Class (pu 5 5l 
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 Copyright N°_ 
 
 COPYRIGHT DEPOSIT. 
 

 
A LABORATORY MANUAL IN PHYSICS 
 
THE MACMILLAN COMPANY 
 
 NEW YORK • BOSTON • CHICAGO • DALLAS 
 ATLANTA • SAN FRANCISCO 
 
 MACMILLAN & CO., Limited 
 
 LONDON • BOMBAY • CALCUTTA 
 MELBOURNE 
 
 THE MACMILLAN CO. OF CANADA, Ltd, 
 
 TORONTO 
 
A LABORATORY MANUAL 
 IN PHYSICS 
 
 TO ACCOMPANY 
 
 BLACK AND DAVIS' "PRACTICAL PHYSICS 
 FOR SECONDARY SCHOOLS" 
 
 BY 
 N. HENRY BLACK, A.M. 
 
 SCIENCE MASTER, EOXBURY LATIN SCHOOL 
 BOSTON, MASS. 
 
 Neto fgotfe 
 
 THE MACMILLAN COMPANY 
 
 1913 
 
 All rights reserved 
 

 COPYBIGHT, 1913, 
 
 By THE MACMILLAN COMPANY. 
 Set up and electrotyped. Published September, 1913. 
 
 Norruooti Stress 
 
 J. S. Cushing Co. —Berwick & Smith Co. 
 
 Norwood, Mass., U.S.A. 
 
 ©CI.A354.277 
 
INTRODUCTION 
 
 It is now more than twenty years since we began to teach 
 elementary physics in the laboratory and we already have 
 many laboratory manuals. Why add another to the list? 
 Every teacher of physics undoubtedly takes up the task of 
 organizing his laboratory with great enthusiasm and high 
 hopes. But sooner or later he finds that this business of 
 teaching young people physics by means of laboratory exer- 
 cises is a very difficult problem. No amount of costly appa- 
 ratus or elaborate laboratory directions will produce that 
 mental activity about physical phenomena that we all want 
 to stimulate in our students. 
 
 Doubtless the ideal method would be for each teacher to 
 make his own laboratory manual, and many have done so. 
 This book is the result of one teacher's attempt to get to- 
 gether a set of experiments that represent a well-balanced 
 course. The aim has been to make the directions so clear 
 and concise that the average boy or girl, who already has in 
 mind a general outline of the problem, can not only do the 
 experiment but can also see the point to it. It is assumed 
 that when the class assembles for the laboratory exercise 
 the teacher will first make a few introductory remarks to 
 indicate just what the problem of the day is and how it 
 is related to the previous work and to the practical affairs 
 of life ; then he will briefly outline just how the problem is 
 to be attacked in the laboratory. If the student has already 
 mastered the written directions, he ought then to be able 
 to proceed intelligently and expeditiously with the work in 
 hand. 
 
vi INTRODUCTION 
 
 One reason why so much of our laboratory work in ele- 
 mentary physics is ineffective seems to be that the students 
 get lost in the multitude of details and forget the point or 
 purpose of the experiment. Sometimes the directions are 
 given with such minuteness that the work is purely me- 
 chanical. This is reflected in the notebooks, which show 
 no individuality and seem to indicate that the work has 
 consisted merely in filling in certain blank spaces in a 
 tabular form. It is, of course, expected that at first the 
 student will need much help in arranging his notes in an 
 orderly way, but these suggestions should be made less and 
 less necessary as time goes on. The great danger in note- 
 book work is artificiality. The student should write down 
 in his own words such notes that when he reviews his work 
 six months or a year later they will recall to his mind just 
 what he did and what were his results. 
 
 In the early days of student laboratory work a very large 
 fraction of the time devoted to physics was spent in the lab- 
 oratory, but in recent years we have come to believe that 
 most subjects can be presented in their qualitative aspects 
 best by the teacher in clean-cut lecture-table demonstrations, 
 while the work of the student in the laboratory should be to 
 perform a few well-selected experiments involving simple 
 measurements. It is, of course, always to be remembered 
 that this elementary work is not primarily physical meas- 
 urements, but physics. Therefore it is hardly worth while 
 at this stage of the work to spend much time in discussing 
 percentage errors which are to be reckoned in tenths of one 
 per cent. The engineer often has to be satisfied with results 
 which check within 5%. Why should we seek for such a 
 high degree of accuracy as can only be attained by compli- 
 cating the apparatus and the manipulation? 
 
 So it has come about that the suggested apparatus is very 
 
INTRODUCTION Vll 
 
 simple and often crude. It is also suggested that the stu- 
 dent do on an average only about one experiment per week. 
 Frequent quizzes and reviews of the laboratory work have 
 been found of great value. In this connection it is urged 
 that the colleges provide for a practical laboratory exam- 
 ination as a part of the admission examination in physics, 
 and that the schools use such practical examinations as 
 a part of the routine work to test the student's achieve- 
 ments in physics. This laboratory examination should not 
 be simply a repetition of experiments already performed, 
 but should also to some extent test the student's originality 
 and power to apply the methods of the laboratory to new 
 problems. 
 
 In his search for the best experiments, each teacher gath- 
 ers ideas from so many sources that he hardly knows to 
 whom he is indebted for the result. In this case, the author 
 owes a great deal to his fellow members of the Eastern Asso- 
 ciation of Physics Teachers, whose meetings have been so 
 fruitful and suggestive. American teachers of elementary 
 laboratory physics are under great obligations to Professor 
 E. H. Hall of Harvard University for his persistent pioneer 
 work in this field, and the author is under special obligations 
 to him as his teacher, adviser, and friend. Professor J. M. 
 Jameson of Pratt Institute has given a practical or engineer- 
 ing aspect to several of the experiments (Nos. 17, 32, and 33) 
 in mechanics and electricity. Finally, it is a great pleas- 
 ure to acknowledge the help of Professor Hermann Hahn 
 of Berlin, Germany, whose " Handbuch fur Physikalische 
 Schuleriibungen " is a mine of suggestions and information 
 about laboratory experiments in physicSo 
 
 N. H. B. 
 
CONTENTS 
 
 EXPERIMENT PAGE 
 
 1. Measurement of a Eight Triangle and a Circle ... 1 
 
 2. Density of a Block of Wood ....... 4 
 
 3. The Straight Lever . 7 
 
 4. The Weight of a Lever and its Center of Gravity . . 9 
 
 5. Parallel Forces . . . . . . . . . . 11 
 
 6. Inclined Plane ....... - . . . 13 
 
 7. Sliding Friction 15 
 
 8. Efficiency of a Commercial Block and Tackle 16 
 
 9. Principle of Archimedes ........ 18 
 
 10. Specific Gravity of a Solid ....... 20 
 
 11. Specific Gravity of a Solid Lighter than Water . . 21 
 
 12. Specific Gravity of a Liquid . . . . . .23 
 
 13. Boyle's Law 25 
 
 14. Density of Air .......... 27 
 
 15. Specific Gravity of a Liquid by Balancing Columns . . 29 
 
 16. Parallelogram of Forces ........ 31 
 
 17. Forces acting on a Simple Truss 33 
 
 18. Breaking Strength of Wire ....... 35 
 
 19. Bending of Rods 37 
 
 20. Accelerated Motion ......... 40 
 
 21. The Fixed Points of a Thermometer ..... 42 
 
 22. Linear Expansion of a Solid 44 
 
 23. Cubical Expansion of Air ........ 47 
 
 24. Specific Heat of a Metal 48 
 
 25. Cooling Curve through the Melting Point . . . .51 
 
 26. Latent Heat of Melting Ice ....... 52 
 
 27. Latent Heat of Steam ........ 53 
 
 28. Lines of Magnetic Force 55 
 
 ix 
 
X CONTENTS 
 
 EXPERIMENT PAGE 
 
 29. The Voltaic Cell 57 
 
 30. Magnetic Effect of a Current .60 
 
 31. Electromotive Eorce 63 
 
 32. The Fall of Potential along a Conductor 6Q 
 
 33. Determination of Kesistance by Ammeter and Voltmeter . 68 
 
 34. Measurement of Eesistance by Wheatstone Bridge . . 70 
 
 35. Internal Resistance of a Battery .73 
 
 36. Measurement of Current by a Copper Coulombmeter . . 75 
 
 37. Induced Currents 77 
 
 38. Efficiency of an Electric Motor 79 
 
 39. Heating Effect of an Electric Current .... 82 
 
 40. Frequency of a Tuning Fork .84 
 
 41. Waye-Length of Sound 86 
 
 42. Bunsen Photometer 88 
 
 43. Image in a Plane Mirror . .90 
 
 44. Images in Cylindrical Mirrors 92 
 
 45. Index of Refraction of Glass ....... 95 
 
 46. Focal Length and Conjugate Foci of a Converging Lens . 97 
 
 47. Size and Shape of a Real Image ...... 99 
 
 48. Magnifying Power of a Simple Lens ..... 102 
 
 49. Telescope and Compound Microscope . 104 
 
 50. Dispersion of Light by a Prism 106 
 
 APPENDIX 109 
 
A LABORATORY MANUAL IN PHYSICS 
 
EXPERIMENT 1 
 
 MEASUREMENT OF A RIGHT TRIANGLE AND A CIRCLE 
 
 What is the relation betiveen the sides of a right triangle and 
 also between the circumference and diameter of a circle? 
 
 Sheet of paper. 
 30 cm. rule. 
 Right triangle. 
 
 Cylinder or brass weight. 
 Strip of thin paper. 
 Pin. 
 
 1. Right Triangle. Draw with a sharp hard lead pencil a 
 right triangle with no two of its sides equal and none less 
 than 10 cm. Make the corners clean and sharp. 
 Label the triangle (Fig. 1) ABC, where is 
 the right angle. Measure each of the three 
 sides and record each length in centimeters 
 and a decimal fraction of a centimeter. The 
 millimeters are to be expressed as tenths of a 
 centimeter (0.1 cm.), and the tenths of milli- 
 meters, which are to be estimated, are to be expressed as 
 hundredths of a centimeter (0.01 cm.). 
 
 Record the measurements as follows : 
 
 Fig. 1 
 
 Sides 
 
 Lengths 
 
 AB 
 BC 
 AC 
 
 . cm. 
 
 . cm. 
 
 To check these measurements, make the following compu- 
 tation : (AB^ 2 = ■■• 
 
 (BC) 2 = ... 
 
 (Acy= ••• 
 
 (Aoy+(Bcy = ... 
 
 Compare (AB} 2 and (AC) 2 + (BC) 2 . 
 
2 LABORATORY MANUAL 
 
 From a well-known proposition in Geometry, we know 
 that in any right triangle the square of the hypothenuse is equal 
 to the sum of the squares on the sides. 
 
 So if the arithmetical computation has been done correctly, 
 the difference between (AB) 2 and (AC) 2 + (BCy must be 
 due to the errors in measurement. Since the measurement 
 of each side is bound to be in doubt as to the hundredths 
 of a centimeter (0.01 cm.), the square of each side can have 
 no more than four significant * figures, and no more should be 
 recorded. 
 
 2. Circle. Measure the diameter across the circular face 
 of a cylinder. Wrap tightly around the cylinder a thin 
 strip of paper and prick a hole with a pin through the paper 
 where it overlaps. Measure the distance between these pin- 
 holes and record thus : 
 
 Circumference = . cm. 
 
 Diameter = . cm. 
 
 Compute the value of 
 
 circumference 
 
 (By experiment.) 
 
 diameter 
 
 True value of ir = 3.14 (By Geometry.) 
 
 Error = . . . . 
 
 *Note. Since in each of the above measurements the tenths of a milli- 
 meter had to be estimated, it follows that each measurement is uncertain to 
 at least 0.01 cm. Eor example, suppose one side of the triangle measured 
 12.46 cm. ; it would mean that we were certain of the first three digits 12.4, 
 but that the 6 was doubtful and probably somewhat in error. 
 
