tsr 
 
 LABORATORY 
 
 OF PHY 
 
 S, ; . C ( ) I 
 
 
RARY OF 
 
 u a 
 
 GIFT OF 
 
 UNIVERSITY FARM 
 
NEW 
 
 LABORATORY MANUAL 
 OF PHYSICS 
 
 BY 
 
 S. E. COLEMAN, S.B., A.M. 
 
 HEAD OF THE SCIENCE DEPARTMENT, AND TEACHER OF 
 PHYSICS IN THE OAKLAND HIGH SCHOOL 
 
 NEW YORK . : . CINCINNATI . : . CHICAGO 
 
 AMERICAN BOOK COMPANY 
 UNIVERSITY OF CALIFORNIA 
 
 LIBRARY 
 
 BRANCH OF THE 
 COLLEGE OF AGRICULTURE 
 
COPYRIGHT, 1908, BY 
 S. E. COLEMAN. 
 
 ENTERED AT STATIONERS' HALL, LONDON,, 
 
 COLEMAN'S NEW LAB. MAN. 
 w. P. 7 
 
PREFACE 
 
 THAT laboratory work is an important part of a course in 
 elementary physics is no longer open to question. The opinion 
 is also practically unanimous that the laboratory work should 
 constitute an organic and integral part of the course, pursued 
 concurrently with the instruction of the class room throughout 
 the subject. Beyond this point, however, there is still a con- 
 siderable diversity of opinion and practice within the limits of 
 good teaching. While the author believes that this Manual 
 will be found adapted to any approved plan of work, it will not 
 be out of place to present the point of view from which the book 
 was written. 
 
 Its scope is that of a laboratory guide for the pupil. It en- 
 croaches as little as possible on the province of the text-book, 
 and does not include class-room experiments to be performed 
 by the teacher. Many such experiments must be presented 
 in any well-conducted course in physics ; but it is unnecessary to 
 place the directions for them in the hands of the pupils. 
 
 Every experiment in the course is a physical experiment. 
 With a superabundance of excellent material within the scope 
 of elementary physics, there would seem to be no valid reason . 
 for spending the first days in the laboratory on manipulation 
 and measurement with vernier and micrometer calipers, the 
 diagonal scale, the spherometer, etc., as is sometimes done, with 
 no physics in sight. 
 
 The course aims to present a maximum of physics with a 
 minimum of manipulation. So far as the teaching of elementary 
 science is concerned, skill in manipulation must be regarded 
 as a means to an end, not as an end in itself. The more simply 
 
 3 
 
 /?3ft 
 
4 PREFACE 
 
 and directly a physical problem is presented to the pupil the 
 better, that his thought and attention may not be diverted from 
 the real point at issue. This principle is especially applicable 
 in the early part of the laboratory course, where it is most 
 frequently and most seriously violated by the use of micrometric 
 instruments, the Jolly balance, etc., in the work on density and 
 specific gravity, eyen before the pupil has had practice in the 
 simpler methods of measuring and weighing. It would seem 
 as if the express purpose of such work were at the outset to 
 throw as many obstacles in the way of progress in physics as 
 the ingenuity of teachers and instrument makers could devise. 
 
 To be entitled to a place, a laboratory experiment must serve 
 a definite purpose in the general plan of the course ; it must 
 contribute something of value in the unfolding of that plan. 
 Perhaps the most striking illustration of what should not be 
 done in this respect is afforded by the familiar quantitative 
 experiments on the breaking strength of wires and on elasticity 
 of stretching, bending, and twisting. These experiments lead 
 absolutely to nothing in most high-school courses. The laws 
 with which they deal are, for the most part, not considered in 
 elementary text-books. A simple qualitative treatment in the 
 class room or the laboratory would serve as an ample experi- 
 mental basis for all the applications that are or need be con- 
 sidered in a general high-school course. 
 
 The qualitative experimental study of phenomena rightly de- 
 mands a large place in an elementary physics course. Economy 
 of time and equipment, convenience, and the advantage of the 
 superior skill of the teacher, are considerations in favor of pre- 
 senting much of this material in the form of class-room experi- 
 ments ; but in a great many instances the laboratory experiment, 
 affording, as it does, immediate sense perception of the phe- 
 nomena in their simplest aspects and at close range, is .greatly 
 superior to any experiment viewed at a distance ; and a labora- 
 tory course which fails to take this into account is necessarily 
 one-sided and incomplete. No apology is therefore necessary 
 
PREFACE 5 
 
 for the large number of qualitative experiments in this Manual. 
 They are entitled to consideration. To lessen the burden of 
 the laboratory record, which rests rather heavily on teacher and 
 pupil alike, it is suggested that many of the qualitative experi- 
 ments may be made nearly, if not quite, as valuable a part of 
 the laboratory course without requiring a written record of them. 
 In such cases the discussion of the observed phenomena in the 
 recitation will suffice. 
 
 Physics should be so taught that the pupil will be led to a 
 correct view of the significance of his laboratory work in its 
 relation to the subject as a science. He should understand 
 that the validity of scientific generalizations, particularly those 
 of a quantitative character, does not depend upon the neces- 
 sarily inaccurate and incomplete data gathered from the experi- 
 ments of the class room and the laboratory. These experiments 
 should be regarded as a limited inquiry into the facts at first 
 hand, not as sources of adequate data for generalizations by the 
 pupil, nor as "verifications" of the laws and principles stated in 
 the text. The pupil's experiment is not a proof of the law, but an 
 aid to the right understanding of it. For example, under Boyle's 
 law the pupil performs an experiment with one gas only (air), 
 at one temperature only, and with only a moderate range of 
 pressure. With the apparatus ordinarily provided, the work 
 is well done if it is not in error by more than two per cent. It 
 would be no less than a complete perversion of the distinctive 
 aims and purposes of scientific instruction to lead the pupil 
 to regard such an experiment as a verification or proof of Boyle's 
 law ; namely, that the inverse proportionality of volume and 
 pressure is true (accurately true) for all gases at any temperature 
 and under all ranges of pressure. It is hardly necessary to say 
 that Boyle's law is not verified until the experiment is repeated 
 at many different temperatures with every gas, and performed 
 with an accuracy equal to that of the ablest experimenters. It 
 would then be found (as the texts state) that the usual state- 
 ment of the law is not exact, and that it wholly fails for any gas 
 
6 PREFACE 
 
 when near a temperature and pressure at which it liquefies. 
 Since the pupil does not undertake such an investigation, he 
 neither proves nor disproves the law. What he really does 
 is to perform an experiment which, within a fair degree of 
 accuracy, illustrates or exemplifies the law ; and he does this 
 in order that he may the better understand it, not because the 
 law is in need of " verification." . 
 
 It is of 'course true that the laboratory work affords a suffi- 
 cient basis for important inferences and conclusions ; but these 
 are necessarily simple, and generally narrow and partial. They 
 must be limited to what follows legitimately from the experi- 
 mental data. To encourage the pupil to draw hasty and unwar- 
 ranted conclusions from insufficient data is a vicious practice. 
 
 This point of view concerning the function of experimental 
 work in elementary physics is maintained throughout the Manual, 
 particularly in the statement of the purpose of each experiment 
 and in the questions asked in the discussions. Consistently 
 with the view that the laboratory course is not a sufficient basis 
 from which to evolve physics as a science, it is assumed in the 
 discussion of experimental results that the pupil has at least 
 carefully read his text-book on the subject of the experiment, 
 and is therefore in a position not only to state the conclusions 
 which are supported by his work, but also to pass judgment on 
 the quality of it by comparing his results with those known to 
 be correct. 
 
 To provide opportunity for choice and to increase the adapt- 
 ability of the Manual to the varying equipment of different 
 laboratories, the number of exercises has been made considerably 
 greater than most teachers will require in a one-year course. 
 A course of sixty exercises, properly distributed over the differ- 
 ent parts of the subject, would constitute a liberal provision of 
 laboratory work, and fifty exercises a reasonable minimum. 
 The following exercises are suggested as, on the whole, the best 
 adapted to such a minimum course, having regard to the cost 
 of equipment and also to the fact that many of the experiments, 
 
PREFACE 7 
 
 or others serving the same purpose, can be performed by the 
 teacher before the class, with satisfactory results : Exercises 1-5, 
 6 (any two of the four experiments), 7, 9, 10, n or 12, 13, 14, 
 16 or 17, 19 or 21, 20, 23-25, 26 (Exp. 50), 29-34, 36, any two 
 of 37 to 41, 42, 43> 45> 47~5 2 > 54 or 55, 56, 57-63, 64 (either 
 experiment), 66 (any one of the experiments), 70, 73. 
 
 The experiments have been chosen and planned with due 
 regard to a reasonable economy in the equipment of the labora- 
 tory and a moderate degree of accuracy in quantitative results. 
 It is far better to have from two to six sets of apparatus of 
 medium cost for each experiment, so that the entire class can 
 be accommodated without running more than from two to four 
 exercises simultaneously, than to provide only one set of expen- 
 sive apparatus for each experiment. On the other hand, it is 
 not a wise economy to spend money on cheap apparatus, lacking 
 in durability and efficiency. The instruments shown in the cuts 
 throughout the book are recommended as of satisfactory grade. 
 
 The grouping of related experiments into exercises will com- 
 mend itself as a convenience both to teacher and pupil. It is 
 intended that, in the regular progress of the work, one laboratory 
 period (either single or double) will be devoted to each exercise. 
 The whole of a single laboratory period will ordinarily be re- 
 quired for the experimental work of the exercise, with only a 
 preliminary record of it in the form of rough notes ; and time 
 outside the laboratory must be taken for writing the permanent 
 record. A double laboratory period (an hour and a half) should 
 be sufficient for both the experimental work and the final record. 
 
 While the present work is in greater part a revision of the " 
 author's " Physical Laboratory Manual," it is newly written 
 throughout ; and full advantage has been taken of the oppor- 
 tunity to make the many improvements in subject-matter, 
 arrangement, and presentation which have been made possible 
 
 by later years of experience. 
 
 S. E. COLEMAN. 
 
 OAKLAND, CALIFORNIA. 
 
CONTENTS 
 
 I. GENERAL DIRECTIONS 
 
 The Laboratory Work . 
 The Laboratory Record . 
 
 PAGE 
 II 
 
 13 
 
 Computations 14 
 
 Measurements ...... 19 
 
 II. DENSITY 
 
 EXERCISE 
 
 I. Density of Solids . ... 24 2. Density of Liquids ... 26 
 III. MECHANICS OF FLUIDS 
 
 3. Gravity Pressure in Liquids 29 
 
 4. Buoyancy of Liquids . . 31 
 
 5. Specific Gravity of Solids . 34 
 
 6. Specific Gravity of Liquids 36 
 
 7. Pressure of Gases ... 40 
 
 8. Boyle's Law 43 
 
 9. The Suction Pump and the 
 
 Siphon 46 
 
 IV. STATICS OF SOLIDS 
 
 10. Equilibrium of Concurrent 
 
 Forces 49 
 
 11. Equilibrium of Parallel 
 
 Forces 52 
 
 12. Moments of Force ... 56 
 
 59 
 
 13. Center of Gravity and Mo- 
 
 ment of Weight . . . 
 
 14. Center of Gravity and the 
 
 States of Equilibrium . 62 
 
 15. Stiffness of Beams. The 
 
 Truss 64 
 
 V. DYNAMICS AND MACHINES 
 
 1 6. Falling Bodies : Whiting's 
 
 Method 67 
 
 17. Falling Bodies: Packard's 
 
 Method 69 
 
 1 8. The Simple Pendulum . . 73 
 
 19. The Wheel and Axle 
 
 20. Pulleys 
 
 21. The Inclined Plane . 
 
 22. Geared Wheels . . 
 
 7 6 
 so 
 83 
 85 
 
 VI. MOLECULAR PHENOMENA 
 
 23. Cohesion and Adhesion 
 
 86 
 
 24. Surface Tension and Capil- 
 larity 88 
 
CONTENTS 
 
 VII. HEAT 
 
 EXERCISE PAGE 
 
 25. Conduction and Convection 91 
 
 26. Radiant Energy .... 93 
 
 27. Coefficient of Linear Ex- 
 
 pansion 96 
 
 28. Coefficient of Expansion of 
 
 Air 99 
 
 29. Specific Heat 101 
 
 30. Melting and Freezing . . 104 
 
 EXERCISE PAGE 
 
 31. Heat of Fusion and Solu- 
 
 tion 106 
 
 32. Cooling by Evaporation ; 
 
 Dew-point 109 
 
 33. Phenomena of Boiling . . m 
 
 34. Heat of Vaporization of 
 
 Water 114 
 
 35. The Steam Engine . . . 116 
 
 VIII. SOUND 
 
 36. The Transmission of Sound 1 18 
 
 37. Ripples. Reflection of 
 
 Sound 121 
 
 38. Vibration Number of a Fork 124 
 
 39. Interference and Beats . . 126 
 
 129 
 
 40. The Law of Lengths 
 
 41. Sympathetic and Forced 
 
 Vibrations 130 
 
 42. Wave Length by Resonance 133 
 
 IX. LIGHT 
 
 Shadows; Pin-hole Images; 
 Law of Intensity . . . 136 
 
 Photometry 139 
 
 Plane Mirrors 143 
 
 46. Multiple Images .... 148 
 
 47. The Concave Mirror . . 149 
 Phenomena due to Refrac- 
 tion 153 
 
 Snell's Law of Refraction ; 
 Index of Refraction of 
 Glass 157 
 
 43 
 
 44, 
 45- 
 
 48. 
 
 49, 
 
 50. Refraction through a Plate 
 
 and through a Prism ; 
 Total Reflection . . . 161 
 
 51. The Convex Lens . . . 165 
 
 52. Convex and Concave Lenses 168 
 
 53. The Eye 171 
 
 54. The Simple and the Com- 
 
 pound Microscope . . 1 72 
 
 55. The Astronomical and the 
 
 Galilean Telescope . . 176 
 
 56. The Spectrum; Color . . 179 
 
 57. Magnets and Magnetic 
 
 Action i 
 
 X. MAGNETISM 
 
 58. Magnetic Fields . 
 
 188 
 
 XI. ELECTRICITY 
 
 59. The Simple Voltaic Cell . 191 
 
 60. The Magnetic Field of a 
 
 Current 194 
 
 61. The Helix, the Electro- 
 magnet, and the Electric 
 Bell 
 
 I 97 
 
10 
 
 CONTENTS 
 
 EXERCISE PAGE 
 
 62. The Electric Telegraph . 200 
 
 63. The Tangent Galva- 
 
 nometer; Polarizing, and 
 Nonpolarizing or Con- 
 stant Cells 202 
 
 64. Measurement of Resistance 
 
 by Substitution ; The 
 Laws of Resistance . . 209 
 
 65. The Resistance of a Cell . 213 
 
 66. The Electro-motive Force 
 
 of Cells 216 
 
 67. The Electro-motive Force 
 
 and Resistance of a Cell 221 
 
 68. The Fall of Potential along 
 
 a Conductor .... 222 
 
 EXERCISE PAGE 
 
 69. Measurement of Resistance 
 with the Wheatstone 
 Bridge ...... 226 
 
 Arrangement of Cells . . 232 
 Measurement of Electrical 
 
 Power 235 
 
 Induced Currents .... 238 
 The Electric Motor and 
 
 Dynamo 241 
 
 The Gilley Gramme Ring 
 
 Dynamo and Motor . . 246 
 
 75. The Telephone . . . , 251 
 
 76. Electrolysis and the Storage 
 
 Cell 254 
 
 70. 
 7 1 - 
 
 72. 
 73- 
 
 74- 
 
 APPENDIX . 
 
 259 
 
 Special catalogues of the apparatus for this manual are issued by the 
 University Apparatus Co., 2229 McGee Ave., Berkeley, California ; and by the 
 Chicago Apparatus Co., 557-559 W. Quincy St., Chicago, Illinois. 
 
NEW LABORATORY MANUAL 
 OF PHYSICS 
 
 I. GENERAL DIRECTIONS 
 
 1. The following general directions should be carefully studied 
 before the laboratory work is begun. It is not to be expected that 
 they will all be fully understood until, by actual experience in the 
 laboratory, the pupil has become somewhat acquainted with the 
 various matters with which they deal. It will therefore be neces- 
 sary to refer to them frequently during the first few weeks, until 
 they become thoroughly familiar. 
 
 THE LABORATORY WORK 
 
 2. Preparation. Finish the record of each laboratory. exercise 
 before beginning the next. It is generally impossible to perform 
 an experiment intelligently unless the lessons to be drawn from the 
 experiments immediately preceding have been definitely learned. 
 
 If the subject with which the exercise deals is not already 
 familiar from previous class-room work, read the text-book on the 
 subject before the laboratory period. Read also the laboratory 
 directions for the exercise. The preliminary information thus 
 gained lessens the danger of misdirected effort in the laboratory 
 and makes the work much easier to understand. 
 
 The references indicated at the beginning of each exercise may 
 be consulted during the laboratory period, as opportunity offers, 
 or at such other times as the instructor may direct. 
 
 To save time in the laboratory, tabular forms for the record of 
 measurements should be prepared in advance. 
 
 3. Apparatus. Before beginning an exercise note whether 
 you have everything called for in the list of apparatus. If any- 
 
12 GENERAL DIRECTIONS 
 
 thing is missing or unsatisfactory, report the fact to the instructor 
 at once. Never take apparatus from other places than your 
 own. 
 
 4. Neatness and Order. A very important incidental benefit 
 of a properly conducted laboratory course is the training it affords 
 in neatness and order. Pupils should feel a personal responsibil- 
 ity for the condition of the apparatus and table where they are at 
 work, and especially for the condition in which these are left at 
 the end of the hour. A proper regard for the comfort and con- 
 venience of others demands that you leave the place you have 
 occupied at least as clean and orderly as you found it. 
 
 5. Damage to Apparatus. Pupils are responsible for all dam- 
 age to apparatus in their possession, and should report such 
 damage to the instructor immediately. 
 
 6. Economy of Time in the Laboratory. It is expected that 
 each exercise will be completed in one laboratory period. To 
 make sure of accomplishing this, no time should be taken in the 
 laboratory for writing discussions or for making computations 
 (unless the results of these computations are needed at the time), 
 until the exercise for the day is completed. The remainder of 
 the period may be spent either in reading the references or in 
 writing up the exercise. No time should be wasted. 
 
 7. Questions. Numerous questions are interspersed with the 
 directions for the experimental work. Do not pass over these 
 questions, leaving them for later consideration. They direct the 
 attention to matters that should be understood at the time with 
 the assistance of the teacher, if necessary. The answers to ques- 
 tions in parentheses may be omitted from the record. 
 
 8. Repetition of Work. An experiment is to be repeated 
 when the results are unsatisfactory. Present doubtful results to 
 the teacher for his decision as soon as possible, so that the experi- 
 ment may be repeated, if necessary, without delay. 
 
THE LABORATORY RECORD 13 
 
 THE LABORATORY RECORD 
 
 9. Specific Directions concerning the manner of taking notes 
 during the progress of experimental work and the form and scope 
 of the final record will be given by the teacher. In addition to 
 these, the following general directions should be carefully observed. 
 
 10. General Form. Copy the number and title of each exer- 
 cise and the purpose of each experiment (printed in italics) from 
 the manual ; and arrange the notes on each experiment under the 
 various heads there indicated. Give proper attention to regular- 
 ity of margins, paragraphing, spacing, numbering, lettering, etc. 
 Do not crowd the notes. Leave a vacant line between the experi- 
 ments of an exercise, and several vacant lines between exercises. 
 Make headings prominent. In all these matters of general form 
 the record should correspond with the manual. 
 
 Measurements, computations, and numerical results should 
 always be set apart by themselves, so as to be easily seen and com- 
 pared. Sets of numbers are best entered in columns, as in Exer- 
 cises i, 8, n, 12, etc. Single items should be given one or more 
 whole lines each, with the numbers at the right-hand side of the 
 page, as in Exercises i, 2, 4, 5, etc. When no form of record is 
 given for an experiment, devise a satisfactory one for yourself. 
 
 N )ll. Clearness and Brevity. The record should be complete 
 in itself, i.e. should not require a knowledge of the directions or 
 the questions asked in the manual to make it fully intelligible. 
 It should be as brief as possible without sacrificing clearness or 
 omitting essentials. The answers to questions inclosed in paren- 
 theses may be omitted from the record ; but these questions 
 should receive no less careful attention on that account. Be pre- 
 pared to answer them orally at any time. 
 
 12. Decimals. Express all fractional quantities decimally. 
 -The relative values of fractions expressed decimally can be de- 
 termined at a glance, but in the form of common fractions this is 
 generally impossible. In the actual work of measuring and com- 
 
14 GENERAL DIRECTIONS 
 
 puting, the decimal fraction is almost without exception more con- 
 venient than the common fraction. This is especially true in 
 using the metric system. 
 
 Express a quantity in terms of one unit only ; e.g. write 15.25 g. 
 instead of 15 g. 2 dg. 5 eg. Express all lengths in centimeters. 
 
 13. What constitutes an Honest Record. Your laboratory 
 notes are accepted upon the supposition that they are a true 
 record of the work done by you in the laboratory. If the results 
 are not satisfactory, the only remedy is to repeat the experiment. 
 Neither borrowing nor lending of note books can be permitted. 
 Where pupils work in pairs each should always take a complete 
 record of all measurements and other necessary data, so as to be 
 wholly independent of his laboratory mate in writing up the ex- 
 ercise, and each should perform all computations for himself. 
 Pupils may, of course, give one another the kind of help that they 
 might expect from the teacher. 
 
 COMPUTATIONS 
 
 14. The Record of Computations. The mathematical pro- 
 cesses by which computed results are obtained must either be 
 fully recorded or indicated by means of the signs of addition, sub- 
 traction, etc. In the first two exercises the computations are 
 indicated in the model form of record, parentheses being used 
 to represent the numbers. You are expected to remember this 
 direction and to observe it in all subsequent work without such a 
 reminder. 
 
 Where results are entered in tabular form, and the computations 
 indicated at the tops of the columns, only the results are to be 
 entered in the columns. 
 
 15. Concrete Numbers. The name of the unit should always 
 be written after the numerical value of a measured or computed 
 quantity. This applies to each quantity recorded in a series of 
 computations as well as to the final result. Failure to keep track 
 of the physical units involved in computations is a fruitful source 
 
COMPUTATIONS 1 5 
 
 of errors in the solution of problems as well as in the laboratory 
 work. 
 
 16. Testing Numerical Results. When an experiment leads 
 to a numerical result the true value of which is known, as the 
 weight of a cubic centimeter of pure cold water (Experiment 3), 
 a comparison of the experimental value with the true value of the 
 quantity serves as a check on the work, to determine whether it 
 has been done with reasonable care and accuracy. The method 
 of making such a comparison is illustrated by the following 
 example. 
 
 If a length of 10.05 cm. is measured and recorded as 10 cm., 
 the error is .05. This is .05-^-10.05, or .005, of the quantity 
 measured, or .5% of it. An equal error (.05 cm.) in measuring a 
 length of 2.5 cm. is 2 % of the quantity measured. In the second 
 case the error is of more consequence because it is a larger 
 fraction of the quantity measured. To illustrate further, if an 
 error of only an inch were made in measuring off a mile, the work 
 would be considered very accurate ; but the measured height 
 of a table would be very inaccurate if it were in error by as much 
 as an inch. It will be seen that the degree of accuracy of a meas- 
 urement is not expressed by the error, but by the percentage of^ 
 error. 
 
 If the percentage of error of any result is unreasonably large, 
 the experiment should be repeated as soon as possible. Only 
 reasonably accurate results should be handed in for inspection. 
 
 17. How the Accuracy of Measurements enters into Computa- 
 tions. To retain either more or fewer decimal places in a com- 
 puted result than the accuracy of the measurements justifies is an 
 error to be carefully avoided. The principles and rules governing 
 correct practice in this matter are illustrated in the following 
 examples. 
 
 In the first laboratory exercise it is required to determine the 
 volume of a rectangular solid. The length is measured near each 
 of the four edges extending in that direction, and the values 
 
l6 GENERAL DIRECTIOiNS 
 
 found are, let us say, 7.25 cm., 7.23 cm., 7.24 cm., and 7.23 cm. 
 The average of these numbers is 7.2375 cm. Now the last figure 
 in each of the four measurements is doubtful, the estimate of 
 hundredths of a centimeter (or tenths of a millimeter) being un- 
 certain by at least one or two hundredths ; hence the 3 in the 
 second decimal place of the average is doubtful, and the last two 
 figures should be dropped. But since the first figure discarded is 
 greater than 5, the last figure retained is increased by one ; i.e. the 
 average is written 7.24 cm. To retain the four decimal places 
 would be wrong, since this would imply a greater accuracy than 
 was actually attained in the measurements. It would also be 
 wrong to drop all but the first decimal figure, since we have good 
 reason for thinking that 7.24 cm. is more nearly right than 7.2 cm. 
 
 Let us suppose further that the average width of the solid is 
 found to be 5.78 cm., and the average thickness 3.18 cm. 
 
 The volume of the body = 7.24 X 5.78 X 3.18 c.c. 
 
 7.24 41.8 
 
 5.78 3-18 
 
 5792 3 344 
 
 5 068 4 18 
 
 36 20 125 4 
 
 41.8472 132-924 
 
 In the above work the doubtful figures are printed in heavy- 
 faced type. Thus, in the first multiplication, since the last figure, 
 8, of the multiplier is in doubt, all that depends upon it is in doubt, 
 t.e. the entire product, .5792. The volume of the body should be 
 written 133 c.c. 
 
 It is easy to see from this example why unreliable figures accu- 
 mulate in multiplication ; but in seeking a practical rule by which 
 to determine what figures should be retained, we must study the 
 question from a different point of view. Suppose in the above ex- 
 ample that each dimension of the block is in doubt by .02 cm. This 
 uncertainty, or possible error, is about y^ of the length, -g-^-g- of the 
 width, and -%%-$ of the thickness. The possible error of the product 
 
COMPUTATIONS 
 
 is the sum of the possible errors of all the factors, i.e. j^ -f- ^ -f- 
 3T o"> or TTTO > or ( rou ghly) a li^ 6 more than i % This clearly 
 renders the units' figure of the computed volume doubtful. If we 
 suppose each dimension of the block to be in doubt by only .01 cm., 
 the product will be in doubt by about -| % ; and, as this also 
 makes the units' figure of the product doubtful, the result should 
 still be written 133 c.c. We should, however, be justified in re- 
 taining the first decimal place in the computed volume if we had 
 reason to believe that the probable error of each factor was less 
 than .01 cm. 
 
 The following table shows how the computed values given in the 
 first column should be written when the probable error is less than 
 i %, when it is between i % and 2 %, and when it is over 2 %. 
 
 COMPUTED VALUE 
 
 ERROR UNDER i% 
 
 ERROR OF i% TO 2% 
 
 ERROR OVER 2% 
 
 214.27 
 
 214.3 
 
 2I 4 . 
 
 214 
 
 93.628 
 
 93-6 
 
 93-6 
 
 94 
 
 10-354 
 
 10-35 
 
 10-35 
 
 10.4 
 
 .09567 
 
 .0957 
 
 .096 
 
 .096 
 
 As a general rule, computations should be carried to the first 
 doubtful figure, and all decimal places beyond this should be dis- 
 carded ; but in some cases the first two doubtful figures should be 
 retained. For example, if the true value of a quantity is 1.19 and 
 the pupil's value is 1.2263, his answer should be written 1.23, not 
 1.2 ; for although the first decimal figure is in error, the omission 
 of the next figure would change the value of the result by 2.5 %,, 
 which is nearly as great as the experimental error. The omission 
 of the .03 would therefore mask the true quality of the experimen- 
 tal work. 
 
 - In division the possible percentage of error of the quotient is the 
 sum of the possible percentage of error of the divisor and dividend, 
 and the same rule holds for retaining decimal places as in multi- 
 plication. The division should always be carried far enough to 
 determine whether the first discarded decimal figure is greater or 
 COLEMAN'S NEW MANUAL 2 
 
1 8 GENERAL DIRECTIONS 
 
 less than 5. If it is 5 or greater, the last figure retained is increased 
 by one, as in the above examples. 
 
 When a result depends upon a series of computations, each 
 computation must be carried far enough to avoid introducing any 
 appreciable error into the work. The safest plan for the beginner 
 is to carry decimal places in excess throughout the computations, 
 and to discard them only in the final result. 
 
 18. Detecting Errors of Computation. Decimal points are fre- 
 quently misplaced. A mere glance at the numbers is generally 
 sufficient to detect such an error. Thus, if 38.2 be divided by 
 .094, it will be evident at once that the quotient is slightly greater 
 than ten times the dividend (since the divisor is slightly less than 
 .1), and that, if the quotient is written 40.64 or 4064., the decimal 
 point is misplaced. 
 
 Misplaced decimal points and other gross errors of computation 
 can often be detected by the absurdity of the results. Thus if one 
 should get .412 g. as the weight of i c.c. of a stone in Experiment 
 2, he should know at once that a serious blunder had been made 
 either in the experimental work or in the computation ; for this is 
 less than half the weight of i c.c. of water (i g.), and the pupil 
 knows that, for equal bulk, stone is much heavier than water. 
 
 The capable student will soon realize that, in such matters as 
 these, the laboratory work furnishes large opportunity for the exer- 
 cise and development of all-round " common sense." 
 
 19. Mathematical Forms. The use of inadmissible mathemat- 
 ical forms should be carefully avoided. Perhaps the most com- 
 mon error of this sort is illustrated in the supposed equation : 
 
 5 X 8 x 10 = 400 -i- 500 = .8. 
 
 This asserts that 400-7- 500 = .8, which is true ; also that 5 X 8 X 
 10 = 400-7- 500, or .8, which is absurd. It is evident, of course, 
 that this is not the meaning intended ; but no other interpreta- 
 tion can be given the supposed equation in accordance with estab- 
 
 < lished mathematical usage, and no departure from this usage can 
 
 ' be tolerated. 
 
MEASUREMENTS IQ 
 
 MEASUREMENTS 
 
 20. Measurement of Length. The customary unit of length 
 in scientific work is the centimeter ; and all lengths are to be 
 recorded in this unit unless otherwise specified. Millimeters are 
 recorded as tenths of a centimeter. 
 
 Fractions of a millimeter are esti- 
 mated in tenths and recorded as 
 hundredths of a centimeter. Thus 
 the length of the block illustrated 
 in Figure i is 2.35 cm. The figure 
 also shows the correct position of a 
 meter rod in measuring. If the rod FlG 
 
 were turned flat, the scale would be 
 
 at a distance and the measurement would be less accurate. It 
 is best not to use the end of the rod, especially if it is worn. 
 Begin at some even centimeter or, better still, even decimeter. 
 
 21. Order of trying Weights in Weighing. Without system in 
 the use of weights much time is wasted in the process of weighing. 
 A full set of weights, such as is always provided in the laboratory, 
 includes all that are necessary to balance any mass from one equal 
 to the sum of all the weights of the set down to one as light as the 
 smallest of the set. But a single set is adequate only when the 
 weights are tried in proper order. 
 
 Begin by trying the weight which you estimate to be most 
 nearly equal to the mass to be balanced. If it seems to be nearly 
 sufficient, add the next smaller ; but if it is evidently much too 
 light, remove it and try the next larger. Proceed thus backward, 
 trying the larger weights till you find that the next larger, used 
 alone, is too large. The secret of rapid weighing is to try out the 
 larger weights first. If the process is begun with too small a 
 weight, this is commonly not discovered till all the smaller 
 weights have been added, when the whole process must be 
 repeated, whereas it would have been discovered by trying the 
 single larger weight. 
 
20 GENERAL DIRECTIONS 
 
 Having thus determined the largest weight to be used, add the 
 smaller weights in succession. If any weight proves to be too 
 great an addition, remove // (not a larger one) and try the next 
 smaller. Continue thus till you come to the smallest weight 
 provided. 
 
 22. Use of the Platform Balance. The platform balance (Fig. 
 2) is provided with a graduated beam, which is to be used instead 
 
 of weights smaller than 
 the maximum reading of 
 the beam (usually 5 g.). 
 The platforms are evenly 
 balanced (with nothing 
 on them) when the 
 weight that slides on 
 the beam is at the zero 
 FIG - 2 ' end of the beam. As 
 
 the weight is moved from this position, it makes the side toward 
 which it is moved heavier, and the platform on that side descends. 
 The object to be weighed must therefore be placed on the other 
 platform, i.e. the one at the zero end of the beam. 
 
 In weighing proceed as follows : Place the article to be weighed 
 on the proper platform. Slide the weight on the beam to the zero 
 end. The beam adjustment is to be held in reserve till the weigh- 
 ing has been brought within the limit of the beam reading. When 
 this has been accomplished, make the final adjustment with the 
 beam. You can save time by steadying the platforms with the 
 hands. Do not waste time waiting for the oscillations to cease 
 entirely. Some platform balances are provided with a vertical 
 pointer between the platforms. If the oscillations are small and 
 this pointer moves to approximately equal distances on both sides 
 of the zero point of the graduated arc behind it, the weighing is 
 sufficiently exact. The weight of the object is the sum of the 
 weights used plus the beam reading. This balance is hardly sen- 
 sitive to less than .1 g., and readings to this fraction are sufficient. 
 
MEASUREMENTS 
 
 21 
 
 FIG. 3. 
 
 23. Use of the Specific Gravity or Beam Balance. The beam 
 of this balance (Fig. 3) is not fastened to the upright, and is 
 easily thrown out of place in putting heavy objects on or remov- 
 ing them from the pans. To avoid 
 
 this, always support the pan on the 
 heavier side by placing a hand 
 under it. When balance is nearly 
 secured, time can be saved by 
 steadying the pans with the hands. 
 Watch the vertical pointer carried 
 by the beam, and adjust the weights 
 according to its indication. The 
 weighing is sufficiently exact when 
 the distances to which the pointer 
 swings on each side of the zero dif- 
 fer by less than one division of the -scale behind it. With this 
 balance weight can be determined to the nearest centigram. 
 
 24. Precautions to be observed in Weighing. (i) Weights, 
 especially heavy ones, should be placed near the center of the 
 platform or pan. 
 
 (2) It is better to handle weights with forceps than with the 
 fingers. If forceps are provided, use them. You will find them 
 more convenient than the fingers, especially in handling the frac- 
 tional weights. 
 
 (3) Always return weights to the proper places in the block as 
 soon as you have finished weighing. The most convenient method 
 of counting weights is to add them up as they are returned to the 
 block, beginning with the largest and taking them in the order of 
 their size. The weights should never be put down anywhere 
 except on the balance and in their proper places in the block. 
 If one of the weights is lost, the whole set is practically useless. 
 
 (4) When fractional weights are provided, they should consist 
 of the following : .5, .2, .1, .1, .05, .02, .02, and .01 g. If any are 
 missing, report the fact to the instructor. 
 
22 GENERAL DIRECTIONS 
 
 (5) Before using a balance observe whether the beam swings 
 freely and comes to rest in a horizontal position. If it does not, 
 a bearing is probably out of adjustment. 
 
 (6) In weighing liquids, see that the outside of the vessel is 
 dry before placing it on the balance. If any liquid is spilled, 
 wipe it up at once. 
 
 25. The Estimation of Tenths. All laboratory measurements 
 should be as accurate as is possible with the apparatus provided. 
 In reading a scale of any sort, as the position of a point on a 
 meter rod, the position of the pointer on the scale of a spring 
 balance, the height of the mercury in a thermometer, etc., the 
 scale should be read to tenths of its smallest division. Even if the 
 pupil has not the skill to do this accurately, the estimate will be 
 considerably more accurate than the nearest whole division ; and 
 it is the universal rule that no error should be unnecessarily intro- 
 duced into the work. 
 
 26. Text-book References. The text-books referred to by 
 paragraph numbers at the beginning of each exercise are named 
 below. The references are limited to the subject-matter of the 
 experiments, their purpose being to indicate the reading that may 
 profitably precede and accompany the laboratory work, without 
 entering upon the equally wide range of topics which fall within 
 the scope of the recitation. 
 
 Adams. Physics for Secondary Schools. Adams. 
 
 American Book Company. 
 Coleman. Elements of Physics. Coleman. 
 
 D. C. Heath and Company. 
 Car. & C. High School Physics. Carhart and Chute. 
 
 (Edition of 1907.) Allyn and Bacon. 
 Ches. G. & T. Physics. Cheston, Gibson and Timmerman. 
 
 D. C. Heath and Company. 
 Hoad. Br. A Brief Course in Physics. Hoadley. 
 
 American Book Company. 
 
MEASUREMENTS 23 
 
 Hoad. El. Elements of Physics. Hoadley. 
 
 American Book Company. 
 Mumper. A Text-book in Physics. Mumper. 
 
 American Book Company. 
 Mil. & G. First Course in Physics. Millikan and Gale. 
 
 Ginn and Company. 
 Went. & H. A Text-book of Physics, Revised. 
 
 Wentworth and Hill. Ginn and Company. 
 Jackson. Elementary Electricity and Magnetism. 
 
 , Jackson and Jackson. Macmillan Company. 
 
II. DENSITY 
 
 EXERCISE i. DENSITY OF SOLIDS 
 
 References. Adams, 1-16; Coleman, 13-20; Car. & C., 
 7-10, 140; Ches. G. &T., 4-8, 15-17, 19-20; Hoad. Br., 13-15, 
 145; Hoad. EL, 12-16, 156; Mumper, 7-9, 16-1 8; Mil. & G., 
 12-18; Went.& H., 11-15. 
 
 Experiment i. To find the mass of one cubic centimeter of a 
 rectangular solid. * 
 
 Apparatus. A rectangular solid, several centimeters in each 
 dimension ; platform balance and weights ; forceps for handling 
 weights ; metric rule (preferably a 3O-cm. rule with beveled edge). 
 
 Experimental Work. Find the dimensions of the solid in 
 centimeters and its weight in grams. Since the solid may not be 
 perfectly rectangular (and very probably is not), four measure- 
 ments of each dimension are to be taken, one near each of the 
 four edges extending in the direction of the length, and similarly 
 for the width and thickness. Record the four measurements of 
 each dimension even if they are all equal. (Why?) In weighing 
 the solid be sure to place it on the proper platform. 
 
 Data and Computations. Compute the volume of the body 
 from its average length, width, and thickness ; then compute its 
 density. Record measurements and computations as follows : 
 
 DIMENSIONS OF THE SOLID 
 
 LENGTH 
 
 WIDTH 
 
 THICKNESS 
 
 cm. 
 
 cm. 
 
 cm. 
 
 cm. 
 
 cm. 
 
 cm. 
 
 cm. 
 
 cm. 
 
 cm. 
 
 cm. 
 
 cm. 
 
 cm. 
 
 Av. cm. 
 
 cm. 
 
 cm. 
 
 1 Use the name of the substance instead of the word " solid." 
 24 
 
DENSITY OF SOLIDS 
 
 Weight of the solid 
 Volume of the solid = ( 
 Density of the solid 
 
 c.c. 
 
 = g. per c.c. 
 
 IG ' 
 
 Experiment 2. To find the density of an irregular solid that 
 sinks in water. 
 
 Apparatus. Platform balance and weights ; overflow can 
 (Fig. 4) ; tumbler ; vessel of water ; cubic 
 centimeter graduate ; irregular solid * with 
 string tied to it ; mop cloth. 
 
 [The copper boiler used in several of the 
 heat experiments serves very well for an 
 overflow can, if a short piece of rubber tub- 
 ing is attached to the spout. A cubic centi- 
 meter graduate having a capacity of 100 c.c. 
 and graduated in single cubic centimeters is 
 recommended as most serviceable for laboratory work.] 
 
 Experimental Work. Weigh the solid before putting it in 
 water; then find its volume by measuring the volume of water 
 
 that it displaces when 
 immersed. If the spout 
 of the overflow can is 
 not high enough to allow 
 the graduate to be placed 
 
 under it, set the can near the edge of the table 
 with the spout projecting over the edge. Fill 
 the can till the water begins to run out of the 
 spout, with the graduate under the spout to catch 
 
 FIG. 5. 
 
 the overflow ; then empty the graduate and again hold it under 
 the spout, as you lower the solid into the can by means of the 
 string. In measuring the overflow, hold the eye on a level with 
 the surface of the water (Fig. 5), and read the scale at the level 
 of the lowest part of the surface (seen through the elevated ridge 
 
 1 Substitute in your record the name of the solid used. 
 
26 DENSITY 
 
 of water at the edge). In taking the reading estimate to tenths 
 of the smallest division. 
 
 Data and Computations. Record each item on a separate 
 line, as in the first experiment, and compute the density of the 
 solid. If its density is given in Table I of the Appendix, compute 
 the percentage of error of your result (Art. 16). 
 
 EXERCISE 2. DENSITY OF LIQUIDS 
 References. The same as for Exercise i. 
 
 Experiment 3. To find the density of water at the temperature 
 of the laboratory. 
 
 Apparatus. Beam balance and set of weights to i eg. (or 
 platform balance and weights to 5 g.) ; forceps; beaker; loo-c.c. 
 graduate ; mop cloth. 
 
 Experimental Work. A measured volume of water is to be 
 weighed in the beaker. Measure in the graduate between 90 and 
 100 c.c. of water (Fig. 5). In reading the volume it is necessary 
 to have the graduate exactly vertical, and to be sure of this it 
 should stand on the table. Read accurately to the nearest tenth 
 of a cubic centimeter. (An error of one tenth of a cubic centi- 
 meter affects the result as much as an error of a decigram in 
 weighing). 
 
 Weigh in the beaker the measured volume of water. Be careful 
 to empty the graduate to the last drop. (There are only about ten 
 drops of water in a cubic centimeter.) Weigh the beaker empty 
 and dry. 
 
 Data and Computations. Compute the density of the water. 
 The true density of pure water at 20 C. (which is about the usual 
 temperature of the laboratory) is .998 g. per cubic centimeter. 
 Compute the percentage of error of your result. If this is over i %, 
 repeat the experiment. (A large error is almost certainly due to 
 an inaccurate reading of the volume. Why ?) Record as follows : 
 
DENSITY OF LIQUIDS 2/ 
 
 Volume of water used = cc. 
 
 Weight of beaker and water 
 
 Weight of beaker empty 
 
 Weight of the water =()() 
 
 Computed density of water = ( ) -5- ( ) 
 
 True value of density (at 20 C.) 
 
 Error =()>() 
 
 Percentage of error =( ) -5- ( ) x 100 % 
 
 Experiment 4. To find the capacity of a bottle, making use of 
 the known density of water. 
 
 Apparatus (for Experiments 4 and 5). Beam balance and set 
 of weights to i eg. (or platform balance and weights to 5 g.); 
 bottle of about 2 oz. capacity, with glass stopper ; supply of pure 
 water; supply bottle of some liquid (saturated solution of zinc 
 sulphate or table salt, alcohol, or mercury) ; a jar of water for 
 rinsing j mop cloth. 
 
 Experimental Work. Weigh the bottle empty with the stopper. 
 Fill it with pure water (not from the jar for rinsing) and insert the 
 stopper, being careful to avoid a bubble of air under the stopper. 
 Wipe the outside of the bottle dry and weigh. Return the water 
 to the supply vessel, and stand the bottle on the table inverted to 
 drain. . 
 
 Data and Computations. Compute the weight of water that 
 the bottle holds. What is the capacity of the bottle in cubic 
 centimeters, assuming the density of water to be i g. per cubic 
 centimeter? Record each item on a separate line, as in the pre- 
 ceding experiment. 
 
 Experiment 5. To find the density of a liquid? using a bottle 
 of known capacity. 
 
 Experimental Work. Fill the bottle used in the preceding 
 experiment with the liquid provided, exercising the same precau- 
 tions as before, and weigh. Return the liquid to the supply bottle, 
 1 Substitute the name of the liquid in your record. 
 
28 DENSITY 
 
 rinse the bottle used, and leave it empty. Use the mop cloth, and 
 leave the table and scale pans dry. 
 
 Data and Computations. Compute the weight of the liquid 
 contained in the bottle, and from this and its volume (the capac- 
 ity of the bottle) compute its density. If its density is given in 
 the Appendix, compute the percentage of error of your result. 
 
 Discussion (Oral). i. Why will more accurate results be ob- 
 tained in Experiment 3 by using about as much water as the 
 graduate will measure instead of only a few cubic centimeters ? 
 
 2. Do you think it would be more or less accurate to find the 
 volume of a liquid by the method of Experiments 4 and 5 than 
 it would be with a graduate, as in Experiment 3 ? Why? 
 
III. MECHANICS OF FLUIDS 
 
 EXERCISE 3. GRAVITY PRESSURE IN LIQUIDS 
 
 References. Adams, 157-159, 163, 165-168 ; Coleman, 21-25 ; 
 Car. & C., 123-124, 127-128; Ches.G.&T., 47-49; Hoad. Br., 
 I 3 I t !34-i37; Hoad. EL, 140-141, 143-146, 151; Mumper, 
 26-27, 29-31; Mil. & G., 57-60; Went. & H., 63-64, 68. 
 
 Experiment 6. To study the pressure of a liquid due to its 
 weight (gravity pressure), with reference especially to the change of 
 pressure with change of depth below the surface. 
 
 Apparatus (for Experiments 6 and 7). Battery jar containing 
 water ; gas-lamp chimney or student-lamp chimney, with an end 
 ground to fit a plane surface ; small square of cardboard ; a stick 
 i ft. long; two beakers, one low and wide, the other tall and 
 slender, of about the same weight but very unequal diameters. 
 
 Experimental Work. a. Place the piece of cardboard over the 
 ground end of the chimney, and lower this end into the jar of water. 
 Hold the chimney loosely so that it will not overturn, and let it 
 sink as far as it will. What keeps it from sinking to the bottom ? 
 Hold the chimney in this position, put the stick down through it, 
 and note the force required to push the cardboard away from the 
 bottom. Is the chimney now sustained by the water as it was 
 when the cardboard was in place? 
 
 Repeat the above or vary the experiment in any way that may 
 occur to you, until you have discovered all that you can in regard 
 to the way in which the chimney is sustained in the water. State 
 briefly the facts observed and your conclusions from them. 
 
 b. With the cardboard over the lower end of the chimney as 
 before, push it slowly down to the bottom of the jar, at the same 
 time noting the change in the tendency of the chimney either to 
 
 29 
 
30 MECHANICS OF FLUIDS 
 
 sink farther or to rise. What relation do you observe between 
 the force (pressure) exerted by the water and the depth at which 
 the force is exerted? (Statements of definite or quantitative re- 
 lations are not supported by this experiment and the two following, 
 since no measurements are made.) 
 
 Experiment 7. To observe whether the total pressure varies 
 with the area of the surface pressed upon. 
 
 Experimental Work. With the beakers empty and one in each 
 hand, push them, bottom down, into the water to equal depths, 
 until the water comes nearly to the top of the shorter one. Note 
 which requires the greater downward pressure to hold it in place. 
 Explain. 
 
 Experiment 8. To observe the effect of the density of a liquid 
 upon the pressure exerted by it at a given depth. 
 
 Apparatus. Tumbler containing mercury ; tumbler of water ; 
 two wooden blocks of the same shape and size, and small enough 
 to go into the tumblers ; piece of iron. 
 
 Experimental Work. a. Compare the weight of the mercury 
 and the weight of the water by lifting the tumblers. (Mercury 
 is 13.6 times as dense as water.) Float one of the blocks on the 
 water and the other on the mercury. Account for the difference 
 in the depths to which the two blocks sink. 
 
 b. Push the blocks down till they are submerged in the liquids. 
 Compare the forces necessary to do this, and account for their 
 difference. 
 
 c. Put the piece of iron into the mercury. What happens to 
 it ? Explain. 
 
 Experiment 9. To measure the pressure in water at different 
 depths with a pressure gauge, or manometer. 
 
 Apparatus. Hydrometer jar filled with water ; two manome- 
 ters, one containing water, the other mercury ; metric rule. 
 
 [To reduce capillary action, the manometer tubes should have 
 an internal diameter of at least one fourth inch.] 
 
GRAVITY PRESSURE IN LIQUIDS 
 
 Experimental Work. a. Lift the manometer containing water 
 out of the jar, and compare the level of the water in the two 
 arms of the bend. Slowly lower the manometer 
 into the jar of water, and observe the behavior of 
 the water in the bend of the tube. Describe and 
 account for its motion. How is the pressure of the 
 water in the jar transmitted to the water in the 
 manometer ? 
 
 b. With the manometer held in a fixed position, 
 measure the difference of level, ab (Fig. 6), of the 
 water in the two arms of the bend, and the differ- 
 ence, cd, between the level of the water in the jar 
 and the water in the lower end of the manometer. 
 Take two other pairs of measurements with the 
 manometer at different depths. 
 
 Copy Figure 6 in your note book," and record the 
 measurements as follows : 
 
 FIG. 6. 
 
 Diff. of level ab 
 Diff. of level cd 
 
 IST POSITION 
 
 cm. 
 
 cm. 
 
 2ND POSITION 
 
 cm. 
 
 cm. 
 
 3RD POSITION 
 
 cm. 
 
 cm. 
 
 How do the distances ab and cd for any position of the ma- 
 nometer compare? Account as fully as possible for this relation. 
 
 c. Repeat the experiment with the mercury manometer, taking 
 three sets of measurements as before. Divide cd by ab for each 
 position. Why is this quotient approximately equal to the density 
 of mercury? Suggest possible reasons why the equality is not 
 exact. 
 
 EXERCISE 4. BUOYANCY OF LIQUIDS 
 
 References. Adams, 183-187; Coleman, 30-32; Car. & C., 
 134-138; Ches. G.&T., 55-57 ; Hoad. Br., 143-144 ; Hoad. EL, 
 154-155; Mumper, 40-41 ; Mil. &G., 74-75 ; Went. &H., 72-74. 
 
 Apparatus. Specific gravity balance and weights to i eg., or 
 platform balance and weights to 5 g. ; for the platform balance a 
 
MECHANICS OF FLUIDS 
 
 support as shown in Figure 7 ; overflow can ; beaker or tumbler ; 
 jar of water ; jar of solution of table salt ; stone with attached 
 
 thread ; block of wood ; 
 
 mop cloth. 
 
 Experiment 10. To find 
 the relation between the buoy- 
 ant force exerted upon a 
 stone in water and the weight 
 of the water it displaces. 
 
 Experimental Work. 
 
 Weigh the stone and the 
 beaker. Catch in the beaker 
 the water displaced by the 
 stone, when lowered by 
 means of a string into the 
 overflow can filled with 
 water (as in Experiment 2). 
 Weigh the displaced water. 
 Suspend the stone from the hook on the under side of the 
 higher scale pan, and let it hang entirely immersed in the jar of 
 water. Be careful to keep it free from the sides and bottom of 
 the vessel. (If a platform balance is used, adjust as shown in 
 Figure 7.) Weigh it thus. This is called the weight of the stone 
 in water. The difference between this and the weight of the stone 
 in air is the buoyant force upon the stone. (Why ?) 
 
 Weigh the stone again, entirely immersed in water as before, but 
 with a greater or a less depth of water above it than before. 
 
 Data and Computations. Record the measurements in the 
 form indicated below, and compute the quantities required : 
 
 Weight of the stone g. 
 
 Weight of the beaker = g. 
 
 Weight of beaker and displaced water = g. 
 
 Weight of stone in water = g. 
 
 Weight of stone at a greater depth in water = g. 
 
 FIG. 7. 
 
GRAVITY PRESSURE IN LIQUIDS 33 
 
 COMPUTATIONS 
 
 Weight of water displaced by the stone = g. 
 
 Buoyant force upon the stone = g. 
 Percentage of difference between the buoyant 
 
 force and the weight of the displaced water = %. 
 
 Discussion. i. Your results should show (within a small 
 error) a simple relation between the weight of the displaced water 
 and the buoyant force upon the stone. State the true relation. 
 
 2. What is likely to be the principal source of error in the ex- 
 periment ? Why? 
 
 3. How is the buoyant force affected by increase of depth after 
 the stone is wholly immersed? Why? 
 
 4. When the stone hangs suspended by the thread in water, 
 what forces sustain its whole weight ? 
 
 Experiment 1 1. To find what difference's, if any, result when a 
 saturated solution of table salt is used instead of water in the pre- 
 ceding experiment. 
 
 Experimental Work. Repeat the above experiment, with the 
 exception of the second weighing in the liquid, using the salt 
 solution instead of water. Be very careful not to mix the water 
 and the solution, and return each to the proper supply vessel. 
 
 Comparisons. i. State the law of buoyancy that holds for 
 both liquids. 
 
 2. In which of the liquids is the buoyant force the greater ? 
 Why? 
 
 Experiment 12. To find the relation between the weight of a 
 block of wood and the weight of water that it displaces when 
 floating. 
 
 Experimental Work. Weigh the block of wood. Find the 
 weight of water that the block displaces when floating, using the 
 overflow can and beaker. Return all liquids to the labeled supply 
 vessels. 
 
 COLEMAN'S NEW MANUAL 3 
 
34 MECHANICS OF FLUIDS 
 
 Data and Computations. Record the measurements in the 
 usual form, and find the percentage of difference between the 
 weight of the block and the weight of the water it displaces. 
 
 What results should you expect to obtain if you floated the 
 block in the salt solution ? 
 
 EXERCISE 5. SPECIFIC GRAVITY OF SOLIDS 
 
 References. Adams, 16, 188-189; Coleman, 33-35; Car. & 
 C., 141-143; Ches. G. & T., 58-60; Hoad. Br., 146-147, 149; 
 Hoad. EL, 157-160; Mumper, 42-45 ; Mil. G., 76-77 ; Went. 
 & H, 75. 
 
 Apparatus. Specific gravity balance and weights to i eg., or a 
 platform balance and support (Fig. 7), or a 25o-g. spring balance ; 
 thread ; tumbler or jar of water ; solid denser and one less dense 
 than water ; sinker \ mop cloth. 
 
 Experiment 13. To find the specific gravity of a solid that 
 sinks in water, applying the principle of Archimedes. 
 
 Experimental Work. Weigh the solid in air. Suspend it from 
 the hook on the under side of the higher scale pan by means of a 
 thread, of such length that the solid will be entirely immersed 
 when the tumbler (or jar) of water is placed beneath the pan. 
 In adjusting the height of the solid, it may be found convenient 
 to change the height of the beam of the balance, which can be 
 done by means of the adjustable rod and thumbscrew. (If a 
 platform balance is used, adjust it as shown in Figure 7.) Air 
 bubbles clinging to the immersed solid must be removed. 
 (Why?) Weigh the solid in water. 
 
 Data and Computations. Compute the specific gravity of the 
 solid. If the specific gravity of the substance is given in Table I 
 of the Appendix, compute the percentage of error of your result. 
 Record as follows, substituting the name of the solid used : 
 
SPECIFIC GRAVITY OF SOLIDS 35 
 
 Weight of the solid in air = g. 
 
 Weight of the solid in water = g. 
 
 COMPUTATIONS 
 
 Weight of an equal volume of water = g. 
 
 Specific gravity of the solid = 
 
 True value of its specific gravity = 
 
 Error = 
 
 Percentage of error = % 
 
 Experiment 14. To find the specific gravity of a solid that 
 floats in water, making use of a sinker. 
 
 Method. In this case a denser body, called a sinker, is at- 
 tached to the solid to keep it wholly immersed when weighed in 
 water. The buoyant force on the solid, when wholly immersed, 
 is greater than its weight ; hence it tends to rise, and so exerts a 
 lifting force on the sinker. The two together, therefore, weigh 
 less in water than the sinker alone. 
 
 Experimental Work. Weigh the solid in air, the sinker in 
 water, and both together in water. Be careful not to leave air 
 bubbles clinging to either immersed body. 
 
 Data and Computations. Record as follows : 
 
 Weight of the solid in air = g. 
 
 Weight of the sinker in water = g. 
 
 Weight of the solid and sinker together in water = g. 
 
 COMPUTATIONS 
 
 Amount by which buoyancy upon the solid exceeds 
 
 its weight = g. 
 
