{"1": {"fulltext": "", "height": "4551", "width": "2897", "jp2-path": "elementarylesson00hall_0001.jp2"}, "2": {"fulltext": "", "height": "4299", "width": "2612", "jp2-path": "elementarylesson00hall_0002.jp2"}, "3": {"fulltext": "", "height": "4299", "width": "2612", "jp2-path": "elementarylesson00hall_0003.jp2"}, "4": {"fulltext": "", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0004.jp2"}, "5": {"fulltext": "ELEMENTARY\\nLESSONS IN PHYSICS\\nMECHANICS {INCLUDING HYDROSTATICS)\\nAND LIGHT\\nBV\\nEDWIN H. HALL, Ph.D.\\nAssistant Professor of Physics in Harvard College\\nNEW YORK\\nHENRY HOLT AND COMPANY\\n1900", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0005.jp2"}, "6": {"fulltext": "TWO COPIES RECEIVED,\\nLibrary of Congre\u00c2\u00ab%\\nOffice of the\\nFEB 7 1900\\nKtglttar of Copyright*\\n54196\\nCopyright, 1900\\nBY\\nHenry Holt Co t\\nSECOND COPY,\\nO O (o\\nROBERT DRUMMOND, ELECTROTYPER AND PRINTER, NEW YORK.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0006.jp2"}, "7": {"fulltext": "INTRODUCTION.\\nThis volume, which is the First Part of Hall and Ber-\\ngen s revised Text-booh of Physics (1897), may be regarded\\nas the second edition of Hair s Elementary Lessons in\\nPhysics. It is intended for the use of pupils in the early\\nyears of a high-school course or even the last year of a\\ngrammar-school course, and it assumes no previous system-\\natic study of physics.\\nThe course of study here given includes laboratory work,\\nto be done by the pupils, combined with a considerable\\namount of general instruction, to be illustrated by lec-\\ntures given by the teacher. The laboratory work is mainly\\nor wholly quantitative, as it must be for large classes, quali-\\ntative laboratory work in such classes making impossible\\ndemands upon the time and energy of the teacher.\\nA First Course made up, as this one is, of simple experi-\\nments in mechanics (including hydrostatics) and optics,\\nmore difficult matters in mechanics, together with heat,\\nsound, electricity, and magnetism, being deferred, is un-\\nusual; but it is here proposed as better suited to many pu-\\npils and to many schools than the more familiar practice of\\ngoing through the whole of mechanics before entering upon\\nany other part of physics, and putting light, or optics, after\\nheat. The laboratory outfit required for these early exer-\\ncises is much less complicated and expensive than that\\nrequired for much of the later laboratory work so that\\nmany schools which would be quite unable to offer a labo-\\niii", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0007.jp2"}, "8": {"fulltext": "iv INTRODUCTION.\\nratory course extending over the whole field of elementary-\\nphysics will find it possible to do what this book requires.\\nMoreover, those teachers w r ho have ample means and facil-\\nities, and who intend to take their pupils through the\\nwhole range of elementary laboratory work, will find it\\nadvantageous to interrupt the course in mechanics lest their\\nclasses grow tired of what is, for many young pupils, the\\nleast interesting part of the study.\\nThe book follows, as a rule, the method of leading up to\\nthe statement of laws by means of carefully chosen experi-\\nments, rather than the opposite one of giving experiments\\nas illustrations or proofs of laws already stated. It can\\nhardly be said for the former method that it teaches the\\nart of making discoveries, that art is as difficult to teach\\nas the art of getting rich, but it has a tendency to keep\\nthe pupil in a more active, self-dependent state of mind\\nthan the latter method, and in particular it prevents iu a\\nlarge measure that state of bias, or preconception, in the\\nperformance of experiments, which is so dangerous not\\nmerely to accuracy of observation but to mental rectitude.\\nOn the other hand, the teacher using the method of this\\nbook must not allow his pupils to think that their experi-\\nments, even when most satisfactory, really demonstrate the\\nrigid accuracy of any numerical law, the law of a balanced\\nlever, for instance. He should ask of them, What law do\\nyour experiments indicate as true and after their answer\\nhe should tell them whether their inference is or is not in\\naccordance with the opinion held by those best qualified\\nto judge of the matter in question.\\nIt is the firm conviction of the writer that class labora-\\ntory work not accompanied by persistent, energetic teach-\\ning is sure to be a failure. We are often told that the\\nfavorite method of the elder Agassiz with a new pupil was", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0008.jp2"}, "9": {"fulltext": "INTROD UCTION. V\\nto set him to gaze in solitude at a single fish for two or\\nthree days. Those who would make this the model for\\nscience-teaching in general forget that pure observation\\nof numerous, minute, varied details plays a much more\\nimportant part in natural history than in physics. The\\nteacher of physics who would produce good and lasting\\nresults must see to it not merely that the laboratory work\\nshall be carefully done, but that the proper lessons shall\\nbe drawn from it and the proper applications made. In\\nfact, the young pupil should give as much time to the\\nstudy of physics in the lecture- or recitation-room as in the\\nlaboratory proper.\\nThe course of study described in this book is intended\\nto run through a school year and to occupy the pupil at\\nleast two school-periods, each forty minutes long, or more,\\nper week; one usually in the laboratory, and the other in\\nthe lecture- or recitation-room. The number of laboratory\\nExercises is considerably less than the number of school-\\nweeks in the year, but some of them may prove to be too\\nlong for a single school-period, and teachers will welcome\\nan occasional opportunity for repetition or review. The\\namount of time required for the course will depend some-\\nwhat upon the age of the pupils taking it, and classes in\\nthe first year of a high-school course may find three\\nschool-periods a week for one year none too much time for\\ndoing the work well.\\nIt is highly desirable that pupils whose laboratory work\\nis confined to that described in this book should have lec-\\nture-room illustrations of many things not here dealt with,\\nelementary facts and principles in heat, sound, electricity,\\nand magnetism. It is therefore recommended that every\\nteacher of such pupils be provided with the means neces-\\nsary for such illustrations, for example much of the appa-", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0009.jp2"}, "10": {"fulltext": "vi INTRODUCTION.\\nrat us designated by Roman numerals in Hall and Bergen s\\nPhysics.\\nThe following estimates of cost for apparatus and ma-\\nterials are only approximate. It is hardly possible to make\\nan accurate estimate, as prices will vary from time to time,\\nand different dealers have somewhat different grades of ap-\\nparatus. The cheapest is not necessarily the best to buy.\\nFOR THIS BOOK.\\nTeacher s apparatus and supplies, pp. 174-178 $78.00\\nStudents apparatus, pp. 170-173, for each member\\nof a laboratory squad 6.00\\nTable, accommodating six workers, p. 178 25.00\\nTotal for all Exercises and Experiments of this\\nbook, with laboratory squads limited to twelve.. 200.00\\nFOR THE SECOND PART OF HALL AND BERGEN S\\nPHYSICS.\\nTeacher s apparatus, pp. 581-586 350.00\\nBy omittiug the thermopile and accompanying\\napparatus and the Roentgen-ray apparatus this ex-\\npense can be reduced about $100.\\nApparatus for the course can be obtained from the fol-\\nlowing well-known manufacturers:\\nThe Chicago Laboratory Supply and Scale Company,\\n39 West Randolph Street, Chicago.\\nThe Franklin Educational Company, Harcourt Street,\\nBoston.\\nThe Knott Company, 16 Ashburton Place, Boston.\\nThe Ritchie Company, Brookline, Mass.\\nThe Ziegler Electric Company, 141 Franklin Street,\\nBoston.\\nE. II. H.\\nJanuary 16, 1900", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0010.jp2"}, "11": {"fulltext": "TABLE OF CONTENTS.\\nPAGE\\nIntroduction iii\\nCHAPTER I.\\nINTRODUCTORY.\\nDefinition of Physics. Use of Physics. Qualitative and\\nQuantitative Knowledge. Object of this Course.\u00e2\u0080\u0094 Preliminary\\nExercises: Measurement of Distance, of Area, of Volume, with\\nEstimation of Errors 1\\nMECHANICS.\\nCHAPTER II.\\nDENSITY AND SPECIFIC GRAVITY.\\nDensity.\u00e2\u0080\u0094 EXERCISE 1: Weight of Unit Volume of a Sub-\\nstance.\u00e2\u0080\u0094 Density of Water.\u00e2\u0080\u0094 Weight.\u00e2\u0080\u0094 Mass.\u00e2\u0080\u0094 EXERCISE 2:\\nLifting Effect of Water.\u00e2\u0080\u0094 EXERCISE 3: Specific Gravity of a\\nSolid that will Sink in Water.\u00e2\u0080\u0094 EXERCISE 4: Specific Gravity of\\nWood by Use of Sinker.\u00e2\u0080\u0094 EXERCISE 5: Weight of Water Dis-\\nplaced by a Floating Body. EXERCISE 6: Specific Gravity by\\nFloating Method.\u00e2\u0080\u0094 EXERCISE 7: Specific Gravity of a Liquid by\\ntwo Methods 15\\nCHAPTER III.\\nFLUID-PRESSURE.\\nFluids: Liquids and Gases\u00e2\u0080\u0094 Experiments with Pressure-\\ngauge in Water. Torricelli s Experiment. Atmospheric Pres-\\nvii", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0011.jp2"}, "12": {"fulltext": "viii TABLE OF CONTENTS.\\nPAGE\\nsure. \u00e2\u0080\u0094Barometer. Boyle s Law.\u00e2\u0080\u0094 Hydraulic Press. Water-\\npumps. Siphon. Balancing Columns 28\\nCHAPTER IV.\\nTHE LEVER,\\nEXERCISE 8 The Straight Lever, First Class, Circular\\nLever.\u00e2\u0080\u0094 EXERCISE 9: Centre of Gravity and Weight of Lever.\\nEXERCISE 10: Levers of the Second and Third Class: s.\u00e2\u0080\u0094 EXER-\\nCISE 11: Force Exerted at the Fulcrum. Pulleys. General Law\\nfor Relation of Power to Weight 41\\nCHAPTER Y.\\nTHREE FORCES ACTING THROUGH ONE POINT THE PARALLELO-\\nGRAM OF FORCES.\\nIntroductory. EXERCISE 12: Errors of a Spring-balance.\\nEXERCISE 13: Parallelogram of Forces.\u00e2\u0080\u0094 The Inclined Plane:\\nWedge, Screw. Equilib i ant aDd Resultant 61\\nCHAPTER VI.\\nFRICTION.\\nEXERCISE 14: Friction between Solid Bodies.\u00e2\u0080\u0094 EXERCISE 15:\\nCoefficient of Friction.\u00e2\u0080\u0094 Friction in Applied Mechanics.\u00e2\u0080\u0094 Rolling\\nFriction. Friction between Solids and Fluids 78\\nCHAPTER VII.\\nTHE PENDULUM.\\nUse in Clocks.\u00e2\u0080\u0094 Experiments.\u00e2\u0080\u0094 Springs in Place of Pendu-\\nlums 86\\nLIGHT.\\nCHAPTER VIII.\\nNature of Light\u00e2\u0080\u0094 Visibility of Objects.\\nLight is Something that Travels. Velocity.\u00e2\u0080\u0094 A Wave-\\nmotion.\u00e2\u0080\u0094 Pencils and Rays.\u00e2\u0080\u0094 Shadows.\u00e2\u0080\u0094 EXERCISE 16: Use of", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0012.jp2"}, "13": {"fulltext": "TABLE OF CONTEXTS. ix\\nPAGE\\nRumford Photometer. Bunsen s Photometer. Effect of Body\\non which Light Falls. Visibility of Objects 90\\nCHAPTER IX.\\nREGULAR REFLECTION OF LIGHT.\\nEXERCISE 17: Images in a Plane Mirror. Images of Images,\\nKaleidoscope. EXERCISE 18: Images Formed by a Convex\\nCylindrical Mirror. EXERCISE 19 Images Formed by a Concave\\nCylindrical Mirror. Relation of Cylindrical to Spherical Mir-\\nrors. The Ophthalmoscope. Formulas relating to Curved\\nMirrors 103\\nCHAPTER X.\\nREFRACTION OF LIGHT.\\nIntroductory Experiments. Angles of Incidence and Re-\\nfraction.\u00e2\u0080\u0094 EXERCISE 20: Index of Refraction of Glass.\u00e2\u0080\u0094 EX-\\nERCISE 21 Index of Refraction of Water.\u00e2\u0080\u0094 Index Different for\\nDifferent Colors. Index of Refraction and Velocity. Internal\\nReflection, Critical Angle. Transparent Plates and Prisms.\\nDispersion, the Spectrum.\u00e2\u0080\u0094 Lenses.\u00e2\u0080\u0094 EXERCISE 22; Focal\\nLength of Converging Lens.\u00e2\u0080\u0094 EXERCISE 23 Conjugate Foci of\\na Lens. EXERCISE 24 Shape and Size of Real Image Formed by\\na Lens. EXERCISE 25 Virtual Image Formed by a Lens.\\nSpherical and Chromatic Aberration in Lenses. Achromatic\\nLenses. 123\\nCHAPTER XL\\nTHE EYE SIGHT AND COLOR.\\nDescription of the Eye.\u00e2\u0080\u0094 Accommodation, etc. The Color-\\nsense. Mixing Color Impressions.;\u00e2\u0080\u0094 Complementary Colors.\\nFatigue of Retina. After-images 152\\nCHAPTER XII.\\nOPTICAL INSTRUMENTS.\\nPhotographer s Camera. Magic Lantern. Projecting a Spec-\\ntrum. Simple Microscope. Compound Micro-cope. Tele-\\nscope 156", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0013.jp2"}, "14": {"fulltext": "X TABLE OF CONTENTS.\\nAPPENDIX I.\\nPAGE\\nFocal Length, etc., of Lenses and Combinations 168\\nAPPENDIX II.\\nIndices of Refraction e 169\\nAPPENDIX III.\\nList of Apparatus, etc., for the Exercises and Experiments of\\nthe Preceding Pages 170", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0014.jp2"}, "15": {"fulltext": "ELEMENTS OF PHYSICS.\\nCHAPTER I.\\nINTRODUCTORY.\\n1. Definition of Physics. Physics is the science of.\\nmechanics, heat, sound, light, electricity, and magnetism,.\\nEverybody knows something about these things before he\\nbegins to study them in a regular way, but sometimes he\\ndoes not know them by the names which are given to them\\nin books.\\n2. Use of Physics. In sailing boats or flying kites, in\\nwalking or swimming, in almost any kind of bodily work or\\nplay, we have to do with physics, that part of physics which\\nis called mechanics. We learn to do many mechanical acts\\nvery well indeed by observation and experience, without\\nthinking very much about them or knowing exactly how we\\ndo them but when w T e have to do something that we have\\nnever done before and have never seen any one else do,\\nsomething, perhaps, that nobody ever did before, we must\\nthink and study.\\n3. Illustrations. Thus no man who has practiced swim-\\nming need study mechanics to improve himself in that art;\\nbut if he would build a ship and make it swim through all\\nkinds of weather and water, he must study mechanics a\\ngood deal in order to know what size and shape to give the\\nvarious parts, how best to put them together, and how to", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0015.jp2"}, "16": {"fulltext": "2 PHYSICS.\\nbalance the whole. If it is to be a steamship, some one\\nmust know a good deal about heat, to make the furnaces\\nand boilers right. We must know about magnetism to\\nmake and use the ship s compass. We may use electricity\\nto furnish light on board at night. We must study sound\\nin order to make the best fog-signals to guard against colli-\\nsions and shipwreck in thick weather.\\nIn short, the science of physics in all its main divisions\\nis not only a very interesting study to many minds, but it\\nis of great use to civilized mankind. Man has become\\ncivilized, indeed, not by merely imitating what his fathers\\nhave done, but by studying, that is, observing and thinking,\\nand gradually improving upon the work of those who have\\ngone before him.\\n4. Qualitative Knowledge. Everybody knows that a\\npiece of wood will float in water, and that a stone will sink.\\nEverybody knows that if a stick and a stone are tied\\ntogether and put into water, the stone tends to sink the\\nstick, and the stick tends to float the stone. This kind of\\nknowledge is called qualitative. It tells in a general way\\nhow the stick and the stone act toward each other.\\n5. Quantitative Knowledge. Some people know enough\\nabout the laws of flotation to calculate with accuracy how\\nlarge a stick of a known kind of wood will be needed to\\nfloat a stone of known size and weight. They have what\\nis called quantitative knowledge of the matter. They can\\ntell how much the stone will pull down on the wood, and\\nthe wood pull up on the stone, when the two are together\\nin water.\\nEverybody knows that a beam has a quality which we call\\nstrength it can bear a load. This is qualitative knowl-\\nedge. Everybody knows that a thick beam is stronger than\\na thin beam. This is quantitative knowledge of a kind, a\\nrather indefinite kind. Some people know how much", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0016.jp2"}, "17": {"fulltext": "INTROD UCTOR Y. 3\\nstronger the thick beam is than the thin beam. They have\\na more complete quantitative knowledge.\\n6. Comparison of the Two Kinds of Knowledge. It is\\nevident that quantitative knowledge is more useful than\\nmere qualitative knowledge. The former includes the latter.\\nThe qualitative man says, I want to build a house. I\\nshall need some land to put it on, and some beams and\\nboards and bricks, etc. The quantitative man says,\\nYes, you will need ail these things, but if you don t make\\nyour ideas more precise you will have a lumber-yard when\\nyou have done, not a house.\\n7. Object of this Course in Physics. The knowledge of\\nphysics which children and older people get by merely\\nknocking about in the world is mostly qualitative. The\\ncourse of work laid out in this book is intended to add greatly\\nto the pupil s stock of this kind of knowledge, and to do\\nsomething more. It aims to make the pupil familiar with\\nquantitative work, and to give him a considerable amount\\nof quantitative knowledge.\\nWe shall begin at once with simple introductory measure-\\nments. All the exercises of this chapter are called Prelim-\\ninary Exercises.\\nMeasurement of Distance.\\n8. The Straight Line. The line to be measured may be\\nalong the edge of a table (or sheet of paper) from one fine\\nscratch to another, a distance of about 15 inches. It is a\\ngreat convenience to have all the pupils\\nmeasure equal distances; accordingly,\\nthe teacher is advised to lay off these\\ndistances by some method like the fol-\\nlowing: A carpenter s square is placed a~\\nalong the edge of the table as in Fig. 1, FlG 1\\nand while it is held firmly in place a fine light scratch is", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0017.jp2"}, "18": {"fulltext": "4 PHYSICS.\\nmade with the point of a sharp knife-blade at right angles\\nwith the edge of the table at the points a and b. The dis-\\ntance from a to i is the one to be measured by the pupil.\\nThe first-described method of using the measuring-stick in\\nthe following Exercise is not a good method, but it is one\\nthat many will use if they are not properly instructed.\\nThe second method is a good one, and the two are here\\nbrought together in order that the pupil may see at once\\nthe right way and the wrong way to use such an instrument.\\nMuch of the interest and profit of this Exercise will come\\nfrom the opportunity given each pupil to compare his own\\nwork with that of others.\\nEXERCISE A.\\nMEASUREMENT OF A STRAIGHT LINE.\\nApparatus A short measuring-stick (No. 1) and a meter-rod\\n(No. 2).\\nTo each pupil is given a measuring-stick about one-fourth as long\\nas the distance from a to b. We will suppose that these sticks are\\nmade by sawing a meter-rod, graduated to millimeters, into ten\\nequal parts. The saw-cut will usually leave the divisions at the\\nvery ends of the sticks imperfect, and these divisions should not be\\nused in the measurements.\\nLet each pupil measure his distance at least twice carefully, with\\nhis measuring-stick laid flat upon the table, the marks upon the\\nstick being thus horizontal, and let him write upon the blackboard\\nthe results of his two measurements.\\nThen let each pupil measure his distance twice again, this time\\nplacing his measuring-stick upon its edge, so that the marks upon it\\nwill be vertical, making a light, fine mark upon the table with a\\nsharp pencil to set the stick by, whenever it is moved forward a\\nlength. These new measurements are also to be placed upon the\\nblackboard under the first ones.\\nFinally let each pupil measure his whole distance at once with his\\nmeter-rod and write this last measurement with the others.\\nAny piece of apparatus to be used in the Exercises will usually\\nbe referred to by the number it bears in the list of apparatus given\\nat the end of the book.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0018.jp2"}, "19": {"fulltext": "INTBODUCTOBT. 5\\n9. Errors. To judge of the accuracy of a set of measure-\\nments it is not enough to know how much these differ\\namong themselves, for the importance of the difference\\nusually depends upon the ratio which the difference bears\\nto the whole quantity measured. A thousandth part of an\\ninch might be a very serious difference to a watchmaker in\\nthe measurement of some small cylinder, while a difference\\nof several inches in the measurement from one mile-post to\\nanother would be of little consequence. The pupil should\\ntherefore form the habit of comparing his errors, or the\\ndifferences of his measurements, with the whole quantity\\nthat he had to measure.\\nLet us suppose, for instance, that in Exercise A the\\nmeasurements made by one pupil are 37.30 cm., 37.00 cm.,\\nand 37.10 cm. The greatest difference is found between\\nthe first and second. It is 0.3 cm., and its ratio to 37.15\\ncm., which is midway between 37.30 cm. and 37.00 cm.,\\nis 0.0081 We see, then, that the difference between the\\ntwo measurements of the line is about eight one-thousandths,\\nnot quite one per cent, of the length of the line.\\nEach pupil should make a similar calculation from his\\nown measurements in Exercise A.\\n10. Units and Standards of Measurement. The impor-\\ntance of having definite units of length, of weight, etc., so\\nthat any man in dealing with his neighbor may know just\\nhow much is meant by the words foot, pound, and the like,\\nis so great that in all civilized countries the exact meaning\\nof such words is fixed by law, and very great care is taken\\nto make and preserve government standards, as they are\\ncalled, standard yard-sticks, standard pound-weights, for\\ninstance, with which as patterns the measuring instruments\\nused in business are compared and tested.\\nInteresting accounts of the foot, the yard, the meter, etc.,\\ncan be found in almost any encyclopedia.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0019.jp2"}, "20": {"fulltext": "6 PHYSICS.\\nMeter-rods for school use are in many cases marked off\\nin inches on one side. With the information given by such\\na rod, the class can find how many centimeters are equal to\\none inch. This number carried to two places of decimals\\nis accurate enough for most purposes.\\n11. The Right Triangle. Eight triangles, that is, tri-\\nangles having one right angle (see Fig. 2), are much used in\\nthe study and application of physics. In such triangles\\nFig. 2.\\nthere is a simple and important relation between the length\\nof the longest side and the length of the other two sides.\\nPart 1 of the following Exercise B is intended to show this\\nrelation and at the same time to give practice in measure-\\nment.\\n12. Circles. The relation between the length of the\\ndiameter of a circle and the length of its circumference is\\nalso very frequently used in physics. Part 2 of Exercise B\\nhas to do with this relation.\\nEXERCISE B.\\nTHE LINES OF THE RIGHT TRIANGLE AND THE CIRCLE.\\nApparatus A 30-cm. measuring- stick (No. 3). A sheet of paper\\nupon which is drawn carefully a right triangle no side of which is\\nless than 10 cm. long. (No two pupils should use exactly similar", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0020.jp2"}, "21": {"fulltext": "INTRODUCTORY. 7\\ntriangles.) A cylinder of wood 4 or 5 cm. in diameter (No. 4). A\\nnarrow straight-edge strip of thin paper.\\nPart 1. Measurement of the Sides of a Right Triangle.\\nLet each pupil measure very carefully all the sides of his triangle,\\nnot being content to read to the nearest 0.1 cm., but striving to note and\\nmeasure 0.05 cm. distances, if he can do so without hurting his eyes.\\nAfter the measurements are made, square the length of each side\\nand compare the greatest square with the sum of the other two\\nsquares. The conclusion drawn from this comparison must not be\\nextended to triangles which are not right-angled.\\nPart 2. Measurement of the Circumference and Diam-\\neter of A Circle. Measure carefully the diameter of one end of\\nthe cylinder. Then wrap the strip of paper around the curved sur-\\nface of the cylinder at the same end, and mark upon the edge of the\\nstrip the point where the second winding of the paper begins to\\noverlap the first. Then unfold the paper and measure upon it that\\ndistance which extended once around the cylinder. Then divide this\\ndistance, which of course is equal to the circumference of the circle,\\nby the length of the diameter. The ratio thus obtained is one which\\nit is important to know, although we shall not have much occasion\\nto use it in this book. Mathematicians, physicists, and engineers\\nuse it so much that thay have a particular sign, it, to denote it.\\nThis sign is a Greek letter and is called pe by students of Greek,\\nbut when used as just described it is often called pi to distinguish\\nit from p.\\n13. Discussion of Exercise B. The measurements of\\nExercise B may be discussed somewhat as follows: The\\nsquare of the longest side of the triangle is found by one\\npupil to be 404.01, and the sum of the squares of the other\\ntwo sides 406.05. If the two short sides were measured\\ncorrectly, how large an error in the measurement of the\\nlongest side would cause the disagreement here found\\nThe long side was measured as 20.10 cm. If it had been\\ncalled 20.20 cm., its square would have been 408.04, which\\nis about as much too large as the square actually found is\\ntoo small. If the distance had been measured as 20.15 cm.,\\nthe square would have been 406.02, a quantity very close", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0021.jp2"}, "22": {"fulltext": "8 physics.\\nindeed to the sum of the other two squares. If, therefore,\\nthe original error lay entirely in the measurement of the\\nlongest side, this error must have been very nearly 0.05 cm.\\nOf course the error may have been made in measuring the\\nother sides, or in drawing the triangle, or in all parts of the\\nwork. An error which mistakes 20.15 for 20.10, or 201.5\\nfor 201.0, or 2015 for 2010, is called in each case an error\\nof 5 parts in 2015, or 1 part in 403, or an error of about\\ni per cent (see remarks following Exercise A).\\nQUESTION.\\nIn the case of the circle, which would make the greater difference\\nin the result (circumference -5- diameter), an error of 0.05 cm. in the\\nmeasurement of the diameter or an error of 0.10 cm. in the measure-\\nment of the circumference\\nMeasurement of Area.\\n14. Unit of Area. Thus far we have been measuring\\nlines. To measure a line, as we see, is merely to find out\\nby trial that it is so many centimeters or inches long. A\\nline 10.6 cm. long is one that could be divided into ten full\\ncentimeters and six tenths of another centimeter. We here\\ncall the centimeter our unit of length.\\nIf we have to measure a surface, the whole table-top, for\\ninstance, our task is to find the number of square centi-\\nmeters, or square inches, or square feet, that would be\\nrequired to cover it, or that it would make if it were cut\\nup without waste into squares. In this case the square\\ncentimeter, or square inch, or whatever square we choose\\nto take, is the unit of area. We might set about to measure\\nsurfaces by actually placing a little square, a square centi-\\nmeter, for instance, on the given surface, marking a line*\\nclose around it, then moving it to a new place, marking\\naround it, and so on till we had marked off the whole sur-\\nface \\\\n\\\\o little squares, with perhaps some fractions of", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0022.jp2"}, "23": {"fulltext": "INTRODUCTORY.\\n9\\nsquares. But this is not the common or the best way of\\nmeasuring surfaces. The common way is to measure the\\nlength of certain lines on the surface and from the lengths\\nof these lines to calculate the extent of the surface.\\n15. Measurement of Rectangles. If the surface is in the\\nform of a rectangle, like Fig. 3, it is plain\\nthat we have merely to multiply the\\nnumber of units, centimeters let us say,\\nin the length by the number of centime-\\nters in the width, and the result, 8x1\\n32 in this figure, is the number of\\nsquare centimeters into which the surface can be divided.\\nThis is called the extent or area of the surface.\\nIn the next Exercise we shall undertake to find rules for\\nthe measurement of surfaces not quite so simple in shape\\nas the rectangle shown in Fig. 3. These will be of the\\nclass called parallelograms.\\nFig. 3.\\n16. Parallelograms. A parallelogram is a flat figure\\nbounded by four straight linos, each line being parallel to\\nthe line opposite. Thus A and B in Fig. 4 are parallelo-\\nB\\nFig. 4.\\ngrams. A is what we have just called a rectangle, and we\\nhave seen how to find the area of any rectangle, but B is\\nnot quite so simple at first sight. A parallelogram like B,\\nwhich contains no right angle, is called an oblique parallel-\\nogram", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0023.jp2"}, "24": {"fulltext": "10 PHYSICS.\\nEXERCISE C.\\nAREA OF AN OBLIQUE PARALLELOGRAM.\\nApparatus: The 30-ciu. measuring-stick (No. 3). An oblique\\nparallelogram of paper about 20 cm. long and 10 cm. wide. (One of\\nthe straight-edged rulers (No. 24) may prove useful in this Exercise.)\\nDraw upon the paper figure a line like c in Fig. 5, taking care\\nto make a right angle with the top line\\nand the bottom line, and then cut or\\ntear the paper along the line c. Take\\nthe small piece thus removed and join it\\nto the larger piece, in such a way as to\\nFig. 5. make a figure that you know how to\\nmeasure. Measure the length and width\\nof the figure thus formed and calculate the extent of its surface.\\nThen put the two pieces together as they were at first and ask\\nyourself whether you could not, if another oblique parallelogram\\nwere given you, find the extent of its surface without cutting it.\\nFor the Class-room.\\nEstimate without measurement the length and width of some\\nvisible and convenient rectangles, a book-cover, a table-top, a win-\\ndow, etc., and calculate the areas from these estimated dimensions.\\nThen take the true dimensions and calculate the true areas.\\nMeasurement of Volume.\\n17. Unit of Volume. We have now to speak of the\\nmeasurement of volume. The unit of volume may be the\\ncubic centimeter, or the cubic inch, or the cubic foot, etc,\\nWe shall generally use the cubic centimeter as our unit.\\nWe mean, then, by the volume of a body the number of\\ncubic centimeters that could be made of that body if it were\\ncut up without waste, as one might cut up a large piece of\\nclay or putty.\\n18. Rectangular Bodies. In the case of a body whose\\nsurface is made up of rectangles, a brick, for instance, it is", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0024.jp2"}, "25": {"fulltext": "INTBODUCTORY. 11\\neasy to see how the volume may be calculated, if we know\\nthe length and the width and the thickness. We have\\nvolume length X width X thickness,\\n19. Irregular Bodies.\u00e2\u0080\u0094 If the body is of less regular\\nshape, like an ordinary stone or a lump of coal, it is not so\\neasy to calculate its volume from measurements of length,\\nwidth, and thickness. There is, however, a very easy way\\nof finding the volume of such a body by the use of water,\\nas will presently be seen.\\n20. Volume of Water.\u00e2\u0080\u0094 It is easy to find the volume of\\na quantity of water in several ways. One way is to pour the\\nwater into a rectangular box. Then we can measure its\\nlength and width and depth and calculate its volume.\\nAnother way is to pour it into a glass measuring-dish having\\nmarks upon it to tell the number of cubic centimeters\\nrequired to fill it to certain depths. Another method is to\\nweigh the water, for i t is known that one cubic centimeter\\nof water weighs one gram. Indeed this is the definition of\\none gram, the to eight of a cubic centimeter of tvater.* If\\nthe balance which we use for weighing reads in ounces\\ninstead of grams, we shall have to remember that 1 oz.\\nabout 28.3 gm., so that 1 oz. of water will be 28.3 cubic\\ncentimeters. We shall commonly find the volume of a\\nbody of water by weighing.\\n21. The Water Method. We will now try the water\\nmethod of finding the volume of a body, a rectangular\\nsolid. We shall find its volume by the water method and\\nalso by direct measurement and calculation, and then see\\nhow well the two results agree. This will test the water\\nmethod, and if we find it to work well, we can use it with\\nirregular solids which we cannot measure directly.\\nTo be exact one must add at 4\u00c2\u00b0 of the centigrade scale of tempera-\\nture. For the purpose of this book such exactness is unnecessary.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0025.jp2"}, "26": {"fulltext": "12\\nPHYSICS.\\nEXERCISE D.\\nVOLUME OF A RECTANGULAR BODY BY DISPLACEMENT\\nOF WATER,\\nApparatus A brass can (No. 5) called G in Fig. 6 A small catch-\\nbucket (No. 6) called p in Fig. 6. A spring-balance (No. 7). A\\nrectangular block of wood (No. 8) so loaded as to sink ia water.\\nClosing the overflow tube t of the can G, pour water into G until it\\nis filled nearly to the brim. Then open the tube and let all the water\\nflow out that will do so, catching it in the small can p, The large\\ncan should rest steadily upon the table, but the small one is better\\nheld in the hand when the flow begins, otherwise some water may\\nbe spilled. The flow should stop rather suddenly at last, with little\\nor no drip.\\nThrow away all the water thus caught in p and then weigh p on\\nthe spring-balance to the nearest gram or the nearest twentieth of\\nan ounce, according to the graduation of the balance.* Then,\\nclosing the tube t as before, lower into the can G the wooden block\\nuntil it rests upon the bottom. Then, or sooner if the can G seems\\nFig. 6.\\nlikely to be overflowed, open the tube t, and as before catch the\\nwater that runs out in the small can p. The water, Fig. 7, now\\nOrdinary small spring-balances now in the market are often\\nmarked off in half-ounce divisions, which are about inch long. The\\npupil will learn to estimate the position of the pointer when it falls\\nbetween two lines, so as to read to about of au ounce.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0026.jp2"}, "27": {"fulltext": "INTRODUCTORY.\\n13\\nstands just as high in G as it did just before the block was put into\\nit. The block has crowded out into the can p just its own bulk of\\nFig. 7.\\nwater. If, then, we can find the volume of the water that the block\\ndrove over into p, we shall have the volume of the block itself.\\nWeigh p and the water it contains.\\nWeight of small can and water\\n11 empty\\nwater alone\\nIf the weight as thus found is in grams, it is equal to the number\\nof cubic centimeters in the block. If the weight as thus found is in\\nounces, we must multiply the number of ounces by 28.3 in order to\\nfind the number of cubic centimeters in the block.\\nNow measure carefully the length, width, and thickness of the\\nblock and calculate the number of cubic centimeters it contains from\\nthese measurements.\\n(Experiments for finding the volumes of irregular bodies by the\\nwater method may well be postponed till the next Exercise, which\\nwould otherwise be a very brief one. Potatoes, stones, lumps of\\ncoal, etc., of suitable size may be used for these further experiments.\\nPractice for the Eye.\\nA line 10 inches long is drawn on a blackboard with a cross-line at\\nany point, and the members of the class estimate the distance from\\neither end to the cross-line. Practice like this helps toward accurate\\nreading of the spring-balance.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0027.jp2"}, "28": {"fulltext": "14 PHYSICS.\\nQUESTIONS.\\n(1) The true length of a certain line is 16.4 cm. One person meas-\\nures it as 16.6 cm., another as 16.3 cm. How great is the error of\\neach in per cents of the true length\\n(2) A certain rectangle is 50 cm. long and 20 cm. wide. It is meas-\\nured by one person as 50 cm. long and 20.2 cm. wide, and by another\\nperson as 50.2 cm. long and 20 cm. wide. If the area is calculated\\nfrom each set of measurements, how great (in per cents) will the error\\nbe in each case\\n(3) A certain rectangle has a base 100 cm. long and an altitude of\\n40 cm. Which will cause the greater error in the estimated area, an\\nerror of 2 cm. in the base or an error of 1 cm. in the altitude\\n(4) A rectangular solid is 40 cm. long, 30 cm. wide, and 20 cm.\\nthick. How great (in per cents) is the error made by calculating the\\nvolume from measurements which give 41 cm. for the length, 31 cm.\\nfor the width, and 19 cm. for the thickness", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0028.jp2"}, "29": {"fulltext": "CHAPTEE II.\\nDENSITY AND SPECIFIC GRAVITY.\\n22. Definition of Density. The weight of unit volume\\nof a substance is called the density of the substance. If\\nwe know the density of a substance we can calculate the\\nweight of any volume of that substance. Engineers and\\nother scientific men often have to find by this method the\\nweight of objects which it would be inconvenient to weigh.\\nThe weights of buildings and bridges, for instance, are\\nfound in this way. Books used by scientific men contain\\ntables giving the densities of many different substances.\\nThe density of a substance may be expressed as the\\nweight in grams of one cubic centimeter, or as the weight\\nin pounds of one cubic foot, or in any one of many other\\nways. For brevity, we call the first method of expression\\njust given the density in grams and cubic centimeters, and\\nthe second, the density in pounds and cubic feet. The\\nfollowing Exercise will make the matter plainer, and will\\ngive good practice in measuring and weighing.\\nEXERCISE I.\\nWEIGHT OF UNIT VOLUME OF A SUBSTANCE.\\nApparatus: A block of wood (No. 9). A spring balance (No. 7).\\nA measuring-stick (No. 3). Thread for suspending the block.\\nFind the weight of the block in grams and also in ounces.\\nMeasure the length of each of the four edges which are parallel to\\nthe grain of the wood, take the average of these measurements and\\ncall it the length of the block.\\n15", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0029.jp2"}, "30": {"fulltext": "16 P TS1C3.\\nMeasure the length of each of the four long edges which are cross-\\nwise to the grain of the wood, and call the average of these four\\nmeasurements the icidth of the block.\\nMeasure the length of each of the four short edges and call the\\naverage of these four measurements the thickness of the block.\\nThe weight in ounces is to be turned into pounds.\\nFrom the length, width, and thickne-s in centimeters the length,\\nwidth, and thickness in feet may be found by the rule that 1 ft.\\n30.5 cm., but it is shorter to find the volume in feet from the volume\\nin cubic centimeters by the rule that 1 cu. ft. 28300 cu. cm.\\nCalculate, 1st, how many grams, or what part of a gram, 1 cu. cm.\\nof the block weighs 2d, how many pounds, or what part of a\\npound, 1 cu. ft. of such wood weighs.\\n23. Density of Water. The density of water in grams\\nand cubic centimeters is 1; that is, 1 cu. cm. of water\\nweighs 1 gm. (see 20). The density of water in pounds\\nand cubic feet is very nearly 62.4; that is, 1 cu. ft. of water\\nweighs 62.4 lbs. These numbers for water should be com-\\nmitted to memory.\\nQUESTIONS.\\n1. What ratio is found from the results* of Exercise 1 between the\\ndensity of wood in grams and cubic centimeters and its density in\\npounds and cubic feet?\\n2. How does this compare with the ratio of the two densities of\\nwater, as given above\\n3. If the ratio is the same for the wood as for water, is this a\\nmere coincidence, or is the same thing true in the case of other\\nsubstances\\nPROBLEMS.\\n(1) If a piece of iron 10 cm. long, 8 cm. wide, and 7 cm. thick\\nweighs 4000 gm., what is its density in gm. and cu. cm, What is\\nits density in lbs. and cu. ft.