34834\\n34883\\n34932\\n34986\\n35029\\n35078\\n35127\\n35175\\n35224\\n35273\\n35321\\n35370\\n35419\\n35467\\n35516\\n35564\\n35613\\n35661\\n35710\\n35758\\n35807\\n35855\\n35904\\n35952\\n36001\\n36049\\n36098\\n36146\\n36194\\n36243\\n36291\\n36340\\n36388\\n36436\\n36484\\n36533\\n3658T\\n36629\\n36678\\n36726\\n36774\\n36822\\n36876\\n36919\\n36967\\n37015\\n37063\\n37111\\n37159\\n3720^\\n37255\\n37303\\nI,nir. Kxser.\\n49\\n48\\n49\\n49\\n49\\n48\\n49\\n48\\n49\\n49\\n48\\n48\\n49\\n48\\n49\\n48\\n49\\n48\\n48\\n48\\n49\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n77\\n10\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n2g\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\no\\n5\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\nr. I\\n6\\n50\\n5.0\\n49\\n4.9\\n7\\n8\\n6 6\\n5-8\\n6.6\\n9\\n10\\n7-5\\n8.3\\n7-4\\n8 2\\n20\\n16.6\\n.6.5\\n30\\n25.0\\n247\\n40\\n33-3\\n33-0\\n50\\n41 6\\n41.2\\n40\\n50\\n20\\n30\\n40\\n50\\n40\\n50\\n20\\n30\\n40\\n50\\n48\\n4.\u00c2\u00a7\\n5-6\\n6.4\\n7-3\\n8.1\\n16. 1\\n24.2\\n3* -3\\n40.4\\n41\\n4.1\\n4-S\\n5-5\\n6.2\\n6.9\\n20.7\\n27-6\\n34.6\\n39\\n3-9\\n4.6\\n5-2\\n.S-9\\n6.6\\n13.1\\n19.7\\n26.3\\n32.9\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n5 3\\n49\\n4.9\\n5-7\\n6.5\\n7-1\\n8.\\n16.3\\n24-5\\n32.^\\n40.8\\n48\\n4.8\\n5.6\\n6.4\\n7.2\\n8.0\\nj6.o\\n24 o\\n32.0\\n40.0\\n41\\n4.1\\n4.8\\n5-4\\ne.i\\nH\\n13-6\\n20. T\\n27.3\\n34-1\\n40 40\\n4\\n4-\\n4-7\\n4-\\n5\\n6\\n4\\nI\\n5-\\n6.\\n6\\n7\\n6.\\n13\\n5\\n3-\\n20\\n2\\n20.\\n27\\n26.\\n33\\n7\\n33\\n39\\n3-9\\n4-5\\n5-2\\n5-8\\n13.0\\n19.5\\n26.0\\n32.5\\n38\\n3-8\\n4-5\\n51\\nS.8\\n6.4\\n12. g\\n19.2\\n25-6\\n32-1\\nI I\\n411", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0463.jp2"}, "464": {"fulltext": "TABLE VIII.-LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS\\n36\u00c2\u00b0 37\u00c2\u00b0\\n_ j Log. Vers. I J JLog. Exseo\\n10\\nII\\n12\\nH\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n9 28099\\n.28138\\n.28177\\n.28216\\n.28255\\n9.28293\\n.28332\\n.28371\\n.28410\\n28448\\n9.28487\\n.28526\\n.28564\\n.28603\\n.28642\\n9.28680\\n.28719\\n.2875;\\n.28796\\n.28835\\n9-28873\\n.28912\\n.28950\\n.28988\\n.29027\\n9.2906^\\n.29104\\n.29142\\n.29180\\n.29219\\n9.29257\\n.29295\\n\u00e2\u0080\u00a229334\\n.29372\\n.29410\\n9-29448\\n29487\\n.29525\\n.29563\\n29601\\n9.29639\\n.29677\\n.2971^\\n\u00e2\u0080\u00a229754\\n.29792\\n9.29830\\n.29868\\n29906\\n.29944\\n.29982\\n9.30020\\n.30057\\n\u00e2\u0080\u00a230095\\n.30133\\n.30171\\n9 30209\\n30247\\n.30285\\n.30322\\n30360\\n9 -30398\\nLog. Vers.\\n39\\n38\\n39\\n39\\n38\\n39\\n38\\n39\\n38\\n39\\n38\\n38\\n39\\n38\\n38\\n38\\n38\\n38\\n39\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n38\\n3f\\n38\\n38\\n38\\n38\\n37\\n38\\n3?\\n38\\n38\\nIT\\n9-37303\\n\u00e2\u0080\u00a237352\\n37400\\n.37448\\n37496\\n37544\\n37592\\n37640\\n37687\\n37735\\nn\\n37783\\n37831\\n37879\\n37927\\n37975\\n38023\\n38071\\n38119\\n38166\\n38214\\n38262\\n38310\\n3835^\\n38405\\n38453\\n38501\\n38548\\n38596\\n38644\\n38692\\n38739\\n38787\\n38834\\n38882\\n38930\\n38977\\n39025\\n39072\\n39120\\n39168\\n39215\\n39263\\n39310\\n39358\\n39405\\n39453\\n39506\\n39548\\n39595\\n39642\\n39690\\n39737\\n39785\\n39832\\n39879\\n39927\\n39974\\n40021\\n40069\\n401 16\\n40163\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n47\\n48\\n48\\n48\\n48\\n48\\n47\\n48\\n48\\n48\\n4?\\n48\\n4^\\n48\\n4f\\n48\\n47\\n48\\n47\\n48\\n47\\n48\\n47\\n47\\n47\\n48\\n47\\n47\\n47\\n47\\n48\\n47\\n47\\n48\\n47\\n47\\n47\\n47\\n47\\n4?\\n47\\n47\\n4f\\n47\\n47\\n47\\n4?\\nAl\\n47\\n4l\\n4l\\n47\\n41\\nLoff. Kxsec.l\\nLog. Vers. I U Log. Exsec.l 2\\n9-30398\\n30436\\n30474\\n.30511\\n30549\\n9-30587\\n30624\\n30662\\n30700\\n-3073?\\n9-30775\\n.30812\\n.30850\\n30887\\n-30925\\n9.30962\\n.31000\\n-31037\\n\u00e2\u0080\u00a231075\\n.31112\\n9.31150\\n.31187\\n.31224\\n.31262\\n.31299\\n9-31336\\n-31374\\n.31411\\n\u00e2\u0080\u00a231448\\n\u00e2\u0080\u00a231485\\n9.31523\\n.31560\\n\u00e2\u0080\u00a231597\\n\u00e2\u0080\u00a231634\\n.31671\\n9-317O8\\n\u00e2\u0080\u00a231746\\n.31783\\n,31820\\n-31857\\n9.31894\\n\u00e2\u0080\u00a231931\\n.31968\\n.32005\\n.32042\\n9-32079\\n.32116\\n.32153\\n.32190\\n-22227\\n9.32263\\n.32300\\n\u00e2\u0080\u00a232337\\n\u00e2\u0080\u00a232374\\n.32411\\n9-32447\\n.32484\\n.32521\\n\u00e2\u0080\u00a232558\\n.32594\\n9-32631\\nLoe. Vers.\\n37\\n38\\n37\\n37\\n38\\n3l\\n3l\\n38\\n37\\n31\\n37\\n3l\\n37\\n37\\n3l\\n37\\n37\\n3l\\n3l\\n3l\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n37\\n36\\n37\\n37\\n36\\n37\\n36\\n37\\n36\\n37\\n36\\n37\\n77\\n9.40163\\n.40216\\n.40258\\n40305\\n.40352\\n40399\\n,40447\\n,40494\\n,40541\\n40588\\n9-40635\\n.40682\\n\u00e2\u0080\u00a240730\\n\u00e2\u0080\u00a240777\\n40824\\n9.40871\\n\u00e2\u0080\u00a240918\\n.40965\\n9-4\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a24\\n.4\\n\u00e2\u0080\u00a24\\n9.4\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a24\\n-4\\n\u00e2\u0080\u00a24\\n9-4\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a24\\n9-4\\n.4\\n.4\\n\u00e2\u0080\u00a24\\n\u00e2\u0080\u00a24\\n012\\n059\\n106\\n153\\n206\\n24^\\n294\\n341\\n388\\n435\\n482\\n529\\n576\\n623\\n670\\n717\\n763\\n816\\n857\\n904\\n951\\n998\\n9.42044\\n.42091\\n.42138\\n.42185\\n-42231\\n9-42278\\n-42325\\n.42372\\n.42418\\n.42465\\n9.42512\\n-42558\\n.42605\\n.42652\\n.42698\\n9-42745\\n.42792\\n.42838\\n.42885\\n-42931\\n9-42978\\nLoar. Kxsec.\\n47\\n41\\n47\\n4l\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n4/\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n46\\n47\\n47\\n47\\n46\\n47\\n47\\n46\\n47\\n47\\n46\\n47\\n46\\n47\\n46\\n47\\n46\\n47\\n46\\n47\\n46\\n46\\n47\\n46\\n46\\n46\\n47\\n46\\n46\\n46\\n46\\n10\\n20\\n21\\n22\\n23\\n24\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n20\\n50\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n40\\n50\\nP. P.\\n48\\n4.8 1\\n5\\n6\\n6\\n4\\n7\\n8\\n3\\n1\\n16\\n1\\n24\\n2\\n32\\n3\\n40\\n4\\n48\\n4^\\n6\\n7\\n8\\n4-7\\n5-5\\n6.3\\n9\\n7-1\\n10\\n7-9\\n20\\n15.\\n30\\n23-7\\n40\\n31-6\\n50\\n39-6\\n16.\\n24.\\n32.\\n40.\\n47\\n4-7\\n5-5\\n6.;\\n7-0\\n7-\\n15.6\\n23-5\\n31-3\\n39-\\n20\\n30\\n40\\n50\\n46\\n4-6\\n5-4\\n6.2\\n7.0\\n7-7\\n15.5\\n23.2\\n31.0\\n38.7\\n39\\n38\\n3-9\\n3-\\n4-5\\n4.\\n5.2\\n5-\\n5-8\\n5;\\n6.5\\n6.\\n13.0\\n12.\\n19^5\\n19.\\n26.0\\n25-\\n32.5\\n32\\n38\\nZl\\n3.8\\n4.4\\n3\\n4\\n50\\n5\\n5-7\\n6.3\\n5-\\n6.\\n12.6\\n12.\\n19.0\\n18.\\n25-3\\n25-\\n31-6\\n31\\n37\\n36\\n3-7\\n3\\n4-3\\n4-\\n4-9\\n4-\\n5-5\\n5-\\n6.1\\n6.\\n12.3\\n12.\\n18.5\\n18.\\n24-6\\n24.\\n30-8\\n30-\\nP. p\\n412", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0464.jp2"}, "465": {"fulltext": "TABLE VIII,\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n10\\nII\\n12\\n14\\n15\\ni6\\ni8\\n19\\n20\\n21\\n22\\n^3\\n24\\n25\\n26\\n27\\n28\\n29\\n80\\n33\\n34\\n33\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44_\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n56\\n57\\n58\\n59\\nGO\\n:58\\n:5i\\nLost. Vers. |li(\u00c2\u00bbsr. Kxsec liOir. Vers, liOC. Kxsec\\n9.32631\\n32668\\n32704\\n32741\\n32778\\n32814\\n32851\\n32888\\n32924\\n32961\\n32997\\n33034\\n33070\\n33107\\n33143\\n33180\\n33216\\n33252\\n33289\\n33325\\n33361\\n33398\\n33434\\n33470\\n33507\\n33543\\n33579\\n33615\\n33652\\n33688\\n33724\\n33766\\n33796\\n33833\\n33869\\n33905\\n33941\\n33977\\n34013\\n34049\\n34085\\n34121\\n34157\\n34193\\n34229\\n34265\\n34301\\n34337\\n34373\\n34408\\n34444\\n34480\\n345 6\\n34552\\n34587\\n34623\\n34659\\n34695\\n34736\\n34766\\n9 34802\\nLog. Vers.\\n36\\n36\\n37\\n36\\n36\\n36\\n37\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n35\\n36\\n36\\n3l\\n36\\n3d\\n36\\n3l\\n36\\n35\\n36\\n35\\n42978\\n43024\\n43071\\n43118\\n43164\\n432 1 1\\n4325^\\n43304\\n43356\\n43396\\n43443\\n43489\\n43536\\n43582\\n43629\\n43675\\n43721\\n43768\\n43814\\n43861\\n43907\\n43953\\n43999\\n44046\\n44092\\n44138\\n44185\\n44231\\n44277\\n44323\\n44370\\n44416\\n44462\\n44508\\n44554\\n44601\\n44647\\n44693\\n44739\\n44785\\n44831\\n44877\\n44924\\n44970\\n45016\\n45062\\n45108\\n45154\\n45200\\n45246\\n45292\\n45338\\n45384\\n45430\\n45476\\n45522\\n45568\\n45614\\n45660\\n45706\\n9-45752\\niOC. Kxsec.\\n46\\n47\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n77\\n9.34802\\n3483?\\n34873\\n34909\\n34944\\n34980\\n35016\\n35051\\n35087\\n35122\\n35158\\n35193\\n35229\\n35264\\n35300\\n35335\\n35376\\n35406\\n35441\\n35477\\n35512\\n35547\\n35583\\n35618\\n35653\\n35689\\n35724\\n35759\\n35794\\n35829\\n35865\\n35900\\n35935\\n35976\\n36005\\n36046\\n36076\\n361 II\\n36146\\n36181\\n36216\\n36251\\n36286\\n36321\\n36356\\n3639\\n36426\\n36461\\n36495\\n36536\\n36565\\n36606\\n36635\\n36670\\n36705\\n36739\\n36774\\n36809\\n36844\\n36878\\n9 369 3\\n3i)\\n36\\n35\\n35\\n35\\n36\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n34\\n35\\n35\\n35\\n34\\n35\\n35\\n34\\n35\\n34\\n35\\n34\\n35\\nVers.\\nIt\\n9\\n45752\\n4579^\\n45843\\n45889\\n45935\\n45981\\n46027\\n46073\\n461 18\\n46164\\n46216\\n46256\\n46302\\n4634^\\n46393\\n46439\\n46485\\n46536\\n46576\\n46622\\n46668\\n46713\\n46759\\n46805\\n46856\\n46896\\n46942\\n4698?\\n47033\\n47078\\n47124\\n47170\\n47215\\n47261\\n47306\\n47352\\n47398\\n47443\\n47489\\n47534\\n47580\\n47625\\n47671\\n477 6\\n47762\\n47807\\n47852\\n47898\\n47943\\n47989\\n48034\\n48080\\n48125\\n48176\\n48216\\n48261\\n48306\\n48352\\n4839?\\n48442\\n48488\\nl,llir. K\\\\K4T.\\n45\\n46\\n46\\n46\\n45\\n46\\n46\\n45\\n46\\n46\\n45\\n46\\n45\\n46\\n45\\n46\\n45\\n46\\n45\\n46\\n45\\n45\\n46\\n45\\n45\\n46\\n45\\n45\\n45\\n46\\n45\\n45\\n45\\n45\\n46\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n5\\n6\\n7\\n8\\n9\\n10\\n1 1\\n12\\n13\\nii_\\n15\\n16\\n17\\n18\\n19\\n\u00e2\u0080\u00a220\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n5\\n52\\n53\\nJ4\\n55\\n56\\n57\\n58\\n4;o\\nV. V\\n20\\n30\\n40\\n50\\n20\\n30\\n40\\n50\\n20\\n30\\n40\\n50\\n40\\n50\\n47\\n4-7\\n5vS\\n6.2\\n7.0\\n7-8\\n15-6\\n23 -5\\n39- 1\\n46\\n4.6\\n5-1\\n6.1\\n6.9\\n7-6\\n15-3\\n23.0\\n30-6\\n38.3\\n46\\n4-6\\n5-4\\n6.2\\n7.0\\n7-7\\n15-5\\n23.2\\n31.0\\n38.7\\n4S\\n4-5\\n5-3\\n6.0\\n6.8\\n7.6\\nJ51\\n22.7\\n30-3\\n37-9\\n9\\n10\\n20\\n30\\n40\\n50\\n45\\n4-5\\n5-2\\n6.0\\n6.7\\n7-5\\n150\\n22.5\\n30.0\\n37-5\\n37\\n3-7\\n4-3\\n4-9\\n5-5\\n6.1\\n12.3\\n18.5\\n24-6\\n30-8\\n36\\n3-6\\n4.2\\n4-8\\n5-5\\n6.1\\n12.1\\n18.2\\n24.3\\n30-4\\n36\\n35\\n3-6\\n3-5\\n42\\n4.1\\n4.8\\n4-7\\n5-4\\n5-3\\ne.o\\n5-0\\nJ2.0\\n18.0\\n17-7\\n24.0\\n23 6\\n30.0\\n29.6\\n35\\n34\\n6\\n3 5\\n3-4\\n7\\n4.1\\n4.0\\n8\\n4-6\\n4.6\\n9\\n5-2\\n5-2\\n10\\n5-\u00c2\u00a7\\n5-7\\n20\\nn-6\\n1 1. 5\\n30\\n7-5\\n17.2\\n40\\n23.3\\n23.0\\n50\\n29.1\\n28.7\\nV. V\\n413", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0465.jp2"}, "466": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n40\u00c2\u00b0 41\u00c2\u00b0\\nLog. Vers. J |Log. Exsec. Z Log. Vers.\\n10\\nII\\n12\\n13\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n^8\\n59\\nGO\\n36913\\n36948\\n36982\\n37017\\n37052\\n37086\\n3712T\\n37156\\n37196\\n37225\\n37259\\n37294\\n37328\\n37363\\n37397\\n37432\\n37466\\n37501\\n37535\\n37570\\n37604\\n37639\\n37673\\n377of\\n37742\\n37776\\n37816\\n37845\\n37879\\n37913\\n37947\\n37982\\n38016\\n38056\\n38084\\n38118\\n38153\\n38187\\n38221\\n38255\\n38289\\n38323\\n38357\\n38391\\n38425\\n38459\\n38493\\n38527\\n3856T\\n38595\\n38629\\n38663\\n38697\\n38731\\n38765\\n38799\\n38833\\n38866\\n38906\\n38934\\n9.38968\\nLoff. Vers.\\n34\\n34\\n35\\n34\\n34\\n35\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n33\\n34\\n34\\n34\\n33\\n34\\n33\\n34\\n48488\\n48533\\n48578\\n48624\\n48669\\n48714\\n48759\\n48805\\n48850\\n48895\\n48946\\n48986\\n49031\\n49076\\n4912T\\n49166\\n492 1 T\\n49257\\n49302\\n49347\\n49392\\n49437\\n49482\\n49527\\n49572\\n49618\\n49663\\n49708\\n49753\\n49798\\n49843\\n49888\\n49933\\n49978\\n50023\\n50068\\n50113\\n50158\\n50203\\n50248\\n50293\\n50338\\n50383\\n50427\\n50472\\n50517\\n50562\\n50607\\n50652\\n50697\\n50742\\n50787\\n5083T\\n50876\\n5092T\\n50966\\n5101 1\\n51055\\n51 106\\n51145\\nQ 5 II 90\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n44\\n45\\n45\\n45\\n45\\n44\\n45\\n45\\n45\\n44\\n45\\n45\\n44\\n45\\n44\\n45\\n45\\n44\\nLog. Hxsec\\n9.38968\\n39002\\n39035\\n39069\\n39103\\n39137\\n39176\\n39204\\n39238\\n39271\\n39305\\n39339\\n39372\\n39406\\n39439\\n39473\\n39507\\n39540\\n39574\\n3960^\\n39641\\n39674\\n39708\\n39741\\n39774\\n39808\\n39841\\n39875\\n39908\\n39941\\n39975\\n40008\\n40041\\n40075\\n40108\\n40 1 41\\n40175\\n40208\\n4024T\\n40274\\n40307\\n40341\\n40374\\n40407\\n40446\\n40473\\n40506\\n40540\\n40573\\n40606\\n40639\\n40672\\n40705\\n40738\\n40771\\n40804\\n40837\\n40870\\n40903\\n40936\\n40969\\nU Loar. Exsec\\n34\\n33\\n34\\n33\\n34\\n33\\n33\\n34\\n33\\n33\\n34\\n33\\n33\\n33\\n33\\n34\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n9\\nLO!. Vers. l.n\\n190\\n235\\n279\\n324\\n369\\nn\\n414\\n458\\n503\\n548\\n592\\n63?\\n682\\n726\\n771\\n816\\n866\\n905\\n950\\n994\\n52039\\n52084\\n52128\\n52173\\n52217\\n52262\\n52306\\n52351\\n52396\\n52446\\n52485\\n52529\\n52574\\n52618\\n52663\\n52707\\n52752\\n52796\\n52841\\n52885\\n52930\\n52974\\n53018\\n53063\\n53107\\n53152\\n53 96\\n53240\\n53285\\n53329\\n53374\\n53418\\n53462\\n53507\\n53551\\n53595\\n53640\\n53684\\n53728\\n53773\\n53817\\n53861\\n45\\n44\\n45\\n44\\n45\\n44\\n45\\n44\\n44\\n45\\n44\\n44\\n45\\n44\\n44\\n45\\n44\\n44\\n44\\n45\\n44\\n44\\n44\\n44\\n44\\n45\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\nExs\\nP. P.\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n60\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\nii_\\n55\\n56\\n57\\n58\\n59\\n({0\\n2D\\n30\\n40\\n50\\n40\\n40\\n50\\n44\\n4.4\\n5-2\\n5-9\\n6.7\\n7-4\\n14.8\\n22.2\\n29-6\\n37-1\\n35\\n7\\n4\\n8\\n4\\n9\\n5\\n10\\n5\\n20\\nII\\n30\\n17\\n40\\n23\\n50\\n29\\n34\\n20\\n40\\n50\\n4S\\n45\\n4-5\\n4-5\\n5 1\\n5-2\\n6.0\\n6.0\\n6.8\\n6.7\\n7.6\\n7-5\\n15. 1\\n15.0\\n22.7\\n22.5\\n303\\n30.0\\n37-9\\n37-5\\n44\\n4.4\\n5-8\\n6.6\\n7-3\\n14-6\\n22 .0\\n29-3\\n36 6\\n34\\n33\\n3-3\\n3-9\\n4.4\\n50\\n5.6\\nt6.\\n27\\n33\\n27\\np. P.\\n414", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0466.jp2"}, "467": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS,\\n4*e 4;r\\nLog. Vers. 1\\n9\\n40969\\n001\\n034\\n067\\n106\\n133\\n166\\n199\\n231\\n264\\n297\\n330\\n362\\n395\\n428\\n461\\n493\\n525\\n559\\n591\\n624\\n657\\n689\\n722\\n754\\n7^7\\n819\\n852\\n885\\n917\\n950\\n982\\n42014\\n42047\\n42079\\n421 12\\n42144\\n42177\\n42209\\n4224T\\n42274\\n42306\\n42338\\n42371\\n42403\\n42435\\n42467\\n42500\\n42532\\n42564\\n42596\\n42629\\n42661\\n42693\\n42725\\n42757\\n42789\\n42822\\n42854\\n42886\\n9-4^9 8\\nLoc. Vers.\\n32\\n33\\njj\\n33\\n32\\n33\\n33\\n32\\n33\\n32\\n33\\n32\\n33\\n32\\n33\\n32\\n33\\n32\\n32\\n32\\n33\\n32\\n32\\n32\\n32\\n32\\n32\\n33\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n32\\n7\\nliOj;. KxHec.\\n53861\\n53906\\n53950\\n53994\\n54038\\n54083\\n54 27\\n54171\\n54215\\n54259\\n54304\\n54348\\n54392\\n54436\\n54480\\n54525\\n54569\\n546-13\\n54657\\n5470T\\n54745\\n54790\\n54834\\n54878\\n54922\\n54966\\n55016\\n55054\\n55098\\n55142\\n55186\\n55230\\n55275\\n55319\\n55363\\n55407\\n55451\\n55495\\n55539\\n55583\\n55627\\n55671\\n55715\\n55759\\n55803\\n55847\\n55890\\n55934\\n55978\\n56022\\n56065\\n561 16\\n56154\\n56198\\n56242\\n56286\\n56330\\n56374\\n5641^\\n5646T\\n56505\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n43\\n44\\n44\\n44\\n44\\n44\\n44\\n43\\n44\\n44\\n44\\n44\\n43\\n44\\n43\\nLos:. Kxseo. J\\nLotr. Vers.\\n9\\n42918\\n42950\\n42982\\n43014\\n43046\\nJ\\n43078\\n43116\\n43142\\n43174\\n43206\\n43238\\n43270\\n43302\\n43334\\n43365\\n4339?\\n43429\\n4346T\\n43493\\n43525\\n43557\\n43588\\n43626\\n43652\\n43684\\n43715\\n43747\\n43779\\n43816\\n43842\\n43874\\n43906\\n43937\\n43969\\n44006\\n44032\\n44064\\n44095\\n44127\\n44 58\\n44190\\n44221\\n44253\\n44284\\n443 6\\n44347\\n44379\\n44416\\n44442\\n44473\\n44504\\n44536\\n44567\\n44599\\n44630\\n4466 T\\n44693\\n44724\\n44755\\n44787\\n448 1 8\\nL(\u00c2\u00bbe. Vers.\\n32\\n32\\n32\\n32\\n31\\n32\\n32\\n32\\n31\\n32\\n32\\n32\\n31\\n32\\n32\\n31\\n32\\n31\\n32\\n31\\n32\\n31\\ny\\n32\\n31\\n32\\n31\\n31\\n31\\n32\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n3\\n31\\n31\\nLoir. K.vNi c\\nW\\n56505\\n5^ 549\\n56593\\n56637\\n56686\\n56724\\n56768\\n56812\\n56856\\n56899\\n56943\\n56987\\n57031\\n57075\\n57 J8\\n57162\\n57206\\n57250\\n57293\\n57337\\n57381\\n57424\\n57468\\n57512\\n57556\\n57599\\n57643\\n57687\\n57730\\n57774\\n57818\\n5786T\\n57905\\n57949\\n57992\\n58036\\n58079\\n58123\\n58167\\n58216\\n58254\\n5829?\\n58341\\n58385\\n58428\\n58472\\n58515\\n58559\\n58602\\n58646\\n58689\\n58733\\n58776\\n58826\\n58S64\\n5890?\\n58951\\n58994\\n59037\\n59081\\nL iiii\\ny Ldir. Kxser.\\n43\\n44\\n44\\n43\\n44\\n44\\n43\\n44\\n43\\n44\\n44\\n43\\n44\\n43\\n44\\n43\\n44\\n43\\n44\\n43\\n43\\n44\\n43\\n44\\n43\\n43\\n44\\n43\\n43\\n44\\n43\\n43\\n44\\n43\\n43\\n43\\n44\\n43\\n43\\n43\\n43\\n44\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n44\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n10\\n1 I\\n12\\n13\\n_LL\\n5\\n16\\n17\\n18\\n19\\n20\\n21\\n-J\\n24\\n25\\n26\\n27\\n28\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n45\\n46\\n47\\n48\\n50\\n31\\n5^\\n53\\n54\\n55\\n5^^\\n57\\n58\\n59\\n;o\\n1 I*.\\n40\\n50\\n40\\n50\\n20\\n30\\n40\\n50\\n40\\n50\\n44\\n4-4 1\\n5\\n2\\n5\\n9\\n6\\n7\\n7\\n4\\n14\\niJ\\n22\\n29\\n6\\n37\\nI\\n33\\n4.4\\n4.9\\n5-5\\n11 .0\\n16.5\\n27-5\\n32\\n3-2\\n3-7\\n4.2\\n4.8\\n5-3\\n10.6\\n16.0\\n21 3\\n26.6\\n7\\n8\\n9\\n10\\n30\\n30\\n40\\n50\\n44\\n4.4\\n5-i\\n5-8\\n6.6\\n7-3\\n14-6\\n22 o\\n29-3\\n36.6\\n43\\n4\\n3\\n5\\nI\\n5\\n8\\n6\\n5\\n7\\n2\\nJ4\\n5\\n21\\n7\\n29\\n36\\n2\\n43\\n28.6\\n35-8\\n32\\n3\\n4-\\n4-\\n5-\\n10.\\n16.\\n27.1\\n31\\n31\\n3-7\\n4.7\\n4-7\\n5-2\\n10.5\\n\u00c2\u00bb5-7\\n21 .0\\n26.2\\n31\\n3-\u00c2\u00bb\\n3-6\\n4\u00c2\u00ab\\n4-6\\n51\\n10.3\\n\u00c2\u00bb5 5\\n20.^\\n25-8\\nI*.\\n415", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0467.jp2"}, "468": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n44\u00c2\u00b0 45\u00c2\u00b0\\nLog. Vers.\\n9.44818\\nI\\n.44849\\n2\\n.44880\\n3\\n.44912\\n4\\n.44943\\n5\\n9-44974\\n6\\n.45.005\\n7\\n\u00e2\u0080\u00a245036\\n8\\n.45068\\n9\\n.45099\\n10\\n9.45130\\nII\\n.45161\\n12\\n.45192\\n13\\n.45223\\n14\\n.45254\\n15\\n9.45285\\ni6\\n.45316\\n17\\n.45348\\ni8\\n.45379\\n19\\n.45410\\n20\\n9.45441\\n21\\n.45472\\n22\\n\u00e2\u0080\u00a245503\\n23\\n\u00e2\u0080\u00a245534\\n24\\n.45565\\n25\\n9.45595\\n26\\n.4562^\\n27\\n\u00e2\u0080\u00a24565?\\n28\\n.45688\\n29\\n.45719\\n30\\n9.45750\\n31\\n.45781\\n32\\n.45812\\n33\\n.45843\\n34\\n.45873\\n35\\n9.45904\\n36\\n.4593!\\n37\\n\u00e2\u0080\u00a245966\\n3\u00c2\u00ab\\n\u00e2\u0080\u00a245997\\n39\\n.46027\\n40\\n9.46058\\n41\\n46089\\n42\\n.46120\\n43\\n.46150\\n44\\n.46181\\n45\\n9.46212\\n46\\n.46242\\n47\\n.46273\\n48\\n.46304\\n49\\n.46334\\n50\\n9.46365\\n51\\n.46396\\n52\\n.46426\\n53\\n.46457\\n54\\n.4648^\\n55\\n9-46518\\n56\\n.46549\\n57\\n.46579\\n58\\n.46610\\n59\\n46646\\nGO\\n9.46671\\nZ Log. Ex sec. J\\nLog. Vers.\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n31\\n30\\n31\\n31\\n31\\n31\\n31\\n30\\n31\\n31\\n30\\n31\\n31\\n30\\n31\\n30\\n31\\n30\\n31\\n30\\n31\\n30\\n30\\n31\\n30\\n30\\n31\\n30\\n30\\n30\\n30\\n31\\n30\\n30\\n30\\n30\\n30\\nIT\\nI. 59124\\n.59168\\n.59211\\n.59255\\n59298\\n59342\\n59385\\n59429\\n59472\\n59515\\n59559\\n59602\\n59646\\n59689\\n59732\\n59776\\n59819\\n59863\\n59906\\n59949\\n9-59993\\n60036\\n.60079\\n.60123\\n.60166\\n60209\\n,60253\\n,60296\\n.60339\\n.60383\\n60426\\n60469\\n,60512\\n,60556\\n60599\\n60642\\n,60685\\n,60729\\n,60772\\n,60815\\n,60858\\n60902\\n60945\\n,60988\\n,61031\\n.61075\\n,61118\\n.61 161\\n,61204\\n.61247\\n,61291\\n.61334\\n61377\\n,61426\\n.61463\\n9-\\n61506\\n61550\\n\u00e2\u0080\u00a261593\\n.61636\\n.61679\\n9.61722\\nLog. Kxsec. I I)\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\nLog. Vers.\\n9 4667 1\\n4670T\\n46732\\n46762\\n46793\\n46823\\n46853\\n46884\\n46914\\n46945\\n46975\\n47005\\n47036\\n47066\\n47096\\n47127\\n4715^\\n4718^\\n47218\\n47248\\n47278\\n47308\\n47339\\n47369\\n47399\\n47429\\n47459\\n47490\\n47520\\n47550\\nn\\n47586\\n47616\\n47646\\n47676\\n47706\\n47731\\n47761\\n47791\\n47821\\n47851\\n47881\\n4791 1\\n47941\\n47971\\n48001\\n48031\\n48061\\n48096\\n48126\\n48156\\n48186\\n48216\\n48240\\n48270\\n48300\\n48329\\n48359\\n48389\\n48419\\n48449\\n48478\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n36\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n30\\n29\\n30\\n30\\n29\\n30\\n30\\n29\\n30\\n30\\n29\\n30\\n29\\nLog. Vers. I J\\nLog. Exsec.\\n9.61722\\n.61765\\n.61808\\n.61852\\n.61895\\n61938\\n,61981\\n.62024\\n.6206^\\n.621 16\\n62153\\n.62196\\n.62239\\n.62282\\n,62326\\n.62369\\n.62412\\n.62455\\n.62498\\n,62541\\n9-\\n62584\\n62627\\n62670\\n62713\\n62756\\n9-\\n62799\\n62842\\n62885\\n62928\\n62971\\n63014\\n,63057\\n,63100\\n63143\\n63186\\n,63229\\n.63272\\n\u00e2\u0080\u00a263315\\n63358\\n63401\\n9-\\n63443\\n63486\\n,63529\\n63572\\n63615\\n\u00e2\u0080\u00a263658\\n\u00e2\u0080\u00a263701\\n\u00e2\u0080\u00a263744\\n,63787\\n,63830\\n,63873\\n\u00e2\u0096\u00a063915\\n\u00e2\u0080\u00a263958\\n,64001\\n64044\\n9.64087\\n64 1 30\\n\u00e2\u0080\u00a264173\\n.64216\\n\u00e2\u0080\u00a264258\\n9-64301^\\nLog. Exsec. J\\nJ)\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n42\\n43\\n43\\n43\\n43\\n43\\n42\\n43\\n43\\n43\\n43\\n42\\n43\\n43\\n43\\n42\\n43\\n43\\n43\\n42\\n43\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n00\\np. P.\\n20\\n40\\n50\\n40\\n50\\n40\\n50\\n43\\n4-3\\n5-1\\n5.8\\n6.5\\n7.2\\n14-5\\n29.\\n36.\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n31\\n3^i\\n3-7\\n4.2\\n4.7\\n5-2\\n10.5\\n15-7\\n21 .0\\n26.2\\n30\\n30\\n3-5\\n4.0\\n4.6\\n5-1\\n10. 1\\n15.5\\n20.3\\n25.4\\n20\\n30\\n40\\n50\\n43\\n4-3\\n5-0\\n5-7\\n6.4\\n7-1\\n14-3\\n21-5\\n28.6\\n35-8\\n42\\n4.2\\n4.9\\n5-6\\n6.4\\n7-1\\n141\\n21 .2\\n28.3\\n35-4\\n31\\n3-1\\n3.6\\n4.1\\n4-6\\n5-1\\n25-8\\n30\\n30\\n3-5\\n4.0\\n4-5\\n5-0\\n10. o\\n15.0\\n20.0\\n25.0\\n29\\n2.9\\n3-4\\n3-9\\n4.4\\n4.9\\n9-8\\n14.7\\n^9-6\\n24.6\\nP. P.\\n416", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0468.jp2"}, "469": {"fulltext": "TABLE V^III.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n40\u00c2\u00b0 47\u00c2\u00b0\\n_9_\\n10\\nII\\n12\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\nLog. Vers. I 1 Los- Kxsef\\n50\\n51\\n52\\n53\\nS\u00c2\u00b1_\\n55\\n56\\n57\\n58\\n59\\n(\u00c2\u00bb0\\n48478\\n4S508\\n48538\\n48568\\n4859?\\n48627\\n48657\\n48686\\n487 1 6\\n48746\\n4877^\\n48805\\n4S835\\n48864\\n48894\\n48923\\n48953\\n48983\\n49012\\n49042\\n49071\\n49101\\n49130\\n49160\\n49189\\n49219\\n49248\\n49278\\n49307\\n49336\\n49366\\n49395\\n49425\\n49454\\n49483\\n49513\\n49542\\n49571\\n49601\\n49630\\n49659\\n49689\\n49718\\n49747\\n49776\\n49806\\n49835\\n49864\\n49893\\n49922\\n;oi\\nD5\\n49952\\n49981\\n50010\\n50039 I\\n50068 I\\n50097\\n50126\\n50185\\n50214\\n9.50243\\nliOff. Vers.\\n29\\n30\\n29\\n30\\n29\\n29\\n30\\n29\\n29\\n30\\n29\\n29\\n29\\n29\\n30\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\nJ\\n9\\n64301\\n64344\\n64387\\n64430\\n64473\\n64515\\n64558\\n,64601\\n64644\\n64687\\n64729\\n,64772\\n64815\\n64858\\n6490 1\\n64943\\n.64986\\n,65029\\n,65072\\n65114\\n9-\\n65157\\n65200\\n65243\\n65285\\n65328\\n65371\\n.65414\\n.65456\\n.65499\\n65542\\n65585\\n,65627\\n,65670\\n.65713\\n6575?\\n9-\\n65798\\n65841\\n65884\\n65926\\n65969\\n,66012\\n.66054\\n66097\\n66 1 40\\n.66182\\nv\\n,66225\\n.66268\\n.66310\\n\u00e2\u0080\u00a266353\\n,66396\\n66438\\n,66481\\n66523\\n.66566\\n66609\\n,66651\\n66694\\n,66737\\n66779\\n66822\\n9.66864\\n43\\n42\\n43\\n43\\n42\\n43\\n43\\n42\\n43\\n42\\n43\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n42\\n42\\n43\\n42\\n43\\n42\\n42\\n43\\n42\\n42\\n43\\n42\\n42\\n43\\n42\\n42\\n43\\n42\\n42\\n42\\n43\\n42\\n42\\n42\\n43\\n42\\n42\\n42\\nliOij. Vers.\\njosr. Kxser.\\n9.50243\\n50272\\n50301\\n50330\\n50359\\n50388\\n50417\\n50446\\n50475\\n50504\\n50533\\n50562\\n50591\\n50619\\n50648\\n50677\\n50706\\n50735\\n50764\\n50793\\n50821\\n50850\\n50879\\n50908\\n50937\\n50905\\n50994\\n023\\n0:;2\\n9-5\\nLost.\\n080\\n109\\n138\\n167\\n195\\n224\\n253\\n281\\n310\\n338\\n367\\n396\\n424\\n453\\n481\\n510\\n539\\n567\\n596\\n624\\n653\\n681\\n710\\n738\\n767\\n795\\n823\\n852\\n886\\n909\\n937\\n90 5\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n28\\n29\\n29\\n29\\n28\\n29\\n29\\n28\\n29\\n29\\n28\\n29\\n28\\n29\\n28\\n29\\n28\\n29\\n28\\n29\\n28\\n28\\n29\\n28\\n28\\n28\\n29\\n28\\n28\\n28\\n28\\n28\\n29\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\nl.dir. Kxscc\\n9-\\n66864\\n66907\\n66950\\n66992\\n67035\\n67077\\n67120\\n67162\\n67205\\n67248\\n,67296\\n67333\\n\u00e2\u0080\u00a267375\\n,67418\\n67466\\n,67503\\n67546\\n.67588\\n,67631\\n,67673\\n67716\\n67758\\n67801\\n67843\\n67886\\n,67928\\n,67971\\n,68013\\n68056\\n68098\\n9-\\n68I4I\\n68183\\n68226\\n68268\\n683! I\\n68353\\n68396\\n68438\\n68481\\n68523\\n,68566\\n,68608\\n.68651\\n,68693\\n.68735\\n,68778\\n,68826\\n,68863\\n,68905\\n,68948\\n68996\\n69033\\n69075\\n69II7\\n69160\\n69202\\n69245\\n69287\\n69330\\n69372\\n60414\\n42\\n43\\n42\\n42\\n42\\n42\\n42\\n43\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n43\\n42\\n42\\n42\\n,1 -7\\nT-\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n9-\\n_9\\n16\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n33\\n34\\nJ5\\n36\\n37\\n3\\n39\\n8\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49_\\nlO\\n5\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n0\\nV. v.\\n20\\n40\\n50\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n43 42\\n6\\n4 3\\n4- -s\\n7\\n5-0\\n4.9\\n9\\n5-7\\n6.4\\n5-6\\n6.4\\n10\\n7-1\\n7\\n20\\n\u00c2\u00bb4-3\\n14.1\\n30\\n40\\n21.5\\n28.6\\n21.2\\n28.3\\n50\\n35-8\\n35-4\\n20\\n30\\n40\\n50\\n30\\n29\\n2.9\\n3 4\\n3-8\\n4-3\\n6\\n7\\n8\\n9\\nlo\\n20\\n30\\n40\\n50\\n42\\n3\\n3\\n5\\n4\\n4\\n5\\n5\\n10\\n15\\n20\\n25\\n29\\n29\\n4\\n9\\n4\\n9\\n28\\n28\\n2.8\\n3-2\\n3-7\\n4-a\\n4-\\n9\\n4\\n18.\\n23.