 Then it obviously follows that the square of 12.46 will also be somewhat 
 in error. Let us see how much. 12 .- 
 
 12.46 
 
 7476 
 
 4984 
 2492 
 1246 
 155.2516 
 
MEASUREMENT OF A BIGHT TRIANGLE AND CIRCLE 3 
 
 Problems. (1) A room is 3.55 meters high, 7.00 meters 
 long, and 4.50 meters wide. Find the length of its diagonal 
 to three significant figures. 
 
 (2) A cow is fastened to a stake by a rope 20 feet long. 
 Find the perimeter of the circle she can graze over, expressed 
 in feet and inches. 
 
 In the above computation, the doubtful digits are printed in black, and 
 it will be seen that in the product we would retain only 155.3, saving only 
 - one doubtful figure. The last figure saved would be written 3 instead of 2, 
 because what was thrown away was more than one-half. 
 
 As a general rule, in multiplying two numbers together, retain in the 
 product only as many significant figures as there are in the least accurate 
 factor. 
 
 In the same way, when we divide two numbers, which are obtained from 
 measurements and so are more or less inaccurate, we keep in the result 
 only one doubtful figure. Thus, suppose the diameter of a circle measured 
 5.25 cm. and the circumference 16.45 cm., then the quotient 3.13 has only 
 three significant figures and the last 3 is somewhat uncertain. 
 
 5.25 | 16.45 1 3. 13 
 15 75 
 700 
 525 
 1750 
 1575 
 175 
 
 In general, then, all numbers obtained from measurement are more or less 
 inaccurate, and we may retain as significant digits only one doubtful digit. 
 The result of an arithmetical computation can never be more accurate than 
 its least accurate factor. 
 
4 LABORATORY MANUAL 
 
 EXPERIMENT 2 
 
 DENSITY OF A BLOCK OF WOOD 
 
 How many grams does one cubic centimeter of wood weigh ? 
 
 Rectangular blocks, such as maple, Platform balance. 
 
 oak, pine, mahogany. Set of weights. 
 
 30 cm. rule. 
 
 To get the density of wood, i.e. the weight per unit 
 volume, it is necessary to get the weight and the volume of 
 a sample block. 
 
 First adjust the balance so that it will just balance evenly 
 with no load in either scale pan. Then place the block of 
 wood on the pan at the zero (left) end of the scale beam and 
 counterbalance with weights. Steady the scale pans with 
 the left hand while adding or removing the larger weights 
 and so avoid jarring the balance and dulling the knife-edges. 
 It will save time to begin by selecting a weight which is prob- 
 ably a bit too heavy, and if so, take it off and replace it with 
 the next smaller weight. Continue in this way until you 
 have the largest weight which is lighter than the object. 
 Add then the next smaller weight to the scale pan and so 
 on until within 10 grams of the weight. To make the final 
 adjustment use the slider. Take great care in counting up 
 the weights used, and record this at once in the notebook 
 as the weight of the block. 
 
 The block of wood, although nearly rectangular, is not 
 geometrically perfect, and therefore it is well to make several 
 measurements of the length, width, and thickness. Then 
 compute the average or mean length, width, and thickness, 
 and so from these values the volume of the block. Finally, 
 knowing the weight in grams of a certain number of cubic 
 
DENSITY OF A BLOCK OF WOOD 
 
 centimeters of wood, we can easily compute the weight of one 
 cubic centimeter, i.e. the density of the wood. 
 
 To measure the block to 0.01 cm. with an ordinary meter 
 stick, requires, however, considerable care. The block should 
 be laid on a sheet of white paper in good light and the meas- 
 uring stick should be placed upon 
 it so that one end of the block is 
 exactly in line with some centimeter 
 mark, such as the 10 cm. mark, as 
 shown in Fig. 2. The other end 
 of the block will probably not lie 
 exactly in line w T ith any millimeter 
 mark on the scale and so it is necessary to estimate the frac- 
 tion of millimeter. Express the result as centimeters and as 
 a decimal fraction thereof, for example, 12.35 cm. To get 
 d the length, measure each of the 
 
 k 
 
 ^^^?^^5^P^5555555^^^^^ 
 
 Fig. 2 
 
 Fig. 
 
 four edges parallel to the grain of 
 the wood, a, 5, <?, and d in Fig. 3. 
 It is not at all likely that each of 
 these measurements, if carefully 
 made, will give exactly the same 
 result to 0.01 cm. In finding the average of four such meas- 
 urements, it is customary to retain but one doubtful figure and 
 if the second doubtful figure be 5 or more, then add one to 
 the first doubtful figure. Thus : 
 
 Length 
 
 12.35 cm. 
 
 12.37 cm. 
 12.33 cm. 
 
 12.38 cm. 
 
 a. 
 b. 
 c. 
 d. 
 
 4 )49.43 cm . 
 12.357 cm. 
 
 Average Length 12.36 cm. 
 
 To get the average width, measure each of the four long 
 edges cross-wise the grain, e,f g, and h. In a similar man- 
 
6 
 
 LABORATORY MANUAL 
 
 ner measure the length of each of the four short edges, i,y, 
 k, and ra, and call the average of these four measurements 
 the thickness of the block. 
 
 In computing the volume of the block, time will be saved 
 if only significant figures are retained, that is, if only the 
 first doubtful figure is kept. It should also be remembered 
 that the result can be no more accurate than its least accurate 
 factor, which is here the shortest side. 
 
 It is very desirable to record all measurements and results 
 in an orderly way and so the following is suggested : 
 
 Weight of block No. = . . . . g. 
 
 Length Width Thickness 
 
 a , ___. cm . e. cm. t. - - cm. 
 
 &. cm. /. cm. j. - cm. 
 
 Ct -____-- cm. g. ------- cm. k. ------- cm. 
 
 d. ------- cm. h. ------- cm. m. ------- cm. 
 
 4) 4 ) 4 ) 
 
 Average cm. Average cm. Average - - - - cm. 
 
 Volume of block cm. 3 
 
 Density of wood g./cm. 3 
 
 Problem. If the density of aluminum is 2.6 g./cm. 3 , how 
 many grams does an aluminum rod 20.0 cm. long and 1.00 
 cm. in diameter weigh ? 
 
THE STRAIGHT LEVEE 
 
 EXPERIMENT 3 
 
 THE STRAIGHT LEVER 
 
 How must the weights on a straight lever be arranged in order 
 
 to balance? 
 
 Meter stick. Set of weights. 
 
 Fulcrum or support for meter stick. Thread. 
 
 Suspend or support a meter stick at its mid-point, and if 
 it does not quite balance, place on the lighter side a piece of 
 bent copper wire at such a point as to produce equilibrium. 
 Hang a 200-gram weight at a distance of 20 centimeters to 
 the right of the fulcrum, and then hang a 100-gram weight 
 at some point on the other side so as to produce equilibrium. 
 Record these weights as W 1 and W 2 and their distances 
 from the fulcrum as d x and d 2 (Fig. 4). 
 
 I I I 1 II II I I I I I I I I : I I I I I I I II 
 
 8 9 J 
 
 I M I I I I I I I I I I I I ' I ' I ' I M I LI I 
 
 w 2 
 
 Fig. 4 
 
 
 The turning effect or moment of a weight depends on the 
 amount of the weight and its distance from the fulcrum. Thus 
 
 Moment = weight x distance. 
 
 Calculate the moment of each of these weights about the 
 fulcrum (.F). 
 
 Repeat, using a different set of weights and calculate the 
 moment of each weight about the fulcrum. Compare these 
 two products. 
 
8 LABORATORY MANUAL 
 
 Then hang two weights at different points on the same 
 side of the fulcrum and balance them with a single weight 
 on the other side. Compute the sum of the moments on one 
 side of the fulcrum and compare this sum with the moment 
 on the other side. 
 
 Finally suspend any convenient object, like a jackknife, 
 screw driver, or monkey wrench, whose weight is not known, 
 on one side of the lever and balance it with a known weight 
 on the other side. Compute the weight of the object by the 
 principle of moments which has just been illustrated. To check 
 this result, weigh the object on the ordinary scales and com- 
 pare the results. 
 
 Arrange these data and results in some convenient tabular 
 form. 
 
 (a) What relation seems to exist between the moment of the 
 weight on the right and that on the left of the fulcrum ? 
 
 (6) How' does the sum of the moments on the right of the 
 fulcrum compare with the sum of those on the left ? 
 
 (c) Why does the weight of an object obtained by the meter- 
 stick lever not agree exactly with that got on the scales ? 
 
 Problem. A seesaw plank is set in an east and west 
 direction. A boy weighing 100 lb. is placed 6 ft. west of 
 the fulcrum ; a girl weighing 60 lb. is placed 6 ft. east of the 
 fulcrum. Where must a second girl weighing 80 lb. be 
 placed to balance the plank ? 
 
WEIGHT OF A LEVER AND ITS CENTER OF GRAVITY 9 
 
 EXPERIMENT 4 
 
 WEIGHT OF A LEVER AND ITS CENTER OF GRAVITY 
 
 Wliere may the iveight of a lever be considered to act ? 
 
 Meter stick loaded at one end. Set of weights. 
 Triangular block of wood. Thread. 
 
 The loaded meter stick AL. (Fig. 5) may be considered 
 an example of a non-uniform lever whose weight cannot be 
 neglected. Hang a known l x f b a 
 
 weight W at some fixed ^^ A i 
 
 point B, and then slide the ^^ ^ w 
 
 meter stick along the tri- IG ' 
 
 angular block of Avood until the whole thing just balances. 
 Call the fulcrum F, and note AF, the distance of the fulcrum 
 from the end of the meter stick. The distance BF is the 
 lever arm of the weight W, and the moment of W about F is 
 equal to W x BF. 
 
 It is evident that part of the weight of the lever tends to 
 turn the lever down on the right side and that the rest of 
 the weight of the lever tends to turn it down on the left side. 
 It would often be very convenient, in dealing with actual 
 levers, if we could find a point where we could consider the 
 whole weight as concentrated, that is, as if the lever weighed 
 nothing and as if we had another weight applied at this 
 point. Let us call such a point, if there be one, JT, and its 
 distance from the fulcrum FX; then its moment is equal to 
 the iveight of the lever times FX. But this moment is equal 
 to the moment on the other side W x BF. In other words 
 we have m ^ ^ x FX = w x BF ^ 
 
 Wx BF 
 
 and therefore FX = 
 
 Wi. of lever 
 
10 
 
 LABORATORY MANUAL 
 
 Weigh the loaded meter stick and compute the value FX 
 and so the position of Jon the meter stick, i.e. the distance 
 AX. 
 
 Repeat this experiment several times, using different 
 known weights and at various positions, but each time com- 
 puting AX. 
 
 Compare the various positions of X and of the center of 
 gravity (<76r) of the lever, which is found by balancing the 
 lever alone without W. 
 
 What does this experiment show about where the weight of a 
 lever may be considered to act ? 
 
 It will be well to arrange the results in some such way as 
 the following : 
 
 Weight of the loaded lever g. 
 
 AB 
 
 AF 
 
 BF 
 
 BFX W 
 
 FX= 
 
 BFXW 
 
 Wt. of Lever 
 
 AX 
 
 100 g. 
 200 g. 
 200 g. 
 500 g. 
 
 10.0 cm. 
 10.0 cm. 
 15.0 cm. 
 
 Center of gravity (CG) is located cm. from A. 
 
 Problem. A boy who weighs 60 lb. uses as a seesaw a 
 15-ft. plank which weighs 70 lb. and which has its center of 
 gravity in the middle. If he sits 1 ft. from one end, how 
 far from this same end must the fulcrum be placed in order 
 to balance ? 
 
PARALLEL FORCES 
 
 11 
 
 EXPERIMENT 5 
 
 PARALLEL FORCES 
 
 What two conditions must always exist in order to have parallel 
 forces in equilibrium ? 
 
 4 spring balances (2000 g.). 
 4 table clamps. 
 
 Meter stick. 
 