\\n(2) The density of mercury in gm. and cu. cm. is about 13.6.\\nHow many lbs. would 1 cu. ft. of it weigh\\nIt is well to take the average of the results found by the various\\nmembers of the class.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0030.jp2"}, "31": {"fulltext": "DENSITY AND SPECIFIC GRAVITY. 17\\n24. Weight. Before going farther we need to think\\ncarefully about the meaning of the word weight, which we\\nhave already used a number of times, and shall have to use\\nvery often. The word has two meanings.\\nSometimes when we speak of the weight of a body we\\nmean the amount of the body, as when we speak of 10 lbs.\\nof butter or 100 lbs. of iron.\\nAt other times we mean by the weight of a body the\\namount of the earth s downward pull upon that body, as\\nshown by the spring-balance, for instance.\\nIt is somewhat hard to remember this distinction,\\nbecause the units in which we tell the amount of a body\\nhave the same name as the units in which we tell the pull\\nwhich the earth exerts upon the body. For instance, we\\nsay that the earth exerts a pull, ov force, of 5 lbs. upon\\n5 lbs. of wood, or 5 lbs. of coal, or anything which consists\\nof, or is, 5 lbs. of substance.\\nOften when we use the word weight it makes no difference\\nwhich of its two meanings we have in mind, but sometimes\\nit does make a difference. Thus, when we put a body\\nunder water, as we shall do in the next Exercise, and say\\nthat it appears to lose weight in going from air to water, we\\ndo not mean that there appears to be any less of the body\\nin water than there was in air. We mean that it requires\\na smaller pull of the spring-balance to keep the body from\\nsinking in water than it does to keep it from sinking in air.\\n25. Mass. In strict scientific language, the word mass\\nis commonly used in speaking of the amount of a substance,\\nand the word iveight in speaking of the earth s pull upon\\nthat substance. For example, a piece of iron the mass of\\nwhich is 50 lbs. is subject to a iveight of 50 lbs. exerted\\nby the earth.\\nSuch distinct ions, which use words in a scientific sense different\\nfrom the popular everyday sense, are often necessary in science, but\\nit would be rather absurd to try to make the popular use of the\\nwords agree with the scientific use in all cases.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0031.jp2"}, "32": {"fulltext": "18 PHYSICS.\\nSpecific Gravity.\\n26, Definition. It is often convenient to know the ratio\\nwhich the weight of a body dears to the tueight of an equal\\nbulk of ivater. This ratio is called the specific gravity of\\nthe body. Gravity comes from a Latin word gravis, mean-\\ning heavy. Specific here means distinctive, or particular.\\nThe specific gravity of a body is its particular heaviness\\nthe degree of heaviness which distinguishes this body from\\nother bodies of the same size but different weight.\\n27. Loss of Weight in Water. In finding specific\\ngravities it is a common practice to weigh bodies under\\nwater. The use of this practice will be made plain by\\nExercise 3. The loss of apparent weight suffered by a body\\nin going from air to water is shown in Exercise 2.\\nEXERCISE 2.\\nLIFTING EFFECT OF WATER UPON A BODY ENTIRELY\\nIMMERSED IN IT.\\nApparatus: Overflow-can (No. 5). Catcli- bucket (No. 6) Spring-\\nbalance (No. 7). Loaded block (No. 8). Thread.\\nFill the can and let it overflow and drip as in Exercise D. Catch\\nthis overflow in the small bucket and throw it away. Then weigh\\nthe empty bucket in grams.\\nWeigh the block in grams before immersing it in the water.\\nLower the block, still suspended from the balance, into the over-\\nflow-can till it is entirely covered, catching the overflow and saving it.\\nWeigh the block in the water, the balance being entirely above the\\nwater.\\nWeigh the bucket with the overflowed water.\\nSubtract the (apparent) weight of the block in water from its\\nweight in air, and call the difference the loss of weight of the block in\\nwater, or the buoyant force exerted upon the block by the water.\\nFind weight of the water in the small bucket, and compare this\\nwith the loss of weight of the block in water.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0032.jp2"}, "33": {"fulltext": "DENSITY AND SPECIFIC GRAVITY. 19\\nIf there is time, make a similar experiment with other bodies.\\nThe law illustrated in this Exercise is called from its discoverer\\nthe law, or principle, of Archimedes. (See any encyclopedia for an\\naccount of Archimedes.)\\nPROBLEMS,\\n(1) A certain body weighs 100 gm. out of water and 50 gm. in\\nwater. How great is the volume of the body?\\n(2) A certain body 5 cm. long, 3 cm. wide, and 2 cm. thick weighs\\n200 gm. in water. How much does it weigh out of water\\nEXERCISE 3.\\nSPECIFIC GRAVITY OF A SOLID BODY THAT WILL SINK IN\\nWATER.\\nApparatus The spring-balance (No. 7). The gallon jar (No. 10)\\nnearJy filled with water. A lump of sulphur (No. 11). Thread.\\nWeigh the sulphur out of water then in water.\\nWe know from Exercise 2 that a body immersed in water loses in\\napparent weight an amount equal to the weight of the water whose\\nplace it has taken. It is easy, therefore, to get from the two weigh-\\nings just made the ratio which we have undertaken to find in this\\nExercise.\\nIf time permits, find in this Exercise, by the same method that\\nis used for the sulphur, the specific gravity of other solids that will\\nsink in water such as glass, coal, etc.\\nQUESTIONS.\\n1. If the specific gravity of 1 cu. cm. of iron is 7, what is the\\nspecific gravity of 50 cu. cm. of the same kind of iron Of 1 cu. ft.\\nof the same kind of iron\\n2. If the sp. gr. of lead is 11.3, what is the weight in grams of\\n1 cu. cm. of lead? What, then, is the density of lead in grams and\\ncubic centimeters (see 22)?\\n3. If the sp. gr. of a certain kind of wood is 0.7, what is the weight\\nin lbs. of 1 cu. ft. of this wood? What, then, is its density in lbs.\\nand cu. ft.\\n4. A certain body weighs 7 lbs. out of water and 4 lbs. in water.\\nWhat is its specific gravity", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0033.jp2"}, "34": {"fulltext": "20 PHYSICS.\\n28, Various Expressions for Specific Gravity. By defi-\\nnition we have\\n7 7 Wt. of the body\\nbp. grav. of a body\\nWt. of an equal volume of water\\nIt is evident that the quantity written below the line in\\nthis definition may be expressed in other ways. We may\\nwrite\\nSp. grav. of a body\\nWt. of the body\\nWt. of water displaced by the body when immersed?\\nor\\na _ Wt. of the body\\n1 Loss of weight of the body token immersed 9\\nor\\nSp. grav.\\nWt. of the body\\nLifting effect of water upon the body when immersed\\nThese expressions all mean the same thing, bat some-\\ntimes one of them is more convenient than the others. In\\nthe Exercise next before us we shall use the last form.\\nEXERCISE 4.\\nSPECIFIC GRAVITY OF A BLOCK OF WOOD BY USE OF A SINKER.\\nApparatus]: A rectangular block of wood (No. 9). The spring-\\nbalance (No. 7). The gallon jar (No. 10) nearly filled with water.\\nA lead sinker (No. 12). Thread.\\nWe have to find two quantities, by experiment 1st, the weight of\\nthe body 2d, the lifting effect of water upon it ichen immersed.\\nWeigh the wood in air and record its weight.\\nNow put the block into water, Jou see tliat it floats, fq mtik$ it", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0034.jp2"}, "35": {"fulltext": "DENSITY AND SPECIFIC GRA VITT.\\n21\\nstay under water you must hold\\nit down. Try this, putting your\\nfingers on the block. In this\\ncase, you see, the lifting effect of\\nthe water, when the block is\\nwholly beneath its surface, is\\ngreater than the weight of the\\nblock. We must find out how\\nmuch it is.\\nWe shalL use the lead sinker to\\nhold the block under water, and\\nwe need to know the weight of\\nthe sinker alone under water.\\nWeigh it in this position and\\nrecord the weight.\\nNow suspend the block from\\nthe balance and the lead sinker\\nfrom the thread under the block,\\nand consider how much the two,\\nblock and sinker, would weigh in\\nthe position shown by Fig. 8, the\\nblock out of water and the sinker\\nin water. You can tell this from\\nthe weighings already made.\\nWrite it down.\\nWt. of block in air -f Wt. of\\nsinker in water\\nNow lower the\\nblock and sinker\\ntill both are cov-\\nFig. 8.\\nF*g. 9.\\nThe success of a difficult experiment like this\\ndepends greatly upon the care with which the details\\nof the work are thought out by the teacher. The\\nfollowing method of attaching the block to the bal-\\nance is recommended Take a thread two feet long\\nand tie the ends together. Then make of it a slip-\\nnoose by passing one end, I (Fig. 9i, through the\\nother end, k. The block may then be placed in the\\nnoose and the loop I slipped upon the hook of the\\nbalance, but to prevent slipping when the lead\\nweight is to be suspended from the loop below the\\nblock it is well to pass tlie loop I twice through at z-", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0035.jp2"}, "36": {"fulltext": "22 PHYSICS.\\nered by the water, and weigh the two together in this position and\\nrecord\\nWt. of block and sinker together in water\\nJust before the block entered the water, the sinker being already\\nin, the weight was Just as soon as the block also was cov-\\nered the weight was only The difference is the lifting effect\\nof the water upon the block. We have now all that we need for cal-\\nculating the specific gravity of the block by means of the formula,\\n_ Wt. of block\\ny Lifting effect of water upon block immersed\\nQUESTIONS.\\n(1) A brick-shaped body 20 cm. long, 10 cm. wide, and 5 cm.\\nthick weighs 1500 grams. What is its density in gram and centi-\\nmeter units\\nWhat would be the weight of an equal bulk of water\\nWhat, then, is the specific gravity of this body?\\n(2) A body whose volume is 700 cu. cm. has the density 8 in gram\\nand centimeter units. How much does it weigh? What is its\\nspecific gravity\\n(3) A body 20 ft. long, 10 ft. wide, and 5 ft. thick weighs 93,600\\nlbs. What is its density in pound and foot units\\nWhat would be weight of an equal bulk of water, one cu. ft. of\\nwater weighing 62.4 lbs What, then, is the specific gravity of the\\nbody\\n(4) A body whose volume is 700 cu. ft. has the density 499.2 in\\npound and foot units. How much does it weigh What is its\\nspecific gravity\\n(5) What numerical relation do we find in these problems, and in\\nthose of page 19, between density in gram and centimeter units and\\nspecific gravity\\n(6) What relation do we find in the same problems between density,\\nin pound and foot units, and specific gravity?\\n29. Flotation. Thus far we have been considering the\\naction of water upon bodies entirely immersed in it. We\\nshall now have to do with floating bodies.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0036.jp2"}, "37": {"fulltext": "DENSITY AND SPECIFIC GRA VII Y. 23\\nEXERCISE 5.\\nWEIGHT OF WATER DISPLACED BY A FLOATING BODY.\\nApparatus: The same as in Exercise 2, with the exception of the\\nsinking body, which is here replaced by one that floats (No. 4).\\nWeigh the cylinder, in grams, in air. Find, in grams, the weight\\nof water which it displaces from the overflow-can. Compare these\\ntwo weights.\\nIt will be well to repeat the overflow operation carefully a number\\nof times.\\nThe fact shown in this Exercise concerning the relation\\nbetween the weight of a floating body and the weight of\\nwater displaced by it should be firmly fixed in the experi-\\nmenter s mind. It leads to a method of finding the specific\\ngravity of floating bodies.\\nEXERCISE 6.\\nSPECIFIC GRAVITY BY FLOATING METHOD.\\nApparatus The gallon jar (No. 10) nearly filled with water. A\\nslender wooden cylinder (No. 13). A support for holding this cylin-\\nder upright in water (No. 14). A measuring- stick (No. 3).\\nIf a cylinder floated upright with its top just level with the top of\\nthe water, we should at once know its specific gravity to be 1. If it\\nfloated just half in and half out of water, we should know its specific\\ngravity to be 0.5. The cylinder that we have to use will not float all\\nin water or exactly half in water, but if we float it, and find the\\nlength of tlie part then in the water, we shall, by comparing this\\nwith the length of the whole cylinder, find some way of ascertaining\\nthe specific gravity of the cylinder,\\nMeasure the length of the whole cylinder.\\nFloat the cylinder in the jar (Fig. 10), keeping it upright by", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0037.jp2"}, "38": {"fulltext": "24\\nPHYSICS.\\nmeans of the holder, which is attached to the side of the jar. Jeggle\\nthe cylinder to make sure that it\\nis free to take its proper posi-\\ntion. After each joggling it\\nshould come to rest at the same\\ndepth as before. The ruigsof the\\nholder must not grip the cylin-\\nder at all. When sure that the\\ncylinder floats as it should, meas-\\nure the length of the submerged\\npart, from the bottom of the\\ncylinder up to the flat surface\\nof the water.\\nTo find the specific gravity\\nfrom the two mi asurements\\nnow made, beg n by recalling\\nthe fact (see Exercise 5) that\\nthe water displaced by the float-\\ning cylinder weighs just as\\nmuch as the cylinder itself.\\nHow many times is the length\\nof the submerged part of the\\ncylinder contained in the whole\\nlength\\nHow ma iy times the weight\\nof the cylinder would be the\\nweight of a like cylinder of\\nwater\\nHow great, then, do you find\\nFig. 10.\\nthe specific gravity of the wooden cylinder to be?\\nPROBLEMS AND QUESTIONS.\\n(1) A block whose specific gravity is 0.6 floats in water. How\\nmuch of it is below the surface\\n(2) A block whose volume is 1000 cu. cm, and whose specific\\ngravity is 0.4, floats in water. How many cu. cm. of the block are\\nbelow the surface\\n(3) A block that weighs 4 oz. in air is fastened to a sinker that\\nweighs 6 oz. in water, and the two together weigh 3 oz. in water.\\nWhat is the specific gravity of the block", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0038.jp2"}, "39": {"fulltext": "DENSITY AND SPECIFIC GRAVITY. 25\\n(4) A block whose specific gravity is 0.5, and which weighs 100\\ngm. alone in air, is fastened to a sinker that weighs 150 gin. alone in\\nwater. How much will both together weigh in water?\\n(5) A certain body has the density 187.2 in pound and foot units.\\nWhat is its specific gravity\\n(6) Is the specific gravity of the human body much greater or\\nmuch less than 1\\n(7) Why doei filling the lungs w r ith air help one to float in water\\nEXERCISE 7.\\nSPECIFIC GRAVITY OF A LIQUID: TWO METHODS.\\nApparatus: The gallon jar (No. 10) nearly filled with water, and\\nthe smaller jar (No. 15) nearly filled with a solution of sulphate of\\ncopper.* The small glass bottle (No. 16). The spring-balance (No.\\n7). Thread.\\nFirst Method.\\nWeigh the bottle empty. Dip the bottle into the jar of sulphate\\nof copper and let it fill with the liquid. Holding the bottle over the\\njar, put the stopper in place, thus crowding out the excess of liquid,\\nthen wipe the outside of the bottle and weigh it carefully with its\\ncontents.\\nPour the sulphate of copper back into its jar, then fill the bottle\\nwith water, just as it was before filled with the other liquid, and\\nagain w r eigh the bottle and its contents.\\nFrom the three weighings now made the specific gravity of sul-\\nphate of copper can easily be found.\\nSecond Method.\\nWe found in Exercise 2 that a body going from air into water lost\\nin apparent w r eight an amount equal to the weight of its own bulk of\\nwater. So a body going from air into a solution of sulphate of copper\\nwill lose in apparent weight an amount equal to the weight of its own\\nbulk of the solution. This gives a method of finding the specific\\ngravity of the solution. As a body to be weighed first in air, then\\nin water, then in the solution, we will use the bottle with enough water\\n*This solution may be made by putting 2 lbs. of sulphate of cop-\\nper crystals into about 3 qts. of warm water in a glass vessel and\\nstirring occasionally till the crystals are dissolved,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0039.jp2"}, "40": {"fulltext": "26 PHYSICS.\\nin it to make it sink in either liquid. We may, indeed, use the bottle\\nfull of water, just as it was left at the end of the first part of this\\nExercise.\\nEXPERIMENTS.\\n1. Exhibit and show in operation two graduated glass hydrometers\\none for determining the specific gravity of liquids less dense than\\nwater (App. No. XI), the other for use with liquids more dense than\\nwater (App. No. XII.\\n2. Show in a bottle together several liquids of different specific\\ngravities that do not tend to mix with each other for instance, mer-\\ncury, chloroform, water, and kerosene.\\n3. Take a small tumbler containing some mercury and drop into\\nit a piece of iron. Do not put into it gold or silver, as mercury at-\\ntacks these metals.\\n4. Place a dry sponge on water. It floats lightly, but is the spe-\\ncific gravity of the fibres of the sponge greater or less than that of\\nwater To answer this question push the sponge beneath the sur-\\nface. What rises from it Squeeze the sponge very hard till noth-\\ning more seems to come from it. Now will it rise to the surface\\nwhen released\\nQTJESTIONS.\\n1. A glass sphere which weighs 100 gm. in air weighs 60 gm. in\\nwater and 40 gm. in sulphuric acid of a certain strength. What is\\nthe specific gravity of the glass\\nWhat is the specific gravity of the sulphuric acid?\\n2. A vessel contains a layer of water 10 cm. deep and above this a\\nlayer of kerosene (sp. gr. 0.8) 10 cm. deep. What is the weight of\\na cube, each edge of which is 10 cm. long, that, if placed in this ves-\\nsel, will sink till one-half its volume is in the water and one-half in\\nthe kerosene? Ans. 900 gm. What is its specific gravity? Arts.\\n0.9.\\n3. A certain ship weighs with its cargo 10,000 tons.\\n(a) How many cubic feet of fresh water would it displace\\n(b) How many cubic feet of sea- water of specific gravity 1.026\\nwould it displace\\n4. If 1 cu. cm. of mercury weighs 13.6 gm. and 1 cu. cm. of cork\\nweighs 0.25 gm., how deep will a cylinder of cork 20 cm. long sink,\\nwhen placed on end in mercury", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0040.jp2"}, "41": {"fulltext": "DENSITY AND SPECIFIC GBAVITT. 27\\n5. Which has the greater specific gravity, cream or skimmed\\nmilk?\\n6. A piece of cloth thrown upon water will float at first and after-\\nward sink. Why does it not sink at once\\n7. Can the pupil tell from his own observation which of the follow-\\ning substances are more dense and which are less dense than water\\nkerosene-oil, ordinary lubricating- oil, butter, cheese, potatoes, eggs,\\nmeat, ice, india-rubber", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0041.jp2"}, "42": {"fulltext": "CHAPTEE III.\\nFLUID-PRESSURE.\\n30. Fluids. Water and air readily floiv from one position\\nor shape to another. They are examples of that class of\\nsubstances called fluids. Fine sand and other like sub-\\nstances flow in a certain way, but examination shows them\\nto consist of little hard or tough particles very different\\nfrom equally small particles of water.\\nFluids are divided into liquids and gases. Water is an\\nexample of the liquids air an example of the gases.\\n31. Fluid-pressure. Fluids settle snugly around solid,\\nthat is, non-fluid, bodies placed in them and act upon these\\nbodies with a peculiarly even pressure. We shall now make\\nsome experiments with liquid-pressure and later with gas-\\npressure.\\nEXPERIMENTS WITH PRESSURE-GAUGE.\\nFill the gallon glass jar (No. 10) with water to a level about one\\ninch from the top. Close the smaller end of a student- lamp chim-\\nney tight with a good cork stopper. Make the pressure-gauge (No.\\nI.) ready for use by the following operation, having first put on a\\nfresh rubber diaphragm if necessary Release the glass tube from\\nthe rubber tube and wet the whole length of the glass tube inside\\nwith water, leaving within it a column of water about one-half inch\\nlong to serve as an index.* Hold the gauge itself under water for a\\nlittle time before reconnecting the glass tube with the rubber tube,\\n*It may be necessary to use water colored by some aniline dye be-\\nfore a large class.\\n28", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0042.jp2"}, "43": {"fulltext": "FLUID-PRESSURE. 29\\nin order to allow the air within the gauge to come to the temperature\\nof the water. On reconnecting the glass tube leave the water-index\\nnear the rubber tube.\\nDifferent Letels. Xow push the gauge down into the jar and\\nraise and lower it repeatedly in the water, keeping the glass tube\\nwith the water-index horizontal, and let the class determine from the\\nmovements of this index whether the pressure of the water against\\nthe rubber diaphragm increases or decreases when the gauge is\\npushed deeper in the water.\\nDifferent Directions. Rest the bottom of the supporting pillar\\nof the gauge upon the bottom of the jar, and, still keeping the glass\\ntube horizontal, turn the upper pulley so that by means of the rubber\\nband the lower pulley will be turned and the rubber diaphragm will\\nface downward, sidewise, and upward in succession, its centre re-\\nmaining practically unchanged in position. Let the class determine\\nby watching the water-index whether the pressure upon the rubber\\ndiaphragm is any greater when it faces upward than when it face?\\ndownward or sidewise.\\nDifferent Points on the S^me Leyel. Push the closed end\\nof the lamp-chimney down into the water till it is near the bottom of\\nthe jar. Move the gauge face about, without changing its level, so\\nas to bring it under this closed end. Move it now out of and now into\\nthis position, thus changing the depth of water immediately above it\\nfrom one-half inch or less to several inches. Let the class determine\\nby watching the index whether such changes of position, without\\nchange of level, make any difference in the pressure against the gauge-\\nface.\\nWe shall make considerable use farther on of the facts\\nbrought out by these experiments. Just here we can see\\nthat they explain, at least in a general way, why a body\\nimmersed in water weighs, or appears to weigh, less than\\nwhen in the air. For we see that there is an upward\\npressure of the water against the under side of the body,\\nand that this upward pressure is greater than the down-\\nward pressure against the upper side of the body.\\n32. Slight Effect of Pressure upon the Density of Water.\\nHaving seen that there is greater pressure on low levels", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0043.jp2"}, "44": {"fulltext": "30 PHYSICS.\\nthan on high levels in water, we may well ask whether this\\ngreater pressure crowds the particles of water closer together\\non the low levels, thus making the water denser than on\\nhigh levels. In fact there is an effect of this kind, but it\\nis so slight that we need take no account of it in any ordi-\\nnary case. It is very difficult to compress water much.\\nEXPERIMENT.\\nFill a bottle with water and close it with, a rubber stopper having\\none hole through it. Then, holding the stopper firmly in place, push\\ndown into the hole a solid brass rod of a size to fit rather closely.\\nThe bottle will probably be broken by this effort to compress the\\nwater within it. (App. No. II.)\\n33. Uniform Increase of Pressure with Depth. We have\\nnot made, and cannot well make with the gauge used, any\\naccurate measurement of the rate at which pressure changes\\nwith change of level in water. The fact is, however, that\\nif we place a surface of 1 sq. cm. horizontal at any depth\\nin water the column of water just above it is resting upon\\nthe given surface.* If we carry the given surface down\\n1 cm. farther, we now have resting upon it a load somewhat\\ngreater than before, greater by the weight of the additional\\n1 cu. cm. of water which is now above it. As 1 cu. cm. of\\nwater weighs 1 gm., the pressure upon a surface of 1 sq.\\ncm. changes by 1 gm. for each 1 cm. change of level in the\\nwater.\\nQUESTIONS.\\nA cubical box, 10 cm. along each edge, has extending from its top,\\nas in Fig. 11, a tube 15 cm. tall and 1 sq. cm. in cross-section (inside).\\n(1) If the box, but not the tube, is full of water, how great is the\\nwater-pressure on the whole of the bottom\\nThe pressure upon the given surface may be greater than the\\nweight of the column of water resting upon it, for there may be, and\\nusually is, a downward pressure of air or something else upon the\\ntop of the water-column.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0044.jp2"}, "45": {"fulltext": "FLUIb-PRBSStmE.\\n31\\n(2) If the tube as well as the box is full of water, how great is the\\npressure upon that one sq. cm. of the bot-\\ntom which lies just beneath the tube\\n(3j Is the pressure equally great per sq.\\ncm. at other parts of the bottom\\n(4) How much is the total pressure now on\\nthe bottom of the box?\\n(5) How great is the pressure per sq. cm.\\nat the top of the box just at the bottom of\\nthe tube\\n(6) How great is the total upward pressure\\nof the water against the top of the box\\n(Disregard the atmospheric pressure upon\\nthe top of the water-column in all these\\nquestions at first. Afterward call this at-\\nmospheric pressure 1000 gm. per sq. cm.,\\nand ask the same questions as before.)\\n34. Gas-pressure. We have made\\nsome experiments with liquid-pressure.\\nWe must now begin to learn some-\\nthing about air-pressure, which in many practical matters\\nof e very-day life has a very important connection with\\nwater-pressure. We will at the start repeat in a slightly\\nvaried form a famous experiment first made by Torricelli,\\nan Italian, about the middle of the seventeenth century.\\nIt is intended to show the pressure of the air about us,\\nwhich is called atmospheric pressure.\\nFig. 11.\\nEXPERIMENT.*\\nTake two pieces of strong glass tubing about 0.7 cm. in inside di-\\nameter, one of them, about 1 m. long, closed at one end, and the other,\\nabout 20 cm. long, open at both ends, and connect them by means of\\na thick- walled piece of rubber tubing about 25 cm. long. The rubber\\ntube should fit tight upon the glass tubes, and for greater security\\nshould be fastened on by means of wire or string.\\nThis experiment can be more conveniently performed with a\\nsingle straight glass tube if a mercury-well is available.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0045.jp2"}, "46": {"fulltext": "32 PHYSIOS.\\nHolding the tubes thus connected (A pp. No. III.) by the\\nfree end of the short glass tube, the closed end of the long\\nglass tube hanging down, pour mercury by means of a small\\nfunnel of glass or paper into the tubes, tapping or shaking\\nthem occasionally to dislodge air-bubbles, until the top of the\\nmercury-column reaches the rubber tube. Then gently raise\\nthe closed end of the long glass tube until this tube points\\nstraight upward (Fig. 12), meanwhile holding the other\\nglass tube upright and taking care that no mercury is spilled.\\nDuring the latter part of this operation it will be noticed\\nthat the mercury begins to fall away from the closed end\\nof the long glass tube, and finally several inches of this\\ntube will be apparently empty.* But the mercury contin-\\nues to stand very much higher in the long glass tube than\\nin the short one.\\ny\\nFig. 12.\\n35. Explanation. It was known before the time of\\nTorricelli that if air was drawn from the upper part of a\\ntube the lower end of which rested in water the water\\nwould rise in the tube, but the true reason for this was not\\nknown. Torricelli maintained, and Pascal, a Frenchman,\\nshowed by experimenting at different heights in the air,\\nthat the pressure of the atmosphere, due to its weight,\\naccounted for the rise of liquids in a vacuum. We have\\nonly to think of the fact that the air, although its density\\nis very small compared with that of water, has, because of\\nits great quantity, a great weight, and we see that the air,\\npressing upon the mercury-surface in the shorter tube,\\nbalances the column of mercury in the long tube.\\n36. Amount of the Atmospheric Pressure Barometer.\\nBy measuring the difference in height of the two mercury-\\nReally this space contains a very little air, from the bubbles that\\nwere in the mercury-column before it was inverted, but so little that\\nwe may at present disregard it and consider the space above the mer-\\ncury as empty. Such a space is called a vacuum, from a Latin word\\nmeaning empty.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0046.jp2"}, "47": {"fulltext": "FL TJID-PBESS USE\\nu\\nsurfaces we can get a measure of the atmospheric pressure.\\nWe find that the atmospheric pressure is about as great\\nupon the surface of the earth as would be the pressure of a\\nlayer of mercury 76 cm. deep, or a layer of water about\\n10.3 m. deep, over the whole earth. The pressure per\\nsquare centimeter at any given part of the earth s surface\\nvaries somewhat from day to day, and even from hour to\\nhour.\\nIf we fasten the apparatus that has just been used to a\\nsuitable support, it will serve permanently as a rude\\nbarometer, indicating the variations of the atmospheric\\npressure.\\n37. Pressure in Different Directions. Air-pressure, like\\nliquid-pressure, is at any given point equal in all direc-\\ntions, if the air is at rest.\\nEXPERIMENT.\\nJ-\\n-J\\nTake a strong thistle-tube (No. IV.) of\\nthe shape shown in Fig. 13 and tie a piece\\nof thick sheet rubber across the mouth,\\nwhich may be about 1 inch in diameter.\\nMake the covering air-tight by means of\\nsome cement, melted beeswax and rosin,\\nfor instance, poured in at the point J. Con-\\nnect this thistle-tube by means of a thick-\\nwalled rubber tube to an air-pump (No.\\nV.), and exhaust the air. The rubber cap,\\nnot being supported by air-pressure beneath,\\nwill now be pushed down by the atmos-\\npheric pressure into a deep cup-shape\\nPinch the rubber tube so that no air shall\\nleak back into the thistle-tube, and then\\nturn the mouth of the latter in all directions,\\nsidewise, downward, and oblique. Observe\\nwhether the depth of the rubber cup\\nchanges during this operation, as it would do if the pressure upon\\nit changed.\\nFig. 13.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0047.jp2"}, "48": {"fulltext": "34 PHYSIOS.\\n38. Air-pressure at Different Levels. We should find\\nby proper experiments that in air at rest, as in water at\\nrest, pressure is equally great at all points on the same\\nlevel. We should find, also, that the air-pressure diminishes\\nwith increase of height from the earth s surface, but, as\\nthe density of air is very little compared with that of\\nwater, it requires a considerable change of level to make\\nmuch difference in the air-pressure.\\nThe rate at which atmospheric pressure decreases with\\nincrease of height being well known, it is a common prac-\\ntice to estimate the height of mountains by noting the\\ndifference of atmospheric pressure at the summit and base.\\nAneroid barometers are frequently used for such work.\\nAneroid means without liquid. An aneroid barometer\\ncontains no mercury nor other liquid. It is an air-tight\\nmetal box with a flexible metal cover. The middle of the\\ncover moves in or out slightly with changes of pressure, and\\nits slight motions are magnified to the eye by various\\nmechanical contrivances. Some aneroid barometers are\\nabout as large as ordinary watches and look much like\\nthem.\\n39. Difference between Liquids and Gases. Liquids are\\nmuch heavier than gases, in most cases. Most liquids are\\neasily seen. Most gases are practically invisible. But per-\\nhaps the most striking difference between liquids and gases\\nis a difference in compressibility. We have seen that it is\\ndifficult to compress water much, but it is very easy to com-\\npress air.\\nEXPERIMENT.\\nTake the bent glass tube (No. VI.), closed at one end, and pour\\ninto it a little mercury, enough to fill the bend. At first the mercury\\nwill stand a little higher in the long arm, but by tipping the tube\\nand letting ont a little of the air imprisoned in the short arm the level\\ncan be made nearly the same in both arms, as in Fig. 14. Now", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0048.jp2"}, "49": {"fulltext": "FLUID-PRESSURE.\\n35\\nmeasure the length of the imprisoned air-column, and write it under\\nthe letter V* on the blackboard.\\nP.\\nFXP.\\nFig. 14.\\nThe pressure upon this air is now, if the mercury- level\\nis the same in both arms, equal to that upon the unim pris-\\noned air. It is as great a pressure as would be exerted by\\nthe weight of a column of mercury as tall as that in the\\nbarometer (Fig. 12). Take, then, a reading of this barom-\\neter and record this reading under the letter P.\\nPour in more mercury till the difference of level in the\\ntwo arms is about 20 cm., then measure again the length\\nof the inclosed air-column. Record this length under V,\\nand record under P the present difference of mercury\\nlevel plus the height of the barometer column.\\nProceed by stages in this way till the volume of the inclosed air-\\ncolumn is about one-half what it was at first. Multiply each number\\nunder Fby the corresponding number under P, and write the prod-\\nucts in the column headed VX P.\\n40. Boyle s Law. An examination of the last column\\nin the table of the preceding section will probably indicate\\na very simple law connecting pressure and volume in the\\ncase of a given body of air. This law is important, and\\nshould be remembered by the pupil. It is sometimes\\ncalled Boyle s law and sometimes Mariotte s law. We shall\\ncall it by the shorter name, Boyle* s lata.\\nIllustrations and Applications of Fluid-pressure.\\n41. Principle of the Hydraulic Press. The questions on\\npp. 30 and 31 have brought out the fact that pressure trans-\\nThe length of the air-column is the same as its volume, if we take\\nfor our unit of volume the space contained in unit length of the tube.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0049.jp2"}, "50": {"fulltext": "36 physics.\\nmitted through a small tube may extend to a broad surface\\nbeyond the tube so as to make the total pressure on this\\nsurface very great. The following experiment will show\\nthat similar effects can be produced with air-pressure.\\nEXPERIMENT.*\\nTake a common rubber football and blow air into it till it is about\\nhalf filled, connecting a rubber tube with the key for greater con-\\nvenience in blowing (App. No. VII). Then rest one end of a board,\\nFig, 15.\\nf S in Fig. 1 5, on the football and the other end upon a box or block\\nof about the same he ght. Then place a weight of 25 lbs. or more\\non the board nearly over the ball, holding the rubber tube attached\\nto the key in such a way that the air cannot escape from the ball.\\nThen blow through the tube into the ball and observe that you can\\nin this way lift the weight.\\n42. Hydrostatic Press. The preceding experiment\\nillustrates the operation of the hydrostatic press, a machine\\nin which a very great force is obtained, for lifting or\\ncompressing bodies, by pumping water through a small\\ntube into a large cylinder, one end of which is closed by a\\nmovable stopper called piston. (See 204.)\\nEXPERIMENTS.\\n1. Take again the pressure-gauge and the accompanying apparatus,\\n31. Fill the lamp-chimney with water, and then, holding a card\\nacross the open end, invert the chimney, lower the end covered\\nby the card into the water, and then remove the card. Most of the\\nwater will now remain in the chimney, although its upper end is nine\\nor ten inches above the surface of the water in the jar.\\nAn experiment with Gage s piston and cylinder apparatus may\\nbe substituted for this to show the same effect.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0050.jp2"}, "51": {"fulltext": "FL UID-PRESSURE.\\n37\\nHow does tlie pressure per sq. cm. inside the chimney on a level\\nwith the outside water surface compare with the pressure per sq.\\ncm. at this outer surface, that is, the atmospheric pressure\\nHow, then, will the pressure per sq. cm. at points higher in the\\nchimney compare with the atmospheric pressure\\nAfter these questions have been answered by the aid of what the\\nclass already knows about liquid-pressure, test the correctness of the\\nanswer by means of the gauge.\\n2. Take a long narrow glass tube open at both ends, and dip one\\nend into a vessel of water. Apply the lips to the other end and\\ndraw the water up till the tube is filled.\\nIn what sense is the water drawn up\\n(The operation begins with an expansion of the lungs which les-\\nsens the air-pressure within them. Then air runs from the place of\\nhigh pressure, the tube, to the place of low pressure, the lungs. So\\nthe air-pressure within the tube is lessened.)\\n3. After nearly filling the tube as in Experiment 2 quickly close\\nthe top with a finger and then lift the lower end from the water.\\nUncover the top of the tube for an instant, then cover it again.\\nExplain the behavior of the water during these operations.\\n4. Fill or nearly fill a tumbler or broad-mouthed bottle with water\\nand then cover it with a sheet of thick paper. Hold the paper firmly\\nin place with the hand and invert the tumbler then take away the\\nhand that holds the paper. (As accidents may happen, the tumbler\\nshould be held over some large dish.)\\nIn this experiment it should be noticed that\\nthe paper does not press close against the rim of\\nthe tumbler after the inversion. It hangs rather\\nloose, having dropped down or sagged a little,\\nthus allowing the air above the water to expand\\na trifle, decreasing in pressure.\\n5. Fig. 16 (App. No. VIlIj shows a bottle\\nclosed with a rubber stopper through which\\ntwo glass tubes, a and b, open at both ends, ex-\\ntend. To one of the tubes, a, is attached a rub-\\nber tube, r. The bottle and the two glass tubes\\nare full of water.\\nBy applying the lips to the outer end of the\\ntube r water can b drawn into the mouth,\\nwhen the tube b is closed by a finger at the top?\\na\\nFig. 16.\\nan this be done", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0051.jp2"}, "52": {"fulltext": "38\\nPHYSICS.\\n6. Show some form of the Cartesian diver (No. XIV), explaining\\nwhy it sinks when greater pressure is put upon the water in\\nwhich it is placed.\\n43. Pumps. Many contrivances for making fluids run\\nfrom one place to another are called pumps. A flow may\\nbe caused by decreasing the pressure at the place where the\\nfluid is to be delivered or by increasing the pressure at the\\nplace from which it is to be removed.\\nEXPERIMENT.\\nShow in operation glass models of the lifting-pump (App.\\nNo. IX, Fig. 17) and force-pump (App. No. X, Fig. 18), dis-\\ncussing their action.\\nL\\nu\\nflflfi\\nD\\nor\\nFig. 17\\nFig. 18.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0052.jp2"}, "53": {"fulltext": "FLUID PRESSURE.\\n39\\n^4\\n44. The Siphon. The apparatus illustrated in the fol-\\nlowing experiment is called the siphon. It is found in a\\ngreat variety of forms and is of much use.\\nEXPERIMENT.\\nTake two glass tubes, each about 6 in. long, connected by a rubber\\ntube about 1 ft. long. Fill the whole with water, then close each\\nend with a finger. Hold one end be-\\nneath the surface of the water in the\\ngallon jar (Fig. 19) remove the fin-\\nger from that end, and bring the\\nother end, still closed, down outside\\nthe jar to a level lower than the water\\nsurface.\\nIs the water-pressure against the\\nfinger that closes the tube now greater\\nor less than the atmospheric pressure\\nupon an equally large surface? If\\ngreater, the water will run out when\\nthe finger is removed. If less, the air\\nwill run in and drive the water up in\\nthe tube when the finger is removed.