{"1": {"fulltext": "\u00e2\u0096\u00a0OYIK\\nwRffl ffi i l. I f^y//\u00c2\u00bb/ym,\\nm iiii. ijji iii i iiiii ui i .i i m i n i\\nmmBmrmmmMmmm A jL iw\\\\-\\\\tnv wmai~Y nm tM[v\u00c2\u00bbijmiui. \u00c2\u00bb-t .i -nrt f p k\\nwmmmmmmommm\\nABMAM", "height": "4406", "width": "2580", "jp2-path": "formulasingearin04stut_0001.jp2"}, "2": {"fulltext": "LIBRARY OF CONGRESS.\\nChapHiM Copyright No*.\\nShell. \u00e2\u0080\u00a2___$_$ 3\\n1 ^oo\\nUNITED STATES OF AMERICA.\\nSe\u00c2\u00a3", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0002.jp2"}, "3": {"fulltext": "SnJ\\nt^e\\nWwM\\n\u00e2\u0080\u00a27^^-\\n\\\\M", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0003.jp2"}, "4": {"fulltext": "", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0004.jp2"}, "5": {"fulltext": "", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0005.jp2"}, "6": {"fulltext": "", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0006.jp2"}, "7": {"fulltext": "", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0007.jp2"}, "8": {"fulltext": "", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0008.jp2"}, "9": {"fulltext": "FORMULAS\\nIN\\nGEAR ING.\\nTHIRD EDITIO\\n-w. ^fctz\\n\\\\x\\nWITH PRACTICAL SUGGESTIONS\\nPROVIDENCE, R. I.\\nBROWN SHARPE MANUFACTURING COMPANY\\n1900.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0011.jp2"}, "10": {"fulltext": "TWO COPIES RECE1\\nLftrtry of C\u00c2\u00a7Bgr\u00c2\u00ab8%\\n1*\u00c2\u00ab of til\\nMAY 7-1880\\nfitter of Cspjrtgkt*\\nG, /J*s6 2.\\n6KCOND COPY,\\n38696\\nEntered according to Act of Congress, in the year 1900 by\\nBRoWX SHAKPEMFti. CO.,\\nIn the Office f the Librarian of Congress at Washington.\\nRegistered at Stationers Hall. London. Eng.\\nAll rights reserved.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0012.jp2"}, "11": {"fulltext": "PREFACE.\\nIt is the aim, in the following pages, to condense as much\\nas possible the solution of all problems in gearing which in the\\nordinary practice may be met with, to the exclusion of prob-\\nlems dealing with transmission of power and strength of\\ngearing. The simplest and briefest being the symbolical\\nexpression, it has, whenever available, been resorted to. The\\nmathematics employed are of a simple kind, and will present\\nno difficulty to anyone familiar with ordinary Algebra and\\nthe elements of Trigonometry.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0013.jp2"}, "12": {"fulltext": "", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0014.jp2"}, "13": {"fulltext": "CONTENTS,\\nFORMULAS IN GEARING.\\nCHAPTER I.\\nPage\\nSystems of Gearing i\\nCHAPTER II.\\nSpur Gearing Formulas Table of Tooth Parts Comparative Sizes\\nof Gear Teeth 4.\\nCHAPTER III,\\nBevel Gears, Axes at Right Angles Formulas Bevel Gears, Axes at\\nany Angle Formulas Undercut in Bevel Gears Diameter Incre-\\nment Tables for Angles of Edge and Angles of Face Tables of\\nNatural Lines 1 r\\nCHAPTER IV.\\nWorm and Worm Wheel, Formulas Undercut in Worm Wheels\\nTable for gashing Worm Wheels 34\\nCHAPTER V.\\nSpiral or Screw Gearing Axes Parallel Axes at Right Angles\\nAxes at any Angle General Formulas Table of Prime Num-\\nbers and Factors 40\\nCHAPTER VI.\\nInternal Gearing Internal Spur Gearing Internal Bevel Gears 5S\\nCHAPTER VII.\\nGear Patterns 64\\nCHAPTER VIII.\\nDimensions and Form for Bevel Gear Cutters 67\\nCHAPTER IX.\\nDirections for cutting Bevel Gears with Rotary Cutter 70\\nCHAPTER X.\\nThe Indexing of any Whole or Fractional Number 73\\nCHAPTER XI.\\nThe Gearing of Lathes for Screw Cutting Simple Gearing Compound\\nGearing Cutting a Multiple Screw 77", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0015.jp2"}, "14": {"fulltext": "", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0016.jp2"}, "15": {"fulltext": "FORMULAS IN GEARING.\\nCHAPTER I.\\nSYSTEMS OF GEARING.\\n(Figs, i, 2.)\\nThere are in common use two systems of gearing, viz.: the\\ninvolute and the epicycloidal.\\nIn the involute system the*outlines of the working parts of a\\ntooth are single curves, which may be traced by a point in a\\nflexible, inextensible cord being unwound from a circular disk\\nthe circumference of which is called the base circle, the disk\\nbeing concentric with the pitch circle of the gear.\\nFig. 1.\\nIn Fig. i the two base circles are represented as tangent to\\nthe line P P. This line (P P) is variously called the line of\\npressure, the line of contact, or the line of action.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0017.jp2"}, "16": {"fulltext": "2 BROWN i 5HARPE MFG. CO.\\nIn our practice this is drawn so as to make with a normal\\nto the center line (O O 14^ or with the center line 75 _\\nThe rack of this system has teeth with straight sides, the two\\nsides of a tooth making, together, an angle of 29\u00c2\u00b0 (twice\\nt/ o.\\nThis applies to gears having 30 teeth or more. For gears\\nhaving less than 30 teeth special rules are followed, which are\\nexplained in our Practical Treatise on Gearing.\\nFig. 2.\\nIn epicydoiaaL or double-curve teeth, the formation of the\\ncurve changes at the pitch circle. The outline of the faces of\\nepicycloidal teeth may be traced by a point in a circle rolling\\non the outside of pitch circle of a gear, and the.flanks by a point\\nin a circle rolling on the inside of the pitch circle. The faces\\nof one gear must be traced by the same circle that traces the\\nflanks of the engaging gear.\\nIn our practice the diameter of the rolling or describing\\ncircle is equal to the radius of a 15-tooth gear of the pitch\\nrequired this is the base of the system. The same describing\\ncircle being used for all gears of the same pitch.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0018.jp2"}, "17": {"fulltext": "PROVIDENCE, R. f. 3\\nThe teeth of the rack of this system have double curves,\\nwhich may be traced by the base circle rolling alternately on\\neach side of the pitch line.\\nAil advantage of the involute over the epicycloidal tooth is,\\nthat in action gears having involute teeth may be separated a\\nlittle from their normal positions without interfering with the\\nangular velocity, which is not possible in any other kind of\\ntooth.\\nThe obliquity of action is sometimes urged as an objection\\nto involute teeth, but a full consideration of the subject will\\nshow that the importance of this has been greatly over-esti-\\nmated.\\nThe tooth dimensions for both the involute and epicycloidal\\ngears may be calcu j.ted from the formulas in Chapter II.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0019.jp2"}, "18": {"fulltext": "BROWN SHARPE MFG. CO.\\nCHAPTER. II.\\nSPUR GEARING.\\n(Figs. 4.)\\nTwo spur gears in action are comparable to two correspond-\\ning plain rollers whose surfaces are in contact, these surfaces\\nrepresenting the pitch circles of the gears.\\nPitch of Gears.\\nFor convenience of expression the pitch of gears may be\\nstated as follows\\nCircular pitch is the distance from the center of one tooth to\\nthe center of the next tooth, measured on the pitch line.\\nDiametral pitch is the number of teeth in a gear per inch of\\npitch diameter. That is, a gear that has, say, six teeth for each\\ninch in pitch diameter is six diameuai pitch, or, as the expres-\\nsion is universally abbreviated, it is six pitch. This is by\\nfar the most convenient way of expressing the relation of\\ndiameter to number of teeth.\\nModule is the pitch diameter of a gear divided by the\\nnumber of teeth.\\nChordal pitch is a term but little employed. It is the dis-\\ntance from center to center of two adjacent teeth measured in\\na straight line.\\nFig. 3.\\nr~t\u00e2\u0080\u0094*i", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0020.jp2"}, "19": {"fulltext": "PROVIDENCE, R. I.\\nFORMULAS.\\nN number of teeth.\\ns addendum and module.\\nthickness of tooth on pitch line,\\nclearance at bottom of tooth,\\nD working depth of tooth.\\nD r whole depth of tqcch.\\nd pitch diameter.\\nd outside diameter.\\nP circular pitch.\\nP^ chord pitch.\\nP diametral pitch,\\nC center distance.\\np _ N 2\\nd\\n71\\nP =P\\nP\\nP 71\\n.318.3 P\\nd _ d\\nN N 2\\n/=^P =:_^L_\\n2 2 P\\ny\\n10\\nt( i 3=- 568sP\\ns\\nP c d sin\\nN\\n360 5 1\\n(J P r\\nP dn where sin d\\nN\\nP\\nd d 2 s\\nNP\\n7t", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0021.jp2"}, "20": {"fulltext": "BROWN SHARPE MFG. CO.\\nGEAR WHEELS.\\nTABLE OF TOOTH PARTS CIRCULAR PITCH IN FIRST COLUMN.\\nThreads or\\nTeeth per inch\\nLinear\\nDiametral\\nPitch.\\nThickness of\\nTooth on\\nPitch Line.\\nAddendum\\nand Modnle.\\nWorking Depth\\nof Tooth.\\nDepth of Space\\nbelow\\nPitch Line.\\nWhole Depth\\nof Tooth.\\nWidth of\\nThread-Tool\\nat End.\\nWidth of\\nThread at Top.\\np\\nl\\np\\nP\\nf\\n8\\nD\\nD\\nP X.31\\nP X.335\\n2\\ni\\n2\\n1.5708\\n1.0000\\n.6366\\n1.2732\\n.7366\\n1.3732\\n.6200\\n.6700\\nIf\\n8\\n15\\n1.6755\\n.9375\\n.5968\\n1.1937\\n.6906\\n1.2874\\n.5813\\n.6281\\n14\\n_4_\\n7\\n1.7952\\n.8750\\n.5570\\n1.1141\\n.6445\\n1.2016\\n.5425\\n.5863\\n1+\\n8\\n13\\n1.9333\\n.8125\\n.5173\\n1.0345\\n.5985\\n1.1158\\n.5038\\n.5444\\nll\\n2\\n3\\n2.0944\\n.7500\\n.4775\\n.9549\\n.5525\\n1.0299\\n.4650\\n.5025\\nit\\n16\\n23\\n2.1855\\n.7187\\n.4576\\n.9151\\n.5294\\n.9870\\n.4456\\n.4816\\nIf\\n8\\n11\\n2.2848\\n.6875\\n.4377\\n.8754\\n.5064\\n.9441\\n.4262\\n.4606\\nif\\n3\\nJ.\\n2.3562\\n.6666\\n.4244\\n.8488\\n.4910\\n.9154\\n.4133\\n.4466\\nIf\\n16\\n21\\n2.3936\\n.6562\\n.4178\\n.8356\\n.4834\\n.9012\\n.4069) .4397\\nH\\n4\\n5\\n2.5133\\n.6250\\n.3979\\n.7958\\n.4604\\n.8583\\n.38751 .4188\\nIt\\n16\\n19\\n2.6456\\n.5937\\n.3780\\n.7560\\n.4374\\n.8156\\n.3681! .3978\\nIf\\n8\\n9\\n2.7925\\n.5625\\n.3581\\n.7162\\n.4143\\n.7724 |.3488| .3769\\nIf\\n16\\n17\\n2.9568\\n.5312\\n.3382\\n.6764\\n.3913\\n.7295\\n.32941 .3559\\n1\\n1\\n3.1416\\n.5000\\n.3183\\n.6366\\n.3683\\n.6866\\n.3100\\n.3350\\n15\\n16\\nli\\n3.3510\\n.4687\\n.2984\\n.5968\\n.3453\\n.6437\\n.2906\\n.3141\\n8\\n1+\\n3.5904\\n.4375\\n.2785\\n.5570\\n.3223\\n.6007\\n.2713\\n.2931\\n13\\n16\\nli 13.8666\\n.4062\\n.2586\\n^,5173\\n.2993\\n.5579\\n.2519\\n.2722\\n4\\n5\\n1-f 13.9270\\n.4000\\n.2546\\n.5092\\n.2946\\n.5492\\n.2480\\n.2680\\n3\\n4\\nli\\n4.1888\\n.3750\\n.2387\\n.4775\\n.2762\\n.5150\\n.2325\\n.2513\\n11\\n16\\n1*\\n4.5696\\n.3437\\n.2189\\n.4377\\n.2532 1 .4720\\n.2131\\n.2303\\n2\\n3\\n1+\\n4.7124\\n.3333\\n.2122\\n.4244\\n.2455; .4577\\n.2066\\n.2233\\n5\\n8\\n1 5\\n5.0265\\n.3125\\n.1989\\n.3979\\n.2301\\n.4291\\n.1938| .2094\\n3\\n5\\n-L 3\\n5.2360\\n.3000\\n.1910 .3820\\n.2210\\n.4120\\n.1860\\n.2010\\n4\\nIf\\n5.4978\\n.2857\\n.1819\\n.3638\\n.2105\\n.3923\\n.1771 .1914\\n9\\n16\\nIf\\n5.5851\\n.2812 11790\\n.3581\\n.2071 .3862\\n.1744 .1884", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0022.jp2"}, "21": {"fulltext": "PROVIDENCE, R. I.\\nTABLE OF TOOTH ARTS.\u00e2\u0080\u0094 Continued.\\nCIRCULAR PITCH IN FIRST COLUMN.\\nf-l\\n1 1 -i\\na\\nIT 1\\nThreads or\\nTeeth per inch\\nLinear.\\nDiametral\\nPitch.\\nThickness of\\nTooth on\\nPitch Line.\\nAddendum\\nand Module.\\nWorking Deptl\\nof Tooth.\\nDepth of Space\\nbelow\\nPitch Line.\\nWhole Depth\\nof Tooth.\\nWidth of\\nThread-Tool\\nat End.\\nWidth of\\nThread at Top.\\nP\\ni\\np\\nP\\nt\\nS fc\\nD\\nJ)\\\\f.\\nPX.31\\nPX.335\\n1\\n2\\n2\\n6.2832\\n.2500\\n.1592\\n.3183\\n.1842\\n.3433\\n.1550\\n.1675\\n7T\\n2t\\n7.0685\\n.2222\\n.1415\\n.2830\\n.1637\\n.3052\\n.1378\\n.1489\\n7\\n1G\\n2f\\n7.1808\\n.2187\\n.1393\\n.2785\\n.1611\\n.3003\\n.1356\\n.1466\\n_3_\\n2i\\n7.3304\\n.2143\\n.1364\\n.2728\\n.1578\\n.2942\\n.1328\\n.1436\\n2\\n5\\n^2\\n7.8540\\n.2000\\n.1273\\n.2546\\n.1473\\n.2746\\n.1240\\n.1340\\n3\\n8\\n2f\\n8.3776\\n.1875\\n.1194\\n.2387\\n.1381\\n.2575\\n.1163\\n.1256\\n4\\n11\\n2f\\n8.6394\\n.1818\\n.1158\\n.2310\\n.1340\\n.2498\\n.1127\\n.1218\\n1\\n3\\n3\\n9.4248\\n.1666\\n.1061\\n.2122\\n.1228\\n.2289\\n.1033\\n.1117\\n5\\n10\\n31\\n10.0531\\n.1562\\n.0995\\n.1989\\n.1151\\n.2146\\n.0969\\n.1047\\n3\\n10\\n31\\n10.4719\\n.1500\\n.0955\\n.1910\\n.1105\\n.2060\\n.0930\\n.1005\\n2\\n7\\n3-\\n10.9956\\n.1429\\n.0909\\n.1819\\n.1052\\n.1962\\n.0886\\n.0957\\n1\\ni\\n4\\n12.5664\\n.1250\\n.0796\\n.1591\\n.0921\\n.1716\\n.0775\\n.0838\\n2\\n9\\n4-\\n2\\n14.1372\\n.1111\\n.0707\\n.1415\\n.0818\\n.1526\\n.0689\\n.0744\\n1\\n5\\n5\\n15.7080\\n.1000\\n.0637\\n.1273\\n.0737\\n.1373\\n.0620\\n.0670\\n3\\n1G\\noy\\n16.7552\\n.0937\\n.0597\\n.1194\\n.0690\\n.1287\\n.0581\\n.0628\\n2\\n11\\n5f\\n17.2788\\n.0909\\n.0579\\n.1158\\n.0670\\n.1249\\n.0564\\n.0609\\n1\\n6\\n6\\n18.8496\\n.0833\\n.0531\\n.1061\\n.0614\\n.1144\\n.0517\\n.0558\\n2\\n13\\n6+\\n20.4203\\n.0769\\n.0489\\n.0978\\n.0566\\n.1055\\n.0477\\n.0515\\n1\\n7\\n7\\n21.9911\\n.0714\\n.0455\\n.0910\\n.0526\\n.0981\\n.0443\\n.0479\\n2\\n15\\n7-\\n2\\n23.5619\\n.0666\\n.0425\\n.0850\\n.0492\\n.0917\\n.0414\\n.0446\\n1\\n8\\n8\\n25.1327\\n,0625\\n.0398\\n.0796\\n.0460\\n.0858\\n.0388\\n.0419\\n1\\n9\\n9\\n28.2743\\n.0555\\n.0354\\n.0707\\n.0409\\n.0763\\n.0344\\n.0372\\n1\\n10\\n10\\n31.4159\\n.0500\\n.0318\\n.0637\\n.0368\\n.0687\\n.0310\\n.0335\\n1\\n16\\n16\\n50.2655\\n.0312\\n.0199\\n.0398\\n.0230\\n.0429\\n.0194\\n.0209\\n1\\n20\\n20\\n62.8318\\n.0250\\n.0159\\n.0318\\n.0184\\n.0343\\n.0155\\n.0167", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0023.jp2"}, "22": {"fulltext": "BROWN SHARPE MFG. CO.\\nGEAR WHEELS.\\nTABLE OF TOOTH PARTS DIAMETRAL PITCH IN FIRST COLUMN.\\n3\\n5^\\n53\\n5^\\nThickness\\nof Tooth on\\nPitch Line.\\nAddendum\\nand Module.\\n5 c\\nDepth of Space\\nbelow\\nPitch Line.\\nWhole Depth\\nof Tooth.\\nP\\nP\\nt\\ns\\nD\\nD\\n4.3142\\n1\\n2\\n6.2832\\n3.1416\\n2.0000\\n4.0000\\n2.3142\\n2.\\n4\\n4.1888\\n2 0944\\n1.3333\\n2.6666\\n1.5428\\n2.8761\\n1\\n3.1416\\n1 5708\\n1.0000\\n2.0000\\n1.1571\\n2.1571\\nii\\n2.5133\\n1.2566\\n.8000\\n1.6000\\n.9257\\n1.7257\\ni*\\n2.0944\\n1.0472\\n.6666\\n1.3333\\n.7714\\n1.4381\\nif\\n1.7952\\n.8976\\n.5714\\n1.1429\\n.6612\\n1.2326\\n2\\n1.5708\\n.7854\\n.5000\\n1.0000\\n.5785\\n1.0785\\n2J\\n1.3963\\n.6981\\n.4444\\n.8888\\n.5143\\n.9587\\n?4\\n1.2566\\n.6283\\n.4000\\n.8000\\n.4628\\n.8628\\n2f\\n1.1424\\n.5712\\n.3636\\n.7273\\n.4208\\n.7814\\n3\\n1.0472\\n.5236\\n.3333\\n.6666\\n.3857\\n.7190\\n3i\\n.8976\\n.4488\\n.2857\\n.5714\\n.3306\\n.6163\\n4\\n.7854\\n.3927\\n.2500\\n.5000\\n.2893\\n.5393\\n5\\n.6283\\n.3142\\n.2000\\n.4000\\n.2314\\n.4314\\nG\\n.5236\\n.2618\\n.1666\\n.3333\\n.1928\\n.3595\\n7\\n.4488\\n.2244\\n.1429\\n.2857\\n.1653\\n.3081\\n8\\n.3927\\n.1963\\n.1250\\n.2500\\n.1446\\n.2696\\n9\\n.3491\\n.1745\\n.1111\\n.2222\\n.1286\\n.2397\\n10\\n.3142\\n.1571\\n.1000\\n.2000\\n.1157\\n.2157\\n11\\n.2856\\n.1428\\n.0909\\n.1818\\n.1052\\n.1961\\n12\\n.2618\\n.1309\\n0833\\n.1666\\n.0964\\n.1798\\n13\\n.2417\\n.1208\\n.0769\\n.1538\\n.0890\\n.1659\\n14\\n_\\n2244\\n.1122\\n.0714\\n.1429\\n.0826\\n.1541", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0024.jp2"}, "23": {"fulltext": "PROVIDENCE, R. I.\\nTABLE OF TOOTH PABTS\u00e2\u0080\u0094 Continued\\nDIAMETRAL PITCH IN FIRST COLUMN.\\n~3\\nQ\\n\u00c2\u00a33\\nThickness\\nof Tooth on\\nPitch Line.\\na.\\na,\\nDepth of Space\\nbelow\\nPitch Line.\\n-4-\\na-;\\nQ\\nM o\\n2\\nP.\\nP\\nt.\\ns.\\nD\\n.0771\\nD\\n.1438\\n15\\n.2094\\n.1047\\n.0666\\n.1333\\n16\\n.1963\\n.0982\\n.0625\\n.1250\\n.0723\\n.1348\\n17\\n.1848\\n.0924\\n.05^8\\n.1176\\n.0681\\n.1269\\n18\\n.1745\\n.0873\\n.0555\\n.1111\\n.0643\\n.1198\\n19\\n.1653\\n.0827\\n.0526\\n.1053\\n.0609\\n.1135\\n20\\n.1571\\n.0785\\n.0500\\n.1000\\n.0579\\n.1079\\n22\\n.1428\\n.0714\\n.0455\\n.0909\\n.0526\\n.0980\\n24\\n.1309\\n.0654\\n.0417\\n.0833\\n.0482\\n.0898\\n26\\n.1208\\n.0604\\n.0385\\n.0769\\n.0445\\n.0829\\n28\\n.1122\\n.0561\\n.0357\\n.0714\\n.0413\\n.0770\\n30\\n.1047\\n.0524\\n.0333\\n.0666\\n.0386\\n.0719\\n32\\n.0982\\n.0491\\n.0312\\n.0625\\n.0362\\n.0674\\n34\\n.0924\\n.0462\\n.0294\\n.0588\\n.0340\\n.0634\\n36\\n.0873\\n.0436\\n.0278\\n.0555\\n.0321\\n.0599\\n38\\n.0827\\n.0413\\n.0263\\n.0526\\n.0304\\n.0568\\n40\\n.0785\\n.0393\\n.0250\\n.0500\\n.0289\\n.0539\\n42\\n.0748\\n.0374\\n.0238\\n.0476\\n.0275\\n.0514\\n44\\n.0714\\n.0357\\n.0227\\n.0455\\n.0263\\n.0490\\n46\\n.0683\\n.0341\\n.0217\\n.0435\\n.0252\\n.0469\\n48\\n.0654\\n.0327\\n.0208\\n.0417\\n.0241\\n.0449\\n50\\n.0628\\n.0314\\n.0200\\n.0400\\n.0231\\n.0431\\n56\\n.0561\\n.0280\\n.0178\\n.0357\\n.0207\\n.0385\\n60\\n.0524\\n.0262\\n.0166\\n.0333\\n.0193\\n0360", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0025.jp2"}, "24": {"fulltext": "IO\\nBROWN SHARPE MFG. CO.\\nComparative Sizes of Gear Teeth.\\nInvolute.\\nJ P\\n18 P\\n16 P\\n14 P\\n12 P\\n7 P\\nIO P\\nS P\\nFig. 4.\\ny p", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0026.jp2"}, "25": {"fulltext": "PROVIDENCE, R. I.\\nII\\nCHAPTER. III.\\nBEVEL GEARS.\u00e2\u0080\u0094 AXES AT RIGHT ANGLES,\\n(Fig. 5.)", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0027.jp2"}, "26": {"fulltext": "12 BROWN 6c SHARPE MFG. CO.\\nFORMULAS.\\n?j a I Number of teeth gea r\\njN I pinion\\nP diametral pitch.\\nP circular pitch.\\na a center angle angle of edge j gear.\\nw b or pitch angie pinion.\\nft angle of top.\\nft angle of bottom.\\nangfle of face r\\ngb pinion.\\n%a =1 4-4.- i f gear.\\n7 v cutting: angle s\\nn b j pinion.\\nA apex distance from pitch circle.\\nA apex distance from large bottom of tooth.\\nd= pitch diameter.\\nd outside diameter.\\ns addendum and module.\\nt thickness of tooth at pitch line.\\nf clearance at bottom of tooth.\\nD working depth of tooth.\\nD -f f whole depth of tooth.\\n2 a diameter increment.\\nb distance from top of tooth to plane of pitch cirde.\\nF width of face.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0028.jp2"}, "27": {"fulltext": "PROVIDENCE, R. I. 13\\nN a N b\\ntan a a tan a b\\nN 6 b N a\\na 2 sin a s\\ntan a or tan B\\nN A\\ntan p sina 2 2 -3 J 4 sin a t g s_ f\\nN N A\\nga 9\u00c2\u00b0\u00c2\u00b0 (ot a 0) g b 90 6 /i)\\nh a\u00e2\u0080\u0094 ft (See Note, page 6 p.\\n2\\nA 2 (S)\\nA\\nN\\n2 P sin\\nA\\nA\\ncos p\\nA\\nsin (a\\nN\\nA N\\n2 P sin a cos /ft\\ncos /i\\np IN\\n2 A sin c*\\nN N P\\nor\\nP 71\\nd d -f 2\\n2 a 2 s cos a\\n(See page 20.)\\na for orear b for pinion\\na tan z r\\nfor pinion b tor gear\\np _5_ p n\\nP P\\n.3183 P s Atan/i\\nP 7T\\nj- 3685 P s A tan\\n2 2 P\\nF\\ni or 2 P to 3 P\\nNote. Formulas containing notations without the designating- letters a and b\\napply equally to either gear or pinion. If wanted for one or the other, the respective\\nletters are simply attached.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0029.jp2"}, "28": {"fulltext": "14\\nBROWN SHARPE MFG. CO.\\nBEVEL GEARS WITH AXES AT ANY ANGLE.\\nFig.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0030.jp2"}, "29": {"fulltext": "PROVIDENCE, R. I, J 5\\nFORMULAS.\\nC angle formed by axes of gears.\\nnumber of teeth J\\nxt numoer 01 teem\\nN b j pinion.\\nP diametral pitch.\\nP circular pitch.\\na angle of edge pitch angle\\na b j e r pinion.\\n(5 angle of top.\\nfi angle of bottom.\\na f- angle of face\\ngb j s pinion.