\\nI V\\n417", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0469.jp2"}, "470": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n48\u00c2\u00b0 49\u00c2\u00b0\\n10\\nII\\n12\\nLos. Vers J\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n3f\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n\u00c2\u00b1L\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n9.51965\\n51994\\n52022\\n52050\\n52079\\n52107\\n52135\\n52164\\n52192\\n52226\\n52249\\n52277\\n52305\\n52333\\n52362\\n52390\\n52418\\n52446\\n52474\\n52503\\n52531\\n52559\\n52587\\n52615\\n52643\\n52671\\n52699\\n5272^\\n52756\\n52784\\n52812\\n52840\\n52896\\n52924\\n52952\\n52980\\n53008\\n53036\\n53064\\n53092\\n53120\\n5314?\\n53175\\n53203\\n53231\\n53259\\n53287\\n53315\\n53343\\n53370\\n53398\\n53426\\n53454\\n53482\\n53509\\n5353?\\n53565\\n53593\\n53620\\n9.53648\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n2?\\n28\\n28\\n28\\n27\\n28\\n28\\n28\\n2f\\n28\\n28\\n2?\\n28\\n2f\\n28\\n2?\\n28\\n27\\n28\\nLog. Vers. J\\nLog. Exsec.\\n9.69414\\n69457\\n69499\\n69542\\n69584\\n69625\\n69669\\n697 1 1\\n69753\\n69796\\n69838\\n69881\\n69923\\n69965\\n70008\\n70050\\n70092\\n70135\\n70177\\n70220\\n2 i Log. Vers.\\n70262\\n70304\\n70347\\n70389\\n70431\\n70474\\n70516\\n70558\\n70601\\n70643\\n70685\\n70728\\n70770\\n70812\\n70854\\n70897\\n70939\\n70981\\n024\\n066\\nI08\\n151\\n193\\n235\\n278\\n320\\n362\\n404\\n447\\n489\\n531\\n573\\n616\\n658\\n706\\n743\\n785\\n82^\\n869\\n912\\n9-71954\\nLog. Exspc.\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n^2\\n42\\n42\\n42\\n42\\n42\\nT\\n53648\\n53676\\n53704\\n53731\\n53759\\n53787\\n53814\\n53842\\n53870\\n5389?\\n53925\\n53952\\n53986\\n54008\\n54035\\n54063\\n54096\\n54118\\n54 45\\n54173\\n1 Los. Exsec.\\n54200\\n54228\\n54255\\n54283\\n543 6\\n54338\\n54365\\n54393\\n54426\\n54448\\n54475\\n54502\\n54530\\n54557\\n54585\\n54612\\n54639\\n54667\\n54694\\n54721\\n54748\\n54776\\n54803\\n54836\\n54858\\n54885\\n54912\\n54939\\n54967\\n54994\\n55021\\n55048\\n55075\\n55103\\n55130\\n55157\\n55184\\n5521T\\n55238\\n55265\\n55292\\n27\\n28\\n27\\n27\\n28\\n27\\n28\\n2?\\n27\\n28\\n27\\n27\\n2?\\n27\\n27\\n27\\n27\\n2?\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n2?\\n27\\n27\\n27\\n27\\n27\\n27\\n2l\\n27\\n27\\n27\\n27\\n2?\\n27\\n2?\\n27\\n27\\n27\\n2?\\n27\\n27\\n27\\n71954\\n71996\\n72038\\n72081\\n72123\\n72165\\n7220^\\n72250\\n72292\\n72334\\n72376\\n72419\\n72461\\n72503\\n72545\\n72587\\n72630\\n72672\\n72714\\n72756\\n72799\\n72841\\n72883\\n72925\\n7296^\\n73010\\n73052\\n73094\\n73136\\n73 78\\n73221\\n73263\\n73305\\n7334?\\n73389\\n73431\\n73474\\n73516\\n73558\\n73606\\n73642\\n73685\\n73727\\n73769\\n73811\\n73853\\n73895\\n73938\\n73980\\n74022\\n74064\\n74106\\n74 48\\n74191\\n74233\\n74275\\n7431?\\n74359\\n7440T\\n74444\\n74486\\n2)\\nVers. D Lour. Exseo\\n418\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\nIt\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n(JO\\np. P.\\n20\\n40\\n50\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n42\\n4.2\\n4.9\\n5-\\n6.\\n7-\\n14-\\n28.3\\n35-4\\n3-3\\n4-3\\n4-7\\n9-5\\n14.2\\n19.0\\n23-7\\n9\\n4\\n10\\n4\\n20\\n9\\n30\\n13\\n40\\n18\\n50\\n22\\n21\\n2.7\\n3-2\\n3-6\\nP. P.\\n42\\n4.2\\n4.9\\n5.6\\n6.3\\n7.0\\n14.0\\n28.0\\n35-0\\n28 28\\n2.8\\n3-2\\n3-7\\n4.2\\n4-6\\n9-3\\n14.0\\n18.6\\n23 3\\n27\\n2,7\\n3-1\\n3.6\\n4.0\\n4.5\\n9.0\\n13-5\\n18.0\\n22.", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0470.jp2"}, "471": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n50\u00c2\u00b0 51\\n10\\n1 1\\n12\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLos. Vers. I 7 Lotf. Kxseo\\n9.55292\\n.55319\\n.55347\\n.55374\\n.55401\\n55428\\n55455\\n55482\\n55509\\n555^.6\\n9.55563\\n.55590\\n.55617\\n.55644\\n.55671\\n9.55698\\n.55725\\n.55751\\n\u00e2\u0080\u00a255778\\n.5580^\\n9.55832\\n.55859\\n.55886\\n\u00e2\u0080\u00a255913\\n.55940\\n9.55966\\n.55993\\n56020\\n56047\\n56074\\n9. 56101\\n.56127\\n.56154\\n.56181\\n56208\\n9.56234\\n56261\\n.56288\\n\u00e2\u0080\u00a256315\\n.56341\\n9.56368\\n56395\\n.56421\\n56448\\n.56475\\n9.56501\\n.56528\\n\u00e2\u0080\u00a256554\\n.56581\\n56608\\n9.56634\\n.56661\\n56687\\n.56714\\n.56741\\n9.56767\\n56794\\n.56826\\n.56847\\n\u00e2\u0080\u00a256873\\n9 56900\\nLotf. Vers.\\n27\\n2f\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n26\\n27\\n27\\n27\\n27\\n26\\n27\\n27\\n26\\n27\\n27\\n26\\n27\\n27\\n26\\n27\\n26\\n27\\n26\\n27\\n26\\n27\\n26\\n26\\n27\\n26\\n26\\n27\\n26\\n26\\n26\\n27\\n26\\n26\\n26\\n26\\n26\\n27\\n26\\n26\\n26\\n26\\n26\\n26\\nJ)\\nJ\\n74486\\n.74528\\n74570\\n,74612\\n74654\\n74696\\n74739\\n74781\\n74823\\n7486^\\n74907\\n74949\\n.74991\\n.75033\\n75076\\n,75118\\n75 1 60\\n,75202\\n75244\\n75286\\n75328\\n75370\\n75413\\n.75455\\n75497\\n75539\\n.75581\\n,75623\\n,7566^\\n.7570^\\n75750\\n75792\\n.75834\\n.75876\\n,75918\\n.75966\\n76002\\n.76044\\n.76086\\n,76128\\n76171\\n,76213\\n,76255\\n,76297\\n.76339\\n7638T\\n,76423\\n.76465\\n,76507\\n.76549\\n,76592\\n.76634\\n76676\\n.76718\\n.76760\\n9.76802\\n.76844\\n.76886\\n.76928\\n.76976\\n9.77012\\nliOC Kxsec I I\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\nLotf. Vers. I 7\\n9. 56900\\n56926\\n56953\\n56979\\n57005\\n57032\\n57058\\n57085\\n5711T\\n57138\\n57164\\n57196\\n57217\\n57243\\n57269\\n57296\\n57322\\n57348\\n57375\\n57401\\n57427\\n57454\\n57480\\n57506\\n57532\\n57559\\n57585\\n57611\\n5763^\\n57664\\n57690\\n57716\\n57742\\n57768\\n57794\\n57821\\n57847\\n57873\\n57899\\n57925\\n57951\\n57977\\n58003\\n58029\\n58055\\n58082\\n58108\\n58134\\n58160\\n58186\\n58212\\n58238\\n58264\\n58290\\n58316\\n58342\\n58367\\n58393\\n58419\\n5^445\\n58471\\nLotr. Vers.\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n25\\n26\\n26\\n26\\n26\\niOi;. Hxsec.l\\n9\\n77012\\n77055\\n77097\\n77139\\n77181\\n7722\\n77265\\n7730^\\n77349\\n77391\\n77433\\n77475\\n77517\\n77560\\n77602\\n77644\\n77686\\n77728\\n77770\\n77812\\n77854\\n77896\\n77938\\n77986\\n78022\\n78064\\n78107\\n78149\\n78191\\n78233\\n78275\\n78317\\n78359\\n7840T\\n78443\\n78485\\n78527\\n78569\\n7861 1\\n78653\\n78696\\n78738\\n78780\\n78822\\n78864\\n78906\\n78948\\n78996\\n79032\\n79074\\n79H6\\n79 58\\n79206\\n79242\\n79285\\n79327\\n79369\\n794 II\\n79453\\n79495\\n79537\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\nLotf. Kxsec.\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\ni2_\\n50\\n5\u00c2\u00ab\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n(iO\\nV. V\\n30\\n40\\n50\\n40\\n50\\n30\\n40\\n50\\n42 42\\n13.2\\n17-6\\n22.1\\n28.0\\n35.0\\n27 27\\n2.7\\n2.\\n3.2\\n3-\\n3-6\\n3\\n4.1\\n4.6\\n4-\\n4.\\ng.i\\n9\\n13-7\\n18.3\\n\u00c2\u00bb3-\\n18.\\n22.9\\n22.\\n2g 26\\n.6\\n3.0\\n3-4\\n3 9\\n4-3\\n17.\\n2S\\n7\\n3.0\\n8\\n3.4\\n9\\n3.8\\n10\\n4.2\\n20\\n8.5\\n30\\n12.7\\n40\\n17.0\\n50\\n21..:\\ni\u00c2\u00bb. r\\n419", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0471.jp2"}, "472": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n52\u00c2\u00b0 53\u00c2\u00b0\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\nLog. Vers.\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n58471\\n5S49?\\n58523\\n58549\\n58575\\n58601\\n58626\\n58652\\n58678\\n58704\\n58730\\n58755\\n58781\\n5880^\\n58833\\n58859\\n58884\\n58916\\n58936\\n58962\\n58987\\n59013\\n59039\\n59064\\n59096\\n59116\\n5914T\\n5916?\\n59193\\n592 1 8\\n59244\\n59270\\n59295\\n59321\\n59346\\n59372\\n5939f\\n59423\\n59449\\n59474\\n59500\\n59525\\n59551\\n59576\\n59602\\n5962^\\n59653\\n59678\\n59704\\n59729\\n59754\\n59780\\n59805\\n59831\\n59856\\n5988T\\n59907\\n59932\\n59958\\n59983\\n9 60008\\nLoj;. Vers.\\nD Log. Exsec. D\\n26\\n25\\n26\\n26\\n26\\n25\\n26\\n26\\n25\\n26\\n25\\n26\\n26\\n25\\n26\\n25\\n26\\n25\\n26\\n25\\n25\\n26\\n25\\n26\\n25\\n25\\n26\\n25\\n25\\n25\\n26\\n25\\n25\\n25\\n25\\n25\\n26\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\nD\\n79537\\n79579\\n7962T\\n79663\\n79705\\n7974^\\n79789\\n79831\\n79874\\n79916\\n79958\\n80000\\n80042\\n80084\\n80126\\n80168\\n80216\\n80252\\n80294\\n80336\\n80378\\n80426\\n80463\\n80505\\n80547\\n80589\\n80631\\n80673\\n80715\\n80757\\n80799\\n8084T\\n80883\\n80925\\n80968\\n010\\n052\\n094\\n136\\n178\\n220\\n262\\n304\\n346\\n388\\n430\\n473\\n515\\n557\\n599\\n641\\n683\\n725\\n76^\\n809\\n851\\n894\\n936\\n978\\n82020\\n82062\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\nLog. Kxsec.i 1)\\nLog. Vers.\\n9 600O8\\n60034\\n60059\\n60084\\n60IIO\\n60135\\n60166\\n60185\\n6021 I\\n60236\\n60261\\n60285\\n60312\\n60337\\n60362\\n6038^\\n60412\\n60438\\n60463\\n60488\\n60513\\n60538\\n60563\\n60589\\n60614\\n60639\\n60664\\n60689\\n60714\\n60739\\n60764\\n60789\\n60814\\n60839\\n60864\\n60889\\n60914\\n60939\\n60964\\n60989\\n014\\n039\\n064\\n089\\n114\\n139\\n164\\n189\\n214\\n239\\n264\\n289\\n313\\n338\\n363\\n388\\n413\\n438\\n462\\n48^\\n512\\nn\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n24\\n25\\n25\\n25\\n24\\n25\\n25\\n25\\n2%\\n25\\n24\\n25\\n25\\nI)\\nLog. Exsec. D\\n82062\\n82104\\n82146\\n82188\\n82236\\n82272\\n82315\\n82357\\n82399\\n82441\\n82483\\n82525\\n8256^\\n82609\\n8265T\\n82694\\n82736\\n82778\\n82820\\n82862\\n82904\\n82946\\n82988\\n83031\\n83073\\n83115\\n83157\\n83199\\n8324T\\n83283\\n83325\\n83368\\n83410\\n83452\\n83494\\n83536\\n83578\\n83626\\n83663\\n83705\\n83747\\n83789\\n83831\\n83873\\n83916\\n83958\\n84000\\n84042\\n84084\\n84126\\n84168\\n842 II\\n84253\\n84295\\n8433?\\n84379\\n84422\\n84464\\n84506\\n84548\\n84596\\nLog. Exsec.\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\nI\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n17\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n40\\n41\\n42\\n43\\n44\\np. P\\n20\\n40\\n50\\n20\\n30\\n40\\n50\\n42\\n4.2\\n4.9\\n5-6\\n6.4\\n7-1\\nM-i\\n21.2\\n28.3\\n35-4\\n7\\n3\\n8\\n3\\n9\\n3\\n10\\n4\\n20\\n8\\n30\\n13\\n40\\n17\\n50\\n21\\n26\\n25\\n16\\n20.8\\n42\\n4.2\\n4.9\\n5 6\\n6.3\\n7.0\\n14.0\\n21 .0\\n28.0\\n35-0\\n2%\\n2-5\\n3-0\\n3-4\\n3-8\\n4-2\\n8-5\\n12.7\\n17.0\\n21.2\\n24\\n2.4\\n2 8\\n3-2\\n3-7\\n4.1\\n16.\\nP. P.\\n420", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0472.jp2"}, "473": {"fulltext": "TABLE VIII, \u00e2\u0080\u0094LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n54\\nr i\\n5\\n6\\n7\\n8\\n9\\n10\\nII\\n12\\n13\\nU\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44_\\n45\\n46\\n47\\n48\\n49\\nL()!r. Vers.\\nIt\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n9.6\\n.6\\n.6\\n.6\\n.6\\n9.0\\n.6\\n.6\\n.6\\n.6\\n9.6\\n.6\\n.6\\n.6\\n.6\\n9.6\\n.6\\n.6\\n.6\\n.6\\n12\\n3\\n537\\n562\\n586\\n61T\\n636\\n661\\n685\\n716\\n735\\n760\\n784\\n809\\n834\\n858\\n883\\n908\\n932\\n957\\n982\\n9.62005\\n.62031\\n.62055\\n.62086\\n.62105\\n9.62129\\n.62154\\n.62178\\n.62203\\n.62227\\n9.62252\\n.62275\\n.62301\\n.62325\\n.62350\\n9.62374\\n.62399\\n.62423\\n.62448\\n.62472\\n9.62497\\n.62521\\n.62546\\n.62576\\n.62594\\n(JO\\n9.62619\\n.62643\\n.62668\\n.62692\\n.627 1 6\\n9.62741\\n.62765\\n.62789\\n.62814\\n.62838\\n9.62862\\n.62887\\n6291T\\n.62935\\n.62960\\n9.62984\\n24\\n25\\n24\\n25\\n24\\n25\\n24\\n25\\n24\\n25\\n24\\n24\\n25\\n24\\n25\\n24\\n24\\n24\\n25\\n24\\n24\\n24\\n25\\n24\\n24\\n24-\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\nIi08?. Kxsec. 1\\n84596\\n84632\\n84675\\n,84717\\n84759\\n8480T\\n84843\\n84886\\n84928\\n84970\\n85012\\n85054\\n85097\\n85139\\n8;i8i\\n9.85223\\n.85265\\n.85308\\n\u00e2\u0080\u00a285350\\n.85392\\n85434\\n85476\\n,85519\\n,85561\\n,85603\\n85645\\n85688\\n85730\\n,85775\\n,85814\\n9-\\n85857\\n85899\\n85941\\n85983\\n86026\\nLost. Vers.\\n,86068\\n86116\\n,86152\\n.86195\\n.86237\\n86279\\n8632T\\n86364\\n86406\\n86448\\n86496\\n86533\\n86575\\n,86617\\n86659\\n86702\\n86744\\n86786\\n.86829\\n,86871\\n86913\\n86956\\n86998\\n87046\\n87082\\n9.87125\\nLos;. Kxspr.\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\nLotf. \\\\i\\nIt I.\\n9.62984\\n\u00e2\u0080\u00a2630O8\\n.63032\\n.63057\\n.63081\\n9.63105\\n.63129\\n\u00e2\u0080\u00a263154\\n.63178\\n.63202\\n9.63226\\n.63256\\n.63274\\n.63299\\n\u00e2\u0096\u00a063323\\n9-63347\\n\u00e2\u0080\u00a263371\\n\u00e2\u0080\u00a263393\\n\u00e2\u0080\u00a263419\\n\u00e2\u0080\u00a263443\\n9.63468\\n.63492\\n.63516\\n\u00e2\u0080\u00a263540\\n\u00e2\u0080\u00a263564\\n9.63588\\n.63612\\n\u00e2\u0080\u00a263636\\n63666\\n\u00e2\u0080\u00a263684\\n9-63708\\n\u00e2\u0080\u00a263732\\n.63756\\n\u00e2\u0080\u00a263786\\n\u00e2\u0080\u00a263804\\n9.63828\\n.63852\\n.63876\\n.63900\\n.63924\\n7\\n9.63948\\n.63972\\n.63996\\n.64019\\n64043\\n9.64067\\n.64091\\n.64115\\n.64139\\n.64163\\n9.64187\\n.64216\\n.64234\\n.64258\\n.64282\\n9.64306\\n.64330\\n.64353\\n.64377\\n6440 1\\n9.64425\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n23\\n24\\n24\\n24\\n24\\n23\\n24\\n24\\n23\\n24\\n24\\n23\\n24\\n24\\n-J\\n24\\n23\\n24\\nI,Off. Vers. I,oc. Kxser\\nKxser\\nn\\nCS7125\\n87167\\n87209\\n87252\\n87294\\n87336\\n87379\\n87421\\n87463\\n87506\\n87548\\n87596\\n87633\\n87675\\n87717\\n87760\\n87802\\n87844\\n87887\\n87929\\n87971\\n88014\\n88056\\n88099\\n88141\\n88183\\n88226\\n88268\\nS8316\\n88353\\n88395\\n88438\\n88486\\n88522\\n88565\\n88607\\n88650\\n88692\\n88734\\n88777\\n88819\\n88862\\n88904\\n88947\\n88989\\n8903 T\\n89074\\n89116\\n89159\\n8920T\\n89244\\n89286\\n89329\\n8937T\\n89414\\n89456\\n89499\\n89541\\n89583\\n89626\\n89668\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n_4_\\n5\\n6\\n7\\n8\\n9\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n\u00e2\u0080\u00a220\\n21\\n2\\n23\\n24\\n-5\\n26\\n27\\n28\\n29\\n30\\n32\\n1\\n34\\n35\\n36\\n37\\n3\\n39\\n8\\n40\\n41\\n42\\n43\\n44\\ni\\n45\\n46\\n47\\n48\\n49\\n5\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n0\\nI I\\n20\\n30\\n40\\n50\\n40\\n20\\n30\\n40\\n50\\n42\\n42\\n4.9\\n5-6\\n6.4\\n7\\n14. 1\\n21 .2\\n28.3\\n35.4\\n24\\n16\\n42\\n4 a\\n4.9\\n56\\n6.3\\n7.0\\n14.0\\n21 .0\\n28.0\\n35.0\\n25\\n24\\n2 5\\n2\\n2\\n9\\n2.\\n3\\n3\\n3.\\n3\\n7\\n3.\\n4\\nI\\n4\\n8\\n3\\n8\\n12\\nS\\n12\\n16\\n6\\n16.\\n20\\n8\\n20\\n23\\n3.\u00c2\u00bb\\n3-5\\n3-9\\n7-8\\nII. 7\\n15-6\\n19.6\\nr. I\\n421", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0473.jp2"}, "474": {"fulltext": "TABLE VIIL\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n56\u00c2\u00b0 57\\n10\\nII\\n12\\n14\\n15\\n16\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n00\\nLog. Vers.\\n9.64425\\n64448\\n64472\\n64496\\n64520\\n64543\\n6456^\\n64591\\n64614\\n64638\\n64662\\n6468I\\n64709\\n64733\\n64756\\n64786\\n64804\\n6482?\\n64851\\n64875\\n64898\\n64922\\n64945\\n64969\\n64992\\nD Lost. Exsec. D\\n650I6\\n65040\\n65063\\n65087\\n651 16\\n65134\\n65157\\n65181\\n65204\\n65228\\n65251\\n65275\\n65298\\n6532T\\n65345\\n65368\\n65392\\n65415\\n65439\\n65462\\n65485\\n65509\\n65532\\n65556\\n65579\\n65602\\n65626\\n65649\\n65672\\n65696\\n65719\\n65742\\n65765\\n65789\\n65812\\n65835\\nLog. Vers.\\n23\\n24\\n23\\n24\\n23\\n24\\n23\\n23\\n24\\n23\\n23\\n24\\n23\\n23\\n24\\n23\\n23\\n23\\n24\\n23\\n23\\n23\\n23\\n23\\n24\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n89668\\n897 1 1\\n89753\\n89796\\n89838\\n89881\\n89923\\n89966\\n90OO8\\n90051\\n90094\\n90136\\n90179\\n90221\\n90264\\n903O6\\n90349\\n90391\\n90434\\n90476\\n90519\\n90561\\n90604\\n90647\\n90689\\n90732\\n90774\\n90817\\n90860\\n90902\\n90945\\n90987\\n030\\n073\\n158\\n200\\n243\\n286\\n328\\n371\\n414\\n456\\n499\\n541\\n584\\n627\\n669\\n712\\n755\\n79?\\n846\\n883\\n926\\n968\\n92011\\n92054\\n92096\\n92139\\n92182\\n92224\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n43\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n42\\n43\\n42\\n42\\n42\\n42\\n42\\n43\\n42\\n42\\n42\\n42\\n43\\n42\\n42\\n42\\n42\\n43\\n42\\n42\\n43\\n42\\n42\\n42\\n43\\n42\\n42\\n43\\n42\\n42\\n43\\n42\\n43\\n42\\n42\\n43\\n42\\n43\\n42\\n42\\nD Log. Exsec.\\nLog. Vers.\\n9.65835\\n.65859\\n.65882\\n.65905\\n.65928\\n9.65952\\n.65975\\n.65998\\n.66021\\n66044\\n9.66068\\n.66091\\n.66114\\n\u00e2\u0080\u00a266i3f\\n66 I 66\\n9.66183\\n.66207\\n.66230\\n\u00e2\u0080\u00a266253\\n.66276\\n9.66299\\n.66322\\n.66345\\n.66368\\n.6639I\\n9.66415\\n.66438\\n6646 I\\n.66484\\n.66507\\nD Log. Exsec. Z\\n9.66530\\n\u00e2\u0080\u00a266553\\n.66576\\n\u00e2\u0080\u00a266599\\n.66622\\n9.66645\\n.66668\\n.66691\\n.66714\\n\u00e2\u0096\u00a066737\\n9.66760\\n.66783\\n.66805\\n.66828\\n.66851\\n9.66874\\n.6689^\\n66926\\n.66943\\n.66966\\n9.66989\\n.67012\\n.67034\\n.6705;\\n.67086\\n9.67103\\n.67126\\n.67149\\n.67171\\n.67194\\n9.67217\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n22\\n23\\n23\\n23\\n22\\n23\\n23\\n22\\n23\\n23\\n22\\n23\\n22\\nLoe. Vers.\\nI)\\n92224\\n92267\\n92310\\n92353\\n92395\\n92438\\n92481\\n92524\\n92566\\n92609\\n92052\\n92695\\n9273?\\n92786\\n92823\\n92866\\n92909\\n92951\\n92994\\n93037\\n93080\\n93123\\n93165\\n932O8\\n9315J\\n93294\\n93337\\n93380\\n93422\\n93465\\n93508\\n93551\\n93594\\n93637\\n93680\\n93722\\n93765\\n93808\\n93851\\n93894\\n93937\\n93980\\n94023\\n94066\\n94109\\n941 51\\n94194\\n94237\\n94286\\n94323\\n94306\\n94409\\n94452\\n94495\\n94538\\n9458T\\n94624\\n9466^\\n94716\\n94753\\n94796\\nLog. Exsec. T\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n42\\n43\\n43\\n42\\n43\\n42\\n43\\n43\\n42\\n43\\n43\\n42\\n43\\n43\\n42\\n43\\n43\\n42\\n43\\n43\\n43\\n42\\n43\\n43\\n43\\n42\\n43\\n43\\n43\\n43\\n43\\n42\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n5\\n6\\n7\\n8\\n_9_\\n10\\nII\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\np. P.\\n40\\n50\\n20\\n40\\n50\\n40\\n50\\n43\\n4\\n3\\n5\\nS\\n7\\n6\\n4\\n7\\nI\\nM\\n3\\n21\\n5\\n28\\n6\\n35\\n8\\n24\\n2-4\\n2.8\\n3.2\\n3-6\\n4 o\\n16.\\n42\\n4.2\\n4.9\\n5-6\\n6.4\\n7-1\\n14. 1\\n21 .2\\n28.3\\n35-4\\n23\\n3.1\\n3-5\\n3.9\\n7-\u00c2\u00a7\\n11.7\\n19.6\\n23\\n2\\n2.3\\n2.\\n2.7\\n2.\\n3.0\\n3\\n3-4\\n3-\\n3-8\\n3.\\n7^6\\n7-\\nII-5\\nII.\\n15-3\\nT.S-\\n19.1\\n18.\\nP. p.\\n422", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0474.jp2"}, "475": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n58\u00c2\u00b0 59\\nLo:;. Vers.\\n1*\\n9\\n10\\n1 1\\n12\\n15\\ni6\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n-5\\n26\\n27\\n28\\n-9_\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n5S\\n59\\n00\\n9.67217\\n.67240\\n.67263\\n.67285\\n\u00e2\u0080\u00a267308\\n9.67331\\n.67354\\n\u00e2\u0080\u00a267376\\n.67399\\n.67422\\n9.67445\\n.67467\\n.67490\\n.67513\\n\u00e2\u0080\u00a267535*\\n9.67671\\n.67694\\n.67717\\n\u00e2\u0080\u00a267739\\n.67762\\n9.67784\\n.67807\\n\u00e2\u0080\u00a267830\\n.67852\\n\u00e2\u0080\u00a267875\\n9.67897\\n.67920\\n.67942\\n.67965\\n.67987\\n9.68010\\n.68032\\n.68055\\n.68077\\n.68 1 00\\n9.67558\\n.67581\\n.67603\\n.67626\\n.67649\\n9.68122\\n.68145\\n.68167\\n68 1 90\\n.68212\\n9.68235\\n.68257\\n.68280\\n.68302\\n\u00e2\u0080\u00a268324\\n9.68347\\n\u00e2\u0080\u00a268369\\n.68392\\n.68414\\n\u00e2\u0080\u00a268436\\n9.68459\\n.68481\\n\u00e2\u0080\u00a268503\\n.68526\\n\u00e2\u0080\u00a268548\\n9-68571\\nLoir. Vers. 1\\nLoir. Kxsec.\\n-^3\\n-3\\n22\\n23\\n22\\n23\\n22\\n23\\n22\\n23\\n22\\n22\\n22\\n22\\n23\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n-IT\\n22\\n9^94796\\n94839\\n94882\\n94925\\n94968\\n95011\\n95054\\n95097\\n95140\\n95183\\n95226\\n95269\\n95313\\n95356\\n95_399\\n95442\\n95485\\n95528\\n95571\\n95614\\n95657\\n95700\\n95744\\n95787\\n95830\\n95873\\n959 6\\n95959\\n96002\\n96046\\n96089\\n96132\\n96175\\n962 1 8\\n9626T\\n96305\\n96348\\n96391\\n96434\\n96478\\n96521\\n96564\\n96607\\n96656\\n96694\\n96737\\n96786\\n96824\\n96867\\n969 1 6\\n96953\\n96997\\n97040\\n97083\\n97127\\n97170\\n97213\\n97257\\n97300\\n97343\\n9^97387\\nIjOjf. Kxser.\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n~~Tr\\n\\\\A)\\\\i. IS.\\nIt\\n68571\\n.68593\\n,68615\\n,68637\\n,68660\\n,68682\\n,68704\\n,68727\\n,68749\\n,68771\\n68793\\n,68816\\n,68838\\n,68866\\n,68882\\n68905\\n,68927\\n68949\\n,68971\\n,68993\\n,69016\\n.69038\\n69060\\n.69082\\n.69104\\n69126\\n69149\\n691 7 1\\n,69193\\n,6921 5\\n69237\\n.69259\\n,69281\\n69303\\n,69325\\n69347\\n,69369\\n,69392\\n.69414\\n,69436\\n,69458\\n,69480\\n.69502\\n,69524\\n,69546\\n,69568\\n69590\\n,69612\\n,69634\\n,69656\\n69678\\n69700\\n,69721\\n69743\\n69765\\n9.6978^\\n69809\\n.69831\\n.69853\\n\u00e2\u0080\u00a269875\\n9 69897\\nliOsr. V rs.\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n2 2\\nO\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n22\\n21\\n22\\n2 2\\n2 2\\n^2\\n21\\nl-o::\\n9\\n10\\nK\\\\MM\\n97387\\n97430\\n97473\\n97517\\n97566\\n97603\\n97647\\n97696\\n97734\\n97777\\n97826\\n97864\\n97907\\n97951\\n97994\\n98038\\n9808 T\\n98125\\n98168\\n982 1 T\\n98255\\n98298\\n983421\\n983851\\n98429\\n98472\\n98516\\n98559\\n98603\\n98647\\n98696\\n98734\\n98777\\n98821\\n98864\\n98908\\n98952\\n98995\\n99039\\n99082\\n99126\\n99170\\n99213\\n99257\\n99300\\n99344\\n99388\\n99431\\n99475\\n995 9\\n99562\\n99606\\n99650\\n99694\\n99737\\n99781\\n99825!\\n99868!\\n99912\\n99956\\n00000 I\\nKxsHr.\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n44\\n43\\n43\\n43\\n43\\n43\\n43\\n43\\n44\\n43\\n43\\n43\\n43\\n44\\n43\\n43\\n43\\n44\\n43\\n43\\n44\\n43\\n43\\n44\\n43\\n44\\n43\\n44\\n43\\n43\\n44\\n43\\n44\\nTT\\n4\\n5\\n6\\n7\\n8\\n_9\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24_\\n25\\n26\\n27\\n28\\n30\\n31\\n32\\n35\\n36\\n37\\n38\\n39\\n40\\n4\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n:a)\\n51\\n52\\n53\\n5-+_\\n55\\n56\\n57\\n58\\n59\\n0\\nv. V.\\n20\\n30\\n40\\nso\\n40\\n50\\n30\\n40\\n50\\n44\\n4.4\\n4-\\n5-1\\n5\\n5.8\\n6.6\\n5\\n6\\n7.3\\n7\\nM.6\\n14.\\n22.\\n21\\n29.3\\n36.6\\n29.\\n36\\n43\\n43\\n6\\n4 3\\n7\\n5.0\\n8\\n5 7\\n9\\n6 4\\n10\\n7-1-\\n20\\n14 3\\n30\\n21-5\\n40\\n28.6\\n50\\n35. 8\\n23\\n2.3\\n2.7\\n3^o\\n19.\\n22\\n2.2\\n2.6\\n15.0\\n18.7\\n22\\n21\\n32\\n3-6\\n7-1\\n10.7\\n14.3\\n17.9\\n423", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0475.jp2"}, "476": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n60\u00c2\u00b0 61\u00c2\u00b0\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n26\\n27\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLog. Vers,\\n9.69897\\n.69919\\n69946\\n69962\\n.69984\\n9 -70005\\n70028\\n70050\\n.70072\\n70093\\n9-70115\\n.70137\\n.70159\\n.70181\\n.70202\\nD\\n9.70224\\n70246\\n.70268\\n.70289\\n.70311\\n9-70333\\n\u00e2\u0080\u00a270355\\n.70376\\n70398\\n.70420\\n9.70441\\n.70463\\n.70485\\n.70507\\n\u00e2\u0080\u00a270528\\n9.70550\\n.70572\\n70593\\n.70615\\n70636\\n9.70658\\n70680\\n.70701\\n.70723\\n.70745\\n9.70765\\n.70788\\n70809\\n.70831\\n.70852\\n9.70874\\n.70896\\n.7091^\\n.70939\\n70966\\n9.70982\\n.71003\\n.71025\\n.71045\\n.71068\\n9.71089\\n.71III\\n.71132\\n.71154\\n.71175\\n9.71197\\nLog. Vers.\\n22\\n21\\n22\\n22\\n22\\n21\\n22\\n22\\n21\\n22\\n21\\n22\\n22-\\n21\\n22\\n21\\n22\\n21\\n22\\n21\\n22\\n21\\n22\\n21\\n21\\n22\\n21\\n22\\n21\\n21\\n22\\n21\\n21\\n21\\n22\\n21\\n21\\n21\\n22\\n21\\n21\\n21\\n21\\n21\\n22\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\nLog. F.xsec.\\n10.00000\\n00044\\n.0008^\\n.00131\\n00 1 7 5\\nI o 002 1 9\\n.00262\\n.00305\\n.00356\\n.00394\\n10.00438\\n.00482\\n.00525\\n.00569\\n006 1 3\\nD Log. Vers. D\\n10.00657\\n.00701\\n.00745\\n.00789\\n.00833\\n10.00875\\n00926\\n00964\\n.oioog\\n.01052\\n10.01 095\\n.01 146\\n.oi 184\\n.OI228\\n.01272\\nIO.OI315\\n.01366\\n.01404\\n\u00e2\u0080\u00a2OI448\\n.01492\\n10.01535\\n.01586\\n.01624\\n.01668\\n.01712\\n10.01755\\n.01806\\n.01844\\n.01889\\n.01933\\n10.01977\\n.02021\\n.02065\\n.02109\\n.02153\\n10.02197\\n.02242\\n.02286\\n.02330\\n.02374\\n1 0.024 1 8\\n.02463\\n.02507\\n.02551\\n.02595\\n10.02639\\nJ Log. Exsec.\\n44\\n43\\n44\\n43\\n44\\n43\\n44\\n44\\n43\\n44\\n44\\n43\\n44\\n44\\n44\\n43\\n44\\n44\\n44\\n43\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n197\\n218\\n239\\n261\\n282\\n304\\n325\\n346\\n368\\n389\\n411\\n432\\n453\\n475\\n496\\n51?\\n539\\n566\\n581\\n603\\n624\\n645\\n667\\n688\\n709\\n730\\n752\\n773\\n794\\n815\\n^1 7\\n858\\n879\\n906\\n922\\n71943\\n71964\\n71985\\n72005\\n72028\\n72049\\n72070\\n7209T\\n721 12\\n72133\\n72154\\n72176\\n72197\\n72218\\n72239\\n72266\\n72281\\n72302\\n72323\\n72344\\n72365\\n72386\\n72408\\n72429\\n72450\\n72471\\nI) I Loff. Vers.\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\nLog. Exsec.\\n10.02639\\n.02684\\n.02728\\n.02772\\n.02815\\n10.02861\\n.02905\\n.02949\\n.02994\\n.03038\\n10.03082\\n.03127\\n.03171\\n.03215\\n.03260\\n10.03304\\n\u00e2\u0080\u00a203348\\n.03393\\n\u00e2\u0080\u00a20343^\\n.03481\\n10.03526\\n.03576\\n.03615\\n.03659\\n.03704\\nI0.03748\\n-03793\\n.03837\\n.03881\\n.03926\\nn\\n10.03970\\n040 1 5\\n.04059\\n.04104\\n.04149\\n10.04193\\n.04238\\n.04282\\n.04327\\n-04371\\n10.04416\\n0446 I\\n.04505\\n.04550\\n-04594\\n10.04639\\n04684\\n.04728\\n.04773\\n.04818\\n10.04862\\n.0490^\\n.04952\\n.04995\\n.05041\\n10.05086\\n.05131\\n.05175\\n,05226\\n.05265\\n10.05310\\nI)\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n44\\n45\\n44\\n44\\n44\\n44\\n44\\n44\\n45\\n44\\n44\\n44\\n45\\n44\\n44\\n44\\n45\\n44\\n45\\n44\\n44\\n45\\n44\\n45\\n44\\n45\\n44\\n45\\n10\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nLog. Exsec. 1\\nGO\\n40\\n50\\n40\\n50\\np. P.\\n45\\n4-5\\n5-2\\n6.0\\n6.7\\n7-5\\n20\\nT5.0\\n30\\n22.5\\n40\\n30.0\\n50\\n37-5\\n44\\n4.4\\n5-i\\n5-8\\n6.6\\n7-3\\n14-6\\n29-3\\n36.6\\n44\\n4.4\\n5-2\\n5.9\\n6.7\\n7-4\\nM-8\\n22.2\\n29-6\\n37.1\\n43\\n4-3\\n5-1\\n5-8\\n6.5\\n7.2\\n14.5\\n21.7\\ng.o\\n36.2\\n22\\n21\\n2.2\\n2.\\n2-5\\n2.\\n2.9\\n2\\n3-3\\n3-\\n,3-6\\n3\\n^7-3\\n7-\\nII.\\n10.\\n14.6\\n14.\\n18.3\\n17-\\n^.6\\nI\\n7\\n3\\n9\\n21\\n20\\n30\\n40\\n50\\nP. P.\\n424", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0476.jp2"}, "477": {"fulltext": "TABLE VIII.-L0GARITHM;C VERSED SINES AND EXTERNAL SECANTS\\n63\u00c2\u00b0 63\u00c2\u00b0\\n10\\nII\\n12\\n13\\n14\\nLop. Vers. I 7\\n9.72471\\n.72492\\n\u00e2\u0080\u00a272513\\n\u00e2\u0080\u00a272534\\n.72555\\n9.72576\\n.72597\\n.72618\\n.72639\\n.72660\\n15\\n16\\n17\\n18\\n19\\n9.72681\\n.72701\\n.72722\\n.72743\\n.72764\\n9.72785\\n.72806\\n.72S2J\\n.72848\\n.72869\\n9.72890\\n.7291 I\\n.72931\\n.72952\\n.72973\\n9.72994\\n.73015\\n\u00e2\u0080\u00a273036\\n.73057\\n\u00e2\u0080\u00a273077\\n9.73098\\n\u00e2\u0080\u00a273119\\n.73140\\n.73161\\n.73181\\n9.73202\\n.73223\\n\u00e2\u0080\u00a273244\\n\u00e2\u0080\u00a273265\\n\u00e2\u0080\u00a273285\\n9-73306\\n\u00e2\u0080\u00a273327\\n.73348\\n.73368\\n\u00e2\u0080\u00a273389\\n9-734IO\\n.73430\\n\u00e2\u0080\u00a273451\\n\u00e2\u0080\u00a273472\\n\u00e2\u0080\u00a273493\\n9-73513\\n\u00e2\u0080\u00a273534\\n\u00e2\u0080\u00a273555\\n.73575\\n\u00e2\u0080\u00a273596\\n,73617\\n.7363^\\n73( S^\\n73679\\n73699\\n9.73720\\nLoer. Vers.