\\nTry the experiment.\\nRepeat the experiment, but now\\nhold the outer end of the tube, before\\nopening it, higher than the level of the water in the jar.\\n45. Balancing Columns. The method of finding specific\\ngravities that is suggested by the following experiment is\\ncalled the method of balancing columns. In the form here\\nshoAvn it cannot well be used with liquids that naturally\\nmix with each other, as alcohol and water do. Later this\\ngeneral method will be used in a form that does not bring\\nthe two liquids into contact with each other.\\nFig. 10.\\nEXPERIMENT.\\nTake a bent glass tube (App. No. XIII, Fig. 20) each arm of which\\nis about one foot long, and pour water into it till both arms are", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0053.jp2"}, "54": {"fulltext": "40\\nPHYSICS.\\nFig. 20.\\nabout half full then pour kerosene into one arm till it is nearly full.\\nDoes the water now stand as high in the other arm as\\nthe kerosene does in the first arm Can you from this\\nexperiment see a third method for finding the specific\\ngravity of a liquid\\nQUESTIONS.\\n(1) Does water stand at the same level in the spout as\\nin the main part of a watering-pot?\\n(2) If one branch of a U tube (see Fig. 20) were larger\\nthan the other, would water stand at the same level in\\nboth?\\n(3) Is it necessary in finding the specific gravity of a\\nliquid by the method indicated in Art. 45 to have the\\ntwo branches of the tube equally large\\n(4) Does the height of mercury in the tube of a barometer depend\\nupon the size of the tube? (We neglect at present w T hat is called\\nthe capillary effect. See Second Part.)\\n(5) If the height of the barometer mercury-column, of specific\\ngravity 13.6, is 76 cm., how tall a column of water could be sustained\\nby the atmospheric pressure if there were a vacuum above the\\nwater (Give the answer in ft. as well as in cm.)\\n(6) A water-tank 10 ft. deep is to be emptied by means of a tube\\nused as a siphon. What is the least length the tube can have?\\n(7) With ordinary atmospheric pressure what is the greatest height\\nto which water may be raised by means of a pump working above it?\\n(8) Do you understand the operation of the trap which allows\\nwater to flow from a sink to a sewer, but does not allow gas to come\\nfrom the sewer to the sink", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0054.jp2"}, "55": {"fulltext": "CHAPTER IV.\\nTHE LEVER.\\n46. Definition and Illustration. Civilized men do most\\nof their work with tools or machines. Many tools and\\nmany parts of machines consist of a piece of iron or wood\\nor other material movable to a certain extent upon a sup-\\nport called a pivot, or axis, or fulcrum, by means of which\\na force applied in one direction at a certain spot may pro-\\ndace another force different in direction or in magnitude,\\nor in both, at another spot. Such a tool or part of a\\nmachine is called a lever.\\nOne of the most familiar examples of the lever is a crow-\\nbar. A hammer, as used to draw out a nail from a board,\\nis another example. Each half of a pair of scissors is a\\nlever. We shall study some very simple forms of the lever\\nto find out what relations hold between the forces exerted\\nat different points.\\nEXERCISE 8.\\nTHE STRAIGHT LEVER: FIRST CLASS.\\nApparatus The lever and supporting bar (Xo. 17) fastened to the;\\nlong horizontal bar that reaches above the table from end to end.\\nTwo scale-pans (Xos. 18a and 18b). A set of weights (No. 19).\\nHang one scale-pan carrying a load of 8 oz. on the right-hand end\\nof the lever at a distance of 14 cm. from the middle, as in Fig. 21.\\nHang the other pan, with an equal load, on the left-hand end of\\nthe lever, at such a distance from the middle that the lever will bal-\\nance, that is, stay horizontal when once placed so, even when the ap-\\n41", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0055.jp2"}, "56": {"fulltext": "42\\nPHYSICS.\\nparatus is jarred somewhat by tapping the short bar to which the\\nlever is attached. Then make a record like this\\nRight dist.\\nfr. centre.\\nLeft wt. fr! centre Ri ht wt\\n(l+8) 9oz. (1 8)= 9 oz. 14.0cm.\\n(The space here left blank (in the record) is to be filled by the left-\\nhand distance which the student finds necessary to make the apparatus\\nbalance.)\\nChange the right-hand weight to 7 oz. keeping its place unchanged,\\nand move the left-hand weight, still 9 oz., to some new position\\nwhich will make the whole balance, in spite of jarring as before.\\nMake a record, as before, of the weights and distances, putting it just\\nbeneath the record for the first arrangement.\\nChange the right-hand weight to 5 oz. without changing its place,\\nand find what position the left-hand weight, still remaining 9 oz.,\\nmust have in order that the lever may balance. Record the distances\\nFig. 21.\\nand weights for this case under the records already made for the\\nfirst and second cases.\\nOne more case may be taken, in which the right-hand weight be-\\ncomes 4 oz., still at 14 cm., which will give a fourth line in the record\\ntable. More observations with different arrangements might be\\nmade, but it is better to make a moderate number of good observa-\\ntions than a large number of hasty or careless ones,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0056.jp2"}, "57": {"fulltext": "THE LEVER.\\n43\\nBy studying the record table now made the student should find a rule\\nby which, when the two weights and one distance are given, the other\\ndistance can be found by calculation or when the two distances and\\none weight are given, the other weight can be found by calculation.\\nQUESTIONS.\\n(1) If a mass of 6 oz. is suspended from a point 4 cm. to the left of\\nthe centre of the lever in Exercise 8, how great a load placed at a\\ndistance of 10 cm. to the right of the centre will make equilibrium\\n(2) A mass of 8 oz. is suspended from a point 5 cm. from the centre\\nof the lever and is balanced by a mass of 10 oz. How far from the\\ncentre is the latter placed?\\n(3j Two masses, 4 oz. and 12 oz. respectively, are to be suspended\\nfrom a lever. Describe three possible arrangements of the masses,\\nany one of which will cause them to balance.\\n(4) A boy pushing down at one end of a lever 6 ft. long pries up a\\nstone weighing 100 lbs. at the other end. The fulcrum is 2 ft. from\\nthe stone. The weight of the lever itself is neglected. How great is\\nthe force exerted by the boy\\n47. More than Two Weights. In the preceding Exer-\\ncise the class found out how to\\nmake the two weights hung\\nfrom the lever balance each\\nother. Let us ask now what the\\nrule for balancing would be if\\nthere were more than two\\nweights in use, as in Fig. 22, for\\ninstance.\\nEXPERIMENTS.\\nWe will make the apparatus balance with four weights, two on\\neach side. We will call the weight nearest the centre on the left\\nhand weight Xo. 1, which we will write TF,, for short. The other\\nweight on the left-hand side we will call Xo. 3, or TT 3\\nweights on the right hand we will call Wz and TF 4\\nWhen the whole balances, we will call\\nThe distance of Wi from the middle, D x\\nW% D* t\\nu M\\\\ D\\ntt3 tt\\nFig. 22.\\nm\\nThe two", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0057.jp2"}, "58": {"fulltext": "44\\nPHYSICS.\\nNow if we go back for a moment to the case of two weights, which\\nthe class has studied, and if we call these Pi and P 2 and their dis-\\ntances from the middle d x and d 2 we can state the rule for balancing\\nin this way\\nPi X ^1 must equal P 2 X d 2\\nIn the new case, where we have four weights, we may guess that\\nthe rale is\\n(Wi X A) (TT 8 X P 3 (TF 2 x D 2 (TF 4 X B A 9\\nand then test the truth of our guess by trial.\\nTry other like cases.\\n48. Circular Lever. In the experiments with which we\\nhave just been engaged the weights have been suspended\\nfrom the top of the lever on a level with that part of the\\npivot upon which the lever rests.\\nIn other experiments which are\\nto follow we shall not always be\\nable to keep this arrangement,\\nI and we have now to find out what\\nwould be the effect of hanging\\none or more of the weights from\\npoints higher or lower than the\\npoint of support of the lever.\\nFor this purpose we shall use No.\\nFlG 3 XV, the piece of apparatus\\nshown in Fig. 23, in which the straight lever thus far used\\nis replaced by a circle of wood about 8 inches in diameter,\\nsupported by a screw passing horizontally through the\\ncentre. Such a circle, or disk, of wood comes under the\\ngeneral definition of a lever.\\nEXPERIMENTS.\\nWe will hang at b and such weights as will balance each\\nShrewd guessing, followed by a test, should be encouraged by the\\nteacher as a means of extending knowledge. In fact, it is the con-\\nstant resource of the investigator.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0058.jp2"}, "59": {"fulltext": "THE LEVER.\\nU\\nother, leaving the disk in equilibrium, and will then move one of\\nthe weights to a point vertically above or vertically below its pres-\\nent place that is, from /to e or g, or from b to a or c. Shall we still\\nhave equilibrium Try.\\nWe will now turn the disk a little, so that the lines ab c and efg\\nwill be no longer quite vertical, and will see whether now a weight\\nat e or at g has just the same effect as if at/. Try.\\nA careful note should be made of conclusions for future use.\\n49. Centre of Gravity. In the experiments upon the\\nlever thus far, the lever itself, whether a bar or a disk, has\\nbalanced, when left to itself without load. We have,\\ntherefore, not had to consider the weight of the lever itself.\\nBut many levers are used in such a way that their own\\nweight helps or hinders the operation to be performed with\\nthem. To understand such cases we must learn something\\nabout what is called the centre of gravity of a body.\\nEXPERIMENT.\\nTake a board, cut in any irregular shape, like Fig. 24, for\\ninstance.\\nFig. 24.\\nBore several small holes straight through the board,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0059.jp2"}, "60": {"fulltext": "46 PHYSICS.\\nand put into each hole a wire nail that will fit close, long enough\\nto project about half an inch on each side of the b ard. Tie a\\nbullet at one end of a thread and make a loop in the other\\nend. Put this loop over one hook of a piece of wire bent\\ninto the shape shown in Fig. 25, and then rest the nail a,\\nFig. 24, in the hooks of the same wire, so that the board and\\nthe string carrying the bullet will both hang free, the string\\nFig. 25. near the face of the board.* Mark with a pencil the course\\nof the string downward across the board.\\nThen suspend the board by the nail b and mark the new course of\\nthe string. Proceed in this way with all the nails and note the point\\nwhere the various pencil-marks cross each other.\\nFinally, place the board horizontal and balance it upon the flat head\\nof a lead-pencil, noting how near the head of the pencil comes to the\\ncrossing of the lines marked on the board.\\nDefinition. By such experiments as this we come to see\\nthat there is within the board a certain point which always\\nhangs just beneath the support when the board comes to\\nrest suspended from any one of the nails. We see that the\\nsame point has to be just above the support when the board\\nrests upon the pencil-top. In short, the board acts in\\nthese experiments as it would if all its weight were concen-\\ntrated at this particular point. This point might be called\\nthe centre of weight or centre of heaviness of the board,\\nbut it is commonly called the centre of gravity.\\n50. Weight of the Lever. The following Exercise is in-\\ntended to make the pupil more familiar with the idea of\\ncentre of gravity, and to show how it may be taken account\\nof in the use of the leyer.\\nEXERCISE 9.\\nCENTRE OF GRAVITY AND WEIGHT OF A LEVER.\\nApparatus The lever of No. 17, detached from its supporting\\nbar, and a small block (No 21), the two being fastened together, as in\\nThe whole apparatus as shown in Fig. 24 will be called No. XVI.)", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0060.jp2"}, "61": {"fulltext": "THE LEVEB. 47\\nFig. 26, so as to make one body, the whole of which will be called\\nFig. 26.\\nthe lever in this Exercise. A slender wooden cylinder (No. 13). A\\n1-oz. scale-pan (18 A or 18 b). A 1-oz. wt. from No. 19.\\nTo find the centre of gravity of the lever, balance it as nearly as\\nyou can, bar and block fastened together, in a horizontal position on\\nthe cylinder laid on the table (see Fig. 26), the cylinder being kept\\nat right angles with the lever. Find in this way at what particular\\nmark of the bar the centre of gravity is, and record this mark for\\nexample, 9.1 cm.\\nThen suspend the 1-oz. scale-pan carrying a 1-oz. wt. 2 oz. in all,\\nfrom any convenient point near the free end of the bar, and letting\\nthis end project beyond the edge of the table-top, balance the whole,\\nas now arranged, as nearly as you can, on the cylinder laid on the\\ntable as before (see Fig. 27).\\nNow record the mark from which\\nthe scale-pan hangs, 33.4 cm., we\\nmay suppose, and the mark which\\nis just over the middle of the cyl-\\ninder when the whole balances,\\n21.6 cm., let us say.\\nZDZ\\nThis case is like that of the lever\\nstudied in Exercise 8. The cylin- p IG# 27.\\nder now taking the place of the screw as a support, we see that\\nthe left-hand weight is 2 oz.,\\ndistance is 33.4 -21.6 11.8 cm.,\\nright-hand weight is the weight of the lever,\\ndistance is 21.6 -9.1 12.5 cm.,\\nthat is, the distance from the support in Fig. 27 to the centre of grav-\\nity of the bar and block.\\nWe do not as yet know the weight of the lever, but we will call it\\nWi and see whether we can find its amount by calculation. If we\\napply the same rule that was found to hold true in Exercise 8, we\\nshall have\\n2 X 11.8 W, X 12.5,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0061.jp2"}, "62": {"fulltext": "48 PHYSICS.\\nwhich gives for the weight of the bar and block\\n2 X 11.8\\nWi =1.89 oz., nearly.\\nThe value of TT 2 obtained in this way by the pupil should be com-\\npared with the weight of the bar and block as found by the teacher\\nwith some balance, e.g. No. XVII, much more sensitive than the\\nspring-balance used by the class; for if the method of this Exercise is\\ncarefully followed it will give the weight of the lever more accurately\\nthan the spring-balance is likely to do.\\nQUESTIONS.\\n(1) An oar, the centre of gravity of which is 3 ft. from the end of\\nthe handle, weighs 4 lbs. It rests in the rowlock at a point 2 ft.\\nfrom the end of the handle. How great a force applied at the end of\\nthe handle will keep it balanced?\\n(2) A boy weighing 100 lbs. is see-sawing alone on a plank 20 ft.\\nlong weighing 50 lbs. The boy s centre of gravity is 1 ft. from one\\nend of the plank. How far from the same end of the plank is the\\nfulcrum (The centre of gravity of the plank is at its middle).\\n(3) If the plank mentioned in the preceding problem is to balance\\non a fulcrum 8 ft. from one end, with a 100 lb. boy 1 ft. from this\\nend and another boy 1 ft. from the other end, how much must the\\nsecond boy weigh (See Art. 47). Ans. 54 T 6 T lbs.\\n51. Remarks. We have now found out how to take\\naccount of the weight of the lever itself, when we need to\\ndo so. We know that all its weight may be regarded as\\nconcentrated at a certain point, which we call the centre of\\ngravity, and we have tried one case in which the weight of\\nthe lever itself, acting at the centre of gravity, balanced a\\ncertain weight suspended from the bar. In common levers,\\nlike the crowbar, the weight of the bar itself is sometimes\\nvery important, when the f alcrum is a long distance from\\nthe centre of gravity of the bar.\\nCentre of gravity will be taken up again, and the differ-\\nent kinds of eqtiilibrium, stable, unstable, and neutral, will\\nbe considered in the Second Part.\\nWe will now return for the present to cases of the lever", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0062.jp2"}, "63": {"fulltext": "THE LEVER.\\n49\\nwhere the centre of gravity lies, as in Exercise 8, just under\\nthe point of support of the bar. In such cases the weight\\nof the lever itself does not tend to make the bar tip in\\neither direction from its horizontal position.\\nClasses of Levers.\\n52. Lever of the First Class. In the levers which we\\nhave studied thus far the support, or fulcrum as it is often\\ncalled, lies between the lines of suspension of two weights.\\nThis kind of lever, whether it is a simple bar or a disk or\\nan object of irregular shape, whether its centre of gravity\\nlies at the point of support or not, is called a lever of the\\nFirst Class.\\n53. The Power, Power-arm, etc.- To take a simple and\\nconvenient case, we will consider in Fig. 28 a circle sup-\\nported at its centre, F. We\\nwill suppose that this lever is\\nused for the purpose of support-\\ning a weight TF, and the force\\nused for this purpose, whether\\nit is applied by means of another\\nweight, as in the figure, or by\\nmeans of the hand, or in any\\nother way, we will call the\\npower.\\nWe have seen in the experi-\\nments of 48 that, as the\\nlever now stands, it makes no\\ndifference whether W is sus-\\npended from the point which now carries it or from some\\npoint higher or lower in the same vertical line, which is\\ncalled the line of action of W. A like statement can be\\nmade for P. We shall call the shortest distance from P s\\nline of action to the fulcrum the power-arm, and the short-\\nFig. 28.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0063.jp2"}, "64": {"fulltext": "50\\nphysics.\\nest distance from JF s line of action to the fulcrum the\\nweight-arm.\\n54, Law for First Class. In order that P and W may-\\njust balance each other we must have, as can be seen from\\nExercise 8,\\npower X power-arm weight X weight-arm.\\nTins is the law for a lever of the first class.\\n55. Levers of the Second and Third Classes. But we\\nmay have a case, like that shown in Fig. 29, in which the\\nline of action of the weight lies between the fulcrum and\\nihe line of action of the power. This arrangement gives us\\nwhat is called a lever of the second class.\\nFig. 29.\\nFig. 30.\\nThere is still a different case, shown in Fig. 30, where\\nthe line of action of the power lies between the fulcrum\\nand the line of action of the weight. This is called a lever\\nof the third class.\\nIn the second and third classes of levers, as in the first\\nclass, the shortest distance from the fulcrum to the line of", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0064.jp2"}, "65": {"fulltext": "THE LEVER. 51\\naction of the weight is called the weight-arm, and the\\nshortest distance from the fulcrum to the line of action of\\nthe power is called the potver-arm.\\nThe pupil is to find out by means of the following Exer-\\ncise whether the laws of the second and third classes of\\nlevers are as simple as the law of the first class.\\nEXERCISE 10.\\nLEVERS OF THE SECOXD AND THIRD CLASSES.\\nApparatus: The lever (No. 17) supported as in Exercise 8. A\\nscale-pan (No. 18). A set of weights (No. 19). A spring-balance\\n(No. 7).\\nSuspend the pan with a load of 8 oz. at a point 5 cm. from the\\nmiddle of the lever, and, on the same arm of the lever, at a distance\\nof 10 cm. from the middle, pull upward with, a spring-balance, con-\\nnected with the lever by means of a loop of thread, until the weight\\nis balanced and the lever becomes horizontal. You have here a lever\\nof the second class. Read the spring-balance and record as follows\\nLever of Second Class.\\nWeight. Weight-arm. Power. Power-arm.\\n9 oz. 5 cm. 10 cm.\\nTry other similar cases, and study them all until you are able to\\nwrite down the law for this class of levers.\\nThen with the same apparatus place the spring balance between\\nthe fulcrum and the line of the weight. You will now have a lever\\nof the third class. Try various cases and record as before\\nLever of Third Class.\\nWeight. Weight-arm. Power. Power-arm.\\nLaw.\\nQUESTIONS.\\n(1) A lever supported at its centre of gravity is used to lift a weight\\nof 100 lbs. applied at a distance of 1 ft. from the fulcrum, The", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0065.jp2"}, "66": {"fulltext": "52 PHYSICS.\\npower is applied 5 ft. from the fulcrum and on the opposite side from\\ntbe weight. How great must the power be Must the power be\\napplied upward or downward\\n(2) If the power were placed on the same side of the fulcrum as\\nthe weight, everything else being as described in the preceding\\nproblem, how great would the power have to be Would it be\\napplied upward or downward\\n(3) If the power were 50 lbs. applied at a point 2 ft. toward the\\nright from the fulcrum, and if the weight were applied 8 ft. toward\\nthe right from the fulcrum, how great could the weight be\\n(4) If a weight of 5 lbs. were placed 4 ft. toward the right from the\\nfulcrum, and a weight of 7 lbs. 6 ft. toward the right from the ful-\\ncrum, how far from the fulcrum toward the left must a force of 10\\nlbs. be applied in order tD make the whole balance Arts. 6.2 ft.\\nIn the four preceding problems the weight of the lever has not been\\nconsidered, because the centre of gravity has been supposed to be at\\nthe point of support. Suppose now that the lever weighs 4 lbs. and\\nthat its centre of gravity is 3 ft. to the right from the fulcrum, and\\nwith this new condition go over each of the four problems again.\\n56. Force at the Fulcrum. If we take a case like that\\nshown in Fig. 31, it is plain\\nthat 4 oz. applied 7 cm. from\\nthe centre will balance 2 oz.\\napplied 14 cm. from the cen-\\ntre, but it may not be per-\\nfectly plain how great the pull\\non the fulcrum itself is. We\\nwill, therefore, in the next\\nFlG si. Exercise try the experiment\\nin one or two simple cases and see what the result will be.\\nEXERCISE II.\\nFORCE EXERTED AT THE FULCRUM OF A LEVER.\\nApparatus: The lever of No. 17 freed from its support. Two\\nscale-pans (Nos. 18a and 18b). Two 1-oz. wts. and one 2-oz. wt.\\nfrom No. 19. The spring-balance (No. 7). A piece of copper wire\\nabout 1 mm. in diameter bent into the form of a hook {h in Fig. 32).\\nA piece of thread about 15 cm. long.\\nID\\no", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0066.jp2"}, "67": {"fulltext": "THE LEVEB. 53\\nSuspend the bar from the balance in the manner indicated by Fig.\\n32. Xote and record the weight\\nof the bar alone. Then suspend\\none scale-pan with a 1-oz. weight\\nfrom one arm of the bar, and the\\nother scale-pan with a 2-oz. weight\\nfrom the other arm in such a way\\nas to balance, taking care not to let\\nthe pans and weights spill. Xote r\\nand record the reading of the bal-\\nance. Then make the loads (pan FlG 32\\nand weight) 2 oz. on one side and 4\\noz. on the other, and read and record. Try any other experiments\\nthat you can with the weights furnished, until you feel reasonably\\nsure that you know the relation between the weights applied and the\\npull on the balance. Then state what this relation is.\\n57. Laws of the Lever. In each of the cases in Exercise\\n11 we have applied two downward forces to the bar in sus-\\npending the two scale-pans with their loads, and have found\\nthese two forces to be balanced by another force exerted\\nupward by the spring-balance. It will be well for us to\\nstudy such cases very carefully, for similar ones are often\\nfound.\\nSuppose we are to make three parallel forces, A y B, and\\n(7, just balance each other when all are applied to the same\\nbody. Can we from what we have now learned tell any-\\nthing about the relative magnitude and the arrangement of\\nthese forces\\nWe know that\\n1st. All the forces cannot point in the\\nsame direction. Let us suppose that G is\\nopposite in direction to A and B.\\n2d. Tlie force C must he equal to the sum\\nof the two forces A and B.\\nB\\\\/ 3d. The line along which C is applied\\nfig. 33. must lie between the lines along ichich A\\nand B are applied.\\nI", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0067.jp2"}, "68": {"fulltext": "51\\nPHYSICS.\\n4zth. A X shortest distance from line of A to line of\\nC B x shortest distance from line of B to line of C. (See\\nFig. 33.)\\nThese rules apply as well to horizontal forces as to ver-\\ntical forces. Try three spring-balances laid parallel to each\\nother on a table and pulling at some light horizontal bar\\na lead-pencil, for instance. (Or try the checker-board\\nwith larger spring-balances, if the apparatus of the Second\\nPart is available.)\\n58. Pulleys. We have already learned to consider a disk\\npivoted at the centre as a kind of lever. When such a lever\\nis worked by means of a cord or band lying upon its cir-\\ncumference, it is called a pulley. We shall now see that\\nthe pulley form of lever has some great advantages.\\nEXPERIMENTS.\\n(1) Take the p alley shown in Fig. 34 (No. XV), and let ns first use\\nthe largest circle only.\\nFig. 34.\\nIf we fasten two equal weights, W x and TT 2 to the ends of a\\nstring and pass the string across the top of the pulley, we shall of\\ncourse find that they balance each other.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0068.jp2"}, "69": {"fulltext": "THE LEVER.\\n55\\nBut suppose we used two strings, one for TFi and the other for\\nTT 2 fastening each string to a pin or tack at point A, but letting\\neach string rest in the groove of the pulley, so that the final position\\nof the two strings will be represented by Fig. 34. Will two equal\\nweights balance each other under these conditions The question\\nis quickly answered by trial, and by turning the pulley a little one\\nway or the other we can try the experiment with A in a variety of\\npositions.\\n(2) Next try the effect of a horizontal pull, P, applied by a spring-\\nbalance at the top of the pulley to balance a weight W, as in Fig.\\n35. (Remember that in this position the reading of the ordinary\\n8-oz. balance is about J oz. less than the real force exerted by it, be-\\nFig. 35.\\ncause the spring of the balance does not now support the weight of\\nthe hook and bar, which is about oz.). Find by experiment\\nwhether the force P must be greater or less than, or equal to, the\\ndirect pull of the weight W.\\n(3) Balance a weight on one circle of the pulley by a weight on\\nanother circle, and find the simple relation which holds between the\\nbalancing weights and the radii of the circles.\\n59. Advantages of a Pulley. We see that the advantage\\nof a pulley, as compared with a simple bar-lever, is that the\\npulley enables us to vary the direction of our power at will", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0069.jp2"}, "70": {"fulltext": "56 PHYSICS.\\nand to lift a weight a much greater distance than we could\\nwith a bar-lever no longer than the diameter of the pulley.\\nIn fact, the distance through which we can lift the weight\\nby means of the pulley depends merely upon the length of\\nthe string that supports the weight.\\n60. Windlass, Capstan, etc. The windlass (see Fig. 36)\\nis a familiar apparatus consist-\\ning of an elongated pulley, d,\\ncalled the drum or cylinder,\\nturned by a power applied at\\nthe handle, A, and acting\\nthrough the lever, or crank, c.\\nThe crank and handle are\\nsometimes called a tvinch. The fig. 36.\\nsame name is sometimes applied to the whole windlass.\\nIf the power is applied at right angles with both h and\\nand if the cord sustaining the weight is small, we have,\\nvery nearly,\\nP X length ofc W X radius of d.\\nA capstan is the same in principle as a windlass, but has\\na vertical drum, so that the lever travels in a horizontal\\ncircle.\\nOn ship-board capstans are frequently worked by means\\nof a number of men walking about the drum and pushing\\nagainst the levers, or capstan-bars, of which there may be\\nseveral applied to one cylinder.\\n61. Movable Pulleys. In the pulleys thus far studied\\nby us the pivot has been fixed in position; but pulleys\\nwith movable pivots are frequently used.\\nEXPERIMENTS.\\n(1) Take the small metal pulley (No. XVIII) and arrange it ac-\\ncording to the indications of Fig. 37, P being the pulley, M a weight", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0070.jp2"}, "71": {"fulltext": "THE LEVEE,\\nOi\\nsuspended from an axis through the centre of the pulley, B a spring\\nbalance, and h sl hook to which one end of the string\\npassing beneath the pulley is attached.\\nTo what class of levers does the pulley in this\\nposition belong? What, then, should be the rela-\\ntion between the weight, which is M plus the weight\\nof the pulley itself, and the pull exerted by the\\nspring-balance? Find by experiment whether the\\nconclusion reached is correct.*\\n(2) Let us now try an arrangement, like that\\nshown in Fig. 38, in which we have one pulley, A,\\nhooked to a bar overhead, and a double pulley\\n(No, XIX), B, which moves up and\\ndown with the load M.\\nLet us consider what should be\\nthe relation between the pull P and\\nthe weight W, which is M plus the\\nweight of B, in this case.\\nIn the case tried in Experiment 1\\nwe had two strings holding up the\\npulley P. We have now four\\nstrings holding up the pulley B.\\nAfter thinking upon the matter for\\na little time, trying to study out\\nwhat is the relation between P and\\nTFwith this arrangement, let us try\\nthe experiment as we have already\\ntried it in the simpler case, noting\\nthe force shown by the spring-balance when M is moving steadily\\nup, and again when it is moving steadily down, and taking the mean\\nbetween these two forces as the one that would be required to bal-\\nance the weight, W, if there were no friction.\\nIn making this trial one must remember that friction is often\\nlarge in pulleys, even when they are well oiled, as this one should\\nbe. Now when the load is being steadily raised the hand carrying\\nthe spring-balance must lift harder than it would if there were no\\nfriction, but when the load is being steadily lowered, the hand, pull-\\ning just hard enough to prevent the load from, hurrying, is assisted\\nby the friction. The mean between the reading of the balance going\\nup and the reading of the balance coming down will show, very\\nnearly, what the pull required to sustain the load would be if there\\nwere no friction.\\nM\\nFig. 38.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0071.jp2"}, "72": {"fulltext": "58 PHYSICS.\\n62. Another Law for Relation of Power to Weight.\\nThe law, 4th in 57, for the relation between potver and\\nlueight is extremely useful, and, properly applied, is suffi-\\ncient for very complicated cases of the lever and pulley but\\nin some cases it is more convenient to make use of a differ-\\nent form or statement of this law, a form which makes use\\nof the relative distances moved over by the power and the\\nweight in any operation of the lever, or pulley, or combina-\\ntion of these, that may be in action.\\n63. Search for the Law. If we study the various cases\\nof lever, pulley, and combination of pulleys that have been\\ndescribed in the preceding pages, we shall see that when-\\never the iveight is greater than the poiver the weight moves\\na less distance than the power does in any given operation\\nof the apparatus; but whenever the weight is less than the\\npower, friction being supposed zero, the weight moves a\\ngreater distance than the power does in the operation of\\nthe apparatus.\\n64. Statement of the Law. If we study the matter\\nmore closely, we shall find the following rule or law sug-\\ngested, though we cannot say that it is proved by our pre-\\nceding experiments:\\nPX D p WxD w9\\nwhere P stands for the power applied\\nW weight lifted;\\nD p distance the power moves\\nD w weight moves.\\nAPPLICATIONS OF THIS LAW.\\n(1) It is evident that this law can be readily applied to a case like\\nthat of Fig. 38. We can see at once that if the pulley B were\\nlifted one inch while P remained stationary there would be four\\ninches of loose string under B. To make the string taut again, P\\nwould have to rise four inches. In actual use P and B rise at the\\nsame time, P moving four times as fast as B,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0072.jp2"}, "73": {"fulltext": "TEE LEVER 59\\n(2) In Fig. 39, representing the rear wheel and gear of a bicycle, let\\nthe diameter of the tire be 28 in.\\nsmall sprocket-wheel be 2 in.\\nlarge sprocket-wheel be 5 in.\\nlength of pedal radius be 6 in.\\nFig. 39.\\nIf the weight of the rider, 150 lbs., rests entirely upon the pedal\\nshown, in its present position, how great a weight acting in opposi-\\ntion, as in the figure, will just neutralize the driving-power\\nThe circumference of the circle described by the pedal is (see Ex.\\nB) 2ft X 6 inches, or 12;r inches.\\nOne revolution of the pedal-crank makes the tire revolve 2 times,\\nwhich drives the bicycle forward\\n2 X 27T X 14 inches 567T inches.\\nThe weight W will be lifted as fast as the bicycle moves forward.\\nIf Dp stands for the distance the power P moves downward from\\nits present position during any very short time, and if D w stands\\nfor the distance W moves upward during the same time, we have\\nDp \\\\D lc :12tt :56tt.\\nHence the law W X D w P X D p (see 64) gives\\nWX 56/r PX 12k,\\nor W=j\\\\P= T 3 T X 150 32. 1 (lbs.)\\nQUESTIONS.\\n(1) A large pair of shears is used to cut a wire. One handle of the\\nshears being held fixed, a power of 25 lbs. is applied to the other\\nhandle at a distance of 2 ft. from the pivot. The wire cut is placed\\n2 in. from the pivot. How great is the resistance offered by the", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0073.jp2"}, "74": {"fulltext": "60 PHYSICS.\\nwiie that is, bow great a force applied just over tlie wire would\\ndrive the blade through it\\n(2) A man lifts 10 lbs. of coal on a shovel. His left hand is at the\\nend of the handle his right hand is 18 in. distant from his left hand\\nthe centre of gravity of the coal is 36 in. distant from the left hand.\\nThe shovel itself weighs 6 lbs. and its centre of gravity is 21 in. from\\nthe left hand.\\n(a) What is the direction and magnitude of the force exerted by\\nthe left hand (Consider the right hand as the fulcrum.)\\nAns. 11 lbs.\\nWhat is the direction and magnitude of the force exerted by the\\nright hand (Answer this question as if the left hand were replaced\\nby a weight.)\\n(3) A body weighing 160 lbs. is suspended from a pole resting on\\nthe shoulders of two men, A and B, of equal height. The point of\\nsuspension is 3 ft. from A s shoulder and 5 ft. from B s. How\\nmuch of the weight does each man bear\\n(4) Six men are working at a capstan, each exerting a force of 20\\nlbs., each at a distance of 6 ft. from the centre. The diameter of\\nthe coils in which the rope is being wound on the drum is 1 ft.\\nHow great is the strain on the rope, all friction being neglected\\n(5) A man finds that by moving one point of a machine, consisting\\nof levers and pulleys, forward 10 in. he can move another point of\\nthe machine 1 in. If a force of 5 lbs. is applied at the first point,\\nhow great a resistance applied at the second point will be required to\\nneutralize it, if there is no friction in the machinery\\n(6) Can the class name any tools or machines, not already men-\\ntioned in this book, in which levers or pulleys are used", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0074.jp2"}, "75": {"fulltext": "CHAPTER V.\\nTHREE FORCES DIRECTED THROUGH ONE POINT: THE\\nPARALLELOGRAM OF FORCES.\\n65. Introductory. In studying the lever we have\\nusually, though not always, had parallel forces to deal with,\\nforces acting straight up or straight down. But very often\\nwe have to do with bodies that are acted upon by forces not\\nparallel to each other. Thus when a ladder standing upon\\nthe ground leans against a house we have at least three\\nforces acting upon the ladder: 1st, the earth s attraction,\\nor, as we call it often, the tv eight of the body, which acts\\nas if the whole substance were at the centre of gravity; 2d,\\nthe push of the ground against the foot of the ladder,\\nwhich push is not straight upward; 3d, the push of the\\nwall against the top of the ladder.\\nAgain, a flying kite is acted upon by the earth s pull,\\nstraight downward by the force exerted by the air, which\\nforce, because of the wind, is not straight upward by the\\npull of the string, which pull is not straight downward.\\nThe way to begin the study of such cases is to study the\\ncase of three forces all acting straight from or straight\\ntoward a single point. We shall take such a case in Exer-\\ncise 13, measuring the forces by means of spring-balances.\\n66. Errors of Spring-balances. It is quite possible in\\nspecific-gravity work to get accurate results with an in-\\naccurate balance for the specific gravity of a body is found\\nby taking the ratio of two quantities, both found by weigh-\\ning with the same balance, and if the balance should give\\n61", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0075.jp2"}, "76": {"fulltext": "62 PHYSICS.\\nthe weight of each as n times its true value the ratio of the\\ntwo false weights would be the same as the ratio of the true\\nweights, whatever the value of n.\\nBut though a balance may give the weight of everything\\nas n times its true weight, n being the same for all parts of\\nthe scale, it is very unlikely that several balances will all be\\nwrong in just the same way; and as in Exercise 13 we\\nshall need to use three balances in combination, it is neces-\\nsary for us to give more careful attention to their errors\\nthan we have given heretofore.\\nThe following Exercise is intended to show how the errors\\nof a spring-balance may be found and may be recorded in a\\nform convenient for future use.\\nEXERCISE 12.\\nERRORS OF A SPRING-BALANCE.\\nApparatus A spring-balance (No. 7). A set of weights (No. 19).\\nThread for suspending the weights. A measuring-stick (No. 3).\\n(Although weights reckoned in ounces are referred to in this Exer-\\ncise, it may be performed equally well with suitable weights reckoned\\nin grams.)\\nBalance in the Vertical Position. Suspend the balance by\\nits ring from some convenient support so that the index will be not\\nhigher than the eye of the observer.\\nMake five careful readings with the loads indicated in the first\\ncolumn below, and record these readings in a second column thus,\\nfor example:\\nTrue Load. Reading. Error.*\\noz. 0.2 oz. 0.2\\n2 2.0 0.0\\n4 4.2 +0 2\\n6 6.3 +0.3\\n8 8.1 +0.1\\nThat is, the quantity which must be subtracted from the reading\\nin order to find the true weight.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0076.jp2"}, "77": {"fulltext": "THE PARALLELOGRAM OF FORGES. 68\\nNow draw in the notebook a straight line a little more than twice the\\nlength of the scale of the balance, and mark off on it points corre-\\nsponding to the loads and readings given above.\\nThen represent the errors by vertical distances, measured down\\nfrom the points indicating the readings when the errors are negative,\\nand up when they are positive, showing these errors on a rather\\nlarge scale, 0.5 cm. per 0.1 oz., for instance.\\nDraw a curve through the extremities of these vertical distances, as\\nin Fig. 40. This curve will enable us to tell with sufficient accu-\\nracy for our present purposes the errors of any other readings made\\nwith the balance in the vertical position for instance, if the balance\\nto which Fig. 40 relates reads 1 oz., we may assume that the error is\\nvery nearly 0.1 oz. and that the true weight is very nearly 1.1 oz.; if\\nthe reading is 3 oz we may assume that the true weight is about 2.9\\noz., and so on, the error for each case being found by measuring\\nfrom the point indicating the reading up to or down to the curve.\\nThe Same Balance in the Horizontal Position. We will\\nsuppose at first that the same index is used for the horizontal as for\\nthe vertical readings.