 Stout cord (fishline). 
 
 Arrange the apparatus flat on the table as shown in the 
 diagram (Fig. 6). Attach cords to the meter stick at vari- 
 
 Fig. 6 
 
 ous points, fasten the spring balances to these cords, and 
 arrange the table clamps so that the meter stick is about 
 parallel to the edge of the table and so that all forces are 
 parallel. 
 
12 LABORATORY MANUAL 
 
 Tighten the cords attached to F 2 and F s until the balances 
 indicate 1000 g. and 1500 g. respectively, and adjust F 1 and 
 F± until the whole is in equilibrium. Then read and record 
 the readings of F v F v _F 3 , and F± and the distances AB, AC, 
 AD, and AF. 
 
 Repeat, using different values for F s and JF 4 , and finally re- 
 peat with different positions for C and D. 
 
 Compute in each case the sum of _F 2 and F s , and the sum 
 of F 1 and F r 
 
 Compute the moment of each force about A and find in 
 each case the sum of the moments tending to produce clock- 
 wise rotation and the sum of the moments tending to produce 
 counterclockwise rotation. 
 
 Compute the moments in one case about F as a turning 
 point. Compare the sum tending to produce clockwise rota- 
 tion with the sum tending to produce counterclockwise 
 rotation. 
 
 When several parallel forces are in equilibrium, (a) how 
 does the sum of the forces in one direction compare with the sum 
 of those in the opposite direction ; (b) how does the sum of the 
 moments of the forces tending to produce clockwise rotation com- 
 pare with the sum of the moments of the forces tending to pro- 
 duce counter clockwise rotation? 
 
 Problem. If forces of 6 lb. north, 8 lb. south, 10 lb. north, 
 and 15 lb. south are applied at distances 4, 8, 12, and 16 ft. 
 respectively from the western end of the rod, what force must 
 be applied to produce equilibrium and at what point and in 
 what direction must it be applied ? 
 
INCLINED PLANE 
 
 13 
 
 EXPERIMENT 6 
 
 INCLINED PLANE 
 
 How does the effort required to pull a loaded car up an in- 
 clined plane depend on the grade ? 
 
 Smooth board. 
 Support for one end. 
 Hall's car. 
 
 Spring balance. 
 Set of weights. 
 Meter stick. 
 
 Tip the board up at some convenient angle, such as 30°, 
 and pull the car (TT), which has been previously weighed, 
 slowly up the incline (Fig. 7). The effort required to do 
 
 Fig. 7 
 
 this is a little more than would be required if friction could 
 be entirely eliminated. But if the car is allowed slowly to 
 roll down the incline, the effort required to hold it back will 
 be slightly less because of the friction. Therefore take the 
 mean or average of these two pulls, as the force (JP) or effort 
 which applied parallel to the incline would be needed to hold 
 the car if there were no friction. 
 
 The grade of an incline is the ratio of the height to the 
 length. For example, a 15 % grade means an incline which 
 
14 
 
 LABORATORY MANUAL 
 
 rises 15 feet in going along the incline 100 feet. To compute 
 the grade, then, measure some convenient height (JET) and 
 its corresponding length (i) along the incline. If, for 
 example, we measure from the table top to the upper side of 
 the inclined board, then we must also measure along the 
 upper side of the board to the point where this surface cuts 
 the table, and so it is usually more convenient to use the 
 lower side of the inclined board in measuring loth height and 
 length. 
 
 Repeat this experiment with different loads in the car, and 
 with the inclined plane at different grades in order to find 
 some relation between the effort (^), the total weight (W) 
 
 XT TT 
 
 (i.e. car + load), and the grade. Compare —-and — • 
 
 W L 
 Tabulate your data and results somewhat as follows: 
 
 
 w 
 
 F 
 
 H 
 
 L 
 
 H 
 L 
 
 F 
 
 W 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Problem. What drawbar pull is necessary to pull a train 
 weighing 350 tons up a grade of 15 ft. rise per mile of track, 
 neglecting friction? 
 
SLIDING FRICTION 15 
 
 EXPERIMENT 7 
 
 SLIDING FRICTION 
 
 How does starting friction compare with sliding friction ? How 
 does sliding friction vary with pressure ? 
 
 Friction board. Set of weights. 
 
 Block of wood or friction box. Spring balance. 
 
 The force needed to cause sliding varies much according 
 to the materials, the condition of the bearing surface, lubrica- 
 tion, etc. 
 
 Place the board on the table and set the friction block or 
 box upon it. Attach the spring balance to the block by a 
 foot or two of cord (Fig. 8). By loading the. block with 
 weights we may get ,p 
 
 any desired pressure f^ 
 
 between the bearing ^— <. ^= >- o I I 
 
 surfaces. We may 
 
 well start with as FlG - 8 
 
 low a pressure as will give a fairly steady reading on the 
 spring balance, and note carefully the force needed to start 
 the loaded block and also the force required to keep it mov- 
 ing slowly at a uniform rate. Then increase the load and 
 measure in the same way the friction at five or six other 
 pressures. 
 
 The ratio between the force (_F) required to cause sliding, 
 and the perpendicular pressure (P) between the bearing sur- 
 faces, is called the coefficient of friction. Compute the coefficient 
 of friction in each case as a decimal fraction. 
 
 Record the results in tabular form : 
 
16 
 
 LABORATORY MANUAL 
 
 Trials 
 
 I 
 
 II 
 
 in 
 
 IV 
 
 V 
 
 VI 
 
 Weight of block 
 
 Load 
 
 Weight of block and load, i.e. 
 pressure ........ 
 
 Starting friction 
 
 Sliding friction 
 
 Coefficient of friction .... 
 
 
 
 
 
 
 
 How does the starting friction compare with the sliding friction ? 
 Does the sliding friction increase with the pressure ? 
 Does the coefficient of friction increase with the pressure ? 
 
 Problem. If the coefficient of friction between two well- 
 lubricated metal surfaces is 0.03, what force is needed to 
 make 500 pounds slide ? 
 
 EXPERIMENT 8 
 
 EFFICIENCY OF A COMMERCIAL BLOCK AND TACKLE 
 
 What fraction of the work put into a commercial block and 
 taxkle is got out under various conditions ? 
 
 Two double pulleys 
 
 (commercial). 
 Rope. 
 
 Weights. 
 Spring balance. 
 Meter stick. 
 
 Attach one block to a ring in the ceiling or to a suitable 
 support from the wall, and apply various loads, such as 5, 
 10, 15, 20 lb., to the movable pulley and determine — using 
 the spring balance (Fig. 9) — the effort (F) required to 
 raise the load (IT) slowly. Determine also the distance 
 through which the effort must be exerted in order to lift the 
 
EFFICIENCY OF COMMERCIAL BLOCK AND TACKLE 17 
 
 weight 1 foot. Compare this distance with that 
 which you would expect from the arrangement 
 of ropes and pulleys. 
 
 Compute the input and output at the different 
 loads for a hoist of 10 feet. The work " put in " 
 is equal to the effort x effort distance, and the 
 work " put out " of a machine is equal to resist- 
 ance x resistance distance. Note that the out- 
 put here means only the useful output, i.e. work 
 done in lifting the load exclusive of the weight 
 of the movable block. 
 
 Finally compute the efficiency, i.e. ratio of out- 
 put to input, of the commercial block and tackle 
 at the different loads. Why is the efficiency not 
 the same at different loads? What becomes of 
 the "wasted ivork" ? 
 
 Plot a curve to show graphically the relation 
 between efficiency (vertical distance to curve) 
 and load (horizontal distance). Explain the 
 form of the curve. 
 
 It will be convenient to record the data and 
 results of this experiment in tabular form, some- 
 what as follows : 
 
 \W 
 
 Fig. 9 
 
 Effort moves through .... ft. when weight is lifted 10 ft. 
 
 Loads 
 (lb.) 
 
 Effort 
 (lb.) 
 
 Output per 10 ft. Lift 
 
 (ft. -lb.) 
 
 Input 
 
 (ft. -lb.) 
 
 Efficiency = 
 (%) 
 
 Output 
 Input 
 
18 
 
 LABORATORY MANUAL 
 
 Problem. If the maximum pull which three men can exert 
 is 400 lb., and if a 1000-lb. piano is to be lifted by a block and 
 tackle whose efficiency is assumed to be 65%, what is the 
 least number of sheaves which can be used in each block? 
 Draw a diagram. 
 
 EXPERIMENT 9 
 
 PRINCIPLE OF ARCHIMEDES 
 
 I. Sow much does a body seem to lose in weight when en- 
 tirely immersed in a liquid ? 
 
 II. Sow much liquid does a floating body displace? 
 
 Overflow can. 
 
 Platform balance with weights and 
 
 support, or spring balance. 
 Solids (denser than water), 100-250 g., 
 
 such as stone, coal, glass, etc. 
 
 Solids (less dense than water) 
 such as blocks of wood, 
 apples, etc. 
 
 Beaker or tumbler. 
 
 Battery jar. 
 
 Thread. 
 
 I. Solids that Sink. By weighing a solid, such as a 
 piece of stone, in air and then when entirely immersed in 
 water, the loss in apparent weight can be computed. This 
 loss of weight evidently depends on the size of the stone and 
 
 so on the weight of the 
 liquid displaced. 
 
 To determine this weight 
 of the liquid displaced, a 
 can with a spout, called an 
 overflow can (Fig. 10), is 
 filled until water runs out 
 of the spout. Then by plac- 
 ing a weighed glass beaker 
 under the spout and care- 
 
 Fig. 10 
 
PRINCIPLE OF ARCHIMEDES 
 
 19 
 
 g- 
 
 g- 
 
 _gl 
 
 g- 
 
 fully lowering the piece of rock into the overflow can, the 
 water which is displaced overflows into the beaker and may 
 be caught and weighed. 
 
 Record these observations and results as follows 
 
 Weight of solid in air 
 
 Weight of solid in water 
 
 Loss of weight of solid in water 
 Weight of catch glass, empty .... 
 Weight of catch glass and water displaced 
 
 Weight of water displaced . . . 
 
 Compare the weight of the displaced water with the loss of 
 weight of the stone in water. 
 
 II. Solids that Float. To find 
 out how the weight of a floating 
 body compares with the weight of 
 liquid displaced by it, first weigh 
 the object, such as an apple or 
 block of wood, and then arrange 
 the overflow can and beaker as in 
 Fig. 11, and determine the weight 
 of water displaced by the floating object. 
 
 The observations to be obtained are as follows : 
 
 Weight of solid 
 
 Weight of catch glass, empty .... 
 Weight of catch glass and water displaced 
 Weight of water displaced . . . 
 
 Compare the weight of a floating object with the weight of the 
 liquid displaced by it. 
 
 Problem. A metal bar, 10 cm. long, 2 cm. wide and 
 1.5 cm. thick, weighs 200 g. in water. How much does it 
 weigh out of water ? 
 
 Fig. 11 
 
 g- 
 g- 
 
20 
 
 LABORATORY MANUAL 
 
 EXPERIMENT 10 
 
 SPECIFIC GRAVITY OF A SOLID 
 
 How many times as heavy as an equal volume of water is a 
 solid which sinks in water ? 
 
 Solids (such as porcelain, solid 
 glass stopper, pieces of metal, 
 stones, sulphur, etc.), weigh- 
 ing 100-250 g. 
 
 Thread. 
 
 Platform balance with weights 
 and support, or spring balance. 
 Battery jar. 
 
 To get the weight of a piece of porcelain, glass, or metal, 
 we have merely to weigh it in the usual way. To get the 
 weight of an equal bulk of water, we make use of Archime- 
 des' principle; namely, that the weight of an equal bulk of water 
 is equal to the loss of weight when immersed in water. The 
 specific gravity of a solid is the ratio of the weight of the solid 
 to that of an equal volume of water. 
 
 Record the observations and results in tabular form : 
 
 
 G LASS 
 
 Marble 
 
 
 Weight of solid in air 
 
 Weight of solid in water -* . 
 