\\ntt gear.\\n7 a y cutting angle\\nn b j pinion.\\nA apex distance from pitch circle.\\nA apex distance from large bottom of tooth.\\nd= pitch diameter.\\nd outside diameter.\\n2 diameter increment.\\nb distance from top of tooth to plane of pitch circle.\\nNote. The formulas for tooth parts as given on page 5 apply equally to these\\ncases.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0031.jp2"}, "30": {"fulltext": "l6 BROWN SHARPE MFG. CO.\\ntan a\u00e2\u0080\u009e\\nsin C\\nN ft\\ncos C\\nsin C\\nX.,\\n-f cos C\\nNi,\\nor cot a a cot C\\nN\u00e2\u0080\u009e sin C\\nor cot r,, cot C\\nX i sin L\\nN,,\\nNote. The above formulas are correct only for values of C less than 90\\nIf C is greater than 90 consult page 18.\\n2 sin Ol s\\ntan P or tan p T\\nX A\\ntan /r Bin 2 3 H sin\\nXX A\\no-, g a a -f- fi for Cases I and II.\\nga fi, for Case III.\\ng a 90 (a a for Case IV.\\n9 o\u00c2\u00b0\u00e2\u0080\u0094 (flf 4 fi)\\na /5 (See page 6p.\\nA p\\n2 P sm a?\\na-= A\\nCos ft\\nN X P\\nor\\nP 7T\\nfor Cases I and II,\\na a 2 a\\nI and pinions in Cases III and IV.\\na a 7 for gear in Case III.\\nd d 2 a, for srear in Case IV.\\n2 5 cos a\\nb s sin\\nNote. Formulas containing notations without the designating letters a and\\napply equally to either gear or pinion. If wanted for one or the other, the\\nrespective letters are simply attached.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0032.jp2"}, "31": {"fulltext": "PROVIDENCE, R. I.\\ni;", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0033.jp2"}, "32": {"fulltext": "l8 BROWN SHARPE MFG. CO.\\nThe formulas given for a a and a h (when C. X\u00e2\u0080\u009e and N 6 are\\nknown) undergo some modifications for values of C greater\\nthan 90\\nFor bevel gears at any angle but 90 we may distinguish\\nfour cases C, X\u00e2\u0080\u009e, N 6 being given.\\nCase. See pages 14 and 16.\\nII. Case. C is greater than 90\\nsin (180 C) sin (180 C\\ntan a a =z 5 tan a b\\nv u v\\n6 cos (180-C) _ a -cos 1S0-C,\\nN N,\\na\\nCase. a a 90 a b C 90\\nIV. Case.\\nsin E sin E\\ntan (Y\u00e2\u0080\u009e _ tan a b\\ncos E b cos E\\nN d X,\\nFor an example to apply to Case III., the following condi-\\ntion must be fulfilled\\nN a sin (C 90\u00c2\u00b0) X,,\\nTo distinguish whether a given example belongs to Case II.\\nor case IV., we are guided by the following condition\\nx XT smaller than X,,, we have Case II.\\nIs X\u00e2\u0080\u009e sin (C 90 7 u XT 6 TTr\\ny larger than N 6j we have case IV.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0034.jp2"}, "33": {"fulltext": "PROVIDENCE, R. I. 19\\nUNDERCUT IN BEVEL GEARS.\\nBy undercut in gears is understood a special formation of\\nthe tooth, which may be explained by saying that the elements\\nof the tooth below the pitch line are nearer the center line of\\nthe tooth than those on the pitch line. Such a tooth outline is\\nto be found only in gears with few teeth. In a pair of bevel\\ngears where the pinion is low-numbered and the ratio high, we\\nare apt to have undercut. For a pair of running gears this\\ncondition presents no objection. Should, however, these gears\\nbe intended as patterns to cast from, they would be found use-\\nless, from the fact that they would not draw out of the sand.\\nWe have stated on page 2 (see Fig. 1) that the base of our\\ninvolute system is the 14^\u00c2\u00b0 pressure angle. If a pair of bevel\\ngears with teeth constructed on this basis have undercut, we\\ncan nearly eliminate the undercut and for the practical work-\\ning this is quite sufficient\u00e2\u0080\u0094 by taking as a basis for the con-\\nstruction of the tooth outline a pressure angle of 20\\nThe question now is When do we, and when do we not\\nhave undercut Let there be\\nN number of teeth in gear.\\n7/ number of teeth in pinion.\\nn V N 2 2\\nP\\nN\\nwhere we have undercut for/ less than 30.\\nThis formula is strictly correct for epicycloidal gears only.\\nIt is, however, used as a safe and efficient approximation for\\nthe involute system.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0035.jp2"}, "34": {"fulltext": "20\\nBROWN SHARPE MFG. CO.\\nDIAMETER INCREMENT.\\n2 a.\\nRule. The ratio being given or determined, to find the outside diameter\\ndivide figures given in table for large and small gear by pitch (P) and add\\nquotient to pitch diameter.\\nGEARS.\\nGEARS.\\nGEARS.\\nRATTO\\nRATTO\\nRATIO\\n1:1\\nLarge\\nSmall\\nLarge\\nSmall\\nLarge\\nSmall\\n1.00\\n1.41\\n1.41\\n1.65\\n1.05\\n1.70\\n4.40\\n.45\\n1M\\n1.05\\n1.37\\n1.42\\n1.67\\n5:3\\n1.03\\n1.72\\n4 50\\n9:2\\n.44\\n1.95\\n1.07\\n1.36\\n1.43\\n1.70\\n1.01\\n1.73\\n4.60\\n.42\\n1 95\\n1.10\\n1.35\\n1.44\\n1.75\\n7:4\\n.99\\n1.74\\n4.80\\n.41\\n1.96\\n1.11\\n10:9\\n1.34\\n1.46\\n1.80\\n9:5\\n.97\\n1.75\\n5.00\\n5:1\\n.39\\n1.96\\n1.12\\n1.33\\n1.46\\n1.85\\n.95\\n1.76\\n5.20\\n.38\\n1.96\\n1.13\\n9:8\\n1.33\\n1.47\\n1.90\\n.93\\n1.77\\n5.40\\n.37\\n1.96\\n1.14\\n8:7\\n1.32\\n1.49\\n1.95\\n.91\\n1.78\\n5.60\\n.36\\n1.97\\n1.15\\n1.31\\n1.50\\n2.00\\n2:1\\n.89\\n1.79\\n5.80\\n.34\\n1.97\\n1.16\\n1.30\\n1.51\\n2.10\\n.87\\n1.80\\n6.00\\n6:1\\n.33\\n1.97\\n1.17\\n7:6\\n1.30\\n1.52\\n2.20\\n.84\\n1.81\\n6.20\\n.32\\n1 97\\n1.18\\n1.29\\n1.53\\n2 25\\n9:4\\n.82\\n1.82\\n6.40\\n.31\\n1.97\\n1.19\\n1.28\\n1.53\\n2.30\\n.80\\n1.83\\n6.60\\n.30\\n1 97\\n1.20\\n6:5\\n1.28\\n1.54\\n2.33\\n7:3\\n.78\\n1.84\\n6.80\\n.29\\n1 98\\n1.23\\n1.27\\n1.55\\n2.40\\n.76\\n1.85\\n7 00\\n7:1\\n.28\\n1.98\\n1.25\\n5:4\\n1.25\\n1.56\\n2.50\\n5:2\\n.75\\n1.86\\n7.20\\n.27\\n1.98\\n1.27\\n1.25\\n1.57\\n2.60\\n.73\\n1.86\\n7.40\\n.27\\n1 98\\n1.29\\n9:7\\n1.24\\n1.58\\n2.67\\n8:3\\n.71\\n1.87\\n7.60\\n.26\\n1 98\\n1.30\\n1.22\\n1.59\\n2.70\\n.69\\n1.87\\n7 80\\n.26\\n1.98\\n1.33\\n4:3\\n1.20\\n1.60\\n2.80\\n.67\\n1.88\\n8 00\\n8:1\\n.25\\n1.98\\n1.35\\n1.18\\n1.61\\n2.90\\n.65\\n1.89\\n8.20\\n.24\\n1.98\\n1 37\\n1.17\\n1.61\\n3.00\\n3:1\\n.63\\n1.91\\n8 40\\n.24\\n1.98\\n1.40\\n7:5\\n1.16\\n1.62\\n3.20\\n.60\\n1.92\\n8.60\\n.23\\n1.98\\n1.43\\n10:7\\n1.15\\n1.63\\n3.33\\n.58\\n1.92\\n8.80\\n.23\\n1.98\\n1.45\\n1.13\\n1.65\\n3.40\\n.56\\n1 92\\n9.00\\n9:1\\n.22\\n1.99\\n1.50\\n3:2\\n1.11\\n1.66\\n3.50\\n7:2\\n.54\\n1.93\\n9.20\\n.22\\n1.99\\n1.53\\n1.10\\n1 67\\n3.60\\n.52\\n1 93\\n9.40\\n.21\\n1.99\\n1 55\\n1.09\\n1 67\\n3.80\\n.50\\n1.94\\n9.60\\n.21\\n2.00\\n1 58\\n1.08\\n1.68\\n4.00\\n4:1\\n.49\\n1.94\\n9.80\\n.20 2.00\\n1.60\\n8:5\\n1.07\\n1.68\\nl\\n4.20\\n.47\\n1.94\\n10.00\\n10:1\\n.20\\n2 00\\nNote. To be used only for bevel gears with axes at right angle.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0036.jp2"}, "35": {"fulltext": "PROVIDENCE, R. I. 21\\nTABLES FOR ANGLES OF EDGE AND ANGLES\\nOF FACE.\\nThe following four tables have been computed for the\\nconvenience in calculating datas for bevel gears with axes at\\nright angle. They do not hold good for bevel gears with axes\\nat any other angle.\\nTo use the tables the number of teeth in gear and pinion\\nmust be known.\\nHaving located the number of teeth in the gear on the\\nhorizontal line of figures at the top of the table, and the num-\\nber of teeth in the pinion on the vertical line of figures on the\\nleft hand side, we follow the two columns to the square formed\\nby their intersections.\\nThe two angles found in the same square are the respective\\nangles for gear and pinion. The tables are so arranged that\\nthe angle belonging to the gear is always placed above the\\nangle for the pinion.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0037.jp2"}, "36": {"fulltext": "22\\nBROWN SHARPE MFG. CO.\\nTABLE i\\nAngle of Edge,\\ngear.\\n41\\n40\\n39\\n38\\n37\\n36\\n35\\n34\\n33\\n32\\n3!\\n30\\n29\\n28\\n27\\n12\\n73V\\n16*19\\n73\u00c2\u00b0i8\\n16*42\\n72V\\n17V\\n72*28\\n17*32\\n72*2\\n17*58\\n71 V\\n18*26\\n71*5\\n18*55\\n70V\\n19*25\\n70 V\\n19V\\n69*26\\n20V\\n68\u00c2\u00b050\\n2l*o\\n68*ie\\n2 1 V\\n67\u00c2\u00b03i\\n22 V\\n66V\\n23*12\\n66*2\\n23*58\\n13\\n72 W\\n17*35\\n71 59\\n18*\\n71*34\\n18*26\\n71 V\\n18*53\\n70*39\\nI9*ei\\n70*9\\n19V\\n69*37\\n20*23\\n69*5\\n20*55\\n68 v 30\\n21*30\\n67*53\\n22*7\\n67 is 1\\n22*45\\n66 V\\n23*26\\n65V\\n24 s\\n65*6\\n24*54\\n64V\\n25*43\\n14\\n71V\\n18*51\\n70*43\\n19*17\\n70*is\\n19*45\\n69V\\n20*14\\n69*16\\n20*44\\n68*45\\n2lV\\n68*12\\n21*48\\n67V\\n22*23\\n67*0\\n23\u00c2\u00b0o\\n66*23\\n23*37\\n6sV\\n24*18\\n64V\\n25* 1\\n64V\\n25*46\\n63 V\\n26V\\n62*36\\n27*24\\n15\\n69V\\n20*6\\n69*86\\n20*34\\n68*58\\n21*2\\n68\u00c2\u00a38\\n21*3*\\n67 V\\n22*4\\n67*23\\n22*3?\\n66*48\\n23*2\\n66 i2\\n23*48\\n65*33\\n24*27\\n64*53\\n25*7\\n64V\\n25\u00c2\u00b0So\\n63*26\\n26*34\\n62*39\\n27*21\\n61*49\\n28*i\\n60V\\n29*3\\n16\\n68V\\n2I*W\\n68 is\\n8148\\n67 V\\ne2V\\n67*10\\n22*so\\n66*37\\n23*23\\n66V\\n23\u00c2\u00b0S8\\n65*26\\n24*34\\n64*48\\n25*12\\n64*8\\n25*58\\n63*2\\n26*34\\n62\u00c2\u00b0V\\n27*\u00c2\u00ab\\n6lV\\n28\u00c2\u00b0*\\n61 V\\n28*53\\n60\u00c2\u00b0is\\n29*45\\n59*2i\\n30*33\\n17\\n67*29\\n22*3 1\\n66*58\\n23*2\\n66*27\\n23*33\\n65*54\\n24*6\\n65*19\\n84V\\n64*43\\n25*7\\n64*6\\n25\u00c2\u00b0S4\\n63 26\\n26*34\\n62V\\n27\u00c2\u00b0is\\n62* r\\n27*59\\n61*15\\n28*45\\n60V\\n29*32\\n59*37\\n30V\\n58V\\n31*16\\n57 V\\n32*12\\n18\\n66V\\n2348\\n6546\\n24\u00c2\u00b0i4\\n65*14\\n24*46\\n64*39\\n25*21\\n64*4\\n25V\\n63V\\n26V\\n62*47\\n27\u00c2\u00b0 i\\n62*6\\n27*54\\n61*5\\n28V\\n60*38\\n29*22\\n59 V\\n30*9\\n59*2\\n30\u00c2\u00b0se\\n58*id\\n31*50\\n57V\\n32*44\\n56V\\n33*4i\\n19\\n65*8\\n24\u00c2\u00b0s*\\n64*3*\\n25*24\\n64V\\n25*58\\n63*26\\n26\u00c2\u00b0B4\\n62*49\\ne7\u00c2\u00b0u\\n62*io\\n27*50\\n61*10\\n28*3\u00c2\u00a9\\n60*48\\n29*12\\n60*4\\n29*56\\n59*18\\n30*42\\n58*30\\n31*30\\n57\u00c2\u00b039\\n32*ei\\n56i6\\n33*4\\n55*Si\\n34*9\\n54*52\\n35*8\\n20\\n64 V\\n26*o\\n63*26\\n26*34\\n62V\\n27*9\\n62*14\\n27*46\\n6l\u00c2\u00b037\\n28*23\\n60*57\\n89**\\nS0\u00c2\u00b0is\\n29*45\\n59V\\n30*28\\n58V\\n31*13\\n58V\\n32V\\n57V\\n32*50\\n56\u00c2\u00b0 19\\n33*41\\n55*24\\n34*36\\n54\u00c2\u00b028\\n35*32\\n53*28\\n36*32\\n21\\n62V\\n27*7\\n62*\\n27*4*:\\n6I*\u00c2\u00ab\\n28*19\\n61*4\\n28*56\\n60\u00c2\u00b025\\n29\u00c2\u00b03s\\n59\u00c2\u00ab\\n30*is\\n59\u00c2\u00b0 Z\\n30*58\\n58*8\\n31*42\\n57*32\\n32*28\\n5\u00e2\u0082\u00acV\\n33*iV\\n55*53\\n34*7\\n55\u00c2\u00b0o\\n35\u00c2\u00b0 0\\n54*5\\n35*55\\n53*7\\n36*53\\n52*8\\n37a\\n22\\n61*47\\n28\u00c2\u00b0i3\\n61 n\\n28*49\\n60\u00c2\u00b034\\n29*26\\n59*56\\n30V\\n59\u00c2\u00b0iS\\n30*45\\n58*34\\n3 1*26\\n575i\\n32*9\\n57*6\\n32*54\\n56\u00c2\u00b0i9\\n33*4)\\n55*29\\n34*3i\\n54*38\\n35*22\\n53*45\\n36*ts\\n52*43\\n37*11\\n51*50\\n38\u00c2\u00b0id\\n50*49\\n39*11\\n23\\n60V\\n29\u00c2\u00b0i8\\n60*6\\n29\u00c2\u00b05*\\n59*28\\n30\u00c2\u00b032\\n5849\\n31*11*\\n58*3\\n31*52\\n57*25\\n32*3S\\nS6*V\\n33*\\n55*55\\n34*s\\n55*7\\n34*53\\n54*\u00c2\u00bb\\n35*42\\n53*26\\n36*V\\n52*3.\\n37\u00c2\u00bb\\n51*35\\n38\u00c2\u00b025\\n50V\\n39*24\\n43\u00c2\u00b0V\\n40\u00c2\u00b026\\n24\\n59*39\\n30*2t\\n59*2\\n30*S8\\n58*23\\n3 1 *37\\n57*44\\n32*16\\n57V\\n32*58\\n56*19\\n33V\\n55*33\\n34*27\\n54V\\n35*3\\n53V\\n3 Y\\n53*7\\n36*53\\n52*15\\n37*45\\n5I\u00c2\u00b020\\n38*40\\n50*23\\n39*37\\n4aV\\n40*36\\n48*22\\n41*38\\n25\\nS8ss\\n31*22\\n58V\\n32*0\\n5720\\n3240\\n56V\\n33*eo\\n55V\\n34*3\\nS5\u00c2\u00b0i3\\n34*47\\n54*28\\n35*32\\n53V\\n36*20\\n52*si\\n37V\\n52V\\n38V\\n51*7\\n38\u00c2\u00b0S3\\n5oV\\n39\u00c2\u00b048\\n49*14\\n40*46\\n48*14\\n41*46\\n47V\\n42*48\\nA\\n26\\n57*37\\n32*23\\n56*58\\n33*e\\n5\u00e2\u0082\u00ac i9\\n33\u00c2\u00b04i\\n55*37\\n34*23\\n54*54\\n35*6\\n54\u00c2\u00b0 id\\n35*5d\\n53*24\\n36*3*\\n52*36\\n37*24\\n51*46\\n38*14\\n50S4\\n39*6\\n50\u00c2\u00b0 r\\n39\u00c2\u00b0S3\\n49*5\\n40*55\\n48*7\\n41*53\\n47 7\\n42*53\\n46*5\\n43*55\\n27\\n56*38\\n33*22\\n55*59\\n34*.\\nss**\\n34\u00c2\u00b042\\n54*36\\n35*24\\n53*53\\n36*7\\n53*7\\n36*53\\n52V\\n37*39\\n51*33\\n38*27\\n50V\\n39*17\\n49\u00c2\u00b0SI\\n40*9\\n4857\\n41\u00c2\u00b0 3\\n48V\\n42\u00c2\u00b0o\\n47*3\\n42V\\n46\u00c2\u00b02\\n43\u00c2\u00b058\\n45*\\n28\\n55*4*\\n34w\\n55*o\\n35*o\\n54\u00c2\u00b0 19\\n35*41\\n53*37\\n36*23\\n52*53\\n37*7\\n52V\\n37*S2\\n51*20\\n38*40\\n50*32\\n39*28\\n49 V\\n40 19\\n48*48\\n41*12\\n47*55\\n42*5\\n46*58\\n43*2\\n46*o\\n44\u00c2\u00b0o\\n45*\\n29\\n54V\\n35*i6\\n54*3\\n35*S7\\n53V\\n36*38\\nS2 C 33\\n37V\\n51*55\\n38\u00c2\u00b0 S\\n51*9\\n38\u00c2\u00b05i\\n5021\\n39*39\\n49*32\\n40*28\\n48\u00c2\u00b04i\\n41*19\\n47V\\n42* w\\n46 V\\n43*6\\n4S 58\\n44*2\\n45*\\n30\\nS3*\u00c2\u00ab\\n36*12\\n53*7\\n36*53\\n52*16\\n37*34\\n51*42\\n38\u00c2\u00b0ie\\n50\u00c2\u00b0S8\\n39*2\\n50*ie\\n39*48\\n49*24\\n40*36\\n48*35\\n41*25\\n4743\\n42*17\\n46*5 1\\n43\u00c2\u00b0 9\\n45*56\\n44V\\n45\u00c2\u00b0\\n31\\n52*54\\n37V\\n52*3\\n37*47\\nSlV\\n58w\\n50*48\\n39*2\\n50V\\n39\u00c2\u00b0S8\\n49\u00c2\u00b0i6\\n40*44\\n48*28\\n41 V\\n47*39\\n42*2f\\n46*47\\n43*13\\n45\u00c2\u00b0S4\\n44*6\\n45*\\n32\\n52V\\n37ss\\n51*20\\n38\u00c2\u00b04o\\n50*38\\n39*22\\n49*54\\n40*6\\n49*9\\n40V\\n48*22\\n41 V\\n47V\\n42*26\\n46 V\\n43*16\\n45V\\n44*7\\n45\u00c2\u00b0\\n33\\nSl io\\n38 so\\n5029\\n39*31\\n49*46\\n40*4\\n43*2\\n40*56\\n48*16\\n41*44\\n47*29\\n42*2 1\\n4641\\n43\u00c2\u00b0i\u00c2\u00bb\\n455\u00c2\u00bb\\n44*9\\n45\u00c2\u00b0\\n34\\n50*20\\n3940\\n49*38\\n40\u00c2\u00b0\u00c2\u00ab\\n48V\\n41*5\\n48V\\n4lV\\n47*25\\n42*35\\n46*38\\n43*22\\n4S so\\n44*i o\\n45*\\n35\\n49*3i\\n40a\\n48*48\\n4l*ie\\n46*5\\n4I\u00c2\u00b055\\n47\u00c2\u00b0n\\n42*39\\n46\u00c2\u00b035\\n43*25\\n45*48\\n44*\u00c2\u00ab\\n4-5\u00c2\u00b0\\n36\\n48*43\\n41*17\\n48\u00c2\u00b00\\n42*o\\n47o\\n4243\\n46*33\\n43*27\\n45*47\\n44*13\\n45\\n37\\n47 56\\n42V\\n47\u00c2\u00b0i4\\n42*46\\n46V\\n43*30\\n454*\\n44V\\n45\u00c2\u00b0\\n38\\n47 io\\n42*so\\n46*a\\n43*32\\n45V\\n44*15\\n45*\\n39\\n46V\\n43V\\n4543\\n44\u00c2\u00b0 7\\n45\\n40\\n45*42\\n44*18\\n45\u00c2\u00b0\\n41\\n45*", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0040.jp2"}, "37": {"fulltext": "PROVIDENCE, R, I.\\n2 3\\nTABLE i. {Continued})\\nAngle of Edge.\\ngear.\\n26\\n25\\n24\\ni23\\n22\\n21\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\n12\\n65\u00c2\u00b0i4\\n24*46\\n64*22\\nZ5\u00c2\u00b038\\n63*26\\n26*34\\n6227\\n27*33\\n61*23\\n28*37\\n60\u00c2\u00b0i5\\n29*45\\n59*2\\n30*58\\n574*\\n32*16\\n56*19\\n33*4i\\n54*47\\n35*13\\n53*7\\n36*53\\n5 1 \u00c2\u00b020\\n38*40\\n49*24\\n40*36\\n47*17\\n42*43\\n45*\\n13\\n63*26\\n26*34\\n62*31\\n27*29\\n61 \u00c2\u00b033\\n28*27\\n60V\\nib ea\\n59*25\\n30*35\\n58*rt\\n3 1 \u00c2\u00b046\\n56*58\\n33\u00c2\u00b0 z\\n55*37\\n34*23\\n54 io\\n35*50\\n52*36\\n37*24\\n50*54\\n39\u00c2\u00b06\\n49*5\\n40SS\\n47*7\\n42*53\\n45*\\n14\\n61*42\\n2 8\u00c2\u00b0 8\\n6045\\n29\u00c2\u00b0 s\\n59\u00c2\u00b04S\\n30*15\\n58*40\\n3 1 \u00c2\u00b020\\n57 32\\n32*28\\n56*19\\n33\u00c2\u00b04i\\n55\u00c2\u00b0 0\\n35*0\\n53*37\\n36*23\\n52*8\\n37*52\\n50*32\\n39*26\\n48 48\\n4I\u00c2\u00b0I2\\n46*58\\n43Y\\n45\u00c2\u00b0\\n15\\n60\u00c2\u00b0i\\n29*53\\n59*2\\n30*58\\n58\\n32V\\n56V\\n33*7\\n55\u00c2\u00b043\\n34 17\\n54*28\\n35*32\\n53*7\\n36*53\\n5t 42\\n38*8\\n50\u00c2\u00b0i2\\n38*48\\n48*35\\n41*25\\n46*51\\n43\u00c2\u00b09\\n45\u00c2\u00b0\\n16\\n58*23\\n31 V\\n57 V\\n32V\\n56*19\\n33*41\\n55\u00c2\u00b0u\\n34*49\\n53*58\\n36*2\\n52*42\\n37*8\\n51*20\\n3840\\n49*54\\n40V\\n48*ez\\n4I\u00c2\u00b038\\n46*44\\n43*16\\n45\\n17\\n56V\\n33*1 1\\n55*47\\n34\u00c2\u00b0i3\\n5441\\n35*9\\n53*32\\n36*28\\n52*18\\n37*42\\n5l*o*\\n39\u00c2\u00b0o\\n49*38\\n40*22\\n48\u00c2\u00b0u\\n41 43\\n46*38\\n43*22\\n45*\\n18\\n5S\u00c2\u00b0ii\\n34*42\\n54*15\\n35*45\\n53*7\\n36*53\\n51V\\n38*3\\n50*43\\n39*|7\\n4a\u00c2\u00b0s\u00c2\u00bb\\n40*36\\n48\u00c2\u00b0o\\n42*0\\n46*33\\n43*27\\n4-5.\u00c2\u00b0\\n19\\n53V\\n36*9\\n52*46\\n37V\\n51*38\\n38*22\\n50*26\\n39*34\\n49*1 1\\n40*49\\n47*52\\n42*8\\n46*28\\n43*32\\n45\u00c2\u00b0\\n20\\ns4W\\n37 34\\n51*20\\n3840\\n50V\\n3948\\n48*59\\n4!\u00c2\u00b0!\\n47*43\\n42V\\n46 24\\n43*36\\n45\\n21\\n51%\\n38*56\\n49*58\\n40Y\\n48*48\\n41\u00c2\u00b0*\\n47*36\\n42\u00c2\u00b0e4\\n46*\u00c2\u00a3o\\n43*40\\n45*\\n22\\n49*46\\n40\u00c2\u00b0 14\\n48*39\\n41 V\\n47*29\\n42*3 r\\n46*16\\n43*44\\n4-5\u00c2\u00b0\\n23\\n48\u00c2\u00b030\\n4\\\\%6\\n4723\\n42V\\n46\u00c2\u00b0i3\\n4347\\n4-5\u00c2\u00b0\\n24\\n47V\\n4243\\n46*10\\n43\u00c2\u00b0so\\n4-5\u00c2\u00b0\\n25\\n46*7\\n43*53\\n45\u00c2\u00b0\\n26\\n4.5\u00c2\u00b0\\ntan a a _ a\\nN 6\\ntan a,\\nN,\\n(See page 13,)", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0041.jp2"}, "38": {"fulltext": "24\\nBROWN SHARPE MFG. CO.\\nTABLE 2.\\nAngle of Edge.\\nGEAR.\\n1\\n72\\n71\\n70\\n69\\n68\\n67\\n66\\n65\\n64\\n63\\n62\\n61\\n60\\n59\\n58\\n57\\n12\\n80*33\\n9* \u00c2\u00a37\\n80*16\\n9*95\\n80W\\n9*46\\n80*6\\n9*52\\n79*58\\nIO*V\\n79*6t\\n10*9\\n79*42\\n10*18\\n79*32\\nlo ae\\n79*23\\n10*37\\n79\u00c2\u00b0 13\\n10*47\\n79*3\\n10*57\\n78*52\\n11\u00c2\u00b0 8\\n78\u00c2\u00b04i\\nU\u00c2\u00b0I9\\n78*30\\n11*30\\n78j9\\nll\u00c2\u00b04l\\n78*7\\n11*53\\n13\\n79*46\\n10*14\\n79*37\\n10*23\\n79*29\\nI0\u00c2\u00b03l\\n79*20\\n10*40\\n79*ll\\n10*49\\n79j.\\n10*59\\n18*51\\n11*9\\n78*4 1\\n11*19\\n78*31\\n11*29\\n78*20\\nll\u00c2\u00b040\\n78*9\\n1 1*51\\n77*58\\n12*2\\n77*46\\n12*14\\n77*34\\n12*26\\n77*22\\ni2\u00c2\u00b038\\n77*9\\n12*51\\n!4\\n79*6\\nII\\n78*51\\n11*9\\n78*41\\n11*19\\n78*32\\nII 28\\n78*22\\nII 38\\n78*\\n11*49\\n76* r\\nII 59\\n77*Sl\\n12*9\\n77*40\\n12 20\\n77*28\\n12 32\\n77*17\\n12 43\\n77*5\\n12 55\\n76*s\u00c2\u00bb\\n13 8\\n76*39\\n13 21\\n76\u00c2\u00b026\\n13*34\\n76 J I2\\n1348\\n15\\n78*1*\\n11*46\\n784\\n77*54\\n12*6\\n77*44\\n12*16\\n77*34\\n12*26\\n77*23\\n12*37\\n77*i2\\n12*48\\n77*o\\n13*0\\n76*48\\n13*12\\n76*36\\n13*84\\n76\u00c2\u00b024\\n13*36\\n76*11\\n13*49\\n7SS8\\n14*2\\n75*44\\n14*16\\n75*30\\n14 30\\n75*15\\n14*45\\n16\\n77*28\\nI*\\n77*8\\n12*42\\n77V\\n12*53\\n76\u00c2\u00b0S7\\n13*3\\n76*45\\n13*15\\n76*34\\n13*26\\n76*22\\n13*38\\n76*10\\n13*50\\n75*58\\n14*2\\n75*45\\n14*15\\n75*32\\n14*28\\n75*18\\n1442\\n75*4\\n14*56\\n74*49\\n15*11\\n74*35\\n15*25\\n74*19\\n15*41\\n17\\n76*43\\n13*17\\n76*32\\n13*28\\n76*2 1\\n13*39\\n76*10\\n13*50\\n75*58\\n14*2\\n75*4*\\n14* 14\\n75*33\\n14*27\\n75*81\\n14*39\\n75*6\\n14*52\\n74*54\\n15*6\\n74\u00c2\u00b04o\\n15*20\\n74*25\\n15*35\\n74*..\\n15*49\\n73*56\\n16*4\\n73*40\\n16*20\\n73*24\\n16 36\\n18\\n75*58\\n14\u00c2\u00b0 i\\n75*46\\n14\u00c2\u00b0 W\\n75*35\\nI4\u00c2\u00b02S\\n75*23\\n14*37\\n7S\u00c2\u00b0i6\\n14*50\\n74\u00c2\u00b0s\u00c2\u00ab\\n15*2\\n74*45\\n15*15\\n74\u00c2\u00b03i\\n15*29\\n74\u00c2\u00b0i7\\n15*43\\n74 3\\n15*58\\n73*49\\nI6\u00c2\u00b0n\\n?3\u00c2\u00b033\\n16*27\\n73*18\\nI6*4z\\n73*2\\n16*58\\n7245\\n17*15\\n72*29\\n17*31\\n19\\n7S*ra\\n14*47\\n75*.