\\nLay the balance flat on its back and tap it gently several times.*\\nThen take its reading, which we will suppose to be 0.5 oz. In this\\ncase it would require a force of 0.3 oz. to pull the index down to the\\nposition it occupied with no load in the vertical test. To bring the\\nindex to any reading in the horizontal use of this balance will, there-\\nfore, require a force 0.3 oz. greater than the weight which, applied\\nto the hook in the vertical use of the balance, would bring the index\\nto the same point.\\nIt would in the case here supposed be sufficiently accurate for our\\npurposes to add 0.3 oz. to any horizontal reading, and then correct\\nthis increased reading by means of the curve given in Fig. 40.\\nWhen a different index is used for horizontal readings, the princi-\\nple is the same. For example, let us suppose the second index reads\\n0.1 without pull in the horizontal use of the balance. We say,\\nthis reading exceeds the vertical reading without load by 0.1 oz. We\\nmust, therefore, subtract 0.1 from all horizontal readings made with\\nthis second index, and then correct these reduced readings by means\\nof the curve in Fig. 40.\\nThis method assumes that the movable parts of the balance are\\nrestrained by friction only, which the tapping overcomes. Sometimes\\nthe slot in the balance-face is not long enough to allow the index to\\nfind its unrestrained position.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0077.jp2"}, "78": {"fulltext": "64\\nPHYSICS.\\nThe curve so often referred to should be marked with the number\\nof the balance and kept for future use.\\nEXERCISE 13.\\nTHREE FORCES IN ONE PLANE AND ALL APPLIED AT ONE\\nPOINT: PARALLELOGRAM OF FORCES.\\nApparatus: Three 8-oz. spring-balances, each provided with two\\nsmall blocks (No. 22) to go under its sides and hold it flat on its back\\nwhen it is lying upon the table. The rectangular block (No. 9).\\nThe measuring-stick (No. 3). A sheet of paper. Thread.\\nTake two pieces of strong thread, one about 12 inches, the other\\nabout 6 inches, long, and tie one end of the short thread to the middle\\nof the long one. Fasten the three loose ends to the hooks of the\\nspring-balances; then lay the latter upon the table, putting the blocks\\nunder their sides, as in Fig. 41, and let one student pull at each bal-\\nFig. 41.\\nance, taking care that the slit of each balance- face is in a straight line\\nwith the thread, until no one of these reads less than 3 oz.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0078.jp2"}, "79": {"fulltext": "THE PARALLELOGRAM OF FORGES.\\n65\\nIt will be found that any variation in the angles which the strings\\nmake with each other will require a change in the forces. Evidently\\nthere is some connection between the directions of the strings and the\\nforces necessary to balance each other. The object of this Exercise\\nis to make out what this connection is.\\nPut under the threads a sheet of paper, and draw on this paper,\\njust under each thread, apencil-mark parallel to the thread, and then\\nwrite down alongside each pencil- mark the force in the direction of\\nthat line, as shown by the spring-balance. The balances must be\\nheld very still while these lines are being drawn, and must be read\\nbefore any change occurs in the direction of the lines.* To draw a\\nline place one side of the block (No. 9) close alongside one branch of\\nthe thread, taking care not to push the thread out of place, and then\\nrun the point of a well-sharpened pencil along the edge of the block\\nunder the thread. Draw the other lines in the same way, doing all\\nvery carefully.\\nEach student in turn should make a set of lines, and record along-\\nFig. 42.\\nside them the proper forces. The directions of the pulls should be\\nvaried somewhat by each experimenter, in order that his lines and\\nforces may not be exactly like those of others.\\nTake now the wooden ruler (Xo 3), and extend the three lines\\ntoward each other till they meet at one point. This they will do if\\nIt is well to fasten the ring of each balance to some object heavy\\nenough to hold the balance in place, thus relieving the experimenters,\\nwho might grow tired and unsteady in holding the balances long\\nenough to permit of drawing the pencil- marks properly.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0079.jp2"}, "80": {"fulltext": "66\\nPHYSICS.\\nthey have been drawn originally just under the threads. If they do\\nnot all meet at one point, a new line should be drawn parallel to one\\nof them in such a position as to pass through the crossing of the other\\ntwo lines, and this new line, the dotted line in Fig. 42, is then to be\\nused in place of the original line. The three lines as now drawn will\\nrepresent accurately the directions of the three forces.\\nNow measure off from the common point along the line A a dis-\\ntance of 1 cm. for each ounce (or each 30 gm., if the forces are meas-\\nured in grams) of the force which was exerted along that line, and\\nput a small arrow-head (see Fig. 42) at the end of this measured dis-\\ntance. Erase that part of line A which lies beyond the arrow-head.\\nDo the same with lines B and C that has been done with A. The\\nthree arrows thus obtained, all reaching from the same point, repre-\\nsent the magnitude and the direction of the three forces exerted by\\nthe spring-balances.\\nNow with A and B of Fig. 42 as two of the sides draw a parallelo-\\ngram, taking pains to make it accurate.* Then make a parallelogram\\nwith B and C as sides, then one with A and G as sides. Compare the\\nOne line may be drawn very nearly parallel to another by means\\nof a device illustrated by Fig. 43. LI is a line already drawn. The\\nblock (No. 9) is so placed that for an eye placed at E the edge mn\\nE\\nFig. 43.\\nappears to be close to LI and parallel to it. Then a pencil-mark is\\nmade along the edge op.\\nA better method is to set the edge op on the line LI and then guide\\nthe block to a new position by sliding it along the straight edge of a\\nruler at right angles with LI.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0080.jp2"}, "81": {"fulltext": "THE PARALLELOGRAM OF FORCES.\\n67\\nlength and direction of the line C with the length and direction of\\nthe diagonal of the parallelogram AB\\\\ the line A with the diagonal\\nof the parallelogram BC; the line B with the diagonal of AG.\\nFrom a study of the Exercise make a rule showing how to find\\nthe direct. on and magnitude of a force G which put with two forces\\nrepresented by the lines A and B (Fig. 44, below) will just balance\\nthem.\\nApplications of the Parallelogram of Forces.\\nThe rale found in the preceding Exercise, and which is called the\\nparallelogram of forces, is peculiarly easy to apply in cases where\\ntwo of the forces are at right angles with each other. A number of\\nsuch cases will now be discussed.\\n(1) A force of 7 lbs. pulls north from a certain point, and a force\\nof 4 lbs. pulls east from the same point. How large must a third\\nforce be to hold them in check, and what will be its general direc-\\ntion?\\nSolution. Fig. 45 indicates the method of working the problem.\\nFig. 44. Fig. 45. Fig. 46.\\nThe directionoi the third force is evidently southwest, in a line with\\nthe diagonal of the rectangle, of which the base is 4 and the height 7.\\nThe magnitude of the third force is evidently equal to the length of\\nthe diagonal, which a simple rule of geometry shows to be\\nv 4 -2 r 8 06\\n(2) A boy weighing 50 lbs., represented by the point b in Fig. 46, is\\nseated in a swing 10 it. long, represented by the line 8b. A horizon-", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0081.jp2"}, "82": {"fulltext": "68\\nPHYSICS.\\ntal pull holds him 4 ft. to one side from the natural position of the\\nswing.\\n(a) How great is the pull of the swing- rope\\n(b) How great is the horizontal pull\\nSolution. Represent the weight of the boy by the line b W, made\\n1 cm. long, we will suppose. The other two forces acting on b must\\nbe such as to make a balance with this force. Draw the line bW\\nexactly equal and opposite to bW, and complete the parallelogram\\nas in the figure.\\nA little geometry shows that the triangle MW is similar to the tri-\\nangle Sbn.\\nThe line bi represents the pull of the swing-rope,\\ntriangles just mentioned are similar, we have\\nU-.bW ::Sb Sn,\\nand, as the\\nbi=(Sb-i-Sn) XbW\\n(10-*- VW^~4: 2 xbW =lMxbW\\nBut b W b W, which represents a force of 50 lbs. Hence bi rep-\\nresents 54.5 lbs. Ans. to {a) 54.5 lbs.\\nThe pull upon the rope is therefore greater than the boy s weight.\\nThe line bh y which is i W, r epresents the horizontal pull.\\nWe have\\nbh .bW :nb:nS,\\nAns. to (b) 21.8 lbs.\\nbh (4 -r- VW -4?)XbW 0.436 X b W\\\\\\nThe force represented by bh is therefore\\n0.436 X 50 lbs. =21,8 lbs.\\n(3) A mass of 20 lbs. is suspended from\\nthe point p (Fig. 47), where a string is bent\\nat a right angle. The ends of the string\\nare fastened to two nails i^i and i\\\\T 2t\\nwhich are at the same height. The part\\nATi^ is 4 ft. long, the part N^p is 8 ft.\\nlong.\\n(a) How great is the pull upon iV a Fig. 47.\\n(b) How great is the pull upon JV 2\\nSolution.\u00e2\u0080\u0094 Represent the weight by pW. Draw p W equal and\\nopposite to pW. Complete the parallelogram.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0082.jp2"}, "83": {"fulltext": "THE PARALLELOGRAM OF FORCES. 69\\nThe triangle pqW is equal to the triangle W rp and similar to the\\ntriangle N*pNi. The side N^N* V _j_ 42 8.94 ft. nearly.\\nThe pull on i\\\\^ is represented by pq, and we have\\npq p W N JMfi, or pg (8 8.94) X p IT\\nTherefore pq represents very nearly 0.895 X 20 lbs. 17.90 lbs.,\\nwhich is the answer to question (a).\\nSimilarly we find the pull on Jjf to be very nearly (4 8.94) X 20\\nlbs. 8.95 lbs., which is the answer to question (5).\\nThe pull along the 8-ft. part of the string is just one-half as great\\nas that along the 4-ft. part.\\nThe LtfCLEN ED Plane.\\n67. Introductory. The parallelogram of forces will\\nenable us to understand a contrivance very often used for\\nraising heavy weights. It is a common thing to see barrels\\nof flour or other heavy objects loaded upon wagons by roll-\\ning them up a plank or a pair of rails, placed with one end\\non the ground and the other upon the wagon, so as to make\\nthe ascent gradual instead of straight up. The flat slanting\\nsurface up which the body is rolled is called an inclined\\nplane.\\nSometimes a body is lifted by forcing an inclined plane,\\nthe slanting face of a wedge under it, as in Fig. 48.\\nFig. 48.\\nSometimes the force used by an experimenter or a work-\\nman with the inclined plane is parallel to the inclined sur-\\nface; sometimes it is parallel to the base-line of the plane,\\nthe horizontal surface of a wedge, for example.\\nWe will consider each case in order, seeking for the con-", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0083.jp2"}, "84": {"fulltext": "70\\nPHYSICS.\\nnection between the weight, steepness of incline, and force\\nto be applied.\\n68. Force Applied Parallel to Incline. This case is illus-\\ntrated by Fig. 40, where\\nL reDresents the length of the incline;\\nB base\\nH height\\nW weight of the body on the incline,\\napplied straight downward from the centre of\\ngravity of the body;\\nW is the equal and opposite of IF;\\nN represents the force exerted upon the body by the\\nplane X, a force which is straight outward\\nfrom the surface of the incline if there is no\\nfriction (see Chap. VI) between the body and\\nthe incline;\\nP represents the pull, parallel to the plane L, which\\nwith the force N will just balance W.\\nBy comparing the dotted triangle with the triangle whose\\nsides are L, B, and H we see that\\nP W (or IF) H: L,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0084.jp2"}, "85": {"fulltext": "THE PARALLELOGRAM OF FORGES.\\n71\\nor\\nPXL=WX H,\\nP= Wx (H+L).\\nEXPERIMENTS.\\nTake apparatus No. XX and adjust it as indicated by Fig. 50, put-\\nting 7 oz. upon the pan, so that P= 7+ 1 8 oz. Then raise or\\nFig. 50.\\nlower the incline till the weight W will barely roll up the incline\\nwhen the apparatus is purposely jarred slightly. (The incline cannot\\nbe quite so steep when this takes place as it might be if there were\\nno friction. If a knot is made in the thread near where it passes over\\nthe pulley at the top of the incline, a very slight movement up or\\ndown the incline can be detected by watching the position of this\\nknot. A slight movement is enough.)\\nAs soon as this adjustment is made read H, the length of the ver-\\ntical scale from the top of the base-board to the under side of the in-\\ncline, and record in the way indicated in the table below (upper row\\nof numbers).\\nThen without changing P rase the incline somewhat more, until W\\nwill, when the apparatus is jarred, barely roll down the incline. (The\\nincline must be somewhat steeper for this than it would have to be\\nif there were no friction.) When the proper adjustment is made, read\\nthe new value of //and record it in the second line of the table below.\\nTo find the //that would make P just balance W if there were no\\nfriction, take the mean between the two values now recorded. Then", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0085.jp2"}, "86": {"fulltext": "72\\nPHYSICS.\\nfind the L that would correspond to this value of H, L being the dis-\\ntance along the inclined scale from the hinge to the point of crossing\\nthe vertical scale.\\nP W H L\\nGoing up. ..8 oz. 16 oz.\\ndown.. 8 16\\nTo balance 8 oz.\\n16 oz.\\nIf time permits, make P 6 oz., then 4 oz. and in each case repeat\\nthe operations just described.\\n69. Force Applied Parallel to Base. This case is illus-\\ntrated by Fig. 51.\\nFig. 51.\\nThe line W is not here, as it is in Fig. 49, the hypothe-\\nneuse of the dotted triangle; but it is evident that the\\ndotted triangle is similar to the triangle made up of X, B,\\nand H. P is the force applied parallel to the base, and just\\nsufficient, with N to balance W. We have, from a com-\\nparison of the triangles,\\nP W (or W) ::I1:B,\\nor\\nP X B= W X H 9\\nP= WX (H+B).", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0086.jp2"}, "87": {"fulltext": "THE PARALLELOGRAM OF FORCES.\\n73\\nEXPERIMENT.\\nFor experiments in which the power is applied parallel to the base-\\nline we cannot well make use of a string running over a pulley. We\\nmust apply the power by means of the spring-balance, as shown in\\nFig. 52, the long slot cut through the incline lengthwise allowing us\\nto do so.\\nFig. 52.\\nFind by trial a steepness of incline that will make P about 7 oz.\\nand, keeping this steepness unchanged for the time, find how large\\nP is when it is pulling W slowly and steadily up the incline, and how\\nlarge when it is letting TFrun with equal slowness and steadiness\\ndown the incline. Take the mean* of these two values as the one\\nthat would be needed to balance W if there were no friction.\\nWe record, then, for this case\\nGoing up...\\n11 down.\\nw\\n16\\n16\\nTo balance.\\n16\\nwhere B is the length of the base-line from the hinge to the foot of\\nthe vertical line, along which IL is measured.\\nIf time permits, lower the incline and try various degrees of steep-\\n*The mean of the two values of P is not, in this case, exactly the\\nquantity wanted, because the greater pull of P when IF is going up\\nthe incline makes W press harder against the incline when going up\\nthan when going down, thus increasing friction. The mean value of\\nP. as now found, is a little greater than the value wanted, but so\\nlittle that the error is not important,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0087.jp2"}, "88": {"fulltext": "74 PHYSICS.\\nness, so that P will be in one case about 5 oz. and in another case\\nabout 3 oz.\\n70. The Wedge. The ivedge, as commonly used (see\\nFig. 48), is a case of the inclined plane with the applied\\nforce parallel to the base. It differs from the case shown\\nin Fig. 51 in one respect. In Fig. 51 the body raised has\\na motion parallel to the base of the plane, while the plane\\nitself has not. A wedge commonly has a motion parallel to\\nits own base, while the body raised or otherwise moved by\\nit does not have a motion in this direction. The principle\\ninvolved in the two cases is quite the same, and for a wedge\\nused to lift a weight we have, leaving friction out of ac-\\ncount as before,\\nP=WX (H+B),\\nwhere H stands for the thickness of the wedge, and B for\\nits length.\\n71. The Screw. The screw is an ingenious form of the\\ninclined plane, as the following experiment will show.\\nEXPERIMENT.\\nCut out a long narrow triangle of paper, (see Fig. 53), and then\\nwind it upon a lead-pencil, beginning at the end \u00c2\u00a3Tand keeping the\\nline B all the time at right angles with the length of the pencil. The\\nline L will make a regular spiral around the pencil, corresponding to\\nthe thread of a screw.\\n72. Pitch of a Screw. The distance from one turn of\\nthe thread to the next turn, measured parallel to the length\\nof the screw, is called the pitch of the screw.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0088.jp2"}, "89": {"fulltext": "THE PARALLELOGRAM OF FORGES. 75\\nIt is evident that in the ordinary use of a screw one\\nrevolution moves it toward or backward the length of its\\npitch.\\n73. Use of the Screw in Lifting. A very large iron\\nscrew, called a jack-screw, is frequently used for lifting\\nvery heavy bodies. The power is applied to such a screw\\nby means of a long handle or lever, which projects from the\\nhead of the screw at right angles with its axis, its central\\nlengthwise line. Leaving friction out of account, we can\\nfind the relation between power applied and weight of the\\nbody lifted thus\\nLet P the power applied to the handle at right angles\\nwith the handle and with the axis of the\\nscrew\\nA the distance from the point of application of P\\nto the axis of the screw\\nr the radius of the screw itself;\\np the pitch of the screw\\nW= the weight of the body lifted.\\nThe force P produces at the thread of the screw a force\\nP P x (A -f- r). (See Exercise 10.)\\nThis force at the thread is like the power used to drive a\\nwedge. The circumference of the screw at the thread,\\nwhich 27rr, corresponds to the length of the base of the\\nscrew, while the pitch corresponds to the thickness of the\\nwedge. We have, then\\nP X 27rr= Wxp,\\nP =z Wx (p 2*r),\\nor\\nPx(iv r) W X (p 27tr)\\nwhence\\nP X 2?rA WXp.\\nObserve that we have here, as we have had so often", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0089.jp2"}, "90": {"fulltext": "76 PHYSICS.\\nbefore, the rule, Power X distance the power moves weight\\nX distance the weight is lifted.\\nDefinitions.\\n74. Equilibrant. A single force that will just balance,\\nor make equilibrium with, two or more others is called their\\nequilibrant.\\nIn Fig. 46 b IF is the equilibrant of hi and bh;\\nU bW bh;\\nbh bW bi.\\n75. Resultant. A single force that can exactly replace\\ntwo or more others, so as to produce the same effect upon\\nthe body acted on, is called their resultant.\\nIn Fig. 46 bW is the resultant of bi and bh.\\nThe resultant and equilibrant in any given case are equal\\nin magnitude, but opposite in direction, so that the two\\nwould exactly balance each other.\\nQUESTIONS.\\n(1) What is tlie resultant of pq and pr in Fig. 47 What is their\\nequilibrant\\n(2) Draw three lines leading from one point, giving to them such\\nmagnitudes and directions that they will represent three forces in\\nequilibrium with each other.\\n(3) Replace two of the lines in the preceding problem by two\\nothers that will also represent equilibrium with the third line.\\n(4) A telegraph-wire pulls north from a post with a force of 12 lbs.\\nanother pulls west from the same post with a force of 16 lbs.\\n(a) How great is the resultant pull on the post?\\n(b) If a third wire is put in to neutralize the pull of the other two,\\nshould it pull more nearly south than east, or more nearly east\\nthan south\\n(5) Two sticks of equal length, OA and OB in Fig. 54, each rest\\ning one end upon the ground, meet at a right angle in a frictionless\\njoint 0. From this joint is suspended a mass of 5 lbs., the weight\\nof which is represented by the line OW.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0090.jp2"}, "91": {"fulltext": "THE PARALLELOGRAM OF FORCES. 11\\n(a) How great is tlie total force exerted by each stick against the\\nground, the weight of the stick being\\nleft out of account Ans. 3.54 lbs.\\n(6) How great is the vertical push ex-\\nerted by each stick against the ground?\\nAns. 2.5 lbs.\\n(c) How great is the horizontal push\\nexerted by each stick against the FlG 54\\nground? Ans. 2.5 lbs.\\n(We see from this problem that the total vertical force exerted at\\nA and B is just equal to the weight of the suspended mass, the\\nweight of the sticks not being considered. If we think of AOB as\\none end of the roof of a house, the answer to (c) shows the tendency\\nof the roof to push the walls apart. This tendency is met in actual\\nroofs by beams or rods connecting A and B.)\\n(6) A wedge 1 ft. long ou its base and 2 in. thick is used to lift a\\nweight of 300 lbs. in a case where friction may be left out of ac-\\ncount. How great is the force, parallel to the base, required to\\ndrive the wedge\\n(Friction not being considered, the force required to keep the\\nwedge moving after it is started is no greater than the force required\\nto hold it in place so as to make equilibrium, as in the discussion of\\n\u00c2\u00a770.)\\n(7) A safe weighing 2000 lbs. is resting on an inclined plane 12 ft.\\nlong, one end of which is 2 ft. higher than the other. How great is\\nthe force, parallel to the incline, required to keep it from sliding\\ndown\\n(8) A jack-screw having a pitch of in. and a handle 2 ft. 1 in.\\nlong is used to lift a mass of 5000 lbs. How great must be the power\\napplied to the end of the handle", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0091.jp2"}, "92": {"fulltext": "CHAPTER VI.\\nFRICTION.\\n76. Introductory. When we push a heavy block along\\non the top of a table we feel a certain resistance. We\\nknow from experience that by making the surface of the\\ntable and the surface of the block yery smooth we can lessen\\nthe resistance. This resistance, the amount of which\\ndepends upon the condition of the rubbing surfaces, is ccdled\\nFriction.\\nFriction always opposes motion, whatever may be the\\ndirection of the motion, that is, it merely tends to stop\\nthe motion. It never helps to push the block back to the\\nposition where it started.\\nWe shall in Exercise 14 measure in a number of cases the\\nforce required to keep a block moving steadily along on a\\nsheet of paper laid upon a level board, and shall study these\\ncases with the purpose of finding out some useful facts, or\\nlaws, concerning friction between solid bodies.\\nEXERCISE 14.\\nFRICTION BETWEEN SOLID BODIES.\\nApparatus A spring-balance (No. 7). A rectangular block (No.\\n9). Set of weights (No. 19). A smooth sheet of paper about 1 ft.\\nwide and 1^ ft. long. Thread.\\nWe shall first consider the velocity of the motion, that is, ice shall\\nask whether the force required to keep up a slow steady motion is\\ngreater or less than that required to keep up a more rapid steady\\nmotion.\\n78", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0092.jp2"}, "93": {"fulltext": "FRICTION-. 79\\nLay the block on one of its broad sides, and attach it to the spring-\\nbalance by a thread passing around but not under the block. Load\\nthe block with weights until the force required to maintain a slow\\nsteady motion is about 3 oz. Draw the block parallel to its grain\\nalong the sheet of paper several times with a very slow steady\\nmotion, and then several times with an equally steady motion two or\\nthree times as fast. (As the paper is likely to grow somewhat\\nsmoother under the repeated rubbing, the experimenter should not\\nmake all his slow trials first, but should change from slow to fast\\nand fast to slow a number of times.)\\nRecord your conclusion as to whether the slow or the more rapid\\nmotion requires the greater force.\\nWe shall next try to find out whether, the total weight being the\\nsame as before, it is easier or harder to draw the block on a narrow\\nside than on a broad side.\\nUse the same block and the same load of weights, pulling it now,\\nas before, parallel to its grain.\\n(The side upon which the block slides should in all cases be clean,\\nand the broad and narrow sides which are compared should be, as\\nnearly as practicable, equally smooth. The thread must not be\\nbetween the rubbing surfaces in any case.)\\nRecord your conclusion as to whether the broad side or the narrow\\nside offers the greater resistance to the motion.\\nFinally y we shall ask what connection there is between the total mass\\ndrawn and the force required to draw it.\\nFor this purpose vary the weights placed upon the block, using\\nnot less than 6 oz. for the least and as much as 16 oz. for the greatest\\nload.\\nAdd to the load in each case the weight of the block itself, and\\nmake the record in the following form, W being the load and b the\\nweight of the block\\nW -f b* F (Force Required).\\nLook for any simple relation between (1F+ b) and F.\\nIt is well to begin with the lightest load, proceed in regular\\norder to the heaviest, then go back in exactly the reverse order to\\nthe lightest, recording both trials made with each load and taking\\nthe mean of the two for final study.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0093.jp2"}, "94": {"fulltext": "80 PHYSIOS.\\nThe experiments just described will teach a number or useful facts\\nabout friction between two solid substances, but one must be careful\\nnot to apply the conclusions here arrived at to extreme cases, ex-\\ntremely slow or very fast motion, for id stance or to cases where the\\npressure is great enough and the edge of the sliding body narrow\\nenough to cause an actual cutting of the body into the surface over\\nwhich it should slide.\\n77. Laws of Friction. The so-called laws of friction\\nbetween solids are:\\n1st. Friction is independent of the velocity of one surface\\nacross the other, other things being equal.\\n2d. Friction is independent of the area of the rubbing\\nsurfaces i other things leing equal.\\n3d. Friction is proportional to the total pressure of one\\nsurface against the other, other things ieing equal.\\nThe experimenter in Exercise 14 need not be surprised\\nor disappointed if his observations do not agree exactly\\nwith these statements. In fact, the laws are not strictly\\ntrue; but they are near enough to the truth to be of very\\ngreat use.\\n78. Coefficient of Friction. If the pressure between two\\nsurfaces, at right angles ivith each of them, is called P, and\\nif the friction between the two surfaces is called F, the ratio\\nF-+- P is called the coefficient of friction.\\nIn Exercise 14 the ratio F (TF+ b) is the coefficient\\nof friction.\\nThere is a method of finding this coefficient without\\nmeasuring either P or F. It makes use of an inclined\\nplane and the parallelogram of forces.\\nIn Fig. 55 is supposed to be a body resting upon the\\nincline AB, which is just steep enough to keep moving\\nwith uniform velocity, in spite of friction, if it is once\\nstarted down the incline.\\nThe line W represents the weight of the body. This", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0094.jp2"}, "95": {"fulltext": "FRICTION,\\n81\\nis equivalent to a force OP at right angles with the incline\\nand a force OM down the incline. It is the force OP that\\nFig. 55.\\ncauses the friction. It is the force OM that maintains\\nmotion in spite of the friction.\\nIf the body moves with uniform velocity down the\\nincline, as we have supposed, the force OM must be exactly\\nequal and opposite to the resistance of friction. For if OM\\nwere greater than the friction, the body would move faster\\nand faster down the incline; while if OM were less than\\nthe friction, the body would move more and more slowly\\ndown the incline.* While the body is moving downward\\nfriction is represented by the arrow pointing from toward\\nA, equal and opposite to OM.\\nTherefore, in accordance with the definition given at the\\nbeginning of this article, we have\\ncoefficient of friction OM -f- OP.\\nIt require- force to set any body in motion and it requires force\\nto stop any body that is in motion. If a body is moving along in a\\nstraight line with uniform velocity we know that the various forces\\nacting on it balance each other. This matter is discussed further in\\nthe Second Part.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0095.jp2"}, "96": {"fulltext": "82 PHYSICS.\\nA comparison of the triangle OWM, in which WM\\nOP, with the triangle ABC shows that they are similar,\\nand hence\\nOM: OP AC: PC.\\nThat is, the\\ncoefficient of friction AC PC.\\nEXERCISE 15.\\nCOEFFICIENT OF FRICTION.\\nApparatus The same block tliat was used in Exercise 14. A\\nflat board (No. 20) about 15 cm. wide and 50 cm. long for the block\\nto slide on. A sheet of paper to cover one side of this board. Some\\nmeans of raising one end of the board and adjusting it so that the\\nblock will just slide down it another block similar to the one which\\nslides, or any similar object, will do for this purpose. A 30-cm.\\nmeasur i ng-stick\\nPlace one end of the board on the table and the other on the sup-\\nport. Vary the steepness of the board by varying the position of\\nthe support, until such an inclination is found that the block, once\\nstarted slowly, will barely continue in motion down the board.\\nThen lay off on the table beneath the board a distance of 30 cm.,\\nmeasured from the edge where the board rests upon the table, and\\nfrom the end of this line measure H, the vertical distance up to the\\nunder side of the board. The coefficient of friction will be H^- 30.\\nIf the same block, the same side of the bloc v, and the same kind\\nof paper are used in this Exercise as in Exercise 14, the value of the\\ncoefficients obtained in the two Exercises should be compared.\\n79. Friction in Applied Mechanics. Friction is one of\\nthe most important conditions in the construction and\\noperation of very many mechanical appliances. It enters\\nlargely into the list of resistances to be overcome, as in the\\nrolling friction of the car-wheels upon the track or of\\nwagon-wheels upon common roads. Every axle revolves in\\nits bearings with a measurable amount of friction, which\\ncan be diminished but not overcome by oiling the surfaces", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0096.jp2"}, "97": {"fulltext": "FRICTION. 83\\nin contact. On the other hand, many machines and\\nmechanical appliances would be valueless without friction.\\nUpon this the efficiency of belting, of brakes, of nails and\\nscrews of every description, is dependent. The driving-\\nwheels of engines or of electric street-cars, the feet of men\\nor of horses, would be unable to produce or maintain loco-\\nmotion without the aid of friction. If its operation were\\nsuspended, every river would become a cataract, soon run-\\nning itself out.\\nRolling Friction.\\n80. Introductory. The friction encountered by a mov-\\ning body is usually much less when it is on wheels or rollers\\nthan when it slides, though it is true that on snow runners\\nare better than wheels. The wheels of ordinary carriages\\ndo not get rid of sliding friction altogether, for the surfaces\\nof the axle and the hub slide over each other. The ball\\nbearings of bicycles do away with this sliding friction\\nalmost completely.\\n81. Coefficient. The coefficient of rolling friction of\\niron wheels on iron rails may be as small as .002,* so that\\na pull of 4 lbs. may keep in motion a carriage weighing\\n2000 lbs.\\nThe coefficient of sliding friction of smooth dry iron upon\\niron is perhaps .15 or .20.\\n82. Slipping of Wheels. When people were first con-\\nsidering the use of steam for dragging railroad trains, they\\nthought it would be necessary to provide the driving-wheels\\nof the locomotive with cogs fitted to a cogged rail along the\\ntrack. This device was found to be unnecessary for ordi-\\nnary work, but it is used on very steep inclines running up\\nthe sides of mountains.\\nRankine, Civil Engineering.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0097.jp2"}, "98": {"fulltext": "84 PHYSICS.\\nEven upon ordinary railroads, when the rails are wet and\\nthere is a heavy train to be set in motion, the driving-\\nwheels sometimes slip and revolve, while the train refuses\\nto start. The frequency of the puffs from a locomotive\\ndepends upon the speed of revolution of the driving-wheels,\\nand when an engine that has been p tiffing very slowly in\\nstarting a train suddenly gives three or four puffs in very\\nquick succession, we may conclude that the driving-wheels\\nare slipping on the rails. Engines are provided with sand-\\nboxes, from which sand can be sprinkled upon the rails in\\nfront of the driving-wheels when slipping occurs.\\nFriction between Solids and Fluids.\\n83. Unlike Friction between Solids. The laws of fric-\\ntion between solids and fluids are very different from those\\nwhich hold between solids. Friction between solids and\\nfluids changes comparatively little with change of pressure,\\nbut it changes a good deal with change of velocity. The\\nresistance of the air is an important obstacle to rapid\\nmotion, as in the case of a railroad train, and the frictional\\nresistance of the water to the hull and propeller of a steamer\\ndemands most of the steam-power required to propel the\\nvessel.\\n84. Friction in Tubes. The friction of liquids or gases\\nflowing rapidly through long tubes is very considerable,\\nas the following experiments will show.\\nEXPERIMENTS.\\n(1) Take a rubber tube 2 or 3 in. long and about 0.6 cm. in diame-\\nter of bore. Cue off a piece about 20 cm. long. Fill a large glass\\n\u00e2\u0096\u00a0Jar with water.\\nUsing the short piece as a siphon, keeping the lower end about\\n10 cm. beneath the surface of the water in the jar, find the number\\nof seconds required to fill a small tumbler with the water delivered,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0098.jp2"}, "99": {"fulltext": "FRICTION, 85\\nTry the same experiment with the long tube, keeping its outlet\\nalso 10 cm. below the surface of the water in the jar.\\nCompare the rates of delivery in these two cases.\\n(2) Take a rubber tube 2 or 3 m. long and about 0.15 cm. in diame-\\nter of bore. Cut off a piece 10 cm. long. Light a candle.\\nPut out the candle-flame by Wowing through the short tube. See\\nhow far from the outlet of the tube the flame must be placed in\\norder to survive the blowing.\\nRepeat the trial, using now the long tube.\\nCompare the distances in the two cases.\\nSomething more concerning friction of water in tubes is\\ngiven in the Second Part.\\nQUESTIONS.\\n(1) A body weighing 20 lbs. rests upon a horizontal surface upon\\nwhich its coefficient of friction is 0.2. How great is the force re-\\nquired to keep the body moving along the surface\\n(2) It requires a force of 20 lbs. to keep a certain body moving\\nalong a horizontal plane, the coefficient of friction being 0.3. What\\nis the weight of the body\\n(3) A sledge weighing 10 lbs. can be drawn along a certain level\\nsurface by a force of 0.25 lb. How great may we expect the force\\nto be which will just maintain motion when a load of 50 lbs. is placed\\non the sledge\\n(4) A sledge weighing 50 lbs., having runners 1 in. wide, is\\ndragged along a floor by a force of 15 lbs. How great a force would\\nbe required if the runners were twice as wide\\n(5) According toRankine s Civil Engineering, the coefficient of slid-\\ning friction of loose earth on earth may be as much as 1, although it\\nis generally less. Suppose a bank of earth, with 1 for the coefficient\\nof friction, to be made of such steepness that the outer surface, if\\nstarted, will continue to slide downward.\\n(a) If a pole reaches 10 ft. straight downward into such a bank,\\nhow far along a horizontal line is the lower end of the pole from the\\nsurface\\n(b) How great is the angle which the surface of such a bank makes\\nwith a horizontal plane", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0099.jp2"}, "100": {"fulltext": "CHAPTEE VII.\\nTHE PENDULUM.\\n85. Use in Clocks. Before leaving the subject of\\nMechanics and going to that of Light it is well to learn\\nsomething about pendulums, which are used to control the\\nmotion of clocks.\\nIf you were to examine the works of an old-fashioned\\nclock, you would find the power which drives it in a heavy\\nweight working upon a kind of pulley by means of a long\\ncord, but the device which governs the speed of the works\\nand allows the motion to be neither too fast nor too slow is\\nthe pendulum. As a crowd of men at a turnstile, however\\nthey may try to force their way, can pass no faster than\\nthe swinging turnstile permits, so the clock-weight, which\\nif the control were removed would run down at once with a\\nfurious buzzing of the wheels, is allowed by the pendulum\\nto descend only very slowly, a very little distance at every\\nswing of the pendulum, and not at all when the pendulum\\ndoes not move.\\nThe rate at which the clock-wheels can move, then,\\ndepends upon the length of time required for each swing\\nof the pendulum. We will try a few simple experiments to\\nfind out something about the laws of pendulum motion.\\nEXPERIMENTS.\\nDescription of Apparatus. A convenient method of suspending a\\nsimple pendulum is shown in Fig. 57, where B is one end of a wooden\\nbar, which is bevelled off ou the side from which the pendulum\\n86", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0100.jp2"}, "101": {"fulltext": "THE PENDULUM.\\n87\\nhangs. G is a cork fastened to the top of the bar and having in it a\\nslit made by a sharp knife, through which slit the silk thread, S,\\no\\n3\\no\\n2\\nFig. 56.\\nI\\nFI .57.\\npasses. If this part of the thread is waxed, the fastening thus ob-\\ntained holds the pendulum securely, although it is very easy to in-\\ncrease or decrease the length of the pendulum at will. The length\\nof the pendulum is to be measured from the under side of the bar to\\nthe centre of the ball. It is intended that the length of No. 2 and\\nNo. 5 in Fig. 56 shall be the same as that of No. 1, that the length\\nof No. 3 shall be one-fourth that of No. 1, and the length of No. 4\\none-ninth that of No. 1. It is therefore convenient to make the\\nlength of No. 1 just 36 inches, which will require 9 inches for the\\nlength of No. 3, and 4 inches for that of No. 4. The suspended\\nbody is a bullet in the case of each pendulum except No. 5, where\\nit is some lighter object a marble, for example.\\nThe whole apparatus is called No. XXI.\\n(1) How does the time required for a single swing depend upon the\\nlengthy or width, of the swing\\nSet No. 1 and No. 2 swinging at the same instant and with the\\nsame width, or length, of swing, and watch them both for a little\\nwhile until it is plain that under these circumstances they keep to-", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0101.jp2"}, "102": {"fulltext": "88 PHYSICS.\\ngether, No. J. taking just as long a time for one swing, or for any\\nnumber of swings, as No. 2 does.\\nThen draw the ball of No. 1 about one inch aside from its position\\nof rest, and the ball of No. 2 about fifteen inches aside from its\\nposition of rest, and release both balls at the same instant. Watch\\nthe two for some little time, a quarter of a minute or longer, and see\\nwhether at the end of that time they begin each swing together, as\\nthey did at first. If they do not, observe which one has gained upon\\nthe other, and, after one or two repetitions of the experiment, write\\ndown an answer to the question which the experiment was intended\\nto meet. This answer should state which swing, the long or the\\nshort, if either, takes the longer time, and whether the difference in\\ntime is large or small compared with the time of either swing.