 
 
 
 Loss of weight in water . . . . . . 
 
 Weight of equal volume water .... 
 
 Specific gravity of solid 
 
 
 
 
 Problem. A brass cylinder (sp. gr. 8.4) weighs 168 
 air. How much will it weigh in water ? 
 
 f. in 
 
SPECIFIC GRAVITY OF SOLID LIGHTER THAN WATER 21 
 
 EXPERIMENT 11 
 
 SPECIFIC GRAVITY OF A SOLID LIGHTER THAN WATER 
 
 Sow many times as heavy as an equal volume of water is a 
 solid which floats in water ? 
 
 Block of wood or paraffine. 
 Spring balance, or platform scales 
 
 with weights and support. 
 Jar of water. 
 30 cm. rule. 
 
 Thread. 
 Lead sinker. 
 Wooden cylinder. 
 Support for cylinder. 
 
 I. Sinker Method. Just as in experiment 10, it is neces- 
 sary to determine the weight of the solid and the weight of 
 an equal volume of water. 
 
 Weigh the block of wood in air. 
 
 To get the weight of an equal volume of water, since the 
 object may be irregular and is lighter than water, attach a 
 sinker large enough to submerge the body. The lifting 
 
 (a) 
 
 Fig. 12 
 
 (b) 
 
22 
 
 LABORATORY MANUAL 
 
 effect of the water on the block is due to the weight of the 
 water displaced by the block. 
 
 To get this lifting effect of the water on the block, get the 
 weight of the block in air with the sinker attached and under 
 water (Fig. 12a). (It maybe more convenient to weigh 
 the sinker under water and add this to the weight of the 
 block in air.) Then weigh both block and sinker submerged 
 (Fig. 12 5) and by subtraction get the lifting effect of the 
 water on the block, i.e. weight of equal volume of water. 
 
 Arrange the data and results as follows : 
 
 Weight of block 
 
 Weight of sinker in water 
 
 Weight of block in air and sinker in water 
 Weight of block and sinker both in water . . . 
 
 Lifting effect of water on block .... 
 Weight of block in air 
 
 Specific gravity of block 
 
 Lifting effect of water on block 
 
 II. Flotation Method. When the object is of regular form, 
 its specific gravity can often be easily determined by finding 
 
 the fractional part of the 
 whole volume which is sub- 
 merged, inasmuch as the 
 volume submerged repre- 
 sents the weight of the 
 block and the whole volume 
 the weight of an equal vol- 
 ume of water. 
 
 To illustrate this method, 
 use a cylinder of wood and 
 float it endwise in water 
 (Fig. 13). Then the specific 
 gravity is equal to length 
 
 Fig. 13 
 
 submerged divided by the whole length. 
 
SPECIFIC GRAVITY OF A LIQUID 23 
 
 Record the data and results as follows : — 
 
 Length of stick under water cm. 
 
 Whole length of stick cm. 
 
 c • ., Length of stick submerged 
 
 Specific gravity = — -£- -= — = . . . 
 
 r 8 J Whole length of stick 
 
 Problems. (1) A cork (sp. gr. 0.25), which weighs 
 50 g. alone in air, is fastened to a sinker that weighs 200 g. 
 alone in water. How much will both together weigh in 
 \yater ? 
 
 (2) A block of wood, 20 cm. x 15 cm. x 10 cm., floats in 
 water. If its sp. gr. is 0.7, how many cubic centimeters are 
 above water ? Which edge floats upright and how many 
 centimeters of it are above the water ? 
 
 EXPERIMENT 12 
 
 SPECIFIC GRAVITY OF A LIQUID 
 
 Sow many times as heavy as water is gasolene? 
 
 Platform balance, weights and Jar of gasolene or other liquid. 
 
 support, or spring balance. Piece of glass or porcelain. 
 
 Glass-stoppered bottle. Thread. 
 
 Jar of water. Cloth. 
 
 I. Bottle Method. If we know the weight of an empty 
 bottle and stopper, and then determine the weight of the 
 bottle full of gasolene (or any liquid) and also the weight of 
 the same bottle full of water, by subtraction we can get the 
 weight of a certain volume of the liquid and also of the same 
 volume of water. Then by division we get the specific 
 gravity of the liquid. 
 
 It is necessary, of course, to wipe the outside of the bottle 
 dry each time and to be sure that there are no air bubbles 
 
24 
 
 LABORATOBT MANUAL 
 
 left in the bottle, i.e. that the bottle is quite full in each 
 case. 
 
 Record the weighings in tabular form : 
 
 Weight of empty bottle with stopper . . 
 Weight of bottle full of liquid (gasolene) 
 Weight of bottle full of water 
 Weight of liquid in bottle . . . 
 Weight of water in bottle . . . 
 Specific gravity of liquid . 
 
 II. Displacement Method. If we weigh some object, like 
 a glass stopper, in air and then in a liquid like gasolene, the 
 loss of weight is equal, according to the Principle of Archi- 
 medes, to the weight of the liquid displaced. In the same 
 way, by weighing the same object in water, the loss of weight 
 gives the weight of an equal volume of water. By compar- 
 ing these losses in weight in the liquid and in water, we can 
 determine the specific gravity of the liquid. 
 Record the weighings as follows : 
 
 Weight of glass stopper in air 
 Weight of glass stopper in liquid 
 Weight of glass stopper in water 
 Loss of weight in liquid . . . 
 Loss of weight in water .... 
 Specific gravity of liquid . 
 
 g- 
 g- 
 g- 
 g. 
 
 g- 
 
 Problems. (1) A sp. gr. bottle weighs 5.25 g. empty 
 and, when full, holds just 50 g. of water. How much will 
 it weigh when filled with mercury (sp. gr. 13.6) ? 
 
 (2) A glass cylinder weighs 100 g. in air and 60 g. in 
 water. What will it weigh in concentrated sulphuric acid 
 (sp.gr. 1.84)? 
 
boyle's law 
 
 25 
 
 EXPERIMENT 13 
 
 BOYLE'S LAW 
 
 How does the volume of a given quantity of gas kept at constant 
 temperature vary with the pressure ? 
 
 Boyle's Law apparatus either with 
 two adjustable tubes connected by 
 rubber tubing, or with a glass 
 J-tube mounted on some conven- 
 ient upright frame. 
 
 Mercury. 
 
 Millimeter cross-section 
 paper. 
 
 The closed tube (i?, Fig. 14) contains a column of air 
 which is imprisoned by the mercury column. The volume 
 of this air is diminished or increased by chang- 
 ing the pressure upon it ; and its volume is 
 determined either directly in cubic centimeters 
 from the graduations on the closed tube or by 
 measuring the length of the air column, assum- 
 ing that the bore of the tube is uniform. 
 
 The pressure exerted on this column of air, 
 when the mercury stands at the same level in 
 the two tubes, is evidently the atmospheric 
 pressure. This is obtained by reading the 
 barometer and is usually expressed as a certain 
 number of centimeters of mercury. When, 
 however, the mercury in the open tube (J.) 
 stands at a lower level than that in the closed 
 tube (5), then the air in the tube is under less 
 than atmospheric pressure, and the pressure is 
 equal to the barometer pressure (centimeters 
 of mercury) minus the difference in level, also expressed as 
 centimeters. But when the level of mercury in the open 
 
 Fig. 14 
 
26 
 
 LABORATORY MANUAL 
 
 tube is higher than it is in the closed tube, then the air is 
 under more than atmospheric pressure and the pressure is 
 equal to the barometric pressure plus the difference in levels. 
 By merely shifting the relative positions of the two tubes 
 (or in the J -form of apparatus by pouring in more mercury), 
 it is possible to vary the pressure on the enclosed air from 
 considerably below that of one atmosphere to nearly two 
 atmospheres and to observe the resulting changes in the 
 volume of the air in the tube. 
 
 Since the volume of a gas is very sensitive to changes in 
 temperature, it is well not to handle the air column. In 
 reading the position of the mercury on the scale, take the top 
 of the mercury each time, as in reading the barometer. 
 Start with the least pressure that your apparatus will give 
 and gradually increase by at least six steps to the maximum. 
 
 Record your readings and results in tabular form somewhat 
 as follows, keeping only the significant figures: 
 
 Atmospheric pressure (E 
 
 ►arometer) . 
 
 
 
 . cm. 
 
 
 V 
 
 Volume of 
 Aik 
 
 Height of 
 
 Mercury in 
 
 Closed Tube (B) 
 
 Height of 
 
 Mercury in 
 
 Open Tube (A) 
 
 Difference 
 
 in 
 
 Levels 
 
 P 
 
 Pressure 
 
 VXP 
 
 . . . cm. 3 
 
 . . . cm. 
 
 . . . cm. 
 
 . . cm. 
 
 . . cm. 
 
 
 From this experiment it will be clear that when the pres- 
 sure increases, the volume decreases. Since, moreover, in 
 the several trials, the product of volume times pressure is 
 nearly constant, i.e. FxP=F'xP'= V n X P", it follows 
 that the volume of the air in the tube varies inversely as the 
 pressure. In other words when the pressure is doubled, the 
 volume is halved. 
 
DENSITY OF AIR 27 
 
 This relation should also be shown by plotting a curve on 
 cross-section paper, using the observed pressures as vertical 
 distances and the volumes as horizontal distances. 
 
 Problem. In a certain experiment of this sort, the data 
 showed that the volume of air was 25.5 cm. 3 when the pressure 
 was 85.5 cm. What would have been the volume when the 
 pressure was 20 lb. per sq. in.? 
 
 EXPERIMENT 14 
 
 DENSITY OF AIR 
 
 What does a liter of air weigh under the conditions of tempera- 
 ture and pressure of the room ? 
 
 Two-liter round bottom flask, Screw pinchcock. 
 
 with rubber stopper and Equal-arm balance 
 connections. sensitive to 0.01 g. 
 
 Air pump. Set of weights. 
 
 Mercury gauge. Barometer. 
 
 First of all, it is assumed that the volume of the flask 
 has been determined by filling it with water and then meas- 
 uring the volume of water with a graduate. When this 
 volume has once been determined, it is marked on the flask 
 and this part of the experiment need not be repeated ; but 
 great care should be taken to have the flask dry and clean 
 inside and out before attempting to weigh its content 
 of air. 
 
 Connect the flask, mercury gauge, and air pump as in- 
 dicated in the diagram (Fig. 15). After pumping out some 
 of the air, pinch the rubber tube connected with the pump 
 and watch the mercury gauge to see whether there is a leak 
 in the connections. A gradual drop of the mercury would 
 
28 
 
 LABORATORY MANUAL 
 
 Air Pump 
 
 indicate such a leak, which must be stopped before proceed- 
 ing. When all the connections are tight, continue pump- 
 ing for at least five minutes and then read the mercury gauge 
 
 {i.e. height of mercury in 
 tube above that in glass). 
 Close the pinchcock (jP) 
 near the bottle tight. 
 
 Disconnect the flask 
 with its tube and pinch- 
 cock, suspend it from one 
 arm of the balance, and 
 counterpoise its weight 
 with great care. Without 
 disturbing the flask or 
 balance, open the pinch- 
 cock and let the air in. 
 Add the necessary weights 
 to make up for the air 
 admitted. This added 
 weight represents the 
 weight of air admitted to the flask. But not quite all the air 
 was removed from the flask by the pump. In fact, only that 
 fraction of total volume of the flask indicated by the height 
 of mercury in the pressure gauge divided by the height of 
 mercury in the barometer, was removed. 
 
 Having calculated, then, the number of cubic centimeters 
 of air admitted and its weight, we may readily compute the 
 weight of 1000 cm. 3 . 
 
 Since the weight of air varies greatly with the temperature 
 and pressure, it is well to record the room temperature and 
 barometric pressure and then check the experimental result 
 of this rather crude method with the results given in the 
 tables in the Appendix. 
 