\\n14*59\\n74*49\\nI5*ll\\n74*36\\n15*24\\n74*23\\n15*37\\n74* K\\n15*50\\n73\u00c2\u00b056\\n16*4\\n73*42\\n16*18\\n73*28\\n16*32\\n73*13\\n16*47\\n72*58\\n17*2\\n7242\\n17*18\\n72jzb\\n17*34\\nit*\\nI7\u00c2\u00b0SI\\n71*52\\n18*8\\n71*34\\n18*26\\n20\\n74*29\\n15*31\\n74*16\\n15*44\\n74*3\\n15*57\\n73*50\\n16\u00c2\u00b0 10\\n73*37\\n16*23\\n73*23\\n16*42\\n73*9\\n16*51\\n72*54\\n17*6\\n72*39\\n17*21\\n72*23\\n17*37\\n72S\\n17*53\\n7I\u00c2\u00b0SI\\n18*9\\n71*34\\n18*26\\n71*16\\n18*44\\n70*59\\n19\u00c2\u00b0 r\\n70*40\\n19*20\\n21\\n73*45\\nIfe lS\\n73*32\\n16*28\\n73 18\\n16*42\\n73 4\\n16*56\\n72*50\\n17* to\\n72*36\\n17\u00c2\u00b024\\n72*21\\n17*39\\n72*6\\n17*54\\n71*50\\nI8*io\\n71*34\\n18*2$\\n71*17\\n18*43\\n71* 0\\n19*0\\n70*43\\nI9\u00c2\u00b0I7\\n70*24\\n19*36\\n70V\\n19*54\\n69*46\\n20*24\\n22\\n73* r\\n16*59\\n72*47\\n17*13\\n72*33\\n17*27\\n72* 19\\n17*4 1\\n72*4\\n17*56\\n71*49\\n18* II\\n71*34\\n18*26\\n71*18\\n18*42\\n71 i\\n18*58\\n70*45\\n19*15\\n70*28\\n19*34\\n70*10\\nI9\u00c2\u00b0S6\\n69*52\\n20*8\\n69*33\\n20*27\\n63*13\\n20*47\\n6B*54\\n21*6\\n23\\nltd\\nr?*\u00c2\u00bb\\n72\u00c2\u00b03\\nI7*$7\\n71*48\\nI8*u\\n71*34\\n18*26\\n71 H\\nI8\u00c2\u00b04l\\n71*3\\n18*57\\n70*47\\n19*13\\n70*90\\n19*30\\n70*14]\\n19*46\\n69*57\\n20 3\\n6939\\n20\u00c2\u00b02l\\n69\u00c2\u00b02(i\\n20*40\\n69*8\\n20\u00c2\u00b058\\n68*42\\n21*18\\n68*22\\n21*38\\n68*2\\n21*58\\n24\\n71*34\\n18 tt\\n71*19\\n18*41\\n71*5\\n18*55\\n70*49\\n19* II\\n70*34\\n19*26\\n70V\\n19*43\\n70* r\\n19*59\\n69*44\\n20*16\\n69*26\\n20*34\\n69*9\\n20*51\\n68*50\\n2l\u00c2\u00b0ib\\n68\u00c2\u00b03i\\n21*24\\n68*12\\n21*48\\n67\u00c2\u00b0S2\\n22*8\\n67*3 1\\n22*29\\n67\u00c2\u00b0io\\n22*50\\n25\\n70V\\n19*9\\n70*36\\n19*24\\n70*ti\\nI9\u00c2\u00b0J9\\n70 5\\n19*55\\n69*49\\n20*11\\n69*32\\n20*28\\n69*15\\n20*4S\\n68*57\\n21 3\\n68*40\\n2 1*20\\n68\u00c2\u00b02i\\n21*39\\n68*3*\\n21*57\\n67*43\\n22*17\\n67*23\\n22*37\\n67*2\\n22*58\\n66*4 1\\n23*19\\n66*19\\n23\u00c2\u00b04i\\n26\\n70*9\\nI9*si\\n69\u00c2\u00bb\\n20*V\\n69*37\\n20*23\\n69*2i\\n20 39\\n69V\\n20*56\\n68*46\\n21*12\\n68*30\\n21*30\\n68*12\\n21*46\\n67*54\\n22*6\\n67*34\\n22*26\\n67*15\\n22*45\\n66*55\\n23*5\\n66*34\\n23*26\\n66*13\\n23*47\\n65*51\\n24*9\\n65*29\\n24*3i\\nV-\\n27\\n69*27\\n20*33\\n69*10\\n20*50\\n68*54\\n21*6\\n68\u00c2\u00b038\\n21*22\\n6820\\n21*40\\n68*3\\n21*57\\n67*45\\n22*15\\n67*26\\n22*34\\n67*8\\n22*52\\n66*46\\n23*12\\n66*28\\n23*32\\n66*7\\n23*53\\n65*46\\n24*14\\n65*25\\n24*35\\n65*2\\n24*58\\n64\u00c2\u00b0 39\\n25*2i\\n28\\n68*45\\nZ 1*15\\n68*29\\n21*31\\n68*12\\n21*48\\n67*55\\n22*5\\n67V\\n22*23\\n67*19\\n22*41\\n67* 1\\n22*S9\\n66*42\\n23*18\\n66*22\\n23*38\\n66*2\\n23*5%\\n65*42\\n24*18\\n66*21\\n24*39\\n64*59\\n25* 1\\n64*37\\n25*23\\n64\u00c2\u00b0i4\\n25*46\\n63\u00c2\u00b0so\\n26*id\\n29\\n88*4\\n21*56\\n6747\\n22*13\\n67*V\\n22*30\\n67*12\\n22*48\\n66*5*\\n23*6\\n66*36\\n23*24\\n66*17\\n23*43\\n65*57\\n24*3\\n65*37\\n24*23\\n65*16\\n24*44\\n64*55\\n25*5\\n4\u00c2\u00b094i\\n25*26\\n64*12\\n25*48\\n63*50\\n26*io\\n63*26\\n26*34\\n63*2\\n26*58\\n30\\n67*\u00c2\u00bb\\n22*37\\n22*54\\n66\u00c2\u00b048\\n23*12\\n66*3\u00c2\u00ab\\n23*30\\n66*12\\n23*48\\n6S\u00c2\u00b0S2\\n24*8\\n65*33\\n24*27\\n65V\\n24*46\\nG4*63\\n25*7\\n64*32\\n25*28\\n64*10\\n25*50\\n63*49\\n26*1 1\\n63\u00c2\u00b026\\n26*34\\n63*3*\\n26*57\\n62*39\\n27*2J\\n62*14\\n27*46\\n31\\n66*42\\n23*18\\n66*23\\n23*35\\n66*6\\n23*54\\n65*46\\n24*\u00c2\u00bb2\\n65*29\\n24*3i\\n65*i6\\n24\u00c2\u00b0si\\n64\u00c2\u00b0so\\n25*io\\n64*30\\n25\u00c2\u00b030\\n64*9\\n25*51\\n63*48\\n26* re.\\n63*26\\n26*34\\n63*3\\n26*57\\n62*40\\n27*20\\n62*8\\n27*42\\n61*63\\n28*7\\n61*25\\n28*31\\n32\\n86*2\\n23*5^\\n65*44\\n24*16\\n65*2*\\n24*34\\n65 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1\\n6048\\n29*12\\n60S*\\n29*34\\n60*4\\n29*56\\n5341\\n30*i9\\n59*18\\n30*42\\n58\u00c2\u00b0S4\\n31*6\\nS8\u00c2\u00b0*o\\n31*30\\n58*S\\n31*55\\n57*39\\n32*21\\n57\u00c2\u00b0i3\\n32*47\\n5646\\n33*14\\n56jt9\\n33*4i\\n39\\n61*33\\n28*27\\n61*13\\n28*47\\n60*53\\n29*7\\n60\u00c2\u00b03l\\n29*29\\n60*10\\n29*50\\n59*48\\n30*12\\n59*25\\n30*95\\n30*5%\\n58*39\\n31*21\\n58\u00c2\u00b0 ia\\n3146\\n5750\\n32*10\\n57*24\\n32*36\\n56*S8\\n33*2\\n56*32\\n33*28\\n56*6\\n33*54\\n55*37\\n34*23\\n40\\n60*57\\n29*3\\n60*56\\n29*4\\n60 J ib\\n2945\\n59*53\\n30\u00c2\u00b0 7\\n5932\\n30*28\\n59*10\\n30\u00c2\u00b0SJ\\n58*47\\n31*13\\nS8\u00c2\u00b0\u00c2\u00bb\\n31*36\\n58* 0\\n32*o\\n57*35\\n32*26\\n57\u00c2\u00b0id\\n32*50\\n56*44\\n33*16\\n56*i9\\n33*4i\\n55*52\\n34*e\\nS5\u00c2\u00b024\\n34 as\\n54*57\\n35*3\\n41\\n60*2*\\n2940\\n60\u00c2\u00b0 0\\n30*0\\n59*39\\n30*21\\n59*17\\n30*43\\n58\u00c2\u00b0SS\\n31*5\\n58*32\\n3t 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12\\n20*48\\n6848\\n21*12\\n68 25\\n21*35\\n67^9\\n22\u00c2\u00b0 1\\n67 34\\n22*26\\n67 6\\n22*54j\\n66 38\\n23*22\\n66 10\\n23*50\\n65*39\\n2**21\\n20\\n70\u00c2\u00b02l\\n19*39\\n70\u00c2\u00b0.\\n19*59\\n69 41\\n20*19\\n69 19\\n20*4i\\n68\\n68*57\\n21*3 2\\n68ji2\\n21*48\\n6748\\n22*12\\n6 V 3\\n22*37\\n66*57\\n23\u00c2\u00b0 3\\n6630\\n23*30\\n66*2\\n23*58|\\n65*33 65*3\\n24*27, 24*$7\\n64*32\\n25*28\\n21\\n69 26 69 o\\n203*\\n20\u00c2\u00b0E\\n68*45\\n21*15\\n6823\\n21*37\\n68\u00c2\u00b0o\\n22*o\\n67j3\\n22*47\\n664s\\n23*12\\n662s\\n23*38\\n65 SS\\n24\u00c2\u00b0S\\n65 28\\n24*32\\n64*59\\n25*1\\n64w\\n25*31\\n63 se|\\n26*8\\n6326\\n2eV\\n22\\n6833\\n2f*27|\\n67 50\\n2\u00c2\u00bb*i| 22*10\\n67 2?\\n22\u00c2\u00b03S\\n67 4\\n22*56\\n6640\\n23*20\\nfefcis\\n23*45\\n65*49\\n24*||\\n6523\\n24*37\\n64 ss\\n25*5\\n64 26\\n25*34\\n63V\\n26*3\\n63*26\\n26*34\\n62*54\\n27*6\\n6221\\n27*39\\n23\\n67V\\n22*19\\n6ria\\n22*42\\n66 SS 66 32\\n23*5 23*28\\n66\u00c2\u00b0 8\\n23*52\\n6544\\n24*16\\n6518\\n24*42\\n64*51\\n25*9\\n64\\n25*361\\n24 63\\n55\\n26* s\\n63 26\\n26*3*\\n62*56\\n27*4\\n62*24\\n27\\n61*52\\ne\\n36 28\\n6f\u00c2\u00b0 e i8\\n2842\\n60*W\\n2945\\n24\\n66*46\\n23*12\\n6626\\n66*2\\n23 34 23 58\\n65 38\\n24*22\\n65\u00c2\u00b0 |4\\n24*4\\n64*48\\n25*12\\n6422\\n25*38\\n635*\\n26*6\\n63\u00c2\u00b02b\\n26*3*\\n62*57\\n27*3\\n6227\\n27*33\\n6I\u00c2\u00b056\\n28*4\\n61*23\\n28*37\\n60 50\\n29*10\\n25\\n65*57\\n24*3\\n65 33\\n24*27\\n65*9\\n24*51\\n6445\\nZ5*i5\\n64 to\\n25*40\\n6353\\n26*7\\n63 26\\n26*34\\nfeTsil\\n27*2\\n62^29\\n27*3\\n61 S9\\n28*.\\n61*29\\n28\u00c2\u00b03i\\n6057\\n29*3\\n60*24\\n29*3\u00c2\u00ab 30 10\\n59 \u00c2\u00bb4\\n30*46\\n26\\n65*6 64*42\\n24*94 25*\u00c2\u00bb\\n64*18\\n25*42\\n63*52\\n26*8\\n6326\\n26 r\\n62*59\\nI\\n34 27\\n62*3i\\n27*29|\\n62 3\\nC 1\\n2757\\n6133\\n28*27\\n61*3\\n28*57\\n60 31\\n29*29\\n5959\\n30\\n59*25\\n30*si\\n58*sd\\n3l*io\\n58\\n31*46\\nS7*i6\\n32\\n2Z,\\n64*16\\n25*44\\n63\u00c2\u00b05i\\n26*9\\n63*26\\n26*34\\n63\u00c2\u00b0o\\n27V\\n62 34\\n27*26\\n62*j6\\n27*5 i\\n61 3a\\n28*22\\n618\\n29*52\\n60m\\n29 f\\n60*7\\nt\\nS3\\n\u00c2\u00bb29\\n59b\\n30*25\\n59*\\n30*S8J\\n5826\\n31*32\\n57*53\\n32*7\\n28\\n29\\n63*26\\n26*34\\n[63V\\n26*59\\n62 36\\n27*24\\n62*9\\n27*si\\n61*42\\n28*18\\n61*14\\n28*46\\n60 45\\n29*5\\n60is\\n29*45\\n5945\\n30*15\\n59 13\\n30*47\\n50*47\\n3l e 2\u00c2\u00bb\\n58*7\\n3I\u00c2\u00b053\\n62*37\\n27*23\\n62*12\\n27*48\\n61*46\\n28*iS\\n61 19\\n2S4i\\n6051\\n29*9\\n60*23\\n29*37\\n5953\\n30*7\\n59 23\\n30*37\\n58 52\\n31*8\\n58 19\\n31*41\\n57*46\\n32*14\\n57*12\\n32*48|\\n57*32\\n3 2*28\\n56*37\\n33*23\\nS6\u00c2\u00b056|\\n33*4\\nS6*i\u00c2\u00bb\\n33V\\n56*^\\n34\u00c2\u00b0 o\\n55*23\\n34*87\\n30\\n61*46\\n28\u00c2\u00b0i 1\\n6rt\u00c2\u00bb\\n28*37\\n60s?\\n29*3\\n60*29\\n29\u00c2\u00b03i\\n60\u00c2\u00b0 1\\n29\\n99\\n59 32 S9 2\\n30*281 30*56\\n58 at\\n31*261\\n58\u00c2\u00b0o\\n32*0\\nS7J7\\n32*33\\n56*53\\n33*7\\n56*19\\n33*4l\\nS5\u00c2\u00b04i|\\n34*17\\n55*7\\n34*531\\n54*28\\n35*32\\n31\\n61* i\\n28*53\\n6016\\n29*a*\\n606\\n29*54\\n59\\\\i\\n30*39\\n5944\\n30*19\\n46\\ni 58*42\\n31*18\\n58*12\\n31*48\\n5741\\n32*19\\n57*8\\n32*\\n56*36 56*\\n24 33*59\\n52 33\\n55*26\\n34*34\\nS4so\\n3S*|0\\nS4i2\\n3S*48|\\n53*34\\n36*26\\ni|57 54\\n32\\n32\\nCO 15\\n29*45\\n59*46\\n5852\\n31*8\\n26\\n5723\\n32*37\\nS6S2,\\n33*8\\n56i9\\n33*41\\n55 45 55 i\u00c2\u00bb\\n34 IS\\n3449\\n54 35\\n3S* 2 i\\n53*s\u00c2\u00bb\\n36*2\\n53*21\\n36*\\n39 37\\n5242\\nIB\\n33\\n5929\\n30*31\\n59*2|58*34|58\u00c2\u00b05\\n31*55\\n30 ss\\n3126\\n36\\n5 57\\n32\\n56*34\\n33\\n56 1\\n33*58\\n55*3C54\u00c2\u00b0\\n34*30 35*\\n^56 54 21\\n35*3\u00c2\u00bb|\\n5345\\n36*ib\\n53*8\\n36*52\\n5229\\n3731\\n5l\u00c2\u00b0so\\no\\n38 9\\n34\\n5844\\n31*16\\n58 16 57*48\\n32*12\\n31 44\\nS7;i9\\n32*4i\\n49\\n56 19\\n33*41\\n5547\\n34*13\\n55ji5\\n34*45\\nS4V\\n35*19\\n54*7\\n35*53\\n53*32\\n36*26\\n52S2\\n37*8\\n52*\u00c2\u00bb\\n37*42\\n51*40\\n38*20\\n51* 0\\n39*0\\n35\\n58 o\\n32*0\\n32 57\\n29 32\\n57\\n5633\\n33*27\\n3 55\\nW34*\\n55o\\n35*0\\n54\u00c2\u00bb\\n35*32\\n5354\\n36*6\\n53 20\\n36*40\\n5244\\n37*i6\\n52\\n37*B2\\nSl\u00c2\u00b030\\n38*30\\n505i\\n39*9\\n50*12\\n39*46\\n36\\n5716\\n5648\\n3244 3912\\n19\\n55*49\\n34*11\\n55\u00c2\u00ab\\n344a\\nis 54\\n35\\n54*15\\n354sl36\\n5342\\n18\\n53*8\\n36*52\\n52 33 51 57\\n37 27\\n38 3\\n51*20\\n38*40\\n50*43\\n39*\u00c2\u00bb7\\nSOV\\n39*\\n49^24\\n36\\n56 40\\n37\\n5632\\n33*28\\n56\\n33\\n*4, S5\\n1*56 34\\n55 5\\n34*55\\n55\u00c2\u00b07\\n34*39\\n34 54\\nI\\n26 35\\nSS\\n53:\\n36\u00c2\u00b0:\\n52 fc\\nO\\n374\\n5223\\n37*37\\n51*47\\n38*13\\n51*12\\n38*48\\n50*35 49*56 49i7\\n39zs40 4\\n4043\\n4837\\n4\u00c2\u00bb\u00c2\u00b023\\n38\\n5 V\\n34*9\\n54*52\\n3S*8\\n5423\\n35*3;\\n5246\\n37*14\\nS2*tt\\n37*46\\n38*22\\n38 5)\\n38*57\\n50 27\\n39*33\\n4949\\n40*ll\\n49 11\\n40*49\\n\u00e2\u0099\u00a6832\\n4l*t\u00e2\u0082\u00ac\\n47la\\n42*8\\n39\\n55*9\\n34*5 i\\n54\u00c2\u00b039| 54*10\\n50\\n35*21\\n35!\\n53 3S\\n36*21\\n53*7\\n36*53\\nf;-\\n5I\u00c2\u00b02\u00c2\u00bb|\\n38*3\\n50 54\\n39*6\\n50 (9\\n39*41\\n49\\n40 _ t8\\n42 49\\nS\\n40~S5\\n48 27\\n41*33\\n4746\\n42*12\\n477\\n42si|\\n40\\n5428 53 \u00c2\u00a38\\n5258\\n3532\\n36 2\\n53*28\\n36\u00c2\u00b032 37*2\\nL\u00c2\u00b026|5I\\n*34\\nS^SI 20\\n5046 SO 12\\n38 6\\n3840\\n3914\\n3948 40\\n49 36J48*59l48\\\\2T47%iJ47 S 5;\\n24 41*1\\n46*24\\n4 r38|42 t6 |42\u00c2\u00b0S5(43 C 36\\n5348\\n36*12\\nS3 17\\n36*43\\n52*48\\n37*2\\n5216\\n37*44\\nI\u00c2\u00b04S|S\\n1\\n15\\nI 12.\\n5039\\n38\\n5 v\\n3848J39 2i 39*55\\n30 48\\n30 41*\\n5446 17\\n6 41\\n43 42\\n47*40\\n20\\n47*1\\n42*\\n4622\\n38\\n59 43\\n45V\\n44*19\\n42\\n53*8\\n36*52\\n52*36\\n37\\n52\\n22 37\\n51*36\\n38*24\\n38\\n1*4 50*S2J49\\n56 39*28 40\\n58 49 24 4649\\n2 40 36 4l*u\\n4813\\n41*47\\n47*36 46*59 46*20\\n42*24|43 l 43*40\\n4^40\\no\\n4420\\n4.5", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0043.jp2"}, "40": {"fulltext": "26\\nBROWN SHARPE MFG. CO.\\nTABLE 3.\\nAngle of Face,\\ngear.\\n41\\n40393837363534\\n333231\\n30292827\\n12\\n13 37\\n70*34\\n13 57\\n70 3 3\\nW- IB\\n70*6\\n14 39\\n69*s4l69*\\n15 a*\\n6832\\n15*9\\n6759\\n16 15\\n67*2 3\\n16 43\\n66*4\u00c2\u00ab i\\n7*13\\nfcfc* s\\n7*3\\n65ii\\n18 is\\n64*\u00c2\u00ab 9\\n18 51\\n6 3*5 3\\n19 27\\n63*3\\n20 5\\n62*9\\n13\\n14 55\\n69*51\\n15.17\\n69*i\u00c2\u00ab\\n15*38\\n68V 7\\n16! 1\\n68\u00c2\u00b0is\\n16 a\\n674 3\\n16*51\\n67*9\\n17 1\\n6633\\n174 6\\n6556\\n18 i\u00c2\u00bb\\n65 16\\n18 V\\n64*34\\n19 2 J\\n63*5\\n19*57\\n63*5\\n20*32\\n62*\\n2T11\\n6I\u00c2\u00b023|\\n21*54\\n60*2\\n14\\n16 w\\n6831\\n16*34\\n66\u00c2\u00b0c\\n16 59\\n6 7*29\\nI 7 U\\n66 4-6\\n17 50\\n6622\\nIB 17\\n6547\\n18 45\\n6,S*s\\n19 16\\n64*30\\n19 48\\n63*48\\n20 to\\n63\u00c2\u00b06\\n205\\n62*20\\n21 s+\\n61*32\\n2 2\u00c2\u00b0\u00c2\u00bb\\n60\u00c2\u00b04i\\n2*5*1\\n59*4\\n23.38\\n58\u00c2\u00b05o\\n15\\n17*28\\n67*6\\n17*53\\n66\u00c2\u00b045\\n1 8\u00c2\u00b0. 8\\n66*14\\n1 8 44\\n65*o\\n)9\u00c2\u00b0n\\n65*3\\nI9 C 40\\n64\u00c2\u00b0 84\\n6349\\n2044]\\n6i\u00c2\u00b06\\nei i8\\n62*14|\\n21 53\\n6i\u00c2\u00b039\\n22*3,\\n60*\u00c2\u00ab,\\n2 3 ,o|\\n60*2\\n24*4.2\\n5 8*3*\\n23*51\\n5S b\\n2435|\\n58*3\\n25*to\\n57?4\\n16\\n18*4 2\\n66 V\\nI9\u00c2\u00b09\\n6533\\n19*35\\n64*41\\n20\u00c2\u00b03\\n64*28\\n63 4\\n2l e s\\n63%\\n2l\u00c2\u00b03e\\n6 2*6 8\\n22\u00c2\u00b09\\n6145\\n22\u00c2\u00b0*\u00c2\u00abi\\n6l 0i\\n23\u00c2\u00b0a\\n60*4\\n27501\\n58 4 2\\n24\u00c2\u00b0 1\\n59 2 5I\\n57\\n2 6\u00c2\u00b0, 2\\n5642\\n27\u00c2\u00b0i\\n55is\\n17\\n19*56\\n64*54\\n20 2 4\\n64*20\\n20\u00c2\u00b0 s\\n6345\\n21*37\\n63*9\\n21 a.\\n639\\n2/*43\\n62j\\n22(4\\n6 I 50\\n2257\\n61*9\\n2333\\n60 25\\n24io\\n5 9 40\\n25\u00c2\u00b03,\\n58*.\\n26 i*J\\n57*i\\n2 759\\n56*13\\n27*7\\n55\u00c2\u00b0 5\\n28 97\\n54*ia\\n18\\n21 9\\n6345\\n22*6\\n6234)\\n22*38\\n6 1*56\\n2o\u00c2\u00b08\\n61*17\\n2343\\n60*3\\n24 ie\\n59\u00c2\u00b05*\\n24\u00c2\u00ab\u00c2\u00ab\\n\u00c2\u00a39*8\\n25 34\\n58 20\\n26(5\\n57*3i\\n26 57\\n56*39\\n5546\\n28 29\\n54*49\\n29 ie\\n53 50\\n309\\n52 47\\n19\\n2 2 to\\n62 3\u00c2\u00ab\\n22 49]\\n6**,\\n23*2\\n61 24\\n23*52\\n60*4\\n24V\\n60*\\n2540\\n58*54\\n25*1\\n59ii\\n2537\\n5837\\n26 1 5\\n57*5f\\n26*56\\n57%\\n2738\\n56*14\\n28*22\\n55*2 1\\n29\u00c2\u00b0a\\n54*24]\\n29 56\\n53*28\\n3043\\n52*28\\n31*40\\n51*2*\\n20\\n23 30\\n61*30\\n24 1\\no\\n6053\\n2432|\\n60 iA.\\n25*6\\nO\\n5934)\\n26 it\\n36\u00c2\u00b0.\\n26 55\\n5 725\\n27e*\\n56*38\\n28)5\\n554\u00c2\u00bb\\n28 58\\n6\\n54 58\\n29\u00c2\u00b044|\\n54\\n30 s.\\n53*9\\n3 1 a,\\n52*9\\n32 iJ\\n51*9\\n33 c\\n50 *A\\n21\\n2439\\n60\u00c2\u00b02s\\n2S\u00c2\u00b0/o\\n59*46\\n2 5*3J\\n59%\\n26 is\\n58*26\\n26*53\\n574S\\n27ao|\\n57*0\\n28*io\\n56*/4\\n28 50\\n6\\n552*\\n29 St\\n54*36\\n30 17\\n53*8\\n31\\n52~so\\n3/52\\n51*32\\n32**s\\n50*53\\n33 36\\n49\\n34 31\\n22\\n25*6\\n59 s \u00c2\u00abo\\n26*9\\n58*4,\\n2653\\n3a*i\\n2727\\n5 7\u00c2\u00b0 9\\n28 v\\n56*3\u00c2\u00ab\\n28**3\\n555\\n2922\\n554\\n30 5\\n54*7\\n3049\\n53\u00c2\u00b026\\n31 34\\nS2\u00c2\u00b03 2J\\n32 2 2\\n5/*3\\n33\u00c2\u00b0 (l\\n50*4i\\n3+\u00c2\u00b03\\n494.\\n34 57\\n48 3 7\\n35*54\\n4732\\n23\\n26 42\\n58*6\\n2 7\u00c2\u00b02\u00c2\u00bb\\n5738\\n28*0\\n56*S6\\n2836\\n56*14\\n29i4\\n55*30\\n2958\\n5\u00c2\u00bb*4j\\n3535\\n5357\\n3l\u00c2\u00b0ie\\n53*8\\n32\u00c2\u00b0i\\nS2*,s\\n324\u00c2\u00ab\\n5/*84\\n33\u00c2\u00b036|\\n50*2\\n34*i\\n8 49*9\\n35 20\\n36 i5\\n4-7*2 7\\n37 2\\n37%o\\n46*. 8\\n24\\n2757\\n5 7*5\\n28 3\\n56*35]\\nE9\u00c2\u00b07\\n2943\\n55*ii\\n30*22\\n54*2\\n3I\u00c2\u00b02\\n3l\u00c2\u00b045\\n52\u00c2\u00b05i\\n32*2a|\\n52*2\\n5/\u00c2\u00b0i\\n34\u00c2\u00b0 1\\n50*5\\n34*3\\n49V\\n42\\n49\u00c2\u00b022\\n36*77\\n47*,\u00c2\u00ab\\n36\u00c2\u00b03i\\n472\\n3B\u00c2\u00b02e\\n45 12\\n25\\n28 ss\\n56*i5\\n29 34\\na\\n5534\\n30T\\n54*34\\n30 c u\\n54*42\\n30*3\\n54*9\\n31 29\\n53*23\\n32\u00c2\u00b0\\n52 36\\n32*5 2\\n51*48\\n33*37\\n50*47\\n34\u00c2\u00b02i|\\n50\u00c2\u00b05\\n34*44\\n496 6\\n35 h\\n49 \u00c2\u00b0n\\n36\u00c2\u00b00\\n4B*6\\n37*7\\n46*i5\\n38\u00c2\u00b04j|\\n4S\u00c2\u00b0!\\n3941\\n6\\niW* 5\\n26\\n30\\nS5 is\\\\\\n3!\\n53\\n3 I 54\\n53\u00c2\u00b0e\\n32\u00c2\u00b03\\n52\u00c2\u00b02i\\n33 is\\n5 1*35\\n33 58\\n50*6\\n3531\\n6\\n49 3\\n35 19\\n4 8%\\n37io\\n47*2\\n38 u 2\\n46\u00c2\u00b0i2\\n4s*io\\n38 46\\n45*0\\n39 54\\n6\\n44 7\\n4052\\n4-3*2\\n27\\n3I U 3\\n54\u00c2\u00b0,9\\n31 39\\n53 37\\n32 ie\\n5 2\u00c2\u00b0\u00c2\u00ab4|\\n32 57\\n5 2\u00c2\u00b09\\n33 37\\n51 23\\n34eo\\n50\\n35\u00c2\u00b0i\\nc\\n49 37\\n35 3\\no\\n45\\n3*49\\n3543\\n48*55\\n3b 36\\n48\u00c2\u00b02\\n3725\\n4.7*7\\n38\\n46*,o\\n41 1\\n4 3*5\\n42 v\\n29\\n32*2\\n53*22\\n32*39\\n52*39\\n33\u00c2\u00b0i8\\n6\\n5IS6\\n33 57\\n51\u00c2\u00b0..\\n34 39\\n50*25\\n36 v 7\\no\\n48 4.7\\n36 42\\no\\n4746\\n3 7*o\\n47\u00c2\u00b02\\n38 20\\n46 b\\n39\\\\,\\n451,\\n40\u00c2\u00b0|4\\n419\\n4-3 9\\n4-2 7\\n29\\n30\\n31\\n32\\n33\\n34\\n35\\n36\\n37\\n38\\n39\\n40\\n41\\n32 59\\n52*27\\n3338\\n5 1 44\\n34.7\\n5l\u00c2\u00b0i\\n3458\\n50 ,6\\n3539\\no\\n49 29\\n36*23\\n|48*4\\n37 a\\n4750\\n3754\\n46*\\n38i\\n8 46 4,\\n39*32\\n45\\n4024\\nIt\\n4l\u00c2\u00b0ie\\n4-3 V i*\\n3367\\n51 as\\n3436\\n50 50\\n35 is\\n50\u00c2\u00b0 r\\n3 556\\n49*2\\n36 38\\n4-834\\n372\\n47^4\\n38\\n36ii\\n46*3\\n394J]\\n45*9\\n40\\n44\u00c2\u00b0i-\\n32 41\\n26\\n43*i7\\n42i\u00c2\u00ab\\n3453\\n5041\\n35 3 1 36ii\\n49*57149\u00c2\u00b0 3\\n36\u00c2\u00b052\\n48\u00c2\u00b0*\\n35*6\\n4950\\n555:\\n49\u00c2\u00b0\\n37 35\\n4739\\n3820\\n4 6 52\\n39 5\\n46*i\\n39\u00c2\u00ab\\n45\\n40*\\no\\n4415\\n4I\u00c2\u00b032\\na\\n43 20\\n42.23\\n37 u 6\\n48*;\\n37*8\\n47j6\\n38 3/\\n4 6 49\\n39*15\\n45*59\\n40\u00c2\u00b0l\\no\\n45 9\\n4049\\n44\u00c2\u00b0! 7\\n4138\\n43*24\\n4228\\n36 6 9\\n48*49\\n373\\n3 7\u00c2\u00b0, 9\\n48*i7\\n38\u00c2\u00b0o\\n47j2\\n38*2\\n4646\\n39*26\\n4558\\n40\u00c2\u00b00\\n45*e\\n4056 4/44\\n44*18 43*1*1\\n4233\\n2\\n48*12\\n38 11\\n47*2 7\\n38*53\\n46**s\\n33*35\\n4547\\n40^\\n45\u00c2\u00b08\\n4I\u00c2\u00b04\\n44\u00c2\u00b0io\\n4149\\n43*29\\n4237\\n38*22\\n4724\\n39\u00c2\u00b03\\n46\u00c2\u00b039l45i4\\n39*4 0 D 26\\n45*a\\n4l\u00c2\u00b0io\\n44 20\\n4 1 ss\\n43*81\\n4241\\nACT**\\n45\u00c2\u00b0e\\n42\\n43*34)\\n42*5\\n40 0\\n4552\\n40 4o|\\n4-5*8\\n40 47\\n45%\\n471\\n4424J\\n4ltt\\n44- i2\\n42 5\\n43\u00c2\u00b0\u00c2\u00bb7\\n42*8\\n42\u00c2\u00b09\\n43*3\\n4132\\n44*24\\n42 14\\n43*40\\n42*4\\n43\u00c2\u00b0,e\\n43*2\\n43\u00c2\u00b0 2\\n42 1", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0044.jp2"}, "41": {"fulltext": "PROVIDENCE, R. I.\\n27\\nTABLE 3. {Continued?)\\nAngle oe Face.\\nGEAR.\\n262524\\n23222\\n20\\n19\\n18\\n17\\n16\\n15\\n14\\n13\\n12\\nO\\n12\\n2 131\\nbO s\\n2Z .B\\n59* o\\n23 a\\n58*2\\n\u00c2\u00a34*3\\n56*4.9\\n25*2\\n55*3 2\\n26*3\\n54 T\\n52*39\\n28*as\\n5/*3\\n29Vi\\n49 V\\n3\\nK7es\\n32*\u00c2\u00ab4. 3426\\n45*24\\n4.3 1*\\n30 16\\n40 io\\n38*i7\\n13\\n22 37\\n59*29\\n23*26\\n58*2 8\\n24*vs\\n5 7\u00c2\u00b0 2\\n25*3\\n56 11\\n2b\\n54\u00c2\u00b05i\\n2 7\u00c2\u00b0s\\n533 6\\n28 m-\\n|52\u00c2\u00b0o\\n29\u00c2\u00b02\\nJ0\u00c2\u00b039\\n30We\\n4-9\u00c2\u00b0a\\n32 V\\n47\u00c2\u00b0 fc\\n333\\n4-5 2 2\\n35 10\\n3o 5S\\n4-3\u00c2\u00b02o4-|\u00c2\u00b09\\n38*o\\n14\\n24 25\\nB\\n574.\\n25\\n5646\\n2 6 s\\n55 38\\n27 5\\n54\u00c2\u00b02 4\\n26 4.\\n53\u00c2\u00b08\\n29s\\n30 20\\nSO20\\n3i 33\\n48\u00c2\u00b04\\n32 52\\n47 \u00c2\u00b0r\\n34 8\\n45*2\\n35so\\n4-32 6\\n3728\\n41 24\\n39 If\\n15\\n26 1\\n56\u00c2\u00b0 3\\n27 a\\n11 se\\n53\u00c2\u00b058\\n28 48\\n\u00e2\u0080\u00a252 44\\n30\u00c2\u00b00\\nSi 26\\n31%,\\n^O^\\n32,9\\n48\\n33 36\\n4 7 o\\n16\\n2 7% 2\\n54\u00c2\u00b03 8\\n28 W \u00c2\u00abM\\n53\u00c2\u00b03\\n294-3\\n52\u00c2\u00b02i\\n30 V*\\n51*6\\n3l\u00c2\u00b0so\\n49*46\\n32\\n48 2 2\\n34- 2\\n46*52\\n3531\\nAS 19\\n34ff\u00c2\u00ab 35 23\\n45 2.o4333\\n3757\\n4 |C 39\\n3938\\n36\u00c2\u00b0.4\\n\u00e2\u0096\u00a043\\n36 4\\n38\u00c2\u00b02j\\n1.51\\n3957\\n17\\n29 ac\\n53*8\\n30 a,\\n52 \u00c2\u00b0o\\n31*2\\n50\u00c2\u00ab8\\n3228\\n49 3 2\\n3335\\n48\\n3447\\n46\u00c2\u00b047\\n36\\n4 5\u00c2\u00b0 6\\n371.,\\n43\u00c2\u00b04 3\\n384s|\\n42\u00c2\u00b0 1\\n40,5\\n18\\n315\\n5141\\n32\\n50 3 2\\nJ3 4\\n4 9\u00c2\u00b0 s\\n34 a\\n48\u00c2\u00b02\\n35,5\\n46a,\\n36\u00c2\u00b02a\\n4 5\\n37js39s\\n43\u00c2\u00b04s42\u00c2\u00b0,i\\n401,\\n19\\n32\u00c2\u00b036|\\n50\u00c2\u00b0, 8\\n3336\\n49\u00c2\u00b08\\n34 38\\n3549\\n47\u00c2\u00ab4 46 36\\n3653\\n4-5\u00c2\u00b05\\n38 6\\n4 3. so\\n39\u00c2\u00b024\\n42%o\\n40*5\\n20\\n54\u00c2\u00b0 s\\n48 si\\n35\u00c2\u00b06\\n4746\\n36*8\\n46*321\\n37,6\\n4-5 ,4\\n38 2 6\\n43*52\\n39 39\\n4-2*27\\n21\\n35 3\\n47*39\\n22\\n23\\n38,2\\n45\u00c2\u00b0, 2\\n24\\n25\\n26\\n3632\\n46*28\\n3 737\\n15\u00c2\u00b0, 3\\n3844\\n4-3 c 56\\n39 54\\n42*34\\n41 e\\n36.52\\n46\u00c2\u00b024-\\n37SS\\n4*\u00c2\u00b03\\n39 u\\n43\u00c2\u00b0se|\\n40 6\\n4-240\\n41 19\\n39 s\\n4-0 20\\n4246\\n41 28\\n39*29\\n44\u00c2\u00b0 3\\n40 32\\n4252\\n41 38\\n4043\\n42 57\\n4(46\\n4153\\ng a 90\u00c2\u00b0 (a a P)\\ng b 90 (a b /3)\\n(See Page ij.)", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0045.jp2"}, "42": {"fulltext": "TABLE 4\\nAngle of Face. Gear.