\\n(2) How does the time required for a single swing depend upon the\\nlength of the pendulum from the support down to the centre of the\\nball?\\nLet one person, holding a watch in his hand, draw ball No. 2\\nseveral inches aside from its position of rest and, releasing it at a\\nconvenient moment, give a signal to the class, and let the class\\ncount the number of single swings till, at the end of 20 seconds from\\nthe start, a signal is given to stop counting.\\nIn a similar manner the number of swings of No. 3 in 20 seconds\\nand the number of swings of No. 4 in an equal time are found, and\\nthe observations for the three pendulums are recorded in a table, as\\nfollows\\nNumber Time of Length Square Root\\nof Swings. One Swing, of Pend. of Length.\\n36 6\\n9 3\\n4 2\\nThe numbers to fill the fourth column must be found from those\\nin the second and third columns. A comparison of the fourth col-\\numn with the sixth column will probably show that there is a close\\nrelation between the time of swing and the length of a pendulum.*\\n(3) Weight of Pendulum-ball. Finally, a comparison of No. 1 and\\nNo. 5, set in motion at the same time and with the same w T idth of\\nIt is interesting and even amusing to watch pendulums 1 and 3\\nor 3 and 4 swinging at the same time, both being started at the end\\nof a swing at the same instant.\\nPendu-\\nWhole\\nlum.\\nTime.\\nNo. 2\\n20 sec.\\n3\\n4\\n(C", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0102.jp2"}, "103": {"fulltext": "THE PENDULUM. 89\\nswing, will show whether the time of swing depends much upon the\\nnature of the suspended body.\\nIt will doubtless be noticed that the width of swing of the lighter\\nbody diminishes more rapidly than that of the heavier one. This\\ngradual loss of motion is due to the resistance of the air. The re-\\nsistance is about the same for both bodies if they have the same size,\\nshape, and velocity, but a light body is more quickly stopped by a\\ngiven resistance than a heavier body. This is the reason why one\\ncannot throw an acorn or a piece of cork so far as one can a stone of\\nthe same size.\\n86. Springs in Place of Pendulums. It has been said\\nabove that pendulums are used to control clocks, but many\\nclocks and all watches are controlled by means of vibrating\\nsprings; for these, like pendulums, are very regular in\\ntheir swings and so are good time-keepers. The controlling\\nsprings (see the balance of a watch, Second Part) must\\nnot be confused with the much larger driving-brings^ or\\nmatw-springs, which are used in watches and in most\\nclocks of the present day.\\nMore will be said about pendulums in the Second Part.\\nQUESTIONS.\\n1. If one pendulum is 9 inches long and another is 64 inches long,\\nhow will the time of vibration of the first compare with that of the\\nsecond\\n2. If pendulum A, 39 in. long, vibrates once in a second and\\npendulum B vibrates once in 5 seconds, what is the length of B", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0103.jp2"}, "104": {"fulltext": "CHAPTEE VIII.\\nNATURE OP LIGHT VISIBILITY OF OBJECTS.\\n87. Light is Something that Travels. We say that a\\nlamp gives, or gives out, light. This is true. Light is\\nsomething that comes to our eyes from any object and\\nenables us to see the object.\\nA substance through which light can travel is called a\\nmedium for light. We have ways of measuring the time\\nrequired by light to travel a given distance in air and in\\nmany other media.\\n88. Measurement of the Velocity of Light. One of the\\nsimplest methods for measuring the velocity of light is that\\ndevised by the French physicist Fizeau.\\nIt consists essentially of a source of light, from which a\\nbright beam may be obtained, a toothed wheel which may\\nbe made to revolve in a plane at right angles to the course\\nof the beam of light, and a plane mirror. Apparatus is\\nprovided by means of which the rate at which the wheel\\nrevolves can be exactly measured.\\nThe beam of light passes through the space between two\\nadjacent teeth of the wheel, travels a distance of several\\nkilometers, is then reflected by the mirror, and returned\\nover the same path by which it passed out. If the wheel is\\nat rest, the beam as it returns will repass the aperture\\nbetween the teeth through which it passed out. But it is\\neasy to see that if the wheel could be revolved fast enough\\na tooth might be brought into the path of the returning\\n90", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0104.jp2"}, "105": {"fulltext": "NATURE OF LIGHT: VISIBILITY OF OBJECTS. 91\\nrays in time to intercept them. Still more rapid revolu-\\ntions would bring a new gap between teeth into the path\\nof the returning rays, and so on. In fact alternate eclipses\\nand appearances of the returning rays are produced when\\nthe wheel is revolved at a high and continually increasing\\nvelocity. From the rate of motion of the wheel and the\\ndistance traversed by the beam it is not difficult to calculate\\nthe velocity of light.\\nAs a result of measurements made by somewhat different\\nmeans from those just described, the velocity of light has\\nbeen ascertained to be about 300,000 kilometers, or 186,000\\nmiles, per second in a vacuum. The velocity in air is a\\nlittle less.\\n89. Light is of Various Kinds. Light as it comes from\\nthe sun, or from most lamps, is of many different kinds, all\\nblended together so that the eye does not distinguish one\\nkind from another; but when this mixture of light falls\\nupon certain objects, pieces of glass called prisms, for in-\\nstance, the mixture is broken up and we see the different\\ncolors,\\nEXPERIMENT.\\nHold a glass prism (No. XXXI) in the direct sunlight in such a\\nposition that light after passing through the prism will fall upon a\\nwhite surface not in the direct sunlight.\\nThis breaking up of light is considered further in 134.\\n90. Light a Wave-motion. Before the nineteenth cen-\\ntury many people believed light to consist of particles of\\nmatter, actually shot out in some way from the luminous\\nbody. These supposed particles were called corpuscles\\n(that is, little bodies), and this theory as to the nature of\\nlight was called the corpuscular theory.\\nWe now believe that light is not a substance, but a kind\\nof wave-motion, a shiver, which is sent along through\\nbodies with great velocity and to very great distances,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0105.jp2"}, "106": {"fulltext": "92 PHYSICS.\\nalthough the particles of the body, or medium, transmitting\\nthis wave-motion travel very small distances on either side\\nof their positions of rest. More will be said about this in\\nthe Second Part of this book.\\n91. Color and Wave-length. The different kinds of\\nlight, which produce in us the sensations of different colors,\\nare distinguished from each other by differences of wave-\\nlength. Waves which produce the sensation of red, and\\nwhich we often call red waves, are longer than the so-called\\nblue waves, which produce the sensation of blue. One tint\\nof red has a wave-length of one thirty-thousandth part of\\nan inch. One tint of blue has a wave-length of one fifty-\\nfive-thousandth of an inch.\\n92. Light Travels in Straight Lines.* When direct\\nsunlight enters a darkened room through a small hole, one\\ncan usually trace its course and boundary in the room by\\nmeans of the air-borne dust particles which are lighted up\\nby it. It is easy to see that the boundary, the side, of the\\nlearn of light is straight. This is one of the familiar facts\\nwhich show that light travels in straight lines. Practical\\napplications of this property of light are found in the. prac-\\ntice of sighting rifles, cannon, and other firearms; in the\\nmethod of glancing along the edge of a board, which the\\ncarpenter adopts to see whether it is straight; and in the\\nvarious surveying operations, in which points are located by\\nsighting with the unassisted eye, or by means of fine slits\\nin metal plates, or by the aid of small telescopes.\\n93. Light Pencils and Rays. If a beam of light is\\nThis statement holds good only in cases in which the light\\ntravels in a medium or substance of uniform composition through-\\nout. Even under such circumstances there are certain exceptions to\\nthe general rule of rectilinear propagation. These occur where\\nlight passes close by the edges of objects, but the effects produced,\\nalthough very interesting and beautiful, are not sufficiently promi-\\nnent to make their study in this book necessary or desirable.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0106.jp2"}, "107": {"fulltext": "NATURE OF LIGHT: VISIBILITY OF OBJECTS. 93\\nslender, it is a pencil of light. If the pencil is very slender\\nindeed, it is called a ray of light, and is represented in\\ndrawings by a single line.\\n94. Camera Obscura^ This name means dark chamber.\\nEXPERIMENT.\\nPush the small tube of No. XXIV, closed end foremost, into the\\nlarger, and then, pointing the apparatus toward a window, look into\\nthe smaller tube and move it back and forth in the other till the best\\nimage of the window or of objects outside is obtained.\\nIt is evident at once that the image is upside down, that\\nis, that the bottom of the image represents the top of the\\nobject. This is due to the fact that the light-rays, coming\\nfrom the object and traversing the very small aperture in\\nthe end of the tube, cross each other in their passage, as in\\nFig. 58, where the object is represented by the arrow AB.\\nFig. 58.\\nFor instance, the cone of rays A A! from the tip of the arrow\\nand the cone of rays BB from the other end, cross at mn,\\nand appear in the image at the spots A and B respectively.\\nIf the aperture mn were gradually made larger, the spots\\nA! and B\\\\ illuminated from A and B respectively, would\\ngrow larger and larger. The same would be true of the\\nspots illuminated from other points of the arrow; and at\\nlast the growing spots would so overlap each other that the\\nimage would be lost in a mere blur of light on the screen.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0107.jp2"}, "108": {"fulltext": "94\\nPHYSICS.\\n95. Shadows. From the fact that light travels in\\nstraight lines, it is easy to see that it will be cat off from a\\nportion of space behind any illuminated opaque object, just\\nas waves of water are cut off by a breakwater, leaving a\\nregion of calm water behind it. The simplest case is that\\nin which the light-giving object is as small as possible.\\nEXPERIMENT.\\nLight a bat- wing gas-jet or a kerosene lamp with a broad, thin\\nflame, and cast the shadow of a lead-pencil, held vertical, on a sheet\\nof white paper, having first the edge and then the broad side of the\\nflame toward the pencil. Note the great difference in the sharp-\\nness of outline in the two cases.\\n96. Umbra. A shadow with a perfectly sharp outline\\ncould only be obtained by using as the source of light a\\nmere point. To illustrate what would be the result if this\\nFig. 59.\\ncould be done, the student should examine Fig. 59.\\nOf the light-rays proceeding from the point the cir-\\ncular opaque object OF intercepts all which strike its sur-\\nface, thus forming a shadow whose shape is in this case the\\nfrustum of a cone, OS TV.* The black space *STin the\\nscreen is not the whole shadow, but a section of the entire\\nshadow OS TV. A perfect shadow like this, equally dark\\nat all points, is called an umbra.\\n97. Penumbra. Suppose now that the source of light\\nis of appreciable size, a candle-flame, for example: then the\\nThat is, a cone with its top sliced off by a section parallel to the\\nbase.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0108.jp2"}, "109": {"fulltext": "NATURE OF LIGHT: VISIBILITY OF OBJECTS. 95\\nopaque object eats off all illumination from some por-\\ntions of the screen, and from other portions cuts off only a\\npart of the light, as in Fig. 60.\\nThat part of the screen which receives light from part of\\nthe flame AB, but not from all of it, will appear a partially\\nshaded ring, P S SP, around the central area of total\\nshadow. This ring forms what is known as the penumbra\\n(from two Latin words meaning almost and shadow).\\nOn account of the comparatively large size of most\\nsources of light most shadows are surrounded by a wide\\nmargin of penumbra. The student will find the best\\nexamples of clear-cut shadows in those cast upon near sur-\\nfaces by opaque bodies exposed to electric arc-lights, and he\\nFig 60.\\nmay compare the dim and indistinct shadows of the leaves\\nof shade-trees exposed to the sun, with those cast by the\\nsame objects exposed to the electric light at night, in which\\neven the serrated margins of the leaves are sometimes clearly\\noutlined.\\n98. How Light Weakens with Distance Law of Inverse\\nSquare- If two equally large surfaces are turned toward\\na very small flame, distant 1 ft. from one and 2 ft. from\\nthe other, the nearer surface will receive very nearly four\\ntimes as much light from the flame as the more distant but-", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0109.jp2"}, "110": {"fulltext": "96 PBTS1CS.\\nface. It is easy to prove that this is true if light travels\\nin straight lines diverging from a point (Second Part).\\nIf one surface is three times as far away as the other it\\nwill receive only one ninth as much light as the nearer\\none, and so on.\\nThe law, which holds when the diameter of the light-\\ngiving spot is very small compared with the distance from\\nit to the receiving surface, may be stated thus The amount\\nof light received on a surface of given area from a given\\nsource of light is inversely proportional to the square of the\\ndistance from the source to the surface.\\nThis is called the law of inverse square.\\nIt follows from this law that if a lamp L sends ,to a given\\nsurface at a distance D 311st as much light as another lamp\\nU sends to the same surface at a distance D\\\\ the light-\\ngiving powers of the two lamps, which powers we will call\\nP and P\\\\ must be such that\\nP: P D 2 D\\nIllustration.\\nA candle-flame 30 cm. from a white card and an incandescent elec-\\ntric lamp 120 cm. from the same card light it up equally. What is\\nthe relative power of the two sources\\nPi (for the lamp) P c (for the candle) 120 2 30 2\\nHence P P c X 16.\\n99. Photometry Rumford s Photometer. It is a matter\\nof great practical importance to compare the illuminating\\npower of different lamps. This operation is called photom-\\netry, or light-measurement. It cannot be done by merely\\nobserving the lamps directly for the eye is unable in this\\nway to distinguish slight differences of power, and if the\\nlights are of somewhat different colors the unaided eye gives\\nonly the vaguest indications in regard to their comparative\\nefficiency.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0110.jp2"}, "111": {"fulltext": "NATURE OF LIGHT: VISIBILITY OF OBJECTS. 91\\nOne of the simplest devices for measuring the relative\\npower of two sources of light is RuniforcTs photometer,\\nwhich compares the shadows cast by a rod placed in front\\nof them.\\nEXERCISE 16.\\nUSE OF RUMFORD PHOTOMETER.\\nApparatus Two small kerosene lamps like No. 33. A cardboard\\nscreen and its support (No. 32 and No. 21). Any opaque rod about\\n1 cm. in diameter and 10 or 15 cm. tall, supported upright e.g., No.\\n13 standing in a hole bored m a small block, or a Bunsen burner, A\\nmeter rod.\\nThe ooject of the experiments will be to find whether a flame sends\\nmore or less light from its broad side than from its edge, and, if so,\\nhow much, The flame should be made as large as they can well be\\nwithout smoking.\\nThe apparatus should be arranged as in Fig. 61,\\nA\\nC\\nFig. 61.\\nJl\\nL is one of the lamps to be compared, and L the other R the\\nrod AB the screen, and Sl and 8 the shadows. The lamps should\\nbe so arranged that lines drawn from their centres to the centre of H\\nwill make nearly equal angles at i? with the line CD, drawn at right\\nangles to the screen through the centre of i?, and on this line the\\nobserver should be placed. The shadows should be near each other,\\nbut must not overlap.\\nIt is plain that the shadow corresponding to L is illuminated by\\nlight from L and that the one corresponding to U is illuminated\\nby light from L.\\nPlace the lamps equidistant from the rod. and, shielding the eyes", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0111.jp2"}, "112": {"fulltext": "98 PHYSICS.\\nfrom the direct light of the flames, adjust the flames, turned edge-\\nwise to the rod, until the shadows are of equal darkness.\\nThen turn one of the lamps about in place until its flame is flat-\\nwise to the rod, and compare the shadows again, fixing the attention\\nupon the middle of the more blurred one. If the shadows still appear\\nto be of equal darkness, record the fact. If they do not, move one of\\nthe lamps toward or from the rod until the shadows appear equally\\ndark, and then record the distance of each flame from the corre-\\nsponding shadow.\\nTry each lamp in turn flatwise, the other being edgewise. Be-\\ntween the trials test the flames again in their original position, to\\nmake sure that they are still equal.\\nIf, on the whole, it appears that one aspect of the flame, broad side\\nor edge, is more effective than the other, estimate the relative light-\\ngiving power of the two aspects from the measured distances, mak-\\ning use of the law of inverse square.\\n100. Bunsen s Photometer. The form of photometer\\ndevised by the German chemist and physicist Bunsen\\nyields, under suitable conditions, more accurate results than\\nthe apparatus just described, and is equally simple, but\\nmore difficult to use in an undarkened room.\\nEXPERIMENT.\\nDrop a little paraffin on a sheet of heavy, unsized, white paper,\\nthin drawing paper, for instance. Heat the paper by placing on it a\\nmoderately hot iron weight or a can of hot water, until the paraffin\\nis entirely melted and soaked evenly into the paper, so as to make a\\nroughly circular spot about 3 cm. in diameter. Cut out of the paper\\na circle about 12 cm. in diameter with the spot just prepared in its\\ncentre. It will be noticed that the spot is translucent that is, it\\nallows some light to pass through it, although objects cannot be\\nclearly seen through it. If one looks from a darker portion of the\\nroom toward a brigther portion with this screen interposed, the\\ntranslucent spot will appear brighter than the ring of opaque paper\\naround it, while, under the reverse conditions of illumination, the\\nopaque ring will appear brighter than the spot.\\nMount the screen in any convenient way for example, in a block\\n(No. 21). In making photometric observations with this screen the", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0112.jp2"}, "113": {"fulltext": "NATURE OF LIGHT: VISIBILITY OF OBJECTS. 99\\nillumination from one source of light is to be allowed to fall at right\\nangles on one side of the screen, and that from the other source is to\\nfall at right angles on the other side. The screen is then to be\\nmoved back and forth between the two lights until a position is\\nfound in which the appearance of the screen, as tested by the con-\\ntrast between the central spot and the rest of the surface, is exactly\\nthe same on both sides when viewed from the same angle. The\\nillumination on the two sides is then equal, and the distances from\\nthe lights to the screen will afford a means of comparing the power\\nof the lights, as already indicated in 98.\\nIt is hardly worth while to attempt this experiment in an\\nundarkened room.\\n101. Effect on Light of the Body on which it Falls.\\nWhen light-rays meet the surface of a body they may be\\na. Regularly reflected that is, sent off from the surface\\nin a direction which can be calculated or foretold, if we\\nknow the direction in which they are to strike the surface,\\nas sunlight is reflected by a mirror.\\nb. Irregularly reflected or scattered: that is, sent back\\nor off from the surface in many different directions, as sun-\\nlight is sent back from the surface of white cloth or white\\npaper.\\nc. Transmitted that is, allowed to pass through as sun-\\nlight through clear window-glass.\\nd. Absorbed that is, neither reflected nor transmitted,\\nbut swallowed up, as sunlight by a lamp-black surface\\nupon which it falls.\\nIt usually happens that more than one of these effects is\\nproduced by the same body at the same time.\\n102. Visibility of Objects.* Very few of the objects we\\nsee shine by their own light, as we can tell by testing them\\nin the dark. They merely give off the light, or some part\\nFor much interesting and valuable matter upon this subject see\\nRood s Text-book of Colo? Appleton Co.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0113.jp2"}, "114": {"fulltext": "100 PHYSICS.\\nof the light, which has fallen upon them from the sun, or\\nfrom some other light-giving body.\\nOf course we see many things every day upon which\\nneither the sun nor any lamp is directly shining. We see\\nthem by what is called daylight. 53 This, however, is\\nsunlight, although it may not have come straight from the\\nsun to the objects that we see lighted up by it. It may\\nhave gone from the sun to a mass of clouds, from the clouds\\nto the surface of fields or streets or walls of houses, and\\nfrom these surfaces into corners where the sun itself is\\nnever seen.\\nIt is extremely fortunate for us that all external objects\\ndo not treat the light which falls upon them in exactly the\\nsame way. If they did, all things would be of one color,\\nand we could distinguish only light and shade. We have\\nsomething like this condition after a fresh fall of snow\\nwhich has covered roofs and trees as well as the ground.\\nThere are always, however, parts of trees and houses not\\ncompletely covered by the snow, and this fact enables us to\\nkeep our bearings fairly well. If everything were covered\\nby the snow, our eyes would not be of much more help to\\nus in broad daylight than they are in the dead of night.\\n103. Colors of Transparent Bodies. Colored pieces of\\nglass, colored liquids, and other transparent bodies, gen-\\nerally owe their color to the fact that they are not trans-\\nparent to all kinds of light. The light which enters them,\\nsunlight, for example, usually consists of many different\\ncolors blended together; and they rob this light of those\\ncolors which suit their own constitution, transmitting the\\nrest. It is the transmitted, the rejected, light which we get\\nfrom them that gives them their apparent color. The\\nlight which they absorb is turned to something else in the\\nabsorption, and is no longer light. It is usually turned\\ninto heat.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0114.jp2"}, "115": {"fulltext": "NATURE OF LIGHT: VISIBILITY OF OBJECTS. 101\\n104. Colors of Opaque Bodies. Most bodies with which\\nwe art? familiar do not appear to transmit light. We cannot\\nsee through them, and we call them opaque bodies.\\nIn fact, most so-called opaque bodies are not perfectly so.\\nIf they are made into very thin sheets, the sun can shine\\nfaintly through them. Even when they are in thick\\nmasses, the light penetrates a very little distance beneath\\nthe surface, where some of it is absorbed, and some, being\\nreflected by interior particles, returns to the outside. This\\nreturning light is usually different in color from the mix-\\nture of lights that entered, certain parts having been\\nabsorbed more than others.\\n105. Light from Surface of Colored Bodies. The light\\nreflected from the real external surface of non-metallic\\ncolored bodies receiving white light is usually not colored.\\nThe following experiment shows an illustration of this fact:\\nEXPERIMENT.\\nLet a beam of direct sunlight, entering a window, fall very ob-\\nliquely upon a sheet of colored glass in such a way that the reflected\\nbeam will fall upon a white surface. Observe the color of the\\nreflected light.\\nCertain materials, silks, for example, may reflect white\\nlight, from the outer surface, together with considerable\\ncolored light that has penetrated this surface and has been\\nsent back from the interior. The white light gives the\\nsheen, but in the spots where this is strong the color is not\\nat the same time very evident, being made to look pale by\\nthe large amount of white light mixed with it.\\nThe following experiment will show how the color coming\\nfrom an object maybe deepened by diminishing the amount\\nof white light reflected from the external surfaces of its\\nnumerous particles.\\nEXPERIMENT.\\nGrind a lump of sulphate of copper to a fine powder and observe\\nhow faint the blue color becomes then wet the powder with water,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0115.jp2"}, "116": {"fulltext": "102 PHYSICS.\\nwhich adds nothing but prevents some of the external reflection,\\nand note the decided deepening of the blue.\\nIn velvet the ends of the fibres, which reflect but little\\nwhite light, are turned outward, and the light which pene-\\ntrates the surface and then returns to the outside is deeply-\\ncolored.\\nSee Rood, p. 79.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0116.jp2"}, "117": {"fulltext": "CHAPTEE IX.\\nREGULAR REFLECTION OF LIGHT.\\n106. Reflectors. Smooth, even surfaces, like the surface\\nof still water, polished glass, or polished metal, reflect light\\nregularly 101).\\nTransparent reflectors are not convenient for ordinary\\nuse: partly because light which we do not want may come\\nthrough them from behind; partly because they reflect\\nreally well only such light as falls upon them very obliquely.\\nEXPERIMENT.\\nLet M t Fig. 62. be a piece of clear window-glass, L a lamp, and E\\nthe position of the observer s eye. The rays LM and J/^rnake a\\nW *T\\nlarge angle with the line 3IX, which is the normal to the surface of\\nthe glass.\\nObserve the comparative brightness of the flame itself, and its\\npicture or image, seen by reflection from 31. Xotice with what\\ndegree of clearness objects back of 31, as, for instance, points on the\\nwall WW, can be seen through 31 in the direction E3I.\\nGradually move the lamp and the eye toward the point X, until at\\nlast both lamp and eye are as nearly as possible on the line X3L\\nWhile making these changes of position observe any resulting\\nchanges in the brilliancy of the image of Z, and in the clearness\\nwith which objects on the line WW are seen through the glass.\\n103", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0117.jp2"}, "118": {"fulltext": "104 PHYSICS.\\nThe reflecting surface which we make use of in a common\\nmirror is not the front surface of the glass, but the metallic\\nsurface at the back. The glass is merely a convenient\\ntransparent support for the metallic layer, keeping it in\\nshape and protecting it from being tarnished, as it soon\\nwould be if exposed to the air.\\nReflection from a Plane Mirror.\\n107. Where the Image Is. A plane mirror is a flat\\nmirror. We shall study curved mirrors later.\\nWhen we place an object in front of a plane mirror and\\nstand in a proper position we see an image, or reflection,\\n.^____ the object, and we say that we\\nsee the object, or its image, in\\nthe mirror. If M, Fig. 63, is\\n\u00e2\u0080\u00a2P t \u00c2\u00bbP A the mirror, a point of the\\n\u00e2\u0080\u00a2P 2 .p 3 object, and P 1? P 2 P 3 and P 4\\nare the positions of four eyes, all\\nfig. 63. may see at the same time an\\nimage of the point in the mirror. Our first Exercise in\\nlight is intended to answer the question whether all these\\neyes see the same image, that is, whether all are looking\\ntoward the same point, and if so, where this point is in\\nfront of the mirror, or behind it, or at its surface.\\nEXERCISE 1 7.\\nIMAGES IN A PLANE MIRROR.\\nApparatus A mirror (No. 23). A rectangular block (No. 9). A\\nrubber band to hold the mirror to the block. Two straight- edged\\nwooden rulers (Nos. 24a and 24b). A meas-\\nuring-stick (No. 3). A sheet of thin white\\npaper about 12 inches by 20 inches. A small\\nblock (No. 25). Attach the mirror to the\\nlarge block by means of the rubber band in\\nthe manner shown by Fig. 64.\\n.i n Fig. 64.\\nDraw a straight pencil -mark across the\\nsheet of paper at its middle, and set the back surface of the mirror", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0118.jp2"}, "119": {"fulltext": "BEGULAR REFLECTION OF LIGHT.\\n105\\n\\\\7*\\n3\\ndirectly over and parallel to this line, the middle of the mirror being\\nvery near the centre of the sheet. See Fig. 65.\\nDraw on the sheet of paper in front of the mirror a triangle, each\\nside of which shall be several inches long, and no corner of which\\nshall be less than three inches from the mirror.\\nIt is well to have one angle of the triangle not\\ndirectly in front of the mirror, but somewhat to\\none side, like point No. 1 in the figure.\\nPlace the small block in such a position that\\nthe vertical pencil-mark which it bears shall be\\ndirectly over point No. 1 of the triangle. Then\\nlay a straight- edged ruler (Fig. 66), upon the\\npaper in such a position that one of its long\\nhorizontal edges, PQ, shall point directly to-\\nward the image of the vertical pencil-mark, as\\nseen in the mirror.* The ruler should be so\\nplaced that the line of sight will strike near\\none end of the face of the mirror. Then with\\na well-sharpened pencil draw upon the paper a\\nfine clear mark alongside that edge of the ruler\\nwhich lies just beneath the line PQ (Fig. 66) along which the\\nsight has been taken. Mark this line 1, because it points toward the\\nimage of the vertical pencil-mark when this\\nmark is over point No. 1.\\nNext, without disturbing anything else,\\nFig. 66. p i ace the ruler in a new position, far removed\\nsidewise from the position just occupied, sight as before, draw\\nanother line alongside the ruler, and mark this line also 1.\\nThen with the ruler in a new position, about half-way between\\nthe first two, if this is convenient, draw a third line in the same\\nway, and mark this also 1.\\nAll this time the small block has remained unmoved, and the\\npencil-mark upon it has pointed straight down at point No. 1.\\nMany persons cannot do this at first unless they are especially\\ninstructed. A person who is not near-sighted should hold his eye\\neight or ten inches distant from P, and should then direct the ruler\\nin such a way that the point P, the point Q, and the image of the\\nvertical pencil-mark seen in the mirror shall all lie in one straight\\nline. Do not try to look along the vertical side of the ruler, but hold\\nthe eye high enough to see all the time the top of the ruler\\nFig. 65.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0119.jp2"}, "120": {"fulltext": "106 PHYSICS.\\nNow place the small block so that the pencil mark shall point\\nstraight down at point No. 2. While it is in this position draw\\nthree straight lines toward the image and mark each one of these 2.\\nFinally, put the pencil mark over point No. 3, draw three straight\\nlines toward its image, and mark each of them 3.*\\nWhen the three sets of lines Lave been drawn, the two blocks and\\nthe mirror are removed from the paper, and each line is then length-\\nened f until it cros es both the others of the same set that is, each\\nNo. 1 line is continued toward or beyond the mirror till it crosses\\nthe two other No. 1 lines. Then the No. 2 set and the No. 3 set are\\ntreated in the same way.\\nAfter each set of lines has been extended in this way, it will be in\\norder to answer the qu* stion whether all the lines of any one set\\nlead to the same point or nearly so, and, if so, where is this point\\nsituated with respect to the mirror and to the point whose image it is.\\nIf the image of each point, No. 1, No. 2, and No. 3, can be thus\\nfound, connect the image-points with each other by straight lines^\\nand thus make an image-triangle.\\nThen fold the sheet of paper carefully along the pencil-mark by\\nwhich the mirror was placed, and holding the folded sheet against\\na window, so that the light from without will shine through it,\\ncompare the size and shape of the two triangles and their relative\\npositions with respect to the line along which the paper is folded.\\nWhile drawing all these lines the experimenter should look fre-\\nquently to see whether the back of the mirror remains in place. It\\nmay be thrown out of place by a little blow or by rubbing the paper\\nhard to remove pencil-marks.\\nf If a line has to be extended far it is well to use two rulers, A\\nand B, as shown in Fig. 67. First A is put into position and a line\\n~7T\\nFig. 67.\\nis drawn alongside it. Then, while A remains unmoved, B is care-\\nfully brought close to it, as the figure shows then B is held firmly\\nin place whil^ A is pushed forward to tLe position indicated by the\\ndotted lints. B is then removed without disturbing A, and again a\\nline is drawn alongside A. In this way a line may be continued\\nnearly straight for a considerable distance,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0120.jp2"}, "121": {"fulltext": "REGULAR REFLECTION OF LIGHT.\\n107\\nI he general rule for placing the image of any point should be\\nrecorded when it is found.\\nThe final result aimed at in this A B\\nExercise should be to enable the\\nstudent to tell, without farther ex-\\nperiment, in any new case given\\nhim (Fig. 68, for instance, in which\\nA B is the line upon which the\\nmirror stands), the position of the\\nimage of points No. 1, No. 2, No. 3,\\nand No. 4, and so the shape and\\nposition of the image of the figure\\nat the corners of which these points\\nlie.\\n108. The Law of Reflection.\u00e2\u0080\u0094 In Fig. 69, MM is a\\nI\\\\\\nmirroi surface, CD a normal to this surface, OC a ray in-\\ncident at the point C, and CP the same ray after reflection.\\nThe angle i is called the angle of incidence.\\nThe angle r is called the angle of reflection.\\nThe law of reflection is, that the angle of reflection\\nis equal to the angle of incidence.\\nThis law is easily proved on the basis of what we have", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0121.jp2"}, "122": {"fulltext": "108 PHYSICS.\\nlearned in the preceding exercise. The line of proof is this\\nThe image of is at I. The angles at E are right angles\\nEI EO EC is common to the two triangles hence the\\ntriangle CEI is similar to the triangle CEO. Then angle\\nangle EOC angle EIC angle r.\\n109. Real and Unreal Images. If the rays of light pro-\\nceeding from a point are by any means really brought\\ntogether again at a different point, as in Fig. 79, then the\\nsecond point is called a real image of the first. A real\\nimage has an actual existence in space, and will show as a\\npicture upon a properly placed white screen.\\nIf the rays of light proceeding from a point are by any\\nmeans made falsely to appear to diverge from a different\\npoint, as in Fig. 70, then the second point is called an\\nv V\\nFig. 70.\\nunreal, or virtual, image of the first. A virtual image has\\nno real existence in space, and would not show upon a screen\\nplaced where it appears to be.\\nEvidently the image formed by a plane mirror is an un-\\nreal image.\\n110. Images of Images. If any of the rays from (Fig.\\n71) after reflection from the mirror A fall upon a second\\nplane mirror i?, they will be treated by this second mirror", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0122.jp2"}, "123": {"fulltext": "REGULAR REFLECTION OF LIGHT.\\n109\\njust as if they really came from I x that is, we shall, look-\\ning into the mirror B in the right direction, see an image\\nof the image and this second image, 7 2 will appear just\\nFig. 71.\\nas if it were the image of an actual object, sending rays\\nfrom I r\\nThe rays reflected first from A and next from B might\\nthen fall upon a third mirror, and give an image of the\\nimage 7 2 and so on; but at each reflection there is some\\nloss of light, and an image formed\\nafter many reflections might be\\ndim.\\n111. Positions of the Various\\nImages. Let A and B in Fig.\\n72 represent the positions of two\\nplane mirrors meeting at right\\nangles with each other at the\\npoint C. Let be a small object\\nplaced between the mirror faces.\\nWe shall have one image, 7 l3 formed by mirror A with-\\nr 3*\u00c2\u00a3_\\nJi\\nFig. 72.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0123.jp2"}, "124": {"fulltext": "110 PHYSICS.\\nout any help from mirror L\\\\ and another, 7 2 formed by\\nB without help from A. There is also 7 3 the image of l5\\nseen in B\\\\ and there is 7 4 the image of 7 2 seen in A, I b\\nand J 4 fail at the same spot.\\nWe cannot with this arrangement of the mirrors get\\nimages of I 2 and 4 because rays leaving mirror A as if\\ndiverging from I A would not strike the face of i?, and rays\\nleaving mirror B as if diverging from 7 3 would not strike\\nthe face of A.\\nObserve that and its images fill the corners of a rec-\\ntangle. If were midway becween the mirrors, the\\nrectangle would be a square, with at its centre.\\nIf the angle between the mirrors were made a bit less\\nthan 90\u00c2\u00b0., I z and 7 4 would fall apart. If the angle were\\nmade 60\u00c2\u00b0, one sixth of a circle, lying half-way between\\nthem, and its images would fill the corners of a regular\\nhexagon having Cat the centre,\\nIf the angle were 30\u00c2\u00b0, one tivelfth of a circle, and its\\nimages would fill the corners of a tweive-sided figure.\\nEXPERIMENT.\\nPlace the hinged mirrors of No. XXV upon the board, with the\\nreflecting surfaces making an angle of 90\u00c2\u00b0,\\nthe point 1, Fig. 73, being midway be-\\ntween them. Place a lighted candle, of\\nsuch length that its flame will not be\\nabove the upper edge of the mirrors, ex-\\nactly over the spot 1.\\nNote the positions of the images of the\\ncandle seen in the mirrors. Put pegs into\\nthe holes behind the mirrors in such posi-\\ntions that to an observer placed in front\\nof the mirrors, so as to see the images in\\nthe mirrors and the pegs over the mirrors, the pegs will appear to\\ncoincide with the images.\\nThen make the angle between the mirrors 60\u00c2\u00b0 and place pegs to\\ncoincide with the images.\\nFinally, try an angle of 30\u00c2\u00b0.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0124.jp2"}, "125": {"fulltext": "REGULAR REFLECTION OF LIGHT, 111\\n112. The Kaleidoscope. The preceding passages give\\nan explanation of the kaleidoscope, No. XXVI, with which\\nmost oeautiful effects of endless variety can be obtained.\\nThe kaleidoscope uses bits of colored glass instead of a\\ncandle flame, and sometimes has three mirrors put together\\nat angles of 60\u00c2\u00b0.\\nQUESTIONS AND PROBLEMS.\\n(1) In a lighted room at night the glass of a window will serve as a\\nmirror. In daylight unsilvered glass with a black cloth behind it\\nmay be used in the same way. Can you explain this\\n(2) Soon after the moons of Mars were discovered in 1877 some one\\nannounced in a newspaper that one of these moons could be seen near\\nMars by looking at the reflection of that planet in a common mirror.\\nIt is true that a faint bright speck appeared near the image of Mars as\\nthus seen, which did not appear when the planet was looked at di-\\nrectly, but the true moons could be seen only by the aid of powerful\\ntelescopes. Can you, after trying the experiment with any bright\\nstar, explain the appearance seen in the mirror\\n(3) Write some short word as it would appear in a mirror if the\\nprinted page containing it were reflected in the mirror.