 Fig. 15 
 
SPECIFIC GRAVITY OF A LIQUID 
 
 29 
 
 Arrange the data and calculated results in an orderly 
 fashion and draw a diagram of the apparatus. 
 
 Problem. If one cubic foot of air weighs about 1.3 ounces, 
 how many pounds of air are contained in a schoolroom which 
 is 40 feet x 30 feet x 12 feet? 
 
 EXPERIMENT 15 
 
 SPECIFIC GRAVITY OF A LIQUID BY BALANCING 
 
 COLUMNS 
 
 « 
 
 How many times as heavy as water is a saturated solution of 
 
 blue vitriol as indicated by the heights to ^ >. 
 
 which the atmospheric pressure will raise || || 
 
 columns of these liquids ? 
 
 Two glass tubes about 
 80 cm. long. 
 
 Glass T-tube with rub- 
 ber connections. 
 
 Screw pinchcock. 
 
 Tumbler of water. 
 Tumbler of solution of 
 blue vitriol (CuS0 4 ). 
 Meter stick. 
 
 Support the T-tube (Fig. 16) at such a 
 height that the ends of the glass tubes will 
 nearly reach the bottoms of the tumblers. 
 Suck out some of the air from the tubes 
 until the water rises about 60 cm. and then 
 close the screw pinchcock (P). Observe 
 carefully the levels of the liquids to see if 
 the apparatus is leaking, as will be shown 
 by a gradual drop of the liquids in the 
 tubes. 
 
 It is evident that the pressure of the air 
 on the liquids in the tumblers is holding 
 
30 
 
 LABORATORY MANUAL 
 
 up the two columns, and the pressure is just balanced by- 
 pressure of the liquid in the tubes plus the air above. That 
 is, each liquid column exerts the same pressure at its base. 
 It is also evident that this pressure depends on the height 
 and density of the liquid, so the liquid of less density will 
 have the greater height ; in other words, the densities of the 
 two liquids (A and i?) vary inversely as the heights of the 
 columns (x and y). So that 
 
 Specific gravity of blue vitriol solution = Density of blue vitriol 
 
 Density of water 
 
 _ Height of water column 
 Height of blue vitriol column 
 
 To obtain these heights we shall need to make the follow- 
 ing measurements and computations : 
 
 
 Trials 
 
 
 #1 
 
 #2 
 
 #3 
 
 Height of water column above the table .... 
 Height of water in tumbler above the table . . . 
 
 Net height of water column raised * 
 
 Height of blue vitriol column above the table . . 
 Height of blue vitriol in tumbler above the table . 
 
 Net height of blue vitriol raised * 
 
 Specific gravity of blue vitriol 
 
 
 
 
 
 
 
 
 * Note. Subtract from the height of each column, as measured, the height 
 to which it was raised by capillary action at the beginning. 
 
 Problem. How high would a glycerine barometer (such 
 as is in the South Kensington Museum, London) stand, 
 when the mercury barometer reads 30 inches ? Sp. gr. of 
 glycerine = 1.26. Sp. gr. of mercury = 13.6. 
 
PABALLELOGBAM OF FOBCES 
 
 31 
 
 EXPERIMENT 16 
 
 PARALLELOGRAM OF FORCES 
 
 When three non-parallel forces are acting on a body, what must 
 be their relative directions and magnitudes in order to pro- 
 duce equilibrium ? 
 
 Three spring balances. 
 Three clamps. 
 30 cm. ruler. 
 
 Fishline. 
 Block of wood. 
 
 To the middle of a piece of fishline about 40 cm. long tie 
 a second piece about half as long. At each of the free ends 
 make a loop and attach the hook of a spring balance. To 
 the ring of each balance attach a strong string, and then 
 arrange the clamps, balances, and strings as shown in Fig. 17. 
 
 Pull each balance until its index is about in the middle of 
 
 Fig. 17 
 
32 LABORATORY MANUAL 
 
 the scale where it is most reliable, and then slip a page of the 
 notebook under the cord connecting the balances, so that 
 the knot conies about in the middle of the page. 
 
 In order to show the direction of each cord on the paper, 
 place a rectangular block alongside and draw a line directly 
 under each cord. Record on each line the pull indicated by 
 the balance, and then relieve the tension on the spring bal- 
 ances. Observe the zero reading of each balance and apply 
 the proper correction to the reading just recorded. If the 
 zero reading is less than zero, add the correction to the bal- 
 ance reading recorded on the paper ; if it is more than zero, 
 subtract the proper amount. 
 
 If the experiment has been carefully done, the three lines 
 representing the three forces will, when prolonged, intersect 
 at a common point. Measure off on each line a distance 
 corresponding to the force, according to any convenient scale, 
 such as 200 g. to 1 cm. Make an arrowhead at the end 
 of each measured line and erase that part of each line which 
 lies beyond the arrowhead. 
 
 On any two of these lines construct a parallelogram, 
 using a ruler and compass to get the lines exactly parallel. 
 Draw the three original force lines as solid lines ( OA, OB, 
 and 00) and the lines needed to complete the parallelo- 
 gram (BR and OR) and the diagonal ( OR) as broken or 
 dotted lines. Draw the diagonal of this parallelogram 
 from the central point, measure its length, and compute the 
 magnitude of the force which it represents. For example, 
 a line 15.6 cm. long represents a force of 3120 g. when the 
 scale is 200 g. to 1 cm. This diagonal line represents the 
 resultant of the two forces which form the sides of the par- 
 allelogram. 
 
 How does the resultant of two forces compare with the third 
 force (a) in magnitude and (b) in direction? 
 
FORCES ACTING ON A SIMPLE TRUSS 
 
 33 
 
 Problem. Find the direction and magnitude of a force 
 needed to balance the effect of 12 lb. acting north and 16 lb., 
 east. 
 
 EXPERIMENT 17 
 
 FORCES ACTING ON A SIMPLE TRUSS 
 
 How much is the thrust 
 exerted by a simple stick 
 when used with a " tie " 
 to support a weight? 
 
 Stick with foot support 
 (Pratt Inst, model). 
 Two spring balances. 
 Scale pan and weights. 
 Large protractor. 
 
 Set up the apparatus 
 as shown in Fig. 18, so 
 that the stick BO is not 
 horizontal. Add enough 
 weights at L to stretch the 
 balance F nearly to its full 
 scale reading. The weight 
 of the stick itself may be 
 neglected because it is so 
 small in comparison with 
 the other forces. 
 
 Measure w r ith a large 
 protractor the angles BCL 
 and ACL and record the 
 weight at L. 
 
 To find the tension in 
 
 Fig. 18 
 
34 
 
 LABORATORY MANUAL 
 
 AC, draw a careful diagram of the three forces with the 
 force OL to some convenient scale. Compare the result of 
 this computation with the reading of the balance F. 
 
 Also by the same diagram, compute the compression on 
 the stick BO. To test this, attach a second balance at 
 and pull out in the line of the stick B O until the end of the 
 stick at B just leaves the wall. Compare this pull (#) with 
 the computed compression in the stick BO. 
 
 Change the angle of the stick to the wall and repeat the 
 experiment, making the necessary diagrams and taking check 
 readings as before. 
 
 Record the readings also in tabular form as follows : 
 
 
 Case 
 
 L 
 
 ABCL 
 
 /.ACL 
 
 F 
 
 S 
 
 Computed 
 
 Measured 
 
 Computed 
 
 Measured 
 
 I 
 
 
 
 
 
 
 
 
 II 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Problem. If the stick BO is 10 ft. long and is placed at 
 an angle of 45° to the wall, what is the tension in the tie 
 OA which is horizontal when the load is 2 tons ? What is 
 the compression in the stick BO? 
 
BREAKING STRENGTH OF WIRE 35 
 
 EXPERIMENT 18 
 
 BREAKING STRENGTH OF WIRE 
 
 Sow many kilograms of force are required to break No. 27 
 spring brass wire, steel wire, and copper wire ? 
 
 Wire-breaking apparatus (Fig. 19). Spools of steel, 
 
 10 kg. spring balance. brass, and copper wire, # 27. 
 
 Micrometer. 
 
 The apparatus (Fig. 19) is so designed that the tension 
 on the wire at the instant it breaks, is recorded on a spring 
 balance (i?). The tension is applied by means of a crank 
 
 (<7) which turns an axle on which the wire is wound. The 
 other end of the wire is attached to the spring balance by 
 means of a frame. As this frame is pulled, a wedge (IF) 
 drops down which holds the index of the balance just where 
 it was at the instant of breaking. 
 
 First slip one end of the wire through the hole in the 
 crank shaft and bend the end over sharply so as to extend 
 along the shaft. In this way one or two turns of the handle 
 will cause the wire to wind over the end and so fasten it 
 
36 LABORATORY MANUAL 
 
 securely. Pass the other end of the wire a couple of times 
 around the wooden post on the sliding frame and clamp the 
 end under the binding post. Let the w r edge rest lightly in 
 the slot of the sliding frame. Set the pawl (P) so that it 
 will rest on the toothed wheel attached to the shaft and so 
 prevent the shaft from turning backward. 
 
 Now turn the crank slowly and cause a slight tension in 
 the wire. Measure with a micrometer the diameter of the 
 wire in at least two places, and increase the tension on the 
 wire by turning the crank and keeping the wedge down in 
 the slot until the wire breaks. As the wedge fills the slot, 
 it holds the spring balance at just the position it was in 
 when the wire broke. Record this force in kilograms. 
 
 Repeat the experiment twice and find the average of the 
 three readings for the breaking strength of ^ 27 brass wire. 
 If time permits, try also steel wire and copper wire. 
 
 Problem. From the result of your experiment calculate 
 the force in kilograms needed to break a wire of the same 
 material 1 mm. 2 in cross section. 
 
BENDING OF BODS 
 
 37 
 
 EXPERIMENT 19 
 
 BENDING OF RODS 
 
 How does the bending of a rod vary under different loads? 
 How is the bending affected, (a) if the rod is shortened to 
 
 one half its original length, (b) if the rod is doubled in width, 
 
 (c) if it is doubled in thickness ? 
 
 Rods of wood, steel, or brass 
 110 cm. x 1 cm. x 1 cm. 
 
 Rods of same material but 
 110 cm. x 2 cm. x 1 cm. 
 
 A Supports. 
 
 Indicator lever, or micrometer screw 
 
 with cell and telephone receiver. 
 Vertical scale. 
 Set of weights. 
 Pan for weights. 
 
 Board to support apparatus. Meter stick. 
 
 Place the board across the gap between two laboratory 
 tables and set up the apparatus as shown in Fig. 20. Of 
 course we should expect a rod to bend more with a heavy 
 
 \U 
 
 Fig. 20 
 
 load than under a light one, and so in this experiment we 
 will try to show just how this bending varies with various 
 loads (Z). Since the rod gets a permanent "set" or bend, 
 when loaded beyond a certain point, called the " elastic 
 limit," we must each time remove the load and read the zero 
 point. The amount of the deflection or bending which a rod 
 will stand and still recover is very small, and so some special 
 
38 
 
 LABORATORY MANUAL 
 
 method has to be adopted to measure this deflection, such as 
 a magnifying lever (Fig. 20) or a micrometer screw (Fig. 21). 
 
 Fig. 21 
 
 Record the loads and deflections of the rod in tabular 
 form somewhat as follows : 
 
 I. Length eetween Supports 100 cm. Width 1.0 cm. 
 Thickness 1.0 cm. 
 
 
 Load 
 
 Indicator Readings 
 
 Actual 
 Deflection 
 
 Deflection per 
 
 Before loading 
 
 After loading 
 
 100 G. 
 
 100 g. 
 200 g. 
 300 g. 
 400 g. 
 500 g. 
 
 
 
 
 
BENDING OF RODS 
 
 39 
 
 II a. Length between Supports 50 cm. Width 1.0 cm. 
 Thickness 1.0 cm. 
 
 500 g. 
 1000 g. 
 
 
 
 
 
 II b. Length between Supports 100 cm. Width 2.0 cm. 
 Thickness 1.0 cm. 
 