\\n7271\\n706968676685 64636261\\n60535857\\n12\\n7\u00c2\u00b0S3\\n8T\\n78\u00c2\u00b05tf\\nWT\\n78*33\\nB-/41\\n73*3*\\n8\u00c2\u00b0Z/\\n78/3\\n8*28\\n78 /6\\n8 35\\n77\u00c2\u00b0 53\\n8*43\\n77*47\\n5 51\\n77\u00c2\u00b037\\n8 53\\n77*25\\n9* o 7\\n77\u00c2\u00b0 I\\n9 n\\n77* r\\n9*26\\n76\u00c2\u00b048\\n9 35\\n76 35\\n9*45\\n76* 23\\n9*55\\n76*8\\n13\\n8\u00c2\u00b040\\n73 12\\n8*48\\n78 2\\n8 54\\n7752\\n9* a\\n7742\\n9 9\\n77\u00c2\u00b034\\n9 V 8\\n77\u00c2\u00b02e\\n9\u00c2\u00b0 26\\n77 3\\n9\u00c2\u00b03i\\n76 56\\n9*/*3 9\u00c2\u00b0 52\\n76*45 76*32\\n10 I\\n76*19\\n10* it\\n76 7\\nVi Zi\\n75*53\\nt0 3l\\n75*33\\n10*42\\n75*26\\n|0*3J\\n7S*il\\n14\\n9*26\\n77*26\\n9*34\\n77\u00c2\u00b0 16\\n9*42\\n77*4\\n9\u00c2\u00b0. 50\\n76 54\\n9 S3\\n76*43\\n10 8\\n76*3*\\n10 16\\n76* 18\\n\\\\0 es\\n76 i\\nI0*3S IQ\u00c2\u00b04S\\n75 55 75 41\\n10 54\\n75*28\\nII* 5\\n7515\\n11*16\\n75*\\nII 27W\u00c2\u00b033\\n7445 74*31\\nII 50\\n74 14\\n15\\n10- 12\\n76\u00c2\u00b04flJ\\n10*21\\n76*23\\n10\u00c2\u00b0 30\\n76\u00c2\u00b0 16\\n76 6\\n|0 A7\\n75*55\\n10 57\\n75*45\\n11*6\\n75*30\\nII 16\\n75 K\\nrer*\\n75 3\\nIf 37\\n74*49\\niiMYirss\\n74\u00c2\u00b0 35 74* 2t\\n12 M\\n74*7\\n12*22\\n7i\u00c2\u00b050\\n12*35\\n73*35\\n12*4$\\n73*18\\n16\\n!0\u00c2\u00b059\\n175*55\\n75 43\\n\u00c2\u00bbr e i7\\n75 31\\n26\\n75 2 6\\n11*37\\n75 7\\n11.46\\n7454\\nII 56\\n74*\\n4*74\\n27\\n2*17\\n74 e 3\\n12*29\\n73*59\\n12*40\\n73\u00c2\u00b044\\n12 52\\n73*28\\n13*5\\n73*i J\\n13* 18\\n72\u00c2\u00b0 561\\n7240\\n13*45\\n7223\\n17\\n44\\n75\u00c2\u00b0 id\\nir\u00e2\u0080\u009e54\\n74 58\\n1 2 4\\n74\u00c2\u00b046\\n2*13\\n74*33\\n1 2\u00c2\u00b0 24\\n74*20\\n12*34\\n74\u00c2\u00b0 S\\n2*46\\n73\u00c2\u00b052\\n12 Sb\\n73 38\\n13\u00c2\u00b0 7\\n73*23\\n13*21\\n73\u00c2\u00b0 9\\n13*32\\n7252\\n13*45\\n72 35\\n13 59\\n7? 2i\\n14* If\\n72\u00c2\u00b0 3\\nWat\\n71*45\\nI4 4e\\n71*26\\n18\\n.2*29|l2\u00c2\u00b040\\n742574*12\\n12 54\\n74*\\n/3*\\n73*46\\n13*12\\n73*32\\n|3\u00c2\u00b023\\n73\u00c2\u00b0 1 3\\n13*34\\n73*4\\n13*47\\n7243\\n13*59^\\n7233\\n14* \\\\i\\n72*18\\n14*24\\n722\\n14*36\\n7144\\n14*52\\n71*28\\n15*6\\n7I H\\n15*21\\n70*51\\n15*36\\n7054\\n19\\n13*14 I3 .2i\\n73*40 73 27\\n13*3$\\n73 14\\n13*48\\n73*\\n14\u00c2\u00b0\\n72*46\\n14* if\\n72\u00c2\u00b03l\\n14\u00c2\u00b0 24\\n72\u00c2\u00b0 16\\n14*36\\n72\u00c2\u00b0\\n14*43\\n71*45\\n15 2\\n7/*28\\n15*15\\n7l n\\n15 so\\n70\\n54 70\\nIV44\\n30\\nI5*S9\\n70 ri\\n16 1 5\\n69\u00c2\u00b059\\n16*31\\n69\u00c2\u00b033\\n20\\ni3;59 |4; ii\\n72*57 72*43\\n14\u00c2\u00b0 23\\n72*29\\nI4 34\\n7214\\n14*46\\n72*\\n5*4\\n7145\\n15\u00c2\u00b0 II\\n71*29\\n15*25\\n7I\u00c2\u00b0I3\\n15\u00c2\u00b0 39\\n70*56\\n15*52\\n70*38\\n16* 7\\n7021\\ni6\u00c2\u00b02i\\n70\u00c2\u00b0 3\\n1 6 37 16*53\\n69*45 69\u00c2\u00b025\\n|7\u00c2\u00ab8\\n69\u00c2\u00b0 6\\nI7*\u00c2\u00bb\\n68*46\\n21\\n443 14\u00c2\u00b0 55\\n72*13 7I 59\\n15 a\\n7/*44\\nI5\u00c2\u00b02J\\n7/29\\n5*33\\n7/ l5\\n15*46\\n70 56\\n15*53\\n7041\\n16*13\\n70*25\\n16\u00c2\u00b0 28\\n70*8\\nI6\u00c2\u00b042\\n69* S 6\\n16*58\\n69\u00c2\u00b0\\n69*n\\nI7\u00c2\u00b028|17\u00c2\u00b046\\n68*54 6V34J6 e i\\n18*2\\n14\\n18\u00c2\u00b0 30\\n167*52\\n22\\n15*2715*40\\n71*29 7l\u00c2\u00b0i4i\\n70*59\\ni6*6;\\n70*44\\n16\u00c2\u00b0 20\\n70*28\\n16 33\\n70 n\\n16*47\\n69*55\\n17*2\\n69*38\\n17*16\\n69*20\\nI7\u00c2\u00b03J\\n63* I\\n17*49\\n68*41\\n16*3\\n68*23\\n18\u00c2\u00b0 zo\\n68*4\\n16\u00c2\u00b0 37\\n67*43\\n18\u00c2\u00b0 56\\n67\u00c2\u00b0;*\\n13* ii\\n67*1\\n66*9\\n23\\n16*12 16*24,\\n70*46 70\u00c2\u00b0 30\\n16\u00c2\u00b0 38\\n70 IS\\n16* 54\\n69*53\\n17*5\\n69*43\\n17*20\\n69*26\\nI7\u00c2\u00b034\\n\u00e2\u0082\u00ac9\u00c2\u00b0 8\\nI7 e 58\\n68 sc\\n18*5\\n68*33\\n18*20\\n68*14\\n18*36\\n67*54\\n18*54\\n67\\n34 67\\n19* 10\\n14\\n19*28\\n66*52\\n19*48\\n66*32\\n65\u00c2\u00b0/8\\n24\\n16*55\\n70*3\\n69*47\\n17*22\\n69*32.\\n17 37\\n63* IS\\n17*51\\n68\u00c2\u00b059\\n18*6\\n68*4fi\\n18*21\\n68*23\\n18*37\\n6ft* S\\n18* S3\\n67*45\\n19*9\\n67*27\\n19*26\\n67V\\n19*44\\n66*46\\n21\u00c2\u00b0 I 20*19\\n66\u00c2\u00b02s 66*3\\n20*33\\n65*41\\n25\\n7*3917*52\\n69 21\\n69 4\\n18*6\\n68 48\\n18\u00c2\u00b0 21\\n68*31\\n18*36\\n68*14\\n18*52\\n67*56\\n19**7\\n67*37\\n13*24;\\n67*\\n19 4*\\n67\u00c2\u00b0\\n13*57\\n66*33\\n2T\u00c2\u00ab4 20;3i\\n66\u00c2\u00b0 20 65\u00c2\u00b0 58\\n20*51\\n65*37\\n21*10\\n65 14\\n2129\\n64\u00c2\u00b0si\\n21*50\\n64*28\\n22*41\\n63\u00c2\u00b03J\\n26\\n\u00c2\u00bb\u00c2\u00b02i 18\u00c2\u00b0 36\\n68*39168*22\\n18*51\\n68*5\\n19*6\\n67*48\\n19*22\\n67* JO\\n13*37\\n67*13\\n19\u00c2\u00b0 53\\n66*53\\n20*10\\n66\u00c2\u00b034\\n\u00c2\u00a30*26 ZQ tf\\n66\u00c2\u00b0 14 65*53\\n21*2 21*21\\n65*32 65* H\\n2l*4i;\\n64*43\\n22\\n64\u00c2\u00b026\\n22*2$\\n64*2\\n27\\n19\u00c2\u00b0 3\\n67*57\\n19* 19\\n6/39\\n19*34\\n67*22\\n19*49\\n67*5\\n20* 6*\\n56*46\\n20*22\\n66*28\\n20 38\\n66*8\\n20*56\\n6S*48\\n21 13\\n65*23\\n2T32\\n65*8\\n21*50\\n54*46\\n20*17\\n66*41\\n22*10\\n54*24\\n22*29\\n64\u00c2\u00b0\\n2243\\n63*33\\n23*10\\n63*14\\n23*31\\n6243\\n28\\nt9 46\\n67*16\\n20*1\\n66*59\\n20 32\\n66*22\\n20*56\\n66*4\\n21*6\\n65*44\\n21*23\\n65*25\\n2l*4f\\n65*5\\n22*\\n64*44\\n22*1*\\n54*22\\n22*57\\n64*1\\n22*56\\n63*38\\n23*17\\n63*15\\n23*38\\n62\u00c2\u00b0 52\\n23*69\\n62*27\\n24 2!\\n62V\\n29\\n20*27\\n66*35\\n2043\\n66*17\\n20*59\\n65*59\\n21*16\\n65*40\\n21*33\\n65* 2 1\\n21 5C\\n65*2\\n22 8\\n64*42\\n22*27\\n64*21\\n22*45\\n63*59\\n23*5\\n63*37\\n23*25\\n63*15\\n23*44\\n62*52\\n24*4\\n62*28\\n24*25\\n62*5\\n24*48\\n64*44\\n25 ia\\n64*14\\n2T5?\\n60 27\\n30\\n21*3\\n65*55\\n21*25\\n65*37\\n21*42\\n65*18\\n21*58\\n64*58\\n22 15\\n64*39\\n22=34\\n64\u00c2\u00b0 18\\n22*52\\n63*58\\n23 10\\n63*38\\n23*3$\\nai lo\\n23*50\\n62*54\\n24*io\\n62* 3d\\n24*30\\n62*7\\n24*51\\n61*43\\n25*12\\n61* 18\\n25*36\\n60*54\\n2?4J\\n55*42\\n31\\n21\u00c2\u00b0 50\\n65*14\\n22*6\\n64*56\\n22*24\\n64*36\\n22*41\\n64*17\\n22 59\\n63*57\\n23*17\\n63*37\\n23*35\\n63*15\\n23*SS\\n62*55\\n24*14\\n52*32\\n24*34\\n62\u00c2\u00b0 10\\n24*54\\n6i\u00c2\u00b046\\n25)7\\n61*23\\n25*38\\n60*56\\n2r5g\\n60\u00c2\u00b0 M\\n26*22\\n645*8\\n32\\n2231\\n64*35\\n2248 23*4\\n64\u00c2\u00b0|^ 63*56\\n23 23\\n63*37\\n23\u00c2\u00b04C\\n63*16\\n23 59\\n62*55\\n24 18\\n62*34\\n24 3S\\n62\u00c2\u00b0 I Z\\n24*58\\n51*50\\n2ri8\\n61\u00c2\u00b0 26\\n25*33 26\u00c2\u00b0 I\\n61* 3 fctfy}\\n26*23 2T43\\n63\u00c2\u00b0 ir 59*49\\n27*9\\n59*21\\n2r 3 4\\n58\u00c2\u00b056\\n33\\n23*io\\n-63*56\\n2T28 123*46\\n63**6lS3*i6\\n24*4\\n62*54\\n24*22\\n62*36\\n24*4l\\n62 15\\n25*/\\ntei s-i\\n2r2i\\n25*42\\n61*8\\n26*2\\n63*44\\n26\u00c2\u00b0 24 26j45\\n60*20 59\u00c2\u00b0 55\\n27*9\\n53*31\\n27*31\\n59*5\\n27*56\\n58*38\\n28*i3\\n58\u00c2\u00b0n\\n34\\n23* Si\\n16317\\n24*8\\n62*5:\\n24*27\\n62*37\\n24 4425\\nS216\\n4;\\n61*56\\n25*23\\n61*33\\n25*42\\n61*12\\n26\u00c2\u00b0 3\\n50*49\\n26\u00c2\u00b024\\n60*26\\n26\u00c2\u00b04*\\n60*2\\n27*7\\n59*37\\nd7 29\\n59\u00c2\u00b0 13\\n27\u00c2\u00b052\\n58*4%\\n28 16\\n5*822\\n28*AO\\n57*.\\n54 37\\na\\n61* IS\\n35\\n24*29\\n62*39\\n24\u00c2\u00b048\\n62*11\\n25*6\\n61*58\\n25*25\\n6 1 37\\n26*4\\n60*54\\n26\u00c2\u00b024\\n60*32\\n26=45\\n60*9\\n27\u00c2\u00b06\\n5944\\n27*28\\n59*22\\n27*50\\n58*56\\n28*13\\n58\u00c2\u00b0 31\\n28\u00c2\u00b036\\n58*6\\n29* f\\n57*39\\n29*25\\n57*11\\n29*56\\n5444\\n36\\n25*9\\n62*1\\n25*27\\n6l*4l\\n25*45\\n61*20\\n26*24\\n60*36\\n26\u00c2\u00b04S\\n60*15\\n27*5\\n59*51\\n2r 26\\n5928\\n27*43\\n59*4\\n28*io\\n58*40\\n28\u00c2\u00b033\\n58 \\\\i\\n28;S6\\n5750\\n29\u00c2\u00b020\\n57*24\\n29*43\\n56\u00c2\u00b0 57\\n30*9\\n56\u00c2\u00b029\\n30*33\\n56\u00c2\u00b0r\\n37\\n25*41\\n61*\\n26\u00c2\u00b0 6\\n61*2\\n26*25 26\\n\u00c2\u00a3041 Z J\\n^44 27 \u00c2\u00b04\\n2C 53*58\\n27*25 27*45\\n59 35 59\u00c2\u00b0 13\\n28\\n58\u00c2\u00b0 43\\n28 23\\n58*25\\n28*51\\n58\u00c2\u00b0 r\\n29 IS\\nS7 35\\n29*38\\n57 10\\n30*7\\n56*42\\n30*27\\n56 15\\n30*52\\n55\u00c2\u00b0 46\\n31*18\\n55M\\n38\\n26*25\\n60*47\\n26*44\\n68*26\\n27*4 27\\n60 4 si\\n27*42 i 28\\n59* 23 59*\\n58*58\\n24|27 c 44\\n42 5920\\n28*4\\n58*56\\n28*26\\n55 34\\n2847\\n58\u00c2\u00b0 9\\n29 q *9\\n57\u00c2\u00b045\\n29*33\\n57\u00c2\u00b02l\\n29*5 i\\n56*55\\n30^20\\n56 30\\n30*44\\n56*2\\n31*9\\n55*35\\n31*35\\n55*7\\n32*1\\n5433\\n39\\n27*5\\n60\u00c2\u00b0 9\\n27 e *22\\n59*48\\n28*22\\n53*42\\n28*43\\n1 58* 1 3\\n29*5\\n5755\\n29*27\\n57*31\\n29*49\\n57\u00c2\u00b0 7\\n30*13\\n56*4i\\n30*36\\n56\u00c2\u00b0 16\\n31*1\\n55*49\\n31*26\\n5522\\n34*50\\n54 54\\n32*16\\n54\\n3243\\n57\\n28 53\\n40\\npr4o\\n59*34\\n2r40\\n59*32\\n29 I\\n58*5\\n29*22\\n57*42\\n29*43\\n57*17\\n30*6\\n56*54\\n30/28\\n56 28\\n30*52\\n56 2\\n31\u00c2\u00b0 17\\n55*37\\n31*42\\n55*i6\\n32*6\\n54*44\\n32 3\\n54*15\\n32*57\\nS3\u00c2\u00b04\u00e2\u0082\u00ac\\n3324\\n53*18\\n41\\n2rir\\n58*57\\n2*Tj7\\n58*37\\n28*S7\\n5*8* is\\n57 39 57\u00c2\u00b0\\n29\u00c2\u00b039\\n57*29\\n30*1\\n57 4\\n30 5 22\\n56*40\\n30*45\\n56*15\\n3i; 9\\n35* 5\\\\\\n3l*5i\\n55* 25\\n31*55\\n54*59\\n32*20\\n5432\\n3246\\n54\u00c2\u00b0 4\\n33*12\\nS3* 36\\n3V 39\\n53*7\\n34 6\\n52 38\\n42\\n26 ii\\n58*22\\n29*t\u00c2\u00a3\\n58* t\\n30*16\\n56*52\\n30*38\\n56*28\\n31\\n56*4\\n31*23\\n55 39\\n31*47\\n55* 13\\n32 10\\n54*48\\n32*35\\n54*21\\n33*\\n53*54\\n33*26\\n53*26\\n33* si\\n52 58\\n34 \u00c2\u00bb9\\n52*23\\n34 46\\n52\u00c2\u00b0", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0046.jp2"}, "43": {"fulltext": "TABLE 4. (Continued?)\\nAngle of Face. Gear.\\n29\\n565554\\n53\\n52\\n51\\n5049484746454443\\n42\\n10\u00c2\u00b0 6\\n7554\\n10; \u00c2\u00bb6\\n7540\\n\u00c2\u00bb*.28\\n7524\\n10\u00c2\u00b0 39\\n75\u00c2\u00b0 9\\n10*52\\n7452\\n11*3\\n7437\\n11\u00c2\u00b0 5\\n74 is\\nIf 30\\n73*58\\n11*43\\n73*39\\nIIM\\n73\u00c2\u00b0 20\\n12* 13\\n72 53\\n72 37\\n12*45*\\n72\u00c2\u00b0 1 5\\n13*1\\n71\u00c2\u00b0 51\\nI3*t9\\n71*25\\n3\\n11*4\\n74 56\\nII 16\\n7443\\nir o 2s\\n742*\\n11*4-2\\n74 8\\n11*54\\n73\u00c2\u00b0 50\\n12 8\\n73*32\\n12* ao\\n73\u00c2\u00b0 12\\n|2\u00c2\u00b037\\n7253\\n12*51\\n72 33\\n13*7\\n72\u00c2\u00b0 II\\n13*23\\n71*49\\n1340\\n7l\u00c2\u00b026\\n13*58*\\n71\u00c2\u00b0 2\\n14*16*\\n70\u00c2\u00b0 38\\n14*35\\n70\u00c2\u00b0 i\\n12* 2\\n73*58\\n12*16\\n7342\\n12*29\\n73*25\\n12*43\\n73 7\\n12 57\\n72 4Q\\n15 II\\n72*29\\n\u00c2\u00bb3*26\\n72 8\\n1S4I\\n71\u00c2\u00b0 4B\\nC3\u00c2\u00b053\\n71*27\\n14\u00c2\u00b0 IS\\n71\u00c2\u00b0 5\\n70\u00c2\u00b04I\\n14*51\\n10\u00c2\u00b0 17\\n15\u00c2\u00b0 10\\n59 52\\n15*30\\n15 51\\n69 26 68 59\\n13\u00c2\u00b0 I\\n73\u00c2\u00b0 I\\n13*16\\n72*44\\n13*28\\n72 26\\n13*43\\n72 7\\n13*59\\n7!*49\\n14*14\\nif 28\\n14*3\u00c2\u00a9\\n71\u00c2\u00b0 6*\\n14*47\\n70*45\\n15\u00c2\u00b0 5\\n70*23\\n15*23\\n69*53\\niS Q 42\\n69*34\\n16\u00c2\u00b0\\n16\u00c2\u00b0 22\\n6842\\n16*43\\n6815\\n17*5*\\n67*47\\n13\u00c2\u00b0 59\\n72*5\\n14*13\\n71*47\\n14*28\\n7I\u00c2\u00b028\\n14*44\\n71\u00c2\u00b0 8\\n15; r\\n70*39\\n15*17\\n7027\\nsras\\n70\u00c2\u00b0 5\\n15*52\\n69*42\\n\u00c2\u00ab6\\n69*19\\n16\u00c2\u00b0 3d\\n54\\n16*56\\n68\u00c2\u00b0 28\\n17*10\\n68*2*\\n17*32\\n67*34\\n17*56\\n67*6\\n18* 18\\n66\u00c2\u00b036\\n7\\n14*57\\n71*9\\nI5*n*\\n70*49\\n\u00c2\u00ab5* sa\\n70*30\\n5*44\\n7010\\n16\u00c2\u00b0 r\\n69*49\\n16*18\\n69*26\\n16\u00c2\u00b0 37\\n69\u00c2\u00b0 3\\n16*56\\n68*39\\n17*15\\nS3* 15\\n17*36\\n67\u00c2\u00b0s6\\n17*57\\n6723\\n58*20\\n66*S4\\n18*43\\n66\u00c2\u00b027\\nK 6\\n65*58\\n19*31\\n65*27\\nis; 52\\n7014\\n16*7\\n69*53\\n16* 26\\n69*34\\n16*42\\n63*12\\n17*1\\n68*43\\n\u00c2\u00bb7\u00c2\u00b02o\\n68*26\\n17*39\\n68*3\\n17*58\\n67*38\\n18*20\\n67\u00c2\u00b0 12\\n18*44\\n66*47\\n19* 3\\n66\u00c2\u00b0 19\\n1927\\n65*5l\\n19*50\\n65\u00c2\u00b02o\\n20*18\\n64\u00c2\u00b05fl\\n2042\\n64 98\\n9\\n16*49\\n69*19\\n17*2\\n68*58\\n\u00e2\u0080\u00a27.23\\n6837\\n17*41\\n68*15\\n18\u00c2\u00b0\\n67*52\\n18*21\\n67*29\\n18*40\\n67*4\\n19*1\\n66*37\\n19*22\\n66*12\\n19.46\\n65*44\\n20\u00c2\u00b0 8\\n65\u00c2\u00b0 16\\n20-.\\n64*4\\n34 20\\n59\\n6415\\n2\u00c2\u00bb\u00c2\u00b024\\n63*44\\n21*52\\n63*|0\\n20\\n17X4\\n68*26\\n1 18* 19\\n\u00c2\u00b03* 67*44\\n18*40\\n67*18\\n66\u00c2\u00b0S4\\n19*20\\n66*36\\n1941\\n66*5\\n20*2\\n65*38\\n20*25\\n65*1 1\\n20*45\\nS443\\n21* 13\\n64*13\\n21*39\\n63*43\\n22 5\\n63*11\\n22*32\\n62*38\\n23\\n62*4*\\n21\\n18*39\\n61\u00c2\u00b0 31\\n18*57\\n679\\n19* 16\\n66 s\\n20*1?\\n65*52\\n4666\\n19*37\\n23\\n19*58\\n65*58\\n20J9\\n65 33\\n20*41\\n85*7\\n21*3\\n64\u00c2\u00b0\\n21*27\\nII\\n39 64\\n21*52\\n63*42\\n22*17\\n63*13\\n22*43\\n6241\\n23\u00c2\u00b0 o\\n62\u00c2\u00b0 8\\n23*38\\n61*34\\n24*8\\nSl\u00c2\u00b0\\n22\\n19*32\\n66 38\\n19*52\\n66 16\\n20 33\\n65*27\\n20*55\\n65\u00c2\u00b0 3*\\n2117\\n6437\\n21*40\\n6410\\n22\u00c2\u00b0 3\\n63V\\n22*0\\n6313\\n22*53 23*19\\n6243 62*11\\n23*46\\n61*40\\n24* l*\\n61*7\\n24*44\\n60*32\\nl*fi4\\n59 56\\n23\\n20*25\\n6547\\n20*47\\n65*23\\n2f8\\n21*29\\n6458 6433\\n21*52\\n64 8\\nZt 13\\n63*41\\n22*37\\n6313\\n23*2*\\n62*44\\n23 27\\n62*15\\n23*54\\n61*44\\n24*21\\n61\u00c2\u00b0 13\\n24*49\\n6044\\n25*18\\n60*6\\n25*47\\n53*31\\n26*18\\n58*54\\n24\\n21* \u00c2\u00bb9\\n64*55\\n21*39\\n64*31\\n22*1\\n64*5\\n22J24\\n63*40\\n46 23\\n22\\n63*14\\n|0\\n6246\\n\u00c2\u00a33*36\\n62* 19\\n24\\n61*48\\n24\u00c2\u00b026\\n61\u00c2\u00b0 18\\n24*53\\n60\u00c2\u00b047\\n25*21 25*49\\n60*15 5941\\n26*26\\n59 6\\n26*51\\n58*31\\n2723\\n57*53\\n25\\n22*11\\n64\u00c2\u00b0 5\\n2233\\n6339\\n22*56\\n63*14\\n23*18\\n62*48\\n23V\\n62*2*\\n24*7\\n61*53\\n24\\n6l\u00c2\u00b024\\n3i24\\n57\\nSO S3\\n25*24\\n60*22\\n25*52\\n59*50\\n26*20\\n59* 18\\n26*50\\n5844\\n27*21\\n58*3*\\n27\u00c2\u00b0tt\\n57*32\\n274? 28*11\\n5747 3/ II\\n28*26\\n56 54\\n29*27\\n55*5S\\no\\nrz;\\nP4\\n26\\n23*3\\n63\u00c2\u00b0\u00c2\u00bb5\\n23*25\\n62*49\\n23*47\\n62*23\\n24\u00c2\u00b0|3\\n61*56\\n24*25\\n61*28\\n25*1\\n60*59\\n25*28*\\n6030\\n25*S3\\n53 59\\n26*ai\\n59*27\\n2T49\\n53*55\\n27\u00c2\u00b0I9\\n58*21\\n28*J4\\n56*34\\n27\\n23*53\\n62*25\\n24*16\\n\u00c2\u00a31*58\\n24*40 25\\n6132\\n*5*\\n6!\u00c2\u00b0 5\\n25*29\\n37\\n25^?\\n6043\\n25*55\\n60*7\\n26*22\\n59\u00c2\u00b0 38\\n26*48\\n59*5\\n27*17\\n58*33\\n27*46\\n21*41\\n57*8\\n28*16\\n57*26\\n28*47\\n56*51*\\n29*19\\n56*15\\n29*52\\n55*38\\n30*2?\\n5459\\n28\\n24*44\\n61*36\\n25*7\\n61*9\\n25*56\\n60 14\\n25*22\\n59\u00c2\u00b046\\n26*48\\n59*16\\n27* J5\\n58*45\\n27*43\\n58* 13\\n28*12\\n57*42\\n29*12\\n56*32\\n29*43\\n1\\n30*16\\n55*2 i\\n30%tf\\n54*42\\n3T25 7\\n54* 3*\\n23\\n25*33\\n60*47\\n25*57\\n60*21\\n26*22\\n59*52\\n26*47\\n59*25\\n27*14\\n58*56\\n27*40\\n58*26\\n28*8\\n57*54\\n28*36*\\n57*22\\n29*5\\n5649\\n29*37\\n56*15\\n30*8\\n55*40\\n30*40\\n55*4\\n3**I3\\n54*27\\n31*48\\n53*4%\\n3221\\n53*9\\n30\\n26* s*\\n60\\n26*47\\n5933\\n59*6*\\n27*38\\n58*36\\n28*4\\n58*6\\n26.3Z\\n57*36\\n29*\\n5/4\\n29*28\\n56*32\\n29*58\\n55*38\\n30*36\\n55*34\\n31*2*\\n5448\\n31*34\\n5412\\n32*8\\n53\u00c2\u00b034\\n32*44\\n[52 54\\n33*19\\n52* I5\\n31\\n27*10\\n59* \u00c2\u00ab4\\n27*34\\n5o\u00c2\u00b046\\n28*3\\n58*15\\n28*27\\n57*4S\\n28*54\\n57 18\\n29*23\\n56*47\\n29*33\\n56 4l\\n29*51\\n56 15\\n3ft* 26\\nS5*42\\n30*52\\n55*8*\\n31 22\\n5434\\n3I\u00c2\u00b0SS\\n53*57\\n3229\\n53*21\\n33*2\\n52\u00c2\u00b042\\n33*39\\n52*3\\n34*15\\n51*23\\n32\\n27*56\\n58*28\\n28*45\\n57*43\\n28*23\\n57*59\\n23*43 23*17\\n57*31 57* I\\n56*\\n3\u00c2\u00a9\u00c2\u00b042\\n55*29\\n31\u00c2\u00b0 10\\n54*54\\n31*42\\n54*20\\n32*14\\n5344\\n32*46\\n53 8\\n33*21\\n52*31\\n33*56\\n51*52\\n34*3i\\n51\u00c2\u00b0 13\\n35*8\\n50*32\\n33\\n29\u00c2\u00b0 0\\n57*14\\n23*37\\n56*45\\n30*5\\n15\\n3032\\n55*49\\n31*1\\n55*13\\n31*31\\n54*39\\n32*1\\n54*5\\n32*32\\n53*32\\n*a*4;\\n58*56\\n33J38\\n52 20\\n34*12\\n51*42\\n33*54 34*28\\n52 8 Sl\u00c2\u00b03\u00c2\u00a3\\n34*47\\n51*3\\n35*z4\\n50 22\\n36\u00c2\u00b0\\n49*41\\n34\\n29*31\\n56*59\\n29*57\\n56*29\\n30*24\\nS6_\\n3\u00c2\u00abJV\\n55*29\\n31*20\\n54*58\\n31*43\\n54*27\\n32JI9\\n53*53\\n32*50\\n53*20\\n33*22\\n5244\\n35\u00c2\u00b0 6\\n50*50\\n35*38\\n50 14\\n36*15\\n49*35\\n36*53*\\n48\u00c2\u00b0S3\\n35\\n30* is;\\n56\u00c2\u00b0 15\\n30*42\\n55*46\\n31*\\n55 16\\n10 31\\n5444\\n3-rr\\n54*13\\nS34C\\n33\u00c2\u00b07\\n53\u00c2\u00b07\\n33*38\\n5234\\n34*14\\n51*58\\n34*42\\n51*22\\n35*n\\n5045\\n35\u00c2\u00b0 51\\n50*7\\n36*27\\n143 27\\n37 S\\n48*47\\n37*42\\n48 6\\n36\\n31\\n55*32\\n31*27\\n55*3\\n31*55\\n5433\\n32 23\\n54*1\\n32*53\\n53\u00c2\u00b0 28\\n33*2^\\n52\u00c2\u00b0 57\\n33*53\\n52*23\\n34 25\\nSl o 40\\n34*57\\n51\u00c2\u00b0 13\\n35*31\\n50*37\\n36*5\\n49 S9\\n49 21\\n37 16\\n148*42\\n37*53\\n48*1*\\n38*32*\\n47*20\\n37\\n31*45\\n5449\\n32*l2\\n54*20\\n32*40\\n5350\\n33*8\\n53*18\\n3338\\n52*46\\n34*9\\n5213\\n34\\n31*40\\n35*\\n51\u00c2\u00b0^\\n12 35\\n43\\n50*29\\n36*13\\n4952\\n36 Sl\\n49 15\\n37 o** 27 J 38 V\\n48\u00c2\u00b037 47*56\\n3842\\n47*16\\n39*26\\n4631\\n38\\n32*27\\nS4 9\\n3Ys?\\n53 38\\n33*24\\n53\u00c2\u00b0 8\\n3352\\n52*38\\n34*22\\n52 4\\n34\u00c2\u00b054\\n51*30\\n35*24\\n5056\\n35*51\\n50 21\\n36*29\\n4945\\n37*3\\n43 9\\n37*38\\n48*32\\n38*14\\n47*52\\n38*51\\n41 13\\n3928\\n46\u00c2\u00b032\\n40*7\\n45*5l\\n40sT\\n45*7\\n39\\n33\u00c2\u00b0 10\\n53*28\\n33\\n52 57\\n39 34\\n7\\n52 27\\n34*36\\n51*54\\n35*7\\n51*2 1*\\n35*37\\n50*49\\n36*9\\n50*15\\n36*41\\n49*39\\n37*15\\n4-9*3\\n37*48\\n48\u00c2\u00b0\\n26 47\\n38*24\\n48\\n39\\n47*io\\n39*36\\n46*30\\n40*i3\\n4545\\n40\\n33*52\\n52*48\\n34*21\\n52*17\\n\u00c2\u00a74?3?\\n52*9\\n34*50\\n51*46\\n35*18\\n5M4\\n35*49\\nS04I\\n36*20\\n50 8\\n36\u00c2\u00b0S3*\\n49 33\\n37*25\\n4\u00e2\u0082\u00acst\\n37*58\\n48*22\\n38*33\\n47*45\\n39*8\\n4/6\\n3944\\n4628\\n40*20\\n45*48\\n40*58\\n43*8\\n41*37\\n44*25\\n41\\n35*3\\n51*37\\n35\u00c2\u00b03i\\nSlV\\n36*1\\n50 33\\n36*31\\nSO* 1\\n37*3\\n49*27\\n37*35\\n48*53\\n38*7\\n48*17\\n38*41\\n47*41\\n39*16\\n47*4\\n39*51\\n46 25\\n40*27\\n45*47\\n41\u00c2\u00b0 5\\n45*7\\n41*42\\n44*26\\n42*22*\\n43*44\\n42\\n35*14\\n35*43\\nSO* 59\\n36* 12*\\n50*28\\n36*42\\n49S4J\\n37*13\\n49* 2l\\n37*44\\n48*48\\n38*17\\n48*13\\n38*49\\n47\u00c2\u00b037\\n39*23\\n47* r\\n39 58\\n46*24\\n40 34\\n45*46\\n41*9\\n45*7.\\n4147\\n4427\\n42 26\\n43*46\\n43*4", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0047.jp2"}, "44": {"fulltext": "30\\nBROWN SHARPE MFG. CO.\\nNATURAL SIXE.\\nDeg.