\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n2r\\n20\\n21\\n21\\n21\\n21\\n21\\n21\\n20\\n21\\n21\\n21\\n20\\n21\\n21\\n21\\n20\\n21\\n21\\n20\\n21\\n21\\n20\\n21\\n26\\n21\\n21\\n20\\n21\\n20\\n21\\n26\\n21\\n20\\n21\\n20\\n20\\n21\\n20\\n21\\n20\\n20\\n21\\n20\\n26\\n21\\n20\\n26\\n21\\n20\\n26\\nLoir. Kxsec J\\n10.05310\\n\u00e2\u0080\u00a205354\\n\u00e2\u0080\u00a205399\\n\u00e2\u0080\u00a205444\\n.05489\\n10.05534\\n.05579\\n\u00e2\u0080\u00a205623\\n.03668\\n.05713\\nI0.05758\\n.05803\\n.05848\\n.05893\\n.05938\\n10.05983\\n.06028\\n.06072\\n06 1 1\\n.06162\\n10.06207J\\n.0625^\\n44\\n45\\n45\\n44\\n45\\n45\\n44\\n45\\n45\\n45\\n44\\n45\\n45\\n45\\n45\\n45\\n44\\n45\\n45\\n.06297\\n.06342\\n.0638^\\n10.06432\\n.0647^\\n.06522\\n.06568\\n.06613\\n10.06658\\n.06703\\n.06748\\n\u00e2\u0080\u00a206793\\n.06838\\n10.06883\\n.06928\\n.06974\\n.07019\\n07064\\n10,07109\\n.07154\\n.07200\\n.07245\\n.07290\\n10.0733$\\n\u00e2\u0080\u00a207380\\n.07426\\n.07471\\n.07516\\n10.07562\\n.07607\\n.07652\\n.0769^\\n\u00e2\u0080\u00a207743\\n10.07788\\n.07834\\n.07879\\n\u00e2\u0080\u00a207924\\n.07970\\n10.08015\\niOir. Kxs\u00c2\u00ab c.l\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\nLoj?. Vers. I 1*\\n9.73720\\n.73740\\n.73761\\n\u00e2\u0080\u00a273782\\n.73802\\n9.73823\\n.73843\\n.73864\\n\u00e2\u0080\u00a27? ^H\\n.73905\\n9.73926\\n.73946\\n.73967\\n.73987\\n74008\\n).74028\\n74049\\n74069\\n74090\\n.74110\\n.74i3i\\n.74151\\n.74172\\n.74192\\n.74213\\n9.74233\\n.74254\\n.74274\\n.74294\\n.74315\\n9-74335\\n\u00e2\u0080\u00a274356\\n\u00e2\u0080\u00a275376\\n\u00e2\u0080\u00a274396\\n.74417\\n9-74437\\n.74458\\n.74478\\n74498\\n\u00e2\u0080\u00a274519\\n9^74539\\n\u00e2\u0080\u00a274559\\n.74580\\n74606\\n.74626\\n9.74641\\n.74661\\n.74681\\n.74702\\n.74722\\n9.74742\\n\u00e2\u0080\u00a274762\\n\u00e2\u0080\u00a274783\\n\u00e2\u0080\u00a274803\\n\u00e2\u0080\u00a274823\\n9.74844\\n.74864\\n\u00e2\u0080\u00a2748S4\\n.74904\\n\u00e2\u0080\u00a274924\\n20\\nI 26\\n21\\nI 26\\n26\\nI\\n26\\n26\\n21\\n20\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n20\\n26\\n20\\n26\\n26\\n26\\n26\\n26\\n20\\n26\\n26\\n26\\n20\\n26\\n26\\n20\\n20\\n26\\n26\\n20\\n26\\n26\\n20\\n26\\n20\\n26\\n20\\n26\\n26\\n20\\n26\\n20\\n26\\n20\\n20\\n26\\nLop. Kxsec.\\n10.0801 5\\n0806 I\\n08 1 06\\n.08151\\n.08197\\n10.08242\\n.0S288\\n\u00e2\u0080\u00a208333\\n\u00e2\u0096\u00a008379\\n,08424\\n10.08470\\n\u00e2\u0080\u00a208515\\n,08561\\n.08605\\n.08652\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n10.08697\\n.08743\\n,08789\\n.08834\\n.08880\\n10.08926\\n.08971\\n.09017\\n,09062\\n-09I08\\n10.09154\\n09200\\n.09245\\n,09291\\n-09337\\n10.09382\\n.09428\\n\u00e2\u0080\u00a209474\\n,09520\\n.09566\\nI0.096IT\\n\u00e2\u0080\u00a20965?\\n09703\\n09749\\n.09795\\n10.09841\\n.09886!\\n.09932!\\n\u00e2\u0096\u00a00997 8:\\n10024\\n10. 10070\\n.10116\\n10162\\nI0208|\\n10254\\n10. 10300\\n.10346\\n.10392\\n.10438\\n10484\\n10. 10530\\n\u00e2\u0080\u00a2I0576\\n10622\\n10668\\n,10714\\n9.74945 10. 10766\\nLoi. .Vors. ILocr. Kxsfr.l\\n425\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n45\\n46\\n45\\n45\\n45\\n46\\n45\\n45\\n45\\n46\\n45\\n46\\n45\\n45\\n46\\n45\\n46\\n46\\n45\\n46\\n45\\n46\\n46\\n45\\n46\\n46\\n45\\n46\\n46\\n46\\n46\\n46\\n46\\n45\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n5\\n6\\n7\\n8\\n_9\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\nI I\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\nJ3\\n36\\n37\\n38\\n39\\n52\\n55\\n56\\n57\\n58\\n59\\n0\\n20\\n40\\n5^\\n30\\n40\\n50\\n20\\n30\\n40\\n50\\n48 46\\n5-4\\n6 2\\n7 o\\n7-7\\n\u00c2\u00ab5-S\\n23.2\\n31.0\\n38.7\\n6 f\\n6.9\\n7 h\\n\u00c2\u00ab5-3\\n23.0\\n30 6\\n38 3\\n45\\n4-5\\n5-3\\n6 o\\n6 8\\n7 6\\n15 I\\n22.7\\n30-3\\n37-9\\n45\\n4-.S\\n5 2\\n6.0\\n6.7\\n7-5\\n150\\n22 5\\n30.0\\n37 5\\n30\\n40\\n50\\n44\\n4-4\\n5 2\\n5 9\\n6 7\\n7 4\\n4. a\\n22.2\\n29-6\\n37 1\\n21\\n2 4\\n2 8\\n31\\n3\\n10.\\nij,\\n7\\n20\\n20\\n6\\n2,0\\n7\\n8\\n\u00e2\u0080\u00a23\\n2-6\\n9\\n3^o\\n10\\n30\\n3-3\\n6-6\\n30\\n10.0\\n40\\n\u00e2\u0080\u00a23 3\\n50\\n16.6\\nI r.", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0477.jp2"}, "478": {"fulltext": "TABLE VIII. LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n64\\n65\\n10\\nII\\n12\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n60\\n51\\n52\\n53\\n54\\nLog. Vers.\\n55\\n56\\n57\\n58\\n59\\n60\\n9-74945\\n74965\\n74985\\n75005\\n75026\\n75046\\n75066\\n75086\\n75106\\n75126\\n75147\\n75167\\n75187\\n75207\\n7522^\\nn Los\\n7524?\\n7526^\\n75287\\n75308\\n75328\\n75348\\n75368\\n75388\\n75408\\n75428\\n75448\\n75468\\n75488\\n75508\\n75528\\n75548\\n75568\\n75588\\n75608\\n75628\\n75648\\n75668\\n75688\\n75708\\n75728\\n75748\\n75768\\n75788\\n75808\\n75828\\n75848\\n75868\\n75888\\n75908\\n75928\\n75947\\n7596^\\n75987\\n76007\\n76027\\n76047\\n76067\\n76087\\n76 log\\n76126\\n76146\\nLog. Vers.\\n20\\n26\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n26\\n20\\n20\\n20\\n20\\n20\\n26\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n19\\n20\\n20\\n20\\n20\\n20\\n19\\n20\\n20\\n20\\n19\\n20\\n20\\n20\\n19\\n20\\n20\\nZ\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\nLog\\nExsec.\\n0766\\n0807\\n0853\\n0899\\n0945\\n0991\\ni03f\\n1084\\n1 1 30\\nIJ76\\n1222\\n1269\\n1315\\n1 361\\n1407\\n1454\\n1506\\n1546\\n1593\\n1639\\n1685\\n1732\\n1778\\n1825\\n187T\\nJD\\nI Log. Vers.\\n191^\\n1964\\n2010\\n2057\\n2103\\n2150\\n2196\\n2243\\n2289\\n2336\\n2383\\n2429\\n2476\\n2522\\n2569\\n2616\\n2662\\n2709\\n2756\\n2802\\n2849\\n2896\\n2942\\n2989\\n3036\\n3083\\n3130\\n3170\\n3223\\n3270\\n3317\\n3364\\n341 1\\n345^\\n3504\\n3551\\nExsec.\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n4g\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n46\\n47\\n46\\n46\\n46\\n46\\n47\\n46\\n46\\n47\\n46\\n46\\n47\\n46\\n47\\n46\\n47\\n47\\n46\\n47\\n46\\n47\\n47\\n47\\n46\\n47\\n47\\n9.76146\\n.76166\\n.76186\\n.76206\\n.76225\\n9.76245\\n.76265\\n.76285\\n76304\\n.76324\\n9.76344\\n76364\\n.76384\\n.76403\\n.76423\\n9.76443\\n.76463\\n.76482\\n.76502\\n.76522\\n9.76541\\n.76561\\n.76581\\n76606\\n.76626\\n9 76640\\n.76659\\n.76679\\n.76699\\n.76718\\nX)\\n9.76738\\n.76758\\n.7677^\\n.76797\\n.76817\\n9.76836\\n.76856\\n.76875\\n.76895\\n.76915\\n9.76934\\n.76954\\n.76973\\n76993\\n.77012\\n9.77032\\n.77052\\n.77071\\n.77091\\n.77116\\n9.77130\\n.77149\\n.77169\\n.77188\\n.77208\\n9.7722^\\n.77247\\n.77266\\n.77286\\n\u00e2\u0080\u00a277305\\n9.77325\\nLog. Vers.\\n19\\n20\\n20\\n19\\n20\\n19\\n20\\n19\\n20\\n20\\n19\\n20\\n19\\n20\\n19\\n20\\n19\\n19\\n20\\n19\\n20\\n19\\n19\\n20\\n19\\n19\\n20\\n19\\n19\\n20\\n19\\n19\\n19\\n20\\n19\\n19\\n19\\n20\\n19\\n19\\n19\\n19\\n19\\n19\\n20\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\nLog\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\nLog\\nExsec.\\n3551\\n3598\\n3645\\n3692\\n3739\\n3786\\n3833\\n3886\\n392?\\n3974\\nD\\n4021\\n4068\\n4115\\n4162\\n4210\\n4257\\n4304\\n4355\\n4398\\n4445\\n4493\\n4540\\n4587\\n4634\\n4682\\n4729\\n4776\\n4823\\n4871\\n491 8\\n4965\\n5013\\n5066\\n5108\\n5155\\n5202\\n5250\\n529?\\n5345\\n5392\\n5440\\n548^\\n5535\\n5582\\n5630\\n5678\\n5725\\n5773\\n5826\\n5868\\n5916\\n5963\\n601 1\\n6059\\n6106\\n6154\\n6202\\n6250\\n6298\\n6345\\n6393\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\n47\\nAl\\n47\\n47\\n47\\n4f\\n47\\nAl\\nA7\\n47\\n4?\\nAl\\nA7\\nAl\\n47\\n4?\\nAl\\n47\\nAl\\nAl\\nAl\\n47\\nAl\\nAl\\nAl\\nAl\\nAl\\nAl\\nAl\\nAl\\nAl\\nAl\\n48\\nAl\\nAl\\nAl\\n48\\nAl\\nAl\\n48\\n47\\nAl\\n48\\nAl\\n48\\n48\\nAl\\n48\\nIT\\n20\\np. p.\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n20\\n40\\n50\\n40\\n50\\n20\\n30\\n40\\n50\\n48\\n4.8\\n5-6\\n6.4\\n7.2\\n8.0\\n16.0\\n24.0\\n32.0\\n40.0\\n47\\n4-7\\n5.5\\n6.2\\n7.0\\n7.8\\n15-6\\n23.5\\n3i\u00c2\u00a7\\n39.1\\n20\\n47\\n4-7\\n5-5\\n6.3\\n7.1\\n7-9\\n15. a\\n23 -7\\n31-6\\n39-6\\n46\\n4.6\\n5.4\\n6.2\\n7.0\\n7.7\\n15-5\\n23.2\\n31.0\\n38.7\\n46\\n6\\n4.6\\n7\\n8\\n5-3\\n6,1\\n9\\n6.9\\n10\\n7-6\\n20\\n15-3\\n30\\n23.0\\n40\\n50\\n30-6\\n38.3\\n20\\n2.0\\n2-3\\n2-6\\n3.0\\n3.3\\n6.6\\n10. o\\n3-3\\n16.6\\n19\\n6\\n1\\n9\\n7\\n8\\n2\\n2\\n3\\n6\\n9\\n2\\n9\\n10\\n3\\n2\\n20\\n6\\n5\\n30\\n9\\n7\\n40\\n50\\n13\\n16\\n2\\nP. p.\\n426", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0478.jp2"}, "479": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\nG6\\n07\u00c2\u00b0\\nLos. Vers.\\n10\\nII\\n12\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n-3\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n77325\\n77344\\n77363\\n77383\\n77402\\n77422\\n77441\\n77461\\n77480\\n774Q9\\n775 9\\n77538\\n7755?\\n77 S9G\\n77616\\n77635\\n77654\\n77674\\n77693\\n77712\\n77732\\n77751\\n77770\\n77790\\n77809\\n77828\\n77847\\n77867\\n77886\\n77905\\n77925\\n77944\\n77963\\n77982\\n78002\\n78021\\n78040\\n78059\\n78078\\n78098\\n78117\\n78136\\n78155\\n78174\\n78194\\n78213\\n78232\\n78251\\n78276\\n78289\\n78309\\n78328\\n78347\\n78366\\n78385\\n78404\\n78423\\n78442\\n78462\\n9-78481\\nLoe. Vers,\\nJ\\nLoK\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n1) I -OK\\n10\\n10\\nxsec. 7\\n6393\\n644 T\\n6489\\n6537\\n6585\\n6633\\n6680\\n6728\\n6776\\n6824\\n6872\\n6926\\n6968\\n7016\\n7064\\n71 12\\n7 1 661\\n7209*\\n72571\\n7305\\n7353\\n7401\\n7449\\n7498,\\n7546I\\n7594\\n7642\\n7696\\n7739\\n778?\\n7835\\n7884\\n7932\\n7986\\n8029\\n807?\\n8126\\n8174\\n8222\\n8271\\n8319\\n8368\\n8416\\n8465\\n8514\\n8562\\n861 1\\n86:^9\\n8708\\n8757\\n8805\\n8854\\n8903\\n895T\\n9006\\n9049\\n9098\\n9146\\n91951\\n92441\\n9293!\\n48\\n47\\n48\\n48\\n48\\n4?\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n48\\n49\\n48\\n48\\n48\\n48\\n48\\n49\\n48\\n48\\n49\\n48\\n49\\n48\\n49\\n48\\n49\\n49\\n48\\nliOjf. Vers.\\n9.78481\\n78500\\n78519\\n78538\\n78557\\n78576\\n78595\\n78614\\n78633\\n78652\\n78671\\n78696\\n78709\\n78728\\n7874?\\n78766\\n78785\\n78804\\n78823\\n78842\\n78861\\n78886\\n78899\\n789I8\\n78937\\n78956\\n78975\\n78994\\n79013\\n79032\\n79051\\n79069\\n79088\\n79107\\n79126\\n79145\\n79164\\n79183\\n79202\\n79226\\n79239\\n79258\\n79277\\n79296\\n79315\\n79333\\n79352\\n79371\\n79390\\n79409\\n7942?\\n79446\\n79465\\n79484\\n79503\\n79521\\n79540\\n79559\\n79578\\n79596\\n0.79615\\n7 liOi:. Vers.\\n\\\\avj:\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n8\\n9\\n9\\n9\\n9\\n9\\n9\\n8\\n9\\n9\\n9\\n9\\n8\\n9\\n9\\n8\\n9\\n9\\n8\\n9\\n9\\n8\\n9\\n9\\n8\\n9\\n8\\n9\\n9\\n8\\n9\\n8\\n9\\n8\\n9\\n8\\n9\\nTT\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\nK\\\\scc\\n\u00e2\u0080\u00a29293\\n19342\\n1 939 1\\n19439\\n19488\\n19537\\n19586\\n19635\\n19684\\n19733\\n19782\\n1983T\\n19886\\n19929\\n19979\\n20028\\n20077\\n20126\\n20175\\n20224\\n20273\\n20323\\n20372\\n2042!\\n20476\\n20520\\n20569\\n206 18\\n20668\\n2071^\\n20767\\n20816\\n20865\\n20915\\n20964\\n014\\n063\\n113\\n162\\n212\\n262\\n3\\n361\\n416\\n466\\n510\\n560\\n609\\n659\\n709\\n759\\n808\\n858\\n908\\n958\\n22008\\n22058\\n22108\\n221581\\n22208\\n22258I\\nKxser.\\n49\\n49\\n48\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n49\\n50\\n49\\n49\\n49\\n49\\n50\\n49\\n50\\n49\\n50\\n49\\n50\\n49\\n50\\n50\\n49\\n50\\n50\\n50\\n50\\n50\\n50\\nIt\\n10\\nI\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n\u00c2\u00b19\\noO\\n51\\n52\\n53\\n55\\n^6\\n57\\n58\\n59\\n;o\\n20\\n30\\n40\\n50\\n6\\n7\\n8\\nq\\n10\\n20\\n30\\n40\\n50\\n20\\n30\\n40\\n50\\nI 1*\\n49\\n4.6\\n5-6\\n6.4\\n7.2\\n8.0\\n16 o\\n24 o\\n32 o\\n40.0\\n19\\n6\\n1.9\\n7\\n2-3\\n8\\n2.6\\n9\\n2.9\\n10\\n3.2\\n20\\n6.5\\n30\\n9-7\\n40\\n13.0\\nSO\\n16.2\\n48\\n4.9\\n4-\\n5-7\\n6 5\\n5-\\n6.\\n7-3\\n8 i\\n7-\\n8\\n.6.3\\n16.\\n24-5\\n24\\n32 6\\n3\u00c2\u00ab\\n40-8\\n40.\\n48 4^\\n4-7\\n5-5\\n6.3\\n71\\n7-9\\n5-8\\n23.7\\n3\u00c2\u00bb-6\\n39-6\\n19\\n1.9\\n3.2\\n2-5\\n2 8\\n3-\u00c2\u00bb\\n6.3\\n9-5\\n12 6\\n5-8\\nIB\\n6\\n1\\n7\\n2\\nI\\n8\\n3\\n4\\n9\\n3\\n8\\n10\\n3\\nX\\n20\\n6\\nI\\n30\\n9\\n3\\n40\\n13\\nJ\\n50\\n15\\n4\\n50\\n49\\n5-0\\n5-8\\n6.6\\n4.9\\n5-8\\n6 6\\n7-\\n8.3\\n7-4\\n8.2\\n.6.6\\n16.5\\n25.0\\n24 7\\n33 3\\n33-0\\n4 6\\n41.2\\nI r.\\n427", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0479.jp2"}, "480": {"fulltext": "TABLE VIIL\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n68\u00c2\u00b0 09\u00c2\u00b0\\n10\\nII\\n12\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n23\\n24\\n^3\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLosj. Ters. I Loe. Exsec; D\\n9.7961S\\n\u00e2\u0080\u00a279634\\n\u00e2\u0080\u00a279653\\n.79671\\n.79690\\n9.79709\\n.7972?\\n\u00e2\u0080\u00a279746\\n.79765\\n\u00e2\u0080\u00a2797S3\\n9.79802\\n.79821\\n\u00e2\u0080\u00a279839\\n.79858\\n.79877\\n9.79893\\n.79914\\n\u00e2\u0096\u00a079933\\n\u00e2\u0080\u00a279951\\n.79970\\n9^79988\\n80007\\n80026\\n.80044\\n.8006^\\n9.80081\\n.80106\\n.80119\\n.8013^\\n.80156\\n9.80174\\n.80193\\n,80211\\n.80230\\n80248\\n9.80267\\n.80286\\n80304\\n\u00e2\u0080\u00a280323\\n.80341\\n9.80360\\n\u00e2\u0080\u00a280378\\n.80397\\n.80415\\n80434\\n9.80452\\n80470\\n80489\\n.8050^\\n.80526\\n9.80544\\n.80563\\n.80587\\n.80600\\n.80618\\n9.80636\\n.80655\\n\u00e2\u0080\u00a280673\\n80692\\n.80710\\n9.80728\\nLog. Vers.\\n18\\n19\\n18\\n18\\n19\\n18\\n19\\n18\\n18\\n19\\n18\\n18\\n19\\n18\\n18\\n18\\n19\\n18\\n18\\n18\\n19\\n18\\n18\\n18\\n18\\n19\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n19\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\n18\\nJ8\\n18\\n18\\n18\\n18\\n10\\n.222581\\n.223081\\n.223581\\n.224081\\n.22458\\n10\\n225081\\n22558!\\n22608\\n22658\\n227O8\\n10.\\n22759\\n22809\\n22859\\n22909\\n22960\\n10.\\n23010\\n23066\\n231 15\\n23161\\n23211\\n10\\n23262\\n23312\\n23362\\n23413\\n23463\\n10.\\n23514\\n23564\\n23615\\n23666\\n23716\\n10\\n23767\\n23817\\n23868\\n23919;\\n239691\\n10.\\n24020\\n24071\\n24122\\n24172\\n24223\\n10.\\n24274\\n24325\\n24376\\n24427\\n24478\\n10.\\n24529\\n24580\\n24631\\n24682\\n24733\\n10.\\n24784\\n24835\\n24886\\n24937\\n24988\\n10.\\n25039\\n25096\\n25142\\n25193\\n25244\\n10.25295\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n50\\n51\\n50\\n50\\n51\\n50\\n51\\n50\\n51\\n51\\n50\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\nTers.! D\\n80728\\n80747\\n80765\\n80783\\n80802\\n80826\\n80839\\n80857\\n80875\\n80S94\\n80912\\n80936\\n80949\\n80967\\n80985\\n003\\n022\\n046\\n058\\n077\\n095\\n113\\n131\\n150\\n168\\n186\\n204\\n223\\n241\\n259\\n27^\\n295\\n314\\n332\\n350\\n368\\n386\\n405\\n423\\n441\\n459\\n477\\n495\\n513\\n532\\n550\\n568\\n586\\n604\\n622\\n646\\n658\\n6/6\\n695\\n713\\n72)^\\n749\\n767\\n785\\n803\\n8182T\\nLog. Exseo.; jf\\n10\\n25295\\n25347\\n25398\\n25449\\n25501\\n10.\\n25552\\n25604\\n25655\\n25707\\n25758\\n10\\n25810\\n25861\\n25913\\n25964\\n26016\\n10\\n2606^\\n26 II 9\\n2617 1\\n26222\\n26274\\n10\\n26326\\n26378\\n26429\\n26481\\n26533\\n10\\n26585\\n26637\\n26689\\n26741\\n26793\\n7 Log. Kxsec i D Log. Vers. 7)\\n428\\n10\\n26845\\n26897\\n26949\\n27001\\n27053\\n10\\n,27105\\n,2715^\\n27209\\n27261\\n27314\\n10\\n27366\\n274I8\\n27476\\n27523\\n2757?\\n10\\n2262^\\n27680\\n27732\\n27785\\n2783?\\n10.\\n27890\\n27942\\n27995\\n2804^\\n28100\\n10.28152\\n.28205\\n.28258\\n.28316\\n.28363\\n10.28416\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n51\\n52\\n51\\n51\\n52\\n51\\n52\\n51\\n52\\n52\\n52\\n51\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n52\\n5-\\n53\\n52\\n52\\n53\\n52\\nLog. Exsec. 1\\n10\\n1 1\\n12\\n13\\n14.\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\np. P\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n40\\n50\\n20\\n30\\n40\\n50\\n20\\n30\\n40\\n50\\n20\\n30\\n40\\n50\\n53 52\\n5.3\\n6.2\\n7.0\\n7.9\\n8.8\\n17-6\\n26.5\\n35-3\\n44.1\\n52\\n5.2\\n6.0\\n6. a\\n7.8\\n8.6\\n17^3\\n26.0\\n34-6\\n43 3\\n51\\n51\\n5-9\\n6.8\\n7-6\\n8.5\\n17.0\\n25.5\\n34-0\\n42.5\\n5.2\\n3.1\\n7.0\\n7.0\\n8.7\\n17-5\\n26.2\\nSS-o\\n43 7\\n51\\n5-1\\n6.0\\n6-8\\n.7-7\\n8.6\\n25-7\\n34^3\\n42.9\\n50\\n5-0\\n5^0\\n6.7\\n7.6\\n8.4\\n16.8\\n25.2\\n33- 6\\n42.1\\n20\\n30\\n40\\n50\\n50\\n5-0\\n16.6\\n25.0\\n33.3\\n41-6\\n19\\nI\\n1.9\\n1.\\n2.2\\n2.\\n2-5\\n2-\u00c2\u00a7\\n2.\\n2.\\n3-1\\n6.3\\n3^\\n6.\\n9-5\\n12.6\\n0.\\n12.\\n^5-1\\n^5-\\n18\\n7\\n2.\\n8\\n2.\\n9\\n2.\\n10\\n3-\\n20\\n6.\\n30\\n9^\\n40\\n12.\\n50\\n15-\\nP. p.", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0480.jp2"}, "481": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\no\\n71\\ni6\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n-5\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n:)5\\n56\\nhi\\n58\\n59\\n0\\nLojf. Vers. I\\n9.8182I\\n.81839\\n.81857\\n.81875\\n.81893\\n9 8 1 9 1 1\\n.81929\\n.81947\\n.8196I\\n.81983\\n9.82001\\n.S2019\\n.82037\\n.82055\\n.82073\\n9.82091\\n.82109\\n.82127\\n.82145\\n.82163\\n9.82449\\n.82467\\n.82485\\n.82503\\n.82526\\n9-82538\\n\u00e2\u0080\u00a282556\\n\u00e2\u0080\u00a282574\\n\u00e2\u0080\u00a282592\\n.82609\\n9.82627\\n\u00e2\u0080\u00a282645\\n.82663\\n.82681\\n.82698\\n9.82716\\n\u00e2\u0080\u00a282734\\n.82752\\n.82769\\n.82787\\n9.82805\\n.82S23\\n.82840\\n.82858\\n.82876\\n9.82181\\n.82199\\n.82217\\n\u00e2\u0080\u00a282235\\n9.8.^276\\n.82288\\n.82306\\n\u00e2\u0096\u00a082324\\n.82342\\n9.82360\\n.82378\\n82396\\n.82413\\n.82431\\n9. 82894\\nliOs;. Vers.\\nliOtf. K.xsec\\nIt\\n10. 28416\\n28469^\\n.28521\\n.28574\\n.28627\\n28680\\n28733\\n28786\\n28839\\n28892\\n10\\n10\\n28945\\n28998:\\n2905 I\\n29104\\n29157\\n10.\\n29210\\n29263\\n293161\\n29370\\n29423\\n10.\\n29476\\n29529\\n29583\\n29636\\n29689\\n10.\\n29743\\n29796\\n29850\\n29903\\n29957\\n10.\\n30010\\n30064\\n30117\\n3o 7i,\\n^0225i\\n10\\n30278|\\n30332\\n30386\\n30440\\n30493\\n10\\n30547\\n30601\\n30655\\n30709\\n30763\\n10. 30817\\n.30871\\n\u00e2\u0080\u00a230925\\n30979\\n\u00e2\u0080\u00a231033\\n10\\n31087\\n31141,\\n31195\\n31249\\n313031\\n10\\n31358;\\n31412\\n31466\\n31521\\n3 575i\\n10. 31629\\n53\\n52\\n53\\n53\\n52\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n53\\n54\\n53\\n53\\n54\\nr\\nDJ\\n54\\n53\\n54\\n53\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\nLot. Vers.\\n|Loc. Kxsec.\\n82894\\n8291 I\\n82929\\n82947\\n82964\\n82982\\n83000\\n83017\\n83035\\n83053\\n83076\\n83088\\n83106\\n83123\\n83141\\n83159\\n83176\\n83194\\n83211\\n83229\\n83247\\n83264\\n83282\\n83299\\n83317\\n83335\\n83352\\n83370\\n83405\\n83422\\n83440\\n83458\\n83475\\n83493\\n83510\\n83528\\n83545\\n83563\\n83586\\n83598\\n83615\\n83633\\n83656\\n83668\\n83685\\n83703\\n83720\\n83737\\n83755\\n83772\\n83790\\n83807\\n83825\\n83842\\n83859\\n83877\\n83894\\n83912\\n83929\\n83946\\nI.OL K\\\\M-C.I 7\\n10\\n10\\n10\\nlioe. Vers. 7\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n31629\\n31684\\n31738\\n3 793\\n31847\\n31902\\n3 956\\n3201 1\\n32066\\n32126\\n32175\\n32230\\n32284\\n32339\\n3239-1\\n32449\\n32504\\n32558\\n32613\\n^2668\\n32723\\n32778\\n32833\\n32888\\n32944\\n32999\\n33054\\n33 09\\n33164\\n33220\\n33275\\n33330\\n33385\\n33441\\n33496\\n33552\\n3360^:\\n33663\\n33718\\n33774\\n33829\\n33885\\n33941\\n339961\\n34052!\\n34108\\n34164;\\n342201\\n34275J\\n34331 1\\n34387\\n34443\\n34499\\n34555\\n34611\\n3466^\\n34723\\n34780,\\n34836I\\n348q2\\n34948!\\n54\\n54\\n54\\n54\\n54\\n54\\n54\\n55\\nh\\\\\\n54\\n55\\n54\\n55\\nhi\\n55\\n55\\n54\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n55\\n56\\n55\\n55\\n56\\n55\\n56\\n56\\n55\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n5\\n6\\n7\\n8\\n_9_\\n10\\n1 1\\n1 2\\n3\\n14\\n15\\n16\\n17\\n18\\n19\\nr. r\\n21\\n22\\n23\\n24\\n26\\n27\\n28\\n29\\n30\\n34\\nj3\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\nii_\\n45\\n46\\n47\\n48\\n49\\noO\\n51\\n52\\n53\\n54\\n^\\\\^\u00c2\u00bbM\u00e2\u0080\u00a2\\n55\\n56\\n57\\n58\\n59_\\n(;o\\n20\\n40\\n50\\n40\\n50\\n20\\n30\\n40\\n50\\n40\\n50\\n56 56\\n5 6\\n6.6\\n7-5\\n8.5\\n9.4\\n18.5\\n28.2\\n37-6\\n47-\u00c2\u00bb\\n5.5\\n6.5\\n7-4\\n8.3\\n9.2\\nT8.5\\n27.7\\n370\\n46.2\\n54\\n53\\n5-3\\n6.2\\n7-i\\n8 o\\n8.9\\n26.7\\n35-6\\n44.6\\n5.6\\n6.5\\n7^4\\n8.4\\n9 3\\ni3.6\\n28.0\\n37-3\\n5S 55\\n5-5\\n6.4\\n7-3\\n8.2\\n9.1\\n18.3\\n27.5\\n36$\\n45-8\\n54\\n4\\n5\\n4\\n5-\\n6.3\\n6.\\n7\\n2\\n7\\n8\\n2\\n8.\\n9\\nr\\n9\\n18\\nI\\n18.\\n27\\n2\\n36\\n3\\n3^\\n45\\n4\\n45-\\n53\\n5-3\\n6.2\\n7.6\\n7-2\\n8.|\\n17-6\\n26.5\\n35-1\\n44 I\\n55\\n6\\n5-2\\n7\\nO.i\\n8\\n7.0\\n7-9\\n10\\n8.7\\n20\\n7-5\\n30\\na6.2\\n40\\n35-0\\n50\\n43-7\\n18 17 17\\n2.4\\n2-7\\n3-0\\n6.0\\n9.0\\n5-8\\n8.7\\nii.fi\\n14 .6\\n\u00e2\u0080\u00a27\\nI r\\n42Q", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0481.jp2"}, "482": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n10\\nII\\n12\\n13\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLoff. Vers.\\n9-83946\\n83964\\n83981\\n83999\\n84016\\n84033\\n84051\\n84063\\n84085\\n84103\\n84126\\n8413^\\n84155\\n84172\\n84189\\n84207\\n84224\\n8424T\\n84259\\n84276\\n84293\\n84316\\n84328\\n84345\\n84362\\n84380\\n84397\\n84414\\n84431\\n84449\\nD Los. Kxsec\\n84466\\n84483\\n84506\\n8451^\\n84535\\n84552\\n84569\\n84586\\n84603\\n84626\\n84638\\n84655\\n84672\\n84689\\n84706\\n84724\\n84741\\n84758\\n84775\\n84792\\n84809\\n84826\\n84844\\n84861\\n84878\\n84895\\n84912\\n84929\\n84946\\n84963\\n9.84986\\nLog. Vers.! J\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\nLog\\n34948\\n35005\\n35061\\n35ii?\\n35174\\n35230\\n35286\\n35343\\n35399\\n35456\\n35513\\n35569\\n35626\\n35683\\n35739\\n35796\\n35853\\n35910\\n35967\\n36023\\n36086\\n36137\\n36194\\n3625T\\n36308\\n36366\\n36423\\n36480\\n36537\\n36594\\n36652\\n36709\\n36766\\n36824\\n36881\\n36938\\n36996\\n37054\\n3711T\\n37169\\nD\\n37226\\n37284\\n37342\\n37399\\n3745?\\n37515\\n37573\\n37631\\n37689\\n37747\\n37805\\n37863\\n37921\\n37979\\n38037\\n38095\\n38153\\n38212\\n38276\\n38328\\n38387\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n56\\n57\\n56\\n56\\n56\\n57\\n56\\n57\\n56\\n57\\n57\\n56\\n57\\n57\\n57\\n57\\n57\\nSJ\\n57\\n57\\nSi\\n57\\n57\\n57\\nSi\\nSi\\nSi\\n57\\n57\\n58\\nSi\\nSi\\nsi\\nsi\\n58\\n57\\n58\\n58\\nSi\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\nLog. Vers.\\n84986\\n8499?\\n85014\\n85031\\n85049\\n85066\\n85083\\n85100\\n85117\\n85134\\n85151\\n85168\\n85185\\n85202\\n85219\\n85236\\n85253\\n85270\\n85287\\n85304\\n85321\\n85338\\n85355\\n85372\\n85389\\n85405\\n85422\\n85439\\n85456\\n85473\\n85496\\n85507\\n85524\\n85541\\n85558\\n85575\\n85592\\n85608\\n85625\\n85642\\n85659\\n85676\\n85693\\n85710\\n85726\\n85743\\n85766\\n85777\\n85794\\n85811\\n8582?\\n85844\\n85861\\n85878\\n8^895\\n8591 I\\n85928\\n85945\\n85962\\n85979\\n85995\\nLog\\nl^lxsec! 7 i Lo:r. Vers. 7\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\nliOi\\nExsec\\n38387\\n38445\\n38504\\n38562\\n38621\\n38679\\n38738\\n38796\\n38855\\n389 4\\n38973\\n39031\\n39096\\n39149\\n39208\\n39267\\n39326\\n39385\\n39444\\n39503\\n39562\\n3962T\\n39681\\n39740\\n39799\\n39859\\n39918\\n3997?\\n40037\\n40096\\n40136\\n40216\\n40275\\n40335\\n40395\\n40454\\n40514\\n40574\\n40634\\n40694\\n40754\\n40814\\n40874\\n40934\\n40994\\n41054\\n41114\\n41 74\\n41235\\n41295\\nj\\n41355\\n41416\\n41476\\n41537\\n41597\\n41658\\n41719\\n41779\\n41840\\n4 1 90 1\\n41962\\n58\\n58\\n58\\n58\\n58\\n58\\n58\\n59\\n58\\n59\\n58\\n59\\n59\\n58\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n59\\n60\\n59\\n59\\n60\\n59\\n60\\n59\\n60\\n60\\n60\\n60\\n60\\n60\\n60\\n66\\n60\\n60\\n66\\n66\\n60\\n66\\n60\\n66\\n66\\n66\\n61\\n66\\n66\\n61\\n61\\nKxsec.\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n00\\nP. P.\\n40\\n50\\n40\\n53\\n40\\n50\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n20\\n30\\n40\\n50\\n6\\nI\\n6.1 1\\n7\\n8\\nI\\nI\\n9\\n10\\n1\\ni\\n20\\n3\\n30\\n5\\n40\\n50\\n6\\n60\\n6.0\\n7.0\\n8.0\\n9.0\\n10.0\\n20.0\\n30.0\\n40.0\\n50.0\\n59\\n5-9\\n6.9\\n5-\\n6.\\n7-8\\n8-8\\n7-\\n8.\\n9-8\\n9-\\nJ9-6\\n39-\\n29-5\\n29.\\n39-3\\n49.1\\n39\\n48.\\n58\\n5-8\\n6.7\\n7-7\\n8.7\\n9-6\\n19-3\\n29.0\\n38.6\\n48.3\\n5-7\\n6.6\\n7.6\\n8.5\\n9-5\\nIQ.O\\n28.5\\n38.0\\n47-5\\n65\\n6.0\\n7.0\\n8.0\\n9.1\\n10. T\\n20.1\\n30.2\\n40- 3\\n50.4\\n59\\n5-9\\n6.9\\n7 9\\n8.9\\n9,9\\ni9-\u00c2\u00a7\\n29.7\\n39-6\\n49.6\\n58\\n57\\n5-7\\n6.7\\n7-6\\n8.6\\n9.6\\n19. 1\\n28.7\\n38.3\\n47-9\\n57 56\\n17\\n17\\n6\\n1-7\\n1-7\\n7\\n2\\n2.0\\n8\\n2\\n3\\n2.2\\n9\\n2\\n6\\n2.5\\n10\\n2\\nQ\\n2-8\\n20\\nS\\nX\\n5 6\\n30\\n8\\n7\\n8.S\\niO\\nII\\n6\\n1^-3\\n50\\n14\\n6\\n14.1\\n5-6\\n6.6\\n7-5\\n8.5\\n9-4\\n38.8\\n28.2\\n37-6\\n471\\n16\\n1-6\\n1.9\\n137\\nP. P\\n430", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0482.jp2"}, "483": {"fulltext": "TABLE VIII. LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n7 4\\n7 a\\n10\\nII\\n12\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n2 2\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44^\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n00\\nLost. Vers.\\n9.85995\\n.86012\\n.86029\\n86046\\n86062\\n9.86079\\n86096\\n.86113\\n.86129\\n.86146\\n7 Log\\n9.86163\\n.86179\\n.86196\\n.86213\\n.86230\\n9.86246\\n.86263\\n.86280\\n.86296\\n.86313\\n9.86330\\n86346\\n.86363\\n.86380\\n\u00e2\u0096\u00a086396\\n9.86413\\n86430\\n86446\\n86463\\n86479\\n86496\\n86513\\n86529\\n86546\\n86s62\\n\u00e2\u0080\u00a286579\\n.86596\\n.86612\\n.86629\\n.86645\\n9.86662\\n.86678\\n.86695\\n.86712\\n\u00e2\u0080\u00a286728\\n9.86745\\n.86761\\n.86778\\n.86794\\n.86811\\n9.86827\\n86844\\n86866\\n.86877\\n.86893\\n9.86910\\n.86926\\n86943\\n.86959\\n86976\\n9.86992\\nLost. Vers.\\n17\\n16\\n17\\n6\\n17\\n16\\n17\\n16\\n17\\n1(5\\n16\\n17\\n16\\n17\\n16\\n16\\n17\\n16\\n16\\n17\\n6\\n16\\n7\\n16\\n16\\n17\\n16\\n16\\n16\\n17\\n16\\n16\\n16\\n16\\n17\\n16\\n16\\n16\\n16\\n16\\n16\\n17\\n16\\n16\\n16\\n16\\n16\\n16\\n16\\n16\\n16\\n16\\n16\\n16\\n6\\n16\\n16\\n16\\n16\\n16\\n10\\nLo:r\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\nExsecj 1)\\n41962\\n42022\\n42083\\n42144\\n42205\\n42266\\n4232?\\n42388\\n42450\\n42511\\n42572\\n42633\\n42695\\n42756\\n42817\\n42879\\n42940\\n43002\\n43063\\n43 25\\n43 87\\n43249\\n43310\\n43372\\n43434\\n43496\\n43558\\n43620\\n43682\\n43744\\n43806\\n43868\\n43931\\n43993\\n44055\\n44118\\n44180\\n44242\\n44305\\n44368\\n44430\\n44493\\n44556\\n446 1 8\\n4468 T\\n44744\\n44807\\n44870\\n44933\\n44996\\n45059\\n45122\\n45185\\n45248\\n45312\\n45375\\n45439\\n45502\\n45565\\n45629\\n45693\\nKxspc.