 Buoyant force upon the solid, or weight of an equal 
 
 volume of water . = g. 
 
 Specific gravity of the solid g. 
 
 True value of its specific gravity = g. 
 
 Percentage of error = % 
 
36 MECHANICS OF FLUIDS 
 
 EXERCISE 6. SPECIFIC GRAVITY OF LIQUIDS 1 
 
 References. Adams, 190; Coleman, 36; Car. & C., 144; 
 Ches. G. & T., 61 ; Hoad. Br., 150; Hoad. EL, 161 ; Mumper, 
 46-47; Mil. & G., 78-80; Went. & H., 75. 
 
 Experiment 15. To find the specific gravity of a liquid by 
 weighing a solid in it and in water. 
 
 NOTE. In Exercise 4 a stone was weighed in water and in a saturated 
 solution of table salt. This gives the necessary data for computing the 
 specific gravity of the salt solution, and hence can be made to serve as the 
 experimental work required in this experiment. 
 
 Apparatus. Specific gravity balance or platform balance and 
 support (Fig. 7) ; weights ; tumbler of water ; tumbler of the 
 liquid whose specific gravity is to be found ; a solid denser 
 than water or the liquid, and insoluble in both (a glass stopper 
 serves well) ; mop cloth. 
 
 Method. By applying the principle of Archimedes, we find 
 the weight of the liquid displaced by the solid when immersed in 
 it and the weight of water displaced by the same solid. These 
 are weights of equal volumes of the liquid and water. (Why?) 
 Hence, dividing the one by the other, we have the specific gravity 
 of the liquid. 
 
 Experimental Work. Weigh the solid in air, then in the liquid 
 whose specific gravity is to be found. Wipe it dry, then weigh it 
 in water. 
 
 Data and Computations. Substitute in your record the name 
 of the solid and the liquid used in the experiment. 
 
 Weight of the solid in air = g. 
 
 Weight of the solid in the liquid = g. 
 
 Weight of the solid in water = g. 
 
 1 It is not expected that the pupils will perform the four experiments of 
 this exercise in one laboratory period. The teacher may select from them 
 material for one laboratory exercise, or devote two periods to the four experi- 
 ments. 
 
SPECIFIC GRAVITY OF LIQUIDS 
 
 -m 
 
 COMPUTATIONS 
 
 Weight of a volume of the liquid equal 
 
 to the volume of the solid = g. 
 
 Weight of an equal volume of water = g. 
 
 Specific gravity of the liquid g. 
 
 Experiment 16. To find the specific gravity of a liquid by bal- 
 ancing columns. 
 
 Apparatus. One or more U-tubes, each containing water and 
 another liquid that will not mix with water (Fig. 8) ; meter stick, 
 or metric scale, attached to the support of the 
 tube. 
 
 Method. Figure 8 represents a tube con- 
 taining kerosene, ab, and water, bnm, extend- 
 ing from b round the bend to m. The column 
 of water below b on the one side exactly 
 balances the water up to the same level, n, on 
 the other side ; hence the column of kerosene 
 ab balances the column of water mn. In other 
 words, these columns cause equal pressures at 
 b and n respectively. 
 
 Let d denote the density of water, d* the 
 density of the kerosene, h the height of the 
 water column mn, and ti the height of the kero- 
 sene column ab. Then the pressure at b is d*h' and the pressure 
 at n is dh. (How do we know this ?) These pressures are equal, 
 as stated above, i.e. 
 
 d*ti = dh ; 
 
 from which = 
 
 d h 1 
 
 By definition, the specific gravity of the kerosene is -. In the 
 
 experiment the lengths of the columns h and h 1 are measured; 
 and the above equation shows that the ratio of one to the other 
 (of which to which?) gives the specific gravity of the kerosene. 
 
 b 
 
 -n 
 
 FIG. 8. 
 
MECHANICS OF FLUIDS 
 
 Experimental Work. Find by the above method the specific 
 gravities of the different liquids provided. The measurements to 
 be taken are the heights of the columns above the level of the 
 surface separating the liquids. Make a drawing of the U-tube 
 and its contents in your note book, lettering it as in Figure 8. 
 
 Experiment 17. To find the specific gravity of a liquid by 
 floating a wooden prism in it and in water, and measuring the 
 displacement. 
 
 Apparatus. Demonstration hydrometer (wood prism of i sq. 
 cm. cross section and graduated in centimeters, or one half inch 
 square and graduated in inches) ; hydrometer jar containing 
 water and one containing a saturated solution of table salt or other 
 liquid ; mop cloth. 
 
 Method. The same body displaces equal weights of all liquids 
 in which it floats. (How do we know ?) Let w denote the weight 
 of the wood prism, d the density of water, d' the density of the 
 other liquid, v the volume of water displaced by the prism when 
 floating, and v' the volume it displaces in the other liquid ; then 
 
 w = z/'//' = z*/. (Why?) 
 
 d ! v 
 
 From which = . 
 
 d v 
 
 Hence by this method the specific gravity of the liquid is the 
 ratio (The ratio of what to what ?) 
 
 Experimental Work. 
 
 Float the prism in water 
 and measure the depth to 
 which it sinks. If the 
 water curves up at the edge 
 
 where it comes in contact with the prism, read the 
 scale while looking through the water along the 
 under side of its surface (Fig. 9). Wipe the prism 
 dry, and measure the depth to which it sinks in 
 the other liquid. Remove the prism and wipe it. 
 
 FIG. 9. 
 
SPECIFIC GRAVITY OF LIQUIDS 39 
 
 Data and Computations. Compute the displaced volume of 
 
 each liquid. (The prism, if graduated in centimeters, has a cross 
 
 section of i sq. cm. ; if graduated in inches, its cross section is 
 
 .5 x .5 in.) Record as follows : 
 
 Depth to which the prism sinks in water = cm. 
 Depth to which the prism sinks in the liquid = cm. 
 
 COMPUTATIONS 
 
 Volume of the displaced water = cc. 
 
 Volume of the displaced liquid = cc. 
 
 Specific gravity of the liquid = 
 
 True value of the specific gravity = 
 
 Percentage of error = cf 
 
 Experiment 18. To find the specific gravity of liquids by means 
 of a* common hydrometer. 
 
 Apparatus. Hydrometer jars containing water and kerosene, 
 alcohol, or other liquids ; two common hydrometers, with specific 
 gravity scale, one for light and one for heavy liquids ; jar of rinse 
 water; mop cloth. 
 
 Experimental Work. Study the scale on either hydrometer. 
 It is graduated so that its reading at the surface of any liquid in 
 which it floats is the specific gravity of the liquid. Does the read- 
 ing increase toward the top or the bottom ? Why ? Find from 
 the numbered divisions the value of ttxe smallest interval. Is this 
 value the same at all parts of the scale ? Why does the space be- 
 tween the lines grow smaller toward the bottom ? Take the read- 
 ing of the hydrometer in water, with the eye in the position shown in 
 Figure 9. If this reading is 1000, call it i. Find the value of the 
 smallest division on the other hydrometer. One of these instruments 
 is for liquids denser than water, and the other for liquids less dense. 
 
 Find the specific gravities of all the liquids provided. Rinse 
 and wipe the hydrometer before putting it from one liquid into 
 another, and before putting it away. 
 
40 
 
 MECHANICS OF FLUIDS 
 
 EXERCISE 7. PRESSURE OF GASES 
 
 References. Adams, 170-174; Coleman, 34-41, 45; Car. & 
 C., 145-147; Ches. G. &T., 66-67, 70, 77; Hoad. Br., 151-160, 
 168; Hoad. EL, 162-173, 180; Mumper, 34-38; Mil. & G., 81- 
 87; Went.&H., 76-73, 80. 
 
 Experiment 19. To study the transmission of pressure in fluids 
 by means of the Cartesian diver. 
 
 Apparatus. An hydrometer jar nearly full of 
 water, in which is floated a short glass tube with a 
 bulb blown at one end, inverted and containing just 
 enough air to float it (the water must only partially 
 fill the tube) ; sheet rubber tied air-tight over the jar. 
 
 [A satisfactory substitute for the tube and bulb is 
 shown in Figure n. It consists of a test tube, fitted 
 with a rubber stopper through which a 
 piece of quarter-inch glass tubing is in- 
 serted. The test tube is partly filled with 
 water, the right amount being determined 
 by trial.] 
 
 Experimental Work. Press down on 
 the rubber cover of the jar with the fingers, and increase 
 the pressure till the floating tube sinks. Diminish the 
 pressure till the tube rises. Repeat and observe the 
 change of level of the water in the tube as you vary 
 the pressure with the fingers. De3cribe and account 
 for this change of level. What does it prove con- 
 cerning the transmission of pressure by air and water ? 
 Explain the sinking and rising of the tube. FIG. n. 
 
 Experiment 20. To study the principle of the barometer. 
 
 Apparatus. A bottle with a two-hole rubber stopper, fitted 
 with a glass .tube in one hole and a round plug in the other; jar 
 of water ; three tumblers, one containing mercury ; a Y-tube, con- 
 
 FIG. 10. 
 
PRESSURE OF GASES 
 
 nected with two glass tubes of unequal diameter and about TOO 
 cm. long, the free end of the Y-tube fitted with a piece of rubber 
 tubing and pinchcock (Fig. 12) ; meter rod ; 
 tall iron stand and clamp, or other support ; 
 mop cloth. 
 
 Experimental Work. a. Fill the bottle 
 with water and insert the stopper. See that 
 no air remains in the bottle. With the glass 
 tube in one hole of the stopper and the plug 
 tightly in the other, apply the mouth to the 
 tube and try to " draw " water from the bottle 
 as you would soda water through a straw. 
 State and account for the result. Do you 
 find any evidence that the " suction " exerted 
 on the water in the tube consists of a pulling 
 force ? 
 
 b. Remove the plug from the second hole 
 of the stopper, and repeat the experiment. 
 State and account for the result, avoiding 
 the use of such indefinite terms as " draw," 
 " suck," and "suction." 
 
 c. Place the long glass tubes in two tum- 
 blers of water, as shown in Figure 12 ; and, with the pinchcock 
 open, apply the mouth to the end of the rubber tube and exhaust 
 the air till the water rises nearly to the top of the tubes. Close 
 the pinchcock and remove the mouth from the tube. Open the 
 pinchcock. Describe and account for all that has taken place in 
 the tubes. 
 
 d. Again exhaust the air as before, and take the following 
 measurements, using the stand and clamp to hold the tubes in 
 the required positions : 
 
 With both tubes vertical, measure the height of the column of 
 water in each, measuring from the level of the water in the 
 tumbler. 
 
 FIG. 12. 
 
42 MECHANICS OF FLUIDS 
 
 With one tube slightly inclined and the other very oblique, 
 measure the length of each column along the tube. 
 
 Without changing the position of the tubes, measure the verti- 
 cal height of each column above the level of the water in the tum- 
 blers. (It will be most convenient to measure the height of the 
 columns above the table, and afterwards subtract the height of the 
 water in the tumblers, also measured from the level of the table.) 
 Record the measurements in tabular form, and make a sketch of 
 the apparatus. 
 
 e. Open the pinchcock and let the water run out of the tubes. 
 Substitute the tumbler of mercury for one of the tumblers of 
 water, exhaust the air from the tubes till the water rises nearly to 
 the top of its tube, and close the pinchcock. With the tubes ver- 
 tical, measure the height of the water and mercury columns above 
 the level of the liquids in the tumblers. Empty the tubes and 
 remove them from the tumblers. 
 
 Compute the ratio of the height of the water column to the 
 height of the mercury column. 
 
 Discussion. i. What causes the water to rise in the tubes 
 when the air is partially exhausted ? 
 
 2. How would you find in grams per square centimeter the dif- 
 ference between the pressure of the air remaining in the tubes and 
 the pressure of the outside air ? 
 
 3. What effect has the diameter of the tube on the height to 
 which the water rises ? How would the result be affected if the 
 larger tube had a diameter of several centimeters? 
 
 4. What effect has the unequal inclination of the tubes on the 
 vertical height of the water in them? Explain. 
 
 5. Account for the relative heights of the water and mercury 
 columns in the last part of the experiment. 
 
 6. Suggest a modification of the experiment by which the tube 
 containing mercury would become a barometer. What further 
 modification would be necessary to make the tube containing 
 water a water barometer? 
 
BOYLE'S LAW 
 
 43 
 
 Experiment 21. To determine the degree of exhaustion that 
 the pupil can produce with his mouth. 
 
 Apparatus. A mounted, open-tube manometer containing 
 mercury (Fig. 13), the arms of which are at least 40 cm. long; a 
 heavy-walled piece of rubber tubing attached 
 to the manometer, with a short piece of glass 
 tubing at its free end. Or, instead of the 
 preceding, a piece of glass tubing 40 to 50 
 cm. long, with a piece of rubber tubing 
 attached, in the other end of which a short 
 piece of glass tubing is inserted; tumbler 
 containing mercury ; meter rod. 
 
 Experimental Work. Apply the mouth to 
 the rubber tube, and exhaust the air as fully 
 as possible. This may be done in stages, 
 closing the tube between the efforts either 
 by placing the tip of the tongue against the 
 end of the tube or by pinching the tube in 
 the fingers. Be very careful not to draw the mercury up into the 
 mouth. Measure, in the most convenient way that occurs to you, 
 the greatest difference of level of the columns that you can pro- 
 duce. (If the straight glass tube and tumbler of mercury are 
 provided instead of the manometer, hold the tube in a vertical 
 position, with its lower end in the mercury, and proceed as above.) 
 
 Assuming that the atmospheric pressure is 76 cm., compute the 
 fraction of the whole pressure that you removed by " suction." 
 
 FIG. 13. 
 
 EXERCISE 8. BOYLE'S LAW 
 
 References. Adams, 177-178; Coleman, 44-47; Car. & C., 
 161-163; Ches. G. & T., 75-76; Hoad. Br., 166; Hoad. EL, 
 178 ; Mumper, 39 ; Mil. & G., 95 ; Went. & H., 79. 
 
 Experiment 22. To find the relation between the volume of a 
 given mass of air and the pressure exerted upon it. 
 
44 
 
 MECHANICS OF FLUIDS 
 
 Apparatus. A Boyle's Law apparatus with adjustable closed 
 and open tubes (Fig. 14). 
 
 Method. NOTE. No record is required of the following ex- 
 perimental study of the method of using the apparatus. If the 
 apparatus has been discussed in class, this ex- 
 perimental study of it may be omitted. 
 
 Adjust the open and closed tubes so that the 
 mercury stands approximately at the same level 
 in both. What evidence is there that the closed 
 tube contains a gas above the mercury ? It is 
 air. How would the mercury stand in the closed 
 tube if the air were removed? 
 
 From the fact that the mercury stands at the 
 same level in the two arms, what do you know 
 concerning the relative value of the air pressure 
 upon the two mercury surfaces ? 
 
 Raise the open tube 20 or 30 cm., and while 
 doing so, observe, the change of level of the 
 mercury in the closed tube. Has the confined 
 air increased or diminished in volume ? Has 
 the pressure upon it been increased or de- 
 creased, and from what cause? If we let H 
 denote the height of the barometer and d the 
 difference of level of the mercury in the two 
 arms, then (H + d) cm. of mercury measures 
 the pressure upon the confined air. Why? 
 
 Lower the open tube 50 cm. or more, while 
 watching the change of level of the mercury in 
 
 FIG. 14. 
 
 the closed tube. How is the volume of the confined air changing? 
 Why is it changing? Again letting d denote the difference of 
 level of the mercury columns, the pressure upon the confined 
 air is now (H d) cm. of mercury. Why? 
 
 Experimental Work. a. Clamp the closed tube near the bot- 
 tom of the standard, and leave it in this position for the first three 
 
BOYLE'S LAW 
 
 45 
 
 sets of readings. Adjust the open tube so that the mercury 
 stands at exactly the same level in both tubes. Take a set of 
 readings as indicated in the tabular form below. " Reading of top 
 of closed tube" means the reading of the meter rod at the level 
 of the top of the air space in the closed tube. If the end of the 
 air space is round, estimate the position to which it would extend 
 if it were squared off without changing the volume. The readings 
 called for will be more accurately found by holding the straight 
 edge of a piece of paper across from the tube to the meter rod. 
 
 b. Raise the open tube and clamp it at about the middle of 
 the standard. Take a second set of readings. 
 
 c. Again raise the open tube and clamp it near the top. Take 
 a third set of readings. 
 
 d. Raise the closed tube and clamp it with its upper end near 
 the top of the standard. Lower the open tube and clamp it at 
 about the middle of the standard. Take a set of readings. 
 
 e. Lower the open tube and clamp it near the bottom. Take 
 a set of readings. Leave the tubes clamped at about the same 
 height, and in such a position that the tube rests upon the base. 
 
 / Read the laboratory barometer. This reading is denoted in 
 one of the headings of the tabular record by H. 
 
 Data and Computations. Record as indicated below, and perr 
 form the indicated computations. Since the closed tube is of uni- 
 form bore, the volume of any portion of it is proportional to the 
 length of that portion ; hence the length of the air column may 
 be taken to represent its volume. This is done in the record, 
 where the length of the air column is denoted by V. 
 
 SET 
 
 READING OF 
 TOP OF CLOSED TUBE 
 
 READING OF TOP OF MERCURY COLUMN 
 
 In closed tube 
 
 In open tube 
 
 a 
 b 
 etc. 
 
 crn. 
 cm. 
 
 cm. 
 cm. 
 
 - cm. 
 - cm. 
 
 
 
 
 / Height of the barometer, H = cm. 
 
46 MECHANICS OF FLUIDS 
 
 COMPUTATIONS 
 
 SET 
 
 LENGTH OF 
 AIR COLUMN, OR V 
 
 DIFFERENCE OF LEVEL 
 OF MERCURY COLS. = d 
 
 PRESSURE 
 = Hd=P 
 
 PV 
 
 a 
 b 
 etc. 
 
 
 cm. 
 
 f ( \ 
 
 
 
 cm. (of mer.) 
 cm. (of mer.) 
 
 
 
 cm. 
 
 cm. 
 
 Discussion. i. According to Boyle's Law, what relation should 
 exist among the numbers of the column headed PV (the product 
 of pressure and corresponding volume) ? 
 
 2. Compute the percentage of difference between the greatest 
 and the least of these numbers. With fair apparatus and reason- 
 ably careful work, this difference will not exceed 2 % . 
 
 EXERCISE 9. THE SUCTION PUMP AND THE 
 SIPHON 
 
 References. Adams, 179-181; Coleman, 49, 51, 53; Car. & 
 C., 157-160 ; Ches. G. & T., 80, 82, 84; Hoad. Br.. 169-170; 
 Hoad. El., 182-184, 189; Mumper, 48-51 ; Mil. & G.,, 99, 102, 
 104 ; Went. & H., 84, 86, 88. 
 
 Experiment 23. To study the action of a suction pump. 
 
 Apparatus. A glass suction pump ; battery jar of water ; mop 
 cloth. 
 
 Experimental Work. CAUTION. In working the piston of the 
 pump, always push and pull directly in line with its length. The 
 rod is easily broken with careless handling. Work the piston 
 slowly, never using more than a moderate force, and be careful 
 not to strike the pump against the bottom or side of the jar. 
 
 Starting with the pump empty, place the lower end in the jar of 
 water, and work the piston slowly. Note when the water begins 
 to rise in the tube of the pump. What causes it to rise ? (Any 
 reference to "suction" explains nothing.) Observe the behavior 
 
THE SUCTION PUMP AND THE SIPHON 47 
 
 of the valves during the downstroke and the upstroke of the 
 piston. Operate the pump till you understand the motion and 
 use of the valves. To empty the pump, raise it above the water, 
 pull the piston up, turn the pump so that the water above the 
 piston will run out of the spout, turn the lower end of the pump 
 slightly upward and shake the lower valve out of position, then 
 turn the lower end slightly downward, and the water will run out. 
 Leave the pump empty and place it on the table. 
 
 Draw two figures of the pump one showing the position of the 
 valves during the upstroke of the piston, the other their position 
 during the downstroke. Write a brief description of the action 
 of the pump, referring to your drawings for illustration. 
 
 Experiment 24. To study the action of a siphon. 
 
 Apparatus. Siphon made of glass tubing of not less than \ in. 
 bore, with arms of unequal length and at an angle of about 50 to 
 each other ; two battery jars with water, or better, one jar and 
 sink at which to work ; small beaker ; mop cloth. 
 
 Experimental Work. a. Invert the siphon and fill it from the 
 beaker by pouring into one arm and closing the end of the other 
 arm with a finger, after it is filled. When both arms are full, stop 
 each end with a finger, and turn the siphon right side up (i.e. 
 with the bend at the top) . Observe the effect of removing the 
 finger from either end, leaving the other end closed. State and 
 account for the result. 
 
 b. Hold the ends of the siphon over the jars, with the end of 
 the longer arm lower than the other, and remove the fingers from 
 both ends. From which end does the water run ? Repeat with 
 the end of the shorter arm lower than the other. Does the water 
 always run out of the longer arm ? Does it always run out of the 
 lower end, whichever that may be ? Repeat till you are sure of 
 the answer. 
 
 c. Place one of the jars, with water in it, on some support 
 above the other jar. Siphon the water from this jar into the lower 
 one. While the siphon is running, note the effect of tilting it so 
 
48 MECHANICS OF FLUIDS 
 
 as to vary the height of the outer end. Try the effect of slowly 
 raising the outer end up to and above the level of the surface of 
 the water. 
 
 Discussion. i. What determines from which end of the siphon 
 the water will run ? Why ? 
 
 2. Is the rate of flow more or less rapid when the outer arm of 
 the siphon is lowered ? Why ? 
 
 3. Why does the water not part at the top and fall from both 
 ends when a siphon is started? 
 
IV. STATICS OF SOLIDS 
 
 EXERCISE 10. EQUILIBRIUM OF CONCURRENT 
 FORCES 
 
 References. Adams, 47-54; Coleman, 57-65 ; Car. & C., 40- 
 44 ; Ches. G. & T., 103-106 ; Hoad. Br., 47, 49 ; Hoad. EL, 54, 
 56; Mumper, 58-60, 64, 67; Mil. & G., 23-26; Went. & H., 
 
 4i-45- 
 
 Experiment 25. To study the conditions for equilibrium of three 
 concurrent forces. 
 
 Apparatus. Three 2OOo-g. spring balances, with flat backs or 
 provided with some simple support to keep them level when lying 
 on the table; three short 
 cords tied to a small ring; 
 rule ; a broad board, with 
 narrow strips on two ad- 
 jacent sides, in which are 
 holes i in. apart, together 
 with two nails and a clamp 
 (Fig. 15). 
 
 [Where clamps can be 
 attached , to both sides of 
 the table (Fig. 16), three 
 clamps and three blocks 
 with hooks can be used 
 instead of the board. With 
 
 three tension clamps (Fig. 
 17) the blocks with hooks are unnecessary.] 
 COLEMAN'S NEW MANUAL 4 49 
 
 FIG. 15. 
 
STATICS OF SOLIDS 
 
 FIRST CASE : Wlien none of the angles between the directions of 
 the forces are specified. 
 
 Experimental Work. If the board shown in Figure 15 is pro- 
 vided, fasten two of the balances by their rings to nails inserted 
 
 FIG. 16. 
 
 in holes in the board, and clamp the third balance in position, 
 passing the screw of the clamp through the ring of the balance. 
 If three clamps and three blocks are provided, clamp the blocks 
 to the table, and adjust as shown in Figure 16. 
 
 Attach the cords on the ring to the hooks of the balances. 
 Fasten the balances in position so that the pull on each is between 
 1000 g. and 2000 g. The forces and the angles 
 may all be unequal. See that the balances lie 
 exactly in line with the cords. (Why?) Place a 
 large sheet of paper under the cords with its center 
 under the ring. Hold the paper in a fixed position 
 while you make a small dot exactly at the point 
 under the ring over which the three cords would 
 intersect if produced across the ring, and a dot 
 directly under each of the cords at a distance of not 
 less than 8 or 10 cm. from the ring. The purpose 
 of these dots is to determine the directions of the 
 cords with the greatest possible accuracy. Have the pencil sharp 
 and make the dots small. In locating a dot, the eyes must be ver- 
 tically above the cord, and the cord should be very near the paper. 
 
EQUILIBRIUM OF CONCURRENT FORCES 51 
 
 Without disturbing the balances, take the reading of each, and 
 record the forces on the sheet beside the corresponding cords. 
 Estimate the readings of the scales to tenths of the smallest division. 
 
 Construction. The diagram based on the above record maybe 
 constructed on the sheet used and transferred later to the note 
 book ; or the record may be transferred to the note book at once 
 by laying the sheet flat on a page of the note book and pricking a 
 pin point through each of the dots. 
 
 The construction must be an accurate record of experimental re- 
 sults. It is as follows : Draw lines through the dots indicating the 
 directions of the three cords (and hence also the directions of the 
 forces exerted upon the ring). Call the point of intersection of 
 the lines O. Measure off on the lines from O distances propor- 
 tional to the forces, using a scale that will give a rather large 
 figure. A scale of 200 g. to the centimeter is about the best. 
 .Record the scale adopted near the diagram. Construct a paral- 
 lelogram upon any two of the lines whose lengths have thus been 
 determined, taking the lines as sides of the parallelogram. For 
 convenience the force represented by the line not used in this con- 
 struction will be referred to as the third force. Draw the diagonal 
 of the parallelogram extending from O. Measure the length of 
 this diagonal, and find, from the scale adopted, the magnitude of 
 the force it represents. 
 
 Record beside each of the four lines extending from O its length 
 in centimeters and the magnitude of the force it represents in 
 grams. Indicate the directions of the forces by arrowheads. 
 
 Discussion. i. What force is represented by the diagonal of 
 the parallelogram? 
 
 2. How should this line compare in magnitude and direction 
 with the line representing the third force ? 
 
 3. In what respects and to what extent do the relations shown 
 in your diagram differ from the true relations? Draw the angle 
 that measures the error in the direction of the diagonal, assuming 
 the direction of the third line from O to be correct. 
 
52 STATICS OF SOLIDS 
 
 SECOND CASE : When the angle between the directions of two 
 of the forces is 90. 
 
 Experimental Work. Repeat the experiment, with the balances 
 adjusted so that two of them will act at an angle of exactly 90 
 after the forces are applied, none of the forces being less than 
 1000 g. Measure the angle with a piece of paper folded so that 
 the two parts of a straight edge coincide. 
 
 Construction. Using the same method as before, find the re- 
 sultant of the two forces acting at an angle of 90. Record all 
 lengths and the forces represented by them in the diagram. 
 
 Computation and Comparison. i. Find the same resultant by 
 computation. (The square on the hypotenuse of a right tri- 
 angle is equal to the sum of the squares on the other two sides.) 
 Remember that the resultant is a force, not a line. 
 
 2. Write down for comparison : 
 
 The resultant found by construction = g. 
 
 The resultant found by computation = g. 
 
 The equilibrant (reading of the third balance) = g. 
 
 Compute the percentage of difference between the largest and 
 the smallest of these quantities. This difference is due to experi- 
 mental errors. What are the probable sources of error? 
 
 EXERCISE ii. EQUILIBRIUM OF PARALLEL FORCES 
 
 References. Adams, 55; Coleman, 67-68; Car. & C., 46; 
 Ches. G. & T., 90-95 ; Hoad. Br., 51 ; Hoad. El., 60; Mumper, 
 64; Went. &H., 53. 
 
 Experiment 26. r To study the conditions for equilibrium of three 
 pa r a lie I forces. 
 
 Apparatus. Meter rod ; two 20oo-g. spring balances ; two 
 unequal weights of about 2000 g. and 3000 g., respectively ; cord ; 
 frame to support the balances (Fig. 34) ; rule. 
 
EQUILIBRIUM OF PARALLEL FORCES 53 
 
 Method. The three parallel forces to be studied act upon a 
 meter rod. Two of them are exerted by spring balances, and the 
 other by a weight (Fig. 18). The weight of the rod itself is an 
 additional force which necessarily affects the readings of the 
 balances ; but since this force is not included in the problem 
 
 FIG. 18. 
 
 under consideration, it is eliminated by subtracting from all read- 
 ings of the balances the forces exerted by the balances in support- 
 ing the rod alone. 
 
 Experimental Work. a. Adjust the balances and meter rod as 
 shown in Figure 18, but without the weight attached. The sup- 
 porting cords must be vertical. For convenience in reading the 
 distances, the balances may be hung 80 cm. apart and the cords 
 attached to the rod 10 cm. from each end. Take the readings of 
 the balances when supporting the rod only. Record the readings 
 as the zero readings of the left and right scales, respectively. 
 These are the forces necessary to support the weight of the rod, 
 and they are to be subtracted from all later readings of the scales 
 in order to obtain the forces necessary to balance the weight that 
 is hung on the rod. In order to keep the zero readings the same 
 throughout the experiment, the rod must always be supported 
 from the same points. 
 
54 
 
 STATICS OF SOLIDS 
 
 In Figure 19, A and B denote the points of support of the rod, 
 and C the point where the weight hangs. In this figure, and also 
 in the record, d l denotes the distance AC, d 2 the distance CB, W 
 the attached weight, and^ and/ 2 the forces necessary to balance 
 
 W (not including the forces 
 
 ^ necessary to balance the 
 
 If weight of the rod). 
 
 b. Hang one of the weights 
 on the rod midway between 
 the supporting cords, and 
 record the readings of the 
 scales and the equal dis- 
 tances d and d> 2 . 
 
 c. Move the weight 10 cm. 
 or more to one side of the 
 
 B 
 
 W 
 
 FIG. 19. 
 
 center, and take a second set of readings (i.e. the scale readings 
 and d l and d^). 
 
 d. Take a third set of readings, using the other weight and 
 placing it in a new position on the rod. Remove the weight. 
 
 Draw a figure for each set of readings taken, similar to Figure 
 19, representing the distances and the forces approximately to 
 scale. (An accurate construction is not required.) 
 
 Data and Computations. Record measurements and computa- 
 tions as follows : 
 
 a. ZERO READINGS: Left Scale =- g. 
 
 Right Scale = 
 
 SET 
 
 SCALE READING 
 
 W 
 
 
 
 
 Left 
 
 Right 
 
 
 
 
 b 
 
 g. 
 
 g- 
 
 g- 
 
 cm. 
 
 cm. 
 
 d 
 
 g* 
 g- 
 
 g* 
 g- 
 
 g- 
 g- 
 
 cm. 
 
 cm. 
 
EQUILIBRIUM OF PARALLEL FORCES 
 COMPUTATIONS 
 
 55 
 
 
 FORCES 
 
 
 
 
 
 
 
 SET 
 
 
 A+A 
 
 4-^1 
 
 Difference 
 
 % of Diff. 
 
 7? /*-i- f 
 
 R - W 
 
 
 
 K yiT/j 
 
 
 /, 
 
 /I 
 
 
 V 
 
 
 
 
 
 b 
 
 g- 
 
 g- 
 
 
 
 
 
 
 o/ 
 ~ /o 
 
 g- 
 
 g. 
 
 
 c 
 
 g- 
 
 g- 
 
 
 
 
 
 
 
 o/ 
 
 ~~ /o 
 
 g- 
 
 g- 
 
 d 
 
 g- 
 
 g- 
 
 ' 
 
 
 
 
 
 / 
 /o 
 
 
 g- 
 
 g- 
 
 Discussion. i. The difference between the ratios^ -r-/ 2 and 
 */ 2 -5- //i is due to experimental errors. It should not exceed 2 % 
 unless the spring balances are very inaccurate. If the difference 
 exceeds this, try to discover the source of the trouble. 
 
 2. Write the proportion that holds between the true values of 
 the quantities',^, d^ 4> an d state the proportion in words. 
 
 3. What relation holds between the true values of ,/ 2 , and Wt 
 What name applied to W expresses its relation to the other two 
 forces? 
 
 ALTERNATIVE METHOD 
 
 Apparatus. Meter rod ; three 2ooo-g. spring balances ; 
 three clamps and blocks with hooks for holding balances (Fig. 
 19), or three tension clamps; cord. 
 
 General Directions. 
 
 Follow the directions 
 
 given above, but with the 
 
 following modifications : 
 
 A third spring balance 
 
 is used instead of the 
 
 weight, and the rod and Jit T h 
 
 balances lie on the table 
 
 (Fig. 20). The three 
 
 cords must be parallel, 
 
 and their lengths are to FIG. 20, 
 
50 STATICS OF SOLIDS 
 
 be so adjusted that the reading of the single opposing balance 
 is nearly 2000 g. No allowance is required for the weight of the 
 rod, since it is not supported by any of the balances ; hence omit 
 the experimental work of paragraph (a) above. 
 
 Before reading the balances, raise the meter rod one or two 
 centimeters, and let it drop. Repeat this several times, so that all 
 parts of the apparatus will come into proper adjustment without 
 hindrance from friction. This is very important. In the dia- 
 grams and the record designate the outer forces as / x and / 2 and 
 the inner force as f. 
 
 EXERCISE 12. MOMENTS OF FORCE 
 
 References. Adams, 108-111; Coleman, 69-71; Car. & C., 
 47 a\ Ches. G. & T., 90-93; Hoad. Br., 96-98; Hoad. El., 
 106-108 ; Mumper, 66 ; Mil. & G., 208-210 ; Went. & H., 49-51. 
 
 Experiment 27. To study the conditions for 
 equilibrium of two forces with respect to rotation 
 about an axis. 
 
 Apparatus. Meter rod with hole at 50 cm.; 
 upright with nail to support the rod ; spring balance ; 
 four weights, two of which are equal ; rule. 
 
 [The hole in the rod should be exactly at 50 cm. 
 and slightly displaced laterally, so that the rod will 
 balance horizontally with slight stability on a nail. 
 If one end of the rod is heavier than the other, the 
 defect can be remedied by boring small holes in 
 the heavier end or by means of a sliding wire rider. 
 A i-kg. weight should be used with a 2OOo-g. balance, 
 and a loo-g. weight with a 25o-g. balance. Either 
 combination will serve. A set of " universal labora- 
 tory weights" (Fig. 21) is very convenient for this 
 exercise and those on machines. The set runs from 
 (C. H. Stocking Co., Chicago, manufacturers.)] 
 
 FIG. 21. 
 
 5 to 1000 g. 
 
MOMENTS OF FORCE 57 
 
 Experimental Work. a. Hang the meter rod on the nail. 
 Hang one of the equal weights near each end of the rod, and 
 adjust them so that the rod balances in a horizontal position. 
 Let w l and w 2 denote the weights, and a v and <z 2 the respective 
 distances from their points of suspension to the axis (the nail). 
 Record the values of these quantities in tabular form, as given 
 below. 
 
 b. Hang two unequal weights on the rod, and adjust them 
 so that they balance. The nearer the weights are to the ends of 
 the rod, the more accurate the results are likely to be. (Why?) 
 
 c. Repeat with two other unequal weights. 
 
 d. With a 25o-g. spring balance use a loo-g. weight for the 
 remaining work ; with a 2Ooo-g. balance use a looo-g. weight, or 
 the largest provided. Hang the weight 20 cm. from an end of 
 the rod, and support the rod on the hook of the spring balance, 
 applied nearer the same end of the rod. Let f denote the force 
 applied by means of the balance and a the distance from its point 
 of application to the axis ; and let w 2 denote the weight and a 2 
 the distance of its point of application from the axis. 
 
 e. Repeat with the balance applied between the weight and 
 the axis. After recording the set of measurements, try the effect 
 of applying the balance nearer and nearer the axis, until it is as 
 near as you can get it. State 
 
 the general result of these 
 
 trials without taking meas- 
 urements. 
 
 Draw a figure for each 
 
 set of readings, similar to P IG 22 
 
 Figure 22, representing the 
 distances and the forces approximately to scale. 
 
 /. Adjust the weight and the balance as in either (//) or (e), with 
 the hook tied to the rod to keep it from slipping, and observe the 
 change in the reading of the balance when the force exerted by it 
 is made more and more oblique to the vertical. Does the moment 
 of the force change as the force changes ? How do you know ? 
 
STATICS OF SOLIDS 
 
 Does its arm change (while it is still applied at the same point) ? 
 What distance is the arm of the force when the force is oblique ? 
 Measurements need not be taken. 
 
 Data and Computations. Record in the form given below. 
 Compute the products w^ (or /^i) and w 2 a 2 for each set of 
 measurements, also their difference and percentage of difference. 
 
 a 
 b 
 c 
 
 d 
 
 e 
 
 V>1 
 
 1V 2 
 
 1 
 
 2 
 
 Wli 
 
 W 2 2 
 
 DifT. 
 
 %ofDiff. 
 
 g- 
 g 
 .g- 
 /i 
 g- 
 g- 
 
 g- 
 g- 
 g- 
 
 g- 
 g. 
 
 cm. 
 cm. 
 cm. 
 
 cm. 
 
 cm. 
 
 /11 
 
 
 
 
 
 % 
 
 % 
 
 o/ 
 /o 
 
 ()/ 
 ~~ fO 
 
 "/ 
 
 
 cm. 
 cm. 
 
 
 cm. 
 
 
 
 /(> 
 
 Discussion. i. Express, both as an equation and as a pro- 
 portion, the relation that holds for the true values of the 
 quantities w l9 w 2 , a lt and a 2 ; and also for the true values of w 2 , 
 /!, a ly and a 2 . 
 
 2. State the two conditions necessary for the equilibrium of two 
 forces with respect to rotation about an axis, and word the state- 
 ment so as to cover every case presented in the experiment. 
 
 3. In this experiment we have not had occasion to consider 
 the force exerted on the rod by the nail. What do you know 
 (from the laws studied in Exercise n) about the magnitude and 
 direction of this force and its effect on the behavior of the rod ? 
 
 4. Does the force exerted by the nail tend to cause the rod to 
 turn in either direction? Why or why not? 
 
 5. In Exercise n what forces tend to cause rotation about C 
 as an axis? Why is there not rotation about this point? Prove 
 your answer correct by making use of any one of the sets of 
 measurements taken in that exercise. 
 
CENTER OF GRAVITY AND MOMENT OF WEIGHT 59 
 
 EXERCISE 13. CENTER OF GRAVITY AND MOMENT 
 OF WEIGHT 
 
 References. Adams, 61-66; Coleman, 73-75; Car. and C., 
 5!-5 2 > 55-5 6 ; Ches. G. & T., 98-100; Hoad. Br., 70-71, 74; 
 Hoad. EL, 82-86; Mumper, 68-69; Mil. & G., 33-34 ; Went. 
 & H., 55-59- 
 
 Experiment 28. To find whether the point of application of the 
 weight of a body, regarded as a single force, changes, or remains 
 the same, under different conditions. 
 
 Apparatus. Meter stick ; wooden or iron clamp ; support 
 with a narrow edge ; platform balance and weights. 
 
 FIRST CASE: A REGULAR BODY 
 
 Experimental Work. Weigh the meter stick. Balance it in a 
 horizontal position on the sharp edge of the support. The weight 
 of the stick, under these conditions, is evidently equivalent to a 
 single force acting at a point vertically above the support, for it is 
 balanced by the upward pressure of the support. This point, then, 
 is, by definition, the center of gravity of the stick when thus 
 balanced. Record its position as the reading of the meter scale 
 at the axis. (On account of slight variations in the density or 
 cross section of the stick, the reading may not be exactly 50 cm.) 
 
 The purpose of the experiment is to determine whether the 
 weight of the stick is equivalent to a single force acting at this 
 same point, or whether it 
 must be regarded as act- 
 ing at some other point, 
 when the stick is bal- 
 anced in a different way ; FJG 
 in other words, to deter- 
 mine whether the center of gravity remains fixed or shifts to a 
 new position when the conditions are changed. Balance the stick 
 in a horizontal position on the support as before, but with a loo-g. 
 
60 STATICS OF SOLIDS 
 
 weight hanging on it i cm. from its zero end (Fig. 23). (It is 
 less convenient to calculate distances from the loo-cm, end.) 
 Record the position of the axis as the reading of the meter scale 
 at that point. 
 
 Data and Computations. When the stick is balanced with the 
 attached weight, this weight tends to pull the shorter end of the 
 stick down ; while the weight of the stick itself tends to pull 
 the longer end down. Obviously, if we regard the weight of the 
 stick as one force, the stick is in equilibrium under the action of 
 two equal and opposite moments of force ; namely, the moment 
 of the attached weight and the moment of the weight of the stick. 
 That is, the product of the attached weight and its arm is equal 
 to the product of the weight of the stick and its arm (the arm of 
 the weight of the stick being the distance from the axis to the 
 point of application of the weight of the stick, wherever that 
 may be). 
 
 Let Wi denote the attached weight, w 2 the weight of the stick, 
 #! the arm of the attached weight, and a 2 the arm of the weight of 
 the stick. Then, as stated above, w^a^ W 2 w 2 . Since a 2 is the 
 only unknown quantity in this equation, it can be computed ; and, 
 measuring off this distance from the axis, we come to the point 
 where the weight of the whole stick must be regarded as acting to 
 produce the observed effect. The point thus found is, therefore, 
 the center of gravity under the conditions of the experiment. Is 
 this second position of the center of gravity the same as the 
 first? 
 
 Copy Figure 22 in your note book, and record data and com- 
 putations as follows : 
 
 Weight of the meter stick, w^ = g. 
 Position of the axis when the stick is balanced alone 
 
 (first position of the center of gravity of the stick) = cm. 
 
 Attached weight, w = g- 
 
 Position of attached weight = i cm. 
 
 Position of axis for equilibrium with weight attached = cm. 
 
CENTER OF GRAVITY AND MOMENT OF WEIGHT 6 1 
 
 COMPUTATIONS 
 
 Arm of attached weight, a = cm. 
 
 Arm of the weight of the stick (distance from the axis 
 to second position of center of gravity of stick), 
 a 2 = w^a^ -r- w 2 = cm. 
 
 Second position of center of gravity of stick = posi- 
 tion of the axis -{- a 2 = cm. 
 
 Difference between the first and second positions of 
 
 center of gravity of stick = cm. 
 
 Conclusion. Assuming that experimental errors may reason- 
 ably account for a difference of .3 cm. in the two positions found 
 for the center of gravity of the stick, what answer have you found 
 to the question under consideration? 
 
 SECOND CASE: AN IRREGULAR BODY 
 
 General Directions. Repeat the above experiment with a 
 clamp firmly attached to the loo-cm, end of the stick, and 
 remaining thus throughout the experiment. The stick and clamp 
 are to be regarded as one irregular body. Weigh this irregular 
 
 FIG. 24. 
 
 body, and find its center of gravity when balanced alone on the 
 axis, and again when it is balanced with a weight of 200 g. to 
 500 g. attached near the lighter end (Fig. 24). If there is time 
 enough, make two trials, either with different attached weights or 
 with the weight in different positions. 
 
 Do the results in this case lead to the same conclusion as before, 
 or to a different one ? 
 
62 STATICS OF SOLIDS 
 
 EXERCISE 14. CENTER OF GRAVITY AND THE 
 STATES OF EQUILIBRIUM 
 
 References. Adams, 61-69; Coleman, 73-80; Car. & C. s 
 51-52, 55-58; Ches. G. & T., 98-101; Hoad. Br., 70, 71, 74, 
 75; Hoad. EL, 82-87; Mumper, 68-69 ; Mil. & G., 33-37 ; 
 Went. & H., 55-57, 60. 
 
 Experiment 29. To find the center of gravity of an irregular 
 piece of cardboard. 
 
 Apparatus (for Experiments 29 and 30). Irregular piece of 
 cardboard ; pins ; small plumb line made of thread and bullet ; 
 rule. 
 
 Experimental Work. a. Stick a pin through the cardboard 
 near one corner, and enlarge the hole enough to allow the card- 
 board to swing freely. Stick the pin, with the cardboard on it, 
 horizontally into the edge of the table or other support. Hang 
 the plumb line on the pin in front of the cardboard, but not quite 
 touching it. When both have come to rest, grasp them together 
 at the bottom, make a dot accurately under the thread, and with 
 a sharp pencil and rule draw a line connecting the dot with the 
 point of suspension. How do you know that the center of gravity 
 of the cardboard is at some point on this line, or, more accurately, 
 at some point directly back of this line, midway between the 
 surfaces? 
 
 b. Suspend the cardboard from another corner, and determine 
 a second line in the same way. Where is the center of gravity of 
 the body. Would this point be vertically under any point of sus- 
 pension from which the cardboard hangs at rest? Test the mat- 
 ter by suspending the body from a third point, chosen at random. 
 State the result. 
 
 c. Trace the outline of the cardboard in your note book, mark 
 the three points of support, and draw the plumb lines. Letter the 
 center of gravity C. 
 
CENTER OF GRAVITY AND STATES OF EQUILIBRIUM 63 
 
 Experiment 30. To study the states of equilibrium of a sus- 
 pended body. 
 
 Experimental Work. a. Hang the cardboard again from one 
 of the holes near the edge, turn it out of the position in which it 
 hangs at rest, and release it. How does it behave as it comes to 
 rest ? Account for this motion as definitely as you can. In what 
 state of equilibrium does it come to rest? How do you know? 
 
 b. Suspend the cardboard exactly at the center of gravity, en- 
 large the hole till it turns freely, and note its behavior when turned 
 out of a position of rest and released. Does it always come to 
 rest in the same position? 
 
 It is not easy to find the center of gravity exactly ; it generally 
 happens that the hole is far enough out of position to affect appre- 
 ciably the behavior of the cardboard. What reason have you, if 
 any, for thinking that such is the case in your experiment ? How 
 would the body behave when turned and released, if it were sus- 
 pended accurately at the center of gravity? Why? In what state 
 of equilibrium would it be when thus suspended and at rest? 
 
 c. Suspend the cardboard at one of the outer holes, and try to 
 balance it with the center of gravity vertically above the support. 
 Why is it practically impossible to secure equilibrium in this posi- 
 tion? What would equilibrium in this position be called? 
 
 Experiment 31. To study the states of equilibrium of bodies 
 supported on a horizontal surface. 
 
 Apparatus. Such bodies as cylinder, cone, sphere, oblate and 
 prolate spheroids ; an empty, round-bottom flask ; a round-bottom 
 flask loaded with shot so that it will stand upright. (The shot can 
 be kept in place by parafftne or wax melted over it.) 
 
 Experimental Work. a. A body may be in different states of 
 equilibrium at the same time with respect to motion in different 
 directions. Experiment with the different bodies provided, and 
 determine their states of equilibrium in different positions, and 
 with respect to motion in different directions for each position. 
 
STATICS OF SOLIDS 
 
 Give a complete account of each case studied, with drawings to 
 illustrate. Include cases of unstable equilibrium, whether you can 
 
 perfectly realize them or not. 
 Locate as closely as possible the 
 center of gravity in each draw- 
 ing, and indicate by a dotted line 
 the path that it would describe if 
 the body were tipped or rolled. 
 
 b. Balance your pencil on its 
 point on your finger, making use 
 of a pocketknife to secure stable 
 equilibrium, as shown in Figure 
 25. Draw a figure showing the 
 position of equilibrium as you 
 secured it, and indicate approxi- 
 mately the position of the center 
 
 of gravity of the knife and pencil regarded as one body. How 
 definitely does the experiment determine this center of gravity? 
 
 EXERCISE 15. STIFFNESS OF BEAMS. THE TRUSS 
 
 References. Adams, 26, 140-143; Coleman, 202-204, 2 6 ; 
 Car. & C., 14-15 ; Hoad. Br., 27 ; Hoad. EL, 27-30 ; Mil. & G., 
 152-156 j Mumper, 22 ; Went. & H., 23-30. 
 
 Experiment 32. To study the effect of the length and the shape 
 of the cross section of a beam upon its stiffness. 
 
 Apparatus. Three meter sticks ; small rod of steel or brass one 
 meter long, and a tube of the same material, length, and weight. 
 
 Experimental Work. a. Note the effort required to bend a 
 meter stick in the hands, while holding it near the ends. Repeat 
 several times, decreasing the distance between the hands with each 
 trial, and observe how difficult the bending becomes as the length 
 of the bent portion is decreased. Account for the observed facts 
 as fully as you can. 
 
STIFFNESS OF BEAMS. THE TRUSS 
 
 b. Holding the rod at the ends, bend it as before in the plane 
 of its smallest dimension (thickness), then in the plane of its 
 width. Compare the stiffness of the rod with respect to bending 
 in these two planes. (Is the stiffness slightly greater, considerably 
 greater, or several times greater in the one case than in the other?) 
 To vary the experiment, rest the ends of the rod on fixed supports 
 (as the edges of two stools), first flatwise, then on edge; and, 
 grasping it firmly at the middle, push down upon it. 
 
 When the rod is bent is its inner side stretched or compressed? 
 Is its outer side stretched or compressed? (If in doubt, mark 
 half-inch spaces on the two sides of a long rubber eraser, and 
 observe the change in the length of these spaces when the rubber is 
 bent in the fingers.) Account as fully as you can for the unequal 
 stiffness of the meter rod with respect to bending in the two planes. 
 
 c. Place the three meter rods together so as to form a compound 
 rod of approximately square cross section. Test the stiffness of 
 this compound rod with 
 
 respect to bending in 
 
 the two planes (Fig. 26). 
 
 In doing this it will be 
 
 necessary to place the 
 
 ends of the rod on fixed 
 
 supports and push down 
 
 hard at the middle. 
 
 Carefully observe whether bending in either position is necessarily 
 
 accompanied by slipping of one surface over another where the 
 
 rods are in contact. Account as fully as you can for the unequal 
 
 stiffness of the set of rods in the two positions. 
 
 If the rods were nailed together along their whole length, do 
 you think the stiffness would be increased for the first position 
 shown in the figure? Do you think it would be for the second 
 position? Give reasons for your opinion. 
 
 d. Test the relative stiffness of the metal rod and tube, and 
 account for the results. (They contain equal quantities of the same 
 material.) 
 
 COLEMAN'S NEW MANUAL 5 
 
 FIG. 26. 
 
66 
 
 STATICS OF SOLIDS 
 
 Experiment 33. To assemble the members of a model bridge 
 truss, and to study their function as parts of the whole. 
 
 Apparatus. A separable model of the Pratt bridge truss 
 (Fig. 27). 
 
 [Short wire rods permanently inserted in the ends of the struts, 
 a, slip loosely through holes in the top and bottom members, b \ 
 the tie-rods, c y are each provided with a thumbscrew at the top, 
 
 FIG. 27. 
 
 by which they are tightened. Suitable dimensions for the truss are : 
 length 100 cm., height 15 cm., cross section of top and bottom 
 members and struts half inch square. The tie-rods are slender 
 rods of iron or steel ; the other members of hard wood.] 
 
 Experimental Work. a. Put the truss together, and test its 
 stiffness when the tie-rods are tight and also when they are loose. 
 Observe whether the tension of the tie-rods increases when the 
 truss is carrying a load. (This can be tested by noting the pitch 
 of the sound when the rods are plucked. The greater the tension 
 the higher the pitch.) 
 
 b. Test the stiffness of the truss when inverted, and account for 
 the result, noting particularly the behavior of the tie-rods. 
 
 c. Observe and account for the curvature of the truss when the 
 rods are overtightened. 
 
 d. The parts or members of the truss are the top and bottom 
 chords, the struts (the vertical members), the end braces, and the 
 tie-rods. Which of these are " tension members " and which are 
 "compression members"? Which require stiffness? Account 
 for the stiffness of the truss as a whole. 
 
V. DYNAMICS AND MACHINES 
 
 EXERCISE 1 6. 
 
 FALLING BODIES: WHITING'S 
 METHOD 
 
 References. Adams, 28-32; Colenian, 91-98; Car. & C., 
 33-34, 60-6 1 ; Ches. G. and T., 114-118; Head. Br., 39, 78- 
 79, 81 ; Hoad. EL, 42-43,45; Mumper, 55-56; Mil. & G., 
 38-47; Went. & H., 168-171. 
 
 Experiment 34. To find the acceleration of a falling body. 
 
 Apparatus. A long stick suspended to swing as a pendulum 
 (Fig. 28); meter rod; ball; carbon paper; thread; pins; 
 matches ; watch or small clock with 
 seconds dial ; large piece of cloth. 
 
 [For the pendulum use a stick from 
 1.5 to 3 m. long, of rectangular cross 
 section about 2 by 4 cm. Suspend it 
 by a strip of canvas or leather, with its 
 wider side turned toward the suspended 
 ball. A strip of carbon paper is fastened 
 at top and bottom of the pendulum, 
 with paper beneath to receive the im- 
 pression. The ball must be heavy 
 enough to hold the pendulum at a con- 
 siderable angle, as shown in the figure; 
 
 if of wood, it should not be less than /////////////////////////////// 
 about 5 cm. in diameter. For a long 
 
 pendulum, an iron ball about 3 cm. in diameter may be neces- 
 sary. The apparatus must be so adjusted that the suspended 
 ball just touches the pendulum when the latter hangs vertical.] 
 
 67 
 
68 DYNAMICS AND MACHINES 
 
 Experimental Work. Fold the cloth into a small mat and 
 place it on the floor so that the ball will fall on it. Place a strip 
 of white paper under the carbon paper at top and bottom of the 
 pendulum. This strip should be as long as the carbon paper 
 and a centimeter or more wider than the pendulum. Fold the 
 extra width over, make a sharp crease, open out the fold at a 
 right angle, and fasten to the side of the pendulum with two pins 
 (out of the way of ihe falling ball). Adjust the ball and pendu- 
 lum as shown in the figure, by means of a thread passing over the 
 three nails. The ball should hang near the middle of the paper. 
 Without letting the thread slip on the nails, strike the ball against 
 the carbon paper, marking its position by the dot thus made on 
 the paper beneath. Stop the swinging of the ball (rotation, due 
 to the untwisting of the thread, does not matter, but the results 
 will be worthless if the ball is swinging at all), then burn the 
 thread between the upper nails. The pendulum should strike the 
 ball, making a dot on the lower paper. Measure the distance 
 between the upper and lower dots. 
 
 Make a second trial ; but before doing so, mark the dots al- 
 ready made on the paper, so they will not be mistaken for 
 new ones. It is better to replace the paper by a new piece 
 after a few trials. If the second result does not differ by more 
 than i cm. from the first, take the average of the two. If the 
 difference is greater than i cm., make further trials till you get 
 three or more results agreeing within i or 2 cm., and take their 
 average. Call the average distance s. 
 
 The ball falls s cm., while the pendulum is swinging to a vertical 
 position, i.e. while it is making half a swing in one direction. To 
 determine this time, set the pendulum swinging, and count the 
 number of swings it makes in exactly 60 sec., timing with the second- 
 hand of a watch. Repeat, if you are at all doubtful of the result. 
 
 Data and Computations. The rate of the pendulum does not 
 change as the arc through which it swings grows less ; hence from 
 the number of swings in 60 sec. you can determine the time of 
 
FALLING BODIES: PACKARD'S METHOD 69 
 
 one swing. Half this time is the time it takes the ball to fall 
 s cm. Compute this time, and call it t. Substitute your values 
 of s and / in the formula for falling bodies, and solve for g. Com- 
 pute the percentage of error of your result. Record as follows : 
 
 Distance the ball falls before striking the pendulum : 
 
 first trial = cm.; second trial = cm.; average, s = cm. 
 
 Number of swings the pendulum makes in 60 sec. : 
 first trial = ; second trial = ; average = 
 
 Time of swing, or time of fall of the ball, /, = sec. 
 
 Value ofg from the experiment = -^j = cm. 
 
 True value of g =980 cm. 
 
 Error = 
 
 Percentage of error = % 
 
 EXERCISE 17. FALLING BODIES: PACKARD'S 
 METHOD 
 
 References. Adams, 28-32, 48-51, 56-60; Coleman, 66, 91- 
 106 ; Car. & C., 33-34, 48, 60-6 1 ; Ches. G. & T., 114-118, 156 ; 
 Hoad. Br., 39, 78-82, in a ; Hoad. El., 42-44, 91 ; Mumper, 55- 
 56, 63, 81, 90 ; Mil. & G., 38-47, 51-52 ; Went. & H., 168-173. 
 