\\n(4) A person standing in the middle of a room 20 ft. wide looks\\nwith one eye into a mirror 2 ft. square set in the wall of one side of\\nthe room. How many square feet of the wall behind himself could he\\nsee reflected in the mirror if his own image did not obstruct the view?\\n{Suggestion Draw a diagram representing the position of the ob-\\nserver, the mirror, the reflected wall and its image, all on a horizon-\\ntal plane.)\\n(5) A candle-flame is placed half-way between two plane mirrors\\nwhich meet at an angle of 40\u00c2\u00b0. How many images appear, and how\\nare they arranged\\nReflection from Curved Mirrors.\\n113. Spherical and Cylindrical. Most curved mirrors\\nare parts of spherical surfaces. We shall, however, study\\nmirrors which are parts of cylinders. They are more con-\\nvenient for our use than spherical mirrors, and they are less\\nexpensive.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0125.jp2"}, "126": {"fulltext": "112 PHYSICS.\\nWe shall use both the convex, or bulging, and the concave,\\nor hollowed, face of the mirror.\\n114. Centre of Curvature, etc. MM, Fig. 74, represents\\na cut through a cylindrical mirror at\\nright angles with the straight lines of its\\n^3i surface. This cut is of course a part of\\na circle.\\nC, the centre of the circle, is called the\\ncentre of curvature of the mirror.\\nThe point is called the centre of the\\nmirror.\\nThe line CO, extended to any distance\\nfig. 74. in either direction, is called the principal\\naxis of the mirror.\\nAny straight line extending, like CR, through C and\\nacross the line MM, but not through the point 0, is called\\na secondary axis of the mirror.\\nEXERCISE 18.\\nIMAGES FORMED BY A CONVEX CYLINDRICAL MIRROR.\\nApparatus The mirror (No. 27). A measuring-stick (No 3). Small\\nblock (No. 25). Rulers (No. 24 A and b). Sheet of white paper.\\nThe plane mirror (No. 23) and its supporting block (No. 9),\\nHold the mirror with its straight edges vertical, and look at the\\nimage of your own face in the convex surface. You will see that the\\nimage is distorted, appearing too narrow for its length. Hold the\\nmirror with its straight edges horizontal, and the image will be dis\\ntorted in the opposite way, appearing too wide for its iength. The\\nobject of the following experiments is to give a better understanding\\nof these curious effects.\\nSet the mirror on the table and bring one end of the plane mirror\\nclose to the surface of the curved mirror, as in Fig 75 Then place\\nthe small block in front of both mirrors, as in Fig. 75, in such a\\nposition that you can see the block reflected in both mirrors at the\\nsame time.\\nDo the two images thus seen appear of the same height\\nDo they appear of the same width", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0126.jp2"}, "127": {"fulltext": "REGULAR REFLECTION OF LIGHT.\\n113\\nFill out, if you can, the following statement Lines of the object\\nwhich are parallel to the straight lines of the cylindrical mirror\\nappear in the cylindrical mirror\\nplane mirror.\\nLines of the object which are at right angles icith the straight lines of\\nthe cylindrical mirror appear in the cylindrical\\nmirror in the plane mirror.\\nFig. 75.\\nRemove the plane mirror. Holding the base of the curved mirror\\nfirmly in place, make a fine, clear, pencil-mark on the paper along\\nthe outer edge of the mirror. Then mark on the paper the point (7,\\nwhich is the centre of curvature of the mirror.\\nAbout 5 cm from the front of the\\nmirror draw an arrow 6 cm. long,\\nmarking the ends and the middle as\\nin Fig. 76. Then place the small\\nblock so that the vertical pencil-mark\\nwhich it carries will point straight\\ndown at point No. 1.\\nWith the straight-edged ruler draw\\ntwo lines, well apart, toward the\\nimage of this vertical line as seen in\\nthe mirror, avoiding parts of the\\nmirror, if there are such, that do not\\ngive a good image of the line. Mark\\neach of these lines 1. Then draw two\\nlines for point No. 2 and two for point No. 3, in the same way.\\n2\\nFig. 76.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0127.jp2"}, "128": {"fulltext": "114\\nPHYSICS.\\nThen clear the paper and prolong each pair of lines till it conies to\\na crossing-point. The three points thus found will locate the images\\nof object-points No. 1, Noi 2, and No. 3, respectively, and a line con-\\nnecting these three image-points will give an idea of the shape of the\\nimage-arrow, whether it is straight or not, and whether its curvature,\\nif it has any, is in the same general direction as the curvature of the\\nmirror or in the opposite direction.\\nDraw a straight line from each marked object-point to the corre-\\nsponding image-point, and prolong these three lines until they cross\\neach other. Note where the crossing occurs.\\nIs the image longer or shorter than the object Is it nearer to,\\nor farther from, the mirror than the object is\\n(It must be understood that the pupil is asked these questions only\\nin regard to the particular case that he has tried. He cannot tell with-\\nout further experiments or further instruction whether the answers he\\ngives in this case would be true for all cases of objects reflected in\\nmirrors such as he is using, for he does not know that the distance of\\nthe object from the mirror may not decide all these questions. The\\nfact is, however, that, if he has found correct answers to the questions\\nasked for his one case, the same answers will be true for the same\\nquestions in all cases with convex cylindrical mirrors. The effects\\nseen with concave mirrors are much more complicated.)\\nFig. 77.\\n115. Law of Reflection Still Holds.\u00e2\u0080\u0094 With curved\\nmirrors, as with plane mirrors, the law 108) angle of in-", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0128.jp2"}, "129": {"fulltext": "REGULAR REFLECTION OF LIGHT. 115\\ncidence angle of reflection holds. With the help of this\\nlaw we can see why the image of a point is nearer the\\nmirror, when this is convex, than the point itself is.\\nLet (Fig. 77) be the object-point in front of the convex\\nmirror JO/, the centre of curvature being at C. A line\\ndrawn from C to any point of the mirror is at right angles\\nwith the mirror at the point of crossing. Two rays going\\nfrom to the mirror-front appear after reflection to come\\nfrom which is nearer the mirror than is.\\n116. Principal Focus and Focal Length. If rays come\\nfrom some very distant point on the principal axis 114),\\nthey are practically parallel to each other when they reach\\nthe mirror. Two such rays are represented by r 1 and r 2\\n(Fig. 77). Applying the law of reflection to them, we find\\nthat after reflection they appear, as r/ and r 2 to diverge\\nfrom a point P, which is very nearly midway between the\\nreflecting surface and the centre of curvature-\\nThe point P is called the principal focus of the convex\\nmirror. It may be defined as the point which marks the\\nimage of an object-point situated a long distance away from\\nthe mirror on the principal axis, or as the point from which\\nrays coming to the mirror parallel to the principal axis\\nappear to diverge after reflection.\\nThe distance, measured along the principal axis, from the\\nprincipal focus to the reflecting face is called the focal\\nlength of the mirror.\\nThe principal focus and the focal length play a very im-\\nportant part in the science of curved mirrors and lenses\\n136). More will be said of this later. See 124.\\n117. Concave Mirrors. If the concave side of the mirror\\nwere used, it is easy to see from Fig. 78 that rays from a\\npoint near the mirror-front would after reflection appear\\nto come from a point which is farther from the mirror", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0129.jp2"}, "130": {"fulltext": "116\\nPHYSICS.\\nthan is. It is evident that the rays from are more\\nnearly parallel to each other after reflection than before.\\nRays from a point 0 somewhat farther from the mirror\\nthan 0, appear after reflection to come from a still more\\ndistant point, I\\\\ and these rays are nearly parallel after\\nreflection. It is easy to see that if the object-point were\\nput somewhat farther still from the mirror, the rays pro-\\nceeding from it might, after reflection, be parallel to each\\nother. They would appear to come from a point as far as\\npossible behind the mirror.\\nIf the object-point is placed still farther away from the\\nmirror, as at in Fig. 79, the rays may after reflection be\\nactually converging, and cross at a point I in front of the\\nmirror. This image I is a real image 109), and if is\\nbright enough, the image /may be seen, like a picture, on\\na piece of white paper or cloth placed in the right position.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0130.jp2"}, "131": {"fulltext": "REGULAR REFLECTION OF LIGHT. 117\\nWe see that the centre of curvature lies between the\\nobject-point and the image-point in the case shown by\\nFig. 79. This is always so in the case of real images\\nformed by concave mirrors, unless the object-point is at\\n(7, in which case the image-point also falls at C.\\nIf the object-point were placed where now is, in Fig.\\n79, the image-point would fall where now is.\\nEXERCISE 19.\\nIMAGES FORMED BY A CONCAVE CYLINDRICAL MIRROR.\\nApparatus: The same as in the preceding Exercise, and in addition\\na common pin.\\nPreliminary\\nRemove the mirror from the base-\\nboard place the latter upon the paper*\\nand mark on the paper the point\\nand the curved outline of the board.\\nMake the distance OA 4.2 cm., and\\ndraw the arrow A 4 cm. long. Draw\\nradii from G through the ends of A.\\nMake the distance GB 3.5 cm., and\\ndraw B from radius to radius.\\nMake the distance GD 1.5 cm., and\\ndraw D from radius to radius.\\n(All this should be done before the\\nregular Exercise begins.)\\nPlace the mirror in position as in\\nFig. 80, and, keeping the eye about 20\\ncm. from it, look at the images of A, B, and D.\\nDo the images of A and B point in the same general direction, from\\nleft to right in the figure, as the arrows themselves\\nIs the same answer true of D and its image\\nAre the images of A and B longer or shorter than the arrows them-\\nselves\\nAt the centre of A stand the pin upright, and laying the two rulers\\non the paper, point one edge of each toward the image of the pin,\\ncontriving to have these edges make a considerable angle with each\\nother. In this way the position of the image is located. Is it behind\\nthe mirror or in front Is it, then, a real image or an unreal one", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0131.jp2"}, "132": {"fulltext": "118\\nPHYSICS.\\nBy the same method locate the image of the pin when erected at\\nthe centre of B and when at the centre of D, asking and answering\\nin each case the same questions that were asked when the pin was at\\nthe centre of A.\\nIf time permits continue the Exercise as follows\\nExtend the two radii r r by the lines r r drawn on the paper, as in\\nFig. 80. Draw the arrow E, 6 or 8 cm. distant from G, marking\\npoints 1, 2, and 3, upon it. Locate the image of each of these points\\nby the method used in the preceding Exercise with the convex side\\nof the mirror, drawing upon the paper the lines of sight and the\\nimage of the arrow.\\n118. Principal Focus of Concave Mirror. Tlie principal\\nfocus of a concave mirror is the point to ivhich rays, coming\\nto the mirror parallel to the principal axis, converge after\\nreflection. In other words, it is the point which marks the\\nimage (real) of a very distant point on the principal axis.\\nAs in the case of a convex mirror, the principal focus lies\\nvery nearly midway between the reflecting surface and the\\ncentre of curvature.\\n119. Rule for Placing Images. Fig. 81 illustrates an\\nFig. 81. Fig. 82.\\neasy rule for finding the position of an image in a convex\\nmirror.\\nLet AB be the object. Draw one ray from A straight\\ntoward the centre of curvature. This ray will return on", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0132.jp2"}, "133": {"fulltext": "REGULAR REFLECTION OF LIGHT. 119\\nitself after reflection, coming as if from C. Draw another\\nray from A parallel to the principal axis. This will after\\nreflection appear to come from P, the principal focus\\n116). Both reflected rays appear to come from A\\\\\\nwhich is therefore the image of A.\\nThe image of B is found in the same way.\\nIf the object is a straight line, as in this figure it is cus-\\ntomary to represent the image by drawing a straight line\\nfrom A to B This is inaccurate, as Exercise 18 should\\nshow.\\nFig. 82 shows the same method applied to a concave\\nmirror.\\n120. Distorted Images. In Exercises 18 and 19, and in\\nall the figures that have been given representing cylindrical\\nmirrors, we have been dealing with rays which are, both\\nbefore and after reflection, parallel to the plane on which\\nthe mirror rests. If we make use of other rays, as we do\\nwhen looking obliquely down at the mirror face, we see\\nthings sadly twisted, the effects thus obtained being too\\ndifficult for oar profitable study.\\n121. Relation of Cylindrical to Spherical Mirrors. If\\nwe were to use a spherical mirror, placed with its principal\\naxis horizontal, and employ only horizontal rays striking\\nthe mirror on a narrow horizontal strip through its middle,\\nwe should get effects quite like those we have already\\nstudied. All the figures from 71 to 82 would apply as well\\nto a spherical mirror so used as to a cylindrical mirror.\\nIndeed, these figures are like those commonly given to show\\nthe effects obtained with spherical mirrors.\\nFor general use spherical mirrors are better than cylindri-\\ncal mirrors, because they can be used from more points of\\nview without giving badly distorted images.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0133.jp2"}, "134": {"fulltext": "120 PHYSICS.\\nEXPERIMENTS.\\nWith a concave spherical mirror 5 or 6 inches wide (No. XXVII)\\n3f-~~ M interesting lecture-table experiments may be\\nmade in a slightly darkened room, the image\\nof a candle-name or, better, gas-flame being\\nthrown upon a screen so as to be visible to all\\nin the room. The screen should be uf tracing\\nLq cloth or oiled paper, so that the image upon it\\nS may be seen from both sides. An opaque screen\\nq 9 should hide the flame itself from the eyes of\\nthe class. Fig. 83 suggests a good arrange-\\nment, MM beng the mirror, G its centre of cur-\\nvature, L the flame, S the opaque screen, and\\nS the tracing- cloth screen.\\nThe positions of L and S may be greatly\\nvaried and may be interchanged, but the least\\ng distance of either from mirror the should be\\nFig. 83. rather more than one half the radius of curva-\\nture of the mirror, if real images are desired.\\n122. Principal Use of Spherical Mirrors. Although\\nspherical mirrors are sometimes used to form images, as in\\ncertain telescopes, probably their most important use is to\\nconcentrate light upon some object that cannot otherwise\\nbe well seen.\\nThus, the small objects which are to be looked at with a\\nmicroscope need to be brightly illuminated, and a concave\\nmirror is commonly used to throw light upon them.\\n123. The Ophthalmoscope. Often a physician wishes to\\nsee what is wrong in the depths\\nof a patient s eye. To do this\\ntfie interior of the eye must be\\nespecially lighted up. If this\\nis done by holding a flame in\\nfront of it, the flame dazzles the\\neye of the observer and therefore\\nis of little use. The difficulty is overcome by means of the", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0134.jp2"}, "135": {"fulltext": "REGULAE REFLECTION OF LIGHT. 121\\nophthalmoscope, Fig. 84, where M is a curved mirror with\\na hole in the centre; L is some source of light, placed so\\nthat the rays proceeding from it to the mirror pass by re-\\nflection into the eye of the patient, represented by E\\\\ and\\nmarks the position of the observer s eye.\\nThis simple application of the concave mirror was made\\nby the great physicist Helmholtz, and it has probably won\\nfor him more popular fame and gratitude than all his other\\nwork. The most remarkable thing about many inventions\\nis the fact that they were not made earlier.\\n124. Formulas Relating to Curved Mirrors. In the fol-\\nlowing formulas, which are here given without proof,\\nD o the distance of object-point from mirror,\\nD t the distance of image of object-point from mirror,\\nF focal length of the mirror.\\nFor a convex mirror we have\\nA A F\\nFor a concave mirror we have\\nA A F\\nwhen the object-point is farther from the mirror than the\\nprincipal focus is, and\\nJ_ JL_ _ 1_\\nA A F\\nwhen the object-point is between the principal focus and\\nthe mirror.\\nIt is doubtful whether work done with the cylindrical\\nmirrors will be accurate enough to give results agreeing\\nwith these formulas. Similar formulas are used with\\nrespect to lenses.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0135.jp2"}, "136": {"fulltext": "122 PHYSICS.\\nQUESTIONS.\\n(1) A small object is placed close to a convex mirror.\\n(a) Is the image real or virtual\\n(b) If the object is moved farther and farther away from the mirror,\\nwill the image at any time become real\\n(2) If one looks at the image of his own face in a convex mirror,\\nwill the nose appear too prominent and the forehead and chin re-\\ntreating, or will the opposite be true\\n(3) If a small object is placed close to a concave mirror\\n(a) Is the image real or virtual\\nIf the object is moved farther and farther away from the mirror,\\nwill it reach such a position that its image will be real If so, what\\nis that position\\n(4) (a) Have you in using any single mirror, plane or curved, seen\\na virtual image that was inverted, as compared with the object?\\n(b) Have you seen any real image, formed by a single mirror, that\\nwas right side up, as compared with the object\\n(5) Do you see anything wrong with the physics of the following\\nstatement, copied from a prominent newspaper\\nThere are times when the public sees things in a convex mirror, in\\nwhich they appear broad, robust, and expanded. There are times\\nwhen the public sees things in a concave mirror, in which they appear\\ncramped, narrow, and contracted.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0136.jp2"}, "137": {"fulltext": "CHAPTER X.\\nREFRACTION OF LIGHT.\\n125. Introductory. In the experiment made with a\\nprism the class may have noticed that the light did not go\\nin the same direction after leading the prism as before\\nentering it. Some members of the class in looking into\\npools or vessels of water may have noticed that objects\\nbeneath the surface are not exactly where they seem to be.\\nEXPERIMENTS.\\n(1) Place a straight stick in an oblique po-ition, partly in and\\npartly out of water. Notice the apparent bendiDg or disconnection\\nof the stick at the surface of the water.\\n(2) Place on a table a pan (No. XXVIII), 15 cm. or more in diam-\\neter and with nearly vertical sides 4 or\\n5 cm. high. Place a small coin on the\\nbottom of the pan, and adjust the head\\nin such a position that the side of the\\npan will just hide the more distant por-\\ntion of the coin from the eye at E (Fig.\\n85). Maintain the head in this position\\nby resting it against any convenient sup-\\nport k:ep one eye closed, and look with\\nthe other into the pan, just beyond the farther edge of the coin, while\\nanother person slowly pours in water. Have the pouring stopped\\nas soon as the whole of the coin becomes visible.\\n(3) Repeat experiment 2 with the eye held vertically above one\\nedge of the coin, with a slender stick or a stout wire laid across the\\ntop of the pan, nearly in the line of vision, to serve as a point of\\ndeparture from which to measure the apparent displacement of the\\ncoin, if any should be observed.\\n123\\nFig. 85.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0137.jp2"}, "138": {"fulltext": "124 PHYSIC 8.\\n126. Interpretation of the Preceding Experiments.\\nObjects always appear to the eye to be in the direction from\\nwhich the rays are travelling at the moment of entering the\\neye. Evidently, then, since the coin appeared to rise when\\nthe water was poured into the jar, in Experiment 2, the\\nlight-rays which proceeded from the coin must have been\\nbent aside in some way by the water.\\nIn Eig. 85 the straight line CE, which passes from the\\nleft-hand edge of the coin C to the pupil of the eye at E,\\nrepresents the course of a light-ray from that point before\\nthe water was poured into the pan. Any ray that passed\\nfarther to the right than CE would be intercepted by the\\nside of the pan any ray that passed farther to the left, or\\nmore nearly vertical than CE, would miss the eye hence it\\nis evident that, so long as the pan is filled with air only,\\nand the eye kept in the position shown, the coin cannot be\\nseen.\\nBut as soon as water is poured into the pan, the rays no\\nlonger travel in straight lines from the object C to the eye.\\n\u00c2\u00a3ach ray suffers an abrupt change of direction at the sur-\\nface of the water, and from this it follows that such rays as\\nthose which take the general course CS in the figure are\\nfinally brought to meet the eye at E. As a result of the\\nbending C becomes visible, and its farther edge is seen\\napparently at 6 y in a position somewhat raised above the\\nbottom of the pan.\\nExperiment shows that the course CSE might be retraced\\nby a ray. That is, a ray leaving E in the direction E8\\nwould reach C by the line SC.\\nQUESTIONS.\\n(1) If normals were drawn to the surface of the water, at the points\\nabout S where the rays emerge, would the bending of each ray be\\ntowards or from the normal (in the air)", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0138.jp2"}, "139": {"fulltext": "REFRACTION OF LIGMT.\\n125\\n(2) If the rays were passing from E to C, would the bending at\\nthe surface of the water be toward or from the normal (in the\\nwater)\\nWhen we look straight clown into\\nwater at any small object it appears\\nto be in its true direction from the eye,\\nbut nearer than it really is. Fig. 86\\nindicates w T hy this is so. represents\\nthe object, E the eye, much magnified,\\nand 0 the apparent position of the\\nobject.\\n127. Angles of Incidence and Refrac-\\ntion. The change of direction which a ray of light under-\\ngoes when it passes obliquely from one medium into\\nanother is called refraction.\\nThe amount of the bending, or refraction, which a ray\\nof light suffers at any surface depends partly upon the two\\nsubstances which meet at this\\nsurface, and partly upon the\\nangle, i (Fig. 87), which the\\nray makes with a line JYjV,\\nwhich is at right angles with\\nthe surface at the point\\nwhere the ray strikes the sur-\\nface.\\nIf the space above the line\\nAB represents the air-space,\\nand that below this line the\\nwater, or glass, or whatever\\nsubstance it may be that lies there, solid or liquid, the\\ncourse of the ray is changed at the surface in such a way\\nthat the angle r which it makes with NN inside the solid\\nor liquid is smaller than the angle\\nC\\n-B\\nN\\nFig. 87.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0139.jp2"}, "140": {"fulltext": "126\\nPHYSICS.\\nThe angle i in Fig. 87 is called the angle of incidence.\\nThe angle r is called the angle of refraction.\\nIf the ray were represented as coming in the opposite\\ndirection, that is, first along R and then along r would\\nbe the angle of incidence and i would be the angle of re-\\nfraction. The ray would be bent just as much at the sur-\\nface as it is when going first along and then along R.\\n128. Index of Refraction, When the direction of I is\\nchanged the direction of R is changed. The way in which\\nthe change of one depends upon the change of the other is\\neasily shown by means of Fig. 88. and I show\\nthree rays all of which come to the point and then sep-\\narate, the first going along i2, the second along i? the\\nthird along R The circle whose centre is at C is drawn\\nwith any convenient length of radius. The dotted lines,\\nw, n\\\\ n and m, m\\\\ m 9 are drawn from the points where\\nthe rays cut the circumference to the line NN 9 at right\\nangles.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0140.jp2"}, "141": {"fulltext": "BEFR ACTION OF LIGHT. 127\\nIf this figure has been drawn so as to acord with the\\nresults of experiments on light-rays, we shall have\\nn __ n _ n\\nm m! m\\nand any one of these equal ratios is called the Index of Re-\\nfraction of the second medium, heloiv AB, with reference to\\nthe first medium, above AB.\\nn\\nIf now we can measure in any given case, we shall\\nhave a quantity which is very useful in physics, for by\\nmeans of it we can calculate at once the value of a new m\\nto go with any new n\\\\ that is, we can, if we know the\\nindex of refraction and the angle which any ray makes with\\nNNvcl one medium, find without further experiment the\\nangle which the same ray makes with NN in the second\\n71\\nmedium. Exercise 20 shows how to find the ratio for\\nm\\nthe case of air and glass.\\nEXERCISE 20.\\nINDEX OF REFRACTION OF GLASS*\\nApparatus A piece of plate glass (Xo. 28). Articles 3, 24a and\\n24b. A sheet of paper and three pins.\\nPlace the glass, G (Fig. 89), on the paper P. Stick one pin up-\\nright at the point 1 close to one of the polished edges of the glass\\nstick the other pin at 2 close to the other polished edge.\\nLook with one eye from the position S through the whole width of\\nthe glass at pin No. 1. Move the eye toward 3, looking all the\\ntime through the glass at the pin. It will presently be noticed\\nthat the pin seen through, the glass is not in the same direction\\nfrom the eye as the same pin seen over the glass. That which is\\nI owe tbe plan of this admirable Exercise to Mr. F. M. Gilley of\\nthe Chelsea High School. It is described in Gilley s Principles of\\nPhysics, Allyn Bacon, Boston. E. H. H.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0141.jp2"}, "142": {"fulltext": "128\\nPHYSIOS.\\nseen through the glass is an image of the real pin, and it is upon this\\nimage that the attention should be fixed.\\nContinue moving the eye in the general direction of 3, keeping it,\\nhowever, about 30 cm. from the glass, until the image of pin No. 1\\nis just hidden behind pin No. 2. Then place a pin at 3, in the same\\nstraight line with the eye, pin No. 2, and the image of No. 1.\\nDraw a fine pencil-line upon the paper close to the glass edge\\ntouched by pin No. 2. Then remove the glass.\\nThe line now drawn marks the position of the refracting surface.\\nThe line 1-2, Fig. 89, shows the direction, within the glass, of a\\n1\\n*L G\\nS\\nA.\\n2\\np\\n\\\\3\\nFig. 89.\\nFig. 90.\\ncertain ray from 1. The line 2-3 shows the course of the same ray\\nafter it leaves the glass at 2. The line NN Fig. 90, is drawn nor-\\nmal to the refracting surface at the point of emergence. From this\\npoint equal distances are laid off, to B and to C. Lines are drawn\\nfrom B and from G to the line i\\\\W at right angles.\\nCE-z- BD the index of refraction from air to glass.\\nEXERCISE 21.\\nINDEX OF REFRACTION OF WATER.\\nApparatus Articles 3, 14, 15, 24a, 24b, 29, 30, and a sheet of\\npaper about 6 inches square.\\nPut the partition i^in place, as shown in Fig. 91, and pour water\\ninto the jar until its surface comes within 1 or 2 mm. of the middle\\ntooth of the partition. Then by means of the plunger (No. 14), at-\\ntached to the side of the jar by means of its clasp, raise the level of", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0142.jp2"}, "143": {"fulltext": "BEFBACTIOjST OF LIGHT.\\n129\\nthe water till the apparent distance between the middle tooth of the\\npartition and its reflection in the water surface is less than 1 mm.\\n(To see this reflection well, one should look through the wall of the\\nempty part of the jar.)\\nThen the brass index b is attached to the jar, as shown in Fig. 91,\\nand is raised or lowered, with the tip p touching the glass, until an\\neye on the line Cg, 20 or 30 cm. from the jar, can barely see p the\\nvery tip of b, apparently in a straight line with Cg. This setting\\nshould be made with care, and after it is made the experimenter\\nmust look to see whether the tooth at G is clear of the water. If its\\nlowest edge touches the water the setting is useless, and all of the\\nadjustments must be made anew before a reading is made.\\nP\\nd/-m-}\\nFig. 91.\\nFig. 92.\\nWhen all the adjustments have been successfully made, measure\\ncarefully the distance from the top of the jar down to the tip, p, of\\nthe index, the measuring-stick being kept outside the jar.\\nMeasure now the inside diameter of the jar.\\nMeasure also, unless it is already known, the distance of G\\nbelow the top of the jar.\\nIt is well to have this distance, which is somewhat troublesome\\nto measure accurately, given by the teacher. Partitions of different\\ndepths might be used in order to vary the angles of incidence and\\nrefraction.\\nIf the jar used in this Exercise is not pretty level at the top, or if\\nthe partition is not just at the middle of the jar, it is well, after\\nmaking one setting of the index and one measurement of its position,\\nto turn the jar about, transferring the index to the other side, and\\nmake a new setting and a new measurement. The mean of the two\\nmeasurements thus made should be nearly free from any error caused\\nby irregularity of the jar or of the partition s position.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0143.jp2"}, "144": {"fulltext": "130 PHYSICS.\\nNow make a drawing, of full natural size, of the sides of the jar\\n(inner lines), the water surface and the partition, as in Fig. 92, con-\\ntinuing the partition line, by means of dots, well down into the jar.\\nPut p in its proper place, and then draw the lines pC and Cg.\\nLay off Cd Cg, and then draw the lines n and m.\\nThe index of refraction from air to water is\\nm\\n129. Index Different for Different Colors. In Exercise\\n20 the observer may have noticed a tint of bine or of red at\\nthe edge of the image of the pin. The fact is that light of\\nvarious colors comes from the pin, and that the rays are not\\nall refracted alike, the blue being refracted more than the\\nred. The index of refraction is therefore different for light\\nof different colors, but for our present purpose we need not\\ndwell upon that fact. We get a sort of average index by\\nthe method of Exercises 20 and 21.\\n130. Relation between Index of Refraction and Velocity\\nof Light. The velocity of light in any transparent sub-\\nstance depends on the nature of the substance. It is\\ngreatest in a so-called vacuum. It is least in the most\\nhighly refractive substances, and, indeed, the index of re-\\nfraction for any given substance depends upon the rate at\\nwhich light travels through it.\\nThis is sometimes illustrated by an analogy suggested by", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0144.jp2"}, "145": {"fulltext": "REFRACTION OF LIGHT.\\n131\\nthe march of troops over ground of various kinds. Suppose\\na column of troops to be marching over smooth ground,\\nrepresented by the space to the left of the line SS in Fig.\\n93. The front of the column being at AB, let the line\\nSS represent the border of a marsh or other difficult ground.\\nUpon entering, the right of the column, B, first encounters\\nthe marsh, and the soldiers at B will fail behind those of\\nthe rest of the front. In consequence of this the column\\nwill, one part after another, wheel to the right until, when\\nthe whole front has entered the marsh, it will have the new\\ndirection shown by the line A B Substitute for the\\ncolumn of troops a beam of light, and for the marsh a\\nhighly refractive transparent substance, and one may get\\nsome notion as to how refraction depends upon the retard-\\ning effect of refractive substances upon light-rays.\\n131. Total Internal Reflection: Critical Angle. \u00e2\u0080\u0094In\\nFig. 94 we have air above the horizontal line and w^ater,\\nFig. 94.\\nglass, or some such transparent medium below the line. A\\nray of light R x may come from beneath to the surface at\\nsuch an angle with the normal that it will after refraction\\nat be parallel to the refracting surface. The ray R t com-\\ning up to at a larger angle with the normal will not pass\\nout to the air, nor will it skim alons; the surface. It will", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0145.jp2"}, "146": {"fulltext": "132\\nPHYSICS.\\nbe reflected at the point 0, the surface acting as a perfect\\nmirror, and will follow the course R the angle of reflec-\\ntion being equal to the angle of incidence.\\nThe angle a, ivhich must not be exceeded if the ray is to\\n2mss ont into the air, is called the Critical Angle.\\nThe reflection which takes place when this angle is ex-\\nceeded is so good that it bears the especial name total\\nreflection.\\nEXPERIMENTS WITH TOTAL REFLECTION.\\n(1) With the eye at E, Fig, 95. look at right angles into a glass\\nprism shaped like ABC, at the same\\ntime holding an object at 0. Note the\\nposition of the image 0 and its re-\\nmarkable distinctness.\\n(2) In Fig. 96 SS is a disk or square\\nof thin wood about 10 cm. wide,\\nLO is a piece of knitting-needle about\\n8 cm. long. The wood floats in water\\nwhich fills a vessel to the brim AB\\nPush the needle down until its upper end is nearly level with the\\nupper surface of the board, and look down obliquely through the\\nwater, close past the margin of the board, at the lower extremity of\\nJE\u00c2\u00b1\\nFig. 96.\\nthe needle. Now draw the needle up, little by little, through the\\nfloating board until the point is reached at which the needle just\\nvanishes from view, the line of sight being made at last as nearly\\nhorizontal as possible. Lift the board from the water, and note how\\nmuch of the needle still projects below the board.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0146.jp2"}, "147": {"fulltext": "REFRACTION OF LIGHT,\\n133\\nWhen the point is at 0 the light-ray going from it to S passes out\\ninto the air. When the point is at 0, a light-ray OS suffers total\\nreflection along SR. The angle OSN 1 or its equal SOL, is nearly\\nequal to the critical angle. Of course no great accuracy can be\\nexpected here.\\nEffect of Transparent Plates and Prisms.\\n132, Transparent Plates. A plate of glass, or other\\ntransparent material, with plane parallel\\nsides, as in Fig. 97, refracts light which\\nenters it obliquely, but refracts it equally and\\nin the opposite direction when it comes out\\nat the opposite side of the glass, so that the\\nentering and emerging rays are parallel to\\neach other, although, as Fig. 97 shows, they\\ndo not lie in one straight line.\\nEvidently a thick plate of glass will, other\\nthings being equal, set the emergent ray\\nfarther to one side, from the line of the original ray, than\\na thin plate will.\\n133. Prisms. A. prism, in the study of light, is usually\\na piece of glass, or other transparent material, bounded by\\nthree rectangular and two triangular faces. DEF in Fig.\\n98 represents one end of such a prism.\\nJ)\\nFig. 97.\\nIt is evident that light entering the face DE from air will\\nbe refracted toward the normal NM. Going through the\\nprism to the face DF it passes out into the air, being re-", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0147.jp2"}, "148": {"fulltext": "134 PHYSICS.\\nfracted again, this time from the normal M N\\\\ so that the\\ntwo refractions have bent the ray far from its original\\ndirection.\\nThe total bending or deviation suffered by a ray in pass-\\ning completely through a prism depends on a number of\\nthings.\\n1st. On the angle which the two faces passed through make\\nwith each other. This angle is called the refracting angle\\nsee D in Fig. 98.\\nThe greater this angle is, other things being equal, the\\ngreater the total deflection will be. We have seen in 132\\nthat if the two faces are parallel the total deviation is zero.\\n2d. On the color of the ray.\\nThis fact has already been noticed. Eed light is deviated\\nless than blue light.\\n3d. On the angle tvhich the ray makes with the first sur-\\nface.\\nThe total deviation is least when the ray strikes in such\\na way as to follow, within the prism, a course parallel to\\nZE7, Fig. 99, which makes the distance AI equal the dis-\\ntance AE, and makes the refraction equally great at both\\nsurfaces.\\nEXPERIMENT.\\nRepeat the experiment of 89, varying the angle at which the\\nsunlight strikes the first face, in order to show that there is one in-\\nA\\nclination which gives a less total deflection of the light than any\\nother position.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0148.jp2"}, "149": {"fulltext": "REFRA CTION OF LIGHT. 135\\n4th. On the material of the prism.\\nAll kinds of glass do not refract equally.\\n134. Dispersion: The Spectrum. The separation of rays\\nof different colors by a prism is called dispersion.\\nThe spot or band of colored light produced by the dis-\\npersion of a sunbeam is called the solar spectrum.\\nIt is customary to divide the spectrum into seven regions,\\ncalled red, orange, yelloiu, green, Hue, indigo, violet, and to\\ncall the general colors of these the primary colors, to dis-\\ntinguish them from those formed by compounding two or\\nmore of them. This division of the spectrum is a mere\\nmatter of convenience. We might name a hundred colors\\nof the spectrum if we chose to do so.\\nSo long as we keep to any one refracting material the\\ndispersion is, in general, greater when the average deviation\\nof all the rays is greater. Thus with a given prism the dis-\\npersion is least when all the rays go through the prism as\\nthe ray IE goes in Fig. 99.\\nWhen prisms of different material are used, two kinds of\\nglass for example, one may disperse the rays more than\\nthe other, while producing no greater average deviation of\\nall the rays or one may disperse the rays about as much as\\nthe other while deviating them, as a whole, much less.\\n135. Achromatic Prisms. Two prisms of nearly equal\\ndispersive power but of unequal deviating power\\nmay be combined, as in Fig. 100, making a com-\\npound prism which produces considerable deviation\\nwith very little final dispersion. Such a combina-\\ntion is called achromatic, that is, colorless.\\nAchromatic combinations of lenses 149) are\\nused in many optical instruments. Fig. ioo.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0149.jp2"}, "150": {"fulltext": "136\\nPHYSICS.\\nLenses.\\n136. Shapes of Lenses. A lens is, usually, a piece of\\nglass whose two faces are parts of spherical surfaces.\\nSometimes there is a cylindrical surface between the two\\nspherical faces.\\nFig. 101 shows various lenses as they would look if cut\\nthrough the middle.\\nFig. 101.\\nLenses are classed as convex, or converging, and concave,\\nor diverging. Convex lenses are all thicker in the middle\\nthan at the margin, and cause parallel light-rays to con-\\nverge, as in Fig. 102. Concave lenses are thinner in the\\nFig. 102. Fig. 103.\\nmiddle than at the margin, and cause parallel light-rays to\\ndiverge, as in Fig. 103.\\nSome of the lenses used in the most accurate optical in-\\nstruments have convex or concave surfaces, which are not\\nstrictly parts of spherical surfaces. Such lenses possess\\ncertain advantages over spherical-surface lenses (see 147).\\n137. Definitions Relating to Lenses. The lenses we\\nshall use will be much like No. 1 in Fig. 101. The two\\nsides are supposed to be just alike.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0150.jp2"}, "151": {"fulltext": "REFRACTION OF LIGHT.\\n137\\nTo understand such a lens better we will make use of\\nFig. 104.\\n(7 is the centre of the spherical surface of which A SB is\\na part. It is called the centre of curvature of the face\\nASB. C is the centre of curvature of the face ABB.\\nThe straight line HCOO K, continued to any distance in\\neach direction, is called the principal axis of the lens.