\\n0\\n10\\n20\\n30\\n40\\n50\\n1\\n60\\n.00000\\n.00291\\n.00581\\n00872\\n.01163\\n01454\\n.01745\\n89\\n1\\n.01745\\n.02036\\n02326\\n.02617\\n.02908\\n.03199\\n.03489\\n88\\n2\\n.03489\\n.03780\\n.04071\\n.04361\\n.04652\\n.04943\\n.05233\\n87\\n3\\n.05233\\n.05524\\n.05814\\n.06104\\n.06395\\n.06685\\n.06975\\n86\\n4\\n.06975\\n.07265\\n07555\\n.07845\\n.08135\\n.08425\\n.08715\\n85\\n5\\n.08715\\n.09005\\n.09295\\n.09584\\n.09874\\n.10163\\n.10452\\n84\\nC\\n.10452\\n.10742\\n.11031\\n.11320\\n.11609\\n.11898\\n.12186\\n83\\n7\\n.12180\\n.12475\\n.12764\\n.13052\\n13341\\n13629\\n.13917\\n82 i\\n8\\n.13917\\n.14205\\n14493\\n14780\\n15068\\n.15356\\n15643\\n81\\n9\\n15643\\n15930\\n.16217\\n16504\\n.16791\\n.17078\\n.17364\\n80\\n10\\n.17364\\n.17651\\n.17937\\n.13223\\n.18509\\n.18795\\n.19080\\n79\\n11\\n.19080\\n.19366\\n.19651\\n.19936\\n.20221\\n20500\\n.20791\\n78\\n12\\n.20791\\n.21075\\n.21359\\n.21644\\n.21927\\n.22211\\n.22495\\n77\\n13\\n22495\\n.22778\\n.23061\\n.23344\\n.23627\\n.23909\\n.24192\\n76\\n14\\n.24192\\n24474\\n.24756\\n.25038\\n.25319\\n.25600\\n.25881\\n75\\n15\\n.25881\\n.26162\\n.26443\\n.26723\\n.27004\\n.27284\\n.27563\\n74\\n16\\n.27563\\n.27843\\n.28122\\n.28401\\n.28680\\n.28958\\n.29237\\n73\\n17\\n.29237\\n.29515\\n.29793\\n.30070\\n.30347\\n.30624\\n.30901\\n72\\n18\\n.30901\\n.31178\\n.31454\\n.31730\\n.32000\\n.32281\\n.32556\\n71\\n19\\n.32556\\n.3283L\\n.33100\\n.33380\\n.33654\\n.33928\\n.34202\\n70\\n20\\n.34202\\n.34475\\n.34748\\n.35020\\n.35293\\n.35565\\n.35836\\n69\\n21\\n.35836\\n.36108\\n.36379\\n.36650\\n.36920\\n.37190\\n.37460\\n68\\n22\\n.37460\\n.37730\\n.37999\\n.38268\\n38536\\n.38805\\n.39073\\n67\\n23\\n.39073\\n.39340\\n.39607\\n.39874\\n.40141\\n.40407\\n.40673 I\\n66\\n24\\n.40673\\n.40989\\n.41204\\n.41469\\n.41733\\n.41998\\n.42261\\n65\\n25\\n.42261\\n42525\\n.42788\\n.43051\\n.43313\\n.43575\\n.43837\\n64\\n26\\n.43837\\n.44098\\n.44359\\n.44619\\n.44879\\n.45139\\n.45399\\n63\\n27\\n.45399\\n.45658\\n.45916\\n.46174\\n.46432\\n.46690\\n.46947\\n62\\n28\\n.46947\\n.47203\\n.47460\\n.47715\\n.47971\\n.48226\\n.48481\\n61\\n29\\n.48481\\n.48735\\n.43989\\n.49242\\n.49495\\n49747\\n.50000\\n60\\n30\\n.50000\\n50251\\n.50503\\n.50753\\n.51004\\n.51254\\n.51503\\n59\\n31\\n.51503\\n.51752\\n52001\\n.52249\\n52497\\n52745\\n.52991\\n58\\n32\\n.52991\\n53238\\n53484\\n.53730\\n53975\\n.54219\\n.54463\\n57\\n33\\n54463\\n54707\\n.54950\\n.55193\\n.55436\\n.55677\\n.55919\\n56\\n34\\n.55919\\n.56160\\n.56400\\n.56640\\n.56880\\n.57119\\n57357\\n55\\n35\\n.57357\\n57595\\n57833\\n.58070\\n.58306\\n58542\\n.58778\\n54\\n36\\n.58778\\n.59013\\n.59243\\n59482\\n.59715\\n.59948\\n.60181\\n53\\n37\\n.60181\\n.60413\\n.60645\\n.60876\\n.61106\\n.61336\\n.61566\\n52\\n38\\n.61560\\n.61795\\n62023\\n.62251\\n.62478\\n62705\\n.62932\\n51\\n39\\n.62932\\n.63157\\n63383\\n.63607\\n.63832\\n.64055\\n.64278\\n50\\n40\\n.64278\\n.64501\\n.64723\\n.64944\\n.65165\\n.65386\\n.65605\\n49\\n41\\n.65605\\n.05825\\n.66043\\n.66262\\n66479\\n.66696\\n.66913\\n48\\n1 42\\n.66913\\n.67128\\n67344\\n.67559\\n.67773\\n.67986\\n.68199\\n47\\n43\\n.68199\\n.68412\\n.68624\\n68835\\n.69046\\n.69256\\n.69465\\n46\\n44\\n69465\\n.69674\\n.69883\\n70090\\n70298\\n70504\\n70710\\n45\\n60\\n50\\n40\\n30\\n20\\n10\\nC\\nDeg.\\nNATURAL COSINE.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0048.jp2"}, "45": {"fulltext": "PROVIDENCE, R. 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CO.\\nNATURAL TANGENT.\\nDeg.\\n0\\n10\\nCO\\nSO\\n40\\n50\\n60\\n.00000\\n.00290\\n.00581\\n.00872\\n.01163\\n.01454\\n.01745\\n89\\n1\\n.01745\\n.02036\\n.02327\\n.02618\\n.02909\\n.03200\\n.03492\\n88\\n2\\n.03492\\n.03783\\n.04074\\n.04366\\n.04657\\n.04949\\n.05240\\n87\\n3\\n.05240\\n.05532\\n.05824\\n.06116\\n.06408\\n.06700\\n.06992\\n86\\n4\\n.06992\\n.07285\\n.07577\\n.07870\\n.08162\\n.08455\\n.08748\\n85\\n5\\n.08748\\n.09042\\n.09335\\n.09628\\n.09922\\n10216\\n.10510\\n84\\n6\\n.10510\\n.10804\\n.11099\\n.11393\\n.11688\\n.11983\\n.12278\\n83\\n7\\n.12278\\n.12573\\n.12869\\n.13165\\n.13461\\n13757\\n.14054\\n82\\n8\\n.14054\\n.14350\\n14647\\n14945\\n.15242\\n.15540\\n.15838\\n81\\n9\\n.15838\\n.16186\\n16435\\n.16734\\n.17033\\n.17332\\n.17632\\n80\\n10\\n.17632\\n.17932\\n.18233\\n.18533\\n.18834\\n.19136\\n.19438\\n79\\n11\\n.19438\\n19740\\n.20042\\n.20345\\n.20648\\n.20951\\n.21255\\n78\\n12\\n.21255\\n.21559\\n.21864\\n.22169\\n.22474\\n.22780\\n23086\\n77\\n13\\n.23086\\n.23393\\n.23700\\n.24007\\n.24315\\n.24624\\n.24932\\n76\\n14\\n.24932\\n.25242\\n.25551\\n.25861\\n.26172\\n.26483\\n.26794\\n75\\n15\\n.26794\\n.27106\\n.27419\\n.27732\\n.28046\\n.28360\\n.28674\\n74\\n16\\n.28674\\n.28989\\n.29305\\n.29621\\n.29938\\n30255\\n.30573\\n73\\n17\\n.30573\\n.30891\\n.31210\\n.31529\\n.31850\\n.32170\\n.32492\\n72\\n18\\n.32492\\n.32813\\n.33136\\n.33459\\n.33783\\n.34107\\n.34432\\n71\\n19\\n.34432\\n.34758\\n.35084\\n.35411\\n.35739\\n.36067\\n.36397\\n70\\n20\\n.36397\\n.36726\\n.37057\\n.37388\\n.37720\\n.38053\\n.38386\\n69\\n21\\n.38386\\n.38720\\n.39055\\n.39391\\n.39727\\n.40064\\n.40402\\n68\\n22\\n.40402\\n.40741\\n.41080\\n.41421\\n.41762\\n.42104\\n.42447\\n67\\n23\\n.42447\\n.42791\\n.43135\\n.43481\\n.43827\\n.44174\\n.44522\\n66\\n24\\n.44522\\n.44871\\n.45221\\n.45572\\n.45924\\n.46277\\n.46630\\n65\\n25\\n.46630\\n.46985\\n.47341\\n.47697\\n.48055\\n.48413\\n.48773\\n64\\n26\\n.48773\\n.49133\\n.49495\\n.49858\\n.50221\\n.50586\\n.50952\\n63\\n27\\n.50952\\n.51319\\n.51687\\n.52056\\n.52427\\n.52798\\n.53170\\n62\\n28\\n.53170\\n.53544\\n.53919\\n.54295\\n54672\\n.55051\\n.55430\\n61\\n29\\n.55430\\n.55811\\n.56193\\n.56577\\n.56961\\n.57347\\n.57735\\n60\\n30\\n57705\\n.58123\\n.58513\\n.58904\\n.59297\\n.59690\\n.60086\\n1 59\\n31\\n.60086\\n.60482\\n.60880\\n.61280\\n.61680\\n.62083\\n.62486\\n1 58\\n32\\n.62486\\n62892\\n.63298\\n.63707\\n.64116\\n.64528\\n.64940\\n1 57\\n33\\n.64940\\n65355\\n.65771\\n.66188\\n.66607\\n.67028\\n.67450\\n56\\n34\\n67450\\n.67874\\n.68300\\n.68728\\n.69157\\n.69588\\n.70020\\n55\\n35\\n.70020\\n.70455\\n.70891\\n.71329\\n.71769\\n.72210\\n.72654\\n54\\n36\\n.72654\\n73099\\n73546\\n.73996\\n.74447\\n.74900\\n75355\\n53\\n37\\n75355\\n75812\\n.76271\\n.76732\\n.77195\\n.77661\\n.78128\\n52\\n38\\n.78128\\n.78598\\n.79069\\n.79543\\n.80019\\n.80497\\n80978\\n51\\n39\\n.80978\\n.81461\\n.81946\\n.82433\\n.82923\\n.83415\\n.83910\\n50\\n40\\n.83910\\n.84400\\n.84900\\n.85408\\n.85912\\n.86419\\n86928\\n1 49\\n41\\n.86928\\n.87440\\n87955\\n.88472\\n.88992\\n.89515\\n.90040\\nI 48\\n42\\n.90040\\n.90568\\n.91099\\n.91633\\n.92169\\n.92709\\n.93251\\n47\\n43\\n.93251\\n.93796\\n.94345\\n.94896\\n95450\\n.96008\\n.96568\\n46\\n44\\n.96568\\n.97132\\n.97699\\n.98269\\n.98843\\n.99419\\n1.0000\\n45\\nGO\\n1\\n50\\n40\\n30\\n20\\n10\\n0\\nDeg.\\nNATURAL COTANGENT.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0050.jp2"}, "47": {"fulltext": "PROVIDENCE, R. I.\\n33\\nNATURAL TANGENT.\\nDeg.\\no\\n10\\n20\\n30\\n40\\n50\\n60\\n45\\n1.0000\\n1.0058\\n1.0117\\n1.0176\\n1.0235\\n1.0295\\n1.0355\\n44\\n46\\n1.0355\\n1.0415\\n1.0476\\n1.0537\\n1 0599\\n1.0661\\n1.0723\\n43\\n47\\n1.0723\\n1.0786\\n1.0849\\n1.0913\\n1.0977\\n1 1041\\n1.1106\\n42\\n48\\n1.1106\\n1.1171\\n1.1236\\n1.1302\\n1.1369\\n1.1436\\n1.1503\\n41\\n49\\n1.1503\\n1.1571\\n1 1639\\n1.1708\\n1.1777\\n1.1847\\n1.1917\\n40\\n50\\n1.1917\\n1.1988\\n1.2059\\n1.2131\\n1.2203\\n1.2275\\n1 2349\\n39\\n51\\n1.2349\\n1.2422\\n1.2496\\n1.2571\\n1.2647\\n1.2723\\n1.2799\\n38\\n52\\n1.2799\\n1.2876\\n1.2954\\n1.3032\\n1.3111\\n1.3190\\n1.3270\\n37\\n53\\n1.3270\\n1.3351\\n1.3432\\n1.3514\\n1.3596\\n1.3680\\n1.3763\\n36\\n54\\n1.3763\\n1.3848\\n1.3933\\n1.4019\\n1.4106\\n1.4193\\n1.4281\\n35\\n55\\n1.4281\\n1.4370\\n1.4459\\n1.4550\\n1.4641\\n1.4733\\n1.4825\\n34\\n56\\n1.4825\\n1.4919\\n1.5013\\n1.5108\\n1.5204\\n1.5301\\n1.5398\\n33\\n57\\n1.5398\\n1.5497\\n1.5596\\n1.5696\\n1.5798\\n1.5900\\n1.6003\\n32\\n58\\n1.6003\\n1.6107\\n1.6212\\n1.6318\\n1.6425\\n1.6533\\n1.6642\\n31\\n59\\n1.6642\\n1.6753\\n1.6864\\n1.6976\\n1.7090\\n1.7204\\n1.7320\\n30\\n60\\n1 7320\\n1.7437\\n1.7555\\n1 7674\\n1.7795\\n1.7917\\n1.8040\\n29\\n61\\n1.8040\\n1.8164\\n1.8290\\n1.8417\\n1.8546\\n1.8676\\n1.8807\\n28\\n62\\n1.8807\\n1.8940\\n1.9074\\n1.9209\\n1.9347\\n1.9485\\n1.9626\\n27\\n63\\n1.9626\\n1.9768\\n1.9911\\n2.0056\\n2.0203\\n2.0352\\n2.0503\\n26\\n64\\n2.0503\\n2.0655\\n2.0809\\n2.0965\\n2.1123\\n2.1283\\n2.1445\\n25\\n65\\n2.1445\\n2.1609\\n2.1774\\n2.1943\\n2.2113\\n2.2285\\n2.2460\\n24\\n66\\n2.2460\\n2.2637\\n2.2816\\n2.2998\\n2.3182\\n2.3369\\n2.3558\\n23\\n67\\n2.3558\\n2.3750\\n2.3944\\n2.4142\\n2.4342\\n2.4545\\n2.4750\\n22\\n68\\n2.4750\\n2.4959\\n2.5171\\n2.5386\\n2.5604\\n2.5826\\n2.6050\\n21\\n69\\n2.6050\\n2.6279\\n2.6510\\n2.6746\\n2.6985\\n2.7228\\n2.7474\\n20\\n70\\n2.7474\\n2.7725\\n2.7980\\n2.8239\\n2.8502\\n2.8770\\n2.9042\\n19\\n71\\n2.9042\\n2.9318\\n2.9600\\n2.9886\\n3.0178\\n3.0474\\n3.0776\\n18\\n72\\n3.0776\\n3.1084\\n3.1397\\n3.1715\\n3.2040\\n3.2371\\n3.2708\\n17\\n73\\n3.2708\\n3.3052\\n3.3402\\n3.3759\\n3.4123\\n3.4495\\n3.4874\\n16\\n74\\n3.4874\\n3.5260\\n3.5655\\n3.6058\\n3.6470\\n3.6890\\n3.7320\\n15\\n75\\n3.7320\\n3.7759\\n3.8208\\n3.8667\\n3.9136\\n3.9616\\n4.0107\\n14\\n76\\n4.0107\\n4.0610\\n4.1125\\n4.1653\\n4.2193\\n4.2747\\n4.3314\\n13\\n77\\n4.3314\\n4.3896\\n4.4494\\n4.5107\\n4.5736\\n4.6382\\n4.7046\\n12\\n78\\n4.7046\\n4.7728\\n4.8430\\n4.9151\\n4.9894\\n5.0658\\n5.1445\\n11\\n79\\n5.1445\\n5.2256\\n5.3092\\n5.3955\\n5.4845\\n5.5763\\n5.6712\\n10\\n80\\n5.6712\\n5.7693\\n5.8708\\n5.9757\\n6.0844\\n6.1970\\n6.3137\\n9\\n81\\n6.3137\\n6.4348\\n6.5605\\n6.6911\\n6.8269\\n6.9682\\n7.1153\\n8\\n82\\n7.1153\\n7.2687\\n7.4287\\n7.5957\\n7.7703\\n7.9530\\n8.1443\\n7\\n83\\nS.1443\\n8.3449\\n8.5555\\n8.7768\\n9.0098\\n9.2553\\n9.5143\\n6\\n84\\n9.5143\\n9.7881\\n10.078\\n10.385\\n10.711\\n11.059\\n11.430\\n5\\n85\\n11.430\\n11.826\\n12.250\\n12.706\\n13.196\\n13.726\\n14.300\\n4\\n86\\n14.300\\n14.924\\n15.604\\n16.349\\n17.169\\n18.075\\n19.081\\n3\\n87\\n19.081\\n20.205\\n21.470\\n22.904\\n24.541\\n26.431\\n28.636\\n2\\n88\\n28.636\\n31.241\\n34.367\\n38.188\\n42.964\\n49.103\\n57.290\\n1\\n89\\n57.290\\n68.750\\n85.939\\n114.58\\n171.88\\n343.77\\n00\\n60\\n50\\n40\\n30\\n20\\n10\\n0\\nBeg.\\nNATURAL COTANGENT.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0051.jp2"}, "48": {"fulltext": "34\\nBROWN SHARPE MFG. CO.\\nCHAPTER. IV.\\nWORM AND WORM WHEEL.\\n(Fig. 8.)", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0052.jp2"}, "49": {"fulltext": "PROVIDENCE, R. I. 35\\nFORMULAS.\\nL lead of worm.\\nN number of teeth in gear.\\nvi threads or turns per inch in worm,\\nd diameter of worm.\\nd diameter of hob.\\nT throat diameter.\\nB blank diameter (to sharp corners).\\nC distance between centers.\\no thickness of hob-slotting cutter.\\nwidth of lands at bottom.\\nb pitch circumference of worm.\\nv width of worm thread tool at end.\\nw width of worm thread at top.\\nP diametral pitch.\\nP circular pitch,\\nj- addendum and module.\\nt thickness of tooth at pitch line.\\nt n normal thickness of tooth.\\nclearance at bottom of tooth.\\nD working depth of tooth.\\nD whole depth of tooth.\\nd angle of tooth of worm wheel with its axis, or the\\nangle of thread of worm with a line at right angles to its axis.\\nIf the lead is for single, double, triple, etc., thread, then\\nIv P 2 F, 3 P etc.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0053.jp2"}, "50": {"fulltext": "36 BROWN SHARPE MFG. CO.\\na 6o\u00c2\u00b0 to 90\\nL l\\nm\\np,_ 7Tl\\nD\\nN 2\\nNP __ N\\n^r P\\nT _ 2 j\\nb 7i {d 2^)\\ntan d _ -I Practical onl y when width of wheel on wheel pitch circle\\n~b is not more than z pitch diameter of worm.\\nn /COS 6\\n1 d\\nr 2 s\\n2\\nr\\nr D\\nC s\\n2\\nB T 4- 2 (r 1 r 1 COS -1 A measurement of sketch is generally\\n2/ sufficient.\\n-335 P\\n2\\nd d 2/\\nz/ .3iP\\nw -335 p\\nNote. The notations and formulas referring- to tooth parts, given on page 5 for\\nspur gears, apply to worm wheels, and are here used.\\nNote. Hob and worm should be marked, as per example\\n4 turns per i single .25 P .25 L.\\n2 turns per 1 double .25 I .50 L.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0054.jp2"}, "51": {"fulltext": "PROVIDENCE, R. I.\\n37\\nUNDERCUT IN WORM WHEELS.\\nIn worm wheels of less than 30 teeth the thread of the worm\\n(being 29 interferes with the flank of the gear tooth. Such\\na wheel finished with a hob will have its teeth undercut. To\\navoid this interference two methods may be employed.\\nFirst Met/iod. Make throat diameter of wheel\\nN\\nT cos 2 14^\\n4 J\\nor\\n\u00e2\u0080\u00a2937 N\\nP\\n4s\\nThis formula increases the throat diameter, and conse-\\nquently the center distance. The amount of the increase can\\nbe found by comparing this value of T with the one as obtained\\nby formula on page 36. To keep the original center distance,\\nthe outside diameter of the worm must be reduced by the\\nsame amount the throat diameter is increased.\\nSecond Method. Without changing any of the dimensions\\nwe found by the formulas given on page 36, we can avoid the\\ninterference to be found in worm wheels of less than 30 teeth\\nby simply increasing the angle of worm thread. We find the\\nvalue of this angle by the following formula\\nLet there be\\n2 y angle oi worm ihreaa.\\nN number of teeth in worm wheel.\\ncos y J _ jL\\ny N\\nFrom this formula we obtain the following values\\nN\\n29\\n3\u00c2\u00b0X\\n28\\n3i\\n27\\n3i#\\n26\\n32X\\n25\\n32%\\n24 23\\n33^34^\\n22\\n35\\n21\\n36\\n20\\n37\\n2 y\\n38 I 39 40 ;4I^\\n15 14\\n13\\n42^44^\\n46\\n2\\n48\\nAs this latter formula involves the making of new hobs in\\nmany cases, on account of change of angle, we prefer to reduce\\nthe diameter of worm as indicated by first method, if the dis-\\ntance of centers must be absolute.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0055.jp2"}, "52": {"fulltext": "5ROWN SHARPS MFG. CO.\\nP\\ni4\\nC\\nH\\nCO\\nto\\nC\\nc\\nC\\nc\\nGO\\nw\\nc\\nc\\nP-l\\ni-l\\n1\\nCD\\nO\\nCD\\n;o\\no\\nCD\\n-i\\nCD\\n;o\\no\\nii n\\nto\\nico\\nCO\\nr:\\nCD\\ncd\\no\\no\\nCD\\n^H\\n-CD\\n-n|-r\\nO\\nCO\\nCD\\n10\\nCD\\nO\\n.0\\nv\\nr^-\\nCO\\nf=l\\no\\ni\\ntO\\nc 1\\ntO\\no\\nCO\\nO\\nen\\niH\\n_\\n10\\nto\\nto\\no\\n\u00c2\u00bb.H\\nS\\nV-\\nCO\\n0\\ncm\\nCD\\n\u00e2\u0096\u00a0*r\\ntO\\nCO\\nC3 CN\\nr~-\\nCO\\n,H\\nc;\\niO O\\n\u00e2\u0080\u00a2\u00c2\u00abr\\nCD\\nCD\\nto\\nCD\\nO\\nCO\\n51\\n,^_\\nCD CD\\nCO\\niO\\nCD\\n1\\n-a-\\nmS-\\nto\\n1\\nCO\\n\u00e2\u0096\u00a0s\\nCO\\nV\\n3\\nIO\\n5\\n51\\nCD\\nV.\\nCM\\nO\\ntO CM\\nCO\\nr\\nCO\\nco\\nCO\\nCM\\nCO\\n-T\\nCO\\n-to\\nCO\\nCM\\nCN\\nO CM\\nCO\\nCO\\nSI\\n0\\ntO\\n-1.\\n-T\\nCD\\nc 4 1 c 4-\\nCO\\nCO\\nCO\\nCO\\nCO\\nCD\\nCO\\nO\\nco\\nCD\\nIO\\nCO\\ns\\n51\\n1\\nZ 1\\n1\\n1\\nCD\\nCO\\nr-\\nCD\\nIO\\nLO\\nCO\\nCO\\nCO\\nCM\\nCO\\nCO\\nl-~\\nCO\\nCO\\nCD\\nto\\nCM\\nto\\nCO\\nCD\\n51\\no\\nCD\\nI--\\na\\n~o\\n1\\nC\\n4\\n\u00c2\u00ab1\\n~o CO\\nCO\\nCO\\nCO\\ncm\\ncm\\nCM\\nr^\\nCO\\nCO\\nCM\\nto\\nCO\\n51\\no\\ni\\n\u00c2\u00b0li\\nCI\\na\\nLTD\\nr 4\\nco\\nco\\nco\\nCO\\nCM\\ncm\\nCM\\nCO\\nco\\nCD\\no\\n%r\\n\\\\_\\nCM\\nCM\\ncd\\nc~\\nee\\nCO\\ntO\\n0:\\ntO\\nCM co\\nCI\\nCM\\nto\\nCO\\nCM\\nCO\\ncO\\nCD\\nto\\nco\\nco\\nCO\\nCs\\nCM\\nCM\\nc.\\nto\\nCO\\nCN\\nm|w\\n10\\nCD\\nCM\\n1^\\nP\u00e2\u0080\u0094 co\\nCD\\nr^\\nCD\\nV\\n00\\nCO\\nC 1\\nIO\\nD\\nCO\\nCO\\nCM\\nD\\nn\\nCO\\nto\\nCM\\nCM\\nO\\nCM\\nCM\\nCM\\nN\\nCM\\ncm\\nCO\\n-s-\\nCD\\nCN\\nCO\\nO\\nCO\\n0\\nIO\\nCM\\nc t\\no\\nCO\\nc\\nCO\\nCO\\nCO\\nCM\\n1\\ncm\\nCO\\nc\\nCM\\nc\\nCM\\nCM\\nCM\\nCN\\nCN\\nCM\\n_ M\\nCO\\nCM\\nCD\\nCM\\nCO\\nCO\\na\\nCO\\nr 1\\nCO\\nCO\\ntO\\nCM\\nCM\\nCM\\nCO\\nD\\nCM\\nCD\\nc\\nCM\\nCD\\nCM\\nCM\\nCM\\nLO\\n1\\n=0\\nCM\\n1\\n1^\\nCO\\n1\\nO\\nIO\\nc\\n\u00e2\u0080\u00a2a\\nJ*\\nJO\\n7\\nCO\\n\u00e2\u0080\u00a27\\n-O\\n7\\n01\\nCO\\nCO\\nCM\\nCN\\nio\\nCO\\nCO\\nCM\\nCM CM\\nCM\\n-J\\nCO\\n34\\nCO\\ntO\\ntO\\ncm\\nO\\nCO\\nCO\\nCO\\nCO\\ni5\\nto\\nc 4\\nCO\\nco\\nCM\\nCM\\nCM\\nCM\\ncm\\n1 1\\n,!_\\n1\\n1\\nCD\\nCO\\nO\\nCM\\nCD\\nCD\\nCM\\nCM\\nCD\\nc 4-\\nCO\\nCO\\ncm\\nCM\\nCM\\nCM\\n~J_\\nCM\\nCM\\nLO\\nx=*-\\nCO\\ncm\\nCM\\nCM\\nLO\\n-T\\nCO CO\\nO\\nCO\\nCM\\nO\\nCO\\n-3\\nC3\\nCM CM\\n7\\n(J?\\nCO\\nCM\\nD.\\nCM\\nOl\\nI-\\nCO\\nTl\\no\\n2\\nCM\\nCD\\nCO\\nCO\\nb\\nto\\ni-\\nCD\\nCO\\nCM\\nCM\\nCM\\nr-\\nCO\\nO\\nCO V)\\nIO\\ncc\\nCO\\nCO\\nCM\\nCO\\n10\\nCM\\nc-\\n^t\\n-\u00e2\u0080\u00a27\\n\u00c2\u00abJ\\nCM CM\\n[5\\n-o\\nCO\\nCM\\nCM\\nCM\\no\\nCD\\n.a\\nCM\\ntO\\nr*-\\nex a\\nto\\nCD\\no\\nI-j\\nCM\\n1\\nCM\\nCM\\nto\\ntO\\nT\\nI\\ni\u00c2\u00ab\\nX\\n11\\nT.\\nC-r \u00e2\u0080\u009e|x\\nX\\nf.\\nD\\nCO o\\nz z\\ncc\\n*H\\np-i\\nT-i\\n\u00c2\u00abH PH\\n51\\n^1\\n\u00e2\u0096\u00a051\\n51\\n5:\\nLli\\n_l\\nQ.\\n\u00e2\u0080\u00a2s\\naai3i/\\\\i\\\\\\n\\\\Q\\nHOlId", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0056.jp2"}, "53": {"fulltext": "PROVIDENCE, R. I.\\n39\\nt o\\nCD\\no\\n-h\\nCN\\nol\\nCO\\ncT\\nLO\\ncj_\\nCM\\nI\\nCO\\nen\\nCO\\nLO\\nO 1\\non\\nCO\\nCM\\no 1\\nen\\no^\\nen\\nSO\\nCD\\nCD\\nCD\\nen\\nCD\\nCO\\nCO\\nol\\nen\\nco\\nen\\ncm\\nCO\\nO 1\\nCO\\nCO\\no 1\\nCO\\nco\\nCO\\no 1\\nLO\\nLO\\n\u00c2\u00b0co\\nco\\nCO\\nOl\\nCO\\nen\\no I\\nCO\\nCO\\nol\\nCO\\niCD\\nCD\\nCD\\nm\\n\u00c2\u00bbi\\nCO\\nc cn\\nCM\\no 1\\ncD\\nc 1\\noT\\nen\\no 1\\nCD\\nco\\nCM\\nc 1\\nCO\\nCO\\n\u00e2\u0096\u00a0=3-\\nLO\\nCN\\nLO\\n~~CM\\noT\\nco\\nLO\\n1\\nlo\\no 1\\nco\\nCO\\nO 1\\ni CO\\nCO\\nCO\\nCO\\nm|-*\\nCN\\n1\\nCO\\nCO\\nol\\ncO\\no 1\\n1^-\\n-3-\\no 1\\nCO\\nW\\nCM\\no 1\\nCO\\nCO\\nCN\\nco\\nCN\\nco\\no 1\\nLO\\nLO\\no 1\\nh-\\nCO\\no\\nlO\\nCM\\nco\\noT\\nCN\\no 1\\no\\no\\no\\ntH\\nlO\\nLO\\nol\\nCO\\nCD\\nCO\\nc 1\\nCO\\nc\u00c2\u00bb\\ncT\\nCO\\nCO\\nol\\nCD\\nco\\nCO\\no 1\\nLO\\ncm\\noT.