 Experiment 35. To 
 
 find the relation between 
 the distance passed over 
 and the time in uniformly 
 accelerated motion. 
 
 Apparatus. A broad 
 inclined plane, with an 
 auxiliary incline (Fig. 
 29) ; steel ball, i in. or 
 
 more in diameter, ac- 
 curately turned and polished ; large sheet of carbon paper ; rule. 
 [The plane should be at ^ast 16 in. square, with a width of at 
 
70 DYNAMICS AND MACHINES 
 
 least ii in. at the side of the auxiliary plane, and must be smooth 
 and even. The auxiliary plane should be about 5 in. long, and 
 provided with a groove running exactly parallel to the top and 
 bottom of the principal plane. This groove is so constructed that 
 the ball does not drop on passing from it to the principal plane. 
 Roth planes are inclined at an angle of about 15. A spring clip 
 to hold the paper in position at the top is desirable. This device 
 for the study of accelerated motion is due to Mr. John C. Packard, 
 of the Brookline, Mass., High School. A very complete and con- 
 venient apparatus for this experiment is manufactured by the 
 L. E. Knott Apparatus Co., Boston.] 
 
 Experimental Work. Place a large sheet of writing paper (not 
 smaller than 8 x 10 in.) on the plane in the position shown in 
 Figure 29. Place the ball in the groove of the auxiliary plane, and 
 let it roll down and over the paper. Observe its path over the 
 paper, and find by trial at what point on the auxiliary plane the 
 ball must be released to cross the bottom of the paper near 
 the farther corner. This is the path that the ball should describe 
 when the record is taken. 
 
 Before taking a record, see that the edges of the sheet are 
 exactly parallel with the edges of the plane, and that it just 
 touches the foot of the auxiliary plane. Hold the paper in this 
 position while taking the record, if a spring clip is not provided. * 
 Lay the carbon paper on the record sheet (with the black side 
 down), and release the ball at the point previously determined* 
 The ball must be freed from the control of the auxiliary plane 
 exactly at the point where it starts across the paper (or at some 
 other definitely marked point), and its path at that point must 
 be parallel to the top edge of the paper. Be sure you have the 
 right adjustment. Repeat till at least two satisfactory traces of 
 the path of the ball are secured. (Use the other side of the 
 paper for a second trace, or take another sheet.) 
 
 Take one or more traces with the paper extending lengthwise 
 from right to left (instead of from top to bottom). In this case 
 
FALLING BODIES: PACKARD'S METHOD 
 
 b' 
 
 start the ball higher up the auxiliary plane, so that it will cross the 
 bottom of the sheet near the farther corner, as before. 
 
 Principle of the Method. If any number of equidistant parallel 
 lines be drawn on a sheet on which the ball has traced its path, 
 taking for the first of these lines the edge of the paper at which 
 the trace begins, these lines will divide the curve into parts ab\ 
 b'J , c'd 1 , d*e' (Fig. 30), which were traversed by the ball in equal 
 times. This is explained as 
 follows : The motion along the 
 curve may be resolved into two 
 components at right angles to 
 each other one across the 
 plane (from left to right in the 
 figure) and the other down 
 the plane. These we shall call 
 the horizontal and the downward 
 components, respectively. The 
 horizontal component was wholly 
 imparted on the auxiliary plane. 
 It remains constant on the prin- 
 cipal plane, since there is no 
 
 B 
 
 FIG. 30. 
 
 force acting to change it (friction, being inappreciably small, is 
 disregarded). If the principal plane were horizontal, the ball would 
 cover the equal distances ab, be, cd y and de in equal times, the 
 velocity being constant. With the principal plane inclined, the 
 direction of the unbalanced force acting on the ball is down 
 the plane, and it affects only the downward component of the 
 motion. Knowing, therefore, that the ball covers equal distances 
 from right to left in equal times, whether the plane is inclined or 
 not, it follows, as stated above, that the equidistant parallel lines 
 divide the curved path into parts which the ball traversed in equal 
 intervals of time. During the first of these equal time intervals 
 the downward distance covered is bb 1 , during the first two intervals 
 it is cc\ during the first three drf, etc. This downward motion 
 
DYNAMICS AND MACHINES 
 
 is in no wise affected by the horizontal motion the ball would 
 make equal progress down the plane if it had a greater horizontal 
 component of motion or if it had no horizontal motion at all. In 
 this experiment the horizontal component of motion merely serves 
 the purpose of marking equal time intervals. 
 
 Construction and Comparison. On one of your record sheets 
 draw very accurately five equidistant parallel lines, as in Figure 30, 
 taking the equal distances such that the fifth line cuts the curve 
 near its lower end. The first line AB must be taken through the 
 point where the ball passes from the control of the auxiliary plane 
 and is free to follow a curved path. Letter the sheet to correspond 
 with Figure 30. The five lines mark off four equal time intervals. 
 Draw the horizontal line abcde. Measure accurately the downward 
 distances bb', cc\ dd* , and ee' . The distance ee' being the greatest, 
 it is probably determined with the greatest accuracy. It is there- 
 fore taken as the basis of comparison. Find the difference between 
 bb* and y 1 ^ ee' , between cc' and -^ ee' , and between dd' and T 9 g- ee 1 . 
 If the work is carefully done, these differences will not exceed i or 
 2 mm. Record as follows : 
 
 TIME TAKEN 
 
 FOR THE 
 RESPECTIVE 
 DISTANCES 
 
 SQUARE OF 
 
 THE TIME 
 
 DOWNWARD DISTANCES 
 
 DIFFERENCE 
 
 Measured 
 
 Computed from ee' 
 
 I interval 
 
 1*= I 
 
 bb 1 = cm. 
 
 l|l6 ee 1 = cm. 
 
 cm. 
 
 2 intervals 
 
 2*= 4 
 
 cJ = cm. 
 
 4|i6 ee' cm. 
 
 cm. 
 
 3 intervals 
 
 3 2 = 9 
 
 dcF = cm. 
 
 9| 1 6 ee r = cm. 
 
 cm. 
 
 4 intervals 
 
 42=16 
 
 ee 1 cm. 
 
 i6|i6 ee' = cm. 
 
 cm. 
 
 Make a similar construction and tabulation of results for the 
 other curves taken, varying the work, however, by marking the 
 curve off into three or five equal time intervals, instead of four, as 
 above. When three intervals are taken, compare the first down- 
 ward distance with ^ of the third, and the second with -| of the 
 
THE SIMPLE PENDULUM 
 
 73 
 
 third ; where five intervals are taken, compare the first downward 
 distance with -% of the fifth, the second with -fa of it, the third 
 with 2^5 of it, and the fourth with if of it. 
 
 Preserve and hand in the sheets on which the curves were 
 taken and the constructions made, as a part of the record of the 
 experiment. 
 
 Discussion (oral except the first question). i. What relation 
 does this experiment establish (within a small limit of error) 
 between the downward distance and the time ? Derive this 
 relation from the tabulated record. 
 
 2. How is it known that the horizontal component of the 
 motion of the ball is constant ? 
 
 3. What is the unbalanced force acting 
 on the ball when it is on the principal plane? 
 What is its direction ? Is it a constant or 
 a variable force ? Prove your answer. 
 
 4. What is the direction of the accelera- 
 tion of the ball? Why? Is it a constant 
 or a variable acceleration? How is this 
 shown by the results? What is the reason 
 for its being so ? 
 
 EXERCISE 1 8. THE SIMPLE 
 PENDULUM 
 
 References. Adams, 76-78, 81-82; 
 Coleman, 130-135; Car. & C., 68-71;, 
 Ches. G. &T., 164-166 ; Hoad. Br., 83-85 ; 
 Hoad. EL, 92-95 ; Mumper, 95 ; Mil. & G., 
 224 ; Went. & H., 189-191. 
 
 Apparatus. A pendulum stand with FlG - Si- 
 
 three pendulums of adjustable length, one with wooden and two 
 with iron or lead bobs (Fig. 31) ; watch or clock with second- 
 hand ; meter rod. 
 
74 DYNAMICS AND MACHINES 
 
 [A convenient and efficient adjustable suspension is shown in 
 Figure 31. A slanting notch is cut at an angle of about 35 to 
 
 receive the thread, and 
 
 | ("gs] iu a cork glued above, in 
 
 ^ which is cut a slit to 
 
 FIG ' 32 ' receive the thread. The 
 
 friction in the cork holds the pendulum. The pendulum clamp 
 shown in Figure 32 is also especially adapted to the requirements 
 of the exercise. It can be clamped to any support rod.] 
 
 Experiment 36. To find whether the amplitude of a pendulum 
 affects its rate. 
 
 Experimental Work. -a. Adjust the two pendulums with iron 
 bobs to exactly the same length, making them about as long as 
 the apparatus will permit. Test the equality of their lengths by 
 careful measurement, and also by starting them together with equal 
 amplitudes. If there is even a very slight difference in their 
 lengths, the shorter will slowly gain on the other, and the differ- 
 ence will begin to be noticeable in a minute or so. 
 
 After securing exact adjustment, start the pendulums together, 
 giving one an amplitude of not more than 5 and the other an 
 amplitude of 30 to 35. Observe whether the pendulums con- 
 tinue for at least a minute to begin and end their swings together. 
 A difference as small as a tenth of a swing can be seen, whereas a 
 difference of one whole swing is the least that would be detected 
 by counting the number of swings made by each pendulum in a 
 given tirtie. Do not count, but observe. Verify the result by a 
 second trial, giving the larger amplitude to the other pendulum. 
 About what difference, if any, do you observe in the rates of the 
 two pendulums? 
 
 b. Again start the pendulums together, giving one an amplitude 
 of about 6 and the other less than 3. Let them swing thus for 
 a minute or more. How do their rates compare ? 
 
 c. What do the above tests show concerning the effect of the 
 amplitude of a pendulum on its rate? 
 
THE SIMPLE PENDULUM 
 
 75 
 
 Experiment 37. To find whether the rate of a pendulum is 
 affected by either its mass or its material. 
 
 Experimental Work. Adjust the pendulum with a wooden 
 bob to the same length as one with an iron bob. The pendulums 
 should be long. The length is measured from the point of sup- 
 port to the middle of the bob. Start the two pendulums together, 
 with equal amplitudes (not above 10), and observe whether one 
 gains on the other in a minute or more. How do you find the 
 rates of the pendulums to be affected by the fact that they are of 
 unequal mass and of different materials ? 
 
 Experiment 38. To find the relation between the period of a 
 pendulum and its length. 
 
 Experimental Work. Adjust the three pendulums to lengths 
 having the ratio of i, \, and ^-. Lengths of 36 in., 9 in., and 4 in. 
 will be most convenient, if the height of the support will permit. 
 Count the number of single vibrations that each of the pendulums 
 makes in exactly 60 sec. 
 
 If you have time, test the ratio of the periods of the pendulums 
 by starting together the 36-in. and the 9-in. pendulums, and observe 
 how many swings of the shorter occur during one swing of the 
 longer. Test the 36-in. and the 4-in. pendulums in the same way. 
 
 Data and Computations. Let / denote the length of a pendu- 
 lum and / the time of one vibration. Compute for each of the 
 pendulums the value of the ratio V/:/ (to be expressed deci- 
 mally) . Record in tabular form, as follows : 
 
 LENGTH = / 
 
 WHOLE TIME 
 
 No. OF SWINGS 
 
 TIME OF i 
 VIBRATION =/ 
 
 V/ 
 
 V/:/ 
 
 36 in. 
 
 60 sec. 
 
 
 
 
 
 
 
 
 
 9 in. 
 
 60 sec. 
 
 
 
 
 
 
 
 
 
 4 in. 
 
 60 sec. 
 
 
 
 
 
 
 
 
 
76 DYNAMICS AND MACHINES 
 
 Discussion. i. If there were no errors, the value of the ratio 
 V7: / would be the same for the three pendulums. Compute the 
 percentage of difference between the greatest and the least of 
 these values. This should not exceed 2 %. 
 
 2. What is the probable source of the greatest error in the 
 experiment ? 
 
 3. From the equal values of the ratio V/:/for all pendulums, 
 derive the proportion between the lengths of any two pendulums, 
 4 and / 2 , and their periods, / A and / 2 
 
 EXERCISE 19. THE WHEEL AND AXLE 
 
 References. Adams, 100-103, 112-113 ;. Coleman, 159-161, 
 168-169; Car. & C., 89-92, 96-97; Ches. G. & T., 143-144, 
 147; Hoad. Br., 93-94, 104-105; Hoad. El., 101-105, 113- 
 114; Mumper, 83-85, 89 ; Mil. & G., 207, 212-213 ; Went. & H., 
 206-211. 
 
 Definitions. In this and the following exercises on machines, 
 the same kind of quantity is always represented by the same 
 letter. The definitions of these quantities and the letters by 
 which they are represented are as follows : 
 
 The body moved by a machine is called the load. The resist- 
 ing force that the load exerts while being moved is called the 
 resistance, and it is denoted by R. In these laboratory exercises 
 the machine is used to raise the load ; in which case the work is 
 done against gravity, and the resistance R is the weight of the load. 
 
 The body that does the work, or supplies the energy for raising 
 the load, is called the agent. The force that the agent must exert 
 to maintain equilibrium, or the force that would be required to 
 do the work if there were no friction, is called the static effort, 
 and is denoted by E 8 . The force that the agent must exert to 
 move the load is necessarily greater than E s . It is called the 
 working effort, and is denoted by E w . In these laboratory exer- 
 cises the agent consists of one or more standard masses (weights) , 
 
THE WHEEL AND AXLE JJ 
 
 and their united weight constitutes the static effort E 8 or the 
 working effort E W9 according to whether it maintains equilibrium 
 or raises the load. 
 
 The distance through which the effort (or the agent) acts is 
 called the effort distance, and is denoted by D e ; and the vertical 
 distance through which the resistance is overcome (or the load is 
 raised) is called the resistance distance, and is denoted by J9 r . 
 
 According to the rule for the measure of work (see text), the 
 work done by the working effort (or the agent) is denoted by 
 E w D e , and the work done against the resistance (or upon the 
 load) is denoted by RD r . In other words, E w D e denotes the 
 energy transferred from the agent to the machine, and RD r 
 denotes the energy transferred from the machine to the load. 
 
 The efficiency of a machine is defined as the ratio of the work 
 done on the load (the useful work) to the total energy expended 
 by the agent ; i.e. 
 
 Efficiency = -^21. 
 E w D t 
 
 Experiment 39. To find the mechanical advantage and the 
 efficiency of a wheel and axle. 
 
 Apparatus. Mounted axle carrying two wheels of different 
 diameters, with cords attached and a hook at the end of each 
 cord ; meter rod ; set of weights running to 500 g. or, better, to 
 1000 g. 
 
 [The " universal laboratory weights" shown in Figure 21 are 
 recommended as most convenient for all experiments with 
 machines. An ordinary set of weights can be used by tying a 
 loop of stout thread to each, by which they can be hung on hooks 
 attached to the ends of the cords. It is more convenient, how- 
 ever, to tie a small bucket or pan to the cord to hold the weights. 
 If the set runs to 1000 g., weights smaller than 10 g. are un- 
 necessary ; if the largest is 500 g., 5 g. is the smallest required. 
 Weights are more accurate and are better in other respects for 
 determining the effort than the draw scale.] 
 
DYNAMICS AND MACHINES 
 
 Experimental Work. a. Hang one or more of the largest 
 weights (the load) on the cord attached to the axle ; and hang 
 just sufficient weights (the agent) on the cord attached to one of 
 the wheels to raise the load slowly (Fig. 33). If a bucket or pan 
 for holding these weights is attached to the cord, its weight must 
 be included as part of the effort. It will probably be found that, 
 on account of varying friction, the motion is not uniform ; but, 
 on the average, the motion should neither be accelerated nor 
 retarded. Record the weight of the load R, and the effort with 
 the load rising. The latter is the working effort E w . 
 
 Find the effort required to maintain steady 
 motion as the load slowly descends. (Reduce 
 the effort by removing weights, but leave the 
 load unchanged.) The average of these two 
 values of the effort is the static effort E s , 
 (Why?) 
 
 Measure the distance D e through which the 
 effort acts (the distance that the agent descends) 
 and the distance D T through which the load is 
 raised, when the load is raised from the lowest 
 to the highest point that the adjustment of the 
 apparatus will permit. (It will be found most 
 convenient and most accurate to measure all 
 distances from the level of the table or the level of the floor, 
 according to the portion of the apparatus. For example, the 
 height of the load above the floor at the start subtracted from 
 its height above the floor after it has been raised, gives the 
 distance D r .) 
 
 Measure the diameters of the wheel and the axle. (If it is 
 inconvenient to measure these diameters directly, measure the 
 length of the cord that goes just once around the circumference, 
 and divide this length by 3.1416.) 
 
 b. If time permits, repeat the experiment, using the axle and 
 the other wheel or the two wheels, regarding the smaller one as the 
 axle in the latter case. 
 
THE WHEEL AND AXLE 
 Data and Computations. Record as follows : 
 
 79 
 
 
 a 
 
 b 
 
 Weight of the load R . . . . 
 
 g. 
 
 g- 
 
 Fff t *th 1 \ ' ' V ff t F 
 
 
 - - ff 
 
 Effort with load descending 
 
 g- 
 g- 
 
 & 
 
 g- 
 
 Distance through which effort acts, D e 
 
 
 cm % 
 
 
 
 Distance through which load is raised, D r 
 
 cm. 
 
 cm. 
 
 Radius of wheel A e (arm of the effort) 
 
 cm. 
 
 cm. 
 
 Radius of axle A r (arm of resistance) 
 
 cm. 
 
 cm. 
 
 COMPUTATIONS 
 
 Average or static effort E s ... 
 
 Mechanical advantage (by definition) = 7? -=- E s 
 
 Mechanical advantage (from the dimensions of 
 the machine) = A e -f- A r 
 
 Work done on the load = RD r . 
 Work done by the agent = E w D e 
 Efficiency of the machine = RD r -f- E lu D e . 
 
 - g.-cm. 
 
 - g.-cm. 
 
 - g.-cm. 
 
 - g.-cm. 
 
 Discussion. i. Show from the principle of moments of force 
 that the ratios R : E 8 and A e : A r should be equal. (The effort 
 and the resistance tend to turn the wheel and axle in opposite 
 directions.) Which of these ratios determines what the value of 
 the other must be for a given wheel and axle? 
 
 2. It can be proved geometrically that D e : D r : : A e : A r . 
 (Prove it.) Compare your experimental values for these ratios. 
 
 3. From the proportions given in the first two questions, show 
 that R\E s \\D e \D r or E 8 D e =RD r . It follows that, 
 
 ~ ffi ' 
 
 Efficiency = 
 
8O DYNAMICS AND MACHINES 
 
 that is, the efficiency is equal to the ratio of the static effort to 
 the working effort. Compute the efficiency from this ratio, and 
 compare the result with the value obtained from RD r -r- E w D e . 
 
 4. Prove that the mechanical advantage of the wheel and axle 
 is equal to the ratio D e : D r . State this relation in words. 
 
 EXERCISE 20. PULLEYS 
 i 
 
 References. Adams, 115-116 ; Coleman, 162-165, 168-169; 
 Car. & C., 98-100; Ches. G. & T., 148-155; Hoad. Br., 107- 
 no; Hoad. EL, 116-119; Mumper, 88; Mil. & G., 204-207; 
 Went. & H., 212. 
 
 Apparatus. A single and two double or triple pulleys ; frame 
 with screw hooks to support the pulleys (Fig. 34); meter rod; 
 stout, flexible cord (heavy fishing-line) ; set of weights to 1000 g. ; 
 small hook or a weight bucket, if the weights are not provided with 
 hooks. 
 
 Experiment 40. To find the mechanical advantage and the 
 efficiency of a single fixed pulley. 
 
 Experimental Work. Suspend a pulley (a single one, if pro- 
 vided), and pass a cord over it. Fasten the largest weight (the 
 load) to one end of the cord. Tie a loop in the cord on the other 
 side of the pulley, at a convenient height (attach the weight 
 bucket or a hook to the loop, if the weights have no hooks), and 
 hang just sufficient weights in it to raise the load slowly and 
 steadily. (If the remaining weights of the set are not sufficient 
 for this, use a smaller weight for the load.) Record the weight 
 of the load R, and the working effort E w (the effort with the load 
 rising). 
 
 Find the effort required to maintain steady motion as the load 
 slowly descends. (Reduce the effort by removing weights, but 
 leave the load unchanged.) The average of these two values of 
 the effort is the static effort E t . (Why ?) 
 
PULLEYS 
 
 81 
 
 FIG. 34. 
 
 Data and Computations. As in the case of the wheel and axle, 
 it can be shown that the efficiency of the fixed pulley is equal to 
 the ratio of the static effort E 8 to the working effort E w . Take 
 this ratio as the measure of the efficiency. Record as follows : 
 
 Weight of the load R = g. 
 
 Effort with load rising, or working effort, E w = g. 
 
 Effort with load descending = g. 
 
 Average or static effort, E s = g. 
 Experimental value of mechanical advantage = R -r- E s = 
 
 True value of mechanical advantage (= number of 
 
 parts of the cord supporting the load) . = i 
 
 Percentage of error = % 
 
 Efficiency of the fixed pulley = E s -+- E w = % 
 COLEMAN'S NEW MANUAL 6 
 
82 
 
 DYNAMICS AND MACHINES 
 
 Experiment 41. To find the mechanical advantage and tht 
 efficiency of a single movable pulley and of a combination of fixed 
 and movable pulleys. 
 
 Experimental Work. a. When a movable pulley is used, it 
 becomes a part of the load to be raised. Weigh every movable 
 pulley used (unless its weight is recorded on it), and add its weight 
 as a part of the resistance R. 
 
 Adjust a fixed and a movable pulley as shown in Figure 34. Use 
 the looo-g. weight (or the largest provided) as the load. Find 
 the working effort and the effort with the load slowly descending, 
 as in the preceding experiment. 
 
 Measure the distance D e through which the effort acts (the dis- 
 tance that the agent descends) and the distance D r through which 
 the. load is raised when the load is raised from the lowest to the 
 highest convenient point (which should be at least 25 cm.). (It 
 will be most convenient and most accurate to measure all dis- 
 tances from the bottom of the support, or from the table top, if 
 that is directly under the pulleys.) 
 
 b. Repeat the experiment, using two or three fixed and two or 
 more movable pulleys. Use two or more of the heaviest weights 
 for the load, and remember to include the weight of the movable 
 pulleys as a part of the resistance R. Make a drawing of the 
 arrangement of pulleys used. 
 
 Data and Computations. Record measurements and computa- 
 tions as follows : 
 
 
 a 
 
 b 
 
 Weight of the load (including weight of mova- 
 
 
 
 ble pulleys) R 
 
 g- 
 
 ' g- 
 
 Effort with load rising (working effort), E w . 
 
 g- 
 
 g- 
 
 Effort with load descending .... 
 
 g- 
 
 g- 
 
 Distance thrgugh which effort acts, D e . 
 
 
 cm. 
 
 cm. 
 
 Distance through which load is raised, D r 
 
 cm. 
 
 cm. 
 
THE INCLINED PLANE 
 
 COMPUTATIONS 
 
 
 a 
 
 b 
 
 Average or static effort, E s 
 Experimental value of mechanical advantage 
 
 True value of mechanical advantage (number 
 of parts of cord supporting load) 
 
 Percentage of error of mechanical advantage . 
 
 2 
 
 g. 
 
 o/ 
 /o 
 
 g.-cm. 
 g.-cm. 
 
 Work done by the agent = E w D e . 
 Efficiency, computed from RD r -E w D e 
 Efficiency, computed from E s -=- E w - . 
 
 g. cm. 
 g.-cm. 
 
 /o 
 
 o/ 
 /o. 
 
 Discussion (Oral). i. By definition, the efficiency of a machine 
 is RD r -r- E w D e . Prove that this is equal to E s -r- E w (a) for a 
 single fixed pulley, (U) for a single movable pulley, (c) for any 
 combination of fixed and movable pulleys. 
 
 2. Prove that the mechanical advantage of any combination of 
 pulleys is equal to the ratio D e : D r . 
 
 EXERCISE 21. THE INCLINED PLANE 
 
 References. Adams, 58, 118; Coleman, 166-169; Car. & 
 C., 101-102 ; Ches. G. & T., 156; Hoad. Br., in ; Hoad. EL, 
 120; Mumper, 90; Mil. & G., 214; Went. & H., 46. 
 
 Experiment 42. To find the mechanical advantage and the 
 efficiency of an inclined plane. 
 
 Apparatus. An inclined plane, with single fixed pulley at top 
 (Fig. 35); roller or car, with its weight marked on it: metric 
 rule set of weights. 
 
8 4 
 
 DYNAMICS AND MACHINES 
 
 Experimental Work. a. Set the plane at an angle of about 
 25. (The angle need not be measured.) Place the roller or 
 car on the plane, pass a cord from it over the pulley, and attach 
 just sufficient weights to the cord to draw the roller (or car) slowly 
 and steadily up the plane (Fig. 35). (If a car and weights to 
 
 1000 g. are provided, 
 more accurate results 
 will be obtained by load- 
 ing the car with one or 
 more of the heavier 
 weights.) Record the 
 weight of the load./?, and 
 the working effort E w . 
 
 Find the effort re- 
 quired to maintain 
 steady motion as the 
 load rolls slowly down 
 the plane. 
 
 Measure the length Z of the plane along its under edge, from 
 its lower end to the straight, vertical edge of the support. Meas- 
 ure the height H of the plane at the vertical edge of the support, 
 from the under edge of the plane to the upper edge of the base. 
 
 b. Repeat the experiment with the plane at an angle of about 
 45. 
 
 Data and Computations. Record as follows : 
 
 FIG. 35. 
 
 
 a 
 
 b 
 
 Weight of the load R . . . . 
 
 g. 
 
 g- 
 
 Effort with the load rising (working effort), E w 
 
 g. 
 
 g- 
 
 Effort with load descending 
 
 
 
 g- 
 
 g- 
 
 Length of the plane L .. . . . 
 
 
 cm. 
 
 cm. 
 
 Height of the plane H 
 
 
 
 
 
GEARED WHEELS 
 
 COMPUTATIONS 
 
 
 a 
 
 b 
 
 Average or static effort E s ... 
 Mechanical advantage, from R -f- E s . 
 Mechanical advantage, from L -r- // . 
 Percentage of difference .... 
 
 Work done on the load in rolling it up the 
 plane - RH 
 
 Work done by the agent E W L 
 Efficiency, computed from RH "-*- E W L 
 Efficiency, computed from E s -f- E w 
 
 g- 
 g.-cm. 
 
 
 g.-cm. 
 g.-cm. 
 
 g.-cm. 
 
 /o 
 
 Discussion (Oral) . Taking RH-^ E W L as the definition of the 
 efficiency of the inclined plane, prove it to be equal to 3 -~- E w . 
 
 EXERCISE 22. GEARED WHEELS 
 ( INVENTIVE) 
 
 Experiment 43. To find the mechanical advantage and the 
 efficiency of a train of geared wheels. 
 
 Apparatus. Set of geared wheels (Fig. 36), mounted on a 
 suitable support, with a 
 cord to support the load 
 and a stout thread to 
 the 
 
 support 
 weights to 
 meter rod. 
 
 agent; 
 TOGO g. ; 
 
 Suggestion. The 
 pupil is left to work out 
 the details of this ex- 
 periment and the form 
 of record for himself. The mechanical advantage can be found 
 experimentally by three independent methods, and the efficiency 
 by two. Employ any or all of these that occur to you. 
 
 FlG * 
 
VI. MOLECULAR PHENOMENA 
 
 EXERCISE 23. COHESION AND ADHESION 
 
 References. Adams, 126-132; Coleman, 188-193; Car. & 
 C., 17-18; Ches. G. & T., 62; Hoad. Br., 28; Hoad. EL, 31, 
 130; Mumper, 22 ; Mil. & G., 157-159 ; Went. & H., 142, 144, 
 146. 
 
 Experiment 44. To study the effect of distance on molecular 
 attraction, and to study the behavior of liqtiids in contact with 
 solids. 
 
 Apparatus. Two pieces of plate glass and two of window 
 glass, each about 6 cm. square ; piece of glass coated with paraf- 
 fme ; bottle containing a little mercury ; sealed bottle containing 
 clean mercury and very small pieces of glass ; vessel of water ; 
 dropping tube ; mop cloth. 
 
 [The pieces of glass should be between 2 mm. and 4 mm. in 
 diameter, and there should be just enough mercury in the bottle 
 to cover about one third of the bottom. The surface of the mer- 
 cury must be clean and bright. Sealing the bottle with wax will 
 preserve the mercury from other use, and keep it clean.] 
 
 Experimental Work. a. Have the pieces of plate glass clean 
 and dry. Press them firmly together, then note the force re- 
 quired to pull them apart. Is cohesion between them great 
 enough to lift one of them by means of the other ? 
 
 b. Try the two pieces of window glass in the same way. How 
 do the results compare with the preceding? The surfaces of the 
 plate glass are quite accurately plane, while those of the window 
 glass are more or less uneven and wavy. The difference in the 
 results in the two cases is due to this difference in the surfaces. 
 
 86 
 
COHESION AND ADHESION 87 
 
 Hence the experiments illustrate a necessary condition for the 
 existence of cohesion. What is this condition ? 
 
 c. Again take the pieces of plate glass, dip them in water to 
 moisten their surfaces, and press them together as before. Note 
 the^ force now required to pull them apart. How does it compare 
 with the force required when the plates are dry ? The thin layer 
 of water adheres to the glass surface on each side, forming a 
 connecting link. 
 
 Is adhesion between water and glass stronger or weaker than 
 cohesion within a piece of glass? How is this shown? Why is 
 adhesion between water and glass stronger than cohesion between 
 the two pieces of plate glass? Is cohesion in water stronger or 
 weaker than adhesion between water and glass? How is this 
 shown ? 
 
 d. CAUTION. In handling mercury, be careful not to get any of 
 it on jewelry. It unites with gold and silver, forming an amalgam 
 which discolors the surface. 
 
 By means of the dropping tube transfer a small drop of mercury 
 from the bottle to a piece of glass. Flatten the drop with the 
 finger, then observe the effect of removing the finger. The be- 
 havior of the drop does not prove that there is no adhesion 
 between mercury and glass. What does it prove? Why does 
 the drop of mercury not flatten out and spread over the glass as a 
 drop of water would ? 
 
 With the finger or the point of your pencil, detach a very small 
 bit from the drop. Is this smaller portion more or less nearly 
 spherical than the larger portion? Why? Pour the drop of 
 mercury into your hand and return it to the bottle. 
 
 e. Take the sealed bottle containing mercury and bits of glass. 
 Incline it slightly from side to 'side so that the mercury will run 
 about over the bottom of the bottle, and note the behavior of the 
 bits of glass toward the mercury. What evidence of adhesion 
 between glass and mercury do you observe? 
 
 /. Observe the behavior of a drop of water on the paraffined 
 surface of the piece of glass. Do you find cohesion within water 
 
88 
 
 MOLECULAR PHENOMENA 
 
 stronger or weaker than adhesion between water and paraffine? 
 Do you infer that adhesion between water and paraffine is greater 
 or less than between water and glass? 
 
 EXERCISE 24. SURFACE TENSION AND CAPILLARITY 
 
 References. Adams, 150-156 ; Coleman, 195-200 ; Car. & C., 
 113-122; Ches. G. & T., 63-65; Hoad. Br., 119-126; Hoad. 
 EL, 130-136; Mumper, 23-25; Mil. & G., 160-167; Went. & 
 H., 145, 147. 
 
 Experiment 45. To study various phenomena due to surface 
 tension. 
 
 Apparatus. Tumbler of clean water; pins; two small slivers 
 of wood (toothpicks) ; very slender rubber band ; lifter made of 
 wire, for placing pins on water (Fig. 37) ; 
 small bottle of alcohol ; glass rod ; dish of soap 
 solution ; wire ring about 3 in. in diameter, 
 with extension of wire for handle, and with 
 thread tied loosely across the ring (Fig. 38) ; 
 bottle containing a drop of oil suspended in a 
 solution of alcohol and water of its own density. 
 [For a good soap solution, put 2 oz. of 
 Castile soap, shaved thin, in i pt. of dis- 
 tilled or rain water. Shake, pour off the 
 clear solution, and add to it \ pt. glyc- 
 erine, and stir. To prepare the sus- 
 pended drop of oil, pour a very little 
 water into the bottle and add an equal 
 or greater quantity of alcohol without 
 shaking. This will leave the mixture 
 somewhat denser at the bottom. Insert 
 2 or 3 large drops of olive or machine 
 oil by means of a dropping tube. Slowly 
 pour in more alcohol, if necessary, till 
 the drop sinks below the surface.] FIG. 38. 
 
 FIG. 37. 
 
SURFACE TENSION AND CAPILLARITY 89 
 
 Experimental Work. a. Place a pin on the lifter (Fig. 37), 
 and lower it gently till the pin floats on the water, then remove 
 the lifter. If the pin sinks now or later in the experiment, take 
 it out with the lifter, wipe it dry with the fingers (which leaves 
 it somewhat oily), and try again. Observe closely the shape of 
 the water about the pin. Describe it, and draw an enlarged figure 
 of a cross section of the pin and adjacent water surface, taken 
 at right angles to the length of the pin. 
 
 Push the pin till it breaks through the surface. Why does it 
 sink now ? Why did it float before ? 
 
 b. Float two wooden toothpicks on the water, placing them 
 parallel and about 2 cm. apart. (Pins can be used, but it is 
 difficult to keep them afloat.) Dip the glass rod into the alcohol, 
 and carry a drop on the end of it to the surface of the water be- 
 tween the toothpicks. What happens ? The alcohol, mixing with 
 the water between the toothpicks, weakens the surface tension. 
 How does this account for the behavior of the toothpicks? 
 
 Repeat the experiment, using the rubber band instead of the 
 toothpicks, and drop the alcohol inside the band. 
 
 Similar results would be obtained if oil were used in these ex- 
 periments, instead of alcohol ; but it would be necessary to change 
 the water after each trial. Why ? 
 
 c. Dip the wire ring into the soap solution, and withdraw it 
 obliquely. Repeat if necessary, till a film is obtained. Observe 
 the behavior of the loose thread as it floats in the film. With 
 the point of a pencil, break the film on one side of the thread. 
 Describe and account for the behavior of the thread. Draw a 
 figure showing the position it takes with a film on only one side 
 of it. 
 
 d. What is the shape of the oil globule suspended in the mix- 
 ture of alcohol and water? What gives it this shape? Disturb 
 the drop by tipping the bottle slightly from side to side, but not 
 so quickly as to break the drop. When the drop is distorted by 
 this motion, does it recover its former shape? Account for this 
 behavior. 
 
QO MOLECULAR PHENOMENA 
 
 Experiment 46. To study capillary action with reference to the 
 effect of the size of the tubes and the direction of the curvature of the 
 liquid. 
 
 Apparatus. Capillary tubes of glass of different sizes ; capillary 
 tubes coated inside with paraffine ; glass of water ; glass containing 
 mercury. 
 
 [To coat a tube with paraffine, put a very small piece of paraffine 
 in one end of the tube, and hold it obliquely in a flame till the 
 paraffine melts and runs down the tube.] 
 
 Experimental Work. a. Observe the shape of the water and 
 mercury surfaces near the glass. Draw figures of vertical sections 
 through the liquids, to illustrate. Account for the difference in 
 the shape of the two surfaces. 
 
 b. In the following work use one set of capillary tubes in water 
 only and the other set in mercury only. Place tubes of different 
 sizes in the tumbler of water. Make a section drawing of the 
 tumbler and tubes, showing the height of the water and the 
 shape of its surface in the tumbler and in the tubes. How does 
 the diameter of a tube affect the height to which water rises in 
 it above the level in the tumbler? How is the water raised and 
 sustained in the tubes? 
 
 c. Repeat the preceding with tubes of different sizes in mer- 
 cury, using only dry tubes. By pressing the tube against the 
 side of the tumbler an unobstructed view of the inside of the 
 tube will be obtained. Describe what is seen and make a section 
 drawing to illustrate. 
 
 d. Place in the tumbler of water the capillary tube coated 
 on the inside with paraffine. Is the water in the tube elevated 
 above or depressed below the level of the water in the tumbler? 
 Is the surface of the water in the tube convex or concave ? 
 
 Discussion. Is the liquid in a capillary tube elevated or 
 depressed when the surface of the liquid is concave? when the 
 surface is convex? State the reason in each case. 
 
VII. HEAT 
 
 EXERCISE 25. CONDUCTION AND CONVECTION 
 
 References. Adams, 374-379 ; Coleman, 215-218; Car. & 
 C-, 343-349; Ches - G - & T -> 213-216; Hoad. Br., 253-256; 
 Hoad. El., 271-276; Mumper, 140-142; Mil. & G., 291-297 ; 
 Went. & H., 115-120. 
 
 Experiment 47. To determine the order in which glass and 
 different metals stand as conductors of heat. 
 
 Apparatus. Rods of brass, iron, copper, and glass (about 
 No. 9 or 10 wire) ; Bunsen burner; vessel of water ; test tube. 
 
 Experimental Work. Test the relative conductivity of the 
 rods, two at a time, holding one in each hand, with an end of 
 each in the Bunsen flame 6 or 8 cm. above the burner, the two 
 being as nearly as possible equally heated. At first hold the rods 
 near the heated end ; then, as they became uncomfortably hot, 
 hold them farther from this end, observing in which the heat 
 travels faster. The method may be varied by holding the rods 
 at the same distance from the heated end, and observing in which 
 the heat first reaches the hand. 
 
 Before trying the same rod a second time, it may be cooled in 
 the vessel of water, except the glass rod, which must be allowed 
 to cool of itself, for it will break if thrust into the water hot. 
 Continue experimenting till you can arrange the rods in the order 
 of their conductivity. 1 Write the names in order, from the best to 
 the poorest conductor. 
 
 1 The rise of temperature along the rods depends upon another property 
 of the substances besides their conductivity. This property, called specific 
 heat, will be studied later. It does not affect the order of conductivity of the 
 materials used in this experiment. 
 
 91 
 
HfiAf 
 
 b. Fill the test tube with water within 2 or 3 cm. of the top. 
 Hold it at the bottom in the fingers, tipping it slightly, and apply 
 
 the Bunsen flame a little 
 / below the top of the water 
 ' If ) ( Fi g- 39), till it boils at the 
 ^^J top for about a minute. 
 
 What do you observe con- 
 cerning the temperature of 
 the water at the bottom of 
 the tube? What do you con- 
 clude concerning the conduc- 
 tivity of water ? 
 
 Experiment 48. To observe whether sensations of heat and cold 
 are affected by the conductivity of the substances touched. 
 
 Apparatus. Two pieces each of several of the following sub- 
 stances : brass, iron, glass, copper, wool, asbestos, stone, and wood ; 
 hot air bath ; ; ice box (unless the weather is cold). 
 
 Experimental Work. a. Place one set of the substances in 
 the air bath and apply a low flame for several minutes. Place the 
 other set in the ice box, or, if the weather is cold, in the open air 
 outside a window. After five minutes or more, when all the sub- 
 stances in the bath have had time enough to come to the same 
 temperature (the temperature of the bath), grasp them in the 
 hand, one at a time, without removing them from the oven, and 
 note the temperature sensation. Repeat until you can write a 
 list of them in order, beginning with the one thatfee/s the hottest. 
 (It is incorrect to say that one is hotter than another.) Note 
 the temperature sensation due to the hot air of the bath, and 
 include air in the list of substances. Account for the seeming 
 difference of temperatures. 
 
 b. Try the same substances cooled in the ice box or outside 
 the window, and arrange a list in order, beginning with the one 
 that feels the coldest. In making this test it is better to press 
 
RADIANT ENERGY 93 
 
 the substances, two at a time, against the forehead, which is much 
 more sensitive than the hands. After testing any substance it 
 must be allowed to cool again before making a further test of it. 
 Account for the seeming difference of temperatures. 
 
 Experiment 49. To study convection currents in water. 
 
 Apparatus. Test tube; Bunsen burner; beaker; sawdust; 
 iron stand ; wire gauze ; mop cloth. 
 
 Experimental Work. a. Put a small pinch of sawdust in the 
 beaker, and fill it nearly full of water. Wipe the outside of the 
 beaker dry, place it on the wire gauze on the ring stand, and apply 
 heat with the Bunsen flame. The gauze should be about 10 cm. 
 above the burner, and the flame turned down so that it will not 
 burn above the gauze. Observe carefully the motion of the parti- 
 cles of sawdust while the water is heating. Give a full account 
 of what is observed, including definite reasons for any motion of 
 the liquid that you may infer from the behavior of the sawdust. 
 
 b. Fill the test tube nearly full of water and hold it in the hand 
 just below the surface of the water, and apply the flame near the 
 bottom. Note the rapidity of the rise of temperature of the water 
 at the top. 
 
 Compare with the experiment in conduction, in which the heat 
 was applied near the top of the tube and the tube was held near 
 the bottom. Account for the difference in the results of the two 
 experiments. 
 
 EXERCISE 26. RADIANT ENERGY 
 
 References. Adams, 381-385 ; Coleman, 219-226 ; Car. & C., 
 350, 352-354; Ches. G. &T., 217 ; Hoad. Br., 258-263 ; Hoad. 
 EL, 280-286; Mumper, 146-151 ; Mil. & G., 299-300; Went. & 
 H., 121-125. 
 
 Experiment 50. To study the transmission, absorption, and 
 reflection of radiant energy. 
 
 Apparatus. Bunsen burner ; a bright tin screen about 8 by 
 8 in., mounted on stand or supported by ring stand and clamp ; 
 
94 HEAT 
 
 mounted tin screen, same size, painted black or coated with soot 
 on one side. 
 
 
 
 Experimental Work. a. Hold the hand in different positions 
 near the flame, at the side and above it. Do you feel convection 
 currents in any position? There may possibly be convection 
 currents that are too weak to be felt as currents, although they 
 warm the hand. Can you suggest any conclusive reason for be- 
 lieving that the hand is not warmed by such a current when held 
 at the side of the flame ? 
 
 b. Hold the hand close beside the flame, and note the intensity 
 of the sensation. With the hand still in this position, insert a 
 sheet of paper between it and the flame, and note the effect on 
 the sensation of heat. How does this effect prove that the hand 
 was not heated by conduction through the air from the flame ? 
 
 c. Place the tin screens on opposite sides of the flame, at equal 
 distances of about 10 cm. from it, with the black side of the one 
 turned toward the flame. After a minute or two, note the tem- 
 perature of the screens by placing a hand flat against each on the 
 side turned from the flame. What do you learn concerning the 
 temperatures of the two screens ? How is this explained ? 
 
 d. Remove the bright screen and hold one hand in its place at 
 the same distance from the flame as the other hand, which is still 
 pressed against the back of the black screen. Which hand be- 
 comes warmer? Explain. 
 
 e. What facts point to the conclusion that the black screen 
 becomes much hotter than the air at that distance from the flame ? 
 Why is this? 
 
 Experiment 51. To find whether radiant energy is transmitted 
 along a straight path, and to test the power of different substances 
 to absorb and transmit luminous and non-luminous radiation. 
 
 Apparatus. Bunsen burner; radiometer; three flat bottles of 
 clear glass, one empty, one filled with water, and one with a solu- 
 tion of iodine in carbon bisulphide. 
 
RADIANT ENERGY 95 
 
 CAUTION. Carbon bisulphide is dangerously inflammable. The 
 bottle must be kept tightly corked and must be handled with care. 
 It should be provided with a support to avoid danger of over- 
 turning. 
 
 Experimental Work. a. Place the radiometer at different dis- 
 tances from the flame, and observe the effect of distance upon the 
 rate of rotation of the vanes. Radiation, both luminous and non- 
 luminous, falling upon the radiometer, will cause the vanes to ro- 
 tate ; and the rate of rotation is an indication of the intensity of 
 the radiation. 
 
 b. Place the radiometer about 30 cm. from the flame and 
 slowly insert a sheet of paper or a book between them. What is 
 the position of the screen when the slower rotation of the vanes 
 indicates that the radiation has been cut off from the radiometer? 
 Does the effect of the screen indicate that radiant energy is or is 
 not transmitted along a straight path ? 
 
 c. Hold the empty flask between the flame and the radiometer, 
 and bring the latter up till the vanes make about one rotation per 
 second. Now remove the flask and note the effect on the radiom- 
 eter. What do you infer in regard to the power of clear glass 
 to absorb radiant energy? 
 
 d. Without moving the radiometer or the flame, hold the flask 
 of water between them. Compare the result with that obtained 
 with the empty flask. A more definite comparison may be made 
 by observing the time of, say, ten rotations ; but where there are 
 easily observable differences, this is not necessary. 
 
 Is water a good or poor absorber of luminous radiation? (Is it 
 transparent?) Does the action of the radiometer show that water 
 is a good or poor absorber of non-luminous radiation? (Probably 
 more than 95 % of the energy radiated from the flame is of the 
 non-luminous variety.) 
 
 e. Substitute the flask containing the solution of iodine in car- 
 bon bisulphide. Compare the results with the preceding. Does 
 the solution transmit light (luminous radiation) ? What evidence 
 
96 HEAT 
 
 is there that it transmits non-luminous radiation? Is it a better or 
 poorer transmitter of non-luminous radiation than water ? better 
 or poorer than glass? 
 
 EXERCISE 27. COEFFICIENT OF LINEAR EXPANSION 
 
 References. Adams, 351; Coleman, 233; Car. & C., 319; 
 Ches. G. & T., 220-221 ; Hoad. Br., 264-265 ; Hoad. EL, 287- 
 288; Mumper, 113-114; Mil. & G., 197; Went. & H., 96. 
 
 Experiment 52. To find the expansion of i cm. of a brass 
 rod due to a rise of temperature of i. 
 
 Apparatus. Linear expansion apparatus (Fig. 40) ; apparatus 
 for generating steam; tumbler; meter rod; Bunsen burner; 
 access to a thermometer. ' 
 
 FIG. 40. 
 
 [For the steam generator use a copper boiler on tripod, with a 
 tight top, or flask with stopper and delivery tube, supported on 
 a ring stand.] 
 
 Experimental Work. a. Fill the steam generator from one 
 third to one half full of water, and with the top off (or the delivery 
 tube disconnected at the generator) begin heating it. While the 
 water is heating, measure the length of the brass rod without 
 removing it from the steam jacket ; then adjust it so that one 
 end rests against the fixed support and the other against the lever. 
 Turn it so that the escape tube will be directed downward. 4 Set 
 the tumbler under this tube to catch the escaping steam and hot 
 water. 
 
 b. Read to .1 mm. the position of the long lever arm on the 
 vertical scale. After taking this reading, be careful not to disturb 
 
COEFFICIENT OF LINEAR EXPANSION 97 
 
 the apparatus in any way, as this would probably move the lever 
 into a new position. 
 
 c. The temperature of the rod is the same as that of the room. 
 Find it by the laboratory thermometer. 
 
 d. Put the top on the steam generator and connect the delivery 
 tube. While the rod is being heated by the steam, observe the 
 motion of the long lever arm. After the steam has been escaping 
 freely from the escape tube for two or three minutes and no further 
 motion of the lever can be detected, read the position of the long 
 lever arm. The temperature of the rod is the same as the tem- 
 perature of the steam, which may be assumed to be 100. 
 
 e. Measure the arms of the lever. These are the distances 
 from the fulcrum (a knife edge or the center of a screw) to the 
 scale and from the fulcrum to the point of contact with the brass 
 rod, respectively. When you have finished, tilt the apparatus so 
 that the water con- 
 densed in the steam 
 
 jacket will run out. 
 
 Data and Computa- 
 tions. The whole ex- 
 pansion of the rod is 
 
 the distance // x (Fig. FIG. 41. 
 
 41) that the short arm 
 
 of the lever is pushed forward. Compute this from the pro- 
 portion d : d> 2 : : a : a 2 . Record data and computations as 
 follows : 
 
 MEASUREMENTS 
 
 Length of brass rod = cm. 
 
 First position of long lever arm = cm. 
 
 First temperature of the rod = C. 
 
 Final temperature of the rod C. 
 
 Final position of long lever arm cm. 
 
 Length of long lever arm a 2 cm. 
 
 Length of short lever arm a = cm. 
 COLEMAN'S NEW MANUAL 7 
 
98 HEAT 
 
 COMPUTATIONS 
 
 Rise of pointer on the index, d^ = cm. 
 Change of temperature of the rod C. 
 Expansion of rod for this change of temperature, d = cm. 
 Expansion of rod for i change of temperature = cm. 
 Expansion of i cm. of rod for i change of temper- 
 ature (coefficient of linear expansion of rod) = cm. 
 True value of coefficient of expansion of brass = .0000188 
 Percentage of error = % 
 
 ALTERNATIVE DIRECTIONS 
 
 If the apparatus is provided with a micrometer screw instead of 
 a lever, the following substitutions are to be made in the directions 
 as given above : 
 
 b. If you do not know how to read the micrometer screw, turn 
 it back and forth and study its action. Note the fixed milli- 
 meter scale and the circular scale on the head ; also that when 
 the head is turned once round, it advances i mm. along the fixed 
 scale. How many divisions are there on the circular scale ? The 
 value of one division on the circular scale is the distance the screw 
 advances when the head is turned through one division. What is 
 this value ? Ask for assistance if necessary. The answers to these 
 questions need not be recorded. 
 
 See that the other end of the rod is against the fixed support, 
 then turn the micrometer screw till it just touches the rod, and 
 take its reading. After taking the reading, turn the screw back 
 2 or $ mm. to make room for the expansion of the rod when heated 
 If this precaution is not observed, the expanding rod will strain 
 and damage the apparatus. Observe the additional precautions 
 given in paragraph b above. 
 
 d. In this paragraph substitute for the reading of the lever a 
 second reading of the screw, after it has been turned up to touch 
 the rod. The difference between the two readings of the screw is 
 the expansion of the rod. 
 
COEFFICIENT OF EXPANSION OF AIR 99 
 
 EXERCISE 28. COEFFICIENT OF EXPANSION OF AIR 
 
 References. Adams, 352-353; Coleman, 237; Car. & C., 
 318-320; Ches. G. &T., 223; Hoad. Br., 268-269; Hoad. EL, 
 293-295 ; Mumper, 118; Mil. & G., 191 ; Went. & H., 97. 
 
 Experiment 53. To find whether the expansion of air is uni- 
 form, and to find by what fraction of its volume at o air expands 
 when its temperature is raised i. 
 
 Apparatus. Copper steam generator with tall top ; Bunsen 
 burner ; hydrometer jar ; stirrer of wire bent into a flat coil at the 
 end ; thermometer ; glass tube containing air and mercury index ; 
 metric rule ; ice. 
 
 [The tube containing air must be of small bore (not greater 
 than i mm.), in order to hold the mercury index in position, and 
 should be 35 to 40 cm. long. Prepare as follows : Thoroughly 
 dry the tube by warming it and passing through it air that has first 
 passed through a calcium chloride drying tube. Insert an end 
 of the tube into clean mercury, withdraw a column about 2 cm. 
 long, and let it run some distance down the tube. Seal an end of 
 the tube in a flame, then work the index into proper position with 
 a fine wire, leaving the confined air column about two thirds the 
 length of the tube.] 
 
 Method. The thread of mercury in the glass tube serves as an 
 air-tight piston to confine a fixed mass of air between it and the 
 closed end of the tube. 
 
 Since the tube is of uniform bore, the volume of this confined 
 air is proportional to its length. This length is determined when 
 the tube is surrounded by melting ice, when it is immersed in 
 warm water, and^ when immersed in steam. The tube is in each 
 case vertical, with the open end up, when the measurements are 
 taken ; hence the confined air is under a constant pressure (the 
 pressure of the atmosphere plus the pressure due to the weight of 
 the mercury index). 
 
1 00 HEAT 
 
 Experimental Work. Handle the tube carefully ; a sudden 
 motion might break the thread of mercury, and this must be 
 avoided. Measure accurately the total length of the bore of the 
 tube (i.e. the distance from the open end to the inside of the 
 closed end), and the length of the mercury index. 
 
 Place the tube, open end up, in the hydrometer jar, and fill the 
 jar with crushed ice or snow up to the index. While waiting a 
 minute or two for the tube to come to the temperature of the ice, 
 fill the steam generator about two thirds full of water and begin 
 heating it. With the tube still in the ice, tap it very lightly to 
 jar the index into its true position, then measure the distance 
 from the top of the index to the top of the tube. Subtracting this 
 distance, together with the length of the mercury index, from the 
 total length of the bore of the tube gives the length of the confined 
 air column. Its length at the other temperatures is found in the 
 same way. 
 
 Remove the tube, pour the water from the jar, and return the 
 remaining ice to the supply vessel. Fill the jar with water from 
 the faucet, and let it stand a moment to warm the jar, then empty 
 and fill with water at 35 to 40 from the supply that is being 
 heated. Be careful not to pour hot water into the jar ; if thick 
 glass is heated suddenly, it will break. Stir the water in the jar 
 thoroughly by moving the stirrer repeatedly from top to bottom 
 of the jar ; place the tube and thermometer in it ; take the 
 temperature accurately ; and after tapping the tube lightly, meas- 
 ure the distance from the top of the index to the top of the 
 tube. 
 
 Place the top on the steam generator, and boil the water. Push 
 the tube through the hole in the cork which closes the top of the 
 generator, and push it farther down as the index rises in the tube, 
 until finally the index appears just above the cork when it has 
 become stationary. After the steam has been escaping from the 
 vent for some time and the index has ceased to rise, measure 
 ';he distance frou the top of the index to the top of the tube. 
 
 Leave the tube standing in the empty hydrometer jar. 
 
SPECIFIC HEAT IOI 
 
 Data and Computations. Record data as follows, and perform 
 the indicated computations : 
 
 MEASUREMENTS 
 
 Total length of bore of tube = cm. 
 
 Length of mercury index = cm. 
 Distance from top of index to top (open end) of tube 
 
 when tube is in ice (temp. o C.) = cm. 
 
 when tube is in water at C. (This tem- 
 perature is denoted below by /) = cm. 
 
 when tube is in steam (temp. 100) = cm. 
 
 COMPUTATIONS 
 
 Length of air column at o = cm. 
 
 Length of air column at / (temp.. in water) = cm. 
 
 Length of air column at 100 = cm. 
 Average expansion of air column per degree 
 
 rise of temperature 
 
 between o and / = cm. 
 
 between / and 100 = cm. 
 
 between o and 100 = cm. 
 Computed coefficient of expansion between o 
 
 and 100 = cm. 
 
 True value of coefficient of expansion of air = .00366 
 
 Percentage of error = % 
 
 Discussion. What information do your results afford on the 
 question whether the expansion of air is uniform within the tem- 
 perature limits of the experiment ? 
 
 EXERCISE 29. SPECIFIC HEAT 
 
 References. Adams, 369, 371-373; Coleman, 239-243; Car. 
 &C., 325-328; Ches. G. & T., 226-230; Hoad. Br., 281-283; 
 Hoad. EL, 312-314, 316; Mumper, 110-112; Mil. & G., 239, 
 250-251 ; Went. & H., 107-109. . 
 
102 HEAT 
 
 Experiment 54. To find the number of calories required to 
 raise the temperature of i g. of i. 
 
 Apparatus. Bunsen burner ; copper vessel on tripod, or other 
 open vessel for boiling water; open roll (Fig. 42) or other mass 
 of metal, with fine wire attached for handle ; calorimeter ; ther- 
 mometer ; platform balance and weights to 500 g. ; mop cloth. 
 
 [The piece of metal whose specific heat is to be found should 
 weigh from 250 to 400 g. A sphere or other compact mass will 
 serve; but an open roll of sheet metal i to 2 mm. thick is 
 better. The space between the surfaces 
 of the roll must be wide enough to avoid 
 holding water by capillary action. A 
 light calorimeter of thin nickel-plated 
 brass or of aluminum is preferable ; but 
 a glass beaker or even a small tin can will 
 serve. It makes a rather better experi- 
 ment to find the specific heat of the metal 
 of which the calorimeter is made, using 
 FIG. 42. a roll or other mass of the same metal.] 
 
