LIBRARY 
 
 OF THK 
 
 UNIVERSITY OF CALIFORNIA. 
 
 IFT OF 
 
 BETA THBTA Pi 
 
 Class 
 
\ 
 
PHYSICAL 
 
 LABORATORY MANUAL 
 
 FOB SECONDARY SCHOOLS 
 
 BY 
 
 S. E. COLEMAN, S.B., A.M. 
 
 HEAD OF THE SCIENCE DEPARTMENT, AND TEACHER OF PHYSICS 
 IN THE OAKLAND HIGH SCHOOL 
 
 FTHE 
 
 { UNIVERSITY ) 
 
 NEW YORK .: CINCINNATI : CHICAGO 
 
 AMERICAN BOOK COMPANY 
 
COPYRIGHT, 1903, BY 
 8. E. COLEMAN. 
 
 ENTERED AT STATIONERS' HALL, LONDON. 
 COLEMAN. PHY. LAB. MAN. 
 
 W. P. 2 
 
OF THE 
 
 UNIVERSITY 
 
 OF 
 
 PREFACE 
 
 THE number and variety of laboratory manuals in physics 
 now on the market are so large that the merits of a new one 
 are hardly to be sought in novelty of content, but rather in 
 the utility of the material chosen from the abundant common 
 store and in the method of presenting it. Believing that these 
 are both matters of great importance and that the possibilities 
 of improvement in them have not yet been exhausted, the 
 author has written this manual in the hope that it will con- 
 tribute toward this end. 
 
 Since both the choice of material and the method of treat- 
 ment are in a large measure determined by the view enter- 
 tained in regard to the place and function of the laboratory 
 work in the course in physics, a brief statement on this point 
 seems desirable. Rejecting the extreme view that little im- 
 portance is to be attached to any part of the work except the 
 laboratory course, as well as the opposite extreme which rele- 
 gates this part of the work to the position of a supplementary 
 adjunct to the old form of text-book instruction, the author 
 has adopted in his teaching and has assumed as the controlling 
 principle in the preparation of this manual the view that the 
 laboratory course should stand in coordinate relationship to 
 the work of the class room; which, in his opinion, should 
 include as important elements qualitative experimental work 
 by the teacher, the systematic study of a good text-book, as 
 large a use of reference books as time and opportunity permit, 
 a constant appeal to the everyday experience of the pupils, 
 and, finally, the recitation or quiz, in which the information 
 gleaned from the several sources is classified, organized into 
 scientific knowledge, and assimilated. 
 
 This point of view presupposes that the laboratory work 
 
 186375 
 
4 PREFACE 
 
 will, iu general, precede the recitation, but may itself be pre- 
 ceded by experimental work by the teacher, presenting funda- 
 mental phenomena as an introduction to either the qualitative 
 or quantitative work of the laboratory. It is also assumed that 
 the text-books and reference books are legitimate aids toward 
 the interpretation of the experiment while it is being performed, 
 and that the reading of the text on the subject of the experi- 
 ment before the laboratory hour will economize time in the 
 laboratory and lead to the best results. 
 
 The choice of experiments has been governed by the fol- 
 lowing considerations : 
 
 (1) The content of the laboratory course should be rich and 
 varied, and the manipulation the simplest that will serve the 
 purpose. Skill in manipulation should not be sought for its 
 own sake, but as a means to an end, the end being a satisfac- 
 tory presentation 'of physical facts and principles. Measure- 
 ments with vernier and micrometer calipers, the diagonal scale, 
 the spherometer, etc., are omitted, since the knowledge of 
 their use finds no important application in elementary physics. 
 
 (2) There are many qualitative experiments such as the 
 reflection or refraction of a beam of sunlight in a darkened 
 room that can be fully appreciated at a distance, and for 
 which the recitation room affords better facilities than the 
 laboratory. Such experiments are not included in the manual, 
 which is limited to experiments best adapted to the laboratory. 
 But the course includes many valuable qualitative experiments 
 that can readily be provided for ; and in a considerable num- 
 ber of cases they present phenomena to the student much more 
 satisfactorily than the equivalent class-room experiments; 
 although, for nearly all of them, the latter may be substituted 
 if the teacher prefers. 
 
 (3) In order that there might be opportunity for choice, the 
 number of experiments has been made considerably greater 
 than most teachers will require of their classes. The alterna- 
 tive experiments serve the same purpose, and increase the 
 
PREFACE 5 
 
 adaptability of the manual to the varying equipment of 
 different laboratories. 
 
 The exercises marked with an asterisk in the Table of Con- 
 tents, exclusive of Part III of Exercise 10 and Part II of 
 Exercises 27, 34, and 76, are suggested as a minimum course. 
 They cover all the essentials of a good laboratory course, yet, 
 for the most part, require only inexpensive apparatus. 
 
 The method of treatment presents the following character- 
 istic features : 
 
 (1) The presentation is in the main inductive, but not ex- 
 clusively so. The laboratory course is regarded as an impor- 
 tant source of information at first hand, which is to serve as a 
 representative (though generally incomplete) basis upon which 
 to establish the theory, rather than as serving merely to illus- 
 trate or exemplify the theory dogmatically presented in the 
 text-book and the recitation. No pains have been spared in 
 the effort to cast the experiments in such form that the pupil 
 will be led by correct reasoning from the observed facts to the 
 legitimate inferences. Where the interpretation of results and 
 the theory of experimental methods can best be arrived at 
 deductively from established theory, this method is employed. 
 
 (2) A persistent effort is made throughout to stimulate 
 thought and to minimize unreasoning, mechanical work. To 
 this end the pupil is generally required to arrive at his results 
 by simple analytical processes, which to be employed must 
 be understood, and the understanding of which involves the 
 physics of the experiment, instead of by means of formulae, 
 which the average pupil will use without verification. 
 
 (3) Economy of time and of effort is sought for both teacher 
 and pupil in making the " exercise " the unit of work. With 
 very few exceptions, each exercise can be performed in a single 
 laboratory period of forty-five minutes. Short experiments on 
 the same or related topics are grouped into an exercise for 
 one laboratory period. This will overcome the tendency of 
 pupils to dawdle over short and simple experiments. 
 
6 PREFACE 
 
 The order of the chapters and, to some extent, of the indi- 
 vidual exercises, may be varied to suit the text or the prefer- 
 ence of the teacher; but generally a definite sequence of 
 exercises within the chapters is necessary for the logical 
 development of the subject, and, in writing the manual, it 
 has been assumed that this sequence will be observed. 
 
 The books referred to throughout the course are the follow- 
 ing: ".A Brief Course in Physics, 77 by George A. Hoadley 
 (American Book Company) ; " High School Physics, 77 by H. S. 
 Carhart and H. N. Chute (Allyn and Bacon) ; " Physics, 77 by 
 Frederick Slate (Macmillan) ; " Elements of Physics, 77 by Fer- 
 nando Sanford (Holt) ; " Heat, Light and Sound, 77 by D. E. 
 Jones (Macmillan); "Heat, 77 by H. ,G. Madan (Rivingtons, 
 London). 
 
 The references are quite narrowly limited to the subject- 
 matter of the experiments ; the aim being to indicate the read- 
 ing 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. 
 
 . The author takes pleasure in acknowledging his great in- 
 debtedness to Mr. George L. Leslie, Head of the Science 
 Department of the Los Angeles High School, under whose 
 helpful direction he obtained his first experience in teaching 
 physics, and whose laboratory course he has, during the years 
 since 1899, developed into the present work. The author 
 regrets to state that circumstances rendered impossible the 
 contemplated cooperation of Mr. Leslie in the preparation of 
 the manual for publication. 
 
 A further acknowledgment is due to Mr. A. G. Van Gorder, 
 a former colleague at Los Angeles, to whom the author is 
 indebted for a number of valuable suggestions. 
 
 S. E. OOLEMAN. 
 OAKLAND, CALIFORNIA. 
 
CONTENTS 
 
 I. DIRECTIONS FOR LABORATORY WORK AND NOTEBOOK 
 KXERCISE II. DENSITY AND MOLECULAR PHENOMENA 
 
 *1 . Density of Solids . . . . . . . 
 
 18 
 
 *2. Density of Liquids . . . . . ' . 
 
 . 20 
 
 *3i. Cohesion and Adhesion . . . . 
 
 . 21 
 
 3 2 . Cohesion and Adhesion (alternative) . 
 
 . 23 
 
 *4. Surface Tension and Capillarity 
 
 . 25 
 
 III. MECHANICS OF FLUIDS 
 
 
 *5. Liquid Pressure 
 
 , 29 
 
 *6i. Buoyancy of Liquids . ... 
 
 , 31 
 
 6 2 . The Buoyant Force of Water (alternative) 
 
 . 34 
 
 *7. Specific Gravity of Solids .* . 
 
 . 35 
 
 *8. Specific Gravity of Liquids ...... 
 
 . 37 
 
 9. Specific Gravity of Liquids 
 
 . 38 
 
 *10. Gas Pressure ....... 
 
 40 
 
 11. Specific Gravity of a Liquid ...... 
 
 . 42 
 
 *12. The Siphon and the Suction Pump 
 
 . 44 
 
 13. The Law of Boyle . . 
 
 . 45 
 
 14. The Density of Air 
 
 . 48 
 
 IV. MECHANICS OF SOLIDS 
 
 
 *1 5. Composition of Forces ....... 
 
 . 51 
 
 16. Equilibrium of Parallel Forces ...... 
 
 . 54 
 
 *17. Moments of Force 
 
 . 57 
 
 *18. Center of Gravity and Equilibrium ..... 
 
 . 60 
 
 19. Equilibrium and Stability ...... 
 
 . 63 
 
 20. Comparison of Masses by Inertia . . . 
 
 . 65 
 
 21. Falling Bodies : Whiting's Method . . 
 
 . 68 
 
 *22. The Simple Pendulum 
 
 . 70 
 
 23. The Wheel and Axle 
 
 . 73 
 
 *24. The Pulley 
 
 . 75 
 
 25. The Inclined Plane 
 
 . 79 
 
 V. HEAT 
 
 
 *26. Expansion by Heat 
 
 . 82 
 
 *27. Conduction of Heat ........ 
 
 . 83 
 
 *28. Convection of Heat 
 
 . 85 
 
 29. Radiant Energy 
 
 . 87 
 
 30. Coefficient of Linear Expansion 
 
 . 90 
 
 31. Coefficient of Expansion of Liquids 
 
 93 
 
 32. Coefficient of Expansion of Air ..... 
 
 . 97 
 
 *33. Melting and Freezing. Solution 
 
 . 99 
 
 *34. Evaporation. Vapor Pressure. Dew-point 
 
 102 
 
 *35. Boiling of Water 
 
 . 105 
 
 36. Boiling Point of a Liquid 
 
 . 107 
 
CONTENTS 
 
 EXERCISE 
 
 *37. Specific Heat 
 
 PAGE 
 
 111 
 
 *38. Latent Heat of Fusion of Ice 
 
 . 113 
 
 39. Latent Heat of Vaporization of Water .... 
 
 116 
 
 VI. SOUND 
 
 
 *40. The Transmission of Sound 
 
 . 118 
 
 41. The Velocity of Sound in Air ...... 
 
 120 
 
 42. The Reflection of Sound 
 
 . 123 
 
 43. Sympathetic and Forced Vibrations .... 
 
 125 
 
 *44. Wave Length by Resonance 
 
 . 128 
 
 45. Interference and Beats 
 
 . 132 
 
 46. Vibrating Strings. Effect of Length 
 
 134 
 
 VII. LIGHT 
 
 
 *47. Some Results of Rectilinear Propagation .... 
 
 . 136 
 
 *48. Photometry 
 
 . 139 
 
 *49i. Plane Mirrors 
 
 145 
 
 49 2 . Plane Mirrors (alternative) . ... 
 
 . 148 
 
 50. Multiple Images ........ 
 
 . 150 
 
 51. The Concave Mirror 
 
 . 153 
 
 *52. Phenomena due to Refraction 
 
 . 157 
 
 *53. Index of Refraction ........ 
 
 . 162 
 
 54. Total Reflection 
 
 . 166 
 
 *55. The Convex Lens 
 
 . 169 
 
 56. The Focal Length of a Lens 
 
 . 172 
 
 *57. The Simple Microscope ....... 
 
 . 176 
 
 *58. Color. 
 
 177 
 
 59. Spectra .......... 
 
 180 
 
 *60. The Astronomical Telescope 
 
 . 185 
 
 61. The Galilean Telescope 
 
 . 187 
 
 62, The Compound Microscope ...... 
 
 . 188 
 
 VIII. MAGNETISM AND ELECTRICITY 
 
 
 *63. Magnets and Magnetic Action 
 
 . 191 
 
 *64. Magnetic Induction. Theory of Magnetism . 
 
 . 192 
 
 *65. The Magnetic Field 
 
 . 195 
 
 *66. The Single-fluid Cell 
 
 . 196 
 
 *67. The Magnetic Effects of a Current 
 
 . 198 
 
 68. The Tangent Galvanometer ...... 
 
 . 204 
 
 69. The Laws of Resistance 
 
 . 207 
 
 *70. Measurement of Resistance 
 
 . 210 
 
 71. The Resistance of a Cell 
 
 . 212 
 
 *72i. The Electromotive Force of Cells 
 
 . 214 
 
 72 2 . The Electromotive Force of Cells (alternative) 
 
 . 216 
 
 73. Arrangement of Cells ....... 
 
 . 217 
 
 *74. Induced Currents 
 
 . 219 
 
 *75 The Motor 
 
 222 
 
 *76. The Electric Bell and the Telegraph .... 
 
 . 224 
 
 77 The Telephone .... 
 
 226 
 
 APPENDIX . 
 
 229 
 
PHYSICAL LABORATORY MANUAL 
 
 I. DIRECTIONS FOR LABORATORY WORK 
 AND NOTEBOOK 
 
 GENERAL DIRECTIONS 
 
 1. On laboratory days the work required of the student 
 outside the laboratory is : (1) the completion of the record for 
 the exercise last performed ; (2) a careful reading of the refer- 
 ence in the text-book and of the laboratory directions for the 
 exercise for the next day. 
 
 2. Check the list of apparatus before beginning any experi- 
 ment, and report any deficiency to the instructor at once. 
 Never borrow apparatus from other places. 
 
 3. Remember that habits of neatness and order are important 
 as well as knowledge. Students should feel a personal respon- 
 sibility for the condition of the apparatus and table where they 
 are at work, and especially for the condition in which they are 
 left at the close of the exercise. Learn to cooperate with the 
 instructor in keeping the laboratory in order. Students are 
 responsible for all damage to apparatus, and should report 
 such damage to the instructor immediately. 
 
 4. Ordinarily no time is to be taken in the laboratory for 
 writing discussions of experiments or for making computations, 
 except in so far as the results of these computations are required 
 for immediate use ; but brief intervals that can not be utilized 
 for experimental work should be so spent. 
 
 9 
 
10 LABORATORY WORK AND NOTEBOOK 
 
 5. All questions asked in connection with the experimental 
 work should receive the immediate and careful attention of the 
 student, as an understanding of them is necessary for the 
 intelligent performance of the experiment. Ask the instructor 
 for help on these questions when it is necessary. 
 
 THE RECORD 
 
 6. At the beginning of the record of each exercise write its 
 number and title. Do not copy the list of apparatus. Copy 
 and number all subheadings. All parts of the record are to be 
 paragraphed, numbered, and lettered to correspond with the 
 directions. 
 
 7. All observations, computations, and results should stand 
 out boldly on the page, separated from all descriptive and 
 explanatory matter. In general, they should be tabulated, or 
 each item should be entered on a separate line. 
 
 8. Do not record results in the manual. Measurements 
 should be immediately recorded (with pencil) in proper form 
 in the notebook. A record taken in any other way, to be 
 copied into the notebook later, is not recommended. 
 
 9. Aim at brevity of statement without omitting essentials. 
 Use only decimal fractions in the metric system, and express 
 a quantity in terms of one unit only; for example, write 
 15.25 g. instead of 15 g 2 dg. 5 eg. Express all lengths in 
 centimeters. 
 
 10. Your record should be complete in itself ; that is, it should 
 not require reference to the directions <to make it fully intelli- 
 gible. The " Form of Record' 7 is intended to serve as a model 
 for the tabulation of numerical data only, and is never to be 
 regarded as indicating the complete record of tho exercise. 
 
COMPUTATIONS 11 
 
 11. A figure drawn for the .purpose of explanation should, in 
 general, represent a plane section through the apparatus, rather 
 than a view in perspective. 
 
 12. In the matter of neatness, as well as of accuracy, the 
 record should be the best that the student is capable of. An 
 untidy page should always be copied. 
 
 COMPUTATIONS 
 
 13. All computations are to be indicated. In the first two 
 exercises the computations are indicated in the form of record 
 as a reminder of this direction. You are expected to remember 
 it thereafter without this hint. Where computations are 
 entered in tabular form in columns, the headings of the 
 columns are a sufficient indication of the operations; hence 
 only the results are to be entered in the columns. Remember 
 that a ratio is an indicated division; always perform the 
 division and express the value of the ratio decimally. 
 
 14. All concrete numbers should be followed by the name of 
 the unit or the units in which they are measured. This applies 
 to all the numbers obtained in a series of computations as well 
 as to the final result. A strict observance of this direction will 
 be very helpful. Completeness of expression compels definite- 
 ness of thought ; the want of it is at the root of the greater por- 
 tion of the difficulties that the average student encounters. 
 
 15. It is important to test the accuracy of numerical results 
 whenever possible. This is done by finding the per cent of 
 error of the result. What is meant by this will be seen from 
 the following example : 
 
 Suppose a length of 10.05 cm. is measured and recorded as 
 10 cm. The error is .05 cm. ; and is .05 -=- 10.05, or .005 of the 
 quantity measured, or .5 % of it. If the same error (.05 cm.) 
 were made in measuring a distance of 2.5 cm., the per cent of 
 
12 LABORATORY WORK AND NOTEBOOK 
 
 error would be .05 -4- 2.5 x 100 %, or 2.5 %. It will be seen 
 that the importance of a given error is greater as the quantity 
 measured is smaller, and that the degree of accuracy of a 
 measurement is expressed not by the error but by the per cent 
 of error. Pupils frequently write the per cent of error 100 
 times too small. 
 
 16. If the per cent of error of any result is too large, the 
 pupil is expected to repeat the experiment without delay. 
 Only reasonably accurate results should be handed in for 
 inspection. 
 
 17. Computations should be carried to the first doubtful 
 figure, and all decimal places beyond this should be dropped, 
 as they are wholly unreliable. For example, suppose that 
 the weight of 1 ccm. of water, computed from the measure- 
 ments obtained in Exercise 2, is found to be .99372 g. ; and 
 that there is a possibility of an error of .5 %, or about .005 g. 
 In this case the third figure (counting from the left) is doubt- 
 ful, and the result should be written .994 g. 
 
 18. Decimal points are frequently misplaced. The most 
 casual inspection of the numbers is often sufficient to detect 
 such an error. Thus, if 38.2 be divided by .094, it will be evi- 
 dent at a glance that the quotient is slightly greater than 10 
 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. 
 
 Gross errors in computation can often be detected by the 
 absurdity of the results obtained. Thus, if one should obtain 
 .412 g. as the weight of 1 ccm. of stone in Exercise 1, he 
 should see at once that a serious blunder had been made 
 either in the experimental work or the computations ; since 
 this is less than half the weight of a cubic centimeter of water 
 (1 g.), and, for equal bulk, stone is much heavier than water. 
 
COMPUTATIONS 13 
 
 19. Work must never be entered in such form as the 
 following : 
 
 5 x 8 x 10 = 400 - 500 = .8. 
 
 This equation expresses the absurdity that 5 x 8 x 10 = .8. 
 Two equations are necessary to express the relations intended; 
 namely : 
 
 5 x 8 x 10 = 400, 
 
 400 -r- 500 =.8. 
 
 20. Finally. All the above directions are important. Al- 
 though some of them can best be understood in connection with 
 the actual work of the laboratory, they are included here for 
 convenience of reference. Study them carefully at the begin- 
 ning, and look them over frequently during the first few weeks, 
 until you are sure you understand them and know that you are 
 following them. 
 
II. DENSITY AND MOLECULAR PHE- 
 NOMENA 
 
 MEASUREMENTS 
 
 21. 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 centi- 
 meter. Fractions of a millimeter 
 are to be estimated in tenths and 
 recorded as hundredths of a centi- 
 meter. Thus the length of the 
 block shown in the figure is 2.35 cm. 
 The figure also shows the correct 
 position of a meter rod in measur- 
 ing. If the rod were turned flat, 
 the scale would be at a distance and the measurement would be 
 less accurate. If the rod is worn at the end, it is better to begin 
 at some other even centimeter or, better still, even decimeter. 
 
 22. Order of trying Weights in Weighing. Without a sys- 
 tematic method of procedure in the use of the weights much 
 time is wasted in the process of weighing. Students often 
 think that they need more small weights than are provided, 
 and resort to the forbidden practice of borrowing. A full set 
 of weights, such as you will always find provided, includes all 
 that are necessary to balance any weight 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. 
 
 14 
 
MEASUREMENTS 15 
 
 Begin by trying the weight which you estimate to be nearest 
 to the weight to be balanced. If it seems to be nearly suffi- 
 cient, add the next smaller; but if it is evidently much too 
 light, replace it and try the next larger. Proceed thus back- 
 ward, trying the larger weights till you are assured that the 
 next larger, used alone, is too large. The secret of rapid 
 iveighing 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 again be repeated ; whereas it would have been 
 discovered by trying the single larger weight. 
 
 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 it (not a larger one) and try the 
 next smaller. Continue thus till you come to the smallest 
 weight provided. 
 
 23. Use of the Platform Balance. The platform balance 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.). In 
 using a platform bal- 
 ance it must be ob- 
 served that the beam 
 adjustment acts with 
 the weights or with the 
 article weighed, depend- 
 ing upon whether the 
 article to be weighed FlG 2 
 
 is placed on the one 
 
 platform or the other. Make the beam adjustment act with the 
 weights, and add the beam reading to the sum of the weights 
 used. 
 
 Proceed as follows : Place the article to be weighed on the 
 proper platform. Slide the weight on the beam to the zero 
 
DENSITY AND MOLECULAR PHENOMENA 
 
 end. The beam adjustment is to be held in reserve till the 
 weighing has been brought within the limit of the beam 
 reading. When this has been accomplished, make the final 
 adjustment with the beam. You can shorten this process 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 sensitive 
 to less than .1 g., and readings to this fraction are sufficient. 
 
 24. Use of the Specific Gravity or Beam Balance. The beam 
 of this balance is not fastened to the upright, and is easily 
 thrown out of place in putting heavy objects on or removing 
 
 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 differ by less than one division of the scale behind it. 
 
 With this balance, weight should be determined to the nearest 
 
 centigram. 
 
 25. Precautions to be observed in Weighing. Weights, 
 especially heavy ones, should be placed, near the center of 
 the platform or pan. 
 
 Fia. 3. 
 
MEASUREMENTS 17 
 
 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 fractional weights. 
 
 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 you return 
 them 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. Remember that if one of the weights is 
 lost the whole set is practically useless. 
 
 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. 
 
 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. 
 
 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. 
 
 26. The Estimation of Tenths. In all laboratory measure- 
 ments it should be remembered that the student is expected to 
 be as accurate as it is possible for him to be with the apparatus 
 provided. In determining the position of points on scales of 
 various sorts, as the position of the end of a line on a meter 
 rod, the point on its scale to which a hydrometer sinks in a 
 liquid, the height of the mercury on a thermometer scale, the 
 position of the pointer on the scale of a spring balance, etc., 
 the scale should be read to tenths of its smallest division. Even 
 if the student has not the skill to do this accurately, the esti- 
 mate will be considerably more accurate than the nearest whole 
 division ; and it is the universal rule that no error should be 
 unnecessarily introduced into the work. 
 COLEMAN'S PHY. LAB. MAN. 2 
 
18 
 
 DENSITY AND MOLECULAR PHENOMENA 
 
 EXERCISE 1. DENSITY OF SOLIDS 
 
 I. To find the weight of one cubic centimeter of a 
 rectangular block of wood. 
 
 Apparatus. A rectangular block of wood; platform balance; 
 weights ; forceps for handling weights ; metric rule. 
 
 [A 30 cm. metric rule is more convenient than a meter stick for this 
 and several other experiments.] 
 
 Definition. The density of a substance is the mass of a unit 
 volume of -the substance. In the metric system it is usually 
 expressed as the number of grams in a cubic centimeter of it 
 (g. per ccm.); in the English system, as the number of pounds 
 in a cubic foot of it (Ib. per cu. ft.). 
 
 Measure with the metric rule the dimensions of the block. 
 (Observe the directions of Arts. 21 and 26.) For each dimen- 
 sion take four measurements one near each of the four 
 parallel edges and take their average. 
 
 Weigh the block. (Observe the directions of Arts. 22, 23, and 
 25.) Does it matter on which platform you place the block? 
 Can the graduated beam at the side be used in the weighing 
 when the block is on either platform ? Always return the 
 weights to their proper places in the block as soon as you have 
 finished weighing. 
 
 Compute the volume of the block and the weight of 1 ccm. 
 of it (its density). 
 
 FORM OF KECORD 
 
 DIMENSIONS OF THE BLOCK 
 
 LENGTH 
 
 WIDTH 
 
 THICKNESS 
 
 cm. 
 
 cm. 
 
 cm. 
 
 Av. cm. 
 
 cm. 
 
 cm. 
 
MEASUREMENTS 19 
 
 Weight of the block = g. 
 
 Volume of the block = ( )x( )x( ) = ccm. 
 
 Density of the block = ( ) ~ ( ) = g. per ccm. 
 
 IIo To find the density of a stone or other irregular 
 body that sinks in water. 
 
 Apparatus. Platform balance and weights ; overflow can ; 
 tumbler ; vessel of water ; cubic centimeter graduate ; stone 
 or other 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 tubing is attached to 
 the spout (Fig. 4).] 
 
 Weigh the solid. (Keturn the weights to the block.) 
 
 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, and catch the over- 
 flow in the graduate ; then empty the latter and again hold it 
 under the spout. Lower the solid into the can by means of 
 the string, and catch the overflow in the graduate. What is 
 the volume of the overflow ? In measuring the water, hold the 
 eye on a level with its surface, and observe 
 where the lowest part of the surface (seen 
 through the elevated ridge of water at the 
 edge) comes to on the scale. Estimate to 
 tenths of the smallest division on the scale. 
 
 How does the volume of the overflow 
 compare with the volume of the solid ? 
 
 Record each item on a separate line, and 
 compute the density of the solid. Indicate 
 the computation. 
 
 If the density of the solid is given in 
 Table I of the Appendix, compute the per cent of error of your 
 result. 
 
20 DENSITY AND MOLECULAR PHENOMENA 
 
 EXERCISE 2. DENSITY OF LIQUIDS 
 
 I. To find the density of water. 
 
 Apparatus. Beam balance and set of weights to 1 eg. (or 
 platform balance and weights to 5 g.) ; forceps ; beaker ; grad- 
 uate with cubic centimeter scale ; mop cloth. 
 
 a. Weigh the beaker empty. (See Arts. 24 and 25.) 
 
 b. Fill the beaker nearly full of water and weigh again. 
 Always record the quantity measured; in this case it is the 
 weight of the beaker and water. The weight of the water is 
 found indirectly by subtraction. The record should be as in- 
 dicated below. By recording the actual observations it is easy 
 to determine whether an error in the final result is due to an 
 error in the experimental work or in the computations. 
 
 c. Measure in the graduate the volume of the water weighed. 
 
 d. Compute the density of the water in grams per cubic cen- 
 timeter. The density of water at 4 C. is 1 g. per cubic centime- 
 ter. At the temperature of the laboratory (about 20) it is 
 .998 g. per cubic centimeter. Assuming the latter to be the 
 true value, find the error (the difference between the true value 
 and your result) and the per cent of error (the per cent that 
 this difference is of .998). The per cent of error should be less 
 than 1%. 
 
 Suggest possible reasons why your result is not perfectly 
 correct. 
 
 FORM OF EECORD 
 
 a. Weight of beaker = g. 
 
 b. Weight of beaker and water = g. 
 
 Weight of water =() () = g. 
 
 c. Volume of the water = ccm. 
 
 d. Computed density of water = ()--() = g. per ccm. 
 True value of density (at 20 C.) = .998 g. per ccm. 
 Error =()-() - g. 
 
 Per cent of error = ()--() x 100% = %. 
 
COHESION AND ADHESION 21 
 
 II. To -find the density of a saturated solution of 
 table salt. 
 
 Apparatus. Beam balance and set of weights to 1 eg. (or 
 platform balance and weights to 5 g.) ; bottle with glass stop- 
 per; bottle of water; bottle of a saturated solution of table 
 salt (or of other liquid) ; jar of water ; beaker ; mop cloth. 
 
 a. Weigh the bottle empty with the stopper. 
 
 b. Fill it with water from the supply bottle and insert the 
 stopper, being careful to avoid a bubble of air beneath the stop- 
 per. Wipe the bottle dry on the outside and weigh it. 
 
 c. Compute the weight of water in the bottle. What is the 
 capacity of the bottle in cubic centimeters, assuming the density 
 of water to be 1 g. per cubic centimeter ? 
 
 d. Empty the bottle (into the supply bottle of water) ; fill 
 with the salt solution (or other liquid provided), exercising the 
 same precautions as before, and weigh. Return the solution 
 to the supply bottle and rinse the bottle in the jar of water. 
 Use the mop cloth, and leave the table and scale pans dry, and 
 everything in order. 
 
 e. Compute the weight of the salt solution used, and from 
 this and its volume (the capacity of the bottle) compute its 
 density. Record each item on a separate line. 
 
 EXERCISE ,% COHESION AND ADHESION 
 
 References. Hoadley, 28 ; Carhart and Chute, 17-18. 
 
 To study the effect of distance upon molecular at- 
 traction, and to determine the relative strength of 
 cohesion and adhesion for a number of substances. 
 
 Apparatus. Two pieces of plate glass ; two pieces of com- 
 mon window glass ; piece of glass coated with paraffine ; vessel 
 of water; small bottle containing a little mercury and some 
 very small bits of glass ; dropping tube. 
 
22 DENSITY AND MOLECULAR PHENOMENA 
 
 a. See that the surfaces of the pieces of plate glass are clean ; 
 then press them firmly together. Now lift the upper piece, 
 and see whether the lower one will stick to it and be lifted with 
 it. Keep one hand in position to catch the lower glass if it 
 falls. Pull the pieces apart after pressing them firmly together, 
 and note the force with which they stick together, or cohere. 
 Describe briefly the observed effects. 
 
 b. Experiment in the same way with the pieces of window 
 glass. The surfaces of the plate glass are quite accurately 
 plane ; those of the window glass are much less so, in fact, are 
 distinctly wavy. The difference in the results of the experi- 
 ments is due to this difference in the surfaces. Hence the ex- 
 periments indicate a necessary condition for the existence of 
 cohesion. State this condition, and show how it follows from 
 the experiments. 
 
 c. Again take the pieces of plate glass, dip them in water to 
 moisten their surfaces, and press them together as before. Now 
 pull them apart. Compare the forces involved with the forces 
 when the plates were dry. The water forms a connecting link, 
 adhering to the glass surface on each side. 
 
 Do you conclude from this that adhesion between water and 
 glass molecules is greater than cohesion between two glass 
 molecules when the molecules are equally near ? 
 
 If your conclusion is different, state it and give reason. (On 
 this point consider whether it is easier to wipe water from 
 a glass surface or to wipe glass molecules from a glass sur- 
 face.) 
 
 d. From the fact that water wets glass, what do you infer 
 concerning the relative strength of the molecular force between 
 two water molecules and that between a water and a glass 
 molecule, the molecules being the same distance apart in both 
 cases ? 
 
 e. Caution. In handling mercury, be careful not to get any 
 of it on jewelry. It unites with gold and silver, forming an 
 amalgam that discolors the surface. 
 
COHESION AND ADHESION 23 
 
 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. 
 
 Why does the drop not flatten out into a thin layer as the 
 result of its own weight ? 
 
 Why does it not spread over the surface as a drop of water 
 would ? 
 
 With the point of your pencil detach a very small bit from 
 the drop. Is this smaller portion more or less nearly spheri- 
 cal than the larger portion ? Why ? Pour the drop of mer- 
 cury into your hand and return it to the bottle. 
 
 /. You may have concluded from the preceding experiment 
 that there is no adhesion between glass and mercury. To test 
 this point, turn the bottle of mercury about and note the 
 behavior of the bits of glass toward the mercury. Describe 
 their behavior and state conclusion. Your conclusion in regard 
 to cohesion in mercury and adhesion between mercury and 
 glass should be consistent with the preceding experiment as 
 well as with this. 
 
 g. Study and describe the behavior of a drop of water on 
 the paraffined surface of the piece of glass. 
 
 Do you find cohesion within water 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 ? 
 
 EXEKCISE 3 2 . COHESION AND ADHESION 
 
 (ALTERNATIVE WITH EXERCISE 3j) 
 References. Hoadley, 28 ; Carhart and Chute, 17-18. 
 
 To measure the force of cohesion or adhesion that 
 must be overcome in pulling a glass disk from water 
 and from mercury, and a copper disk from* mercurj/. 
 
24 DENSITY AND MOLECULAR PHENOMENA 
 
 Apparatus. Specific gravity balance ; weights to 1 eg. ; fine 
 shot or coarse sand ; disk or square of glass about 5 cm. in 
 diameter, with 3 or 4 threads attached for suspending it 
 (Fig. 5) ; disk or square of copper of same size, amalgamated 
 with mercury, with threads for suspension; tumbler of clean 
 water ; tumbler containing some clean mercury. 
 
 [To amalgamate the copper, put it in a dish containing a little mercury 
 and dilute sulphuric acid, and rub the acid and mercury over its surface 
 with a rag tied to a stick. Mercury will wet such an amalgamated sur- 
 face if it is kept clean. Avoid touching it with the fingers. ] 
 
 a. Suspend the glass disk from the hook on the under side 
 of the higher scale pan ; and adjust the standard of the balance 
 or the glass of water so that the disk just touches the water 
 when the beam is horizontal. The disk must be exactly hori- 
 zontal when all the cords are stretched ; but, to 
 avoid air bubbles under it, touch one side of it to 
 the water first, then gradually lower the other. 
 Pour the shot (or sand) slowly into the scale pan 
 on the opposite side till the disk is torn away from 
 the water. Eemove the tumbler of water, and 
 restore equilibrium by placing weights in the 
 
 scale pan from which the disk is still suspended. These 
 weights measure the force exerted in tearing the disk from 
 the water. 
 
 b. Is the under surface of the disk dry or wet ? Was the 
 force that was overcome adhesion between the disk and the 
 water or cohesion between a thin layer of water in contact 
 with the disk and the water beneath ? 
 
 Which is the stronger, cohesion in water or adhesion between 
 water and glass ? 
 
 c. In the same way measure the force necessary to tear the 
 glass disk from the mercury. The glass must be dry and the 
 
 'surface of the mercury very clean. Impurities on the surface 
 may be removed by skimming it with a bit of paper pushed 
 into the mercury and drawn across the surface. 
 
SURFACE TENSION AND CAPILLARITY 25 
 
 d. Did the mercury wet the disk ? Which joint was broken 
 when the disk was torn away, the adhesion joint between glass 
 and mercury, or the cohesion joint between adjacent layers of 
 mercury ? 
 
 e. Measure in the same way the force necessary to tear the 
 amalgamated copper disk from the mercury. Do not touch 
 the under surface of the disk with the lingers ; the oil from 
 them would atfect the adhesion of the mercury to the surface. 
 If the disk is clean, as it should be, its surface will be wet 
 with mercury when it is torn away. 
 
 Have you measured cohesion in mercury or adhesion between 
 mercury and the amalgamated surface of the copper ? 
 
 Discussion. a. Which is stronger, adhesion between glass 
 and mercury, or cohesion in mercury ? Show how your answer 
 follows from the results of this exercise. 
 
 b. Arrange in their order of magnitude, cohesion in mer- 
 cury, cohesion in water, adhesion between mercury and glass, 
 and adhesion between the amalgamated copper and mercury. 
 What do you know of the position of adhesion between water 
 and glass in this list ? 
 
 EXERCISE 4. SURFACE TENSION AND 
 CAPILLARITY 
 
 References. Hoadley, 119-126; Carhart and Chute, 113- 
 122 ; Slate, 80-82 ; Sanford, pp. 102-103. 
 
 I. To study various phenomena due to surface tension. 
 
 Apparatus. Pins; tumbler of clean water; lifter made of 
 wire, for placing pins on water (Fig. 6) ; small bottle of alco- 
 hol ; glass rod ; small rubber band ; dish of soap solution ; 
 wire ring about 3 in. in diameter, with extension of wire for 
 handle, and with a thread tied across the ring and carrying a 
 loop at its middle (Fig. 7) ; bottle containing a drop of oil sus- 
 pended in a solution of alcohol and water of its own density. 
 
26 
 
 DENSITY AND MOLECULAR PHENOMENA 
 
 FIG. 6. 
 
 [To prepare the suspended drop of oil, pour a very little water into 
 the bottle ; add two or three drops of oil ; then pour in alcohol till 
 the oil sinks part way. Tip the bottle and pour the alcohol in gently 
 to avoid breaking the oil up into minute globules.] 
 
 a. Place a pin on the lifter (Fig. 6) and lower it slowly till 
 
 the pin floats on the water, then remove 
 the lifter carefully. If the pin sinks now 
 or later during the experiment, take it out 
 with the lifter, wipe it dry, and try again. 
 Observe closely the shape of the surface of 
 the water about the pin. Describe it. Draw 
 an enlarged figure of a cross section of the 
 pin and adjacent water surface. 
 
 Push the pin till it breaks through the 
 surface. Why does it sink now ? Why did it float before ? 
 
 b. Float two pins on the water, placing them parallel and 
 about 2 cm. apart. Dip the glass rod into the alcohol, and 
 carry a drop on the end of it to the surface of the water 
 between the pins, at the same time watching the behavior 
 of the pins. (If you do not succeed in 
 
 the experiment after a few trials, you 
 may substitute the rubber band for the 
 pins, and drop the alcohol inside of 
 it.) What happens ? In trying to 
 understand what happens, think of the 
 water surface as a stretched membrane, 
 attached (by adhesion) to both sides 
 of the pin and pulling it equally on 
 both sides. 
 
 What is the effect of the alcohol on 
 the surface tension or stretch ? 
 
 c. Dip the wire ring into the soap solution and withdraw it 
 obliquely. Repeat, if necessary, till a film is obtained. Hold 
 the ring so that the loop of thread will attach itself to the 
 film ; then, with the point of your pencil, break the film inside 
 
 FIG. 7. 
 
SURFACE TENSION AND CAPILLARITY 27 
 
 the loop. Describe and explain the behavior of the loop when 
 the film inside it is broken. 
 
 d. Describe the appearance of the oil globule suspended in 
 the solution of alcohol and water. An inflated rubber balloon 
 and a soap bubble take the same shape for similar reasons. 
 Describe, compare, and explain. Shake the bottle very gently 
 so as to distort the drop, and note its behavior. Be careful 
 not to shake so hard as to break up the drop. Describe and 
 explain its motion. 
 
 II. To study capillary action with reference to the 
 effect of the size of the tubes and the relative strength 
 of cohesion and adhesion. 
 
 Apparatus. Capillary tubes of glass of different sizes; 
 capillary tube coated inside with paraffine ; glass of water ; 
 glass containing a little mercury ; blotting paper. 
 
 [To coat a tube with paraffine, put a very small piece of paraffine in 
 one end of the tube ; hold it obliquely in a flame till the paraffine melts 
 and runs down the tube.] 
 
 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. Do not use the same tubes in the water and the mercury. 
 Insert tubes of different sizes into the water, and observe the 
 rise of the water in the tubes. The forces that produce this 
 motion are the molecular forces of cohesion and adhesion that 
 were studied in the preceding exercise. Describe the shape of 
 the water surface in the tubes. Remember that the surface is 
 under a tension, and is attached by adhesion to the glass. 
 
 Explain how the rise of the water is brought about. 
 
 Draw a figure in cross section showing the height of the 
 water and the shape of the surface in the tumbler and in tubes 
 of different sizes inserted in it. 
 
28 DENSITY AND MOLECULAR PHENOMENA 
 
 c. Kepeat the preceding with tubes of different sizes in mer- 
 cury, using only dry tubes. By pressing the tube against the 
 side of the glass, an unobstructed view of the inside of the tube 
 will be obtained. Describe what is seen and draw figures to 
 illustrate. 
 
 d. The rise of the water and the fall of the mercury in the 
 tubes are due to the direction of curvature of their surfaces. 
 Explain how. 
 
 What determines the direction of curvature of the surfaces ? 
 
 Test these matters further by trying in water the capillary 
 tube coated on the inside with paraffine. Describe and account 
 for the result, bearing in mind the behavior of the drop of 
 water on the piece of glass covered with paraffine in Ex- 
 ercise 3!. 
 
 e. Pour a few drops of water upon the mercury, and remove 
 it with the blotting paper. Observe the difference in the 
 behavior of the water and the mercury toward the blotting 
 paper. Describe and explain. 
 
III. MECHANICS OF FLUIDS 
 EXERCISE 5. LIQUID PRESSURE 
 
 References. Hoadley, 131-142 ; Carhart and Chute, 123- 
 133 ; Slate, 45-47. 
 
 I. To observe the effect of the depth of a liquid upon 
 the pressure exerted by it. 
 
 Apparatus (for Parts I and II). Battery jar filled with 
 water ; Welsbach or student lamp chimney ; small square of 
 cardboard ; stick 1 ft. long ; two beakers, one low and wide, 
 the other tall and slender, of about the same weight, but very 
 unequal diameters. 
 
 a. Hold the cardboard over an end of the chimney, and 
 lower this end into the jar of water. Remove the hand from 
 the cardboard when you find that it will remain in place with- 
 out being held. What keeps it in place ? 
 
 b. With the -cardboard covering the lower end of the chim- 
 ney, lower it till it no longer tends to sink. Steady it, but do 
 not support it with the hands. What sustains the chimney ? 
 It may help you to understand this if you put the stick down 
 through the chimney and push the cardboard from the end of 
 it, at the same time noting the force necessary to do so. 
 
 c. Replace the cardboard over the end of the chimney, and 
 push the latter slowly into the water, at the same time noting 
 the change in the force you must exert to keep it in place. 
 State any relation that you discover between the depth and the 
 force (pressure) exerted by the water. Do not make your state- 
 ment more explicit than the crude nature of your experiment 
 will warrant. The exact relation between depth and pressure 
 
 29 
 
30 MECHANICS OF FLUIDS 
 
 can be obtained experimentally only - by careful measurement 
 of the depths and pressures. 
 
 What is the direction of the pressure you have been investi- 
 gating ? 
 
 II. To observe whetlier the total pressure is affected by 
 the area of the surface pressed upon. 
 
 Push the two beakers, one in each hand, bottom down, into 
 the water to the same depth ; and notice which requires the 
 greater force to keep it in place. Explain. 
 
 III. To observe the effect of the density of the liquid 
 upon the pressure exerted by it. 
 
 Apparatus. Tumbler containing mercury ; tumbler of water ; 
 two blocks of the same size and shape and small enough to go 
 into the tumblers ; chunk or ball of iron. 
 
 a. Lift the tumbler of mercury ; handle it carefully. Lift 
 the tumbler of water. Mercury is 13.6 times as dense as water. 
 Float one of the blocks on the water and the other on the mer- 
 cury. 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 chunk or ball of iron into the mercury. What 
 happens to it ? Explain. 
 
 IV. To measure liquid pressure with a pressure gauge, 
 or manometer. 
 
 Apparatus. Hydrometer jar of water ; a water and a mer- 
 cury manometer ; metric rule. 
 
 a. A bent tube containing a liquid and used to measure pres- 
 sures exerted by liquids or gases is called a pressure gauge or 
 manometer (Fig. 8). Lift the water manometer out of the jar. 
 
BUOYANCY OF LIQUIDS 31 
 
 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 trans- 
 mitted to the water in the manometer ? 
 
 While moving the manometer up and down, com- 
 pare the difference of level of the water in the 
 two arms of the bend with the difference between 
 the level of the water in the jar and in the lower 
 end of the manometer. Make two or three exact 
 measurements of these distances with the manom- 
 eter at different depths. How do they compare ? 
 
 b. Repeat with the mercury manometer, except 
 the measurements, which need not be taken. State 
 the points of similarity with the preceding. State ' 
 and account for the differences. 
 