 200 g. 
 
 400 g. 
 
 ! 
 
 
 II c. Length between Supports 100 cm. Width 1.00 cm. 
 Thickness 2.0 cm. 
 
 500 g. ! 
 1000 g. 
 
 
 
 
 
 From a comparison of the results shown in the last column 
 under "Deflection per 100 g.," in case I, state how the deflection 
 varies with the load. 
 
 By comparing the average deflection per 100 g. in cases I 
 and II a, state how the hending decreases when the length is 
 halved. 
 
 By comparing the average deflection per 100 g. in cases I and 
 115, state how the bending decreases when the width is doubled. 
 
 Finally by comparing the average deflection per 100 g. in 
 cases I and II <?, state how the bending decreases when the depth 
 is doubled. 
 
 Note . If metal rods are used with a micrometer screw and heavier loads, 
 which are needed, the results will be more consistent. 
 
 Problem. If a beam 10 ft. long, 4 in. wide, and 6 in. 
 thick, is bent 0.5 in. under a load of 300 lb., how much load 
 would it take to bend a beam 5 ft. long, 2 in. wide, and 3 in. 
 thick, the same amount ? 
 
40 
 
 LABORATORY MANUAL 
 
 EXPERIMENT 20 
 
 ACCELERATED MOTION 
 
 How does the distance traversed by a moving body under con- 
 stant acceleration vary with the time? 
 
 Grooved plank according to 
 
 Duff. 
 Steel ball, 1.5" diam. 
 Blocks to support one end of 
 
 incline. 
 
 Meter stick. 
 
 Pepper box with lycopodium 
 
 powder. 
 Cloth. 
 
 When the grooved plank (Fig. 22) is placed horizontally 
 on the table, a steel ball placed on one edge will, when re- 
 leased, oscillate back and forth like a pendulum. Although 
 
 Fig. 22 
 
 the swings decrease in amplitude, yet the time of each swing 
 remains constant. When the plank is tilted so that one end 
 is higher than the other, a ball placed at the top in the 
 middle of the groove will roll down, going faster and faster 
 until it reaches the bottom. 
 
 In this experiment we shall combine this oscillatory motion 
 back and forth across the groove with the accelerated motion 
 down the incline in such a way as to make the oscillatory 
 motion mark off equal intervals of time for the study of the 
 accelerated motion. 
 
 First wipe off the trough with a damp cloth and rub it 
 thoroughly dry, then sprinkle it with lycopodium powder. 
 
ACCELEBATEB MOTION 
 
 41 
 
 Tilt the plank with blocks, taking care to keep the under 
 edges at the upper and lower ends exactly horizontal. Place 
 the ball at the top of the groove against the metal 
 strip ($) which serves as a guide until it reaches the 
 middle line. When the ball is released, it goes zig- 
 zagging down the groove. If the powder is blown 
 off, we see distinctly the path traced on the black- 
 board, somewhat as shown in Fig. 23. We have now 
 simply to measure certain distances along the mid- 
 line to understand the relation of distance to time in 
 a case of accelerated motion. 
 
 In the second column we record the distances trav- 
 ersed in 1 interval of time, 2 intervals, 3, and so on, 
 that is, AB, AC, AD, AE, etc. 
 
 In the third column we record the separate dis- 
 tances covered in the 1st interval of time, in the 2d 
 interval, and so on, that is, AB, BO, (7D, etc. 
 
 From a study of the result given in the fourth col- 
 
 umn [—J, what relation seems to exist between the space, 
 s, and the time, t? From a study of the results in the 
 
 last column ( ], what relation seems to exist be- fig. 23 
 
 \2t-lJ 
 
 tween the separate distances (c?) and the odd numbers given by 
 the expression (2 t — 1)? 
 
 Time 
 
 Space 
 Traversed (s) 
 
 Distance covered 
 
 in Each Time 
 Interval (d) 
 
 s 
 P 
 
 d 
 
 Intervals (t) 
 
 02* -1) 
 
 1 
 
 
 
 
 
 2 
 
 
 
 
 
 3 
 
 
 
 
 
 4 
 
 
 
 
 
 5 
 
 
 
 
 
42 LABORATORY MANUAL 
 
 Problem. As the board is tilted more and more, the value 
 
 — increases, until when the board is vertical and the ball falls 
 t 2 
 
 freely, — = 16.1, where' t is expressed in seconds and s in feet. 
 How far would a body fall freely in 3 seconds? 
 
 EXPERIMENT 21 
 
 THE FIXED POINTS OF A THERMOMETER 
 How to test the fixed points of a thermometer, i.e. 0° and 
 
 ioo° a 
 
 How much is the boiling point of water affected by a change of 
 1 centimeter in the barometric pressure ? 
 
 Steam boiler and Bunsen burner. Small glass tumbler. 
 
 Mercury U-tube gauge. Cracked ice (clean). 
 
 Thermometer (— 10° to 110° C). Screw pinchcock. 
 
 Fill the boiler about half full of water, screw the chimney 
 or top down firmly, and attach the necessary gauge (Fig. 24). 
 Open up the pinchcock (A) near the top of the chimney 
 and start heating the water. 
 
 I. Freezing Point. Fill a glass tumbler with clean cracked 
 ice and pour over it enough water to fill the spaces around 
 the pieces of ice. Put the thermometer bulb down into the 
 melting ice, so that you can just see the mercury. After a few 
 minutes, when the mercury has ceased to fall and has come 
 to a definite position, read the thermometer to one tenth of 
 a degree, and record this as the freezing point of your ther- 
 mometer. The error is the difference between this reading 
 and zero. 
 
 II. Boiling Point. Carefully insert the thermometer in 
 the stopper of the steam boiler, so that the 100° mark on 
 
THE FIXED POINTS OF A THERMOMETER 
 
 43 
 
 the scale projects just a little above the stopper. Let the 
 steam flow around the bulb and stem for several minutes 
 until the thermometer has come to a fixed reading, then, 
 read and record its position and also the barometer height. 
 
 Fig. 24 
 
 III. Pressure of Steam and its Temperature. Since the 
 boiling point of water is much affected by changes in pres- 
 sure, it has been necessary to fix on some standard barometric 
 pressure, and this is 760 mm. As the barometer is very sel- 
 dom just at this point, it is necessary to know how to com- 
 pute the true boiling point of water at any pressure. To 
 do this we need to know the effect on the temperature of 
 steam of a change in pressure of 1 cm. 
 
 When the steam is escaping freely into the air, the mer- 
 cury in the gauge ((r) reads the same in each arm. Now 
 
44 LABORATORY MANUAL 
 
 gradually close the steam exit (A) by screwing up the 
 pinchcock until the pressure gauge shows a difference in 
 levels of about 6 or 8 cm. and has become fairly steady, then 
 read the thermometer, and remove the burner. 
 
 How much has the temperature of the steam been raised by 
 increasing the pressure ? 
 
 Hoiv much is the temperature of steam raised per centimeter 
 increase of pressure? 
 
 Very careful and repeated experiments of this sort have 
 shown that the temperature of steam is changed about 0.37° 
 for each centimeter of change of pressure. Compute, then, 
 the true temperature of steam to-day and then the error in 
 your thermometer. 
 
 Problem. A standard thermometer was found on a certain 
 day to read in steam 98.5° C. ; what was the pressure ? 
 
 EXPERIMENT 22 
 
 LINEAR EXPANSION OF A SOLID 
 
 How much does one centimeter of aluminum expand when 
 heated one degree Centigrade ? 
 
 Linear expansion apparatus according Thermometer. 
 
 to Hall or Co wen. Barometer. 
 
 Boiler and burner. Meter stick. 
 
 Since the amount which a solid expands is exceedingly 
 small, it is difficult to measure it with great precision. One 
 of the many methods of measurement of this slight expan- 
 sion makes use of a lever to magnify the actual expansion as 
 shown in Fig. 25.* The metal tube is heated by passing 
 
 * This form of apparatus was designed by Mr. C. M. Hall of Springfield, 
 Mass. 
 
LINEAR EXPANSION OF A SOLID 
 
 45 
 
 steam through it. One end of the tube is made fast with a 
 pin (P), and the other end, as the rod expands, turns a bent 
 lever (£) about a point (A). The expansion of the tube 
 
 Steam 
 
 '^^ 
 
 r 
 
 A Fig. 25 
 
 is magnified as many times as the short arm (AB) of the 
 lever is contained in the long arm (CD). Therefore to get 
 the actual expansion we have only to divide the movement 
 of the pointer by the magnifying power of the lever. 
 
 In another form of apparatus the expansion is measured 
 by allowing the tube (T) to rest on a needle (iV), which in 
 turn rests on roller bearings (BB) as shown in Fig. 26.* 
 
 Fig. 26 
 
 The rotation of the needle is measured on a circular scale by 
 a pointer. Evidently if the needle turns around once, the 
 tube has expanded a distance equal to the circumference of 
 the needle ; and if it turns less than a complete revolution, 
 the tube has expanded the corresponding fraction of the 
 circumference of the needle. 
 
 * This form of apparatus was designed by Mr. G. A. Co wen of Jamaica 
 Plain, Boston. 
 
46 LABORATORY MANUAL 
 
 In the first method the short arm of the bent lever, and 
 in the second method the diameter of the needle, can be meas- 
 ured with great precision by means of a micrometer. 
 
 The length of the tube between the fixed point (P) and 
 the indicating device can be easily measured to three signifi- 
 cant figures with an ordinary meter stick. 
 
 The temperature of the tube at first may be assumed to be 
 that of the room, and the temperature of the tube when hot 
 will be the temperature of steam, which can be computed 
 from the barometric reading. 
 
 Record the measurements and computations somewhat as 
 follows : 
 
 Length of metal tube cm. 
 
 Temperature of room °C. 
 
 Height of the barometer mm. 
 
 Temperature of steam °C. 
 
 Length of short arm of pointer . . . , cm. 
 
 Length of long arm of pointer cm. 
 
 Magnifying power of pointer 
 
 Reading of pointer before cm. 
 
 Reading of pointer after cm. 
 
 Rise of the pointer cm. 
 
 Actual expansion of the metal tube cm. 
 
 Expansion of tube per degree rise in temperature . . cm. 
 Expansion of one centimeter of tube per degree 
 
 (coefficient of linear expansion) 
 
 o 
 
 Problem. If the melting temperature of aluminum is 1157 
 F., how much must be allowed for shrinkage in making 
 patterns for aluminum castings? (For coefficient of ex- 
 pansion of aluminum, see tables in Appendix.) 
 
CUBICAL EXPANSION OF AIR 47 
 
 EXPERIMENT 23 
 
 CUBICAL EXPANSION OF AIR 
 
 What fraction of its volume at 0°(7. does a certain quantity of 
 air expand when heated 1° (?. under constant pressure ? 
 
 Glass tube of dry air according Boiler with top. 
 
 to Waterman. Bunsen burner. 
 
 Thermometer. Pail or battery jar of cracked ice 
 
 Meter stick. or snow. 
 
 A thick-walled glass capillary tube with a uniform bore 
 of about 1 mm. is closed at one end (Fig. 27). Near the 
 middle of the tube is a thread of mercury (M) about 
 2 cm. long. The distance QA3T) from the closed end 
 of the bore up to the mercury represents the volume 
 of air. (The volume of the air is measured in terms 
 of the volume of a unit length of the tube.) 
 
 Stand the air tube in the battery jar so that the air 
 column is surrounded by cracked ice and allow it to 
 stand until the mercury index ceases to go down fur- ||L f 
 ther. Then mark the position of the lower end of the 
 thread of mercury with a rubber band. Remove the 
 tube from ice, lay it alongside the meter stick, and 
 measure the distance from the closed end of the bore 
 to the rubber band. This represents the volume of 
 the air at 0° C. 
 