\\n60\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n61\\n6!\\n61\\n61\\n61\\n61\\n61\\n61\\n62\\n61\\n62\\n61\\n62\\n61\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n62\\n63\\n62\\n62\\n63\\n62\\n63\\n62\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n63\\n64\\nLojf. Vers.\\n9.86992\\n87009\\n.87025\\n.87042\\n.870 58\\n9.87074\\n.87091\\n.87107\\n.87124\\n.87146\\n9.87157\\n.87173\\n.87189\\n.87206\\n.87222\\n9.87239\\n.87255\\n.8727!\\n.87288\\n87304\\n9.87326\\n.87337\\n\u00e2\u0080\u00a287353\\n.87370\\n.87386\\n9.87402\\n.87419\\n.87435\\n.87451\\n.87468\\n9.87484\\n.87506\\n.875I6\\n\u00e2\u0080\u00a287533\\n.87549\\n9.87565\\n.87582\\n.87598\\n.87614\\n.87631\\n9.87647\\n.87653\\n.87679\\n.87696\\n.87712\\n9.87728\\n.87744\\n.87761\\n.^7777\\n.87793\\n9.87809\\n.87825\\n.87842\\n.87858\\n.87874\\n9.87896\\n87906\\n.87923\\n\u00e2\u0080\u00a287939\\n.87955\\n9.87971\\nK\\\\s\u00c2\u00bb o.\\n10\\n10\\n\u00e2\u0080\u00a245^93\\n\u00e2\u0080\u00a245756\\n.45820\\n.45884\\n.45947\\n.4601 1\\n.46075\\n\u00e2\u0080\u00a246139\\n.46203\\n.4626^\\n10\\n\u00e2\u0080\u00a246331\\n46395;\\n46460\\n.46524\\n.46588\\n10\\n,46652\\n,46717\\n,46781\\n46846\\n46916\\n10\\n\u00e2\u0080\u00a246975\\n47040\\n.47104\\n,47169\\n.47234\\n10\\n.47299\\n\u00e2\u0080\u00a247364\\n.47429\\n\u00e2\u0096\u00a047494\\n\u00e2\u0096\u00a047559\\n10\\n.47624\\n,47689\\n.47754\\n,47820\\n47885\\n10\\n.47950\\n.48016,\\n.48081\\n.48147\\n\u00e2\u0080\u00a248213\\n10\\n\u00e2\u0080\u00a248278\\n.48344\\n.48410\\n.48476\\n,48542\\n10\\n.48607\\n.48674\\n48740;\\n.48806,\\n.48872\\n10\\n.48938\\n49004\\n,49071\\n.4913?,\\n,49204!\\n10\\n,49270\\n.49337\\n49403\\n49476\\n49537\\n10.49604\\n7 i liO tf. V p r s I J) IliO g Kx\u00c2\u00bb er.\\nI*, r\\n67\\n66\\n6\\n6.7\\n6.^\\n7\\n7.8\\n7.7\\n8\\n8.9\\n8.8\\nq\\n10.\\n10.\\n10\\nII. I\\nII. I\\n20\\n\u00e2\u0096\u00a022.3\\n22.1\\n30\\n33.5\\n33.2\\n40\\n44.6\\n44-3\\n50\\n55.8\\n554\\n65\\n65\\n6\\n6. .5\\n6.5\\n7\\n7-6\\n7.6\\n8\\n87\\n\u00c2\u00abf?\\n9\\n9.8\\n9.7\\n10\\n10. 9\\n10. 8\\n20\\n21. g\\n21.6\\n30\\n32-7\\n32.5\\n40\\n43-6\\n43-3\\n50\\n54^b\\n54 I\\n66\\n6.6\\n7.7\\n8.8\\n9.9\\nI I o\\n33.0\\n44.0\\n55.0\\n64\\n6.4\\n64\\n63\\n63\\n6\\n6.4\\n6.3\\n6.3\\n7\\n74\\n7-4\\n73\\n8\\n8.5\\n8.4\\n8.4\\n9\\n9.6\\n9 5\\n9.4\\n10\\n10.6\\n10.6\\nJO-5\\n20\\n21.3\\n21 1\\n21 .0\\n30\\n32\\n3 .7\\n31-5\\n40\\n42-6\\n42.3\\n42.0\\n50\\n53 3\\n52-9\\n52.5\\n62 62 61\\n6\\n6.2\\n6.2\\n6.\\n7\\n8\\n7.3\\n8.3\\n7.2\\n8.2\\n7\\n8\\n9\\n10\\n9.4\\n10.4\\n9-3\\n10.3\\n9-\\n10.\\n20\\n20.\\n31.2\\n4J-6\\n52.1\\n20.6\\n20.\\n30\\n40\\n50\\n31.0\\n41 3\\n5i^6\\n30.\\n4t\\n5\\n20\\n30\\n40\\n50\\n61\\n6.1\\n7-1\\n8.1\\nQ.I\\n10. i\\n20.3\\n30-5\\n40\\n50-8\\n17\\n16\\n6\\n1-7\\n^\u00e2\u0080\u00a26\\n7\\n2.0\\n19\\n8\\n2.2\\n2.2\\n9\\n2-5\\n2.5\\n10\\n2.3\\n2-7\\n20\\nS-6\\n5-5\\n30\\n8.5\\n8.5\\n40\\nII. 3\\n1 1,0\\n50\\n14.1\\n13.^\\n66\\n6.5\\n7.5\\n8.5\\n9.1\\n10. 1\\n20.1\\n30.2\\n40 3\\n50.4\\n16\\n1.6\\n2.^,\\n8.0\\n10.^\\n\u00c2\u00bb3-3\\nP. P.", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0483.jp2"}, "484": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\nLop. Vers.\\n10\\nII\\n12\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n=;8\\n59\\n(JO\\n9.87971\\n.87987\\n88003\\n88020\\n.88036\\n9.88052\\n88068\\n88084\\n.88100\\n.88116\\n9.88133\\n.88149\\n.88165\\n.88181\\n.88197\\n9.88213\\n.88229\\n.88245\\n.88261\\n.8827^\\n9.88294\\n.88310\\n.88326\\n.88342\\n.88358\\n9.88374\\n.88390\\n88406\\n.88422\\n.88438\\n9.88454\\n.88470\\n.88486\\n.88502\\n.88518\\n9.88534\\n.88556\\n.88566\\n.88582\\n.88598\\n9.88614\\n.88636\\n.88646\\n.88662\\n.88678\\n9.88694\\n.88710\\n.88726\\n.88742\\n.88758\\n9,88774\\n.88790\\n.88805\\n.88821\\n.8883^\\n9.88853\\n.88869\\n.88885\\n88901\\n.88917\\n9.88933\\nLojj. Vers.\\nJ\\n6\\n6\\n6\\n6\\n6\\n6\\n6\\n6\\n6\\n6\\n6\\n6\\n6\\n6\\nTT\\nliOP\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\nKxsec. D\\n49604\\n49670\\n4973?\\n49804\\n49871\\n49939;\\n50006\\n50073\\n50146\\n50208;\\n50275\\n50342\\n50410\\n5047?\\n50545\\n50613\\n5068 1 j\\n50748;\\n508 1 6\\n50^\\n50952\\n51026\\n51088\\n51157\\n51225\\n51293\\n51361\\n51430\\n51498\\n51567\\n51636\\n51704\\n51773\\n51842\\n51911\\n51980\\n52049\\n52118\\n52187\\n52256\\n52325\\n52394\\n52464\\n52533\\n52603\\n52672\\n52742\\n52812\\n52881\\n52951\\n53021\\n53091\\n5316T\\n53231\\n53301\\n53372\\n53442\\n53512\\n53583\\n53653\\n53724\\nKxsec.\\n66\\n67\\n67\\n67\\n6?\\n67\\n67\\n67\\n6f\\n67\\n6f\\n6f\\n67\\n68\\n6f\\n68\\n6?\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n68\\n69\\n68\\n68\\n69\\n69\\n69\\n69\\n6q\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n69\\n70\\n69\\n69\\n70\\n70\\n70\\n70\\n70\\n70\\n76\\n70\\n76\\n70\\n76\\n70\\nTT\\nLos. Vers.\\n88933\\n88949\\n88964\\n88986\\n88996\\n89012\\n89028\\n89044\\n89060\\n89075\\n89091\\n8910^\\n89123\\n89139\\n89155\\n89176\\n89186\\n89202\\n89218\\n89234\\n89249\\n89265\\n89281\\n89297\\n893 2\\n89328\\n89344\\n89360\\n89376\\n89391\\n89407\\n89423\\n89438\\n89454\\n89470\\n89486\\n89501\\n8951^\\n89533\\n89548\\n89564\\n89580\\n89596\\n896 11\\n89627\\n89643\\n89658\\n89674\\n89690\\n89705\\n89721\\n89737\\n89752\\n89768\\n89783\\n89799\\n89815\\n89836\\n89846\\n89862\\n9.8987?\\nliOsr. Vers.\\nU Lo;r. Exsec. JJ\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\nT) ihuii\\n53724\\n53794\\n53865\\n53936\\n54007\\n54078\\n54149\\n54220\\n54291\\n54362\\n54433\\n54505\\n54576\\n5464?\\n54719\\n5479\\n54862\\n54934\\n55006\\n55078\\n55150\\n55222\\n55294\\n55366\\n55438\\n5551^\\n55583\\n55655\\n55728\\n55801\\n55873\\n55946\\n56019\\n56092\\n56165\\n56238\\n563 1 T\\n56384\\n5645?\\n5653\\n56004\\n56678\\n56751\\n56825\\n56899\\n56973\\n57047\\n57126\\n57195\\n57269\\n57343\\n5741?\\n57491\\n57566\\n57646\\n57715\\n57790\\n57864\\n57939\\n58014\\n58089\\nKxsec. T\\n70\\n71\\n76\\n71\\n71\\n71\\n71\\n71\\n71\\n7T\\n71\\n71\\n71\\n72\\n71\\n71\\n72\\n71\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n72\\n73\\n72\\n72\\n73\\n72\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\n73\\n74\\n73\\n74\\n74\\n73\\n74\\n74\\n74\\n74\\n74\\n74\\n74\\n75\\n74\\n74\\n75\\n75\\n75\\nI\\n25\\n26\\n27\\n28\\nao\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\nP. P.\\n75\\n74\\n72\\nt\\n7.-S\\n7-4\\n7.\\n7\\n8.7\\n8\\n6\\n8.\\n8\\n10.\\n9\\n8\\n9\\n9\\nII. 2\\nII\\nI\\n10.\\n10\\n12.5\\n12\\n3\\n12.\\n20\\n25.0\\n24\\n6\\n24.\\n30\\n37.5\\n37\\n3b.\\n40\\n50.0\\n49\\n3\\n48.\\n50\\n62.5\\n61\\n6\\n60.\\n20\\n30\\n40\\n50\\n66\\n6.6 1\\n7\\n7\\n8\\n8\\n9\\n9\\n1 1\\n22\\n33\\n44\\n55\\n16\\n13\\n16\\nT.6\\n2.4\\n\u00e2\u0080\u00a2^\u00e2\u0080\u00a26\\n5-3\\n8.0\\n10. 6\\nJ3-3\\n72\\n71\\n6\\n7.2\\n7.1\\n7\\n8.4\\n8.3\\n8\\n9.6\\n9.4\\n9\\n10.8\\n10. 6\\n10\\n12 .0\\n.8\\n20\\n24.0\\n23-6\\n30\\n36.0\\n35.5\\n40\\n48\\n47.3\\n50\\n60.0\\n59-1\\n70\\n7.0\\n8.2\\n9.4\\n10.6\\n11.7\\n23.3\\n35-2\\n47.0\\n58.7\\n69 68 67\\n6\\n6.Q\\n6.8\\n7\\n8,5\\n7-9\\n8\\n9.2\\n9.0\\n9\\n10.3\\n10 2\\n10\\n5\\n.3\\n20\\n2:!.0\\n22-6\\n30\\n34. s\\n34\\n40\\n46.0\\n45-3\\n50\\n57.5\\n50-6\\n6.-\\n7.8\\n8.9\\n100\\nII. i\\n2P.3\\n33-5\\n44-6\\n55.8\\n0.0\\n0.0\\n0.0\\no. 1\\nO. I\\no. i\\n0.2\\n0.3\\n0.4\\n15\\nP. P.\\n432", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0484.jp2"}, "485": {"fulltext": "TABLE Vlll. LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n78\\nly c\\n1)\\nLo?. Vers. 7\\n9.8987^\\n15\\nI?\\n10.58089\\nI\\n.89893\\n.58164\\n2\\n89908\\n\u00e2\u0080\u00a258239\\n3\\n.89924\\n\u00e2\u0080\u00a258315\\n4\\n89939\\n16\\n3\\n58390\\nS\\n9.89955\\n10.58465\\n6\\n.89971\\n2\\n.58541\\n7\\n.89986\\nI\\n\u00e2\u0080\u00a2586I6\\n8\\n.90002\\n58692\\n9\\n.90017\\nt6\\n.58768\\n10\\n9.90033\\n10.58844;\\n1 1\\n90048\\n.58920\\n12\\n90064\\n.58995\\n13\\n90080\\nI 2\\n.59072\\nU\\n.90095\\nI?\\n.59148\\n10.59224\\n15\\n9.901 1 1\\ni6\\n.90125\\nI\\n.59300\\n17\\n.90142\\n3\\nI\\n\u00e2\u0080\u00a259377;\\ni8\\n\u00e2\u0080\u00a290157\\nT\\n\u00e2\u0080\u00a259453\\n19\\n.90173\\n\u00e2\u0080\u00a259530\\n20\\n9.90188\\n10.59606\\n21\\n90204\\nT\\n\u00e2\u0080\u00a259683\\n22\\n.90219\\n59760;\\n23\\n\u00e2\u0080\u00a290235\\n5\\n1\\n\u00e2\u0080\u00a259837,\\n24\\n.90250\\nT\\n59914;\\n10.59991\\n25\\n9.90266\\n26\\n.90281 1\\n5\\nT P\\n.60068\\n27\\n.902971\\nI5\\n3\\n.60145\\n28\\n.90312 j\\n5\\n.60223\\n29\\n.90328\\n.60306\\n30\\n9 \u00e2\u0080\u00a290343\\n10.60378\\n31\\n\u00e2\u0080\u00a2903591\\n5\\nT r\\n.60455,\\n32\\n\u00e2\u0080\u00a290374\\n\u00e2\u0080\u00a260533\\n33\\n.90389\\n606 1 1 1\\n34\\n\u00e2\u0080\u00a290405\\nId\\np\\n.60688\\n35\\n9 90426\\n10.60765\\n36\\n.90436\\nI3\\nT\\n60844\\n37\\n.90451\\nI 3\\nP\\n.60923\\n3^\\n.90467\\nI 5\\np\\n6 I 00 I\\n39\\n.90482\\nI3\\n15\\n.61079\\n40\\n9.90497\\n10.61158\\n41\\n\u00e2\u0080\u00a290513\\nr P\\n.61236\\n42\\n\u00e2\u0080\u00a290528\\nr\\n.61315\\n43\\n\u00e2\u0080\u00a290544\\n1\\n\u00e2\u0080\u00a261393\\n44\\n\u00e2\u0080\u00a290559\\n3\\n15\\n.61472\\n45\\n9.90574\\n10.61551\\n46\\n.90590\\n.61630\\n47\\n.9060 5\\nP\\n.61709\\n48\\n9062 1\\n5\\n1 p\\n.61788\\n49\\noO\\n\u00e2\u0080\u00a290636\\n15\\np\\n.6186^\\n9.90651\\n10.61947\\n51\\n90667\\n3\\n.62026\\n52\\n.90682\\nI 3\\n.62105\\n53\\n90697\\nT\\n.62185\\n54\\n907 1 3\\nT P\\n.62265\\n55\\n9.90-28\\n10.62345\\n56\\n90744\\n15\\n15\\n.62424\\n57\\n\u00e2\u0080\u00a290759\\n.62504\\n5^\\n.90774\\n.62585\\n59\\n90790\\n.62665\\nGO\\n9.90805\\n10.62745\\nliOtf. Vers.\\n1\\nliOe. Kxsec.\\nLoff. Kxsec. J\\n75\\n75\\n75\\n71\\n75\\n75\\n75\\n76\\n75\\n76\\n76\\n75\\n75\\n76\\n76\\n76\\n76\\n76\\n76\\n76\\n77\\n76\\n77\\n77\\n77\\n77\\n77\\n71\\n77\\n77\\n77\\n77\\n78\\n77\\n78\\n78\\n78\\n78\\n78\\n78\\n78\\n78\\n78\\n79\\n78\\n79\\n79\\n79\\n79\\n79\\n79\\n79\\n80\\n79\\n80\\n79\\n80\\n86\\n80\\n80\\nLoir. Vers.\\n90805\\n90826\\n90835\\n90851\\n90865\\n7\\n90881\\n90897\\n90912\\n90927\\n90943\\n90958\\n90973\\n90988\\n91004\\n9IOI9\\n91034\\n91049\\n9 1 06 5\\n91080\\n91095\\n91 1 10\\n91 126\\n91141\\n91156\\n91171\\n91 187\\n91202\\n91217\\n91232\\n91247\\n91263\\n91278\\n91293\\n91308\\n91323\\n91338\\n91354\\n91369\\n91384\\n9 399\\n91414\\n91429\\n9 445\\n91460\\n91475\\n91490\\n91505\\n91520\\n91535\\n91556\\n91565\\n91581\\n91596\\n9161 1\\n91626\\n91641\\n91656\\n91671\\n91685\\n91701\\n9 7 r\\nliOjr. Kxser.\\n10\\n62745\\n.62825\\n,62906\\n,62985\\n,6306^\\n10\\n,63148\\n,63229\\n.63310\\n.63391\\n,63472\\n10\\n63553\\n63634\\n63716\\n6379?\\n63879\\n10\\n63961\\n64043\\n,64125\\n,64207\\n,64289\\n1)\\n10\\n.64371\\n64453\\n\u00e2\u0080\u00a264536\\n,64618;\\n,64701!\\n10\\n10\\n64784\\n64867\\n64950\\n65033\\n,651 16\\n^5199\\n65283\\n65366\\n,65450\\n65534\\n10\\n6561^\\n,657oT\\n.65785\\n,65870\\n\u00e2\u0080\u00a265954\\n10\\n66038 J\\n,66123\\n,6620^1\\n.66292\\n,66377\\n10\\n10\\n10\\n,66462\\n.66547\\n,66632\\n.66717\\n.66803\\n66888\\n,66974\\n.67059\\n,67145\\n.6723T\\n673\\n.67403\\n67490\\n.67576\\n67663\\n10,^7749\\nI IjOtr. Vers. l, iir- Kxser\\n433\\n86\\n86\\n81\\n85\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n81\\n82\\n82\\n82\\n82\\n82\\n82\\n82\\n82\\n82\\n83\\n82\\n83\\n83\\n83\\n^1\\n83\\n83\\n83\\n83\\n84\\n83\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n84\\n85\\n85\\n85\\n85\\n85\\n85\\n85\\n85\\n85\\n86\\n86\\n86\\n86\\n86\\n86\\n86\\n86\\n5\\n6\\n7\\n8\\n_9_\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n^9\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n50\\n5\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nr\u00c2\u00bbo\\n1 I\\n86 85 84\\n6\\n8.6\\n8.5\\n7\\n10.\\n9\\n8\\n11.4\\n11.3\\n9\\n12. g\\n12.7\\n10\\n14.3\\n14. 1\\n20\\n28.6\\n28.3\\n^0\\n43.0\\n42.1;\\n40\\n57-3\\n56.6\\n50\\n7\u00c2\u00bb^6\\n70.8\\n8.\\n9.8\\nII .2\\n12.6\\n14.0\\n28.0\\n42.0\\n56.0\\n70.0\\n83 82 81\\n6\\n8.3\\n8.2\\n8.\\n7\\n9-7\\n9-5\\n9-\\n8\\n11 .0\\n10. 2\\n10.\\n9\\n12.4\\n12.3\\n12.\\n10\\n20\\ni3-\u00c2\u00a7\\n27-6\\nX3-6\\n27-3\\n3-\\n27.\\n30\\n41. s\\n41.0\\n40\\n40\\n50\\n55-3\\n69.1\\n54\\n68.3\\n54\\n67\\n80\\n79\\n6\\n80\\n7-9\\n7\\n9-3\\n9.2\\n8\\n10.6\\n10.5\\n9\\n12.0\\n10\\n133\\n13-1\\n20\\n26.6\\n26.3\\n30\\n40.0\\n39-5\\n40\\n53-3\\n52-6\\n50\\n66.6\\n65-8\\n78\\n78\\n9.1\\n10.4\\n11.7\\n13.0\\n26.0\\n39-0\\n52.0\\n65.0\\n77 76 75\\n6\\n7^7\\n7.6\\n7\\n9.0\\n8.8\\n8\\n10.2\\n10. 1\\n9\\n\u00e2\u0080\u00a25\\nII. 4\\n10\\n12.\\n20\\n25 6\\n253\\n30\\n38.5\\n38.0\\n40\\n5 -3\\n50.\\n50\\n64.1\\n63.3\\n7-5\\n8.7\\n10. o\\n1 1 .2\\n12.5\\n25.0\\n37-5\\n50.0\\n62.5\\n20\\n30\\n40\\n50\\n0.3\\n0.4\\n16\\n15\\n6\\n1.6\\ni 5\\n7\\n8\\n3.1\\n1.8\\n2.6\\n9\\n2-4\\n23\\n10\\n2.5\\n2.6\\n20\\n5-3\\n5^\u00c2\u00bb\\n30\\n8.0\\n7-7\\n40\\n10$\\n10.3\\n50\\n133\\n12.9\\n15\\n\u00e2\u0080\u00a25\\n\u00e2\u0080\u00a27\\n2.0\\n2.3\\n2-5\\n7-5\\nto.o\\n12.5\\nI r", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0485.jp2"}, "486": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n80^\\n81\\n10\\n1 1\\n12\\n14\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLog. Vers\\n7I6\\n731\\n746\\n761\\n776\\n791\\n807\\n822\\n837\\n852\\n867\\n882\\n897\\n912\\n927\\n942\\n957\\n972\\n987\\n92002\\n92016\\n9203!\\n92046\\n92061\\n92076\\n92091\\n92106\\n92121\\n92136\\n92151\\n92166\\n921 81\\n92196\\n9221 r\\n92226\\n92240\\n92255\\n92276\\n92285\\n92306\\n92315\\n92330\\n92345\\n92360\\n92374\\n92389\\n92404\\n92419\\n92434\\n92449\\n92463\\n92478\\n92493\\n92508\\n92523\\n92538\\n92552\\n9256^\\n92582\\n92597\\n9.92612\\nLog. Vers.\\nX) Loff. Exsec.\\n10\\n67749\\n67836\\n67923\\n.68010\\n68097\\n10\\n,68184\\n.6827\\n68359\\n.68447\\n.68534\\n10\\n,68622\\n68716\\n,68798\\n,68886\\n68975\\n10\\n69063\\n,69152\\n69246\\n69329\\n694 1 8\\n10\\n69507\\n69596\\n69686\\n69775\\n69865\\n10\\n69955\\n70044\\n\u00e2\u0096\u00a070134\\n,70224\\n.70315\\n10\\n70405\\n70495\\n70586\\n70677\\n70768\\n10\\n70859\\n70950\\n7104T\\n71133\\n71224\\n10\\n,71316\\n,71408\\n7 1 500\\n71592\\n,71684\\n10\\n71776\\n71869\\n7 1 96 1\\n72054\\n72147\\n10\\n,72240\\n72333\\n72427\\n,72526\\n72614\\n10\\n,7270^\\n7280T\\n72895\\n72990\\n73084\\n10.73178\\nLog. Kxsec.\\nI)\\n86\\n87\\n87\\n^7\\n8^\\n8?\\n87\\n8?\\n87\\n88\\n88\\n89\\n89\\n89\\n89\\n89\\n89\\n89\\n90\\n89\\n90\\n90\\n96\\n90\\n90\\n91\\n96\\n91\\n91\\n91\\n91\\n91\\n91\\n91\\n92\\n92\\n92\\n92\\n92\\n92\\n92\\n93\\n92\\n93\\n93\\n93\\n93\\n93\\n93\\n94\\n94\\n94\\n94\\n94\\nLog. VerS\\nI)\\n92612\\n92626\\n92641\\n92656\\n92671\\n92686\\n92706\\n92715\\n92730\\n92745\\n92759\\n92774\\n92789\\n92804\\n92818\\n92833\\n92848\\n92862\\n9287^\\n92892\\n92907\\n9292T\\n92936\\n92951\\n92965\\n92986\\n92995\\n93009\\n93024\\n9.3039\\n93053\\n93068\\n93083\\n9309^\\n93II2\\n93127\\n9314I\\n93156\\n9317I\\n93185\\n93200\\n93214\\n93229\\n93244\\n93258\\nJ Log. Exsec.\\n93273\\n93287\\n93302\\n93317\\n93331\\n93346\\n93366\\n93375\\n93389\\n93404\\n93419\\n93433\\n93448\\n93462\\n93477\\n9.93491\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\n10\\nLoe. V\u00c2\u00ab*rs.l 7 |Loi\\n73178\\n73273\\n73368\\n73463\\n73558\\n73653\\n73748\\n73844\\n73940\\n74035\\n74131\\n7422^\\n74324\\n74426\\n74517\\n74613\\n74716\\n7480^\\n74905\\n75002\\nij\\n75099\\n7S^9l\\n75295\\n75393\\n7549\\n75589\\n75688\\n75786\\n75885\\n75984\\n76083\\n76182\\n76282\\n76382\\n76481\\n76581\\n76681\\n76782\\n76882\\n76983\\n77083\\n77184\\n77286\\n77387\\n77488\\n77590\\n77692\\n77794\\n77896\\n77998\\n78101\\n78203\\n78306\\n78409\\n78513\\n78616\\n78720\\n78823\\n78927\\n79031\\n79136\\nExsec.\\n95\\n94\\n95\\n95\\n95\\n95\\n95\\n96\\n95\\n96\\n96\\n96\\n96\\n96\\n96\\n97\\n97\\n97\\n97\\n97\\n98\\n9l\\n98\\n98\\n98\\n98\\n98\\n99\\n99\\n99\\n99\\n99\\n100\\n99\\n00\\n00\\n06\\n06\\n06\\n06\\n01\\n01\\n01\\n01\\n01\\n02\\n02\\n02\\n02\\n02\\n02\\n03\\n03\\n03\\n03\\n04\\n03\\n04\\n04\\n04\\n10\\nI\\n2\\n3\\n4\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n\u00c2\u00ab0\\np. r\\n20\\n40\\n50\\n6\\n7\\n8\\n9\\n10\\n20\\n30\\n40\\n50\\n40\\n50\\n20\\n30\\n40\\n50\\n20\\n30\\n40\\n50\\n90\\n9\\nTO\\n5\\n12\\n13\\n5\\n15\\n30\\n45\\n60\\n75\\n0-5\\n0.6\\no.g\\n0.7\\no\u00c2\u00a7\\n1-6\\n2.5\\n3-3\\n41\\nIS\\n40\\n50\\n7\\n0.\\n8\\nQ\\n0.\\nI\\nI\\nI\\n1.\\n2\\n3\\n2.\\n3\\n4\\n5\\n6\\n3-\\n4-\\n5\\n8\\n5-\\n80\\n8.0\\n9-3\\n13-3\\n26.6\\n40.0\\n53 3\\n66.6\\n0.8\\n0.9\\n1 .0\\n1.2\\n1-3\\n2.6\\n4.0\\n5-3\\n6.6\\nIS\\nI\\nS\\n1.\\nI\\n8\\nI.\\n2\\na.\\n2\\n3\\n2.\\n2\\n6\\n2.\\n5\\n7\\n10\\nI\\n7\\n.3\\n5-\\n7-\\n10.\\n12\\n9\\n12.\\n14\\n1.4\\n1-7\\n1.9\\n2.2\\n2.4\\n4-8\\n7.2\\n9-6\\n12. 1\\n434", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0486.jp2"}, "487": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n83\u00c2\u00b0 8:r\\n10\\nII\\n12\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nL( S. Vers. I 7\\n9-93491\\n93506\\nJ3-\\n93535\\n93549\\n93564\\n93578\\n93593\\n93607\\n93622\\n93636\\n93651\\n93665\\n93680\\n93694\\n93709\\n93723\\n93738\\n93752\\n93767\\n93781\\n93796\\n93816\\n93824\\n93839\\n93^53\\n93868\\n93882\\n93897\\n9391 1\\n93925\\n93940\\n93954\\n93969\\n93983\\n93997\\n94012\\n94025\\n94041\\n940 s 5\\n94069\\n94084\\n94098\\n941 12\\n94127\\n94141\\n94155\\n94170\\n94184\\n94198\\n94213\\n94227\\n94241\\n94256\\n94270\\n94284\\n94299\\n94313\\n9432?\\n94341\\n9 94356\\nliOe. Vers. I 7\\n14\\nu\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\nu\\n14\\nu\\n14\\n14\\n14\\n14\\n14\\n14\\nu\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\nLog. Ex sec. I D\\nIO.79F36J\\n.792401\\n\u00e2\u0080\u00a279345\\n\u00e2\u0080\u00a279450\\n\u00e2\u0080\u00a279555\\n10.79666\\n.79766\\n.79871\\n\u00e2\u0080\u00a279977\\n80083\\n10.80189\\n80296\\n80402\\n.80509\\n.806 16\\n10.80723\\n.50831\\n\u00e2\u0080\u00a280938\\n.81046\\n.81154\\n10,81202\\n.813711\\n.81479\\n.8i:;88\\n.81697\\nio.8i8o6\\n.81916\\n.82025\\n.82135\\n.82245\\n10.82356\\n.82466\\n.82577\\n.82688\\n.82799\\n10.82916\\n.83022\\n\u00e2\u0080\u00a283133\\n.83245\\n833vS\\n10.83470\\n.83583\\n.83695\\n.83809\\n.83922\\n10.84035\\n.84149\\n\u00e2\u0080\u00a284263\\n84492\\n10.84607\\n.84721\\n.84837\\n.84952\\n.85068\\n10.85183\\n.85299\\n.85416\\n\u00e2\u0080\u00a285532\\n85649\\n10.85766\\n104\\n105\\n104\\n105\\n105\\n105\\n105\\n106\\n106\\n106\\n106\\n106\\n107\\n107\\n107\\nI of\\n\\\\oJ\\n108\\n108\\n108\\nlog\\nlog\\n109\\n109\\n109\\n109\\n109\\n1 10\\nno\\nno\\n1 16\\n116\\n1 1 1\\nIII\\nIII\\n1 11\\n1 11\\nI 12\\nI 12\\n112\\nI 12\\nI 12\\n113\\n113\\n113\\n114\\n114\\n114\\n114\\nU5\\n114\\n115\\n116\\n116\\n116\\n116\\n117\\n117\\nLog. Vers. I L(\u00c2\u00bb;r. Kxscc.\\nKxspr.l 7\\n9 -943 56\\n94370\\n94384\\n94398\\n94413\\n94427\\n94441\\n94456\\n94470\\n94484\\n94498\\n94512\\n94527\\n94541\\n94555\\n945 ^9\\n94584\\n94598\\n94612\\n94626\\n94646\\n94655 j\\n94669\\n94683\\n94697 I\\n947 1 1\\n94726\\n94740\\n94754\\n94768\\n94782\\n94796\\n94816\\n94825\\n94839\\n94853\\n94867\\n9488T\\n94895\\n94909\\n94923\\n94938\\n94952\\n94966\\n94980\\n94994\\n95008\\n95022\\n95036\\n95050\\n95064\\n95078\\n95093\\n95107\\n95121\\n95135\\n95M9\\n95163\\n95177\\n95191\\n995205\\nliOR. Vers. 7\\n10.85766\\n.85884\\n86001\\n.861 19\\n.86237\\n10\\n86355\\n,86474\\n,86592\\n,86711\\n,86831\\n10\\n.86956\\n.87076\\n.87196\\n,87316\\n.87431\\n10\\n87552\\n87673\\n87794\\n.8;;9i6\\n,88038\\n10.\\n88160\\n88282\\n88405\\n88528\\n8865T\\n10\\n88775\\n,88898\\n,89022\\n.89147\\n,89271\\n10\\n89396\\n,89521\\n,89647\\n.89773\\n.89899\\n117\\niif\\n117\\n118\\n118\\n118\\n118\\n119\\n119\\n119\\n120\\n120\\n120\\n126\\n121\\n121\\n121\\n121\\n122\\n122\\n122\\n122\\n123\\n123\\n124\\n123\\n124\\n124\\n124\\n125\\n125\\n125\\n126\\n126\\n10\\n.90025\\n90 1 5 2\\n,90279\\n90406\\n90533\\n10\\n,90661\\n.90789\\n,90917.\\n,91046\\n91175\\n10\\n91304\\n.91434\\n.91564;\\n.91694,\\n91825,\\n10\\n91956\\n,92087\\n,92218\\n.92350\\n,92482;\\n10\\n92614\\n92747\\n92886\\n93014\\n9314 71\\n93281I\\n126\\n126\\n127\\n127\\n127\\n128\\n127\\n128\\n129\\n129\\n129\\n1 130\\n129\\n136\\n130\\n131\\n131\\n3\\n3\\n13\\n131\\n132\\n132\\n133\\n133\\n133\\n133\\n134\\n4\\n5~\\n6\\n7\\n8\\n9\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n21\\n23\\n24\\n10\\nl.fijr. Kxsec\\n25\\n26\\n27\\n28\\n30\\n31\\n32\\n33\\n34\\nI r.\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\no\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\nio\\n6\\n130\\n13.0\\n7\\n8\\n\u00c2\u00bb5-J\\n\u00c2\u00bb7^3\\n9\\n19.5\\n10\\n2\u00c2\u00bb f,\\n20\\n40\\n50\\n43 3\\n65.0\\n108.3\\n120\\n12. (J\\n14.0\\n16.0\\n18.0\\n20.0\\n40.0\\n60.0\\n\u00c2\u00a30 o\\nlUO.O\\nno 100\\n10.0\\nII. 6\\n3-3\\n15.0\\n16.^\\n33.3\\n50.0\\n66.6\\n83.3\\n6\\nII .0 1\\n7\\n2.^1\\n8\\nM.6\\n16. s\\nTO\\n,8.3\\n20\\n36.6\\n30\\n55.0\\n40\\n73 3\\n50\\n91-6\\n6\\n3\\n0.3\\n7\\n8\\n0.3\\n0.4\\nq\\n0.4\\n10\\n0.5\\n20\\n1 .0\\n30\\n1.5\\n40\\n2.0\\n50\\n2-5\\nI\\n6\\n0.. 1\\n7\\nI\\n8\\nI\\n9\\nI\\n10\\nI\\n20\\n3\\n30\\n5\\n40\\n50\\n8\\n14\\n6\\n1.4\\n7\\n\u00c2\u00bb.7\\n8\\n9\\n9\\n2.2\\n10\\na. 4\\n20\\n4.?\\n30\\n7.2\\n40\\n9-6\\n50\\n12. 1\\n0.1\\nO.I\\no.i\\no.a\\n0.3\\n0.4\\n14\\n1.4\\n15\\n8\\na. I\\n2-3\\n4 6\\n7.0\\n9.3\\n11.6\\nr. r.\\n435", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0487.jp2"}, "488": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n84\u00c2\u00b0 85\u00c2\u00b0\\n10\\nII\\n12\\n15\\ni6\\n17\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\nLost. Vers.\\n9.95205\\n95219\\n95233\\n9524f\\n9526T\\n95275\\n95289\\n95303\\n9531^\\n95331\\n95345\\n95359\\n95373\\n95387\\n95401\\n95415\\n95429\\n95443\\n95457\\n95471\\n2\\nLog. Exsec.\\n95485\\n95499\\n95513\\n95527\\n95540\\n95554\\n95568\\n95582\\n95596\\n95610\\n95624\\n95638\\n95652\\n95666\\n95680\\n95693\\n95707\\n95721\\n95735\\n95749\\n95763\\n95777\\n95791\\n95804\\n95818\\n95832\\n95846\\n95860\\n95874\\n95888\\n95901\\n95915\\n95929\\n95943\\n95957\\n95970\\n9598^\\n95998\\n96012\\n96026\\n9.96039\\nLog. Vers.\\nn\\n10\\n93281\\n93416\\n\u00e2\u0080\u00a293551\\n93686\\n93821\\n10\\n93957\\n.94093\\n,94229\\n94366\\n94503\\n10\\n,94641\\n94778\\n.94917\\n.95055\\n95194\\n10,\\n95333\\n95473\\n95613\\n95753\\n95894\\nJD\\n10\\n,96035\\n.96176\\n.963I8\\n9646 1\\n96603\\n10\\n96746\\n,96889\\n97033\\n97177\\n97322\\n10\\n.97467\\n,97612\\n.97758\\n,97904\\n,98056\\n10\\n.9819?\\n.98345\\n,98492\\n98646\\n.98789\\n10\\n98938\\n.9908^\\n.9923^\\n.9938^\\n\u00e2\u0080\u00a299538\\n10\\n10\\n1 1\\n99689\\n,99841\\n99993\\n,00145\\n,00293\\nII\\n00451\\n00605\\n00759\\n00914\\n01069\\nII\\n01225\\n01381\\n0153^\\n01694\\n01852\\n1 1 .02010\\nLog. Kxsen.\\n34\\n35\\n35\\n35\\n35\\n36\\n36\\n37\\n37\\nZl\\n3l\\n38\\n38\\n39\\n39\\n39\\n40\\n40\\n40\\n41\\n41\\n42\\n42\\n42\\n43\\n43\\n44\\n44\\n44\\n45\\n45\\n45\\n46\\n46\\n47\\n4^\\n4?\\n48\\n49\\n49\\n49\\n50\\n50\\n51\\n51\\n51\\n52\\n52\\n53\\n53\\n54\\n54\\n55\\n55\\n55\\n56\\n56\\n57\\nS7\\n58\\n7\\nLog. Vers.\\n9.96039\\n96053\\n96067\\n96081\\n96095\\n96 log\\n96122\\n96136\\n96150\\n96163\\n9617^\\n9619I\\n96205\\n962 1 8\\n96232\\n96246\\n96259\\n96273\\n96287\\n96301\\n96314\\n96328\\n96342\\n96355\\n96369\\n96383\\n96397\\n96416\\n96424\\n96438\\n1 Log\\n96451\\n96465\\n96479\\n96492\\n96506\\n96519\\n96533\\n96547\\n96566\\n96574\\n96588\\n9660T\\n96615\\n96629\\n96642\\n96656\\n96669\\n96683\\n96697\\n96716\\n96724\\n9673^\\n96751\\n96764\\n96778\\n96792\\n96805\\n96819\\n96832\\n96846\\n9.96859\\nI I\\n1 1\\nII\\n1 1\\nI I\\nI I\\nII\\nII\\nII\\n1 1\\nII\\nII\\nI I\\nLotf. Vers. 7 |L \u00c2\u00bber\\n436\\nExsec.\\n02010\\n02163\\n0232^\\n02487\\n02646\\n02807\\n02968\\n03129\\n03291\\n03453\\n036 1 6\\n03780\\n03944\\n04108\\n04273\\n04438\\n04604\\n04771\\n04938\\n05106\\n1)\\n05274\\n05443\\n05612\\n05782\\n05952\\n06123\\n06295\\n06467\\n06640\\n06813\\n06987\\n07 161\\n07336\\n07512\\n07688\\n07865\\n08043\\n08221\\n08400\\n08579\\n08759\\n08940\\n09121\\n09303\\n09486\\n09669\\n09853\\n10038I\\n10223I\\n10409\\n10595\\n10783\\n1097 1\\n1 1 160\\n1 1 349\\n1 1 539\\n1 1 736\\n11922\\n12114\\n1230^\\n12501\\nKxs\u00c2\u00ab\\n58\\n59\\n59\\n59\\n66\\n61\\n61\\n61\\n62\\n63\\n63\\n64\\n64\\n65\\n65\\n66\\n67\\n67\\n67\\n68\\n69\\n69\\n69\\n70\\n71\\n71\\n72\\n73\\n73\\n74\\n74\\n75\\n76\\n76\\n77\\n71\\n78\\n79\\n79\\n80\\n86\\n81\\n82\\n82\\n83\\n84\\n85\\n85\\n86\\n86\\n87\\n88\\n89\\n89\\n90\\n91\\n91\\n92\\n93\\n93\\n5\\n6\\n7\\n8\\n10\\n1 1\\n12\\n13\\n14\\n15\\n16\\n17\\n18\\n19\\n20\\n21\\n22\\n23\\n24\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n0\\nJ)\\np. p.\\n6\\n190\\n19.0\\n7\\n8\\n22.1\\n25-3\\n9\\n28.5\\n10\\n20\\n63-3\\n30\\n95 -o\\n40\\n50\\n126.6\\n158.3\\n170\\n17.0\\n19-8\\n22.6\\n25-5\\n28.3\\n56.6\\n85.0\\n3-3\\n141-6\\n180\\n18.0\\n21.0\\n24.0\\n27.0\\n30.0\\n60.0\\n00. o\\n120.0\\n150.0\\n160\\n16.0\\n18. 6\\n21.3\\n24 .0\\n26.6\\n53-3\\n80.0\\n106.6\\n^33-3\\n150 140\\n15.0\\n17-5\\n20.0\\n22.5\\n25.0\\n50,0\\n75-0\\nlOO.O\\nI2S.O\\n14.0\\n16.3\\n18.6\\n21 .0\\n23 -3\\n46.5\\n70.0\\n93-3\\n116.6\\n130\\n9\\nb\\n6\\n13.0\\n0.9\\n0.\\n7\\n15-1\\n1\\n0.\\n8\\n17-3\\nI\\n2\\nI\\n9\\n19-5\\nI\\n3\\n1.\\n10\\n21.6\\nI\\n5\\nI.\\n20\\n43-3\\n3\\n2.\\n.30\\n65.0\\n4\\n5\\n4-\\n40\\n86.6\\n60\\n5-\\n5\u00c2\u00ab\\n108.3\\n7\\n5\\n6.\\n6\\n7\\n0.7\\n6\\n0.6\\n7\\n8\\n0.8\\n0.9\\n0.7\\n0.8\\n9\\nI.O\\n0.9\\n10\\nI.I\\n1 .0\\n2D\\n2.3\\n2.0\\n30\\n3-5\\n3-0\\n40\\n4-6\\n4.0\\n50\\n5-8\\n5-0\\n5\\n05\\n0.6\\n0.6\\n0.7\\n0-8\\n1-6\\n2-5\\n3-3\\n4.1\\n14\\n14\\nI\\n6\\n1.4\\n1.4\\nI.\\n7\\n1-7\\n1-6\\nI.\\n8\\n1.9\\n1-8\\nI.\\n9\\n2.2\\n2.1\\n2.\\n10\\n2.4\\n2-3\\n2.\\n20\\n4-8\\n4 6\\n4-\\n30\\n7.2\\n7.0\\n6.\\n40\\n9-6\\n9-3\\n9-\\n50\\n12. 1\\n11.6\\nII.\\nr.", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0488.jp2"}, "489": {"fulltext": "TABLE VIII. -LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS\\n80\u00c2\u00b0 S7\\n10\\nII\\n12\\n14\\n15\\ni6\\nI?\\ni8\\n19\\n20\\n21\\n22\\n23\\n24\\n^5\\n26\\n27\\n29\\n30\\n31\\n32\\n33\\nJ\u00c2\u00b1.\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n4B\\n49\\n50\\n51\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n5?_\\nGO\\nLoar. Vers.\\nJ)\\n9.96859\\n.96873\\n.96887\\n.96900\\n.96914\\n,96927\\n,96941\\n96954\\n96968\\n96981\\n9.96995\\n.970O8\\n97022\\n\u00e2\u0080\u00a29703?