 Experimental Work. Begin heating water in the copper boiler. 
 Weigh the piece of metal whose specific heat is to be found. 
 
 Weigh the calorimeter. Put the roll into the calorimeter, and 
 pour in enough water to cover it. The water should be about 3 
 below the temperature of the room, for best results. Put the roll 
 into the water that is being heated, and see that there is enough 
 water in the boiler to cover it. Weigh the calorimeter and the 
 water in it. 
 
 After the above has been done and the water in the vessel is 
 boiling, thoroughly stir the water in the calorimeter with the ther- 
 mometer and take its temperature to a tenth of a degree. (The 
 temperature must be read as accurately as possible. An error of . i 
 in determining a temperature change of 5 is an error of 5 %.) 
 
 As soon as the temperature is taken, remove the thermometer, 
 hold the calorimeter close beside the boiler, and transfer the roll 
 
SPECIFIC HEAT 1 03 
 
 to the calorimeter as quickly as possible. (It is assumed that the 
 temperature of the roll is 100 when it is put into the calorimeter ; 
 but it cools with great rapidity during the transfer, and a delay 
 of even a second will cause a considerable error in the result.) 
 Place the calorimeter on the table at a distance from the flame, 
 move the roll about in it to stir the water, then insert the ther- 
 mometer and take the temperature near the top and the bottom 
 of the water and on opposite sides of the roll. If differences are 
 found, stir again. Record the highest uniform temperature. 
 
 If time permits, the experiment should be repeated. Having 
 become familiar with the method of procedure, you will very prob- 
 ably secure better results. Leave the calorimeter empty. 
 
 Data and Computations. Let s denote the specific heat of the 
 roll. If the calorimeter is of the s^ame metal as the roll, its spe- 
 cific heat is also denoted by s. That is, s denotes the number of 
 calories lost by each gram of the roll as its temperature falls one 
 degree, and also the number of calories received by each gram 
 of the calorimeter as its temperature rises one degree. If the 
 calorimeter and the roll are of different metals, the specific 
 heat of the calorimeter is treated as a known quantity in the com- 
 putations, and its value is taken from a table of specific heats. 
 
 The calorimeter is assumed to be at the temperature of its con- 
 tents. The heat gained by the water and the calorimeter is 
 assumed to come entirely from the roll (any transfer of heat be- 
 tween the vessel and outside bodies is disregarded) ; i.e. 
 
 Heat lost by roll = heat received by water 
 
 -f heat received by calorimeter. 
 
 The algebraic statement of this relation (i.e. with the quantities 
 expressed numerically or algebraically) is called the heat equation. 
 The specific heat is found by solving this equation for s. 
 
 Be careful to specify in the record what metal is used in the 
 experiment and of what metal the calorimeter is made. Record 
 as follows : 
 
104 HEAT 
 
 Weight of roll of = g . 
 
 Weight of calorimeter = g. 
 
 Weight of calorimeter and water = g. 
 
 Initial temperature of water and calorimeter = C. 
 
 Initial temperature of roll of- =100 C. 
 
 Final temperature of calorimeter and contents = C 
 
 COMPUTATIONS 
 
 Weight of water used = g. 
 Rise of temperature of water and calorimeter 
 
 Heat received by water = cal. 
 
 Heat received by calorimeter =()x()XJ = cal. 
 
 Fall of temperature of roll = 
 
 Heat given out by roll =()x()XJ cal. 
 Heat equation and its solution : 
 
 Computed specific heat of , s = 
 
 True value of the specific heat = 
 
 Percentage of error = % 
 
 EXERCISE 30. MELTING AND FREEZING 
 
 References. Adams, 386-388 ; Coleman, 231, 244-247 ; Car. 
 & C., 311, 329-332; Ches. G. &T., 207, 232-237; Hoad. Br., 
 240, 271-273; Hoad. El., -257, 298-300; Mumper, 105, 122- 
 123 ; Mil. & G., 180, 264-269, 273 ; Went. & H., 94, 99-101. 
 
 Apparatus. Thermometer, numbered for identification ; tum- 
 bler or beaker ; test tube ; supply of ice and salt. 
 
 Experiment ^. To find the error of the zero point on a 
 thermometer scale. 
 
 Experimental Work. a. Fill the beaker about half full of fine 
 crushed ice. Insert the thermometer, and pack the ice about it 
 nearly to the zero of the scale. After the mercury ceases to fall, 
 take the temperature to .1. Record the number of the ther- 
 mometer and its reading in melting ice. The graduation of 
 thermometers, except expensive ones, may be in error by several 
 
MELTING AND FREEZING 10$ 
 
 
 
 tenths of a degree. The temperature of melting ice (when by 
 itself) is exactly zero. The reading of a centigrade thermometer 
 in melting ice is therefore the error of its zero point. 
 
 b. What evidence is there that the ice you used was melting? 
 Was the ice receiving or losing heat during the experiment? 
 How and why? 
 
 Experiment 56. To find whether freezing and melting take 
 place at the same temperature. 
 
 Experimental Work. a. Mix with the ice in the beaker about 
 one fourth its volume of table salt. Put enough water into the 
 test tube to cover the bulb of the thermometer when inserted in 
 it, and place it in the freezing mixture of salt and ice. Stir the 
 water in the test tube with the thermometer, keeping watch of 
 its temperature. At what temperature does it begin to freeze? 
 Continue the stirring and take the temperature from time to time 
 as the freezing continues. What is the reading of the thermometer 
 in freezing water ? How do the temperatures of melting ice and 
 freezing water compare? 
 
 b. After a third or a half of the water in the tube is frozen, allow 
 the remainder to freeze round the bulb of the thermometer. What 
 change of temperature do you observe after the water is all frozen? 
 
 To free the thermometer from the ice, let water from the faucet 
 run on the test tube. Take the temperature of the freezing mix- 
 ture. Was the water in the test tube receiving or losing heat 
 while it was freezing? Why? 
 
 Experiment 57. To observe the effect of pressure upon* the 
 melting point of ice. 
 
 Apparatus. A block of ice supported at the ends ; a heavy 
 weight suspended from the block of ice by means of a loop of 
 fine wire passed over it. 
 
 [The most convenient procedure with this experiment is for the 
 teacher to set it up, at or just before the beginning of the labora- 
 tory period, and have all the members of the class observe its 
 progress from time to time during the hour.] 
 
IO6 HEAT 
 
 
 Experimental Work. a. When the weight was hung upon the 
 
 ice, the wire rested upon its surface. How do you find it now? 
 
 Look at it from time to time during the hour, and note any change 
 
 in the position of the wire. 
 
 b. How is the cut that the wire makes in the ice mended ? 
 
 What is the cause of the melting under the wire? What is the 
 
 source of the heat required for this melting? Why does the water 
 
 above the wire freeze? (Heat received by the ice from the air 
 
 and other bodies does not reach the interior.) 
 
 EXERCISE 31. HEAT OF FUSION AND SOLUTION 
 
 References. Adams, 389-392 ; Coleman, 248-250 ; Car. & 
 C., 332-334; Ches. G. & T., 238-240; Hoad. Br., 284; Hoad. 
 EL, 315 ; Mumper, 124-125 ; Mil. & G., 264-265, 281 ; Went. & 
 H., i lo-m. 
 
 Experiment 58. To find the number of calories required to 
 change i g. of ice at o into water at o. 
 
 Apparatus. Calo- 
 rimeter ; thermometer 
 an d stirrer (Fig. 43) ; 
 FlG 3 platform balance and 
 
 weights to 500 g. ; 
 cloth ; ice plane ; supply of ice and of hot water. 
 
 [For a stirrer use a piece of very thin sheet copper about 
 i x 1.5 in., with two holes large enough to slip it on the end 
 of the thermometer.] 
 
 Experimental Work. Weigh the calorimeter to .1 g. Put into 
 it about 150 g. of water at a temperature between 45 and 50. 
 Take hot water from the supply and add cold water till the tem- 
 perature is right. Weigh the calorimeter and water. During the 
 remainder of the experiment the calorimeter should stand on wood 
 or paper (poor conductors), and should be touched by the hands 
 as little as possible. 
 
HEAT OF FUSION AND SOLUTION IO/ 
 
 Have at hand a quantity of shaved or crushed ice. This must 
 be dry. (Why?) It is best prepared by shaving it with an ice 
 plane immediately before using it. The quantity required will 
 have a volume about equal to the volume of water used. If a 
 supply of crushed ice is provided, dry it as much as possible by 
 spreading it out on a cloth and wiping each piece with a corner 
 of the cloth. 
 
 Thoroughly stir the water in the calorimeter with the stirrer on 
 the thermometer, and take the temperature to .1. Immediately 
 put in nearly all of the ice, and stir the water constantly while the 
 ice is melting. If ice remains after the temperature has fallen to 
 about 8, remove it with the stirrer ; if the ice is all melted before 
 the temperature has fallen to 10 or 12, add more without delay. 
 As soon as the temperature has fallen to about 8 and no ice 
 remains in the calorimeter, stir the water thoroughly and take the 
 temperature at top and bottom. If there is a difference, stir and 
 read again. Record the lowest uniform temperature of the water. 
 
 Weigh the calorimeter and contents. Leave the calorimeter 
 empty, and the table dry. 
 
 Data and Computations. The experiment is planned so that 
 the heat lost from the calorimeter and contents by radiation and 
 conduction while they are warmer than the air is approximately 
 balanced by the heat gained by the same means after they have 
 become colder than the air. We may therefore assume that the 
 heat received by the ice in melting and the heat received by the 
 ice water in warming to the final temperature comes entirely from 
 the warm water and the calorimeter, and that the heat received 
 by the ice and the ice water is equal to the heat lost by the warm 
 water and the calorimeter. Let /denote the heat of fusion of ice 
 (the number of calories required to melt one gram of ice without 
 change of temperature). Take the specific heat of the calorimeter 
 from the table of specific heats in the Appendix. Write the heat 
 equation and solve it for /. Record data and computations as 
 follows : 
 
108 HEAT 
 
 Weight of the calorimeter = g. 
 
 Weight of calorimeter and water = g. 
 Temperature of calorimeter and water just before 
 
 adding ice = C. 
 
 Final temperature of calorimeter and water = C. 
 Final weight of calorimeter and water (including 
 
 water from the ice) = g. 
 
 COMPUTATIONS 
 
 Weight of water before adding ice = g. 
 
 Weight of ice added = g. 
 
 Fall of temperature of calorimeter and water = 
 
 Heat given out by warm water = cal. 
 
 Heat given out by calorimeter = cal. 
 
 Heat received by the ice in melting = ( ) X/ = cal. 
 Heat received by the ice water in warming to the 
 
 final temperature = cal. 
 Heat equation and its solution : 
 
 Computed heat of fusion of ice,/ = cal. 
 
 True value of heat of fusion of ice = 79.25 cal. 
 
 Percentage of error /o 
 
 Experiment 59. To observe the change of temperature when 
 ammonium chloride or ammonium nitrate is dissolved in water. 
 
 Apparatus. Thermometer; test tube; ammonium chloride 
 or ammonium nitrate. 
 
 Experimental Work. Fill the test tube about one third full 
 of water and take its temperature. Add a teaspoonful or more 
 of ammonium chloride or ammonium nitrate, stir with the ther- 
 mometer, and note the change of temperature. What inference 
 may be drawn from this change of temperature? 
 
 If there is time, repeat the experiment with ice-water. Compare 
 the fall of temperature in the two cases, and note particularly 
 whether the temperature falls below the freezing point of pure water. 
 
COOLING BY EVAPORATION; DEW-POINT 1 09 
 
 EXERCISE 32. COOLING BY EVAPORATION; DEW- 
 POINT 
 
 References. Adams, 393, 397, 401-403 ; Coleman, 251-252, 
 256-259; Car. & C., 335-336, 339, 341 ; Ches. G. & T., 243- 
 249; Hoad. Br., 274-276 ; Hoad. El., 302-305 ; Mumper, 126- 
 127, 134-136; Mil. & G., 133-143, 145-146; Went. & H., 102- 
 103, 113, 127-128. 
 
 Experiment 60. To compare the rate of evaporation of water, 
 alcohol, and ether, and to observe the change of temperature due to 
 evaporation. 
 
 Apparatus. Small bottles containing water, alcohol, and ether ; 
 thermometer ; absorbent cotton. 
 
 Experimental Work. a. Pour a few drops of water on the 
 palm of the hand, and move the hand back and forth edgewise. 
 Note the temperature sensation and the rapidity with which the 
 water evaporates. Try the same experiment with alcohol. 
 
 Compare the rapidity of evaporation of water and alcohol and 
 the temperature sensations. Account for the difference in the 
 temperatures. 
 
 b. Repeat the experiment, using ether. Compare results with 
 those obtained with water and alcohol. Account for the differ- 
 ence in the temperatures. 
 
 c. Take the temperature of the air. Wrap a small quantity of 
 cotton round the bulb of the thermometer, and insert it in the 
 bottle of water. Take the temperature of the water. Raise the 
 bulb out of the water, but leave it still inside the bottle, and after 
 about half a minute take the temperature. Remove the ther- 
 mometer from the bottle, and observe any change in the reading 
 as it is held in the air for a short time. After the temperature 
 has become constant, move the thermometer to and fro several 
 times, and again read the temperature. Record the observed 
 temperatures on separate lines. 
 
110 HEAT 
 
 Account for the equality of or the difference between the 
 various temperatures. 
 
 d. Replace the cotton on the bulb of the thermometer with a 
 dry piece, and repeat the preceding experiment, using ether in- 
 stead of water. 
 
 Compare the results with those obtained with water. Why 
 does the temperature cease to fall before all the ether has evapo- 
 rated from the cotton? 
 
 Experiment 61. To find the dew-point of the air in the 
 laboratory. 
 
 Apparatus. Thermometer; stirrer of thin copper; bright 
 calorimeter ; two beakers ; ice. 
 
 Experimental Work. a. Put water in the calorimeter to a 
 depth of about three centimeters. Have at hand a beaker of 
 water, and a small quantity of shaved or finely crushed ice in the 
 other beaker. Add ice to the calorimeter, a very little at a time, 
 stirring constantly with the stirrer on the thermometer. Watch 
 closely meanwhile for the first deposit of moisture on the calorim- 
 eter near the bottom ; and when it appears, take the tempera- 
 ture of the water. It is the highest temperature at which 
 moisture is deposited that is to be found. If the moisture 
 gathers quickly and abundantly, the water is too cold. If this 
 happens, add warmer water to the calorimeter, wipe the outside 
 dry, and repeat, being careful to cool the water more gradually. 
 Avoid breathing on the calorimeter. (Why?) If the dew-point 
 is below zero, it will be necessary to add salt with the ice. If in 
 the course of the experiment the calorimeter becomes more than 
 half full, pour out part of the contents. 
 
 b. Starting with a thin film of moisture on the calorimeter, stir 
 the water constantly till the moisture disappears, then take the 
 temperature. The temperatures at which the dew appears and 
 disappears should not differ by more than i. Take their aver- 
 age as the dew-point of the air in the laboratory at the time of 
 the experiment. 
 
PHENOMENA OF BOILING 
 
 III 
 
 EXERCISE 33. PHENOMENA OF BOILING 
 
 References. Adams, 393-395; Coleman, 261-262; Car. & 
 C., 337 ; Ches. G. & T., 251-254 ; Hoad. Br., 277 ; Hoad. EL, 
 306; Mumper, 128-129; Mil. & G., 278-280; Went. & H., 104. 
 
 Apparatus. Ther- 
 
 mometer, numbered 
 
 for identification ; ring 
 
 stand, ring and clamp ; 
 
 wire gauze ; large flask, 
 
 and stopper to fit, with 
 
 two holes ; delivery 
 
 tube (Fig. 44) ; hy- 
 
 drometer jar ; Bunsen 
 
 burner ; closed -tube 
 
 pressure gauge con- 
 
 taining water in the 
 
 closed tube above the 
 
 mercury (Fig. 45). 
 [To make the pres- 
 
 sure gauge, take a 
 
 piece of small glass tubing about a foot long ; seal one 
 end, and bend about 3 in. from the closed end, as shown 
 in Figure 45, making the bend narrow enough to pass 
 through the neck of the flask. A slight bend in the 
 open arm of the tube, at right angles to the two arms, as 
 shown in the figure, will keep the mercury from running 
 out when the tube is laid on the table. Pour in enough 
 mercury to fill the short arm and extend just past the bend. 
 By holding the tube horizontal, with the closed end below, 
 and inclining it first in one direction then in the other, 
 the air can be gradually displaced from the closed end 
 by the mercury. Next pour in water to a depth of 
 about half an inch, and work a little of it into the closed 
 
 FIG. 45. arm by inclining the tube with the closed arm above.] 
 
 FlG - 
 
112 HEAT 
 
 Experiment 62. To observe the phenomena preceding and ac- 
 companying boiling; and to find the temperature of the boiling 
 water and the steam. 
 
 Experimental Work. Fill the flask about half full of fresh 
 water (not water that has been boiled), wipe the outside dry, 
 place it on the wire gauze on the stand, and apply heat. The 
 flame must not be high enough to burn above the gauze. While 
 the water is heating, conduct simultaneously the observations 
 called for in paragraphs a, b, and c. 
 
 a. Place the thermometer in the flask, letting it rest on the 
 bottom, and occasionally observe the temperature. Observe the 
 water while heating, and note the first formation of bubbles. 
 These are bubbles of air which was dissolved in the water and 
 which is now being driven off by the heat. Describe their size, 
 abundance, and behavior ; and state through what range of tem- 
 perature (approximately) they continue to be given off. (The 
 
 " flat " taste of boiled water is due to the fact that it contains 
 little or no dissolved air.) 
 
 b. Note any gathering of moisture on the inside of the flask 
 and on the thermometer. Does it occur before the water boils ? 
 How do you account for it? 
 
 c. Note the temperature when sounds begin to come from the 
 flask. What is their cause ? Is the water boiling when the sounds 
 begin ? Watch closely for the first formation of bubbles larger 
 than the air bubbles first observed. What are they? Where are 
 they formed ? What becomes of them ? Note the temperature. 
 Watch closely for any change in the phenomena as the tempera- 
 ture approaches 100. 
 
 d. Regulate the flame so that the water boils slowly, and record 
 its temperature. Record its temperature when it is boiling 
 rapidly. 
 
 e. Raise the thermometer till the bulb is just out of the water. 
 Take the temperature as accurately as possible and record it as 
 the temperature of the steam. 
 
PHENOMENA OF BOILING 113 
 
 Experiment 63. To find the vapor pressure of steam at the 
 
 boiling point. 
 
 Experimental Work. The closed-tube pressure gauge (Fig. 45) 
 contains water in the closed arm above the mercury. If there is 
 a bubble at the top of the closed tube, it is air, and mast be 
 removed. Have this done by the instructor. Lower the gauge 
 into the steam above the boiling water in the flask, and note the 
 formation of water vapor in the closed arm. How do the levels 
 of the mercury in the two arms compare? What does this 
 prove concerning the relative values of the atmospheric pressure 
 and the pressure of the water vapor in the closed arm ? Observe 
 the effect of removing the gauge from the flask. Explain. 
 
 Conclusions. State the conclusions to be drawn from the 
 experiment. 
 
 Experiment 64. To observe the effect of increase of pressure 
 upon the boiling point ; and to find the correction for the boiling 
 point on the thermometer used. 
 
 Experimental Work. Remove the burner from under the flask 
 while you are making the following adjustment. Push the ther- 
 mometer through the hole in the stopper till the bulb is but little 
 above the water when the stopper is in the flask. Be careful ; if 
 you have difficulty, call for assistance. Press the stopper firmly 
 into the flask. Connect the delivery tube as shown in Figure 44, 
 and let it extend to the bottom of the hydrometer jar, which 
 should be nearly full of water. Boil the water in the flask, and 
 take the temperature of the steam while it is escaping into the 
 bottom of the jar of water. (The noise of the condensing steam 
 can be greatly reduced by standing the jar on a book.) Gradually 
 raise the delivery tube out of the jar while observing the effect 
 upon the temperature of the steam. Raise and lower the tube 
 till you are sure of the effect. Take the temperature while the 
 steam is escaping into the air. Empty the flask and return the 
 thermometer to its case. 
 
 Read the barometer. 
 
 COLEMAN'S NEW MANUAL 8 
 
114 
 
 HEAT 
 
 Discussion. i. Discuss the experiment as an illustration of 
 the effect of pressure on the temperature at which water boils. 
 
 2. At a pressure of one atmosphere (76 cm.) the true value of 
 the boiling point is 100. For pressures either slightly greater or 
 less than one atmosphere, the temperature of steam from boiling 
 water varies .37 for a change of pressure of i cm. Compute the 
 true value of the temperature of steam at the observed barometric 
 pressure. 
 
 3. What is the error of the boiling point on this thermometer? 
 
 EXERCISE 34. HEAT OF VAPORIZATION OF WATER 
 
 References. Adams, 396; Coleman, 266-267; Car. & C., 
 342 ; Ches. G. & T., 245, 255 ; Hoad. Br., 285-286; Hoad. El., 
 317-318; Mumper, 133 ; Mil. & G., 275-277 ; Went. & H., 112. 
 
 Experiment 65. To find the number of calories given out by 
 i g. of steam at 100 in condensing to water at 100. 
 
 Apparatus. Flask or other steam-generating apparatus, with 
 rubber tube and condensation trap (Fig. 46) or side-neck test 
 
 tube ; Bunsen burner ; calorim- 
 eter ; thermometer and stirrer ; 
 platform balance and weights; 
 ice ; mop cloth. 
 
 Experimental Work. Fill 
 the steam generator about half 
 full of water, and begin heating 
 it. Connect the delivery tube 
 and condensation trap. Sup- 
 port the delivery tube on some 
 object so that the escaping 
 steam will not damage the table. 
 
 Weigh the calorimeter to .1 g. 
 
 FIG ' 46 ' (It is especially important ir 
 
 this experiment that the weighing be carefully done.) Fill 
 
HEAT OF VAPORIZATION OF WATER 1 15 
 
 calorimeter about two thirds full of water at o to 5. Add ice to 
 water from the faucet till the required temperature is obtained. 
 (If ice is not provided, use the coldest water obtainable.) 
 Weigh the calorimeter and water, and remove at once from the 
 balance. 
 
 Place the stirrer on the thermometer, and as soon as the steam 
 is escaping freely from the delivery tube, stir the water in the 
 calorimeter and take the temperature. Wipe off any dew that has 
 gathered on the calorimeter, and immediately place the delivery 
 tube in the water to a depth of an inch or two. The calorimeter 
 should be at some distance from the burner and protected from 
 its radiation by a screen. Stand your note book between them 
 for this purpose. There should be no considerable loss of steam 
 on account of poorly adjusted apparatus. If the steam is delivered 
 properly, the temperature will rise rapidly. Stir the water con- 
 stantly, keeping the hands off the calorimeter. The condensation 
 trap must not overflow and admit hot water into the calorimeter. 
 To empty it, remove the burner from under the boiler and lift the 
 delivery tube till the water in the trap runs back into the boiler. 
 
 When the temperature has risen to about 40, turn off the gas, 
 remove the delivery tube from the calorimeter immediately, stir 
 the water thoroughly, and take the temperature as quickly as 
 possible. 
 
 Weigh the calorimeter and contents. Leave the calorimeter 
 empty and the table dry. 
 
 Data and Computations. The temperatures in the experiment 
 are so chosen that the heat received from outside bodies while the 
 calorimeter and water are colder than the air is as nearly as possi- 
 ble equal to the heat gained after they have become warmer than 
 the air. Hence the heat gained by the water and calorimeter is 
 assumed to come only from the steam, first in condensing to water 
 at 100, second in cooling to the final temperature. Let v denote 
 the heat of vaporization of water (the number of calories given 
 out by one gram of steam in condensing to water at 100). Write 
 
Il6 HEAT 
 
 the heat equation, and solve it for v. Record data and computa- 
 tions as follows : 
 
 Weight of calorimeter = g. 
 
 Weight of calorimeter and water g. 
 
 Temperature of calorimeter and water just before add- 
 ing steam = 
 
 Final temperature of calorimeter and water = 
 
 Final weight of calorimeter and water (including water 
 
 from steam) = g. 
 
 COMPUTATIONS 
 
 Weight of water before adding steam = g. 
 
 Weight of steam added = g. 
 
 Rise of temperature of calorimeter and water = 
 
 Heat received by the calorimeter = cal. 
 
 Heat received by the water = cal. 
 
 Heat given out by the steam in condensing to water at 
 
 ioo= ( ) x v cal. 
 
 Heat given out by water from condensed steam in cool- 
 ing to final temperature cal 
 
 Heat equation and its solution : 
 
 Computed heat of vaporization of water, v cal. 
 
 True value of heat of vaporization of water = 536 cal. 
 
 Percentage of error = % 
 
 EXERCISE 35. THE STEAM ENGINE 
 (INVENTIVE) 
 
 References. Adams, 362-368 ; Coleman, 275-276 ; Car. & C., 
 .357; Ches. G. & T., 257-260; Hoad. Br., 289; Hoad. EL, 
 321-322; Mumper, 156; Mil. & G., 252-258; Went. & H., 230- 
 233- 
 
 Experiment 66. To study the mechanism of a steam engine. 
 
 Apparatus. Section model of a steam engine (Fig. 47). 
 
 
THE STEAM ENGINE 
 
 117 
 
 Suggestions. Study the model in connection with the text 
 and reference books. Describe the points illustrated by the 
 model, referring to lettered diagrams of its various parts. A model 
 like that shown in the 
 figure is provided with 
 the reversing gear used 
 on locomotives. The 
 reversing gear is oper- 
 ated by means of the 
 lever. Find the direc- 
 tion in which the driv- 
 ing wheel of the actual 
 engine represented by 
 the model would turn 
 when the lever is in 
 
 FIG. 47 . 
 
 the extreme front and back positions. What would be the effect 
 of placing the lever midway between these positions ? Study the 
 effect of setting the lever part way forward and part way back. 
 In discussing the reversing gear, refer to lettered diagrams of it. 
 
VIII. SOUND 
 
 EXERCISE 36. THE TRANSMISSION OF SOUND 
 
 References. Adams, 208 ; Coleman, 277-280,290; Car. & 
 C., 174-179, 198-199; Ches. G. & T., 167-170; Hoad. Br., 
 181-184; Hoad. EL, 195-198; Mumper, 162-165; Mil. & G., 
 444-445 ; Went - & H., 333-334. 
 
 Experiment 67. To study the transmission of sound through 
 solids. 
 
 Apparatus. Meter rod ; large tuning fork ; rubber mallet for 
 striking the fork ; cord four or five feet long. 
 
 [For a rubber mallet bore a half-inch hole in a large rubber 
 stopper, and insert a stick about 10 in. long for a handle ; or slip 
 a short piece of large, thick rubber tubing on the end of a stick.] 
 
 Experimental Work. a. To set a tuning fork in vibration, 
 hold it by the stem in one hand and strike one of the prongs a 
 sharp, quick blow near its end, in the direction of the other prong. 
 (Touching a prong of a sounding fork immediately stops it.) 
 Hold one end of the meter rod close to the ear while your com- 
 panion holds the stem of the vibrating fork against the other end 
 of the rod. Note the loudness of the sound. Listen to the sound 
 of the fork through the air at the same distance, the rod being 
 removed. Compare the loudness of the sound transmitted through 
 the rod and through the air. 
 
 b. Hold an end of the rod between your teeth while the stem 
 of the sounding fork is held against the other end. The sound 
 travels through the rod, the teeth, and the bones of the head to 
 the ear. Describe the result. Do you feel the vibrations? 
 
 118 
 
THE TRANSMISSION OF SOUND Iig 
 
 c. Hold the stem of the vibrating fork against the teeth ; against 
 the top of the head. State the result. 
 
 d. Tie a string one or two meters long to the stem of the fork. 
 Press one end of the string into your ear, while your companion 
 sets the fork vibrating and holds it so as to stretch the string moder- 
 ately tight. Try the effect of slackening the string ; also the 
 effect of removing it from the ear when tightly stretched. What 
 have you learned about the transmission of sound by the string? 
 
 e. Touch the stem of the vibrating fork to the table top. The 
 loud sound comes from the table, which is set in vibration by the 
 fork. Hold an end of the meter rod against the side of the table, 
 and the vibrating fork against the other end of the rod. State and 
 account for the result. 
 
 /. Place the rubber stopper of the mallet between the vibrating 
 fork and the table. How does the stopper compare with the rod 
 in its power to transmit sound? To what is the difference due? 
 
 Experiment 68. To study the construction and use of an 
 acoustic telephone line. 
 
 Apparatus. An acoustic telephone line, with stations at oppo- 
 site ends of the laboratory or in adjacent rooms j tuning fork ; 
 mallet. 
 
 [To make an acoustic telephone, make a small hole in the mid- 
 dle of the bottom of two small tin cans or chalk boxes, fasten 
 them up at some distance apart, and stretch a cord or small copper 
 wire rather tightly between them, fastening the ends to some small 
 object, as a button, on the inside of the bottom of the cans. The 
 cord must not be supported by fastening it rigidly to any object. 
 It may be supported at any point by a short cord, and may be 
 carried round a corner by giving it three or four such supports at 
 the corner, making each bend slight. The acoustic telephones 
 supplied by dealers are more satisfactory.] 
 
 Experimental Work. Listen at one end of the telephone line, 
 while your companion places the stem of a vibrating fork against 
 
120 SOUND 
 
 the telephone at the other end. Try speaking to each other 
 through the telephones. 
 
 Note the construction of the telephones and the manner in 
 which the connecting wire (or cord) is supported. Describe the 
 various details observed, and explain their purpose. 
 
 Experiment 69. To find whether water transmits sound. 
 
 Apparatus. Battery jar of water ; large tuning fork ; large 
 cork or small block of wood with hole to fit the stem of the fork ; 
 rubber mallet. 
 
 Experimental Work. Place a jar of water on the table. In- 
 sert the stem of the fork into the hole in the cork (or block). 
 Set the fork in vibration and hold it with the cork immersed in 
 the water, but not touching the glass. Raise the cork out of the 
 water and again immerse it, repeating the process a number of 
 times, and note the effect on the loudness of the sound. State 
 the result. 
 
 With the fork sounding and its stem in the water, try the effect 
 of lifting the jar from the table and again replacing it. Does the 
 sound come principally from the jar of water or from the table 
 when the jar stands on the table? 
 
 How does the experiment answer the question whether water 
 transmits sound? 
 
 Experiment 70. To study the transmission of sound through 
 a speaking tube. 
 
 Apparatus. A tin or large glass tube 6 ft. to 10 ft. long; roll 
 of cotton or soft cloth ; watch. 
 
 Experimental Work. Lay a watch on a roll of cotton or soft 
 cloth (to prevent the transmission of the sound through the table) 
 at one end of the tube, and listen at the other end to the sound 
 of the ticking. About how near to the watch must you hold the 
 -ear to hear it as distinctly directly through the air as through the 
 tube ? 
 
 Explain the effect of the tube. 
 
RIPPLES. REFLECTION OF SOUND 121 
 
 EXERCISES 37. RIPPLES. REFLECTION OF SOUND 
 
 References. Adams, 195-196, 213; Coleman, 281-283, 2 93 > 
 Car. & C., 164-165, 167, 169-172, 184-186; Ches. G. &T., 170- 
 173, 181; Hoad. Br., 185-188, 193-195; Hoad. EL, 200-203, 
 209-211; Mumper, 157-160, 165, 167; Mil. & G., 448-455, 
 459-460; Went. & H., 334-33 8 . 340-34L 
 
 Experiment 71. To study the origin, transmission, and reflec- 
 tion of ripples. 
 
 Apparatus. Ripple trough, strip of tin about 2 in. wide and 
 about the width of the trough, bent into an arc of about 70 ; thin 
 board about 3 in. wide and a trifle shorter than the width of the 
 trough. 
 
 [The ripple trough is a shallow box with a glass bottom. For 
 the sides use 1.5 x 2.5 in. wood or larger, and for the bottom 
 a window pane not smaller than 20X24 in., larger, up to 
 24 x 30 in., is preferable. Plate glass gives a uniform depth of 
 water, which is very desirable. The wooden sides should be 
 given two or three coats of boiled oil or a coat of hot paraffine 
 to prevent absorption of water. An inch hole should be bored 
 in one end and closed with a cork, for convenience in emptying 
 the trough.] 
 
 Experimental Work. a. Origin and propagation of waves. 
 Spread a large sheet of white or very light colored paper on 
 a table near a window where 'the light is strong, and place the 
 trough on the paper. This arrangement makes the ripples 
 distinctly visible. Fill the trough with, water to a depth of about 
 i cm. Start a wave at the center of the trough by dipping the 
 finger into the trough and quickly removing it. Observe the shape 
 of the wave and the direction or directions in which it travels. 
 Repeat till sure of the results. Describe what is observed. 
 
 b. Start a series or train of waves by tapping rapidly with 
 the finger at the center of the trough. Describe the appearance 
 of the train of waves and their behavior. 
 
122 
 
 SOUND 
 
 FIG. 48. 
 
 c. Place the board on edge in the trough in the position shown 
 at ab (Fig. 48). With a slight forward and backward motion of 
 
 the board, start a wave down the trough. 
 
 Describe the shape and behavior of the 
 
 wave, and compare it with the wave 
 
 set up by the finger. 
 
 d. Start a train of waves by means 
 
 of the board. Compare with the train 
 
 of waves set up by rapid tapping with 
 
 the finger. 
 
 Reflection of Waves. e. Start a 
 straight wave with the board, as in c, and observe what happens 
 when the wave reaches the farther end of the trough. Start a 
 train of three or four waves, and observe 
 whether they are all reflected. Can 
 two sets of waves travel over the same 
 surface in opposite directions and at 
 the same time? 
 
 f. Start a train of waves with the 
 board at an angle with the side of the 
 trough, as in the position ab (Fig. 49). 
 Draw a diagram showing the course of 
 these waves before and after reflection, 
 waves by a number of parallel lines.) 
 
 FIG. 50. 
 
 FIG. 49. 
 
 (Represent a train of 
 Describe the reflection 
 of an oblique wave and its change of 
 direction*. 
 
 g. Start a circular wave at the center 
 of the trough by a tap with the finger, 
 and observe its reflection by the sides 
 of the tank. Start a train of waves, 
 and observe. Describe, with a diagram 
 to illustrate. 
 
 h. Place the curved strip of tin as 
 
 shown at cd (Fig. 50), and observe the reflection of a single 
 straight wave and also a train of straight waves from its concave 
 
RIPPLES. REFLECTION OF SOUND 123 
 
 side. Describe the shape and behavior of the reflected waves, and 
 draw a diagram to illustrate. 
 
 Experiment 72. To study the reflection of sound from concave 
 surfaces. 
 
 Apparatus. Two large concave reflectors; large funnel with 
 rubber tube attached, for use as an ear trumpet ; watch. 
 
 [This experiment can be performed only in a very quiet room. 
 It should be set up in a room by itself, if possible.] 
 
 Experimental Work. a. Stand one of the reflectors (A, Fig. 
 51) at one end of the table, and turn it so as to face toward the 
 other reflector B, placed at a distance of 3 or 4 m. B is set 
 
 FIG. 51. 
 
 obliquely, as shown in the figure. Hang a watch in front of 
 the center of reflector A at a distance from it equal to half the 
 radius of its spherical surface. This point F is called the 
 principal focus of the reflector. 
 
 Hold the ear at E, being careful to cover as little of the reflector 
 with the head as possible, so as not to intercept the sound waves 
 as they travel from A to B. Move the head slightly in different 
 directions to find the position where the sound is loudest. When 
 the ear is properly placed, the watch should be heard distinctly. 
 
 b. Instead of placing the ear at E, the reflector B may be turned 
 so as to face squarely toward A, and the ear trumpet used to con- 
 vey the sound to the ear. Place the funnel at the focus of B, and 
 facing toward it, and the end of the tube in the ear. Try both ways. 
 
 c. With the ear at E or with the ear trumpet in position, 
 observe the effect of turning A about a vertical axis toward one 
 side, then toward the other. 
 
124 
 
 SOUND 
 
 EXERCISE 38. VIBRATION NUMBER OF A FORK 
 
 References. Adams, 231-239 ; Coleman, 294-296 ; Car. & C., 
 204-205 ; Ches. G. & T., 185-186 ; Hoad. Br., 205-207 ; Hoad. 
 EL, 201, 222 ; Mumper, 172 ; Mil. G., 456-457 ; Went. & H., 
 344- 
 
 Experiment 73. To find the number of vibrations per second 
 of a tuning fork. 
 
 FIG. 52. 
 
 Apparatus. Vibrograph with tuning fork, as shown in Figure 
 52 ; rubber mallet; watch or small clock with second-hand; fluid 
 paste of whiting (or chalk dust) and alcohol ; small paint brush. 
 
 [The pendulum of the vibrograph should make not less than two 
 double vibrations per second, and must have a heavy bob in order 
 that the friction of the stylus may not affect its rate or stop it too 
 quickly. The fork must be large and of low pitch, preferably not 
 above 128, and capable of vibrating with a large amplitude for 
 several seconds. Dealers supply forks especially designed for 
 this purpose. The glass plate should be a foot or more in length, 
 so as to accommodate at least two double vibrations of the pendu- 
 
VIBRATION NUMBER OF A FORK 125 
 
 him. The experiment is intolerably dirty in the hands of most 
 pupils, if smoked glass is used. If smoked glass is preferred, it 
 is recommended that the teacher smoke the plates and take the 
 traces for the class.] 
 
 Method. A stylus of fine wire or bristle is attached at the 
 lower end of the pendulum, and another at the end of one of the 
 prongs of the fork. These styluses lightly touch a plate of glass 
 placed under them on the board. The glass is covered on its 
 upper side with a thin coating of whiting and alcohol (or is 
 smoked). With the fork and the pendulum vibrating, the glass is 
 drawn quickly along the board to the right, and each stylus traces 
 a wavy line on the glass, as shown in Figure 53, the line traced by 
 the pendulum crossing and recrossing at regular intervals the one 
 
 made by the fork. The time interval from A to C in the figure 
 is the time of a double vibration of the pendulum, which is com- 
 puted from the number of double vibrations which the pendulum 
 makes in one minute. The number of vibrations made by the 
 fork during one or more double vibrations of the pendulum is 
 found from the trace on the glass. Having thus the number of 
 vibrations of the fork in a known interval of time, the number of 
 vibrations per second is easily computed. 
 
 Experimental Work. Paint one side of the glass plate uniformly 
 with the whiting and alcohol paste, and lay the plate aside to dry. 
 
 Count the number of vibrations that the pendulum makes in 
 60 sec., and compute the time of one double vibration. 
 
 After the glass is dried, place it in position with its right end 
 under the styluses, being careful not to bend them. Adjust the 
 
126 SOUND 
 
 fork and the pendulum so that the styluses touch the glass lightly, 
 within 2 or 3 mm. of each other at points which are in a line 
 parallel to the sides of the base. Set the pendulum swinging 
 through an arc of about 3 cm., strike the fork a vigorous blow to 
 give it a large amplitude, and immediately draw the glass with a 
 quick, steady motion to the right. Repeat, if necessary, till you 
 have obtained a good trace of the fork covering not less than two 
 double vibrations of the pendulum (from A to E in the figure), 
 if this seems to be possible with the apparatus provided. 
 
 Count the double vibrations of the fork (estimating tenths) for 
 the greatest number of whole double vibrations of the pendulum 
 recorded on the glass (A to C, A to E, or A to G in the figure). 
 Only whole double vibrations of the pendulum are considered, 
 since, if the traces of the fork and the pendulum do not lie on 
 exactly the same axis, adjacent spaces (as BC and CD) will not 
 be exactly equal, one representing more and the other less than a 
 single vibration of the pendulum. 
 
 Data and Computations. Record as follows: 
 
 No. of double vibrations of pendulum in 60 sec. = 
 
 Time of one double vibration of pendulum = 
 
 No. of vibrations of fork to double vibrations of 
 
 pendulum (counted) = 
 
 No. of vibrations of fork to one double vibration of pen- 
 dulum (computed) = 
 No. of vibrations of fork per second = 
 
 EXERCISE 39. INTERFERENCE AND BEATS 
 
 References. Adams, 201, 220-223; Coleman, 298-299; Car. 
 & C., 201-203; Ches. G. & T., 195, 200; Hoad. Br., 196-197, 
 204; Hoad. El., 212, 219; Mumper, 171, 177; Mil. & G., 468; 
 Went. & H., 353-354- 
 
 Experiment 74. To study the interference of sound waves 
 about a tuning fork. 
 
INTERFERENCE AND BEATS 127 
 
 Apparatus (for Experiments 74 and 75). Two tuning forks 
 nominally of the same pitch, but giving from one to three beats 
 per second ; cylinder about 10 cm. in length and 2 cm. in diam- 
 eter, consisting of an open roll of writing paper fastened with 
 paste or a rubber band ; rubber mallet ; soft wax. 
 
 [To make the soft wax, melt together about nine parts, by 
 weight, of beeswax and one part of Venice turpentine. Pour the 
 melted wax into slender cylindrical paper molds. The paper 
 may be removed as the wax is used.] 
 
 Experimental Work. a. Hold a vibrating fork in a vertical 
 position near the ear, and rotate it slowly. Have your companion 
 tell you the position of the plane of the prongs (whether parallel 
 with the side of the face, perpendicular to it, or at a greater or 
 less angle) when the sound is loudest and when it is faintest to 
 you. Describe the variations in the intensity of the sound, and 
 the corresponding positions of the fork, during one rotation. 
 Note whether there are positions in which the sound is inaudible. 
 
 b. With the vibrating fork held to the ear in the position in 
 which the sound is faintest, have your companion cover one of the 
 prongs with the paper cylinder, being careful not to touch the 
 fork with it. Repeat till you are sure of the effect. State it. 
 
 Discussion. State briefly the cause of the phenomena 
 observed in these experiments. The full discussion may be left 
 for the recitation. 
 
 Experiment 75. To study beats by means of two tuning forks 
 of very nearly the same pitch. 
 
 Experimental Work. a. Sound both forks and hold them 
 facing each other, about 2 cm. apart and close to the ear, with the 
 planes of the prongs perpendicular to the side of the face. Note 
 the frequency of the beats. Sound the forks and touch their 
 stems to the table. Are beats produced? 
 
 b. Stick a piece of soft wax about the size of a pea to a prong 
 of one of the forks, near the end, and note the effect on the fre- 
 
128 
 
 SOUND 
 
 quency of the beats. If the effect is too small to be noticed, 
 use more wax. It is better to stick some wax on both prongs 
 than a large quantity on one. The effect of the wax on the fre- 
 quency of the beats will depend upon whether it has been put on 
 the fork of the lower or the higher pitch. Prove this by remov- 
 ing the wax and putting it on the other fork. Does loading a 
 fork raise or lower its pitch ? Why ? 
 
 c. Tune the forks accurately to the same pitch by loading the 
 right one till the beats cease. Do the 
 beats become more or less frequent as 
 the forks approach unison? 
 
 Experiment 76. To study a mechan- 
 ical illustration of beats. 
 
 Apparatus. As shown in Figure 54. 
 
 \_BC is a light, thin board about 20 cm. 
 long, having a light pointer about 50 cm. 
 long fastened to one end. The lower end 
 of the pointer carries a small white card. 
 The board is free to swing from a fixed 
 support E, and carries two pendulums, 
 one 80 to 100 cm. in length, the other 
 about f as long. The bobs of the pendu- 
 lums are of equal mass, between 50 and 
 200 g. This experiment is due to Pro- 
 fessor Will C. Baker, of Queen's University, Kingston, Ont] 
 
 Experimental Work. Start the pendulums together, giving the 
 longer one an amplitude of about 15 and the shorter an ampli- 
 tude a few degrees greater. Carefully observe : (i) the gradual 
 and regular alternation of the pendulums between vibration 
 together (in the same phase) and in opposition (in opposite 
 phase) ; (2) the behavior of the pointer; (3) the correspond- 
 ence between the behavior of the pendulums and the behavior of 
 the pointer. 
 
 FIG. 54. 
 
THE LAW OF LENGTHS 129 
 
 Describe the observed phenomena, and show how the behavioi 
 of the pointer results from the behavior of the pendulums. 
 
 Class Discussion. This experiment affords visible illustration 
 of the mechanical relations involved in the production of beats in 
 sound. Study the experiment from this point of view, and discuss 
 it in the recitation. 
 
 EXERCISE 40. THE LAW OF LENGTHS 1 
 
 References. Adams, 245; Coleman, 305-307; Car. & C., 
 210-211 ; Ches. G. & T., 199; Hoad. Br., 220-222; Hoad. EL, 
 233-234; Mumper, 181 ; Mil. & G., 475 ; Went. & H., 347. 
 
 Experiment 77. To find the relation between the length of a vi- 
 brating string and its pitch, the tension remaining constant, 
 
 Apparatus. Sonometer (Fig. 55); rubber mallet; three or 
 more forks, including c 1 (256 vibrations) and c" (512); meter rod. 
 
 55. 
 
 Experimental Work. Adjust the bridge of the sonometer so 
 that the vibrating segment of the wire is between 60 and 70 cm. 
 long. Vary the tension till the wire is brought nearly into unison 
 with the c 1 fork, then complete the adjustment to unison by vary- 
 ing the position of the bridge. In doing this, the vibrating fork 
 may be held close to the ear (if the pupil is working alone) 
 or touched to the sonometer or to the top of the table. The wire 
 gives a better sound and one easier to compare with the fork if it 
 
 1 The only law of vibrating strings requiring quantitative treatment in ele- 
 mentary physics is the law of lengths. This law underlies the discussion of 
 the fundamental tone, overtones, and quality, both of strings and vibrating air 
 columns, and may therefore be conceded a place in the laboratory course, 
 although the other laws receive only qualitative illustration in the classroom. 
 COLEMAN'S NEW MANUAL 9 
 
130 
 
 SOUND 
 
 is plucked near the middle with the end of the finger (not the 
 nail). When the wire and the fork are nearly in unison, note the 
 beats and tune till they disappear. Measure the length of the vi- 
 brating segment of the wire when unison is exact. The tension 
 must now remain unchanged throughout the exercise. Displace 
 the bridge and make a second trial. Make further trials if the 
 disagreement exceeds 3 mm. 
 
 Repeat the above work with each of the forks provided, tuning 
 only by varying the length of the wire. 
 
 Data and Computations. Tabulate measurements and compu- 
 tations as indicated below. By length ratio for any tone is meant 
 the ratio of the length of the wire for that tone to the length of 
 the wire for c* . Compute the length ratio in each case, carrying 
 to three decimal places. Find the true values of the length ratios 
 from the law of lengths and the known vibration ratios of the forks 
 used. For example, if the fork is g', the vibration ratio is f, and, 
 by the law of lengths, the length ratio is the reciprocal of this, or f . 
 
 
 LENGTH OF WIRE 
 
 
 LENGTH RATIO 
 
 
 
 TONE 
 
 
 MEAN 
 LENGTH 
 
 
 ERROR 
 
 PERCENTAGE 
 OF ERROR 
 
 
 
 
 
 
 ist Trial 
 
 2 d Trial 
 
 
 By Exp. 
 
 True 
 
 
 
 c > 
 
 
 
 
 
 
 
 
 e> 
 
 cm. 
 
 cm. 
 
 cm. 
 
 
 
 .800 
 
 
 
 
 
 jf 
 
 cm. 
 
 cm. 
 
 cm. 
 
 
 
 .667 
 
 
 
 
 
 etc. 
 
 cm. 
 
 cm. 
 
 cm. 
 
 
 
 
 
 
 
 
 
 EXERCISE 41. SYMPATHETIC AND FORCED 
 VIBRATIONS 
 
 References. Adams, 214-215 ; Coleman, 310-315 ; Car. & C., 
 189-193; Ches. G. & T., 194-196; Hoad. Br., 198, 202-203, 
 205; Hoad. El., 213-215,217-218; Mumper, 168-169; Mil. & G., 
 456, 463, 467 ; Went. & H., 351-352. 
 
SYMPATHETIC AND FORCED VIBRATIONS 131 
 
 Experiment 78. To study the sympathetic vibration of tuning 
 forks and resonators. 
 
 Apparatus. Two tuning forks of exactly the same pitch 
 (shown by the absence of beats when sounded together) ; 
 rubber mallet; soft wax; set of three or four tin tubes, or 
 short pieces of large glass tubing, of different length and 
 diameter. 
 
 [Forks giving a few beats per second can be permanently 
 tuned to unison by filing a little off the inside of the prongs at the 
 base of the higher fork or the free ends of the lower one. It will 
 be more interesting if the tubes are of such sizes as to sound a 
 major chord. A set of four tin tubes haying lengths of 10, 8, 6.7, 
 and 5 in., and diameters in proportion to the lengths, will do 
 this.] 
 
 Experimental Work. a. Place the stem of a sounding fork 
 against the teeth. What evidence do you find that the stem 
 vibrates as well as the prongs? Is the vibration of the stem 
 longitudinal or transverse ? 
 
 b. With one fork sounding and the other silent, place the ends 
 of their stems together ; and after they have been in contact one 
 or two seconds, hold the fork that was silent close to the ear. It 
 will be found to be vibrating audibly. How was its vibration 
 produced ? 
 
 c. Sound one of the forks and hold it and the other fork close 
 together, facing each other, but not touching. After one or two 
 seconds, hold the fork that was silent close to the ear. It should 
 be sounding ; if it is not, repeat. Explain. 
 
 d. Stick a bit of wax about twice the size of a pea near the end 
 of a prong of one of the forks. This will slightly change the rate 
 of vibration of the fork (see Experiment 75). Now repeat the 
 experiments of paragraphs b and <r, sounding either of the forks, 
 and observe whether the silent fork is made to vibrate. State and 
 account for the result. 
 
 e. Blow across the ends of the tubes in succession. Note that 
 
132 SOUND 
 
 each tube gives forth a sound of definite pitch. Hold the tubes 
 close to the ears, using both ears at once, and note the faint 
 sounds, like the roar of a sea shell, coming from them. Note 
 whether the loudness of the sounds coming from the tubes is 
 affected by scraping the foot on the floor while the tubes are at 
 the ears. Note the pitch of these sounds. Is it the same in 
 each case as that produced by blowing across the end cf the 
 tube? 
 
 The continuous sounds from the tubes are due to the various 
 noises in the room. Consult texts for the explanation. 
 
 Experiment 79. To study the sympathetic and forced vibra- 
 tion of a sonometer wire. 
 
 Apparatus. Sonometer (Fig. 55) with two wires of the same 
 size, and without a bridge. 
 
 Experimental Work. a. Tighten one of the sonometer wires 
 till it sounds a note of medium pitch, and tune the other wire to 
 perfect unison with it. When the wires are nearly in unison, 
 listen for a periodic pulsation of the sound (beats) when both 
 wires are plucked. Tune till the beats cease. Now sound one of 
 the wires, and the other will immediately begin to vibrate visibly. 
 Stop the first wire, and the sound will be continued with consider- 
 able intensity by the other. Is this a case of sympathetic or forced 
 vibration? How is it produced? 
 
 b. With the wires of the sonometer so nearly in unison that 
 they give less than one beat per second when sounded together, 
 sound only one of them and observe the behavior of the other. 
 It should vibrate visibly for brief intervals, which alternate with 
 intervals of rest. Observe that, as the difference in pitch 
 is increased, these alternations of rest and vibration become 
 more rapid, and the maximum amplitude of vibration becomes 
 less, until presently the silent wire ceases to respond at all to 
 the vibrations of the other. Account for this behavior of the 
 wire. 
 
WAVE LENGTH BY RESONANCE 133 
 
 EXERCISE 42. WAVE LENGTH BY RESONANCE 
 
 References. Adams, 216-219 ; Coleman, 313 ; Car. & C., 193; 
 Ches. G. & T., 194-197; Hoad. Br., 198-201 ; Hoad. EL, 216; 
 Mil. & G., 463-466 ; Went. & H., 349. 
 
 Experiment 80. To find, by means of a resonance tube, the 
 length of the sound waves set up by a tuning fork of known vibra- 
 tion rate ; and to compute the velocity of sound in air frcm these 
 quantities. 
 
 Apparatus. Some form of resonance tube having an adjustable 
 length (Figs. 56, 57, and 58) ; tuning fork; rubber mallet; rub- 
 ber band; meter rod; access to a thermometer. 
 
 "FIG. 56. 
 
 [For second resonance, the tube must be at least 105 cm. long 
 with a f 1 fork (256), 85 cm. long with an <?' fork, 75 cm. long with 
 a,g-' fork, and 55 cm. long with a c" fork (512).] 
 
 Formula. As explained in the text-books, the length of an air 
 column giving maximum resonance, in a tube closed at one end, 
 is \ of the wave length of the sound for first resonance, and f of 
 the wave length for second resonance. The vibrating air column, 
 however, extends beyond the open end of the tube a distance 
 approximately equal to .3 of the inside diameter of the tube. Let 
 L denote the wave length, ^ the length of the tube for first reso- 
 nance, and / 2 for second resonance, and d its inside diameter; 
 then the algebraic statement of these relations is ^-f .$d=\L, 
 and / 2 + .3 d= f L ; from which 
 
 L = 4 (/! 4- .3 </), for first resonance, 
 L = 2 (/ 2 / T ), for second resonance. 
 
 It should be noted that the formula for second resonance does 
 
134 
 
 SOUND 
 
 not involve the "correction for the diameter," the increase of 
 length for second resonance being exactly half a wave length. 
 
 Method. The vibrating fork is held within 
 i or 2 cm. of the end of the tube, with the 
 plane of the prongs either parallel or perpen- 
 dicular to the axis of the tube. There will be 
 almost no response from the tube unless the 
 length of the air column is nearly that neces- 
 sary for maximum resonance, the length of the 
 column being determined by the position of 
 the piston (which is of water with the apparatus 
 shown in Figures 57 and 58). As the piston 
 nears the correct position, the sound rapidly 
 becomes louder. When this position is ap- 
 proximately located, the piston should be 
 moved quickly but steadily (not with sudden 
 jerks) back and' forth past it several times, 
 through a gradually diminishing distance, the 
 experimenter being guided by the regular 
 swelling and dying away of the sound. Mean- 
 while the rubber band, which is used to mark 
 
 FIG. 57. 
 
 the correct position, is gradually shifted 
 into place. The adjustment is difficult 
 and requires care. 
 
 In using the apparatus shown in Figure 
 5 7, water is poured in till it stands within 
 25 or 30 cm. of the top of the tube when 
 the funnel is about half full. The height of 
 the water in the tube is adjusted by raising 
 and lowering the funnel, which is undamped 
 and held in the hand. With the apparatus 
 shown in Figure 58, the length of the air 
 column is adjusted by raising and lowering 
 the tube in the jar of water. 
 
 ;. 58. 
 
WAVE LENGTH BY RESONANCE 135 
 
 Experimental Work. Two pupils will work together, one man- 
 aging the fork and the other the piston. The vibrating fork must 
 not be permitted to touch the tube, as the tube may be broken. 
 Find the length of the tube for first resonance. Make a second 
 trial, after moving the rubber band and piston out of position. If 
 the two results do not differ by more than 3 mm., take their aver- 
 age as the value of 4 If the difference is more than this, repeat. 
 
 Find the length of the tube for second resonance, making two 
 or more trials as before, and call their average / 2 . (If the appa- 
 ratus of Figure 5 7 is used, it may be necessary to pour out part of 
 the water. With the apparatus of Figure 58, the tube is too short 
 for second resonance ; in which case determine the length for first 
 resonance with a fork of different pitch.) 
 
 Measure the inside diameter of the tube d\ record the vibra- 
 tion number of the fork n, and the temperature of the laboratory /. 
 