 EXERCISE G!. BUOYANCY OF LIQUIDS 
 
 References. Hoadley, 143-144; Carhart and Chute, 134- 
 138. 
 
 Apparatus. Specific gravity balance and weights to 1 eg., 
 or platform balance and weights to 5 g. ; for the platform 
 balance a support as shown in Fig. 9 ; overflow can ; beaker 
 or tumbler; jar of water; jar of solution of table salt; stone; 
 block of wood ; mop cloth. 
 
 I. To find the relation between the loss of weight of 
 a stone in water and the weight of the water that it 
 displaces. 
 
 a. Weigh the stone. 
 
 b. Weigh the beaker, and place it under the spout of the 
 overflow can. Fill the can with water till it begins to overflow. 
 
32 
 
 MECHANICS OF FLUIDS 
 
 Empty the beaker, replace it under the spout, lower the stone 
 
 into the can by means 
 of a thread, and catch 
 beaker 
 
 in the 
 
 and 
 
 FIG. 9. 
 
 weigh the displaced 
 wa+er. 
 
 c. 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 plat- 
 form balance is used, 
 Weigh it thus. This is called 
 
 adjust as shown in Fig. 9.) 
 the weight of the stone in water. 
 
 d. Weigh the stone again, entirely immersed in water as 
 before, but with a greater or less depth of water above it than 
 before. 
 
 After the stone is wholly immersed, does further lowering 
 affect its weight in water ? Explain. 
 
 FORM OF RECORD 
 
 a. Weight of stone in air 
 
 b. Weight of beaker 
 
 g. 
 g. 
 
 Weight of beaker and displaced water -- g. 
 Weight of water displaced g. 
 
 c. Weight of stone in water = - g. 
 
 d. Weight of stone with a greater depth 
 
 of water above it - g. 
 
 Loss of weight of stone in water = - g. 
 
BUOYANCY OF LIQUIDS 83 
 
 e. Account for the loss of weight of the stone in water. 
 
 When the stone hangs suspended by the thread in water, 
 what forces sustain its whole or true weight ? 
 
 /. Your results should show (within 1% of error) a simple 
 relation between the weight of the displaced water and the 
 loss of weight of the stone. State the relation and compute 
 the per cent of error. 
 
 II. To find the relation between the loss of weight of 
 the stone in a solution of table salt and the weight of 
 the solution that it displaces. 
 
 Repeat the above work (omitting paragraph d) with the 
 solution of table salt. When you have finished, return the solu- 
 tion to the proper jar. 
 
 Compare the results with those of Part I. In what respects 
 are they alike ? 
 
 III. To find the relation between the weight of a blook 
 of wood and the weight of water that it displaces when 
 floating. 
 
 a. Weigh the block of wood. 
 
 b. Determine with the overflow can and scales the weight of 
 the water that the floating block displaces. Return the water 
 to the proper jar, and leave the can and beaker empty and the 
 table dry. 
 
 c. What force or forces sustain the weight of the floating 
 block? 
 
 State and account for the resemblances and differences between 
 these results and those of Parts I and II. 
 
 Discussion. a. Assuming that the relation that is seen to 
 hold in the experiments of this exercise is true for all solids in 
 all liquids, how would you state it, (1) for immersed bodies ; 
 (2) for floating bodies ? 
 
 b. Account for the buoyancy of liquids. 
 COLEMAN'S PHY. LAB. MAN. 3 
 
34 MECHANICS OF FLUIDS 
 
 EXERCISE 6 2 . THE BUOYANT FORCE OF WATER 
 (ALTERNATIVE WITH EXERCISE 61) 
 
 References. Hoadley, 143-144 ; Carliart and Chute, 134- 
 138. 
 
 Apparatus. Specific gravity balance and weights ; brass 
 cylinder and bucket ; tumbler or jar of water ; beaker ; ring 
 stand ; dropping tube. 
 
 I. To find the relation between the loss of weight of a 
 brass cylinder in water and the weight of the water 
 that it displaces. 
 
 a. Observe whether the cylinder fills the bucket. How do 
 the volume of the cylinder and the capacity of the bucket 
 compare ? 
 
 b. Attach the cylinder to the hook on the bottom of the 
 bucket, and attach the bucket to the hook on the under side of 
 the higher scale pan. Weigh the cylinder and bucket in air. 
 
 c. With the balancing weights still in the pan, lower the 
 cylinder into the tumbler (or jar) of water by adjusting the 
 standard of the balance. If the balance is not adjustable, raise 
 the tumbler on blocks or other supports. 
 
 Why is equilibrium destroyed ? 
 
 d. With the cylinder still in the water, 
 fill the bucket exactly level full of water, 
 by means of the beaker and the drop- 
 ping tube. Use the dropping tube for 
 adding or removing a few drops. Adjust 
 the balance till the beam of the balance 
 is horizontal when the top of the cylin- 
 der is just submerged. With this ad- 
 justment equilibrium should be restored. 
 Explain the restoration of equilibrium. 
 
 e. State the principle illustrated by the experiment. 
 
SPECIFIC GRAVITY OF SOLIDS 35 
 
 II. To find what becomes of the weight lost by the 
 cylinder in water. 
 
 a. Place a beaker on one pan of the balance, with enough 
 water in it to cover the cylinder completely when this is placed 
 in it ; and place the empty bucket in the other pan. Without 
 the cylinder in the beaker, add weights to the lighter side till 
 balance is secured. 
 
 b. Suspend the cylinder from the ring stand by means of a 
 thread, so that it hangs immersed in the water of the beaker 
 (Fig. 10). Why does immersing the cylinder destroy equilib- 
 rium? 
 
 c. Fill the bucket in the opposite pan with water. When 
 it is level full equilibrium should be restored. Why ? 
 
 What forces are sustaining the whole or true weight of the 
 cylinder ? 
 
 EXERCISE 7. SPECIFIC GRAVITY OF SOLIDS 
 References. Hoadley, 46; Carhart and Chute, 140-141. 
 
 Apparatus. Specific gravity balance and weights to 1 eg., 
 or a platform balance and support (Fig. 9), or a 250-g. 
 spring balance ; thread ; tumbler or jar of water ; solid denser 
 and one less dense than water ; sinker ; mop cloth. 
 
 [Fairly satisfactory results can be obtained with a 250-g. (or 8-oz.) 
 spring balance, if the objects are of such weight and density as to make 
 the readings of the balance as large as may be.] 
 
 I. To find the specific gravity of a solid from its loss 
 of weight in water. 
 
 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 it will be entirely immersed when the tumbler 
 (or jar) of water is placed beneath the pan. (If a platform 
 balance is used, adjust it as shown in Fig. 9.) Weigh the 
 solid in water. Use the name of the solid in the record. 
 
36 MECHANICS OF FLUIDS 
 
 Compute its specific gravity. If the true value of the specific 
 gravity is given in Table I of the Appendix, compute the error 
 and the per cent of error of your result. 
 
 FORM OF RECORD 
 
 Weight of solid 1 in air = g. 
 
 Weight of solid in water = g. 
 
 Weight of an equal volume of water = g. 
 
 Specific gravity of the solid = 
 
 True value of its specific gravity = 
 
 Error = 
 
 Per cent of error = of c 
 
 II. To find the specific gravity of a solid by submer- 
 sion with a sinker. 
 
 Weigh the sinker in air and in water. Weigh the solid in 
 air. Fasten the sinker to the solid so that both will be en- 
 tirely immersed when suspended from the balance. Weigh the 
 two together in water. 
 
 FORM OF RECORD 
 
 Weight of sinker in air = g. 
 
 Weight of sinker in water = g. 
 
 Weight of solid 1 in air = g. 
 
 Weight of solid and sinker in water = g. 
 
 COMPUTATIONS 
 
 Weight of water equal in volume to solid and sinker = g. 
 
 Weight of water equal in volume to sinker = g. 
 
 Weight of water equal in volume to solid - g. 
 
 Specific gravity of the solid = 
 True value of its specific gravity 
 
 Error = 
 
 Per cent of error = % 
 
 1 Use the name of the solid in your record. 
 
SPECIFIC GRAVITY OF LIQUIDS 87 
 
 EXEECISE 8. SPECIFIC GEAVITY OF LIQUIDS 
 
 References. Hoadley, 144-146 and 150 (c) ; Car hart and 
 Chute, 144. 
 
 Apparatus. Demonstration hydrometer (wood prism of 1 
 scm. cross section and graduated in centimeters) ; common 
 hydrometer (specific gravity scale) for light and heavy liquids 
 or one for each; hydrometer jars containing water, saturated 
 solution of table salt, kerosene, alcohol, or other liquids ; jar of 
 rinse water ; mop cloth. 
 
 I. To find the specific gravity of a liquid by meas- 
 uring the depth to which a woomn prism sinks in it 
 and in water. j, 
 . -( - 
 
 a. Float the demonstration hydrometer in water and meas- 
 ure the depth to which it sinks. Record each item on a sepa- 
 rate line. The cross section of the hydrometer is 1 scm. What 
 is the volume ( F) of the displaced water ? How does the 
 weight of the water displaced compare with the weight of the 
 hydrometer ? 
 
 b. Measure the depth to which the hydrometer sinks in the 
 salt solution. What is the volume (v) of the displaced solution ? 
 
 c. How does the weight of the displaced solution compare 
 with the weight of the displaced water ? Why ? Why is v 
 less than V ? 
 
 d. Let w denote the weight of the hydrometer, D the density 
 of water, and d the density of the salt solution. The correct 
 answers to the above questions will give the relations : w = 
 VD vd. Show that this is so. 
 
 e. From the above equation derive the proportion d : D : : V: 
 v. This proportion expresses the relation between the volume 
 of the liquid displaced by a floating body and the density of the 
 liquid. Express the relation in words. This is the principle 
 upon which the use of the hydrometer depends. 
 
38 MECHANICS OF FLUIDS 
 
 /. By definition, the specific gravity of the salt solution is 
 d -T- D. The densities are not measured in the experiment, but 
 the volumes V and v are; and from the above proportion 
 d -f- D = V H- v. Compute the specific gravity of the solu- 
 tion. 
 
 I.I. To find the specific gravity of liquids by means of 
 a common hydrometer. 
 
 a. Observe whether the hydrometer sinks to the mark 1 
 (or 1000) in water. Does the reading of the scale increase 
 toward the top or bottom ? Why must it be so ? 
 
 b. Determine the specific gravity of the liquids provided, 
 including the salt solution. Wipe the hydrometer before put- 
 ting it from one liquid into another and before putting it away. 
 Kinse it in the jaj of rinse water after using it in the salt 
 solution. 
 
 Discussion. a. What changes, if any, would be necessary 
 in the experiment of Part I and in the discussion of it, if 
 English units were used instead of metric ? Would the specific 
 gravity be different ? 
 
 b. The specific gravity of ice is .917. What fraction of an 
 iceberg is above water ? 
 
 EXERCISE 9. SPECIFIC GEAVITY OF LIQUIDS 
 
 I. To find the specific gravity of a liquid by weighing 
 a solid in it and in water. 
 
 Apparatus. Specific gravity balance or platform balance 
 and support (Fig. 9) ; weights ; tumbler of water ; tumbler of 
 the liquid; a solid denser than water or the liquid, and in- 
 soluble in them (a glass stopper is convenient) ; mop cloth. 
 
 Make the measurements called for in the record, and com- 
 pute the specific gravity of the liquid. 
 
SPECIFIC GRAVITY OF LIQUIDS 
 
 39 
 
 FORM OF RECORD 
 
 Weight of solid 1 in air 
 Weight of solid in water 
 Weight of solid in the liquid 1 
 
 COMPUTATIONS 
 
 Weight of water equal in volume to solid = g. 
 Weight of liquid equal in volume to solid = g. 
 Specific gravity of the liquid 
 
 II. To find the specific gravity of a liquid by balancing 
 columns. 
 
 Apparatus. A U-tube with water and kerosene or other 
 liquid that will not mix with water (Fig. 11) ; meter stick, or 
 metric scale on the support of the tube. 
 
 a. Measure the height of the liquid col- 
 umns above the level (L) of the surface 
 separating them (Fig. 11). The liquid 
 below that level serves as a support for the 
 two columns ; and, since it is free to move, 
 it would immediately respond to any differ- 
 ence in the pressures exerted upon it by 
 these columns. Since the liquid is at rest, 
 these pressures are evidently equal. 
 
 b. Let D denote the density of water, d 
 the density of the liquid, JT the height of the 
 water column above the level Z/, and h the 
 height of the column of the liquid. Then 
 
 the pressures (per square centimeter) at the bottom of these 
 columns are DH and dh respectively. Why ? From this derive 
 the formula and compute the specific gravity of the liquid. 
 Remember that, by definition, specific gravity is d -+- D. 
 
 1 Use the name of the solid and the liquid in your record. 
 
 FIG. 11. 
 
40 
 
 MECHANICS OF FLUIDS 
 
 EXERCISE 10. GAS PRESSURE 
 
 References. Hoadley, 151-161 ; Carhart and Chute, 145-150. 
 
 I. To study the transmission of pressure by means of 
 a Cartesian diver. 
 
 Apparatus. An hydrometer jar nearly full of water, in 
 which is floated a short glass tube with bulb blown 
 at one end, inverted and containing just enough 
 air to float it (the air must only partly fill the 
 tube) ; sheet rubber tied air-tight over the jar. 
 
 a. Press the fingers on the rubber cover of the 
 jar, and increase the pressure till the floating tube 
 sinks. Diminish the pressure till it again rises. 
 Repeat, and look for any change of level of water 
 in the ' tube during the process. Describe and 
 account for this change. 
 
 b. What must be true of the average density of 
 bodies that float ? Of bodies that sink ? Explain 
 
 FIG. 12. the sinking and rising of the tube. 
 
 II. To study atmospheric pressure. 
 
 Apparatus. Bottle; battery jar of water; glass tube. 
 
 a. Fill the bottle level full of water and cover it with a 
 small piece of paper, being careful to exclude air bubbles. 
 Press the paper smoothly against the mouth of the bottle, then 
 remove the hand and invert the bottle. The paper should 
 remain in place. Tarn the bottle in different directions. With 
 the bottle inverted, observe the shape of the paper. Does 
 it bulge as you would expect it to if it were sustaining the 
 weight of the water ? Explain all that you have observed. 
 
 b. Hold a finger over an end of the glass tube and fill it with 
 water. Invert it and insert the lower end into the jar of water. 
 Why does the water remain in the tube ? Remove the finger 
 from the top. Why does the water in the tube fall ? 
 
GAS PRESSURE 
 
 41 
 
 FIG. 13. 
 
 III. To measure the pressure of the gas in the gas 
 pipes. 
 
 Apparatus. A water and a mercury manometer (Fig. 13) ; 
 rubber tube. 
 
 a. By means of the rubber tube connect 
 the water manometer with the gas jet and 
 turn on the gas. Describe and explain 
 the effect upon the water in the manom- 
 eter. Measure the difference of level of 
 the tops of the water columns in the two 
 arms of the manometer. 
 
 b. How does the pressure at the top of 
 the lower column (the pressure of the gas) 
 compare with the pressure at the same 
 level in the opposite column? To what 
 two causes is the latter pressure due ? 
 
 Show that the total pressure of the gas 
 upon the water exceeds that of the air by an amount equal to 
 the weight of the water column sustained by the gas. 
 
 By how many grams per square centimeter does the pressure 
 of the gas exceed that of the air ? 
 
 c. Repeat the experiment, using the mercury manometer. 
 Why is the difference of level so much less than before ? 
 Leave the gas turned off. 
 
 IV. To study the barometer. 
 
 Apparatus. Two barometer tubes of different diameters, 
 filled and supported vertically by ring stand and clamp. 
 
 a. What occupies the space above the mercury in the 
 barometer ? 
 
 What is the pressure upon the top of the mercury column of 
 the barometer ? 
 
 What measures the transmitted pressure of the air exerted 
 upward in the tube at the bottom of the mercury column ? 
 
42 MECHANICS OF FLUIDS 
 
 b. Measure the heights of the barometers. The height is 
 measured from the surface of the mercury in which the tube 
 stands to the top of the mercury column. 
 
 How is the height of a barometer affected by its diameter ? 
 
 c. Compute the pressure in grams per square centimeter 
 indicated by a barometer column of 76 cm., taking 13.596 g. 
 per cubic centimeter as the density of mercury. 
 
 EXEECISE 11. SPECIFIC GEAVITY OF A LIQUID 
 
 To find the specific gravity of a liquid 
 by means of the inverted \J-tube. 
 
 Apparatus. Hare's apparatus, as shown in 
 Fig. 14; water in one tumbler, and the liquid 
 whose specific gravity is to be determined in the 
 other"; meter rod. 
 
 a. Open the pinchcock, apply the mouth to 
 the tube, and slowly exhaust the air, while watch- 
 ing the ascent of the liquids. Be careful not 
 to carry the exhaustion so far as to cause the 
 higher column to overflow into the other. When 
 the higher column is within a few centimeters 
 of the top, close the pinchcock. 
 
 b. If the tubes were long enough and the air 
 completely removed from them, how high (ap- 
 proximately) would the water column stand ? 
 What would be the appropriate name for it ? 
 
 c. Does the air remaining in the tube exert 
 the same or different pressure upon the tops of 
 
 FIG. 14. tne two co i unms 9 
 
 What balances the transmitted pressure of the outside air at 
 the bottom of the two columns ? (The bottom of the column is 
 at the level of the surface of the liquid in the tumbler.) 
 
 d. Let D denote the density of water, and H the height of 
 the water column ; d the density of the liquid, and h the height 
 
 C_ 
 
SPECIFIC GRAVITY OF A LIQUID 43 
 
 of its column. The correct answer to the above questions 
 should lead easily to the proof that DH is equal to dh. Prove 
 it, and from it derive the formula for the specific gravity of the 
 liquid in terms of the heights of the columns. 
 
 e. Measure the heights of the columns. Lower the columns 
 slightly by admitting a little air, and measure them again. 
 Again lower the columns slightly and measure. 
 
 /. Open the pinchcock, and measure the heights of the 
 liquids in the tubes due to capillarity. If capillarity causes 
 depression of the liquid (as with mercury), the height is to be 
 recorded as negative. For computing the specific gravity of 
 the liquid, the heights of the columns as they would have been 
 if there were no capillary action are wanted. These corrected 
 heights are found by subtracting from the measured heights 
 the elevations due to capillarity and adding the depressions. 
 
 Compute the specific gravity from each of the pairs of 
 values, and take their average. 
 
 FORM OF RECORD 
 
 123 
 
 e. Height of water column = cm. cm. cm. 
 
 Height of liquid l column = cm. cm. cm. 
 
 /. Height of water due to 
 
 capillarity cm. 
 
 Height of liquid due to 
 
 capillarity cm. 
 
 Corrected height of water 
 
 column = cm. cm. cm. 
 
 Corrected height of liquid 
 
 column = cm. cm. cm. 
 
 Specific gravity of the 
 
 liquid = 
 
 Av. specific gravity of the 
 
 liquid = 
 
 1 Use the name of the liquid in your record. 
 
44 MECHANICS OF FLUIDS 
 
 EXERCISE 12. THE SIPHON AND THE 
 SUCTION PUMP 
 
 References. Hoadley, 169-170, 176-177 ; Carhart and 
 Chute, 157-160. 
 
 I. To study the action of a siphon. 
 
 Apparatus Siphon made of glass tubing, with arms of un- 
 equal length and at an angle of about 50 to each other ; two 
 battery jars and water, or, better, one jar, and sink at which to 
 work ; small beaker ; mop cloth. 
 
 a. Invert the siphon and fill it from the beaker by pouring 
 into the long arm and closing the end of the short 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 (that is, 
 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 and remove 
 the fingers from both ends. From which end (the higher or 
 the lower) does the water run ? Eepeat, and observe whether the 
 order in which the fingers are removed affects the result. 
 
 What determines which way the water runs out ? Explain. 
 Why does the water not part at the top and fall from both 
 ends? 
 
 c. Put water in the jar and place it on some support above 
 the other jar. Fill the siphon, and, with a finger closing the 
 long arm, insert the short arm into the water of the higher jar. 
 Remove the finger, and siphon the water into the other jar. 
 
 Note the effect of tilting the siphon so as to vary the dis- 
 tance of the end of the long arm below the level of the water 
 surface. Try the effect of raising it up to and above the level 
 of the water. 
 
 State and explain the observed effect. 
 
 d. What has air pressure to do with the action of a siphon ? 
 
THE LAW OF BOYLE 45 
 
 II. To study the action of a suction pump. 
 
 Apparatus. A glass suction puinp; battery jar of water; 
 mop cloth. 
 
 NOTE. This pump is called a lifting pump in some text-books, in 
 order to avoid the misconception that commonly attaches to the word suc- 
 tion. This is that suction is a drawing or pulling process (that is, one in- 
 volving a pulling force). This is never the case. Suction is always a 
 process by means of which a pressure or push is utilized. With a correct 
 conception of what the word means, there is no objection to its applica- 
 tion to this kind of pump. 
 
 a. Beginning with the pump empty, push the piston down, 
 while observing the behavior of the valve in the piston. 
 Explain it. 
 
 Lower the pump into the jar of water and raise the piston 
 slowly, while observing the two valves and the water in the 
 pump. Describe and explain what happens. Avoid the use of 
 ambiguous words, such as draw, suck, and suction. State clearly 
 what the force is that makes the water rise, and how it acts. 
 
 b. Operate the pump till you understand the motion and use 
 of the valves. Draw figures showing their action when the 
 piston is ascending and when it is descending, and write a 
 brief description of the action. 
 
 EXEECISE 13. THE LAW OF BOYLE 
 
 References. Hoadley, 166; Carhart and Chute, 161-163. 
 
 To find the relation between the volume of a confined 
 body of air and the pressure exerted upon it. 
 
 Apparatus. A Boyle's-law apparatus with adjustable closed 
 and open tubes (Fig. 15). 
 
 I. a. Adjust the open and closed tubes so that the mercury 
 stands approximately at the same level in both. What evi- 
 dence is there that the closed tube contains a gas above the 
 mercury ? It is air. 
 
46 
 
 MECHANICS OF FLUIDS 
 
 How would the mercury stand in the closed tube if the air 
 were removed? 
 
 How would it then differ from a barometer ? 
 
 b. From the fact that the mercury stands at 
 the same level in the two arms, what do you 
 infer concerning the relative value of the air 
 pressure upon the two mercury surfaces ? 
 
 The pressure of the outside air is given by 
 the barometer; read and record it for use 
 later, and call it H. 
 
 What is the pressure of the air in the closed 
 tube, measured in centimeters of mercury ? 
 
 c. Raise the open tube 20 to 30 cm. ; and 
 while doing so, observe the change of level 
 in the closed tube. Has the confined air in- 
 creased or diminished in volume ? Has the 
 pressure upon it been increased or decreased, 
 and from what cause? 
 
 The pressure upon the confined air is now 
 the transmitted pressure of the outside air 
 (H) plus the pressure due to the difference of 
 level of the mercury columns. Let d denote 
 this difference of level. This added pressure 
 may be expressed as the pressure of d cm. of 
 mercury. Hence the total pressure sustained 
 by the confined air is measured by (H+ d) cm. of mercury. 
 
 d. Lower the open tube about 50 cm., while watching the 
 change of level in the other. How is the volume changing ? 
 Why is it changing ? 
 
 Again letting d denote the difference of level of the mercury 
 
 columns, what is now the pressure upon the confined air ? 
 
 4 
 
 II. a. Clamp the closed tube near the bottom of the stand- 
 ard and leave it in this position for the first three sets of read- 
 ings. Adjust the open tube so that the mercury stands at the 
 
 FIG. 15. 
 
THE LAW OF BOYLE 
 
 47 
 
 same level in both tubes. Take a set of readings as indicated 
 in the form of record. " Reading of top of closed tube " means 
 the reading of the point on the meter rod on a level with the 
 top of the bore or hole of the closed tube. Since the closed 
 tube is of uniform bore, the volume of any portion of it is pro- 
 portional to the length of that portion ; hence the length of 
 the air column may be taken to represent its volume. 
 
 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. Eaise 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 rubber tube is supported by the base. 
 
 FORM OF RECORD FOR PART II 
 
 SET 
 
 READING OF 
 TOP OP CLOSED TUBE 
 
 READING OP TOP OF MERCURY COLUMN 
 
 In closed tube 
 
 In open tube 
 
 a. 
 
 cm. 
 
 cm. 
 
 cm. 
 
 b. 
 
 
 
 -^ 
 
 
 
 etc. 
 
 
 
 
 
 
 
 COMPUTATIONS 
 
 SET 
 
 LENGTH OF 
 AIR COLUMN OR V 
 
 DIFFERENCE OF LEVEL 
 OF MERCURY COLS. = d 
 
 TOTAL PRESSURE 
 = fId=P 
 
 PV 
 
 a 
 
 cm. 
 
 cm. 
 
 cm. (of mer . ) 
 
 
 
 b 
 
 
 
 
 
 
 
 
 
 etc. 
 
 
 
 
 
 
 
 
 
48 MECHANICS OF FLUIDS 
 
 Discussion. a. According to Boyle's law, what relation 
 should exist among the numbers of the column headed PV? 
 
 b. Compute the greatest per cent of difference between these 
 numbers. This per cent represents the error, and should not 
 exceed 2%. If it exceeds 4% repeat the experiment. 
 
 c. Is it necessary that the open and the closed tubes should 
 be of the same diameter ? Explain. 
 
 d. Would the accuracy of the result be affected by any un- 
 evenness in the diameter of the open tube ? In the diameter 
 of the closed tube ? Give reasons in each case. 
 
 e. When the mercury stands at the same level in the two 
 arms of a Boyle's-law apparatus, the air column is 20 cm. long. 
 What will be its length (a) when the mercury stands 25 cm. 
 higher in the closed than in the open tube ; and (b) when it 
 stands 30 cm. lower ; the atmospheric pressure being 75 cm. ? 
 
 EXEKCISE 14. THE DENSITY OF AIR 
 
 Reference. Hoadley, 155. 
 
 To find the weight of one cubic centimeter of air at 
 the temperature and pressure of the laboratory. 
 
 Apparatus. Air pump; closed mercury pressure gauge; 
 strong balance, sensitive to 1 eg. ; weights to 1 eg. ; forceps ; 
 heavy rubber tubing for connections ; brass cylinder with stop- 
 cock at each end (or bottle with rubber stopper, in which is 
 fitted a short piece of glass tubing with Y-tube, pinchcock, and 
 connections as shown in Fig. 16). 
 
 [The cylinder should be strengthened with braces or partitions (not 
 air-tight), and should have a capacity of 1500 to 2000 ccm. The capacity 
 should be given the students. A bottle holding 3 to 5 pts. will serve instead 
 of the cylinder. The pressure gauge has no air in the closed tube.] 
 
 a. The capacity of the cylinder (or bottle) is marked on it. 
 Record it. 
 
 b. Attach the cylinder by a rubber tube to the air pump, 
 and by another to the pressure gauge (Fig. 16) ; and exhaust 
 
THE DENSITY Off AIR 
 
 FIG. 10. 
 
 the air till the mercury falls a few centimeters in the gauge, 
 or until the difference of level of the mercury column is not 
 more than 10 or 15 cm. The 
 gauge acts as a short barometer 
 to measure the greatly reduced 
 pressure in the cylinder. Quickly 
 read the heights of the mercury 
 columns of the gauge; then close 
 the stopcocks. Very slowly re- 
 move the tube connecting with the 
 gauge. If it is removed quickly, 
 the sudden inrush of air may make 
 the mercury strike the closed end with sufficient force to break 
 it. Disconnect the other tube and weigh the cylinder. If the 
 balance is provided with a lever or other device for raising 
 and lowering the beam and pans, always lower the beam before 
 placing anything on or removing anything from the pans, except 
 weights lighter than 1 g. See that the pans are suspended 
 from the knife edges on the beam. They sometimes slip off. 
 
 c. Open the stopcocks and weigh again. Kecord each item 
 on a separate line. The difference between the two weighings 
 is the weight of the air pumped out. Compute it. 
 
 d. Eead the barometer. At the second weighing, the air in 
 the cylinder was under this pressure ; at the first weighing, it 
 was under the pressure measured by the difference of level of 
 the mercury columns of the gauge. The weight of air in a 
 given space and at a given temperature is proportional to its 
 pressure. (This follows from Boyle's law.) 
 
 e. From the known pressures, find what (decimal) fraction 
 of the air was pumped out. 
 
 /. Compute the weight of the air in the cylinder when under 
 atmospheric pressure. 
 
 g. Compute the density of the air (in grams per cubic 
 centimeter) at the temperature and pressure of the laboratory. 
 
 COLEMAN'S PHY. LAB. MAN. 4 
 
 OF THE 
 
IV. MECHANICS OF SOLIDS 
 FORCES i 
 
 27. A force is a push or a putt, and tends to cause motion of 
 the body on which it acts or to change the existing motion of 
 that body. It will do so unless prevented by the equal and 
 opposite tendency of another force or other forces. 
 
 28. Balanced Forces. Equilibrium. If two or more forces 
 act upon a body at rest so as completely to neutralize each 
 other's tendency to produce motion, the body will remain at 
 rest, and is said to be in equilibrium. The forces also are said 
 to be in equilibrium or to balance each other ; and are often 
 called balanced forces. A large part of the work of this chapter 
 consists in a study of the conditions of equilibrium ; that is, of 
 the relations that must exist among several forces in order that 
 they shall balance each other. 
 
 29. The resultant of two or more forces is the single force 
 that would produce the same effect as the given forces, if it 
 were substituted for them. The given forces are called com- 
 ponents (that is, parts) of the resultant. The resultant of any 
 number of forces in equilibrium is zero ; for, being in equilib- 
 rium, they do not affect the state of rest or of motion of the 
 body upon which they act. 
 
 30. In any problem concerning the conditions of rest or of 
 motion of a body, we are always at liberty to replace given 
 
 1 The summary presented in these articles is intended to serve for con- 
 venient reference in the laboratory, not as a substitute for the detailed 
 treatment to be found in text-books. 
 
 50 
 
COMPOSITION OF FORCES 51 
 
 forces by their resultant or a given force by its components ; 
 since, if such a substitution were actually made, the behavior 
 of the body, as regards rest or motion, would not be affected 
 in the least. 
 
 31. The equilibrant of any number of forces (one or more) 
 is the single force that would hold the given forces in 
 equilibrium. 
 
 32. The elements of a force are, (1) its point of application; 
 (2) its direction; (3) its magnitude. A force is not completely 
 known or determined till these three things are known about 
 it. A comparison of two forces consists in a comparison of 
 their three elements. 
 
 33. Representation of Forces. A force may be represented 
 in all its elements by a straight line. One end of the line 
 represents the point of application of the force ; the direction 
 of the line (with an arrow head on it, since a line has two 
 directions) represents the direction of the force; and the 
 length of the line represents the magnitude of the force on 
 a definite scale, arbitrarily adopted to suit convenience. 
 
 BALANCED FORCES: STATICS 
 EXEECISE 15. COMPOSITION OF FORCES 
 
 References. Hoadley, 47-49 ; Carhart and Chute, 45-47. 
 I. To study the conditions of equilibrium of two forces. 
 
 Apparatus. Three 2000-g. spring balances, preferably with 
 flat backs ; two nails ; three cords attached to small ring ; large 
 board on which to perform the experiment, with narrow strips 
 on two adjacent sides, in which are bored holes 1 in. apart to 
 hold the nails (Fig. 17) ; rule. 
 
52 
 
 MECHANICS OF SOLIDS 
 
 a. Attach two of the spring balances to cords on the ring, 
 and, with one in each hand, stretch the cords and leave the 
 ring at rest. The ring is now in equilibrium under the action 
 of two pulls. 
 
 How do these pulls compare in their three elements 
 (Art. 32)? 
 Do you alter these relations when you vary the pulls ? 
 
 b. Either of two forces in equilibrium is the equilibrant of 
 the other (Art. 31). What is the resultant of the two ? 
 
 II. To study the conditions of equilibrium of three 
 concurrent forces. 
 
 a. Attach the cords on the ring to the hooks of the three 
 balances. Fasten two of the balances by their rings to the 
 nails, inserted in holes in the board, and placed so that the 
 
 angle between these bal- 
 ances will be between 60 
 and 120 (Fig. 17). Place 
 your record sheet under 
 the cords. Pull on the 
 ring of the third balance 
 with sufficient force and 
 in the proper direction to 
 cause each of the balances 
 to register not less than 
 1000 g. and not more 
 than 2000 g. Adjust the 
 paper under the cords, 
 hold the third balance 
 steadily, and make a dot 
 on the paper at the middle of the ring and one exactly under 
 each of the cords at a considerable distance from the ring. Kead 
 each of the balances and record on the sheet beside the cords. 
 
 b. Remove the sheet, draw lines through the dots indicating 
 the directions of the cords (and hence also the directions of 
 
 FIG. 17. 
 
COMPOSITION OF FOKCES 53 
 
 the forces), and measure off on these lines, from their point 
 of intersection, distances proportional to the forces, using a 
 scale that will give a rather large figure (Art. 33). The remain- 
 der of the construction may be left for home work. Con- 
 struct accurately, by the parallelogram of forces, the resultant 
 of any two of these forces ; and compare it with the third force 
 (Art. 32). 
 
 The third force is the equilibraut of the other two (Art. 31). 
 Is it the equilibrant of their resultant ? 
 
 c. Arrange the balances so that two of them will act at 
 an angle of exactly 90 after the forces are applied. For an 
 angle to measure by, fold a piece of paper twice. Draw a 
 figure to scale as in the first case, marking in the figure the 
 magnitude of each force. Record the scale adopted for the 
 figure. 
 
 d. Obtain by construction the resultant of the two forces 
 acting at an angle of 90, and mark the value of the resultant 
 in the figure. 
 
 Find the same resultant by computation. (The square on 
 the hypotenuse of a right triangle is equal to the sum of the 
 squares on the other two sides.) 
 
 Find the per cent of difference between these two results. 
 The error should not exceed 2%. 
 
 Discussion. a. In the above work, how should the resultant 
 of any two of the forces compare with the third force ? Give 
 a full and satisfactory reason for your answer. 
 
 b. What is the resultant of the three forces applied to the 
 ring ? Give reasons for your answer. 
 
 c. As the angle between two forces increases from to 180, 
 how does their resultant vary ? What ^is the value of the 
 resultant at the beginning ? At the end ? 
 
 d. Two equal forces act at an angle of 120. What is the 
 magnitude and direction of their resultant? Answer from 
 geometry. 
 
54 MECHANICS OF SOLIDS 
 
 EXERCISE 16. EQUILIBRIUM OF PARALLEL 
 FORCES 
 
 References. Hoadley, 51 ; Carhart and Chute, 47. 
 
 To study the conditions of equilibrium of three 
 parallel forces. 
 
 Apparatus. Meter rod; two 2000-g. spring balances; two 
 unequal weights of 2000 to 3000 g. ; cord ; frame to support 
 the balances (Fig. 28) ; rule. 
 
 a. Adjust the balances and meter rod as shown in Fig. 18. 
 The supporting cords must be parallel and the rod horizontal. 
 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 sup- 
 
 FIQ. 18. 
 
 porting the rod only. Estimate to tenths of the smallest scale 
 division (Art. 26). Record the readings as the zero readings 
 of the left and right scales respectively. They are the forces 
 necessary to support the rod, and are to be subtracted from 
 subsequent readings of the scales in order to obtain the forces 
 (/ and jP, Fig. 19) necessary to balance the weight (W) hung 
 
EQUILIBRIUM OF PARALLEL FORCES 
 
 55 
 
 upon the rod. In order to keep the zero readings the same 
 throughout the exercise, the rod must always be supported 
 from the same points. 
 
 b. In Fig. 19, A and B denote the points of support of the 
 rod, and C the point of application of the weight. In the 
 record let the distances AC 
 
 and CB be denoted by d f 
 and D respectively. Hang 
 one of the weights on the - 
 rod midway between the 
 supporting cords, and record 
 the readings of the scales 
 and the equal distances d w 
 
 and D. Draw a figure simi- 
 lar to Fig. 19, representing 
 the distances and the forces approximately to scale. (An 
 accurate construction is not required.) 
 
 c. Move the weight from 10 to 20 cm. toward one end, and 
 take a second set of readings. Draw a figure as before. 
 
 d. Use the other weight. Hang it so that d and D are un- 
 equal, and take a third set of readings. Draw figure to illus- 
 trate. When you have finished, remove the weight from the 
 rod. 
 
 FORM OF RECORD 
 
 a. Zero reading of left scale = 
 Zero reading of right scale = 
 
 FIG. 19. 
 
 
 SCALE I 
 
 IEADINO 
 
 If 
 
 t / 
 
 /) 
 
 
 Left 
 
 Riffht 
 
 
 
 
 J) 
 
 g- 
 
 % 
 
 g. 
 
 cm. 
 
 cm. 
 
 d 
 
 
 
 
 
 
 
 
 
 
 
MECHANICS OF SOLIDS 
 
 COMPUTATIONS 
 
 Cp-p 
 
 FOKOKS 
 
 f F 
 
 D ' d 
 
 DlFFKR- 
 
 
 R f+ F 
 
 R W 
 
 
 / 
 
 F 
 
 
 
 i \i i: 
 
 
 
 
 b 
 
 <v 
 
 tv 
 
 g. 
 
 
 
 
 
 =- 
 
 % 
 
 &' 
 
 
 
 d 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Discussion. a. Enter in the record, as indicated, the com- 
 puted values (expressed decimally) of the ratios /: F and D : d ; 
 and compute the per cent of difference between them for each 
 set of readings. This difference is due to experimental errors, 
 and should not exceed 1%. If it is greater than 2% in any 
 case, repeat the set of readings. 
 
 6. Since the ratios are equal, they form a proportion. 
 Write it, using the letters /, F, d, and D ; arid state it in words 
 also. 
 
 c. What is the magnitude, direction, and point of application 
 of the equilibrant (W) of two parallel forces acting in the 
 same direction ? 
 
 c?. How should R, the resultant of / and F, compare with 
 W in magnitude, direction, and point of application ? 
 
 ALTERNATIVE METHOD 
 
 Apparatus. Meter rod ; three 2000-g. spring balances ; cord. 
 
 Follow the above directions with the following modifications : 
 A third spring balance is used instead of the weight W, and 
 the rod and balances lie upon the table. There will be no zero 
 reading of the balances. The reading of the single opposing 
 balance should in every case be near its maximum, in order to 
 secure the best results. The two balances acting in the same 
 direction may be fastened to nails driven into the table, and 
 the third balance held in the hand. 
 
MOMENTS OF FORCE 57 
 
 EXERCISE 17. iMOME>s T TS OF FORCE 
 
 Reference. Hoadley, 96-98. 
 
 To study the conditions of equilibrium of two forces 
 about an axis. 
 
 Apparatus. Meter rod with hole at 50 cm.; upright with 
 nail to support the rod ; 2000-g. 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. Few meter rods are uniform enough in cross section and density 
 to balance exactly at 50 cm. ; but this defect is remedied by boring small 
 holes in the heavier end.] 
 
 a. Hang the rod on the support. Hang the equal weights 
 on the rod, one on each side, and adjust them so that the rod 
 will balance in a horizontal position. In the record and in the 
 figure let W and iv denote the weights, and A and a respec- 
 tively their arms (the dis- 
 tances from the weights to A 
 
 W FIG. 20. 
 
 the axis of rotation). The 
 axix of rotation is also called 
 the fulcrum. The product 
 of either weight and its arm 
 is called the moment of the weight about the fulcrum ; thus 
 the moment of the weight w about the fulcrum is wa, and 
 that of W is WA. Draw a figure similar to Fig. 20, approxi- 
 mately to scale, and in it record the values of the weights and 
 their arms. 
 
 b. Hang unequal weights on the rod and adjust them so 
 that they balance. Better results will be obtained by making 
 the arms rather long. Compute the moments of these fordes. 
 Within a very small error (less than .5%), a simple relation 
 should hold between them. What is it? Draw a figure as 
 before. 
 
58 
 
 MECHANICS OF SOLIDS 
 
 c. Repeat the preceding with other unequal weights. 
 
 d. Hang the heaviest weight on the rod, and balance by 
 holding up the same end of the rod by the hook of the spring 
 balance, applied nearer the end of the rod than the weight. 
 Let W denote the weight and A its arm ; and let / denote the 
 force applied through the balance and a its arm. Eemember 
 that the arm is the distance from the point of application of 
 the force to the axis of rotation. Compute the moments of W 
 and / about the axis, and find the per cent of difference between 
 these moments. 
 
 A larger error may be expected than in the previous work. 
 Why? 
 
 Draw a figure showing W and / drawn approximately to 
 scale and in the proper directions. 
 
 e. Repeat the preceding with the balance nearer the axis 
 than the weight is. ' Draw figure as before. 
 
 FORM OF RECORD 
 
 
 W 
 
 W 
 
 a 
 
 A 
 
 wa 
 
 WA 
 
 DlFF. 
 
 %OFDIFF. 
 
 
 
 
 
 
 
 
 
 o/ 
 
 b 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 7o 
 
 a 
 
 / 
 
 
 
 
 fa 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Discussion. a. Express algebraically, both as an equation 
 and as a proportion, the relation that should hold for the four 
 quantities W, w, a, and A ; and also for W, f, A, and a. 
 Express the same relation in words. 
 
 b. Compare the conditions of equilibrium when the forces 
 are applied on opposite sides of the fulcrum with the condi- 
 tions when they are applied on the same side. 
 
CENTER OF GRAVITY 59 
 
 c. In Exercise 16 find the moments of the forces / and F 
 about an axis through the rod at C (the point of application 
 of the weight) for one set of observations. 
 
 d. Compare Exercises 16 and 17. In what respects are they 
 alike ? What and where is the equilibrant of w and W in this 
 exercise ? 
 
 34. Center of Gravity. The attraction of the earth is exerted 
 on all parts of a body, an exceedingly .small pull upon each 
 particle. These pulls are directed toward the center of the 
 earth; hence they are practically parallel. The resultant of 
 these parallel forces is equal in magnitude to their sum ; and 
 we call it the weight of the body. (This is not strictly 
 accurate except for bodies at the poles.) The direction of this 
 resultant is the same as the direction of its components, 
 vertically down. Its point of application is named the center 
 of gravity of the body. Hence we have the following definition : 
 
 The center of gravity of a body is the point of application 
 of the resultant of all the forces of gravity acting upon the 
 body. 
 
 35. Properties of the Center of Gravity. The center of gravity 
 of a body has several important properties, two of which are 
 fundamental, and, if clearly grasped, will greatly assist in the 
 understanding of all questions that may arise under this topic. 
 They are the following : 
 
 (1) So long as a body remains intact and of the same shape, 
 its center of gravity is a fixed point relative to the body, how- 
 ever the body may be turned and in whatever situation it may 
 be placed. 
 
 (2) The second property follows directly from the definition 
 of a resultant force (Art. 29). It is that, under all conditions 
 affecting the state of rest or of motion of a body, the body 
 behaves exactly as it would if the actual forces of gravity (in- 
 definite in number) were replaced by a single force (the weight 
 of the body) applied at the center of gravity and acting verti- 
 
b'O MECHANICS OF SOLIDS 
 
 cally downward. In problems in equilibrium this substitution 
 of the resultant for the actual forces is always assumed at the 
 outset. 
 
 EXERCISE 18. CENTER OF GRAVITY AND 
 EQUILIBRIUM 
 
 References. Hoadley, 70, 71, 74, and 75 ; Carhart and Chute, 
 51-52 and 55-58. 
 
 I. To find the center of gravity of an irregular piece 
 of cardboard. 
 
 Apparatus (for Parts I and II). Irregular piece of card- 
 board ; pin ; small plumb line made of thread and bullet or 
 button; rule. 
 
 a. Stick the pin through the cardboard near the edge, and 
 enlarge the hole till the cardboard swings freely on the pin. 
 Hang the plumb line on the pin near 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 this 
 dot with the point of suspension. Do all this with care. Sus- 
 pend the cardboard at a different point, also near the edge, 
 and determine a second line in the same way. 
 
 6. What single point of the cardboard was vertically under 
 the point of suspension in both cases ? Do you think it would 
 be vertically under any point of suspension from which the 
 cardboard hangs at rest ? Test the matter by suspending it 
 from a third point chosen at random. State the result. 
 
 c. If the pull of the earth upon the molecules of the card- 
 board were replaced by their resultant (the weight of the card- 
 board), where would it have to be applied to cause the cardboard 
 to behave as it does when suspended from different points? 
 Give reason for your answer. Trace the outline of the card- 
 board in your notebook, locate the three points of support, and 
 draw the plumb lines. Letter the center of gravity C. 
 