\\n97049\\n.97062\\n.97076\\n.97089\\n97103\\n97116\\n97 1 30\\n\u00e2\u0096\u00a097143\\n\u00e2\u0096\u00a097157\\n,97170\\n97183\\n\u00e2\u0096\u00a097^97\\n.97216\\n,97224\\n,9723^\\n97251\\n,97264\\n,97277\\n,97291\\n97304\\n97318\\n997331\\n\u00e2\u0080\u00a297345\\n\u00e2\u0080\u00a297358\\n\u00e2\u0080\u00a297371\\n\u00e2\u0080\u00a297385\\n9^97398\\n.97412\\n\u00e2\u0080\u00a297425\\n\u00e2\u0080\u00a297438\\n\u00e2\u0080\u00a297452\\n9.9746S\\n\u00e2\u0080\u00a297478\\n.97492\\n\u00e2\u0080\u00a297505\\n\u00e2\u0080\u00a297519\\n9-97532\\n\u00e2\u0080\u00a297545\\n\u00e2\u0080\u00a297559\\n\u00e2\u0080\u00a297572\\n\u00e2\u0080\u00a297585\\n9^97599\\n.97612\\n.97625\\n\u00e2\u0080\u00a297639\\n.97652\\n9.9766:\\n13\\n14\\n13\\n13\\n13\\nJ3\\nf3\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\nJ3\\n13\\n13\\nliOp. Kxsec. 7\\nI I\\n12501\\n12696\\nI2891\\n.13087\\n.13284\\nI I 1^482\\nI 3680\\n\u00e2\u0080\u00a213879\\n.14079\\n14286\\n95\\n195\\n96\\n96\\n198\\n198\\n199\\n200\\n201\\n1 1\\n14482\\n14684\\n14887\\n15092\\n15297\\n1 1\\n15502\\n15709\\n1-5917\\n16125\\n6334\\n1 1\\n16544\\n16755\\n16967\\n17186\\n17394\\n1 1 1 7609\\n17824\\n1 804 1\\n.18259\\n.1847^\\nII 18697\\n.1891^\\n\u00e2\u0080\u00a2i9 38\\n9361\\n.19584\\nII\\n19809\\n20034\\n.20261\\n20489I\\n.20717,\\n11.20947,\\n.211781\\n.21410I\\n.21643\\n.21877:\\nI I .221 I2j\\n.22349\\n.22586\\n.22825\\n.230651\\nI 233O6\\n\u00e2\u0080\u00a223548\\n23792\\n-240371\\n.24283!\\n11.24530\\n\u00e2\u0080\u00a224778\\n\u00e2\u0080\u00a225028\\n.25279\\n\u00e2\u0080\u00a2255311\\n11.25785\\n201\\n202\\n203\\n204\\n205\\n205\\n206\\n208\\n208\\n209\\n210\\n21 1\\n212\\n213\\n214\\n214\\n215\\n216\\n218\\n218\\n219\\n226\\n221\\n222\\n223\\n224\\n225\\n227\\n227\\n228\\n230\\n236\\n232\\n233\\n234\\n235\\n236\\n237\\n239\\n239\\n24?\\n242\\n243\\n245\\n246\\n247\\n248\\n250\\n251\\n252\\n254\\nLojf. Vers. I It\\n9.97665\\n.97679\\n.97692\\n\u00e2\u0080\u00a297705\\n\u00e2\u0080\u00a2977I8\\n9.97732\\n\u00e2\u0080\u00a297745\\n\u00e2\u0080\u00a297758\\n.97772\\n\u00e2\u0096\u00a097785\\n9^97798\\n.97811\\n.97825\\n\u00e2\u0080\u00a297838\\n\u00e2\u0080\u00a297851\\n9.97864\\n\u00e2\u0080\u00a297878\\n.97891\\n97904\\n-97917\\n9-97931\\n\u00e2\u0080\u00a297944\\n\u00e2\u0080\u00a297957\\n.97976\\n.97984\\n9-97997\\n.98016\\n.98023\\n98036\\n.98050\\n9.98063\\n.98076\\n98089\\n.98102\\n.98116\\n9.98129\\n.98142\\n\u00e2\u0080\u00a298155\\n.98168\\n.98181\\n9.98195\\n.98208\\n.98221\\n\u00e2\u0080\u00a298234\\n\u00e2\u0080\u00a29824?\\n9.98266\\n\u00e2\u0080\u00a298273\\n.98287\\n.98300\\n\u00e2\u0080\u00a298313\\n9.98326\\n\u00e2\u0080\u00a298339\\n.98352\\n.98365\\n\u00e2\u0080\u00a298378\\n9.98392\\n98405\\n.98418\\n.98431\\n\u00e2\u0080\u00a2984-14\\nf). 984^7\\nLoir. Vers. I \\\\\\\\,nK. Kxser. k Loir. Vers.\\n3\\n13\\n3\\n13\\n3\\n13\\n13\\n13\\n3\\n3\\n3\\n13\\n13\\n13\\n13\\n3\\n13\\n13\\n3\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n3\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n3\\n3\\n13\\n13\\n13\\n13\\nM\\n13\\n13\\n3\\n3\\nK\\\\\\n\u00e2\u0080\u00a225785 _\\n.26046 ^5\\n.26297 ^0\\n\u00e2\u0080\u00a226554\\n.26814\\n1 1\\n27074\\n27336\\n27599\\n27864\\n28131,\\n1 1\\n\u00e2\u0080\u00a228398\\n.28668\\n.28938\\n.2921 1\\n\u00e2\u0080\u00a229485\\n1 1\\n.29766\\n3003^\\n.30316\\n\u00e2\u0080\u00a230596\\n\u00e2\u0080\u00a230878\\n1 1\\n^,1 162\\n\u00e2\u0080\u00a23 447\\n\u00e2\u0080\u00a231734\\n.32023\\n\u00e2\u0080\u00a232313\\nII\\n.32606\\n32900\\n\u00e2\u0080\u00a233196\\n\u00e2\u0080\u00a233494\\n\u00e2\u0080\u00a233793\\n1 1 34095\\n\u00e2\u0096\u00a034398\\n34704\\n.35011\\n\u00e2\u0080\u00a235321\\n\u00e2\u0080\u00a2356321 ^I^\\n-5/\\n259\\n266\\n262\\n263\\n265\\n266\\n267\\n269\\n276\\n272\\n274\\n275\\n277\\n278\\n279\\n282\\n2S3\\n285\\n287\\n288\\n296\\n292\\n294\\n296\\n298\\n299\\n301\\n303\\n305\\n307\\n309\\n10\\n1 1\\n12\\n3\\n14\\n5\\n16\\n17\\n18\\n9\\nI I\\n35946\\n.36261\\n\u00e2\u0080\u00a236579\\n36899\\n1 1\\n.37221\\n\u00e2\u0080\u00a237546\\n.37872\\n.38201\\n\u00e2\u0080\u00a238532\\n1 1 38866\\n.3920I\\n\u00e2\u0080\u00a239540\\n\u00e2\u0080\u00a239886\\n.40224\\n1 1 .40569\\n409 1 8\\n.41269\\n.41622\\n\u00e2\u0080\u00a241979\\n7\\n11.42338\\n.42699\\n.43064\\n\u00e2\u0080\u00a24343\\n.43802\\n-44175\\n3^3\\n3 5\\n318\\n320\\n-7 2\\n324\\n326\\n328\\n33\\n333\\n335\\n338\\n340\\n343\\n345\\n348\\n351\\n353\\n356\\n359\\n361\\n36.1\\n37 5\\n20\\n21\\n22\\n23\\n3_\\n25\\n26\\n27\\n28\\n29\\n;iO\\n31\\n32\\n33\\nii\\n35\\n36\\n37\\n3^\\n39\\nj\\n40\\n41\\n42\\n43\\nJ4\\n45\\n46\\n47\\n48\\n49\\n50\\n51\\n52\\n53\\n55\\n56\\n57\\n58\\n59\\n(;o\\n6\\n250\\n25.0\\n7\\n8\\n29.1\\n33-3\\n9\\n37-5\\n10\\n20\\n83.3\\n30\\n40\\n50\\n125.0\\n166.^\\n208.3\\n230\\n23.0\\n26.\\n30 6\\n34-5\\n38^3\\n76.6\\n115. o\\n53^3\\n191. 6\\n210\\n6\\n21 .0\\n7\\n24^5\\n8\\n28.0\\n9\\n3i^5\\n10\\n35^o\\n20\\n70.0\\n20\\n105.0\\n40\\n140.0\\n50\\n\u00c2\u00bb75-o\\n240\\n24 .0\\n28.0\\n32 o\\n36.0\\n40.0\\n80.0\\n120.0\\n160.0\\n200.0\\n220\\n22.0\\n25-6\\n29.3\\n33^o\\n36.^\\n73-3\\n1 10. o\\n83.3\\n200\\n20.0\\n2^-3\\n26.6\\n30.0\\n33-3\\n66.6\\n100.0\\n133.3\\n166.6\\n0.1\\n0.1\\n0-3\\n0.5\\no.^\\n14\\n13\\n6\\n1.4\\n\u00e2\u0080\u00a23\\n7\\n\u00e2\u0080\u00a26\\ni.ti\\n8\\n1-8\\n1.8\\n9\\n2.1\\n2.0\\n10\\n2-3\\n3.2\\n20\\n4.6\\n4..S\\n30\\n7.0\\n6.7\\n40\\n9.3\\n9.0\\n50\\n.6\\nII. 2\\n0.1\\no. t\\n13\\n\u00e2\u0080\u00a23\\n\u00e2\u0080\u00a27\\n1.5\\n2. 1\\n4-3\\n6..S\\n8.6\\n10. 8\\nr. r.\\n190\\n4\\n3\\n6\\nig.o\\n0.4\\no^3\\n7\\n8\\n9\\n22. 1\\n25^3\\n28.5\\n0.4\\n0-5\\n0.6\\n0-3\\n0.4\\n0.4\\n10\\n20\\n3 -6\\n633\\n6\\n^\u00e2\u0080\u00a23\\n0-5\\nI.O\\n30\\n40\\n50\\n95-0\\n126.6\\n15S.3\\n2.0\\n3.3\\n\u00e2\u0080\u00a25\\n2.0\\n\u00e2\u0080\u00a25 1\\n437", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0489.jp2"}, "490": {"fulltext": "TABLE VIII.\u00e2\u0080\u0094 LOGARITHMIC VERSED SINES AND EXTERNAL SECANTS.\\n88\u00c2\u00b0 89\\nLo\\nVers.\\nJ Loi:.\\nExsec. 1 J Loj\\nJ. Vers.\\nI)\\nLoff. Exsec.\\n2\\nP. P.\\n9\\n9845^\\nI^\\n44175] 376 9\\n44551! :^7a\\n99235\\n11.75050\\n742\\n755\\n768\\n781\\nI\\n98476\\n13\\n99248\\n1 Z\\n.75792\\nI\\n2\\n3\\n4\\n98483\\n98496\\n.98509\\n13\\n13\\n13\\n44931 ^g\\n45313 ^86\\n45699\\n99261\\n99274\\n99287\\n13\\n13\\n13\\n.7654^\\n.77316\\n.78097\\n2\\n3\\n4\\n5 9\\n.98522\\n\\\\l\\n46088 9\\n99299\\n12\\n11.78892\\n795\\n809\\n825\\n840\\n856\\n872\\n896\\n908\\n927\\nS\\n6\\n.98535\\n13\\n46486 ^92\\n\u00e2\u0080\u00a246876 395\\n99312\\n13\\n.79702\\n6\\n7\\n\u00e2\u0080\u00a298548\\n13\\n99325\\n13\\n.80527\\n7\\n8\\n.98562\\n^3\\n\u00e2\u0080\u00a247275 ii^\\n99338\\n1 z\\n.81367\\n8\\n9\\n\u00e2\u0080\u00a298575\\n13\\n\u00e2\u0080\u00a247677\\n99351\\n13\\n.82223\\n9\\n10 9\\n.98588\\n48083 4-^ 9\\n99363\\n12\\n11.83095\\n10\\nII\\n.98601\\nij\\n48493 jj^\\n99376\\n13\\n.83986\\nII\\n12\\n98614\\n13\\n\u00e2\u0080\u00a248906 4 3\\n99389\\n13\\n84894\\n12\\n13\\n.98627\\n^j\\n\u00e2\u0080\u00a249323 l^Q\\n99402\\n.85821\\n13\\n14\\n98640\\n13\\n49743\\n\u00e2\u0080\u00a299415\\n13\\n13\\n12\\n.86768\\n947\\n967\\n989\\n14\\n15\\n16\\n15 9\\ni6\\n98653\\n98666\\n\\\\l\\n50168 9\\n50597 f:^\\n99428\\n99446\\n11.87735\\n.88724\\n17\\n98679\\n13\\n51029 2:^:\\n99453\\n13\\n\u00e2\u0080\u00a289735\\n17\\ni8\\n19\\n98692\\n98705\\n13\\n13\\n5H66 436\\n51906\\n99466\\n\u00e2\u0080\u00a299479\\n1 2\\n13\\n90769\\n.91829\\n1 1034\\n1059\\n1085\\n1112\\n1 146\\n1171\\n1203\\n1236\\n18\\n19\\n20 9\\n21\\n98718\\n98731\\n\\\\i\\n52351 445 g\\n53713\\n54176 4 3\\n\u00e2\u0080\u00a299491\\n\u00e2\u0080\u00a299504\\n12\\n13\\nI 1 .92914\\n.94026\\n20\\n21\\no -7\\n98744\\n13\\n13\\n13\\n\u00e2\u0080\u00a299517\\ni^\\n\u00e2\u0080\u00a295167\\n22\\n23\\n24\\n98757\\n98770\\n\u00e2\u0080\u00a299530\\n\u00e2\u0080\u00a299543\\n13\\n12\\n\u00e2\u0080\u00a296338\\n\u00e2\u0080\u00a297541\\n23\\n24\\n25\\n25 9\\n98783\\nM\\n54643!^? 9\\n99555\\n11.98777\\n26\\n98796\\n13\\n\u00e2\u0080\u00a299568\\n^3\\nI 2 00048\\n26\\n27\\n98809\\n13\\n5|5^l 485\\n56076 4\\n56563 ^^l\\n99581\\n.01358\\n1309\\n27\\n28\\n29\\n98822\\n98835\\n13\\n99594\\n99606\\n13\\n12\\n13\\nT\\n.02707\\n04098\\n1349\\n1 391\\n1436\\n1485\\n28\\n29\\n30\\n30 9\\n98848\\n=3\\n57334 roi\\n99619\\n12.05535\\n31\\n98861\\n99632\\n.07020\\n31\\n32\\n98874\\n13\\n58058 504\\n58567; 1^:1\\n59082 513\\n99645\\n3\\n\u00e2\u0080\u00a208557\\n1537\\n32\\n33\\n34\\n98887\\n98900\\n13\\n99657\\n99670\\n13\\nIOI49\\nII80I\\n1592\\n1652\\n1716\\n33\\n34\\n35 9\\n98913\\nII\\n?20\\n59602 J 9\\n60129 527\\n60662 533\\n99683\\nI 2\\nI2.I3517\\n35\\n36\\n98925\\n99695\\n15302 :^^f\\n36\\n37\\n98938\\n13\\n99708\\n13\\n.17163\\n37\\n38\\n39\\n98951\\n98964\\nI J\\n13\\n61202 539\\n61747. 545\\n99721\\n99734\\n13\\n12\\n13\\n12\\n.19106\\n.21139\\n1943\\n2033\\n2I3I\\n2246\\n2361\\n38\\n39\\n10\\n41\\n42\\n10 9\\n41\\n42\\n98977\\n98996\\n99003\\n13\\n62300 ^52 Q\\n99746\\n99759\\n99772\\n12.23271\\n.25511\\n.27872\\n6\\n7\\nI\\nI\\nI\\n3\\n3\\n.6\\n13\\n^\u00e2\u0080\u00a23\\n1.5\\n43\\n44\\n990 1 6\\n99029\\n13\\n12\\nS5g:\\n99784\\n99797\\n13\\n.3036^\\n\u00e2\u0080\u00a233013\\n2495\\n2645\\n2815\\n43\\n44\\n9\\nlO\\n2\\n2\\n2\\n1-7\\n2.1\\n45 9\\n99042\\n5 II\\n65167\\nsoo\\n99810\\n12\\n12.35828\\n45\\n30\\n4\\n6\\n\u00e2\u0080\u00a27\\n4-3\\n6.5\\n46\\n99055\\nij\\n65762\\n99823\\n3\\n\u00e2\u0080\u00a23883?\\n3009\\n46\\n40\\n9\\n.0\\n8.6\\n47\\n99068\\n13\\n66366 ^Vl\\nf 978 ^4\\n67598\\n99835\\n1 2\\n42068\\n3231\\n3489\\n3791\\n4152\\n4588\\n512^\\n5812\\n6707\\n47\\n50\\n1 1 J 1\\n10.\\n48\\n49\\n99081\\n99093\\n13\\n12\\n99848\\n99861\\n13\\n12\\n12\\n13\\n12\\n12\\n\u00e2\u0080\u00a24555^\\n\u00e2\u0080\u00a249349\\n48\\n49\\n50\\n51\\n52\\n53\\n54\\n1\\n50 9\\n51\\n52\\n53\\n54\\n99106\\n991 19\\n99132\\n99H5\\n99158\\n13\\n13\\n12\\n68227l^;8 9\\n68865I ^38\\n695ii 6t^\\n70168 ^56\\n70834: f\\n99873\\n99886\\n99899\\n9991 1\\n99924\\n12.53501\\n58089\\n.63217\\n.69029\\n\u00e2\u0080\u00a275736\\n6\\n7\\n8\\n9\\n[2\\n1.2\\n1.4\\n1-6\\n1.9\\n55 9\\n56\\n57\\n58\\n59\\n99171\\n99184\\n99197\\n99209\\n99222\\n13\\n12\\n13\\n1 1\\n7^509J68| 9\\n728921 96\\n736001\\n74319 II\\n99937\\n99949\\n99962\\n99974\\n99987\\n13\\n12\\n12\\n12\\n13\\n12\\n12.83667\\n\u00e2\u0080\u00a293371\\n13.05877\\n\u00e2\u0080\u00a2234991\\n\u00e2\u0080\u00a253615\\n7931\\n9704\\nI25O6\\nI762T\\n301 16\\n55\\n56\\n57\\n58\\n59\\n00\\n10\\n20\\n30\\n40\\n50\\nI\\n2. 1\\n4.1\\n6.2\\n8.3\\n0.4\\n0 9\\n99235\\nII\\n75050 10\\n00000\\nInfinity\\n1\\nLo\\nu. Vers.\\nD Log.\\nKxsec T Lo!\\nVers.\\nj\\nLoar. Exsec.\\n1\\nP. P. 1\\n438", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0490.jp2"}, "491": {"fulltext": "TABLE IX.\u00e2\u0080\u0094 NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS.\\nlO\\n20\\n30\\n40\\n50\\n1\\n10\\n20\\n30\\n40\\n50\\n2\\n10\\n20\\n30\\n40\\n50\\n3\\n10\\n20\\n30\\n40\\n50\\n4\\n10\\n20\\n30\\n40\\n50\\n5\\n10\\n20\\n30\\n40\\n50\\ne\\n10\\n20\\n30\\n40\\n7\\n10\\n20\\n30\\n40\\n50\\n8\\n10\\n20\\n30\\n40\\n50\\n9\\n10\\n20\\n30\\n40\\n50\\n10\\nSin.\\n0.0000\\n0.0029\\n0.0058\\no.ooSf\\no.ci 15\\n0.0I4I\\n0.0174\\n0.0203\\n0.0232\\n0.0262\\n0.0291\\n0.0320\\n0.0349\\n0.0378\\n0.0407\\n0.0436\\n0.0465\\n0.0494\\n0.0523\\n0.0552\\n0.0581\\n0.0610\\n0.0639\\n0.0663\\n0.0697\\n0.0726\\n0.0755\\n0.0784\\n0.0813\\n0.0842\\n0.0871\\no. 0900\\n0.0929\\n0.0958\\n0.0987\\no. 1016\\n0.1045\\n0.1074\\nO.I 103\\nO.I 1 32\\n0.II6I\\no. 1 190\\n0.I2I8\\no. 1 247\\nO.I276\\n0.1305\\n0.1334\\n0.1363\\n0.I39I\\n0.1420\\n0.1449\\n0.1478\\no. 1 507\\n0.1535\\n0.1564\\no. 1 593\\n0.1622\\n0.1656\\n0.1679\\n0.1708\\n0.1736\\nCos.\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n28\\n29\\n29\\n29\\n29\\n28\\n29\\n29\\n29\\n28\\n29\\n28\\n29\\n29\\n28\\n29\\n28\\n29\\n28\\n29\\n28\\n2\u00c2\u00a7\\n29\\nd.\\nTan.\\nJ). 0000\\n0.0029\\n0.0058\\n0.0087\\no.oi 16\\n0.014.5\\n0.0174\\n0.0203\\n0.0233\\n0.0262\\n0.0291\\n0.0320\\nd.\\n0.0349\\n0.0378\\no. 040^\\n0.0436\\n0.0466\\n0.0495\\n0.0524\\n0-0553\\n0.0582\\n0.061 1\\n0.0641\\n0.0670\\n0.0699\\n0.0728\\n0.0758\\n0.0787\\n0.0816\\n0.0845\\n0.0875\\no. 0904\\n0.0933\\n0.0963\\n0.0992\\no. 102T\\n0.I05I\\no. 1 080\\no. mo\\n0.1139\\no. 1169\\n0.1 198\\n0.1228\\n0.1257\\n0.1287\\n0.1316\\n0.1346\\n0.1376\\no.i4og\\n0.1435\\n0.1465\\n0.1494\\no. 1524\\n0.1554\\n0.1584\\n0.1613\\n0.1643\\n0.1673\\n0.1703\\n0.1733\\n0.1763\\nCot.\\nCot.\\n00\\n343.773\\n171.885\\n114.588\\n85. 9398\\n68.7501\\n;57_^89\u00c2\u00a7\\n49.1039\\n42.9641\\n38.1884\\n34-367^\\n31.2416\\n28.6362\\n26.4316\\n24. 54 if\\n22.903^\\n21.4704\\n20.2055\\n19.0811\\n18.0750\\n17. 1693\\n16.3498\\n15.6048\\n14.9244\\n14.3005\\n13.726^\\n13.1969\\n12.7062\\n12.2505\\n11.8261\\n11.4300\\n11.0594\\n10.71 19\\n10.3854\\n10.0786\\n9.788T\\n9.5143\\n9-2553\\n9.0098\\n8.7769\\n8.5555\\n8.3449\\n8.1443\\n7-9530\\n7.7703\\n7-595?\\n7.4287\\n7.268^\\n7- 1 153\\n6.9682\\n6.8269\\n6.6911\\n6.5605\\n_6^3j+8\\n^,3i3 7.\\n6. 1976\\n6.0844\\n5-9757\\n5.8708\\n5-7693\\nd.\\n5-6713\\ni860\\n1398\\n7756\\n8217\\n1261\\n6053\\n2046\\nTan.\\n6380\\n4333\\n2648\\n1244\\n0061\\n9056\\n8 95\\n7450\\n6804\\n6237\\n5739\\n5298\\n4907\\n4557\\n4243\\n3961\\n3706\\n3475\\n3265\\n3073\\n2899\\n2738\\n2590\\n2454\\n2329\\n2213\\n2106\\n2006\\n1913\\n1826\\n1746\\n1670\\n1599\\n1534\\n1471\\n1413\\n1358\\n1306\\n1257\\n1211\\n1 1 67\\n1126\\n1087\\n1049\\n1014\\n986\\n1.\\nCos.\\n1. 000\\n1. 0000\\nI.GOOO\\n0.9999\\n0-9999\\n0.9999\\n^9998\\n0.9998\\n0.999?\\n0-9996\\n0.9996\\n0.9995\\n0-9994\\n0.9993\\n0.9991\\n0.9996\\n0.9989\\n0.9988\\no.998g\\n0.9984\\n0.9983\\n0.9981\\n0.5979\\n0.9977\\n0997g\\n0.9973\\n0.9971\\n0.9969\\n0.9967\\n0.9964\\n0.9962\\n0.9959\\n0-9956\\n0.9954\\n0.9951\\n0.9948\\n0.9945\\n0.9942\\n0.9939\\n0.9935\\n0.9932\\n0.9929\\n0992g\\n0.9922\\n0.9918\\n0.9914\\n0.9916\\n^.9906\\n0.9902\\n0.9898\\n0.9894\\n0.9890\\n0.9886\\n0.9881\\nJ\u00c2\u00b0^9l77:\\n0.9872\\n0.9867\\n0.9863\\n0.9858\\no.98y_\\n0.9848\\nSin.\\nd.\\nyo\\n50\\n40\\n30\\n20\\n10\\nso\\n50\\n40\\n30\\n20\\n10\\n88\\n50\\n40\\n30\\n20\\n10\\n87\\n50\\n40\\n30\\n20\\n10\\n86\\n50\\n40\\n30\\n20\\n10\\n85\\n50\\n40\\n30\\n20\\n10\\n84\\n50\\n40\\n30\\n20\\n10\\n83\\n50\\n40\\n30\\n20\\n10\\n82\\n50\\n40\\n30\\n4\\n5\\n20\\n6\\n10\\n7\\n81\\n8\\nQ\\n50\\n40\\n30\\n20\\n10\\n80\\nr. I\\n30 29 29\\n3-0\\n6.0\\n9.0\\n12.0\\n15.0\\n18.0\\n21 .0\\n24.0\\n27.0\\n14.7\\n17.7\\n20-6\\n23.6\\n26.5\\n2.9\\n5-8\\n8.7\\n11.6\\nM-5\\n17.4\\n20.3\\n23.2\\n26.1\\n28 5 4 4\\n2-8\\n05\\n0.4\\n5-7\\n8.5\\nI.O\\n1-5\\n0.9\\n1.3\\n11.4\\n2.0\\n1.8\\n14.2\\n2.5\\n2.2\\n17. 1\\n3.0\\n2.7\\n19.9\\n3-5\\n31\\n22.8\\n4.0\\n3-t\\n25.6\\n4-5\\n4.0\\n0.4\\n1.6\\n3.2\\n3-6\\n3322\\n4\\n5\\n62\\n72\\n82\\n9I3\\n3 0.3\\n70.6\\n0.9\\n1.2\\n1.5\\n2.1\\n2.4\\nI 2.7\\n1.5\\n1.7\\n2.0\\n1-4\\n1.6\\n1.8\\n0.4\\n0.5\\n0.6\\n.ojo.7\\n.20.8\\n.310.9\\n0.0\\n0.1\\nI X O\\n0.1\\n0.3\\n0.4\\n0.6\\n0.7\\n0.9\\n0.2\\n0.3\\n0.3\\n0.4\\n0.4\\nP. P.\\n80-90\\n439", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0491.jp2"}, "492": {"fulltext": "TABLE IX.\u00e2\u0080\u0094 NATURAL SINES,\\nCOSINES, TANGENTS, AND COTANGENTS.\\n10-20\u00c2\u00b0\\nSin.\\nd.\\n28\\nTan.\\nd.\\nCot.\\nd.\\nCos.\\nd:\\np. p.\\n10\\n10\\n0.1736\\n0.1763\\n30\\n5-6713\\n949\\n0.9848\\n5\\n80\\n50\\n0.1765\\n0.1793\\n5-5764\\n0.9843\\n20\\n0.1793\\n^8\\n0.1823\\ni^\\n5.4845\\n919\\n890\\n862\\n8^A\\n0.9838\\nb\\n40\\n30\\n40\\n0.1822\\nO.1851\\n29\\n28\\n0.1853\\n0.1883\\n30\\n30\\n30\\n30\\n30\\n5-3955\\n5-3093\\n0.9832\\n0.9827\\n5\\n5\\n30\\n20\\n33 32 31\\n50\\n11\\n10\\n0.1879\\n28\\n28\\nO.1913\\n5-2256\\n811\\n787\\n764\\n742\\n0.9822\\n5\\n6\\n10\\n79\\n50\\nI\\n2\\n3\\n3-3 3\\n6.6 6\\n9-9 9\\n.2 3.1\\n.4 6.2\\n.6 9.3\\n0.1908\\n0.1944\\n0.1974\\n5-I44S\\n0.9816\\n01 936\\n5.0658\\n0.9816\\n20\\n0.1965\\n^8\\n28\\n0. 2004\\n3^\\n30\\n4.9894\\n0.9805\\n5\\n6\\n40\\n4\\n5\\n13.2 12\\n16.5 16\\n.8 12.4\\n\u00e2\u0080\u00a20 15.5\\n30\\n0.1993\\n2R\\n0.2034\\n30\\n4.9151\\n721\\n0.9799\\n5\\n30\\n6\\n19.8 19\\n.2 18.6\\n40\\n50\\n12\\n10\\n20\\n0.2022\\n0.2050\\n28\\n28\\n28\\n28\\n0.2065\\n0.2095\\n30\\n30\\n.30\\n30\\n4.8430\\n4-7728\\n7o\u00c2\u00a3\\n682\\n664\\n646\\n620\\n0.9793\\n0.978^\\n6\\n6\\n6\\n6\\n6\\n20\\n10\\n78\\n50\\n40\\n7\\n8\\n9\\n23.1 22\\n26.4 25\\n29.7 28\\n.4 21-7\\n.6 24.8\\n.827.9\\n0.2079\\n0.2125\\n47046\\n0.9781\\n0.9775\\n0.9769\\n0.2I0f\\n0.2136\\n0,2156\\n0.2185\\n4.6382\\n4-5736\\n30\\n40\\n0. 2 1 64\\n0.2193\\n28\\n0.2217\\n0.224^\\n30\\n4.5107\\n4.4494\\n613\\n0.9763\\n0.97 56\\n6\\n30\\n20\\n1\\n36 30 29 1\\n3.0 3.0I 2.9\\n50\\n13\\n10\\n20\\n0.2221\\n28\\n28\\n28\\n28\\n0.2278\\n3^\\n30\\n31\\n30\\n4-3897\\n597\\n582\\n568\\n553\\n0.9750\\n6\\n6\\n6\\n6\\n10\\n77\\n50\\n40\\n2\\n3\\n4\\n5\\n6\\n6.1 6\\n9.1 g\\n12.2 12\\n15-2 15\\n18.3 18\\n.0 5.8\\n.0 8.7\\n.0 II. 6\\n.0 14.5\\n.0 17.4\\n2249\\nO.23O8\\n43315\\n09743\\n0.2278\\n0.2306\\n0.2339\\n0.2370\\n4-2747\\n4.2193\\n0-9737\\n0.9736\\n30\\n40\\n0.2334\\n0.2362\\n28\\n28\\n0.2401\\nO.243T\\n3i\\n30\\n4-1653\\n4.1125\\n540\\n527\\n515\\n0.9723\\n0.9717\\ny\\n6\\n30\\n20\\n7\\n8\\n21.3 21\\n24-4 24\\n.0 20.3\\n.0 23.2\\n50\\n0.2391\\n23\\n0. 2462\\n31\\n4.0616\\n0.Q710\\n10\\n9\\n27.4 27\\n.0 26.1\\nU\\n10\\n20\\n0.2419\\n28\\n28\\n0.2493\\n31\\n30\\n31\\n4.0108\\n491\\n480\\n469\\n0.9703\\n7\\n7\\n7\\n76\\n50\\n40\\n20 28 2*7\\n0.2447\\n0.2475\\n0.2524\\n0.2555\\n3-9616\\n3-9136\\n0. 9696\\n0.9688\\n30\\n0.2504\\n^8\\n0.2586\\n31\\n3.8667\\n0.9681\\n7\\n30\\nI\\n2.\u00c2\u00a7 2\\n.8 2.7\\n40\\n0.2532\\n28\\n0.2617\\n31\\n3.8208\\n458\\n0.9674\\n7\\n20\\n2\\n5.2 5\\n.6 5.4\\n50\\n15\\n0.2560\\n28\\n28\\n0. 2648\\n3i\\n31\\n3-7759\\n449\\n439\\n42Q\\n0. 9665\\n7\\n7\\n8\\n10\\n75\\n3\\n4\\n8.5 8\\nII. 4 II\\n.4 8.1\\n.2 10.8\\n0.2588\\n0.2679\\n3.7326\\n0.9659\\n10\\n0.2615\\n?8\\n0.2716\\n31\\n3.6891\\n420\\n0.9651\\n7\\n50\\n6\\n17.1 16\\n.8^16. 2\\n20\\n30\\n0.2644\\n0.2672\\n28\\n8\\n0.2742\\n0.2773\\n31\\n3.6470\\n3.6059\\n411\\n403\\n0.9644\\n0.9636\\n7\\n8\\n40\\n30\\n7\\n8\\n19.9 19\\n22.8 22\\n.618.9\\n.4 21.6\\n40\\n0.2700\\n28\\n0.2804\\n3-565?\\n\u00e2\u0096\u00a0^94\\n0.9628\\n8\\n20\\n9\\n25-525\\n.2 24.3\\n50\\n16\\n10\\n0.2723\\n28\\n28\\n?8\\n0.2836\\n31\\n31\\n31\\n3.5261\\n387\\n379\\n371\\n0.9626\\n8\\n8\\n8\\n10\\n74\\n50\\n10 8\\n0.2758\\n0.286^\\n3-4874\\n0.9612\\n0.2784\\n0.2899\\n3-4495\\n0. 9604\\n20\\n0.2812\\n0. 2930\\n3-4123\\n0-9596\\n8\\n8\\n40\\n3\\ni.o 0.\\n90.8\\n30\\n40\\n0.2840\\n0.2868\\n\u00e2\u0096\u00a01\\n28\\n0.2962\\n0.2994\\n32\\n3-3759\\n3-3402\\n357\\n0.9588\\n0.9580\\n30\\n20\\n2.0 I.\\nJ 3.02.\\n8 1.6\\n72.4\\n50\\n17\\n10\\n0*2896\\n28\\n27\\n28\\n0.3025\\n3i\\n32\\n31\\n3-3052\\n350\\n343\\n337\\n0.9571\\n8\\n8\\n8\\n10\\n78\\n50\\nM-o 3-\\n504-\\n3 6.0 5.\\n6 3.2\\n5 4-0\\n44.8\\n2923\\n0.3057\\n0.3089\\n32708\\n09563\\n0.2951\\n3.2371\\n0.9554\\n20\\n0.2979\\n28\\n0.31 21\\n32\\n3.2040\\n331\\n0.9546\\n8\\n40\\nr 7.0 6.\\ni 8.0 7.\\n3 5-6\\n2 6.4\\n30\\n0. 3007\\n2y\\n0.3153\\n32\\n3-1716\\n324\\n0.9537\\ny\\n30\\nc\\n9.0 8.\\nI 7.2\\n40\\n0.3035\\n28\\n0.3185\\n32\\n3-1397\\n319\\n0.9528\\n8\\n20\\n50\\n0.3062\\n2y\\n0.3217\\n32\\n3.1084\\n313\\n0.9519\\ny\\n10\\n18\\n0.3090\\n27\\n0.3249\\n32\\n3.0777\\n307\\n0.9516\\ny\\n72\\nA \u00c2\u00bbv A v\\n10\\n20\\n0.31 18\\n0.3145\\n27\\n0.3281\\n0.3313\\n32\\n32\\n3-0475\\n3-OI78\\n302\\n296\\n0.950T\\n0.9492\\n9\\n9\\n50\\n40\\n1 c\\n2 I\\n.70.7\\n\u00e2\u0080\u00a25 1-4\\nD.60.5 1\\n1.2 1.0\\n30\\n0.3173\\n27\\n0.3346\\n32\\n2.9887\\n0.9483\\n9\\n30\\n32\\n.22.1\\n1.8 1.5\\n40\\n0.3200\\n\u00e2\u0080\u00a2I]\\n0.3378\\n32\\n2.9606\\n286\\n0.9474\\ny\\n20\\n4 3\\n.0 2.8\\n2.4 2.0\\n50\\n19\\n10\\n3228\\n27\\n27\\n27\\n27\\n0.3411\\n32\\n32\\n32\\n32\\n2.9319\\n277\\n272\\n267\\n0.9464\\ny\\n9\\n9\\nQ\\n10\\n71\\n50\\n53\\n64\\n7 5\\n86\\n-73-5\\n.5 4-2\\n.2 4.9 t.\\n-0 5.6\\n3-02.5\\n?.6 3.0\\n^23-5\\nI..8 4.0\\n0.3255\\n03443\\n2.9042\\n0.9455\\n03283\\n0.3476\\n2.8770\\n0.9445\\n20\\n0.3310\\n27\\n0-3508\\n2.8502\\n263\\n0.9436\\n5\\n40\\n96\\n\u00e2\u0080\u00a276.3\\n5.4 4-5 1\\n30\\n0-3338\\n0-354I\\n2.8239\\n0.9425\\n30\\n40\\n0-3365\\n27\\n0-3574\\n33\\n2.7980\\n0.9415\\n20\\n50\\n0.3393\\n\u00e2\u0096\u00a0^\u00e2\u0096\u00a07\\n27\\n0.3607\\nii\\n32\\n2.7725\\n254\\n250\\n0.9407\\ny\\n10\\n10\\n70\\nI20\\n0.3420\\n0.3639\\n2-7475\\n0.9397\\nCos. 1\\nd.\\nCot.\\nd.\\nTaB. I\\nd.\\nSin. 1\\nd. P. p. 1\\n70\u00c2\u00b0-80\\n440", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0492.jp2"}, "493": {"fulltext": "TABLE IX.\u00e2\u0080\u0094 NATURAL SINES, COSINES. TANGENTS, AND COTANGENTS.\\n20\\nlo\\n20\\nI 30\\nI 40\\n30\\n21\\n10\\n20\\n30\\n40\\n50\\n22\\n10\\n20\\n30\\n40\\n50\\n23\\nj 20\\nI 30\\n40\\n24\\nJO\\nI 20\\nI 30\\n40\\n50\\n25\\n10\\n20\\n30\\n40\\n50\\n26\\n10\\n20\\n30\\n40\\n50\\n27\\n10\\n20\\n30\\n40\\n50\\n28\\n10\\n20\\n30\\n40\\n50\\n29\\n10\\n20\\n30\\n40\\n50\\n30\\nSin.\\nd.\\no 3420\\n0-3447\\n0.3475\\n0.3502\\n0.3529\\n0-3556\\n035 83\\no. 36 1 I\\n0.3638\\n0.3665\\n0.3692\\n0.3719\\n03746\\n0.3773\\n0.3800\\n0.3827\\n0-3853\\n0.3880\\no 3907\\n0.3934\\n0.3961\\n0.398^\\n0.4014\\no. 404 1\\n0.406^\\n0.4094\\n0.4120\\n0.4147\\n0.4173\\n0.4200\\no 4226\\n0.4252\\n0.4279\\n0.4305\\n0.4331\\n0.4357\\n04383\\n0.4410\\n0.4436\\n0.4462\\n0.4488\\n0.4514\\n04540\\n0.4566\\n0.4591\\n0.4617\\n0.4643\\n0.4669\\n0.4694\\n0.4720\\n0.4746\\n0.4771\\n0.4797\\n0.4822\\n0.4848\\n0.4873\\n0.4899\\n0.4924\\n0.4949\\n0.4975\\n0.5000\\nCos.\\nTan.\\n3 639\\n0.3672\\n0.3705\\n0.3739\\n0.3772\\n0.3805\\n03838\\n0.3872\\n0.3905\\n0.3939\\n0.3972\\no. 4005\\n0.4040\\n0.4074\\n0.4108\\n0.4142\\n0.4176\\n0.4216\\n0.4244\\n0.4279\\n0.4313\\n0.4348\\n0.4383\\no.44if\\n04452\\n0.4487\\n0.4522\\n0.455?\\n0.4592\\n0.462^\\n0.4663\\n0.4698\\n0.4734\\n0.4770\\n0.4805\\n0.484T\\n0487^\\n0.4913\\n0.4949\\n0.4986\\n0.5022\\n0.5058\\n0.5095\\n0.5132\\n0.5169\\n0.5205\\n0.5242\\n0.5280\\n05317\\n0.5354\\n0.5392\\n0.5429\\n0.546?\\n0.5505\\n0-5543\\n0.5581\\n0.5619\\n0.565?\\no. 5696\\n0.5735\\n05773\\nCot.\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n33\\n34\\n34\\n33\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n34\\n35\\n34\\n35\\n34\\n35\\n35\\n35\\n35\\n35\\n35\\n35\\n36\\n35\\n36\\n36\\n36\\n36\\n36\\n36\\n36\\n37\\n36\\n37\\n36\\n37\\n37\\n37\\n37\\n37\\n37\\n38\\n37\\n38\\n38\\n38\\n38\\n38\\n39\\n38\\n(1.\\nCot.\\n2-7475\\n2.7228\\n2.6985\\n2.6746\\n2.6511\\n2.6279\\n2.6051^\\n2:7826\\n2.5604\\n2.5386\\n2.517T\\n2.4959\\n24751\\n2.4545\\n2.4342\\n2.4142\\n2-3945\\n2.3750\\n2.3558\\n2.3369\\n2.3182\\n2.2998\\n2.2815\\n2.263^\\n2.2466\\n2.2285\\n2.21 13\\n2.1943\\n2.1775\\n2. 1609\\n2. 1445\\n2. 1283\\n2.II23\\n2.0965\\n2.0809\\n2.0655\\n2.0503\\n2.0352\\n2.0204\\n2.0057\\n.9911\\n.9768\\n9626\\n.9486\\n\u00e2\u0080\u00a29347\\n.9210\\n.9074\\n.8940\\nr88oy\\n.8676\\n.8546\\n.841?\\n.8296\\n^8165\\n.8040\\n-791?\\n\u00e2\u0096\u00a0119%\\n.7675\\n.7555\\n.743?\\n7320\\nTan.\\n247\\n245\\n239\\n235\\n232\\n238\\n225\\n221\\n218\\n215\\n212\\n208\\n206\\n203\\n200\\n197\\n194\\n192\\n189\\n187\\n184\\n182\\n179\\n177\\n175\\n172\\nI70\\n168\\n166\\n164\\n162\\n159\\n158\\n156\\n^54\\n152\\n\u00c2\u00bb5o\\nM8\\n147\\n145\\n143\\n142\\n140\\n139\\n137\\n136\\n134\\n132\\n131\\n130\\nI2\u00c2\u00a7\\n127\\n125\\n124\\n123\\n122\\n126\\n119\\n118\\n117\\nCos.\\nI.\\n0.9397\\n0.9387\\n0.9366\\n0.9356\\n0.9346\\n0.9336\\n0.9325\\n0.9315\\n0.9304\\n0.9293\\n0.9282\\n0.9272\\n0.9261\\n0.9250\\n0.9239\\n0.922^\\n0.9216\\n0.9205\\n0.9193\\n0.9182\\n0.9170\\n0.9159\\n0.9147\\n0.913S\\n0.9123\\n0.911T\\no. 9099\\n0.9087\\n0.9075\\n0.9063\\n0.9050\\n0.9038\\n0.9026\\n0.9013\\n0.9006\\n0.8988\\n0.8975\\n0.8962\\no. 8949\\n0.8936\\n0.8923\\n0.8910\\n0.8897\\n0.8883\\n0.8870\\n0.8856\\n0.8843\\n0.8829\\n0.8816\\n0.8802\\n0.8788\\n0.8774\\n0.8766\\n0.8746\\n0.8732\\n0.8718\\n0.8703\\n0.8689\\n^8675^\\no. 8666\\nSin.\\n13\\n12\\n13\\n12\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\nIS-\\nIS\\n13\\n13\\n14\\n14\\n13\\n14\\n14\\nM\\n14\\n14\\n14\\nI-?\\nd.\\n70\\n50\\n40\\n30\\n20\\n10\\n69\\n50\\n40\\n30\\n20\\n10\\n68\\n50\\n40\\n30\\n20\\n10\\n67\\n50\\n40\\n30\\n20\\n10\\n66\\n50\\n40\\n30\\n20\\n10\\n65\\n50\\n40\\n30\\n20\\n10\\n64\\n50\\n40\\n30\\n20\\n10\\n63\\n50\\n40\\n30\\n20\\n10\\n62\\n50\\n40\\n30\\n20\\n10\\n61\\n50\\n40\\n30\\n20\\n10\\n60\\nP. P.\\nZ% 35 34 33\\n1 3-5\\n2| 7.1\\n3 \u00c2\u00bbo-6\\n4J14.2\\n5,17-7\\n6 21.3\\n7 24.8\\n8;28.4\\n9131.9\\n3-5\\n7.0\\n10.5\\n14.0\\n17-5\\n21.0\\n24-5\\n28.0\\n31.5\\n3-4\\n6.8\\n3-3\\n6.6\\n9-9\\n13.6,13.2\\n17.0 16.5\\n20.4 IQ.8\\nI\\n23.8 23.1\\n27.2 26.4\\n30.6[29.7\\n2^ 27 26 25\\n2.7\\n2-7\\n2.6\\n5-5\\n8.2\\n5-4\\n8.1\\n5-2\\n7.8\\nII.\\n10.8\\n10.4\\n13-7\\n16.5\\n13-5\\n16.2\\n13.0\\n15.6\\n19.2\\n18. q\\n18.2\\n22.0\\n21.6\\n20.8\\n24.7\\n243\\n23-4\\n1.4\\n2,9\\n1.4\\n2.8\\n1-3\\n2.6\\n4-3\\n4.2\\n3-9\\n5-8\\n7-2\\n8.7\\n5-6\\n7.0\\n8.4\\n5-2\\n6.5\\n7.8\\n10. i\\nII. 6\\n9.8\\n11.2\\n9.1\\n10.4\\n13.0\\n12.6\\nII. 7\\n39\\n38\\n37\\n36\\nI\\n3-9\\n3-8\\n3-7\\n3-6\\n2\\n7-8\\n7-6\\n7-4\\n7-2\\n3\\n11.7\\nII. 4\\n10. 1\\n10.8\\n4\\n15-6\\n15.2\\n14.8\\n14.4\\n5\\n19-5\\n19,0\\n18.5\\n18.0\\n6\\n23-4\\n22.8\\n22.2\\n21.6\\n7\\n27-3\\n26.6\\n25-9\\n25.2\\n8\\n31.2\\n30-4\\n29.6\\n28.8\\n9\\n35-1\\n34-2\\n33-3\\n32.4\\n2-5\\n5-0\\n7-5\\nirf.o\\n12.5\\n15-0\\n17-5\\n20.0\\n5\\n14 14 13 12\\n2.4\\n3-6\\n4.8\\n6.0*\\n7-2\\n8.4\\n9.6\\n10.8\\n10\\ni.o\\n2.0\\n3-0\\n4.0\\n5-0\\n6.0\\n7.0\\n8.0\\n9.0\\nII II\\nil I\\n9\\n10.3\\n2.2\\n3-3\\n4.4\\n5-5\\n6.6\\n7-7\\n8.8\\n9-9\\nP. P.\\n60-70\\n441", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0493.jp2"}, "494": {"fulltext": "TABLE IX.\u00e2\u0080\u0094 NATURAL SINES, COSINES, TANGENTS. AND COTANGENTS.\\n30-40\u00c2\u00b0\\no\\nlO\\n20\\n30\\n40\\n50\\n31\\n10\\n20\\n30\\n40\\n50\\n32\\n10\\n20\\n30\\n40\\n50\\n33\\n10\\n20\\n30\\n40\\n50\\n34\\n10\\n20\\n30\\n40\\n50\\n85\\n10\\n20\\n30\\n40\\n50\\n36\\n10\\n2.0\\n30\\n40\\n50\\n37\\n10\\n20\\n30\\nI 40\\n50\\n|3$\\n10\\n20\\n30\\n40\\n50\\n39\\n10\\n20\\n30\\n40\\n50\\n40\\nSin.\\n0.5000\\n0.5025\\n0.5056\\n0.5075\\n0.5106\\n0.5125\\n0.5150\\n0.5175\\n0.5200\\n0.5225\\n0.5250\\n0.5274\\n0.5299\\n0.5324\\no. 5348\\n0.5373\\n0.539^\\no. 5422\\n0.5446\\n0.5471\\n0.5495\\n0.5519\\n0.5543\\no.:;568\\n0.5592\\n0.5616\\no. 5640\\no. 5664\\n0.5688\\n0.5712\\n0.5736\\n0.5759\\n0.5783\\no. 5807\\no. 5836\\n0.5854\\n0.5878\\n0.5901\\n0.5925\\n0.5948\\n0.5971\\n0.5995\\n0.6018\\n0.6041\\n0.6064\\n0.6087\\n0.61 15\\n0-6133\\no6i5g\\n0.6179\\n0.6202\\n0,6225\\n0.6248\\n0.6276\\n0.6293\\n0.6316\\n0.6338\\n0.6361\\n0.6383\\n0.6405\\n0.6428\\nCos.\\nd.\\nTan.\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n24\\n25\\n25\\n24\\n24\\n25\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n23\\n24\\n2\u00c2\u00a7\\n23\\n24\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n22\\n23\\n22\\n22\\n23\\n22\\n0.5773\\n0.5812\\n0.5851\\n0.5896\\n0.5929\\n0.5969\\nO.6OO8\\nd.