 Data and Computations. Record as follows : 
 
 Length of tube for first resonance = cm. 
 
 Ditto, second trial = cm. 
 
 Ditto, average value, J L = cm. 
 
 Length of tube for second resonance = cm. 
 
 Ditto, second trial = cm. 
 
 Ditto, average value, / 2 = cm. 
 
 Diameter of the tube (inside) d = cm. 
 Vibration number of the fork n = 
 
 Temperature of the room / = C. 
 
 Length of wave L = 4(4 -f .3 (?) = cm. 
 
 Length of wave L = 2(/ 2 /j) = cm. 
 
 Discussion. i . From the known vibration number of the fork 
 and the value of L given by the experiment, compute the velocity 
 of sound in air at the temperature of the room. 
 
 2. Compute the true value of the velocity at the temperature 
 of the room, by adding to the velocity at o (332 m. per second) 
 .6 m. for each degree above o. 
 
 3. Compute the percentage of error of your result. 
 
IX. LIGHT 
 
 EXERCISE 43. SHADOWS; PIN-HOLE IMAGES; 
 LAW OF INTENSITY 
 
 References. Adams, 258-262, 304; Coleman, 332, 334, 337- 
 338; Car. & C., 231-236; Ches. G. & T., 274-278, 280-281; 
 Hoad. Br., 443-445, 447-448 ; Hoad. EL, 489-491, 493 ; Mum- 
 per, 190, 192, 194; Mil. & G., 500-502 ; Went. & H., 362-364, 
 366. 
 
 Apparatus. A flat gas jet, or lamp with flat wick ; meter rod 
 attached to a board (Fig. 59), or rod alone ; three screens, referred 
 to in tHe directions as A, B, and C, A is 5 cm. square and 
 
 FIG. 59. 
 
 mounted on a wire (Fig. 59), B and C are about 18 or 20 cm. 
 square, B having a broken horizontal row of small holes (Fig. 59), 
 and C a small hole in the center ; short metric rule. 
 
 A gas burner on a low support should be provided for this and 
 other exercises in light. The low form of Bunsen burner can be 
 adapted to the purpose ; but a tip mounted on a block, such as is 
 used for the screens and lenses, is preferable. It will be most con- 
 
 136 
 
SHADOWS; PIN-HOLE IMAGES; LAW OF INTENSITY 137 
 
 venient to have the screens, lenses, spherical mirrors, photometer, 
 gas jet, and candles for the experiments in light mounted at the 
 center of blocks of uniform size, in which a groove is cut so that 
 they fit loosely on a meter rod, placed on edge. The rod thus 
 serves as a guide to keep the parts of the apparatus in alignment, 
 and the distances between them will be the distances between 
 the corresponding ends (right or left) of the blocks upon which 
 they are mounted. A board 100 cm. long and 8 or 10 cm. wide, 
 with the meter rod fastened to it, makes a better support for the 
 apparatus (Fig. 59). 
 
 Experiment ST. To study the formation of shadows. 
 
 Experimental Work. a. The room must be darkened for this 
 exercise. Place the gas jet at an end of the meter rod, and place 
 the screens A and B on the rod about 30 cm. and 80 cm. respec- 
 tively from the same end, so that the shadow of the smaller screen 
 falls on the larger. Turn the flame flatwise (parallel) to the screens, 
 and adjust its height so that the darker part of the shadow (the 
 umbra) covers all of the lower holes on B, but none of the higher 
 holes on either side ; some, if not all, of the latter will then lie in 
 the lighter part of the shadow (the penumbra), which borders the 
 umbra. Now look toward the flame through each of the holes in 
 succession, and observe what portion of the flame, if any, is 
 visible from these different positions. State the connection between 
 what you observe through each hole and the character of the 
 shadow at that place. Draw a diagram of a horizontal section of 
 the flame, screens, and parts of the shadow illustrating your 
 explanation. 
 
 b. Turn the flame edgewise (perpendicular) to the screens, and 
 note the change in the appearance of the shadow on B. Account 
 for this change, and draw a section diagram to illustrate. 
 
 c. Remove A, and in its place hold a lead pencil vertically. 
 Observe the shadow of the pencil on B, with the flame turned 
 edgewise, then flatwise. With the flame flatwise, observe the vary- 
 ing width of the umbra and penumbra as the screen is moved up 
 
138 LIGHT 
 
 to the pencil. Describe the observed changes in the appearance 
 of the shadow, and draw diagrams to illustrate. (Remember that 
 what we commonly call a shadow is only a cross section of it. A 
 shadow is really the space from which the light is wholly or partly 
 excluded by an opaque body.) 
 
 Experiment 82. To study the formation of images by small 
 openings. 
 
 Experimental Work. a. Place the gas jet, turned flatwise, 
 a short distance from the screen C (the one with the single hole at 
 its center), and place the screen B close behind C. The light 
 from the jet that passes through the hole in C forms an image of 
 the jet on B. Move B toward and from C, and observe the effect 
 on the size and brightness of the image. Account for the inver- 
 sion of the image and its change of size when B is moved, refer- 
 ring to a diagram of a vertical section of the apparatus, the flame, 
 and the image. 
 
 Account for the change in brightness when B is moved away 
 from C. 
 
 b. Replace C with a sheet of paper in which you have made a 
 small hole with the point of your pencil. Hold the paper so that 
 the light through this hole will form an image on J3 9 and note the 
 effect of gradually enlarging the hole till it is 2 cm. or more in 
 diameter. Describe and explain the changes in the image as the 
 hole is made larger. 
 
 Experiment 83. To find how the intensity of light is affected 
 by distance. 
 
 Experimental Work. a. Since this experiment deals with nu- 
 merical relations, measurements must be made accurately. Place 
 the screen B so that it (not its support) is exactly 60 cm. from the 
 center of the gas jet, and place the small screen A exactly midway 
 between them (i.e. 30 cm. from the center of the flame). Turn 
 the flame down so as to get as nearly as possible a point source of 
 light without losing the outline of the shadow of A on B. Meas- 
 
PHOTOMETRY 
 
 ure the dimensions of A and the dimensions of its shadow on B. 
 How do the dimensions of A and of its shadow on B compare ? 
 How do their areas compare ? If A were removed, the light which 
 now illuminates it would fall upon B and would cover the area 
 now occupied by the shadow. How would the intensity of illumi- 
 nation on B then compare with the present illumination on A? 
 Why? Does the relative brightness of A and of the illuminated 
 part of B seem to be in agreement with this conclusion? Both 
 screens are partly illuminated by light from other sources than the 
 gas jet. (How do you know?) Does this other light make the 
 illumination of the screens more or less nearly equal than would 
 be the case if the gas jet were the only source? 
 
 b. Repeat the experiment with A 30 cm. and B 90 cm. from 
 the flame. Answer all the questions, changing them, where neces- 
 sary, to agree with the present distances. 
 
 State the general relation between intensity of illumination and 
 distance from the source. 
 
 EXERCISE 44. PHOTOMETRY 
 
 References. Adams, 261-264 ; Coleman, 338-340 ; Car. & C., 
 235-238; Ches. G. T., 281-282 ; Hoad. Br., 447-449; Hoad. 
 1,494-496; Mumper, 192-193; Mil. & G., 502-505; Went. 
 & H., 366-367. 
 
 Apparatus. A Rumford's or Bunsen's photometer (Figs. 60 
 and 61) ; i large candle and 5 small ones; 3 blocks for support- 
 ing candles ; flat gas jet or lamp ; meter rod. 
 
 [A Rumford's photometer, consisting of a screen of \vhite card- 
 board and a rod, each supported vertically, is the most satisfactory 
 form of photometer for elementary laboratory work, as it is least 
 affected by the diffused light in an imperfectly darkened room or 
 a room in which more than one piece of apparatus is in use. 
 The box form of the Bunsen photometer is effective, but bulky 
 and rather troublesome to manipulate. The author is of the 
 opinion that laboratory work in photometry is hardly worth the 
 
140 
 
 LIGHT 
 
 trouble. If a laboratory is not already equipped with satisfactory 
 apparatus or a separate dark room for this work, he would recom- 
 mend that such work be omitted, and that the principles of 
 photometry be illustrated in the classroom only.] 
 
 Method. We can make no reliable estimate of the relative 
 brightness of unequally illuminated surfaces, but are able to judge 
 with considerable accuracy whether two adjacent surfaces, seen at 
 the same time, are equally illuminated ; hence, with all forms of 
 photometers, the distances of the lights compared are adjusted so 
 as to give equal illumination. 
 
 Rumford's Photometer. Figure 60 shows the adjustment of 
 this apparatus in comparing the illuminating powers of a candle 
 
 FIG. 60. 
 
 and a gas jet. The rod casts two shadows on the screen, one 
 being due to the exclusion of the candle light, the other to the 
 exclusion of the gas light. Each source of light illuminates the 
 shadow due to the other; hence, when their relative distances 
 from the screen are such that the shadows are equally dark (i.e. 
 equally illuminated), we know that the lights give equal intensity 
 of illumination at these distances ; and, knowing the law, we can 
 compute their relative illuminating powers from these measured 
 distances. Conversely, if we know the relative illuminating powers 
 of the two lights, the experiment demonstrates the law. (This is 
 the problem of Experiment 84.) The room must be quite dark, 
 or other sources of light will make the shadows too faint for 
 comparison. 
 
PHOTOMETRY 
 
 141 
 
 Bunsen's Photometer. The box form of this photometer is 
 shown in Figure 61. The box serves the purpose of shutting out 
 diffused light from other sources. The essential part of the photom- 
 eter is a vertical screen of white paper, having a translucent spot 
 made by applying a drop of hot paraffine. If the two sides of the 
 paper are unequally illuminated, the spot will appear darker than 
 the rest of the paper when viewed from the more strongly illumi- 
 nated side, and lighter when viewed from the less strongly illu- 
 minated side. The spot appears darker in the first case because 
 it reflects less light to the eye than the rest of the paper does ; in 
 
 FIG. 61. 
 
 the second case it appears bright on account of the light it trans- 
 mits from the other side. When both sides are equally illuminated, 
 the spot nearly disappears and looks exactly alike on both sides. 
 The adjustment of the photometer consists in moving the screen 
 from side to side along the line between the two lights that are 
 being compared, until the position is found where the spot has 
 the same appearance from both sides. We know then that the 
 two lights give equal illumination at their respective distances. 
 The adjustment of the screen is much more accurately made with 
 the aid of two small mirrors, so placed that the two sides of the 
 spot can be seen in them at the same time. 
 
 Experiment 84. To find the relation between the illuminating 
 pouters of two lights and the distances at which they give equal 
 illumination. 
 
 Experimental Work. Mount a small candle at the center of 
 one block- and four small candles in a line on another. With the 
 Rumford photometer, place the single candle at a distance of 
 
142 
 
 LIGHT 
 
 about 40 cm. from the screen, and the four candles at such a 
 distance that the two shadows are equally dark. The rod that 
 casts the shadow should be within a few centimeters of the screen, 
 and the lights so placed that the shadows are separated only by 
 a narrow line. The line of four candles should be parallel to the 
 screen. In making the adjustment, move one of the lights toward 
 the screen till one of the shadows is lighter than the other, then 
 move it away till the same shadow is darker than the other. 
 Repeat several times, gradually diminishing the distance covered 
 in the to-and-fro motion, and finally estimate the correct position 
 as closely as possible. With the Bunsen photometer, place the 
 lights at the ends of the meter rod, and move the screen to one 
 side till that side of the spot is darker than the other, then back 
 again till the other side is darker ; and repeat through a gradually 
 diminishing distance till you have found the position where the 
 two sides of the spot look just alike. 
 
 Care must be taken to see that the five candles are burning 
 as nearly equally as possible ; for the light from any one of them 
 may vary, if left to itself, 50 / or more in the course of a few 
 minutes, and the experiment is based upon the assumption that 
 the four candles give four times as much light as the single candle. 
 Use scissors to trim the wicks before adjusting the distances, if 
 the candles are burning unequally. 
 
 When the adjustment for equal illumination has been made, 
 measure the distances of the lights from the screen. Make and 
 record two or three trials, leaving the position of one of the lights 
 unchanged with the Rumford photometer, and the position of both 
 lights unchanged with the Bunsen. 
 
 Data and Computations. Let P l denote the illuminating power 
 of the single candle and D l its average distance from the screen ; 
 /2 the illuminating power of the group of four candles and D z its 
 average distance. It is assumed that P 2 = 4 P\- This assumption 
 may, however, be in error by as much as 10 or 15 %, even with 
 careful attention to the candles. Record as follows : 
 
PLANE MIRRORS jj* 
 
 Distance of single candle s- cmt 
 
 Ditto, second trial cm> 
 
 Ditto, average, D l cm> 
 
 Distance of group of four candles = cm . 
 
 Ditto, second trial = cm< 
 
 Ditto, average, Z> 2 = cm. 
 
 Ratio of illuminating powers of the lights P l -f- P 2 = .25 
 
 Ratio of distances of the lights D -:- D 2 = 
 
 Ratio of the squares of the distances D? -~ D/ = 
 
 Percentage of difference between P l -+- P 2 and D l -~ Z> 2 = cf 
 
 Percentage of difference between P 1 -f- P 2 and D* -r- D = cj 
 
 Is the difference between either of these pairs of ratios within a 
 reasonable limit of experimental error (say 15 %)? If so, what is 
 the answer suggested to the question stated as the object of the 
 experiment? 
 
 Experiment 85. To measure the candle power of a small 
 candle and a gas jet or a lamp. 
 
 Experimental Work. a. Use the photometer to find the ratio 
 of the illuminating power of a small candle to the large one, i.e. 
 taking the large candle as the standard, find the candle power of 
 the small candle. 
 
 b. Find the candle power of the gas jet or the lamp (which- 
 ever is provided), when turned to a moderate height, by compar- 
 ing it with the large candle. Have the flame turned flatwise 
 toward the screen. 
 
 EXERCISE 45. PLANE MIRRORS 
 
 References. Adams, 265-266, 304-307; Coleman, 342-348; 
 Car. & C., 239-245 ; Ches. G. & T., 283-290; Hoad. Br., 450- 
 455 > Hoad. EL, 497-503; Mumper, 195-197; Mil. & G., 506- 
 508, 528-530; Went. & H., 369-371. 
 
 Apparatus. A small, rectangular plane mirror, with support 
 (if mounted with a free space of about 5 mm. under it, as shown 
 
144 
 
 LIGHT 
 
 FIG. 62. 
 
 in Figure 62, it will serve for both experiments following) ; metric 
 rule ; protractor ; pins. 
 
 [In using common mirrors for the study of images, an error is 
 involved, due to two refractions of the light at the front surface. 
 
 These refractions diminish the dis- 
 tance of the image by about two 
 thirds the thickness of the mirror. 
 Hence thin mirrors are to be pre- 
 ferred. The error is reduced one 
 half, if, in locating the image by 
 the method of Experiment 87, the 
 pin that is made to coincide with 
 the image is viewed through an unsilvered portion of the glass. 
 The error will be entirely avoided if the front surface of a piece of 
 plate or window glass is used as the reflecting surface. The image 
 thus obtained will be quite distinct if the glass is backed with black 
 paper or cloth. Since both surfaces reflect, two images will be 
 seen. The rear image will disappear and the other will be more 
 distinct if the back of the glass is painted black.] 
 
 Experiment 86. To find the position of a point image in a 
 plane mirror by sight lines ; and to find the relation between the 
 position of the point and its image, and the relation between the 
 angles of incidence and reflection. 
 
 Method. A sheet of paper is 
 
 laid on the table, and the mirror 
 placed on it in a vertical position 
 marked by the line AB (Fig. 63). 
 A pin is stuck in a vertical position 
 at O in front of the mirror, and the 
 point where it pierces the paper is 
 taken as the object whose image in 
 the mirror is to be located. If this image has a fixed position 
 behind the mirror, all lines drawn on the paper in front of the 
 mirror and extending in the direction of the image will intersect 
 
 FIG. 63. 
 
PLANE MIRRORS 
 
 145 
 
 at the position of the image when produced; and this position 
 will be determined by the intersection of any two such lines. 
 Lines thus drawn are called sight lines, i.e. lines along which the 
 observer sights toward the image. A sight line is determined by 
 means of two pins, placed vertically several centimeters apart 
 (as at C and D in the figure) and exactly in line with the image 
 of O, the pin at C being placed first, at any point near the mirror 
 and on either side of O. A line is then carefully drawn with a 
 rule and a sharp pencil through the points C and Z>, and pro- 
 duced after the mirror is removed. 
 
 Experimental Work. Draw a line AB about 10 cm. long on a 
 large sheet of paper, leaving a space of not less than 8 cm. on 
 each side of it. Stand the mirror so that the plane of its reflect- 
 ing surface passes exactly through this line. In doing this, look 
 vertically down along the reflecting surface. (The reflecting sur- 
 face of a common mirror is, of course, the rear surface. If unsil- 
 vered glass is used, either with or without the back painted black, 
 its front surface is the reflecting surface. If the back surface is 
 not painted or ground, it, too, will cause an image, slightly 
 farther back than the first ; but this image is to be disregarded.) 
 Stick a pin vertically 3 or 4 cm. in front of the mirror, and mark 
 the point where it pierces the paper O. This point is the object 
 whose image is to be located. 
 
 Draw four sight lines directed accurately toward the image, and 
 determined in the manner described above, two of them lying on 
 each side of O. In sighting, place the eyes on a level with the 
 paper, close one of them, and have the pins parallel. The sight 
 lines should all make wide angles with each other ; since, if any 
 two are nearly parallel, a slight error in the direction of either 
 will make a relatively large error in their point of intersection. If 
 necessary in order to get wide angles, the mirror may be shifted 
 parallel to itself along the line AB. 
 
 Remove the mirror and produce the sight lines on the other 
 side of AB. If the image has the same position when viewed 
 COLEMAN'S NEW MANUAL 10 
 
146 LIGHT 
 
 from different directions, the sight lines, if accurately determined, 
 will all intersect at the same point. Repeat the experiment if the 
 points of intersection do not coincide within 2 mm. With care- 
 ful work they should coincide within i mm. 
 
 Mark the point of intersection of the sight lines /. Draw the 
 line OI. Measure with the protractor, and record in the figure, 
 one of the angles formed by AB and OI. What should this angle 
 be? Measure the segments of OI formed by its intersection with 
 AB, and record in the figure. How should these segments 
 compare ? 
 
 It is evident that, when you were looking along any one of the 
 sight lines, the light by which you saw the image came to the eye 
 along that line, having been reflected by the mirror at the point 
 where the sight line meets AB. Mark this point N. Draw the 
 line ON, representing the incident ray; and draw the perpen- 
 dicular to AB at N (using the protractor). Measure with the 
 protractor, and record in the figure the angles of incidence and 
 reflection. Repeat this construction and measurement for one 
 other sight line. How nearly do the constructed angles of inci- 
 dence and reflection agree with the law? With careful work the 
 error will be less than i. 
 
 The sheet on which this work is done may be pasted in your 
 record book, or an accurate copy of the figure made by placing 
 the sheet on the one to which the figure is to be transferred, and 
 pricking two pin points through to mark the position of each 
 line. 
 
 Experiment 87. To find the position of a point image in a 
 plane mirror by direct observation. 
 
 Preliminary Study (to precede the laboratory hour). Hold a 
 pencil at arm's length, pointing upward, in one hand, and a sec- 
 ond pencil at about two thirds that distance, pointing downward, 
 in the other hand. Bring the points of the pencils into line with 
 one eye, the other eye being closed. The points will seem to 
 touch, although they are really 15 cm. or more apart. Without 
 
PLANE MIRRORS 
 
 147 
 
 moving either pencil, look at them with the other eye, closing the 
 first, and note the change in the apparent positions of the pen- 
 cils. Repeat, closing first one eye, then the other, with the pen- 
 cils in line with each eye in turn, until you are familiar with the 
 effects, and have discovered the reason for the apparent shifting 
 of the pencils when you change the eye with which you look. 
 Now look with both eyes, first at the nearer pencil, then at the 
 farther one, and note that when you are looking at either pencil, 
 the other appears double ; note also that while looking with both 
 eyes, there is no misjudgment of distances. Look again with 
 each eye in turn, as you gradually move either pencil toward the 
 other ; and note that the apparent shifting of the pencils from side 
 to side becomes less, and ceases only when the points are actually 
 in contact. 
 
 Familiarity with these phenomena of vision will be of great 
 assistance in the following experiment, and in several later ones as 
 well, where the work has to do with the actual position of images. 
 The apparent displacement of an object, due to a change in the 
 position from which it is viewed, is called parallax. 
 
 Experimental Work. Draw a line AB across the middle of a 
 large sheet of paper, and stand the mirror with its reflecting sur- 
 face vertically over it. Stick a pin in a vertical position at a dis- 
 tance of several centimeters in front of the mirror. With the eyes 
 just above the level of the table, look under the mirror at a second 
 pin, held vertically in the fingers behind the mirror ; and place 
 this pin where it appears to coincide with the image of the pin in 
 front. In doing this, look with both eyes, and move the head into 
 various positions. When the pin is correctly placed, it will accu- 
 rately fit the image from all points of view. 
 
 When the image is correctly located, draw a line connecting it 
 with the object. Measure and record the segments into which 
 this line is divided by AB, and the angle between the lines. If 
 time remains, see if you can get more accurate results by further 
 trials, placing the object in a different position each time, 
 
148 LIGHT 
 
 EXERCISE 46. MULTIPLE IMAGES 
 (INVENTIVE) 
 
 References. Adams, 308-309 ; Coleman, 349 ; Car. & C., 
 246-247; Hoad. Br., 456-458; Hoad. EL, 504-506; Mil. & G., 
 532 ; Went. & H., 373. 
 
 Experiment 88. To study the formation of images by multiple 
 reflection from two plane mirrors. 
 
 Apparatus. Two plane mirrors, each with a support to hold it 
 in a vertical position ; rule ; candle, mounted ; some small object 
 having right side distinguishable from left and front from back ; etc. 
 
 Suggestions. In performing this experiment it is necessary to 
 bear in mind that the reflected light travels from the direction of 
 
 the image, just as if the 
 image were the real source. 
 The principal points that 
 come within the scope of 
 the experiment are as fol- 
 lows : 
 
 i. With the mirrors at a 
 given angle, to note the 
 number of images formed 
 and their exact location with 
 respect to the object, the 
 FIG. 64. mirrors, and the images of 
 
 the mirrors. 
 
 2. To determine the number of reflections by which each 
 image is formed, and the order in which these reflections occur 
 (/>. from which mirror first). 
 
 3. To account for the number and position of the images, 
 from the known reflections of the light and the law of reflection. 
 
 4. To observe which of the images have their right and left 
 sides reversed and which have not, and to determine why. 
 
THE CONCAVE MIRROR 
 
 5. To determine the path of a ray of light from the object to 
 the eye, in viewing any one of the images from a given position. 
 
 6. To construct dia- 
 grams illustrating the an- I L N 
 
 swers to these questions. 7, x " 
 
 Make a study of these l Q ^>, x X s 
 questions and of others that 
 may occur to you, devising 
 methods of procedure for 
 yourself. The mirrors may | f 
 be at any angle, an angle 
 of 90 being the simplest 
 case. The case of parallel i 
 mirrors should be included. ~v 
 
 -ni r- 9f' FlG. 6s. 
 
 Ihe accompanying figures 
 
 will afford suggestions as to the character of the diagrams. If a 
 
 kaleidoscope is provided, investigate its construction and action. 
 
 EXERCISE 47. THE CONCAVE MIRROR 
 
 References. Adams 310-316; Coleman, 350-355 ; Car. &C., 
 249-255; Ches. G. & T., 295-298; 302-305; Hoad. Br., 460- 
 466 ; Hoad. EL, 507-512 ; Mumper, 198; Mil. and G., 538-545 ; 
 Went. & H., 374-376, 379- 
 
 Experiment 89. To find the focal length and radius of curva- 
 ture of a concave mirror, and to study the formation of real and 
 virtual images by it. 
 
 Apparatus. Concave mirror ; meter rod ; mounted candle ; 
 cardboard screen. 
 
 [A silvered mirror of glass having a diameter of 10 or n cm. 
 is adapted to this experiment. These can be obtained in a 
 wooden frame with a handle, and also in a light metal frame, 
 which is preferable. It will be found convenient to have them 
 mounted on blocks, uniformly with the screens, lenses, etc., as 
 suggested under Exercise 43.] 
 
1 50 LIGHT 
 
 Experimental Work. a. Hold the mirror in the sunlight and 
 facing exactly toward the sun, and focus the light on a piece of 
 paper. In doing this, hold the paper a little to one side, so as 
 not to cut off the light from the mirror ; turn the mirror so that 
 the reflected light falls upon the paper and move the paper toward 
 or from the mirror into the position where the spot of light is the 
 smallest. The spot is an image of the sun, and if the adjustment 
 is right, it will be round. 
 
 b. Stand the mirror on the table near a window, and turn it 
 facing toward some distant object, as a house or a tree, at least 
 200 ft. away. Stand the cardboard screen on the table in front 
 of the mirror and a little to one side of the direct line between 
 the minor and the object (in order not to intercept the light), and 
 adjust its distance from the mirror till the image of the distant 
 object is sharply denned upon it. If the weather is not too cold, 
 raise the window in making this adjustment, for the light is dis- 
 torted by the wavy surfaces of common window glass, and this 
 makes perfect focusing impossible. Measure the distance from 
 the image to the mirror. This is the focal length f of the mirror 
 (the rays from any point of the object being sensibly parallel). 
 
 c. Move the screen a little to one side, leaving it in the plane 
 of the image and near it so as to mark its position. Place the 
 head very nearly in line between the mirror and the object, at a 
 distance of about a meter from the mirror, and look toward the 
 mirror at the place in the air beside the screen, where the image is. 
 If this is correctly done, the image will be very distinctly seen in 
 its real position in front of the mirror. It is difficult for the be- 
 ginner to avoid looking beyond the image into the mirror ; in 
 which case the image will appear to be in the mirror and will be 
 blurred, just as the finger appears blurred and double when you 
 hold it before you and look at something beyond it. If you are 
 unsuccessful after a brief trial, pass this for the present, and try 
 again after finishing the exercise. 
 
 d. The remainder of the exercise requires a darkened room. 
 Place the lighted candle at one end of the meter stick, and stand 
 
THE CONCAVE MIRROR 151 
 
 the mirror at the other end. Place the eyes on a level with the 
 candle, and look past it toward the mirror. A number of real and 
 inverted images of the candle will be seen in line between it and 
 the mirror. The one that is the largest, the farthest from the 
 mirror, and the brightest is the one that is formed by a single 
 reflection at the concave silvered surface, and is the one to be 
 studied. The others are due to multiple reflections within the 
 mirror. Turn or tip the mirror a little, if necessary, to bring the 
 images into line with the candle, and be careful to find the princi- 
 pal one. Ignore the others. Move the candle along the meter 
 rod till the tip of the flame coincides with the tip of the image, 
 turning or tilting the mirror, if necessary. Object (the tip of the 
 flame) and image are now at the center of curvature of the mirror. 
 (Why?) Measure their distance from the mirror. This is the 
 radius of curvature r. Compare r/2 wiihf, found in paragraph b. 
 
 e. Starting with the candle at the center of curvature, carry it 
 slowly across the room as far as you can from the mirror, while 
 your companion, standing near the mirror, observes the simul- 
 taneous change of size and position of the image. Measure the 
 distance of the image from the mirror when the object is farthest 
 away, focusing the image on the screen for the purpose, if found 
 more convenient. Compare this distance with /. What would 
 be the final position of the image if the object were carried farther 
 away indefinitely? 
 
 / Again starting with the candle near the center of curvature, 
 move it slowly toward the principal focus, meanwhile keeping 
 watch of the changing size and position of the image by focusing 
 it on the screen. Continue till the image is focused upon a 
 distant wall of the room, or as far away as it can be seen. With 
 this adjustment, measure the distance of the candle from the 
 mirror, and compare with the distance of the image when the 
 candle was at its greatest distance. If the candle were moved up 
 to the principal focus, where would the image be ? 
 
 g. Move the candle from the principal focus toward the mirror, 
 while observing the change in the size and position of the image, 
 
152 LIGHT 
 
 which is now virtual, erect, and behind the mirror. (A faint vir- 
 tual image of constant size will also be seen. This is due to par- 
 tial reflection from the front surface of the mirror, which is plane.) 
 Estimate the relative distances of image and object from the 
 mirror. 
 
 Discussion. From a study of the text you will learn how the 
 facts observed in this exercise result from the law of reflection 
 and the curvature of the reflecting surface. The text also dis- 
 cusses the construction of explanatory diagrams. From a study 
 of the text and the results of the experiment, find the answers to 
 the following questions : 
 
 1. What happens, after reflection, to the diverging cone of light 
 that falls upon the mirror from any one point of the object (a) 
 when the distance of the object is greater than the focal length ; 
 (b) less than the focal length ; (c) equal to the focal length? 
 
 2. What behavior of the reflected light gives rise to (a) a real 
 image ; (b) a virtual image ? (Remember that a focus is a point, 
 and that images have size. Be definite in your answer.) 
 
 3. Under what conditions is (a) a real image formed; (b) a 
 virtual image? 
 
 4. With rule and compass draw accurate figures showing the 
 size and position of the image formed by a concave mirror 
 
 When the object is large and at a relatively great distance (illus- 
 trating paragraph b of the experiment). 
 
 When the object is a point at the center of curvature (illus- 
 trating paragraph d\ 
 
 When the object is beyond the center of curvature, but not at a 
 great distance (illustrating paragraph e). 
 
 When the object is between the principal focus and the center 
 of curvature (illustrating paragraph/). 
 
 When the object is only slightly nearer the mirror than the 
 principal focus (illustrating paragraph ). 
 
 When the distance of the object from the mirror is about \ the 
 focal length (illustrating paragraph^). 
 
PHENOMENA DUE TO REFRACTION 153 
 
 Use the same radius of curvature in all the above figures, and 
 in all but the first two represent the object by an arrow of the 
 same length. The object cannot be represented in the first dia- 
 gram, being too far away and too large to be represented to 
 scale. 
 
 EXPERIMENT 48. PHENOMENA DUE TO REFRACTION 
 
 References. Adams, 267-268; Coleman, 358-359; Car. & 
 C., 256-257; Ches. G.&T., 310-311 ; Hoad. Br., 467-470, 474 ; 
 Hoad. EL, 515-518, 522; Mumper, 200; Mil. & G., 510; Went. 
 & H., 381-382. 
 
 Experiment 90. To study the refraction of light in passing from 
 glass into air, and the apparent displacement of objects resulting 
 from such refraction. 
 
 Apparatus. A rectangular piece of thick plate glass, ground 
 and polished on two opposite ends; glass prism with flat ends 
 and wide faces ; rule ; pins. 
 
 Experimental Work. a. Stand the prism on end on this page, 
 and look at the printing through it. Note the apparent elevation 
 of the part of the page seen through the prism. Estimate the 
 ratio of the real length of the prism to its 
 apparent length, as you look through it. Lay 
 the piece of plate glass on the page, and 
 observe whether there is a similar apparent 
 elevation of the part seen through it. Stand 
 the plate on one of its polished ends and 
 look down through the width of the glass at 
 the printing. Result? 
 
 b. Lay a sheet of paper on the table, and 
 
 lay the glass plate on it near the farther end FlG 66 
 
 (Fig. 66), with its polished ends at front and 
 rear. Stick pins vertically at A, B, and C, close to the glass 
 A at the middle of the farther end, B and C about 2 cm. apart 
 
154 LIGHT 
 
 at the front end. Place the eyes just above the level of the table, 
 close one of them, and move the other into line with B and the 
 apparent position of A, seen through the glass. Place another pin 
 exactly in this line, 5 or 6 cm. toward the eye from B ; and mark 
 its position D. The line DB indicates the direction in which A 
 is seen through the glass, when the eye is in its present position. 
 Obviously, the light by which A is seen from this position emerges 
 from the glass at B (since B appears to be in line with A), and 
 traverses the path BD to the eye. Its path through the glass is 
 along the straight line AB. Since A, B, and D are not in a 
 straight line, it follows that the light undergoes a change of direc- 
 tion (refraction) at B. It is important to note that A is seen in 
 the direction from which the light is traveling as it enters the eye, 
 a general truth that has become familiar in the study of images 
 formed by reflection. In fact, what is seen through the glass is an 
 image of A formed by refraction. 
 
 In the same way place a pin (at E in the figure) in line with 
 C and the apparent position of A. 
 
 Draw the outline of the glass plate pn the paper ; remove the 
 plate; draw the lines DB and EC, and produce them as dotted 
 lines to their point of intersection; letter this -point A 1 ; draw 
 the lines AB and AC '; and place arrowheads on the parts of 
 the broken lines ADB and ACE. These broken lines with the 
 arrowheads represent actual paths of light from A through the 
 glass and into the air; the dotted lines AB and A'C indicate 
 apparent paths of light from the image A'. 
 
 Is the refraction to the right or the left at Bt Does this cause 
 A to appear to the right or the left of its true direction ? Answer 
 the same questions for the refraction at C. 
 
 c. Replace the glass plate in its former position, and find the 
 apparent direction and position of A when viewed through the 
 glass along the line perpendicular to the front surface. Is its 
 apparent position the same as when viewed along the lines DB 
 and C? (Answer from direct observation with one eye and 
 also with both.) Does it appear to be to the right, to the left, or 
 
PHENOMENA DUE TO REFRACTION 
 
 155 
 
 in its real direction? What does this indicate concerning the 
 refraction (bending) of the ray that is perpendicular to the surface 
 of the glass? 
 
 d. Move the head to one side so as to view A more obliquely 
 through the glass than DB or EC, and note the change in its 
 apparent position, using both eyes for the observation and without 
 placing pins. State the result. 
 
 Copy the figure accurately or paste the sheet in your record 
 book. 
 
 Experiment 91. To study the apparent displacement of objects 
 under water, due to refraction at. the surface. 
 
 Apparatus. Glass jar, preferably rectangular; bit of tin or 
 other small object that sinks in water ; large jar of water ; beaker ; 
 rule ; mop cloth. 
 
 Experimental Work. a. Pour water, a little at a time, into 
 the smaller jar, while looking down at the bottom of the jar 
 through the water ; and observe the apparent eleva- 
 tion of the bottom above the level of the table top. 
 How does the apparent elevation of the bottom 
 change as the depth of the water increases? 
 Estimate the ratio of the real depth of the water 
 to its apparent depth as you look vertically down 
 through it. Does this ratio appear to change or 
 to remain constant as you increase the depth of 
 the water? Figure 67 represents a pencil of light 
 from a point of the bottom. Copy and complete 
 the figure so as to explain the apparent elevation 
 of the bottom. Represent the apparent path of 
 light by a dotted line. 
 
 b. Fill the jar nearly full of water. With the rule held exactly 
 vertical, gradually lower an end of it into the water, observing any 
 change in the apparent length of the immersed portion, when 
 viewed through the surface of the water. Repeat the observation, 
 
 FIG. 67. 
 
156 
 
 LIGHT 
 
 raising and lowering the rule several times. Does the immersed 
 portion appear to be in its real direction (vertical) or does it 
 appear to be oblique? Does the appearance of the immersed 
 portion indicate an apparent oblique or 
 vertical displacement of any point from its 
 real position? Copy and complete Figure 68 
 so as to explain the apparent displacement 
 of the immersed end of the rule. 
 
 c. Observe any change in the appearance 
 of the immersed portion of the rule, held 
 in a fixed vertical position, as you view it 
 more and more obliquely through the sur- 
 face of the water, gradually lowering the 
 head till the eyes are nearly on a level 
 with the surface. Draw a figure represent- 
 
 FIG. 68. 
 
 ing and explaining the appearance, 
 when the line of sight is very 
 oblique. 
 
 d. Hold the rule or a pencil 
 oblique and partly immersed in 
 water, and note the apparent length 
 and direction of the immersed por- 
 tion as seen through the surface. 
 Copy Figure 69 and complete it, 
 showing the apparent position of 
 the immersed part of the pencil. 
 
 Pupils often confuse the actual 
 direction of bending of the light 
 with the apparent direction of bend- 
 ing of the object. Referring to your completed copy of Figure 
 69, show the relation between these directions. 
 
 e. Drop the piece of tin (or other small object) into the jar of 
 water, and look down at it while disturbing the water with your 
 finder. Describe and explain the effect of the motion of the 
 Surface. 
 
 FIG. 69. 
 
SNELL'S LAW OF REFRACTION 
 
 157 
 
 EXERCISE 49. SNELL'S LAW OF REFRACTION; 
 INDEX OF REFRACTION OF GLASS 
 
 References. Adams, 268-270; Coleman, 360-362; Car. & 
 C, 258-260; Ches. G. & T., 312; Hoad. Br., 468-471 ; Hoad. 
 EL, 515-519; Mumper, 202; Mil. & G., 523-525; Went. & H., 
 381. 
 
 Apparatus Rectangular piece of thick plate glass, ground 
 and polished on two opposite ends, and having scratches perpen- 
 dicularly across the polished ends at A, JB, C, and O (Fig. 70) ; 
 pencil compass ; metric rule ; pins. 
 
 Experiment 92. To study the relation between the directions of 
 the incident and refracted rays for different angles of incidence; 
 and to find the index of refraction of a piece of plate glass. 
 
 CAUTION. In this experiment the numerical values are obtained 
 from a diagram, which must therefore be constructed as accurately 
 as possible. Points are to be located by means of minute dots, 
 lines drawn very thin with a rule and sharp pencil, perpendiculars 
 accurately at 90, and distances measured to tenths of a milli- 
 meter. A pupil who has had practice in 
 mechanical drawing should be able to get 
 results agreeing with the law within i % ', 
 for others an accuracy of 2 % is very good 
 and an error of 3% satisfactory. 
 
 Experimental Work. Have the pencil 
 very sharp, and keep it so. Draw a thin 
 straight line MN (Fig. 70) across the 
 middle of a large sheet of paper, and lay 
 the glass plate on it with one of the 
 polished ends exactly at the line, as shown 
 in the figure. The plate should have 
 scratches perpendicularly across the polished ends at A, B, C, 
 and O. Locate the exact position of these scratches on the paper 
 by minute dots. If there are not scratches on the glass, stick pins 
 
 ABC 
 
 FIG. 70. 
 
LIGHT 
 
 vertically at these points, close to the glass. The glass must be 
 left exactly in this position until pins have been located at D, E, 
 and F, as follows : 
 
 Place the eyes on a level with the table, close one of them, 
 and place a pin near the front edge of the paper exactly in line 
 with the scratch (or pin) at O and the image of the scratch at A. 
 Letter this point D. Similarly, locate a pin at E in line with O 
 and the image of B, and another at F in line with O and the 
 image of C. 
 
 Remove the plate and draw very accurately the broken lines 
 DO A, EOB, and FOC, extending them in both directions to 
 the edge of the paper. To distinguish the different incident 
 and the corresponding refracted rays, place a single arrowhead 
 on DO and on OA y two arrowheads on E O and on OB, and 
 three on FO and on OC. 
 
 Fold a straight edge of a sheet of paper to form an accurate 
 right angle, and use it to erect a perpendicular to MN at O. 
 
 (Do this with the great- 
 est care.) Letter this 
 perpendicular X Y. 
 
 Use the pencil com- 
 pass to describe a circle 
 with O as a center and 
 a radius of 8 cm. or 
 more. From the six 
 points of intersection of 
 this circumference with 
 the lines representing 
 the incident and re- 
 fracted rays, drop per- 
 
 FlG pendiculars to XY, as 
 
 shown in Figure 71. 
 
 Let P l9 P 2 , and P z denote the perpendiculars constructed for the 
 three refracted rays, and /V> ^V> and P 3 ' the perpendiculars for 
 the corresponding incident rays. Measure these perpendiculars, 
 
SNELL'S LAW OF REFRACTION 
 
 159 
 
 estimating carefully the tenths of a millimeter, and record their 
 lengths beside them. 
 
 Paste or copy this figure in your record book. 
 
 Data and Computations. Compute the ratios P^/PJ, RJPJ, 
 and P s /P 3 f to three decimal places, and find the percentage of 
 difference between the greatest and the least of them. According 
 to the law of refraction, they should be equal. 
 
 Any one of these ratios is an experimental value of the index 
 of refraction of the glass plate, and their average is to be taken 
 as the value of this quantity as given by your experiment. Com- 
 pute it. 
 
 Discussion SnelPs Law, as commonly stated, involves the 
 
 use of the term " sine of an angle." In any right triangle the ratio 
 
 of either leg to the hypothenuse 
 
 is called the sine of the angle 
 
 opposite to that leg. Thus in 
 
 Figure 72 the sine of angle A 
 
 is BC/AB or ffC/Aff or 
 
 B"C"/AB" (all of which ratios 
 
 are equal, since the triangles are 
 
 similar), and the sine of angle B 
 
 is AC/AB. The usual form of 
 
 writing this is sine A = BC/AB, and sine B = AC/AB. The 
 
 sine of an angle increases as the angle increases from o to 90, but 
 
 they do not increase proportionally. In other words, while the 
 
 greater of two acute angles always has the greater sine, the angles 
 
 and the sines are not in proportion. 
 
 Let the radius of the circle in Figure 71 be denoted by R ; then 
 the sine of the smallest angle of incidence is P\/R, and the sine 
 of the corresponding angle of refraction is Pi/R. The ratio of 
 the sine of the angle of incidence to the sine of the angle 
 of refraction is therefore P^/R : P\/R, or P\/P^. If we suppose 
 the light to be traveling from air to glass (reversing the arrow- 
 heads in your figure), the angles of incidence and refraction will 
 
 B" 
 
 FIG. 72. 
 
160 LIGHT 
 
 simply be interchanged. We shall then have as the ratio of 
 the sine of the angle of incidence to the sine of the angle 
 of refraction PJP, Py/P*, and P 3 /P 3 ' for the three cases, 
 respectively, and we have learned that these ratios should be 
 equal. In the customary language, we have found that the ratio 
 of the sine of the angle of incidence to the sine of the angle 
 of refraction is constant (within a certain limit of experimental 
 error) for air and the glass plate, for the different angles of 
 incidence. 
 
 It should be noted that the index of refraction of a substance 
 is defined as the ratio of the sine of the angle of incidence to 
 the sine of the angle of refraction for light traveling from a vacuum 
 (or air) into the substance. This is why we have assumed the 
 direction of the light in the above experiment to be reversed. 
 
 Experiment 93. To find whether the ratio of the real width 
 of the piece of plate glass to its apparent width, viewed through it 
 perpendicularly to a polished end, is equal to its index of refraction. 
 
 Experimental Work. Paste a strip of paper B (Fig. 73) on 
 one side of the glass plate used in Experiment 92, so as to over- 
 lie the perpendicular from one of the 
 scratches A. Hold the plate in one 
 hand on a level with the eyes, and look 
 with both eyes at the scratch through the 
 polished end CD, along the line NA 
 perpendicular to CD\ and at the same 
 time look through the air at the sharp 
 point of your pencil, as you place it in 
 apparent coincidence with the scratch. 
 
 In doing this you will find it helpful to move the pencil forward 
 until it is evidently a little nearer than the image of the scratch, 
 then back till it is a little farther than the image, gradually diminish- 
 ing the distance till the exact point is located. Shifting the head 
 very slightly from side to side is sometimes helpful. It should be 
 possible to locate the image of the scratch within .2 or .3 mm. 
 
REFRACTION THROUGH A PLATE AND A PRISM l6l 
 
 Make a dot on the paper marking the position of the image. 
 Measure the distance from this dot to the surface CD. This is 
 the apparent width of the glass. Measure its real width. 
 
 Computation and Conclusion Divide the real width by the 
 
 apparent width ; and compare the quotient with the index of 
 refraction of the glass as found in Experiment 92. 
 
 It can be shown mathematically that the quotient of the real 
 width of a transparent body by its apparent width, when viewed 
 perpendicularly to 'the refracting surface, is the index of refraction 
 of the substance. 
 
 EXERCISE 50. REFRACTION THROUGH A PLATE 
 . AND A PRISM ; TOTAL REFLECTION 
 
 References. Adams, 272-276, 278; Coleman, 365-369; Car. 
 & C., 262-263, 266-268; Ches. G. & T., 315-318; Hoad. Br., 
 472-473, 475-476 ; Hoad. EL, 520-524 ; Mumper, 200-201, 203 ; 
 Mil. & G., 511-515 ; Went - & H -> 383-385- 
 
 Experiment 94. To find the path of a ray of light through a 
 glass plate and through a glass prism ; and to observe the apparent 
 displacement of objects seen through each. 
 
 Apparatus. A rectangular piece of thick plate 
 glass ; a triangular prism with flat ends and wide 
 faces ; rule. 
 
 Experimental Work. a. Draw a straight line 
 AB (Fig. 74) a few centimeters long on a page 
 of your note book ; stand the glass plate on end 
 obliquely to the line, and mark its outline CD on 
 the paper. Lay the rule on the paper in front _ 
 
 of the glass ; and, sighting along its edge with 
 one eye, place the edge in line with AB as seen through the 
 glass. Draw a line on the paper in this position, and letter it EF. 
 Raise the plate so as to view AB under it, and note the actual 
 COLEMAN'S NEW MANUAL n 
 
1 62 LIGHT 
 
 position of AB relative to EF. Note the apparent shifting of AB 
 parallel to itself as the plate is again lowered. Try the effect of 
 gradually turning the plate round to a position at right angles to 
 the lines. Result? 
 
 Continue the lines AB and EF to the lines representing the 
 surfaces of the plate, and draw a straight line (between the parallel 
 lines of CD] joining their extremities. The broken line ABEF 
 now represents the path of a ray of light passing obliquely through 
 the plate. Place an arrowhead on each part of the broken line. 
 Produce FE as a dotted line to represent the apparent position 
 of AB, when viewed through the plate. 
 
 b. Stand the prism on end on a page of your note book, with 
 its rear face at an angle of about 45 with a line AB (Fig. 75); 
 
 and, as with the glass plate, draw a lir^e FG in 
 front of the prism and in line with the apparent 
 position of AB as seen through the prism. 
 Draw the outline of the base of the prism, and 
 complete the construction, showing the path of 
 a ray of light through the prism. Produce GF 
 backward as a dotted line to represent the 
 apparent position of AB. Draw perpendiculars 
 to CD and ED at the points of entrance and 
 emergence of the ray ; letter the two angles of 
 incidence z, the two angles of refraction r, and 
 the angle of total deviation d (the acute angle 
 between AB and FG produced). 
 
 c. Hold the glass plate up before you with your pencil behind 
 it, both vertical, and the plate turned obliquely to the line of sight. 
 Compare the apparent position of the pencil, viewed thus obliquely 
 through the glass, with its real position, as shown by the upper end 
 of it, viewed above the plate. Move the pencil to a distance of 
 a fpot or more back of the plate, and observe whether the dis- 
 tance between its real and apparent positions changes. 
 
 d. Repeat with the prism in place of the plate. In moving the 
 pencil away from the prism, move it in such a direction that it 
 
REFRACTION THROUGH A PLATE AND A PRISM 163 
 
 continues visible through the prism. Compare the results with 
 those obtained with the plate, and account for the difference. 
 
 e. Look at any distant straight lines, as the* outline of a build- 
 ing, through a common window pane, and note their apparent 
 wavy distortion. Observe their apparent wriggling motion as the 
 head is moved from side to side. Explain. 
 
 Experiment 95. To study phenomena due to total reflection in 
 glass and in water. 
 
 Apparatus. Triangular glass prism with flat ends ; glass jar, 
 preferably rectangular large jar of water ; beaker ; rule ; mop 
 cloth. 
 
 Experimental Work. a. Lay a glass prism down on a side on 
 a printed page. Look at the page through the prism, with the 
 eyes at first directly above it. Slowly lower the head so as to 
 view the page more and more ob- 
 liquely through the near side of the 
 prism until the printing is no longer 
 visible. Describe arid account for 
 the appearance of the lower face of 
 the prism and the disappearance of 
 the printing, referring to a copy 
 of Figure 76. Remember that there 
 is a thin layer of air between- the 
 prism and the paper. 
 
 b. With the eyes in such a posi- 
 tion that the printing is invisible, 
 
 test the reflecting power of the lower face of the prism by viewing 
 in it the image of your pencil, held near the farther face of the 
 prism. While still viewing this image, slowly raise the head till 
 the printing becomes visible, and note the change in the bright- 
 ness of the image. Explain. 
 
 c. Moisten a part of the lower face of the prism with a drop 
 of water on the finger, and press this face down on the printed 
 page. Can the printing be seen through the moistened part of 
 
164 
 
 LIGHT 
 
 the surface when the eyes are in position to receive total reflec- 
 tion from the remainder of it? Find whether there is total reflec- 
 tion from the moistened part of the surface at any angle. With 
 the eyes in position to see the printing through the moistened part 
 of the surface but not through the remainder, observe the gradual 
 disappearance of the printing as the moisture is absorbed by the 
 paper. 
 
 In this experiment water takes the place of air between the 
 paper and the moistened part of the lower face. From the 
 observed phenomena do you find the critical angle at a glass- 
 water surface greater or less than at a glass-air surface? 
 
 d. Stick a bit of gummed paper on the outside of the smaller 
 jar 5 or 6 cm. from the top. Fill the jar level full of water, and 
 
 stand it near the edge of the 
 table with the bit of paper on 
 the side opposite you. Look at 
 the paper through the surface 
 of the water, while gradually 
 lowering the eyes till they are 
 on a level with the surface, and 
 note the continuous change in 
 the apparent position of the 
 paper. Continue to lower the 
 head while looking upward 
 through the side of the jar at 
 
 the under side of the surface of the water. Presently an image 
 of the paper will be seen by reflection in this surface. Copy 
 Figure 77 and finish it, showing the position of the image of the 
 paper for different positions of the eye. Why does the image by 
 reflection not appear as soon as the eyes are too low to see it 
 by refraction through the surface of the water? 
 
 e. With the eyes directed upward toward the surface of the 
 water, observe in it the image of your pencil, held partly under 
 water. What evidence is there that this image is formed by total 
 reflection ? 
 
THE CONVEX LENS 
 
 I6 5 
 
 EXERCISE 51. THE CONVEX LENS 
 
 References. Adams, 318-326; Coleman, 374-379; Car. & 
 t., 269-274 ; Ches. G. & T., 321-329 ; Hoad. Br., 477-480, 483- 
 484; Hoad. EL, 525-528, 530-532; Mumper, 204-206; Mil. & 
 G., 546-549 ; Went. & H., 386-388, 390. 
 
 Experiment 96. To find the focal length of a convex lens; and 
 to study the formation of real and virtual images by it. 
 
 Apparatus. Meter rod ; mounted lens, having a focal length 
 of 10 to 15 cm.; two mounted cardboard screens, one having a 
 circular hole about 5 cm. in diameter at the same height as the 
 lens ; mounted candle. 
 
 [Various inexpensive supports for lenses are supplied by dealers. 
 Figure 78 shows very satisfactory metal supports for lens and 
 screen. The support for the lens should have a neck, as shown 
 
 FIG. 78. 
 
 in the figure, to hold the lens several centimeters above the meter 
 rod. This is much more convenient than to have the lens down 
 on the rod. Figure 79 shows another form of support, consisting 
 of a wooden block and upright strips of brass.] 
 
 Experimental Work. a. Place the lens at about the middle 
 of the meter rod, and turn it toward some distant object, visible 
 through an adjacent window. If it is not too cold, open the 
 window, to avoid the unequal refraction of the glass. Place the 
 screen with the hole close behind the lens (i.e. on the side oppo- 
 
1 66 LIGHT 
 
 site to the object). Place the other screen back of the first, and 
 adjust its distance so that a distinct image of the distant object 
 is focused on it. The screen with the hole is to intercept as 
 much of the light from other sources as possible. Note the effect 
 of removing it. 
 
 Measure the distance from the lens to the image. (If the lens 
 
 and screen are mounted at the middle of blocks of the same 
 
 length, take the readings of the meter scale at corresponding ends 
 
 of these blocks, and subtract one from the other.) This distance 
 
 is the focal length /of the lens. 
 
 b. Remove the screen on which the image is focused, and stand 
 the other screen in its place, so that the image will be in the air 
 in the hole of this screen. Place the head a foot or two back 
 of the screen, and look at the image with both eyes, focusing 
 them on the hole (not on the more distant lens). The screen 
 serves merely as an aid in focusing the eyes on the real position 
 of the image. You may succeed without it, though this is difficult 
 for the beginner. If not quickly successful in trying to view the 
 image directly, pass it. 
 
 c. Take the apparatus to a darkened corner of the room, or, 
 better, to a room where all the shades can be drawn. Place the 
 lens near the middle of the rod and the lighted candle at one 
 end. Focus the image of the candle on the screen to determine 
 its position, then remove the screen and view it directly. Observe 
 the change in the size and position of the image (either viewing it 
 directly or focusing it on the screen) as your companion slowly 
 carries the candle from its present position to a distance of several 
 meters. Repeat a number of times, comparing roughly the dis- 
 tances through which the candle and the image move. Does the 
 position of the image change more or less rapidly for a given 
 motion of the candle as the distance of the candle becomes large? 
 
 Measure the distance of the image from the lens when the 
 candle is at its greatest distance, and compare with trie focal 
 length of the lens. What point would the image approach if the 
 distance of the candle were increased indefinitely? 
 
THE CONVEX LENS 1 67 
 
 d. Move the candle slowly toward the lens from a distance of 
 about half a meter, and follow the change in the size and position 
 of the image, by focusing it on the screen. Does it move more or 
 less rapidly than the object? 
 
 Focus the image, if possible, on a distant wall of the room, and 
 measure the distance of the candle from the lens. Compare this 
 distance with the focal length. What would become of the image 
 if the candle were moved up to the principal focus? 
 
 e. Place the eye close to the lens and look through it at the 
 candle, and observe the change in its apparent size and position 
 as you move it toward the lens from a position beyond the prin- 
 cipal focus. What appears to be the " magnified candle " is the 
 magnified virtual image of the candle. 
 
 /. Standing in a well-lighted part of the room, hold the lens in 
 one hand at a distance of about 30 cm., and hold your pencil 
 close behind it. Look with both eyes through the lens at the 
 image of the pencil, and compare its size and position with the 
 part of the pencil seen above the lens, as you slowly move 
 the pencil back from the lens. Continue the observation as you 
 move the pencil back and forth through the whole distance within 
 which the image remains distinct. If you have difficulty in seeing 
 the image in its true position, keep the eyes steadily on it as you 
 start with the pencil close to the lens and move it slowly back. 
 A slight shifting of either the lens or the pencil from side to side 
 is also helpful. Find frorn 1 these observations the answers to the 
 following questions : 
 
 Is the distance of the image ever greater than that of the 
 object? Is it always greater? Which increases more rapidly, the 
 distance of the object or the distance of the image? 
 
 How does the size of the image change as the object is moved 
 back from a position close to the lens? 
 
 What is the greatest distance of the object at which the image 
 remains distinct? (Measure it and compare with the focal length 
 of the lens.) Why is the image indistinct when the object is at 
 a greater distance than this? 
 
1 68 LIGHT 
 
 Discussion. From the results of the experiment, together with 
 a study of the text, find answers to the following questions : 
 
 1. What happens after refraction to the diverging cone of light 
 that falls upon the \ens/r0m any one point of the object, (a) when 
 the distance of the object is greater than the focal length? (b) less 
 than the focal length? (c) equal to the focal length? 
 
 2. What behavior of the refracted light results in (a) a real 
 image? (b) a virtual image? 
 
 3. (a) Under what conditions is a real image formed? (b) a 
 virtual image? 
 
 4. With rule and compass draw accurate figures showing the 
 size and position of the image in the following cases. Use the 
 same focal length in all the figures, and in all but the first an 
 arrow of the same length as object. The object cannot be rep- 
 resented in the first figure. (Why not?) 
 
 Object large and at a relatively great distance (illustrating 
 paragraph a). 
 