CENTER OF GRAVITY AND EQUILIBRIUM 61 
 
 II. To study the different kinds of equilibrium by 
 means of the cardboard suspended from a pin. 
 
 a. Hang the cardboard again from a hole near the edge and 
 set it swinging. Describe the path of the center of gravity. 
 
 Where is the center of gravity with respect to the lowest 
 point of that path when the cardboard hangs at rest ? 
 
 Is the center of gravity raised or lowered when the cardboard 
 is moved from its position of equilibrium ? 
 
 What name is given to this kind of equilibrium ? Define it. 
 
 b. Hang the cardboard on the pin through the center of 
 gravity; enlarge the hole till it moves freely; and observe 
 its behavior when it is set rotating. Does it always come to 
 rest in the same position ? It is not easy to find and pierce 
 the center of gravity exactly with the pin. It generally happens 
 that the hole is far enough to one side to affect appreciably the 
 behavior of the cardboard. Have you reason to think that 
 such is the case in your experiment ? If so, state it. 
 
 How would the cardboard behave with respect to positions 
 of rest if it were suspended accurately at the center of gravity ? 
 
 In what kind of equilibrium would it be ? Define this kind 
 of equilibrium. 
 
 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 this kind of equilibrium difficult to secure ? 
 Name and define this kind of equilibrium. 
 
 III. To study weight as a resultant force by means 
 of a stick of uniform cross section. 
 
 Apparatus Meter stick ; platform balance and weights ; 
 fulcrum to support the meter rod. 
 
 a. Weigh the meter rod on the platform balance, and let w 
 denote its weight. Find the center of gravity of the rod by 
 balancing it horizontally upon the support. Do not waste 
 time trying to secure a perfect balance : the equilibrium is 
 unstable. When balanced, the center of gravity is above the 
 
62 MECHANICS OF SOLIDS 
 
 support. Record its position as the reading of the meter scale 
 at that point. On account of slight variation in the density 
 or cross section of the rod, its center of gravity may be appre- 
 ciably to one side of 50 cm. 
 
 b. The purpose of this experiment is to determine whether, 
 under different conditions of equilibrium, the weight of the 
 whole rod may still be regarded as a single force whose point 
 of application is the center of gravity of the whole rod. 
 
 c. Hang a 100-g. weight (denoted by W) 1 cm. from the 
 zero end of the rod; then balance the rod on the support. 
 Assuming that W is balanced by w (which, remember, is the 
 weight of the whole rod), we can find the point where w must 
 be applied ; for, if W and w balance each other about the axis 
 of support, their moments about that axis must be equal. Let 
 A and a denote the arms of W and w, respectively. Measure 
 A, and record it and the position of the axis of support. Com- 
 pute a from the equation wa = WA. 
 
 d. We have now found that, in order to balance W, the 
 weight of the rod must be applied a cm. from the axis of 
 support. What is this position on the rod? Is it the same 
 point as the center of gravity ? It should be, within a reason- 
 able limit of experimental error (2 or 3 mm.). 
 
 e. What answer have you found for the question stated in 
 paragraph b ? (See Art. 35.) 
 
 FORM OF RECORD 
 
 a. Weight of meter rod (w) 
 Position of center of gravity 
 
 c. Attached weight (W) = g. 
 
 Position of attached weight = I cm. 
 
 Position of axis of support = cm. 
 
 Arm of W (A) = cm. 
 
 Arm of the weight of the rod (a) = WA -5- W cm. 
 
 d. Point of application of the weight of the rod 
 
 position of the axis of support -f- a = - - cm. 
 
EQUILIBRIUM AND STABILITY 63 
 
 EXEECISE 19. EQUILIBRIUM AND STABILITY 
 References. Hoadley, 76-77; Carhart and Chute, 57-59. 
 
 I. To study the different kinds of equilibrium by 
 means of bodies supported on a level surface. 
 
 Apparatus Such bodies as cylinder, cone, sphere, oblate 
 and prolate spheroids, an empty round-bottomed flask, a round- 
 bottomed flask loaded with shot so that it will stand upright. 
 
 [The shot can be kept in place by paraffine or wax that has been 
 melted over it.] 
 
 a. A body may have different kinds of equilibrium at the 
 same time with respect to motion in different directions. 
 Experiment with the different bodies provided, and determine 
 their kinds of equilibrium in different positions and with 
 respect to motion in different directions for each position. 
 Give a complete account of each case investigated, with draw- 
 ings 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 drawing, and 
 indicate by a dotted line the path that it would describe if 
 the equilibrium of the body were disturbed. 
 
 b. Balance your pencil on its point on your finger, making 
 use of a pocketknife to secure stable equilibrium. The blade 
 should be half open and stuck into the pencil near its point so 
 that the handle hangs below the finger. Draw a figure, and in 
 it locate the center of gravity of the pencil and knife regarded 
 as one body. 
 
 How definitely does the experiment determine this center 
 of gravity ? 
 
 II. To study the conditions affecting the stability of 
 bodies. 
 
 Apparatus. A rectangular and a trapezoidal block (Figs. 22 
 and 21), cut from a 2-in. board, the former heavily loaded 
 
64 MECHANICS OF SOLIDS 
 
 with lead at one end, and the latter loaded on the shorter of 
 the parallel sides so as to bring the center of gravity midway 
 between these sides. In one of the broad sides of each of these 
 blocks drive a nail over the center of gravity for the suspension 
 of a plumb line ; and bore two holes in each near vertices for 
 suspension in verifying the location of the center of gravity. 
 
 a. A nail is driven in a side of each of the blocks, presum- 
 ably over the center of gravity (which, of course, is within the 
 block). Verify the location of the center of gravity of each 
 block by suspending it by a nail or a short wire from each of 
 the holes in succession, and noting the direction of the plumb 
 line suspended from the same support. 
 b. Investigate the degree of diffi- 
 culty in overturning the trapezoidal 
 block on a short edge from a position 
 of equilibrium on each of its parallel 
 bases (Pig. 21). 
 
 What relation do you discover be- 
 FIG 21 tween the area of the base and the 
 
 stability of the body (the height of 
 the center of gravity remaining the same) ? 
 
 Draw a figure of the block in each position, and show by a 
 dotted line the path of the center of gravity in the process of 
 overturning. 
 
 What relation do you discover between the vertical distance 
 through which the center of gravity must be raised before the 
 body falls over and the difficulty of overturning it? (The 
 nature of the experiment does not justify the statement of 
 definite relations, such as proportionality.) 
 
 c. Investigate the degree of difficulty in overturning the 
 rectangular block on a short edge from a position of equi- 
 librium on each end. 
 
 What relation do you discover between the height of the 
 center of gravity of a body and its stability (the area of 
 the base remaining the same) ? 
 
COMPARISON OF MASSES BY INERTIA 65 
 
 Draw figures as before, showing the path of the center of 
 gravity in overturning. 
 
 Is the distance through which the center of gravity must be 
 raised to overturn the block the same or different for the two 
 ends? What suggestion does the answer to this question 
 afford in regard to the cause of the difference in stability 
 in the two positions ? 
 
 d. Experiment with either block 
 (both, if time permits), to determine 
 how far it must be turned on any of its 
 short -edges before it will fall over 
 (Fig. 22). For this purpose, suspend 
 the plumb line from the nail at the 
 center of gravity, adjusting the length 
 of the line so as to free the bob from 
 the table (or stand the block at the 
 
 edge of the. table, so that the plumb line hangs free in front of 
 it), and observe where the line passes, with reference to the 
 base of support, at the instant the block falls. Write your 
 conclusion in the form of a general statement that covers all 
 the cases that you have tried. 
 
 e. Explain this behavior of bodies in overturning them. 
 
 UNBALANCED FORCES: DYNAMICS 
 
 EXERCISE 20. COMPARISON OF MASSES BY 
 INERTIA 
 
 References. Hoadley, 15, 26, and 40-44 ; Carhart and Chute, 
 9, 13, and 39-43 ; Slate, 175-176 ; Sanford, pp. 26-28. 
 
 To measure a mass by the effect of a force upon it. 
 
 Apparatus. Torsion apparatus (Fig. 23), with weights to 
 fit the cups ; clamp to fasten it to the table or other support ; 
 tumbler or beaker; shot; balance and weights. 
 COLEMAN'S PHY. LAB. MAN. 6 
 
66 MECHANICS OF SOLIDS 
 
 [The torsion apparatus consists of a piece of spring brass or steel wire, 
 about No. 12 and a foot or more in length, attached rigidly to a small 
 block at the upper end and to the middle of a light, horizontal bar of wood 
 at the lower end. This bar is 8 or 10 in. long, and carries at each end cups 
 of tin or brass in which fit snugly equal brass weights. Cylinders of lighter 
 metal than brass (as zinc or iron) are to be preferred, if obtainable, as 
 the distinction between equality of mass and of volume would be more 
 strikingly illustrated. Weights of 200 g. are perhaps best suited to the 
 experiment, but either 100-g. or 500-g. weights may be used. For 500-g. 
 weights the supporting wire should be No. 10 or 11. The wire should be 
 of such size and length that, with the weights used, there are from 80 to 
 120 single vibrations per minute.] 
 
 a. Place the brass weights (hereafter called cylinders) in 
 
 the cups, and set the bar vibrat- 
 ing in a horizontal plane by 
 rotating it through 10 or 15. 
 Count the number of single vi- 
 brations made in exactly two 
 minutes, keeping time by the 
 second hand of a watch. 
 
 b. Set the bar vibrating through 
 a considerably smaller (or larger) 
 arc, and count the number of 
 
 vibrations as before. What effect has the extent of swing, or 
 amplitude, on the rate of swing ? 
 
 c. Kemove the cylinders from the cups and set the bar 
 vibrating. How has the removal of the cylinders affected the 
 rate ? (The rate need not be determined.) The vibration 
 is maintained by the elasticity of the supporting wire; and 
 the force brought into action by twisting it is the same 
 whether the cylinders are in the cups or not. After the 
 cylinders were removed, there was less mass (or matter) to 
 be moved by the force; hence the change in the rate. The 
 weight of the cylinders is not what affects the rate of vibra- 
 tion. The attraction of the earth plays no part whatever in 
 the experiment, not even causing friction, as is generally the 
 
COMPARISON OF MASSES BY INERTIA 67 
 
 case with moving bodies. The pull of the earth is balanced 
 by the tension of the wire ; the motion is caused by the torsion, 
 which is entirely independent of the tension, and hence of the 
 weight also. In fact, if the experiment could be performed 
 away from the attraction of the earth or of any heavenly 
 body, the effect of the cylinders would be the same as before, 
 although they would then weigh nothing. 
 
 d. From the above determined number of vibrations in 2 
 inin. with the cylinders in, compute the number of vibrations 
 in 1 min., and also in 30 sec. These numbers are wanted for 
 comparison in the next step. 
 
 e. Fill the cups about half full of shot. Set the apparatus 
 vibrating and count the number of vibrations in 30 sec. If the 
 rate is faster than with the cylinders, add more shot to each 
 cup, always keeping them equally full ; if the rate is slower, 
 remove part of the shot. In this way, by repeated trials, 
 adjust the quantity of shot till the rate of vibration is the 
 same as with the cylinders. When a difference can no longer 
 be detected in 30 sec., count for 1 min. and, finally, for 2 min. 
 Time is saved by making the period of counting short at first, 
 and greater accuracy is secured by making it longer. 
 
 /. When the adjustment called for has been made as closely 
 as possible, unclamp the apparatus and empty the shot into the 
 empty tumbler or beaker, keeping a hand over one cup to avoid 
 spilling while emptying the first cup. Weigh the shot used. 
 
 g. The experimental errors should not exceed 1% or 2%. 
 Within this limit, how do the masses of the shot used and 
 the cylinders compare ? Mass is really measured inertia (Slate, 
 224). 
 
 Discussion. This experiment teaches that : 
 
 (1) The inertia of a body is not to be confounded with its 
 weight, and is in no way dependent upon it. 
 
 (2) When equal (unbalanced) forces produce equal effects 
 upon different bodies, these bodies have equal masses. 
 
MECHANICS OF SOLIDS 
 
 (3) When equal forces act upon unequal masses, a less effect 
 is produced upon the larger mass. That is, the greater the 
 mass of a body, the greater its inertia. 
 
 Discuss each of these points, showing how they follow from 
 the experiment. 
 
 EXERCISE 21. FALLING BODIES: 1 WHITING'S 
 METHOD 
 
 References. Hoadley, 35-39, 78-79, and 81 ; Carhart and 
 Chute, 29-34 and 60-61. 
 
 I. To find the acceleration of a falling body. 
 Apparatus. A stick suspended to swing as a pendulum 
 (Fig. 24); meter rod; iron or lead ball; thread; matches. 
 
 [For the pendulum use a stick 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 impression. 
 The ball must be heavy enough to hold the 
 pendulum at a considerable angle, as shown 
 in the figure. For a long pendulum a lead 
 ball about 4 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 vertically.] 
 
 a. Place a strip of white paper 
 under the carbon paper at the top and 
 bottom of the pendulum. Adjust the 
 ball and pendulum, as shown in the 
 FIG. 24. figure, by means of a thread passing 
 
 1 Parts II and III may be omitted if a pendulum of different length 
 is not provided. Part I is complete in itself. If Parts II and III are 
 included, the exercise is complete (from a different point of view) without 
 Part I. d, which may be omitted. 
 
FALLING BODIES: WHITING'S METHOD 69 
 
 over the three nails. The ball should hang near the middle 
 of the paper. Without disturbing the adjustment of the 
 pendulum, strike the ball against the carbon paper, marking 
 its position by the dot thus made on the paper beneath. 
 When the ball is perfectly at rest 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. 
 
 b. Repeat the experiment ; but before doing so mark out 
 the dots already made on the paper, so they will not be mis- 
 taken for the 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 1 cm. from the first, take the average of 
 the two. If the difference is greater than 1 cm., make fur- 
 ther trials till you get three or more results agreeing within 
 1 or 2 cm., and take their average. Call the average dis- 
 tance S. 
 
 c. S is the distance the ball fell while the pendulum was 
 swinging to a vertical position; that is to say, while it was 
 making half a swing or vibration. To determine this time, 
 set the pendulum swinging, and count the number of swings 
 it makes in exactly 1 min., using the second hand of a watch. 
 The time of a swing does not change as the arc through which 
 the pendulum swings grows less ; hence from the number of 
 swings in 60 sec. you can determine the time of one swing. 
 Half this time is the time it takes the ball to fall S cm. 
 Compute this time and call it t. 
 
 d. Substitute your values of S and t in the formula for fall- 
 ing bodies and solve it for g. Compute the per cent of error of 
 your result. 
 
 II. To find the relation between the distance and the 
 time of fall. 
 
 Apparatus. The same as for Part T, except that the pendu- 
 lum is considerably longer (or shorter). 
 
TO MECHANICS OF SOLIDS 
 
 a. Repeat all the work of Part I with the longer (or shorter) 
 pendulum. Let the distance fallen be denoted by ^ and the 
 time of fall by t t . 
 
 b. Compute the ratios S : S l9 t : t ly (t : ^) 2 and (t : ^) 3 . Assum- 
 ing that the distance fallen by a freely falling body starting 
 from a state of rest is proportional to some integral power of 
 the time of fall, what power is it, as indicated by these ratios? 
 
 c. Compute the per cent of difference between the ratios that 
 should be equal. 
 
 Mention probable sources of error in the experiment. 
 
 III. To compute the acceleration of a falling body 
 from the data of Parts I and II. 
 
 a. In the proportion that you have formed from the quan- 
 tities S, $!, t, and t l9 let S and t denote, as before, the distance 
 and time respectively for Part I, and let Si denote the distance 
 fallen when ^ = 1 sec. Substitute these values in the propor- 
 tion and solve it for S^ 
 
 b. Since the distance fallen in one second from a state of 
 rest is one half the acceleration (g) of a freely falling body, we 
 
 have g = 2Si = cm. 
 
 Compute the per cent of error of your experimental value of 
 g, assuming the true value to be 980 cm. 
 
 EXERCISE 22. THE SIMPLE PENDULUM 
 
 References. Hoadley, 83-86 ; Carhart and Chute, 68-73. 
 
 Apparatus. A pendulum stand with three pendulums, one 
 with wooden and two with iron bobs (Fig. 25) ; watch or clock 
 with second hand. 
 
 [A convenient and efficient adjustable suspension is shown in the figure. 
 A slanting notch is cut to receive the thread at an angle of about 35, and 
 a cork glued above, in which is cut a slit to receive the thread. The fric- 
 tion in the cork holds the pendulum.] 
 
THE SIMPLE PENDULUM 
 
 71 
 
 I. To -find whether the amplitude of a pendulum 
 affects its time of vibration, or period. 
 
 a. Adjust the pendulums with iron 
 bobs so that, when started together with 
 equal amplitudes, they keep together. 
 It is better to have the pendulums about 
 as long as the apparatus will permit. 
 The adjustment will be sufficiently 
 accurate if one has not visibly gained 
 on the other in half a minute. After 
 securing this adjustment, start the pen- 
 dulums together, giving one an amplitude 
 of 4 or 5 and the other an amplitude 
 about one third as great. Let them 
 swing together for half a minute or 
 more. Does one gain on the other? 
 
 b. Again start the pendulums to- 
 gether, giving one an amplitude of 2 
 or 3 and the other an amplitude of 25 
 to 30. Observe which gains on the 
 other. Verify the result by a second 
 trial, giving the larger amplitude to the 
 other pendulum. 
 
 How does a large amplitude affect the period of a pendulum? 
 
 II. To find whether the mass and material of a pen- 
 dulum affect its period. 
 
 Adjust the pendulum with the 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 support 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 half a minute or more. 
 
 How do you find the period of a pendulum to be affected by 
 its weight or the material of which it is made ? 
 
 FIG. 25. 
 
72 
 
 MECHANICS OF SOLIDS 
 
 III. To find the relation between the period of a 
 pendulum and its length. 
 
 Adjust the three pendulums to lengths having the ratio of 
 1, ^, and %. Lengths of 36 in., 9 in., and 4 in. will be most con- 
 venient. Determine the number of vibrations that each of the 
 pendulums makes in exactly 60 sec. Compute for each of the 
 pendulums the value of the ratio VZ : t (to be expressed deci- 
 mally). 
 
 If there is time, test the ratio of the periods of the pendulums 
 by starting together the 36-in. and the 9-in. pendulums, and 
 observing 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. 
 
 FORM OF BECORD FOR PART III 
 
 Length = L 
 
 Whole Time 
 
 No. of Swings 
 
 Time of 1 
 Vibration = t 
 
 V^ 
 
 \/2 : t 
 
 36 in. 
 
 60 sec. 
 
 
 
 
 
 
 
 
 
 9 
 
 60 
 
 
 
 
 
 
 
 
 
 4 
 
 60 
 
 
 
 
 
 
 
 
 
 Discussion. a. The ratios VZ : t should be equal within 
 the limits of experimental errors (1% or 2%). Compute the 
 per cent of difference between the greatest arid the least of 
 them. 
 
 b. From the equality of these ratios determine the relation 
 between the lengths of two pendulums (L x and Z/ 2 ) and their 
 periods (^ and 2 ). 
 
 c. How should the pendulum of a clock be adjusted when it 
 is losing time ? When it is gaining time ? 
 
 d. Why does a pendulum such as you used in this exercise 
 come to rest after a time ? 
 
 What is the usual shape of the bobs of clock pendulums ? 
 What is the advantage of this shape ? 
 
THE WHEEL AND AXLE 
 
 73 
 
 MACHINES: WORK AND ENERGY 
 EXERCISE 23. THE WHEEL AND AXLE 
 
 References. Hoadley, 92-106 ; Carhart and Chute, 89-97. 
 To study the laws of the wheel and axle. 
 
 Apparatus. Wheel and axle mounted in any convenient 
 way, and with cord attached to the axle and each wheel ; 250-g. 
 spring balance with its weight recorded on 
 its back ; weights of about 1 kg. and 2 kg. 
 respectively (2000-g. balance and heavier 
 weights may be used) ; meter rod. 
 
 a. Weigh the small weight with the spring 
 balance, and call it W. Suspend it from 
 the axle, and tie the balance, right end up, 
 to the cord on the smaller wheel (Fig. 26). 
 Hold the balance by the hook. The sus- 
 taining force (/) includes the weight of the 
 balance (recorded on its back) in addition 
 to the scale reading. Observe that the 
 latter can be made to vary appreciably with- 
 out causing any motion of the apparatus. 
 This is due to friction, for which allowance 
 must be made in order to find what the 
 balancing force would be if there were no 
 friction. This is accomplished by reading 
 
 the balance while slowly and steadily raising the weight and 
 again while lowering it. Since friction always opposes motion, 
 it will be eliminated by taking the average of these readings. 
 To this average add the weight of the balance for /. Record 
 observations as indicated below. 
 
 b. In considering the condition for equilibrium of the wheel 
 and axle, it is to be regarded as a modified form of a lever of 
 the first class, as shown in Figure 27, where A denotes the 
 
 I 
 
 FIG. 26. 
 
74 MECHANICS OF SOLIDS 
 
 radius of the axle and a the radius of the wheel. Measure 
 (unless given) the diameters of the axle and the wheel. Write 
 the condition for equilibrium and see 
 whether your observations are in agree- 
 ment with it. 
 
 c. Eaise the weight a measured distance 
 (D), not less than 30 cm., and measure the 
 distance (d) through which the force acts 
 (the distance between the positions of a 
 corner of the balance before and after the 
 weight was raised). Compute the work done 
 upon the weight ( WD ) and the work done by the applied force 
 (fd). How should they compare? Find the per cent of error. 
 Record measurements and computations as indicated. 
 
 FORM OF RECORD 
 
 a. Weight of spring balance g. (or oz.) 
 Weight raised (W) - g. (or oz.) 
 Reading of balance, W rising 
 
 Reading of balance, W falling 
 Sustaining force (/) 
 
 b. Radius of axle (A) = cm. (or in.) 
 Radius of wheel (a) 
 
 Moment of weight ( WA ) = 
 
 Moment of the sustaining force (fa) 
 
 Error 
 
 Per cent of error - % 
 
 c. Distance weight is raised (U) cm. (or in.) 
 Distance through which / acts (d) - 
 
 Work done upon the weight (Wdfy = - kgm. (or ft. Ib.) 
 
 Work done by / (fd) 
 
 Error 
 
 Per cent of error = % 
 
THE PULLEY 75 
 
 Repeat the whole experiment with the larger weight and the 
 larger wheel. Make a section drawing and in it indicate the 
 quantities A, a, W, /, d, and D. 
 
 Discussion. a. With any wheel and axle the applied force 
 will support a weight how many times greater than itself? 
 (See paragraph 6.) 
 
 b. With any wheel and axle the applied force must act 
 , through a distance how many times farther than the weight is 
 
 lifted ? 
 
 c. From your answers to the preceding questions show that 
 the work done upon the weight (Wd) must always be equal 
 to the work done by the applied force (fd), disregarding 
 friction. 
 
 Taking friction into account, which of the two is necessarily 
 the greater ? Why ? 
 
 EXERCISE 24. THE PULLEY 
 References. Hoadley, 107-110 ; Carhart and Chute, 98-100. 
 
 Apparatus. A single and two double or triple pulleys ; 
 frame with screw hooks to support the pulleys (Fig. 28); 
 meter rod ; a weight of 2 to 4 Ib. and one of 6 to 16 Ib. ; cord ; 
 2000-g. spring balance. 
 
 I. To study the laws of the single fixed pulley. 
 
 NOTE. Use only metric or only English units throughout the exercise. 
 
 a. Suspend the pulley and pass a cord over it. Attach the 
 smaller weight ( W ) to one end of the cord, and tie the balance, 
 right end up, to the other end. The force (/) necessary to 
 balance the weight equals the reading of the balance plus its 
 weight (recorded on the back). Observe that the scale reading 
 can be made to vary appreciably without moving the weight. 
 This is due to friction, for which allowance must be made in 
 
76 
 
 MECHANICS OF SOLIDS 
 
 order to find what the sustaining force would be if there were 
 no friction. To eliminate the effect of friction, read the balance 
 while slowly and steadily raising the weight and again while 
 lowering it, and take the average. To this average add the 
 weight of the balance. Kecord W. In the form of record n 
 
 S 
 
 -A\ 
 
 FIG. 28. 
 
 denotes the number of parts of the cord supporting the weight. 
 (In this case n = 1.) 
 
 b. Starting with the balance near the pulley, pull it down 
 through a measured distance of 50 fern, to 80 cm., and measure 
 the distance the weight rises. The former is recorded as the 
 distance through which the force acts (d), and the latter as the 
 distance through which the weight moves (Z>). 
 
THE PULLEY 77 
 
 Compute the work done by the force (fd) and the work done 
 upon the weight (WD), using the kilogram-meter (or foot-pound) 
 as the unit. How do they compare ? 
 
 What advantage is there in using a single fixed pulley ? 
 
 II. To study the laws of the single movable pulley. 
 
 a. Weigh the single pulley and adjust it as 
 shown in Fig. 29, using the larger weight if not 
 greater than 4 kg. With this adjustment, W in- 
 cludes the weight of the pulley. Does / include 
 the weight of the balance ? In determining / 
 eliminate friction as before. Record /, W, and 
 n (n = 2). 
 
 What relation is there between the mechanical 
 advantage ( W : /) and n ? Account for this 
 relation, bearing in mind that the tension is the 
 same in all parts of the cord. 
 
 b. Starting with the weight low, raise the 
 balance through a measured distance not less 
 than 50 cm. How far is the weight lifted ? 
 
 Discover the connection between the ratio of 
 these distances and the number of parts of -the 
 cord supporting the weight. 
 
 What is gained by using a movable pulley ? G ' 
 
 Make a section drawing and in it indicate /, TF, d, and D. 
 
 III. To study combinations of fixed and movable 
 pulleys. 
 
 a. With the two double or triple pulleys arrange any com- 
 bination that you may choose. Use the heavier weight or, 
 if convenient, both. Weigh the movable pulley and remember 
 to include it as part of W. Follow directions and answer 
 questions of Part II. a. 
 
 b. Pull the balance down through a measured distance of 
 50 cm. or more, and measure the distance through which the 
 
78 
 
 MECHANICS OF SOLIDS 
 
 weight is lifted. Answer the questions of Part II, b. Make a 
 drawing of the arrangement of pulleys. 
 
 c. If time remains, arrange other combinations of pulleys, 
 and record the observations, together with drawings of the 
 combinations. 
 
 FORM OF RECORD 
 
 
 SCALE READING 
 
 / 
 
 W 
 
 n 
 
 Wif 
 
 ERRORS 
 n-W :f 
 
 %OF 
 
 ERROK 
 
 t'p 
 
 Down 
 
 I 
 
 g. 
 
 g- 
 
 g. 
 
 g- 
 
 
 
 
 
 
 
 % 
 
 II 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 III 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 d 
 
 'D 
 
 WORK DONE j ERRQR 
 
 %OF 
 
 
 
 
 By/ (-/<*) 
 
 Upon W(=\VD) J d WI) 
 
 ERROR 
 
 I 
 
 cm. 
 
 cm. 
 
 kgrn. 
 
 
 o/ 
 
 
 10 
 
 II 
 
 
 
 
 
 
 
 I 
 
 
 
 III 
 
 
 
 
 
 
 
 
 
 
 
 Discussion. a. Draw a figure of a single fixed pulley with 
 a force / supporting a weight W. Draw the horizontal diameter 
 of the pulley ; and regard this as a lever and the axis of the 
 pulley as its fulcrum. Express the condition for equilibrium 
 and show why / must be equal to W. 
 
 b. With any combination of pulleys a given force will sup- 
 port a weight how many times greater than itself ? Why ? 
 Word your answer so as to apply to all cases. 
 
 c. With any combination of pulleys the applied force must 
 act through a distance how many times farther than the weight 
 is raised ? Why ? 
 
 d. From your answers to b and c show that, neglecting friction, 
 there is neither saving nor loss of work by the use of pulleys. 
 
 What is the advantage gained by their use ? 
 
THE INCLINED PLANE 
 
 79 
 
 EXERCISE 25. THE INCLINED PLANE 
 References. Hoadley, 111 ; Carhart and Chute, 101-102. 
 
 Apparatus. An inclined plane (Fig. 30) ; roller or car ; 
 250-g. spring balance. 
 
 I. To find the ratio of the weight to the force neces- 
 sary to sustain it when the latter is applied parallel 
 to the plane. 
 
 a. Set up the plane at an angle of about 20. It is not 
 necessary to have the angle exact or to measure it. Measure 
 the height (H) and the length (L) of the plane. Since we 
 need only the ratio of these quantities, we may take for meas- 
 
 urement the right triangle formed by the under edge of the 
 plane, the upper edge of the base, and the straight vertical edge 
 of the support of the plane. With the balance determine the 
 force (/), parallel to the plane, necessary to hold the roller (or 
 car) in equilibrium on the plane. This may be taken as the 
 
80 
 
 MECHANICS OF SOLIDS 
 
 average of the readings when the roller is moving slowly up 
 the plane and slowly down it. Friction is thus eliminated. 
 Weigh the roller and call its weight W. 
 
 b. Repeat the set of measurements with the plane at a con- 
 siderably greater angle. (The angle must not be so large that 
 /exceeds the maximum reading of the balance.) 
 
 II. To find the ratio of the weight to the force neces- 
 sary to sustain it when the latter is applied parallel 
 to tlw base. 
 
 a. Take a set of readings with the applied force parallel to 
 the base, and the plane at the same angle as for I 6 ? unless the 
 force needed is greater than the balance will register, in which 
 case lower the plane. Instead of L record the length of the 
 base (B). 
 
 b. For a given angle of the plane, is the applied force greater 
 when applied parallel to the plane or parallel to the base ? 
 
 FORM OF RECORD 
 
 
 SCALE READING 
 
 
 
 
 
 
 
 f 
 
 W 
 
 
 ff 
 
 
 Up 
 
 Down 
 
 
 
 
 
 I a 
 
 f. 
 
 g. 
 
 g- 
 
 g- 
 
 L = cm. 
 
 cm. 
 
 b 
 
 
 
 
 
 
 
 
 
 L = cm. 
 
 
 
 II a 
 
 
 
 
 
 
 
 
 B= cm. 
 
 
 
 
 
 W:f 
 
 
 ERROR 
 
 % OF ERROR 
 
 I a 
 
 
 
 L: H= 
 
 W: 
 
 f-L: PI= 
 
 o /o 
 
 r 
 
 
 L - H 
 
 W - 
 
 / ' H 
 
 
 II a 
 
 
 
 B: H= 
 
 W: 
 
 f J) . TT 
 
 
 
THE INCLINED PLANE 81 
 
 Discussion. a. Make a section drawing of the plane, and in 
 it indicate the quantities /, W, B, L, and H. Resolve W into 
 components respectively perpendicular and parallel to the in- 
 clined plane. Write the relation that holds among the quan- 
 tities f 9 W) L, and H. Test your results by this relation, as 
 indicated in the form of record. 
 
 b. Make a similar drawing in which W is resolved into com- 
 ponents respectively perpendicular to the inclined plane and 
 parallel to the base ; and write the relation that holds for f 9 
 W, B, and H. 
 
 c. A plane is inclined at an angle of 30. What is the value 
 of L : H? What force parallel to the plane would be neces- 
 sary to support a 200-lb. barrel on it ? 
 
 d. How much work would be done in rolling the barrel 10 ft. 
 up the plane ? Through what vertical distance would the 
 barrel be raised ? 
 
 e. How much work would have been done if the barrel had 
 been lifted vertically that distance without the aid of any 
 machine ? 
 
 / What advantage is derived from the use of the plane ? 
 
 COLEMAN'S PHY. LAB. MAN. 6 
 
V. HEAT 
 EXERCISE 26. EXPANSION BY HEAT 
 
 References. Hoadley, 235-238 ; Carhart and Chute, 305-307. 
 
 I. To observe and compare the effect of heat on brass 
 and iron. 
 
 Apparatus. Ball and ring of brass; Bunsen burner; jar of 
 water ; compound bar of iron and brass riveted together. 
 
 a. To heat either the ball or ring, hold it in the Bunsen flame 
 about a minute ; to cool them, thrust them into the jar of water. 
 Do not lay the hot' ball or ring on the table. Find by trial 
 whether the ball will pass through the ring, (1) when both 
 are cold ; (2) when the ball is hot and the ring cold ; (3) when 
 both are hot. 
 
 State and account for the result in each case. 
 
 6. Heat both strips of the compound bar as nearly equally 
 as possible. Hold them in the flame so that they are side by 
 side, not one above the other. What does the bending of the 
 bars indicate ? 
 
 II. To observe the effect of heat on the volume of 
 water. 
 
 Apparatus A small flask or bottle of water, fitted with 
 
 stopper and small glass tube, with small rubber band for an 
 index (narrow section of small rubber tubing) ; vessel for heat- 
 ing water ; Bunsen burner. 
 
 Heat the vessel of water about as hot as you can bear with 
 your hand. See that the water stands a few centimeters high 
 in the glass tube inserted in the flask (Fig. 31). Its height 
 can be increased by pushing the stopper in farther. Mark the 
 
 82 
 
CONDUCTION OE HEAT 
 
 83 
 
 FlG 3 
 
 height of the water by the rubber band on the tube. 
 Lower the flask of water into the hot water, keep- 
 ing a sharp watch for the first motion of the water 
 in the tube. State and account for the observed 
 changes of level. 
 
 III. To observe the effect of gain and loss 
 of heat on the volume of air. 
 
 Apparatus. Small flask with stopper and glass 
 tube inserted ; tumbler of water. 
 
 a. With the flask inverted, thrust the end of the 
 glass tube into the tumbler of water ; and inclose 
 the flask in the hands so as to heat it and the air 
 inside. Observe whether bubbles rise in the tum- 
 bler ; and if they do, account for them. 
 
 b. With the tube still in the water, remove the 
 
 hands from the flask and observe any movement of air or 
 water in the tube. Explain. 
 
 c. Which was raised to the higher temperature, the flask of 
 water or the flask of air ? 
 
 From your observations which do you think would expand 
 more for equal changes of temperature, water or air ? 
 
 EXERCISE 27. CONDUCTION OF HEAT 
 
 References. Hoadley, 253-254; Carhart and Chute, 343- 
 347 ; Sanford, p. 170 ; Jones, 2 ; Madan, pp. 2-5 and 252-253. 
 
 I. To determine the order in which glass and different 
 metals stand as conductors of Iwcut. 
 
 Apparatus. Rods of brassy iron, glass, and copper (use wires 
 of the different metals of about No. 9 to 12) ; Bunsen burner ; 
 vessel of water ; test tube. 
 
 a. 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 about 6 cm. above the burner ; the two being as nearly as 
 
84 HEAT 
 
 possible equally heated. At first hold the rods near the heated 
 end ; and, as they become 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. 
 
 b. Fill the test tube with water within an inch of the top. 
 Hold it at the bottom with the fingers, tipping it slightly, and 
 apply the Bunsen flame a little below the top of the water, till 
 it boils at the top for about a minute. 
 
 What do you observe concerning the temperature of the 
 water at the bottom of the tube ? 
 
 What do you conclude concerning the conductivity of water? 
 
 II. To observe whether sensations of heat and cold are 
 affected by the- conductivity of the substance touched. 
 
 Apparatus. Some or all of the following substances, heated 
 to the same temperature in an air bath : brass, iron, glass, cop- 
 per, wool, asbestos, stone, wood. The same substances, cooled 
 to equal temperatures in an ice box. 
 
 a. Eemove from the air bath and cautiously feel the differ- 
 ent substances, two at a time, one in each hand. Arrange 
 them as nearly as you can in order, beginning with the one 
 that feels the hottest. 
 
 1 The rise of temperature along the rods depends upon another property 
 of the substances (not yet studied) besides their conductivity. But this 
 property (specific heat) would not affect the order of conductivity of the 
 materials used in this experiment. 
 
CONVECTION OF HEAT 85 
 
 These substances were really equally hot, all being at the 
 temperature of the hot air of the bath, to which they had been 
 exposed for a considerable time. Account for their seeming 
 difference of temperature. 
 
 b. Feel the same substances cooled in the ice box, and arrange 
 in order, beginning with the one that feels the coldest. In 
 doubtful cases press the substances, two at a time, against the 
 forehead, which is more sensitive than the hands. 
 
 Were their temperatures really different ? Explain. 
 
 Discussion. a. Why is woolen clothing warmer than cotton 
 or linen ? 
 
 b. Why is a carpet more comfortable to the bare feet in 
 cold weather than the floor ? 
 
 c. Why is asbestos used as wrapping for steam pipes and 
 boilers ? 
 
 d. An overcoat is said to " keep out the cold." What is it 
 that it really does ? 
 
 EXERCISE 28. CONVECTION OF HEAT 
 
 References. Hoadley, 255-257; Carhart and Chute, 348- 
 349. 
 
 I. To study convection currents in water. 
 
 Apparatus. Test tube; Bunsen burner; beaker; sawdust; 
 iron stand ; wire gauze ; mop cloth. 
 
 a. Put a very little 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 particles 
 of sawdust while the water is heating. What does this motion 
 indicate ? 
 
HEAT 
 
 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. (Consider the results of Part II 
 of Exercise 26.) 
 
 6. Fill the test tube nearly full of water, 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 
 where held. Compare with the experiment in conduction in 
 which the heat was applied near the top of the tube and was 
 held near the bottom. 
 
 Account for the difference in the results of the two experi- 
 ments. 
 
 II. To study convection currents of air. 
 
 Apparatus. Two student lamp chimneys ; a chalk or paste- 
 board box, with lidr that fits closely, and with a hole about an 
 inch in diameter in the lid near one end, and a group of small 
 holes that can be covered by the chimney near the other end 
 (Fig. 32) ; candle ; touch-paper ; jar of 
 water ; cloth and stick. 
 
 [Touch-paper is made by soaking filter 
 paper in a strong solution of saltpeter and 
 drying.] 
 
 a. Light the candle and place it on 
 the box over the group of small holes, 
 and place a student lamp chimney 
 over it, being careful to cover all the 
 holes with the chimney. Any wax or 
 tallo^ that keeps the chimney from 
 
 fitting tightly must be scraped off. Place the other chimney 
 over the large hole, and study the air currents by holding 
 burning touch-paper over the tops of the chimneys. When the 
 paper has burned nearly to the fingers, throw it into the jar of 
 water. Describe and account for the currents of air discovered. 
 b. Observe the effect upon the candle when the chimney is 
 
RADIANT ENERGY 87 
 
 removed from the large hole and the hole tightly covered with 
 the hand. Describe the result and explain it. If the burning 
 paper has soiled the chimneys, clean them with the cloth and 
 stick. Leave the apparatus and the table clean and in order. 
 
 36. Radiant Energy. Tt should be understood that so-called 
 " radiant heat " is not heat at all, but a wholly different form 
 of energy which is readily transformable into heat by absorp- 
 tion, a process analogous to the transformation of the kinetic 
 energy of a flying bullet into heat when it strikes a steel target. 
 Hence, of course, the " radiation of heat " is not a process of 
 heat transmission, but is the transmission of this other form 
 of energy. Its correct name is radiant energy, and the process 
 of transmission is radiation (not radiation of heat). 
 
 But light is also radiant energy, and its transmission is called 
 radiation ;' and it is desirable to be able to distinguish without 
 too many words between light and so-called " radiant heat." 
 Since the latter does not affect the eye, it is appropriately 
 called invisible radiation; and is thus distinguished from light, 
 which is visible radiation. 
 
 In general, the energy of invisible radiation is greater than 
 that of light, and hence has greater heating power when ab- 
 sorbed ; but the energy of light is also transformed into heat 
 by absorption. 
 
 EXERCISE 29. RADIANT ENERGY 
 
 References. Hoadley, 258-263; Carhart and Chute, 350- 
 354 ; Slate, 154-155 ; Sanf ord, pp. 17 -177 ; Jones, 86, 92. 
 
 Apparatus. Radiometer; Bunsen burner ; pasteboard screen 
 about 8 in. wide and 10 in. high, mounted on block; two 
 mounted tin screens, one bright, the other painted black or 
 coated with soot on one side ; three flat bottles of clear glass, 
 one empty, one filled with water, and one with a solution f 
 iodine in carbon bisulphide. 
 
88 HEAT 
 
 I. To study radiation and to distinguish it from con- 
 duction and convection. 
 
 a. Hold the hands beside the Buusen flame at different dis- 
 tances and above it. Note the intensity of the sensation of 
 heat in the different positions ; also note whether you can feel 
 convection currents in any position. In what position does 
 the hand receive heat by convection ? 
 
 b. Hold the hand beside the flame and within a few inches 
 of it, and note the intensity of the sensation. Insert the 
 pasteboard screen between your hand, still in this position, 
 and the flame. How does this affect the sensation of heat ? 
 
 If the heat came to the hand by conduction or convection, 
 could it get round the screen ? 
 
 State all the facts pointing to the conclusion that the hand 
 is not heated by conduction or convection when it is beside the 
 flame. 
 
 Does the radiation reach the hand by a straight or a bent path ? 
 
 c. Place the radiometer at different distances from the flame, 
 and observe the effect of distance upon the rate of rotation of 
 the vanes. Eadiation, both visible and invisible, falling upon 
 the radiometer, will cause the vanes to rotate ; and the rate of 
 rotation is an indication of the energy of the radiation. How 
 this effect is produced need not concern you here. 
 
 d. Place the radiometer 25 or 30 cm. from the flame and 
 slowly insert the pasteboard screen 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 ? 
 
 What evidence does this afford on the question how radia- 
 tion travels ? 
 
 II. To test the power of different substances to absorb 
 and transmit visible and invisible radiation. 
 
 a. Place the tin screens on opposite sides of the flame, about 
 10 cm. from it, with the black side of the one toward the flame. 
 
RADIANT ENERGY 89 
 
 After a minute or two, note the temperatures of the screens by 
 placing a hand flat against each on the side turned from the 
 flame. State and account for what is observed. 
 
 b. Eemove the bright screen and hold the hand in its place 
 at the same distance from the flame as the other hand, which 
 is still held against the back of the black screen. Which 
 hand becomes warmer ? Explain. 
 
 Note and account for the difference of temperature of the 
 palm and back of the hand that receives the direct radiation. 
 
 Do you think that the palm or back of the hand or the black 
 screen is more nearly at the temperature of the air at that dis- 
 tance from the flame ? Give reasons for your opinion. 
 
 c. Hold the empty flask between the flame and the radi- 
 ometer, and bring the latter up till the vanes make about one 
 rotation per second. Now remove the flask and note the effect 
 on the radiometer. What do you infer in regard to the be- 
 havior of clear glass toward radiation ? 
 
 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. 
 
 e. Substitute the flask containing the solution of iodine in 
 carbon disulphide. Compare the result with the preceding. 
 
 Does the solution transmit visible radiation ? (Can you see 
 through it ?) 
 
 What evidence is there that it transmits invisible radiation ? 
 
 Is it a better or a poorer transmitter of light than water ? 
 Is it a better or poorer transmitter of invisible radiation ? 
 
 Substances that transmit light readily are called transparent; 
 those that do not transmit light are called opaque. Substances 
 that readily transmit invisible radiation are called diaiher- 
 manous; those that absorb instead of transmitting it are 
 called athermanous. 
 
90 HEAT 
 
 III. To find in what direction radiation is reflected 
 by a smooth surface. 
 
 a. Adjust the flaine (F), the pasteboard screen (AB), and 
 the bright tin screen (CD) in the relative positions shown in 
 
 Fig. 33. AB should be within 10 or 12 cin. 
 
 C D 
 
 of the flame and within 2 cm. of CD. Com- 
 pare the rates of rotation of the radiometer 
 at a, b, and c. Observe that the flame and 
 the radiometer, when the latter is at a, are 
 symmetrically situated with respect to the 
 B screens. With the radiometer at a, try the 
 
 effect of turning CD at different angles, 
 always keeping it near the edge of AB. On what part of CD 
 does the radiation fall that is reflected into the space CAB ? 
 
 What does this experiment show concerning the law of reflec- 
 tion of radiation ? 
 
 b. Eeplace CD by the black screen, using the black surface. 
 Place the radiometer at a. State and account for the result. 
 
 c. Compare the reflecting powers of the two screens and 
 their powers of absorption as determined in II a. 
 