\\no. 6048\\n0.6088\\n0.6128\\n0.6168\\n0.6208\\n0.6248\\n0.6289\\n0.6330\\n0.6376\\n0.641T\\n0.6453\\n0.6494\\n0.6535\\n0.6577\\n0.6619\\n0.6661\\n0.6703\\n0.6745\\n0.678^\\n0.6830\\n0.6873\\n0.6915\\n0.6959\\n0.7002\\n0.7045\\no. 7089\\n0.7133\\n0.7177\\n0.7221\\n0.7265\\n0.7310\\n0.7354^\\n0.7399\\n0.7444\\n0.7490\\n0.7535\\n0.7581\\n0.7627\\n0.7673\\n0.7719\\n0.7766\\n0.7813\\n0.7860\\no. 7907\\n0.795^\\no. 8002\\n0.8050\\n0.8098\\n0.8146\\n0.8194\\n0.8243\\n0.8292\\n0.8341\\n0.8391\\nCot.\\nd.\\n39\\n39\\n39\\n39\\n39\\n39\\n40\\n39\\n40\\n40\\n40\\n40\\n40\\n41\\n40\\n41\\n41\\n41\\n41\\n41\\n42\\n42\\n42\\n42\\n42\\n42\\n43\\n42\\n43\\n43\\n43\\n43\\n44\\n44\\n44\\n44\\n44\\n44\\n45\\n45\\n45\\n4\u00c2\u00a7\\n4S\\n46\\n46\\n46\\n46\\n47\\n47\\n47\\n47\\n47\\n48\\n48\\n48\\n4\u00c2\u00a7\\n49\\n49\\n49\\n49\\ndT\\nCot.\\n1.7320\\n1.7204\\n1.7090\\n1.6976\\n1.6864\\n1.6753\\n1.6643\\n1-6533\\n1.6425\\nI.63I8\\n1. 6212\\n1.610^\\n1.6003\\n1.5900\\n1.5798\\n1.5697\\n1-5596\\n1-5497\\n1-5398\\n1.5301\\n1.5204\\nI-5108\\n1-5013\\n1-4919\\n1.4825\\n1-4733\\n1. 4641\\n1.4550\\n1.446c\\n1.4370\\n1.4281\\n1-4193\\n1. 4106\\n1. 4019\\n1-3933\\n1.3848\\n1-3764\\n1.3680\\n1-3597\\nI-35H\\n1.3432\\n1. 3351\\n1.3270\\n1. 3190\\n1.3111\\n1.3032\\n1.2954\\n1.2876\\nd.\\n1.2799\\n1.2723\\n1 2647\\n1. 2571\\n1.2497\\n1.2422\\nI 2349\\n1.2276\\n1.2203\\nI.2131\\n1.2059\\n1. 1988\\nTan.\\n99\\n98\\n97\\n96\\n96\\n95\\n94\\n93\\n92\\n92\\n91\\n90\\n87\\n86\\n86\\n85\\n84\\n84\\n83\\n83\\n81\\n81\\n80\\n80\\n79\\n78\\n78\\n77\\n77\\n76\\n76\\n75\\n74\\n74\\n73\\n73\\n73\\n72\\n71\\n71\\n70\\nd.\\nCos.\\n0.8660\\no. 8645\\n0.8631\\n0.86I6\\no.86oi\\n0.8586\\nd.\\n08571\\n0.8556\\n0.8541\\n0.8526\\nO.851I\\no. 8496\\n0.8486\\n0.8465\\no. 8449\\n0.8434\\n0.8418\\n0.8/|02\\n0.8388\\n0.8371\\n0.8355\\n0.8339\\n0.8323\\n0.8306\\n0.8290\\n0.8274\\n0.825^\\n0.824T\\n0.8225\\n0.8208\\n0.8I9I\\n0.8175\\n0.8158\\n0.8I4I\\no. 8 1 24\\n0.8107\\n0.8090\\n0.8073\\n0.8056\\n0.8038\\n0.8021\\no. 8004\\n0.7988\\n0.7969\\n0.7951\\n0.7933\\n0.7916\\n0.7898\\n0.7880\\n0.7862\\n0.7844\\n0.7826\\n0.7808\\n0.7789\\n0-7771\\n0.7753\\n0.7734\\n0.7716\\n0.769^\\n0.7679\\n0.7666\\nSin.\\nd.\\nF. P.\\n60\\n50\\n40\\n30\\n20\\n10\\n59\\n50\\n40\\n30\\n20\\n10\\n58\\n50\\n40\\n30\\n20\\n10\\n57\\n50\\n40\\n30\\n20\\n10\\n56\\n50\\n40\\n30\\n20\\n10\\n55\\n50\\n40\\n30\\n20\\n10\\n54\\n50\\n40\\n30\\n20\\n10\\n53\\n50\\n40\\n30\\n20\\n10\\n52\\n50\\n40\\n30\\n20\\n10\\n51\\n50\\n40\\n30\\n20\\n10\\n50\\n49 49 48 47 46\\n49 4-9\\n9-9i 9-8\\nI4-8I4-7\\n19.8 19.6\\n24.724.5\\n29.7,29.4\\n34 6 34-3\\n39.639.2\\n44.544.1\\n4.8^ 4.7 4.6\\n9.6 9.4 9.2\\nI4.4 i4.i|i3.8\\n19.\\n24.0\\n^28.8\\n18.8 18.4\\n23-523.0\\nz8.2 27.6\\n33.632.9 32.2\\n38.437.6,36.8\\n43.2|42.3!4i.4\\n4S 45 44 43 42\\n4-5\\n9.1\\n13-6\\n4-5\\n9.0\\n13-5\\n4.4\\n8.8\\n13.2\\n4-3\\n8.6\\n12.9\\n18.2\\n18.0\\n17.6\\n17.2\\n22.7\\n22.5\\n22.0\\n21-5\\n27-3\\n27.0\\n26.4\\n25.8\\n31.8\\n36.4\\n40.9\\n31-5\\n36.0\\n40.5\\n30.8\\n35-2\\n39-6\\n30.1\\n34-4\\n38.7\\n4.2\\n8.4\\n12.6\\n16.8\\n21 .0\\n25.2\\n29.4\\n33-6\\n37.8\\n41 41 40 39\\n4.1\\n8.3\\n12.4\\n16.6\\n20.7\\n24.9\\n29.0\\n33-2\\n37-3\\n4-1\\n8.2\\n12.3\\n16.4\\n20.5\\n24.6\\n28.7\\n32.8\\n36-9\\n4.0\\n8.0\\n16.0\\n20.0\\n24.0\\n28.0\\n32.0\\n36.0\\n3-9\\n7-8\\n11.7\\n15.6\\n19-5\\n23-4\\n27-3\\n31.2\\n35-1\\n2% 25 24 23\\n2-3\\n4.6\\n6.9\\n2.5\\n2.5\\n2.4\\n5-1\\n5-0\\n4.8\\n7-6\\n7-5\\n7.2\\n10.2\\n10.\\n9.6\\n12.7\\n12-5\\n12.0\\n15.3\\n15.0\\n14.4\\n17.8\\n17-5\\n16.8\\n20.4\\n20.0\\n19.2\\nI22.9\\n22.5\\n21.6\\n22 22 18\\n2.2\\n2.2\\n1-8\\n6.7\\n4-4\\n6.6\\n3-7\\n5-5\\n9.0\\nII. 2\\n8.8\\nu.o\\n7-4\\n9.2\\n13-5\\n13.2\\nII. I\\n15-7\\n18.0\\n15-4\\n17.6\\n12.9\\n14.8\\n20.2\\n19.8\\n16.6\\nIf\\n17\\n16\\n15\\n1\\n1.7\\n1-7\\n1.6\\n1-5\\n2\\n3-5\\n3-4\\n3-2\\n30\\n3\\n5.2\\n5.1\\n4.8\\n4-5\\n4\\n7.0\\n6.8\\n6.4\\n6.0\\n5\\n8.7\\n8.5\\n8.0\\n7-5\\n6 10.5\\n10.2\\n9.6\\n9.0\\n7 12.2\\nII. 9\\nII. 2\\n10.5\\n8 14.0\\n13.6\\n12.8\\n12.0\\n9\\n15-7\\n15-3\\n14.4\\n13-5\\n9.2\\n.5\\n1^.8\\n16.1\\n18.4\\n20.7\\n18\\nI. a\\n3.6\\n5-4-\\n7. a\\n9.0\\n10. a\\n12.6\\n14.4\\n16.2\\n14\\n1-4\\n2.9\\n4-3\\n6.8\\n7.2\\n8.7\\nII. 6\\n13.0\\nP.P.\\n50-60\\n442", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0494.jp2"}, "495": {"fulltext": "TABLE IX.\u00e2\u0080\u0094 NATURAL SINES, COSINES, TANGENTS, AND COTANGENTS.\\n40\u00c2\u00b0-45\u00c2\u00b0\\n40\\nlO\\n20\\n30\\n40\\n50\\n410\\n10\\n20\\n30\\n40\\n50\\n42\\n10\\n20\\n30\\n40\\n50\\n43\\n10\\n20\\n30\\n40\\n50\\n44\\n10\\n20\\n30\\n40\\n50\\n45\\nSin.\\n0.6428\\n0.6450\\n0.6472\\no. 6494\\nO.65I6\\n0-6538\\n0.6566\\n0.658!\\no. 6604\\n0.6626\\n0.6648\\n0.6669\\n0.6691\\n0.6713\\n0.6734\\n0.6756\\n0.6777\\n0-6798\\n0.6820\\n(1.\\n0.6841\\n0.6862\\n0.6883\\no. 6904\\n0.692^\\n0.694^\\n0.6967\\n0.6983\\no. 7009\\no. 7030\\n0.7050\\n0.7071\\nCos.\\n21\\n22\\n21\\n22\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n20\\n21\\n20\\n20\\nd.\\nTan.\\nd.\\n08391\\no. 8446\\n0.8496\\n0.8541\\n0.8591\\no. 8642\\n0.8693\\n0.8744\\n0.8795\\n0.8847\\n0.8899\\n0.8951\\n0.9004\\n0.9057\\n0.9IIO\\n0.9163\\n0.9217\\n0.9271\\n09325\\n0.9379\\n0-9434\\n0.9489\\n0.9545\\n0.9601\\n0.9657\\n0.9713\\n0.9770\\n0.9827\\n0.9884\\n0.9942\\n1. 0000\\n49\\n50\\n50\\n50\\n51\\n51\\n51\\n51\\n52\\n51\\n52\\n52\\n53\\n53\\n53\\n53\\n54\\n54\\n54\\n55\\n55\\n5S\\n56\\n56\\n56\\n56\\n57\\n57\\n57\\n58\\nCot.\\nd.\\nCot.\\nd.\\n191-7\\niS4f\\n1777\\n1708\\n1640\\n1571\\n1503\\n1436\\n1369\\n1303\\n1237\\n1171\\n.1106\\n.1041\\n.0977\\n.0913\\n.0849\\n.0723\\n.0661\\n.0599\\n.0538\\n\u00e2\u0080\u00a20476\\n.0416\\n0355\\n.0295\\n.0235\\n.0176\\n.0117\\n.0058\\n0000\\n70\\n70\\n69\\n68\\n68\\n68\\n67\\n67\\n66\\n66\\n65\\n65\\n64\\n64\\n64\\n63\\n63\\n^3\\n62\\n62\\n61\\n61\\n66\\n66\\n65\\n59\\n59\\n59\\n58\\n58\\nCos.\\n0.7666\\nTan.\\nd.\\n0.764!\\n0.7623\\no. 7604\\nO.75S5\\n0.7566\\n0-7547\\n0.7528\\n0.7509\\n0.7489\\n0.7476\\n0.7451\\n0.7431\\n0.7412\\n0.7392\\n0.7373\\n0-7353\\n0-7333\\n^7313\\n0.7293\\n0.7273\\n0.7253\\n0.7233\\n0.7213\\n0.7193\\n0.7173\\n0.7153\\n0.7132\\n0.71 12\\n0.7091\\n0.7071\\nSin.\\n19\\n18\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n19\\n20\\n19\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n26\\n20\\n26\\n26\\n26\\n26\\n50\\n50\\n40\\n30\\n20\\n10\\n49\\n50\\n40\\n30\\n20\\n10\\n48\\n50\\n40\\n30\\n20\\n10\\n47\\n50\\n40\\n30\\n20\\n10\\n40\\n50\\n40\\n30\\n20\\n10\\n45\\np. r.\\n70\\n22\\n22\\n21\\n21\\n7.0\\n2.2\\n2.2\\n2.1\\n2. 1\\n14.0\\n21 .0\\ni:l\\n4-4\\n6.6\\n4-3\\n6.4-\\n42\\n6.3\\n28.0\\n9.0\\n8.8\\n8.6\\n8.4\\n42.0\\nII .2\\n13-5\\n11 .0\\n13.2\\n10.7\\n12.9\\n10.5\\n12.6\\n49.0\\n56.0\\n63.0\\n15-7\\n18.0\\n20.2\\n15-4\\n17.6\\n19.8\\n15.0\\n17.2\\n19-3\\n14.7\\n16.8\\n18.9\\n69 20 20 19 19\\nI\\n6.9\\n2.0\\n2.0\\n1.9\\n2\\n3\\n13S\\n20.7\\n4-1\\n6.1\\n4.0\\n6.0\\n3-9\\n5\u00c2\u00a7\\n4\\n27.6\\n8.2\\n8.0\\n7.8\\n5\\n34-5\\n10.2\\n10.\\n9-7\\n6\\n41.4\\n12.3\\n12.0\\nII. 7\\n7\\n8\\n9\\n48.3\\n55-2\\n62.1\\n14-3\\n16.4\\n18.4\\n14.0\\n16.0\\n18.0\\n13-6\\n15-6\\n17-5\\n5-7\\n7.6\\n9-5\\nII. 4\\n133\\n15.2\\n17. 1\\n68 68 67 66 18\\n68\\n6.8\\n6.7\\n6.6\\n13-7\\n20.5\\n13-6\\n20.4\\n134\\n20.1\\n13.2\\n19.8\\n27.4\\n34-2\\n41. 1\\n27.2\\n34-0\\n40.8\\n26.8\\n33-5\\n40.2\\n26.4\\n33\\n39-6\\n47-9\\n54-8\\n61.6\\n47.6\\n54.4\\n61.2\\n46.9\\n60.3\\n46.2\\n52.8\\n59-4\\n3-7\\n5-5\\n7-4\\n9.2\\n12.9\\n14.8\\n16.6\\n6S 64 64 63 62 61 66 59 59 58 58 5l 57 56 56 55 54 54 53 53 52 52\\nI\\n6.5\\n6.4\\n2\\n3\\n19-6\\n12.9\\n19-3\\n4\\n26.2\\n25.8\\n5\\n6\\n327\\n39-3\\n32.2\\n38.7\\n7\\n8\\n9\\n45-8\\n52.4\\n58.9\\n45-1\\n5t.6\\n58.6\\n6.4\\n12.8\\n19.2\\n25.6\\n32.0\\n38.4\\n44-8\\n51.2\\n57-6\\n6.3\\n12.6\\n18.9\\n25.2\\n31-5\\n37-8\\n44. 1\\n50-4\\n56.7\\n12.4\\n18.6\\n24.8\\n31.0\\n37-2\\n43.4\\n49.6\\n55-8\\n6.1: 6.0\\n12.3 1 2 1\\n18.4 18. I\\ni\\n24.6 24.2\\n30.7 30.2\\n36.9 36-3\\n43.0 42.3\\n49.2 48.4\\n55-31 54-4\\n5-9\\nII. 9\\n17-8\\n23.8\\n29.7\\n35-7\\n41-6\\n47.6\\n53-5\\n5-9\\nII. 8\\n17.7\\n23.6\\n29-5\\n35-4\\n41.3\\n47.2\\n53-1\\n5-8\\nII. 7\\n17-5\\n23.4\\n29.2\\n35-1\\n40.9\\n46.8\\n52-6\\n5-8\\nII. 6\\n17.4\\n23.2\\n29.0\\n34.8\\n40.6\\n46.4\\n52.2\\n5-7\\n\u00e2\u0080\u00a25\\n17.2\\n23.0\\n28.7\\n34-5\\n40.2\\n46.0\\n51.7\\n5-7\\nII. 4\\n17. 1\\n22.8\\n28.5\\n34-2\\n39-9\\n45-6\\n51-3\\n5-6\\n\u00e2\u0096\u00a03\\n16.9\\n22.6\\n28.2\\n33-9\\n39-5\\n45-2\\n50-8\\n5.6\\nII .2\\n16.8\\n22.4\\n28.0\\n33.6\\n39-2\\n44.8\\n50.4\\n5-5\\nII .0\\n16.5\\n22.0\\n275\\n33-0\\n38.5\\n44.0\\n49-5\\n5-4\\n10.\\n16.3\\n21.8\\n27.2\\n32-7\\n38.1\\n43-6\\n49.0\\n5-4\\n10.8\\n16.2\\n21 .6\\n27.0\\n32.4\\n37-8\\n43-2\\n48.6\\n5-3\\n10.7\\n16.0\\n21.4\\n26.7\\n37-4\\n42.8\\n48.1\\n5-3 5-2\\n10.6 10.5\\n159 15-7\\n5-2\\n10.4\\n15.6\\n21 .2 21 .0 20.8\\n26.5 26.2 26.0\\n31.8 31.5 31.2\\n371 36.7\\n42.4: 42.0\\n47-7I47-2\\n36-4\\n41.6\\n46.8\\nS? 51 so 50 49\\n5-i\\n10.^\\n5-1\\n10.2\\n5-0\\n10. 1\\n50\\n10.\\n154\\n15-3\\n15.1\\n15-0\\n20.6\\n20.4\\n20.2\\n20.0\\n257\\n30.9\\n25 -5\\n30.6\\n25.2\\n30.3\\n25.0\\n30.0\\n36.0\\n41.2\\n46.3\\n35-7\\n40.8\\n45-9\\n35-3\\n40.4\\n45-4\\n350\\n40.0\\n45.0\\n4.9\\n9.9\\nI4\u00c2\u00a7\\n19.8\\n24.7\\n29.7\\n34-6\\n39-6\\n44-5\\nTable for passing from Sexagesimal to Circular\\nMeasure.\\n100\\n200\\n300\\n40\\n50\\n60\\n70\\n80\\n90\\nCircular Meas,\\n1.74 532 9\\n3-49 065 8\\n5.235988\\n0.69 813 T\\n0.87 266 4\\n1.04 719 7\\n1.22 173 6\\n1.39 626 3\\n1.570796\\nCirt ular Moas. Circular Meas.\\n10\\n20\\n30\\n40\\n50\\n6\\n7\\n8\\n9\\n0.00 290 9\\n0.00 581 8\\n0.00 872 6\\no.oi 163 5\\n0.0 1 454 4\\n0.00 174 5\\n0.00 203 6\\n0.00 232 7\\n0.00 261 8\\n10\\n20\\n30\\n40\\n50\\n6\\n7\\n8\\n9\\n45-50\\no. 00 004 8\\no. 00 009 7\\n0.00 014 5\\n0.00 019 4\\n0.00 024 2\\n0.00 002 9\\n0.00 003 4\\n0.00 003 9\\n0.00 004 3\\n443", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0495.jp2"}, "496": {"fulltext": "TABLE X.\u00e2\u0080\u0094 NATURAL VERSED SINES AND EXTERNAL SECANTS.\\n0\u00c2\u00b0-10\u00c2\u00b0 10\u00c2\u00b0-20\u00c2\u00b0\\nlo\\n20\\n30\\n40\\n50\\n1\\n10\\n20\\n30\\n40\\n50\\n2\\n10\\n20\\n30\\n40\\n50\\n3\\n10\\n20\\n30\\n40\\n50\\n4\\n10\\n20\\n30\\n40\\n50\\n5\\n10\\n20\\n30\\n40\\n50\\n6\\n10\\n20\\n30\\n40\\n50\\n7\\n10\\n20\\n30\\n40\\n50\\n8\\n10\\n20\\n30\\n40\\n50\\n9\\n10\\n20\\n30\\n40\\n50\\n10\\nTers.\\n00000\\n00000\\n0000 I\\n00004\\n00007\\n,00016\\n.00015\\n00020\\n.00027\\n.00034\\n00042\\n.00051\\n00061\\n0007 I\\n.00083\\n.00095\\n.OOIOg\\n.00122\\n00137\\n.00152\\n.00169\\n.00185\\n00204\\n.00223\\n00243\\n00264\\n.00286\\n00308\\n,00331\\n\u00e2\u0096\u00a0003Sg\\n00386\\n00405\\n.00433\\n00460\\n00483\\n.00518\\n00548\\n.00578\\n.00616\\n.00643\\n.00676\\n007 1 6\\n00745\\n.00781\\n.00818\\n.00855\\n.00894\\n.00933\\n00973\\n.01014\\n.01056\\n.01098\\n.01142\\n.01186\\n.01231\\n.01277\\n.01324\\n,01371\\n,01420\\n01469\\n(1.\\n10\\n16\\nII\\n12\\n13\\n13\\n15\\n15\\n16\\nI?\\n18\\n19\\n20\\n21\\n21\\n22\\n23\\n24\\n25\\n26\\n26\\n2?\\n28\\n29\\n30\\n30\\n32\\nExsec. d.\\n.00000\\n00000\\n0000 I\\n00004\\n00007\\n.00016\\n.00015\\n00020\\n.00027\\n.00034\\n00042\\n.00051\\n.00061\\nOI519\\nVers.\\n33\\n33\\n35\\n36\\n36\\n37\\n38\\n39\\n40\\n41\\n42\\n42\\n43\\n44\\n45\\n46\\n47\\n47\\n48\\n49\\n50\\n(1.\\n0007 1\\n.00083\\n.00095\\n.00108\\n.00122\\n00137\\n.00153\\n.00169\\n.00187\\n.00205\\n.00224\\n00244\\n.00265\\n.00285\\n00309\\n.00332\\n\u00e2\u0080\u00a200357\\n.00382\\n00408\\n\u00e2\u0080\u00a200435\\n00462\\n.00491\\n.00526\\n00551\\n.00582\\n.00614\\n00647\\n0068 I\\n007 1 5\\n00751\\n.0078^\\n.00824\\n.00863\\n00902\\n00942\\n00983\\n.01024\\n.01067\\n.01116\\n.01155\\n.01206\\n0I24g\\n.01293\\n.01341\\n\u00e2\u0080\u00a201396\\n.01446\\n.01491\\n01542\\nExsec.\\nTO\\n16\\nli\\n12\\n13\\n14\\n14\\n16\\n16\\n17\\n18\\n19\\n20\\n21\\n21\\n22\\n23\\n24\\n25\\n26\\n27\\n2?\\n28\\n29\\n30\\n31\\n32\\n33\\n34\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n41\\n42\\n43\\n44\\n45\\n46\\n47\\n48\\n49\\n50\\n50\\n^1\\n10\\n10\\n20\\n30\\n40\\n50\\n11\\n10\\n20\\n30\\n40\\n50\\n12\\n10\\n20\\n30\\n40\\n50\\n13\\n10\\n20\\n30\\n40\\n50\\n14\\n10\\n20\\n30\\n40\\n50\\n15\\n10\\n20\\n30\\n40\\n50\\nIG\\n10\\n20\\n30\\n40\\n50\\n17\\n10\\n20\\n30\\n40\\n50\\n18\\n10\\n20\\n30\\n40\\n50\\n19\\n10\\n20\\n30\\n40\\n50\\n20\\nVers. I d.\\nO1519\\n.01570\\n.01622\\n.01674\\n.01728\\n.01782\\noi83 7\\n.01893\\n.01950\\n02007\\n02066\\n.02125\\n,02185\\n.02246\\n.02308\\n.02376\\n.02434\\n02498\\n02563\\n.02629\\n.02695\\n.02763\\n.02831\\n.02906\\n02970\\n\u00e2\u0080\u00a203041\\n\u00e2\u0080\u00a203113\\n.03185\\n\u00e2\u0080\u00a203258\\n\u00e2\u0080\u00a203332\\n03407\\n03483\\n\u00e2\u0080\u00a203559\\n.03637\\n.03715\\n\u00e2\u0080\u00a203794\\n\u00e2\u0080\u00a203874\\n\u00e2\u0080\u00a203954\\n.04036\\n.04118\\n.04201\\n.04285\\n04369\\n\u00e2\u0080\u00a204455\\n.04541\\n.04628\\n.04716\\n04805\\n04894\\n04984\\n.05076\\n.0516^\\n.05266\\n\u00e2\u0080\u00a205354\\n05448\\n\u00e2\u0080\u00a205543\\n.05639\\n.05736\\n\u00e2\u0080\u00a205833\\n\u00e2\u0096\u00a005931\\n51\\n52\\n52\\n53\\n54\\n55\\n55\\n57\\n5?\\n58\\n59\\n60\\n61\\n62\\n62\\n63\\n64\\n65\\n66\\n66\\n6^\\n68\\n69\\n70\\n76\\n72\\n72\\n72\\n74\\n75\\n75\\n76\\n7?\\n78\\n79\\n80\\n80\\n81\\n82\\n83\\n84\\n84\\n85\\n86\\n8?\\n8?\\n89\\n89\\n90\\n91\\n91\\n93\\n93\\n94\\n95\\n95\\n97\\n9?\\n98\\n99\\nExsec.\\n06036\\nVers. I d.\\n01542\\n.01595\\n.01648\\n.01703\\n\u00e2\u0080\u00a2OI758\\n.01814\\n.01871\\n.01929\\n.01988\\n02048\\n.02109\\n.02171\\n02234\\n.0229^\\n.02362\\n.02428\\n02494\\n.02562\\n02636\\n.02700\\n,02770\\n,02841\\n.02914\\n.02987\\n.03061\\n\u00e2\u0080\u00a203136\\n.03213\\n.03290\\n.03368\\n\u00e2\u0080\u00a20344?\\n03527\\n03609\\n.03691\\n\u00e2\u0080\u00a203774\\n\u00e2\u0080\u00a203858\\n\u00e2\u0080\u00a203943\\n04030\\n.04117\\n.04205\\n.04295\\n.04385\\n.04475\\n04569\\n04662\\n\u00e2\u0080\u00a20475^\\n.04853\\n.04949\\n.0504?\\n05146\\n.05246\\n\u00e2\u0080\u00a205347\\n\u00e2\u0080\u00a205449\\n.05552\\n.05655\\n05762\\n.05868\\n.05976\\n.06085\\n06 I 94\\n.06305\\n06418\\nExsec.\\n52\\n53\\n54\\n55\\n56\\n57\\n58\\n59\\n60\\n61\\n62\\n62\\n63\\n65\\n65\\n66\\n6f\\n68\\n69\\n70\\n71\\n72\\n73\\n74\\n75\\n76\\n77\\n78\\n79\\n80\\n81\\n82\\n83\\n84\\n85\\n86\\n87\\n88\\n89\\n96\\n91\\n92\\n93\\n95\\n95\\n96\\n98\\n98\\n100\\nloi\\n102\\n103\\n104\\n105\\n105\\nI of\\n109\\n109\\nIII\\n112\\nP. P.\\n110 100 90 80 70 60 50 40\\nII\\n10\\n9\\n8\\n7\\n6\\n5\\n22\\n20\\n18\\n16\\n14\\n12\\n10\\n33\\n30\\n27\\n24\\n21\\n18\\n15\\n44\\n40\\n36\\n32\\n28\\n24\\n20\\n55\\n50\\n45\\n40\\n3S\\n30\\n25\\n66\\n60\\n54\\n48\\n42\\n36\\n30\\n77\\n70\\n63\\n56\\n49\\n42\\n35\\n88\\n80\\n72\\n64\\n56\\n48\\n40\\n99\\n90\\n81\\n72\\nb3\\n54\\n45\\n30 20 10 9 9 8 8 :7\\n3\\n2\\nI\\n0.9\\n0.9\\n0-8\\n0.8\\n6\\n4\\n2\\n1.9\\n1.8\\n1-7\\n1.6\\n9\\n6\\n3\\n2-8\\n2.7\\n2.5\\n2.4\\n12\\n8\\n4\\n3^8\\n3^6\\n3-4\\n3^2\\n15\\n10\\n5\\n4-7\\n4^5\\n4.2\\n4.0\\n18\\n12\\n6\\n5-7\\n5.4\\n5-1\\n4.8\\n21\\n\u00c2\u00bb4\\n7\\n6-6\\n6.3\\n5.q\\n5.6\\n24\\n16\\n8\\n7.6\\n7.2\\n6.8\\n6.4\\n27\\n18\\n9\\n8.5\\n8.1\\n7-6\\n7.2\\n0.7\\n1-5\\n2.2\\n3-0\\n3-7\\n4-5\\n5-2\\n6.0\\n6.7\\n7 6 6 5 5 4 4\\n0.7 0.5 0.6 0.5 0.5 0.4 0.4\\n1.4 1.311.2 I.I 1.00.9 0.8\\n3.1 1.9 1.8 1. 6 1.5 1.3 1.2\\n2.8 2.6 2.4 2.2 2.0 1.8 1.6\\n3.5 3.2 3.0 2.7 2.5 2.2 2.0\\n4.2 3.9 3.6 3.3 3.0 2.7 2.4\\n4.9 4.5 4-2 3-8 3-5 3-1 2-8\\n5.6 5.2 4.8 4.4 4.0 3.6 3.2\\n6.3 5-8 5-4I4.9 4^5 4-03-6\\n3 3 2 2 I I o\\n03\\n0-7\\n1 .0\\n2.4\\n2.8\\n3-1\\n.2\\n\u00e2\u0080\u00a25\\n.8\\n2.1\\n\u00e2\u0080\u00a24\\n2.7\\n0.2\\n0.5\\n0.7\\n1 .0\\n1.2\\n1.5\\n1-7\\n2.0\\n0.4\\n0.6\\n0.3\\n0.4\\n0.6\\n0.7\\n0.9\\ni.o\\no. 1\\n0.2\\n0-3\\n0.4\\n0-5\\n0.6\\n0.3\\n70-3\\n0.8 0.4\\n9I0.4\\nP. P.\\n444", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0496.jp2"}, "497": {"fulltext": "TABLE X. NATURAL VERSED SINES AND EXTERNAL SECANTS.\\n2ir-:ur M) ur\\n20\\nlO\\n20\\n30\\n40\\n50\\n21\\n10\\n20\\n30\\n40\\n50\\n22\\n10\\n20\\n30\\n40\\n50\\n23\\n10\\n20\\n30\\n40\\n50\\n24\\n10\\n20\\n30\\n40\\n50\\n2o\\n10\\n20\\n30\\n40\\n50\\n2G\\n10\\n20\\n30\\n40\\n50\\n27\\n10\\n20\\n30\\n40\\n50\\n28\\n10\\n20\\n30\\n40\\n50\\n29\\n10\\n20\\n30\\n40\\n50\\n80\\nVers.\\nd.\\n0603\\n0613^\\n.0623\\n\u00e2\u0080\u00a20633\\n.0643\\n.0654\\n.0664\\n.0674\\n.0685\\n,0696\\n07O6\\n,0717\\n0728\\n0739\\n,0750\\n.0761\\n.0772\\n.0783\\n,079 s\\n.0S05\\n,0818\\n.0829\\n.0841\\n.0853\\n0864\\n,0876\\n,0888\\n,0906\\n.0912\\n.0024\\n0937\\n,0949\\n.0961\\n,0974\\n,0986\\n.0999\\nI0I2\\n1025\\n103^\\n1050\\n1063\\n1077\\n1090\\nI 103\\n.1116\\n.1130\\n.1143\\nII 57\\n1170\\n.1184\\n.1198\\n1212\\nI22\u00c2\u00a7\\n.1239\\n^i25_4_\\n.1268\\n.1282\\n.1296\\n131 1\\n\u00e2\u0080\u00a21325\\n1339\\nVers.\\n10\\n10\\n10\\n10\\nid\\n10\\n16\\n16\\nII\\n10\\nII\\n10\\nII\\nII\\nII\\nII\\nI I\\niT\\nII\\nII\\nII\\nII\\n12\\nII\\n12\\n12\\n12\\n12\\n12\\n12\\n12\\n12\\n12\\n12\\n13\\n12\\n13\\n12\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n14\\n14\\n13\\n14\\n14\\n14\\n14\\nI ^4\\n14\\nKxsec.\\n0642\\n,0653\\n,0664\\n0676\\n,0688\\n.0699\\n^711\\n.0723\\n.0735\\n.0748\\n.0760\\n.0772\\n078g\\n.0798\\n,0811\\n.0824\\n.0837\\n.0850\\n,0863\\n.0877\\n.0890\\n.0904\\n.0918\\n.0932\\n.0948\\n,0966\\n,0975\\n.0989\\n1004\\n1019\\n1034\\n1049\\n1064\\n1079\\n1094\\n1 1 16\\n1126\\n1 142\\n1 1 58\\n1174\\n1196\\n1206\\n1223\\n1240\\n.1257\\n.1274\\n1291\\n.1308\\n1325\\n\u00e2\u0080\u00a21343\\n1361\\n\u00e2\u0080\u00a21379\\n\u00e2\u0080\u00a21397\\n.1415\\n\u00e2\u0080\u00a21547\\nKxsec.\\nd.\\n1 1\\niT\\nII\\n12\\niT\\n12\\n12\\n12\\n12\\n12\\n12\\n13\\n12\\n13\\n13\\n13\\n13\\n13\\n13\\n13\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n14\\n15\\n15\\n15\\n15\\n15\\n15\\n16\\n15\\n16\\n16\\n16\\n16\\n16\\n17\\n16\\n17\\n17\\n17\\n17\\n17\\n18\\n17\\n18\\n18\\n18\\n18\\n18\\n18\\n19\\n19\\n19\\n19\\nd.\\n30\\n10\\n20\\n30\\n40\\n50\\n31\\n10\\n20\\n30\\n40\\n50\\n32\\n10\\n20\\n30\\n40\\n50\\n33\\n10\\n20\\n30\\n40\\n50\\nU\\n10\\n20\\n30\\n40\\n50\\n35\\n10\\n20\\n30\\n40\\n50\\n3(1\\n10\\n20\\n30\\n40\\n50\\n37\\n10\\n20\\n30\\n40\\n50\\n38\\n10\\n20\\n30\\n40\\n50\\n39\\n10\\n20\\n30\\n40\\n50\\n40\\nVers.\\n1339\\n1354\\n1369\\n1383\\n1398\\n1413\\n_14^8\\n1443\\n.1458\\n1473\\n,1489\\n.1504\\nKxsec\\n1519\\n1535\\n1550\\n1566\\n1582\\n159^\\n1613\\n1629\\n1645\\n1661\\n1677\\n1693\\n1709\\n1726\\n1742\\n1758\\n1775\\n1792\\n1808\\n1825\\n1842\\n1859\\n1876\\n1893\\n1910\\n1927\\n1944\\n1 961\\n1979\\n1996\\n2013\\n.2031\\n,2049\\n.2066\\n.2084\\n.2102\\n2120\\n2138\\n2156\\n2174\\n2192\\n.2216\\n222g\\n.2247\\n2265\\n.2284\\n.2302\\n.2321\\n~233\u00c2\u00a7\\nVers.\\n\u00e2\u0080\u00a21547\\n.1566\\n.1586\\n1606\\n1626\\n1646\\n.166S\\n1687\\nI/O?\\n1728\\n1749\\n1776\\n1792\\n1813\\n.1835\\n.1857\\n.1879\\n1 901\\n\u00e2\u0080\u00a21923\\n.1946\\n.1969\\n.1992\\n.201 5\\n2038\\n.2062\\n.2086\\n.2110\\n.2134\\n\u00e2\u0080\u00a22158\\n.2183\\n.2207\\n22 12\\n.2258\\n.2283\\n.2309\\n2334\\n2366\\n.2387\\n\u00e2\u0080\u00a22413\\n.2440\\n.2467\\n\u00e2\u0080\u00a22494\\n2521\\n2549\\n\u00e2\u0080\u00a22576\\n.2604\\n2633\\n.2661\\n2690\\n.2719\\n2748\\n.2778\\n.280^\\n.2837\\n.286^\\n.2898\\n.2928\\n\u00e2\u0080\u00a22959\\n.2991\\n3022\\n3054\\nKxsec.\\n19\\n19\\n20\\n20\\n20\\n26\\n26\\n26\\n21\\n21\\n21\\n2T\\n21\\n21\\n22\\n22\\n22\\n22\\n23\\n22\\n23\\n23\\n23\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n25\\n25\\n25\\n25\\n25\\n26\\n26\\n26\\n26\\n27\\n27\\n27\\n27\\n2f\\n28\\n28\\n28\\n28\\n29\\n29\\n29\\n29\\n30\\n30\\n30\\n30\\n31\\n31\\n31\\n31\\nd.\\nV. V\\n31 30 29 28\\n3-\u00c2\u00bb\\n6.2\\n30\\n6.0\\n2.9\\n5.8\\n9-3\\n9.0\\n8.7\\n12.4\\n12.0\\nII. 6\\n15-5\\n18.6\\n15-0\\n18.0\\n14.5\\n17-4\\n21.7\\n21 .0\\n20.3\\n24.8\\n24.0\\n23.2\\n27.9\\n27.0\\n26.1\\n5.6\\n8.4\\n14.0\\n16.8\\n19.6\\n22.4\\n25.2\\n27 26 25 24\\n2.7\\n2.6\\n2.5\\n5-4\\n8.1\\n5-2\\n7.8\\n5.0\\n7 5\\n10.8\\n10.4\\n10\\n135\\n16.2\\n13.0\\n15.6\\n12.5\\n15\\n18.9\\n18.2\\n7-5\\n21.6\\n20.8\\n20.0\\n24-3\\n23-4\\n22.5\\n24\\n4.8\\n7.2\\n9.6\\nT2 .0\\n14 4\\n16.8\\n19.2\\n21.6\\n23 22 21 20\\n2.-,\\n2.2\\n2.1\\n4.6\\n4.4\\n42\\n6.9\\n6.6\\n6.3\\n9.2\\n8.8\\n8.4\\nII. s\\nIT.O\\niO.,S\\n13-8\\n13.2\\n13.6\\n16. 1\\niS-4\\n14.7\\n18.4\\n17.6\\n16.8\\n20.7\\n19.8\\n18.9\\n19 18\\n1.9\\n1.8\\n^\u00e2\u0080\u00a27\\n3^\u00c2\u00ab\\n3^6\\n3^4\\n5 7\\n5-4\\n51\\n7 6\\n7.2\\n6.8\\n9-5\\n9.0\\n8.5\\nII 4\\nI0.8\\n10.2\\n\u00c2\u00ab3-3\\n12.6\\n11 .0\\n15-2\\n14.4\\n13-^\\n17.1\\n16.2\\n15-3\\n17 16\\n1.6\\n3-2\\n4.8\\n9.6\\nII. 2\\n12.8\\n14.4\\n15 14 13 12\\n1.5\\n1.4\\n13\\n30\\n2.8\\n2.6\\n4-5\\n4.2\\n3^9\\n6.0\\n5-6\\n$\u00e2\u0080\u00a22\\n7-S\\n7.0\\n(^\u00e2\u0096\u00a05\\n9.0\\n8.4\\n7.8\\n10.5\\n9.8\\n9.1\\n12\\n11 .2\\n10.4\\n13-5\\n12.6\\n11.7\\n2-4\\n3^6\\n4.8\\n6.0\\n7.2\\n8.4\\n9.6\\n[0.8\\nII 10 O\\n1 .1 [i .0 0.0\\n2 .2|2 .0\\n3-? 30\\nI\\no\\n4-4 4\\n5-5 5\\n6.6,6.0\\n7-7 7-\\n8.8 8.\\n9.9I9.\\n0.3\\n0-3\\n0.4\\n0.4\\nr. V.\\n445", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0497.jp2"}, "498": {"fulltext": "TABLE X.\u00e2\u0080\u0094 NATURAL VERSED SINES AND EXTERNAL SECANTS.\\n40\u00c2\u00b0-50 50-60\\nI Vers, j d. Exsec. d.\\n40\\nlO\\n20\\n30\\n40\\n50\\n41\\n10\\n20\\n30\\n40\\n50\\n42\\n10\\n20\\n30\\n40\\n50\\n43\\n10\\n20\\n30\\n40\\n50\\n44\\n10\\n20\\n30\\n40\\n50\\n45\\n10\\n20\\n30\\n40\\n50\\n46\\n10\\n20\\n30\\n40\\n50\\n47\\n10\\n20\\n30\\n40\\n50\\n48\\n10\\n20\\n30\\n40\\n50\\n49\\n10\\n20\\n30\\n40\\n50\\n50\\n2339\\n2358\\n2377\\n2396\\n2415\\n2434\\n2453\\n2472\\n2491\\n2510\\n2529\\n2549\\n2568\\n2588\\n26of\\n2627\\n2647\\n266,^\\n2686\\n2706\\n2726\\n274\u00c2\u00a7\\n2765\\n2786\\n28og\\n2827\\n2847\\n286f\\n2888\\n2908\\n2920\\n2949\\n2970\\n2991\\n301 T\\n30^2\\n3053\\n3074\\n3095\\n3116\\n313?\\n315^\\n3180\\n3201\\n3222\\n3244\\n3265\\n3287\\n3308\\n3330\\n3352\\n3374\\n3395\\n34if\\n3439\\n346T\\n3483\\n3505\\n352?\\n3550\\n3572\\nVers.\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n9\\n20\\n19\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n20\\n26\\n20\\n20\\n20\\n20\\n21\\n20\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n21\\n22\\n21\\n22\\n21\\n22\\n22\\n22\\n22\\nj 22\\n22\\n22\\n3054\\n3086\\n3II8\\n315I\\n3183\\n3217\\n3250\\n3284\\n331^\\n3352\\n3386\\n3421\\n345S\\n3491\\n352^\\n35^3\\n3599\\n3636\\n3673\\n3710\\n3748\\n3786\\n3824\\n3863\\n3901\\n3941\\n3980\\n4020\\n4066\\n4101\\n4142\\n41^3\\n4225\\n4267\\n4309\\n4352\\n439^\\n4439\\n4483\\n452^\\n4572\\n461^\\n4663\\n4945\\n4993\\n5042\\n5091\\n514T\\n5192\\n5242\\n5294\\n534?\\n539?\\n5450\\n5503\\n4708\\n4755\\n4802\\n4849 I 4^\\n4896 I 48\\n32\\n32\\n32\\n32\\n33\\n33\\n34\\n33\\n34\\n34\\n34\\n3l\\n35\\n36\\n36\\n36\\n37\\n37\\n37\\n37\\n38\\n38\\n39\\n38\\n39\\n39\\n40\\n40\\n40\\n41\\n41\\n41\\n42\\n42\\n43\\n43\\n43\\n44\\n44\\n44\\n4?\\n4?\\n45\\n46\\n47\\n47\\n48\\n48\\n49\\n50\\n50\\n50\\n51\\n51\\n52\\n53\\n53\\n53\\n5557\\nExsec. d.\\n50\\n10\\n20\\n30\\n40\\n50\\n51\\n10\\n20\\n30\\n40\\n50\\n52\\n10\\n20\\n30\\n40\\n50\\n53\\n10\\n20\\n30\\n40\\n50\\n54\\n10\\n20\\n30\\n40\\n50\\n55\\n10\\n20\\n30\\n40\\n50\\n56\\n10\\n20\\n30\\n40\\n50\\n57\\n10\\n20\\n30\\n40\\n50\\n58\\n10\\n20\\n30\\n40\\n50\\n59\\n10\\n20\\n30\\n40\\n50\\n60\\nVers.\\n3572\\n3594\\n3617\\n3639\\n3661\\n3684\\n3707\\n3729\\n3752\\n3775\\n379f\\n3820\\n3843\\n3866\\n3889\\n3912\\n3935\\n3958\\n3982\\n4005\\n4028\\n4052\\n4075\\n4098\\n4122\\n4145\\n4169\\n4193\\n4216\\n4246\\n4264\\n4286\\n4312\\n4336\\n4360\\n4384\\n4408\\n4432\\n4456\\n4486\\n4505\\n4529\\n4553\\n4578\\n4602\\n4627\\n465T\\n4676\\n4701\\n4725\\n4750\\n4775\\n4800\\n4824\\n4849\\n4874\\n4899\\n4924\\n4949\\n4975\\n5000\\nVers.\\n22\\n22\\n22\\n22\\n22\\n23\\n22\\n22\\n23\\n22\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n23\\n24\\n23\\n23\\n24\\n23\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n24\\n25\\n24\\n24\\n25\\n25\\n24\\n25\\n25\\n25\\n25\\n25\\n25\\n2 5\\nExsec.\\nd.\\n5557\\n561 1\\n5666\\n5721\\n5777\\n5833\\n5890\\n594?\\n6005\\n6064\\n6123\\n6182\\n6242\\n6303\\n6365\\n6427\\n6489\\n6552\\n6618\\n6681\\n6746\\n6811\\n6878\\n6945\\n7013\\n708T\\n7156\\n7220\\n7291\\n7362\\n213\u00c2\u00a3\\n750?\\n7581\\n7655\\n7730\\n7806\\n7883\\n7966\\n8039\\n8118\\n8198\\n8279\\n8361\\n8443\\n8527\\n8611\\n8697\\n8783\\n8871\\n8959\\n9048\\n9139\\n9230\\n9322\\n0416\\n9510\\n9606\\n9703\\n9801\\n9900\\nI 0000\\nFxsec.\\n53\\n54\\n54\\n55\\n56\\n56\\n5?\\n58\\n58\\n59\\n59\\n60\\n61\\n61\\n62\\n62\\n63\\n64\\n64\\n65\\n65\\n66\\n67\\n68\\n68\\n69\\n70\\n76\\n71\\n72\\n73\\n73\\n74\\n75\\n75\\n77\\n71\\n7l\\n79\\n80\\n81\\n82\\n82\\n83\\n84\\n85\\n86\\n89\\n96\\n91\\n92\\n93\\n94\\n95\\n97\\n98\\n99\\n100\\nd.\\nl\u00c2\u00bb. P.\\n987654\\n0.9\\n1.8\\n2.7\\n3-6\\n4-5\\n5-4\\n6.3\\n7.2\\no.8|o.7\\n611 .4\\n42.1\\n5-6 4.9\\n6.4 5.6\\n7-216.3\\n2.4\\n3-0\\n3-6\\n4.2\\n4.8\\n5-4\\n0.5 0.4\\n1.00.8\\n1.5 1.2\\n2.0 1.6\\n2.5 2.0\\n3.0 2.4\\n3-5\\n4.0\\n4-5\\n2.8\\n32\\n3-6\\n3 2 19 8 7\\nI\\n0.3\\n0.2\\n0.1\\n0.9\\n0-8\\n2\\n3\\no.b\\n0.9\\n0.4\\n0.6\\n0.2\\n0.3\\n1.9\\n2-8\\n1-7\\n2-5\\n4\\n1 .2\\n0.8\\n0.4\\n3.8\\n3-4\\n5\\n6\\n1-5\\ni..t\\n1 .0\\n1.2\\n0.5\\n0.6\\n4-7\\n5-7\\n4 2\\n5-1\\n7\\n8\\n2.1\\n2.4\\n1.4\\n1.6\\n0.7\\n0.8\\n6.6\\n7.6\\n5-9\\n6.8\\n9\\n2-7\\n1.8\\n0.9\\n\u00c2\u00ab.5\\n7-6\\n07\\nI.. 5\\n2.2\\n3-0\\n3-7\\n4-5\\n5-2\\n6.0\\n6.7\\n6 5\\n4\\n3\\n2\\nI\\no.go.g\\n0.4 03\\n0.2\\ni\\n1.3 1 1\\n1.9 1.6\\n0.9\\n1-3\\n0.7\\n1 .6\\n0.5\\n0.7\\n0.3\\n0.4\\n2.6 2.2\\n1.8\\n1.4\\n1 .0\\n0.6\\n3.2 2.7\\n2.2\\ni-7\\n1 .2\\n0.7\\n3-9 3-3\\n2-7\\n2.1\\n1 .5\\n0.9\\n4-5 3-8\\n3-i\\n2.4\\n1-7\\n1 .0\\n5.2 4-4\\n5-8 4-9\\n3 t^\\n4.0\\n2.\\n3-1\\n2.0\\n2.2\\nT .2\\n1-3\\n25 25 24 24 23 23\\n2.5\\n2.5\\n2.4\\n2.4\\n2-3\\n5-1\\nS-c\\n4-9\\n4.!\\n4-7\\n7-6\\n7-5\\n7 3\\n7-2\\n70\\n10. 2\\n12.7\\n10.0\\n12.5\\n9\\n12.2\\n9.6\\n12.0\\n9.4\\nIt. 7\\n15.3\\n150\\n14 7\\n14.4\\n14.1\\n^7-8\\n17-5\\nJ7.1\\n16.8\\n16.4\\n20.4\\n22.9\\n20.0\\n22.5\\n19. t\\n22.6\\n10.2\\n21.6\\n:8.8\\n21 .1\\n2-3\\n4.6\\n6.9\\n9.2\\nlis\\n13-8\\n4\\n20.7\\n22 22 21 21 20 20\\n4.4\\n6.6\\n13.21\\n4-3\\n6.4-\\n4 2\\n6.3\\n8.6 8.4\\n[0.710.5\\n12.9 12.6\\n41\\n6.1\\ne.o\\n8.0\\n10. o\\n12.31 12 .0\\n15.4I15.0 14.7 14-3 M-\\n17.6117.21 16.8 I6.4J16\\n19.8119.3 18.9ll8.4il8\\n19 19 18\\n3-9\\n5 8\\n7.8\\n9 7\\n13-6 3\\ni5-6|i5\\ni7-5i 7\\nP. P.\\n3-7\\n5-5\\n7-4\\ng.2\\n12.9\\n14.8\\n16.6\\n446", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0498.jp2"}, "499": {"fulltext": "TABLE X.