 Distance of object greater than twice the focal length (illustrating 
 paragraph c). 
 
 Distance of object greater than the focal length and less than 
 twice the focal length (illustrating paragraph </). 
 
 Distance of object slightly less than the focal length, and 
 also when only a small fraction of the focal length (illustrating 
 paragraph/). 
 
 EXERCISE 52. CONVEX AND CONCAVE LENSES 
 
 References. Adams, 319-327; Coleman, 380, 382; Car. & 
 C., 271-274; Ches. G. & T., 330; Hoad. Br., 481-482; Hoad. 
 EL, 525-532; Mumper, 206-207; Mil. & G., 550-551; Went. 
 & H., 386-390. 
 
 Experiment 97. To find the focal length of a convex lens from 
 its relation to conjugate focal distances ; and to compare the rela 
 five size of image and object with their respective distances from 
 the lens. 
 
CONVEX AND CONCAVE LENSES 
 
 169 
 
 Apparatus. Lens of 10 to 15 cm. focal length; meter rod; 
 two mounted screens, one having a round hole about i in. in 
 diameter, with cross wires (Fig. 79) ; flat gas jet or lamp. 
 
 Experimental Work. Find the focal length /of the lens by 
 focusing the image of a distant object on a screen, as in the pre- 
 ceding exercise. 
 
 Draw the window shades, at least those near the apparatus, so 
 as to make the room rather dark. Stand the screen with the 
 
 FIG. 79. 
 
 cross wires at an end of the rod, and turn the gas jet flatwise 
 toward it. Place the lens at a distance exactly equal to twice its 
 focal length from this screen, and adjust the other screen so that 
 the image of the cross wires is exactly focused upon it. The 
 image of the cross wires may be red, black, or greenish blue, de- 
 pending upon the position of the screen. Adjust for a black 
 image. Let / denote the distance from the lens to the cross 
 wires, and /' from the lens to the image. Record as indicated 
 below. Measure carefully the diameter of the hole contain- 
 ing the cross wires and the diameter of the image. Call the 
 first the length of the object /, and the second the length of the 
 image /'. 
 
 Move the screen on which the image is caught to the farther 
 end of the rod ; then move the lens toward the cross wires till the 
 image is again distinct on the screen. Measure/,/', and /'. 
 
LIGHT 
 
 Without changing the position of either screen, move the lens 
 away from the cross wires till the image again falls upon the other 
 screen ; and measure p, /', and /'. 
 
 Data and Computations. Consult the text-book for the deri- 
 vation of the lens formula \/p + i//' = i//. Solved for f, this 
 gives /=//'/(/+/'). The average of the three values of/ com- 
 puted from this formula is the focal length of the lens as found by 
 the method of conjugate foci. Compare this with the value ob- 
 tained by focusing on a distant object. 
 
 Consult the text, also, for the geometrical proof that the true 
 values of the ratios p'/p and /// are equal. Write all ratios in 
 the tabulated record as quotients expressed decimally. Record 
 as follows : 
 
 ft 
 
 ft f 
 
 tt 
 
 // 
 
 j.r Ij. 
 
 1' 17 
 
 DIFFERENCE 
 
 PER CENT 
 
 p 
 
 P 
 
 p+p> 
 
 
 P IP 
 
 i ft 
 
 P'lP ~ I'/i 
 
 OF DlFF. 
 
 
 
 
 
 
 
 
 o/ 
 
 
 
 
 
 
 
 
 /o 
 o/ 
 
 cm. 
 
 cm. 
 
 
 
 
 
 
 
 
 
 
 
 /o 
 
 / 
 
 /o 
 
 Focal length of lens / found by focusing on 
 
 a distant object 
 Average value of focal length, computed from 
 
 conjugate focal distances 
 Percentage of difference between focal lengths 
 
 by the two methods 
 Diameter of circular hole (length of object) / 
 
 = cm. 
 
 = cm. 
 
 = cm. 
 
 Discussion. a. Show from the formula that/ and /' should 
 be equal in the first set of measurements. 
 
 b. How do / and/' of the second set of measurements com- 
 pare with / and / respectively of the third set ? What principle 
 of conjugate foci is illustrated by these two pairs of values? 
 
THE EYE 
 
 171 
 
 Experiment 98. To study the formation of images by a con- 
 cave lens. 
 
 Apparatus. Concave lens. 
 
 Experimental Work. a. Try to focus a beam of sunlight on 
 a sheet of paper with the concave lens, as you do with a convex 
 lens. State and account for the result. 
 
 b. Hold the lens up before a window (preferably open) at a 
 distance of a foot or more from the face, and look through it 
 with both eyes at the image of distant objects. Shift the lens 
 slightly from side to side to aid in locating the image. The dis- 
 tance of the image is the focal length of the lens. Estimate this 
 distance as closely as you can. 
 
 c. Look at nearer objects through the lens, as the window, 
 the floor, a page of your book, your hand, a pencil, etc., always 
 with both eyes and with the lens a foot or more from the face. 
 Compare the relative size and distance of object and image in 
 each case. As the object approaches the lens, what change takes 
 place in the size and position of its image? Where is the image 
 when the object is close to the lens? 
 
 Draw three diagrams showing the formation of an image by a 
 concave lens ; the first with a large object at a relatively great 
 distance (the object not shown in the figure); the second with 
 the object (represented by an arrow) at about twice the focal 
 length ; the third with the distance of the object about one fourth 
 the focal length. Take the same focaHength in the three diagrams. 
 
 EXERCISE 53. THE EYE 
 
 (INVENTIVE) 
 
 References. Adams, 331-333; Coleman, 383-386; Car. & 
 C., 301-302; Hoad. Br., 520-521; Hoad. EL, 570-572; Mum- 
 per, 215 ; Mil. & G., 555 ; Went. & H., 403-404. 
 
 Experiment 99. To study the structure of the eye by means of 
 a dissected model. 
 
 Apparatus. A large anatomical model of the eye, separable. 
 
1/2 LIGHT 
 
 Suggestions. Examine the model in connection with the 
 study of the text and any school physiology on the subject of the 
 eye. Handle the model only with clean hands and as little as 
 will serve the purpose, to avoid unnecessarily soiling it. Make 
 note of any points not fully understood, and bring them up for 
 discussion in the recitation. The parts of the eye, their appear- 
 ance, shape, relative position, physical properties, structure, and 
 function should all receive attention, primarily from the point of 
 view of the eye as an optical instrument. 
 
 Experiment 100. To examine a dissected eye of an ox. 
 Material. An ox's eye, dissected by the teacher. 
 
 Suggestions. If several pupils are to study the same eye, it 
 should be disturbed but little. At the most, use the scalpel or 
 other dissecting instrument to move the parts slightly, if neces- 
 sary to get a good view of them, or to test their texture, rigidity, 
 etc. Examine the specimen closely in connection with a study 
 of the text or any physiology. 
 
 EXERCISE 54. THE SIMPLE AND THE COMPOUND 
 MICROSCOPE 
 
 References. Adams, 335-336; Coleman, 393-395 ; Car.&C., 
 295-296; Hoad. Br., 513-514; Hoad. EL, 562-563; Mumper, 
 
 206, 211 ; Mil. & G., 556-558, 560 ; Went. & H., 406, 411-412. 
 
 
 
 Apparatus. Two mounted -lenses, preferably of equal focal 
 length not over 10 cm. ; meter rod; two small mounted screens 
 with printing and metric scale. 
 
 [Lenses and screens mounted as in Figure 78 are preferable. 
 The screens are better small not over 6 by 8 cm. Printing in 
 the same size of small type is pasted on one side of each screen 
 and a paper metric scale 5 cm. long at the left edge of the other 
 side. The screens should be held in their supports only by the 
 pressure of the springs, so that they can be shifted to right or 
 left.] 
 
THE SIMPLE AND THE COMPOUND MICROSCOPE 173 
 
 Experiment 101. To find the magnifying power of a simple 
 microscope. 
 
 Experimental Work. - a. Place a lens at an end of the meter 
 rod, and adjust one of the screens back of it so as to read the 
 fine printing with one eye, placed close to the lens. Estimate 
 the magnification. 
 
 b. Place both of the screens behind the lens on the rod, with 
 the metric scales turned toward the lens, and the farther screen at 
 a distance of 25 cm. from the lens. Adjust the nearer screen so 
 that the scale is distinctly seen through the lens, with the eye 
 close to it. 
 
 With the screens remaining at these distances and the scales at 
 the left side of each (invert if necessary), shift the nearer screen 
 to the right until the scale is directly over the meter rod. Look 
 at this scale with the right eye, placed close to the lens, and 
 at the same time look through the air with the left eye at the 
 farther scale. While looking thus with both eyes, slip the farther 
 scale to the left till it appears to the left and close beside the 
 image of the nearer scale. (If you prefer to look through the lens 
 with the left eye, read right instead of left, and vice versa, in the 
 above directions.) If you have difficulty in seeing both scales 
 distinctly at the same time, winking with one eye or the other, 
 or both, will help. Note as accurately as possible the length on 
 the farther scale that is equal to a centimeter on the magnified 
 image of the nearer scale. 
 
 This gives the magnification produced by the lens when used to 
 the best advantage as a simple microscope. For example, if the 
 magnified centimeter has the same length as 2 cm. on the scale 
 which is viewed with the naked eye at 25 cm. (the least distance 
 of distinct vision), the magnification is 2. 
 
 c. Compare the magnification, thus determined, with the ratio 
 of the distance of the farther screen (25 cm.) to the distance of 
 the nearer screen from the lens. Record the latter distance as 
 well as the ratio. 
 
1 74 LIGHT 
 
 d. Find the focal length of the lens / by focusing it on a dis- 
 tant object. Compute the ratio of 25 cm. to the focal length. 
 This ratio (2$//, the distances being measured in centimeters) is 
 the formula for computing the approximate .value of the magnifica- 
 tion from the known focal length (see text). 
 
 Oral Discussion. i. Is the ratio determined in c or in d more 
 nearly equal to the magnification as determined by direct com- 
 parison ? 
 
 2. Which should you expect to be more nearly equal, and why? 
 
 Experiment 102. To adjust and use a pair of lenses as a com- 
 pound microscope; and to determine the magnification. 
 
 Experimental Work. a. Leave the lens that you have been 
 using at the end of the rod, to serve as the eye lens. Place the 
 other lens (the objective) on the rod at a distance of four or five 
 times the focal length from the first. (The two lenses are of equal 
 or nearly equal focal length.) Place one of the screens beyond 
 the objective, with the printing turned toward you ; and adjust its 
 distance so that the printing is distinct when viewed through the 
 two lenses. Probably not more than two or three letters v/ill be 
 visible, the field of view being very small. Note the distortion 
 and coloring of the image. These imperfections and their remedy 
 are discussed in the text. The image will appear greatly magni- 
 fied in comparison with the printing viewed directly with the 
 other eye at that distance (50 to 60 cm. with lenses of 10 cm. 
 focal length) ; but the correct comparison is made with the print- 
 ing as it appears to the unaided eye at a distance 0/2$ cm. The 
 metric scales will be used for this purpose in the work of the next 
 paragraph. 
 
 b. Reverse the screen, and slip it to right or left till as much of 
 the scale as possible is distinctly visible through the lens. Hold 
 the other screen in the hand 25 cm. from the eye lens and in such 
 a position that the scale on it, 'viewed directly with one eye, 
 appears close beside the image of the farther scale, viewed through 
 the lenses with the other eye. From a comparison of the scales, 
 
THE SIMPLE AND THE COMPOUND MICROSCOPE 175 
 
 determine the magnification. For example, if 2 mm. of the mag- 
 nified scale appear as long as 9 mm. on the other, the magni- 
 fication is 9/2, or 4.5. 
 
 c. Measure the distance between the lenses and the distance 
 from the objective to the screen used as object. 
 
 Let/ denote the latter distance (represented by AO in Figure 
 80) and/' the distance from the objective to the real image formed 
 
 FIG. 80. 
 
 by it (Oa in the figure). This real image ba is approximately at 
 the principal focus of the eye lens (really at a somewhat less dis- 
 tance from the eye lens, as an object would be when viewed 
 through the eye lens alone) ; hence the approximate value of/' is 
 found by subtracting the focal length of the eye lens from the dis- 
 tance between the lenses. 
 
 Since / and /' are conjugate focal distances, the magnification 
 due to the objective alone is /'//. The magnification due to the 
 eye lens is the same as when that lens is used alone, its approxi- 
 mate value being 25/7. Hence the magnification due to objective 
 and eye lens together is/'// x 2$/f. Compute the magnification 
 from this formula, and compare with the value found by direct 
 observation. 
 
 Record data and computations in the usual form. 
 
176 LIGHT 
 
 EXERCISE 55. THE ASTRONOMICAL AND THE GALI- 
 LEAN TELESCOPE 
 
 References. Adams, 337-338; Coleman, 396, 398; Car. 
 C., 297-298 ; Hoad. Br., 515-517 ; Hoad. EL, 564-566 ; Mumper, 
 212, 214; Mil. & G., 559, 562; Went. & H., 413-415. 
 
 Apparatus. Convex lens of long focal length; two convex 
 lenses of unequal short focal length ; concave lens of short focal 
 length; two mounted screens, one with a hole of 1.5 in. diameter 
 at height of lenses ; meter rod ; metric rule. 
 
 [The lenses commonly supplied for laboratory work have a 
 focal length of 10 to 15 cm. If these are used as eye lenses in 
 this experiment, the objective should have a focal length of 40 cm. 
 or more ; but a diameter of 4 cm. is quite sufficient. Dealers 
 will supply such lenses, made to order, at a moderate price. 
 Lenses of 15 to 16 cm. focal length can be used as objectives 
 with lenses of 3 to 8 cm. focal length for eye lenses. The latter 
 
 can be obtained, mounted in various ways, as simple microscopes.] 
 
 
 
 Experiment 103. To adjust and use a pair of lenses as an 
 astronomical telescope ; and to determine the magnification. 
 
 Experimental Work. a. Find the focal lengths of the three 
 convex lenses by focusing on a distant object. The screen with 
 the hole, placed just back of the lens to cut off diffused light, 
 will probably not be sufficient to make the image visible with the 
 lens of long focal length, as the image is large and correspond- 
 ingly faint. Lower the window shade nearly to the level of the 
 table, and stand before the window so as to cut off light from the 
 side as much as possible. Let/ denote the greatest focal length, 
 / the next, and / the shortest. The lenses will be referred to 
 as lens/j, lens/, and lens/. 
 
 b. Place lens / as eye lens at an end of the meter rod, and 
 lens/ as objective at a distance from the first, approximately equal 
 to the sum of their focal lengths. Turn the telescope thus formed 
 
ASTRONOMICAL AND GALILEAN TELESCOPE 
 
 177 
 
 toward a distant object ; and, with the eye close to the lens, adjust 
 the objective till the image is distinct. The window should be 
 raised if the weather will permit. Note the border of color round 
 the edges of objects. Is the color stronger when you look through 
 the centers of the lenses or through their marginal portions? This 
 defect and its remedy is discussed in the text under chromatic 
 aberration and achromatic lenses. 
 
 c. Turn the telescope toward a distant chimney, tower, water 
 tank, or other regular object of moderate size. A window will 
 
 J. 
 
 FIG. 81. 
 
 serve, or a letter of a large sign ; but an isolated object having the 
 sky as a background is much the best. Support the meter rod 
 upon books or blocks, or with a stand and clamp, so that it 
 can be pointed steadily toward the object. While looking at the 
 object directly with one eye and through the telescope with 
 the other, turn the telescope so that the image directly overlies 
 the object, and estimate the magnification. 
 
 d. Measure the distance between the lenses. This is the 
 length / of the telescope. 
 
 e. Repeat the above work with the same objective and lens f 2 
 as the eye lens ; and again with lens^ as the objective and lensy^ 
 as the eye lens. 
 
 Data and Computations. Compare the estimated magnification 
 in each case with the ratio of the focal length of the objective to 
 the focal length of the eye lens. Compare also the length of 
 COLEMAN'S NEW MANUAL 12 
 
LIGHT 
 
 the telescope with the sum of the focal lengths of objective and 
 eye lens. Record as follows : 
 
 Focal length/ = cm., / 2 = cm., / 3 = 
 
 cm. 
 
 ESTIMATED 
 MAGNIFICATION 
 
 COMPUTED 
 MAGNIFICATION 
 
 DIFFERENCE 
 
 I 
 
 SUM OF 
 FOCAL LENGTHS 
 
 DIFFERENCE 
 
 
 
 /1//3= 
 
 
 
 cm. 
 
 /!+/=- 
 
 
 
 
 
 /!//*= 
 
 
 
 cm. 
 
 /1+/2-- 
 
 
 
 
 
 /2 // 3 = 
 
 
 
 
 /- . r 
 
 
 
 
 - 
 
 Discussion. i. Discuss the first and second combinations of 
 lenses as an illustration of the effect of the focal length of the eye 
 lens on the magnification. 
 
 2. Discuss the first and third combinations as an illustration of 
 the effect of the focal length of the objective on the magnification. 
 
 3. Discuss the relation between the lengths of the telescopes 
 and the sum of the focal lengths of the objective and eye lens. 
 
 4. Copy Figure 81 and answer the following questions : 
 
 a. Which rays come from a point at the top of the object, and 
 which from a point at the bottom? 
 
 b. What (in the figure) is the focal length of the objective? 
 of the eye lens? 
 
 c. What is the visual angle with the naked eye ? with the 
 telescope ? 
 
 </. What ratio (of lengths) measures the magnification? 
 
 Experiment 104. To adjust and use a convex and a concave 
 lens, as a Galilean telescope ; and to determine the magnification. 
 
 Experimental Work. a. To find the focal length of the con- 
 cave lens, hold it about a foot from the face, look through it with 
 both eyes at the image of a distant building, and measure with 
 the rule the distance between the image and the lens. In doing 
 this, look at the farther end of the rule directly (not through the 
 lens), and extend it just to the image. (The method is similar to 
 
THE SPECTRUM; COLOR 
 
 179 
 
 that of finding the apparent width of a glass plate or the apparent 
 depth of water in a vessel.) 
 
 b. Place the concave lens at the end of the t meter rod. This 
 is the eye lens. Use the lens of long focal length / x as the ob- 
 r 
 
 H 
 
 FIG. 82. 
 
 jective, and place it at the greatest distance from the eye lens 
 that will give a distinct image of a distant object. Estimate the 
 magnification and measure the distance between the lenses. 
 
 Discussion. i . Compare the length of the telescope with 
 the difference between the focal lengths of the lenses. 
 
 2. Compare the estimated magnification with the ratio of the 
 focal length- of the objective to that of the eye lens. 
 
 3. Copy Figure 82 and answer the questions under 4 of the 
 discussion at the end of the preceding experiment. 
 
 EXERCISE 56. THE SPECTRUM; COLOR 
 
 References. Adams, 277-280, 286-291, 299-300; Coleman, 
 401, 403-404, 407-408, 410, 419; Car. & C., 277-278, 287-289, 
 291-293; Ches. G. & T., 33 J -332, 339, 341-352; Hoad. Br., 
 486-487, 494-496, 498-499, 508-509 ; Hoad. EL, 534~53 6 > 543- 
 546, 556-557; Mumper, 209, 217-221; Mil. & G., 565-574; 
 Went. & H., 392-394, 417-418, 422-425. 
 
 Experiment 105. To determine by analysis with a prism the 
 elementary or prismatic colors of sunlight, of light transmitted 
 through colored glass, and of light reflected from colored surfaces. 
 
1 80 LIGHT 
 
 Apparatus. Prism of flint glass ; square of black cardboard 
 (Fig. 83) with a slit i mm. by 2 cm. and a slit i cm. by 2 cm.; 
 pieces of colored glass 3 to 5 cm. square ; 
 strips of colored paper i mm. wide and 2 cm. 
 long, pasted on black cardboard. 
 
 [A prism of crown glass will serve, but . 
 flint glass gives nearly twice the dispersion, 
 which is an advantage. Pieces of cardboard 
 10 or 12 cm. square serve for the slits and 
 the strips of colored paper. For these strips 
 use white and several of the spectrum colors ; 
 and arrange them on the card so that their spectra can be easily 
 distinguished from one another. The squares of colored glass 
 should include ruby, yellow, and blue. The ruby is a fine 
 example of a nearly pure spectrum color. The yellow and blue 
 should be selected to give bright green by transmission through 
 both.] 
 
 Experimental Work. a. Stand facing a window, and hold the 
 cardboard with the slits out nearly at arm's length, with the slits 
 horizontal and strongly illuminated by sunlight (having the sky for 
 a background). Look at the narrow slit through the prism, held 
 close to the eye with its long edges 
 horizontal and its faces turned, as 
 shown in Figure 84. Looking 
 obliquely down at an angle of 
 about 35 to the direction of the 
 
 FIG. 84. 
 
 slit, you will see the overlapping 
 colored images of it which together constitute the spectrum of 
 sunlight. Copy Figure 84 on a large scale, and mark by the 
 initial letters R, O, .Y, etc., the colors of the spectrum in the 
 observed order. What color is refracted most? what least? 
 
 b. Look at the wide slit in the same way. Record the colors 
 in their observed order in a figure similar to Figure 84, but with 
 a wide beam of light represented instead of a ray. The figure 
 
THE SPECTRUM; COLOR 
 
 181 
 
 should account for the fact that the central portion of the slit 
 appears white. Explain. 
 
 c. Cover one end of the narrow slit with the blue glass, and 
 view the slit with the prism, as before. You now observe side by 
 side the complete spectrum and the spectrum of the light that is 
 transmitted through the blue glass. What colors besides spectrum 
 blue are transmitted by the glass? The colors not transmitted 
 are absorbed. Record as shown below, designating the colors by 
 initials. 
 
 Make a similar analysis of the light transmitted by the yellow 
 glass, by the blue and yellow together, and by the other pieces 
 provided. 
 
 COLOR OF GLASS 
 
 COLORS TRANSMITTED 
 
 COLORS ABSORBED 
 
 Blue 
 
 
 
 Yellow 
 
 
 
 Blue and yellow 
 
 
 
 Red 
 
 
 
 
 Etc. 
 
 
 
 d. Look through the blue and yellow pieces of glass placed 
 together (not using the prism), and note the color. Explain. 
 
 e. Hold the colored strips on the cardboard in a strong light 
 (direct sunlight, if possible), and analyze with the prism the light 
 reflected by them. Record in tabular form, as in paragraph c, 
 heading the first column "color of the strip," the second " colors 
 reflected," and the third " colors absorbed." Colors that appear 
 very faint in the spectrum are to be recorded as absorbed. 
 
 Experiment 106. To determine the color resulting from the 
 synthesis (union) of various colored lights; and to distinguish 
 complementary colors. 
 
 Apparatus. Several pieces of black cardboard on each of 
 
182 
 
 LIGHT 
 
 which are pasted two squares of colored paper (Fig. 85) ; piece 
 
 of window glass about 6 by 10 cm. 
 
 [On pieces of black cardboard about 8 by 12 cm., paste colored 
 
 papers 4 or 5 cm. square, two on each card, close together. 
 Some of these pairs of colors are to be 
 complementary, others not. Any of the 
 following are good : blue and yellow, red 
 and bluish green, green and purple, violet 
 and yellowish green, red and yellow, green 
 and violet, violet and red, orange and 
 green.] 
 
 Experimental Work. Stand the piece 
 of window glass between the yellow and 
 blue squares on one of the cards, with 
 the yellow color toward you, as shown in 
 Figure 85. Look through the glass at 
 Superposed on it will be an image of the 
 
 FIG. 85. 
 the blue square. 
 
 yellow square, due to partial reflection from the window glass ; 
 and the blue paper will appear to be of the color it would have if 
 all the light that enters the eye from its direction actually came 
 from it. Inclining the glass forward increases the amount of re- 
 flected yellow light and decreases the amount of transmitted blue 
 light, causing the appearance of the blue paper to change from 
 blue through white or light gray to yellow. Inclining the glass 
 backward produces the opposite effect. Observe the nearest 
 approach to white that can be obtained in this way. 
 
 Repeat the experiment with the red and yellow papers. (It is 
 immaterial in any case which paper is in front.) An intermediate 
 white or gray is impossible in this case. What color is produced 
 instead ? 
 
 Try in the same way all the pairs of colors provided. Name in 
 one group all those pairs of colors which, like the blue and yellow, 
 give white or gray. All such pairs are complementary colors. 
 Record the component and resultant colors in tabular form. 
 
THE SPECTRUM; COLOR 
 
 183 
 
 PURPLE 
 
 Discussion. i. Compare all results with the arrangement of 
 colors shown in Figure 86, and state the results in general terms 
 with reference to this arrangement. 
 
 2. How is it possible that the yel- 
 low and blue pieces of glass together 
 transmit green, while the light from 
 the yellow and blue papers gives 
 white when combined ? 
 
 Experiment 107. To study the 
 production of color by interference. 
 
 Apparatus. Two pieces of thick 
 plate glass ; small iron clamp ; soap- 
 bubble solution in a jar; wire loop 
 with handle. 
 
 Experimental Work. a. Clamp the two pieces of glass firmly 
 together, being careful to have the surfaces that are in contact 
 thoroughly clean. Hold them in a strong light, and look at them 
 from the illuminated side. Observe the curved bands of spectrum 
 colors which surround the spot where the clamp is applied. Ac- 
 count for them after consulting the text. 
 
 How do these bands of colors change as you apply additional 
 pressure at the edges of the plates with the fingers? How do 
 they change as you turn the plates about and view them at dif- 
 ferent angles ? Explain. 
 
 b. Cover the wire loop with a film of the soap solution, and 
 hold it in a strong light, with the film vertical. Note the gradual 
 appearance of bands of color in the upper side of the film. These 
 interference colors are due to the gradual thinning of the upper 
 part of the film under the action of gravity. Describe. 
 
X. MAGNETISM 
 
 EXERCISE 57. MAGNETS AND MAGNETIC ACTION 
 
 References. Adams, 436-443, 449-451; Coleman, 420-428; 
 Car. & C., 358-369; Ches. G. & T., 354~359 ; Hoad. Br., 291- 
 298, 307; Hoad. EL, 326-336, 345-346; Mumper, 222-228; 
 Jackson, 68-83 ; Mil. & G., 305-311; Went. & H., 240-243, 
 245-246. 
 
 Apparatus Bar magnet; magnetic needle on stand (Fig. 87); 
 coarse iron filings or very small tacks in a box longer than the 
 
 magnet ; small .pieces 
 _MAGNETIC__ of various substances. 
 
 MERIDIAN 
 
 as iron, steel, brass, 
 copper, lead, glass, 
 paper, etc. ; pieces 8 
 or 10 cm. square of 
 cardboard, glass, thin 
 
 wood, sheet iron (or tin), zinc, lead, and brass ; rods of soft 
 iron, steel (knitting needle), and brass or wood of equal length 
 (15 to 20 cm.). 
 
 Experiment 108. To determine the distribution of attracting 
 power in a magnet, the polarity of a magnet, and the law of 
 magnetic action. 
 
 Experimental Work. a. Lay the magnet in the box of iron 
 filings, so that its whole length comes in contact with the filings. 
 Lift the magnet and observe the distribution of the filings that 
 cling to it. Draw a sketch to illustrate. The regions where the 
 power of attraction is greatest are called poles. Is there any 
 evidence of attraction at the center? Remove the filings by 
 wiping them toward the middle of the magnet. 
 
 184 
 
MAGNETS AND MAGNETIC ACTION 185 
 
 b. Test the attracting power of the magnetic needle (Fig. 87) 
 in the same way. (Do not let it come in contact with the bar 
 magnet.) The needle is a magnet adapted in its form to special 
 uses. Replace it on its stand. 
 
 c. Remove all magnetic substances to a distance not less than 
 a meter from the magnetic needle, and observe its behavior when 
 disturbed and free to turn on its support. Does it always 
 come to rest with the same end pointing in the same direction? 
 The end that points north in the position of equilibrium is called 
 the north pole. Note its color (commonly blue), which serves 
 to distinguish it from the south pole. 
 
 The bar magnet, if supported so as to be free to turn in a 
 horizontal plane, would behave like the needle. 1 The end that 
 would point north is marked N. The south pole is sometimes 
 marked S, sometimes left unmarked. 
 
 d. Observe the effect of bringing each of the poles of the bar 
 magnet near each of the poles of the magnetic needle. What 
 action is observed between like poles? between unlike poles? 
 Remember that the action between two bodies is always mutual 
 (Newton's third law). Is there any evidence of action on the bar 
 magnet? Why or why not? If not, can you suggest any means 
 by which it might be detected? 
 
 e. Note roughly the rapidity of vibration of the magnetic needle 
 when removed from all magnetic substances and disturbed from 
 the position of equilibrium. Note the change in the rate of 
 vibration as a pole of the bar magnet is slowly brought up 
 toward the unlike pole of the needle. The increased rate indicates 
 increased magnetic force. It can be shown mathematically that 
 the magnetic force acting on a needle is proportional to the 
 square of its rate of vibration. Thus, if the rate increases to 
 twice its original value, we know that the magnetic force is four 
 
 1 It will not serve in testing this to suspend the magnet by a thread, for the 
 tension on the thread causes it to untwist with a force that is commonly greater 
 than the magnetic force that tends to set the magnet north and south. An untwisted 
 fiber should be used for the suspension. 
 
!86 MAGNETISM 
 
 times as great as at first. The more or less rapid vibration of 
 the magnetic needle often serves to indicate roughly the relative 
 magnitude of magnetic forces. It is unnecessary in elementary 
 physics to measure them. 
 
 What do your observations indicate concerning the effect of 
 distance from a magnet on the magnetic force exerted by it. 
 
 Experiment 109. To distinguish magnetic and nonmagnetic 
 substances ; and to determine which of these act as magnetic screens. 
 
 Experimental Work. a. Find which of the small pieces of 
 various substances provided are attracted by a magnet, and which 
 are not. Classify the former as magnetic and the latter as non- 
 magnetic. 
 
 b. Put a small quantity of iron filings (or tacks) on the card- 
 board, and move a pole of the magnet about against the under 
 side of the cardboard beneath the filings. What evidence is there 
 of magnetic action through the cardboard ? Repeat with the 
 piece of sheet iron in place of the cardboard, and try all the sub- 
 stances provided in the same Tjay. Classify them in two groups 
 according as they do or do not act as a screen to cut off magnetic 
 action. What relation do you find between this classification and 
 that of magnetic and nonmagnetic substances ? 
 
 Gather up with the magnet any scattered filings. 
 
 c. Hold a pole of the bar magnet about i cm. from* the unlike 
 pole of the magnetic needle, and note the rate of vibration. Slip 
 the piece of sheet iron between, and observe the effect on the rate 
 of vibration. Conclusion ? Try the other substances in the same 
 way. 
 
 Experiment no. To study phenomena of magnetic induction. 
 
 Experimental Work. a. Find whether the soft iron rod at- 
 tracts iron filings. Try again with an end of the magnet against 
 the upper end of the rod. What happens to the load of filings on 
 the end of the rod when the magnet is removed from the other 
 end ? What does this indicate concerning the magnetic condition 
 of the rod ? 
 
MAGNETS AND MAGNETIC ACTION 187 
 
 b. With an end of the bar magnet against an end of the soft 
 iron rod, test the polarity of the other end of the rod by bringing 
 it up to the magnetic needle. Is this pole like or unlike the pole 
 of the magnet which is in contact with the other end of the rod ? 
 With the rod still in place, reverse the magnet, bringing its other 
 pole in contact with the rod, and note the effect on the needle. 
 
 The iron rod is itself a magnet while in contact with the bar 
 magnet, and has two unlike poles. You have tested one of these 
 poles, and hence by inference know the other. Is the pole of the 
 rod at the end touched by the magnet like or unlike that with 
 which it is touched ? Draw a figure showing the arrangement of 
 poles in the magnet and the rod, when they are placed end 
 to end. 
 
 c. Repeat the work of paragraph a with the steel rod. Do you 
 find it already magnetized ? If so, how do you account for this 
 condition ? Determine its polarity by testing with the magnetic 
 needle. Find whether the polarity of one end of it is reversed by 
 merely changing the pole of the magnet with which its other end 
 is touched. If not, find whether you can reverse its polarity by 
 repeatedly rubbing it from the center to one end with one pole of 
 the magnet, and from the center to the other end with the other 
 pole. Are the poles of the rod like or unlike the poles of the 
 magnet that were applied to produce them ? 
 
 d. Test the brass (or wooden) rod as you did the iron rod in a 
 and b. In repeating , hold a pole of the magnet so that the 
 distance between it and the needle is a little greater than the 
 length of the rod, and observe whether interposing and removing 
 the brass rod between them has any effect on the needle. Try 
 the same with the iron rod. 
 
 Does a nonmagnetic substance in the form of a rod affect mag- 
 netic action ? Does it in the form of a sheet (Exp. 109, b} ? 
 Compare the effects of a magnetic substance in the two forms. 
 In this connection make a further test of the sheet iron by hold- 
 ing an end of the magnet against its center, while touching its edge 
 to iron filings. 
 
!88 MAGNETISM 
 
 EXERCISE 58. MAGNETIC FIELDS 
 
 References. Adams, 452-455 ; Coleman, 431-432 ; Gar. & C., 
 374-377; Ches. G. &T., 363-367; Hoad. Br., 299-300; Hoad. 
 EL, 334-337; Mumper, 230; Jackson, 84-90; Mil. & G., 312- 
 314; Went. & H., 249-251. 
 
 Apparatus. Two bar magnets; small compass; board about 
 
 10 by 15 in. with parallel 
 grooves about 2 in. apart, 
 in the direction of the 
 length (Fig. 88) ; one or 
 more pieces of thick card- 
 board 9 by ii in. ; fine 
 iron filings in pepper box 
 
 r IG. oo. 
 
 or other sifter ; with or 
 
 without blue-print paper and rubber bands to fasten it to the 
 cardboard. 
 
 Experiment in. To determine the shape and direction of the 
 lines of force in the magnetic field about a bar magnet. 
 
 Experimental Work. Without Blue-print Paper. Place a mag- 
 net in one of the grooves of the board, and note the position of 
 its north and south poles. Lay the cardboard over the magnet, 
 and sprinkle iron filings thinly and evenly over it from the height 
 of about a foot. Gently tap the cardboard at different points with 
 the finger (not the finger nail), while holding it in place. The 
 slight jarring helps to overcome friction, and enables the filings to 
 arrange themselves in lines under the action of the magnet. 
 
 Place the compass at different points about the magnet, and 
 compare the direction of the needle in each position with the 
 direction of the lines of filings at that place. The lines of filings 
 are more or less irregular and broken ; the magnetic lines of force 
 which they imperfectly sketch are really smooth, continuous curves. 
 Draw a diagram on a reduced scale, representing the magnet and 
 several lines of force about it, as indicated by the lines of filings. 
 
MAGNETIC FIELDS 189 
 
 Mark the poles of the magnet N and S. Be careful to represent 
 the position and curvature of the lines of force, as correctly as 
 possible, by regular, unbroken lines. Place an arrowhead on each 
 line, indicating the direction along the line in which the north pole 
 of the compass needle points. 
 
 With Blue-print Paper. Fasten a sheet of the blue- print 
 paper, prepared side up, to the cardboard by means of rubber 
 bands, and proceed as above, sprinkling the filings on the blue- 
 print paper and omitting the pencil sketch. Keep unused blue- 
 print paper in the dark. Mark the positions of the north and 
 south poles of the magnet on the paper, and place arrowheads 
 here and there, indicating the direction in which the north pole 
 of the needle points. 
 
 Lift the cardboard vertically from the magnet, and place it in 
 a strong light (direct sunlight, if possible) for a few minutes. 
 
 A . B CD 
 
 FIG. 89. 
 
 When the uncovered parts of the paper have turned dark, return 
 the filings to the box and wash the paper immediately by moving 
 it about in clean water, or letting water run over it from the faucet 
 for a few minutes. Spread it out on a flat surface to dry, and 
 when dry, fasten it in your note book. If left in the laboratory till 
 the following day to dry, write your name on it for identification. 
 
 Experiment 112. To determine the shape and direction of the 
 lines of force between and about two bar magnets in different rela- 
 tive positions. 
 
 Experimental Work. Proceed as above, either with or with- 
 out blue-print paper, to study and make a record of the magnetic 
 fields between and about two bar magnets in the different positions 
 shown in Figure 89. For the positions shown in A and B, place 
 the magnets about 4 cm. apart in the same groove of the board, 
 
190 MAGNETISM 
 
 and determine the lines of force between and about their adjacent 
 ends. For the arrangements shown in C and D, determine the 
 lines of force between and all round the magnets. The last one 
 or two cases may be omitted if one laboratory period does not 
 give time enough for all of them. Mark the poles of the magnets 
 in the figure or blue print, and place arrowheads on the lines, as 
 in the preceding experiment. 
 
 Be careful to gather up all iron filings and return them to the 
 sifter. 
 
 Discussion. The following questions are to be answered from 
 a study of the diagrams or blue prints you have made : 
 
 1. Do the lines of force converge to a common point at or near 
 the end of a magnet, or to different parts of a small area near the 
 end? 
 
 2. Do any lines of force cross each other? What reasons have 
 you for thinking that they can or cannot cross in any case ? 
 
 3. Do lines offeree extend between like poles or unlike poles, 
 or both? What reasons have you for thinking that they can or 
 cannot extend between like poles in any case ? 
 
XI. ELECTRICITY 
 
 EXERCISE 59. THE SIMPLE VOLTAIC CELL 
 
 References. r- Adams, 456-463 ; Coleman, 441-447, 453 ; Car. 
 & C., 428-431, 433-435; Ches. G. & T., 376-379; Hoad. Br., 
 346-350; Hoad. EL, 387-39!; Mumper, 251-253, 257; Jack- 
 son, 30-37, 51-52; Mil. & G., 35 I ~35 2 > 375~376; Went. & H., 
 
 271-274. 
 
 Apparatus. Tumbler of dilute sulphuric acid (about i part by 
 volume of concentrated acid to 20 parts of water) ; copper strip ; 
 an amalgamated and an unamalgamated zinc plate, rod, or strip; 
 copper wire ; double connector (if necessary) ; 
 magnetic needle (Fig. 87) ; glass tray or 
 empty tumbler. 
 
 [The tumbler battery shown in Figure 90 
 is most convenient for this exercise ; but a 
 wooden block with slots to support the plates 
 will serve. The wires may be soldered or 
 clamped to the plates ; but soldering will 
 not hold in contact with an amalgamated 
 surface of zinc. A photographer's developing 
 tray of glass is very satisfactory for holding the plates when not in 
 use. It should be large enough to hold the tumbler battery, also.] 
 
 Experiment 113. To study the action of a simple voltaic cell ; 
 and to test the presence of an electric current by its action on a 
 magnetic needle. 
 
 Experimental Work. a. Keep the zinc and copper plates, 
 when not in use, in the glass tray or empty tumbler provided for 
 the purpose ; and keep the amalgamated zinc (the one of lighter 
 
 191 
 
I Q2 
 
 ELECTRICITY 
 
 color) from contact with the other plates, to avoid any amalgama- 
 tion of their surfaces. If the glass tray is large enough, stand the 
 tumbler of acid on it. Avoid getting any of the acid on the table, 
 the clothing, or the fingers. 
 
 Place the unamalgamated zinc plate (the darker one) in the 
 tumbler of acid, and note the size and abundance of the bubbles that 
 form on its surface. What becomes of them ? They are bubbles 
 of hydrogen (a constituent of the acid) which has been displaced 
 by zinc, forming zinc sulphate. The zinc sulphate (a white solid) 
 remains dissolved in the liquid, forming a colorless solution. 
 Remove the zinc, and observe whether it has the appearance of 
 having been partly consumed through previous use. Place it in 
 the tray or empty tumbler. 
 
 b. Place the strip of copper in the acid, and observe whether 
 any hydrogen bubbles form on its surface. Remove the copper, 
 and observe whether it has been partly consumed through pre- 
 vious use. 
 
 When sulphuric acid acts on copper, copper sulphate is formed. 
 This is a blue solid, which would remain dissolved in the liquid 
 and would color it a greenish blue. Do you find the liquid thus 
 colored? What conclusion do you draw from these observations? 
 
 c. Support the copper and the unamalgamated zinc plates in 
 the acid by means of the clamps (or other device), and connect 
 the copper wire with either of them, leaving its other end free. 
 Do bubbles form at either or both plates? Press the free end 
 of the wire against the other plate, and observe whether bubbles 
 form at both plates. Remove the end of the wire, and observe. 
 Repeat till sure of results. Avoid inhaling the unpleasant fumes 
 from the battery. 
 
 The appearance of bubbles on the copper plate is not in itself 
 evidence of chemical action on that plate. If there is such chemi- 
 cal action, the copper plate will be consumed after repeated use, as 
 the zinc is, and the liquid will become greenish blue. Conclusion? 
 
 d. Connect the plates by means of the wire, using the clamps 
 or double connector. (Do not twist wires together. Connections 
 
THE SIMPLE VOLTAIC CELL 
 
 193 
 
 must always be made to the bare wire ; for the current will not 
 pass through the insulation covering the wire.) Extend a portion 
 of the wire parallel to the magnetic needle and several inches 
 above it. Lower the wire without changing its direction (Fig. 91), 
 and note the behavior 
 of the needle as the wire 
 approaches it. Note 
 the effect of holding the 
 wire under the needle. 
 Disconnect the wire 
 from one of the plates, 
 and repeat. Result? 
 
 The deflection of the 
 needle indicates the ex- 
 istence of a magnetic 
 field about the wire, due 
 to an electric current flowing through the wire from the copper 
 to the zinc. (Since copper is not magnetic, it is evident that the 
 wire is not magnetized.) 
 
 e. Connect the plates again, and estimate the relative amounts 
 of hydrogen liberated at the two plates. The hydrogen liberated 
 at the copper plate represents chemical action (of the acid on the 
 zinc plate) which maintains the electric current in the wire. This 
 is useful action, i.e. action by which an electric battery serves its 
 intended purpose. The hydrogen liberated at the zinc plate 
 represents local action (see text), which plays no part in main- 
 taining the current in the wire, and hence results in wasted 
 energy. Estimate the relative amounts of useful and wasteful 
 action. Remove the zinc from the acid. 
 
 Experiment 114. To determine the effect of amalgamating the 
 zinc. 
 
 Experimental Work. a. Place the amalgamated zinc and the 
 copper plates in the acid. With the plates disconnected (circuit 
 open), observe the size and abundance of the bubbles forming on 
 COLEMAN'S NEW MANUAL 13 
 
194 ELECTRICITY 
 
 the zinc plate. Compare with the results obtained with the un- 
 amalgamated zinc in a above. 
 
 b. Connect the plates with the wire, and test the presence of 
 an electric current, as in d above. 
 
 c. Estimate the relative amount of useful and wasteful action, 
 as you did with the unamalgamated zinc in e above. 
 
 Place all the plates on the tray (or in the empty tumbler), being 
 careful not to let the amalgamated zinc touch the other plates. 
 
 EXERCISE 60. THE MAGNETIC FIELD OF A 
 CURRENT 
 
 References. Adams, 472-473, 475 ; Coleman, 453-455 ; Car. 
 & C., 433-434, 452-454; Ches. G. & T., 373; Hoad. Br., 371- 
 373 ; Hoad. EL, 408-409 ; Mumper, 257-258 ; Jackson, 119-124 ; 
 Mil. & G., 355, 394-395 j Went. & H., 278, 281. 
 
 Apparatus. Small compass; wire rectangle (Fig. 92); square 
 of cardboard with slit from edge to hole at center ; electric cell ; 
 tangent galvanometer or a flat, circular coil, with cardboard to fit, 
 as in Figure 93 ; fine iron filings in sifter ; contact key (useful, 
 but may be omitted). 
 
 [The wire rectangle should consist of 8 or 10 turns of No. 16, 
 or 20 to 30 turns of No. 20 to 24 copper wire. The galvanometer 
 should have 15 turns. A flat, circular coil of 15 to 20 turns and 
 12 to 15 cm. in diameter will serve instead. A good dry cell (as 
 the Columbia), a Grenet, or a Fuller cell will furnish sufficient 
 current. These cells all have a very low resistance, which is 
 necessary.] 
 
 CAUTION. Throughout this exercise the circuit should be open 
 when the current is not required, to avoid waste and to reduce 
 polarization. If a Grenet cell is used, the circuit is closed by 
 lowering the zinc into the liquid, and opened by raising it. Keep 
 the zinc raised when the current is not in immediate use. If a dry 
 cell is used and a contact key provided, always include the con- 
 
THE MAGNETIC FIELD OF A CURRENT 
 
 195 
 
 tact key in the circuit. The circuit is opened and closed at the key. 
 If a key is not provided, close the circuit by holding an end of 
 the wire against a post of the cell. If the wire is not fastened, 
 there will be less probability of keeping the circuit closed unnec- 
 essarily. A good dry cell furnishes a large current through cir- 
 cuits of low resistance, as in this exercise, if the service required 
 is brief, with intervals of rest to permit recovery from polarization. 
 
 Experiment 115. To find the shape and direction of the lines 
 of force about a straight conductor carrying a current, and the 
 relation between their direction and the direction of the current. 
 
 Experimental Work. a. Support the cardboard in a horizon- 
 tal position with one side of the wire rectangle passing through 
 the hole at its center, and sprinkle 
 iron filings on it. Connect the rec- 
 tangle with the electric cell, including 
 the contact key in the circuit, if one 
 is provided. 
 
 The current leaves the cell from the 
 carbon terminal and returns through 
 the zinc terminal. Determine from 
 this fact whether the current flows / 
 up or down on the side of the rec- / 
 tangle where the cardboard is placed. 
 (The current flows in the same direc- 
 tion round the rectangle through all the turns composing it.) 
 
 With the circuit closed, tap the cardboard gently until the 
 filings are arranged in distinct lines. Use the compass to deter- 
 mine the direction of the lines of force round the wire (i.e. the 
 direction round the wire in which the north pole of the needle 
 points). Break the circuit. Raise the zinc, if you are using a 
 Grenet cell. Return the filings to the sifter. 
 
 Draw a figure in perspective, showing with arrowheads the 
 direction of the current and the direction of the lines of force. 
 
 Several turns of wire are used in the rectangle merely to increase 
 
 FIG. 92. 
 
196 ELECTRICITY 
 
 the effect of the current. The magnetic field is strengthened in 
 proportion to the number of turns, but is otherwise the same as 
 that about a single wire. 
 
 b. Grasp the wire above the cardboard with the right hand, 
 with the thumb extended (up or down) in the direction in which 
 the current was flowing. Do the fingers point round the wire in 
 the direction of the lines of force (as the north pole of the com- 
 pass needle points) or in the opposite direction ? The relation 
 between the direction of an electric current in a straight con- 
 ductor and the direction of the lines of force round the conductor, 
 when stated with reference to the thumb and fingers of the right 
 hand, is known as the right-hand rule. State it in full. 
 
 c. Close the circuit, and use 
 the compass to determine the 
 direction of the lines of force 
 round the opposite side of the 
 rectangle. Is their direction in 
 agreement with the right-hand 
 rule? 
 
 d. Observe the direction of 
 the north pole of the needle 
 with reference to the wire, when 
 held just above the upper side 
 
 of the rectangle and when held just below it. Repeat with the rec- 
 tangle standing in various directions, including east-west and north- 
 south. Is the behavior of the needle in agreement with the rule ? 
 
 Experiment 116. To study the magnetic field within and 
 about a coil of wire carrying a current, with special reference to 
 the relation between the direction of the current round the coil and 
 the direction of the lines of force at its center. 
 
 Experimental Work. a. Connect the cell to the two binding 
 posts of the galvanometer between which all the turns of the coil 
 are included. Adjust the cardboard to the middle of the coil 
 (Fig. 93), and close the circuit. Sprinkle filings on the card- 
 
THE HELIX, ELECTRO-MAGNET, AND ELECTRIC BELL 197 
 
 board, and tap with the finger. Determine with the compass 
 the direction of the lines of force through the coil. Break 
 the circuit. 
 
 If the direction in which the wire is wound round the coil from 
 one post to the other is open to view, find from the connections 
 with the cell in which direction the current was flowing round the 
 coil. If the winding of the coil is not open to view, find the 
 direction of the current round the coil from the right-hand rule 
 and the known direction of the lines of force. (The rule applies 
 to the parts of a curved conductor as well as to a straight one, as 
 the change in the field caused by the .bending of the conductor 
 does not alter the relation expressed by the rule.) Draw a figure 
 in perspective, showing the direction of the current and the di- 
 rection of the lines of force within and about the coil. Return 
 the filings to the sifter. 
 
 b. As applied to coils, a different statement of the right-hand 
 rule is more convenient. Close the right hand and place it within 
 the coil, with the extended thumb pointing in the direction of the 
 lines of force through the coil. Do the fingers point in the direc- 
 tion of the current round the coil or in the opposite direction? 
 State the rule in full. 
 
 EXERCISE 61. THE HELIX, THE ELECTRO-MAGNET, 
 AND THE ELECTRIC BELL 
 
 References. Adams, 478-483 ; Coleman, 456-458 ; Car. & C., 
 455,457-458,515; Ches. G. & T., 393, 442 ; Hoad. Br., 373-376, 
 418; Hoad. EL, 410-414, 460; Mumper, 262, 266; Jackson, 124- 
 129, 319; Mil. & G., 396-400; Went. & H., 282, 284-285. 
 
 Experiment 117. To study the helix and the electro-magnet: 
 
 Apparatus. Soft iron rod of smaller diameter than a lead pen- 
 cil; 3 m. of small (No. 20 to 24) double-covered, copper wire; 
 coarse iron turnings, tacks or small nails ; magnetic needle ; dry, 
 Grenet, or Fuller cell. 
 
198 ELECTRICITY 
 
 Experimental Work. a. Wrap half the wire round a lead 
 pencil, forming a close coil of one or more layers and about 5 cm. 
 long. Connect the wire with the cell, and find by means of the 
 magnetic needle which end of the coil acts like the north pole 
 of a magnet and which like the south pole. Break the circuit. 
 Trace the direction of the current from the cell, and find which 
 way it flowed round the coil. Grasp the coil in the right hand, 
 with the fingers pointing round it in the direction of the current, 
 and the thumb extended. Does the thumb point in the direction 
 of the north pole or the south pole of the coil? State the rela- 
 tion in full. 
 
 Show that this relation amounts to the same thing as the one 
 obtained with the flat coil in the preceding experiment. 
 
 b. Remove the helix from the pencil, and slip it over the iron 
 rod, leaving about 2 cm. of an end of the rod exposed. With 
 the circuit open, test the rod for magnetization by dipping an 
 end of it into the iron turnings (or tacks). Close the circuit 
 through the helix and repeat the test, noting carefully the quan- 
 tity of turnings that cling to the rod. Observe the behavior of 
 these turnings as you break the circuit. What does this behavior 
 indicate? -The helix and the rod together constitute an electro- 
 magnet. 
 
 c. Wrap the remainder of the wire round the rod, leaving 
 only a few inches at the ends for convenient connection with 
 the cell. (If more convenient, replace the helix on the pencil 
 to complete the winding.) Note the quantity of turnings that 
 the electro-magnet will now pick up when the circuit is closed. 
 How has the strength of the electro-magnet been affected by 
 increasing the number of turns in the helix? Account for this 
 effect. 
 
 d. With the circuit closed, test the polarity of the electro- mag- 
 net by means of the magnetic needle. Do like poles of the elec- 
 tro-magnet and the helix point in the same or in opposite directions? 
 (If necessary, repeat the test of the helix alone.) Leave the cell 
 
 . disconnected. 
 
THE HELIX, ELECTRO-MAGNET, AND ELECTRIC BELL 199 
 
 Experiment 118. To study the construction and action of an 
 electric bell. 
 
 Apparatus. An electric bell with a short piece of rubber tub- 
 ing on the clapper to deaden the sound ; push button ; connect- 
 ing wires ; dry, Leclanche*, or Fuller cell. 
 
 Experimental Work. a. Connect the cell with the bell, 
 including the push button in the circuit. If the push button is 
 not provided, close the circuit by touching an end of the wire to 
 one of the poles of the cell. Ring the bell, and observe the sparks 
 at the point where the spring that is attached to the clapper touches 
 the point of a screw. The current crosses at this point ; hence 
 the circuit is broken whenever the spring leaves the screw. 
 
 Trace the circuit through the bell from either binding post to 
 the other. The metal frame of the bell commonly forms a part 
 of the circuit. Does it in this bell? There are four posts whose 
 attachment to the base must be carefully examined. They are 
 the two binding posts, the post that carries the screw that touches 
 the spring, and the upright to which the clapper is attached. 
 One or more of these will be found to be electrically insulated 
 from the base by means of hard rubber washers. Such a post is 
 not in metallic contact with the base, and the current cannot pass 
 between them. The current is thus compelled to follow a definite 
 course through the. bell. Describe this course, referring to a sim- 
 plified lettered diagram. Mark the insulated posts in this diagram, 
 and represent by a dotted line the part of the circuit formed by 
 the metal base of the bell. 
 
 What wires would you supply to complete the circuit if the base 
 were of wood, and hence could not 'be utilized as a part of the 
 circuit? 
 
 b. Explain the action of the bell. How would the bell behave 
 if the circuit were such as to send the current through the electro- 
 magnet without crossing between the screw and the spring? 
 
 c. Unscrew the cap of the push button, and observe its con- 
 struction. Describe. 
 
200 ELECTRICITY 
 
 EXERCISE 62. THE ELECTRIC TELEGRAPH 
 
 References Adams, 484-486 ; Coleman, 459-463 ; Car. & C., 
 507-514 ; Ches. G. & T., 444-445 ; Hoad. Br., 419-427 ; Hoad. 
 EL, 461-468; Mumper, 264-265 ; Jackson, 290-299; Mil. & G., 
 401-403 ; Went. & H., 286. 
 
 Experiment 1 19. - To set up a short distance telegraph line, and 
 to study the construction and action of the instruments. 
 
 Apparatus. Two sounders ; two keys ; two gravity cells ; con- 
 necting wires. 
 
 Experimental Work. a. Examine the sounder. Send the cur- 
 rent from a gravity cell through it alone.* The lever should be 
 drawn down. Why? If it is not, the spring probably needs 
 adjusting. Does the movement of the lever break the circuit, as 
 it does in the electric bell? 
 
 b. Examine the key. Find the insulation that keeps the circuit 
 open in the key when the switch is open and the lever up. Trace 
 the circuit through the key (i) when the switch is open and the 
 lever depressed ; (2) when the lever is up and the switch closed. 
 Place the key in circuit with the sounder, and operate the sounder 
 by means of it. 
 
 c. Connect up a telegraph line of two stations, having a sounder, 
 a key, and a gravity cell at each station. The cells must be 
 connected so as to act in the same direction round the circuit. 
 Operate the line from each station in turn. Why is one key kept 
 closed by means of the switch while the other key is in use ? 
 
 Make a diagram of the circuit. 
 
 If gravity cells are used, leave them on closed circuit through 
 the sounders when you have finished. 
 
 Experiment 1 20. To set up a long distance telegraph line ; and 
 to study the construction and action of the relay. 
 
 Apparatus. Two sounders ; two keys ; two relays ; four to six 
 gravity cells, as needed ; connecting wires. 
 
THE ELECTRIC TELEGRAPH 
 
 201 
 
 Experimental Work. a. Examine the relay. Find the posts 
 by which the line circuit is connected with the electro-magnet. 
 The local circuit, consisting of the sounder and the local battery, 
 is connected with the other two posts. Trace the local circuit 
 between these posts, and find where and how it is closed and 
 opened by the movement of the vertical lever. 
 
 b. Connect the local circuit with the relay, using only one cell, 
 if this is sufficient to operate the sounder. Operate the sounder 
 by moving the lever of the relay back and forth by hand. How 
 is this possible ? 
 