 What relation is shown between absorbing and reflecting 
 powers ? Account for this relation. 
 
 EXERCISE 30. COEFFICIENT OF LINEAR 
 EXPANSION 
 
 References. Hoadley, 264-265; Carhart and Chute, 319. 
 
 To find the expansion of 1 cm. of a brass rod for T 
 rise of temperature. 
 
 Apparatus. Linear expansion apparatus (Fig. 34); appa- 
 ratus for generating steam ; access to a thermometer; tumbler; 
 meter rod ; Bunsen burner. 
 
 [For the steam generator use a copper boiler on tripod, with tight top, 
 or flask with stopper and delivery tube, supported on a ring stand.] 
 
COEFFICIENT OF LINEAR EXPANSION 
 
 91 
 
 a. Fill the steam generator from one-third to one-half full 
 of water, and with the top off (or the delivery tube discon- 
 nected 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. 
 Set the tumbler under this tube to catch the escaping steam 
 and hot water. 
 
 6. Read to .1 mm. the position of the top of the long lever 
 arm on the vertical scale near its end. After taking this read- 
 ing be careful not to disturb the apparatus, as any change in 
 the relative position of the parts (for example, a slight rotation 
 
 of the steam jacket) may cause an appreciable change in the 
 reading just taken. 
 
 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 rod can be detected, read 
 the position of the long lever arm. The temperature of the 
 rod is the same as the temperature of the steam, which may 
 be assumed to be 100. 
 
 e. Measure the arms of the lever. These are the distances 
 from the fulcrum (the center of the screw) to the scale and 
 
92 HEAT 
 
 from the fulcrum to the point of contact with the rod respec- 
 tively. When you have finished, tilt the apparatus so that 
 the water condensed in the steam jacket will run out. 
 
 In finding the whole expansion of the rod, called for in the 
 computations, make use of the fact that the ends of the lever 
 arms move through distances that are proportional to the 
 lengths of the arms. 
 
 OBSERVATIONS 
 
 a. Length of brass rod = cm. 
 
 b. First position of long lever arm = cm. 
 
 c. First temperature of the rod = - C. 
 
 d. Final temperature of the rod = C. 
 
 Final position of long lever arm = cm. 
 
 e. Length of long lever arm = cm. 
 
 Length 'of short lever arm = cm. 
 
 COMPUTATIONS 
 
 Change of temperature of rod = C. 
 
 Expansion of the rod for this change of temp. = cm. 
 
 Expansion of the rod for 1 change of temp. = cm. 
 
 Expansion of 1 cm. of rod for 1 change of temp. = cm. 
 
 The last quantity is the coefficient of linear expansion of 
 brass, the correct value of which is .0000188. Compute the 
 per cent of error of your result. 
 
 ALTERNATIVE DIRECTIONS 
 
 If the apparatus is provided with a micrometer screw instead 
 of a lever, the following modifications of the directions will 
 apply :- 
 
 b. If you do not know how to read the micrometer screw, 
 turn it back and forth and study its action. Note the fixed 
 millimeter scale and the circular scale on the head ; also that 
 when the head is turned once round it advances 1 mm. along 
 
COEFFICIENT OF EXPANSION OF LIQUIDS 93 
 
 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 neces- 
 sary. The answers to these questions need not be recorded. 
 
 c. Turn the micrometer screw till it just touches the rod, 
 and take its reading. After taking the reading, turn the screw 
 back 2 or 3 mm. to make room for the expansion of the rod when 
 heated. If this precaution is not taken, the expanding rod will 
 strain and damage the apparatus. Eead the additional precau- 
 tion 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. Omit paragraph e. 
 
 EXEKCISE 31. COEFFICIENT OF EXPANSION OF 
 LIQUIDS 
 
 References. Hoadley, 266-267; Carhart and Chute, 317, 
 319. 
 
 Apparatus. Flask fitted with stopper and delivery tube and 
 supported on stand (Fig. 35) ; Bunsen burner ; three hydrom- 
 eter jars; stirrers; thermometers, each with a tube attached 
 containing the liquids for the exercise (Fig. 36) ; ice. 
 
 [For the tube to contain the liquids take a piece of quarter inch glass 
 tubing a little longer than the thermometer and seal at one end. Fasten 
 the tube firmly to the thermometer with fine wire or thread. As the 
 thermometer scale is to be used for measuring the length of the liquid 
 column, the lower end of the tube must not be below the bottom of the 
 thermometer scale. The measurement will be simplified by placing the 
 end of the bore of the tube exactly at the zero of the scale. The stirrer 
 may be made of a piece of wire about 30 in. long, bent into a close flat 
 coil that fits loosely into the jar ; with the remainder of the wire at right 
 angles to the coil for a handle. Alcohol, kerosene, olive oil, turpentine, 
 and ether are suitable liquids for the study of expansion. ] 
 
94 
 
 HEAT 
 
 I. To find the expansion (in 'com.} of 1 ccm. of a 
 liquid 1 for 1 rise of temperature. 
 
 a. Fill one of the jars about half full of crushed ice; 
 then fill with water full enough to cover the liquids in the 
 
 tubes fastened to the 
 thermometers. Fill 
 the flask about half 
 full of water, and sup- 
 port it on the ring 
 stand with the gauze 
 under it (Fig. 35). 
 The gauze should be 
 about 10 cm. above the 
 burner, and the flame 
 adjusted so that it 
 does not burn above 
 the gauze ; it is liable 
 to break the flask if 
 it does. Insert the 
 stopper and delivery 
 tube, being careful to 
 press the stopper in firmly. Fill the other two hydrometer 
 jars with water. 
 
 In the experimenting that follows, one jar is to be used for 
 temperatures between and 4, another for temperatures 
 between 20 and 40, and the third for temperatures between 
 50 and 80. Each set of jars will serve for more than one 
 student. 
 
 The temperatures of the jars are raised by passing in steam 
 from the flask, and lowered either by allowing to stand or 
 by pouring out part of the water and adding cold water. The 
 jars must not be subjected to large and sudden changes of tem- 
 perature or they will break. 
 
 1 Insert the name of the liquid used. 
 
COEFFICIENT OF EXPANSION OF LIQUIDS 95 
 
 Turn off the gas when not using steam, and immediately 
 remove the delivery tube from the jar. If this precaution is 
 not observed, the water in the jar will be "sucked" 
 over into the flask when the steam in the latter 
 cools. 
 
 b. Take a thermometer and tube containing any of 
 the liquids provided except water ; and, after thor- 
 oughly stirring the ice water by moving the stirrer 
 several times up and down through the length of the 
 jar, place the thermometer and tube in it. Read 
 the temperature and the height of the liquid on the 
 thermometer scale. The latter must be read as accu- 
 rately as possible to a tenth of a degree division, 
 reading the bottom of the curved surface. Be careful 
 not to cause the tube to slip along the thermometer. 
 Unless securely fastened, it may slip far enough to 
 cause a very large error in determining the expansion, 
 which will be only a few divisions. 
 
 c. Read and record the position of the bottom of 
 the liquid column. (The tube need not be in the 
 water when this reading is taken.) 
 
 d. Find the length of the liquid column, measured 
 in degree divisions on the thermometer scale. Thus, 
 if the bottom is at 10 and the top at 91.3, the 
 length is 101.3 (not marked with the degree sign). 
 
 e. After thoroughly stirring a jar of hot water, 
 put the thermometer and tube into it. The hot water 
 must be below the boiling point of the liquid in the tube; 
 otherwise it will boil. If you are experimenting 
 
 with ether the temperature must not exceed 33. Test by 
 inserting only the bulb of the thermometer at first. Ether 
 must be kept away from the flame, as its vapor is very in- 
 flammable. If alcohol is used, the water must not be above 
 7.V. Read the temperature and the height of the liquid as 
 before. 
 
96 HEAT 
 
 / Since the bore of the tube is uniform, the volume of the 
 liquid is proportional to its length. In fact the volume of the 
 tube between two adjacent marks on the thermometer scale 
 may be taken as the unit of volume. 
 
 The observed expansion is not linear, although indicated by 
 an increase of length, but cubical. Why ? 
 
 Compute the average expansion per degree of rise of temper- 
 ature. 
 
 g. The average expansion per degree is what fraction of 
 the volume at the lower temperature ? This is the average 
 coefficient of (cubical) expansion of the liquid between the 
 observed temperatures. 
 
 Compare the value you have obtained with the value given 
 in Table V of the Appendix. 
 
 II. To find the average coefficient of expansion of 
 water for the different intervals of temperature specified 
 in the record. 
 
 a. Proceed in a similar manner with the thermometer and 
 tube of water. Eead the position of the bottom of the water 
 column. 
 
 b. After thorough stirring, take the temperature and read 
 the position of the top of the water column as accurately as 
 possible: (1) in a jar of ice water; (2) in water at about the 
 temperature of the laboratory; (3) in water at 45 to 50; in 
 water at 75 to 80. 
 
 c. Compute the average coefficient of expansion of water: 
 (1) between the first and second observed temperatures; (2) 
 between the first and third observed temperatures ; (3) between 
 the third and fourth observed temperatures. 
 
 d. What do your results indicate in regard to the uniformity 
 of the expansion of water at different temperatures ? (See 
 values given in Table V of the Appendix.) 
 
 What can you say of the accuracy of this method for deter- 
 mining the expansion of water below 20 ? 
 
COEFFICIENT OF EXPANSION OF AIR 97 
 
 EXERCISE 32. COEFFICIENT OF EXPANSION 
 OF AIR 
 
 References. Hoadley, 268-270; Carhart and Chute, 318- 
 320. 
 
 To find by what fraction of its volume at air ex- 
 pands when Us temperature is raised 1 
 
 Apparatus. Copper boiler on tripod, with tall top ; Bunsen 
 burner; hydrometer jar; stirrer; thermometer, with attached 
 tube containing air and a mercury index ; ice. 
 
 [The tube containing the air must be of small bore (1 mm. or less), in 
 order to hold the mercury index in position, and should be 10 or 12 in. 
 long. Prepare as follows : Thoroughly dry the tube by passing dried air 
 through it. Insert an end of the tube into mercury, withdraw a column 
 about 3 mm. long, and let it run some distance down the tube. Seal an 
 end of the tube in a flame ; fasten the tube to a chemical thermometer as 
 for the preceding exercise (see directions). Work the index into proper 
 position with a fine wire, allowing for an expansion of somewhat more 
 than one fourth without exceeding the thermometer scale. Stick a 
 wooden plug in the end (not air tight) to keep out moisture.] 
 
 a. The tube fastened to the thermometer contains air which 
 is confined by means of the drop of mercury. Any considerable 
 jarring or rough handling is apt to displace the mercury index 
 and vary the amount of air confined below it. If this happens, 
 the whole set of observations will be worthless. With any 
 expansion or contraction of the confined air the index changes 
 its position without permitting any, air to pass it (unless it is 
 jarred). The length of the air column is to be measured by 
 the thermometer scale. If the tube extends below the zero 
 of the scale, the length of the air column will be the sum of 
 the readings of the lower end of the bore of the tube and of the 
 lower end of the index. For example, if these are respectively 
 12 and 74.3, the length of the column is 86.3 (not marked 
 with the degree sign). 
 
 COLEMAN'S PHY. LAB. MAN. 7 
 
98 HEAT 
 
 Without handling the thermometer or lube (to avoid impart- 
 ing heat from the hands) read the lower end of the air column, 
 the lower end of the index, and the temperature, all to .1. 
 
 b. Fill the hydrometer jar half full of crushed ice, and pour 
 in water enough to reach the top of the scale of the ther- 
 mometer when it is inserted. While the water is cooling, fill 
 the boiler two thirds full of water, and heat it as hot as you 
 can conveniently bear with the hand. 
 
 Thoroughly stir the water in the jar, pushing the ice to the 
 bottom of the jar with the stirrer several times. When the 
 temperature has fallen to 1 or 2, hold the ice at the bottom 
 of the jar with the stirrer, and insert the thermometer and air 
 tube. Take the temperature and the length of the air column 
 as before, after first assuring yourself that the readings of 
 the thermometer and of the mercury index have become 
 stationary. 
 
 c. Empty the jar (into the supply vessel of ice water if one 
 is provided), fill it with water from the faucet and empty it 
 several times, then rinse it with water from the boiler not 
 hotter than you can comfortably bear with the hands. (If 
 thick glass is heated suddenly it will break.) Now heat the 
 water in the boiler to about 60, fill the jar with it, and insert 
 the thermometer and air tube. Put the top on the boiler and 
 apply heat to boil the remaining water. (The boiler should be 
 at least one third full.) 
 
 After thoroughly stirring the water in the jar, take the tem- 
 perature and the position of the index as soon as they have 
 become stationary. 
 
 d. Insert the thermometer and tube into the top of the 
 boiler. Hold it by the cord and be careful not to burn your- 
 self with the steam, which must be escaping freely from the 
 top. As soon as the thermometer and index are stationary, 
 take a set of readings as before. 
 
 Empty the water from the jar and leave the thermometer 
 and tube in it. 
 
COEFFICIENT OF EXPANSION OF AIR 99 
 
 Discussion. a. Compute to three decimal places the con- 
 traction of the air column per degree fall of temperature be- 
 tween the first and second temperatures. 
 
 b. Compute the expansion of the air column per degree rise 
 of temperature between the first and third temperatures. 
 
 c. Compute the same between the third and fourth tem- 
 peratures. 
 
 d. Except for experimental errors the change of length per 
 degree should be the same by the three computations. (The 
 expansion of gases is uniform.) How great is the per cent of 
 difference between your results ? 
 
 e. Take the average of your three values of the expansion 
 (or contraction) per degree change of temperature. This is the 
 most reliable value obtainable from your observations. 
 
 /. Assuming the same contraction per degree, compute the 
 length of the air column at 0. 
 
 g. The expansion per degree (e) is what fraction of the 
 length at ? This is the coefficient of expansion of air (and 
 of all gases). Its true value is .00366. Compute the per cent 
 of error of your result. 
 
 EXEECISE 33. MELTING AND FKEEZING. 
 SOLUTION 
 
 References. Hoadley, 271-273; Carhart and Chute, 329- 
 332 and 334; Sanford, pp. 152-154 ; Slate, 123-124 ; Jones, 45; 
 Madan, pp. 39-42, 150-153, and 158-159. 
 
 Apparatus. Thermometer, numbered for identification ; 
 tumbler or beaker ; test tube ; access to ice and salt. 
 
 [It is suggested that all the thermometers used by the students be 
 numbered, and that a table of corrections for their freezing and boiling 
 points be posted in the laboratory for convenient reference. Such a 
 table may be compiled from the records of this exercise and Exercise 35 ; 
 and, when once compiled, will serve as a check on the work of future 
 classes. ] 
 
100 HEAT 
 
 I. To find the correction for the melting point of a 
 thermometer. 
 
 a. Fill the tumbler about half full of fine crushed ice. In- 
 sert the thermometer, and pack the ice about it nearly to the 
 zero of the scale. After the mercury becomes stationary, read 
 the temperature accurately to .1. Record the number of the 
 thermometer and the reading in melting ice. The graduation 
 of most thermometers, except expensive ones, is appreciably in- 
 accurate. In melting ice the reading should be exactly zero. 
 The reading you obtained is therefore the error of the melting 
 point of this thermometer. 
 
 b. What evidence is there that the ice you used was melting ? 
 Was the ice receiving or losing heat during the experiment ? 
 
 Give reason for your opinion. 
 
 II. To find whether ice freezes and melts at the same 
 temperature. 
 
 a. Mix with the ice about one third its volume of table salt. 
 Put enough water into the test tube to fill it about one fourth 
 full after the thermometer is inserted, and place it in the freez- 
 ing mixture of salt and ice. Stir the mixture with the test 
 tube, keeping watch of the temperature of the water in it. At 
 what temperature does it freeze ? Sometimes the temperature 
 of water falls a few degrees below the freezing point before it 
 begins to freeze ; but as soon as freezing begins, the tempera- 
 ture very quickly rises to the freezing point and remains sta- 
 tionary till the process is completed. Observe -whether this 
 happens in your experiment. Read accurately and record the 
 freezing point. 
 
 b. Does the temperature fall below the freezing point after 
 the water is all frozen ? 
 
 To melt the ice in the test tube let water run on it from the 
 faucet. Insert the thermometer into the freezing mixture and 
 take its temperature. 
 
MELTING AND FREEZING. SOLUTION 101 
 
 Was the water in the test tube receiving or losing heat during 
 the experiment ? Give reasons for your answer. 
 
 c. How do the temperatures of melting ice and freezing 
 water compare ? 
 
 What determines whether, in a mixture of the two, the ice 
 will melt or the water freeze ? 
 
 III. To observe the effect of pressure on 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. 
 
 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 posi- 
 tion 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 ? 
 
 IV, To observe the effect on temperature of dissolving 
 ammonium chloride or ammonium nitrate in water. 
 
 Apparatus. Thermometer ; test tube ; ammonium nitrate or 
 ammonium chloride. 
 
 a. Fill the test tube about one third full of water and take 
 its temperature. Add a teaspoonful or more of ammonium 
 nitrate or ammonium chloride, stir with the thermometer, and 
 note the change of temperature. 
 
 b. What inference may be drawn from this change of tem- 
 perature ? 
 
 What points of similarity are there between solution and 
 melting ? What transformation of heat is involved in either 
 process ? (See references.) 
 
102 HEAT 
 
 EXERCISE 34. EVAPORATION: VAPOR PRESSURE. 
 DEW-POINT 
 
 References. Hoadley, 274-276; Carhart and Chute, 335- 
 336 and 339-341 ; Slate, 125, 128-129, and 133-135 ; Sanford, 
 pp. 162-165 ; Jones, 48-49, 59-63, and 95-96; Madan, pp. 165- 
 168, 220-223, and 342-348. 
 
 I. To compare the evaporation of water, alcohol, and 
 ether with respect to rapidity and effect upon tempera- 
 ture. 
 
 Apparatus. Water ; small bottles of alcohol and ether. 
 
 a. Wet the palm with water and move the hand rapidly 
 back and forth edgewise. What is the temperature sensation? 
 Explain it. 
 
 b. Repeat with alcohol. Wet the palm by placing it over 
 the mouth of the bottle and inverting the bottle. Compare the 
 rapidity of evaporation of alcohol and water. Compare the 
 temperature sensations. Account for the difference. 
 
 c. Again moisten the palm with alcohol, and compare the 
 temperature sensations when the hand is still and when it is 
 moved rapidly to and fro. Account for the difference. 
 
 d. Repeat with ether. Compare results with those obtained 
 with alcohol. Account for the difference. 
 
 II. To find the pressure of saturated vapor of water, 
 alcohol, and ether at the temperature of the ldboratoj*y ; 
 and to observe the effect of change of temperature on tlxe 
 pressure of a saturated vapor. 
 
 Apparatus. Three barometer tubes set up, one with water, 
 one with alcohol, and one with ether in the tube above the 
 mercury, each supported with ring stand and clamp ; meter 
 rod; access to a barometer. 
 
 [To set up a tube fill it up with clean mercury within an inch or less 
 of being full, then finish filling with the liquid (water, alcohol, or ether). 
 
EVAPORATION. VAPOR PRESSURE. DEW-POINT 103 
 
 Invert a few times to gather up air bubbles in the mercury by means of the 
 lighter liquid as it runs from end to end. Fill the tube again completely 
 full and invert it over a dish of mercury. If all air has been removed, 
 the liquids will rise and completely till the tubes when they are inclined.] 
 
 a. Read the laboratory barometer and thermometer. 
 
 b. Measure the height of the mercury columns in the tubes 
 with water, alcohol, and ether respectively at the top. 
 
 c. Unclamp the tube containing alcohol or ether, and incline 
 it, being careful to hold the lower end firmly under the surface 
 of the mercury in the dish. Incline it till the space at the top 
 entirely disappears. Clamp the tube in a vertical position again. 
 
 What evidence is there that the space above the liquid does 
 not contain any air ? 
 
 What evidence is there that it is not a vacuum ? It does 
 contain the vapor of the liquid above the mercury. 
 
 How high would the mercury stand in the tube if the vapor 
 were not present ? 
 
 What became of this vapor when the tube was inclined ? 
 
 d. How great a pressure (measured in centimeters of mer- 
 cury) is exerted by the vapors of water, alcohol, and ether at 
 the temperature of the room ? 
 
 e. Warm the tube containing the ether by holding the hands 
 on it, and observe the effect on the height of the mercury. 
 (No measurements need be taken.) The observed effect is 
 partly due to the heating of the vapor already in the tube, 
 but chiefly to the evaporation of more ether. So long as any 
 liquid ether remains it will continue to evaporate till the space 
 above it is saturated; that is, contains all the ether vapor that 
 it can hold at that temperature. 
 
 Is the pressure of saturated ether vapor greater or less at 
 a higher temperature ? 
 
 /. Try the effect of warming the other tubes with the hands. 
 State results and compare with that obtained, with ether. 
 
 g. Point out the agreement between the results of these 
 experiments and those on evaporation. 
 
104 HEAT 
 
 III. To find the dew-point of the air in the laboratory. 
 Apparatus. Thermometer j bright calorimeter or tin can; 
 
 two beakers or tumblers; ice, or ammonium nitrate or ammo- 
 nium chloride. 
 
 a. Fill the calorimeter with water to about an inch in depth. 
 Have at hand a tumbler of water and a little finely crushed ice 
 in the other tumbler. Add ice to the calorimeter, a very little 
 at a time, stirring constantly with the thermometer. Watch 
 closely meanwhile for the first deposit of moisture on the calo- 
 rimeter near the bottom ; and, when it appears, take the tem- 
 perature of the water. 
 
 If the dew-point is below 0, it will be necessary to add salt 
 with the ice. If the calorimeter becomes filled to a depth 
 of over 2 in., pour out part of the contents. 
 
 Wipe the dew off with a cloth or your finger, and observe 
 whether it quickly gathers again. If it does, warm the 
 water in the calorimeter slightly by pouring in a little water 
 from the tumbler. Try to find the highest temperature 
 at which the dew will form at all. The warm, moist breath 
 will .cause the dew to form, on the side of the calorimeter 
 toward you before it will elsewhere. Test this by holding 
 the mouth close to the calorimeter and breathing against it. 
 To get the dew-point of the air in the room, avoid this error 
 by turning the calorimeter and quickly observing the appear- 
 ance of the farther side. 
 
 b. Wipe the calorimeter ; and, starting with the temperature 
 low enough to- deposit a thin film of dew, stir constantly till 
 it disappears, then quickly note the temperature. The tem- 
 peratures at which the dew appears and disappears should not 
 differ by more than 1. Take their average as the dew-point 
 of the air in the laboratory at the time of the experiment. 
 
 NOTE. Water, taken at the temperature of the laboratory, can gen- 
 erally be lowered to the dew-point by dissolving ammonium nitrate or 
 ammonium chloride in it. If ice is not provided, use one of these salts 
 instead, adding it slowly while stirring with the thermometer. 
 
BOILING OF WATER 105 
 
 EXERCISE 35. BOILING OF WATER 
 
 References. Hoadley, 277-280; Carhart and Chute, 337- 
 338. 
 
 Apparatus. Chemical thermometer, numbered for identifi- 
 cation ; ring stand, ring, and clamp ; wire gauze ; large flask, 
 and stopper to fit, with two holes ; delivery tube (Fig. 35) ; 
 hydrometer jar ; Bunsen burner ; closed tube pressure gauge 
 containing water in the closed tube above the mercury (Fig. 37). 
 
 [To make the pressure 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 Fig. 41, making the bend narrow enough to pass through the 
 neck of the flask. 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 tilting first one end, then the other, the air can 
 be gradually displaced from the closed tube by the mercury. Next pour 
 in water to a depth of about half an inch, and work a little of it into the 
 closed arm by inclining the tube with the closed arm above. ] 
 
 I. To observe the phenomena preceding and accom- 
 panying boiling; and to find the temperature of the 
 boiling water and the steam. 
 
 a. Fill the flask about half full of water from the faucet, 
 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. Insert the thermometer into the flask, and 
 occasionally observe the temperature. Observe the water care- 
 fully from the moment when you begin to apply the heat, and 
 note the first formation of bubbles. They are bubbles of air 
 which were dissolved in the water and are now being driven 
 off by the heat. Describe their size, abundance, and behavior; 
 and state through what range of temperature (approximately) 
 they continue to be given off. 
 
 6. 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 ? 
 
106 HEAT 
 
 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 temperature approaches 100. 
 
 d. Cause the. water to boil slowly and note the tem- 
 perature. Boil rapidly and again note the temperature. 
 
 e. Raise the thermometer till the bulb is just out 
 of the water. What is the reading of the thermometer ? 
 Read this as accurately as possible and record it as the 
 temperature of the steam. 
 
 II. To find the vapor pressure of steam at the 
 boiling point. 
 
 a. The closed tube pressure gauge (Fig. 37) contains 
 water in the closed arm above the mercury. Lower it 
 into the steam above the boiling water in the flask, 
 and note the formation of water vapor in the closed 
 arm. Observe the level of the mercury in the two arms. 
 
 How does the pressure of the water vapor in the 
 closed arm compare with the atmospheric pressure ? 
 What is its temperature ? 
 
 b. Observe the effect of removing the tube from the 
 flask. Explain. 
 
 c. What determines the temperature at which any 
 FIG. 37. liquid boils? 
 
 III. To observe the effect of increase of pressure upon 
 the boiling point; and to find the correction for the 
 boiling point of the thermometer used. 
 
 (L Remove the burner from under the flask while you are 
 making the following adjustment. Push the thermometer 
 through the hole in the stopper till the bulb is but little above 
 
BOILING OF WATER 107 
 
 the water when the stopper is in the flask. Be careful not to 
 break the thermometer by prying or using too much force. If 
 you have difficulty, call for assistance. Press the stopper 
 firmly into the flask. Connect the delivery tube as shown in 
 Fig. 35, 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. Gradually raise 
 the delivery tube out of the jar while observing the effect upon 
 the temperature of the steam. Raise and lower the delivery 
 tube till you are sure of the effect. 
 
 b. What change in the atmospheric pressure would produce 
 the same effect upon the temperature of the steam as lowering 
 the delivery tube into the jar of water? Estimate roughly the 
 change in the barometer corresponding to the water pressure 
 in the bottom of the jar. 
 
 Empty the flask and return the thermometer to its case. 
 
 c. Head the barometer. 
 
 d. 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 boiling point varies 
 .37 for a change of pressure of 1 cm. Compute the true value 
 of the boiling point at the observed barometric pressure. 
 
 e. What is the error of the boiling point of this thermometer ? 
 
 /. You will find in text-books a description of better appara- 
 tus for the accurate location of the boiling point on a thermom- 
 eter. Will the boiling point as determined by this apparatus 
 be a very little too high or too low ? Why ? 
 
 EXERCISE 36. THE BOILING POINT OF A LIQUID 
 (DETERMINED BY MEANS OF ITS VAPOR PRESSURE) 
 
 Apparatus. Flask fitted with stopper and delivery tube 
 and supported on a ring stand (Fig 35) ; Bunsen burner ; hy- 
 drometer jar; stirrer; thermometer; pressure gauges contain- 
 ing the liquids whose boiling points are to be determined. 
 
108 HEAT 
 
 [The pressure gauges are like that of the, preceding exercise except that 
 the closed arm should be 8 or 9 in. long, and the open arm a foot or 
 more. See the preceding exercise for directions for filling. Any liquid 
 whose boiling point lies between 30 and 90 may be used. ] 
 
 I. To find the boiling point of 
 
 a. Fill the flask about half full of water, and adjust the 
 apparatus as shown in (Fig. 35), being careful to press the 
 stopper in firmly . Apply heat. Fill the hydrometer jar nearly 
 full of water, and place in it the pressure gauge containing the 
 liquid whose boiling point is to be determined. The water 
 must cover the closed tube of the gauge. Pass steam into the 
 jar till the mercury stands at the same level in the arms of the 
 gauge. Remove the flame from under the flask and the delivery 
 tube from the jar ; and stir the water in the jar thoroughly. 
 If the mercury levels in the gauge now indicate that the water 
 is below the boiling point of the liquid, pass in a little more 
 steam. If the temperature is too high, allow to cool, stirring 
 occasionally, till the mercury stands exactly at the same level 
 in the two arms ; then take the temperature, calling it the 
 boiling point of the liquid. 
 
 b. How do you know that this is the boiling point of the 
 liquid ? 
 
 II. To find the boiling point of . 
 
 In the same way find the boiling point of another liquid. 
 
 CALORIMETRY 
 
 37. The Heat Unit. In the following experiments it is 
 required to measure definitely (although indirectly) the quan- 
 tity of heat transferred from one body to another. For this 
 purpose it is necessary to adopt a definite quantity of heat as 
 the unit of measurement. The one that we shall use is the 
 quantity of heat required to raise the temperature of 1 g. of 
 water 1 C. ; and it is called the calorie. 
 
Thus, to raise^fche temperature of 20 g. of water from 5 to 
 12 would require 140 calories ; for the rise of temperature is 
 7, which would require 7 calories per grain, or 20 x 7 calories 
 for 20 g. 
 
 38. Specific Heat. Equal quantities of heat are not re- 
 quired to raise the temperature of equal weights of different 
 substances the same number of degrees. For example, it is 
 found that only one ninth as much heat is required to raise a 
 given weight of iron 1 as is necessary to raise the same weight 
 of water 1. This is expressed by saying that the specific heat 
 of iron is one ninth or .11. It will be seen that specific heat 
 (like specific gravity) is a ratio. If, however, we take for 
 comparison 1 g. of each of the substances, it follows that, 
 since it takes one calorie to raise 1 g. of water 1, it will take 
 one ninth of a calorie to raise 1 g. of iron 1. Hence the specific 
 heat of a substance may be defined as the number of calories 
 of heat necessary to raise the temperature of 1 g. of the 
 substance 1 C. 
 
 To illustrate : If the specific heat of a substance is .04 
 (calories), to raise the temperature of 50 g. of it from 2 to 6 
 would require 50 x 4 x .04, or 8 calories. The same body in cool- 
 ing from 50 to 30 would give out 50 x 20 x .04, or 40 calories. 
 
 39. The Heat Equation. In experiments in calorimetry 
 (heat measurement) two bodies at different temperatures are 
 brought together in the same vessel (the calorimeter), and 
 mixed so that their temperatures are quickly equalized. The 
 calorimeter, of course, shares in the transfer of heat. In addi- 
 tion to this, there will be a transfer of heat to or from bodies 
 outside the calorimeter by conduction and radiation ; and for 
 accurate results allowance must be made for this, or the con- 
 ditions of the experiment must be so adjusted that the gains 
 and losses of heat by these processes balance each other. The 
 latter method is adopted in the following experiments. (How 
 this is accomplished will be left for consideration in the ex- 
 
110 UK AT 
 
 periments themselves.) By this method it is assumed that 
 the transfers of heat take place only among the calorimeter and 
 its contents ; hence it follows that the heat given out by the 
 body or bodies that fall in temperature is equal to the heat 
 gained by the bodies that rise in temperature. 
 
 For example, let it be required to find the specific heat (s) 
 of iron from the following data : 
 
 A brass calorimeter weighing 100 g. contains 400 g. of water 
 at 18. Into this is put a roll of iron at a temperature of 100 
 and weighing 190 g. The temperature of the calorimeter and 
 water rises and that of the iron falls to 22. It is further 
 given that the specific heat of brass (the material of the calo- 
 rimeter) is .09. 
 
 SOLUTION 
 
 Rise of temp, of calorimeter and water = 22 18 = 4 
 Gain of heat by calorimeter =100 x 4 x .09 = 36 cal. 
 
 Gain of heat by water = 400 x 4 = 1600 cal. 
 
 Fall of temperature of iron = 100 - 22 = 78 
 
 Loss of heat by iron = 190 x 78 x * = 14820 seal. 
 
 Loss of heat by iron = gain of heat by calorimeter 
 + gain of heat by water ; 
 14820s = 36 + 1600 
 Specific heat of iron (*)= 1636 -s- 14820 = .110 
 
 The method of treating the experimental data, as illustrated 
 by the above example, may be stated as follows : 
 
 (1) Find numerical or algebraic expressions for the separate 
 quantities of heat involved in the equalization of temperatures. 
 
 (2) With these heat quantities form the heat equation, which 
 expresses the equality of heat lost and heat gained. This equa- 
 tion contains as an unknown quantity the quantity sought 
 (specific or latent heat) ; and this is found by solving the 
 equation by the usual algebraic processes. 
 
OF THE 
 
 UNIVERSITY 
 
 OF i SPECIFIC HEAT 111 
 
 EXERCISE 37. SPECIFIC HEAT 
 
 References. Hoadley, 281-283 ; Carhart and Chute, 325- 
 327 ; Slate, 113. 
 
 To find the number of calories given out by 1 g. of 
 brass or copper in cooling 1. 
 
 Apparatus. Bunsen burner ; copper vessel on tripod, or 
 other open vessel for boiling water ; roll of copper or brass 
 with fine wire attached for handle ; brass or copper calorim- 
 eter; thermometer; platform balance and weights ; mop cloth. 
 
 [The roll of copper or brass should weigh from 200 to 400 g. , and must 
 be an open roll with a space of about one fourth in. between the sur- 
 faces, to avoid holding water by capillary action (Fig. 38). It would 
 better be made from sheet metal at least 1 mm. thick. ] 
 
 a. Begin heating the water in the 
 copper boiler. Weigh the roll of copper 
 (or brass) to .1 g. 
 
 b. Weigh the calorimeter. Put the 
 roll into the calorimeter and pour in 
 enough water to cover it. The water 
 should be 2 or 3 below the tempera- 
 ture 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. FIG. 38. 
 
 c. Weigh the calorimeter and the water in it, and remove 
 it from the balance. 
 
 d. After the above has been done and the water in the copper 
 vessel is boiling, thoroughly stir the water in the calorimeter 
 with the thermometer and take its temperature to .1. Kemove 
 the thermometer, hold the calorimeter close beside the boiler, 
 and as quickly as possible transfer the roll to the calorimeter. 
 Place the calorimeter on the table at a distance from the flame; 
 move the roll about in it to stir the water; insert the ther- 
 
112 HEAT 
 
 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. 
 
 NOTE. It is assumed that the roll is at a temperature of 100 when 
 put into the calorimeter ; but it cools with great rapidity during the trans- 
 fer, and a delay of a second in this process will cause an error of from 
 5% to 10% in the result. The small quantity of hot water clinging to the 
 roll and transferred with it partly compensates for the loss of heat by the 
 roll. The temperatures must be read as accurately as possible. An error 
 of .1 in determining a temperature change of 5 is an error of 2 %. 
 
 It will be well, if time permits, to repeat the experiment. It 
 will take but a few minutes to do so; and, having become 
 familiar with the method of procedure, you will very probably 
 secure better results. 
 
 The specific heat of copper and of brass are equal within the 
 limits of your experimental errors ; hence the roll and the 
 calorimeter, either of which may be of brass or copper, are 
 considered together in this experiment, and their specific heat 
 (s) determined. Remember that s denotes the number of calories 
 of heat lost by 1 g. of either metal when its temperature falls 1 
 and the number of calories gained when its temperature rises 1. 
 
 The heat that caused the rise of temperature of the calo- 
 rimeter and water is assumed to come entirely from the roll, 
 and hence to be equal to the heat lost by it. Form the heat 
 equation with these equal quantities of heat and solve it for s. 
 Include the equation and its solution in the record. 
 
 OBSERVATIONS 
 
 a. Weight of copper (or brass) roll = g. 
 
 b. Weight of calorimeter = g. 
 
 c. Weight of calorimeter and water = g. 
 
 d. Initial temperature of water and calorimeter = - C. 
 Initial temperature of copper roll = 100 C. 
 Final temperature of calorimeter and contents = C. 
 
LATENT HEAT OF FUSION OF ICE 113 
 
 COMPUTATIONS 
 
 Weight of water = g. 
 
 Rise of temperature of calorimeter 
 
 Gain of heat by calorimeter = ( ) x ( ) X s= calories 
 
 Fall of temperature of roll = 
 
 Loss of heat by roll =( )x( ) x s calories 
 
 Specific heat of copper or brass (s) = 
 
 To find the specific heat of any metal. 
 
 Use a roll of the metal as above. Instead of the brass calo- 
 rimeter a small tin can or glass beaker may be used. In 
 any case the specific heat of the calorimeter must be known. 
 (See Table of Specific Heats in the Appendix.) 
 
 Follow the above directions and form of record ; but in the 
 expression for the gain of heat by the calorimeter substitute its 
 known specific heat. 
 
 EXERCISE 38. LATENT HEAT OF FUSION OF ICE 
 
 References. Hoadley, 284; Carhart and Chute, 329-333; 
 Sanford, pp. 152-153. 
 
 To find the number of calories required to change 1. g. 
 of ice at into water at 0. 
 
 Apparatus. Calorimeter; thermometer and stirrer (Fig. 39); 
 platform balance and weights ; cloth ; supply of ice and of hot 
 water. 
 
 [For a stirrer use a piece of very thin copper (thickness of writing 
 paper) about 1 x 1.5 in. with two holes large enough to slip it on the end 
 of the thermometer. ] 
 
 a. Weigh the calorimeter to .1 g. 
 
 6. Fill the calorimeter about half full of water (about 200 g.) 
 at about 45 C. Take hot water from the supply and add cold 
 water as needed. Weigh the calorimeter and water and remove 
 from the balance. 
 
 COLEMAN'S PHY. LAB. MAN. 8 
 
114 HEAT 
 
 c. Have at hand a large handful of crushed ice on a cloth 
 (to keep it dry). There should be no pieces larger than small 
 
 marbles. Stir the water with the copper stirrer on 
 the thermometer till the temperature is uniform, 
 then take it accurately. Quickly dry the ice by 
 spreading it out thin and wiping it with the cloth, 
 and immediately put nearly all of it into the calo- 
 rimeter. Stir the water constantly while the ice is 
 melting. Keep the hands off the calorimeter during 
 the process to avoid conduction from the hand. 
 
 If ice remains after the temperature has fallen to 
 8 or 10, 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 ice has all disappeared, 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. 
 
 d. Weigh the calorimeter and contents. 
 
 It will be advisable to repeat the experiment if there is time. 
 Do not leave ice to melt on the table. Leave the calorimeter 
 empty and the table dry. 
 
 e. The experiment is planned so that the loss of heat from 
 the calorimeter and contents by radiation and conduction in the 
 
 . first part of the experiment is approximately balanced by the 
 gain by the same means in the latter part. Hence the heat 
 necessary to melt the ice and to raise its temperature after 
 melting is assumed to come entirely from the hot calorimeter 
 and water, and to be equal to the heat lost by them. Form the 
 heat equation containing all these quantities of heat, and solve 
 it for Z, which is used to denote the latent heat of fusion of ice 
 (or the latent heat of water). If the calorimeter is of brass, 
 take .094 for its specific heat; if of other material, find its 
 specific heat in Table VIII of the Appendix. 
 
LATENT HEAT OF FUSION OF ICE 
 
 115 
 
 OBSERVATIONS 
 
 a. Weight of calorimeter 
 
 b. Weight of calorimeter and initial water 
 
 c. Initial temp, of calorimeter and water 
 Final temp, of calorimeter and water 
 
 d. Final weight of calorimeter and water 
 
 (including water from ice) 
 
 COMPUTATIONS 
 
 Weight of water before adding ice 
 
 Weight of ice added 
 
 Fall of temperature of calorimeter and 
 
 initial water 
 
 Loss of heat by calorimeter 
 Loss of heat by initial water 
 Heat required to melt the ice = ( ) x L 
 Heat required to raise temperature of 
 
 melted ice from to final temp. 
 Latent heat of fusion of ice (L) 
 True value of latent heat of fusion of ice 
 Per cent of error 
 
 = g- 
 
 'C. 
 
 = g. 
 
 = g- 
 
 calories 
 
 calories 
 = calories 
 
 calories 
 calories 
 80 calories 
 
 EXEKCISE 39. 
 
 LATENT HEAT OF VAPORIZATION 
 OF WATER 
 
 References. Hoadley, 285-286; Carhart and Chute, 342; 
 Slate, 152. 
 
 To find the number of calories given out by 1 g. of 
 steam at 100 in condensing to water at 100. 
 
 Apparatus. Calorimeter ; steam generating apparatus ; Bun- 
 sen burner; rubber tube and condensation trap (Fig. 40) or 
 side-neck test tube ; thermometer and stirrer ; platform balance 
 and weights ; mop cloth. 
 
116 HEAT 
 
 a. Fill the steam generator about half full of water, and 
 heat. Connect the delivery tube and condensation trap. Sup- 
 port the delivery tube on some object so that the escap- 
 ing steam will not damage the table. 
 
 b. Weigh the calorimeter to .1 g. (It is especially 
 important in this experiment that the weighing be 
 carefully done.) 
 
 c. Fill the calorimeter about two thirds full of water 
 at 5 to 8. Add ice to water from the faucet till the 
 
 . 40. re q u i re d temperature is obtained. (If no ice is pro- 
 vided, use the coldest water obtainable ; and carry the tem- 
 perature with the steam, as directed in the next paragraph, 
 up to about 40.) Weigh carefully the calorimeter and con- 
 tents, and remove from the balance. 
 
 d. Place the stirrer on the calorimeter ; and, as soon as the 
 stearn is escaping freely from the delivery tube, stir the water 
 in the calorimeter and take the temperature, and immediately 
 place the delivery tube in it to a depth of an inch or two. The 
 calorimeter should be as far as possible from the burner, and 
 protected from its radiation by a screen. Stand your note- 
 book between them for this purpose. There should be no con- 
 siderable loss of steam on account of poorly adjusted apparatus. 
 If the steam is being delivered properly, the temperature will 
 rise rapidly. 
 
 Stir the water continuously, keeping the hands off the calo- 
 rimeter. Be careful not to let the condensation trap over- 
 flow 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 is about as far above the tem- 
 perature of the room as it was below it at the start, turn 
 off the gas, remove the delivery tube, and immediately, 
 while stirring, observe the highest uniform temperature 
 attained. 
 
 e. Weigh the calorimeter and contents. 
 
LATENT HEAT OF VAPORIZATION OF WATER 117 
 
 Repeat the experiment if there is time. Leave the calo- 
 rimeter empty and the table dry. 
 
 /. How has loss or gain of heat by radiation and conduction 
 been provided for in this experiment ? L is used to denote the 
 latent heat of vaporization of water ; which is also the amount 
 of heat given out by 1 g. of steam in condensing to water at 
 100. Write the heat equation and solve for L, as in the pre- 
 ceding experiment. 
 
 OBSERVATIONS 
 
 b. Weight of calorimeter 
 
 c. Weight of calorimeter and initial water = 
 
 d. Initial temp, of calorimeter and water 
 Final temp, of calorimeter and water = 
 
 e. Final weight of calorimeter and water 
 
 (including water from steam) 
 
 COMPUTATIONS 
 
 Weight of water before adding steam 
 
 Weight of steam added 
 
 Eise of temperature of calorimeter and 
 
 initial water 
 
 Gain of heafc by calorimeter 
 Gain of heat by initial water = 
 
 Heat given out by steam in condensing to 
 
 water at 100 = ( ) X L 
 Heat given out by water from steam in 
 
 falling to final temperature 
 Latent heat of vaporization of water (L) = 
 True value of latent heat of vaporization 
 
 of water 
 Per cent of error 
 
 
 calories 
 
 calories 
 
 - calories 
 
 - calories 
 
 - calories 
 
 = r>37 calories 
 
VI. SOUND 
 EXEECISE 40. THE TRANSMISSION OF SOUND 
 
 References. Hoadley, 181-184; Carhart and Chute, 174- 
 179 and 198-199 ; Jones, Sound, 10. 
 
 Apparatus (for Parts I and II). Meter rod ; tuning fork ] ; 
 tumbler or jar of water ; large cork or small block of wood 
 with hole to fit the stem of the fork ; rubber mallet for strik- 
 ing the fork ; an apoustic telephone. 
 
 [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. To make an acoustic 
 telephone, make a small hole in the middle of the bottom of two small 
 tin cans or chalk boxes, fasten them up at some distance apart, and 
 stretch a cord or small wire rather tightly between them, fastening the 
 ends to some small object (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 cord, and may be carried 
 round a corner by giving it three or four supports at the corner, making 
 each bend slight. It is rather better to replace the bottom of the can or 
 box by a piece of parchment.] 
 
 I. To investigate the transmission of sound through 
 solids. 
 
 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 to drive it toward the other 
 
 1 Tuning forks for experimental purposes should be large and heavy. 
 Small forks do not vibrate long enough nor with sufficient energy. 
 