\u00e2\u0080\u0094 NATURAL VERSED SINES AND EXTERNAL SECANTS.\\nG0\u00c2\u00b0-70 7()\u00c2\u00b0-8()\\nVers.\\nGO\\nlo\\n20\\n30\\n40\\n50\\nGl\\n10\\n20\\n30\\n40\\n50\\nG2\\n10\\n20\\n30\\n40\\n50\\nG3\\n10\\n20\\n30\\n40\\n50\\n64\\n10\\n20\\n30\\n40\\n50\\nG5\\n10\\n20\\n30\\n40\\n50\\nG6\\n10\\n20\\n30\\n40\\n50\\n67\\n10\\n20\\n30\\n40\\n50\\n68\\n10\\n20\\n30\\n40\\n50\\n69\\n10\\n20\\n30\\n40\\n50\\n70\\n5000\\n5025\\n5050\\n5076\\n5101\\n5126\\n5152\\n5177\\n5203\\n5228\\n5254\\n5279\\n530g\\n5331\\n5356\\n53^2\\n5408\\n5434\\n5460\\n5486\\n5512\\n5538\\n5564\\n5590\\n5616\\n5642\\n5668\\n5695\\n5721\\n574^\\n5774\\n5800\\n5826\\n5853\\n5879\\n5906\\n5932\\n5959\\n5986\\n6012\\n6039\\n6066\\n6092\\n61 19\\n6i46\\n6173\\n6200\\n6227\\n6254\\n6281\\n6308\\n6335\\n6362\\n6389\\n6416\\n6443\\n6476\\n6498\\n6525\\n6552_\\n6580\\nVers.\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n25\\n2S\\n2S\\n25\\n26\\n25\\n25\\n26\\n26\\n2l\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n26\\n27\\n26\\n26\\n27\\n26\\n27\\n27\\n26\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n27\\n2^\\n27\\n27\\n27\\n27\\n2f\\nd.\\nKxsec.\\n,0000\\n.0101\\n.0204\\n.030^\\n\u00e2\u0080\u00a20413\\n.0519\\n062\u00c2\u00a7\\n.073S\\n.0846\\n.0957\\n1076\\n,1184\\n1300\\nI4I8\\ni53\u00c2\u00a7\\n1657\\n1902\\n2027\\n2153\\n2281\\n2411\\n2543\\n2676\\n28ii\\n2948\\n3087\\n3228\\n3371\\n351?\\n3662\\n3810\\n3961\\n4114\\n4269\\n4426\\n4586\\n4747\\n4912\\n5078\\n5247\\n5419\\n5593\\n5770\\n5949\\n613T\\n6316\\n6504\\n6694\\n6888\\n7085\\n.7285\\n,7488\\n7694\\n7904\\n811^\\n8334\\n8554\\n.8778\\n9006\\n9238\\nKxsec.\\n01\\n02\\n03\\n05\\n06\\n07\\n09\\n16\\nII\\n13\\n14\\n16\\n18\\n26\\n21\\n23\\n25\\n26\\n28\\n30\\n31\\n33\\n35\\n37\\n39\\n40\\n43\\n44\\n46\\n48\\n51\\n52\\n55\\nSi\\n59\\n61\\n64\\n66\\n69\\n71\\n74\\n77\\n79\\n82\\n85\\n88\\n96\\n94\\n96\\n200\\n203\\n206\\n210\\n213\\n216\\n226\\n224\\n22^\\n232\\n(I.\\n70\\n10\\n20\\n30\\n40\\n50\\n71\\n10\\n20\\n30\\n40\\n50\\n72\\n10\\n20\\n30\\n40\\n50\\n73\\n10\\n20\\n30\\n40\\n50\\n74\\n10\\n20\\n30\\n40\\n50\\n75\\n10\\n20\\n30\\n40\\n50\\n76\\n10\\n20\\n30\\n40\\n50\\n77\\n10\\n20\\n30\\n40\\n50\\n78\\n10\\n20\\n30\\n40\\n50\\n79\\n10\\n20\\n30\\n40\\n50\\n80\\nVers.\\n6580^\\n6607\\n6634\\n6662\\n6689\\n67j7_\\n^744.\\n6772\\n6799\\n6827\\n6854\\n6882\\n6910\\n7104\\n7132\\n7160\\n7187\\n7215\\n7243\\n6271\\n7299\\n732^\\n7355\\n7383\\n21\\n12\\n7440\\n7468\\n7496\\n7524\\n7552\\n7581\\n7609\\n763?\\n7665\\n7694\\n7722\\n775o_\\n7779\\n7807\\n7835\\n7864\\n7892\\n7921\\n7949\\n7978\\n8005\\n8035\\n8063\\n8092\\n8126\\n8149\\n817^\\n8206\\n8235\\n8263\\nVers.\\n27\\n2^\\n27\\n2?\\n27\\n27\\n2^\\n2?\\n27\\n27\\n27\\n28\\n27\\n27\\n28\\n27\\n28\\n28\\n2?\\n28\\n28\\n2^\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n2g\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n28\\n29\\n28\\n28\\n(1.\\nKxsec.\\n9238\\n\u00e2\u0080\u00a29473\\n\u00e2\u0080\u00a29713\\n\u00e2\u0080\u00a2995^\\n.0205\\n0458\\n097 1\\n.1244\\n.1515\\n.1792\\n.2073\\n.2366\\n7265^\\n.2951\\n3255\\n3565\\n.3881\\n2.4203\\n\u00e2\u0080\u00a24531\\n.4867\\n.5209\\n\u00e2\u0080\u00a25558\\nJ9i,5\\n.6279\\n.6651\\n.7031\\n.7420\\n.7816\\n8222\\n8637\\n.9061\\n.9495\\n.9939\\n.0394\\n.0859\\n1335\\n1824\\n2324\\n2836\\n3362\\n3901\\n4454\\n5021\\n5604\\n6202\\n6816\\n7448\\n809f\\n8765\\n9451\\nOI58\\n0885\\nj[636\\n2408\\n3205\\n4026\\n4874\\n5749\\n6653\\n758?\\nKxsec.\\n235\\n240\\n244\\n248\\n253\\n257\\n262\\n26^\\n276\\n276\\n281\\n287\\n292\\n298\\n304\\n310\\n316\\n322\\n328\\n33^\\n342\\n349\\n356\\n364\\n372\\n380\\n388\\n396\\n406\\n414\\n424\\n434\\n444\\n454\\n465\\n476\\n488\\n500\\n512\\n525\\n539\\n553\\n56?\\n582\\n598\\n614\\n631\\n649\\n667\\n686\\n707\\n728\\n749\\n772\\n796\\n821\\n847\\n^7l\\n904\\n934\\n(I.\\nI 1*\\n9\\n0.9\\n8 7\\n2.7\\n3-6\\n5-4\\n6.3\\n7.2\\n0.8\\n1.6\\n2.4\\n0.7\\n1.4\\n2. 1\\n3.2 2.8\\n4-0 3.5\\n4.8 4.2\\n5-6\\n6.4\\n7.2\\n4.9\\n5.6\\n1.8\\n2.4\\n3-0\\n3.6\\n4.2\\n4.8\\n\u00e2\u0080\u00a23 5-4\\n5 4\\n).S 0.4\\n.0\\n-5\\n1.2\\n2.0 1.6\\n2.5 2.0\\n302. 4\\n3.52.8\\n40 3.2\\n4.513.6\\n3 2 19 8 7\\n0-3\\n0.2\\n0.1\\n0.9\\n0-8\\n0.\\n0.6\\n0.4\\n0.2\\n1.9\\n1.7\\nI.\\n0.9\\n0.6\\n0.3\\n2-8\\n2.5\\n2.\\n1 .2\\n0.8\\n0.4\\n3.8\\n3-4\\n3-\\n1-5\\nI.O\\n0.5\\n4-7\\n4.2\\n3-\\ni.fc\\n1.2\\n0.6\\n5-7\\n5-1\\n4-\\n2.1\\n2.4\\n1.4\\n1.6\\n0.7\\n0.8\\n6.6\\n7.6\\n5-9\\n6.8\\n5-\\n6.\\n2.7\\n1.8\\n0.9\\n8-5\\n7-6\\n6.\\n6 5 4 3 2 1\\n0.6 0.5 0.4 0.3 0.2 oi\\ni.3|i.i 0.9 0.7 0.5 o 3\\ni.9|i.6 10 0-7 0.4\\n2.6|2.2 1.8 1.4 1.00.6\\n3.2 2.7 2.21.7 \u00e2\u0080\u00a22 0.7\\n3.9 3.3 2.7|2.1 l.S 0.9\\n4.5 3\u00c2\u00a7 3-1 2.4 1.7 1.0\\n5.2 4.4 3.62.^ 2.0 1.2\\n5-8 4 94-ol3-i 2.2 r.3\\n29 28 28 2f\\n2.9\\n5.8\\n8.7\\nII. 6\\n14.5\\n17.4\\n20.3\\n23.2\\n26. 1\\n2-8\\n5-7\\n8.5\\nII. 4\\n14.2\\n17.1\\n19.9\\n22.8\\n25-6\\n2.8\\n5.6\\n8.4\\n14.0\\n16.8\\n19.6\\n22.4\\n252\\n27 2g 26 2^\\n2.7\\n2-6\\n2.6\\n2-5\\n5^4\\n.S 3\\n5-2\\n51\\n8.1\\n7-9\\n7.8\\n7-6\\n10.8\\n10.6\\n10.4\\n10.2\\n\u00c2\u00bbJ 5\\n13-2\\n13.0\\n12.7\\n16.2\\n5-9\\n15.6\\n\u00c2\u00bb5-3\\n18.9\\n18.5\\n18 2\\n17-8\\n21.6\\n21.2\\n20.8\\n30.4\\n24.3\\n23-8\\n23.4\\n22.9\\n447", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0499.jp2"}, "500": {"fulltext": "TABLE X.\u00e2\u0080\u0094 NATURAL VERSED SINES AND EXTERNAL SECANTS.\\n80\u00c2\u00b0-85 85^-90\u00c2\u00b0\\nso\\nlO\\n20\\n40\\n50\\n81\\n10\\n20\\n30\\n40\\n50\\nS2\\n10\\n20\\n30\\n40\\n50\\n83\\n10\\n20\\n3\u00c2\u00ab\\n40\\n50\\n84\\n10\\n20\\n30\\n40\\n50\\n85\\nVers.\\n8263\\n8292\\n8321\\n8349\\n8378\\n8407\\n8435\\n8464\\n8493\\n8522\\n8550\\n8579\\n8608\\n8637\\n8666\\n8694\\n8723\\n8752\\n8781\\n8810\\n8839\\n8868\\n8897\\n8926\\n8954\\n8983\\n9012\\n9041\\n9070\\n9099\\n9128\\nVers.\\n29\\n28\\n28\\n29\\n28\\n29\\n28\\n29\\n28\\n29\\n29\\n28\\n29\\n28\\n29\\n29\\n29\\n28\\n29\\n29\\n29\\n29\\n28\\n29\\n29\\n29\\n29\\n29\\n29\\nd.\\nExsec.\\n(1.\\n4 7587\\n4-8554\\n4.9553\\n5.0588\\n5 1 666\\n5.2772\\n5-3924\\n5.5121\\n5-6363\\n5-7654\\n5.8998\\n6.0396\\n6.1853\\n6.3372\\n6.4957\\n6.6613\\n6.8344\\n7.0I56\\n7-2055\\n7 4046\\n7.6138\\n7.8336\\n8.0651\\n8.309T\\n8.5667\\n8.8391\\n9.1275\\n9-4334\\n9-7585\\n10. 1045\\n10-4737\\nExsec.\\n966\\n999\\n035\\n072\\nIII\\n152\\n196\\n242\\n291\\n343\\n398\\n456\\n519\\n585\\n656\\n731\\n812\\n898\\n991\\n2091\\n2198\\n2315\\n2440\\n2576\\n2723\\n2884\\n3059\\n3250\\n3466\\n3691\\n85\\n10\\n20\\n30\\n40\\n50\\n86\\n10\\n20\\n30\\n40\\n50\\n87\\n10\\n20\\n30\\n40\\n50\\n88\\n10\\n20\\n30\\n40\\n50\\n89\\n10\\n20\\n30\\n40\\n50\\n90\\nVers.\\n9123\\n9157\\n9186\\n9215\\n9244\\n9273\\n9302\\n9331\\n9366\\n9389\\n94I8\\n9447\\n?47i\\n9505\\n9534\\n9564\\n9593\\n9622\\n9651\\n9680\\n9709\\n9738\\n9767\\n9796\\n982S\\n9854\\n9883\\n9912\\n9942\\n9971\\n0000\\nVers.\\n(1.\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\n29\\nd.\\nExsec.\\n0-4737\\n0.8683\\nI .2912\\n1-7455\\n2.2347\\n2.7631\\nd.\\n3-3356\\n3-9579\\n4.6368\\n5-3804\\n6. 1984\\n7. 1026\\n8.1073\\n9.2303\\n20.4937\\n21 .9256\\n23. 5621\\n25-4505\\n27.6537\\n30.2576\\n33.3823\\n37.2015\\n41-9757\\n48, 1 146\\n56.2987\\n67-7573\\n84.9456\\n113-5930\\n170.8883\\n342..7752\\n00\\nExsec.\\n.3946\\n.4229\\n.4542\\n.4892\\n.5284\\n\u00e2\u0080\u00a25725\\n.6223\\n-6789\\n-7436\\n.8180\\n.9041\\nI 0047\\nI 1230\\nI .2634\\nI. 4319\\nI .6365\\n1.8884\\n2.2032\\n2.6039\\n3.1247\\n3.8192\\n4.7741\\n6. 1383\\n8.1846\\nd.\\nP. P.\\n29 29 28\\n2.9\\n5.9\\n8.8\\n11.8\\n14.7\\n17.7\\n20-6\\n23.6\\n26.5\\n2.9\\n5.8\\n8.7\\nII. 6\\nM-5\\n17.4\\n20.3\\n23.2\\n26.1\\n5-7\\n8-5\\n11.4\\n14.2\\n17.1\\n19.9\\n22.8\\n25.6\\n448", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0500.jp2"}, "501": {"fulltext": "TABLE XL\u00e2\u0080\u0094 USEFUL TRIGONOMETRICAL FORMUL.\u00e2\u0082\u00ac.\\nlo\\nII\\nsin a\\nI _ tan a\\ncosec a |/i tan\\ncos 2a\\nVi cot a\\ncos a tan a Vi cos z 2 sin z cos la\\nI cos a 2 tan\\ncot ^a I tan z\\nI cot a\\nvers ^z cot ^a.\\ncos iZ\\nsec a i/i _|_ cot a Vi tan^\\nI vers a sin a cot ^z i^i sin^ a 2 cos J^ i\\nsin a cot la 1 cos^ Ja sin la \u00e2\u0080\u00941 2 sin la.\\ntana\\nsin d5 sec a\\ncot (Z cos a cosec a Vcosec^ a i\\nvers 2a cosec 2a cot a 2 cot 2a sin a sec a\\nsin 2^\\nI cos 2a\\nexsec cot ^a exsec 2^z cot 2a.\\ncot tZ\\ncos a\\nsin 2(Z\\n_ I -f- cos 2a\\ntan a sin a\\nI cos 2a sin 2a\\nV^cosec^ a I cot la cosec\\nvers a 1 cos sin tz tan ^a 2 sin^ ^tz cos a\\nexsec iz sec a i tan a tan la vers a sec a.\\nexsec (Z.\\nsin 4^\\ncos la\\ntan 1^\\ncot ^a\\ni/\\nvers _ sin a __ vers ^z cos la\\n2\\n2 cos 2\\nsin a\\na/ I cos rt; _ sin dz _ sin sin la\\n2 2 sin la\\nvers\\nvers a cosec a cosec a cot a\\ntan a\\nI cos a\\ncosec a cot a\\nI 4 sec a\\ntan a\\nsin a\\nexsec cosec a cot\\nvers la i V|(i cos a).\\n12\\nexsec\\n1/7\\ni^|(i -j- cos\\nI.\\n449", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0501.jp2"}, "502": {"fulltext": "TABLE XL\u00e2\u0080\u0094 USEFUL TRIGONOMETRICAL FORMULA.\\n13\\n2 tan\\nI tan*^ a\\n14\\ncos 2a cos sin^ i 2 sin^ a 2 cos a i\\nI tan^\\nI tan^ a\\n15\\n2 tan a\\nIdn 2tf\\nI tan^ a\\n16\\ncot I I tan^ a\\ncot 2^ i cot a 1 tan\\n2 cot a 2 tan a\\n17\\nvers 2^ =2 sin a 1 cos 2^ 2 sin cos a tan\\n18\\ntan 2a 2 tan^ a 2 sin a\\ncot a I tan^^ 1 2 sm a\\n19\\nsin sin cos cos sin L\\n20\\ncos cos a cos sin a sin\\n21\\nsin tz sin =2 sin cos l{a\\n22\\nsin a sin (5=2 sin ^{a b) cos |(a\\n23\\ncos cos 5 2 cos cos J(^ /5).\\n24\\ncos a cos b 2 sin ^5) sin \\\\{a b).\\nCall the sides of any triangle A^ B^ C, and the opposite angles a, b, and\\nc. Call J i(^ C).\\n25\\njI jg\\ntan l(a _^ tan _^ cot Jr.\\n26\\n27\\n28\\nC B) f (A BfJ \\\\f I\\ncos ^(rt sin ^(a b)\\nsin i\u00c2\u00ab\\ncosi\u00c2\u00ab y\\n29\\n30\\nArea Vs{s A){s B){s C)\\n2 sin\\n1\\n450", "height": "4304", "width": "2598", "jp2-path": "railroadconstruc00webb_0502.jp2"}, "503": {"fulltext": "INDEX.\\nAbutments for trestlef?, 1G7.\\nAccuracy of earthwork computations,\\n109.\\nAccuracy of tunnel surveying, 189.\\nAdjustments of instruments, 303.\\nAdvantages of tie-plates, 260.\\nAllowance for shrinkage of earth-\\nwork, 113.\\nAmerican system of tunnel excava-\\ntion, 197.\\nAngle-bar (rail-joint) efficiency, 255.\\nArch culverts, 215.\\nArea of culverts method of compu-\\ntation, 204.\\nArea of culverts results based on\\nobservation, 206.\\nArea of the waterway culverts, 203.\\nA. S. C. E. standard rail section, 245.\\nAustrian system of tunnel excavat on,\\n197.\\nAveraging end areas for volume of\\nearthwork, 79.\\nBallast, 220.\\nBallast\u00e2\u0080\u0094 cost, 224.\\nBallast methods of laying, 223.\\nBarometric elevations, 6.\\nBelgian system of tunnel excavation,\\n197.\\nBlasting, 142.\\nBlasting cost, 147.\\nBorrow-pits earthwork, 102.\\nBowls (ties), 241.\\nBox CULVERTS, 212.\\nBracing trestles, 16G.\\nBracing (trestles) design, 184.\\nBridge-joints (rail), 257.\\nBridge spirals, 4.\\nBroken-stone ballast, 221.\\nBurnettizing wooden ties, 234.\\nCaps (trestle) design, 184.\\nCars and horses use in hauling\\nearthwork cost, 134.\\nCars and locomotives use in hauling\\nearthwork cost, 136.\\nCarts use in hauling earthwork\\ncost, 130.\\nCattle-guards, 216.\\nCattle-passes, 218.\\nCenter of gravity of side-hill pactions\\nearthwork, 107.\\nCentral angle of a curve, 21.\\nChemical composition of rails, 251.\\nCinders (ballast), 221.\\nCircular lead-rails switches, 278.\\nClassification of excavate I material,\\n148.\\nCompound curves, 37.\\nCompound curves application of tran-\\nsition curves, 56.\\nCompound sections earthwork, 07.\\nCompulations (approximate) from\\n})rofiles earthwork. 111.\\nComputation of j)roducts earthwork,\\n90.\\nComputation cf volu^me of earth-\\nwork, 76.\\n451", "height": "4321", "width": "2521", "jp2-path": "railroadconstruc00webb_0503.jp2"}, "504": {"fulltext": "452\\nINDEX.\\nConnecting curve from a curved track\\nto the inside, 291.\\nConnecting curve from a curved track\\nto the outside, 290.\\nConnecting curve from a straight\\ntrack, 290.\\nConstruction of tunnels, 195.\\nContractor s profit earthwork, 140.\\nCorbels trestles, 1G8.\\nCost of ballast, 224.\\nCost of earthwork, 126.\\nCost of framed timber trestles, 174.\\nCost of metal cross-ties, 240.\\nCost of pile trestles, IGl.\\nCost of rails, 254.\\nCost of ties, 232.\\nCost of treating wooden ties, 236.\\nCost of tunneling, 201.\\nCreosoting wooden ties, 233.\\nCross-country route, 3.\\nCrossings, 300.\\nCrossing one straight and one curved\\ntrack, 301.\\nCrossing two curved tracks, 301,\\nCrossing two straight tracks, 300.\\nCross-over between two parallel curved\\ntracks reversed curve, 296.\\nCross-over between two parallel curved\\ntracks straight connecting curve,\\n295.\\nCross-over between two parallel\\nstraight tracks, 293.\\nCross-sectioning field-work, 10.\\nCross-sectioning for volume of earth-\\nwork, 73.\\nCross-sectioning irregular sections\\nearthwork, 100.\\nCross-section method of obtaining con-\\ntours, 9.\\nCross-sections ballast, 222.\\nCross-sections of tunnels, 190.\\nCulverts, 202.\\nCurvature correction volume of\\nearthwork, 103.\\nCurve location by deflections, 23.\\nCurve location by middle ordinates,\\n27.\\nCurve location by offsets from the\\nlong chor i, 28.\\nCurve location by tangential offsets,\\n26.\\nCurve location by two transits, 26.\\nDeflections for a spiral, \u00e2\u0096\u00a049.\\nDesign of culverts elements, 202.\\nDesign of nut-locks, 268.\\nDesign of pile trestles, 161.\\nDesign of ti3-plates, 261.\\nDesign of track-bolts, 267.\\nDesign of tunnels, 190.\\nDesign of wooden trestles, 174.\\nDimensions of wooden ties, 229.\\nDitch -s, 69.\\nDrains tunnels, 195.\\nDrill-holes, position and direction\\nblasting, 145.\\nDrilling blasting, 144.\\nDriving spikes, 264.\\nDurability of metal ties, 238.\\nDurability of wooden ties, 228.\\nEarly forms of rails, 243.\\nEarthwork cost, 126.\\nEarthwork surveys, 72.\\nEccentricity of the center of gravity\\nof an earthwork ^rcss-section, 104.\\nEconomics of treated ties, 236.\\nElements of a 1\u00c2\u00b0 curve, 22.\\nElements of a simple curve, 21,\\nEnglish system of tunnel excavation,\\n197.\\nEnlargement of headings tunnels,\\n196.\\nEquivalent level sections eartliwork,\\n85.\\nEquivalent sections earthwork, 83.\\nExisting track determination of cur-\\nvature, 35.\\nExpansion of rails, 249,\\nExploding the charge blasting, 147,\\nExplosive, amount required in blast-\\ning, 146.\\nExplosives blasting, 142,\\nExtent of use metal ties, 238.", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0504.jp2"}, "505": {"fulltext": "INDEX.\\n453\\nExtent of use of trestles, 153.\\nExternal distances for a 1\u00c2\u00b0 curve, 318.\\nExternal distance simple curve, 21.\\nFactors of safety design of timber\\ntrestles, 180.\\nFailures of rail-joints, 258.\\nFastenings for metal cross-ties, 240.\\nField-work for locating a spiral, 52.\\nFire protection on trestles, 173.\\nFive-level sections earthwork, 92.\\nFloor systems of trestles, 1G7.\\nFormation of embankmekts. 111.\\nForming embankments methods, 115.\\nForm of excayatioxs and embank-\\nments, 64.\\nForms of rail sections (standard), 244.\\nFormulae for re(|uired area of culverts,\\n205.\\nFoundations trestles, 1G5.\\nFramed timber trestles cost, 174.\\nFramed trestles, 162.\\nFree haul\u00e2\u0080\u0094 limit, 124.\\nFrench system of tunnel excavation,\\n197.\\nFrogs, 272.\\nFrog angles trigonometrical func-\\ntions, 321.\\nFrog number, 273.\\nGerman system of tunnel excavation,\\n197.\\nGrade line change, based on mas3\\ndiagram, 123.\\nGrade of tunnels, 192.\\nGravel (ballast), 221.\\nGround-levers, 276.\\nGuard-rails switches, 277.\\nGuard-rails trestles, 169.\\nHauling earthwork cost, 130.\\nHaul of earthwork computations,\\n116.\\nHaul of earthwork method depend-\\nent on distance, 137.\\nHaul of earthwork profitable limit,\\n140.\\nHeadings tunnels, 195.\\nI-beam bridges, 219.\\nInstrumental work of locating curves,\\n24.\\nIron-pipe culverts, 209.\\nIrregular prisinoid volume, 94.\\nIrregular sections earthwork, 93.\\nJoints of framed trestles, 162.\\nKyanizing wooden tics, 234.\\nLateral bracing trestles, 167.\\nLength of a simple curve, 20.\\nLength of rails, 248.\\nLevel adjustments, 309.\\nLevel sections earthwork, 81.\\nLimitations in location, 34.\\nLining of tunnels, 193.\\nLoading\u00e2\u0080\u0094 design of timber trestles,\\n179.\\nLoading earthwork cost, 128.\\nLocation surveys, 13.\\nLogarithmic sines and tangents of\\nsmall angles\u00e2\u0080\u0094 table of, 345.\\nLogarithmic sines, cosines, tangents,\\nand cotangents table of, 348.\\nLogarithmic versed sines and external\\nsecants table of, 393.\\nLogarithms of numbers talb of, 325.\\nLong chords for a 1\u00c2\u00b0 curve, 318.\\nLong chord simple curve, 21.\\nLongitudinal bracing\u00e2\u0080\u0094 trestles, 166.\\nLongitudinals, 241.\\nLoosening earthwork cost, 127.\\nMathematical DESIGN of switches,\\n278.\\nMass curve area, 121.\\nMass curve properties, 118.\\nMass diagram, 117.\\nMass diagram value, 122.\\nMetal cross-ties cost, 240.\\nMetal cross-ties fastenings. 240.\\nMetal ties, 238.\\nMetal ties form and dimensions. 239.\\nMiddle areas for volume of earth-\\nwork, 79.", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0505.jp2"}, "506": {"fulltext": "454\\nINDEX.\\nMiddle ordinate simple curve, 21.\\nModifications of location compound\\ncurves, 40.\\nModifications of location simple\\ncurves, 31.\\nMountain route, 3.\\nMud ballast, 220.\\nMud-sills\u00e2\u0080\u0094 trestle foundations, 166.\\nMultiform compound curves, 47.\\nMultiple-story construction trestles,\\n163.\\nNatural sines, cosines, tangents, and\\ncotangents table of, 439.\\nNatural versed sines and external se-\\ncants table of, 444.\\nNotes location surveys, 16.\\nNumber of a frog\u00e2\u0080\u0094 to find, 273.\\nNut-locks, 266.\\nObstacles to location, 29.\\nObstructed curve curve location, 31.\\nOld-rail culverts, 213.\\nOpen cuts vs. tunnels, 200.\\nOrdinates of a spiral, 48.\\nPaper location, 13.\\nPile bents, 155.\\nPile-driving formulae, 159.\\nPile-driving methods, 157.\\nPile foundations for trestles, 165.\\nPile-points and pile-shoes, 160.\\nPile trestles, 155.\\nPile trestles cost, 161.\\nPipe culverts, 208.\\nPipe culverts construction, 208.\\nPit cattle-guards, 216.\\nPloughs use in loosening earth, 127.\\nPoint of curve, 21.\\nPoint of curve inaccessible curve lo-\\ncation, 33.\\nPoint of tangency, 21.\\nPoint of tangency inaccessible\u00e2\u0080\u0094 curve\\nlocation, 30.\\nPoint-rails of switches construction,\\n275.\\nPoint-switches, 275.\\nPortals (tunnel) excavation, 199.\\nPosts (trestle) design, 1S2.\\nPreliminary surveys, 8.\\nPreservation of ties cost, 236.\\nPreservative processe 5 for wood-\\nen ties, 232.\\nPrismoidal correction (approximate)\\nfor irregular prismoids, 99.\\nPrismoidal correction (true) for ir-\\nregular prismoids, 95.\\nPrismoids, 72.\\nRadii of curves table, 314.\\nRails, 243.\\nRail expansion, 249.\\nRail-gap at joints effect, 256.\\nRail-joints, 255.\\nRails chemical composition, 25L\\nRails cost, 254.\\nRail testing, 252.\\nRail wear on curves, 253.\\nRail wear on tangents, 252.\\nReconnoissance surveys, 1.\\nRenewals of ties regulations, 231.\\nRepairs, etc., of plant for earthwork\\ncost, 139.\\nReplacement of a compound curve by\\na curve with spirals, 58.\\nReplacement of a simple curve by a\\ncurve with spirals, 53.\\nRequirements for a perfect rail- joint,\\n255.\\nRequirements spikes, 263.\\nRequirements track-bolts, 266.\\nRoadbed width, 67.\\nRoadways for earthwork cost, 138.\\nRock ballast, 221.\\nRules for switch-laying, 298.\\nRuling grade, 2.\\nScrapers use in earthwork cost, 133.\\nScrews and bolts (rail-fastenings),\\n264.\\nSetting tie-plates methods, 262.\\nShafts tunnels, 193.\\nShaft (tunnel) surveying, 187.", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0506.jp2"}, "507": {"fulltext": "INDEX.\\n455\\nShells and small coal\u00e2\u0080\u0094 ballast, 221.\\nShoveling: (hand) of earthwork cost,\\n128.\\nShrinkage of oartliwork, 111.\\nSide-hill work^cartliwork, 100.\\nSills (trestle)\u00e2\u0080\u0094 design, 184.\\nSimple curves, 18.\\nSlag (ballast), 221.\\nSlide-rule for earthwork computa-\\ntions, 90.\\nSlopes earthwork, G5.\\nSlope-stakes position, 75.\\nSodding efl ect on slopes, 70.\\nSpacing of ties, 229.\\nSpan trestles, 164.\\nSpecifications for earthwork, 148.\\nSpecifications for wooden ties, 230.\\nSpikes, 203.\\nSpikes driving, 204.\\nSpirals required length, 48.\\nSpreading earthwork cost, 138.\\nStadia method of obtaining topog-\\nraphy, 12.\\nStandard angle-bars, 259.\\nStandard stringer bridges, 219.\\nSteam-shoveling earthwork, 129.\\nStifiness of rails efl ect on traction,\\n247.\\nStone box culverts, 212.\\nStone foundations for framed trestles,\\n166.\\nStraight connecting curve from a\\ncurved main track, 292.\\nStraight frog-rails\u00e2\u0080\u0094 effect, 280.\\nStraight point-rails effect, 281.\\nStrength of timber, 176.\\nStrength, required elements trestles,\\n175.\\nStringers for trestles design, 180.\\nStringers trestles, 167.\\nStub switches, 273.\\nSubchord\u00e2\u0080\u0094 length, 19.\\nSubgrade\u00e2\u0080\u0094 form, 68.\\nSuperelevation of the outer rail on\\ncurves general principles, 43.\\nSuperelevation of the outer rail on\\ncurves on trestles, 170.\\nSuperelevation of th? outer rail on\\ncurves practical rules, 45.\\nSuperintendence of earthwork cost.\\n139.\\nSupported joints, 257.\\nSurface cattle-guards, 217.\\nSurface survey s tunneling, 185.\\nSUKYEYIXG TUNNELS, 185.\\nSuspended joints, 257.\\nSwitchbacks, 4.\\nSwitch consteuction, 271.\\nSwitch-laying practical rules, 298.\\nSwitch leads and distances, 321.\\nSwitch-stands, 276.\\nTamping blasting, 146.\\nTangent distance simple curve, 21.\\nTangents for a 1\u00c2\u00b0 curve, 318.\\nTemperature allowances rails, 250.\\nTerminal pyramids and wedges\\nearthw ork, 65.\\nTesting rails, 252.\\nThree-level sections earthwork, 87.\\nThrown of a switch, 279.\\nTie-plates, 260.\\nTie-rods, 276.\\nTies, 226.\\nTies cost, 232.\\nTies on trestles, 170.\\nTile pipe culverts, 211.\\nTimber for framed trestles, 173.\\nTimber for pile trestles, 157.\\nTimber, strength, 176.\\nTopographical maps, use of, 5.\\nTkack-bolts, 266.\\nTransit adjustments, 304.\\nTransition curves, 43.\\nTransition curves fundamental prin-\\nciple, 43.\\nTransition curves tables of, 322.\\nTrestles, 153.\\nTrestles framed, 162.\\nTrestles pile, 155.\\nTrestles posts design, 182.\\nTrestles required elements of\\nstrength, 175.", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0507.jp2"}, "508": {"fulltext": "456\\nINDEX.\\nTrestles sills design, 184.\\nTrestles stringers design, 180.\\nTrestles vs. embankments, 154.\\nTunnels, 185.\\nTunneling cost, 201.\\nTunnel spirals, 5.\\nTurnout (double) from a straight\\ntrack, 287.\\nTurnout from the inner side of a\\ncurved track dimensions, 286.\\nTurnout from the outer side of a\\ncurved track dimensions, 284.\\nTurnouts with straight point-rails and\\nstraight frog-rails table of, 321.\\nTwo-level ground for volume of\\nearthwork, 80.\\nTwo turnouts on the same side, 289.\\nUnderground surveys, 188.\\nUnit chord simple curves, 19.\\nUpright switch-stands, 270.\\nUseful trigonometrical formulae table\\nof, 449.\\nValley route, 2.\\nVentilation (tunnel) during construc-\\ntion, 199.\\nVertex inaccessible curve location,\\n30.\\nVertex of a curve, 21.\\nVertical curves, 01.\\nVertical curves\u00e2\u0080\u0094 form of curves, 62.\\nVertical curves requ r.d length, CI.\\nVulcanizing wooden ties, 232.\\nWaterway required for culverts, 203.\\nWear of rails on curves, 253.\\nWear of rails on tangents, 252.\\nWeight of rails, 246.\\nWellhouse process for preserving\\nwooden ties, 235.\\nWheelbarrows use in hauling earth-\\nAvork cost, 132.\\nWooden box culverts, 212.\\nWodden spikes, 266.\\nWooden ties, 227.", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0508.jp2"}, "509": {"fulltext": "SHORT-TITLE CATALOGUE\\nOF TlIK\\nPUBLICATIONS\\nOF\\nJOHN WILEY SONS,\\nNew York.\\nLondon: CHAPMAX HALL, Limited.\\nARRANGED UNDER SUBJECTS.\\nDescriptive circulars sent on application.\\nBooks marked with an asterisk are sold at net prices ouly.\\nAll books are bound in cloth unless otherwise stated.\\nAGRICULTURE.\\nCattle Feeding\u00e2\u0080\u0094 Dairy Practice Diseases of Animals\\nGardening, Etc.\\nArmsby s Manual of Cattle Feeding 12mo, |1 75\\nDowning s Fruit and Fruit Trees 8vo, 5 00\\nGrotenfelt s The Principles of Modern Dairy Practice. (Woll.)\\n12mo, 2 00\\nKemp s Landscape Gardening 12mo, 2 50\\nMaynard s Landscape Gardening 12mo, 1 50\\nSteel s Treatise on the Diseases of the Dog 8vo, 3 50\\nTreatise on the Diseases of the Ox 8vo, 6 00\\nStockbridge s Rocks and Soils Svo, 2 50\\nWoU s Handbook for Farmers and Dairymen 12mo, 1 50\\nARCHITECTURE.\\nBuilding Carpentry\u00e2\u0080\u0094 Stairs\u00e2\u0080\u0094 Ventilation Law, Etc.\\nBerg s Buildings and Structures of American Railroads 4to, 7 50\\nBirkmire s American Theatres\u00e2\u0080\u0094 Planning and Construction. Svo, 3 00\\nArchitectural Iron and Steel Svo, 3 50\\nCompound Riveted Girders Svo, 2 00\\nSkeleton Construction in Buildings Svo, 3 00\\n1", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0509.jp2"}, "510": {"fulltext": "Birkmire s Planniog and CoDstruction of High OflQce Buildings.\\n8vo, 13 50\\nBriggs Moderu Am. School Building 8vo, 4 00\\nCarpenter s Heating and Ventilating of Buildings 8vo, 3 00\\nFreitag s Architectural Engineering *8vo, 2 50\\nThe Fireproofing of Steel Buildings 8vo, 2 50\\nGerhard s Sanitary House Inspection 16mo, 1 00\\nTheatre Fires and Panics 12mo, 1 50\\nHatfield s American House Carpenter 8vo, 5 00\\nHolly s Carpenter and Joiner 18mo, 75\\nKidder s Architect and Builder s Pocket-book. 16mo, morocco, 4 00\\nMerrill s Stones for Building and Decoration. 8vo, 5 00\\nMonckton s Stair Building\u00e2\u0080\u0094 Wood, Iron, and Stone 4to, 4 00\\nWait s Engineering and Architectural Jurisprudence 8vo, 6 00\\nSheep, 6 50\\nWorcester s Small Hospitals Establishment and Maintenance,\\nincluding Atkinson s Suggestions for Hospital Archi-\\ntecture 12mo, 1 25\\nWorld s Columbian Exposition of 1893 Large 4to, 2 50\\nARMY, NAVY, Etc.\\nMilitary Engineering Ordnance Law, Etc.\\n^Bruff s Ordnance and Gunnery 8vo, 6 00\\nChase s Screw Propellers 8vo, 3 00\\nCronkhite s Gunnery for Non-com. Officers 32mo, morocco, 2 00\\nDavis s Treatise on Military Law 8vo, 7 00\\nSheep, 7 50\\nElements of Law 8vo, 2 50\\nDe Brack s Cavalry Outpost Duties. (Carr.). 