 Now put the air tube into the top of the steam 
 boiler, in such a way as to surround the air column 
 with steam. When the mercury ceases to rise in the tube, 
 again mark the position of the lower end of the mercury 
 with a rubber band. Remove the tube from the boiler and 
 measure the distance, which is the length of the air column 
 
 'A 
 Fig. 27 
 
48 LABORATORY MANUAL 
 
 when hot. Read the barometer and compute from this the 
 temperature of the steam. 
 
 Compute the expansion of the air, the rise in temperature, the 
 expansion per degree rise in temperature, and finally the ex- 
 pansion of 1 cm. per degree. This last result represents the 
 coefficient of cubical expansion of air. 
 
 Problem. A room 20 m. x 10 m. x 5 m. would contain 
 1290 kg. of air at 0° C. ; how much air will it contain at 30° C? 
 
 EXPERIMENT 24 
 
 SPECIFIC HEAT OF A METAL 
 
 How many calories does one gram of a metal give out 
 in cooling l°C.f 
 
 Blocks of metal, such as aluminum, Thermometer. 
 
 brass, or copper. Platform balances and 
 
 Boiler and burner. sets of weights. 
 Calorimeter. 
 
 The thermal unit commonly employed in heat measure- 
 ments in the laboratory is the calorie. This is the amount of 
 heat needed to raise the temperature of one gram of water 
 one degree Centigrade. Experience shows that more heat 
 is required to heat one gram of water one degree than is re- 
 quired to heat one gram of almost any substance one degree. 
 To find out just what fraction of a calorie is absorbed or 
 given out when one gram of a metal changes its temperature 
 one degree is the purpose of this experiment. 
 
 If hot metal is plunged into cold water, the metal gives 
 out heat and the water absorbs heat ; and if no heat is 
 lost during the process, the number of calories given out 
 
SPECIFIC HEAT OF A METAL 49 
 
 by the metal is equal to the number of calories absorbed 
 by the water. But it must also be remembered that the 
 vessel which holds the water, the calorimeter, absorbs heat. 
 Experiments show that brass (the metal commonly used for 
 the calorimeter) absorbs about one tenth as much heat as the 
 same weight of water. Therefore one tenth the weight of 
 the calorimeter, called the water equivalent of the calorimeter, 
 is to be added to the weight of water used. 
 
 To compute the number of calories absorbed by the water 
 and calorimeter, multiply the number of grams of water plus 
 the water equivalent of the calorimeter by the number of 
 degrees which it is raised in temperature. This quantity of 
 heat was furnished by a certain number of grams of metal 
 in cooling a certain number of degrees. From this we can 
 compute how much heat was furnished by one gram of metal 
 in cooling one degree. This is called the specific heat of the 
 metal. 
 
 The metal for this experiment may be finely divided like 
 shot, which may be heated in a dipper set in a boiler, or per- 
 haps more conveniently may be in the form of a cylinder or 
 ball which is heated directly in the water of the boiler. 
 Weigh the metal and then put it into the boiler to heat. In 
 the meantime measure out a certain quantity of cold water, 
 about 300 cm. 3 at from 5° to 10° C. Record the weight of 
 water used, considering 1 cm. 3 as equal to 1 g. 
 
 When the metal has reached the temperature of the boil- 
 ing water, which is to be computed from the barometric 
 reading, first read and record the temperature of the cold 
 water and then quickly lift the metal by means of a thread 
 out of the boiler and put it in the cold water. Stir the 
 water and take its final temperature as soon as it becomes 
 constant. 
 
 These data should be recorded in tabular form. 
 
50 
 
 LABORATORY MANUAL 
 
 Weight of metal g. 
 
 Weight of cold water . . . . g. 
 
 Weight of calorimeter g. 
 
 Temperature of metal °C. 
 
 Temperature of cold water ° C. 
 
 Temperature of water and metal °C. 
 
 From these facts calculate the following results : 
 
 Water equivalent of calorimeter 
 
 Weight of water and water equivalent of cal. 
 Rise of temperature of water and calorimeter 
 Calories absorbed by water and calorimeter 
 
 Drop in temperature of metal 
 
 Calories given out by metal in cooling 1° C. 
 Calories given out by 1 g. of metal in cooling 1° C 
 
 g- 
 g- 
 
 °C. 
 cal. 
 °C. 
 cal. 
 cal. 
 
 What do you find the specific heat of the metal used to be? 
 Compare this with the result given in the tables in the Ap- 
 pendix and try to explain the difference. 
 
 Note. Experiments in heat measurements are especially difficult and 
 great precautions must be taken. Each time read the thermometer correctly 
 not only to whole degrees, but also to tenths of a degree. Avoid han- 
 dling the calorimeter during the experiment or in any way transferring heat 
 to or from it. Check up each step in the arithmetical computation. 
 
 Problem. A 10-gram ball of platinum (sp. ht. 0.04) is 
 taken from a furnace and dropped into 40 g. of water at 
 10° C. The temperature is raised to 25° C. How hot was 
 the furnace ? 
 
COOLING CURVE THROUGH THE MELTING POINT 51 
 
 EXPERIMENT 25 
 
 COOLING CURVE THROUGH THE MELTING POINT 
 
 Sow does a change of state, such as from a liquid to a solid, 
 affect a cooling curve ? 
 
 Test tube and clamp. Acetamide or naphthaline. 
 
 Bunsen burner. Millimeter cross-section paper. 
 
 Thermometer. Boiler. 
 
 Fill a test tube about three quarters full of acetamide and 
 place the tube down in the boiling water of the boiler. In- 
 sert the thermometer in the test tube and heat until all the 
 crystals are melted and the liquid has reached a temperature 
 of about 100° C. Then lift the test tube out of the boiler 
 and clamp it in a convenient position to observe the tempera- 
 ture as the liquid cools. Do not disturb the liquid or ther- 
 mometer in any way. 
 
 As the substance cools from 100° C. to 50° C, record every 
 half minute the temperature and the time. Then plot these 
 results on cross-section paper, representing temperatures by 
 vertical distances (1 mm. for 1°) and times by horizontal dis- 
 tances (4 mm. for 1 min.). Study the curve carefully so as 
 to answer such questions as the following : 
 
 (a) What portion of the curve represents the cooling of the 
 
 substance in the liquid state ? 
 
 (b) What portion of the curve represents the condition dur- 
 
 ing the process of crystallization ? 
 
 (c) What portion of the curve represents the cooling of the 
 
 substance in the solid state ? 
 
 (d) Is there any part of the curve which indicates " subcool- 
 
 ing " t 
 
 (e) What would you consider the freezing point of the sub- 
 
 stance used? 
 
52 
 
 LABORATORY MANUAL 
 
 Question. Does the process of freezing water evolve or 
 absorb heat from the surroundings ? 
 
 EXPERIMENT 26 
 
 LATENT HEAT OF MELTING ICE 
 
 How many calories are required to change one gram of ice at 
 0° 0. into water at 0° 0. ? 
 
 Calorimeter. 
 
 Thermometer. 
 
 Platform scales and set of weights. 
 
 Supply of hot water (teakettle). 
 Cracked ice. 
 Cloth or towel. 
 
 First weigh the calorimeter empty and then with about 
 300 g. of warm water, the temperature of which is about 
 25° C. above that of the room. Break or grind up enough 
 clean ice to fill a 150-cm. 3 beaker with pieces less than 2 cm. 
 in diameter. Stir the water in the calorimeter thoroughly 
 and determine its temperature as precisely as possible. At 
 once add the ice, taking care to wipe each piece on the cloth 
 and not to spatter the water. Stir the water continually, 
 and when the temperature of the water has fallen 10° or 
 more below that of the room, stop adding ice and just as soon 
 as the last piece melts, read the temperature again with great 
 precision. To find out how much ice has been used, weigh 
 the calorimeter with its water and melted ice. 
 
 Record the following data : 
 
 Weight of calorimeter (c) . . 
 Weight of calorimeter + water 
 
 Weight of water (w) 
 Initial temperature of water (/) 
 Final temperature of water (?) 
 Weight of calorimeter + water + ice 
 
 Weight of ice (i) .... 
 
 C C. 
 °C. 
 
LATENT HEAT OF STEAM 53 
 
 The water and calorimeter in cooling give out heat which 
 is used, first, to melt the ice, and, second, to raise the water 
 which is formed, from zero to the final temperature. If each 
 gram of ice in changing from ice at 0° C. to water at 0° C. 
 requir.es x calories, then i grams of ice would require ix 
 calories. But after the ice is melted, it becomes i grams of 
 water at 0°C, and this water is raised to the final tempera- 
 ture t' which requires it 1 calories in addition. This heat is 
 supplied by W grams of water and by c grams of calorimeter 
 (whose specific heat is about 0.1) in cooling from the initial 
 temperature t to the final temperature th This heat is equal 
 to (w + 0.1 c.) (t — £') calories. If we make an equation 
 between the heat absorbed by the ice and the heat given out by 
 the water and calorimeter, we can easily solve for x, the latent 
 heat of melting ice. 
 
 Problem. If the latent heat of melting ice is 80 calories, 
 how many B. t. u. are needed to melt 1 lb. of ice ? 
 
 EXPERIMENT 27 
 
 LATENT HEAT OF STEAM 
 
 How many calories of heat are liberated when one gram of 
 steam at 100° O. condenses into water at 100° C? 
 
 Boiler and burner. Calorimeter. 
 
 Water trap. Thermometer. 
 
 Balance and weights. 
 
 Fill the boiler half full of water and start heating. Then 
 fill the calorimeter, whose weight has already been deter- 
 mined, two thirds full of cold water (about 5° C), and 
 determine the weight of the water with great precision. 
 
54 
 
 LABORATORY MANUAL 
 
 Fig. 28 
 
 Set up a book or wooden screen between the boiler and 
 calorimeter and place a thermometer in the water. 
 
 As soon as the steam is ready, attach the water trap (T, 
 Fig. 28) to the delivery tube to catch any condensed steam. 
 
 Stir the water in the calorimeter 
 with the thermometer and read 
 its temperature to one tenth of a 
 degree. Then quickly put the de- 
 livery tube of the water trap (T 7 ) 
 into the water so that its end pro- 
 jects under water about 2 cm. 
 Continue to stir the water slowly 
 until the water gets to a tempera- 
 ture about as much above that 
 of the room as the initial temperature was below it. Re- 
 move the delivery tube from the calorimeter and after 
 stirring read the highest temperature which the water 
 reaches. 
 
 Finally, as soon as convenient, weigh with great care the 
 calorimeter, water, and condensed steam and compute the 
 weight of the steam used. 
 Record the following data : 
 
 Weight of calorimeter (c) . . 
 Weight of calorimeter + water 
 Weight of water (w) . . . 
 Initial temperature of water (t) 
 Final temperature of water (t') 
 Weight of cal. + water + condensed stea 
 Weight of condensed steam (s) . . . 
 Water equivalent of calorimeter (0.1 c.) 
 
 °C. 
 
 °c. 
 g- 
 
 g- 
 
 Computation : 
 
 (a) How many degrees was the water raised in tempera- 
 
 ture? 
 
LINES OF MAGNETIC FORCE 55 
 
 (6) How many calories have the calorimeter and water 
 received ? 
 
 (<?) How many grams of steam were condensed ? 
 
 (d) How many calories did s grams of condensed steam 
 give out in cooling from 100° C. to t'° C. ? 
 
 (e) How many calories did the s grams of steam give out 
 in condensing ? 
 
 (/) How many calories did one gram of steam give out 
 in condensing to water at 100° C. ? 
 
 Problem. How many B. t. u. are required to change 100 
 pounds of water at 45° F. into steam at 212° F. ? (Assume 
 the latent heat of steam to be 540 cal. for 1 g. of water at 
 100° C). 
 
 EXPERIMENT 28 
 
 LINES OF MAGNETIC FORCE 
 
 What is the direction of the lines of magnetic force which are 
 produced by the earth and a bar magnet? 
 
 Bar magnet (15 cm. x 1 cm. x 1 cm.). Thumb tacks. 
 
 Tracing compass (Hahn form). Hard, sharp lead pencil. 
 