 118 
 
THE TRANSMISSION OF SOUND 119 
 
 prong. Hold one end of the meter rod (or other long stick) 
 close to the ear while your companion holds the stem of the 
 vibrating fork against the other end of the rod. Remove the 
 ear from the rod and listen for the sound of the fork through 
 the air. 
 
 Compare the loudness of the sound transmitted through the 
 rod and through the air. 
 
 b. Hold the end of the rod between your teeth while the 
 fork is sounded against the other end. The vibrations travel 
 through the rod, the teeth, and the bones of the head to 
 the ear. 
 
 Describe the result. Do you feel the vibrations ? 
 
 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 moderately tight. Try the effect of slackening the 
 string and of removing it from the ear. 
 
 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 vibrat- 
 ing fork and the table. 
 
 How does the stopper compare with the rod in its power to 
 transmit sound ? Account for the difference. 
 
 g. If an acoustic telephone is set up in the laboratory, listen 
 at one end of it while your companion sounds the fork against 
 the bottom of the can or box at the other end. Try speaking 
 to each other through the telephone. 
 
120 SOUND 
 
 II. To find whether water transmits sound. 
 
 Place a tumbler of water on the table. Insert 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 tumbler from the table and again replacing 
 it. State and account for the effect upon the sound when the 
 tumbler is lifted. 
 
 How does the experiment answer the question whether 
 water transmits sound? 
 
 III. To investigate the transmission of sound through 
 a speaking tube. 
 
 Apparatus. A tin or large glass tube 6 ft. to 10 ft. long ; a 
 roll of cotton or soft cloth. 
 
 Lay a watch on a roll of cotton or soft cloth (to prevent 
 transmission of the sound through the table) near one end of 
 the tube, and listen at the other end for 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. 
 
 EXERCISE 41. THE VELOCITY OF SOUND IN AIR 
 
 References. Hoadley, 189-192; Carhart and Chute, 180- 
 183 ; Jones, Sound, 24-27. 
 
 Apparatus. Pendulum that beats half seconds ; hammer ; 
 piece of iron or other object that gives a loud, sharp sound 
 when struck ; tape measure or long cord of measured length. 
 
THE VELOCITY OF SOUND IN AIR 121 
 
 To determine the velocity of sound in open air by 
 timing an echo. 
 
 a. This method is to be preferred if there is a large building 
 that can be utilized as a reflector for obtaining an echo. This 
 will require a free space of about 300 ft. beside the building. 
 
 Adjust a pendulum to beat half seconds. It will be about 
 25 cm. long ; but find the exact length by trial. A stone tied 
 to a string will serve. 
 
 Stand facing the building at a considerable distance from it 
 and in line with the perpendicular to the middle of the side of 
 the building. Start the pendulum swinging. Hold the hammer 
 in one hand and the object to be struck in the other ; swing the 
 hammer to and fro horizontally in exact time with the pendu- 
 lum ; and strike the object once per second exactly at the instant 
 that the pendulum completes its swing to one side (the left). 
 
 b. Listen for the echo, and find by trial the distance from 
 the building at which you hear it exactly at the instant the 
 pendulum completes its swing to the opposite side (the right). 
 The echo must divide the time between the blows exactly in 
 half. Repeat the blows many times in succession, carefully 
 watching the pendulum and listening to the echo. 
 
 c. When you have found the distance from the building that 
 gives the best results, measure it. Since the echo was heard 
 one half second after the blow was struck, the sound traveled 
 twice this distance (to the building and back) in one half a 
 second. Hence four times this distance is your experimental 
 value of the velocity of sound at the temperature when the 
 experiment was performed. 
 
 d. Record the temperature if you have access to a thermom- 
 eter ; if not, record your estimate of the temperature. 
 
 e. Compute the true value of the velocity of sound from the 
 formula v = ( 1090 + p _ 32 ] ) f t ., 
 
 in which t is the temperature by the Fahrenheit thermometer ; 
 and from this find the per cent of error of your result. 
 
122 SOUND 
 
 To determine the velocity of sound in open air by 
 timing a sound made at a distance. 
 
 a. This method requires two stations between 500 and 600 ft. 
 apart with an unobstructed view between them. It is de- 
 sirable to have an opera glass or a spy glass for observing 
 the pendulum at a distance. 
 
 At one station set up a pendulum that beats half seconds 
 (see paragraph a of the first method) with a screen behind 
 it so that it can be more easily seen at a distance. Use a 
 white screen if the bob of the pendulum is dark and a black 
 screen if it is light. The bob must be large if it is to be 
 observed with the naked eye. 
 
 One person stands beside the pendulum and makes a loud 
 sound once per second as directed in paragraph a of the first 
 method ; and another finds by trial the distance at which he 
 hears the sound exactly one half second after the blow is struck; 
 that is, at the instant the pendulum completes its swing to the 
 opposite side. As noted above, it will be better to use an 
 opera glass or a spy glass for observing the pendulum. 
 
 b. Exchange places and repeat the experiment. It will be 
 evident that the probable error in determining the distance 
 is rather large ; but the estimates of the two observers should 
 agree within 50 ft. By repeated trial secure agreement within 
 this limit if possible. 
 
 c. Measure the distance between the stations, taking the 
 average if the estimates differ; and double this distance for 
 the velocity of sound at the temperature when the experiment 
 was performed. 
 
 d. Kecord the temperature if you have access to a thermom- 
 eter ; if not, record your estimate of the temperature. 
 
 e. Compute the true value of the velocity of sound from the 
 formula 
 
 o _ 32 -] ) f t> ^ 
 
 in which t is the temperature by the Fahrenheit thermometer ; 
 and from this find the per cent of error of your result, 
 
THE REFLECTION OF SOUND 123 
 
 EXERCISE 42. THE REFLECTION OF SOUND 1 
 
 i 
 
 References. Hoadley, 193-195 ; Carhart and Chute, 184- 
 186. 
 
 I. To study the reflection of sound from a plane sur- 
 face. 
 
 Apparatus. Two large glass or tin tubes, 2 to 3 ft. long ; 
 screen or other vertical plane surface to serve as a reflector; 
 roll of cotton or soft cloth ; watch. 
 
 a. Lay the tubes on the table so as to form an angle between 
 50 and 60, the ends at the vertex of the angle being close 
 together but not touching. Lay a watch 
 
 on the roll of cotton at the end A (Fig. 41), 
 of one of the tubes, or just inside it if 
 the tube is large enough. Be sure that the 
 watch does not touch the tube. Listen at 
 B for the ticking, first with the reflector 
 in position at (7, making equal angles 
 with the tubes, then with the reflector 
 removed. 
 
 State and account for the result in each case. 
 
 b. While listening at B as before, gradually turn the re- 
 flector about a vertical axis till it makes very unequal angles 
 with the two tubes. State the result. 
 
 c. Set the tubes at a wider angle (80 to 90) and repeat 
 paragraphs a and b. 
 
 d. What do you learn from the experiment concerning the 
 direction in which sound is reflected from a plane surface? 
 
 II. To study the reflection of sound from concave sur- 
 faces. 
 
 Apparatus. Two concave reflectors; large funnel with rub- 
 ber tube attached, for use as an ear trumpet ; watch. 
 
 1 This exercise can be performed only in a very quiet room. It should 
 be set up in a room by itself, if possible. 
 
124 SOUND 
 
 a. Stand one of the reflectors (yi/Fig. 42) 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 obliquely, as shown 
 in the figure. Hang a watch in front of the center of reflector 
 A Sit a, distance from it equal to about half the radius of the 
 spherical surface. This point (F) is called the focus of the 
 
 FIG. 42. 
 
 reflector. It is easily found by turning the reflector toward 
 the sun and catching the reflected light on a piece of paper. 
 By moving the paper to and fro, find the position where the 
 spot of light is the smallest. This is the focus. 
 
 Hold the ear at jEJ, being careful to cover as little of the 
 reflector with the head as possible. 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. 
 
 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 convey the sound to the ear. Place the funnel at the 
 focus of B and facing toward it, arid the end of the tube in 
 the ear. Try both ways. 
 
 b. With the ear at E or with the ear trumpet in position, 
 observe the effect on the loudness of the sound when your 
 companion moves the watch closer to and farther from A. 
 State the result in each case. 
 
 c. With the ear in position as before, observe the effect of 
 turning A about a vertical axis toward one side and toward 
 the other. 
 
 In what direction does A reflect the sound most distinctly ? 
 
SYMPATHETIC AND FORCED VIBRATIONS 
 
 125 
 
 EXERCISE 43. 
 
 SYMPATHETIC AND FORCED 
 VIBRATIONS 
 
 References. Hoadley, 198-199 and 202-203; Carhart and 
 Chute, 189-192 ; Slate, 185 ; Sanford, p. 211, on Forced Vibra- 
 tion; Jones, Sound, 56-57. 
 
 I. To study sympathetic and forced vibrations (not 
 sonorous} by means of pendulums. 
 
 Apparatus. Four pendulums supported as shown in Fig. 43. 
 CD is a light rod 2 or 3 ft. long, suspended by short cords from 
 any convenient fixed sup- fe ^.^ ^ s ^ as _ g= ^..^^. J ^ rf== ,_. 3ja ,, , . 
 
 _L 
 
 T 
 
 FIG. 43. 
 
 port. From CD two pairs 
 of pendulums are sus- 
 pended, the pendulums of 
 each pair being of equal 
 length and the shorter pair 
 about half the length of 
 the longer. 
 
 a. Set one of the longer 
 pendulums vibrating in the 
 direction of the supporting 
 rod (CD, Fig. 43), and 
 
 observe the effect upon the other pendulums. Describe and 
 account for the observed effects, noting particularly any 
 difference in the effect upon the longer and the shorter 
 pendulums. 
 
 What examples of sympathetic or of forced vibrations are 
 afforded by the motions of the pendulums ? 
 
 b. Bring the pendulums to rest and repeat, this time start- 
 ing one of the shorter pendulums. Describe and discuss the 
 result. 
 
 c. Again bring the pendulums to rest and set a long one and 
 a short one vibrating at the same time. Describe and account 
 for the motion of the other two pendulums. 
 
120 SOUND 
 
 d. Bring the pendulums to rest and give the supporting rod 
 a slight push in the direction of its length. Observe its rate 
 of vibration. 
 
 Is it the same as that of any of the pendulums ? 
 
 Are the motions impressed upon it by the pendulums, when 
 vibrating, examples of forced or sympathetic vibrations ? 
 
 II. 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; short pieces of large glass tubing 
 of different length and diameter. 
 
 [To make the soft wax, melt together about nine parts, by weight, of 
 beeswax and one part of Venice turpentine. Forks giving a few beats 
 per second may 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 glass tubes are of such sizes 
 as to sound a major chord. The longer tubes should have the greater 
 diameter.] 
 
 a. 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 will be found to be vibrating audibly. Explain. 
 
 b. Sound one of the forks and hold the stems of both against 
 the table top. After one or two seconds stop the fork that was 
 sounded. The other fork should now be sounding audibly. 
 If it is not, try again until you are successful. How was 
 the vibration set up in the second fork ? 
 
 c. 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, as can be shown by sounding 
 both of the forks and holding them side by side near the oar. 
 The pulsation of the sound (called beats) is due to a slight 
 difference in the vibration rates of the forks. Now repeat the 
 
SYMPATHETIC AND FORCED VIBRATIONS 1:27 
 
 experiments of paragraphs a and b, sounding either of the 
 forks, and observe whether the silent fork- is made to 
 vibrate. State and explain the result. 
 
 d. Blow across the ends of the glass tubes in succession. 
 Observe that each tube gives forth a sound of definite pitch. 
 Hold the tubes, two at a time, close to the ears, and note the 
 faint sounds, like the roar of a sea shell, coming from 
 them. 
 
 How does the pitch of the sound coming from each tube 
 compare with that produced by blowing across the end of it ? 
 
 Account for these faint sounds coming from the tubes. 
 
 III. To study the sympathetic and forced vibration 
 of a sonometer wire. 
 
 Apparatus. Sonometer with two wires of the same size and 
 without a bridge. 
 
 a. Tighten one of the sonometer wires to a moderate ten- 
 sion, and tune the other wire in 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. As the 
 sounds approach unison the pulsations become slower, and 
 they disappear when unison is secured. Tune the wires till 
 the pulsations 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 considerable 
 intensity by the other. 
 
 Is this a case of sympathetic or forced vibration? How 
 was it set up? 
 
 b. With the wires of the sonometer so nearly in unison that 
 they give less than one pulsation 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 these 
 alternations of rest and vibration become more rapid as the 
 difference in pitch is increased; the amplitude simultaneously 
 
128 SOUND 
 
 decreasing, until presently the wire- ceases to respond at all 
 to the vibrations of the other. 
 
 Account for the behavior of the second wire under the dif- 
 ferent conditions, and compare with the experiments with the 
 pendulums. 
 
 EXERCISE 44. WAVE LENGTH BY RESONANCE 
 
 References. Hoadley, 198-201; Carhart and Chute, 189- 
 194 ; Jones, Sound, 62. 
 
 Apparatus. Some form of resonance tube or jar with 
 adjustable length (Figs. 44-47); one or more tuning forks; 
 rubber mallet ; rubber band ; meter rod. 
 
 I. To find, by ^neans of a resonance tube, the length 
 of tlw sound waves set up by a tuning fork of known 
 vibration rate. 
 
 Theory. From a study of the text you will learn that the 
 resonance tube sounds when the length of the confined air 
 column is very nearly equal to one fourth the length of the 
 waves set up by the fork used ; and that the " correction for 
 the diameter" is one half the diameter or the radius of the 
 tube, which is to be added to the length of the air column. 
 The tube will again sound when the length is further increased 
 by exactly half a wave length. Let L denote the wave length 
 of the fork, l : the length of the air column for first resonance, 
 and ? 2 f r second resonance, and r the radius of the tube; 
 
 then L = 4 (^ + r), for first resonance, 
 
 and L = 2 (1 2 7^, for second resonance. 
 
 The latter will probably be more exact, as it does not involve 
 the correction for the diameter of the tube, which is somewhat 
 uncertain. 
 
WAVE LENGTH BY RESONANCE 1^9 
 
 DIRECTIONS FOR TUBE WITH PISTON 
 
 a. It is better for two students to work together in this 
 exercise, one operating the piston and the other the fork. 
 Sound the fork and hold it at the end of the tube in the posi- 
 tion shown in Fig. 44. At the same time, starting with the 
 piston near the same end of the tube, pull it slowly and steadily 
 back till the tube responds to the vibrating fork. Mark this 
 position of the front of the piston with the rubber band on 
 the tube. Move the piston back and forth several times past the 
 position of maximum reinforcement, gradually diminishing the 
 
 FIG. 44. 
 
 range of motion. When you have secured the best adjustment 
 possible, measure the distance from the end of the tube to the 
 piston. This is recorded as the length of the air column (IJ. 
 Move the rubber band and piston out of position, and make 
 a second and entirely independent trial. If it does not differ 
 from the first by more than 3 mm., the work is sufficiently 
 accurate, and the average of the two results may be taken as 
 the correct value. If the difference is more than this, repeat 
 till consistent results are obtained. 
 
 b. In the same way find the position of the piston for second 
 resonance. The correct position can be more quickly found by 
 remembering that the air column will now be approximately 
 three times as long as before. Make at least two trials, and 
 more if necessary, as before. 
 
 c. Measure the diameter of the tube and take the temperature 
 of the room. Kecord the vibration number (2V) of the fork used. 
 Compute the wave length by both formulas as indicated below. 
 
 COLEMAN'S PHY. LAB. MAN. 9 
 
180 
 
 SOUND 
 
 cm. 
 
 cm. 
 
 cm. 
 
 FORM OF RECORD 
 
 a. Length of air column for first resonance = 
 Ditto, second trial = 
 Ditto, average value (7j) 
 
 b. Length of air column for second resonance = cm. 
 
 Ditto, second trial = cm. 
 
 Ditto, average value (7 2 ) = cm. 
 
 c. Radius of the tube = 
 
 Temperature of the room = C. 
 
 Vibration number of the fork (N) = 
 
 Length of wave (L) = 4 (^ -f r) = cm. 
 
 Length of wave (L) = 2 (1 2 li) = cm. 
 
 DIRECTIONS FOR APPARATUS SHOWN IN FIG. 45 
 
 a. With the third clamp, support the funnel so that its top 
 is about lo cm. below the top of the glass 
 tube. Pour water into the funnel till it 
 stands about half full. Remove the funnel 
 from the clamp ; hold it in the hand ; and 
 while the vibrating fork is held just above 
 the tube, raise and lower the funnel,, causing 
 the water to rise and fall in the tube till the 
 adjustment giving the loudest reenforcement 
 of the sound is obtained. Mark the height 
 of the water in the tube by the rubber band. 
 Cause the water to rise and fall several times 
 past the position of greatest reenforcement, 
 each time trying to adjust the position of 
 the rubber band more accurately. Measure 
 the length of the air column and record the 
 result as the first trial. 
 
 Repeat the process of adjusting the rubber 
 band, first displacing it several centimeters, 
 FIG. 45. so that the judgment will not be influenced 
 
WAVE LENGTH BY RESONANCE 
 
 181 
 
 by the first trial. If the second result does not differ from 
 the first by more than 3 inm., the work is sufficiently accurate, 
 and the average of the two results may be taken as the cor- 
 rect value. If the difference is more than this, repeat till 
 consistent results are obtained. 
 
 b. Draw off the water in the tube till the funnel is about 
 half full when the air column is about three times as long as 
 for first resonance. Find the length of the air column for sec- 
 ond resonance in the same manner as before, repeating till two 
 results are obtained which do not differ by more than 3 mm. 
 When you have finished, clamp the funnel in place. 
 
 c. Follow the directions of paragraph c above and the above 
 form of record. 
 
 DIRECTIONS FOB OTHER FORMS OF EESONATORS 
 
 a. Insert a glass cylinder (student lamp chimney) into a bat- 
 tery or hydrometer jar filled with water (Fig. 46). The length 
 
 of the air column is varied 
 
 by raising and lowering the 
 
 cylinder. 
 
 Or an hydrometer jar may 
 
 be used for the resonator, and 
 
 the level of the water in it 
 
 adjusted by means of a siphon, 
 
 using a rubber tube for this 
 
 purpose (Fig. 47). 
 
 In either case read para- 
 graph a of the first directions 
 for the general plan of the experiment, and make the obvious 
 modifications of the method of procedure. 
 
 b. Both the tube and the jar are too short for second reso- 
 nance. Instead of this part, the wave length of a fork of different 
 pitch may be found, using first resonance as before. 
 
 c. Follow the directions of paragraph c of the first directions. 
 
 FIG. 46. 
 
 FIG. 47. 
 
132 SOUND 
 
 II. To compute the velocity of sound from the data of 
 Part I. 
 
 a. From the known vibration number (N) of the fork, and 
 the value of L determined by the experiment, compute the 
 velocity of sound at the temperature of the room from the 
 relation v = NL. 
 
 b. Compute the true value of v at the temperature of the 
 room from the formula v = (332 -f- .6 1) meters, in which t is 
 the temperature of the room by the Centigrade thermometer. 
 
 c. Compute the per cent of error of your result. 
 
 EXERCISE 45. INTERFERENCE AND BEATS 
 
 References. Hoadley, 196-197 and 204 ; Carhart and Chute, 
 201-203 ; Sanf ord, p. 215, Interference of Sound Waves to (6). 
 
 Apparatus. Two tuning forks giving from one to three beats 
 per second ; paper cylinder about 10 cm. in length and 2 cm. in 
 diameter ; rubber mallet ; soft wax. 
 
 I. To study the interference of the sound waves about 
 a tuning fork. 
 
 a. Hold a vibrating fork near the ear and parallel to the 
 face, and rotate it slowly. Your companion will tell you the 
 position of the fork when the sound is loudest and when it is 
 faintest to you. How many times does the sound swell and 
 die away during one rotation ? 
 
 Can you find 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, let your companion cover one of 
 the prongs with the paper cylinder, being careful not to touch 
 the fork. Repeat till you are sure of the effect. State it. 
 
 c. Figure 48 represents the sound waves about a vibrating 
 fork, as seen with the ends of the fork pointing toward the 
 observer. The prongs always move toward and from each 
 
INTERFERENCE AND BEATS 
 
 133 
 
 other simultaneously ; hence, in separating, a condensed half 
 wave is set up on the outside of each, and a rarefied half wave 
 between them ; and, on approaching each other, the opposite 
 conditions are produced. If the space about the fork were 
 partitioned off into four compartments, as shown at the left, 
 there would be condensations and rarefactions on opposite sides 
 
 FIG. 48. 
 
 of the partitions, at equal distances from the fork. But as 
 there are no partitions to keep the condensations and rarefac- 
 tions apart, their opposing tendencies are mutually destructive 
 in these regions, causing silence, as shown at the right. 
 
 Why was sound restored when one of the prongs was cov- 
 ered by the paper cylinder ? 
 
 II. To study beats by means of two tuning forks of 
 very nearly the same pitch. 
 
 a. Sound both forks and hold them facing each other close 
 to the ear, in the position for loudest sound. Estimate roughly 
 the frequency of the beats. Sound the forks and touch them 
 to the table. Can you distinguish the beats ? 
 
 b. Stick a small bit of soft wax to a prong of one of the 
 forks, near the end, and observe the effect on the frequency 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 
 
134 
 
 SOUND 
 
 large quantity on one. The effect of the wax on the frequency 
 of the beats will depend upon whether it has been put on the 
 fork of the lower or the higher pitch. Prove this by observ- 
 ing the beats with the wax on the other fork. 
 
 c. Tune the forks accurately to the same pitch by loading 
 one of them till the beats cease. 
 
 Does loading a fork raise or lower its pitch? Why ? 
 
 FIG. 49. 
 
 d. Figure 49 presents an explanation of beats. Copy the 
 top and middle parts of it, and write a brief explanation. 
 
 Why are beats less frequent as unison becomes more nearly 
 perfect ? 
 
 EXERCISE 46. VIBRATING STRINGS. 
 EFFECT OF LENGTH 
 
 References. Hoadley, 220-222; Carhart and Chute, 210- 
 212. 
 
 To find the relation between the length of a vibrat- 
 ing string and its pitch. 
 
VIBRATING STRINGS. EFFECT OF LENGTH 185 
 
 Apparatus. Sonometer; rubber mallet; several tuning 
 forks, including c' (256 vibrations), and c" (512 vibrations); 
 meter rod. 
 
 a. Tighten the wire till a length of 60 cm. or more vibrates 
 in unison with the c' fork. To make the sound of the fork 
 audible, touch its stem to the sonometer or to the top of the 
 table. The wire gives a better sound and one easier to com- 
 pare with the fork if it is plucked near the middle with the end 
 of the ringer or the thumb (not the nail). Tune the wire by 
 varying its length by means of the bridge. When the wire 
 and fork are nearly in unison, listen for beats and tune till 
 they disappear. Measure the length of the wire ; then dis- 
 place the bridge, tune again (without changing the tension), 
 and again measure. (If the difference is more than 3 mm., 
 make further trials.) The tension of the wire must remain the 
 same throughout the experiment. 
 
 b. Adjust the length of the wire so as to bring it successively 
 into unison with the other forks, making at least two trials for 
 each. Eecord as indicated. 
 
 c. 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. 
 
 d. From the law of lengths and the known vibration ratios 
 of the forks used (see the text), find the true values of the 
 length ratios. 
 
 FORM OF RECORD 
 
 TONI 
 
 LENGTH 
 OF WIRE 
 
 MEAN 
 LENGTH 
 
 LENGTH RATIO 
 
 KKKOI; 
 
 PER CENT 
 OF ERROR 
 
 By Exp. 
 
 True 
 
 c 1 
 
 
 
 
 
 
 
 r 1 
 
 
 
 
 
 
 
 e' 
 
 
 
 
 
 
 
 
 r f 
 
 
 
 
 
 
 
 .8 
 
 
 
 
 
 etc. 
 
 
 
 
 
 
 
VII. LIGHT 
 
 EXERCISE 47. SOME RESULTS OF RECTILINEAR 
 PROPAGATION 
 
 References. Hoadley, 443-445 and 447-448 ; Carhart and 
 Chute, 231-236 ; Jones, Light, 4-8. 
 
 Apparatus. A flat gas jet or lamp with flat wick ; optical 
 bench or meter rod ; a screen 5 cm. square, mounted on a wire 
 (A, Fig. 50) ; a screen (B) with horizontal rows of holes, and 
 a screen (0) with a, hole in the center, both about 18 or 20 cm. 
 square ; short metric rule. 
 
 [A very convenient burner for this exercise and the one on photom- 
 etry is made by attaching the short tube and tip of an ordinary 
 gas jet to the base of a Bunsen burner. The connection is made air- 
 tight with a little paint or melted wax. It will be most convenient to 
 have the screens, lenses, spherical mirrors, diffusion photometer 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 will fit loosely 
 upon a meter rod (placed on edge or lying flat). The rod thus serves 
 as a guide to keep the several parts of the apparatus in alignment, 
 and the distances between them will be the distances between the cor- 
 responding ends (right or left) of the blocks upon which they are 
 mounted. A board 110 cm. long and 8 or 10 cm. wide, with the 
 meter rod fastened to it, makes a better support for the apparatus. 
 Such a board with the attached rod is called an optical bench or, 
 simply, bench, in the following exercises.] 
 
 I. To study the formation of shadows. 
 
 a. The room must be at least partially darkened for this 
 exercise. Place the gas jet at an end of the optical bench (or 
 
 136 
 
SOME RESULTS OE RECTILINEAR PROPAGATION 137 
 
 meter rod), and place the screens A and B on it about 30 cm. 
 and 80 cm. respectively from this end. Turn the flame first 
 edgewise then flatwise to the screens, and observe the appear- 
 ance of the shadow of A upon B. In which case is the darker 
 part of the shadow (the umbra) bordered on its vertical sides 
 by a strip of fainter shadow (the penumbra) ? 
 
 b. Again place the flame flatwise, and adjust the distance of 
 B so that the line between the umbra and the penumbra falls 
 upon B at the break in the line of holes. The upper holes 
 now lie in the penumbra, and the lower in the umbra (Fig. 50). 
 Look toward the flame through each of the holes in succes- 
 sion. 
 
 State what you see, (1) when looking through the different 
 upper holes ; (2) when looking through the lower holes. 
 
 FIG. 
 
 From your observations state the cause of the umbra and of 
 the penumbra. 
 
 Draw figures of horizontal sections explaining the appear- 
 ance of the shadows with the flame in the two positions. (Fol- 
 low models found in the text and reference books. Drawings 
 that explain are not mere pictures of what is seen.) 
 
 c. Remove A and in its place hold a lead pencil vertically. 
 Observe the shadow of the pencil with the flame turned edge- 
 wise then flatwise. With the flame in the latter position, 
 observe the varying width of the umbra and penumbra as the 
 
138 LIGHT 
 
 screen is moved toward and from the pencil. Move the screen 
 so that the umbra disappears. 
 
 Describe the observed changes in the appearance of the 
 shadow, and explain them with the aid of drawings. 
 
 II. To study the formation of images by small 
 openings. 
 
 a. Stand the gas jet, turned flatwise, at the end of the optical 
 bench. Place the- screens B and C on the bench with C nearer 
 the light. Move the screens, together and separately, toward 
 and from the light, and observe the image of the flame on B. 
 Account for the inversion of the image and its varying size, 
 with drawings of vertical sections to illustrate the explanation. 
 
 b. Replace C with a sheet of paper in which you have made 
 a small hole with a pin or the point of your pencil. Hold the 
 paper so that the light through this hole will form an image on 
 B, and note the effect of gradually enlarging the hole till it is 
 2 cm. or more in diameter. Describe and explain the effect on 
 the image. 
 
 c. Make a few small holes in a group in another place in the 
 paper, and hold it so that images will be formed by them. 
 Increase the number of holes in the group from time to time, 
 until finally there are many of them very near together, and 
 observe the effect on the images. How would the images be 
 affected if the number of holes were indefinitely increased ? 
 
 III. To find the relation between the area of the sur- 
 face covered, by a given pencil of light and the distance 
 of the surface from the source of the light. 
 
 a. Place A 30 cm. and B 60 cm. from the flame, turned very 
 low and placed edgewise at the end of the optical bench. 
 (Measure from the ./fame, not from the end of the bench.) 
 Measure the height and width of the shadow. 
 
 How do its dimensions compare with those of A ? 
 
 How do their areas compare '/ 
 
PHOTOMETRY 
 
 139 
 
 If A were removed, the light which now falls upon it would 
 cover how many times as great an area at B ? 
 
 How would the intensity of illumination upon B then com- 
 pare with the present illumination upon A ? 
 
 b. Repeat the preceding with A 30 cm. and B 90 cm. from 
 the flame. 
 
 c. What is the relation between the distance from a source 
 of light and the area covered by a given pencil of light, from 
 that source ? Draw a figure (in perspective) to illustrate. 
 
 d. State the law of intensity of illumination, and show how 
 it follows from your answer to the preceding question. 
 
 EXEECISE 48. PHOTOMETKY 
 
 References. Hoadley, 447-449; Carhart and Chute, 235- 
 238 ; Sanford, pp. 333-335 ; Jones, Light, 6-10. 
 
 DIRECTIONS FOR BUNSEN'S PHOTOMETER 
 
 Apparatus. A Bunsen's photometer, box form (Fig. 51) ; 
 gas jet ; large and small paraffine candles ; blocks for supporting 
 the candles. 
 
 I. To find the relation between the intensity of illumi- 
 nation and the distance. 
 
 a. Mount a small candle at the center of one block and four 
 of the same size on another block. Place the single candle 
 
 o 
 
 FIG. 
 
 exactly at one end of the meter rod in the photometer and the 
 center of the group of four candles at the other end. With the 
 
140 LIGHT 
 
 lid of the photometer partly closed to shut out external light, 
 move the sliding piece of the photometer back and forth be- 
 tween the lights ; and, while doing so, observe in the mirrors 
 the changing appearance of the two sides of the oiled spot on 
 the screen. 
 
 Is the side of the spot upon which the stronger light falls 
 the brighter or the darker ? Why ? 
 
 When the two sides of the spot look alike, the two sides of 
 the screen are equally illuminated. (The candles should burn 
 as nearly equally as possible. To make them do so it may be 
 necessary to trim the wicks occasionally.) Find the position 
 of equal illumination, and measure the distances from the lights 
 to the screen. Let D denote the distance of the four candles 
 and d the distance of the single candle. 
 
 b. Without moving the candles, displace the screen and 
 make a new adjustment. If the new position does not differ 
 by more than 1 cm. from the first, average these distances with 
 the first for the true values of D and d. The results of differ- 
 ent trials may differ considerably. This is principally due to 
 the fact that the candles do not burn steadily. If the differ- 
 ences-are large, take the average of several trials. 
 
 c. Assuming that all the candles give equally strong light, 
 the illumination on the side of the screen toward the four 
 candles is four times as great as it would be if illuminated by 
 a single candle at the same distance. That is, the illumination 
 of the screen by a single candle D cm. from it is \ as great as 
 it would be at a distance of d cm. Or thus : for distances in 
 the ratio D : d, the intensities of illumination due to equal 
 sources (or the same source) are in the ratio 1 : 4. Compute 
 D : d and (D : d) 2 , and compare the latter with the ratio (or the 
 reciprocal of the ratio) of the illuminating power of a light at 
 these distances. 
 
 How should these ratios compare? Compute the per cent 
 of error. 
 
 Mention probable sources of error in the experiment. 
 
PHOTOMETRY 
 
 141 
 
 II. To measure the candle power of a small candle 
 and a gas jet. 
 
 a. Compare the intensity (illuminating power) of a small 
 candle and a large one. Let D and d denote respectively the 
 distance of the large and the small candle from the screen for 
 equal illumination, and I and i their respective illuminating 
 powers. Taking the larger candle as the standard, the candle 
 power of the small one is i -~- I, which is measured by (d -f- Z>) 2 . 
 Make two or more trials, and record as indicated. 
 
 b. Find the candle power of the gas jet when turned to a 
 moderate height, by comparing it with the large candle. Stand 
 the burner on a block so that the flame is exactly at the end 
 of the rod and turned flatwise toward the screen. 
 
 c. If there is time, turn the flame edgewise toward the screen 
 and measure its candle power in this position. 
 
 FORM OF RECORD FOR PART II 
 
 SOURCE OF 
 LIGHT 
 
 
 D 
 
 d 
 
 d+D 
 
 CANDLE POWER 
 
 (i -r /)=(<* -5- />) 
 
 small 
 
 1 
 
 CHI. 
 
 cm. 
 
 
 
 candle 
 
 2 
 
 
 
 
 
 
 
 
 Av. 
 
 
 
 
 
 
 
 
 
 gas jet 
 
 1 
 
 
 
 
 
 
 
 (flatwise) 
 
 2 
 
 
 
 
 
 
 
 etc. 
 
 Av. 
 
 
 
 
 
 ^^^~" 
 
 
 
 DIRECTIONS FOR THE DIFFUSION PHOTOMETER 
 
 Apparatus. A diffusion photometer; optical bench; flat gas 
 jet; large and small paraffine candles; blocks for supporting 
 candles. 
 
 [The diffusion photometer consists of two cakes of paraffine about 5 cm. 
 square and 1 cm. thick, separated by tin foil and mounted on a block 
 (Fig. 52). To insure equal optical properties, they must be cut from the 
 
142 
 
 LIGHT 
 
 same piece of paraffine. The cakes are attached to the foil by warming 
 a surface of each till it begins to melt, then pressing the warmed surfaces 
 quickly together with the foil between. Attach to the block with a few 
 drops of melted paraffine. The photometer in this form gives good results 
 if the room is well darkened and there are no lights from other experi- 
 ments to interfere ; but it is generally better to inclose the paraffine blocks 
 in a cylinder of black cardboard with a hole just above them through 
 which they can be observed, as shown at the right in the figure.] 
 
 a. Take the photometer (the mounted paraffine blocks) in 
 the hand, and turn it about at different angles to any source of 
 light. Observe that the less strongly illuminated side always 
 appears the darker. Since the tin foil separating the blocks is 
 
 FIG. 52. 
 
 opaque, each block is illuminated only from its own side. 
 They have the same tint when they are equally illuminated. 
 
 Darken the room as much as possible, place the photometer 
 on the optical bench, and turn the latter so that the two sides 
 of the photometer are equally illuminated by the diffused light 
 of the room. Mount a small candle at the center of one block 
 and four of the same size on another. Light them and place 
 them on the optical bench near each end. Move the photome- 
 ter back and forth between the lights till the position of equal 
 illumination is found. If necessary, trim the candle wicks to 
 make them burn equally before making this adjustment. Meas- 
 ure the distance from the lights to the photometer. If the 
 supporting blocks are of uniform length, the distance from 
 center to center of two blocks is the same as the distance from 
 either end of one to the corresponding end of the other. The 
 latter distance is the more convenient one to measure. 
 
PHOTOMETRY 143 
 
 b. Without moving the candles, displace the photometer 
 and make a new adjustment. For the remainder of the exer- 
 cise, follow the directions for the Bunsen photometer, begin- 
 ning with I b. 
 
 DIRECTIONS FOB B-UMFORD'S PHOTOMETER 
 
 Apparatus. A Bumford's photometer, consisting of a screen 
 of white cardboard and a rod, each supported vertically ; large 
 and small candles ; blocks for supporting the candles ; flat gas 
 jet or lamp ; meter rod. 
 
 Figure 53 is a diagram of a horizontal section showing the 
 arrangement of the apparatus. AB represents the screen, C 
 the vertical rod, i and / the two lights to be compared, and 
 s and S the shadows cast by i and / respectively. The rod 
 
 FIG. 53. 
 
 should be within a few centimeters of the screen, and the 
 lights placed so that the shadows are close together, but not 
 touching. The screen should be turned so as to make ap- 
 proximately equal angles with the lines si and SI. 
 
 It is evident that each light illuminates the shadow cast by 
 the other ; hence, when the shadows are equally dark (that is, 
 equally illuminated), the two lights give equal illumination at 
 their respective distances from the screen. The room must be 
 rather dark, or other sources of light will make the shadows 
 too faint for satisfactory comparison. 
 
144 LIGHT 
 
 Follow the directions for the Bunsen photometer, with the 
 necessary modifications of I. a. The weaker light should be 
 placed at a distance of 30 to 40 cm., and the other moved back 
 and forth till the position is found for which the shadows 
 appear equally dark. Measure the distances SI and si (denoted 
 by D and d respectively). Displace / and make a new trial. 
 
 40. Parallax. Hold a pencil out at arm's length toward 
 some object at a distance of several feet, and study carefully 
 the apparent change in the position of the pencil with respect 
 to the object beyond, as you look at it, first with one eye, then 
 with the other (keeping one eye closed). Discover the cause 
 of this apparent change of position. 
 
 While looking steadily with one eye at the pencil, move the 
 head from side to side, and observe that the pencil seems to 
 move to and fro in front of the object beyond, although it is 
 really held at rest. Does the pencil seem to move in the same 
 direction as your eye, or the opposite ? 
 
 Hold the pencil nearer the object (or observe its apparent 
 motion with respect to a nearer object), and continue to shorten 
 the distance between them till they are close together. How 
 does the decrease of distance affect the apparent motion of the 
 pencil ? 
 
 Study in the same way the apparent motion of the pencil 
 with respect to an object (a finger) held between it and the eye. 
 Observe that the apparent motion of the finger with respect to 
 the pencil is the opposite of the apparent motion of the pencil 
 with respect to the finger. 
 
 Continue experimenting till yon have established for your- 
 self the following : (1) With respect to the more distant object, 
 the apparent motion of the nearer one is opposite to the motion of 
 the eye; (2) as the distance between the objects diminishes, the 
 apparent motion of either with respect to the other also dimin- 
 ishes; and (3) these apparent motions disappear when the 
 objects are brought together. 
 
PLANE MIRRORS 145 
 
 Kecall the apparent motions of near and distant objects when 
 viewed from a window of a rapidly moving car; and find 
 whether they agree with these conclusions. 
 
 The apparent displacement of an object caused by a change 
 in the position of the observer is called parallax. The fact 
 that parallax between two objects disappears when they are 
 brought together is a very useful one in locating images ; and 
 for this purpose it will be necessary to remember the relation 
 stated just above in italics. 
 
 EXERCISE 49 P PLANE MIRRORS 
 
 References. Hoadley, 450-455 ; Carhart and Chute, 239- 
 245 ; Slate, 196-197. 
 
 Apparatus. A rectangular piece of plane mirror attached to 
 a block at the back to support it vertically ; 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. On account of 
 these refractions the distance of the image is diminished 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 parallax, 
 the object 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 w'indow glass is used as the reflecting 
 surface. The image 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. ] 
 
 I. 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. 
 
 a. Draw a line AB (Fig. 54) about 10 cm. long on your 
 record sheet, and stand the mirror with the edge of its reflect- 
 ing surface on this line. (The reflecting surface of a common 
 COLEMAN'S PHY. LAB. MAN. 10 
 
14ti LKJ1IT 
 
 mirror is, of course, the rear surface. If unsilvered 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, more distant 
 than the first, but it is to be disregarded.) Stick a pin verti- 
 cally about 6 or 8 cm. in front of 
 
 B the mirror (at 0). You are to 
 
 determine accurately the position 
 of the image of the point of this 
 pin, seen in the mirror. Stick a 
 second pin near the mirror and a 
 few centimeters to one side of 
 (at (7), and another pin (at D) 6 or 
 8 cm. from C and exactly in line 
 
 with the pin at C and the image of the pin at 0. The pins 
 should be as nearly vertical as possible, and the eye, in sight- 
 ing, placed on a level with the paper. Draw the line CD. 
 The image of the pin at lies somewhere on this line pro- 
 duced. 
 
 b. Without disturbing the position of the mirror, determine 
 in the same way two other lines directed toward the image, at 
 different angles with AB. one on each side of 0. If the image 
 has the same position when viewed from different directions, 
 these lines (and all others similarly drawn) should intersect in 
 the point which is the position of the image. 
 
 Has the image a fixed position ? 
 
 c. Let I denote the position of the image. Draw a line con- 
 necting / and 0. 
 
 What angle does this line make with AB ? (Measure with 
 the protractor.) 
 
 How is it divided by AB ? 
 
 Describe definitely the position of the image with reference 
 to the mirror and the position of the point object. 
 
 d. Eepeat the experiment with the point taken either a 
 greater or less distance from the mirror. 
 
PLANE MIRRORS 147 
 
 II. To find the relation between the angle of incidence 
 and the angle of reflection. 
 
 a. It is evident that, when you were sighting along the line 
 DC at the image, the light by which you saw it came to the 
 eye along that line, 1 having been reflected by the mirror at the 
 point where DC meets it. Call this point N. Draw the incident 
 ray ON and the perpendicular at N. Measure with the protractor 
 and record in your figure the angles of incidence and reflection. 
 Repeat this construction and measurement for the other two 
 reflected rays. 
 
 6. Within what limits (expressed as a per cent) do your 
 results agree with the law of reflection ? 
 
 c. What is meant by the plane of the angle of incidence and 
 of the angle of reflection ? What is the plane of these angles 
 in this experiment ? 
 
 III. To find the relation between the position and 
 appearance of an object and its image. 
 
 a. Write your name on a piece of paper and look at its 
 image in the mirror. Describe and account for its appearance. 
 
 6. Draw a line (AB) on your record sheet, and a short dis- 
 tance below it draw a triangle and letter the vertices (7, Z>, and 
 E. Leave sufficient space above AB for the proper location 
 of the image of the triangle. Stand the mirror on AB, and 
 study the image of the triangle, noting the order and position 
 of its sides and the appearance of the letters at the vertices. 
 The vertices of the triangle may be located experimentally as 
 in I a, two lines for each vertex being sufficient, or by the 
 geometrical construction indicated by your answers to I c. 
 Place the letters C, D, and E in the drawing of the image just 
 as they appear in the mirror. 
 
 1 CD is, strictly speaking, the axis of the pencil or cone of light that 
 enters the eye. It must be remembered that the eye locates the image at 
 the point from which this cone of light seems to come. 
 
148 
 
 LIGHT 
 
 EXERCISE 49 2 . PLANE MIRRORS 
 
 References. The same as for Exercise 49]. 
 
 I. To find the position of a point iunt^c in a plane 
 mirror by parallax; and to find the relation between fhr 
 position of the point and its image. 
 
 Apparatus (for Parts I and II). The same as for Exercise 9 } 
 with the exception that the mirror is supported with a free 
 space about half an inch high under it (Fig. 55). 
 
 a. Draw a line AB about 10 cm. long on your record sheet, 
 leaving a blank space of equal width above it, and stand the 
 mirror so that its reflecting surface is in the vertical plane 
 through AB. Adjust it accurately. (The reflecting surface of 
 
 a common mirror is, of course, 
 the rear surface. If un silvered 
 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, more distant 
 than the first, but it is to be disregarded.) Stick a pin verti- 
 cally 6 or 8 cm. in front of the mirror. Place a second pin 
 behind the mirror, and find by parallax (Art. 40) the position 
 in which the portion of it that is seen under the mirror (the 
 eyes being nearly on a level with the table) fits accurately to 
 the portion of the image of the pin in front that is seen at the 
 same time in the mirror. Use both eyes, and move the head 
 from side to side. When the correct position is found, the pin 
 and the image fit from all points of view. Let Oj denote the 
 position of the pin in front and 7 X the position of its image. 
 
 b. Place the pin at a different distance from the mirror, and 
 again locate the image. Let 2 and/ 2 denote the position of 
 object and image respectively. 
 
 c. Follow the directions of I c of Exercise 49 P 
 
 FIG. 55. 
 
PLANE MIRRORS 149 
 
 II. To find the relation between the position and ap- 
 pearance of an object and its image. 
 
 Follow the directions of Part III of Exercise 49i locating 
 the vertices of the triangle by parallax or by geometrical con- 
 struction. 
 
 III. To find the relation between the angle of in- 
 cidence and the angle of reflection. 1 
 
 Apparatus. Reflection apparatus (Fig. 56). 
 
 a. Hold a finger over the first hole on either side of the 
 middle hole of the reflection apparatus (Fig. 56). (If the room 
 is darkened for other experiments, a lighted candle may be 
 used instead of the finger.) 
 