\\nLO\\nLO\\n1\\nco\\nCO\\noT\\nCO\\no 1\\nLO\\no 1\\nCO\\nCO\\no 1\\nCO\\nco\\nCM\\no 1\\nCO\\noT\\nCO\\no\\n\u00c2\u00b0co\\nCM\\nol\\no\\nCD\\nCD\\nCO\\ncm\\nCO\\nOl\\nLO\\noT\\nLO\\no 1\\nLO\\n5\\nen\\nCM\\n1\\ncD\\noT\\nco\\no 1\\nCO\\nen\\nCO\\nc 1\\nCO\\nCO\\nCM\\nol\\nCO\\noT\\nCO\\no 1\\nCO\\n~LO\\nLO\\nO\\nCN\\nCM\\nen\\nCO\\no 1\\nCN\\nCO\\no 1\\nCN\\nco\\nCM\\no\\no\\nLO\\n1\\nr-\\\\\\nv4\\noT\\nCO\\nLO\\nol\\n-4-\\nLO\\nol\\nCO\\nCO\\n0|\\nCM\\nC T\\nLO\\nCO\\nCO\\no 1\\nCO\\nLO\\nCM\\no 1\\nCO\\noT\\nCM\\no 1\\nCO\\nLO\\no I\\nCM\\nCN\\nCO\\nCO\\nCM\\nCM\\nCM\\no 1\\nCM\\no 1\\nCM\\nco\\nCO\\nCO\\nCO\\nHoi\\nCO\\nCN\\ncl\\nco\\noT\\nCO\\nco\\nco\\noV\\nCO\\noT\\nCO\\nCM\\no 1\\nCO\\nCM\\nLO\\nCM\\n~CM\\no 1\\nCM\\nco\\nCO\\no 1\\nCN\\nCN\\nCN\\ncn\\noT\\nCM\\nco\\noT\\nCM\\nl\\no 1\\no 1\\nCM\\n5 o\\nCD\\nCD\\nCO\\no\\noT\\nLO\\nel\\nCO\\n-3-\\nol\\nCO\\nCO\\nol\\nCO\\nCN\\no 1\\nCO\\nr-^\\n1\\no 1\\nCM\\nCO\\nc 1\\nCM\\no 1\\nCM\\noT\\nCM\\n:z\\nLO\\no 1\\nLO\\no 1\\no 1\\nol\\nLO\\nOD\\nol\\nCO\\nol\\nCO\\n1\\nCO\\nol\\nCO\\nCO\\nCM\\n1\\nCO\\nCM\\noT\\nCO\\nCn\\no i\\nCM\\nCO\\nCO\\nCM\\nCM\\nen\\noT\\nCM\\nCM\\noT\\nCM\\nLO\\no 1\\nCM\\nen\\nLO\\nLO\\nOj_\\nen\\no 1\\nol\\nCD\\nCD\\nCD\\nto\\n\u00c2\u00a91\\ncO\\nCN\\nol\\nCO\\nT\\ncT\\nCO\\no\\noT\\nCO\\ncN\\nol\\nCO\\ncO\\no 1\\nCM\\nco\\nCO\\nCM\\nco\\nCN\\nol\\nCM\\noT\\nCM\\ncn\\no I\\nCM\\nCM\\no 1\\nCM\\nLO\\no l\\nen\\no 1\\no 1\\nen\\nCO\\nO 1\\nLO\\nCO\\no 1\\nCO\\nol\\n-3\\n\u00c2\u00a93\\nol\\nCO\\nol\\n\u00e2\u0096\u00a0en\\nol\\nCN\\nCM\\nol\\nCN\\no\\nCO\\nol\\nCM\\nen\\nCM\\no\\noT\\ncm\\nCM\\n1\\nco\\ncm\\n\u00e2\u0080\u00a2=3-\\nc|\\nCO\\nco\\nCO\\nL 0-\\nco\\nc 1\\nCM\\no 1\\nCM\\no 1\\nlo\\nCO\\nOl\\nH\u00c2\u00ab\\n\u00c2\u00a9i\\nen\\nLO\\nol\\nCN\\no\\nol\\nCN\\nCO\\nCN\\nCO\\nCO\\n1\\nCM\\nCM\\nol\\noT\\nLO\\no 1\\nCD\\nLO\\nO 1\\nol\\nCO\\no 1\\nCO\\no 1\\nCD\\nCN\\n1\\nLO\\nCM\\no 1\\nCM\\nol\\nCO\\noT\\nCD\\nO\\nO\\n\u00c2\u00a9i\\noT\\nCN\\nol\\nCN\\nCO\\nCN\\nCN\\nCM\\noT\\nCM\\nLO\\nLO\\n0|\\non\\nol\\nol\\nCO\\nol\\nCN\\nCO\\no 1\\nCN\\nO 1\\nCM\\no 1\\nCD\\n1\\nCO\\noT\\nCO\\no\\nLO\\n1\\nCO\\n\u00c2\u00a91\\ncO\\nCO\\nol\\nCN\\nen\\nCN\\n01\\nCN\\ncO\\nCN\\n1\\nCN\\noT\\nCM\\nCD\\n1\\nr-~\\nol\\nen\\noT\\nco\\n1\\nCO\\no I\\nCO\\nol\\nco\\nCM\\no 1\\nCM\\noT\\noo\\nlO\\noT\\noT\\ncb\\no I\\ns co\\nCO\\nCO\\nCO\\n\u00c2\u00a91\\nCO\\n01\\nCN\\nCN\\nCM\\nol\\nCN\\nCO\\noT\\nCM\\nCN\\nO 1\\nCM\\nLO\\nel\\nCO\\no 1\\na\\nCO\\no 1\\nCO\\nCO\\nCM\\n1\\nCM\\no 1\\nCD\\no\\nCO\\noT\\nCM\\noT\\nen\\n1\\nco\\nol\\n^co\\nCO\\nCO\\nCO\\nCO\\nC\u00c2\u00bb\\nCO\\ncT\\nCN\\nl-~-\\nol\\nC4\\nC 1\\nCM\\nO 1\\nol\\nCO\\no 1\\nCO\\no 1\\nCO\\noT\\nCM\\nol\\noT\\nCO\\noT\\nen\\no 1\\nco\\no 1\\nco\\no 1\\noT\\nLO\\nCO\\nCN\\n\u00c2\u00a95\\nen\\nLO\\nol\\nLO\\nol\\nen\\nol\\no 1\\ncO\\nCO\\no 1\\nen\\nCM\\nco\\nCN\\no 1\\nco\\noT\\n0*i~\\nen\\no 1\\nCO\\no 1\\nCO\\no 1\\noT\\n1\\nLO\\nLO\\nLO\\nCO\\nO\\nLO\\nCN\\nol\\nOD\\nCO\\nol\\nLO\\nCO\\no 1\\nCO\\nol\\nCN\\no 1\\nCO\\noT\\nCO\\noT\\no 1\\no I\\nCO\\nLO\\nLO\\nLO\\nL.3\\no\\nLO\\nCO\\nCO\\nCN\\nCN\\nCN\\nCN\\nco\\nCO\\ncO\\nc 1\\nlO\\no|\\nCN\\no 1\\nLO\\no 1\\nol\\noT\\nLO\\ns\\nLO\\nen\\nco\\ncm\\no\\nCD\\nCD\\nCD\\nCM\\nW3\\nCO\\nCN\\no!\\no\\nCN\\nol\\nCD\\noT\\nco\\noT\\no 1\\nCO\\no 1\\nCO\\nLO\\nLO\\nLO\\no\\nCD\\ns?\\nCD\\nCD\\nCO\\nco\\nCO\\nt\u00c2\u00a9\\nCD\\nCN\\noT\\nen\\nol\\nCO\\nol\\noT\\nr~-\\nCO\\nLO\\no\\nLO\\n5\\n5\\no\\nCO\\nCO\\nCD\\nCD\\nCO\\nCO\\nCO\\nes\\nol\\nco\\nCO\\noT\\nCD\\nLO\\nCM\\nCD\\nCO\\no\\nCD\\nCD\\nCD\\nCO\\nLO\\nCD\\nCO\\nCO\\nlo\\no\u00c2\u00a9\\nol\\noT\\ncd\\nLO\\nCD\\nLO\\nCN\\nLO\\nCO\\nLO\\nCM\\no\\nCO\\nLO\\nC J\\nCO\\no\\nt\\nol\\nis\\ns\\nLO\\nCO\\nLO\\n5\\nO\\nCD\\nCO\\nLO\\nCO\\nCD\\n^co\\nCO\\nCO\\nCD\\nLO\\nCO\\nLO\\nLO\\no\\nLO\\nCM\\nCD\\nCD\\nCO\\nC3\\nCO\\no\\nlO\\nCN\\nCO\\nLO\\no\\nLO\\nCO\\nCO\\n3\\no\\nCO\\nCD\\nCO\\n-3\\nCO\\ncN\\nCO\\np\\nd\\nCD\\n5\\n3\\nCD\\n-3-\\nCO\\nCO\\nLO\\nCO\\nCD\\nCD\\nCO\\no\\no\\nCD\\nCN\\nCD\\nCO\\nCO\\nCO\\nCO\\nCO\\nCM\\no\\nCD\\nCO\\nQ\\nUl\\nsi\\nC\u00c2\u00a3\\nr- uj\\n0.\\n*\u00c2\u00ab9|ce\\n\u00c2\u00a91\\n\u00c2\u00a91\\nt-|ao\\n\u00c2\u00a91\\nco\\n!-l|-*\\neo\\ni-l|oi\\n\u00c2\u00a90\\nsol-*\\nCO\\n^H\\nJL\u00c2\u00a9\\ni.\u00c2\u00a9\\nt\u00c2\u00a9\\no\\n\u00e2\u0096\u00a0sya\u00c2\u00b13iAivia HOiid", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0057.jp2"}, "54": {"fulltext": "40\\nBROWN SHARPE MFG. CO.\\nCHAPTER V\\nSPIRAL OR SCREW GEARING.\\n(Figs. 9, 10, ii.\\nFig. 9.\\nRIGHT HAND SPIRAL GEARS.\\nIn spiral gearing the wheels have cylindrical pitch surfaces,\\nbut the teeth are not parallel to the axis. The line in which\\nthe pitch surface intersects the face of a tooth is part of a\\nscrew line, or helix, drawn at the pitch surface. A screw\\nwheel may have one or any number of teeth. A one-toothed\\nwheel corresponds to a one-threaded screw, a many-toothed\\nwheel to a many- threaded screw. The axes may be placed at\\nany angle.\\nConsider spiral gears with\\nI. Axes parallel.\\nII. Axes at right angles.\\nIII. Axes any angle.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0058.jp2"}, "55": {"fulltext": "PROVIDENCE, R. I.\\n4*\\nLet th\\nN a\\nN ft\\nC\\nP\\nP\\nP\\nY\\nL,\\nL 2\\nT\\nD\\nB\\nFig. 10.\\nLEFT HAND SPIRAL GEAR.\\nere be\\nnumber of teeth in gears\\ncenter distance.\\ndiametral pitch\\ncircular pitch.\\nnormal diametral pitch.\\nnormal circular pitch.\\nangle of axes.\\nexact lead of spiral on pitch surface.\\napproximate lead of spiral on pitch surface.\\nnumber of teeth marked on cutter to be used when\\nteeth are to be cut on milling machine.\\npitch diameter.\\nblank diameter.\\na n\\nt\\ns\\nangle of teeth with axis\\nthickness of tooth.\\naddendum and module.\\nwhole depth of tooth.\\nD\\nNote. Letters a and b occurring- at bottom of notations refer to gears a and b.\\nI. Axes Parallel.\\nGears of this class are called twisted gears. The angle of\\nteeth. with axes in both gears must be equal and the spirals\\nrun in opposite directions. The angles are generally chosen\\nsmall (seldom over 20 to avoid excessive end thrust. End\\nthrust may, however, be entirely avoided by combining two\\npairs of wheels with right and left-hand obliquity. Gears of\\nthis class are known as Herringbone gears. They are com-\\nparatively noiseless running at high speed.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0059.jp2"}, "56": {"fulltext": "42 BROWN SHARPE MFG. CO.\\nII. Axes at Right Angles.\\nHere we must always have\\ni. The teeth of same hand spiral\\n2. The normal pitches equal in both gears and\\n3. The sum of the angles of teeth with axes 90\u00c2\u00b0.\\nChoosing Angle of Teeth with Axes.\\n1. If in a pair of gears the ratio of the number of teeth is\\nequal to the direct ratio of the diameters, i. e., if the number of\\nteeth in the two gears are to each other as their pitch diame-\\nters, then the angles of the spirals will be 45\u00c2\u00b0 and 45\u00c2\u00b0 for, this\\ncondition being fulfilled, the circular pitches of the two gears\\nmust be alike, which is only possible with angles of 45\u00c2\u00b0. In\\nsuch a combination either gear may be the driver.\\n2. If the ratio of the diameters determined upon is larger\\nor smaller than the ratio of the number of teeth, then the\\nangles are\\ntan a a tan a b b Nq\\nD 6 N a D N\\\\\\nIn such gears the velocity ratio is measured by the number\\nof teeth, and not by the diameters.\\n3. Given N a N 6 and C\\nIf P a is made P 6 then we have case 1 and\\nP n\\n~^(N a +N 6\\nBut if P a is assumed, then\\np r C n\u00e2\u0080\u0094yi N a P a\\nb i/^NJ\\nand\\ntan a n tan a b\\nThe gear whose P or a is larger will ordinarily be the\\ndriver, on account of the greater obliquity of the teeth.\\n4. Given N a N 6 and C or D.\\nSee case 7 under III., considering y 90\\nIII. Axis at any Angle (y).\\n5. Given case 1, under II., then angles of spirals j4 y,\\nfor the same reason.\\n6. Analogous cases to 2 and 3, under II., may be\\nworked out, when angles of axes y, but they have been", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0060.jp2"}, "57": {"fulltext": "PROVIDENCE, R. I.\\n43\\nomitted, partly because the formulas are too cumbersome, and\\npartly because they are to some extent covered by cases 5\\nand 7.\\n7. Given N a N b and C, or one of the pitch diameters. We\\nfind the angles by a graphic method, which for all practical\\npurposes is accurate enough ro and v o are the axes of gears\\nforming angle y (see diagram, Fig. 11.) On these axes we\\nlay off lines o r and v representing the ratio of the number\\nof teeth (velocity ratio), so that N a N 6 r s s v, and\\nFig. 11.\\nconstruct parallelogram o r s v. Then, according to Mc-\\nCord,* the angles formed by the tangent s o in the pitch con-\\ntact with the axes of the gears insures the least amount of\\nsliding. In bisecting angle y by tangent u o and using angles\\nproduced in this manner we equally distribute the e?id thrust on\\nboth shafts. Both methods have their advantages to profit\\nby both we select angles a a and a h produced by tangent x,\\nbisecting angle u s.\\nThus we have when angles are found and C given,\\n2 C 7t cos a a cos al\\np/ i\\nand when D Cf given\\np/\u00c2\u00bbi\\nD,\\nN a cos a b Nfccosa^\\nD\u00e2\u0080\u009e 7t cos a\u00e2\u0080\u009e\\nP n N 6\\nit cos a h\\nand\\nMcCord, Kinematics, page 378.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0061.jp2"}, "58": {"fulltext": "44\\nEROWX 5HARPE MFG. CO.\\nGeneral Formulas.\\ny a a a\\nn D n\\nD or\\nB D 2J\\nP or\\nX\\n-tcos a\\nor D\\nP\\nP\\ncos a\\nP\\nP\\nP cos a\\n7T\\nt\\nF\\npn.\\nT\\nor\\ni Piich of cutter.)\\nr\\nD 2 j\\nL\\nL\\ncos a\\nX P\\ntan a\\nic WG.\\ni J\\\\~ ?fe 7.)\\n:r\\nx-\\nL X P i\\nS G\\nPtan\u00c2\u00abr L; X P\\nNote 2 and examph\\ns 45\u00c2\u00b0= 7071 1\\ncos 45= 5\\ntan 45 1.000\\nNote i. Cutters of regular involute system.\\nL sr No. 1 cutter for T from 135 up.\\n2 55 *-o 134\\n$5 to 54\\n4 26 to 34\\nNo. 5 cutter for T from\\n6\\n21 te\\n17 t: _\\n14 to 16\\n12 tO 13\\nNote 2. Gears used on spiral head and bed for Brown 3l Sharpe milling\\nmachine\\nW number of teeth in gear on worm.\\nG is: d.\\nG: 2d stud.\\n5 screw.\\nShould a spiral head of different construction be used, the formula might not\\napply.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0062.jp2"}, "59": {"fulltext": "PROVIDENCE, R. I.\\n45\\nThe following data are usually required in cutting spiral\\ngears in a Universal Milling Machine, and it will be found\\nconvenient to arrange them in tabular form as follows\\n1\\nGEAR.\\nPINION.\\nNo. of Teeth\\nPitch Diameter\\nOutside Diameter\\nCircular Pitch\\nAngle of Teeth with Axis\\nNormal Circular Pitch\\nPitch of Cutter\\nAddendum s\\nThickness of Tooth t\\nWhole Depth D f\\nNo. of Cutter\\nExact Lead of Spiral\\nApproximate Lead of Spiral\\nGears on Milling Machine to Cut Spiral\\nGear on W T orm\\nist Gear on Stud\\n2nd Gear on Stud\\nGear on Screw\\nIf the exact lead L x can be obtained by the gears at hand,\\nLj will equal L 2 and we shall have from the formula\\n10 W Go\\n,L o\\nS G L\\nW Go\\n-g-g^ (for B. S. Milling Machine.)\\n10\\nExample I.\\nRequired the gears for cutting a spiral of 2% lead.\\nfactoring, in the most simple way, we have\\ni i x i i x 28 32 x 28 W G 2\\n4 ~2X2~ 56x2~ 56 x~64 S G!", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0063.jp2"}, "60": {"fulltext": "46 BROWN SHARPK MFG. CO.\\nThus the gearing will be 32 T.. on worm, 64 T. ist, on stud,\\n28 T. 2nd on stud 3 and 56 T. on screw.\\nTrying these gears on the Milling Machine we find that\\nthey cannot be used, and as we have no other regular gears\\nin the ratio of 2 to 1 that can be used we must try, by factor-\\ning, to get such ratios for the two pairs of gears as to be able\\nto use the gears at hand, bearing in mind that the combined\\nratio must be J.\\n1 18 3x6 24 x 6 24 x 48\\n4~~~ 72 ~~9x8 __ 9x 64 72 X64\\nThese gears are at hand and the combination can be used\\non the machine, giving the exact lead of 2J\\nExample II.\\nRequired the gears for cutting a spiral of 8.639 lead.\\n8.639 8 T 6 3 (H) reducing, by continued fractions, to a\\nsmaller fraction of approximately the same value, as described\\non pages 74 and 75\\n639 1000 1\\n639\\n361 )639( 1\\n361\\n278 361 1\\n278\\n3) 278 3\\nJ 49_\\n29 83 2\\n58\\n25 29 1\\n25\\n4)25 (6\\n24\\ni)4(4\\n4", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0064.jp2"}, "61": {"fulltext": "PROVIDENCE, R. I. 47\\n112. _7_ 1.6 .2 3. J_5.4 6 3!)\\n1 2 3 11 2 5 3 6 2 4 110 TJTT\\nSelecting ^-f as an approximation near enough for our\\npurpose, and in fact as near as we are likely to find gears for,\\nwe have for our lead 8i|. Applying the formula as in Ex-\\nample I.\\nSjj __ W G,\\nio S Gi\\n8||- 216 108 f\\nfactoring we have\\nio 250 125\\n9 X 12 9 X 48 72 X 48\\n^r z T 7Z~: 7: the gears required,\\n25 x 5 100 x 5 100 x 40 H\\nthese being regular gears furnished with the Milling Machine.\\nProof\\n72 x 48 x 10\\n8.640 L,\\n100 X 40 T\\n8-639 Li\\n.001 error in lead.\\nIn shops where much work is done in milling spirals it is\\ndesirable to have a full set of gears for the milling machine,\\nfrom the smallest to the largest numbers of teeth that can be\\nused. This makes it possible, in most cases, to get closer\\napproximations than could be otherwise obtained, and often\\nsaves a great deal of figuring.\\nWhen the use of continued fractions does not bring a\\nclose enough approximation, one method to secure a closer\\nresult is to add to or substract from the numerator and de-\\nnominator of the fraction to be reduced, any numbers nearly\\nin proportion to the given fraction, seeing that the numbers\\nadded or substracted are such as to make the fraction reduc-\\nible to lower terms. By a little ingenuity and patience ex-\\ntremely close approximations can generally be reached in\\nthis way.\\nTake, as an illustration, the fraction in Example II.\\n8tVo 9 o 8639\\n10 1 0000\\nAdding 9 to the numerator and 10 to the denominator, these", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0065.jp2"}, "62": {"fulltext": "48 BROWN SHARPE MFG. CO.\\nbeing in about the same ratio to each other as the numerator\\nand denominator of the fraction, we have\\n8639+9 8648 __ 4324 _ 47 x 92\\n10000+10 10010 5005 55 x 91\\nAll of the gears in this case are special.\\nApplying the same proof as in Example II. we find that\\nthis train of gears will give a lead of 8.6393+, making an\\nerror of .0003 in the lead.\\nXo doubt a much closer approximation even than this\\ncould be obtained by further trial.\\nAnother method is to multiply both terms of the fraction\\nby some number which will make one term of the fraction\\neasily reducible, and adding one to or subtracting it from the\\nother term to make it possible to reduce that also.\\nThere is an element of uncertainty in both these methods,\\nas we never feel sure that we have obtained the best combina-\\ntion practical work, however, rarely requires accuracy beyond\\na point that can readily be reached.\\nThe accompanying list of prime numbers and factors will\\nbe found useful in reducing: and factoring fractions.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0066.jp2"}, "63": {"fulltext": "PROVIDENCE, R. I.\\n49\\nPRIME NUMBERS AND FACTORS.\\n1 TO lOOO,\\n1\\n26\\n2x13\\n51\\n3x17\\n76\\n1\\n2 2 xl9\\n2\\n27\\n3\\n52\\n2 2 xl3\\n77\\n7x11\\n3\\n28\\n2 2 x7\\n53\\n78\\n2x3x13\\n4\\n2 2\\n29\\n54\\n2x3\\n79\\n30\\n2x3x5\\n55\\n5x11\\n80\\n2 4 x5\\n6\\n2x3\\n31\\n56\\n2 x 7\\n81\\n3 4\\n7\\n32\\n2 5\\n57\\n3x 19\\n82\\n2x41\\n8\\n2 3\\n33\\n3x11\\n58\\n2x29\\noo\\n9\\n3-\\n34\\n2x17\\n59\\n84\\n2 2 x 3 x 7\\n10\\n2x5\\n35\\n5x7\\n60\\n2 2 x 3 x 5\\n85\\n5x 17\\n11\\n36\\n2 2 x3 2\\n61\\n86\\n2x43\\n12\\n2 2 x3\\n37\\n62\\n2x31\\n87\\n3 x 29\\n13\\n38\\n2x19\\n63\\n3 2 x7\\n88\\n2 3 xll\\n14\\n2x7\\n39\\n3x13\\n64\\n2\u00c2\u00b0\\n89\\n15\\n3x5\\n40\\n2 3 x5\\n65\\n5x13\\n90\\n2x3 2 x5\\n16\\n2 4\\n41\\n66\\n2x3x11\\n91\\n7x13\\n17\\n42\\n2x3x7\\n67\\n92\\n2 2 x23\\n18\\n2x3 2\\n43\\n68\\n2 2 xl7\\n93\\n3x31\\n19\\n44\\n2 2 xll\\n69\\n3x23\\n94\\n2x47\\n20\\n2 2 x5\\n45\\n3 2 x5\\n70\\n2x5x7\\n95\\n5x19\\n21\\n3x7\\n46\\n2x23\\n71\\n96\\n2 5 x3\\n22\\n2x11\\n47\\n72\\n2 3 x3 2\\n97\\n23\\n48\\n2 4 x3\\n73\\n98\\n2x7 2\\n24\\n2 3 x3\\n49\\nf-9\\nr\\n74\\n2x37\\n99\\n3 2 xll\\n25\\n5 2\\n50\\n2x5 2\\n75\\n3x5 2\\n100\\n2 2 x5 2", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0067.jp2"}, "64": {"fulltext": "5o\\nBRCTSYX SHARPE MFG. CO.\\n101\\n131\\n161\\n7 x 23\\n191\\n102\\n2x3x17\\n132\\n2-x3xll\\n162\\n2x3 4\\n192\\n2 x3\\n103\\n133\\n7x19\\n163\\n193\\n104\\n2\u00c2\u00b0xl3\\n134\\n2 x 67\\n164\\n2 2 X41\\n194\\n2x97\\n105\\n3x5x7\\n135\\n3 3 x 5\\n165\\n3 x 5 x 11\\n195\\n3x5x13\\n106\\n2x53\\n136\\n2 3 xl7\\n166\\n2 x 83\\n196\\n2-x7-\\n107\\n137\\n107\\n197\\n108\\n2-x3 3\\n138\\n2 X 3 x 23\\n168\\nx 3 x 7\\n198\\n2x3^x11\\n109\\n139\\n169\\n13-\\n199\\n110\\n2X5X11\\n140\\n2- x 5 x 7\\ni7\\n2x5x17\\n200\\n2 3 x5 2\\n111\\n3x37\\n141\\n3x47\\n171\\n3-xl9\\n201\\n3x67\\n112\\n2 4 x7\\n142\\n2x71\\n172\\n2 2 x43\\n202\\n2x101\\n1J3\\n143\\n11x13\\n173\\n203\\n7x29\\n114\\n2x3x19\\n144\\n2 4 x3^\\n174\\n2x3x29\\n204\\n2-x3xl7\\n115\\n5x23\\n145\\n5 x 29\\n175\\n5- x 7\\n205\\n5x41\\n116\\n2-X29\\n146\\n2 x 73\\n176\\n2 4 xll\\n206\\n2 x 103\\n117\\n3-X13\\n147\\n3 x 7-\\n177\\n3 x 59\\n207\\n3^x23\\n118\\n2x\\n148\\n2 2 x37\\n178\\n2x89\\n2 U.s\\n2 4 xl3\\n119\\n7x17\\n149\\n179\\n11 xl9\\n120\\n2 s x 3 x 5\\n150\\n2 x 3 x 5-\\n180\\n2 2 x 3- x 5\\n210\\n2x3x5x7\\n121\\n11-\\n151\\n181\\n211\\n122\\n2x61\\n152\\n2 3 xl9\\n182\\n2x7x 13\\n212\\n2-X53\\n123\\n3x41\\n153\\n3 J xl7\\n183\\n3x61\\n213\\n3x71\\n124\\n2-X31\\n154\\n2x7x11\\n184\\n2-X.23\\n214\\n2x107\\n125\\n5 3\\n155\\n5x31\\n185\\n5x37\\n215\\n5x43\\n126\\n2x3^x7\\n156\\n2 2 X3X13\\n186\\n2x3x31\\n216\\n2 3 x3 8\\n127\\n157\\n187\\n11 X17\\n217\\n7x31\\n128\\n2\\n158\\n2x79\\n188\\n2-x47\\n218\\n2 x 109\\n129\\n3 x -43\\n159\\n3 x 53\\n189\\n3 x 7\\n219\\n3 x 73\\n130\\ni\\n2x5x13\\n160\\n2 s x 5\\n19(\\n2x5x19\\n220\\n2- x 5 x 1 1", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0068.jp2"}, "65": {"fulltext": "PROVIDENCE, R. I.\\n51\\n1\\n221\\n13x17\\n251\\n281\\n311\\n222\\n2x3x37\\n252\\n2 2 x3 2 x7\\n282\\n2x3x47\\n312\\n2 3 x3xl3\\n223\\n253\\n11x23\\n283\\n313\\n224\\n2 5 x7\\n254\\n2X127\\n284\\n2 2 x71\\n314\\n2x157\\n225\\n3 2 x5 2\\n255\\n3x5x17\\n285\\n3x5x19\\n315\\n3 2 x5x7\\n226\\n2x113\\n256\\n2 8\\n286\\n2x11x13\\n316\\n2 2 x79\\n227\\n257\\n287\\n7x41\\n317\\n228\\n2 2 x3xl9\\n258\\n2 X 3 X 43\\n288\\n2 5 x3 2\\n318\\n2x3x53\\n229\\n259\\n7x37\\n289\\n17 2\\n319\\n11x29\\n230\\n2x5x23\\n260\\n2 2 x5xl3\\n290\\n2x5x29\\n320\\n2 6 x5\\n231\\n3X7X11\\n261\\n3 2 x29\\n291\\n3x97\\n321\\n3x107\\n232\\n2 3 x29\\n262\\n2x131\\n292\\n2 2 x73\\n322\\n2x7x23\\n233\\n263\\n293\\n323\\n17x19\\n234\\n2x3 2 xl3\\n264\\n2 3 x3xll\\n294\\n2 X 3 x 7 2\\n324\\n2 2 x3 4\\n235\\n5 x47\\n265\\n5 x53\\n295\\n5x59\\n325\\n5 2 X13\\n236\\n2 2 x59\\n266\\n2x7x19\\n296\\n2 3 x37\\n326\\n2x163\\n237\\n3x79\\n267\\n3x89\\n297\\n3 3 xll\\n327\\n3x109\\n238\\n2x7x17\\n268\\n2 2 X67\\n298\\n2x149\\n328\\n2 3 x41\\n239\\n269\\n299\\n13x23\\n329\\n7x47\\n240\\n2 4 x3x5\\n270\\n2x3 3 x5\\n300\\n2 2 x3x5 2\\n330\\n2X3X5X11\\n241\\n271\\n301\\n7x43\\n331\\n242\\n2xll 2\\n272\\n2 4 xl7\\n302\\n2x151\\n332\\n2 2 x83\\n243\\nr 5\\n273\\n3x7x13\\n303\\n3x101\\n333\\n3 2 x37\\n244\\n2 2 X61\\n274\\n2x137\\n304\\n2 4 X19\\n334\\n2x167\\n245\\n5X7 2\\n275\\n5 2 Xll\\n305\\n5x61\\n335\\n5x67\\n246\\n2x3x41\\n276\\n2 2 x3x23\\n306\\n2x3 2 xl7\\n336\\n2 4 x3x7\\n247\\n13x19\\n277\\n307\\n337\\n248\\n2 3 x31\\n278\\n2x139\\n308\\n2 2 x7xll\\n338\\n2X13 2\\n249\\n3x83\\n279\\n3 2 x31\\n309\\n3x103\\n339\\n3x113\\n250\\n2x5 3\\n280\\n2 3 x 5 X 7\\n310\\n2x5x31\\n340\\n2 2 X5X17", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0069.jp2"}, "66": {"fulltext": "BROWN SHARPE MFG. CO.