\\nAny straight line going, like LM, obliquely through the\\ncentre of the lens is called a secondary axis of the lens.\\nIf the two faces of a lens are exactly alike, as we suppose\\nthem to be here, any ray of light going through the centre\\nof the lens, the point 0, will hare the same direction after\\nleaving the lens as before entering it, because the two little-\\nspots of surface at which it enters and leaves the lens are\\nparallel to each other, so that the ray is affected just as if\\nit were going through a plate with parallel faces.* is\\ncalled the optical centre of the lens.\\nEays entering a convex lens parallel to its principal axis,\\nas in Fig. 102, are refracted in such a way that after leav-\\ning the lens they will cross this axis. They do not all cross\\nat one point, but if the faces are near together, and are very\\nsmall parts of spherical surfaces, as in our lenses, such rays\\nwill cross at or near a certain point, F, on the principal\\nThe direction of the ray within the lens is, of course, not quite\\nthe same as its direction before entering. This fact is not shown in\\nFig. 104.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0151.jp2"}, "152": {"fulltext": "138\\nPHYSICS.\\naxis, and this point is called the principal focus of the\\nlens. There are two principal foci, one on each side of the\\nlens. See points i^and F in Fig. 104.\\nThe distance from the principal focus to the nearer face\\nof the lens is called the focal length of the lens.\\nFocal length is a quantity of very great importance in\\ndealing with lenses, and the next Exercise will show how\\nto find it by experiment. For this purpose we need to have\\nthe light come to the lens in rays nearly parallel to each\\nother and to the principal axis. This we can do by taking\\nthe light from any small spot of any distant but distinct\\nobject; for instance, a chimney or a church-spire outlined\\nagainst the sky.\\nEXERCISE 22.\\nFOCAL LENGTH OF A CONVERGING LENS.\\nApparatus The lens (No. 31) mounted on a block. A meter-rod\\n(No. 2). A small block (No. 21) bearing a white cardboard screen\\n(No. 32). A common pin.\\nFig. 105.\\nFirst Method. Place the lens and the screen upon the rod, as in\\nFig. 105, and point the rod at some distant object, seen against the\\nsky, in such a way that the light from this object will pass from the\\nlens and then fall upon the screen. Move the screen back and forth\\nBee Appendix I,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0152.jp2"}, "153": {"fulltext": "REFRACTION OF LIGHT. 139\\nuntil that part of the image which lies on or near the principal axis\\nof the lens is made as distinct as possible. Then by means of the grad-\\nuations of the meter-rod, or by an independent measuring-stick if this\\nis preferred, note the distance from this part of the image to the\\nnearer face of the lens. This is the focal length.\\nSecond Method. Remove the screen from its block and put the\\npin upright in its place. Let the pin, thus mounted, be placed on\\nthe meter-rod, about as far from the end of the rod as the pupil\\nusually holds a book from his eyes when reading. Place the lens\\nsomewhat farther from the same end of the rod.\\nPlace the eye at this end of the rod and, looking sharply at thepm,\\ndirect the rod and adjust the lens in such a way that the light from\\nsome distant object will pass through the lens and form an image in\\nthe air close to the pin. To decide whether the image is nearer the\\neye than the pin is, move the eye to and fro, to the right and the left,\\nwatching the pin and the image. f If the pin is more distant than\\nthe image, it will, when the eye is moved toward the right, appear\\nto move across the image toward the right. If the pin is nearer than\\nthe image, it will, when the eye is moved toward the right, appear\\nto move across the image toward the left. The rod should not be\\nheld in the hands during this test, but should be placed on some\\nsteady support.\\nContinue the adjustments until the test described fails to show\\nwhich of the two, the pin or the image, is nearer the eye. Then meas-\\nure the distance from the pin to the lens. It should be the focal\\nlength of the lens.\\nCompare the values of the focal length given by the two methods.\\nThe second method is more difficult, but it is instructive, and it\\n*The image is formed because light coming from anyone small\\nspot of the object is brought to a small spot again by the lens. The\\nimage is made up of such small spots each in its own place. For the\\npurposes of this Exercise the distant object need not be more than 30\\nor 40 feet from the experimenter. The images on the screen will\\nbe much more distinct if the apparatus is used in the back part of\\nthe room, well away from the windows.\\nf To see the reason of the test just described, close one eye and hold\\nthe two forefingers, some inches apart, in line with the other eye, so\\nthat one finger hides the other. Then move the eye to the right\\nand left, and notice the apparent movement of the fingers with\\nrespect to each other.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0153.jp2"}, "154": {"fulltext": "140 PHYSICS.\\ncan be used in cases where the image is too faint to show clearly upon\\nthe screen.\\n138. Discussion of Exercise 22. It is common to speak\\nof the rays coming to a lens from a distant object as parallel\\nrays. This does not mean that rays coming from different\\nparts of the object to the lens are parallel to each other. It\\nmeans merely that rays coming from any one spot of the\\nobject to the lens are parallel, or very nearly parallel, to\\neach other. In fact, if rays from the different parts of a\\nluminous body could be converged to the same point, the\\nresult would not be an image repeating the features of the\\noriginal objects. It would be a mere point, or very small\\npatch of light.\\nThe image seen in the Second Method is, like that of the\\nFirst Method i a real image 109), but it is in the air.\\nAs there is an image in the air, we may well inquire why\\nthis image cannot be seen by a whole class at once without\\nthe use of a screen. It is because the light forming the\\nimage in the air goes straight on through this image, and\\ncan be received only by placing one s self behind the image.\\nThe light which forms an image upon a screen is by the\\nthreads of the screen reflected back in all directions, and\\ntherefore some part of it reaches every eye.\\nQUESTION.\\nIf a bright point were placed at the principal focus of a lens, what\\ndirection would the rays going from this point to the lens have after\\npassing through the lens\\n139. Object-distance and Image-distance: Conjugate\\nFoci. Two points so placed tvith respect to a lens that an\\nobject placed at either of them will have an linage at the\\nother are called Conjugate Foci of the lens.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0154.jp2"}, "155": {"fulltext": "REFRACTION OF LIGHT. 141\\nEXERCISE 23.*\\nRELATION OF IMAGE-DISTANCE TO OBJECT-DISTANCE\\nCONJUGATE FOCI OF A LENS.\\nApparatus The same lens that was used in Exercise 22. A\\nmeter-rod. Block (No. 9). Small block (No. 21), with a cardboard\\nscreen (No. 32). Small kerosene lamp with an asbestos band around\\nthe chimney (No. 33).\\nArrange the apparatus according to Fig. 106. The hole in the as-\\nFig. 106.\\nbestos band, lighted up by the name behind, is the object the image\\nof which is to be received upon the screen. One end of the meter-\\nrod is placed vertically beneath this illuminated hole.\\nPlace the screen at first at a distance from the object about equal\\nto three times the focal length of the lens. Then move the lens back\\nand forth on the rod between the object and the screen, and see\\nwhether in any position it gives upon the screen a clear image of the\\nobject. If it does, measure the distance from the lens in this position\\nto the object, and write this distance as the first number in a record-\\ncolumn headed D (object-distance). Measure also the distance from\\nthe lens to the screen, and put this distance as the first number in a\\nrecord-column headed Di (image-distance).\\nIf, with the present position of the screen and object, there is no\\nposition of the lens that will cause a distinct image of the object\\nto fall upon the screen, move the screen one or two centimeters far-\\nther from the object, and then try again to get a good image. If still\\nnone is found, move the screen still farther away, continuing the\\ntrial till a distinct image is obtained. Then measure and record the\\nTo economize space upon the laboratory- tables it will probably\\nbe necessary to have pupils work in pairs in this Exercise. Each pair\\nshould know the focal length of its lens at the outset, so as to lose no\\ntime in beginning the Exercise.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0155.jp2"}, "156": {"fulltext": "142 PHYSICS.\\nD and Di as already described. (Very little time need be spent upon\\nthese first successive trials.)\\nThen at one move place the screen about 10 cm. farther still from\\nthe object, find a position of the lens that will give a distinct image,\\nmeasure and record D Q and Di as before. Without moving the screen,\\nsee whether there is any other position of the lens that will give a\\ndistinct image if there is, measure and record the D Q and the Di for\\nthis position of the lens.\\nMove the screen 10 cm. farther away, and then do exactly as\\nbefore.\\nIf there is time, move the screen two or three more times, adjust-\\ning the lens, measuring, and recording each time. It is better to\\nmake a moderate number of settings and readings well than a large\\nnumber carelessly, but an error of one or two millimeters in these\\nreadings will be of no great consequence.\\n140. Discussion of Exercise 23. The distance from\\nobject to image in any case of Exercise 23 is D Q D and\\nwe may call this D oi This distance was shortest in the\\nfirst case recorded. Let each member of the class divide\\nthe D oi of this case by the focal length of his lens. Is there\\nany general agreement between the quotients thus found\\nWhen the screen was farther away, was there usually\\nmore than one position of the lens that would give a distinct\\nimage, the screen remaining unmoved\\nIf you were told that in a given case the D Q was 20 cm.\\nand the A 60 cm., could you tell what the other possible\\nD Q and Di would be for the same positions of object and\\nscreen Look at your record-columns for Exercise 23, and\\nsee whether they help you to answer this question.\\nLet each member of the class call F the focal length of\\nthe lens which he used, and let him test the truth of the\\nformula.\\n1 1 1", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0156.jp2"}, "157": {"fulltext": "REFRACTION OF LIGHT. 143\\nor, what means the same,\\nD xD =F(D +A),\\nfor all cases tried and recorded Ly himself in Exercise 23.\\nPROBLEMS.\\n(1) Do for a certain case is 50 cm. and Dx is 100 cm. How great is\\nFt\\n(2) If Di is 80 cm. and Fis 20 cm., how great is D\\n(3) If D Q =Di, we will call each D.\\n(a) What in this case is the relation between F and D1\\n(b) How does this agree with your observations in Exercise 23?\\n141. Real Image Formed by a Lens. In the preceding\\nExercises the object presented to the lens has been small,\\nor has been at such a distance as to give a rather small\\nimage. It is now desirable to study larger images, and to\\nstudy them with especial reference to their shape and size,\\nrather than their distance from the lens. We shall in the\\nnext Exercise find the shape and size of an image of an\\narrow placed at right angles with the principal axis of the\\nlens and not far from the lens. We shall not attempt to\\nfind the whole image at once, but shall find separately the\\nimages of several points of the arrow, and then make an\\napproximate image of the arrow by connecting these points.\\nEXERCISE 24.\\nSHAPE AND SIZE OF A REAL IMAGE FORMED BY A LENS.\\nApparatus: The lens (No. 31). Measuring-stick (No. 3). Block\\n(Xo. 21) carrying in the narrow slot on its top a piece of wire (No.\\n34) extending first horizontally and then downward (see Fig. 108).\\nA ruler (No. 24). Block (No. 25). A sheet of paper about 30 cm.\\nwide and 1 m. long, having near one end an arrow 8 cm long, drawn\\nat right angles with a pencil-mark about 30 cm. long, and marked, or\\nnumbered, as shown by Fig. 107. Weights (No. 19) to hold the cor-\\nners of this sheet in place on the table.\\nArrange the apparatus as shown by Fig. 108, the centre of the lens\\nover a point on the long pencil-mark, at a distance from the centre of", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0157.jp2"}, "158": {"fulltext": "144\\nPHYSICS.\\nthe arrow about equal to one and a half times the focal length of the\\nlens, and block Xo. 25 in such a position that the vertical mark upon\\nits face points straight down to point Xo. 3 of the arrow. This ver-\\ntical mark will now cross the principal axis of the lens, if the lens is\\naccurately placed.\\nPlace the other block near the other end of the paper in such po-\\nsition that the vertical part of the wire it carries shall be near the\\nA1\\n\u00e2\u0096\u00a0m\\nFig. 107. Fig. 108.\\nprincipal axis of the lens. Keep the eye 20 or 30 cm. distant from\\nthis part of the wire, on a level with the centre of the lens and in line\\nwith the centre of the lens and the vertical part of the wire. Look\\nat this part of the wire so as to see it distinctly, and note whether\\nyou can see at the same time, near the wire, the image of the pencil-\\nmark on the farther block. If so, find out by moving the eye to the\\nright or left, as in Exercise 23, whether this image is more or less\\ndistant from the eye than the vertical wire is. Then move the block\\ncarrying the wire into such a position that the image and the wire\\nseem to keep close together when the eye is moved a considerable\\ndistance to the right or left. When this adjustment is made, put a\\ndot on the paper just beneath the vertical wire and mark this dot 3.\\nIt represents the image of object-point Xo. 3.\\nFind in a similar manner the image-points 1, 2, 4, 5, corresponding\\nto the object -points 1,2, 4, 5. The experimenter must take care not\\nto let any idea he may have as to the position where an image-point\\nought to be affect his judgment in deciding where it is.\\nAfter all the five image-points are found, connect them, No. 1 to\\nNo. 2, No. 2 to Xo. 3, etc., by means of straight lines, thus getting\\na rough representation of the whole image.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0158.jp2"}, "159": {"fulltext": "REFRACTION OF LIGHT. 145\\nDraw from each object-point toward the corresponding image-point\\na straight line as long as the ruler (No. 23), and note the point where\\n^hese lines cross each other.\\n142. Formation of the Image in Exercise 24. The for-\\nmation of the image-points in Exercise 24 is illustrated by\\nFig. 109. One ray from the object-point A follows a\\nsecondary axis 137) passing through the centre of the\\nlens, and its direction after leaving the lens is the same as\\nbefore entering it. (Its direction inside the lens is not\\nquite the same, but the figure does not show this.)\\nAnother ray from A runs parallel to the principal axis\\n137) before entering the lens, and will therefore pass\\nFig. 109.\\nthrough the principal focus, on the farther side of the\\nlens. The crossing of these two rays at A shows the posi-\\ntion of the image of A.\\nIn a similar way B\\\\ the image of i?, is located.\\n143. Size and Shape of Image. If a straight line is\\ndrawn from A to B in Fig. 109, we mav call this the\\nlength of the image, although the images of points between\\nA and B will not lie on this line. It is evident from Fig.\\n109, and also from the figure obtained in Exercise 21, that\\nthe distance A B is to the distance AB as the distance of\\nA B from the lens is to the distance of AB from the lens.\\nThe curved shape of the image obtained in Exercise\\n24, if the work has been correctly done, is due to the\\nfact that the ends of the object-arrow are farther from the\\nlens than the centre of the arrow, and to the further fact", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0159.jp2"}, "160": {"fulltext": "146 PHYSIOS.\\nthat the focal length along a secondary axis is less than the\\nfocal length along the principal axis. This latter fact can\\neasily be shown by direct experiment with either method\\nof Exercise 22.\\n144. Virtual Image Formed by a Lens. We see in\\nExercise 24 and in Fig. 109, where the object-point is\\nfarther from a lens than its principal focus is that the rays\\ngoing from this object-point to the lens are bent by the lens\\nin such a way that, after leaving it, they converge to a point\\nagain. We know, too, that if the object-point were placed\\nat the principal focus the rays going from it to the lens\\nwould emerge from the lens parallel to each other.\\nIt is not difficult to see that, if the object-point were\\nplaced letiueen the lens and its principal focus, the rays\\ngoing from it to the lens would be divergent still, after\\nleaving the lens, though less divergent than before entering\\nit. In the next Exercise we shall have a case of this kind.\\nEXERCISE 25,\\nVIRTUAL IMAGE FORMED BY A LENS.\\nApparatus: The same as for the preceding Exercise except that\\nthe sheet of paper need not be more than one half as long, and that\\nthe arrow upon it should be 4 cm. long and about 20 cm. distant from\\none end.\\nPlace the lens between the arrow and the nearer end of the sheet\\nof paper, at a distance from the arrow equal to about two-thirds of\\nits focal length, and in such a position that its principal axis extends\\nover the middle point of the arrow. Place the small block (No. 25)\\nwith vertical pencil-mark pointing straight down at the middle\\npoint, No, 3. of the arrow. Turn the vertical part of the wire on the\\nother block so that it will point up instead of down, and place this\\nblock some distance behind the other one.\\nHolding the eye 20 or 30 cm. from the lens, look through the lens\\nat the image of the vertical pencil-mark, and at the same time oxer\\nthe lens at the vertical part of the wire. Bring the wire into line\\nwith the image, and then by the usual test find which of them is the\\nmore distant. Move the wire back and forth until it coincides in", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0160.jp2"}, "161": {"fulltext": "REFRACTION OF LIGHT. 147\\nposition with the image. Then mark with a figure 3 the point just\\nunder the vertica lpart of the wire. This represents the image of\\nobject-point No. 3.\\nIn a similar manner locate the images of points 1, 2, 4, and 5.\\nConnect the image- points by straight lines, from 1 to 2, from 2 to\\n3, etc.. thus forming an image of the arrow.\\nDraw a straight line from each image point to its corresponding\\nobject-point, and note where these lines will cross each other if con-\\ntinued.\\n145, Formation of the Image in Exercise 25. The\\nimages observed in Exercise 25 were virtual images. They\\ncould not be shown tipon a screen, and were not formed by\\nthe actual crossing of light rays. Fig, 110 will serve to\\nillustrate the way in which virtual image-points are formed.\\nLet AB be the object, placed between the lens LL and\\nthe principal focus F\\\\ To find the position of the virtual\\nimage of the point A, draw ^[/parallel tc the principal axis\\nof the lens, This ray will, after leaving the lens, pass\\ntoward F, the principal focus on the farther side, and so\\nwill appear to have come along the path 31 F.\\nDraw another ray, AC\\\\ passing through the centre of the\\nlens This ray will, after leaving the lens, have the same\\ndirection as before entering it, and will be represented by\\nthe line CiV If, then, we carry back the line CiVtill it\\ncrosses the line MF, also carried backward, the point A\\\\\\nwhere the crossing occurs, is a point from which both of\\nthe rays appear to come. A is, then, the virtual image\\nof A.\\nBy a similar process B is found to be the virtual image\\nof B.\\nP\\\\ the image of the point P, is here represented as lying\\nin the straight line between A and B It is usually so\\nThe dotted lines drawn from M and N to F in Fig 110 are not\\nintended to show the actual course of the rays within the eye.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0161.jp2"}, "162": {"fulltext": "148 PHYSICS.\\nrepresented in books. Exercise 25 shows that it does not\\nlie there,\\nThe image A B is evidently larger than the object AB.\\nWhenever a virtual image is forced by a convex lens, this\\nimage appears, to an eye placed in any ordinary position on\\nthe other side of the lens, larger than the real object would\\nA\\ni\\nFig. 110.\\nlook if held at a comfortable seeing-distance from the eye.\\nHence the name magnifying-glass^ so commonly given to a\\nlens used as in Fig. 110.\\n146. Application of Formula. The formula used in\\n140 to express the relation betweeen focal length, object-\\ndistance, and image-distance in the case of real images, can\\nbe adapted to use with virtual images by merely changing\\nthe sign of one term, so as to make\\ni A A\\nTo illustrate the use of this formula it will be well to\\nmeasure the distance from lens to object-point 3, and from\\nlens to image-point 3, in the diagram made in Exercise 25,\\nand try them in the formula, with the known value of F,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0162.jp2"}, "163": {"fulltext": "REFRACTION OF LIGHT. 149\\n147. Spherical Aberration in Lenses. All the rays going\\nfrom a point to a lens A do not, after passing through\\nthe lens, converge to a single point 7. Those which go\\nthrough the lens near its margin converge to a nearer point\\nJ\\\\ This imperfection of a lens is called spherical aberra-\\ntion.\\nWhen a very clear-cut image is needed, it is customary\\nto put a stop in front of the lens; that is, a thin metal\\nplate with a hole which permits only those rays to pass\\nwhich are near the principal axis of the lens.\\nLenses can be so constructed, with surfaces not quite\\nspherical, as to do away with this defect in great part, for\\nlight of any one color, but such lenses are difficult to make\\nand are uncommon except in large telescopes.\\n148. Chromatic Aberration in Lenses. Ordinary lenses,\\nmade of a single piece of glass, give rise to colored fringes\\nor borders about the images which they produce. The\\ncause for this defect, which is called chromatic aberration,\\nis this, that the objects looked at send more than one kind\\nof light to the lens and that rays of different colors are\\nnot refracted equally by the lens, and so do not come to a\\nfocus equally near the lens.\\nBut little trouble from this source is experienced in the\\nuse of lenses of slight convexity, whose images are not to be\\nfurther magnified; as, for instance, in spectacles and ordi-\\nnary magnify ing-glasses. Stopping out the greater", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0163.jp2"}, "164": {"fulltext": "150 PHYSICS.\\nportion of the surface of a lens with a circular diaphragm,\\nwhich allows light to pass only through a small portion of\\nthe lens near its centre, improves its performance greatly.\\nHow much help such diaphragms give by reducing spherical\\nand chromatic aberration, may be learned by taking out\\nsome or all of the diaphragms of an ordinary cheap spy-\\nglass, and then looking with it at distant objects in bright\\nsunlight.\\n149. Achromatic Lenses.\u00e2\u0080\u0094 Fortunately for the manufac-\\nturers and users of optical instruments, it is possible to\\nmake an achromatic lens, or one, at any rate,\\nwhich is practically achromatic. This is usually\\n|b accomplished by uniting into one lens two sepa-\\nrate lenses,* one, A, of flint-glass, and the other,\\nB, of crown-glass, as shown in Fig. 112. A con-\\nvex lens made in this way has, on the whole, a\\nconverging effect on parallel rays, while at the\\nsame time the superior dispersive power 134) of\\nthe flint-glass enables the lens A, though of less\\nfig. 112. refractive power than the lens i?, just to coun-\\nteract the dispersive tendency of the latter. Many of the\\nlenses used in optical instruments of the best quality are\\nachromatic. Eye-pieces 164), however, of the ordinary\\npattern do not require achromatic lenses.\\nA large lens practically free from spherical and chromatic\\naberration is a marvel of skillful and patient work. Grlass\\nsuitable for making a large lens of the best quality is very\\ndifficult to procure, as a very slight flaw or unevenness of\\nquality may spoil a large block. The shaping and polish-\\ning and testing of the largest lenses, after the proper kind\\nof glass is obtained, is a work of years, and men who are\\nSometimes more than two pieces are employed in making an\\nachromatic lens.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0164.jp2"}, "165": {"fulltext": "REFRACTION OF LIGHT. 151\\nskillful and patient enough to do it become known through-\\nout the world.\\nFor many years the largest and best lenses for great\\ntelescopes have been made by Alvan Clark and his two sons\\nof Cambridge, Massachusetts; but now all of these famous\\nmen are dead. The largest lenses ever made, 40 inches in\\nwidth, were placed in the great telescope of the Observa-\\ntory of Chicago University by the last of the Clarks a few\\nweeks before his death in 1897.\\nQUESTIONS AND PROBLEMS.\\n(1) An object is placed at a great distance from a converging lens\\nand on its principal axis.\\n(a) What changes of position will the image of this object undergo\\nwhile the object is moved along the principal axis up to the surface\\nof the lens\\n(b) In what part of this operation will the image be erect and in\\nwhat part inverted\\n(c) In what part will it be real and in what part virtual\\n(2) In Exercise 25 the .virtual image of a straight line was found\\nto be a curve. How should a line be curved with respect to the lens\\nin order to make its virtual image a straight line\\n(3) The focal length of a certain convex lens is 15 cm.\\n(a) How far from the lens will the image be if the object is 30\\ncm. from the lens\\n(b) How far if the object is 10 cm. from the lens\\n(4) An object is 40 cm. from a convex lens and the image equally\\nfar from the lens. What is the focal length of the lens\\n(5) If the object mentioned in problem 3 is 5 cm. long, how long\\nwill each of the images there mentioned be (In answering this\\nquestion disregard the curvature of the images.)\\n(6) A bright point, which is more distant from a converging lens\\nthan its principal focus is, sends white light to the lens. Which falls\\nnearer the lens, the red image of the point or the blue image Why\\n(7) What would be the answer to the questions in (6) if the point\\nwere between the lens and its principal focus?", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0165.jp2"}, "166": {"fulltext": "CHAPTEE XI.\\nTHE EYE: SIGHT AND COLOR.\\n150. Parts of the Eye. The eye as an optical instru-\\nment consists of a liquid lens A (Fig.\\n113) called the aqueous humor, a solid\\nlens, B, called the crystalline lens, a\\ntransparent jelly-like mass 0, called\\nthe vitreous humor, and a screen rr,\\ncalled the retina, upon which the\\nimage of the object looked at falls.\\nThe aperture at the back of the\\nFlG 118 eye is occupied by the optic nerve\\nleading from the retina to the brain.\\n151. Accommodation. Muscles attached to the lens B\\nhave power to change its form to some extent, thus adapt-\\ning the eye to see distinctly near or distant objects at will.\\nThis is called the power of accommodation.\\nA normal eye, that is, an eye approved by physicians, has\\nsuch shape as to give upon the retina distinct images of\\nvery distant objects without effort. In accommodating\\nitself to see nearer objects such an eye has to make an effort,\\nwhich grows greater as the distance lessens, but does not\\nbecome painful until the object looked at is less than eight\\nor ten inches from the eye.\\n152. Far-sight and Near-sight. Some eyes lack the\\npower of accommodation for near objects, and are called\\nfar-sighted, or long-sighted, although they cannot see dis-\\ntant objects any better than normal eyes can.\\n152", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0166.jp2"}, "167": {"fulltext": "THE EYE: SIGHT AND COLOR. 153\\nSome eyes are slightly egg-shaped, the retina being\\nfarther back than in normal eyes. These eyes are called\\nnear-sighted, or short-sighted, because they are well adapted\\nfor seeing near objects, while they cannot see distant objects\\ndistinctly.\\nFor some purposes near-sighted eyes have a certain\\nadvantage over normal eyes, for they enable their possessor\\nto hold an object very near, when there is need, and so\\nmake it look larger than it would look to the normal eye.\\n153. Eye-glasses. Ear-sighted eyes must wear convex\\nlenses to help them converge the rays from a near object to\\nan image upon the retina. Near-sighted eyes must wear\\nconcave lenses to prevent the rays sent by a distant object\\nfrom coming to an image in front of the retina.\\nThe Perception of Color.\\n154. The Color-sense. In the retina are found the ends\\nof the nerves through which we get the sensation of light\\nand of color.\\nAlthough the eye can distinguish scores of different tints,\\nit is believed that the sets of nerves operating in the percep-\\ntion of colors are very few, probably not more than three\\nor four. Each set of nerves is supposed to give one peculiar\\ncolor sensation and only one but the combination of these\\nfew primary color sensations in various proportions is sup-\\nposed to give all the other color sensations.\\nIt is very generally believed that the primary color sensa-\\ntions are three red, green, and violet.\\n155. Mixing Color Impressions. The most convenient\\nway to find the effect of mixing color sensations is to place\\nvariously colored pieces of paper on some body which can\\nbe made to spin rapidly before the observer s eyes. Tops\\nor other whirling apparatus No. XXXV, for example, can", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0167.jp2"}, "168": {"fulltext": "154 PHYSICS.\\nbe used for this purpose, and indeed the whole outfit for\\nthis kind of experimentation is now readily obtained.\\nEXPERIMENT.\\nPlace a red paper, a green paper, and a violet paper upon a whirl-\\ning apparatus, and so vary the proportions of the visible parts of\\nthese papers that when rapidly whirled before the eye they will\\nproduce the effect of gray. (In the study of color all shades of gray,\\nfrom brilliant white to dead black, must be classed together as white,\\nthe difference between them being merely a difference of brightness.)\\n156. Complementary Colors. It has already been shown\\nthat ordinary white light is composed of many different\\ncolors, ranging from red to violet, but it is not necessary to\\nput together all of these colors in order to get the sensation\\nof white. There are many pairs of colors, any one pair of\\nwhich will give the sensation of white when its elements\\nare mixed in the right proportions. The two colors making\\nsuch a pair are called complementary to each other. Thus,\\naccording to Eood,\\nred is complementary to green-blue,\\norange cyan-blue (between blue-green\\nand blue),\\nyellow ultramarine-blue,\\ngreenish-yellow violet,\\ngreen te purple.\\nEXPERIMENT.\\nPlace blue and yellow disks upon the whirling apparatus, and so\\nproportion the visible parts that when revolving rapidly they will\\nproduce the effect of gray.\\nTry the same experiment with other pairs of complementary\\ncolors.\\n157. Fatigue of the Retina. If one looks steadily for a\\nshort time at some strongly colored object held against a\\nbackground of gray or white, that spot of the retina upon\\nwhich the image of the colored object falls loses in part, for", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0168.jp2"}, "169": {"fulltext": "THE EYE: SIGHT AND CO LOB. 155\\nthe time being, the power of giving the particular color\\nsensation which it is furnishing, while its power of giving\\nother color sensations may remain as great as ever. This\\ntemporary loss of power is called fatigue of the retina, and\\nit may give rise to curious effects.\\nEXPERIMENT.\\nHold a piece of bright green paper against a white background,\\nand look very steadily at one spot on this paper for thirty seconds.\\nThen look steadily at some one spot of the white surface for a few\\nseconds and note any peculiar color effect that is observed. The\\ncolor complementary to green will probably appear as a patch upon\\nthe white, the shape of this patch being exactly like that of the\\ngreen paper.\\nTry the same experiment with other colors.\\n158. After-images. The effects observed in the follow-\\ning experiment are still more curious than those of 157.\\nEXPERIMENT.\\nLook steadily for half a minute at some particular spot on a win-\\ndow haying the sky as a background. Then close the eyes and wait\\na few seconds for the figure on the window to show out against the\\ndarkness. Watch the changes of color the figure undergoes. Ob-\\nserye that details appear in this persisting image which were not\\nnoticed while the eyes were open.\\n11 After-images like the one here mentioned, cannot be\\nthe work of memory. They must be due to some change\\nof state in the retina, some real impression made there,\\nwhich lasts for a considerable time but gradually passes\\naway.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0169.jp2"}, "170": {"fulltext": "CHAPTER XII.\\nOPTICAL INSTRUMENTS.\\n159. Importance of Optical Instruments. Much of the\\nprogress of science during the nineteenth century has been\\ndue to improvements in the construction of optical instru-\\nments and their more general use in scientific investigations.\\nImprovements in telescopes and the invention and per-\\nfection of the spectroscope have enabled the astronomer to\\ndiscover, and even to measure, objects and motions whose\\nexistence was unsuspected by the observers of two genera-\\ntions ago. The chemist is to-day able by means of the\\nspectroscope to ascertain in a few minutes the presence, in\\na substance of unknown composition, of elements which it\\nwould have taken him days to detect by purely chemical\\nmeans.\\nTo the physician, the food-analyst, the manufacturing\\ndruggist, and to those engaged in many other professional\\nor technical occupations, the microscope is a necessary piece\\nof apparatus, a tool of daily, almost hourly, use.\\nOptical instruments comprise a great variety of combina-\\ntions of mirrors, lenses, and prisms. Only some of the\\nsimpler ones can be referred to in an elementary book on\\nphysics.\\n160. The Photographer s Camera. This instrument\\nconsists essentially of a box, in the front of which is fastened\\na convex lens or a combination of lenses, L (Fig. 114), the\\ndistance of which from a ground-glass screen, P, at the\\n156", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0170.jp2"}, "171": {"fulltext": "OPTICAL INSTRUMENTS.\\n157\\nother end of the box. may be varied at will. An inverted\\nand usually diminished real image of any o.itside object not\\ntoo near L may be formed on P. When this adjustment\\nlias been precisely made, the lenses are covered with an\\nopaque cap; a plate of ordinary glass, coated with a film of\\ngelatine made sensitive to light by the presence in it of cer-\\ntain compounds, usually of silver, is substituted for P; the\\ncap is then- removed, and the light is allowed to act for a\\nA\\np\\nL\\n\\\\J\\nFig. 114.\\nsufficient time upon the sensitive plate, after which the cap\\nis replaced and the plate removed and developed into a\\nphotographic t; negative/*\\nThose who are interested in practical photography will\\nfind in Exercise *24 some explanation of the difficulty ex-\\nperienced in making all parts of the ground-glass screen\\nshow clear images at the same time; and in 1-47 there is\\na suggestion as to the effect of diaphragms with larger\\nor smaller holes.\\n161. The Magic-lantern. This instrument, known also\\nby various other names, stereapticon, for instance, requires\\na powerful source of light, such as a large kerosene-flame,\\nor some form of calcium-light A (Fig. 115), in which a\\ncylinder of quicklime is heated by a flame formed by burn-\\ning together oxygen ami coal-gas, or. bust of all. the electric\\narc-light. By means of a large lens B (Kg. 115), called", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0171.jp2"}, "172": {"fulltext": "158\\nPHYSICS.\\nthe condenser, a powerful beam of light from this source\\nis thrown upon the painted or photographed slide, the\\nFig. 115.\\nimage of which is to be exhibited. This slide is pushed\\ninto the opening (7, a little outside the focus of a smaller\\nconvex lens or a pair of such lenses, D, and a greatly\\nenlarged real image of the slide is thrown upon the screen.\\nThe throwing of large images upon a screen is called pro-\\njection of these images and apparatus used for this purpose\\nis called projecting apparatus.\\n162. Projecting a Spectrum. A kind of spectrum has\\nbeen shown in the experiment of 89, but a better disper-\\nsion of the colors can be obtained by means of some device\\nlike that described in the following experiment. If sunlight\\nis not available, the stereopticon, if provided with a calcium\\nlight or an electric arc-light, can be successfully used, the\\nprism being placed in the path of the rays after they have\\ntraversed the projecting lens.\\nEXPERIMENT.\\nBy means of a porte-lumiere (No. XXX throw a beam of sunlight\\nthrough a narrow slit at S, Fig. 116. Place a lens, L, in the path of\\nthe beam, and adjust it so as to throw a distinct image of the slit\\non a screen at I. Now introduce a prism, P (2s o. XXXII), in the", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0172.jp2"}, "173": {"fulltext": "OPTICAL INSTRUMENTS. 159\\nposition shown in the figure, and then place the screen at RR\\nmaking the distance PR equal to PI The prism used may be of\\nflint-glass, or, better, may be hollow and filled with the highly dis-\\npersive liquid bisulphide of carbon.\\nExamine the spot of colored light on the screen. (1) How many\\ncolors can be distinctly seen (2) Do they blend, or are they sharply\\nFig. 116.\\nseparated from each other? (3) Which color is most refracted?\\nleast refracted? Try the effect of passing the emergent pencil\\nthrough a second prism similar to the first, and placed so as to re-\\nfract the light in the same direction as the first.\\nTry the effect with a second prism so placed as to refract in the\\nopposite direction from the first.\\n163. The Simple Microscope. In its least complicated\\nform the simple microscope, or magnify] ng-glass, consists\\nof a convex lens used, as explained in 145, to form an\\nupright magnified image of any small object. When much\\nmagnifying-power is required, two or even three convex\\nlenses, mounted one over the other with their surfaces only\\na few millimeters apart, are often used. Such combinations\\nare called doublets or triplets, according to the number of\\nlenses composing them. They have certain advantages over\\nsingle lenses of equal magnifying-power.\\nThe discussion in 145 will helj) the student to see that\\nthe magnifying-power of a simple microscope is greater as\\nits focal length is less.\\n164. The Compound Microscope, For viewing objects\\nunder any but the lowest magnifying-powers, that is, in all", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0173.jp2"}, "174": {"fulltext": "160\\nPHYSICS.