 By trial find the hole 
 through which the image 
 of the covered (or illumi- 
 nated) hole can be seen 
 in the mirror. Place the FlG - 56< 
 
 finger over the next hole, and repeat the observation. Try all 
 the holes on one side of the center in the same way ; and in 
 each case observe how the arc of the rim between the middle 
 hole and the covered hole compares in length with that between 
 the middle hole and the one through which the image is seen. 
 
 How do the angles subtended at the center of the mirror by 
 these arcs compare ? These angles at the center are the angles 
 of incidence and reflection respectively, for the line from the 
 middle hole to the center of the mirror is perpendicular to it. 
 State the relation that holds for these angles. 
 
 b. Draw a diagram showing an incident and the reflected r;i y 
 and the perpendicular to the mirror at the point of incidence; and 
 indicate the angles of incidence and reflection by i and r. 
 
 What is meant by the plane of these angles ? What does the 
 experiment show concerning these planes ? 
 
 1 This part may be omitted and the law of reflection deduced geometri- 
 cally from the results of Part I. 
 
150 LIGHT 
 
 EXERCISE 50. MULTIPLE IMAGES 
 
 References. Hoadley, 456-458; Carhart and Chute, 246-247; 
 Slate, 200 ; Jones, Light, 22-24. 
 
 Apparatus. Two plane mirrors with support at the back to 
 hold them in a vertical position ; bits of colored glass or paper ; 
 rule ; candle ; an object with distinguishable right and left sides 
 and front and back. A small block with some printed matter 
 pasted on one side (called the front) will serve. 
 
 I. To study tlie formation of images by two mirrors 
 at right angles. 
 
 a. Stand the mirrors at right angles to each other with a 
 vertical edge of each together. To do this, adjust the mirrors 
 so that the image of each is in the same plane as the mirror 
 itself. Place the block between the mirrors and turn it so 
 that the printing is visible in both of them. Observe the ap- 
 pearance of the printing in each of the images. Note also the 
 location of the images with respect to the mirrors, the images 
 of the mirrors, and the object. Study these matters further as 
 you move the block about between the mirrors. 
 
 Draw a diagram of what is seen with the block in one posi- 
 tion, representing the block by a rectangle with the vertices 
 lettered A, B, C, and D. (To locate the image of a point, draw 
 a perpendicular from the point to the line representing the 
 mirror, and extend it an equal distance beyond.) Letter the ver- 
 tices of the images to correspond. The correct lettering of the 
 vertices will show which images are reversed and which are not. 
 
 Any corner of the object and its three images form the ver- 
 tices of what geometrical figure ? 
 
 b. Cover first one of the mirrors then the other with a sheet 
 of paper, and observe which of the images remain. Which 
 images are formed by one mirror only ? Which by both? Num- 
 ber the images in your diagram, and answer by reference to 
 these numbers. 
 
MULTIPLE IMAGES 151 
 
 c. The light by which you see the image that is formed by 
 both mirrors is reflected from the mirror in which the image is 
 seen, after a previous reflection from the other mirror. After 
 the first reflection, the light falls upon the second mirror at pre- 
 cisely the same angle that it would if it came from the image 
 in the first mirror. This will be understood from a study of 
 Fig. 57; in which O is a point object and I I its image in the 
 
 mirror AB. A pencil of light from 0, after reflection from AB, 
 will seem to come from the image I l9 and will fall upon the 
 mirror CD and be reflected by it just as if it did come from /,. 
 Hence J 2 , the image in CD that is formed by reflection from 
 CD after reflection from AB, is most simply located by first 
 locating I 19 then treating it as the object whose image is 7,,. 
 In this sense J 2 is an image of the first image 7j. 
 
 Use this method in locating images in parallel mirrors or in 
 mirrors at any angle. 
 
 II. To study the formation of images by two mirrors 
 at an angle of 60*. 
 
 a. Stand the mirrors at an angle of 60. To do this, turn 
 the mirrors gradually together till each is in line with tin- 
 second mirror image in the other mirror. Plar<- tin- M"<-k 
 
152 
 
 LIGHT 
 
 between the mirrors and study its images as before. Draw 
 a diagram of the observed arrangement of object and images, 
 and indicate corresponding vertices by lettering. 
 
 b. Place a few small objects (such as bits of colored glass 
 or paper) between the mirrors and near the vertex of the angle 
 between them. Move the objects into different positions, and 
 observe the symmetry of the different patterns formed by the 
 objects and their images. This illustrates the principle of the 
 kaleidoscope. Draw one or two of the patterns. 
 
 If a kaleidoscope is provided, look through it. 
 
 III. To study the formation of images by two parallel 
 mirrors. 
 
 a. Stand the mirrors parallel to each other and a few centi- 
 meters apart. Place the block between them, and observe its 
 images in each mirror. Draw a diagram of the block and mir- 
 rors and their images. 
 
 b. Light the candle and place it between the parallel mir- 
 rors. Why are there more images of the candle than there 
 were of the block ? 
 
 c. Hold the candle near one of the mirrors, and look at its 
 image obliquely to the mirror. What fainter images are seen 
 near the principal one ? Account for them. 
 
 Discussion. a. Draw a figure of two mirrors at right angles, 
 
 showing the images of a 
 point object and a ray 
 from the object to the eye 
 for each image. Place 
 both the object and the 
 eye at unequal distances 
 from the mirrors. Locate 
 the images by the method 
 
 described in I c. Draw 
 t 
 
 the last part of the ray 
 FIG. 58. first, from the eye to the 
 
THE CONCAVE MIRROR 153 
 
 mirror, in the direction of the image from which it seems to 
 
 come; then, if this image is a second image, draw the next 
 
 part of the ray to the rr 
 
 other mirror, in the direc- * ^ 
 
 tion of the corresponding Tr -vr-- 
 
 first image. Vx -^ x v x 
 
 b. Draw a similar figure - 
 for two mirrors at an angle 
 
 of 60, nsing Fig. 58 as a . 
 
 model. In constructing 
 
 the figure, locate first the ."'"'.'' 
 
 point object (unequally ^"' ^' 
 
 distant from the mirrors), * &' ^-' 
 
 then the two first images, ~J"~~' 
 
 ,_, I 9 FIG. 59. 
 
 ii and /!, then the two 
 
 second images, i z and I 2 , and lastly the third image, i s or J 3 , 
 according to the position of the eye. It will be a help in the 
 construction to make use of the fact that the object and its 
 images lie on the circumference of a circle. 
 
 c. Draw a figure for parallel mirrors and a point object. 
 Draw rays from the object to the eye for a few of the images. 
 
 EXERCISE 51. THE CONCAVE MIRROR 
 
 References. Hoadley, 460-466; Carhart and Chute, 249- 
 255 ; Slate, 201 and 203 ; Jones, Light, 32-35. 
 
 Apparatus. Optical bench or meter rod ; mounted candle ; 
 concave mirror ; cardboard screen with hole 5 or 6 cm. in 
 diameter. 
 
 [It will be convenient to have the mirror mounted uniformly with 
 the screens, lenses, etc.' (See suggestions under Exercise 47.) The 
 hole in the screen should be at the same height as the central portion 
 of the mirror; so that light from more distant objects, after passing 
 through the hole, will fall upon the mirror and be reflected by it to 
 the rear surface of the screen.] 
 
154 LIGHT 
 
 I. To find the focal length of a concave mirror; and to 
 study the real images formed by it. 
 
 a. Hold the mirror in the sunlight and facing the sun, and 
 focus the light on a piece of paper. To do this, move the 
 paper to and fro till the place is found where the spot of light 
 is the smallest. This small, round spot of light is a real 
 image of the sun. Its position is called the principal focus of 
 the mirror. (See definition in text.) 
 
 b. Kaise a window and turn the optical bench so that the 
 mirror, when placed upon it, will face some distant object. 
 Focus the image of this object upon the screen by placing the 
 screen upon the bench and adjusting its distance from the mir- 
 ror till the image is sharply defined upon it. A screen with- 
 out a hole may be used by placing it a little to one side of a 
 direct line between the object and the mirror. If the object 
 is at a distance of 200 ft. or more, the image is very nearly at 
 the principal focus. Try to discover a reason for this while 
 studying conjugate foci in Part III. Measure the distance of 
 the image from the mirror. Assuming the image to be at the 
 principal focus, this distance is the focal length (/) of the 
 mirror. 
 
 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. 
 Now stand at a distance of about 2 m. from the mirror and 
 very nearly in line between it and the object, and look at the 
 screen. You should see the image of the distant object beside 
 the screen and in the air where it really is ; and, when seen 
 thus, it will be very distinct. The natural tendency is to 
 look in the mirror for the image ; and it will seem to be 
 in the mirror and will appear blurred if the eyes are so 
 directed. 
 
 d. Try viewing the image directly from different positions. 
 Can you see it from as many different directions as you can 
 when it is caught upon a screen ? Explain. 
 
THE CONCAVE MIRROR 155 
 
 II. To find the center of curvature of the mirror. 
 
 a. Close the window and blinds, or carry the apparatus to a 
 darker room. Light the candle and place it upon the bench at 
 one end and the mirror at the other. Stand about 2 m. in 
 front of the mirror, and with the eye on a level with the can- 
 dle, look for real images of it in front of the mirror. The one 
 that is the largest and the most distant from the mirror is 
 much the brightest, and is the one to be studied. The others 
 are due to multiple reflections within the mirror. A faint, 
 unmagnified, virtual image will also be visible. It is due to 
 reflection from the front surface of the mirror, which is a plane 
 surface. 
 
 b. Move the candle on the bench till the image is directly 
 above it. If you have difficulty in seeing the image where it 
 actually is, locate it by catching it upon the screen. If the 
 candle is adjusted to the proper height, the tip of the flame 
 and its image can be made to coincide. They are then at the 
 center of curvature of the mirror. Why? Make this adjust- 
 ment and measure the distance of the candle from the mirror. 
 This is the radius of curvature (r) of the mirror. 
 
 c. What simple relation (within 2% or 3%) do you discover 
 between r and / ? 
 
 III. To study the relation between the position of the 
 object and the size and position of its real or virtual, 
 image. 
 
 a. Starting with the candle at the center of curvature, move 
 it slowly across the room as far as you can from the mirror, 
 and observe the simultaneous movement of the image and 
 change in its size. 
 
 Describe this motion of the image with reference to the 
 center of curvature and the principal focus. 
 
 Where is the image with reference to the principal focus 
 when the object is most distant? 
 
156 LIGHT 
 
 What would be the final* position of the image if the object 
 were carried farther away indefinitely ? 
 
 6. Again starting with the candle at the center of curvature, 
 move it slowly toward the principal focus ; and study the image 
 as before, except that it is to be caught upon the screen. Con- 
 tinue till the image is focused upon the wall or as far away as 
 it can be seen. 
 
 Where is the candle now with reference to the principal focus 
 and the center of curvature? 
 
 If it were moved up to the principal focus, where would the 
 image be ? 
 
 Whenever a real image is formed, the rays from any point 
 of the object converge to the corresponding point of the image 
 after reflection from the mirror. Do the rays after reflection 
 become more or less convergent as the candle is moved from 
 the center of curvature toward the principal focus ? 
 
 Are they convergent, divergent, or parallel when the candle 
 is at the principal focus ? 
 
 c. Move the candle from the principal focus toward the 
 mirror ; and at the same time study the image, which is now 
 virtual and must be looked for in the mirror. Describe its 
 change of size and position during the motion. 
 
 Are the rays convergent or divergent after reflection ? 
 
 d. With the mirror at one end of the bench and the screen 
 at the other, place the candle so that its image is distinct upon 
 the screen. Interchange the positions of the candle and the 
 screen, placing each exactly where the other was before. Is 
 the image now distinct upon the screen ? 
 
 What property of conjugate foci does this illustrate? 
 
 Discussion. The point of convergence of a pencil of rays 
 after reflection from the mirror (or the point from which the 
 pencil seems to come, if it is diverging after reflection) is de- 
 termined by the intersection of any two rays of the pencil. Now 
 there are certain rays whose directions after reflection are very 
 
PHENOMENA DUE TO REFRACTION 157 
 
 simply determined without the construction of angles of inci- 
 dence and reflection ; and, on the ground of simplicity, these 
 rays should always be used in drawing figures showing the 
 formation of images by concave (or convex) mirrors. They are 
 the following : 
 
 (1) The ray (from the chosen point of the object) parallel to 
 the principal axis ; which passes through the principal focus 
 (F) after reflection. 
 
 (2) The ray through F\ which is reflected parallel to the 
 principal axis. 
 
 (3) The ray through the center of curvature (0) ; which is 
 reflected back along the same path. 
 
 With an arrow as object, draw figures showing the formation 
 of the image by a concave mirror, (1) when the object is be- 
 yond C; (2) when it is between F and (7; (3) when it is a 
 little nearer the mirror than F; (4) when it is very near the 
 mirror. 
 
 EXERCISE 52. PHENOMENA DUE TO REFRACTION 
 
 References. Hoadley, 467-470 and 474-476; Carhart and 
 Chute, 256-259 and 261-265; Slate, 207-209 and 213-214; 
 Jones, Light, 42. 
 
 I. 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; beaker; jar of water; mop 
 cloth. 
 
 a. Place the bit of tin (or other small object) in the empty 
 jar at the side farthest from you, and hold the eye a very little 
 too low to see it over the edge of the jar. Keep the eye 
 steadily in this position while your companion slowly pours 
 water into the jar, being careful not to displace the tin, and 
 observe any change in its apparent position. 
 
158 
 
 LIGHT 
 
 Is the direction of the apparent displacement horizontal, 
 
 vertical, or oblique ? 
 
 The light that enters the eye is bent (refracted) on passing 
 
 from the water into the air, as shown in Fig. 60. The object 
 
 appears to be on the line 
 determined by the direction 
 of the ray as it enters the eye. 
 Its position on that line is 
 the point from which the 
 diverging cone of light that 
 enters the eye seems to come. 
 This point is determined from 
 the experiment by noting the 
 
 direction of the apparent displacement. Draw a figure similar 
 
 to Fig. 60, and complete it, showing the real and the apparent 
 
 position of the tip. 
 
 b. Look at the piece of tin through the surface of the water 
 while disturbing the water with your finger. Describe and 
 explain the effect of the motion of 
 
 the surface. 
 
 c. Put your pencil into the 
 water obliquely half its length, 
 and note its appearance as seen 
 through the surface of the water. 
 Draw a figure similar to Fig. 61, 
 and complete it, showing the 
 apparent position of the portion 
 of the pencil under water. 
 
 Study further the direction of 
 apparent displacement by noting 
 the appearance of the pencil when 
 held vertical and partly under 
 water. This should leave no possibility of doubt. (The illus- 
 trations in many text-books are very inaccurate and misleading 
 on this point.) 
 
 FIG. 61. 
 
PHENOMENA DUE TO REFRACTION 159 
 
 d. Look vertically into the jar of water, and observe the 
 apparent elevation of the bottom above the level of the 
 table top. Figure 62 represents a pencil of 
 light from a point of the bottom. Draw and 
 complete the figure so as to explain the 'ap- 
 parent elevation of the bottom. Represent the 
 apparent path of light by a dotted line. 
 
 II. To study the apparent displacement 
 of objects seen through plate glass. 
 
 Apparatus. A rectangular piece of thick 
 plate glass, preferably ground and polished on 
 two opposite edges. 
 
 a. Hold the piece of plate glass up before 
 
 you, and hold your pencil behind it so as to see part of the 
 pencil above the glass and part through it. Turn the glass 
 
 from side to side about the 
 pencil as an axis, and note the 
 
 effect on the apparent position 
 
 of the part of the pencil seen 
 through it. 
 
 What is the direction of the 
 rays through the glass when 
 FIG. 63. \ there is no apparent lateral 
 
 displacement of the pencil ? 
 
 Figure 63 represents a section taken at right angles to the 
 pencil. Complete it so as to explain the apparent lateral dis- 
 placement of the pencil, representing its apparent position by 
 a dotted circle. 
 
 b. Compare the real thickness of the glass with the apparent 
 thickness when you look through it. 
 
 Compare its width with its apparent width as you look 
 through it from edge to opposite edge. Draw a figure explain- 
 ing the observed effect. 
 
 o 
 
160 LIGHT 
 
 III. To find the path of a ray ^ of light passing from 
 air through a triangular prism and into the air again. 
 
 Apparatus. A triangular glass prism with flat ends; pins. 
 Stick two pins vertically in your record sheet about two- 
 thirds as far apart as the width of a side of the prism, and 
 stand the prism between them, as shown in Fig. 64. With 
 the eye in position to see the two pins 
 in line (the farther one through the 
 faces AB and AC), stick a third pin 
 behind the prism and a fourth in front 
 of it, all about equally spaced and all 
 apparently in a straight line when the 
 two farther ones are seen through the 
 prism. Draw an outline of the base of 
 the prism ; remove it and draw straight 
 lines connecting the positions of the 
 pins. This broken line is the path of a ray from the farthest- 
 pin to the eye. 
 
 Draw perpendiculars to the refracting surfaces at the point 
 of entrance and emergence of the ray, and indicate the angles 
 of incidence and refraction of the rays and the angle of devia- 
 tion. 
 
 State the direction of deviation (toward or from the per- 
 pendicular) in passing into and out of the prism. 
 
 41. The Sine of an Angle. In a right triangle, the ratio of a 
 leg to the hypotenuse is called the sine of the angle opposite 
 the leg. Thus, in the right triangle .AB C, BC: BA is the sine 
 of angle A and CA: BA is the sine of angle B. The usual 
 form of expression is 
 
 sine A = BC + BA, sine B = CA -+- BA. 
 
 The three right triangles ABC, AB'C', and AB"C' f are simi- 
 lar; hence 
 
 BC:BA = B'C' : B'A = B"C" :B"A = sine A. 
 
INDEX OF REFRACTION 
 
 161 
 
 the sine of an angle is 
 
 From which it will be seen that 
 
 independent of the size of the 
 
 triangle. It does, however, 
 
 depend upon the size of the 
 
 angle ; increasing as the angle 
 
 increases (up to 90), but not 
 
 proportionally. The student 
 
 should assure himself of the 
 
 truth of this statement by 
 
 drawing angles of different 
 
 sizes and roughly comparing the angles and their sines. 
 
 42. Index of Refraction. The index of refraction of a sub- 
 stance is defined as the ratio of the sine of the angle of inci- 
 dence to the sine of the angle of refraction when light enters 
 the substance from a vacuum. That is : 
 
 Index of refraction = sine i : sine r = : 
 
 AO CO 
 
 If the distances AO and OC, along the incident and refracted 
 rays respectively, are taken equal, this expression for the index 
 of refraction reduces to : 
 
 Index of refraction = sine i : sine r = AB : CD. 
 
 The methods employed in elementary 
 physics are not accurate enough to detect 
 any difference between the index of refrac- 
 tion from a vacuum into a substance and 
 from air into the same substance. Hence 
 such differences may be neglected. 
 
 43. Index of Refraction by Apparent 
 Depth. In Fig. 67, EOB represents a sec- 
 tion of a narrow cone of rays from a 
 point on the surface of some substance. OA, the axis of the 
 cone, is perpendicular to the opposite surface, at which the light 
 COLEMAN'S PHY. LAB. MAN. 11 
 
 FIG. 66. 
 
162 
 
 LIGHT 
 
 passes into the air. It was by such a cone of rays that you 
 observed the apparent elevation of the bot- 
 tom of the jar of water in Part I c?, of the 
 last exercise. The figure applies also to Part 
 II b. The angles of incidence and refraction 
 in the figure are taken for light traveling in 
 the opposite direction. 
 
 NM is the perpendicular to the surface at 
 BJ hence it is parallel to AO. 
 
 Hence, also, angle ACB = angle NED and 
 angle AOB = angle OEM. 
 
 Index of refraction = sine i : sine r = : = 
 
 CB OB CB 
 
 For a narrow pencil of light (such as enters the eye) the 
 error is altogether inappreciable when we write OB = OA and 
 CB= CA-, hence 
 
 Index of refraction =^|^^4 _ 
 
 CB CA apparent depth 
 
 FIG. 67. 
 
 EXEECISE 53. INDEX OF KEFRACTION 
 
 References. Hoadley, 467-471 ; Carhart and Chute, 256-260. 
 
 I. To find the index of refraction of a piece of plate 
 glass. 
 
 Apparatus. Piece of thick plate glass with at least one 
 straight, polished edge ; pins ; metric rule. 
 
 First Method. a. In this experiment the numerical values 
 are obtained from the geometrical figures ; hence they should 
 be constructed as accurately as possible with a sharp pencil. 
 
 Draw a straight line AB about 8 cm. long on your record 
 sheet, and lay the piece of plate glass flat on the sheet with a 
 polished edge on this line (Fig. 68). Stick two pins vertically 
 against the edges of the glass at C and D. If a scratch or 
 other mark has been made across an edge of the glass, use it 
 
INDEX OF REFRACTION 
 
 163 
 
 instead of the pin at C. The line CD must be quite oblique 
 
 to AB. With the eye on a 
 
 level with the paper, move 
 
 it into line with the pin at 
 
 D and the image of the pin 
 
 at C, seen through the glass; 
 
 and place a third pin in 
 
 this line at E, 5 or 6 cm. 
 
 from D. (The three pins Fm ' 68> 
 
 must seem to stand exactly in a straight line.) 
 
 b. Eemove the glass and draw straight lines connecting (7, 
 D, and E. This is the path by which light came to the eye 
 
 from C. Draw a line (NM) per- 
 pendicular to AB at D. (For a 
 right angle to measure by, fold 
 a piece of paper so that the two 
 parts of a straight edge of it fit 
 B accurately together.) Lay off on 
 DC and DE equal distances DF 
 and DG (not less than 5 cm.) ; 
 and from F and G drop perpen- 
 diculars to NM (FH and GI). 
 Measure FH and GI as accurately 
 as possible, and compute GI: FH. This is the index of refrac- 
 tion of the plate glass (Art. 42). 
 
 c. Repeat the experiment with the point D taken nearer the 
 corner of the glass (if possible) so that the angles of incidence 
 and refraction will be larger. 
 
 d. Compute the per cent of difference between the two 
 values of the index of refraction. This difference is due to 
 experimental errors or to errors of construction and measure- 
 ment, and should not exceed 3r% or 4%. 
 
 Second Method. The piece of plate glass should have a 
 scratch or other mark (A, Fig. 70) across the edge opposite to 
 a polished edge. Paste a strip of paper (B) on a side of tin- 
 
 M 
 
 FIG. 09. 
 
164 
 
 LIGHT 
 
 /N 
 FIG. 70. 
 
 glass with a straight edge of it in line with the perpendicular 
 (AN) from the mark to the polished edge CD. Hold the 
 plate on a level with the eyes, and look with both eyes at 
 the mark through the edge CD, along 
 the line NA; and at the same time 
 through the air at the sharp point of 
 your pencil, held against the glass at 
 the edge of the strip of paper. Adjust 
 the position of the pencil by parallax, 
 shifting the eyes a little to right and 
 left, till the pencil point, seen through 
 the air, coincides with the image of the 
 mark, seen through the glass. When 
 the correct adjustment is secured, mark on the paper strip the 
 position (E) of the pencil. Make at least two or three trials. 
 Measure accurately the width of the glass and its apparent 
 width when viewed through it ; and compute its index of 
 refraction (Art. 43). 
 
 II. To find the index of refraction of water. 
 
 Apparatus. Battery jar ; board, with crosspiece to support 
 
 it on the jar; pins; metric rule; 
 
 mop cloth. 
 
 First Method. a. Stick a pin 
 perpendicularly into the board at C 
 (Fig. 71) and place the board in the 
 jar. Fill the jar nearly full of water, 
 and stick a pin perpendicularly into 
 the board near each side of the jar 
 (at A and B) exactly at the water 
 level. The pins must mark as accu- 
 rately as possible the general level 
 of the water, not the raised edge in 
 contact with the board. Stick a pin at Z>, toward the opposite 
 side of the jar from C and within 1 cm. of the water, but not 
 
 FFC. 71. 
 
INDEX OF REFRACTION 165 
 
 touching it. Look with one eye along the surface of the board, 
 and place a pin at E in line with D and the apparent position 
 of C, so that the three pins appear to be exactly in a straight 
 line. 
 
 Remove the board, wipe it dry, and see that the pins are 
 stuck in firmly. Push the pins through a sheet of paper, and 
 spread the paper smoothly over the board. Being careful not 
 to let the paper slip about, draw with a sharp pencil a straight 
 line between the pins at A and B and another between E and 
 D. Continue the latter till it meets the line AB, and call the 
 point of intersection 0. Draw a straight line connecting 
 and the pin at G. The broken line COE is the path of the 
 light from C to the eye when the pins were seen apparently in 
 a straight line. 
 
 Remove the sheet of paper from the board, place it over the 
 record sheet, and locate on it the point and the lines AB, 
 C0 } and OE by pricking pinholes through at two points on 
 each line (where the paper is not torn). The lines must be 
 accurately located; the points where 
 the pins were need not be. Draw the 
 lines AB, CO, and OE on the record 
 sheet. Erect a perpendicular (MN) to 
 AB at 0. (For a right angle to meas- 
 ure by, fold a piece of paper so that 
 the two parts of a straight edge of it 
 fit accurately together.) Lay off on 
 OC and OE equal distances OF and 
 OG (not less than 5 cm.) ; and from F 
 and G drop perpendiculars to MN (FH and GI). Measure 
 FH and GI as accurately as possible and compute GI:FH. 
 This is the index of refraction of water (Art. 42). 
 
 b. Repeat the experiment with the point D in a different 
 position, so that the angles of incidence and refraction will be 
 different (larger if possible). 
 
 c. Compute the per cent of difference between the two re- 
 
166 LIGHT 
 
 suits. This difference is due to experimental errors or to errors 
 of construction and measurement, and should not exceed 3%. 
 
 Apparatus. Battery jar; bit of tin or other bright metal; 
 metric rule. 
 
 Second Method. Fill the jar nearly full of water and drop 
 the bit of tin into it. Place the tin (with the rule) so that 
 it lies flat on the bottom and touches the side of the jar. 
 Look with both eyes vertically down through the water at the 
 tin and through the air at the point of your pencil held against 
 the outside of the jar. Move the head slightly from side to 
 side, and, by means of parallax, place the point of the pencil 
 on a level with the apparent position of the tin. Measure 
 (outside the jar) the distance from the pencil to the top of the 
 water. Make several trials. Practice till independent measure- 
 ments agree within 2 or 3 mm., and take the average of two 
 or three of these. Measure (inside the jar) the depth of the 
 water. Compute the index of refraction of water (Art. 43). 
 
 EXERCISE 54. TOTAL REFLECTION 
 
 References. Hoadley, 472-473 ; Carhart and Chute, 266- 
 268 ; Slate, 210-211. 
 
 To study phenomena due to total reflection and the 
 conditions under which they occur. 
 
 Apparatus. Glass jar, preferably rectangular ; test tube ; 
 prism. 
 
 NOTE. It will be useful, both in explaining the following experiments 
 and in drawing the figures, to know that the critical angle for water is 
 48.5, for crown glass about 41, and for flint glass about 37. 
 
 a. Stick a bit of gummed paper on the outside of the 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 nearly vertically through 
 
TOTAL REFLECTION 
 
 167 
 
 the surface of the water, then gradually more and more ob- 
 liquely, till the eyes are on a level with the surface of the 
 water ; observing all the time the simultaneous 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. 
 Draw a figure similar to Fig. 
 73 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 
 
 , FIG. 73. 
 
 as the eyes are too low to 
 
 see it by refraction through the surface of the water ? 
 
 b. With the eyes directed upward toward the surface of the 
 water, observe in it the image of your pencil, held partly under 
 the water. 
 
 Briefly describe its appearance. What evidence is there 
 that the image is formed by total reflection ? 
 
 Try to look through the surface of the water at the portion 
 of the pencil above it. State and explain the result. (If the 
 part of pencil above the water is not seen, it is not because no 
 light enters the water from it, but because the light that does 
 so does not enter the eye.) 
 
 c. Put a strip of paper into the test tube ; and thrust the 
 tube, slightly inclined, into the jar of water with the closed 
 end down. Observe the appearance of the portion of the test 
 tube under water when viewed from above; and note the 
 effect of laying a sheet of white paper on the table beside 
 the jar on the side toward which the lower end of the tube 
 points. 
 
168 
 
 LIGHT 
 
 FIG. 74. 
 
 From what direction does the light come that is reflected 
 
 into the eye by the tube ? 
 
 Figure 74 represents a 
 section of the test tube (the 
 thickness of the glass being 
 magnified) and its effect 
 upon several rays falling 
 upon it, one being from 
 the paper inside the tube. 
 Study this figure for an 
 explanation of what you 
 see when you look at the 
 tube and the paper inside 
 it from different positions. 
 
 Describe and explain 
 what you have observed, re- 
 ferring to a copy of Fig. 74. 
 
 d. Eepeat with the tube partly filled with water. Compare 
 results with the preceding, and explain. 
 
 e. Lay a glass prism, face downward, 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 obliquely 
 
 through the near side of the prism 
 until the printing is no longer 
 visible. 
 
 Describe the appearance of the 
 lower face of the prism and ex- 
 plain the disappearance of the 
 printing, referring to a copy of 
 Fig. 75. 
 
 /. 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 a finger, 
 
 FIG. 75. 
 
THE CONVEX LENS 169 
 
 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 brightness of the image. 
 Give a brief account of what you have observed, and explain. 
 
 EXERCISE 55. THE CONVEX LENS 
 
 References. Hoadley, 477-480; Carhart and Chute, 269- 
 274; Jones, Light, 60-64, 68, and 72-74. 
 
 Apparatus. Optical bench or meter rod ; lens ; two card- 
 board screens, one having a circular hole about 5 cm. in diameter 
 at the same height as the lens ; mounted candle. 
 
 I. To find the focal length of a convex lens; and to 
 study real images formed by it. 
 
 a. Turn the optical bench (or rod) toward some distant 
 object seen through an adjacent window. (A more distinct 
 image is obtained if the window is open.) Place the lens about 
 the middle of the bench, and place near it, on the side opposite 
 the object, the screen with the hole. Place the other screen 
 behind this, and adjust it so that a distinct image of the distant 
 object is formed upon it. The screen with the hole is to inter- 
 cept as much of the light from other sources as possible. Try 
 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, measure from an end of one block to the corre- 
 sponding end of the other.) This is the focal length (/) of 
 the lens. Make three settings of the screen and average the 
 readings. 
 
 b. Kemove the screen on which the image was focused, and 
 stand the screen with the hole in its place, so that the image is 
 now in the air in the hole of this screen. Stand a meter or 
 more from the lens on the same side as the screen, and view 
 the image in the hole directly with both eyes. The eyes must 
 
170 LIGHT 
 
 be in line with the hole in the screen and the lens. The screen 
 serves merely to locate the image, thus helping the observer to 
 direct his eyes toward its real position. Without the screen, 
 the observer naturally looks at the lens ; in which case the 
 image seems to be in the lens and appears blurred, just as your 
 finger does if you hold it up before you and look at some object 
 a foot or two beyond it. Remove the screen and try to see the 
 image where it really is. When the eyes are properly directed, 
 the image appears perfectly distinct and definitely located at 
 the principal focus. 
 
 Try viewing the image directly from different positions. 
 Can you see it from as many different directions as you can 
 when it is caught upon a screen ? Explain. 
 
 II. To study tJw relation between the position of the 
 object and the size, and position of its real image. 
 
 a. Draw the blinds so as to darken the room (or carry the 
 apparatus to a darker room), turn the bench lengthwise with the 
 table, place the lens near the middle of the bench, and set 
 the lighted candle near one end. Stand a short distance beyond 
 the opposite end of the bench, and look for the image of the 
 candle in front of the lens. If you have difficulty in focusing 
 the eyes properly, use the screen to locate the image. 
 
 Let one student slowly move the candle from the lens, while 
 the other observes the simultaneous change in the size and 
 position of the image. Eecord the changes observed. 
 
 b. Continue these observations till the candle is so far away 
 that the image almost ceases to be visible. 
 
 Does the image continue to change in size and position as it 
 did at first ? Does it change as rapidly ? 
 
 Which moves the faster, the object or the image ? 
 
 What is the least distance of the image from the lens ? How 
 does this distance compare with the focal length of the lens ? 
 
 c. Now move the candle slowly toward the lens and follow 
 the behavior of the image. To study a large arid distant image 
 
THE CONVEX LENS 
 
 171 
 
 it is necessary to catch it on the screen. Record the observed 
 changes in the size and position of the image. 
 
 Which moves the faster, the object or the image when the 
 object is near the lens ? 
 
 When you have a distinct image as far from the lens as you 
 can get it, how far is the candle from the lens ? 
 
 d. What reciprocal relations have you discovered between 
 the image and the object ? 
 
 44. Formula for Convex Lenses. For the present purpose 
 (that of establishing certain geometrical relations), there is no 
 appreciable error in drawing rays as if light were refracted once 
 halfway between the surf aces "of a lens instead of at each sur- 
 
 FIG. 76. 
 
 face. The rays are so drawn in Fig. 76. Let p denote the 
 distance of the object (CO), p' the distance of the image (OD), 
 and / the focal length of the lens (OF). From similar triangles 
 prove that AB:ab = CO:OD or p:p'-, also that MN:ab = 
 OFiFDoTfi(p'-f). 
 Since AB = MN 9 we have from these proportions 
 
 AB : ab = MN: ab =p:p' =/: (p' -/). 
 From the last proportion derive the formula 
 
 1 + 1=1. 
 p P' f 
 
 Expressed in words, this means that the sum of the recipro- 
 cals of a pair of conjugate focal distances of a convex lens is 
 equal to the reciprocal of its focal length. 
 
172 
 
 LIGHT 
 
 EXERCISE 56. THE FOCAL LENGTH OF A LENS 
 
 References. The same as for the preceding exercise. 
 
 To find the -local length of a lens from its relation to 
 conjugate focal distances. 
 
 Apparatus. Optical bench or meter rod ; two screens, one 
 with small hole and cross wires; flat gas jet or lamp; lens. 
 
 a. Find the focal length (/) of the lens by focusing it on a 
 distant object, as in the preceding exercise. 
 
 b. Draw the blinds so as to make the room rather dark. 
 Stand the burner at the end of the optical bench, light it, and 
 turn the flame flatwise toward the bench. Set the screen with 
 the cross wires on the end of the bench near the light (Fig. 77). 
 Place the lens at a distance from the cross wires equal to twice 
 
 FIG. 77 
 
 its focal length. Place the other screen so that the image of 
 the cross wires is sharply focused upon it. The image of the 
 wires may be red, black, or greenish blue, depending upon 
 the position of the screen. The adjustment should be such 
 that the image is as nearly black as possible. Let p denote the 
 distance of the lens from the cross wires, andp' the distance of 
 the image from the lens. Eecord as indicated below. 
 
 c. Move the screen on which the image is caught 30 to 40 cm. 
 farther from the cross wires ; then move the lens toward the 
 
THE FOCAL LENGTH OF A LENS 
 
 173 
 
 cross wires till the image is again distinct upon the screen. 
 Measure p and p'. 
 
 d. Without changing the position of either screen, move the 
 lens away from the cross wires till the image is again distinct 
 upon the other screen. Measure p andp'. 
 
 Perform the computations indicated in the form of record. 
 This will show how nearly your results agree with the formula 
 derived in Art. 44. 
 
 FOKM OF EECORD 
 
 
 
 
 
 
 
 
 ERROR =- 
 
 
 
 
 \ 
 
 1 
 
 1 1 
 
 1 
 
 
 
 p 
 
 !>' 
 
 P 
 
 
 _i+-L 
 p p? 
 
 
 -(Ul) 
 
 v y 
 
 
 
 
 
 
 
 
 c 
 
 
 
 
 
 
 
 
 
 
 
 
 d 
 
 
 
 
 
 
 
 
 
 
 
 
 Discussion. a. Why should p and p' be equal in the first 
 set of measurements? (Find the answer from the formula.) 
 
 b. Why should p 1 and p in the last set of measurements be 
 respectively equal to p and p' of the preceding set ? 
 
 c. Average the numbers in the column headed - H , and 
 
 p p 1 
 
 compute the reciprocal of this average. The result is the 
 focal length of the lens found by the method of conjugate foci. 
 
 d. Prove geometrically from a drawing like Fig. 76 that 
 
 Length of image : length of object = p' : p. 
 
 e. From a study of the drawing discover whether, for a given 
 object at a given distance, the size and distance of the image 
 would be greater or less if a lens of greater focal length were 
 used. Prove that, under these conditions, the size of the image 
 is proportional to its distance from the lens. 
 
174 
 
 LIGHT 
 
 45. Angular Size and Visual Angle. It is a familiar fact 
 that the distinctness with which an object is seen depends 
 upon its distance from the observer as well as upon its size. 
 The reason for this is shown in Fig. 78. The crystalline lens 
 (aided by the other refractive media of the eye) forms upon the 
 back part of the eyeball (the retina) a real, inverted image of 
 objects within view. The nearer an object is to the eye the 
 larger is its image on the retina. In fact, the size of the image 
 is proportional to the angle under which the object is seen 
 (angles AOB and A' OB' in the figure) ; and this angle is (very 
 nearly) inversely proportional to the distance of the object. 
 
 FIG. 78. 
 
 The angle under which an object is seen is called the visual 
 angle, and it measures the angular size of the object. The 
 distinctness with which an object is seen (so long as the image 
 is clearly defined upon the retina) is determined by the visual 
 angle ; and this, as we have seen, varies inversely as the 
 distance of the object for vision with the naked eye. 
 
 The various forms of telescopes and microscopes serve the 
 purpose of increasing the visual angle. 
 
 46. Magnification of a Simple Microscope. In using a convex 
 lens as a simple microscope, it is commonly held close to the 
 eye; hence the angle under which the image is seen is approxi- 
 mately a Ob (Fig. 79). It might be supposed that the angular 
 size of the image, and hence its distinctness, would be no 
 greater than that of the object, since angle aOb and angle AOB 
 
THE SIMPLE MICROSCOPE 
 
 175 
 
 are identical. But in order to view the object directly, its 
 distance must be at least as great as EO (about 25 cm.), for at 
 a less distance the eye is unable to focus the image distinctly 
 upon the retina and the object appears blurred. At this dis- 
 tance the visual angle of the object would be-4'OJB'; hence the 
 magnification is 
 
 angle a Ob : angle A' OB'; 
 and this is approximately equal to 
 
 abiA'B' orab-.AB. 
 From similar triangles, 
 
 ab:AB::EO:DO. 
 
 FIG. 79. 
 
 Hence the magnification is equal to the ratio of the distance 
 of the image to the distance of the object. 
 
 JEJO, the nearest distance of distinct vision, is about 25 cm. 
 for the normal eye ; and, for lenses of short focus (5 cm. and 
 under), DO is but little less than the focal length of the lens; 
 hence the magnifying power of such lenses is approximately 
 expressed by the ratio 
 
 25:/, 
 
 where / is the focal length of the lens in centimeters. 
 
17fi LIGHT 
 
 EXERCISE 57. THE SIMPLE MICROSCOPE 
 
 References. Hoadley, 513 ; Carhart and Chute, 295 ; Slate, 
 216. 
 
 To study the formation of virtual images by a convex, 
 lens. 
 
 Apparatus. Optical bench; mounted lens of short focal 
 length ; mounted candle ; screen. 
 
 a. Find the focal length of the lens by focusing on a distant 
 object. 
 
 b. Place the lighted candle on the end of the optical bench 
 and the lens in front of it at a distance considerably greater 
 than its focal length. Catch the image of the candle on the 
 screen (or a sheet of paper). (It may be necessary to go to 
 a dark corner of the room for this.) Remember that a real 
 image is formed Jby the convergence of light from each point 
 of the object to the corresponding point of the image. Move 
 the candle slowly toward the lens, meanwhile following the 
 image with the screen. 
 
 As the candle is moved up, does the cone of light that 
 falls upon the lens from any point of it become more or less 
 divergent ? 
 
 Does the refracted cone become more or less convergent ? 
 
 c. Move the candle up to the principal focus of the lens. 
 What has become of the image meanwhile ? 
 
 What is now the shape of the cone of light from a point of 
 the candle after passing through the lens ? 
 
 d. With the eye close to the lens, look through it at the 
 candle while you are moving it up close to the lens. What 
 you see is not the candle, but its image. 
 
 On which side of the lens is it ? 
 Can it be caught on a screen ? Is it real or virtual ? 
 Are the rays from a point of the candle convergent or 
 divergent after passing through the lens ? 
 
 How does the image compare in size and position with 
 
COLOR 177 
 
 the object? Be careful as to its position; the eye is easily 
 deceived on this point. Locate the image by parallax by 
 holding a pencil just above it, looking at the pencil over the 
 lens. Moving the head slightly from side to side will help. 
 
 e. What change takes place in the size and position of the 
 image as the object is brought up toward the lens from the 
 principal focus ? Explain this change of size and position 
 by means of two drawings, one with the distance of the object 
 (an arrow) only slightly less than the focal length and one 
 with the object very near the lens. 
 
 /. Use the lens as a simple microscope in viewing various 
 objects, as the back of your hand, cloth, printing, etc. Hold 
 the lens close to the eye and vary the distance of the object 
 till it is seen distinctly. While looking at the different objects 
 estimate the magnification of the lens. jMagnification is always 
 the ratio of corresponding linear dimensions of image and ob- 
 ject, never of surfaces or volumes. 
 
 g. How does the estimated magnification compare with the 
 value given by the formula 25 -s-/? 
 
 EXERCISE 58. COLOE 
 
 References. Hoadley, 486-487 and 495-499; Carhart and 
 Chute, 277-278 and 287-292 ; Slate, 218-221 ; Jones, Light, 97. 
 
 Apparatus. Glass prism ; small square of black cardboard 
 with a slit 1 mm. by 2 cm. and a slit 1 cm. by 2 cm.; strips 
 of colored paper 1 mm. wide on black cardboard ; small squares 
 or other patterns of complementary colors pasted on opposite 
 sides of black cardboard (yellow and blue on one and purple 
 and green on another) ; pieces of colored glass (blue and 
 yellow) ; colored disks and top. 
 
 I. To separate li$ht into its elementary, or prismatic, 
 colors. 
 
 a. Stand facing a window and hold the cardboard with the 
 slits at about the height of the eyes, with the slits horizontal 
 COLEMAN'S PHY. LAB. MAN. 12 
 
178 
 
 LIGHT 
 
 FIG. 80. 
 
 and strongly illuminated by sunlight (having the sky for a 
 background). Look at the narrow slit through the prism, held 
 
 as shown in the figure, 
 with its edges parallel to 
 the slit. The prism should 
 be held near the eye, and 
 the slit at a distance of 
 about a foot. Make a 
 drawing like Fig. 80, but larger, and complete it, showing the 
 apparent position and the appearance of the slit. The drawing 
 should account for the relative position of the red and blue 
 ends of the spectrum a. it appears upon the cardboard. 
 
 b. Look at the wide slit in the same way. Account for the 
 absence of color from the central portion of the slit, and draw 
 a figure to illustrate. ^ 
 
 c. Cover one end of the narrow slit with the blue glass, and 
 view the slit through the prism as before. Compare the spec- 
 tra of the covered and the uncovered portions of the slit. 
 
 What colors are transmitted through the glass ? What 
 colors are absorbed by it ? 
 
 Why does the glass appear blue when it transmits other 
 colors also ? 
 
 d. Analyze in the same way the light transmitted by the 
 other pieces of glass. 
 
 e. Hold the colored strips on the black cardboard so that 
 they are illuminated by direct sunlight, and with the prism 
 analyze the light reflected by them. Record as follows, using 
 the initial letters V, I, B, Gr, Y, 0, and E to denote the colors: 
 
 COLOR OF 
 STRIP 
 
 Col.OKS COMPOSING 
 
 REFLECTED LIGHT 
 
 ('oU)RS AP.SOKBKI) 
 
 BY STRIP 
 
 white 
 red 
 
 
 
 etc, 
 
 
 
COLOR 179 
 
 II. To observe the colors produced when different colors 
 are combined by rapid rotation. 
 
 a. Fasten a red and a yellow disk to the top, leaving half 
 of each exposed. Spin the top, and observe the resultant 
 color. Try in the same way the red and violet and the blue 
 and green disks. If you try other combinations, make a record 
 of them, also. Note the relative positions of the colors used 
 and of the resultant color in the chart of complementary colors 
 given in the text or reference books. 
 
 What is the position on the chart of the resultant color, 
 relative to the colors combined to produce it ? 
 