\\n341\\n11x31\\n371\\n7x53\\n401\\n431\\n=:_\\n342\\n2x3 2 Xl9\\n372\\n2 2 x3x31\\n402 2x3x67\\n432\\n2 4 x3 :i\\n343\\n7 ,J\\n373\\n403 13x31\\n433\\n344\\n2^X43\\n374\\n2x11x17\\n404\\n2 2 xl01\\n434\\n2x7x31\\n345\\nX5 x23\\n375\\n3 X 5 s\\n|405\\n3 4 x5\\n435\\n3 X 5 X 29\\n346\\n2x173\\n376\\n2 3 x47\\n406 2x7x29\\n436\\n2 2 xl09\\n347\\n377\\n13x29\\n407\\n11x37\\n437\\n19x23\\n348\\n2 2 X 3 x 29\\n378\\n2 x 3 3 x 7\\n408\\n2 3 x3xl7\\n438\\n2x3x73\\n349\\n879\\n409\\n439\\n350\\n2x5-x7\\n380\\n2 2 x5xl9\\n410 2x5x41\\n440\\n2 x5x 11\\n351\\n3 3 X13\\n381\\n3x127\\n411 3x137\\n441\\n3 2 x 7 2\\n352\\n2 5 Xll\\n382\\n2X191\\n412 2 2 xl03\\n412\\n2x13x17\\n353\\n883\\ni\\n413 7x59\\n443\\n354\\n2 X 3 X 59\\n384\\n2 X o\\n414 2x3 2 x23\\n444\\n2 2 x3x37\\n355\\nox 71\\n385\\n5x7x11\\n415 5x83\\n445\\n5 X 89\\n356\\n2 2 X 89\\n386\\n2x193\\n416 2 xl3\\n446\\n2 x 223\\n357\\n3x7x17\\n387\\n3 2 x43\\n417\\n3x139\\n447\\n3x149\\n358\\n2x179\\n388\\n2 2 x97\\n418\\n2x11x19\\n448\\n2 6 x7\\n359\\n389\\n419\\n__\\n449\\n360\\n2-x3 2 x5\\n390\\n2X3X5X13\\n420\\n2 2 X3X5X7\\n450\\n2x3 2 x5 2\\n361\\n19 2\\n391\\n17x23\\n421\\n451\\n11X41\\n362\\n2x181\\n392\\n2 3 X7 2\\n422\\n2x211\\n452\\n2 2 xH3\\n363\\n3xll 2\\n393\\n3x131\\n423\\n3 2 x47\\n453\\n3x151\\n364\\n2 2 x7xl3\\n394\\n2x197\\n424\\n2 3 X53\\n454\\n2x227\\n365\\n5x73\\n395\\n5 x 79\\n425\\n5 2 x 1 7\\n455\\n5x7x13\\n366\\n2x3x61\\n396\\n2 2 x3 2 xll\\n426\\n2x3x71\\n456\\n2 x3xl9\\n367\\n397\\n427\\n7x61\\n457\\n368\\n2 4 x 23\\n398\\n2x199\\n428\\n2 2 X107\\n458\\n2x229\\n369\\n3 2 x41\\n399\\n3x7x19\\n429\\n3xllXl3\\n459\\n3 3 xl7\\n370\\n2x5x37\\n400\\n2 4 X5 2\\n430\\n2x5x43\\n460\\n2 2 x5x23", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0070.jp2"}, "67": {"fulltext": "PROVIDENCE, R. I.\\n461\\n491\\n521\\n551\\n19x29\\n462\\n2X3X7X11\\n492\\n2 2 x3x41\\n522\\n2x3 2 x29\\n552\\n2 3 x3x23\\n463\\n493\\n17X29\\n523\\n553\\n7x79\\n464\\n2 4 X 29\\n494\\n2x13x19\\n524\\n2 2 xl31\\n554\\n2x277\\n465\\n3x5x31\\n495\\n3 2 x5xll\\n525\\n3 x 5 2 x 7\\n555\\n3x5x37\\n466\\n2 X 233\\n496\\n2 4 x31\\n526\\n2x263\\n556\\n2 2 xl39\\n467\\n497\\n7x71\\n527\\n17x31\\n557\\n468\\n2 2 x3 2 xl3\\n498\\n2x3x83\\n528\\n2 4 x3xll\\n558\\n2x3 2 x31\\n469\\n7x67\\n499\\n529\\n23 2\\n559\\n13x43\\n470\\n2x5x47\\n500\\n2 2 x 5 3\\n530\\n2x5x53\\n560\\n2 4 x5x7\\n471\\n3x157\\n501\\n3x167\\n531\\n3 2 X59\\n561\\n3x11x17\\n472\\n2 3 x59\\n502\\n2x251\\n532\\n2 2 x7xl9\\n562\\n2x281\\n473\\n11x43\\n503\\n533\\n13x41\\n563\\n474\\n2x3x79\\n504\\n2 3 x3 2 x7\\n534\\n2 x 3 x 89\\n564\\n2 2 x3x47\\n475\\n5 2 X19\\n505\\n5x101\\n535\\n5x107\\n565\\n5x113\\n476\\n2 2 x 7 X 1 7\\n506\\n2x11x23\\n536\\n2 3 x67\\n566\\n2x283\\n477\\n3 2 x53\\n507\\n3xl3 2\\n537\\n3x179\\n567\\n3 4 x7\\n478\\n2 x 239\\n508\\n2 2 xl27\\n538\\n2 x 269\\n568\\n2 3 X71\\n479\\n509\\n539\\n7 2 xll\\n569\\n480\\n2 5 x 3 x 5\\n510\\n2X3X5X17\\n540\\n2 2 x3 3 x5\\n570\\n2x3X5X19\\n481\\n13.X37\\n511\\n7x73\\n541\\n571\\n482\\n2x241\\n512\\n2 9\\n542\\n2x271\\n572\\n2 2 xllxl3\\n483\\n3 x 7 x 23\\n513\\n3 X19\\n543\\n3x181\\n573\\n3x191\\n484\\n2 2 xll 2\\n514\\n2x257\\n544\\n2 5 xl7\\n574\\n2x7x41\\n485\\n5x97\\n515\\n5x103\\n545\\n5x109\\n575\\n5 2 x23\\n486\\n2 x 3 5\\n516\\n2 2 x3x43\\n546\\n2X3X7X13\\n576\\n2 6 x3 2\\n487\\n517\\n11x47\\n547\\n577\\n488\\n2 s x61\\n518\\n2x7x37\\n548\\n2 2 xl37\\n578\\n2xl7 2\\n489\\n3x163\\n519\\n3x173\\n549\\n3 2 x61\\n579\\n3x193\\n490\\n2 x 5 x 7 2\\n_ L\\n520\\n2 3 x5xl3\\n550\\n2x5 2 xll\\n580\\n2 2 x5x29", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0071.jp2"}, "68": {"fulltext": "54\\nBROWN SHARPE MFG. CO.\\n581\\n7x83\\n611 13x47\\n1\\n611 671\\n11x61\\n582\\n2x3x97\\n612 2 2 x3 2 xl7\\n642\\n2x3x107\\n672\\n2 5 x 3 x 7\\n583\\nllx-33\\n613\\n643\\n673\\n584\\n2 a x73\\n614\\n2x307\\n644\\n2 2 x7x23\\n674\\n2x337\\n585\\n3-x5xl3\\n615\\n3x5x41\\n645 3x5x43\\n075\\n3 3 X5 2\\n586\\n2 x 293\\n616\\n2 3 x7xll\\n646\\n2x17x19\\n676\\n2 2 xl3 2\\n587\\n617\\n617\\n677\\n588\\n2 2 x 3 x 7 2\\n618\\n2x3x103\\n648\\n2 x3 4\\n678\\n2x3x113\\n589\\n19x31\\n619\\n649\\n11X59\\n679\\n7x97\\n590\\n2 x5x59\\n020\\n2 2 xox31\\n650\\n2x5 2 xl3\\n680\\n2x5 x 17\\n591\\n3x197\\n621\\n3 x23\\n651\\n3x7x31\\n681\\n3x227\\n592\\n2 4 x37\\n622\\n2x311\\n652\\n2 2 xl63\\n682\\n2x11x31\\n593\\n623\\n7x89\\n653\\n683\\n594\\n2 x 3 x 1 1\\n624\\n2 4 x3xl3\\n654 2x3x109\\n684\\n2 2 x3 2 xl9\\n595\\n5x 7 x 17\\n625\\n5 4\\n655 5x131\\n685\\n5x137\\n596\\n2 2 xl49\\n626\\n2x313\\n656 2 4 x41\\n686\\n2 x 7\\n597\\n3 x 199\\n627 3x11x19\\n657 3 2 x73\\n687\\n3x229\\n598\\n2x13x23\\n628 2 2 xl57\\n658 2 x 7 x47\\n688\\n2 4 x43\\n599\\n629 17x37\\n659\\n689\\n600\\n2 s x 3 x 5 2\\n630\\n2X 3 X 5X7\\n660\\n2 2 X3X5xll\\n690\\n2X3x5X23\\n601\\n631\\n661\\n691\\n602\\n2x7x43\\n632\\n2 x79\\n662\\n2x331\\n692\\n2 2 xl73\\n603\\n3-x67\\n633\\n3x211\\n663\\n3x13x17\\n693\\n3 2 x7xll\\n604\\n2-xlol\\n634\\n2x317\\n664\\n2 x83\\n694\\n2 x 347\\n605\\n5xll 2\\n635 5x127\\n665 5x7x19\\n695\\n5x139\\n606\\n2x3x101\\n636 2 2 x3x53\\n666 2x3 2 x37\\n696\\n2 x3x29\\n607\\n637\\n72 1 Q\\n1 X 1 3\\n667 23x29\\n697\\n17x41\\n608\\n2 5 xl9\\n638 2x11x29\\n668 2 2 xl67 698\\n2 x 349\\n609\\n3x7x21\\n639 3-X71\\n669 3x223 699\\n3 x 233\\n610\\n2x5x61\\n640 2 7 X 5\\n670 2x5x67 700\\n2 2 x 5 2 X 7", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0072.jp2"}, "69": {"fulltext": "PROVIDENCE, R. I.\\n55\\n701\\n731\\n17x43\\n761\\n791\\ni\\n7x113\\n702\\n2x3 3 xl3\\n732\\n2 2 x3x61\\n762\\n2x3x127\\n792\\n2 3 x3 2 xll\\n703\\n19x37\\n733\\n763\\n7x109\\n793\\n13x61\\n704\\n2 c xll\\n734\\n2x367\\n764\\n2 2 xl91\\n794\\n2x397\\n705\\n3x5x47\\n735\\n3 x 5 x 7 2\\n765\\n3 2 x5xl7\\n795\\n3x5x53\\n706\\n2x353\\n736\\n2 5 x23\\n766\\n2x383\\n796\\n2 2 xl99\\n707\\n7x101\\n737\\n11x67\\n767\\n13x59\\n797\\n708\\n2 2 x3x59\\n738\\n2x3 2 x41\\n768\\n2 8 x3\\n798\\n2X3X7X19\\n709\\n739\\n769\\n799\\n17x47\\n710\\n2x5x71\\n740\\n2 2 x5x37\\n770\\n2X5X7X11\\n800\\n2 5 x5 2\\n711\\n3 2 X79\\n741\\n3x13x19\\n771\\n3x257\\n801\\n3 2 x89\\n712\\n2 3 x89\\n742\\n2x7x53\\n772\\n2 2 xl93\\n802\\n2x401\\n713\\n23x31\\n743\\n773\\n803\\n11X73\\n714\\n2X3X7X17\\n744\\n2 3 x3x31\\n774\\n2x3 2 x43\\n804\\n2 2 x3x67\\n715\\n5x11x13\\n745\\n5x149\\n775\\n5 2 x31\\n805\\n5 X 7 X 23\\n716\\n2 2 xl79\\n746\\n2x373\\n776\\n2 3 x97\\n806\\n2x13x31\\n717\\n3x239\\n747\\n3 2 x83\\n777\\n3x7x37\\n807\\n3x269\\n718\\n2 x 359\\n748\\n2 2 xllxl7\\n778\\n2x389\\n808\\n2 3 X101\\n719\\n749\\n7x107\\n779\\n19x41\\n809\\n720\\n2 4 x3 2 x5\\n750\\n2 x 3 x 5 3\\n780\\n2 2 X3X5X13\\n810\\n2x3 4 x5\\n721\\n7x103\\n751\\n781\\n11X71\\n811\\n722\\n2xl9 2\\n752\\n2 4 x47\\n782\\n2x17x23\\n812\\n2 2 x7x29\\n723\\n3x241\\n753\\n3x251\\n783\\n3 3 x 29\\n813\\n3x271\\n724\\n2 2 xl81\\n754\\n2x13x29\\n784\\n2 4 x7 2\\n814\\n2x11x37\\n725\\n5 2 x29\\n755\\n5x151\\n785\\n5 x 157\\n815\\n5x163\\n726\\n2x3xll 2\\n756\\n2 2 x3 3 x7\\n786\\n2x3x131\\n816\\n2 4 x3xl7\\n727\\n757\\n787\\n817\\n19x43\\n728\\n2 3 x7xl3\\n758\\n2x379\\n788\\n2 2 xl97\\n818\\n2x409\\n729\\n3 6\\n759\\n3x11x23\\n789 3x263\\n819\\n3 2 X7X13\\n730\\nI\\n2x5x73\\n760\\n2 3 x5xl9\\n790 2x5x79\\n820\\n2 2 x5x41", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0073.jp2"}, "70": {"fulltext": "BROWN cS: SHARPE MFG. CO.\\n821\\nI\\n851\\n23x37\\n881\\n911\\n1\\n822\\n2x3x137\\n852\\n2 2 x3x71\\n882\\n2x3 2 x7 2\\n912\\n2 4 x3xl9\\n823\\n853\\n883\\n913\\n11x83\\n824\\n2 3 xl03\\n854\\n2x7x61\\n884\\n2 2 xl3xl7\\n914\\n2x457\\n825\\n3x5 2 xll\\n855\\n3 2 x5xl9\\n885\\n3x5x59\\n915\\n3x5x61\\n826\\n2 x 7x59\\n856\\n2 3 xl07\\n886\\n2x443\\n916\\n2 2 x229\\n827\\n857\\n887\\n917\\n7x131\\n828\\n2 2 x3 2 x23\\n858\\n2x3x11x13\\n888\\n2 3 x3x37\\n918\\n2x3 3 xl7\\n829\\n859\\n889\\n7x127\\n919\\n830\\n2x5x83\\n860\\n2 2 x5x43\\n890\\n2x5x89\\n920\\n2 3 x5x23\\n831\\n3x277\\n861\\n3x7x41\\n891\\n3 4 xll\\n921\\n3x307\\n832\\n2 G xl3\\n862\\n2x431\\n892\\n2 2 x223\\n922\\n2x461\\n833\\n7 2 xl7\\n863\\n893\\n19x47\\n923\\n13x71\\n834\\n2x3x 139\\n864\\n2 5 x 3 3\\n894\\n2x3x149\\n924\\n2 2 x3X7XH\\n835\\n5xl 67\\n865\\n5x173\\n895\\n5x179\\n925\\n5 2 x37\\n836\\n2 2 xllxl9\\n866\\n2x433\\n896\\n2 7 x7\\n926\\n2x463\\n837\\n3 s x31\\n867\\n3xl7 2\\n897\\n3x13x23\\n927\\n3 2 xl03\\n838\\n2x419\\n868\\n2 2 x7x31\\n898\\n2x449\\n928\\n2 5 x29\\n839\\n869\\n11x79\\n899\\n29x31\\n929\\n840\\n2 3 X3X5X7\\n870\\n2X3X5X29 900 2 2 x3 2 x5 2\\n930 2X3X5X31\\n841\\n29 2\\n871\\n13x67 901 17x53\\n931 7 2 xl9\\n842\\n2x421\\n872\\n2 3 xl09\\n902\\n2x11x41\\n932 2 2 x233\\n843\\n3x281\\n873\\n3 2 x97\\n903\\n3x7x43\\n933 3x311\\n844\\n2 2 x211\\n874\\n2x19x23\\n904\\n2 3 xll3\\n934 2x467\\n845\\n5X13 2\\n875\\n5 3 x 7\\n905\\n5x181\\n935 5x11x17\\n846\\n2x3 2 x47\\n876\\n2 2 x 3 x 73\\n906\\n2x3x151\\n936\\n2 3 x3 2 Xl3\\n847\\n7xll 2\\ns;;\\n907\\n937\\n848\\n2 4 x53\\n878\\n2x439\\n908\\n2 2 x227\\n938\\n2x7x67\\n849\\n3x283\\n879\\n3x293\\n909\\n3 2 xl01\\n939\\n3x313\\n850\\n2 X 5 2 X 1 7 880\\n2 4 X0Xll 910\\n2X5X7X13\\n940\\n2 2 x5x47\\ni", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0074.jp2"}, "71": {"fulltext": "PROVIDENCE, R. I.\\no7\\n941\\n956\\nl\\n2 2 x239\\n971\\n986\\n2x17x29\\n942\\n2x3x157\\n957\\n3x11x29\\n972\\n2 2 X 3 5\\n987\\n3x7x47\\n943\\n23x41\\n958\\n2x479\\n973\\n7x139\\n988\\n2 2 x 13x19\\n944\\n2 4 X59\\n050\\n7x137\\n974\\n2x487\\n989\\n23 X 43\\n945\\n3 3 x 5 x 7\\nI960\\n2 fi x3x5\\n975\\n3x5 2 xl3\\n990\\n2x3 2 X5Xll\\n946\\n2x11 X43\\n961\\n31 2\\n976\\n2 4 x61\\n991\\n947\\n962\\n2x13x37\\n977\\n992\\n2 5 x31\\n948\\n2 2 x3x79\\n963\\n3 2 xl07\\n978\\n2x3x163\\n993\\n3x331\\n949\\n13x73\\n964 2-X241\\n979\\n1 1 X 89\\n994\\n2 x 7 x 71\\n950\\n2X5-X19\\n965 5x193\\n980\\n2 2 X 5 x 7 2\\n995\\n5x199\\n951\\n3x317\\n966\\n2X3X7X23\\n981\\n3 2 xl09\\n996\\n2 2 x3x83\\n952\\n2 3 x7xl7\\n967\\ni\\n982\\n2x491\\n997\\n953\\n968\\n2 Xll 2\\n983\\n998\\n2x499\\n954\\n2x3 2 x53\\n969J 3x17x19\\n984\\n28 x 3x41\\n999\\n3 3 x37\\n955\\nc-\\n5x191\\n970 2x5x97\\n985\\n5x197\\n1000\\ni\\n2 3 x 5 3", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0075.jp2"}, "72": {"fulltext": "58 BROWN SHARPE MFG. CO.\\nCHAPTER VI.\\nINTERNAL GEARING.\\nPART A.\u00e2\u0080\u0094 INTERNAL SPUR GEARING.\\n(Figs. 12, 13, 14, 15, 16.)\\nA little consideration will show that a tooth of an internal\\nor annular gear is the same as the space of a spur external\\ngear.\\nWe prefer the epicycloidal form of tooth in this class of\\ngearing to the involute form, for the reason that the difficulties\\nin overcoming the interference of gear teeth in the involute\\nsystem are considerable. Special constructions are required\\nwhen the difference between the number of teeth in gear and\\npinion is small.\\nIn using the system of epicycloidal form of tooth in which\\nthe gear of 15 teeth has radial flanks, this difference must be\\nat least 15 teeth, if the teeth have both faces and flanks. Gears\\nfulfilling this condition present no difficulties. Their pitch\\ndiameters are found as in regular spur gears, and the inside\\ndiameter is equal to the pitch diameter, less twice the adden-\\ndum.\\nIf, however, this difference is less than 15, say 6, or 2, or 1,\\nthen we may construct the tooth outline (based on the epicy-\\ncloidal system) in two different ways.\\nFirst Method. To explain this method better, let us sup-\\npose the case as in Fig. 12, in which the difference between\\ngear and pinion is more than 15 teeth. Here the point o of\\nthe describing circle B (the diameter of which in the best\\npractice of the present day is equal to the pitch radius of a 15\\ntooth gear, of the same pitch as the gears in question) gene-\\nrates the cycloid o, o 1 o a o 3 etc., when rolling on pitch circle\\nL L of gear, forming the face of tooth and when rolling on\\nthe outside of L L the flank of the tooth. In like manner is the\\nface and flank of the pinion tooth produced by B rolling out-\\nside and inside of E E (pitch circle of pinion). A little study", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0076.jp2"}, "73": {"fulltext": "PROVIDENCE, R. I.\\n59\\nof Fig. 12 (in which the face and flank of a gear tooth are\\nproduced) will show the describing circle B divided into 12\\nS\\n\u00c2\u00ab0\\n\u00c2\u00abfc\\nH\\nfe\\nIS*\\nequal parts and circles laid through these points (1, 2, 3, etc.),\\nconcentric with L L. We now lay off on L L the distances\\n0-1, 1-2, 2-3, etc., of the circumference of B, and obtain points", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0077.jp2"}, "74": {"fulltext": "6o\\nBROWN SHARPE MFG. CO.\\ni 1 2 1 3 1 etc. [Ordinarily it is sufficient to use the chord.] It\\nwill now readily be seen that B in rolling on L L will success-\\nively come in contact with i 1 2 1 3 1 etc., c meanwhile moving\\nto c\\\\ r, c\\\\ etc. (points on radii through i 1 2 1 3 1 etc.), and the\\ngenerating point o advancing to o 1 o 2 o 3 etc., being. the inter-\\nsections of B with c\\\\ c~, c etc., as centers and the circles laid\\nthrough 1, 2. 3, etc. Points o, o\\\\ o 2 o 3 etc., connected with a\\ncurve give the face of the tooth in like manner the flank is\\nobtained.\\nIn this manner the form of tooth is obtained, when the\\ndifference of teeth in gear and pinion is less than 15, with the\\nexception that the diameter of describing circle B\\n4^\\nwhere P diametral pitch, N and n number of teeth in gears.\\nThe distances of the tooth above and below the pitch line\\nas well as the thickness are determined as in regular spur\\ngears by the pitch, except when the difference in gear and\\npinion is very small, where we obtain a short tooth, as in Figs.\\n13 and 14. In such a case the height of tooth is arbitrary and\\nonl3 T conditioned by the curve. In internal gears it is best to\\nallow more clearance at bottom of tooth than in ordinary spur\\ngears.\\n29 Teeth\\n8 P.\\nII\\nFig. 13.\\n42 T.\\nIn a construction of this kind it is suggested to draw the\\ntooth outline many times full size and reduce by photography.\\nAn equally multiplied line A B will help in reducing.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0078.jp2"}, "75": {"fulltext": "PROVIDENCE, R. I.\\n61", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0079.jp2"}, "76": {"fulltext": "62 BROWN SHARPE MFG. CO.\\nSeco7id Method. The difference between gear and pinion\\nbeing very small, it is sometimes desirable to obtain a smooth\\naction by avoiding what is termed the friction of approach-\\ning action. This is done, the pinion driving, by giving gear\\nonly flanks, Fig. 15, and the gear driving, by giving gear only\\nfaces, Fig. 16. In both these cases we have but one describ-\\ning circle, whose diameter is equal to the difference of the two\\npitch diameters. The construction of the curve is precisely\\nthe same as described under A. The describing circle has\\nbeen divided into 24 parts simply for the sake of greater\\naccuracy.\\nPART B.\u00e2\u0080\u0094 INTERNAL BEVEL GEARS.\\n(Fig- 170\\nThe pitch surfaces of bevel gears are cones whose apexes\\nare at a common point, rolling upon each other. The tooth\\nforms for any given pair of bevel gears are the same as for a\\npair of spur gears (of same pitch) whose pitch radii are equal to\\nthe respective apex distances of the normal cones (i. e., cones\\nwhose elements are perpendicular upon the elements of the\\nbevel gear pitch cones). (Compare Fig 19, page 68-)\\nThe same is true of internal bevel gears, with the modifica-\\ntion that here one of the pitch cones rolls inside of the other.\\nThe spur gears to whose tooth forms the forms of the bevel\\ngear teeth correspond, resolve themselves into internal spur\\ngears (Fig. 17). The problem is now to be solved as indicated\\nin the first part of this chapter.\\nMcCord, Kinematics, pages 107, 108.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0080.jp2"}, "77": {"fulltext": "PROVIDENCE, R. I.\\n63\\n8 P.\\nGear 40 Teeth\\nPinion 40 Teeth\\nFig. 17.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0081.jp2"}, "78": {"fulltext": "64 BROWN SHARPE MFG. CO.\\nCHAPTER VII.\\nGEAR PATTERNS.\\n(Fig. 18.)\\nTo place in bevel gears the best iron where it belongs, the\\ntooth side of the pattern should always be in the nowel, no\\nmatter of what shape the hubs are.\\nHubs, if short, may be left solid on web if long they should\\nbe made loose. A long hub should go on a tapering arbor, to\\nprevent tipping in the sand. i c taper for draft on hubs when\\nloose, and 3\u00c2\u00b0 when solid is considered sufficient.\\nCoreprints as a rule are made separate, partly to allow the\\npattern to be turned on an arbor, partly for convenience,\\nshould it be desirable to use different sizes.\\nPut rap- and draw-holes as near to center as possible.\\nReferring to Fig. 18, make L D for D from y A to i% t or\\neven more, should hubs be very long. Otherwise if D is more\\nthan 1 *4 leave L i%\\nIron pattern before using should be marked, rusted and\\nwaxed.\\nShrinkage For cast-iron, J 5 per foot.\\nFor brass, j^\\nCast-iron gears, especially arm gears, do not always shrink\\nper foot. In making iron patterns the following allow-\\nances have been found useful\\nUp to 12 diameter allow no shrink.\\nFrom 12 to 18 JA regular shrink.\\n18 tO 24 V2\\n24 to 48 2 A\\nAbove 48 .10\\nfor cast-iron.\\nu u", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0082.jp2"}, "79": {"fulltext": "PROVIDENCE, R. 1.\\n65", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0083.jp2"}, "80": {"fulltext": "66\\nBROWN SHARPE MFG. CO.\\nIf in gears the teeth are to be cast, the tooth thickness in\\nthe pattern is made smaller than called for by the pitch, to avoid\\nbinding of the teeth when cast. No definite rule can be given,\\nas the practice varies on this point. For the different diam-\\netral pitches we would advise making smaller by an amount\\nexpressed in inches, as given in the following table\\nDiam. Pitch.\\nAmount t\\nis Smaller.\\nDiam, Pitch.\\nAmount t\\nis Smaller.\\n16\\n12\\nIO\\n8\\n6\\n.oio\\n.012\\n.014\\n.016\\n-ci8\\n5\\n4\\n2\\nI\\n.020\\n.022\\n.026\\n\u00e2\u0080\u00a203c\\n.040", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0084.jp2"}, "81": {"fulltext": "PROVIDENCE, R. I.\\n67\\nCHAPTER VIII.\\nDIMENSIONS AND FORM FOR BEVEL GEAR\\nCUTTERS.\\n(Fig. 19.)\\nThe data needed to determine the form and thickness of a\\nbevel gear cutter are the following\\nP pitch.\\nN number of teeth in large gear.\\nn\u00e2\u0080\u0094 number of teeth in small gear.\\nF length of face of tooth, measured on pitch line,\\nAfter having laid out a diagram of the pitch cones a b c and\\na bf, and laid off the width of face, the problem resolves itself\\ninto two parts\\nPart I. Determine Proper Curve for Cutter.\\nIt will be remembered that in the involute system of cutters\\n(the only one used for bevel gears that are cut with rotary\\ncutter), a set of eight different cutters is made for each\\npitch, numbering from No. 1 to No. 8, and cutting from\\na rack to 12 teeth. Each number represents the form of\\na cutter suitable to cut the indicated number of teeth. For\\ninstance, No. 4 cutter (No. 4 curve) will cut 26 to 34 teeth.\\nIn order to find the curve to be used for gear and pinion\\nwe simply construct the normal pitch cones by erecting\\nthe perpendicular p q through b, Fig. 19. We now measure the\\nlines b q and b p, and taking them as radii, multiplying each by\\n2 and P we obtain a number of teeth for which cutters of\\nproper curves may be selected. From example we have\\nGear b q 9^ 2 X P X 9.75 97 T No. 2 curve.