\\ncases wher^ the apparent diameter of the image is to be\\nanywhere from 50 to 5000 times the actual diameter of the\\nobject, the compound microscope is employed. The essen-\\ntial optical parts of this instrument, as usually constructed,\\nare (see Fig. 117), an eye-piece, LL\\\\ here represented as\\nsingle, but generally consisting of two convex lenses, and\\nan objective, 11, frequently consisting of from two to six\\npieces. These lenses are fixed in a brass tube so arranged\\nthat the distance between the eye-piece and the objective\\ncan be varied at will, within certain limits. A mirror, not\\nhere shown, which is adjustable to any desired angle, is\\nasually employed for throwing light upon the object.\\nThe object to be viewed is placed on a platform beneath", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0174.jp2"}, "175": {"fulltext": "OPTICAL INSTRUMENTS. 161\\nthe objective, and is strongly illuminated by light reflected\\nfrom the mirror. A real, inverted, magnified image, A x B l9\\nof the object is formed within the tube of the instrument\\nat a position somewhat nearer to the eye-piece than its\\nprincipal focus. This real image is therefore magnified by\\nthe eye-piece, which forms an enlarged virtual image, A B\\\\\\nof it at a position not far from the object.\\nThe foci of the object-glass are at/ and/ those of the\\neye-piece at F and F.\\nThe total magnifying -power of the instrument is that of\\nthe objective multiplied by that of the eye-piece. In\\ngeneral, the shorter the focal length (see Appendix I) of a\\nmicroscope objective, the greater its magnifying-power.\\nAn objective of one inch focal length will, on a tube 10\\ninches long, give, with the lowest power eye-piece in com-\\nmon use (the A eye-piece), a magnification of about 50\\ndiameters; with an eye-piece of double the magnifying-\\npower B eye-piece) the total magnification will be\\nabout 100 diameters, and so on.\\nEXPERIMENT.\\nFasten a page of fine print, P in Fig. 118, upright on a table in a\\ngood light. Set up in front of it a short-focus convex lens, L, at a\\ndistance from the page somewhat greater than the focal length.\\nIf\\nFig. 118.\\nHold another short-focus convex lens, L\\\\ in various positions farther\\nfrom the page until one position is found in which an eye close to L\\nsees through it an inverted, magnified image of the print, this being\\na virtual image of the real image formed by the lens L. This appa-\\nratus is a rude model of the compound microscope.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0175.jp2"}, "176": {"fulltext": "162\\nPHYSIOS.\\n165. The Astronomical Refracting Telescope. This in-\\nstrument consists essentially of the long-focns object-glass,\\nor objective, L (Fig. 119), mounted in one end of a tube, at\\nFig. 119.\\nthe other end of which is placed an eye-piece, L\\\\ precisely\\nsimilar to that of the compound microscope. The eye-\\npiece can be moved toward or away from the object-glass\\nin order to make the image appear most distinct.\\nThe real image of any distant object is, of course, always\\nformed by the objective very near its principal focus. The\\nfoci of the eye-piece are at i^and F\\nAstronomical telescopes are always furnished with achro-\\nmatic object-glasses 149).\\nEXPERIMENT.\\nMount upon blocks two convex lenses, one of 30 or 40 cm. focal\\nlength, the other of about o cm. focal length. Set them up on the\\ntable with their principal axes coincident\u00e2\u0080\u0094 that is, with their centres\\non the same straight line at right angles to the centres of their faces.\\nMount a bit of tracing-paper or greased writing-paper, and place\\nthis screen in such a position between the lenses that the one of\\ngreatest focal length shall throw upon it a distinct image of some\\ndistant bright object. Look at this image on the translucent paper\\nthrough the 5-cm. lens Choose such a position and distance as to\\ngive a clea- virtual image, as much magnified as possible, of the\\nreal image on the screen. Now remove the screen, and observe that\\nthe virtual image of the real image is still visible.\\n166. Efficiency of the Telescope. The usefulness of the\\ntelescope as an aid to vision depends upon the following", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0176.jp2"}, "177": {"fulltext": "QUESTIONS AXD PROBLEMS. 163\\npoints: (a) the clearness and sharpness of the image, or\\nwhat is called the definition of the instrument; (b) the\\nbrilliancy of the image; (c) the amount of allowable mag-\\nnification.\\nGood definition depends upon the accuracy with which\\nthe leas is shaped and finished, and upon the quality of the\\nglass, which should be free from flaws.\\nBrightness depends upon the amount of light which can\\nbe concentrated in the different parts of the image. Hence\\na large objective will, other things being equal, give the\\nbest illumination. In some recent telescopes the objective\\nhas a diameter of 3 feet or more.\\nThe magnification, with a given eye-piece, is evidently\\nvery nearly proportional to the focal length of the objec-\\ntive; but unless the objective is large, and furnishes much\\nlight, it is useless to give it great focal length, for the\\nreason that the much-magnified image would be too faint\\nto be seen to advantage.\\nQUESTIONS AND PROBLEMS.\\n(1) How could you find the weight of a body that will float, if you\\nhad no balance but had a vessel filled with water and a graduated\\nglass flask that is, a flask with marks upon it showing the number\\nof cu. cm. required to fill it to certain depths\\n(2) If a liter of hydrogen weighs .0896 gin. and if the sp. gr. of\\noxygen as compared with hydrogen is 16, what is the weight of 1\\ncu. m. of oxygen\\n(3) A certain volume of mercury of density 13.6 weighs 216 gm.,\\nand the same volume of another liquid weighs 14.8 gin. Find the\\ndensity of the second liquid.\\n(4) A piece of iron weighs 200 lbs. in air and 172.5 lbs. in water.\\nHow great is its sp. gr.\\n(5) A given body weighs 500 gm. in air and 400 gm. in water.\\n(a) How great is its volume\\n(b) How great is its sp. gr.\\n(6) A board 12 X 6 X 1 in. weighs 1.5 lbs. What is its density in\\nlbs. per cu. ft.?", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0177.jp2"}, "178": {"fulltext": "164 PHYSICS.\\n(7) A cubical block of wood 15 cm. along the edge weighs 1125\\ngm. What is its density\\n(8) A 30 cu. cm. body weighs 10 gm. in water. How great is its\\nsp. gr.\\n(9) What is the volume of a body which weighs 25 gm. in air and\\n20 gm. in water\\n(10) A body weighs 180 lbs. in water and 120 lbs. in a liquid that\\nis 1.8 times as dense as water. Find the volume and the sp. gr. of\\nthe body\\n(11) How much will a kgm. weight of sp. gr. 7 weigh in a liquid\\nwhich is 0.8 as dense as water\\n(12) A cubical box, 3 ft. square on a side, made of 2 in. plank of\\nsp. gr. 0.5, has a bottom but no top. It contains a body weighing\\n100 lbs. To what depth will this box sink, upright, in water\\nAns. 6.7 in. nearly.\\n(13) The sp. gr. of air, as compared with water, is about .00129 at\\n0\u00c2\u00b0 C. under ordinary atmospheric pressure. How many grams\\nwould equal the buoyant force exerted by air in this condition upon\\na cu. m. of any substance?\\n(14) If the sp. gr. of a certain block is 0.3 and its volume 100 cu.\\ncm. how much of it would be submerged if it were floating in a\\nliquid of sp. gr. 2.\\n(15) A rod floats one-half submerged in a liquid of sp. gr. 0.9.\\nHow much of it would be submerged in a liquid of sp. gr. 3?\\n(16) There is a uniform rod 6 ft. long and 4 in. square, of sp. gr.\\n0.5. What must be the sp. gr. of a cubical piece of metal 4 in. on\\nthe edge which, when attached to the rod, would just hold it sub-\\nmerged in water\\n(17) If a diver with his suit weighs 200 lbs. and it takes of a\\ncu. ft. of lead, sp. gr. 11.4, to keep him submerged in fresh water,\\nhow many cu. ft. of water does he, in his suit, displace?\\n(18) Two boys are pulling at a rope in opposite directions, each\\nwith a force of 25 lbs.\\n(a) How great is the tension on the rope?\\n(b) How great would you call the tension if the rope were tied to a\\nbeam and supported a weight of 25 lbs.\\n(19) A uniform beam, 12 ft. long and weighing 300 lbs., rests,\\nhorizontal, on a fulcrum 2 ft. from one end. How much weight\\nmust be applied at this end to make the beam balance in its present\\nposition\\n(20) (a) Find the direction, position, and magnitude of the equil-", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0178.jp2"}, "179": {"fulltext": "QUESTIONS AND PROBLEMS. 165\\nibrant 74) of two forces, parallel and in the same direction, one of\\nwhich is 10 lbs. and the other 12 lbs., their lines of action being 3 ft.\\napart.\\n(b) Find the direction, position, and magnitude of the resultant\\n75) of the same two forces.\\n(21) One end of a horizontal beam 20 ft. long and weighing 50 lbs.\\nrests upon a wall, and the other end is supported by a rope that will\\nbear only 85 lbs. A boy weighing 100 lbs. walks slowly along the\\nbeam from the wall toward the rope. How far from the rope will\\nthe boy be when it breaks\\n(22) A hammer is use! to draw out a nail from a board. The\\nhead of the hammer rests against the board at a distance of 3 in.\\nfrom the nail. A force of 50 lbs. is applied at right angles with the\\nhandle at a point 12 inches from the boar^l. How great is the force\\nexerted by the hammer on the nail (This case is similar in principle\\nto some of those discussed in connection with the pulley. See Ex-\\nperiments under 58.)\\n(23) If a force of 50 lbs. is applied at the end of the handle of a\\njack-screw 18 in. from the centre of the screw, and if one revolu-\\ntion of this screw lifts a weight 0.5 in., how great is this weight,\\nif there is no frict.on\\n(24) A sled weighing with its load 50 lbs. rests on the side of a\\nhill rising 1 ft. in a distance of 5 ft. along the incline.\\n(a) How great a force acting parallel to the incline is needed to\\nkeep the sled from sliding downward if there is no friction\\n(b) If the crust on the snow is just strong enough to bear the sled\\nunder these conditions, how much would the load on the sled have\\nto be lightened in order that a similar crust might bear the sled on a\\nlevel\\n(25) An inclined plane rising at an angle of 45\u00c2\u00b0 has a load of 50\\nlbs. resting upon it. How large a horizontal force will be needed to\\nkeep this load moving up the incline if there is no friction\\n(26) A horizontal force of 10 lbs. is required to keep a certain body\\nmoving along a horizontal surface with which its coefficient of fric-\\ntion is 0.2. How great is the weight of the body\\n(27) A mass of 100 lbs. rests upon an inclined plane 10 ft. long and\\n4 ft. high.\\n(a) How great must be the resistance of friction to keep the body\\nfrom sliding down the incline\\n(b) How great must the coefficient of friction be\\n(28) If a simple pendulum 1 m. long vibrates 58 times a minute,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0179.jp2"}, "180": {"fulltext": "166 PHYSICS.\\nwhat is the length, of a simple pendulum that vibrates 116 times in\\na second\\n(29) The length of a simple pendulum vibrating once a f econd in\\nthe latitude of New York is about 39.1 in. How many seconds a\\nday would a clock lose if controlled by a simple pendu um 40 in. long\\n(30) Two lights, A and B, are placed 20 ft. apart. The power of A\\nis to that of B as 4 to 9. At what point between them must a screen\\nbe placed in order to be equally lighted up on both sides\\n(31) The distance of the planet Neptune from the sun being\\n2,800,000,000 miles, nearly, how long does it take a wave of light to\\ngo from the sun to Neptune\\n(32) What is the height of a tree which casts a shadow 100 ft. long,\\nwhen an upright rod 5 ft. tall casts a shadow 7 ft. long\\n(33) The image of an upright stake 8 ft. tall, and 10 ft. from a\\nwindow-shutter appears on a screen 4 ft. beyond the shutter. The\\naperture in the shutter through which the light passes from the stake\\nto the screen is very small. How great is the length of the image\\n(34) The clock on a wall indicates 9.30. What time will it appear\\nto indicate if the observer sees the reflection of the clock in a\\nmirror on the opposite wall but does not distinguish the numerals\\n(35) A plane mirror lies up m a table and a pencil 6 in. tall stands\\nupright on one edge of the mirror. How wide must the mirror be\\nin order that a person whose eyes are 5 in. above its surface and 20\\nin. distant from the pencil may just see the whole length of the\\npencil reflected in the mirror (To be solved by drawing and meas-\\nuring. The thickness of the glass is to be neglected.\\n(36) Prove that if an object is placed in front of a plane mirror and\\nthe mirror is moved either toward or from the object, without turning,\\nthe image will move twice as far as the mirror.\\n(37) Prove that if a candle is placed in front of a vertical plane\\nmirror and the mirror is turned 45\u00c2\u00b0 about a vertical axis, the image\\nof the candle will move through an arc of 90\u00c2\u00b0 around the axis of\\nthe mirror.\\n(38) Two plane mirrors, A and B, are placed 12 cm. apart, facing\\neach other and parallel. A small object is placed between them 4 cm.\\ndistant from A. Calculate the distance from A to the first and\\nsecond images seen in it. Do the same for B.\\n(39) Two plane mirrors, placed vertical, make with each other an\\nangle of 60\u00c2\u00b0. A candle is placed between them, but nearer one than\\nthe other. Draw a figure showing the positions of the various images\\nof the candle.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0180.jp2"}, "181": {"fulltext": "QUESTIONS AND PROBLEMS. 167\\n(40) If the radius of curvature of a concave spherical mirror is 50\\ncm., and if a candle is placed 40 cm. distant from the mirror,\\n(a) How far from the mirror will the image of the candle be\\n(b) Will this image be real or virtual\\n(c) Will it be erect or inverted\\n(d) If the candle-flame is 2 cm. long, what will be the length of its\\nimage\\n(41) If the candle mentioned in the preceding problem was 10 cm.\\nfrom the mirror, what would be the answers to the questions there\\nstated\\n(42) What would be the answers in problems 40 and 41 if the\\nmirror were convex\\n(43) Have you ever seen curved mirrors used except in a class-room\\nor laboratory? If so, for what purposes were they used?\\n(44) Define the term index of refraction.\\n(45) The index of refraction of the earth s atmosphere is little greater\\nthan 1 with respect to the space outside this atmosphere. Does this\\nfact delay, or does it hasten, the first glimpse of the rising sun\\n(46) For which of the colors here named is the index of refraction\\nof glass the greatest red, green, yellow, blue For which of them\\nis it least\\n(47) How could you find by experiment the color complementary to\\nany given tint\\n(48) Show that the image formed by a convex lens may be either\\nlarger or smaller than the object.\\n(49) Prove algebraically, and also graphically (after the manner of\\n142), that when thy distance of an object from a convex lens is\\ntwice the focal length, the image is at the same distance on the other\\nside.\\n(50) A rod 5 cm. long held in front of a convex lens, at right angles\\nwith the principal axis, has an image 25 cm. long upon a screen dis-\\ntant 100 cm. from the lens. How great is the focal length of the\\nlens?\\n(51) An object 4 cm. long, placed 20 cm. from a certain lens and\\nat right angles with the principal axis, has a real image 10 cm. dis-\\ntant from the lens. If the same object were placed 5 cm. distant\\nfrom the same lens,\\n(a) Would the image be real or virtual\\n(b) How far from the lens would the image be\\n(c) How great would the length of the image be", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0181.jp2"}, "182": {"fulltext": "APPENDIX I.\\nFOCAL LENGTH, ETC., OF LENSES AND COMBINATIONS OF\\nLENSES.\\nIt is customary to define the focal length, F y of a single lens as the\\ndistance from the focus to the nearest point of the surface of the lens,\\nand in the formula -f- to consider D and Di as measured\\nJo JJo JJ\\\\\\nfrom the object and image, respectively, to the nearest point of the\\nlens. With this interpretation of the letters, the formula is not ex-\\nactly fulfilled by any actual lens. It holds strictly true only for the\\nideal case of a lens of zero thickness, but it is sufficiently near the\\ntruth for common purposes in the case of ordinary lenses. The for-\\nmula is about equally accurate, for a4ouble convex lens, at least, when\\nall the distances, F, D and Di, are measured to the optical centre of\\nthe lens 137).\\nWhen a combination of lenses is used, as in a microscope-objective\\nor a photographic camera, a formula similar to that just given can be\\napplied, but the F, D and Di occurring in it are not now measured\\neither to the nearest point of the combination or to the optical centre.\\nThey are measured to certain other points determined by the radii of\\ncurvature, thickness, and refractive index of each lens, and the dis-\\ntance between the two lenses. In the ordinary use of such a combi-\\nnation, its magnifying power is substantially equivalent to that of a\\nsingle ideal thin lens having a focal length equal to what is called\\nthe focal length of the combination. The calculation of the focal\\nlength of the combination is frequently very laborious.\\nDealers in photogiaphic objectives very frequently state as the\\nfocal length of a combination of lenses the distance from the principal\\nfocus to the near, r surface of the nearest lens. They sometimes call\\nthis the back focal length, or, rather, the back focus of the coni-\\n168", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0182.jp2"}, "183": {"fulltext": "APPENDIX I.\\n169\\nbination. It is a convenient quantity to use in the description of a lens,\\nbut it is not intended for use in the formula 4- -=r\\nF D G Z i\\nThe term equivalent focal length/ or equivalent focus, is\\nsometimes applied, in the case of a combination of two equal lenses,\\nto the distance from the principal focus to a point midway be-\\ntween the two lenses.\\nAPPENDIX II.\\nINDICES OF REFRACTION OF VARIOUS SUBSTANCES\\nCOMPARED WITH A VACUUM. (See 128.)\\nAgate 1.540\\nCanada balsam 1.53\\nDiamond 2.5\\nFluor spar 1.434\\nGlass (ordinary crown). 1.53\\nflint)... 1.61*\\nIce 1.31\\nQuartz 1.544\\nRock salt 1.544\\nSelenium (crystals)\\n2.98\\nAlcohol 1.36\\nPetroleum (heavy) 1.45\\n(light) 1.4\\nWater 1.333\\nNitrogen 1.000298\\nOxygen 1.000371\\nThe dispersive power 134) of flint glass is nearly twice as great\\nas that of crown glass.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0183.jp2"}, "184": {"fulltext": "APPENDIX III.\\nAll the articles in the first list here given should be furnished to\\neach member of the laboratory section.\\nLIST OF ARTICLES REFERRED TO BY NUMBER IN THE\\nEXERCISES OF THIS BOOK.\\nNo. 1. A 10-cni. section of a meter-rod.\\nNo. 2. A meter-rod, marked on one side in feet and inches.\\nNo. 3. A 30- cm. bevel- edged measuring-stick, marked on one side\\nin inches.\\nNo. 4. A waterproofed wooden cylinder about 8 cm. long and 4.5\\ncm. in diameter, loaded internally with shot so that it will float\\nnearly submerged in water.\\nNo. 5. A brass can about 14 cm. tall and 7 cm. in diameter, having\\na slightly declining, straight, overflow-tube, about 6 cm. long and\\n0.8 cm. in internal diameter, extending from a point about 1.5 cm.,\\nclear, below the top of the can (see Fig. 6). To prevent dribbling\\nthe junction of tube and can should be covered, internalJy, with a\\ncoat of paraffin melted on.\\nNo. 6. A braes catch-bucket with a wire handle, capable of holding\\nabout 175 gm. of water, and weighing not more than 50 gm.\\nNo. 7. An 8-oz. spring-balance graduated to 0.5 oz. (There is now\\nin the market an improved balance, graduated on one side in 10-gm.\\n[Tni^iiiliinfiinjiinf 1\\nFig. 120.\\nintervals and on the other side in 0.25-oz. intervals. It is, moreover,\\nespecially adapted for use in the horizontal position. This improved\\nbalance is desirable for this course.)\\n170", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0184.jp2"}, "185": {"fulltext": "APPENDIX III 171\\nNo 8. A rectangular waterproofed block of wood, about 7 cm.\\nlong and 4.5 cm. square on the end, so loaded internally with shot\\nthat it will sink in water, but not enough to make it weigh more\\nthan 225 gm.\\nNo. 9. A rectangular waterproofed cherry block about 7.5 cm. X 7.5\\ncm. X 3.8 cm. This block should be smooth, and therefore the water-\\npr ioflng should be done by soaking it in very hot paraffin. For the\\nbest results this soaking should be done in a vacuum. Excess of\\nparaffin should be scraped off before the block is used.\\nNo. 10. A one-gallon glass jar of good quality. (It is poor economy\\nto buy a poor jar and have it break with a liquid in it.)\\nNo. 11. A lump of roll sulphur weighing about 175 or 200 gm.\\nIt is not worth while to cast these lumps into regular cylindrical\\nform.\\nNo. 12. A lead sinker with w r ire handle, weighing about 175 gm.\\nNo. 13. A waterproofed wooden cylinder about 1 cm. in diameter\\nand 20 cm. long. Doweling-rod, furnished by hardware dealers,\\nserves well when waterproofed.\\nNo. 14. A holder for keeping No. 13 upright in water. It consists\\nof a waterproofed wooden rod about 12 cm. long and 1.3 cm. square\\non the end, provided with a clasp for attaching it to the side of a jar,\\nand with two screw-eyes projecting from one side, the rings of which\\nare large enough to let the cylinder No. 13 slip easily through them,\\nbut not large enough to allow the cylinder to tip far from the vertical\\nposition (see Fig. 10).\\nNo. 15. A cylindrical glass jar, about 14 cm. tall and 10 cm. in\\ndiameter, with level top.\\nNo. 16. A broad-mouthed bottle with ground-glass stopper, stand-\\ning not much more than 11 cm. tall with stopper, and weighing,\\nwhen filled with water, about 175 or 200 gm.\\nNo. 17. A lever and supporting-bar. The lever is a 30-cm. section\\nfrom a meter-rod, pivoted upon the smoothed cylindrical body of a\\nbrass screw which is driven horizontally into the end of a bar of\\nhard wood about 25 cm. long, 5 cm. wide, and 3 cm. thick. A\\nbrass plate projecting from this bar and overhanging the middle of\\nthe lever prevents the lever from tipping far, while it allows suffi-\\ncient freedom of motion. The lever itself, except for a distance of\\n2 cm. each side of the middle, is cut away so that its top is level with\\nthe upper part of the hole through the centre. There should be a", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0185.jp2"}, "186": {"fulltext": "172 PHYSICS.\\nscrew-hole running downward through, the middle of the supporting-\\nbar, to facilitate in attaching it, as shown in Fig. 21.\\nNo. 18 (A and B). Two brass scale-pans about 6.5 cm. square,\\neach with its suspending threads weighing accurately 1 oz. (that is,\\nnot differing from this weight by more than .01 oz.). Each pan is\\nsuspended by four strong linen threads meeting in a knot about 20\\ncm. above the pan, two of them continuing in a loop about 4 cm.\\nlong above this knot. (Fig. 21.)\\nNo. 19. A set of iron weights, 8 oz 4 oz., 2 oz., and two 1 oz.\\nmaking a total of 16 oz. No weight should be in error more than\\n.01 oz.\\nNo. 20. A flat pine board about 50 cm. long and 15 cm. wide for\\nuse in the Exercises on Friction.\\nNo. 21. A cubical block of wood about 3.7 cm. on each edge. A\\ngroove about 1 cm. wide and 2 cm. deep extends through the lower\\npart of the block with the grain of the wood. An ordinary short\\nscrew extends through one side of the block into this groove, and\\nserves to fix the block in position upon a meter- rod. Across the grain\\nat the top of the block is a slot about 0.1 cm. wide and 0.5 cm. deep.\\n(Figs. 26 and 105.)\\nNo. 22. Two bits of wood, each about 8 cm. long and 1 cm. square\\non the end, for supporting the spring- balance in a horizontal position.\\n(Fig. 41.)\\nNo. 23. A plate-glass mirror about 15 cm. long, 3.8 cm. wide, and\\n0.2 cm. thick, the coating on the back protected by paint or varnish.\\nNo. 24 (A and B). Two straight- edged rulers of some wood that\\nwill keep its shape well white pine, for instance each about 30\\ncm. long, 5 cm. wide, and 1 cm. thick.\\nNo. 25. A block like No. 21, but without the large slot and the\\nscrew. One side of this block is coated with white paper, and a\\nvertical pencil-mark or ink-mark is made across the middle of this\\npaper. (Fig. 108.)\\nNo. 26. A Walter Smith school {rquare, or other equally good\\nprotractor.\\nNo. 27. A cylindrical mirror of nickel-plated brass, about 5 cm.\\ntall and 8 cm. wide, cut from seamless tubing 4 inches in diameter\\nand J inch thick, mounted upon a sem circular base-board of wood\\nof the proper radius of curvature. The base-board should be about\\n1.5 cm. thick.\\nNo. 28. A piece of plate-glass about 7 cm. square and 0.6 cm. thick,", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0186.jp2"}, "187": {"fulltext": "APPENDIX III. 178\\nfor Exercise 20 on Index of Refraction. Two opposite edges or narrow\\nsides of the glass should be ground tolerably plane and polished\\nsufficiently to allow seeing readily through the whole width of the\\nplate (see Fig. 89).\\nNo. 29. A brass partition made to fit the small glass jar (No. 15)\\nand to extend downward into the jar a distance equal to about one-\\nthird the diameter of the jar. It should be made of sheet brass\\nFig. 121.\\nabout .07 cm. thick, The method of shaping and adjusting the par-\\ntition is suggested by Fig. 121, where A shows a side view and B an\\nend view of the partition. The flanges shown in B are bent more or\\nless in adjusting the partition to fit the jar closely, but without too\\nmuch pressure.\\nNo. 30. An index of thin sheet brass made to clasp the side of the\\njar (No. 15). This index is a strip about 15 cm. long, before bending,\\nand 1 cm. wide, tapered to a point at one end. To enable it to clasp\\nthe jar, about 3 cm. at the untapered end is bent over. (See pb in\\nFig. 91.)\\nNo. 31. A circular (not elliptical) double-convex spectacle-lens,\\nhaving a focal length not less than 12 cm. and not more than 16 cm.\\nThe lens is mounted on a block similar to No. 21. (See Fig. 105.)\\nNo. 32. A white cardboard screen about 8 cm. square, of such\\nthickness as to be held firmly in the narrow slot of the small block\\nNo. 21. (Fig. 105.)\\nNo. 33. A small kerosene lamp of such size and shape as to fit it\\nfor the use shown in Fig. 106. The lower partof the chimney is sur-\\nrounded by a thin sheet of asbestos paper, having a hole 3 or 4 mm.\\nin diameter at the height of the flame.\\nNo. 34. A wire, of the right size to fit into the narrow slot of No.\\n21, bent at a right angle, one arm about 6 cm. long, the other about\\n4 cm, (Fig. 108.)", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0187.jp2"}, "188": {"fulltext": "174\\nPHYSICS.\\nARTICLES USED BY THE TEACHER, BUT NOT TO BE\\nFURNISHED TO STUDENTS.\\n(Most of them are referred to by number in the Experiments of\\nthis book.)\\nNo. I. A gauge for testing pressure at various points and in vari-\\nous directions in a jar of water. In Fig. 122, P is a pillar of wood or\\nmetal about 25 cm. tall G is a small glass thistle-tube about 1.7 cm.\\nwide m is a tbin rubber membrane fastened water-tigbt across the\\nmouth of C p and p are hard-rubber pulleys about 1.7 cm. in diam-\\neter, fitting closely on their axes r is a small rubber tube g is a\\nglass tube i is a short column of water serving as an index. A band\\nof strip-rubber, such as toy stores supply, connects the two pulleys p\\nand p, so that by turning a, the axis of the upper pulley, between the\\nthumb and finger, the gauge-face m may be turned upward, down-\\nward, or sidewise, without changing level. A student-lamp chimney,\\nwith stopper for one end, accompanies this gauge.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0188.jp2"}, "189": {"fulltext": "APPENDIX III 175\\nNo. II, Apparatus for bursting a bottle by an attempt to compress\\nwater within it.\\nThe essentials are a glass bottle, with a perforated rubber stopper\\nwhich fits the bottle well when driven in its full length a strong\\nframe for holding the bottle and keeping the stopper in place a rod,\\nwith convenient handle, to be driven water-tight down through the\\nhole in the stopper,\\nNo. III. Glass tube about 1 m. long, closed at one end, connected\\nby a strong rubber tube 25 cm. long with another glass tube 20 cm.\\nlong. .See Fig. 12.)\\nNo. IV. Strong thistle-tube (Fig. 13) about 2.5 cm. wide, covered at\\nthe mouth with strong sheet rubber and furnished with a thick-\\nwalled rubber tube about 20 cm. long.\\nNo. V. Small air-pump suitable for both exhaustion and compres-\\nsion.\\nSuch a pump is frequently sold without base, but it is well to have\\na base, bell-jar plate, and one or two bell-jars. For many purposes a\\nlarger pump is desirable.\\nNo. VI. Bent glass tube for Boyle s law, the whole tube about 1.5 m.\\nlong (Fig. 14).\\nNo. VII. Common large rubber foot-ball, with a rubber tube about\\n30 cm. long attached to the key. (Fig. 15.)\\nNo. VIII. Small bottle provided with rubber stopper fitted with\\ntwo glass tubes as in Fig. 16.\\nNo. IX. Glass model of lifting-pump (Fig. 17).\\nNo. X Glass model of force-pump (Fig. 18).\\nNo. XI. Hydrometer for liquids less dense than water.\\nNo. XII. Hydrometer for liquids more dense than water.\\nNo. XIII. Glass U tube (Fig. 20) about 60 cm. long before bending.\\nNo. XIV. Some form of the Cartesian Diver.\\nNo. XV. Eight-inch and four-inch wooden disks combined in one\\npiece for use as a pulley. This piece is fitted with various pins (re-\\nmovable) for suspending weights. It is mounted much like the lever\\nof No. 17. (See Fig. 34).\\nNo. XVI. Centre-of-gravity board, with suspension and plummet.\\n(Fig. 24.)\\nNo. XVII. Platform balance weighing from 1 kgm. to 0.1 gm.,\\nprovided with a set of brass weights.\\nNo. XVIII. Well-made small brass pulley with a hook or loop.\\n(Fig. 37.)", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0189.jp2"}, "190": {"fulltext": "1Y6\\nPHYSICS.\\nNo. XIX. Well-made small double brass pulley with hook or loop.\\n(Fig. 38.)\\nNo. XX. An inclined plane,* shown about one-fourth natural size\\nin Fig. 123. The roller should be of brass, accurately turned. It\\nweighs with its frame jus 16 oz. The graduations of the scale may\\nbe in millimeters. The apparatus should be made with care.\\nNo. XXI. Pendulum-support and pendulum-balls (Figs. 56 and 57).\\nFig. 123.\\nNo. XXII. Three small packages of dyestuffs soluble in water,\\nvarious colors.\\nNo. XXIII. Three glass plates, red, green, and blue, about 10 cm.\\nsquare.\\nNo. XXIV. Camera obscura consisting of two pasteboard tubes\\neach about 25 cm. long. The larger, about 5 cm. in diameter, is\\nclosed at one end save at the centre, where there is a hole about 0.1\\ncm. in diameter in a thin partition. The smaller tube, about 4 cm.\\nin diameter, is closed at one end by thin tracing-paper. (See 94.)\\nA number of excellent features in this apparatus are due to Mr.\\nSweet, formerly of the Rindge Manual-Training School in Cambridge.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0190.jp2"}, "191": {"fulltext": "APPEXDIX II J 177\\nNo. XXV. Make according to the following directions On a board\\nabout 35 cm. square (Fig. 73) lay off a circle 30 cm. in diameter.\\nBore 12 holes, 1, 2, 3, etc., dividing the circumference in 30\u00c2\u00b0 parts.\\nFrom the centre draw radii, making the angle a of 90\u00c2\u00b0, /3 of 60\u00c2\u00b0, and\\ny of 30\u00c2\u00b0. Provide pegs, about 15 cm. tall, to fit in all the holes.\\nMount two strips of thin silvered glass, each about 20 cm. long\\nand 10 cm. wide, on two boards hinged together in such a way that\\nthe angle between them may be varied from 30\u00c2\u00b0 or less to 90 D or\\nmore, the longer edges of the mirrors being horizontal.\\nNo. XXVI. An inexpensive kaleidoscope.\\nNo. XXVII A concave spherical mirror 12 or 15 cm. in diameter.\\nNo. XXVIII. A granite-ware ba^in 15 cm. or more in diameter.\\nNo. XXIX. Thin waterproofed board, pierced by knitting-needle\\nfor experiment on the critical angle. (Fig. 96.)\\nNo. XXX. A porte-lumiere.\\nNo. XXXI. Right-angled glass prism about 5 cm. long, for show-\\ning total reflection. (Fig. 95.)\\nNo. XXXII. A pair of equilateral prism?, for experiment on pro-\\njecting the solar spectrum. 162.)\\nNo. XXXIII. Set of about half a dozen lenses of various shapes 4\\nor 5 cm. in diameter. Fig. 101.)\\nNo. XXXIV. Set of about half a dozen convex lenses varying from\\n2 cm. to 50 cm. in focal length, the largest 6 or 8 cm. in diameter.\\nNo. XXXV. Rotating apparatus* suitable for carrying Maxwell s\\ncolor-disks, etc.\\nNo. XXXVI. Set of color-disks, e.g. those made by Milton Bradley.\\nMISCELLANEOUS ARTICLES.\\nTwo pounds of clean mercury.\\nTwo pounds of assorted soft glass tubing, from 2 mm. to 8 mm.\\ninside diameter.\\nSix feet of rubber tubing, about 5 mm. inside, that will not col-\\nlapse when connected with the air- p am p.\\nAn ounce or two of very small rubber tubing.\\nPiece of thin sheet rubber about 6 in. square, for use with the\\ngauge. (No. I.)\\nSet of cork- borers.\\nThree-cornered file for cutting glass tubing.\\nThe well-known little tops with color-disks serve very well if\\nlarger forms of XXXV and XXXVI are not available.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0191.jp2"}, "192": {"fulltext": "178 PHYSICS.\\nScrew-driver.\\nPair of wire-cutting pliers.\\nOne- half pound of naked copper- wire about 1 rnm. in diameter.\\nLABORATORY TABLES.\\nThe laboratory tables used in the Cambridge grammar-schools are\\nwell suited to the work of this course. They are about 10 ft. long,\\n4 ft. wide, and 2 ft. 10 in. tall. They have white- pine tops about 1^\\nin. thick, and heavy white- wood legs. Extending from end to end\\nover each table are two horizontal bars, about 2 in. by 3 in., ad-\\njustable at various heights (which should range from 1| ft. to 3\u00c2\u00a3\\nft. by 3-iu. intervals) above the table-top, their ends, which are\\ncut in tenons, sliding in grooves in the supporting posts. These\\nposts are fastened to the frame of the table and rise through slots in\\nthe table-top, being flush with the ends of this top and about 10\\nin. distant from the sides. Pins of iron or wood placed in holes\\nin these posts support the ends of the horizontal bars. To adapt\\nthese tables to Exercises 29 and 30 (Second Part of book), holes\\nabout 1-J in. in diameter should be bored through the top.\\nFor Exercises in heat (see Second Part) this table should have a\\ngas-pipe running along the middle of the top from end to end, with\\nthree stop-cocks leading to the right and three leading to the left.\\nThis pipe should be readily detachable, as its pre c ence would be in-\\nconvenient in many experiments.\\nEach table is intended to accommodate six independent experi-\\nmenters.", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0192.jp2"}, "193": {"fulltext": "APPENDIX IV.\\nA FEW EQUIVALENTS IN THE ENGLISH AND METRIC\\nSYSTEMS.\\n1 meter 1.0936 yards.\\n1 3.2809 feet.\\n1 39.3705 inches.\\n1 kilometer 0.6214 mile.\\n1 gram 15.4323 grains 0.0353 ounce-\\n1 kilogram 2.2046 pounds avoirdupois.\\n1 yard 0. 9144 meter.\\n1 foot 0.3048\\n1 inch 0.0254\\n1 mile 1.6093 kilometers.\\n1 pound avoirdupois 0.4536 kilogram.\\n1 ounce 28.35 grams.\\nThe following are approximate equivale\\n1 decimeter 4 inches.\\n1 meter 1.1 yards.\\n1 kilometer f of a mile.\\n1 kilogram 24 pounds.\\n179", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0193.jp2"}, "194": {"fulltext": "", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0194.jp2"}, "195": {"fulltext": "INDEX.\\nAberration, chromatic, spherical,\\n149\\nAchromatic, prism, 135 lens,\\n150\\nAngle, of incidence and of re-\\nflection, 107; of refraction, 125;\\ncritical, 131 refracting, of\\nprisms, 134\\nArchimedes, principle of, 19\\nAtmospheric pressure, 31\\nAxis of lens, 137\\nBalance, spring-, errors of, 61\\nBarometer, Aneroid, 34; Torri-\\ncelli s 31\\nBoyle s law, 35\\nBunsen s photometer, 98\\nCamera, obscura, 93 photog-\\nrapher s, 156\\nCentre, of curvature, 112; optical,\\n137\\nChromatic aberration, 149\\nCoefficient of friction, 80\\nColors, 92, 100 complementary,\\n154 mixing, 153\\nComposition of forces, 76\\nConjugate foci, 140\\nCritical angle, 131\\nCurvature, centre of, in mirror,\\n112; in lens, 137\\nDensity, definition of, 15 of\\nwater, 16\\nDispersion, 135\\nDistance, measurement of, 3, 4\\nobject- and image-, 140\\nEnglish and metric units, App V\\nEquilibrant, definition of, 70\\nEye, 152\\nEyepieces, 161\\nFloating bodies, specific gravity\\nof, 23\\nFluids, definition of, 28 liquid\\nand gas, 34\\nFocal length, of mirrors, 115 of\\nlenses, 138 formula for, 142,\\n148, 168\\nFoci, conjugate, 41\\nFocus, principal, of mirrors, 115,\\n118 of lens, 138\\nFoot, relation to meter, App. V\\nForces, parallelogram of, 61-69\\nFriction, 78 between solids, 80\\ncoefficient of, 80 between\\nsolids and fluids, 84 rolling,\\n83 in tubes, 84\\nFulcrum, definition of, 49 force\\nat, 52\\nGas, 28, 34\\n(rases, pressure of, 31, 35\\nGravity, specific, 18 centre of,\\n46\\nHydrostatic press, 36\\nIllumination, measure of, 96\\nImages, in plane mirrors, 104-\\n111 by convex mirror, 112 by\\nconcave, 117 distorted, 119\\nof lenses, 143-148 after, 155\\nInch, relation to cm., App. V\\nInclined planes, 69-75\\nIncident angle 107\\nIndex of refraction, 126\\nInverse square, law of, 95\\nKaleidoscope, 111\\n181", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0195.jp2"}, "196": {"fulltext": "182\\nINDEX.\\nLantern, magic, 157\\nLength, focal, of mirrors, 115\\nof lenses, 138 formula for,\\n142, 148, 168\\nLenses, definitions relating to,\\n136-138; shapes of, 136; achro-\\nmatic, 150\\nLever, definition of, 41 circular,\\n44; weight of, 46; laws of, 50,\\n51, 53, 58 pulley, windlass,\\ncapstan, 56\\nLight, 90 velocity of, 90 theory\\nof, 91 colors, 92, 100 pencils\\nand rays, 92 weakens with\\ndistance; 95\\nLiquid, 28, 34\\nLiquids, pressure of, 28-30, 36\\nMachines, 41\\nMagic latern, 157\\nMass, 17\\nMeter, relation of, to foot, App.\\nV\\nMetric system, App. V\\nMicroscope, 159\\nMirrors, plane, 104; cylindrical\\nand spherical, 111, 121 con-\\nvex, 112; concave, 115; for-\\nmulas for, 121\\nObjectives, 160\\nOptical instruments,\\n156\\nParallel rays, 140\\nParallelogram, measurement of,\\n9, 10; of forces, Chap. V\\nPendulum, 86\\nPenumbra, 94\\nPhotometry, 96\\nPhysics, definition of, 1\\nPlane mirrors, 104\\nPorte-lumiere, 160\\nPressure, at different levels,\\nliquids, 29, 30 gases, 34 in\\ndifferent directions, liquids, 29;\\ngases, 33\\nPrincipal axis of lens, 137\\nPrisms, achromatic, 135 defini-\\ntion of, 133\\nProjection, of images and of spec-\\ntruim. 158\\nPulley, 54-57\\nPumps, 38\\nRays, parallel, 140\\nReflection, of light, 103; from\\nplane mirror, 104 law of, 107,\\n114 total internal, 131\\nRefraction, 125 index of, 126; of\\nglass, 127, 133; of water, 138;\\nof air, 129; of different colors,\\n130; relation to velocity, 130\\nResultant of forces, 76\\nRumford photometer, 97\\nScrew, 74\\nShadows, 94\\nSiphon, 39\\nSpecific gravities, definition of,\\n18; formulas, 20; methods of\\nobtaining, 18-27, 39\\nSpectrum, 35\\nSpring-balance, errors of, 61\\nSprings, in watches, 89\\nStereopticon, 157\\nTelescope, 162\\nTorricelli s barometer, 31\\nTriangle, 6\\nTubes, flow of fluids in, 84\\nUmbra, 94\\nUnits of measurement, 5\\nVelocity of light, 90\\nVirtual image, of mirrors, 108\\nof lenses, 146\\nVolume, measurement of, 10-13\\nWater, density of, 16\\nWave-lengths varying in differ-\\nent colors, 92\\nWedge, 74\\nWeight, compared with mass, 17", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0196.jp2"}, "197": {"fulltext": "", "height": "4188", "width": "2619", "jp2-path": "elementarylesson00hall_0197.jp2"}, "198": {"fulltext": "", "height": "4428", "width": "2732", "jp2-path": "elementarylesson00hall_0198.jp2"}, "199": {"fulltext": "", "height": "4428", "width": "2732", "jp2-path": "elementarylesson00hall_0199.jp2"}, "200": {"fulltext": "", "height": "4542", "width": "2983", "jp2-path": "elementarylesson00hall_0200.jp2"}}