 COMPONENT COLORS 
 
 KESULTANT COLOK 
 
 red and yellow 
 red and violet 
 blue and green 
 
 
 6. When united in this way, complementary colors, if suffi- 
 ciently intense, will produce white. Generally, however, the 
 whole amount of light reflected is so small that the resulting 
 color is gray, or even as dark as slate. That such colors are 
 really shades of white (that is, white of a low degree of lumi- 
 nosity) may be shown by rotating together the white and the 
 black disks, first with but little of the black exposed, then with 
 more and more of the black. Test the white and black in this 
 way. 
 
 Try the different pairs of complementary colors provided. 
 The yellow and blue disks will probably give the best result. 
 If in any case the resulting color is not a neutral gray or slate, 
 vary the portion of each color. Draw circles and divide them so 
 as to show the portion of each color when the resultant is gray. 
 
 c. Try to produce white (gray) with a combination of the 
 primary colors, red, green, and violet. Make a drawing as 
 before. 
 
180 LIGHT 
 
 III. To observe after images-; and to -find whether a 
 color and its after image are complementary. 
 
 a. Look steadily, without moving the eyes, for about half a 
 minute at the green paper on the black cardboard, with as 
 strong a light on the paper as you can get (direct sunlight if 
 possible) ; then quickly look at a sheet of white paper. 
 
 What is the shape and color of the spot observed ? 
 
 Does the spot follow the eye as you look at different parts of 
 the paper ? The spot is called an after image. 
 
 (Consult the text or a reference book for the cause of after 
 images.) 
 
 After again looking steadily at the paper for half a minute, 
 close the eyes quickly and hold the hand over them to exclude 
 the light that would otherwise penetrate the eyelids. 
 
 What is the shape and color of the spot observed ? 
 
 b. Repeat the 'experiment with the bit of purple paper. (If 
 purple is not provided, use violet.) 
 
 What relation does the color of the after image bear to that 
 of the object ? 
 
 c. Try the yellow and the blue papers, observing the after 
 images with the eyes closed or by looking at white paper. 
 
 EXERCISE 59. SPECTRA 
 
 References. Hoadley, 500-506; Carhart and Chute, 283- 
 286; Sanford, pp. 392-398. 
 
 Apparatus. Spectroscope ; Bunsen burner ; flat gas jet ; 
 ring stand ; asbestos ; blue, yellow, and red glass ; solutions 
 of strontium, barium, calcium and potassium salts ; platinum 
 wire for each solution ; platinum foil ; black screen. 
 
 [Make a hole about 2 cm. in diameter in the middle of a small piece of 
 sheet asbestos, and rub salt into the asbestos about the hole. A Bunsen 
 flame rising through this hole will be strongly colored with sodium. Fuse 
 pieces of platinum wire 7 or 8 cm. long and the platinum foil into short 
 pieces of glass tubing for handles. Roll 2 cm. of the wire at the end into 
 a small, tight coil.] 
 
SPECTRA 181 
 
 I. To study and adjust a spectroscope. 
 
 a. If the prism is covered, remove the cover and observe the 
 position of the prism. Find from its position what the direc- 
 tion of deviation must be, and in what position the telescope 
 must be placed to receive the light from the collimator after it 
 has passed through the prism. 
 
 The telescope must be focused for parallel rays ; hence the 
 eyepiece is to be adjusted so that distant objects (viewed 
 through the open window) are seen distinctly. With some 
 instruments an unobstructed view of distant objects can be 
 obtained by removing the prism (do not touch the refracting 
 surfaces) ; with others it will be necessary to unscrew the tele- 
 scope. If the telescope is removed, be very careful in replacing 
 it not to damage the thread by starting it the wrong way and 
 forcing it. This adjustment of the telescope for distant ob- 
 jects is to remain unchanged throughout the exercise. 
 
 b. If the telescope is in a fixed position, omit this para- 
 graph. If it is carried on a movable arm, turn it into line 
 with the collimator ; and, with the prism removed, move the 
 adjustable end of the collimator so that the slit is seen dis- 
 tinctly through the telescope. 
 
 c. Light the Bunsen burner, and place it in line with the 
 collimator about 10 cm. beyond its end. Support the asbestos 
 on the ring stand, and adjust it so that it is a little below the 
 level of the collimator and so the flame of the burner rises 
 through the hole in the asbestos. If the flame is not strongly 
 colored yellow, rub more salt into the asbestos about the hole. 
 The yellow color is due to sodium vapor. Place the black 
 screen a short distance beyond the burner, so as to shut out 
 other light from the collimator. Open the slit of the collimator 
 a little way by turning the thumbscrew at the side, and look 
 through the telescope. If the apparatus is properly adjusted, 
 you will see a yellow image of the slit. If this image is not 
 distinct, move the adjustable end of the collimator in or out 
 till it is. The slit should be vertical. This adjustment of the 
 
iXiJ LIGHT 
 
 distance of the slit is to remain unchanged throughout the 
 exercise; but the width of the slit may be changed as desired. 
 Observe the effect of varying the width of the slit, and leave it 
 finally about the width of a fine hair. 
 
 cl This paragraph is to be included or omitted with para- 
 graph b. If b is omitted, c is done with the prism in place. 
 If b is included, replace the prism now, and cover it and the 
 adjacent ends of the telescope and collimator so as to exclude 
 as much light as possible. Turn the telescope in the proper 
 direction till the image of the slit is seen. 
 
 Has the prism affected its size or color ? What is the effect 
 of the prism ? 
 
 e. If the spectroscope has a third tube carrying a scale, 
 light the gas tip in front of it. Look in the telescope, and 
 adjust the sliding piece at the end of the third tube till the 
 scale that it carries is seen distinctly. If this scale is not 
 horizontal, turn the end piece till it is. Again remove the 
 cover of the prism, and observe that the scale is seen by reflec- 
 tion from the front surface of the prism. 
 
 II. To study continuous spectra. 
 
 a. Observe the spectrum of the Bunsen flame with the 
 asbestos removed. The screen should be in position to shut 
 out other light. If the flame is nearly non-luminous, as it 
 should be, it will give no spectrum, or, at the most, only a 
 very faint one. Hold a piece of platinum foil in the flame 
 and in line with the slit. 
 
 What kind of spectrum does it give when incandescent ? 
 What classes of bodies give this kind of spectrum ? (See 
 references.) 
 
 b. Substitute the flat gas jet for the Bunsen burner and 
 observe its spectrum. 
 
 Why is it continuous ? (Consult any chemistry on the 
 cause of the luminosity of a gas flame.) 
 
 For what color is the angle of deviation greatest ? Least ? 
 
SPECTRA 183 
 
 III. To study discontinuous or bright-line spectra. 
 
 The bright-line spectrum of sodium has already been ob- 
 served. Dip the wire for the strontium salt into the solution of 
 that salt ; then hold it in the Bunsen flame and observe the spec- 
 trum. Compare with the colored plate of the spectrum in 
 some reference book. Draw a figure, locating the lines of the 
 spectrum by the scale of the instrument, if it has one, and 
 name their color in the figure. 
 
 Try the other salts, using for each the wire provided for it ; 
 and compare with colored plates of the spectra. In each case 
 the spectrum observed is that of the metal in the salt. Draw 
 figures. 
 
 Is the metal in the solid or gaseous state while emitting the 
 light ? 
 
 IV. To study absorption spectra. 
 
 a. Obtain a continuous spectrum from the flat gas jet; then 
 hold the blue glass between the flame and the slit. What 
 colors are most strongly absorbed by the glass ? Which are 
 transmitted ? 
 
 6. Test the red and the yellow glass in the same way. 
 
 c. What colors are transmitted by the blue and the yellow 
 glass together ? Answer from the results obtained with the 
 two separately, and test your conclusion by holding them both 
 together before the slit and observing the spectrum of the 
 transmitted light. 
 
 Look through the two together toward the light. What is 
 the color of the transmitted light ? 
 
 d. Turn the collimator toward the sky, and observe the 
 spectrum of skylight (the solar spectrum). If the slit is narrow 
 and the telescope properly focused, many dark lines (Fraun- 
 hofer lines) will be seen. 
 
 Where are the substances that absorb the colors that would 
 otherwise occupy the places in the spectrum where the Fraun- 
 hofer lines are ? (See references.) 
 
184 
 
 LIGHT 
 
 Observe and explain the effect upon these lines of widening 
 the slit. 
 
 e. If the spectroscope has a comparison prism, do the follow- 
 ing ; if not, omit it. Narrow the slit till the lines are distinctly 
 visible. Cover half the slit with the comparison prism, and 
 stand the sodium flame at the side so that its light is reflected 
 by the prism into the slit. You now have the solar spectrum 
 with the spectrum of sodium beside it. Observe whether the 
 sodium line is continuous with a dark line in the solar spectrum. 
 Explain. 
 
 47. The Astronomical Telescope. In Fig. 81 MO and HI 
 represent rays from the top of a distant object, and NO and JK 
 rays from the bottom. The inverted arrow ab represents the 
 real, inverted image formed by the objective. Since the object 
 is at a considerable distance, the distance of the image (0(7) is 
 the focal length of the objective (F). The eye lens is used as a 
 
 FIG. 81. 
 
 simple microscope to form a magnified, virtual image (a'b 1 ) of 
 the real image ; hence CE is approximately equal to the focal 
 length of the eye lens (/). 
 
 By the use of the eye lens the visual angle becomes a'Eb' or 
 aEb. The magnifying power of the telescope is the ratio of the 
 visual angle when the object is viewed through it (angle aEb) 
 to the visual angle with the naked eye (angle MON or its equal 
 
THE ASTRONOMICAL TELESCOPE 185 
 
 angle a Ob). But, for small angles, the visual angle is (very 
 nearly) inversely as the distance (Art. 45) ; hence 
 
 the magnifying power = angle aEb : angle a Ob 
 
 = OC:GE or F:f (very nearly). 
 
 Stated in words this means that the magnifying power of a 
 telescope is directly proportional to the focal length of the 
 objective and inversely proportional to the focal length of 
 the eyepiece. For example, the magnifying power would be 
 doubled either by doubling the focal length of the objective 
 (which would double the size of the real image ab) or by reduc- 
 ing the focal length of the eyepiece one half (which would 
 double the size of the virtual image a'b'). Some elementary 
 text-books make the erroneous statement that the magnification 
 is due entirely to the eyepiece. 
 
 EXERCISE 60. THE ASTRONOMICAL TELESCOPE 
 
 References. Hoadley, 515-516; Carhart and Chute, 297; 
 Slate, 216-217 ; Jones, Light, 87-88. 
 
 To study, by means of two convex lenses, the use of 
 the objective and the eyepiece of an astronomical tele- 
 scope and the relation between their focal lengths and 
 the magnifying power of the instrument. 
 
 Apparatus. Optical bench ; mounted screen ; three mounted 
 convex lenses, one of long focal length (the longer the better 
 up to 40 cm.), and two of unequal short focal length. 
 
 a. Find the focal length of each of the lenses by focusing 
 the image of a distant object on the screen. Let F denote the 
 longest focal length, /j the next, and/ 2 the shortest. 
 
 b. Tarn the bench toward a distant building, and stand the 
 lens having the shortest focal length (the eye lens) on the bench 
 at the end farthest from the object. Use the lens having the 
 
18G LIGHT 
 
 longest focal length as the objective. Place it on the bench at 
 a distance from the eye lens approximately equal to the sum 
 of the focal lengths of the two lenses ; and, with the eye close 
 to the eye lens, adjust the objective till the image is distinct. 
 It will be better to raise the window, as the wavy surface of 
 common window glass interferes seriously with the formation 
 of distinct images. 
 
 View the object directly with one eye, and the image, at the 
 same time, with the other; and estimate the magnification 
 (the ratio of the apparent length of any part of the image to 
 the length of the corresponding part of the object). The best 
 object for this purpose is one bounded by short, straight lines, 
 as a window. 
 
 c. Compute the magnification from the focal lengths (Art. 
 47), and compare with the estimated value. 
 
 d. Measure the distance between the lenses, and compare 
 this distance with the sum of the focal lengths of the lenses. 
 
 Why should these quantities be equal ? (See Art. 47.) 
 
 e. Why is the image bordered with red and blue ? 
 
 Is the coloring greater or less for parts of the image seen 
 through the central portion of the eye lens ? Why ? 
 
 /. Repeat the experiment with the same objective and the 
 other lens for the eye lens. Estimate and compute the magni- 
 fication as before ; but omit paragraph d. 
 
 g. Is chromatic aberration greater or less than before ? Why ? 
 
 h. Repeat the experiment with the lens of medium focal 
 length (/j) for the objective and the one of shortest focal 
 length for the eye lens. 
 
 How does the magnification compare with that of the first 
 combination, where the same eye lens was used ? 
 
 What is the advantage of an objective of long focal length? 
 
 Discussion. Copy Fig. 81, and prove, referring to the figure, 
 that the size of the image formed by the objective is proportional 
 to its focal length. 
 
THE GALILEAN TELESCOPE 187 
 
 EXEKC1SE 61. THE GALILEAN TELESCOPE 
 
 References. Hoadley, 482 and 517 ; Carhart and Chute, 
 271-272 and 298; Jones, Light, 90. 
 
 Apparatus. Optical bench ; convex lens of long focal length ; 
 concave lens. 
 
 I. To study the effect of a concave lens on parallel 
 and diverging light. 
 
 a. Try to focus a beam of sunlight with a concave lens as 
 you did with a convex lens. State and explain the result. 
 
 b. Look at near and distant objects through the lens, noting 
 the effect of the lens on the apparent size and position of the 
 object. 
 
 State this effect and explain it by a figure showing the for- 
 mation of an image by a convex lens. 
 
 c. It is evident that, since a concave lens makes parallel 
 rays divergent, it will make convergent rays less convergent, 
 and may even make them parallel or divergent. In the Gali- 
 lean telescope its function is to intercept the converging rays 
 from the objective and make them very slightly divergent 
 (practically parallel). 
 
 II. To adjust and use a convex and a concave lens as 
 a Galilean telescope. 
 
 a. The focal length of a concave lens can be found experi- 
 mentally, but not so simply as that of a convex lens. On this 
 account measurements and computations are omitted from this 
 exercise. 
 
 Turn the optical bench toward a distant building, and place 
 the convex lens (the objective) at the nearer end. Find ap- 
 proximately the position of the real image formed by the objec- 
 tive, and place the concave lens (the eye lens) on the bench at 
 about this point. While looking through the eye lens, move 
 it slowly toward the objective till the image is distinctly seen. 
 
188 
 
 LIGHT 
 
 b. Direct the telescope toward a window of the distant 
 building so that it can be seen directly with one eye and 
 through the telescope with the other, and estimate the magni- 
 fication as you did for the astronomical telescope. 
 
 FIG. 82. 
 
 Discussion. Copy Fig. 82 and write a brief explanation, 
 answering the following questions: 
 
 a. Which rays come from the top of the object and which 
 from the bottom ? 
 
 6. What (in the figure) is the focal length of the objective ? 
 
 c. What is the focal length of the eye lens ? 
 
 d. W r hat is the visual angle with the naked eye ? 
 
 e. What is the visual angle with the telescope? 
 
 /. What ratio (of lengths) measures the magnification ? 
 
 EXERCISE 62. THE COMPOUND MICROSCOPE 
 
 References. Hoadley, 514; Carhart and Chute, 296; Jones, 
 Light, 89. 
 
 To study, by means of two convex lenses, the use of the 
 objective and the eyepiece of a compound microscope; (in (I 
 to compute the magnifying power. 
 
 Apparatus. Optical bench ; two lenses of short focal length, 
 preferably, of the same size and focal length ; printed page, 
 inverted and fastened to a mounted screen. 
 
THE COMPOUND MICROSCOPE 
 
 189 
 
 a. Find the focal length of the lenses by focusing the image 
 of a distant object on the screen. Let F denote the shorter 
 focal length (if they differ) and /the longer. 
 
 b. Place the lens of longer focal length (/) at one end of 
 the bench for the eye lens, and the object (the inverted printed 
 page) at the other. Starting with the other lens near the 
 
 FIG. 83. 
 
 object, slowly move it toward the eye lens till a distinct image 
 of one or more letters is seen. 
 
 c. Measure the distance from the object to the objective (p) 
 and the distance between the lenses (M). 
 
 Let p f denote the distance between the objective and the real 
 image formed by it ; then M should be very nearly equal to 
 / + />'. Why? 
 
 To test this relation, compute p' from the formula 
 
 . 
 p p' F 
 
 To p' add the focal length of the eye lens (/), and compare the 
 
 sum with M. 
 
 p 
 d. The magnification by the objective is . Why? 
 
190 LIGHT 
 
 95 
 The magnification by the eye lens is ~- Why ? 
 
 /r>'\ /^'i 
 
 The total magnification is ( *L ) x ( ^ 
 
 Compute the magnification from the measurements taken. 
 
 e. Move the eye lens a few centimeters nearer the object, 
 then move the objective toward the eye lens till the image is 
 again distinct. 
 
 Is the magnification more or less than it was before ? Ex- 
 plain. 
 
 /. Eeplace the eye lens exactly in its first position; and 
 move the objective toward the eye lens till a second position 
 is found for which the image is distinct. 
 
 Is the magnification more or less than in the first instance ? 
 Explain. 
 
 g. With this adjustment you should find that the distances 
 p and p' of paragraph c are interchanged, the distance between 
 the object and the objective being p' and the distance between 
 the lenses/-!- p. Why should this be so ? 
 
 Measure the distance between the object and the objective 
 and compare it with p'. 
 
 h. The lenses in this adjustment make an astronomical tele- 
 scope for viewing the printing. In what respects does it differ 
 from the microscope ? 
 
VIII. MAGNETISM AND ELECTRICITY 
 EXERCISE 63. MAGNETS AND MAGNETIC ACTION 
 
 References. Hoadley, 291-298 ; Carhart and Chute, 358-366 
 and 377. 
 
 Apparatus. Bar magnet ; small pieces of iron, brass, copper, 
 zinc, lead, wood, glass, paper, etc. ; small pieces (about 8 or 10 
 cm. square) of cardboard, glass, thin wood, sheet iron (or tin), 
 zinc, brass, and lead ; coarse iron filings or small tacks ; mag- 
 netic needle, mounted or suspended (a magnetized sewing, 
 darning, or knitting needle will serve). 
 
 I. To observe the distribution of attracting power in a 
 magnet. 
 
 Lay the bar magnet in a box of coarse iron filings (or small 
 tacks), so that its whole length comes in contact with the fil- 
 ings. Lift the magnet and observe the distribution of the 
 filings that cling to it. 
 
 What does the experiment show concerning the distribution 
 of magnetic attraction in a bar magnet? The regions of 
 greatest attraction are called poles. Remove the filings by 
 wiping them toward the middle of the magnet. 
 
 II. To find which of certain substances are attracted 
 by a magnet and which are not. 
 
 Try to lift with the magnet small bits of various substances ; 
 and classify them as magnetic and non-magnetic according to 
 whether they are or are not attracted by the magnet. 
 
 191 
 
192 MAGNKTISM AM) KLiiCTKUTFY 
 
 III. To find whether tlierc /A < it traction or repulsion 
 between like poles; between unlike pole*. 
 
 The end of the bar magnet marked N is the north-seeking or 
 north pole. It is like the pole of the magnetic needle that 
 points toward the north. (This may be tested by suspending 
 the bar magnet by a thread at the middle, and observing the 
 direction in which the marked end points when it comes to 
 rest.) 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 un- 
 like poles ? 
 
 IV. To find which of certain substances act as screens 
 to cut off magnetic action, and which do not. 
 
 a. Put a small quantity of iron filings (or tacks) on the card- 
 board, and move" a pole of the magnet to and fro against the 
 under side of the cardboard beneath the filings. What evidence 
 is there of magnetic action through the cardboard ? Test in the 
 same way the different substances provided, and classify them 
 in two groups according as they do or do not act as a screen to 
 cut off magnetic action. Substances that act as a screen are 
 said to be very permeable, for reasons that will appear in the 
 next exercise. 
 
 Gather up with the magnet any scattered filings. 
 
 b. Compare these lists with your lists of magnetic and non- 
 magnetic substances. 
 
 EXERCISE 64. MAGNETIC INDUCTION. THEORY 
 OF MAGNETISM 
 
 References. Hoadley, 307-309 ; Carhart and Chute, 367-373 ; 
 Slate, 224. 
 
 Apparatus. Bar magnet ; magnetic needle; piece of soft iron 
 rod (Norway iron); piece of wood of same size and shape as the 
 
MAGNETIC INDUCTION. THEORY OF MAGNETISM 198 
 
 iron rod; piece of steel; iron wire 10 in. long with an inch at 
 each end bent at right angles ; iron filings ; slender test tube 
 nearly full of iron filings. 
 
 [A satisfactory magnetic needle for this and the following exercise can 
 be made by magnetizing a piece of a large sewing or darning needle an 
 inch long and suspending it by a silk thread or, better, by a single strand. 
 Waxing the thread at the end before tying it to the needle will keep it 
 from slipping. It will be still better if the thread is run through a piece 
 of small glass tubing 5 in. long and fastened with wax at the farther end 
 so as to permit the needle to hang freely a little below the tube when it is 
 held vertically. The tube prevents lateral motion of the needle.] 
 
 I. To find what is meant by magnetic permeability 
 and to study magnetic induction in iron and steel. 
 
 a. Try to pick up iron filings with the soft iron rod. Does 
 it show magnetic properties? Try again with a pole of the 
 magnet held against the other 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 ? 
 
 6. Test the piece of wood as you did the iron rod. 
 
 c. The magnetic action permeates the iron, extending from 
 end to end, the rod serving as a carrier for the action. This is 
 what is meant by calling magnetic substances permeable. 
 Compare the results obtained here with those of Part IV of 
 the preceding exercise. 
 
 d. Hold a pole of the magnet against an end of the soft iron 
 rod, and test the polarity of the magnetism induced in the iron 
 by bringing the other end of it near the magnetic needle. 
 Repulsion rather than attraction should be made the test. 
 \Vliy? Repeat with the other end of the magnet held to the 
 iron. 
 
 If a more complete test of the magnetism induced in the 
 iron were made, it would be found to have unlike poles at its 
 ends. Assuming this to be true, is the pole at the end touched 
 by the magnet like or unlike the inducing pole ? 
 
 COLKMAN'S PHY. LAP.. MAN. 13 
 
194 MAGNETISM AND ELECTRICITY 
 
 How does the polarity of the magnetism induced in soft iron 
 account for its attraction by the magnet ? 
 
 e. Repeat the tests of paragraphs a and d using the piece of 
 steel instead of the soft iron. State the results and compare 
 them with those obtained with the iron. Account for the 
 differences. 
 
 IT. To study the magnetic action of magnetized filings 
 when arranged with tJieir like poles pointing in the same 
 direction, and when lying irregularly f to observe the effect 
 of twisting a magnetized wire. 
 
 a. Shake the filings away from the bottom of the test tube ; 
 then, with the tube in a horizontal position, jar them back by 
 gentle and repeated tapping of the bottom of the tube against 
 the north pole of the magnet. The filings are thus brought 
 into their new positions under the action of the north pole 
 of the magnet. 'The filings at the bottom of the test tube 
 should now repel one pole of the magnetic needle. If they 
 do, what is the polarity at this end of the tube ? If they do 
 not, repeat the experiment till successful. 
 
 Apply the same test to the filings again after thoroughly 
 shaking the tube. Remember that, where the magnetic action 
 is weak, repulsion is the only test for magnetism not induced 
 by the presence of the testing needle itself. 
 
 State and explain the result of the test. 
 
 b. Briefly discuss the experiment as an illustration of the 
 theory of magnetism. 
 
 c. Magnetize the long piece of wire by rubbing it from the 
 center to one end with one pole of the magnet and to the other 
 end with the other pole. Test the amount of magnetism de- 
 veloped in the wire by the quantity of filings that it will pick 
 up. Twist the wire both ways a few times, and again test its 
 magnetism. 
 
 How does the theory of magnetism account for the observed 
 effect of the twisting ? 
 
THE MAGNETIC FIELD 195 
 
 EXERCISE 65. THE MAGNETIC FIELD 
 
 References. Hoadley, 299-300 ; Carhart and Cluite, 374-376. 
 
 To study and to make maps of magnetic fields, show- 
 ing the shape and direction of the lines of force. 
 
 Apparatus. Magnetic needle suspended by a thread ; two 
 bar magnets ; piece of thick cardboard about 9 by 11 in. ; board 
 of the same size or larger, with parallel grooves, about an inch 
 apart, in which the magnets will lie flush with the surface ; 
 blue-print paper ; iron filings in pepper box or other sifter. 
 
 a. Move the magnetic needle around and over a pole of 
 a bar magnet upon the table. Observe the behavior of the 
 needle. Do the same at the other end of the magnet and 
 compare results. Move the needle over the magnet from end 
 to end, also along the sides of the magnet and beyond the ends ; 
 and observe the direction of the needle in all positions. 
 
 b. Place a magnet in a groove of the board. If blue-print 
 paper is provided, fasten a piece of it by means of rubber 
 bands to the cardboard with the prepared side up, and place it 
 over the magnet. Keep unused paper in the dark. Sprinkle 
 filings thinly and evenly over the paper, and gently tap the 
 card with the finger while holding it in place. 
 
 Move the magnetic needle about just above the paper. How 
 does it set itself with respect to the lines of filings ? 
 
 Why are these lines called lines of force ? 
 
 Lift the cardboard vertically from the magnet, and place it 
 in the sun for about three minutes. If the sun is not shining, 
 place it in the strongest daylight available for five minutes or 
 more. Return the filings to the box, and wash the paper im- 
 mediately by moving it about in clean water or letting water 
 run over it from the faucet for a few minutes. After it has 
 dried, fasten it in your notebook. If left to dry in the labora- 
 tory till the following day, write your name on it for identi- 
 fication. 
 
196 MAGNETISM AND ELECTRICITY 
 
 If blue-print paper is not provided, sprinkle the filings on 
 the cardboard and make a drawing of the magnet and its field 
 in your notebook, sketching in a number of the lines shown 
 by the filings. 
 
 c. In the same way make a blue print (or drawing) of the 
 magnetic field about two bar magnets placed parallel in the 
 grooves with like poles turned in the same direction. Mark 
 the poles N and S in the print or drawing. 
 
 Repeat with like poles in opposite directions. 
 Do you find in these prints lines of force connecting unlike 
 poles ? Do you find them connecting like poles ? 
 
 d. Place arrowheads on some of the lines of force in all 
 of the prints or drawings, pointing from the north pole. What 
 do these arrowheads denote ? (See references.) 
 
 EXERCISE 66. THE SINGLE-FLUID CELL 
 
 References. Hoadley, 346-351; Carhart and Chute, 428- 
 431 and 433-435 ; Sanford, pp. 281-282. 
 
 Apparatus. Two test tubes ; small pieces of zinc and cop- 
 per ; bottle of dilute sulphuric acid ; matches ; tumbler of dilute 
 sulphuric acid (about one part by volume of concentrated acid 
 to twenty parts of water) ; strip of copper and two of zinc, 
 one amalgamated, with a wire soldered to each strip ; wooden 
 block to hold the strips (Fig. 84) ; double connector; magnetic 
 needle. 
 
 I. To study the chemical action of dilute sulphuric 
 acid on zinc and copper. 
 
 a. Put a few pieces of zinc in a test tube and pour on them 
 a little sulphuric acid. Invert the other test tube over the 
 first to collect the gas liberated. Observe the action. After a 
 minute or two, remove the upper test tube, keeping it still in- 
 verted, and hold a lighted match to its mouth. There should 
 
THE SINGLE-FLUID CELL 
 
 197 
 
 be a small explosion, indicating the presence of a combustible 
 gas. This is hydrogen, which has been set free from the acid 
 by the zinc. Return the acid to the bottle and remove the 
 zinc. 
 
 b. Try the action of the acid on some pieces of copper in a 
 test tube. State the result. 
 
 II. To study the action of a simple voltaic cell with 
 unarnal^amated zinc; and to test the presence of a 
 current by its magnetic action on a compass needle. 
 
 a. Insert the strips of copper and unamalgainated zinc into 
 the slits of the supporting block and place them in the tumbler 
 of acid. (The darker piece of 
 zinc is the unamalgamated one.) 
 Avoid all metallic connections 
 between the strips. Observe for 
 a short time and record what 
 happens at the surface of each 
 strip. Avoid inhaling the escap- 
 ing gas, as it contains irritating 
 impurities. 
 
 6. Connect the copper and 
 zinc strips outside the cell by 
 means of the wire and connec- 
 tor. (Connections must always 
 be firmly made to the bare 
 wire. The current will not pass 
 through the insulation covering 
 the wire.) Observe and record 
 what happens at the surface of 
 each strip. Explain briefly after consulting the references. 
 
 c. Turn and bend the connecting wire so that a portion of it 
 is horizontal and extends north and south. Hold the magnetic 
 needle very close to this portion of the wire and just below it. 
 Observe whether the needle comes to rest in a different direc- 
 
 FIG. 84. 
 
108 MAGNETISM AND ELECTRICITY 
 
 tion when brought near the wire. , If there is a deflection of 
 the needle, it is evidence of an electric current in the wire. 
 How is the deflection of the needle affected by holding it just 
 above the wire ? Remove the zinc from the acid at once. 
 
 III. To study the action of a simple voltaic cell with 
 amalgamated zinc. 
 
 a. Place the amalgamated zinc in the cell instead of the 
 unamalgamated, and observe the action at its surface with the 
 wires disconnected. Compare with the action on unamalga- 
 mated zinc under the same conditions, and account for the dif- 
 ference. (See references.) 
 
 b. Connect the strips with a wire and observe what happens 
 at their surfaces. Compare with the results of II b. and 
 account for the difference. 
 
 c. Test the presence of a current in the wire by the de- 
 flection of the needle, as before. 
 
 Disconnect the wire and remove the strips from the acid. 
 
 EXERCISE 67. THE MAGNETIC EFFECTS OF A 
 CURRENT 
 
 References. Hoadley, 355 and 371-376 ; Carhart and Chute, 
 433-434, 441, and 452-458. 
 
 Apparatus. Magnetic needle (see Exercise 64) ; wire 
 rectangle of several turns and about 25 cm. in diameter 
 (Fig. 85) ; Grenet cell (or other cell that will furnish a current 
 of several amperes); cardboard; tangent galvanometer with- 
 out the needle (or a circular coil of 15 to 20 turns and about 
 15 cm. diameter) ; helix on cardboard and soft iron rod for core 
 (Fig. 87); electromagnet consisting of the core of the helix 
 and a long coil of small wire of about 200 turns wound on a 
 cardboard tube ; nail or other piece of iron ; two double con- 
 nectors. 
 
THE MAGNETIC EFFECTS OF A CURRENT 199 
 
 I. To find the shape and direction of the lines of force 
 of a current in a straight wire; and to find the relation 
 between the direction of the lines of force and the direc- 
 tion of the current. 
 
 a. Support the wire rectangle in a vertical plane extending 
 north and south, and connect it with the cell. If a Grenet 
 cell is used the circuit is closed by lowering the zinc into the 
 liquid. Keep the zinc out of the liquid as much as possible. 
 Place the cardboard in position around ,____ ,__ 
 one of the sides of the rectangle and 
 close the circuit. Sift filings upon the 
 cardboard, and tap it gently until the 
 filings are arranged in distinct lines. 
 
 Determine from the battery connec- 
 tions whether the current is flowing up 
 or down in the wires through the card- 
 board. (It flows through the wire from 
 the carbon to the zinc.) Use the mag- ' 
 netic needle to determine the direction 
 
 of the lines of force about the wire (the direction indicated by 
 the north pole of the needle). Raise the zinc. Draw a figure 
 in perspective, showing the direction of the current and the 
 lines of force. 
 
 6. Grasp the wire with the right hand, with the thumb ex- 
 tended and pointing in the direction in which the current was 
 flowing. Do the fingers point in the direction of the lines of 
 force round the wire or in the opposite direction ? Remember 
 this relation. It is called the right-hand rule. State it in full. 
 
 c. Close the circuit ; and, by means of the needle, determine 
 the direction of the lines of force about the opposite side of 
 the rectangle. Is their direction in agreement with the right- 
 hand rule ? 
 
 d. Observe the deflection of the needle when held just above 
 the upper side of the rectangle and when held just below it. 
 Are the deflections in agreement with the rule ? 
 
200 
 
 MAGNETISM AND ELECTRICITY 
 
 Several turns are used in the rectangle merely to intensify 
 the effect. With the same current, the magnetic field about a 
 single wire would be weaker, but otherwise the same. 
 
 II. To find the shape and direction of the lines of 
 force about a coil of wire in which a current is flow- 
 ing ; and to find the relation between tJie direction of the 
 cuwcnt and the direction of the lines of force at the 
 center of the coil- 
 
 a. Connect the cell to the two binding posts of the galva- 
 nometer between which all the turns of the coil are included. 
 Adjust the cardboard to the middle of the coil (Fig. 80), and 
 close the circuit. Sprinkle filings on the cardboard, and tap 
 with the finger. Determine with the needle the direction of 
 
 the lines of force through the 
 coil. Eaise the zinc. If pos- 
 sible, find from the galvanom- 
 eter and battery connections 
 and the winding of the coil 
 the direction of the current 
 through the coil. If the wind- 
 ing of the coil is not open to 
 view, find the direction of the 
 current 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 affect the relation expressed by the 
 rule.) Draw a figure in perspective showing the direction of 
 the current and the lines of force. Return the filings to 
 the box. 
 
 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 
 
 FIG. 
 
THE MAGNETIC EFFECTS OF A CURRENT 201 
 
 direction of the lines of force through the coil. Do the fingers 
 point in the direction of the current through the coil or in the 
 opposite direction ? State the rule in full. 
 
 III. To find the shape and direction of the lines of 
 force within and about a helijo ; and the relation betwee?i 
 the polarity of the helijo and the direction of the current 
 round it. 
 
 Pass the current through the helix on the cardboard, and 
 use filings to show the lines of force. Determine the direction 
 of the current round the helix from the battery connections, 
 and the polarity of the helix by means of the needle. (As the 
 
 FIG. 87. 
 
 field of the coil is weak, it should lie east and west to dis- 
 tinguish its action from that of the stronger field of the 
 earth.) Draw a figure in perspective showing the polarity of 
 the helix and the direction of the current. 
 
 Are the observed relations in agreement with the right-hand 
 rule for coils ? 
 
 IV. To jnalce an electromagnet and test its strength. 
 
 a. Again pass the current through the helix, and place the 
 soft iron core inside it. Study the field with filings and deter- 
 mine the polarity as before. What is the effect of the core ? 
 
 b. Connect the coil of the electromagnet to the battery and 
 insert the iron core. Test the strength of the electromagnet 
 
202' 
 
 MAGNETISM AND ELECTRICITY 
 
 thus formed. How does it compare in strength with the 
 permanent magnets previously used ? 
 
 Raise the zinc and return all filings to the box. 
 
 48. The Tangent of an Angle. In a right triangle the ratio 
 of one leg to the other is called the tangent of the angle opposite 
 
 to the first leg. Thus, in the 
 right triangle ABC (Fig. 88), 
 BC:AC is the tangent of 
 angle A, and AC: EC is the 
 tangent of angle E\ or, as 
 usually expressed, 
 
 tan A = BC: AC 
 FIG. 88. and tan B = AC : BC, 
 
 in which the abbreviation tan is used for tangent. 
 Since triangles' AB C and AB'C' are similar, 
 
 BC:AC=B'C':AC'', 
 and hence tan A = B'C' : AC'. 
 
 From which it will be seen that the tangent of an angle, like 
 its sine (Art. 41), is independent of the size of the triangle. 
 
 Draw right triangles with angle A of different sizes, the 
 largest near 90, and find whether the angle and its tangent 
 increase proportionally. The comparison is simplified by 
 making the side adjacent to the angle the same in all the 
 triangles. 
 
 As an angle increases (up to 90), which increases the faster, 
 its sine or its tangent ? 
 
 What is the tangent of 45 ? 
 
 As an angle approaches 90, what value does its tangent 
 approach ? 
 
 49. The Tangent Galvanometer. In Exercise 67 it was found 
 that the lines of force of the current in a tangent galvanometer 
 for circular coil) were approximately straight near the middle 
 
THE TANGENT GALVANOMETER 
 
 203 
 
 FlG 89 
 
 of the coil, where the needle of the instrument is placed, and 
 were at right angles to the plane of the coil. In using the 
 instrument it is always set with the plane of the coil in the 
 magnetic rneridan; hence, at the center of the coil, the lines of 
 force of the current are at right angles to those of the earth's 
 field. 
 
 In Fig. 89 let denote the center of the galvanometer coil, 
 ON the strength and direction of the earth's field, and OC 
 the strength and direction 
 
 of the field of the current N , *A N, ^A 
 
 in the coil. The direction 
 
 of the resultant of these 
 
 forces is OA\ which is 
 
 therefore the direction of 
 
 the resultant force upon 
 
 the north pole of the needle. Since the resultant force upon the 
 
 south pole is equal and opposite to that upon the north pole, 
 
 the needle will come to rest in the line OA. 
 
 Now suppose the strength of the field of the current to be 
 doubled (which would be the case if the current were doubled, 
 since a current is measured by its magnetic effect). ON re- 
 mains the same, as the earth's field is not changed. The angle 
 of deflection is increased, but is not doubled. In fact, if at 
 first OC is equal to ON, angle NO A is 45, and can never be 
 quite doubled however great OC may become. Clearly the 
 currents are not proportional to the deflections that they 
 produce. 
 
 Let C and C 1 denote two currents through the same number 
 of turns of the same galvanometer, and let OC and OC' 
 (or NA and NB, Fig. 90) denote the strengths of their fields 
 (at the center of the galvanometer). ON, as before, is the 
 strength of the earth's field. Then angles a and a' are the 
 deflections caused by C and C' respectively. 
 
 Since the currents are measured by their magnetic effects, 
 C : C 1 : : NA : NB. 
 
204 
 
 MAGNETISM AND ELECTRICITY 
 
 C 
 
 FIG. 90. 
 
 If the terms of the second ratio are divided by the same 
 quantity OJV, the value of the ratio is not altered j hence 
 
 r .^..NA.NB 
 
 "ON' ON 1 
 
 or C: C' : : tan a: tan a'. (1) 
 
 That is, the currents are proportional to the tangents of the 
 
 angles of deflection. This is why 
 the instrument is called a tangent 
 galvanometer. 
 
 To illustrate: A current (C) 
 causes a deflection of 50 and 
 another current (C") a deflection 
 of 25. By referring to the Table 
 of Tangents in the Appendix, 
 
 it is found that fan 50 = 1.19 and tan 25 = .466. 
 
 Hence C: C' : : 1.19 : .466; 
 
 from which C=2.55 C'. 
 
 While the tangent galvanometer may be thus used to com- 
 pare currents, it does not give their value in amperes (unless 
 provided with a calibrated tangent scale). The deflections can 
 be reduced to amperes ; but the methods by which this is done 
 lie beyond the scope of an elementary course. 
 
 Is the deflection affected by the strength of the magnetic 
 needle ? 
 
 EXERCISE 68. THE TANGENT GALVANOMETER 
 
 References. Hoadley, 356-357 and 382 ; Carhart and Chute, 
 460, 464-466, and 471-472 ; Slate, 230. 
 
 To learn to use a tangent galvanometer; and to find 
 the relation between the number of turns of the coil 
 through which the current is sent and the strength of 
 the magnetic field of the current. 
 
THE TANGENT GALVANOMETER 205 
 
 Apparatus. A tangent galvanometer with three different 
 connections (usually for 5, 10, and 15 turns of the coil) ; con- 
 stant cell (gravity or Daniell) ; wires for connections ; two 
 double connectors ; two " compensating coils " having resist- 
 ances equal respectively to 5 and 10 turns of the galvanometer 
 coil; another resistance coil, if necessary (see the experi- 
 ment). 
 
 [The coils are easily made by winding the necessary amount of wire 
 on spools. They serve the purpose better than a resistance box at this 
 stage of the work.] 
 
 a. Turn the galvanometer so that the ends of the pointer 
 attached to the needle (or the ends of the needle, if it does not 
 carry a pointer) stand as nearly as possible at zero. Tap the 
 galvanometer gently with the finger to overcome friction, which 
 might otherwise hold the needle in a wrong position. (Always 
 observe this precaution before ' reading a deflection.) When 
 adjusted as directed, the coil of the galvanometer will be in 
 the plane of the magnetic meridian. Care must be taken not 
 to disturb this adjustment during the exercise. 
 
 The three binding posts on the galvanometer make possible 
 three different connections by which the current is sent through 
 the number of turns of the coil marked on the base. Connect 
 the cell with the galvanometer so as to include all the turns 
 of the coil ; and, if necessary, introduce resistance into the cir- 
 cuit to prevent a deflection exceeding 65. Do not use the 
 " compensating coils " for this purpose. Any resistance intro- 
 duced here must be retained in the circuit throughout the exercise. 
 After tapping the galvanometer, read the position of both ends 
 of the pointer. In taking the reading, close one eye and look 
 vertically down upon the pointer with the other. E/ead to the 
 nearest .5. Keverse the connections with the galvanometer 
 (using the commutator, if one is provided), thus causing a 
 deflection in the opposite direction, and take readings as be- 
 fore. Take the average of these four readings as the true 
 deflection. 
 
206 
 
 MAGNETISM AND ELECTRICITY 
 
 b. Connect with the galvanometer so as to send the current 
 through the next small number of turns ; and, in addition to 
 the resistance previously included (if any), include the smaller 
 compensating coil, whose resistance is equal to the resistance 
 of the turns of the galvanometer coil that have been dropped 
 from the circuit. 
 
 The purpose of this adjustment is to keep the resistance of 
 the circuit the same as before. For a constant current is 
 required throughout the exercise, and this is furnished by a 
 constant cell (E.M.F. constant) through a constant resistance. 
 (See Ohm's law.) 
 
 Find the average deflection from four readings as before. 
 
 c. Connect with the smallest number of turns of the galva- 
 nometer, and replace the smaller compensating coil with the 
 larger, leaving the circuit otherwise unchanged. Determine 
 the deflection as,, before. 
 
 d. In order to test the constancy of the cell throughout the 
 exercise, connect again as for the first set of readings. If the 
 deflection is appreciably different from that first obtained, it 
 will be desirable to repeat the whole exercise if time permits. 
 If this is done, record both series of observations, and com- 
 pute the results called for from both. 
 
 Leave the cell disconnected. 
 
 FORM OF EECORD 
 
 
 
 DEFLECTION 
 
 
 
 
 
 No. OF 
 
 or POINTER 
 
 Av. DEFLEC- 
 
 TAN a 
 
 n -f- TAN a 
 
 
 
 E. end 
 
 W. end 
 
 
 
 
 a 
 
 
 
 N. 
 
 S. 
 
 
 
 
 
 
 S 
 
 N 
 
 
 
 
 b 
 
 
 
 N. 
 
 S_ 
 
 
 
 
 
 
 S. 
 
 N. 
 
 
 
 
 
 
 
 
 
 \r 
 
 
 
 
 
 
 
 S. 
 
 N. 
 
 
 
 
 
 
 
THE LAWS OF RESISTANCE 207 
 
 Discussion. From the Table of Tangents in the Appendix find 
 the tangents of the average deflections. The numbers in the 
 last column of the record are found by dividing the number of 
 turns used in each case by the tangent of the corresponding 
 deflection. These three quotients should be equal. If the 
 cell is fairly constant, the per cent of difference between the 
 greatest and the least of the quotients should not exceed 5%. 
 Compute it. 
 
 The equality of these quotients is expressed by the formula 
 
 n : tan a : : n' : tan a', 
 or, n : n' : : tan a : tan a 1 . 
 
 From this it follows that, for a constant current) the strength 
 of the field of the current is proportional to the number of 
 turns through which it flows. Compare this with the relation 
 
 C : C' : : tan a : tan a', 
 
 established in Art. 49. The latter relation holds when the cur- 
 rents are sent through the same number of turns of the coil. It 
 will be seen that the same effect (upon the field and the deflec- 
 tion) would be produced by doubling the number of turns 
 through which a given current is sent, or by sending twice 
 the current through the original number of turns ; and similarly 
 for an increase (or decrease) in any ratio. 
 
 EXEKCISE 69. THE LAWS OF KESISTAISTCE 
 
 References. Hoadley, 356-357 and 379-380; Carhart and 
 Chute, 460-462 and 464-466 ; Slate, 234-235. 
 
 Apparatus. A low-resistance galvanometer; constant cell; 
 board with wires (Fig. 91) ; sliding-contact piece ; meter rod ; 
 connecting wires. 
 