32mo, morocco, 2 00\\nDietz s Soldier s First Aid 16mo, morocco, 1 25\\nDredge s Modern French Artillery Large 4to, half morocco, 15 00\\nRecord of the Transportation Exhibits Building,\\nWorld s Columbian Exposition of 1893.. 4to, half morocco, 10 00\\nDurand s Resistance and Propulsion of Ships 8vo, 5 00\\nDyer s Light Artillery 12mo, 3 00\\nHoff Naval Tactics 8vo, 1 50\\nIngulls s Ballistic Tables 8vo, 1 50\\n2", "height": "4967", "width": "2909", "jp2-path": "railroadconstruc00webb_0510.jp2"}, "511": {"fulltext": "Ingalls s Handbook of Problems iu Direct Fire 8vo,\\nMahau s Permanent Fortifications. (Mercur.).8vo, half morocco,\\nMercur s Attack of Fortified Places 12mo,\\nElements of the Art of War 8vo,\\nMetcalfe s Ordnance and Gunnery 12mo, with Atlas,\\nMurray s A Manual for Courts-Martial IGmo, morocco,\\nInfantry Drill Regulations adapted to the Springfield\\nRifle, Caliber .45 32mo, paper,\\nPhelps s Practical Marine Surveying 8vo,\\nPowell s Army Oflicer s Examiner 12mo,\\nSharpens Subsisting Armies 32mo, morocco,\\nWheeler s Siege Operations. 8vo,\\nWinthrop s Abridgment of Military Law 12mo,\\nWoodhull s Notes on Militar}^ Hygiene 16mo,\\nYoung s Simple Elements of Navigation 16mo, morocco,\\nfirst edition\\nASSAYING.\\nSmelting Ore Dressing Alloys, Etc.\\nPletcher s Quant. Assaying with the Blowpipe.. 16mo, morocco, 1 50\\nFurman s Practical Assaying 8vo, 3 00\\nKunhardt s Ore Dressing 8vo, 1 50\\nO Driscoll s Treatment of Gold Ores 8vo, 2 00\\nRicketts and Miller s Notes on Assaying 8vo, 3 00\\nThurston s Alloys, Brasses, and Bronzes 8vo, 2 50\\nWilson*s Cyanide Processes. 12mo, 1 50\\nThe Chlorination Process 12mo*, 1 50\\nH 00\\n7 50\\n2 00\\n4 00\\n5 00\\n1 50\\n10\\n2 50\\n4 00\\n1 50\\n2 00\\n2 50\\n1 50\\n2 00\\n1 00\\nASTRONOMY.\\nPractical, Theoretical, and Descriptive.\\nCraig s Azimuth 4to, 3 50\\nDoolittle s Practical Astronomy 8vo, 4 00\\nGore s Elements of Geodesy Svo, 2 50\\nHay ford s Text-book of Geodetic Astronomy 8vo. 3 00\\nMichie and Harlow s Practical Astronomy 8vo, 3 00\\nWhite s Theoretical and Descriptive Astronomy 12mo, 2 00\\n3", "height": "4967", "width": "2909", "jp2-path": "railroadconstruc00webb_0511.jp2"}, "512": {"fulltext": "BOTANY.\\nGardening for Ladies, Etc.\\nBaldwin s Orchids of New England Small 8vo, $1 50\\nThome s Structural Botany 16mo, 2 25\\nWestermaier s General Botany. (Schn^der.) 8vo, 2 00\\nBRIDGES, ROOFS, Etc.\\nCantilever Draw Highway Suspension.\\n{See also Engineering, p. 8.)\\nBoiler s Highway Bridges 8vo, 2 00\\nThe Thames River Bridge 4to, paper, 5 00\\nBurr s Stresses in Bridges. 8vo, 3 50\\nCrehore s Mechanics of the Girder 8vo, 5 00\\nDredge s Thames Bridges 7 parts, per part, 1 25\\nDu Bois s Stresses In Framed Structures Small 4to, 10 00\\nFoster s Wooden Trestle Bridges 4to, 5 00\\nGreene s Arches in Wood, etc 8vo, 2 50\\nBridge Trusses 8vo, 2 50\\nRoofTrusses 8vo, 125\\nHowe s Treatise on Arches 8vo, 4 00\\nJohnson s Modern Framed Structures Small 4to, 10 00\\nMerriman Jacoby s Text-book of Roofs and Bridges.\\nPart I., Stresses 8vo, 2 50\\nMerriman Jacoby s Text-book of Roofs and Bridges.\\nPart n., Graphic Statics. 8vo, 2 50\\nMerriman Jacoby s Text-book of Roofs and Bridges.\\nPar.t III., Bridge Design 8vo, 2 50\\nMerriman Jacoby s Text-book of Roofs and Bridges.\\nPart lY., Continuous, Draw, Cantilever, Suspension, and\\nArched Bridges 8vo, 2 50\\nMorison s The Memphis Bridge Oblong 4to, 10 00\\nWaddell s Iron Highway Bridges 8vo, 4 00\\nDe Pontibus (a Pocket-book for Bridge Engineers).\\n16rao, morocco, 3 00\\nWood s Construction of Bridges and Roofs 8vo, 2 00\\nWright s Designing of Draw Spans. Parts I. and II..8vo, each 2 50\\nComplete.... ....8vo, 3 50\\n4", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0512.jp2"}, "513": {"fulltext": "CHEMISTRY\u00e2\u0080\u0094 BIOLOGY- PHARMACY.\\nQualitative Quantitative Organic Inorganic, Etc.\\nAdriance s Laboralory Calculations 12in(),\\nAllen s Tables for Iron Analysis Svo,\\nAusten s Notes for Chemical Students 12mo,\\nBolton s Student s Guide in Quantitative Analysis Svo,\\nBoltwood s Elementary Electro Chemistry {I/i the jjress.)\\nClassen s Analysis by Electrolysis, (Ilcrrick and Boll\\\\vood.).8vo,\\nCohu s Indicators and Test-papers 12mo\\nCrafts s Qualitative Analysis. (Schaeiler.) 12mo,\\nDavenport s Statistical Methods with Special Reference to Bio-\\nlogical Variations 12nio, morocco,\\nDrechscl s Chemical Reactions. (Merrill.) 12mo,\\nFresenius s Quantitative Chemical Analysis. (Allen.) Svo,\\nQualitative (Johnson.) Svo,\\n(Wells.) Trans.\\n16th German Edition Svo,\\nFuertes s Water and Public Health 12mo,\\nGill s Gas and Fuel Analysis 12mo,\\nHammarsten s Physiological Chemistry. (Mandel.) Svo,\\nHelm s Principles of Mathematical Chemistry. (Morgan). 12mo,\\nLadd s Quantitative Chemical Analysis 12mo,\\nLandaucr s Spectrum Analysis. (Tingle.) Svo,\\nLob s Electrolysis and Electrosyn thesis of Organic Compounds.\\n(Lorenz.) 12mo,\\nMf ndel s Bio-chemical Laboratory 12mo,\\nMason s Water-supply Svo,\\nExamination of Water 12mo,\\nMeyer s Radicles in Carbon Compounds. (Tingle. 12mo,\\nMiller s Chemical Physics Svo,\\nMixter s Elementary Text-book of Chemistry 12mo,\\nMorgan s The Theory of Solutions and its Results 12mo,\\nElements of Physical Chemistry 12mo,\\nNichols s Water-supply (Chemical and Sanitary) Svo,\\nO Brine s Laboratory Guide to Chemical Analysis Svo,\\nPerkins s Qualitative Analysis 12mo,\\nPinner s Organic Chemistry. (Austen.) 12mo,\\n$1 25\\n3 00\\n1 50\\n1 50\\n3 00\\n2 00\\n1 50\\n1 25\\n1 25\\n6 00\\n3 00\\n5 00\\n1 50\\n1 25\\n4 00\\n1 50\\n1 00\\n3 00\\n1 00\\n1 50\\n5 00\\n1 25\\n1 00\\n2 00\\n1 50\\n1 00\\n2 00\\n2 50\\n2 00\\n1 00\\n1 50", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0513.jp2"}, "514": {"fulltext": "Poole s Calorific Power of Fuels 8vo, $3 00\\nRicketts and Russell s Notes on Inorganic Clieniistry (Non-\\nmetallic) Oblong 8vo, morocco, 75\\nRuddimau s Incompatibilities in Prescriptions 8vo, 2 00\\nScliimpfs Volumetric Analysis 12mo, 2 50\\nSpencer s Sugar Manufacturer s Handbook 16mo, morocco, 2 00-\\nHandbook for Chemists of Beet Sugar Houses.\\n16mo, morocco, 3 00\\nStockbridge s Rocks and Soils 8vo, 2 50\\nTillman s Descriptive General Chemistry 8vo, 3 00\\nVan Deventer s Physical Chemistry for Beginners. (Boltwood.)\\n12mo, 1 50\\nWells s Inorganic Qualitative Analysis 12mo, 1 50\\nLaboratory Guide in Qualitative Chemical Analysis.\\nSvo, 1 50\\nWhipple s Microscopy of Drinking-water 8vo, 3 50\\nWiechmanu s Chemical Lecture Notes 12mo, 3 00\\nSugar Analysis Small Svo, 2 50\\nWulling s Inorganic Phar. and Med. Chemistry 12mo, 2 00\\nDRAWING.\\nElementary Geometrical Mechanical Topographical.\\nHill s Shades and Shadows and Perspective Svo, 2 00\\nMacCord s Descriptive Geometry. Svo, 3 00\\nKinematics Svo, 5 00\\nMechanical Drawing Svo, 4 00\\nMahan s Industrial Drawing. (Thompson.) 2 vols., Svo, 3 50\\nReed s Topographical Drawing. (H. A.) 4to, 5 00\\nReid s A Course in Mechanical Drawing Svo. 2 00\\nMechanical Drawing and Elementary Machine Design.\\nSvo. {In the press.)\\nSmith s Topographical Drawing. (Macmillan.) Svo, 2 50\\nWarren s Descriptive Geometry 2 vols., Svo, 3 50\\nDrafting Instruments 12mo, 125\\nFree-hand Drawing 12mo, 1 00\\nLinear Perspective 12mo, 1 00\\nMachine Construction 2 vols., Svo, 7 50\\n6", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0514.jp2"}, "515": {"fulltext": "Warren s Pl.ine Problems 12ino, $1 25\\nPrimary Geometry 12mo, 75\\nProblems aud Theorems 8vo, 3 50\\nProjection Drawing 12mo, 150\\nWarren s Shades and Shadows 8vo, 3 00\\nStereotomy\u00e2\u0080\u0094 Slone-cuttiug 8vo, 2 50\\nWhelpley s Letter Engraving 12mo, 2 00\\nELECTRICITY AND MAGNETISM.\\nIllumination Batteries Physics Railways.\\nAnthony and Brackett s Text-book of Physics. (Magie.) Small\\nSvo, 3 00\\nAnthony s Theory of Electrical Measurements 12mo, 1 00\\nBarker s Deep-sea Soundings Svo, 2 00\\nBenjamin s Voltaic Cell Svo, 3 00\\nHistory of Electricity Svo, 3 00\\nClassen s Analysis by Electrolysis. (^Ilerrick and Boltwood.) Svo, 3 00\\nCrehore and Squier s Experiments with a New Polarizing Photo-\\nChronograph Svo, 3 00\\nDawson s Electric Railways and Tramways. Small, 4to, half\\nmorocco, 12 50\\nDredge s Electric Illuminations. .2 vols., 4to, half morocco, 25 00\\nVol.11 4to, 7 50\\nGilbert s De magnete. (Mottelay.) Svo, 2 50\\nHolman s Precision of Measurements Svo, 2 OO\\nTelescope-mirror-scale IVIethod Large Svo, 75\\nLob s Electrolysis and Electrosynthesis of Organic Compounds.\\n(Lorenz.) 12mo, 1 00\\n*Michie s Wave Motion Relating to Sound and Light Svo, 4 00\\nMorgan s The Theory of Solutions a,nd its Results 12mo, 1 00\\nNiaudet s Electric Batteries. (Fishback.) 12mo, 2 50\\nPratt and Alden s Street-railway Road-beds Svo, 2 00\\nReagan s Steam and Electric Locomotives 12mo, 2 00\\nThurston s Stationary Steam Engines for Electric Lighting Pur-\\nposes Svo, 2 50\\n*Tillman s Heat Svo, 1 50", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0515.jp2"}, "516": {"fulltext": "ENGINEERING.\\nCivil Mechanical Sanitary, Etc.\\n{See also Bridges, p. 4 Hydraulics, p. 9 Materials of En-\\ngineering, p. 10 Mechanics and Machinery, p. 12 Steam\\nEngines. AND Boilers, p. 14.)\\nBaker s Masonry Constructiou 8vo, $5 00\\nSurveying luslruments 12mo, 3 00\\nBlack s U. S. Public Works Obloug 4to, 5 00\\nBrooks s Street-railway Location 16mo, morocco, 1 50\\nButts s Civil Engineers Field Book 16mo, morocco, 2 50\\nByrne s Highway Construction 8vo, 5 00\\nInspection of Materials and Workmanship 16mo, 3 00\\nCarpenter s Experimental Engineering 8vo, 6 00\\nChurch s Mechanics of Engineering Solids and Fluids Svo, 6 00\\nNotes and Examples in Mechanics Svo, 2 00\\nCrandall s Earthwork Tables Svo, 1 50\\nThe Transition Curve 16 mo, morocco, 1 50\\nDredge s Penn. Railroad Construction, etc. Large 4to,\\nhalf morocco, 20 00\\nDrinker s Tunnelling 4to, half morocco, 25 00\\nEissler s Explosives Nitroglycerine and Dynamite Svo, 4 00\\nFolwell s Sewerage Svo, 3 00\\nFowler s Coffer-dam Process for Piers Svo. 2 50\\nGerhard s Sanitary House Inspection 12mo, 1 00\\nGodwin s Railroad Engineer s Field-book 16mo, morocco, 2 50\\nGore s Elements of Geodesy Svo, 2 50\\nHoward s Transition Curve Field-book 16mo, morocco, 1 50\\nHowe s Retaining Walls (New Edition. 12mo, 1 25\\nHudson s Excavation Tables. Vol. II Svo, 1 00\\nHutton s Mechanical Engineering of Power Plants Svo, 5 00\\nHeat and Heat Engines Svo, 5 00\\nJohnson s Materials of Construction Large Svo, 6 00\\nTheory and Practice\u00c2\u00bbof Surveying Small Svo, 4 00\\nKent s Mechanical Engineer s Pocket-book IGmo, morocco, 5 00\\nKiersted s Sewage Disposal 12mo, 1 25\\nMahan s Civil Engineering. (Wood.) Svo, 5 00\\nMerriman and Brook s Handbook for Surveyors. .16mo, mor., 2 00\\nMerriman s Precise Surveying and Geodesy Svo, 2 50\\nRetaining Walls and Masonry Dams Svo, 2 00\\nSanitary Engineering Svo, 2 00\\nNagle s Manual for Railroad Engineers 16mo, morocco, 3 00\\nOgden s Sewer Design 12mo, 2 00\\nPatton s Civil Engineering Svo, half morocco, 7 50\\n8", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0516.jp2"}, "517": {"fulltext": "Patton s Fouudations 8vo,\\nPratt and Aldeu s Street-railway Road-beds 8vo,\\nRockwell s Roads and Pavements iu France 12mo,\\nSearles s Field Engineeriii j 16mo, morocco,\\nRailroad Spiral 16mo, morocco.\\nSiebert and Biggin s Modern Stone Cutting and Masonry. .8vo,\\nSmart s Engineering Laboratory Practice 12ino,\\nSmith s Wire Manufacture and Uses Small 4to,\\nSpalding s Roads and Pavements 12mo,\\nHydraulic Cement 12iuo,\\nTaylor s Prismoidal Formulas and Earthwork Svo,\\nThurston s Materials of Construction Svo,\\nTrautwiue s Civil Engineer s Pocket-book. .16mo, morocco,\\nCross-section Sheet,\\nExcavations and Embankments Svo,\\nLaying Out Curves 12mo, morocco,\\nWaddell s De Pontibus (A Pocket-book for Bridge Engineers).\\n16mo, morocco,\\nWait s Engineering and Architectural Jurisprudence Svo,\\nSheep,\\nLaw of Field Operation in Engineering, etc Svo.\\nWarren s Stereotomy Stone-cutting Svo,\\nWebb s Engineering Instruments. New Edition. 16mo, morocco,\\nWegmann s Construction of Masonry Dams 4to,\\nWellington s Location of Railways Small Svo,\\nWheeler s Civil Engineering. Svo,\\nWolff s Windmill as a Prime Mover Svo,\\nHYDRAULICS.\\nWater-w^heels Windmills Service Pipe Drainage, Etc.\\n{See also Engineering, p. S.)\\nBazin s Experiments upon the Contraction of the Liquid Vein.\\n(Trautwine.) Svo, 2 00\\nBovey s Treatise on Hydraulics Svo, 4 00\\nCoffin s Graphical Solution of Hydraulic Problems 12mo, 2 50\\nFerrel s Treatise on the Winds, Cyclones, and Tornadoes. .Svo, 4 00\\nFol well s Water Supply Engineering Svo, 4 00\\nFuertes s Water and Public Health 12mo, 1 50\\nGanguillet Kutter s Flow of Water. (Hering Trautwine.)\\nSvo, 4 00\\nHazen s Filtration of Public Water Supply Svo, 3 00\\nHerschel s 115 Experiments Svo, 2 00\\n9\\n0\\n00\\n2\\n00\\n1\\n25\\n3\\n00\\n1\\n50\\n1\\n50\\n2\\n50\\n3\\n00\\n2\\n00\\n2\\n00\\n1\\n50\\n5\\n00\\n5\\n00\\n25\\n2 00\\n2\\n50\\n3 00\\n6\\n00\\n6\\n50\\n2\\n50\\n1\\n25\\n5 00\\n5\\n00\\n4 00\\n3 00", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0517.jp2"}, "518": {"fulltext": "Kiersted s Sewage Disposal 13mo, $1 25-\\nMason s Water Supply 8vo, 5 00\\nExamination of Water 12mo, 1 25\\nMerriman s Treatise on Hydraulics 8vo, 4 00\\nNichols s Water Supply (Chemical and Sanitary) 8vo, 2 50\\nWegmann s Water Supply of the City of New York 4to, 10 00\\nWeisbach s Hydraulics. (Du Bois.) Svo, 5 00\\nWhipple s Microscopy of Drinking Water Svo, 3 50-\\nWilson s Irrigation Engineering Svo, 4 00\\nHydraulic and Placer Mining 12mo, 2 00^\\nWolff s Windmill as a Prime Mover Svo, 3 OO\\nWood s Theory of Turbines Svo, 2 SO\\nMANUFACTURES.\\nBoilers Explosives\u00e2\u0080\u0094 Iron Steel Sugar\u00e2\u0080\u0094 Woollens, Etc.\\nAllen s Tables for Iron Analysis Svo, 8 OO\\nBeaumont s Woollen and Worsted Manufacture 12mo, 1 50\\nBolland s Encyclopaedia of Founding Terms 12mo, 3 00-\\nThe Iron Founder 12mo, 2 50\\nSupplement 12mo, 2 50^\\nBouvier s Handbook on Oil Painting 12mo, 2 00\\nEissler s Explosives, Nitroglj^cerine and Dj-namite Svo, 4 00\\nFord s Boiler Making for Boiler Makers ISmo, 1 00\\nMetcalfe s Cost of Manufactures Svo, 5 00\\nMetcalf s Steel\u00e2\u0080\u0094 A Manual for Steel Users 12mo, 2 OO\\nReisig s Guide to Piece Dyeing Svo, 25 00\\nSpencer s Sugar Manufacturer s Handbook .16mo, morocco, 2 00-\\nHandbook for Chemists of Beet Sugar Houses.\\n16mo, morocco, 3 OO\\nThurston s Manual of Steam Boilers Svo, 5 00\\nWalke s Lectures on Explosives Svo, 4 00\\nWest s American Foundry Practice 12m o, 2 50\\nMoulder s Text-book 12mo, 2 50\\nWiechmann s Sugar Analysis Small Svo, 2 50\\nWoodbury s Fire Protection of Mills Svo, 2 50\\nMATERIALS OF ENGINEERING.\\nStrength Elasticity Resistance, Etc.\\n{See a^s(? Engineering, p. 8.)\\nBaker s Masonry Construction Svo, 5 00\\nBeardslee and Kent s Strength of Wrought Iron Svo, 1 50\\nBovey s Strength of Materials Svo, 7 50\\nBurr s Elasticity and Resistance of Materials Svo, 5 OO\\n10", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0518.jp2"}, "519": {"fulltext": "$5\\nGO\\n6\\noa\\n10\\nGO\\nG\\nGO\\n7\\n50\\n50\\n5\\n00\\n4\\n00\\n1\\n00\\n5\\nGO\\n1\\n25\\no\\n00\\n5\\nGO-\\n8 oa\\n3\\n00-\\n3\\n50\\no\\n50\\n2\\noa\\nByrue s Highway Construction 8vo,\\nChurch s Mechanics of Engineering Solids and Fluids 8vo,\\nDu Bois s Stresses in Framed Structures Small 4to,\\nJohnson s Materials of Construction 8vo,\\nLanza s Applied Mechanics 8vo,\\nMarlens s Testing Materials. (Ilenning.) 2 vols., 8vo,\\nMerrill s Stones for Building and Decoration 8vo,\\nMerriman s Mechanics of Materials 8vo,\\nStrength of Materials 12uio,\\nPatton s Treatise on Foundations 8vo,\\nRockwell s Roads and Pavements in France 12mo,\\nSpalding s Roads and Pavements 12mo,\\nThurston s Materials of Construction 8vo,\\nMaterials of Engineering 3 vols., 8vo,\\nVol. I. Non-metallic 8vo,\\nVol. II., Iron and Steel 8vo,\\nVol. III., Alloys, Brasses, and Bronzes 8vo,\\nWood s Resistance of Materials 8vo,\\nMATHEMATICS.\\nCalculus\u00e2\u0080\u0094 Geometry Trigonometry, Etc.\\nBaker s Elliptic Functions 8vo,\\nBarnard s Pyramid Problem 8vo,\\n*Bass s Differential Calculus 12rao,\\nBriggs s Plane Analytical Geometr)- 12mo,\\nChapman s Theory of Equations 12mo,\\nCompton s Logarithmic Computations 12mo,\\nDavis s Introduction to the Logic of Algebra 8vo,\\nHalsted s Elements of Geometry 8vo,\\nSynthetic Geometry 8vo,\\nJohnson s Curve Tracing 12mo,\\nDifferential Equations Ordinary and Partial.\\nSmall 8vo,\\nIntegral Calculus 12mo,\\nUnabridged. Small 8vo.\\n(In the press.\\nLeast Squares. 12mo,\\n*Ludlow s Logarithmic and Other Tables. (Bass.) 8vo,\\nTrigonometry with Tables. (Bass.) 8vo,\\n*Mahan s Descriptive Geometry (Stone Cutting) 8vo,\\nMerriman and Woodward s Higher ]\\\\Iathematics 8vo,\\nMerriman s Method of Least Squares 8vo,\\nRice and Johnson s Differential and Integral Calculus,\\n2 vols, in 1, small 8vo, 2 50\u00c2\u00bb\\n11\\n1\\noa\\n1\\nsa\\n4 GO\\n1\\noa\\n1\\n5a\\n1\\n50\\n1\\n50\\n1\\n75\\n1\\n50\\n1\\n00\\n3\\nsa\\n1\\nsa\\n1\\nsa\\n00\\n3 oa\\n1\\n50\\n5\\n00\\noa", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0519.jp2"}, "520": {"fulltext": "Rice aud Jobuson s Differential Calculus Small 8vo, $3 00\\nAbricigmeut of Differential Calculus.\\nSmall 8vo, 1 50\\nTotteu s Metrology 8vo, 2 50\\nWarren s Descriptive Geometry 3 vols., Svo, 3 50\\nDrafting Instruments 12mo, 1 25\\nFree-band Drawing 12mo, 100\\nLinear Perspective 12mo, 100\\nPrimary Geometry 12mo, 75\\nPlane Problems .12mo, 125\\nProblems and Theorems Svo, 2 50\\nProjection Drawing 12mo, 1 50\\nWood s Co-ordinate Geometry Svo, 2 00\\nTrigonometry 12mo, 100\\nWoolf s Descriptive Geometry .Large Svo, 3 00\\nMECHANICS-MACHINERY.\\nText-books and Practical Works.\\n{See also Engineering, p. S.)\\nBaldwin s Steam Heating for Buildings 12mo,\\nBarr s Kinematics of Machinery Svo,\\nBenjamin s Wrinkles and Recipes 12mo,\\nChordal s Letters to Mechanics 12mo,\\nChurch s Mechanics of Engineering, Svo,\\nNotes and Examples in Mechanics Svo,\\nCrehore s Mechanics of the Girder Svo,\\nCromwell s Belts and Pulleys 12mo,\\nToothed Gearing 12mo,\\nCompton s First Lessons in Metal Working 12mo,\\nCompton and De Groodt s Speed Lathe 12mo,\\nDana s Elementary Mechanics 12mo,\\nDingey s Machinery Pattern Making 12mo,\\nDredge s Trans. Exhibits Building, World Exposition.\\nLarge 4to, half morocco,\\nDu Bois s Mechanics. Vol. I., Kinematics Svo,\\nVol. II., Statics Svo,\\nVol. III., Kinetics Svo,\\nFitzgerald s Boston Machinist ISmo,\\nPlather s Dynamometers 12mo,\\nRope Driving 12mo,\\nHall s Car Lubrication 12mo,\\nHolly s Saw Filing ISmo,\\nJohnson s Theoretical Mechanics. An Elementary Treatise.\\n(Li the press.)\\nJones s Machine Design. Part I., Kinematics. Svo, 1 50\\n12\\n2 50\\n2 50\\n2 00\\n2 00\\n6 00\\n2 00\\n5 00\\n1 50\\n1 50\\n1 50\\n1 50\\n1 50\\n2 00\\n10 00\\n3 50\\n4 00\\n3 50\\n1 00\\n2 00\\n2 00\\n1 00\\n75", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0520.jp2"}, "521": {"fulltext": "$3 00\\n7 50\\n5 00\\n4 00\\n5 00\\n4 00\\n1 50\\n8 00\\n00\\n3 00\\n1 00\\n7 50\\n5 00\\nJones s Macbiue Desigu. Part II., Strength and Proportion of\\nMachine Parts 8vo,\\nLanza s Applied Mechanics 8vo,\\nMacCord s Kinematics 8vo,\\nMerriman s Mechanics of Materials 8vo.\\nMetcalfe s Cost of Manufactures 8vo,\\n*Michie s Analytical Mechanics 8vo,\\nRichards s Compressed Air 12mo,\\nRobinson s Principles of Mechanism 8vo,\\nSmith s Press-M orking of Metals 8vo,\\nThurston s Friction and Lost Work 8vo,\\nThe Animal as a Machine 12mo,\\nWarren s Machine Construction 2 vols., 8vo,\\nWeisbacli s Hydraulics and Hydraulic Motors. (Du Bois.)..8vo,\\nMechanics of Engineering. Vol. III., Part I.,\\nSec. I. (Klein.) 8vo, 5 00\\nWeisbach s Mechanics of Engineering. Vol. III., Part I.,\\nSec. n. (Klein.) 8vo, 5 00\\nWeisbach s Steam Engines. (Du Bois.) 8vo, 5 00\\nWood s Analytical Mechanics 8vo, 3 00\\nElementary Mechanics 12mo, 125\\nSupplement and Key 12mo, 125\\nMETALLURGY.\\nIiiON\u00e2\u0080\u0094 Gold\u00e2\u0080\u0094 Silver Alloys, Etc.\\nAllen s Tables for Iron Analysis 8vo, 3 00\\nEgleston s Gold and Mercury Large 8vo, 7 50\\nMetallurgy of Silver Large 8vo, 7 50\\nKerl s Metallurgy Copper and Iron 8vo, 15 00\\nSteel, Fuel, etc 8vo, 15 00\\nKunhardl s Ore Dressing in Europe 8vo, 1 50\\nMetcalf s Steel\u00e2\u0080\u0094 A Manual for Steel Users 12mo, 2 00\\nO Driscoll s Treatment of Gold Ores 8vo, 2 00\\nThurston s Iron and Steel 8vo, 3 50\\nAlloys Svo, 2 50\\nWilson s Cyanide Processes 12mo, 1 50\\nMINERALOGY AND MINING.\\nMine Accidents Ventil.\\\\tion Ore Dressing, Etc.\\nBarringer s Minerals of Commercial Value. ..Oblong morocco, 2 50\\nBeard s Ventilation of Mines 12mo, 2 50\\nBoyd s Resources of South Western Virginia Svo, 3 00\\nMap of South Western Virginia Pocket-book form, 2 00\\nBrush and Penfield s Determinative Mineralogy. New Ed. Svo, 4 00\\n13", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0521.jp2"}, "522": {"fulltext": "Chester s Catalogue of Minerals 8vo,\\nPaper,\\nDictionary of the Names of Minerals 8vo,\\nDana s American Localities of Minerals Large 8vo,\\nDescriptive Mineralogy. (E.S.) Large Svo. half morocco,\\nFirst Appendix to System of Mineralogy. .Large Svo,\\nMineralogy and Petrography. (J. D.) 12mo,\\nMinerals and How to Study Them. (E. S.) 12mo,\\nText-book of Mineralogy. (E. S.).. .New Edition. Svo,\\nDrinker s Tunnelling, Explosives, Compounds, and Rock Drills.\\n4to, half morocco,\\nEgleston s Catalogue of Minerals and Synonyms Svo,\\nEissler s Explosives Nitroglycerine and Dynamite Svo,\\nHussak s Rock-forming Minerals. (Smith.) .Small Svo,\\nIhlseng s Manual of Mining Svo,\\nKuuhardt s Ore Dressing in Europe Svo,\\nO Driscoll s Treatment of Gold Ores Svo,\\nPenfield s Record of Mineral Tests Paper, Svo,\\nRosenbusch s Microscopical Physiography of Minerals and\\nRocks. (Iddings.) Svo,\\n:Sawyer s Accidents in Mines Large Svo,\\n\u00e2\u0080\u00a2Stockbridge s Rocks and Soils Svo,\\nTValke s Lectures on Explosives Svo,\\nWilliams s Lithology Svo,\\nWilson s Mine Ventilation 12mo,\\nHydraulic and Placer Mining 12mo,\\nSTEAM AND ELECTRICAL ENGINES, BOILERS, Etc.\\nStationaky Marine\u00e2\u0080\u0094 Locomotive Gas Engines, Etc.\\n(See also Engineering, p. S.)\\nBaldwin s Steam Heating for Buildings 12mo, 2 50\\nOlerk s Gas Engine Small Svo, 4 00\\nFord s Boiler Making for Boiler Makers ISmo, 1 00\\nHemeu way s Indicator Practice 12mo, 2 00\\nHoadley s Warm-blast Furnace Svo, 1 50\\nUneass s Practice and Theory of the Injector Svo, 1 50\\nMacCord s Slide Valve Svo, 2 00\\nlleyer s Modern Locomotive Construction 4to, 10 00\\nPeabody and Miller s Steam-boilers Svo, 4 00\\nPeabody s Tables of Saturated Steam Svo, 1 00\\nThermodynamics of the Steam Engine Svo, 5 00\\nValve Gears for the Steam Engine Svo, 2 50\\nPray s Twenty Years with the Indicator Large Svo, 2 50\\nPupin and Osterberg s Thermodynamics 12mo, 1 25\\n14\\n$1 25\\n50\\n3 00\\n1 00\\n12 50\\n1 00\\n2 00\\n1 50\\n4 00\\n25 00\\n2 50\\n4 00\\n2 00\\n4 00\\n1 50\\n2 00\\n50\\n5 00\\n7 00\\n2 50\\n4 00\\n3 00\\n1 25\\n2 50", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0522.jp2"}, "523": {"fulltext": "Heagan s Steam and Electric Locomotives 12mo, f 2 00\\nRoutgeu s Thermodynamics. (Du Bois. 8vo, 5 00\\nSinclair s Locomotive liunuiug 12mo, 2 00\\nSnow s Steam-boiler Practice 8vo. 3 00\\nThurston s Boiler Explosions 12mo, 1 50\\nEngine and Boiler Trials 8vo, 5 00\\nManual of the Steam Engine. Part L, Structure\\nand Theory Svo, 6 00\\nManual of the Steam Eugine. Part IL, Design,\\nConstruction, and Operation Svo, 6 00\\n2 parts. 10 00\\nThurston s Philosophy of the Steam Engine 12mo, 75\\nReflection on the Motive Power of Heat. (Caruot.)\\n12mo, 1 50\\nStationary Steam Engines Svo, 2 50\\nSteam-boiler Construction and Operation Svo, 5 00\\nSpaugler s Valve Gears Svo, 2 50\\nAYclsbach s Steam Eugine. (Du Bois.) Svo, 5 00\\nWhitham s Constructive Steam Engineering Svo, 6 00\\nSteam-engine Design Svo, 5 00\\nWilson s Steam Boilers. (Flather.) \u00e2\u0080\u00a2..12mo, 2 50\\nWood s Thermodynamics, Heat Motors, etc Svo, 4 00\\nTABLES, WEIGHTS, AND MEASURES.\\nFor Actuaries, Chemists, Engineers, Mechanics\u00e2\u0080\u0094 Metric\\nTables, Etc.\\nAdriance s Laboratory Calculations 12mo, 1 25\\nAllen s Tables for Iron Analysis Svo, 3 00\\nBixby s Graphical Computing Tables Sheet, 25\\nCompton s Logarithms 12mo, 1 50\\n\u00e2\u0096\u00a0Crandall s Railway and Earthwork Tables Svo, 1 50\\nEgleston s Weights and Measures ISmo, 75\\nFisher s Table of Cubic Yards Cardboard, 25\\nHudson s Excavation Tables. Vol. II Svo, 1 00\\nJohnson s Stadia and Earthwork Tables Svo, 1 25\\nLudlow s Logarithmic and Other Tables, (Bass.) 12mo, 2 00\\nTotten s Metrology Svo, 2 50\\nVENTILATION.\\nSteam Heating House Inspection Mine Ventilation.\\nBaldwin s Steam Heating 12mo, 2 50\\nBeard s Ventilation of Mines 12mo, 2 50\\nCarpenter s Heating and Ventilating of Buildings Svo, 3 00\\nGerhard s Sanitary House Inspection 12mo, 1 OC\\nWilson s Mine Ventilation 12rao, 1 25\\n15", "height": "4279", "width": "2478", "jp2-path": "railroadconstruc00webb_0523.jp2"}, "524": {"fulltext": "MISCELLANEOUS PUBLICATIONS.\\nAlcott s Gems, Sentiment, Language Gilt edges, $5 00\\nDavis s Elements of Law 8vo, 2 00\\nEmmou s Geological Guide-book of the Rocky Mountains. .8vo, 1 50\\nFerrel s Treatise on the Winds 8vo, 4 00\\nHaines s Addresses Delivered before the Am. Ry. Assn. ..12mo, 2 50\\nMott s The Fallacy of the Present Theory of Sound. .Sq. IGmo, 1 00\\nRichards s Cost of Living 12mo, 1 00\\nRicketts s Historj^ of Rensselaer Polytechnic Institute 8vo, 3 OO\\nRotherham s The New Testament Criticall}^ Emphasized.\\n12mo, 1 50\\nThe Emphasized New Test. A new translation.\\nLarge 8vo, 2 00\\nTotteu s An Important Question in Metrology 8vo, 2 50\\nWiley s Yosemite, Alaska, and Yellowstone 4to, 3 00\\nHEBREW AND CHALDEE TEXT=BOOKS.\\nFor Schools and Theological Seminaries.\\nGesenius s Hebrew and Chaldee Lexicon to Old Testament.\\n(Tregelles. Small 4to, half morocco, 5 00\\nGreen s Elementary Hebrew Grammar 12mo, 1 25\\nGrammar of the Hebrew Language (New Edition). 8 vo, 3 00\\nHebrew Chrestomathy 8vo, 2 00\\nLetteris s Hebrew Bible (Massoretic Notes in English).\\n8vo, arabesque, 2 25\\nMEDICAL.\\nHammarsten s Physiological Chemistry. 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