 SOUNDER 
 
 SOUNDER 
 
 KEY 
 
 -H 
 
 LOCAL BATTERY 
 
 EARTH 
 
 LOCAL BATTERY 
 
 EARTH 
 
 FIG. 94. 
 
 c. Connect up the local circuits at the two stations and the line 
 circuit between them, as shown in Figure 94, using wire for the 
 entire line circuit instead of the earth for the return. Open the 
 switch at one station and operate it, at the same time observing 
 the action of the relay and the sounder, another pupil also ob- 
 serving the action of the instruments at the other station. Now 
 let the other pupil operate the key at his station, both observing 
 as before. 
 
 Make a diagram of the entire telegraph system as you have 
 arranged it. 
 
 If gravity cells are used, leave the switches closed when you 
 have finished ; if other cells are used, disconnect them or leave 
 the switches open. 
 
202 
 
 ELECTRICITY 
 
 EXERCISE 63. THE TANGENT GALVANOMETER; 
 POLARIZING AND NONPOLARIZING OR CONSTANT 
 CELLS 
 
 References Adams, 465-470, 489 ; Coleman, 448-452, 464- 
 
 467; Car. & C., 436-442, 464-466, 471-472; Ches. G. & T., 
 384-386, 400-402; Hoad. Br., 351-355, 382; Hoad. EL, 392- 
 398; Mumper, 254-256, 260, 282 ; Jackson, 40-50, 145 ; Mil. & 
 G., 378-383; Went. & EL, 275-276, 280. 
 
 Principle of the Tangent Galvanometer. In the tangent gal- 
 vanometer (Fig. 95) the current is sent through a vertical circular 
 * coil, consisting of one or more 
 
 turns of insulated wire. A com- 
 pass, with a scale graduated in 
 degrees, is placed at the center 
 of the coil. In Experiment 116 
 it was found that the lines of 
 force due to a current in a cir- 
 cular coil are approximately 
 straight near the center of the 
 coil, and are at right angles to 
 the plane of the coil. The 
 magnetic field of the current is 
 of sensibly uniform strength 
 throughout this small space at 
 the center ; and, in a good 
 FIG. 95. instrument, the compass needle 
 
 is short (not above 2 cm.) in 
 
 order that it may lie wholly in this uniform field, in whatever 
 direction it may turn. The deflection of the needle is found by 
 means of a long pointer, which is attached at right angles to the 
 needle, and turns with it. All parts of the instrument except the 
 needle must be nonmagnetic. The pointer is generally of alu- 
 minum, on account of its lightness. 
 
THE TANGENT GALVANOMETER 
 
 203 
 
 In using a tangent galvanometer it must be placed with the 
 
 plane of its coil in the magnetic meridian ; in which position the 
 
 lines of force of the coil at its center (where 
 
 the needle is) are at right angles to the lines 
 
 of force of the earth's field. When the 
 
 galvanometer is in this adjustment and no 
 
 current is flowing, the earth's field brings 
 
 the needle to rest in the plane of the coil 
 
 (along the line NS in Figure 96). When 
 
 the current is flowing, its magnetic field 
 
 tends to set the needle a't right angles to 
 
 this position. Thus two forces, acting at 
 
 right angles to each other, are exerted on 
 
 each pole of the needle, as shown in the 
 
 figure ; and the needle comes to rest in the R 
 
 direction of the resultant of these forces. 
 
 The deflection of the needle caused by the 
 
 current is the angle NOR. FlG - 9 6 - 
 
 In Figure 97 ON represents the earth's magnetic force (acting 
 
 on the north pole of the compass needle), and OB the magnetic 
 
 force due to a current 
 
 N A X A" in the coil. The de- 
 
 flection in this case is 
 NO A or a. Now, if 
 the current is doubled, 
 its magnetic force is 
 doubled, as represented 
 by O' ; and the de- 
 flection becomes NO A 
 or a'. Similarly, if the 
 
 B 
 
 FIG. 97 . 
 
 B 
 
 B 
 
 current is increased to three times its first strength, its magnetic 
 force is also trebled, as represented by OB 11 , and the deflection 
 becomes NOB" or a". It is evident from the figure that the 
 deflection increases less rapidly than the current (a' <2 a and 
 a" < 3 #) the current is not proportional to the deflection. But 
 
204 ELECTRICITY 
 
 the- tangent 1 of angle a f is twice the tangent of angle a (i.e. 
 NA'/ON= 2 NA/ON), and the tangent of a" is three times the 
 tangent of a (i.e. NA"/ON = 3 NA/ON}. This relation is 
 expressed in general terms as follows : When currents of different 
 strengths are sent through the same number of turns of the coil of a 
 tangent galvanometer, the currents are proportional to the tangents 
 of the angles of deflection which they produce. This is why the 
 instrument is called a tangent galvanometer. 
 
 To express this relation algebraically, let C and O denote the 
 strengths of two currents (measured in amperes), and let a and a' 
 denote the deflections which they produce when sent through the 
 same number of turns of a tangent galvanometer ; then 
 
 C \ O : : tan a : tan a', 
 
 in which "tan a " is the usual abbreviation for "tangent of 
 angle a. 11 
 
 EXAMPLE. A current C causes a deflection of 50, and another 
 current C causes a deflection of 25. It is found from a table of 
 tangents that tan 50 = 1.19 and tan 25 = .466. 
 
 Hence C: C : : 1.19 : .466 ; 
 
 from which C= 2.55 C. 
 
 1 The ratio of one leg of a right triangle to the other is called the tangent of 
 the angle opposite to the first leg. Thus the tangent of angle A (Fig. 98) is 
 
 BCiACor: B'C': AC', BC and B'C 
 being any line perpendicular to either 
 side of the given angle. Since triangles 
 AB C and AB 1 C 1 are similar, the ratios 
 BC/AC&nd B'C'/AC' are equal. It 
 is evident, therefore, that the tangent 
 of an angle is a definite quantity, the 
 value of which depends only upon the 
 size of the angle. Angles are not pro- 
 
 FIG. 98. portional to their tangents, although 
 
 small angles are very nearly so. The 
 
 tangent of any angle from o to 90 may be found from a table of tangents 
 (Appendix, Table XV). 
 
THE TANGENT GALVANOMETER 
 
 205 
 
 A tangent galvanometer having a scale graduated in degrees 
 may be thus used to determine the relative strengths of currents, 
 but it does not give their numerical values. The numerical value 
 (in amperes) may, however, be obtained by multiplying the tangent 
 of the angle of deflection by a constant factor, found by experiment. 
 
 To adjust the Galvanometer. - The galvanometer is turned so 
 that the two ends of the pointer stand at the two zero points of 
 the circular scale. Since the two zero points are in a line per- 
 pendicular to the plane of the coil and the pointer is at right 
 angles to the magnetic needle, this adjustment brings the plane 
 of the coil into the magnetic meridian. . This adjustment must not 
 be disturbed during an experiment. All magnetic substances must 
 be kept at a distance in adjusting and using the galvanometer. 
 
 To find the Deflection. With most instruments it will be 
 found that the two ends of the pointer do not stand exactly at 
 the zero points at the same time, that the two ends of the pointer 
 give slightly different readings for the same deflection, and that 
 when the current is reversed in the coil, causing a deflection in 
 the opposite direction, the two readings of this deflection differ 
 not only from each other, but also from the first two readings. 
 These discrepancies frequently amount to one or two degrees, and 
 are due to various slight imperfections in the construction of the 
 compass, and to an inexact adjustment of the instrument. To 
 find the true value of the deflection due to a given current it is 
 therefore necessary to read the position of both ends of the 
 pointer, then to reverse the current and take two readings as 
 before, and finally to take the average of these four readings as 
 the true deflection. 
 
 Before taking a reading, the cover of the compass should be 
 gently tapped with the finger to overcome friction, which might 
 otherwise hold the needle in a wrong position 
 
 A reading should be taken with one eye closed and the other 
 held vertically above the pointer, otherwise the pointer will not 
 appear in its true position over the scale.' The eye is in the cor- 
 
206 ELECTRICITY 
 
 rect position when the faint image of it, formed by reflection 
 from the glass cover of the compass, is directly under the pointer. 
 If the scale is graduated in single degrees, the reading should be 
 estimated to tenths of a degree ; if graduated in intervals of two de- 
 grees each, the reading should be taken to the nearest half degree. 
 
 Use of Different Numbers of Turns of the Coil. The coil of a 
 tangent galvanometer usually consists of fifteen turns, which are 
 connected in groups of five to binding posts, so that the current 
 can be sent through five,, ten, or all fifteen turns, as desired. 
 The number of turns used in any experiment should be the one 
 giving deflections nearest to 45, for the work is less accurate 
 with either very large or very small deflections. A given error 
 in reading the deflection involves the least error in the computed 
 current when the deflections are between 30 and 60. 
 
 It is important to understand why the deflection varies with the 
 number of turns used. The tangent of the angle of deflection is 
 proportional to the magnetic force of the current ; and, with a 
 current of given strength, this magnetic force is proportional to 
 the number of turns through which the current flows. 
 
 Experiment 121. To determine the decrease of current strength 
 due to polarization in different cells under the same conditions. 
 
 Apparatus. Tangent galvanometer; constant cell (gravity or 
 Daniell) ; simple cell, as in Exercise 59; one or more cells for 
 open circuit work (dry, Leclanche*, Grenet, etc.) ; coil of wire 
 having a resistance of about 3 ohms, with double connectors ; 
 connecting wires; watch or clock with second-hand. 
 
 [A tangent galvanometer to be satisfactory for students' use 
 must conform to the following requirements : coil not less than 
 6 in. in diameter, having 10 or 15 turns in at least three combina- 
 tions (usually 5, 10, and 15); short magnetic needle, with agate 
 cap and light aluminum pointer ; dial not less than 3 hi. in diam- 
 eter, and graduated in single degrees. Such an instrument will 
 cost from $6.00 to $10.00.] 
 
 CAUTION. With considerable resistance in the circuit, the cur- 
 
THE TANGENT GALVANOMETER 2O/ 
 
 rent from a cell is small, and there is but little chemical action in 
 the cell. Under such conditions polarization takes place slowly. 
 When a cell is short-circuited (i.e. placed in a circuit having 
 almost no resistance), the current is as large as the cell is capable 
 of, and polarization takes place rapidly, if at all. When a simple 
 cell is short-circuited, polarization is practically instantaneous. 
 Hence in connecting up the different cells in the following ex- 
 periment, care must be taken to include the resistance coil in the 
 circuit before the circuit is closed. The experiment with the 
 simple cell will fail completely if this precaution is not observed. 
 The copper plate can be depolarized by heating it in a Bunsen 
 flame. Wiping it with a cloth is not effective. 
 
 Experimental Work. Adjust the galvanometer. Connect the 
 simple cell with ten turns of the galvanometer coil, including the 
 resistance coil (3 ohms) in the circuit. Read the deflection in- 
 dicated by one end of the pointer as quickly as possible; and 
 after one minute (by a clock or watch), read the deflection again, 
 meanwhile observing the behavior of the needle. Remember 
 always to tap the cover of the compass lightly with the finger be- 
 fore taking a reading. (In this exercise it is sufficiently accurate 
 to take only one reading of a deflection, always reading the same 
 end of the pointer, with the deflection in the same direction.) 
 
 Immediately after taking the second reading, bring the binding 
 screws (double connectors) at the ends of the resistance coil to- 
 gether, and hold them in firm contact for one minute. This 
 throws the resistance coil out of the circuit, and short-circuits 
 the cell. Polarization, if not already completed before the short- 
 circuiting, will now take place very rapidly (for reasons stated in 
 the caution above). After one minute separate the binding screws, 
 thus restoring the circuit as at first, and read the deflection. 
 Record as indicated below. Remove the plates from the cell. 
 
 Repeat the above experiment with each of the cells provided, 
 using in each case the number of turns of the galvanometer coil 
 that will give a deflection between 30 and 60, or as nearly 
 
208 
 
 ELECTRICITY 
 
 within these limits as possible. With a dry or a Grenet cell, try 
 5 turns first; with a Leclanche" cell, 10 turns; with a gravity or 
 a Daniell cell, 15 turns. 
 
 Data and Computations. Record observations and computa- 
 tions as follows : 
 
 
 SIMPLE 
 
 GRAVITY 
 
 DRY 
 
 ETC. 
 
 
 
 
 
 
 No. of turns of galvanometer coil used 
 
 Deflection on closing circuit through resist- 
 ance coil of 3 ohms .... 
 
 Deflection, same circuit, after it has been 
 
 
 
 
 
 
 
 
 
 Deflection, same circuit, after cell has been 
 on short circuit I min. 
 
 
 
 
 
 
 
 
 
 COMPUTATIONS 
 
 
 
 
 
 Tangent of first deflection 
 Tangent of second deflection . . . 
 Tangent of third deflection 
 
 Percentage of decrease of current in I min. 
 through resistance coil 
 
 Percentage of decrease of current in I min. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Discussion. i. Name the cells used in the order of rapidity 
 v/ith which they polarize. 
 
 2. Account for the positions that the simple cell and the 
 gravity (or Daniell) cell occupy in this list. 
 
 3. With which cells is the decrease of current greater on short 
 circuit than with the resistance coil in the circuit? Why? With 
 which cells (if any) is it less, and why? 
 
 4. What means are employed in the different cells to reduce 
 or prevent polarization ? (See text.) 
 
MEASUREMENT OF RESISTANCE BY SUBSTITUTION 2OQ 
 
 EXERCISE 64. MEASUREMENT OF RESISTANCE BY 
 SUBSTITUTION; THE LAWS OF RESISTANCE 1 
 
 References Adams, 492-495; Coleman, 468-471; Car. & 
 
 C., 460-462, 464-466; Ches. G. & T., 406-407, 409-410; 
 Hoad. Br., 377-380, 388; Hoad. El. 421-424; Mumper, 275- 
 277 ; Jackson, 91-101, 160-161 ; Mil. & G., 363-365 ; Went. & 
 H., 290, 294. 
 
 Method. The resistance to be measured is connected in circuit 
 with the galvanometer and a constant cell, and the deflection 
 read as accurately as possible. The unknown resistance is then 
 removed from the circuit, and a resistance box (Fig. 99) put 
 in its place. Different resist- 
 ances are introduced into the 
 circuit through the box, by 
 removing plugs, till the de- 
 flection of the galvanometer 
 is the same as before. The 
 sum of the resistances of the 
 box then included in the cir- 
 cuit is equal to the unknown 
 resistance. For the equal 
 deflections of the galvanom- 
 eter indicate that the same 
 amount of current flows through the circuit in the two cases, 
 and the cell has a constant E. M. F. ; hence, according to Ohm's 
 Law, the total resistance of the circuit must be the same in the 
 two cases (R = E/C)- y hence, further, the resistance introduced 
 from the box must be equal to the unknown resistance, no change 
 having been made in the remainder of the circuit. The two 
 deflections being equal and in the same direction, a single reading 
 (of the same end of the pointer) for each deflection is sufficient. 
 
 FIG. 99. 
 
 1 Either experiment of this exercise may be taken, and the other omitted. 
 COLEMAN'S NEW MANUAL 14 
 
210 ELECTRICITY 
 
 Resistances obtained by this method may be in error by as 
 much as 10%, even with careful work. This inaccuracy is due 
 to the fact that, with a resistance of several ohms already in 
 the circuit, a change of a few tenths of an ohm causes hardly a 
 perceptible change in the deflection. For example, the deflec- 
 tion may be right, as nearly as it can be read, with a resistance 
 of 3 ohms introduced in the box, while an additional resistance 
 of .2 ohm causes no perceptible change. Consequently, the 
 true value of the resistance may be 3 ohms, 3.2 ohms, or anything 
 between, making a possible error of about 7%. 
 
 Use of the Resistance Box The resistance of the row of brass 
 plugs and blocks on the resistance box is practically zero ; but 
 wherever a plug is removed, the resistance of the coil that bridges 
 
 the gap (Fig. 100) is introduced in 
 the circuit. The amount of this re- 
 sistance is marked on the top of 
 the box. When two or more plugs 
 are removed, the resistance intro- 
 duced is the sum of the resistances 
 of the coils where the plugs are out. 
 In finding the required resistance, 
 
 the coils are tried in order from larger to smaller, as weights are 
 tried in weighing. 
 
 Before using a resistance box, turn each plug in its hole, while 
 exerting a moderate pressure. This insures good electrical con- 
 nection between the plugs and the blocks, which is necessary, as 
 the resistance at the points of contact between a loose plug and the 
 adjacent blocks will make a set of measurements wholly unreliable. 
 A switch resistance box consists of three series of resistances, 
 with a switch for each series. A resistance is introduced by turn- 
 ing a switch so as to rest upon the contact block beside which the 
 desired number of ohms is marked. The total resistance intro- 
 duced is the sum of the numbers at the three contact blocks with 
 which the switches connect. 
 
MEASUREMENT OF RESISTANCE BY SUBSTITUTION 211 
 
 Experiment 122. To measure the resistance of a wire by the 
 method of substitution. 
 
 Apparatus A low resistance galvanometer; constant cell; 
 resistance box ; two coils of unknown resistance ; connecting 
 wires. 
 
 [Any low-resistance galvanometer that gives a suitable deflec- 
 tion may be used instead of a tangent instrument. An error 
 of less than 15% or 20% is not to be expected, however, unless 
 the dial is graduated in single degrees. With a gravity or a 
 Daniell cell and a tangent galvanometer having a coil of 15 turns, 
 the best results are obtained with resistance of 2 to 6 ohms.] 
 
 Experimental Work Adjust the galvanometer. Complete 
 
 the circuit through the cell, the galvanometer, and one of the 
 unknown resistances. Use the number of turns of the galva- 
 nometer coil which gives a deflection nearest to 45. Read the 
 deflection indicated by one end of the pointer, estimating tenths 
 of a degree as accurately as possible. Substitute the resistance 
 box for the unknown resistance, and adjust the resistance in 
 it till the deflection (of the same end of the pointer in the 
 same direction) is exactly the same as before. If the required 
 resistance is uncertain by one or more tenths of an ohm, find 
 and record the least and the greatest resistance in the box that 
 give the correct deflection, and take their average as the value 
 of the unknown resistance. If the deflection is seen to vary when 
 no change has been made in the resistance of the circuit, the cell 
 is at fault and dependable results are impossible. Record as indi- 
 cated below. 
 
 Measure in the same way the other unknown resistance. 
 
 Find in the same way the resistance of the two wires when 
 placed together in the circuit so that the whole current passes 
 through one after the other. (This is called connecting in series.) 
 The resistance of the two wires in series is the sum of their 
 separate resistances. This will serve as a test of the accuracy of 
 your results. 
 
2 1 2 ELECTRICITY 
 
 Data and Computations. 
 
 
 FIRST 
 WIRE 
 
 SECOND 
 WIRE 
 
 BOTH IN 
 SERIES 
 
 Deflection 
 Least resistance in box giving an equal deflection 
 
 Greatest resistance in box giving an equal 
 deflection ....;.. 
 
 Average resistance in box giving an equal de- 
 flection ( = resistance of wire) . 
 
 
 
 
 
 
 
 Sum of the separate resistances of wires 
 Percentage of difference between sum of the separate 
 resistances and resistance of both in series 
 
 = ohms. 
 
 Experiment 123. To study the relation between the resistance 
 of a wire and its length and diameter, and to determine the relative 
 resistance of German silver or other wire and copper wire of the 
 same length and diameter. 
 
 Apparatus. Low-resistance galvanometer; constant cell; re- 
 sistance box ; three pieces of wire of high specific resistance, of 
 equal length, and two of them of the same diameter ; copper wire 
 of same diameter as one of the others, and long enough to have a 
 nearly equal resistance. 
 
 [Two pieces, i m. each, of No. 26 and i m. of No. 30, all of 
 German silver, and 15 m. of insulated copper wire of either num- 
 ber are suitable. They may be in coils or stretched on a board. 
 If stretched, the German silver wires may be bare or covered. 
 See suggestions under Experiment 129 for making a piece of 
 apparatus (Fig. 101) especially suited to both of these experi- 
 ments.] 
 
 Experimental Work. Following the directions of the preced- 
 ing experiment, find the resistance (a) of one of the two larger 
 high-resistance wires ; () of the two larger high- resistance wires 
 
THE RESISTANCE OF A CELL 
 
 213 
 
 (of the same diameter), placed together in the circuit so that the 
 whole current passes through one after the other ; (c) of the 
 smaller high-resistance wire ; (d) of the copper wire. In each 
 case find the least and the greatest resistance in the box that give 
 the correct deflection, but record only their average. 
 
 Measure (unless given), and record the length and diameter of 
 each wire. 
 
 If a gravity cell is provided for the work, leave it on a closed 
 circuit through the resistance box, with the 2o-ohm coil in the 
 circuit. (The small current in such a circuit prevents the mixing 
 of the two liquids by diffusion.) 
 
 Data. Record as follows : 
 
 
 XlND OF 
 
 s WIRE 
 
 LENGTH OF 
 WIRE 
 
 DIAMETER OF 
 WIRE 
 
 DEFLECTION OF 
 GALVANOMETER 
 
 RESISTANCE OF 
 WIRE 
 
 a 
 
 
 
 
 
 
 
 
 
 
 
 b 
 
 
 
 
 
 
 
 
 
 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 d 
 
 
 
 
 
 
 
 
 
 
 
 Discussion. i. How nearly are the resistances found in a and 
 b proportional to the lengths of the wires (considering the two 
 wires in series in b as one wire) ? 
 
 2. How nearly are the resistances found in a and c inversely 
 proportional to the squares of the diameters of the wires? 
 
 3. Compute the ratio of the resistance of the high-resistance 
 wire to the resistance of an equal length of the copper wire of the 
 same diameter. 
 
 EXERCISE 65. THE RESISTANCE OF A CELL 
 
 Principle of the Method. Let C (amperes) denote the current 
 which an electro- motive force E (volts) maintains in a circuit 
 whose total resistance is R (ohms), and C denote the current 
 
214 
 
 ELECTRICITY 
 
 which the same electro-motive force maintains in a circuit whose 
 resistance is R' ; then, by Ohm's Law, 
 
 E = CR = C'R', 
 from which we have the proportion, 
 
 C : C : : R 1 : R. (E constant.) 
 
 That is, the current due to a given E. M. F. is inversely pro- 
 portional to the total resistance of the circuit (including the resist- 
 ance of the battery). 
 
 In the following experiment a constant cell (E constant) is 
 connected in circuit with a tangent galvanometer and a resistance 
 box. Let r denote the resistance of the cell, g the resistance of 
 the galvanometer coil, and R and R 1 resistances introduced in 
 the box at different times. The resistance of the connecting 
 wires is disregarded. The total resistance of the circuit will then 
 be r -f- g -|- R in the first case, and r + g 4- R' in the second. 
 Letting C and C' denote the currents maintained through these 
 resistances respectively, the above proportion becomes 
 
 C : C : : (r + g + R') : (r + g + R). 
 
 If a and a' denote the deflections caused by the currents C and 
 C respectively, then 
 
 C : C : : tan a : tan a\ (Exercise 63.) 
 From these two proportions we have 
 
 (r + g + R 1 ) : (r + g + R) : : tan a : tan a\ 
 
 That is, with a constant E. M. F., the total resistance of the 
 circuit is inversely proportional to the tangent of the angle of 
 deflection. 
 
 Experiment 1 24. To find the resistance of a constant cell by 
 the method of reduced deflection. 
 
 Apparatus. A tangent galvanometer of low resistance ; con- 
 stant cell (gravity or Daniell) ; resistance box ; commutator 
 (useful but not essential) ; connecting wires. 
 
THE RESISTANCE OF A CELL 
 
 215 
 
 Experimental Work. Adjust the galvanometer, and connect 
 it in circuit with the cell and the resistance box. Include the 
 commutator in the circuit, if one is provided. Connect with the 
 number of turns of the galvanometer that gives a deflection 
 nearest to 50 or 60 when no resistance is introduced in the box, 
 and use only this connection throughout the experiment. 
 
 With no resistance introduced in the box (R = o), read the 
 position of both ends of the pointer as accurately as possible ; re- 
 verse the current, and read again. The average of these four 
 deflections is taken as the true deflection a. 
 
 Repeat with a resistance of 2 ohms in the box (R 1 = 2), and 
 again with 4 ohms in the box (R" = 4). 
 
 Record the resistance of the number of turns of the galvanom- 
 eter used, as marked on the instrument or given by the teacher. 
 
 Data and Computations. 
 
 Resistance, g, of the number of turns of the 
 
 galvanometer coil used = ohms. 
 
 Box 
 RESISTANCE 
 
 DEFLECTION OF POINTER 
 
 AVERAGE 
 DEFLECTION 
 
 TAN a 
 
 E. end 
 
 W. end 
 
 E. end 
 
 W. end 
 
 R =o 
 
 -N. 
 
 S. 
 
 - o. 
 
 N. 
 
 a = 
 
 
 
 R' =2 
 
 
 
 
 
 
 
 
 
 a' = 
 
 
 
 R" = 4 
 
 
 
 
 
 
 
 
 
 a" = 
 
 
 
 a. Compute the resistance r of the cell from the values of a, a', 
 R, and R\ substituting in the proportion 
 
 (r + g + R')i (r+g+R) : : tan a : tan a'. 
 
 b. Compute r from a, a", R, and R 11 . 
 
 c. Compute r from a', a", R', and R". 
 
 d. With careful work these three independently determined 
 values of r should differ by less than 6 %. Find the percentage 
 of difference between the greatest and the least of them. 
 
2I 6 ELECTRICITY 
 
 EXERCISE 66. THE ELECTRO-MOTIVE FORCE OF 
 CELLS 1 
 
 References. Adams, 495 ; Coleman, 472-478 ; Car. & C., 465, 
 478; Ches. G. &T., 390-392,404; Mumper, 278-279, 285; Jack- 
 son, 106-107, 182 ; Mil. & G., 359-362 ; Went. & H., 292, 296. 
 
 Experiment 125. To find the E. M. F. of cells with a tangent 
 galvanometer having a high resistance. 
 
 Apparatus. A tangent galvanometer of high resistance ; grav- 
 ity or Daniell cell ; one or more cells for the measurement of 
 their E. M. F. ; commutator (useful but not essential). 
 
 [The galvanometer must have a resistance of at least 100 ohms ; 
 200 ohms or more is better. The E. M. F. of the gravity or 
 Daniell cell should be found with a voltmeter from day to day, 
 and marked on the cell.] 
 
 The Principle of the Method. The fall of potential in the dif- 
 ferent parts of a circuit (including the liquid of the cell) is every- 
 where proportional to the resistance of the different parts. For 
 example, if the resistance of the cell is i ohm and that of the ex- 
 ternal circuit 99 ohms, the fall of potential in the liquid of the cell 
 from the zinc to the carbon plate is i % of the E. M. F. of the 
 cell, and the fall of potential in the external circuit is 99 % of it. 
 There is, therefore, an error of i % in assuming that the fall of 
 potential in the external circuit is equal to the E. M. F. of the 
 cell. But if the resistance of the external circuit is 999 ohms, 
 the error in this assumption is only .1 %. 
 
 It will be seen from the above that, if the coil of a tangent gal- 
 vanometer has a resistance of at least two or three hundred ohms, 
 the potential difference between its terminals when connected 
 with a cell will be sensibly equal to the E. M. F. of the cell, and 
 the tangents of the angles of deflection will be proportional to this 
 
 1 It is intended that only one of the experiments of this exercise be taken, 
 the choice depending upon the laboratory equipment. 
 
THE ELECTRO-MOTIVE FORCE OF CELLS 
 
 E. M. F. If a denotes the deflection when the galvanometer is 
 connected with a cell whose E. M. F. is E, and a 1 the deflection 
 when it is connected with a cell whose E. M. F. is E 1 , then 1 
 
 E : E [ : : tan a : tan a'. (Resistance constant.) 
 
 Experimental Work. Adjust the galvanometer, and connect 
 with the gravity or the Daniell cell. Read both ends of the 
 pointer, reverse the current, and read again. Record the E. M F. 
 of the cell, as marked on it by the instructor. 
 
 Connect each of the cells in turn with the galvanometer, and 
 read the deflections as before. 
 
 Data and Computations. Compute the E. M. F. of each cell 
 from the formula 
 
 :E':: tan a : tan a 1 , 
 
 in which E and a refer to the gravity or the Daniell cell, and 
 E 1 and a? to each of the other cells in turn. Record as 
 follows : 
 
 
 DEFLECTION 
 
 
 
 
 KIND OF CELL 
 
 
 Av. DEFLEC- 
 TION a 
 
 TAN a 
 
 E. M. F. 
 
 
 
 
 E. end 
 
 W. end 
 
 
 
 
 Gravity 
 
 N. 
 
 s 
 
 
 
 
 
 
 g 
 
 N. 
 
 
 
 
 
 (given) 
 
 Leclanche 
 
 N. 
 
 g 
 
 
 
 
 
 S. 
 
 N. 
 
 
 
 
 
 
 
 Etc. 
 
 
 
 
 
 
 
 
 
 
 
 1 This relation does not hold with a low-resistance galvanometer, for in 
 that case the resistance of the cells would be a large part of the whole resist- 
 ance of the circuit, and the currents (and the tangents of the angles of deflec- 
 tion) would be as largely affected by the unequal resistances of the cells as by 
 their unequal electro-motive forces. 
 
2 1 8 ELECTRICITY 
 
 Experiment 126. To find the E. M. F. of cells by the method 
 of equal deflections. 
 
 Apparatus. A high-resistance galvanometer (not necessarily 
 a tangent instrument) with its resistance marked on it ; resistance 
 box ; gravity or Daniell cell, with its E. M. F. marked on it ; one 
 or more cells for the measurement of their E. M. F. 
 
 [Any simple galvanoscope will serve, provided it has a sufficient 
 number of turns to give a suitable deflection in a circuit with one 
 cell and a total resistance of 200 ohms or more.] 
 
 Principle of the Method. Let E denote the E. M. F. that 
 maintains a current C in a circuit whose total resistance is R, and 
 E' the E. M. F. that maintains an equal current through a total 
 resistance R' ; then, by Ohm's Law, 
 
 from which E : E 1 : : R : R 1 . (Current constant.) 
 
 That is, the E. M. F. necessary to maintain a given current is 
 proportional to the total resistance of the circuit. 
 
 Experimental Work. Adjust the galvanometer and connect it 
 in circuit with the gravity or Daniell cell and the resistance box ; 
 but before closing the circuit introduce a high resistance in the box, 
 to avoid possible damage to the galvanometer by too large a cur- 
 rent. Adjust the resistance in the box so as to make the deflec- 
 tion between 40 and 50, and read one end of the pointer as 
 accurately as possible. Record the deflection, the resistance R 
 introduced in the box, and the resistance g of the galvanometer 
 coil. If R+g is greater than TOO ohms, the resistance of the 
 cell may be disregarded ; but its approximate value, if known, 
 may be added as a part of the resistance of the circuit. 
 
 Substitute each of the cells in turn for the one just used, and 
 repeat the above work, in each case adjusting the resistance R in 
 the box so that the deflection of the same end of the pointer in 
 the same direction is exactly equal to the first deflection. 
 
THE ELECTRO-MOTIVE FORCE OF CELLS 
 
 219 
 
 Data and Computations. Let E denote the known E. M. F. of 
 the gravity cell and R the box resistance used with it, ' the E.M. F. 
 of any one of the other cells, and R 1 the box resistance used with 
 it. The currents were equal (how do we know?) ; hence, dis- 
 regarding the resistances of the cells, 
 
 E:E'::R+g:R ! +g. (Why?) 
 
 From this proportion compute the E. M. F. of each of the cells 
 used. Record as follows : 
 
 Deflection for each adjustment = 
 Resistance of galvanometer coil g = 
 
 ohms. 
 
 KIND OF CELL 
 
 Box 
 
 RESISTANCE R 
 
 R+g 
 
 E. M. F. 
 
 Gravity 
 
 ohms 
 
 ohms 
 
 volts (given) 
 
 Etc. 
 
 
 
 
 
 
 
 Experiment 127. To find the E. M. F. of cells by the method 
 of reduced deflection. 
 
 Apparatus. Galvanometer; resistance box; gravity or Dan- 
 iell cell with its E. M. F. marked on it; one or more cells for the 
 measurement of their E. M. F. 
 
 [Almost any galvanometer will serve, of either low or high re- 
 sistance. A tangent galvanometer with a 15 -turn coil is as 
 good as any. A very sensitive galvanometer, as an astatic or a 
 D'Arsonval, requires the use of a shunt or of very high resistances.] 
 
 Principle of the Method. Let C denote the current that an 
 E. M. F. E maintains through a total resistance R, and Q the 
 current when the resistance is increased by R ; t.e. 
 
 C=- and Ci 
 R 
 
220 ELECTRICITY 
 
 Let R* denote the total resistance through which an E. M. F. 
 ' maintains the first current C, and R the added resistance 
 necessary to reduce the current to Ci ; i.e. 
 
 and 
 
 Hence C= = ' 
 
 <p. P\ f 
 
 (-"+-"1) (f 
 From (i) = . (3) 
 
 Fro m(2 ) 
 
 Subtracting the members of (3) from the corresponding mem- 
 bers of (4) we have 
 
 Ri = R 
 E E' 9 
 
 or E : E 1 : : ^ : Rj. 
 
 That is, the two electro- motive forces are proportional to the 
 added resistances which reduce the equal currents equally. 
 
 Experimental Work. Adjust the galvanometer, and connect 
 all the turns of its coil in circuit with the gravity or Daniell cell 
 and the resistance box. If necessary, introduce resistance in the 
 box to reduce the deflection to about 50. Read one end of the 
 pointer as accurately as possible. Record the deflection and 
 the box resistance. Increase the box resistance till the deflection 
 is reduced nearly one half. Record the exact deflection and the 
 box resistance. 
 
 Substitute each of the cells in turn for the one just used ; and 
 in each case adjust the box resistance so as to give first and sec- 
 ond deflections (of the same end of the pointer in the same direc- 
 tion) exactly equal to the two deflections in the first case. 
 Record the box resistances. 
 
ELECTRO-MOTIVE FORCE AND RESISTANCE OF A CELL 221 
 
 Data and Computations. Compute the E. M. F. of each cell 
 from the proportion 
 
 in which E denotes the E. M. F. of the gravity cell and ' the 
 E. M. F. of any other cell used, R l the added resistance causing 
 the reduced deflection with the gravity cell, and RJ the added 
 resistance with the other cell. The resistances of the galva- 
 nometer and of the different cells are not required. Record as 
 follows : 
 
 First deflection (for all cells) = 
 Second deflection (for all cells) = 
 
 KIND OF CELL 
 
 Box RESISTANCE 
 
 ADDED RESIST- 
 ANCE, R l 
 
 E. M. F. 
 
 ISt 
 
 2 d 
 
 Gravity 
 
 ohms 
 
 ohms 
 
 ohms 
 
 volts (given) 
 
 Etc. 
 
 
 
 
 
 
 
 
 
 EXERCISE 67. THE ELECTRO-MOTIVE FORCE AND 
 RESISTANCE OF A CELL 
 
 References. Adams, 495-496 ; Coleman, 472-478 ; Car. & C., 
 465,474,478; Ches. G. & T., 390-392, 403-404; Hoad. Br., 
 386, 39<>> 393-394; Hoad. EL, 430, 436; Mumper, 273, 278- 
 279, 285 ; Jackson, 171, 175, 182; Mil. & G., 358-362, 369-370; 
 Went. & H., 292, 296. 
 
 Experiment 128. To find the E. M. F. and the resistance of a 
 cell by means of a voltmeter and an ammeter. 
 
 Apparatus. Voltmeter; ammeter; cells of different kinds; 
 short connecting wires. 
 
222 
 
 ELECTRICITY 
 
 Experimental Work. Find the E. M. F. of a cell by connect- 
 ing its poles directly to the voltmeter ; then connect the cell with 
 the ammeter, to determine the current that the cell gives when 
 short-circuited (the resistance of the ammeter being negligible). 
 Repeat with each of the cells provided, always connecting with 
 the voltmeter first, as most of the cells will begin rapidly to polar- 
 ize when connected with the ammeter, thus diminishing their 
 E. M. F. 
 
 Data and Computations. When a cell is connected with the 
 ammeter, the external resistance may be disregarded, with very 
 little error; i.e. the resistance of the cell may be taken as the 
 whole resistance of the circuit. Upon this assumption, the resist- 
 ance of the cell is found by dividing the E. M. F. of the cell by 
 the reading of the ammeter (R=E j C). Record as follows : 
 
 KIND OF CELL 
 
 E. M. F. OF CELL 
 
 CURRENT THROUGH 
 AMMETER 
 
 RESISTANCE OF 
 CELL, R = E/ C. 
 
 
 volts 
 
 amperes 
 
 ohms 
 
 EXERCISE 68. FALL OF POTENTIAL ALONG A 
 CONDUCTOR 
 
 References. Adams, 497; Coleman, 475-478; Car. & C., 
 478 ; Ches. G. & T., 390-392, 404 ; Hoad. Br., 386, 394 ; Hoad. 
 El., 430, 433 ; Mumper, 285 ; Jackson, 106-107, 171, 175, 182 ; 
 Mil. & G., 359-362 ; Went. & H., 292, 296. 
 
 Experiment 129. To study the relation between the fall of 
 potential in the different parts of a circuit and the resistances of 
 those parts. 
 
FALL OF POTENTIAL ALONG A CONDUCTOR 
 
 223 
 
 Apparatus. Tangent galvanometer of high resistance, or volt- 
 meter ; board with stretched wires ; one or more cells, as needed ; 
 connecting wires. 
 
 [The directions for the experiment are adapted to the tangent 
 galvanometer. A voltmeter simplifies the work, but the smallest 
 divisions of the scale must not be greater than . i volt. A d'Ar- 
 sonval galvanometer may be used, if provided with a suitable 
 shunt to reduce the deflections. Three German silver wires, 
 two of No. 26 and one of No. 30, each stretched between 
 binding posts i m. apart, and 15 m. of No. 30 insulated copper 
 wire, also connected with a pair of binding posts (Fig. 101), are 
 
 1 
 
 U 
 
 o 
 
 
 o 
 
 
 
 
 
 FIG. 101. 
 
 suitable for this experiment and also for Experiment 123. The 
 No. 30 German silver wire must be bare, and should be stretched 
 over a meter stick, for convenience in measuring off lengths. The 
 distances between the binding posts can be reduced to 50 cm. 
 by using wire having a specific resistance of 40 to 50 instead of 
 German silver ; and with such wire somewhat larger sizes can be 
 used, giving greater durability. It is only necessary that the resist- 
 ances of the wires be large enough to give good results (2 to 5 
 ohms each), and that the copper wire be of the same diameter as 
 one of the others.] 
 
 Experimental Work. a. Connect the cell (or two or more 
 cells in series) with the binding posts a and b (Fig. 101), between 
 which the smaller high-resistance wire is stretched. Connect one 
 
224 
 
 ELECTRICITY 
 
 terminal of the high-resistance coil of the galvanometer (or the 
 voltmeter) with the post a. Connect a short wire with the other 
 terminal of the galvanometer, and press the other end of this wire 
 firmly down upon the stretched wire exactly 25 cm. from a. 
 Read the deflection indicated by both ends of the pointer. Re- 
 peat, taking the point of contact c 50 cm., 75 cm., and 100 cm. 
 from a. (If the length of the wire is 50 cm., reduce each of these 
 distances one half.) 
 
 Reverse the connections with the galvanometer, so that the 
 deflections will be in the opposite direction, and repeat the read- 
 ings for each of the above adjustments. The average of the four 
 
 ^n 
 
 -n 
 
 
 
 
 
 readings for each adjustment is taken as the true deflection. If a 
 voltmeter is used, a single reading for each adjustment is all that 
 is required. 
 
 b. Connect the battery in series with the stretched copper 
 wire, one of the larger high-resistance wires, and the smaller high- 
 resistance wire, as shown in Figure 102, using short connecting 
 wires between the posts. Find the deflection of the galvanometer 
 when connected with the binding posts at the ends of the smaller 
 high-resistance wire (see figure). Reverse the current through 
 the galvanometer, and take the average of the four readings as 
 the true deflection. 
 
FALL OF POTENTIAL ALONG A CONDUCTOR 225 
 
 In the same way find the deflection of the galvanometer when 
 connected with the ends of the larger high-resistance wire (mak- 
 ing no change in the main circuit), and when connected with the 
 ends of the copper wire. 
 
 Record the lengths and diameters of the different wires. 
 
 Data and Computations. Let /denote the length of stretched 
 wire between the terminals of the galvanometer in Part a of the 
 experiment. Record as follows : 
 
 PART a 
 
 
 DEFLECTION 
 
 
 
 
 I 
 
 
 Av. DEFLEC- 
 TION a 
 
 TAN a 
 
 /-T-TAN a 
 
 
 
 
 E. end 
 
 W. end 
 
 
 
 
 25 cm. 
 
 N. 
 
 S. 
 
 
 
 
 
 CJ 
 
 "NT 
 
 
 
 
 50 cm. 
 
 N. 
 
 S. 
 
 
 
 
 
 S. 
 
 -N. 
 
 
 
 
 
 
 
 75 cm. 
 
 N. 
 
 S. 
 
 
 
 
 
 S. 
 
 N. 
 
 
 
 
 
 
 
 100 cm. 
 
 JsJ 
 
 S. 
 
 
 
 
 
 S. 
 
 
 
 
 
 
 
 
 
 PART b 
 
 STRETCHED WIRE BETWEEN 
 GALVANOMETER TERMINALS 
 
 DEFLECTION 
 
 Av. DEFLEC- 
 TION a 
 
 TAN* 
 
 Kind 
 
 Length 
 
 Diameter 
 
 E. end 
 
 W. end 
 
 
 
 cm. 
 
 cm. 
 
 N. 
 
 S. 
 
 
 
 
 
 
 S. 
 
 N. 
 
 
 
 
 
 
 
 
 
 
 
 N. 
 
 S. 
 
 
 
 
 
 
 S. 
 
 N. 
 
 
 
 , 
 
 Copper 
 
 
 
 
 
 N. 
 
 S. 
 
 
 
 
 
 
 S. 
 
 N. 
 
 
 
 
 COLEMAN'S NEW MANUAL 15 
 
226 ELECTRICITY 
 
 Discussion. i. The resistance of any portion of the stretched 
 wire is proportional to its length ; the fall of potential in any 
 portion is proportional to its resistance (Ohm's Law as applied to 
 the parts of a circuit) ; and the potential difference between the 
 terminals of the galvanometer (i.e. the fall of potential in the part 
 of the stretched wire between these terminals) is proportional to 
 the tangent of the angle of deflection (why?) ; hence the lengths 
 of the parts of the stretched wire between the terminals of the 
 galvanometer in Part a should be proportional to the tangents of 
 the angles of deflection (i.e. the quotient /-=- tan a should be con- 
 stant). Within what percentage of difference do you find this 
 relation to hold? 
 
 2. Do the deflections of the galvanometer indicate equal or 
 unequal fall of potential in the whole length of the smaller high- 
 resistance wire in Parts a and bl How do you account for this? 
 
 3. From the measured diameters of the two high-resistance 
 wires, compute the ratio of the resistances of i m. of each. 
 Compute the ratio of the fall of potential in one to the fall of 
 potential in the other in Part b (given by the ratio of the tangents 
 df the deflections). How should these ratios compare, and why? 
 Is the fall of potential more or less rapid in the larger wire than 
 in the smaller? Why? 
 
 4. Assuming Ohm's Law, find, from the data obtained in Part b 
 with the copper wire and the high-resistance wire of the same 
 diameter, the ratio of the resistance of the latter to the resistance 
 of an equal length of the copper wire. This ratio is the specific 
 resistance of the high-resistance wire referred to copper. 
 
 EXERCISE 69. MEASUREMENT OF RESISTANCE WITH 
 THE WHEATSTONE BRIDGE 
 
 References : The Wheatstone Bridge 
 
 Adams, 498; Car. & C., 476-479; Ches. G. & T., 412; 
 Hoad. Br., 389; Hoad. EL, 434; Mumper, 284-286; Jackson, 
 106, 162-168; Went. & H., 291-293. 
 
THE WHEATSTONE BRIDGE 227 
 
 The d'Arsonval Galvanometer 
 
 Adams, 490; Coleman, 484; Car. & C., 473; Ches. G. & T., 
 405 ; Hoad. Br., 385 ; Hoad. EL, 429 ; Mumper, 261 ; Jackson^ 
 151-152; Mil. & G., 356; Went. & H., 280. 
 
 The Astatic Galvanometer 
 
 Coleman, 483 ; Hoad. Br., 383 ; Hoad. EL, 427 ; Jackson, 149; 
 Went. & H., 280. 
 
 Principle of the Bridge. When two points, A and B (Fig. 103), 
 on an electric circuit are connected by two branches, as AMB and 
 ANB, the fall of potential 
 is the same in both branches, Jv; 
 
 since in both it is the po- A^/^ ^/) "^^-5. 
 
 tential difference between 
 the points A and B. Let 
 N be the point in one 
 branch whose potential is 
 the same as that of a given 
 point M in the other 
 branch. Then the fall of 
 
 potential in AM is equal to that in AN, and the fall in MB 
 is equal to that in NB. But, by Ohm's Law, the fall of potential 
 in AM is to that in MB as the resistance of AM, or r l9 is to 
 the resistance of MB, or r 2 : and similarly in the other branch. 
 Hence r : r 2 : : r s : r 4 . If any three of these resistances are 
 known, the fourth can be computed from this proportion. 
 
 The equipotential points M and TV are found experimentally by 
 means of a sensitive galvanometer placed in the " bridge " joining 
 the two branches. The resistances are varied (as described below) 
 till the deflection of the galvanometer is zero. We then know 
 that there is no current through the wire joining M and N, and 
 consequently that these points are at equal potentials. The two 
 branches of the divided battery circuit AMB and ANB, together 
 
228 
 
 ELECTRICITY 
 
 with the cross branch MN 9 constitute a Wheatstone bridge. The 
 parts AM, MB, AN, and NB are the four arms of the bridge. 
 The Wheatstone bridge is made in various forms, but the above 
 statement of the principle holds for all. 
 
 The Slide Wire Bridge. This form of the Wheatstone bridge 
 (Figs. 104 and 105) derives its name from a stretched bare wire, 
 
 FIG. 104. 
 
 the parts of which, 4 and L 2 , constitute two arms of the bridge. 
 The resistance to be measured (^ in the figure) is placed in 
 either of the arms AM or MB, and a resistance box is placed in 
 the other. The resistance of the large brass connecting bars 
 in these arms is, of course, negligible. The battery terminals are 
 
 /3W&wflp*r\ 
 
 FIG. 105. 
 
 connected to posts at A and B. One terminal of the galvanom- 
 eter is connected with a post at M, and the other is brought in 
 contact with any desired point of the stretched wire by means of 
 the sliding contact key N. 
 
THE WHEATSTONE BRIDGE 22Q 
 
 When the position of the key ^V is such that there is no deflec- 
 tion of the galvanometer on closing the circuit through it, the 
 resistances of the segments /j. and / 2 into which the wire is divided 
 by the point of contact of the key are in the same ratio as ^ and 
 r 2 ; or, since the lengths / x and / 2 are in the same ratio as their 
 resistances, / x : / 2 : : ^ : r%. Hence if r v is the unknown resistance, 
 it is computed from the equation r = /i^ 2 /4- 
 
 The lengths / x and / 2 can be more accurately determined when 
 neither is small ; it is therefore best to have them nearly equal. 
 This requires that the box resistance be nearly equal to the 
 resistance to be measured. Hence in measuring a resistance, 
 begin by introducing in the box a resistance estimated to be 
 somewhere nearly equal to it. With the battery circuit closed, 
 touch the slide wire with the contact key near one end, and note 
 the direction of the deflection. Slide the key to about an equal 
 distance from the other end, and repeat. (Do not slide the key 
 when closed : the wire would be damaged by scraping it.) If the 
 deflection is in the same direction a's before, the resistance in the 
 box is much too large or too small. If you are doubtful which is 
 the case, make contact nearer either or both ends, till an oppo- 
 site deflection is obtained. Having properly adjusted the box 
 resistance, and having found two points between which the cor- 
 rect point of adjustment lies (the two points giving deflections 
 in opposite directions), the adjustment is completed by noting the 
 decreasing deflection of the galvanometer in either direction as 
 the points of contact are taken at diminishing distances on each 
 side of the point sought. With a sensitive d'Arsonval galvanom- 
 eter, the adjustment should be right within i mm. 
 
 The Resistance-coil Bridge. In each of the arms AM and AN 
 of this form of bridge a resistance coil (i, 10, or 100 ohms) is 
 introduced by removing a plug, as in a resistance box. The re- 
 sistance of the brass connecting bars is negligible. The resist- 
 ance to be measured (; 2 in the figure) is placed in either of the 
 arms ME or NB, and a resistance box r (in the figure) is placed 
 
230 
 
 ELECTRICITY 
 
 in the other. The box resistance is adjusted to give a zero deflec- 
 tion of the galvanometer. 
 
 The results are most accurate when the coil used for r^ is the 
 one most nearly equal to r> 2 and when the ratio r^/r^ is so taken 
 
 that ?\ is not far from 
 the full capacity of the 
 box. It is generally 
 better to begin with 
 equal values for ^ and 
 > B r 3 , and to change the 
 ratio later if this is 
 found to be desirable. 
 The circuit through the 
 galvanometer is mo- 
 mentarily closed, by 
 means of the contact 
 key, after each adjust- 
 ment of the resistance. The battery circuit may be kept closed ; 
 but if a key is provided for this circuit, it is closed before and 
 opened after the galvanometer circuit. 
 
 In measuring a resistance, note first the direction of the deflec- 
 tion when the box resistance is zero ; then introduce a resistance 
 estimated to be about equal to the one you are measuring. If 
 the deflection is in the same direction as before, introduce more 
 resistance ; if it is in the opposite direction, replace the plug 
 firmly and introduce a smaller resistance. Proceed thus down 
 to the smallest resistance in the box, or until there is no deflec- 
 tion. When the correct adjustment is secured, r s is found from 
 the equation r 2 = ; 
 
 FIG. 106. 
 
 Experiment 130. To measure electrical resistance by means of 
 a Wheatstone bridge. 
 
 Apparatus. A Wheatstone bridge ; d'Arsonval or astatic gal- 
 vanometer ; dry (or other) cell ; resistance box ; resistance to be 
 measured ; connecting wires. 
 
THE WHEATSTONE BRIDGE 
 
 231 
 
 [The slide wire bridge is recommended unless the laboratory 
 is already supplied with the other form. A satisfactory d'Arson- 
 val galvanometer, similar to Figure 
 107, very sensitive, suitable for use 
 with the bridge and for experiments 
 on induced currents, can be bought 
 for $7.00 to $12.00. These are 
 dead-beat instruments, which is a 
 very important advantage over the 
 astatic type.] 
 
 Experimental Work. In measur- 
 ing any resistance with a Wheatstone 
 bridge, follow the directions given 
 above. Find the resistance of such 
 of the following conductors as are 
 provided : 
 
 1. The filaments of incandescent 
 
 lamps; e.g. a i6-candle, no-volt lamp; a 32-candle, no-volt 
 lamp; a i6-candle, 22O-volt lamp; a 32-candle, 22O-volt lamp. 
 
 2. Coils of electro-magnets ; e.g. of a telegraph sounder, tele- 
 graph relay, electric bell, and the armature of a motor or dynamo. 
 
 3. The coil of a galvanometer or a voltmeter. 
 Experiment 131. To measure the resistance of a cell. 
 Apparatus. As for Experiment 130; also two of the cells 
 
 whose resistance is to be found. 
 
 Experimental Work. The two cells whose resistance is to be 
 determined must be of the same kind and, as nearly as possible, 
 in the same condition, in order that their electro-motive forces 
 may be equal. Place them, connected in series and opposing each 
 other, in one arm of the bridge. When thus connected their 
 combined E. M. F. is zero, and their effect in the bridge is that 
 of a simple resistance equal to the sum of their separate resist- 
 ances. A third cell must, of course, be used in the usual manner 
 to supply a current to the bridge. 
 
232 ELECTRICITY 
 
 Experiment 132. To find the relative resistance of different 
 metals, referred to copper. 
 
 Apparatus. As for Experiment 130; also copper and other 
 wires of the same diameter and any convenient lengths. 
 
 Experimental Work. Find and record the length, diameter, 
 and resistance of each wire. Compute the ratio of the resistance 
 of each wire to the resistance of a copper wire of the same length 
 and diameter. Compare the values obtained with the values 
 given in tables. Enter data and computations in tabular form. 
 
 Experiment 133. To study the relation between the resistance 
 of a wire and its cross section. 
 
 Apparatus. As for Experiment 130; also two or more wires 
 of the same material and length, but of different diameters ; mi- 
 crometer screw (unless the diameters of the wires are given). 
 
 Experimental Work. Find the lengths, diameters, and resist- 
 ances of the different wires. Find within what percentage of error 
 the measured resistances and diameters agree with the known law. 
 Enter data and computations in tabular form. 
 
 EXERCISE 70. ARRANGEMENT OF CELLS 
 
 References. Adams, 499-504 ; Coleman, 477, 479-482 ; Car. 
 &C., 467-470; Ches. G. & T, 396-399 ; Hoad. Br., 358-362 ; 
 Hoad. El., 401-405; Mumper, 283; Jackson, 38; Mil. & G., 
 384-386; Went. & H., 297. 
 
 Experiment 134. To study the arrangement of cells in series 
 and in parallel; and to find which arrangement gives the larger 
 current through a given external resistance. 
 
 Apparatus. Tangent galvanometer of low resistance and one 
 of high resistance (the latter can be dispensed with), or a volt- 
 meter and an ammeter ; two cells of the same kind ; resistance 
 box ; double connectors ; connecting wires. 
 
 [The cells should be of the same size and as nearly as possible 
 
ARRANGEMENT OF CELLS 
 
 233 
 
 FIG. 108. 
 
 in the same condition, in order that they may have equal E. M. F. 
 and approximately equal resistance. The resistance of good dry 
 cells is so small that they fail to show the advantage of connec- 
 tion in parallel, unless the whole external resistance is only a few 
 hundredths of an ohm). 
 
 Experimental Work. Find the ratio of the E. M. F. of a bat- 
 tery of two like cells in series 
 (Fig. 108) to that of one cell, and 
 the ratio of the E. M. F. of the 
 two cells in parallel (Fig. 109) to 
 that of one cell. If a tangent 
 galvanometer of high resistance is 
 provided for this purpose, follow 
 the method of Experiment 125 and the form of record given 
 below ; with a high-resistance galvanometer, which is not a tangent 
 instrument, follow the method of^Experiment 
 126; with a low-resistance galvanometer, follow 
 the method of Experiment 127; with a volt- 
 meter, measure directly the E. M. F. of each cell 
 separately, of both in series, and of both in 
 parallel, as in Experiment 128. 
 
 Connect the low-resistance galvanometer (or 
 the ammeter) in circuit with the resistance box 
 and one cell. Use the number of turns of the 
 coil which gives a deflection nearest to 45 with 
 no box resistance ; and use the same connection 
 in all that follows. Read to the nearest degree the deflection 
 (of one end of the pointer in one direction) with a box resistance 
 R of o ohms ; with R = 3 ohms ; and with R=2O ohms. Repeat 
 with a battery of two cells in series and the same box resistances. 
 Read the same end of the pointer as before, with the deflection 
 in the same direction. Repeat with a battery of two cells in paral- 
 lel and the same box resistances. Record as indicated below. If 
 an ammeter is used, all the readings will be in amperes. 
 