 [For the resistances, stretch on a long board, between binding posts, 
 three bare German silver wires of different sizes (Nos. 25 to 30 are suit- 
 able) and about a meter long, and 8 to 10 in. of insulated copper wire 
 of the same size as one of the German silver wires. Steel wire may be 
 
208 MAGNETISM AND ELECTRICITY 
 
 used instead of the German silver ; but it should be of smaller sizes or 
 longer, as its resistance is less. For ttte measurement or comparison of 
 resistances by substitution with a galvanometer of 15 turns and a gravity 
 or a Daniell cell, resistances between '2 and 6 ohms give the best results ; 
 and beyond a range of 1 to 10 ohms the probable error is large. For this 
 exercise and the following a tangent galvanometer is not essential. Any 
 low-resistance galvanometer that gives a suitable deflection may be used. 
 The sliding-contact piece may be any device similar to that used with a 
 slide-wire bridge. The diameters of the wires arid the length of the copper 
 wire should be accurately measured and recorded beside them.] 
 
 I. To observe the effect of length on the resistance of a 
 conductor. 
 
 Adjust the galvanometer. (See directions at the beginning 
 of Exercise 68.) Connect the cell with the 15 turns of the 
 galvanometer and with one end of one of the German silver 
 (or steel) wires. Complete the circuit as shown in Mg. 91, 
 
 using the sliding-contact piece 
 for the second connection 
 with the German silver wire. 
 (In diagrams a cell is usually 
 represented by two parallel 
 lines, as shown at C in the 
 figure, the short, heavy line 
 representing the zinc and the lighter and longer line the carbon 
 or copper. A galvanometer of any form is represented by a 
 circle with a short line at the center, representing the needle, 
 as at 6r.) Make contact at different places along the stretched 
 wire, and observe the effect upon the deflection of the gal- 
 vanometer needle. Explain. No readings or measurements 
 need be taken. 
 
 It is not possible by this method to determine the definite 
 relation between the resistance of a wire and its length, because 
 other resistances are necessarily included in the circuit, and 
 they too affect the strength of the current, In the remainder 
 of the exercise it will be assumed that the resistance of a wire 
 (of given size and material) is proportional to its length. 
 
THE LAWS OF RESISTANCE 209 
 
 II. To find the relative resistance of (reriYian silver and 
 copper. 
 
 a. Connect the cell and galvanometer in circuit with the 
 copper wire on the board. Tap the galvanometer and read 
 the deflection of one end of the pointer as nearly to a tenth 
 of a degree as possible. Kecord the length and diameter of 
 the wire and the deflection. 
 
 b. Substitute for the copper wire the German silver wire 
 of the same diameter, connecting as in Part I. The deflection 
 must be in the same direction as with the copper wire. Adjust 
 the sliding contact till the reading of the same end of the 
 pointer is exactly the same as before ; and measure the length 
 of German silver wire included in the circuit (that is, from the 
 end where connection is made to the sliding contact). 
 
 The resistance of this portion of the wire is equal to that 
 of the copper wire. Why ? 
 
 Why is it unnecessary to take the average of four readings 
 for the deflection, as in the preceding exercise ? 
 
 c. How many times greater than this would be the resistance 
 of a German silver wire of the same diameter and as long as 
 the copper wire ? This is the relative resistance of German 
 silver and copper as determined by your experiment. Com- 
 pare with the value given in Table XIII of the Appendix. 
 
 III. To find the relation between the area of the cross 
 section of a conductor and its resistance. 
 
 a. Include in the circuit the whole of the German silver 
 wire of largest diameter, and read the position of one end of 
 the pointer as accurately as possible. Record the deflection 
 and the length (^) and diameter (dj of the wire. 
 
 b. Substitute the next smaller German silver wire for the 
 first, using the sliding contact, and adjust the contact till the 
 deflection is the same as before. Eecord the diameter (c? 2 ) of 
 the wire and the length (7 2 ) included in the circuit. 
 
 c. Substitute the smallest wire and repeat. 
 
 PHY. LAB. MAN. 14 
 
210 MAGNETISM AND ELECTRICITY 
 
 FORM OF RECORD FOR PART III 
 
 
 LENGTHS OF 
 WIRE USED 
 
 DIAMETERS 
 OF WIRES 
 
 KATIO OF RESIST- 
 ANCES FOR EQUAL 
 LENGTHS (/ x ) 
 
 CROSS SECTIONS 
 OF WIRES 
 
 KATIO OF 
 CROSS SEC- 
 TIONS 
 
 a 
 
 ll = Cm. 
 
 di = mm. 
 
 
 a\ smin. 
 
 
 b 
 
 1 2 = 
 
 d. 2 = 
 
 r 2 :ri = 
 
 a 2 = 
 
 ai :a 2 = 
 
 c 
 
 h = 
 
 ^ 3 
 
 ,. 3 :ri = 
 
 3 = 
 
 di :a s = 
 
 Discussion. a. The lengths /j, 1 2 , and 1 3 of the three wires 
 have equal resistances. Why ? Let r denote this resistance. 
 
 b. Assuming that resistance is proportional to length, find 
 from these lengths how many times r t would be the resistance 
 of lengths of the second and third wires equal to that of the 
 first (7j). Let r 2 and r s respectively denote these resistances. 
 
 c. Let a ly a 2 , and a s denote the areas of the cross sections of 
 the wires. Compute them, (a = Trd 2 .) 
 
 d. Compute the ratios a-i : a 2 and a T : a s . 
 
 e. Test the proportionality of the ratios r 2 : n and % : a 2 ; 
 also the ratios r 3 : i\ and % : a s . Their difference is due to 
 experimental errors, and should riot exceed 5%. 
 
 /. State the relation in words, being careful to iiiclude in 
 the statement all the necessary conditions. 
 
 EXEECISE 70. MEASUREMENT OF EESISTANCE 
 
 References. The same as for Exercise 69. 
 
 To ineaswre the resistance of a conductor by the method 
 of substitution. 
 
 Apparatus. A low-resistance galvanometer ; constant cell ; 
 connecting wires ; resistance box ; two coils of unknown re- 
 sistance (from 3 to 6 ohms). 
 
 a. Adjust the galvanometer. Complete the circuit through 
 one of the coils whose resistance is to be measured and the 
 
MEASUREMENT OF RESISTANCE 211 
 
 fifteen turns of the galvanometer coil. Tap the galvanometer 
 gently, and read one end of the pointer as nearly to one tenth 
 of a degree as possible. A single reading for each adjustment 
 will be sufficient if, throughout the exercise, the same end of 
 the pointer is read and the connections are made so as to have 
 all the deflections in the same direction. 
 
 b. Remove the coil from the circuit, insert the resistance 
 box in its place, and remove plugs till the deflection is the 
 same as for the unknown resistance. While trying to get an 
 equal deflection with the resistance box, observe what is the 
 least resistance that will cause a visible change in the deflec- 
 tion ; and, by comparing this with the resistance to be measured, 
 estimate the probable accuracy of your result. 
 
 The total resistance in ohms introduced by the coils of the 
 box is the sum of the numbers at the places where the plugs 
 have been removed. This is equal to the unknown resistance. 
 Why ? 
 
 c. Measure in the same way the resistance of the other coil. 
 
 d. Measure in the same way the resistance of the two coils, 
 connected so that the whole current passes through the two 
 coils in succession. (This is called connecting in series.) The 
 resistance of the two coils in series is the sum of their separate 
 resistances. This will serve as a test of the accuracy of your 
 results. Even with careful experimenting, the error may be 
 as great as 6%. If it exceeds this limit and time permits, 
 repeat the experiment. 
 
 This method of measuring resistance is instructive; but 
 other methods are used where accuracy is required. 
 
 50. Let C denote the current that an electromotive force E 
 sends through a (total) resistance R, and C' the current that 
 the same electromotive force sends through a resistance IV \ 
 then, by Ohm's law, 
 
212 MAGNETISM AND ELECTRICITY 
 
 Dividing the members of the first equation by the corre- 
 sponding members of the second gives 
 
 (L^HL^E-^w 
 
 C'~ R '' R'~ R' 
 or C:C'::R':R. (1) 
 
 This means that the current due to a given E.M.F. is 
 inversely proportional to the resistance of the entire circuit 
 (including the resistance of the battery). 
 
 It is sometimes necessary, as in the following exercise, to 
 consider separately the different parts of the total resistance 
 of the circuit. Let r denote the resistance of the battery 
 (internal resistance), g the resistance of the galvanometer, 
 and R the remainder of the external resistance. With the 
 resistance thus denoted in parts, Ohm's law takes the form 
 
 C- E 
 
 (R + r + g)' 
 
 and (1) becomes 
 
 (2) 
 
 If a and a' are the deflections caused by the currents C and 
 C' respectively, then 
 
 C : C' : : tan a : tan a'. (Art. 49.) (3) 
 
 Hence, from (2) and (3), 
 
 (R 1 -h r 4- g) : (R + r + g) : : tan a : tan a'. (4) 
 
 Note the fact that this is an inverse proportionality, and 
 that it is true only for a constant E.M.F. 
 
 EXERCISE 71. THE RESISTANCE OF A CELL 
 
 To find the resistance of a constant cell (gravity or 
 Daniell} by the method of reduced deflection. 
 
 Apparatus. A tangent galvanometer of low resistance ; 
 gravity or Daniell cell ; resistance box. 
 
THE RESISTANCE OF A CELL 
 
 213 
 
 a. Adjust the galvanometer, and connect it in circuit with 
 the cell and the resistance box. Connect with the number of 
 turns of the galvanometer that gives a deflection nearest to 
 50 to 60 when no resistance is introduced in the box, and use 
 only this connection throughout the exercise. 
 
 Let g denote the resistance of the number of turns of the 
 galvanometer used, and record its value as given you. Let r 
 denote the (unknown) resistance of the cell ; R, R', and R" 
 the resistances successively introduced in the resistance box ; 
 and a, a', and a" the corresponding average deflections of the' 
 galvanometer. The resistance of the connecting wires may be 
 neglected. 
 
 With no resistance introduced in the box (R = 0)., read the 
 position of both ends of the pointer as accurately as possible; 
 reverse the current (using the commutator, if one is provided) 
 and read again. 
 
 Repeat with R' = 2 ohms and again with R" = 4 ohms. 
 
 b. The resistance of the cell can be computed by substi- 
 tuting in (4) of Art. 50 any two pairs of values of tana and R 
 and the value of g, and solving for r. 
 
 Compute r from a, a', R, and R'. 
 
 c. Compute r from a, a", R, and R". 
 
 d. Compute r from a', a", R', and R 1 '. 
 
 e. These three independent determinations of r should agree 
 within 5 %. Find the greatest per cent of difference between 
 them. 
 
 FORM OF RECORD 
 
 Box RE- 
 
 
 DEFLECTION 
 
 OF POINTE 
 
 a 
 
 AVERAGE 
 
 
 SISTANCE 
 
 E. end 
 
 W. end 
 
 E. end 
 
 W. end 
 
 DEFLECTION 
 
 
 R 
 
 N 
 
 05 
 
 <^ 
 
 N' 
 
 
 
 E' 2 
 
 
 
 
 
 a 
 
 
 R" 4 
 
 
 
 
 
 n tl 
 
 
 
 
 
 
 
 
 
21 I MAGNETISM AND ELECTRICITY 
 
 51. Let C denote the current that an electromotive force E 
 sends through a (total) resistance R, and C' the current that 
 an electromotive force E' sends through the same resistance; 
 
 then (7 = | and C'=^- 
 
 H K 
 
 From which 
 
 C:C'::E:E' (1) 
 
 That is, /or a constant resistance, the current is proportional 
 to the E. M. F. 
 
 From this and equation (1) of Art. 49 it follows that 
 
 E : E' : : tan a : tan a 1 . (2) 
 
 Thus, if two batteries are separately connected with a tan- 
 gent galvanometer and the total resistance of the two circuits 
 is the same, the E.M.F. of the two batteries will be proportional 
 to the tangents of the angles of deflection. 
 
 EXEECISE 72,. THE ELECTROMOTIVE FOKCE OF 
 
 CELLS 
 
 References. Hoadley, 381 and 394 ; Carhart and Chute, 465. 
 
 To find the electromotive force of cells by the method 
 of constant resistance. 
 
 Apparatus. A tangent galvanometer of high resistance ; 
 gravity or Daniell cell ; one or more cells for the measurement 
 of their E.M.F. 
 
 [The galvanometer should have a resistance of at least 100 ohms ; the 
 greater the better. The E.M.F. of the gravity or Daniell cell should be 
 determined with a voltmeter by the teacher from day to day, and marked 
 on the cell. ] 
 
THE ELECTROMOTIVE FORCE OF CELLS 
 
 215 
 
 a. Adjust the galvanometer, and pass the current from the 
 gravity or Daniell cell through it. Read both ends of the 
 pointer, reverse the current and again read. Record the E.M.F. 
 of the cell. 
 
 Find in the same way the deflection caused by each of the 
 other cells provided. 
 
 b. The resistance of the galvanometer is very large compared 
 with the other resistances of the circuit ; hence the difference 
 in the resistances of the cells may be neglected, and the total 
 resistance of the circuit may be regarded as constant through- 
 out the exercise. 
 
 Hence the E.M.F. of each of the cells can be computed by 
 substituting in (2), Art. 51, the tangent of the deflection caused 
 by it (tan a') and by the cell of given E.M.F. (tan a) and the 
 E.M.F. (E) of the latter. 
 
 FORM OF RECORD 
 
 KIND OF CELL 
 
 DEFLECTION 
 
 Av. DEFLEC- 
 TION (a) 
 
 TAN a 
 
 E.M.F. 
 
 E. end 
 
 W. end 
 
 Gravity 
 
 N. 
 
 S. 
 
 
 
 
 
 S. 
 
 N 
 
 
 
 f re\ c\v\\ 
 
 
 
 
 \ given; 
 
 Leclanche" 
 
 N. 
 
 S. 
 
 
 
 
 
 S. 
 
 N. 
 
 
 
 
 
 
 
 52. Let E be the E.M.F. that sends a current C through 
 a resistance R, and E 1 the E.M.F. that sends an equal current 
 through a resistance R' ; then 
 
 r _E_E' 
 -- 
 
 Hence E:E'::R:R' (1) 
 
 This means that, to maintain a given current, the E.M.F. 
 must be proportional to the resistance. 
 
21(3 MAGNETISM AND ELECTRICITY 
 
 EXERCISE 72 2 . THE ELECTROMOTIVE FORCE OF 
 
 CELLS 
 
 References. Hoadley, 381 and 394 ; Carhart and Chute, 465. 
 
 To find tlw electromotive force of cells by tlie method 
 of equal deflections. 
 
 Apparatus. A high-resistance galvanometer (not neces- 
 sarily a tangent instrument) with its resistance marked on 
 it, or an astatic galvanometer of low resistance , 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. 
 
 a. Adjust the galvanometer and connect with the gravity or 
 Daniell cell, including the resistance box in the circuit ; but 
 before closing the circuit introduce a high resistance in the 
 box to avoid the danger of passing too large a current through 
 the galvanometer. Adjust the resistance in the box so that 
 the deflection is between 40 and 50, and read one end of the 
 pointer as accurately as possible. 
 
 Let R denote the resistance introduced in the box, and g the 
 resistance of the galvanometer. If R -f- g is more than 100 
 ohms, the battery resistance may be neglected. 
 
 b. Substitute another cell for the one just used, and adjust 
 the resistance in the box so that the deflection of the same 
 end of the pointer in the same direction is equal to the first 
 deflection. 
 
 Let R' denote the resistance introduced in the box, and E' 
 the E.M.F. of the cell ; then, since the currents were equal, we 
 have from (1), Art. 52, 
 
 From which compute the E.M.F. of the cell. 
 
 c. Find in the same way the E.M.F. of the other cells 
 
 provided. 
 
ARRANGEMENT OF CELLS 
 
 217 
 
 FORM OF RECORD 
 
 Deflection for each adjustment = - 
 Resistance of galvanometer (g) = ohms 
 
 KIND OF CELL 
 
 Box RESIST- 
 ANCE (H) 
 
 R+g 
 
 E.M.F. 
 
 Gravity 
 Leclanch, etc. 
 
 
 
 
 
 
 
 
 
 
 EXERCISE 73. ARRANGEMENT OF CELLS 
 
 References. Hoadley, 358-362; Carhart and Chute, 467- 
 470 ; Sanf ord, pp. 318-319. 
 
 To find when cells should be connected in parallel and 
 when in series to obtain the larger current. 
 
 Apparatus. A tangent galvanometer of low resistance ; two 
 gravity or Daniell cells (as nearly alike as possible in E.M.F. 
 and resistance) ; resistance box ; two double connectors ; con- 
 necting wires. 
 
 a. Connect one of the cells with the resistance box and 
 ten turns of the galvanometer coil, after adjusting the galva- 
 nometer. Throughout the exercise make connections for de- 
 flection in the same direction, and read the same end of the 
 pointer. If care is taken not to disturb the position of 
 the galvanometer, this single reading of each deflection (to 
 the nearest degree) will be sufficient. 
 
 Read the deflections for resistances of 0, 1, 2, 4, 10, and 
 20 ohms in the resistance box. 
 
 b. Substitute the other cell and repeat. If, however, the 
 deflections with the second cell are within one or two degrees 
 of the first, this part may be omitted. 
 
218 
 
 MAGNETISM AND ELECTRICITY 
 
 c. Repeat with the same series* of resistances and the two 
 cells in parallel. Make a diagram of the connections. 
 
 d. Repeat with the cells in series. Make a diagram of the 
 connections. 
 
 FORM OF RECORD 
 
 
 DKKLECTION WITH 
 
 
 DEFLECTION FOR CELLS 
 
 
 
 AV. FOR THE 
 
 
 
 
 
 Two CELLS 
 
 
 
 
 ONE CULL 
 
 OTHER CELL 
 
 
 Ix PARALLEL 
 
 IN SKUIF.S 
 
 Q 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 etc. 
 
 
 
 
 
 
 
 
 TANGENTS FOR CELLS 
 
 
 TAXGEXT OF AVERAGE OF 
 
 
 
 SINGLE CELL 
 
 
 
 
 
 IN PARALLEL 
 
 IN SERIES 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 
 etc. 
 
 
 
 
 Discussion. a. If the deflections were found for both cells 
 separately, find their average deflection for each resistance. 
 Find the tangents of these average deflections and of the 
 deflections with the cells in parallel and in series, and record 
 as indicated. 
 
 b. Since the currents are proportional to the tangents of the 
 deflections, the relative advantage of joining the cells in series 
 and in parallel for the different resistances is shown at once by 
 the tangents. 
 
 Within what limits does connection in parallel give the 
 larger current? 
 
INDUCED CURRENTS 219 
 
 c. Does the advantage of connection in series become more 
 or less marked as the external resistance is increased ? 
 
 d. Let r denote the resistance and E the E.M.F. of each of 
 the cells, R the external resistance, and C the current. Using 
 these letters, write the formula for the current, (1) when the 
 two cells are connected in parallel ; (2) when they are con- 
 nected in series. 
 
 With the aid of these formulas show : 
 
 e. Why two cells in series are but little better than one 
 when the external resistance is a small fraction of an ohm. 
 
 /. Why two cells in parallel are but little better than one 
 when the external resistance is 20 ohms. 
 
 g. Why two cells in series give nearly twice the current 
 through 20 ohms that a single cell does. 
 
 EXEKCISE 74. INDUCED CURRENTS 
 
 References. Hoadley, 397 ; Carhart and Chute, 480-482 ; 
 Slate, 232 ; Sanford, p. 291. 
 
 Apparatus. An astatic or D'Arsonval galvanometer ; in- 
 duction coil with movable primary and iron core ; bar magnet ; 
 connecting wires. 
 
 [With a high-resistance induction coil a D' Arson val or an astatic 
 galvanometer of high resistance gives the best results. For a low-resist- 
 ance coil a low-resistance astatic galvanometer is best.] 
 
 I. To find the direction of the current induced in a 
 coil of wire by inserting into it or withdrawing either 
 pole of a bar magnet. 
 
 a. Only very small currents should be sent through an 
 astatic or a D'Arsonval galvanometer; otherwise the action 
 on the needle is violent, and the instrument may be damaged. 
 Since the galvanometer is to be used to determine the direc- 
 tion of the induced currents as well as to detect their presence, 
 it is necessary first to determine what the direction of the 
 
220 MAGNETISM AND ELECTRICITY 
 
 deflection will be for a current of known direction. With 
 an astatic galvanometer this can be done by applying the 
 right-hand rule, if the connections and the direction of winding 
 are open to view. Otherwise, proceed as follows : Send a 
 current from one cell through a meter or more of wire, and 
 
 connect the galvanometer as a shunt 
 between two points a few centi- 
 meters apart on this circuit (A and 
 B y Fig. 92). If necessary, increase 
 the distance AB till there is a 
 visible deflection. Note its direc- 
 tion, and find from the connections which is the positive post 
 of the galvanometer. If the current entered by the other post, 
 the current would of course be reversed. Hence, in the fur- 
 ther work, the direction of the deflection will indicate which 
 is the positive post of the galvanometer; and from this the 
 direction of the current can be traced through the entire 
 circuit. 
 
 &. Adjust the galvanometer and connect it 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 watching the galvanometer needle. 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 magnet. Test this by inserting and withdraw- 
 ing the magnet with the circuit broken.) 
 
 From the direction of the deflections, determine the direc- 
 tion of the current round the coil (clockwise or counter clock- 
 wise, as you look down upon it), (1) when the north pole of 
 the magnet is inserted ; (2) when it is removed. 
 
 Is there a current when the magnet is at rest within the 
 coil? 
 
INDUCED CURRENTS 221 
 
 c. Applying the right-hand rule, find the polarity of the 
 coil due to the current, (1) when the north pole is inserted ; 
 (2) when it is removed. 
 
 d. Does the magnetic field due to the current aid or oppose 
 the insertion and removal of the magnet ? 
 
 e. The induced current that would magnetize the magnet 
 with its existing polarity is called direct, and the opposite 
 current indirect or inverse. Is the current direct or inverse, 
 (1) on inserting the north pole ? (2) on removing it ? 
 
 /. Eepeat the experiment, inserting and removing the south 
 pole ; and answer the preceding questions for this case. 
 
 II. To find the direction of the current induced in a 
 coil of wire by inserting or withdrawing the north pole 
 of another coll in which a current is flowing ; and to find 
 the direction of the induced current when the current in 
 the inner coil is started and when it is stopped. 
 
 a. If more than one cell is provided, connect them in paral- 
 lel, and send the current through the smaller coil (called the 
 primary) in the direction that makes the lower end of it a 
 north pole. The galvanometer is to be left connected with 
 the secondary coil as before. 
 
 Determine, from the deflection of the needle, the direction 
 of the current in the secondary coil, (1) when the north pole of 
 the primary is inserted into it; (2) when it is removed. 
 
 6. A current in the secondary coil in the same direction as 
 that in the primary is called direct, and a current in the 
 opposite direction is called inverse. Is the induced current 
 direct or inverse, (1) when the coil is inserted ? (2) when it 
 is removed ? 
 
 c. With a primary coil at rest in the secondary, study the 
 currents induced, (1) when the circuit is closed through the 
 primary ; (2) when it is broken. (Make and break the circuit 
 by touching the connecting wire to one of the binding posts 
 and removing it.) 
 
2*22 MAGNETISM AND ELECTRICITY 
 
 Compare the directions of the, induced currents with the 
 directions of the currents induced when the primary coil was 
 inserted and removed. 
 
 d. Repeat the work of paragraph c with the iron core within 
 the primary coil. State the results and account for the effect 
 of the core. 
 
 Discussion. a. State the different ways in which you ob- 
 tained, (1) an inverse induced current; (2) a direct induced 
 current. 
 
 b. In whatever way produced, the inverse induced current 
 is due to an increase in the number of lines of force within 
 the coil, and the direct induced current to a decrease in them. 
 When the number of lines of force within the coil is increas- 
 ing, is the direction of the induced current clockwise or counter 
 clockwise to an observer looking at it in the direction of the 
 lines of force (that is, in the direction in which the north pole 
 of the magnet or primary coil points) ? 
 
 What is the direction of the induced current to such an 
 observer when the number of lines of force within the coil is 
 decreasing ? 
 
 These relations find application in the study of the dynamo 
 and motor, and should be remembered. 
 
 c. What is the source of the energy of the currents induced 
 by the magnet ? (See the question of I d. for a suggestion.) 
 
 EXERCISE 75. THE MOTOR 
 
 References. Hoadley, 406-415 and 439 ; Carhart and Chute, 
 494-500. 
 
 Apparatus. Small motor, preferably one that can readily 
 be taken apart and put together again (Fig. 93) ; one or more 
 cells as needed ; magnetic needle. 
 
 I. To study the construction and action of a small 
 inotor. 
 
THE MOTOR 
 
 223 
 
 FIG. 93. 
 
 a. Starting at either of the binding posts of the motor, trace 
 the circuit through the coil of the field magnet and through 
 the armature to the other 
 
 post. If the coils of the 
 field magnet and armature 
 are connected in series, the 
 motor is said to be series 
 wound; if they are con- 
 nected in parallel, it is 
 shunt wound. Is this motor 
 shunt or series wound ? 
 
 b. Connect the battery 
 with the motor, and note 
 by which binding post the 
 current enters it. While 
 the motor is running, note 
 
 the direction of rotation, and determine the polarity of the field 
 magnet with the magnetic needle. Is the relation between its 
 polarity and the direction of the current in its coil in agree- 
 ment with the right-hand 
 rule? 
 
 c. Disconnect the bat- 
 tery. If Grenet cells are 
 used, raise the zincs. 
 Study carefully the action 
 of the commutator ; and 
 determine the direction 
 
 FIELD MAGNET WIRE 
 
 ARMATURE WIRE 
 
 PULLEY TUBES FOR 
 
 FIG. 94. 
 
 which the current is reversed, 
 covered. 
 
 the coils of the armature 
 and the polarity of its 
 core during one complete 
 rotation, noting particu- 
 larly the positions in 
 State briefly the facts dis- 
 
224 MAGNETISM AND ELECTRICITY 
 
 d. From the polarity of the poles of the armature (that is, 
 the cores of the armature coils) in different positions about the 
 axis, account for the rotation of the armature. 
 
 e. Draw a simplified diagram of the motor showing the 
 direction of the current in the coils of the field magnet and 
 armature, the polarity of the field magnet and of the poles of 
 the armature, and the direction of rotation. 
 
 /. Connect the battery with the motor so that the current in 
 it is reversed with respect to its first direction. Is the direc- 
 tion of rotation reversed ? Explain. 
 
 II. To take a small inotor apart and put it together 
 again. 
 
 If the motor is dissectable, let the student take it apart and 
 put it together again ; or, beginning with it taken apart, let 
 him put it together, following directions adapted to the motor 
 provided or following as a model a similar motor, finished 
 (one of which will serve for several students). 
 
 EXERCISE 76. THE ELECTEIC BELL AKD 
 THE TELEGRAPH 
 
 References. Hoadley, 418-425 ; Carhart and Chute, 507-515. 
 
 I. To study the construction and action of an electric 
 bell. 
 
 Apparatus. An electric bell with rubber tubing on the clap- 
 per to deaden the sound ; push button ; a Leclanche battery. 
 
 a. Trace the circuit from the battery through the several 
 parts of the bell and the push button to the battery again. 
 The metal frame of the bell commonly forms a part of the 
 circuit. Does it in this bell ? Look carefully for insulation 
 that compels the current to cross where the spring that carries 
 the armature touches the end of a screw. 
 
 b. Unscrew the cap of the push button and study its con- 
 struction. Describe it. 
 
THE ELECTRIC BELL AND THE TELEGRAPH 225 
 
 c. Connect the battery to the bell and ring it. Observe the 
 sparks at the point where the spring touches the screw. What 
 causes them ? 
 
 Why would the bell not ring if the current did not cross at 
 this point ? 
 
 Briefly explain the action of the bell in connection with a 
 simplified drawing showing the actual connections as you find 
 them. 
 
 II. To set up a telegraph line and study the construc- 
 tion and action of the instruments. 
 
 Apparatus. A complete telegraph line. 
 
 a. Connect up the local circuits and the line circuit, with 
 the aid of the figure in the text or a reference book. If the 
 connections are already made, trace them out. Find the insula- 
 tion in the key which keeps the circuit open except when the 
 lever is depressed or the switch closed. Find the insulation 
 in the relay which keeps the local circuit open when the line 
 circuit is open. 
 
 b. Observe that the line battery is in two sections, one at 
 each end of the line. Which poles of the two sections must 
 be connected together ? Why ? 
 
 Make a simplified diagram of the local and line circuits just 
 as you find them, including the instruments and batteries. 
 
 c. Open the switch at one end of the line and operate it, at 
 the same time observing the action of the sounder and the 
 relay ; another student also observing the action of the instru- 
 ments at the other station. Now let the other student operate 
 the key at his station, both observing as before. 
 
 d. Try to operate the line with both switches open. Ac- 
 count for your success or want of success. If gravity cells 
 are used, leave the switches closed when you have finished ; if 
 other cells are used, leave the switches open. 
 
 e. Write a brief statement of the action and use of the key, 
 sounder, and relay, and the use of the local and line batteries. 
 
 COLEMAN'S PHY. LAB. MAN. 15 
 
22l> MAGNETISM AND ELECTRICITY 
 
 EXERCISE 77. THE TELEPHONE 
 
 References. Hoadley, 429-431; Carhart and Chute, 520- 
 522, 
 
 I. To study the construction and action of a telephone 
 receiver, and the action of a telephone line consisting of 
 two receivers. 
 
 Apparatus. A sensitive, high-resistance galvanometer 
 (astatic or D'Arsonval) ; two telephone receivers connected 
 with long wires ; tuning fork ; rubber mallet. 
 
 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 ma- 
 terial is it ? 
 
 b. Connect the receiver with the galvanometer. Place the 
 disk in position on the receiver and press it lightly at the 
 center with the finger so as to bring it nearer to the magnet. 
 If the galvanometer indicates a current, account for it. 
 
 c. Connect the two receivers with long wires. This is the 
 original form of the Bell telephone, and is the simplest tele- 
 phone line. Let one student lightly touch the stem of a 
 sounding tuning fork to the disk of one receiver while another 
 listens at the other receiver. Try speaking to one another, 
 using the receivers alternately as receiver and transmitter. 
 
 Explain the action of such a telephone line. 
 
 II. To study the construction and action of a micro- 
 phone. 
 
 Apparatus. A telephone receiver; galvanic cell; two bat- 
 tery or electric light carbons ; microphone ; tuning fork ; 
 rubber mallet. 
 
 a. Connect the pieces of carbon, the receiver, and the bat- 
 tery, as shown in Fig. 95, so that the circuit is completed by 
 
THE TELEPHONE 
 
 227 
 
 touching the carbons together. Place the receiver to the ear, 
 and rub one carbon lightly upon the other. The receiver 
 should give out a loud, 
 rattling sound. The re- 
 sistance at the points of 
 contact of the carbons 
 varies with the pressure. 
 How does this account 
 for the sounds from the 
 receiver ? Draw a dia- 
 gram of the apparatus. 
 
 In this experiment the 
 pieces of carbon play the part of a microphone or the trans- 
 mitter of a telephone. 
 
 b. The microphone shown in Fig. 96 is a simplified trans- 
 mitter together with an induction coil and receiver. Complete 
 
 FIG. 95. 
 
 FIG 
 
 the battery circuit through the primary coil and the trans- 
 mitter. Connect the receiver with the secondary coil. 
 
228 MAGNETISM AND ELECTRICITY 
 
 A simpler form of microphone has no induction coil. If one 
 of this type is provided instead of one like the figure, connect 
 the receiver in the battery circuit with the microphone. 
 
 Hold the receiver to the ear, and tap lightly upon the base 
 of the microphone or rub the finger over it. Touch a vibrating 
 tuning fork to it. Listen to a watch lying on the microphone. 
 
 Draw a figure of the microphone and explain its action. 
 
 III. To study tlie construction and action of a com- 
 plete telephone line. 
 
 Apparatus. A telephone line consisting of two telephones 
 made for laboratory use. 
 
 The principles of the telephone have been covered by the 
 preceding experiments. The rest is a matter of detail of con- 
 struction, in respect to which telephones differ greatly from 
 one another. Study in detail the laboratory telephone line, 
 including the points covered by the following directions : 
 
 a. Trace out the connections by which the bell is included 
 in the line circuit when the receiver is on the hook. 
 
 Trace the circuit when the button is pushed to ring the bell 
 of the other telephone. Is the bell of either telephone rung by 
 the battery of the same or the other telephone ? 
 
 b. With the receiver off the hook, trace, (1) the local circuit 
 through the transmitter and the primary coil ; (2) the line 
 circuit through the secondary coil and the receiver. 
 
 c. 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. 
 Write a brief description of this telephone line, and explain 
 its operation, including any points not covered by the directions. 
 
APPENDIX 
 
 TABLE I 
 
 DENSITIES IN GRAMS PER CUBIC CENTIMETER 
 
 Aluminum . 
 
 2.67 
 
 Alcohol (95%) . 
 
 .82 
 
 Antimony, cast . 
 
 6.7 
 
 Blood 
 
 1.06 
 
 Beeswax 
 
 .96 
 
 Carbon di sulphide . 
 
 1.29 
 
 Bismuth, cast 
 
 9.8 
 
 Chloroform 
 
 1.5 
 
 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 C. 
 
 13.596 
 
 Glass, crown 
 
 2.5 
 
 Milk . - . 
 
 1.03 
 
 Glass, flint . 
 
 3 to 3.5 
 
 Nitric acid 
 
 1.5 
 
 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.) . 
 
 1.000 
 
 Lead . 
 
 11.3 to 11.4 
 
 Water, sea 
 
 1.026 
 
 Marble 
 
 2.72 
 
 
 
 Mercury, at C. 
 
 13.596 
 
 GASES AT C. AND 76 CM. 
 
 Platinum . 
 
 21.5 
 
 PRESSURE 
 
 
 Quartz 
 
 2.65 
 
 
 
 Silver . 
 
 10.4 to 10.5 
 
 Air ... 
 
 .001293 
 
 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 
 
 
 229 
 
 
230 
 
 APPENDIX 
 
 TABLE II 
 DENSITY OF WATER AT VARIOUS TEMPERATURES 
 
 TEMPERATURE 
 
 DENSITY 
 
 TEMPERATURE 
 
 DENSITY 
 
 . 
 
 .99987 
 
 16 . 
 
 .99900 
 
 4 . 
 
 1.00000 
 
 20 . 
 
 .99826 
 
 8 . 
 
 .99989 
 
 50 . 
 
 .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 
 15 
 12 
 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 . 
 Hardwood 
 
 TABLE V 
 COEFFICIENT OF CUBICAL EXPANSION 
 
 Acetic acid 
 Alcohol (5 to 6) . 
 Alcohol (49 to 50) 
 Ether 
 Glycerine . 
 Mercury . 
 
 .00105 Olive oil. 
 
 .00105 Petroleum 
 
 .00122 Turpentine . 
 
 .0015 Water (5 to 6) . 
 
 .0005 Water (49 to 50) . 
 
 .0001 8 Water (99 to 100) 
 
 2 
 
 0.2 
 
 0.15 
 
 0.14 
 
 0.05 
 
 0.01 
 
 0.007 
 
 .000012 
 
 .000028 
 
 .0000088 
 
 .000019 
 
 .000006 
 
 .0008 
 
 .0009 
 
 .0007 
 
 .000022 
 
 .00046 
 
 .00076 
 
APPENDIX 
 
 231 
 
 
 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 . 
 
 
 
 Sulphur 
 
 . 115 
 
 Iridium . 
 
 . 1950 
 
 Tin . 
 
 . 230 
 
 Iron, cast 
 
 . 1100 to 1200 
 
 Wax, white 
 
 65 
 
 
 TABLE VII 
 
 
 
 BOILING POINTS 
 
 
 Acetic acid 
 
 . 117 C. 
 
 Water . 
 
 100 C. 
 
 Alcohol, ethyl 
 
 . 78.4 
 
 Air 
 
 . -191 
 
 Alcohol, methyl 
 
 . 66 
 
 Ammonia . 
 
 . -39 
 
 Ether . 
 
 . 34.9 
 
 Carbon dioxide . 
 
 . -78 
 
 Mercury . 
 
 . 357 
 
 Hydrogen . 
 
 . -238.5 
 
 Sulphur . 
 
 . 447 
 
 Nitrogen 
 
 . -194.5 
 
 Sulphuric acid 
 
 . 325 
 
 Oxygen 
 
 . -182 
 
 
 TABLE VIII 
 
 
 
 SPECIFIC HEATS 
 
 
 Alcohol (0 to 50) 
 
 . .615 Iron 
 
 . .114 
 
 Aluminum (15 to 
 
 97) . .21 
 
 Lead . . . 
 
 . .031 
 
 Brass . 
 
 . .094 
 
 Marble . 
 
 . .21 
 
 Copper . 
 
 . .095 
 
 Mercury 
 
 . .033 
 
 Ether . 
 
 . .52 
 
 Silver . 
 
 . .056 
 
 Glycerine 
 
 . .55 
 
 Steel . 
 
 . .118 
 
 Glass . 
 
 . .19 
 
 Turpentine . 
 
 . .426 
 
 Ice 
 
 .504 
 
 Zinc 
 
 .094 
 
232 
 
 APPENDIX 
 
 TABLE IX 
 LATENT HEATS OF FUSION 
 
 Beeswax 
 Ice 
 
 Lead . 
 Mercury 
 
 Alcohol . 
 Ether . 
 Mercury 
 
 Brass 
 
 Glass 
 
 Granite 
 
 Iron 
 
 Lead 
 
 Oak 
 
 Steel 
 
 Air . 
 
 Alcohol 
 
 Canada balsam 
 
 Carbon bisulphide 
 
 Diamond . 
 
 Ether 
 
 Glass, crown . 
 
 Glass, flint 
 
 Glycerine . 
 
 CALORIES 
 
 
 CALORIKS 
 
 . 97 
 
 Silver . 
 
 . 21.07 
 
 . 79.25 
 
 Sulphur 
 
 . 9.37 
 
 5.37 
 
 Tin . 
 
 . 14 9 5 
 
 2.83 
 
 Zinc . 
 
 , 28.13 
 
 TABLE X 
 
 LATENT HEATS OF VAPORIZATION 
 
 CALORIES 
 
 . 208 
 
 . 90 
 
 62 
 
 Sulphur 
 Turpentine 
 Water . 
 
 CALORIES 
 
 . 362 
 
 . 74 
 
 536 
 
 TABLE XI 
 VELOCITY OF SOUND IN METERS PER SECOND 
 
 3394 
 
 4965 to 5564 
 
 1664 
 
 5016 to 5127 
 
 1319 to 1368 
 
 3287 to 3991 
 
 4768 to 5016 
 
 GASES AT 
 Air .... 
 Carbon dioxide . 
 Hydrogen . 
 Oxygen 
 
 TABLE XII 
 INDICES OF REFRACTION 
 
 1.000294 Ice 
 
 1.36 Iceland spar, ordinary ray . 
 
 1.54 Iceland spar, extraordinary 
 
 1.68 ray .... 
 
 2.47 to 2.75 Water . 
 
 1.36 The eye: 
 
 1.53 to 1.56 Aqueous humor 
 
 1.58 to 1.64 Vitreous humor 
 
 1.47 Crystalline lens 
 
 332 
 
 261 
 
 1269 
 
 317 
 
 1.31 
 1.65 
 
 1.48 
 1.336 
 
 1.337 
 1.339 
 1.384 
 
APPENDIX 233 
 
 TABLE XIII 
 
 ELECTRIC RESISTANCE 
 
 (Ohms to 1 m. length and 1 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 j VOLTS 
 
 Bunsen .... 1.9 Grenet ... 2 
 
 Daniell .... 1.07 
 
 Edison-Lalande . . .7 
 
 Gravity .... 1 
 
 Grove .... 1.9 
 Leclanche .... 1.4 
 
 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. 
 
234 
 
 APPENDIX 
 
 ANGLE 
 
 TANGENT 
 
 ANGLE 
 
 TANGENT 
 
 ANGLE 
 
 TANGENT 
 
 ANGLE 
 
 TANGENT 
 
 
 
 .0000 
 
 23 
 
 .424 
 
 46 
 
 1.036 
 
 69 
 
 2.61 
 
 1 
 
 .0175 
 
 24 
 
 .445 
 
 47 
 
 1.072 
 
 70 
 
 2.75 
 
 2 
 
 .0349 
 
 25 
 
 .466 
 
 48 
 
 1.111 
 
 71 
 
 2.90 
 
 3 
 
 .0524 
 
 26 
 
 .488 
 
 49 
 
 1.150 
 
 72 
 
 3.08 
 
 4 
 
 .0699 
 
 27 
 
 .510 
 
 50 
 
 1.192 
 
 73 
 
 3.27 
 
 5 
 
 .0875 
 
 28 
 
 .532 
 
 51 
 
 1.235 
 
 74 
 
 3.49 
 
 6 
 
 .1051 
 
 29 
 
 .554 
 
 52 
 
 1.280 
 
 75 
 
 3.73 
 
 7 
 
 .1228 
 
 30 
 
 .577 
 
 53 
 
 1.327 
 
 76 
 
 4.01 
 
 8 
 
 .1405 
 
 31 
 
 .601 
 
 54- 
 
 1.376 
 
 77 
 
 4.33 
 
 9 
 
 .1584 
 
 32 
 
 .625 
 
 55 
 
 1.428 
 
 78 
 
 4.70 
 
 10 
 
 .1763 
 
 33 
 
 .649 
 
 56 
 
 1.483 
 
 79 
 
 5.14 
 
 11 
 
 .194 
 
 34 
 
 .675 
 
 57 
 
 1.540 
 
 80 
 
 5.67 
 
 12 
 
 .213 
 
 35 
 
 .700 
 
 58 
 
 1.600 
 
 81 
 
 6.31 
 
 13 
 
 .231 
 
 36 
 
 .727 
 
 59 
 
 1.664 
 
 82 
 
 7.12 
 
 14 
 
 .249 
 
 37 
 
 .754 
 
 60 
 
 1.732 
 
 83 
 
 8.14 
 
 15 
 
 .268 
 
 38 
 
 .781 
 
 61 
 
 1.804 
 
 84 
 
 9.51 
 
 16 
 
 .287 
 
 39 
 
 .810 
 
 62 
 
 1.88 
 
 85 
 
 11.43 
 
 17 
 
 .306 
 
 40 
 
 .839 
 
 63 
 
 1.96 
 
 86 
 
 14.30 
 
 18 
 
 .325 
 
 41 
 
 .869 
 
 64 
 
 2.05 
 
 87 
 
 19.08 
 
 19 
 
 .344 
 
 42 
 
 .900 
 
 65 
 
 2.14 
 
 88 
 
 28.64 
 
 20 
 
 .364 
 
 43 
 
 .933 
 
 66 
 
 2.25 
 
 89 
 
 57.29 
 
 21 
 
 .384 
 
 44 
 
 .966 
 
 67 
 
 2.36 
 
 90 
 
 CO 
 
 22 
 
 .404 
 
 45 
 
 1.000 
 
 68 
 
 2.48 
 
 
 
 
 TABLE XVI 
 
 
 
 EQUIVALENTS 
 
 
 1 cm. 
 
 = 0.3937 in. 
 
 1 in. 
 
 = 2.54 cm. 
 
 1 km. 
 
 = 0.6214 mi. 
 
 1m. 
 
 = 1.609km. 
 
 1 sq. cm. 
 1 c. cm. 
 
 = 0.1550 sq. in. 
 = 0.0610 cu. in. 
 
 1 sq. in. 
 1 cu. in. 
 
 = 6.452 sq. cm. 
 = 16.387 ccm. 
 
 1kg. 
 11. 
 1 1. 
 
 = 2.20 Ib. avoir. 
 = 1.0567 qt. (liquid). 
 = 0.908 qt. dry. 
 
 1 oz. avoir. 
 1 Ib. avoir. 
 
 = 28.35 g. 
 = 453.6 g. 
 
A Brief Course in General Physics 
 
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Botany all the Year Round 
 
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A DESCRIPTIVE CATALOGUE OF HIGH 
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UNIVERSITY OF CALIFORNIA LIBRARY 
 
 THIS BOOK IS DUE ON THE LAST DATE 
 STAMPED BELOW 
 
 23 191 > 
 23 Wl'i 
 
 181 
 
 JAN 21 1918 
 
 
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