\\nPinion: b p 3^ 2 X P X 3.5 35 T No. 3 curve.\\nThe eight cutters which are made in the involute system\\nfor each pitch are as follows\\nNo. 1 will cut wheels from 135 teeth to a rack.\\n2\\na\\na\\n55\\na\\na\\n134 teeth\\n3\\n1 u\\na\\n35\\na\\na\\n54\\n4\\na\\na\\n26\\n11\\na\\n34\\n5\\nt a\\na\\n21\\na\\na\\n25\\n6\\n1 u\\nit\\n17\\na\\na\\n20\\n7\\n1 a\\na\\n14\\nu\\na\\n16\\n8\\ni u\\nit\\n12\\na\\na\\n13", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0085.jp2"}, "82": {"fulltext": "68\\nBROWX SHARPE MFG. CO.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0086.jp2"}, "83": {"fulltext": "PROVIDENCE, R. I. 69\\nPart II. Determine Thickness of Cutter.\\nIt is very evident that a bevel gear cutter cannot be thicker\\nthan the width of the space at small end of tooth the practice\\nis to make cutter .005 thinner. Theoretically the cutting angle\\n(h) is equal to pitch angle less angle of bottom (or h a ft\\nPractically, however, better results are obtained by making\\nh a fi (substituting angle of top for angle of bottom), and\\nin calculating the depth at small end, to add the full clearance\\nto the obtained working depth, giving equal amount of\\nclearance at large and small end. This is done to obtain a\\ntooth thinner at the top and more curved. As the small end\\nof tooth determines the thickness of cutter, we shall have to\\nfind the tooth part values at small end. From the diagram it\\nwill be seen that the values at large end are to those at small\\nend as their respective apex distances (a b and a I). The\\nnumerical values of these can be taken from the diagram and\\nthe quotient of the larger in the smaller is the constant where-\\nwith to multiply the tooth values at large end, to obtain those\\nat small end. In our example we find\\n.6^ constant t? t\\nafr=c.8 For 5 P we have\\n2057\\n1310\\n\u00c2\u00b03\u00c2\u00a34\\n1624\\n1310\\n3 i 4 i f\\nS .2COO\\n/=.o 3 i4\\n2 3 I 4\\nD +/=.43i4- s= _\\nD +/=.2934\\nFrom the foregoing it is evident that a spur gear cutter\\ncould not be used, since a bevel gear cutter must be thinner.\\nIf in gears of more than 30 teeth the faces are proportion-\\nately long, we select a cutter whose curve corresponds to the\\nmidway section of the tooth. The curve of the cutter is found\\nby the method explained in Part I. of this Chapter.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0087.jp2"}, "84": {"fulltext": "ro BROWN SHARPE MFG. CO.\\nCHAPTER IX.\\nDIRECTIONS FOR CUTTING BEVEL GEARS\\nWITH ROTARY CUTTER.\\n(Fig. 20.)\\nIn order to obtain good results, the gear blanks must be of\\nthe right size and form. The following sizes for each end of\\nthe tooth must be given the workman\\nTotal depth of tooth.\\nThickness of tooth at pitch line.\\nHeight of tooth above pitch line.\\nThese sizes are obtained as explained in Chapter VIII.\\nThe workman must further know the cutting angle (see\\nformula on page 13 and compare Chapter VIII.), and be pro-\\nvided with the proper tools with which to measure teeth, etc.\\nIn cutting a gear on a universal milling machine the opera-\\ntions and adjustments of the machine are as follows\\n1. Set spiral bed to zero line.\\n2. Set cutter central with spiral head spindle.\\n3. Set spiral head to the proper cutting angle.\\n4. Set the index on head for the number of teeth to be cut,\\nleaving the sector on the straight or numbered row of holes,\\nand set the pointer (or in some machines the dial) on cross-feed\\nscrew of milling machine to zero line.\\n5. As a matter of precaution, mark the depth to be cut for\\nlarge and small end of tooth on their respective places.\\n6. Cut two or three teeth in blank to conform with these\\nmarks in depth. The teeth will now be too thick on both their\\npitch circles.\\n7. Set the cutter off the center by moving the saddle to or\\nfrom the frame of the machine by means of the cross-feed\\nscrew, measuring the advance on dial of same. The saddle\\nmust not be moved further than what to good judgment", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0088.jp2"}, "85": {"fulltext": "PROVIDENCE, R. I.\\n7*\\nFig. 20.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0089.jp2"}, "86": {"fulltext": "72 BROWN SHARPE MFG. CO.\\nappears as not excessive at the same time bearing in mind\\nthat an equal amount of stock is to be taken off each side of\\ntooth.\\n8. Rotate the gear in the opposite direction from which the\\nsaddle is moved off the center, and trim the sides of teeth (A)\\n(Fig. 20.)\\n9. Then move the saddle the same distance on the opposite\\nside of center and rotate the gear an equal amount in the\\nopposite direction and trim the other sides of teeth (C).\\n10. If the teeth are still too thick at large end E, move the\\nsaddle further off the center and repeat the operation, bearing\\nin mind that the gear must be rotated and the saddle moved\\nan equal amount each way from their respective zero settings.\\nIt is generally necessary to file the sides of teeth above the\\npitch line more or less on the small ends of teeth, as indicated\\nby dotted lines F F. This applies to pinions of less than 30\\nteeth.\\nFor gears of coarser pitch than 5 diametral it is best to\\nmake one cut around before attempting to obtain the tooth\\nthickness.\\nThe formulas for obtaining the dimensions and angles of\\ngear blanks are given in Chapter III.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0090.jp2"}, "87": {"fulltext": "PROVIDENCE, R. I.\\n73\\nCHAPTER X.\\nTHE INDEXING OF ANY WHOLE OR FRAC-\\nTIONAL NUMBER.\\n(Fig. 21\\nIn indexing on a machine the question simply is How-\\nmany divisions of the machine index have to be advanced to\\nadvance a unit division of the number required. To which\\nis the\\ndivisions of machine index\\nanswer\\nnumber to be indexed\\nSuppose the number of divisions in index wheel of machine\\nto be 216.\\nExample I. Index 72.\\nAnswer: 216\\n72\\n3 (3 turns of worm).", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0091.jp2"}, "88": {"fulltext": "74 BROWN SHARPE MFG. CO.\\nExample II. Index 123.\\n1 .93\\n123 123\\nIf now we should put on worm shaft a change gear having\\n123 teeth, give the worm shaft, Fig. 21, one turn, and in addi-\\ntion thereto advance 93 teeth of the change gear (to give the\\nfractional turn), we would have indexed correctly one unit of\\nthe given number, and so solved the problem. Should we not\\nhave change gear 123 we may try those on hand. The ques-\\ntion then is How many teeth (x) of the gear on hand (for\\ninstance 82) must we advance to obtain a result equal to the\\none when advancing 93 teeth of the 123 tooth gear We have\\nwhere x 62\\n123 82\\nExample III. Index 365, change gear 147.\\nwhere j 87 -2-\\n3 6 5 J 47 3 6 5\\nHere 147 is the change gear on hand. In indexing for a unit\\nof 365 we advance87teeth of our 147 tooth gear. It is evident\\nthat in so doing we advance too fast and will have indexed\\nthree teeth of our change gear too many when the circle is\\ncompleted. To avoid having this error show in its total amount\\nbetween the last and the first division, we can distribute the\\nerror by dropping one tooth at a time at three even intervals.\\nExample IV. Index 190.\\n216 26\\nYqo Too Change gear on hand 88 T\\nwhere j 12\\n190 88 190\\nTo distribute the error in this case we advance one additional\\ntooth ot a time of the change gear at eight even intervals.\\nExample V. Index 117.3913.\\n216 _ ^86087\\nH7-39 T 3 ll 739 1 3\\nThis example is in nowise different from the preceding\\nones, except that the fraction is expressed in large numbers.\\nThis fraction we can reduce to lower approximate values,\\nwhich for practical purposes are accurate enough. This is\\ndone by the method of continued fractions. [For an explana-", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0092.jp2"}, "89": {"fulltext": "PROVIDENCE, R. I. 75\\ntion of this method we refer to our Practical Treatise on\\nGearing.\\n986087\\n739 x 3\\n986087)\\nI I 73913\\n986087\\n(1\\n187826) 986087 (5\\n939 J 30\\n46957) 187826 (3\\n140871\\n46955) 46957 (1\\n46955\\n2) 46955 (23477\\n46954\\nj) 2 (2\\n2\\n739*3\\n1 1\\n5 i\\n3 i\\n1 1\\n23477\\n2\\nr=3 1 23477\\n1 b 5 16 21 493033 986087\\nl =i 6 n 19 25 586944 n739 T 3\\nNote.. Find the first two fractions by reduction and z the\\n11 1 1 6\\n5\\nothers are then found by the rule c a\\nJ b y c a 1 ^d 1\\nThe fraction is a good approximation; putting therefore\\na change gear of 25 teeth on worm shaft, we advance (beside\\nthe one full turn) 21 teeth to index our unit.\\nOf course, in using any but the correct fraction we have an\\nerror every time we index a division so that when indexed\\naround the whole circle, we have multiplied this error by the\\nnumber of divisions.\\nIn the present example this error is evidently equal to the\\ndifference between the correct and the approximate fraction\\nused. Reducing both common fractions to decimal fractions\\nwe have\\n9S6087 Q\\n.84000006\\nn739 r 3\\nM\\n1 2I\\n=.84000000\\n.uoooooo6 error in each division.\\nv", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0093.jp2"}, "90": {"fulltext": "76 BROWN SHARPE MFG. CO.\\n.00000006 X 1 1 7.3913 .00000704348 total error in complete\\ncircle. This error is expressed in parts of a unit division. (To\\nfind this error expressed in inches, multiply it by the distance\\nbetween two divisions, measured on the circle.) In this case\\nthe approximate fraction being smaller than the correct one,\\nin indexing the whole circle we fall short .00000704348 of a\\ndivision.\\nExample VI.\\nIndex 15.708\\n216 11706\\n13 1\\n15.708 15708\\n11796 _ 983\\n15708 1309\\n983 1309 1\\n983\\n326) 983 (3\\n978\\n5) 326 (65\\n30\\n26\\n25\\n1) 5 (5\\n5\\n983 _,\\n1309 r^-r\\n3+i\\n65 1\\n5\\n1 3 65 5\\n1 3 196 983\\n1 4 261 1309\\nIn using the approximation JJ-J the error for each division\\n(found as above) will be .000002927, for the whole circle\\n.0000460. In this case, the approximation being larger than\\nthe correct fraction, we overreach the circle by the error.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0094.jp2"}, "91": {"fulltext": "PROVIDENCE, R. I.\\n77\\nCHAPTER XI.\\nTHE GEARING OF LATHES FOR SCREW\\nCUTTING.\\n(Figs. 22, 23.)\\nThe problem of cutting a screw on a lathe resolves itself into\\nconnecting the lathe spindle with the lead screw by a train of\\ngears in such a manner that the carriage (which is actuated by\\n^vrvrv-TL/iy^\\nSimple Gearing.\\nFig. 22.\\nV ofC.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0095.jp2"}, "92": {"fulltext": "78\\nBROWN SHARPK MFG. CO.\\nthe lead screw) advances just, one inch, cr some definite dis-\\ntance, while the lathe spindle makes a number of revolutions\\nequal to the number of threads lo be cut per inch.\\nThe lead screw has, with the exception of a very few cases,\\nalways a single thread, and to advance the carriage one inch it\\ntherefore makes a number of revolutions equal to its number\\nCompound Gearing-\\nFig. 23.\\nof threads per inch. Should the lead screw have double\\nthread, it will, to accomplish the same result, make a number\\nof revolutions equal to half its number of threads per inch. It\\nfollows that we must know in the first place the number of\\nthreads per inch on lead screw.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0096.jp2"}, "93": {"fulltext": "PROVIDKNCE, R. I. 79\\nIt ought to be clearly understood that one or more inter-\\nmediate gears, which simply transmit the motion received from\\none gear to another, in no wise alter the ultimate ratio of a\\ntrain of gearing. An even number of intermediate gears\\nsimply change the direction of rotation, an odd number do not\\nalter it.\\nThe gearing of a lathe to solve a problem in screw cutting\\ncan be accomplished by\\nA. Simple gearing.\\nB. Compound gearing.\\nReferring to the diagrams, Figs. 22 and 23, we have in Fig.\\n22 a case of simple, and in Fig. 23 a case of compound gear-\\ning.\\nIn simple gearing the motion from gear E is transmitted\\neither directly to gear Ron lead screw or through the interme-\\ndiate F. In compound gearing the motion of E is transmitted\\nthrough two gears (G and H) keyed together, revolving on the\\nsame stud n, by which we can change the velocity ratio of the\\nmotion while transmitting it from E to R. With these four\\nvariables E, G, H, R, we are enabled to have a wider range of\\nchanges than in simple gearing.\\nB and C, being intermediate gears, are not to be considered.\\nIf, as is generally the case, gear A equals gear D, we disregard\\nthem both, simply remembering that gear E (being fast on\\nsame shaft with D) makes as many revolutions as the spindle.\\nSometimes gear D is twice as large as gear A, then, still con-\\nsidering gear E as making as many revolutions as the spindle,\\nwe deal with the lead screw as having twice as many threads\\nper inch as it measures.\\nSIMPLE GEARING,\\nLet there be the number of teeth in the different gears\\nexpressed by their respective letters, as per Fig. 22, and\\ns threads per inch to be cut,\\nL threads per inch on lead screw then\\n1. s _ R\\nL E", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0097.jp2"}, "94": {"fulltext": "SO BROWN SHARPE MFG. CO.\\nIf now one of the two gears E and R is selected, the other\\nwill be\\nL\\nThe two gears may be found by making\\nR\\nE\\nP _P where/ may be any number.\\n3. The above holds good when a fractional thread is to be\\ncut, but if the fraction is expressed in large numbers, as, for\\ninstance, j- 2.833 C 2 ^mr)\u00c2\u00bb we nrst reduce this fraction (y^ 3 t0\\nlower approximate values by the process of continued fraction\\n(see pages 73 and 74).\\n833 ICOO\\n833\\n167)\\n(I\\n8l3 4\\n66S\\n165) 167 (1\\n165\\n2) 165 (82\\n16\\n5\\n4_\\n1)2(2\\n2\\nI\\n4 I 82\\n2\\nI\\nI\\nA JL ill\\n5 6 497\\n833\\n1000\\n.8^^ (nearly) and s 2^\\nu 6\\nIf in this case L 4, and we select E 48, then, since\\nR fJE R 34\\nCOMPOUND GEARING.\\n4. In a lathe geared compound for cutting a screw the\\nproduct of the drivers (E and H, Fig. 2^) multiplied by the num-\\nber of threads per inch to be cut must equal the product of the\\ndriven (G and I\\\\) multiplied by the number of threads on lead\\nscrew. This is expressed by\\nF H s\\nE H s r G R L or f 1", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0098.jp2"}, "95": {"fulltext": "PROVIDENCE, R. I. 8 1\\nIf three of the gears E, H, G, R have been selected, the\\nfourth one would be either\\nGRL\\nH s\\nH\\nGRL\\nE s\\nG-\\nE H s\\nK L\\nR\\nE H s\\nG L\\nR G L\\nor\\nor\\nor\\nL\\nE H\\n/J^GX\\nVL.E.H/\\nIf a fractional thread is to be cut, as under 3, we reduce\\nthe fraction to lower approximate values.\\nExample.\u00e2\u0080\u0094 Gear for 5.2327 threads per inch, lead screw is\\n6 threads.\\n2^27\\n.2327 -^\u00e2\u0080\u0094L\\nIOOOO\\n2327) iooco (4\\n93o8\\n692) 2327 (3\\n2076\\n251) 692 (2\\n502\\n190) 251 (1\\n190\\n~6t) 19c (3\\n183\\n7) 61 (8\\n56\\n5)7(i\\n5_\\n2; 5 (2\\n4\\n1)2 (2\\n2\\n10 37 3\u00c2\u00b0 6 343 99 2 2 3 2 7\\n4 13 3\u00c2\u00b0 43 x 59 !3!5 J 474 4263 10000\\n10 1 j IO\\n.2327 (nearly) and 5.2327 5\\n43 43\\nSelecting E 43, H 52, R 50, and\\nG we have G 3\u00c2\u00a3 xJJ ?q.\\nR L 50 6 y", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0099.jp2"}, "96": {"fulltext": "82 BROWN SHARPE MFG. CO.\\n5. The examples so far given all deal with single thread.\\nThe pitch of a screw is the distance from center of one thread to\\nthe center of the next. The lead of a screw is the advance for\\neach complete revolution. In a single thread screw the pitch\\nis equal to the lead, while in a double thread screw the pitch\\nis equal to one-half the lead in a triple thread screw equal to\\none-third the lead, etc.\\nIf we have to gear a lathe for a many-threaded screw\\n(double, triple, quadruple, etc.), we simply ascertain the lead,\\nand deal with the lead as we would with the pitch in a single\\nthread screw, i. we divide one inch by it, to obtain the num-\\nber of threads for which we have to eear our lathe.\\nExample. Gear for double thread screw, lead .4654.\\nNumber of threads per inch to be geared for is\\n2.1487\\nLead -4654\\nLead screw is four threads per inch.\\nAs in previous examples, we reduce the fraction .14%? -f\u00c2\u00a3\u00c2\u00a3f6\\nto lower approximate values by the process of continued frac-\\ntion.\\nFrom the different values received in the usual way we\\nselect\\n4} .1487 (nearly) and 2.1487 2AJ\\nWe have therefore\\nS 24-1\\nL 4\\nE 74\\nSelecting G 30\\nH 40\\nR\\nE H. s _ 74 -40. 2H_.\\n3J\\nG L\\nNote. In using any but the original fraction we commit an error. This error\\ncan be found by reducing the approximate fraction used to a decimal fraction, and\\ncomparing it with the original fraction. In the above example the original fraction is\\n.14S7 and\\nH I4S64\\nError .oooc6 inch in lead.\\nIn cutting a multiple screw, after having cut one\\nthread, the question arises how to move the thread tool the\\ncorrect amount for cutting the next thread.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0100.jp2"}, "97": {"fulltext": "PROVIDENCE, R. I. 83\\nIn cutting double, triple, etc., threads, if in simple or com-\\npound gearing the number of teeth in gear E is divisible by\\n2, 3, etc., we so divide the teeth then leaving the carriage\\nat rest we bring gear E out of mesh and move it forward one\\ndivision, whereby the spindle will assume the correct position.\\nWhen E is not divisible we find how many turns (V) of\\ngear R are made to each full turn of the spindle. Dividing\\nthis number by 2 for double, by 3 for triple thread, etc., we\\nadvance R so many turns and fractions of a turn, being careful\\nto leave the spindle at rest.\\nFor compound gearing\\nG R\\nWhen the gear D is twice as large as the gear A (ss ex-\\nplained in fifth paragraph, page 78.) the formula would be\\ny= E. H.\\n_ 2 G. R.\\nIf in simple gearing both E and R are not divisible, one\\nremedy would be to gear the lathe compound or the face-\\nplate may be accurately divided in tw T o, three or more slots,\\nand all that is then necessary is to move the dog from one slot\\nto another, the carriage remaining stationary.", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0101.jp2"}, "98": {"fulltext": "", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0102.jp2"}, "99": {"fulltext": "", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0103.jp2"}, "100": {"fulltext": "", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0104.jp2"}, "101": {"fulltext": "", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0105.jp2"}, "102": {"fulltext": "P !b", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0106.jp2"}, "103": {"fulltext": "Wftp", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0107.jp2"}, "104": {"fulltext": "", "height": "4241", "width": "2509", "jp2-path": "formulasingearin04stut_0108.jp2"}}