234 
 
 ELECTRICITY 
 
 Data and Computations. Make diagrams of the series and 
 parallel arrangements, representing the resistance box and the 
 galvanometer in the circuit. With a tangent galvanometer of 
 high resistance and a low-resistance instrument (tangent or other), 
 record as follows : 
 
 E. M. F. OF TWO CELLS IN SERIES AND IN PARALLEL COMPARED WITH THAT 
 OF A SINGLE CELL. (HiGH-RESISTANCE GALVANOMETER.) 
 
 NO. AND 
 
 ARRANGEMENT 
 OF CELLS 
 
 DEFLECTION 
 
 Av. DEFLECTION 
 
 TANGENT 
 
 RATIO OF 
 ELECTRO- 
 MOTIVE 
 FORCES 
 
 E. end 
 
 W. end 
 
 I 
 
 N. 
 
 ; o 
 
 
 
 
 
 S. 
 
 N. 
 
 
 
 tan a 
 
 
 2, in series 
 
 N. 
 
 S. 
 
 
 
 
 
 S. 
 
 N. 
 
 
 
 tan a- 
 
 tan a f -Man a 
 
 2, in parallel 
 
 * N. 
 
 S. 
 
 
 
 
 
 S. 
 
 N. 
 
 
 
 tan a" 
 
 tan a' 1 -4- tan a 
 
 CURRENT FROM TWO CELLS IN SERIES AND IN PARALLEL COMPARED WITH 
 THAT FROM SINGLE CELL. (LOW-RESISTANCE GALVANOMETER.) 
 
 No. AND ARRANGE- 
 MENT OF CELLS 
 
 DEFLECTION WITH Box RESISTANCE R 
 
 ARRANGEMENT 
 GIVING THE 
 LARGER CURRENT 
 
 R=o ohms 
 
 R=3 ohms 
 
 K = 2o ohms 
 
 I 
 
 2, in series 
 2, in parallel 
 
 
 
 
 
 
 
 
 
 
 
 Discussion. i. How does the E. M. F. of the two cells in 
 series compare with that of one cell? the E. M. F. of the two 
 cells in parallel? 
 
MEASUREMENT OF ELECTRICAL POWER 235 
 
 2. From the known law of resistances in series and in parallel 
 (which holds for cells as well as for other conductors), how does 
 the resistance of a battery of two like cells in series compare with 
 that of one cell? the resistance of a battery of two like cells in 
 parallel ? 
 
 3. Letting E denote the E. M. F. and r the resistance of one 
 cell, R the external resistance, and C the current, write the 
 formula for the current from a battery of two cells in series ; 
 also the formula for the current from a battery of two like cells 
 in parallel. 
 
 4. Show from the results of the experiment which arrangement 
 of cells gives the larger current through a very low external re- 
 sistance (R = o) ; and which arrangement gives the larger current 
 through a considerable external resistance (R = 20). 
 
 5. Account for these results by means of the formulas given in 
 answer to the third question. 
 
 EXERCISE 71. MEASUREMENT OF ELECTRICAL 
 POWER 
 
 References. Adams, 541-544 ; Coleman, 486-491 ; Ches. G. 
 & T., 387 ; Hoad. Br., 395 ; Hoad. El., 437 ; Mumper, 280-281 ; 
 Jackson, no, 112-113, 331; Mil. & G., 404-407; Went. & H., 
 299-302. 
 
 Electrical Power. The unit of electrical power is the energy 
 expended per second by a current of i ampere in any part of 
 the circuit in which the fall of potential is i volt. This unit is 
 called the watt. The power of an electric current, or the total 
 energy expended by it in the entire circuit in one second, meas- 
 ured in watts, is equal to the product of the E. M. F. and the 
 current; i.e. P= EC watts, in which P denotes the electrical 
 power, E the E. M. F. in volts, and C the current in amperes. 
 
 The power used in any part of a circuit is measured in watts 
 by the product of the current and the fall of potential in that 
 
ELECTRICITY 
 
 part of the circuit. For example, if a i6-candle lamp takes a 
 current of .5 ampere and the potential difference between its 
 terminals is no volts, the power expended in it is .5 x no, or 
 55 watts. This is 3.44 watts per candle power (55 -r- 16 = 3.44). 
 
 Experiment 135. To measure the power generated by a battery 
 when lighting an incandescent lamp ; and to determine the percent- 
 age of the total power consumed in the battery and in the lamp. 
 
 Apparatus. A small incandescent lamp; a sufficient number 
 of cells to light the lamp ; voltmeter ; ammeter ; two double 
 connectors ; connecting wires. 
 
 [Dry cells are best and most convenient. Lamps requiring 
 from two to four dry cells in series are suitable. If the laboratory 
 is not provided with such lamps, the coil of an electro-magnet or 
 any resistance coil may be used instead.] 
 
 Experimental Work. Connect the lamp and the ammeter in 
 circuit with one cell. If the current is not sufficient to light the 
 lamp, add a second cell in series with the first, and, if necessary, 
 
 a third and a fourth cell. 
 Use only a sufficient num- 
 ber of cells to light the 
 lamp brightly ; if too 
 many are used, the fila- 
 ment will be burned out 
 and the lamp destroyed. 
 
 Connect the voltmeter 
 as a shunt to the lamp 
 A (V, Fig. no) to deter- 
 mine the potential differ- 
 ence between its termi- 
 nals. Read the ammeter and the voltmeter. Do not keep the 
 circuit closed longer than is necessary. Make a diagram of the 
 circuit. 
 
 Find the E. M. F. of the battery by connecting its terminals 
 
 FIG. no. 
 
MEASUREMENT OF ELECTRICAL POWER 237 
 
 directly to the voltmeter (the lamp and the ammeter being re- 
 moved from the circuit). 
 
 Record the candle power of the lamp. 
 
 Data and Computations. Let P t denote the fall of potential in 
 the lamp and P b the fall or loss of potential in the battery, when 
 on the lamp circuit. (The loss of potential in the battery is practi- 
 cally zero when connected directly with the voltmeter, as explained 
 in Experiment 125.) Hence, letting E denote the E. M. F. of 
 the battery, and assuming the loss of potential in the ammeter and 
 the connecting wires to be negligible, E = P b -f P l (i.e. the total 
 fall of potential in the whole circuit is equal to the E. M. F. of the 
 battery). 
 
 If the current through the lamp circuit is denoted by C, the 
 total power generated by the battery when on the lamp circuit is 
 EC watts, the power expended in the lamp is P t C, and the power 
 lost in the battery, due to internal resistance, is P b C. 
 
 Record data as follows, and perform the indicated computa- 
 tions : 
 
 Current supplied to the lamp C = amperes. 
 
 Potential difference between the lamp terminals P l = volts. 
 
 E. M. F. of battery E = volts. 
 
 Candle power of the lamp = 
 
 Loss of potential in the battery when on the lamp 
 
 circuit P b = E-P l = volts. 
 
 Total power generated by the battery when on the 
 
 lamp circuit EC = watts. 
 
 Power expended in the lamp P t C = watts. 
 
 Power lost in the battery P b C = watts. 
 
 Percentage of total power utilized in the lamp = % 
 
 Percentage of total power lost in the battery = % 
 
 Discussion. i. By Ohm's Law, the losses of potential in the 
 battery and in the lamp are proportional to their respective resist- 
 ances, and the total resistance is E/ C. From this compute the 
 
238 ELECTRICITY 
 
 resistance of the battery and the resistance of the lamp. (Since 
 P b , as found, really includes the loss of potential in the ammeter 
 and the connecting wires, the computed battery resistance will 
 include the resistance of the ammeter and the connecting wires.) 
 2. Compute the watts per candle power consumed by the lamp. 
 
 EXERCISE 72. INDUCED CURRENTS 
 
 References. Adams, 505-512, 524 ; Coleman, 492-495 ; Car. 
 & C., 480-482 ; dies. G. & T., 415-422 ; Hoad. Br., 397 ; Hoad. 
 EL, 439-440; Mumper, 287-291; Jackson, 132-137; Mil. & G., 
 412-417 ; Went. & H., 313-315- 
 
 Apparatus. A d'Arsonval or astatic galvanometer ; induction 
 coil with movable primary and iron core ; dry cell ; bar magnet ; 
 connecting wires. 
 
 [The usual form of separable induction coil, in which the sec- 
 ondary coil consists of many turns of fine wire, requires a d'Arson- 
 val or an astatic galvanometer of fairly high resistance. With an 
 astatic galvanometer of low resistance, the secondary coil should 
 consist of a few turns of large wire, like the primary.] 
 
 Experiment 136. To study the laws of current induction by 
 magnets. 
 
 Experimental Work. a. Since the galvanometer is to be 
 used to determine the direction as well as the existence of induced 
 currents, it is first necessary to observe the direction of the de- 
 flection due to a current whose direction is known. Use the cell 
 for this purpose ; but before closing the circuit, connect the termi- 
 nals of the galvanometer with a short wire, which will act as a 
 shunt to the galvanometer, permitting only a small fraction of the 
 current to pass through it. (This is a necessary precaution with 
 a sensitive instrument.) Observe the direction of the deflection, 
 and note (from the battery connections) by which terminal the 
 
INDUCED CURRENTS 
 
 239 
 
 current enters the galvanometer. A current entering by the other 
 terminal would cause a deflection in the opposite direction. 
 Hence in the following experiments the direction of the deflection 
 will indicate by which terminal the current enters the galvanom- 
 eter ; and from this the direction of the current can be traced 
 through the entire circuit. 
 
 b. Connect the galvanometer with the larger coil of wire (called 
 the secondary coil), placed at a distance of a meter or more. 
 The circuit consists only of the coil, the galvanometer, and the 
 connecting wires. 
 
 Thrust the north pole of the magnet suddenly into the coil, 
 while observing the galvanometer. Note the direction of the 
 deflection. Observe the effect of removing the magnet. Repeat 
 till you are sure of the results. (The galvanometer must be far 
 enough away not to be directly affected by the motion of the mag- 
 net. Test this by inserting and withdrawing the magnet with the 
 circuit broken.) From the direction of the deflection, determine 
 the direction of the current round the coil (clockwise or counter 
 clockwise as you look down upon it), when the north pole of the 
 magnet is inserted and when it is removed. Applying the right- 
 hand rule, determine whether the current induced in the coil 
 makes its upper end N or S when the north 
 pole of the magnet is inserted and when it is 
 removed. 
 
 Draw diagrams similar to Figure in, show- 
 ing the polarity of the magnet and the direc- 
 tion in which it is moving, and the resulting 
 polarity of the coil and direction of the current 
 round it. 
 
 c. Is there a current when the magnet is at 
 rest within the coil? What is the experimental 
 evidence ? 
 
 d. Study the effect of inserting and removing the south pole of 
 the magnet. Answer all the questions of (^) for this case, and draw 
 diagrams as before. 
 
240 
 
 ELECTRICITY 
 
 Experiment 137. To study the laws of current induction by 
 currents. 
 
 Experimental Work. a. Connect the cell with the smaller 
 coil (called the primary) so as to make the lower end of the coil a 
 north pole. The galvanometer is to be connected with the sec- 
 ondary coil as before. 
 
 Determine, from the deflection of the needle, the direction of 
 the current in the secondary coil when the north pole of the pri- 
 mary coil is inserted into and when it is removed from the sec- 
 ondary coil. Make diagrams similar to Figure 112, showing the 
 direction of the current in the secondary coil in 
 each case and the resulting polarity of this coil. 
 b. With the primary coil at rest in the 
 secondary, study the currents induced when 
 the circuit is closed through the primary, and 
 when it is broken. (Make and break the cir- 
 cuit by touching the connecting wire to one of 
 the binding posts, and removing it.) 
 
 Compare the directions of the induced cur- 
 rents with the directions of the currents induced 
 when the primary coil was inserted and removed. 
 Repeat the work of (b) with the iron core within the primary 
 Note whether the deflections are greater or less than be- 
 State and account for the effect of the core. 
 d. With the primary circuit closed, insert and remove the pri- 
 mary coil and the iron core together, first quickly, then more and 
 more slowly, and note the effect of the rate of motion on the 
 amount of the deflection. What law of electro-magnetic induc- 
 tion is illustrated? 
 
 FIG. 112. 
 
 c. 
 
 coil, 
 fore. 
 
 Discussion. The induced current in the secondary coil is 
 called direct if its direction round the coil is such that like poles 
 of the secondary coil and the magnet or the primary coil point in 
 the same direction; inverse, if their -like poles point in opposite 
 
THE ELECTRIC MOTOR AND DYNAMO 241 
 
 directions. Thus a direct induced current flows in the same 
 direction round the coil as the inducing current in the primary 
 coil, and an inverse induced current flows in the opposite direc- 
 tion. State the different ways in which you obtained 
 
 1. An inverse induced current. 
 
 2. A direct induced current. 
 
 3. Does the magnetic field due to the induced current aid or 
 oppose the insertion and removal of the magnet or the primary 
 coil? (Consult the text and reference books for a discussion of 
 the connection of this fact with the principle of the conservation 
 of energy.) 
 
 4. In which cases in these experiments was the induced cur- 
 rent due to an increase in the strength of the magnetic field 
 within the secondary coil? Was the induced current in these 
 cases direct or inverse? 
 
 5. In which cases was the induced current due to a decrease in 
 the strength of the magnetic field within the secondary coil ? Was 
 the induced current in these cases direct or inverse? 
 
 6. What law of electro-magnetic induction is illustrated by the 
 effect of the iron core ? 
 
 EXERCISE 73. THE ELECTRIC MOTOR AND 
 DYNAMO 
 
 References. Adams, 513-523 ; Coleman, 500-505 ; Car. & C., 
 493-500; Ches. G. & T., 428-436, 439-441; Hoad. Br., 406- 
 415, 439; Hoad. El., 445-459; Mumper, 292-295; Jackson, 
 195-215 ; Mil. & G., 416-427 ; Went. & H., 314-325. 
 
 Experiment 138. To study the construction and action of a 
 small motor. 
 
 Apparatus. Small motor (Fig. 113); dry cell; compass; 
 small square of cardboard; iron filings in sifter; screw-driver; 
 connecting wires. [The cheapest grade of motor is not recom- 
 mended. One costing $2.00 to $3.00 gives much better service.] 
 COLEMAN'S NEW MANUAL 16. 
 
242 
 
 ELECTRICITY 
 
 FIG. 113. 
 
 Experimental Work. a. Trace the circuit from one binding 
 post of the motor to and from the armature, and through the 
 
 coil of the field magnet to 
 the other post. (The cir- 
 cuit through the armature 
 will be studied later.) If 
 the armature and the coil 
 of the field magnet are con- 
 nected in series, the motor 
 is said to be series-wound ; 
 if they are connected in 
 parallel, it is shunt-wound. 
 Is this motor shunt or series 
 wound? 
 
 b. Connect the motor 
 with the dry cell, and note 
 by which post the current enters it. Determine the polarity of the 
 field magnet from the known direction in which the current flows 
 round its coil (applying the right-hand rule), and test your con- 
 clusion by means of the compass. 
 
 Note the brush (upper or lower) by which the current enters 
 the armature, and the direction in which the armature rotates. 
 
 c. Interchange the battery connections with the binding posts 
 of the motor. Does this reverse the direction of the current 
 in the coil of the field magnet? Is the polarity of the field 
 magnet reversed? (Test with the compass.) Does the cur- 
 rent enter the armature by the same brush as before or by 
 the other one? Does the armature rotate in the same direction 
 as before? 
 
 d. Unscrew the horizontal bar that supports the armature on 
 the side opposite the commutator brushes. (The upper side 'of 
 this bar should be distinguished by a file mark, to assist in re- 
 placing it with the same side up. There are commonly slight 
 inequalities in the bar which throw the armature slightly out of 
 position and hinder or even prevent its rotation, if the bar is 
 
THE ELECTRIC MOTOR AND DYNAMO 243 
 
 reversed when it is replaced.) Remove the armature and inspect 
 the winding of its coils and their connection with the segments of 
 the commutator. Pass a current through the armature by hold- 
 ing the ends of the connecting wires from the cell against any two 
 segments of the commutator; and, while doing so, test the 
 polarity of each pole of the armature by means of the compass. 
 Draw a diagram of the armature, indicating the segment of the 
 commutator by which the current enters and the one by which it 
 leaves the armature, the direction of the current in each coil, and 
 the polarity of the different poles. 
 
 e. Test the polarity of the poles of the armature when the con- 
 necting wires are pressed with thumb and finger against opposite 
 sides of the commutator and the armature is turned into different 
 positions, bringing different pairs of the commutator segments 
 into contact with the connecting wires. Continue this study 
 until you have determined at what two points in a complete rota- 
 tion the current is reversed in any one coil (the wires being held 
 opposite to each other in fixed positions, like the brushes of the 
 motor). 
 
 /. Send the current from the cell through the coil of the field 
 magnet, turn the magnet into a horizontal position with the 
 brushes underneath, place the cardboard over the magnet, and 
 study the magnetic field in the space where the armature belongs, 
 by means of iron filings sprinkled on the cardboard. (If the 
 motor is series-wound, the circuit through the field magnet will 
 be broken by the removal of the armature. It can be closed by 
 bringing the brushes into contact with each other.) Make a 
 diagram of the poles of the magnet and the lines of force between 
 them. Test the strength of the magnet after breaking the cir- 
 cuit, by observing its effect on the iron filings and the compass. 
 This residual magnetism, as it is called, is important in most 
 forms of dynamos, but is of no value in motors. 
 
 g. Replace the armature in position, and test it by finding 
 whether it will run as before. Trace the direction of the current 
 (with the circuit open) from either post to the other, round the 
 
244 
 
 ELECTRICITY 
 
 coil of the field magnet and all the coils of the armature ; and 
 determine by the right-hand rule the resulting polarity of the 
 field magnet and the polarity of any coil of the armature in the 
 different parts of a complete rotation. If this is correctly done, 
 it will be seen that the commutator reverses the current in each 
 coil of the armature as it passes two fixed positions in each 
 
 rotation, and that this keeps the 
 armature in continuous rotation by 
 the attraction of unlike poles and the 
 repulsion of like poles of armature 
 and field magnet. 
 
 Make a section diagram of the 
 motor, similar to Figure 114, and in 
 it indicate the direction of the cur- 
 rent in the coils of the field magnet 
 and the armature, the polarity of the 
 field magnet and the poles of the 
 armature, and the direction of rota- 
 tion. 
 
 FIG. 114. 
 
 h. Account for the direction of rotation (the same or opposite) 
 when the direction of the current through the motor is reversed. 
 
 Experiment 139. To study the action of the motor when run 
 as a dynamo. 
 
 Apparatus. The same as for the preceding experiment, to- 
 gether with a low-resistance galvanometer or galvanoscope and a 
 piece of stout cord four or five feet long. 
 
 Experimental Work. a. Connect the motor with the gal- 
 vanometer, using all the turns of the coil. Pass an end of the 
 cord half round the pulley attached to the axle of the armature ; 
 and, while another pupil holds the motor on the table, set the 
 armature in rapid rotation by drawing the cord quickly from end 
 to end over the pulley. This should generate sufficient current to 
 deflect the galvanometer. 
 
THE ELECTRIC MOTOR AND DYNAMO 245 
 
 
 Note the direction of the deflection when the armature is 
 rotated in the same direction as that in which it turns as a motor, 
 and also when rotated in the opposite direction. From the direc- 
 tion of the deflection in each case, determine the direction of the 
 current through the galvanometer (making a test of the galvanom- 
 eter by means of the cell, if necessary), and from this the direction 
 of the current through the armature. 
 
 b. The current generated by the rotation of the armature in 
 this experiment is too weak either to materially strengthen or 
 weaken the residual magnetism of the field magnet. The polar- 
 ity of this residual magnetism is determined by the direction of 
 the much stronger current last sent through the coil from the 
 cell. Find this polarity by means of the compass, and indicate 
 it in a diagram like that of the motor in the preceding experi- 
 ment. 
 
 In running the machine effectively as a dynamo, the direction 
 of the current generated must be such as to strengthen the exist- 
 ing polarity of the field magnet. In which direction (the same 
 as that in which it turns as a motor or the opposite) must the 
 armature be turned to accomplish this result ? When the rotation 
 is in this direction, does the current flow through the armature in 
 the same direction as when it is running as a motor, or in the 
 opposite direction? (The answers to these questions are not the 
 same for shunt-wound as for series-wound machines. Remember 
 that the current enters the armature by the positive brush when 
 the machine is run as a motor, and leaves by the positive brush 
 when it is run as a dynamo.) 
 
 c. Represent the above facts in the diagram of the dynamo. 
 State the points of resemblance and the points of difference 
 between the diagrams of the motor and the dynamo. 
 
 Discussion (Oral). i. Does the current generated in a dynamo 
 help or hinder the rotation of its armature? Answer from the 
 facts of the experiment, as shown in your diagrams. 
 
 2. Show that the laws of electro-magnetic induction apply in 
 the generation of a current by a dynamo. 
 
246 
 
 ELECTRICITY 
 
 EXERCISE 74. THE GILLEY GRAMME RING DYNAMO 
 AND MOTOR 
 
 References. The same as for Exercise 72. 
 
 Experiment 140. To study the construction and action of a 
 model Gramme ring dynamo and motor. 
 
 Apparatus. Gilley's model Gramme ring and motor (Fig. 115) ; 
 two dry cells ; cardboard ; iron filings in sifter ; compass ; con- 
 necting wires. 
 
 [The Gilley model Gramme ring and motor is manufactured by 
 the L. E. Knott Apparatus Co., Boston. It is a very instructive 
 
 piece of apparatus, espe- 
 cially designed for labora- 
 tory work. The following 
 directions are adapted 
 from Mr. Gilley's exer- 
 cises on the machine.] 
 
 FIG. 115. 
 
 Experimental Work. 
 
 The Field Magnet. a. 
 Lift the armature off and 
 set it aside. Send the cur- 
 rent from one cell through 
 the coil of the field mag- 
 net. Lay the cardboard 
 over it, and study the 
 magnetic field by means of iron filings and the compass. Make a 
 diagram of the field magnet, showing the direction of the current 
 round the coil, the north and south poles of the magnet, and the 
 lines of force between the poles. 
 
 b. Note the behavior of the compass needle and the iron filings 
 when the circuit is closed, and when it is open. The stronger the 
 magnetic force, the more rapidly will the compass needle vibrate 
 
THE GILLEY GRAMME RING DYNAMO AND MOTOR 247 
 
 when disturbed. The magnetism remaining in the electro-magnet 
 when there is no current through its coil is called residual 
 magnetism. What do you infer concerning the relative amount 
 of the residual magnetism? 
 
 c. Reverse 'the current through the coil, and note the effect on 
 the polarity of the field magnet. Result? 
 
 The Armature. d. Remove the field magnet and replace the 
 armature. Send the current from one cell through the armature 
 by connecting the cell with the binding posts on the brush holder. 
 Observe that there is a continuous coil, wound throughout in the 
 same direction round the iron ring of the armature, and that this 
 coil is connected at four equidistant points with the correspond- 
 ing sections of the commutator on the under side. The current 
 divides in passing through the armature from one brush to the 
 other, part going through one half of the coil and part through 
 the other half. The current flows in opposite directions round 
 these two parts of the coil. (Why?) A Gramme ring armature 
 is, therefore, a double electro- magnet, with like poles of the two 
 semicircular magnets together. 
 
 Place the cardboard over the armature, and study its magnetic 
 field by means of the iron filings and the compass. The double 
 north and south poles of the armature are where the lines of 
 force extend radially (i.e. where the compass points exactly toward 
 the center of the armature). Make a diagram of the armature, 
 representing its north and south poles, the lines of force, and the 
 direction of the current round the halves of the coil. 
 
 The Commutator. e. With the current flowing through the 
 armature and the cardboard removed, hold the compass close 
 beside the armature at one of its poles ; and, keeping it in this 
 position, note the behavior of the needle as you slovyly turn the 
 armature. Stop the armature at the instant when the needle sud- 
 denly changes its direction, and observe whether this is a position 
 in which the brushes change contact from one section of the 
 commutator to the next. 
 
 Again turn the armature slowly, moving the compass at the 
 
248 ELECTRICITY 
 
 same time, so as to keep it exactly at one of the poles. Stop the 
 armature at the instant when the needle indicates a sudden change 
 in the position of the pole, and find the point to which the pole 
 has shifted. Find what change of contact between the commuta- 
 tor and brushes caused the shifting of the pole. Does the other 
 pole shift at the same time so as to remain opposite to the first? 
 
 /. How many times during a complete rotation do the poles 
 shift to a new position? Why? 
 
 Through what angle do the poles turn with the armature before 
 shifting to a new position? Through what angle do they shift? 
 Do they shift in the direction of rotation or in the opposite 
 direction? 
 
 What is the greatest angle that the straight line through the poles 
 of the armature makes in either direction with the line through 
 the points of contact of the brushes with the commutator? 
 
 g. How would these results differ if the commutator had eight 
 sections? sixteen sections? (The commutators of dynamos and 
 motors for practical use have many sections.) 
 
 h. Find the north and south poles of the armature ; then, 
 without changing its position, turn the brush holder through 180. 
 What is the effect on the position of the north and south poles? 
 Explain. 
 
 The Complete Motor, Series-wound. /. Place the armature and 
 the field magnet in position. Connect the two cells in series, and 
 join one pole of the battery to a binding post of the field magnet, 
 and the other pole to one of the binding posts on the brush holder. 
 Connect the other binding posts of the field magnet and brush 
 holder by a short wire. The motor is now series -wound. Turn 
 the brush holder till the points of contact of the brushes are in a 
 line parallel to the two arms of the field magnet. The armature 
 should rotate. 
 
 Make a diagram of the motor, showing the connections, the 
 direction of the current round the coil of the field magnet and 
 the two branches of the armature coil, the polarity of the field 
 magnet and the armature, and the direction of rotation. If you 
 
THE GILLEY. GRAMME RING DYNAMO AND MOTOR 249 
 
 have difficulty in determining the polarity of the armature either 
 by the right-hand rule or the compass, test it with the compass 
 after removing the coil of the field magnet from the circuit. 
 
 Referring to your diagram, show whether all the attractions: 
 and repulsions between the poles of the field magnet and the 
 poles of the armature are such as to cause rotation in the observed 
 direction. 
 
 j. With the connections the same as before, turn the brush 
 holder through 180. Account for the reversal of the rotation. 
 
 k. Turn the brush holder back through 90, bringing the points 
 of contact of the brushes into a line at right angles to the arms of 
 the field magnet. Why does the armature not rotate ? 
 
 The Complete Motor, Shunt-wound. /. Connect the battery 
 wires to the binding posts of the field-magnet coil, and connect 
 the armature as a shunt to this coil. The motor is now shunt- 
 wound. The position of the brush holder is the same as with 
 series winding. Make a diagram showing connections, direction 
 of rotation, etc., as before. 
 
 m. Is the rotation reversed on turning the brush holder through 
 180? Give reason. 
 
 n. Is the rotation reversed on interchanging the battery con- 
 nections ? Explain. 
 
 Experiment 141. To study the action of the model Gramme 
 ring machine when run as a dynamo. 
 
 Apparatus. The same as for the preceding experiment, to- 
 gether with a low-resistance galvanometer. 
 
 Experimental Work. a. Restore the connections and the 
 adjustment of the brush holder exactly as shown in your diagram 
 under (/) in the preceding experiment. See that the direction of 
 rotation is the same as before, and note by which binding post 
 the current enters the armature. (This is the positive armature 
 
 post.) 
 
 Disconnect the armature from the battery circuit, leaving the 
 
250 ELECTRICITY 
 
 field magnet in the circuit as it was ; and connect the armature 
 with the galvanometer, using all its turns. Rotate the armature 
 as rapidly as possible, by a sudden push of the finger, in the direc- 
 tion in which it previously turned as a motor, and note the direc- 
 tion of the galvanometer deflection. From the direction, of the 
 deflection, find the direction of the current in the armature circuit 
 (testing the galvanometer with a cell, if necessary), and note the 
 post by which the current leaves the armature. This is the posi- 
 tive post, since the E. M. F. is generated in the armature coil and 
 the rise of potential must therefore be in it. 
 
 Does the current flow in the same direction in the armature as 
 it did when the machine was running as a motor, or in the oppo- 
 site direction? Draw a diagram as for the motor, representing 
 the direction of the current in the coils of the field magnet and 
 armature, the polarity of the field magnet, and the polarity of the 
 armature resulting from the current generated by its rotation. 
 
 b. Find in the same way the direction of the current generated 
 by rotating the armature in the opposite direction, all the other 
 conditions remaining the same as before. 
 
 Leave the cells disconnected. 
 
 Discussion. i. Is the polarity of the armature such as to aid 
 or oppose its rotation when it is run as a dynamo? Show that the 
 answer is in agreement with the principle of the conservation of 
 energy, and that if the opposite were true, it would be an excep- 
 tion to this principle. 
 
 2. From a comparison of your diagrams, show whether (the 
 connections remaining the same) the armature of a shunt-wound 
 dynamo must be turned in the direction in which it would run as 
 a motor, or in the opposite direction, if it supplies the current for 
 its own field magnet. (The direction of the current that a dynamo 
 sends through its field magnet must be such as to strengthen the 
 existing polarity of the residual magnetism. Why?) 
 
 3. What is the advantage of a large number of segments in the 
 commutator of a motor? 
 
THE TELEPHONE 
 
 EXERCISE 75. THE TELEPHONE 
 
 251 
 
 References. Adams, 530-532 ; Coleman, 508-510; Car. & C., 
 520-523 ; Ches. G. & T., 446 ; Hoad. Br., 429-431 ; Hoad. EL, 
 469-471 Mumper, 299 ; Jackson, 308-316 ; Mil. & G., 441-443 ; 
 Went. & H., 332. 
 
 Experiment 142. To study the construction and action of a 
 telephone receiver. 
 
 Apparatus. A d'Arsonval or astatic galvanometer of high 
 resistance ; telephone receiver. 
 
 Experimental Work. a. Unscrew and remove the cap that 
 covers the disk of the receiver. Remove the disk. Describe the 
 parts exposed to view. Is the disk attracted by the magnet? Of 
 what material is it? Make a section diagram of the receiver. 
 
 b. Connect the receiver with the galvanometer. Note the be- 
 havior of the galvanometer when you touch the magnet with the 
 disk, and again when you remove the disk. Do the deflections 
 indicate currents in the same or in opposite directions in the two 
 cases? Account for these currents. 
 
 c. Place the disk in position on the receiver, and observe 
 whether the galvanometer indicates a current when you press the 
 disk lightly at its center with the finger, so as to bring it nearer 
 the magnet, and again when you remove the pressure. 
 
 If you should speak into the receiver when it is on a closed 
 circuit, what currents would be generated, and why? Why would 
 such currents not cause a deflection of the galvanometer? 
 
 Experiment 143. To study the action of a telephone line con- 
 sisting of two receivers. 
 
 Apparatus. Two telephone receivers at opposite ends of the 
 laboratory or in adjacent rooms, connected with long wires ; tun- 
 ing fork ; rubber mallet. 
 
 [The circuit may be permanently set up between two binding 
 
252 ELECTRICITY 
 
 posts at each end of the line, so that it is only necessary for the 
 pupil to connect the receivers with the binding posts.] 
 
 Experimental Work. a. Listen at one receiver while your 
 companion touches the stem of a vibrating fork to the disk of the 
 receiver at the other end of the line. 
 
 b. Try speaking to one another, using the receivers alternately 
 as receiver and transmitter. 
 
 Explain the action of such a telephone line. 
 
 Experiment 144. To study the construction and action of a 
 microphone. 
 
 Apparatus. Telephone receiver; dry cell; two battery or 
 electric light carbons ; microphone ; tuning fork and rubber mal- 
 let ; watch. 
 
 Experimental Work. a. Connect the pieces of carbon, the 
 receiver, and the battery as shown in Figure 116, so that the circuit 
 
 will be closed by touching 
 the carbons together. Place 
 the receiver to the ear, and 
 touch one carbon to the 
 other, varying the pressure, 
 or rub one carbon lightly 
 over the other. The re- 
 ceiver should give out a 
 
 loud, rattling sound. The 
 FIG. 116. . ' 5 
 
 resistance at the points of 
 
 contact of the carbons with each other varies with the pressure. 
 How does this account for the sounds from the receiver? 
 
 b. If the microphone is without an induction coil, connect it 
 in series with the receiver in the battery circuit (Fig. 117) ; if 
 it has an induction coil, connect the cell with the primary coil 
 and the telephone receiver with the secondary. (The microphone 
 is permanently connected in series with the primary coil.) 
 
 Hold the receiver to the ear, and tap lightly on the base of the 
 
THE TELEPHONE 
 
 253 
 
 microphone, or rub the finger lightly over it. Listen to a watcn 
 lying on the microphone. Touch a faintly sounding tuning fork 
 to the microphone. 
 
 FIG. 117. 
 
 How does the microphone reproduce these different sounds? 
 Is the reproduction like the original sound in character? Is it 
 louder ? 
 
 Experiment 145. To study the construction and action of a 
 complete telephone line. 
 
 Apparatus. A telephone line consisting of two telephones 
 made for laboratory use. 
 
 [A battery call telephone (Fig. 118), costing from $5 to $7 
 each, is suitable for this experiment.] 
 
 Experimental Work. The principles of the modern telephone 
 are covered by the preceding experiments ; the details of con- 
 struction differ in different telephones. The following general 
 directions indicate the principal matters of detail to be made out 
 in the study of the laboratory telephone. 
 
254 
 
 ELECTRICITY 
 
 a. Trace out the connections by which the bell is included in 
 th.e line circuit when the receiver is on the hook. 
 
 b. Trace the line circuit through the telephone when the button 
 
 is pushed to ring the bell of the 
 other telephone. Is the bell of 
 one telephone rung by the bat- 
 tery of the other, or by its own? 
 
 c. With the receiver off the 
 hook, trace the local circuit 
 through the transmitter and the 
 primary coil, and the line cir- 
 cuit through the secondary coil 
 and the receiver. 
 
 What connections are broken 
 and what made by the lever 
 when the receiver is removed 
 from the hook? 
 
 d. Study and use the line till 
 you understand its operation. 
 Draw one or more diagrams of 
 
 the telephone, showing the various circuits and connections that 
 you have found. Describe the telephone and its action, referring 
 to your diagrams. 
 
 FIG. 118. 
 
 EXERCISE 76. ELECTROLYSIS AND THE STORAGE 
 
 CELL 
 
 References. Adams, 533-538 ; Coleman, 511-513; Car. &C., 
 
 445-44 7> 449-45 1 ', Ches. G. & T., 395~395 a \ Hoad - Br -> 365- 
 370; Hoad. El., 415-420; Mumper, 269-271 ; Jackson, 56-67, 
 370-387 ; Mil. & G., 387-393 ; Went. & H., 306-307, 309-312. 
 
 Experiment 146. To study the effect of passing an electric cur- 
 rent through solutions of zinc sulphate and copper sulphate, between 
 copper and other electrodes. 
 
ELECTROLYSIS AND THE STORAGE CELL 255 
 
 Apparatus. Two dry or chromic acid cells; tumbler of zinc 
 sulphate in solution (colorless) ; tumbler of copper sulphate in 
 solution (blue) \ copper wires, No. 16 or larger, bare or bared for 
 about 10 cm. at the ends ; piece of emery cloth or sandpaper. 
 
 Experimental Work. a. Connect the cells in series, and use 
 the bare copper wires (or wires bared for about 10 cm. at the ends) 
 as the battery terminals. Brighten with the emery cloth the free 
 end of the negative terminal. The free end of the positive termi- 
 nal should be dull from exposure to the air. If it is bright or 
 plated with zinc from previous use, cut this portion off or use 
 another wire. 
 
 Hold the battery terminals some distance apart in the solution 
 of zinc sulphate, and close the circuit. Note any immediate 
 change in the appearance of either terminal. Remove them occa- 
 sionally for better observation. Which terminal (the positive or 
 the negative) receives a coating of zinc? What evidence do you 
 find that copper from the other terminal has gone into solution? 
 The electric current causes copper to replace zinc in the com- 
 pound, forming copper sulphate and depositing zinc. 
 
 b. Place a brightened end of copper wire in the zinc sulphate 
 solution without electrical connection. Is it coated with zinc? 
 Do you infer that electrical energy is or is not necessary for this 
 displacement of zinc by copper? 
 
 c. Place the zinc-covered terminal in the solution of copper 
 sulphate for an instant, without electrical connections, and observe 
 whether the coating of zinc is removed. If so, is there any evi- 
 dence that a deposit of copper has taken its place ? Wipe the 
 wire with a cloth to be sure of results. Is a supply of energy from 
 some outside source necessary for this displacement of copper 
 from the sulphate by zinc? 
 
 d. Take for battery terminals wires whose free ends have not 
 been used or brightened ; and, with the circuit closed* hold these 
 ends for a minute or two in the solution of copper sulphate. De- 
 termine from the appearance of the wires which (the positive or 
 
256 ELECTRICITY 
 
 the negative) has received a deposit of copper and which has been 
 partly consumed. Was the transfer of copper between the termi- 
 nals in the direction of the current or in the opposite direction? 
 
 e. If you wish to plate a nickel or a dime with copper, attach 
 it to the terminal that receives the deposit. To attach the coin, 
 wrap the end of the wire four or five times round a lead pencil, 
 making the turns close together, and slip the coin between them. 
 To make the plating uniform, it will be necessary to slip the wire 
 into a new position on the coin three or four times. 
 
 How could the current be made to remove the plating? 
 
 Experiment 147. To study the construction and action of a 
 storage cell 
 
 Apparatus. Tumbler containing dilute sulphuric acid (about 
 10% acid by volume) ; two lead plates, with support as in Exer- 
 cise 59; two dry cells; electric bell; high-resistance galvanom- 
 eter or voltmeter ; piece of emery cloth or sandpaper ; connecting 
 wires ; two double connectors. 
 
 Experimental Work. a. Clean the lead plates with the emery 
 cloth or scrape them with a knife, till the surfaces are bright. 
 Place them in the tumbler of acid, using the support to keep them 
 in position, and connect their terminals with the galvanometer (or 
 voltmeter). If all deposits due to previous use have been removed 
 from the plates, there will be no deflection. The tumbler of acid 
 and the lead plates constitute a storage cell. In its present con- 
 dition its E. M. F. is zero. (Why?) 
 
 b. Connect the storage cell in circuit with the battery of dry 
 cells, and connect the galvanometer as a shunt to the storage cell 
 (Fig. 119). Note the deflection (exact reading not required). 
 After about half a minute disconnect one of the battery terminals, 
 and note the behavior of the galvanometer. Does it indicate an 
 E. M. F. in the storage cell? If so, note the rapidity with which 
 the deflection decreases as the cell loses its slight charge in send- 
 ing a current through the galvanometer. 
 
ELECTROLYSIS AND THE STORAGE CELL 257 
 
 c. Again close the battery circuit through the storage cell for 
 about half a minute, and repeat the previous observations. Note 
 the formation of bubbles on the plates during the charging. Do 
 they gather more abundantly on the positive or the negative 
 plate ? The bubbles at the positive plate are of oxygen ; those at 
 the negative plate, of hydrogen. Raise 
 
 the lead plates out of the liquid and 
 note their color, especially the inside 
 surface of each, when the cell is charged 
 and also when it is discharged. 
 
 d. Repeat all these processes and ob- 
 servations five or six times, noting care- 
 fully the growing color of the plates 
 when charged, the difference between 
 the color of the plates when charged 
 and when discharged, and the increas- 
 ing time required to discharge the cell. Repeated charging and 
 discharging increases the quantity of reddish brown peroxide of 
 lead (PbO) that can be formed on the one plate (which?), and 
 the quantity of spongy lead that can be formed on the other. 
 The cell thus becomes capable of receiving a greater charge. 
 
 e. Determine from the direction of the galvanometer deflection 
 whether the plate that is positive while the cell is being charged 
 is also the positive plate while the cell is generating a current. 
 Does the current generated by the cell flow through it in the same 
 direction as the charging current or in the opposite direction? 
 
 f. If a voltmeter is used, find the voltage of the cell when 
 charged. 
 
 g. Charge the cell, and connect it with the electric bell. It 
 should furnish current enough to ring the bell for several 
 seconds. 
 
 Discussion. i. Compare the chemical changes that take place 
 in the zinc sulphate cell, under the action of the electric current, 
 with those that take place in the gravity or the Daniell cell in gen- 
 ^OLEMAN'S NEW MANUAL 17 
 
258 ELECTRICITY 
 
 crating a current. What transformation of energy do you infer 
 takes place in the electrolytic cell? Give reasons. 
 
 2. What transformation of energy takes place in a storage cell 
 while it is being charged? while it is generating a current? 
 
 3. To what extent do the facts established in this exercise lend 
 support to the principle of the conservation of energy ? 
 
APPENDIX 
 
 TABLE I 
 DENSITIES IN GRAMS PER CUBIC CENTIMETER 
 
 Aluminum . 
 
 2.67 
 
 Alcohol (95 %) . 
 
 .82 
 
 Antimony, cast . 
 
 6.7 
 
 Blood 
 
 i. 06 
 
 Beeswax 
 
 .96 
 
 Carbon disulphide , 
 
 1.29 
 
 Bismuth, cast 
 
 9.8 
 
 Chloroform 
 
 i-5 
 
 Brass . 
 
 8.4 
 
 Copper sulphate solution 
 
 1.16 
 
 Copper 
 
 8.8 to 8.9 
 
 Ether 
 
 .72 
 
 Cork . 
 
 .14 to .24 
 
 Glycerine . 
 
 1.27 
 
 Galena 
 
 7.58 
 
 Hydrochloric acid 
 
 1.22 
 
 German silver 
 
 8-5 
 
 Mercury, at o C. . i 
 
 3-59 6 
 
 Glass, crown 
 
 2.5 
 
 Milk 
 
 1.03 
 
 Glass, flint . 
 
 3 to 3.5 
 
 Nitric acid 
 
 15 
 
 Gold . 
 
 19-3 
 
 Oil of turpentine 
 
 .87 
 
 Ice ... 
 
 .917 
 
 Olive oil . 
 
 .915 
 
 Iron, bar 
 
 7.8 
 
 Sulphuric acid (15 %) 
 
 1. 10 
 
 Iron, cast . 
 
 7.2 to 7.3 
 
 Sulphuric acid . 
 
 1.8 
 
 Ivory . 
 
 1.9 
 
 Water (4 C.) . 
 
 I.OOO 
 
 Lead . 
 
 11.3 to 11.4 
 
 Water, sea 
 
 1.026 
 
 Marble 
 
 2.72 
 
 
 
 Mercury, at o C. 
 
 I3-59 6 
 
 GASES AT o C. AND 
 
 76 CM. 
 
 Platinum 
 
 21.5 
 
 PRESSURE 
 
 
 Quartz 
 
 2.65 
 
 
 
 Q'l 
 
 , _ - 
 
 Air 
 
 OOI293 
 
 Steel . 
 
 7.8 to 7.9 
 
 Carbon dioxide 
 
 .001977 
 
 Sulphur, native . 
 
 2.03 
 
 Hydrogen 
 
 .0000896 
 
 Tin . 
 
 7-3 
 
 Nitrogen . 
 
 .001256 
 
 Zinc, cast . 
 
 6.86 
 
 Oxygen 
 
 .001430 
 
 
 25 
 
 9 
 
 
260 
 
 APPENDIX 
 
 TABLE II 
 DENSITY OF WATER AT VARIOUS TEMPERATURES 
 
 TEMPERATURE 
 
 DENSITY 
 
 TEMPERATURE 
 
 DENSITY 
 
 . 
 
 .99987 
 
 1 6 . 
 
 .99900 
 
 4 
 
 I .OOOOO 
 
 20 . 
 
 .99826 
 
 8 . 
 
 .99989 
 
 5 0^ . . 
 
 .9882 
 
 12 . 
 
 99955 
 
 100 . 
 
 .9586 
 
 TABLE III 
 
 RELATIVE CONDUCTIVITIES FOR HEAT 
 (Silver taken as the standard of comparison = 100.) 
 
 Silver 
 
 Copper 
 
 Brass 
 
 Zinc 
 
 Tin 
 
 Iron 
 
 Lead 
 
 Aluminum 
 Brass . 
 Copper . 
 Glass . 
 Gold 
 
 100 
 
 74 
 27 
 
 20 
 
 8. 5 
 
 Bismuth 
 Ice 
 
 Marble . 
 Water . 
 Glass 
 Wood . 
 Air 
 
 TABLE IV 
 COEFFICIENTS OF LINEAR EXPANSION 
 
 .000023 
 
 .0000188 
 
 .0000172 
 
 .0000085 
 
 .0000144 
 
 Iron and steel 
 Lead . 
 Platinum 
 Silver . 
 Hard wood . 
 
 TABLE V 
 COEFFICIENT OF CUBICAL EXPANSION 
 
 Acetic acid 
 
 Alcohol (5 to 6) . 
 
 Alcohol (49 to 50) 
 
 Ether 
 
 Glycerine . 
 
 Mercury . 
 
 .00105 
 
 .00105 
 
 .00122 
 
 .0015 
 
 .0005 
 
 .00018 
 
 Olive oil 
 
 Petroleum 
 
 Turpentine 
 
 Water (5 to 6) . 
 
 Water (49 to 50) . 
 
 Water (99 to 100) 
 
 2 
 
 O.2 
 
 0.15 
 
 0.14 
 
 0.05 
 
 O.OI 
 
 0.007 
 
 .000012 
 
 .000028 
 
 .0000088 
 
 .000019 
 
 .000006 
 
 .0008 
 .0009 
 .0007 
 
 .000022 
 
 .00046 
 
 .00076 
 
APPENDIX 
 
 26l 
 
 
 TABLE VI 
 
 
 
 MELTING POINTS 
 
 
 Aluminum . 
 
 . 657 C. 
 
 Lead 
 
 327 c. 
 
 Beeswax 
 
 62 
 
 Mercury . 
 
 -39 
 
 Butter . 
 
 33 
 
 Paraffine . 
 
 45 to 50 
 
 Copper . 
 
 . 1084 
 
 Platinum . 
 
 1775 
 
 Glass 
 
 . 1000 to 1400 
 
 Rose's fusible metal . 
 
 94 
 
 Gold . 
 
 . 1064 
 
 Solder, soft 
 
 225 
 
 Ice 
 
 o 
 
 Sulphur 
 
 115 
 
 Iridium . 
 
 . 1950 
 
 Tin . 
 
 230 
 
 Iron, cast 
 
 . IIOO tO I2OO 
 
 Wax, white 
 
 65 
 
 
 TABLE VII 
 
 
 
 BOILING POINT 
 
 
 Acetic acid 
 
 . ii7C. 
 
 Water 
 
 100 C. 
 
 Alcohol, ethyl 
 
 . 78.4 
 
 Air . 
 
 - 191 
 
 Alcohol, methyl 
 
 . 66 
 
 Ammonia . 
 
 -39 
 
 Ether . 
 
 - 34 9 
 
 Carbon dioxide . 
 
 -78 
 
 Mercury 
 
 - 357 
 
 Hydrogen . 
 
 -2385 
 
 Sulphur . 
 
 . 447 
 
 Nitrogen . 
 
 - 194-5 
 
 Sulphuric acid 
 
 325 
 
 Oxygen 
 
 - 182 
 
 
 TABLE VIII 
 
 
 
 SPECIFIC HEATS 
 
 
 Alcohol (o to 50 
 
 ) . . .615 
 
 
 .114. 
 
 
 
 Aluminum (15 to 
 
 97) -2i 
 
 Lead 
 
 .0^1 
 
 
 
 Brass . 
 
 . .094 
 
 Marble 
 
 . .21 
 
 Copper 
 
 . .095 
 
 Mercury 
 
 -033 
 
 Ether . 
 
 . .52 
 
 Silver .... 
 
 . .056 
 
 Glycerine 
 
 . .55 
 
 Steel 
 
 .118 
 
 
 
 Glass . 
 
 . .19 
 
 Turpentine . 
 
 . .426 
 
 Trp 
 
 .COA 
 
 Zinc , 
 
 .094 
 
262 
 
 APPENDIX 
 
 TABLE IX 
 HEATS OF FUSION 
 
 
 CALORIES 
 
 
 CALORIES 
 
 Ice . 
 
 7Q 2C 
 
 Silver 
 
 2 1 .07 
 
 Iron 
 
 23 to 3O 
 
 Sulphur ... 
 
 
 Lead . 
 
 **j cw o w 
 
 5-37 
 
 Tin . 
 
 . 14.25 
 
 
 . 2.83 
 
 7i n r . 
 
 28 13 
 
 
 
 
 
 TABLE X 
 
 
 
 HEATS OF VAPORIZATION 
 
 
 
 CALORIES 
 
 
 CALORIES 
 
 Alcohol . 
 
 . 208 
 
 Sulphur 
 
 . 362 
 
 Ether . 
 
 . 9 
 
 Turpentine 
 
 - 74 
 
 Mercury . . 
 
 62 
 
 Watpr 
 
 r?6 
 
 
 TABLE XI 
 
 
 VELOCITY 
 
 OF SOUND IN METERS PER SECOND 
 
 
 Brass 
 
 3394 
 
 GASES AT o 
 
 
 Glass 
 
 4965 to 5564 
 
 Air .... 
 
 332 
 
 Granite . 
 
 1664 
 
 Carbon dioxide . 
 
 . 261 
 
 Iron 
 
 5016 to 5127 
 
 Hydrogen . 
 
 . 1269 
 
 Lead 
 
 1319 to 1368 
 
 Oxygen 
 
 317 
 
 Oak ... 
 
 3287 to 3991 
 
 
 
 Steel . 
 
 4768 to 5016 
 
 
 
 
 TABLE XII 
 
 
 
 INDICES OF REFRACTION 
 
 
 Air . 
 
 i .000294 
 
 Ice 
 
 1-31 
 
 Alcohol . 
 
 1.36 
 
 Iceland spar, ordinary ray . 
 
 1.65 
 
 Canada balsam 
 
 1.54 
 
 Iceland spar, extraordinary 
 
 
 Carbon bisulphide 
 
 1.68 
 
 ray . 
 
 1.48 
 
 Diamond . 
 
 2.47 to 2.75 
 
 Water . 
 
 I-336 
 
 Ether 
 
 1.36 
 
 The eye : 
 
 
 Glass, crown 
 
 1.53 to 1.56 
 
 Aqueous humor 
 
 1-337 
 
 Glass, flint 
 
 1.58 to 1.64 
 
 Vitreous humor 
 
 1-339 
 
 Glycerine 
 
 1.47 
 
 Crystalline lens 
 
 1.384 
 
APPENDIX 263 
 
 TABLE XIII 
 ELECTRIC RESISTANCE 
 
 (Ohms to i m. length and i sq. mm. cross section.) 
 
 Aluminum, annealed . .0289 
 
 Copper, annealed . . .0157 
 
 Copper, hard . . . .0150 
 
 German silver . . .2076 
 
 Iron, pure . . . .0964 
 
 Iron, telegraph wire . .15 
 
 Lead . . . .196 
 
 Manganin. . . .475 
 
 Mercury . . . .943 
 
 Platinum . . . .0898 
 
 Silver, annealed . .0149 
 
 Carbon, graphite . 24 to 420 
 
 TABLE XIV 
 ELECTROMOTIVE FORCE OF CELLS 
 
 These are only approximate values. The E.M.F. of cells varies 
 considerably with the condition of the plates and the liquid. 
 
 VOLTS 
 
 Bunsen . . . . 1.9 
 
 Daniell . . . . 1.07 
 
 Edison-Lalande . . .7 
 
 Gravity I 
 
 VOLTS 
 
 Grenet .... 2 
 Grove . . . . 1.9 
 Leclanche' . . . . i .4 
 
 TABLE XV 
 TANGENTS OF ANGLES 
 
 To find the tangent of an angle not measured by a whole number 
 of degrees, find first the tangent of the integral part of the number, 
 and add to this the product obtained by multiplying the difference 
 between this tangent and the tangent of the next whole number of 
 degrees by the decimal part of the angle. For example, to find the 
 tangent of 38 .7, proceed thus : 
 
 tan 38 = .781, tan 39 = .810. 
 
 .810 - .781 = .029, 
 
 .7 x .029 = .020. 
 
 tan 38 .7 = .781 + .020 = .801. 
 
264 
 
 APPENDIX 
 
 ANGLE 
 
 TANGENT 
 
 ANGLE 
 
 TANGENT 
 
 ANGLE 
 
 TANGENT 
 
 ANGLE 
 
 TANGENT 
 
 
 
 .OOOO 
 
 2 3 
 
 .424 
 
 46 
 
 .036 
 
 69 
 
 2.6l 
 
 I 
 
 .0175 
 
 24 
 
 445 
 
 47 
 
 .072 
 
 70 
 
 2.75 
 
 2 
 
 .0349 
 
 25 
 
 .466 
 
 48 
 
 .III 
 
 71 
 
 2.90 
 
 3 
 
 .0524 
 
 26 
 
 .488 
 
 49 
 
 .150 
 
 72 
 
 3.08 
 
 4 
 
 .0699 
 
 27 
 
 .510 
 
 50 
 
 .192 
 
 73 
 
 3-27 
 
 5 
 
 .0875 
 
 28 
 
 532 
 
 5i 
 
 235 
 
 74 
 
 3-49 
 
 6 
 
 .1051 
 
 2 9 
 
 554 
 
 52 
 
 .280 
 
 75 
 
 3-73 
 
 7 
 
 .1228 
 
 3 
 
 577 
 
 53 
 
 327 
 
 76 
 
 4.01 
 
 8 
 
 .1405 
 
 3i 
 
 .601 
 
 54 
 
 376 
 
 77 
 
 4-33 
 
 9 
 
 .1584 
 
 32 
 
 .625 
 
 55 
 
 .428 
 
 78 
 
 4.70 
 
 10 
 
 .1763 
 
 33 
 
 .649 
 
 56 
 
 483 
 
 79 
 
 5.14 
 
 ii 
 
 .194 
 
 34 
 
 .675 
 
 57 
 
 540 
 
 80 
 
 5.67 
 
 12 
 
 .213 
 
 35 
 
 .700 
 
 58 
 
 .600 
 
 81 
 
 6-31 
 
 13 
 
 .231 
 
 36 
 
 727 
 
 59 
 
 .664 
 
 82 
 
 7.12 
 
 H 
 
 .249 
 
 37 
 
 754 
 
 60 
 
 732 
 
 83 
 
 8.14 
 
 15 
 
 .268 
 
 38 
 
 .781 
 
 61 
 
 .804 
 
 84 
 
 9.51 
 
 16 
 
 .28 7 
 
 39 
 
 .810 
 
 62 
 
 .88 
 
 85 
 
 u-43 
 
 17 
 
 .306 
 
 40 
 
 839 
 
 63 
 
 .96 
 
 86 
 
 14.30 
 
 18 
 
 325 
 
 4i 
 
 .869 
 
 64 
 
 2.05 
 
 87 
 
 19.08 
 
 19 
 
 344 
 
 42 
 
 .900 
 
 65 
 
 2.14 
 
 oo 
 oo 
 
 28.64 
 
 20 
 
 364 
 
 43 
 
 933 
 
 66 
 
 2.25 
 
 89 
 
 57.29 
 
 21 
 
 384 
 
 44 
 
 .966 
 
 67 
 
 2-36 
 
 90 
 
 00 
 
 22 
 
 .404 
 
 45 
 
 1. 000 
 
 68 
 
 2.48 
 
 
 
 
 TABLE XVI 
 
 
 
 EQUIVALENTS 
 
 
 cm. 
 
 = 0-3937 in. 
 
 in. 
 
 2.54 cm. 
 
 km. 
 
 = 0.6214 m i- 
 
 m. 
 
 = 1. 609 km. 
 
 sq. cm. 
 
 = 0.1550 sq. in. 
 
 sq. in. 
 
 = 6.452 sq. cm. 
 
 c. cm. 
 
 = 0.0610 cu. in. 
 
 cu. in. 
 
 = 16.387 ccm. 
 
 kg- 
 
 = 2. 20 Ib. avoir. 
 
 oz. avoir. 
 
 = 28.35 g. 
 
 1. 
 
 - 1.0567 qt. (liquid). 
 
 Ib. avoir. 
 
 = 453-6 g- 
 
 1. 
 
 = 0.908 qt. (dry). 
 
 
 
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