 White paper. 
 
 Fasten a sheet of white paper to the table with thumb tacks 
 and lay the magnet on the paper near the middle so that its 
 axis lies nearly north and south and its north-seeking pole is 
 turned toward the south. Trace around the bar magnet 
 with a pencil and mark the position of its poles with the 
 letters N and S. Indicate with dots the starting points of 
 about a dozen lines of magnetic force, grouping them mostly 
 around the N-pole. 
 
56 
 
 LABORATORY MANUAL 
 
 Fig. 29 
 
 Place the tracing compass on the paper near the magnet in 
 such a way that the S-pole notch in its rim (see Fig. 29) 
 lies as nearly as possible right over a starting point, and then 
 turn the compass around this point until 
 the needle stands exactly over the line on 
 the compass base. Then mark with a lead 
 pencil the position of the N-pole notch in 
 the rim. Move the compass in the direc- 
 tion in which the N-pole points until the 
 S-pole notch lies exactly over the mark 
 that has just been made. Then turn as 
 before the compass about this point until 
 the needle lies exactly over the north- 
 south line made on the bottom of compass, and again mark 
 the position of N-pole notch. Continue this until the edge 
 of the paper is reached. Connect all these points with a 
 line of dashes and arrows to show the path and direction of 
 the compass. Such a line is called a magnetic line of force. 
 
 Draw other lines of force, beginning each time with a 
 point near the N-pole of the magnet. 
 
 Draw lines of force which start on the south edge of the 
 paper but do not hit the magnet at all. 
 
 On another sheet of paper, repeat this experiment with the 
 S-pole pointing south. 
 
 Fold up the sheets of paper and glue them into the regular 
 notebook. 
 
 Questions. Are there any points in the magnetic field 
 about the bar magnet where the force of the earth and mag- 
 net are exactly equal but opposite in direction ? How did 
 you detect them ? 
 
THE VOLTAIC CELL 
 
 57 
 
 EXPERIMENT 29 
 
 THE VOLTAIC CELL 
 
 How can chemical energy he converted into electrical energy ? 
 
 Glass tumbler. 
 
 Zinc strip, unainalgamated. 
 
 Zinc strip, amalgamated. 
 
 Copper strip. 
 
 Board top for tumbler. 
 
 2 binding posts. 
 
 Sulphuric acid (1 : 20). 
 
 Commercial sal-ammoniac cell. 
 
 Connecting copper wire. 
 
 Simple galvanoscope. 
 
 Large copper plate. 
 
 Zinc wire. 
 
 Porous cup. 
 
 Copper sulphate solution. 
 
 Zinc sulphate solution. 
 
 I. Action of Dilute Sulphuric Acid on Copper and Zinc. 
 
 (1) Open circuit. Fill a tumbler about three fourths full of 
 dilute sulphuric acid (1 to 20) and put a strip of copper 
 and a strip of zinc into the acid in such a way as to avoid 
 all metallic connections between the strips. Observe for a 
 few minutes the action of the acid on each strip and then 
 record just what is seen on the 
 surface of each metal. (The bub- 
 bles are hydrogen.) 
 
 (2) Closed circuit. Connect the 
 tops of the strips (Fig. 30) and 
 notice what change, if any, takes 
 place on the surface of each metal. 
 Record the results. FlG - 3° 
 
 II. Effect of using Amalgamated Zinc. Replace the or- 
 dinary zinc which has just been used by an amalgamated 
 zinc plate or rod (i.e. zinc which has been dipped in mer- 
 cury and rubbed until it is covered with a smooth coating 
 of mercury). Repeat the experiment with the circuit open 
 
58 
 
 LABORATORY MANUAL 
 
 Fig. 31 
 
 and closed, and record any differences which are observed in 
 the action. 
 
 III. Magnetic Effects observable about the Wire connect- 
 ing the Strips. Place a very simple form of galvanoscope 
 (coil of wire with compass in the center, Fig. 31, a or J) so 
 
 that the plane of the coil is north 
 and south. Connect the binding 
 posts of the metal strips by means 
 of copper wire to 
 the binding posts of 
 the 15- or 25-turn 
 coil of the galvan- 
 oscope. Assuming 
 that the current 
 comes from the cell 
 by way of the copper strip, note the direction of the current 
 as it goes over the top of the galvanoscope coils and the posi- 
 tion of the needle. Reverse the currents in the coils by 
 interchanging the wire connections of the galvanoscope. 
 Observe the new position of the needle due to the change 
 in direction of the current. 
 
 IV. Polarization of a Simple Cell. Set up the cell as used 
 in III, but use a copper plate of large surface (rolled into 
 cylindrical form) and a very narrow strip or wire of zinc. 
 Arrange the coils of the galvanoscope so that the coils are 
 north and south, and turn the compass so that its zero is 
 directly under the north end of the needle. When all the 
 connections are made, immerse the plates in the acid and 
 read the deflection of the needle as soon as it stops swinging 
 violently. (If this deflection is more than about 45° insert 
 into the circuit enough No. 36 German silver wire to reduce 
 the deflection to about 40°.) Tap the galvanoscope lightly 
 
THE VOLTAIC CELL 
 
 59 
 
 
 E3 
 
 Nut 
 
 _=^ 
 
 =£~HI 
 
 s 
 
 
 
 ~fz 
 
 3= 
 
 ^^ 
 
 -:^ 
 
 d^fl 
 
 fe 
 
 
 Fig. 32 
 
 This is known as 
 
 to allow the needle to take its proper position. Watch the 
 needle carefully for two minutes and record what you ob- 
 serve. Short-circuit the cell for half a 
 minute by holding a stout, short copper 
 wire in contact with both the copper and 
 zinc plates (Fig. 32). Of course the de- 
 flection is reduced nearly to zero because 
 most of the current now goes through the 
 stout copper wire. Remove this wire and 
 see if the needle returns quite to its old 
 value. By short-circuiting the cell, the 
 hydrogen was generated in greater abun- 
 dance. Judging from this experiment, 
 what effect does an accumulation of hy- 
 drogen upon the copper plate seem to 
 have upon the strength of the current ? 
 the polarization of the cell. 
 
 V. Daniell Cell. Replace the simple cell with a Daniell 
 cell, which has the zinc plate standing in zinc sulphate 
 solution and the copper plate in copper sulphate solution 
 and the two solutions separated by a po- 
 rous cup as shown in Fig. 33. (Fill the 
 porous cup nearly full of zinc sulphate 
 solution and allow it to stand three or 
 four minutes so that the solution fills the 
 pores of the cup and so lets the electricity 
 pass through it easily.) Repeat the ex- 
 periment of IV and record the behavior of 
 this two-fluid cell. Can the Daniell cell 
 be called a non-polarizing cell ? Lift up the copper plate 
 and examine its surface. Does the fact that copper instead 
 of hydrogen has been deposited on the copper plate account 
 for the steadiness of the current of the Daniell cell ? 
 
 -r 
 
 mGu 
 
 ZriSOi CxiSOi 
 [Porous cup _ 
 
 Fig. 33 
 
60 LABORATORY MANUAL 
 
 VI. Sal-ammoniac Cell. If time permits, repeat the ex- 
 periment of IV using a commercial sal-ammoniac cell (zinc 
 and carbon). Does this cell recover after being short-cir- 
 cuited ? Break the circuit entirely for a few minutes and 
 then connect and read the deflection. 
 
 Question. What kind of cell would you use to operate an 
 ordinary electric bell ? Why ? 
 
 EXPERIMENT 30 
 
 MAGNETIC EFFECT OF A CURRENT 
 
 What is the direction of the magnetic lines of force about a wire 
 
 carrying an electric current? 
 What is the direction of the magnetic lines of force about a coil 
 
 carrying an electric current? 
 How is the distribution of magnetic flux passing through a coil 
 
 changed by inserting a soft iron core? 
 How should the windings of an electromagnet be connected? 
 
 Dry cell. Compass (2.5 cm. needle). 
 
 Reversing switch (or commutator). Soft iron rod or core. 
 Connecting wires. U-shaped iron core. 
 
 I. Magnetic Field about a Wire Carrying Current. Assum- 
 ing that the N-pole of the magnetic needle points in the 
 direction of the magnetic lines of force and that the direction 
 in which the electricity flows through a zinc-copper (or zinc- 
 carbon) cell is from zinc to copper (or carbon) inside the liquid 
 said from copper to zinc in the external circuit, we will inves- 
 tigate the magnetic field around a wire carrying a current. 
 
 (<z) Connect a simple cell, such as a dry cell, to a revers- 
 ing switch (Fig. 34) or commutator (Fig. 35) and then lead 
 
MAGNETIC EFFECT OF A CURRENT 
 
 61 
 
 the current from south to north 
 over a compass. Close the 
 circuit by closing the switch 
 (or commutator) and record 
 the deflection. 
 
 (J) Turn the switch so as 
 to reverse the current, caus- 
 ing it to flow from north to 
 south over the compass. Record the deflection. 
 
 Compare these results with what might be expected from 
 the so-called thumb rule. 
 
 If one grasps the ivire with the right hand so that the thumb 
 points in the direction of the current, the fingers will point in 
 the direction of the magnetic field. 
 
 Fig. 35 
 
 (<?) Put the wire under the compass and without chang- 
 ing the direction of the current note the direction of the 
 deflection. 
 
 (c?) Pass the current froni the cell over the compass from 
 south to north, holding the wire close to the face of the com- 
 pass and make the return wire pass under the compass so 
 that a loop is made around the compass. Is the deflection 
 greater or less than in (a) ? Why? 
 
 II. Magnetic Field about a Coil Carrying Current, (a) Loop 
 the wire used in I (d) several times around the compass in 
 such a way that the plane of the coil is north and south. 
 
62 LABOEATOBY MANUAL 
 
 What change in the deflection is produced by increasing the 
 number of turns in the coil ? 
 
 (6) Make a helix (Fig. 36) by wrapping the wire say 
 fifty times around a lead pencil. Connect this to the switch 
 
 or commutator as in I, 
 and see whether or not 
 such a helix carrying a 
 current acts as a mag- 
 *" net with one end at- 
 tracting the north pole of the compass and the other repell- 
 ing it. Reverse the current through the helix by means of 
 the commutator and record the effect that is produced upon 
 the poles. 
 
 Compare these results with what might be expected from 
 the thumb rule for a coil. 
 
 Grrasp the coil with the right hand so that the fingers point in 
 the direction of the current in the coil, and the thumb will point 
 to the north pole of the coil. 
 
 - (<?) Make an electromagnet by putting a large iron nail 
 or bolt inside the helix. Does this iron core make the poles 
 stronger or weaker than before ? How do you know ? 
 
 (d!) Wind the two sides of the U-shaped piece of iron 
 with a wire carrying a current, in such a way that one end 
 which has been already marked shall be an N-pole and the 
 other an S-pole. 
 
 Test the polarity of this horseshoe with a compass. 
 
 In recording the results of these experiments make very 
 simple but clear diagrams, showing the polarity and the 
 direction of the current in each case. 
 
 Question. An ordinary twisted lamp cord, connected to a 
 lighted electric reading lamp, passes over a pocket compass. 
 What effect will the current have on the magnetic needle ? 
 
ELECTBOMOTIVE FORCE 
 
 63 
 
 EXPERIMENT 31 
 
 ELECTROMOTIVE FORCE 
 
 How does the JE. M. F. of a cell depend upon the size and 
 character of the electrodes and on the solution or electrolyte ? 
 
 How does the JE. M. F. of a group of cells depend on their 
 arrangement (series and parallel) ? 
 
 D'Arsonval galvanometer and 
 high resistance coil (1000 
 ohms), or voltmeter (0-5). 
 
 Simple voltaic cell (Exp. 29). 
 
 Carbon rod or plate for cell. 
 
 Lead rod or plate for cell. 
 
 Sulphuric acid (1 :20). 
 Hydrochloric acid dil. 
 Brine, solution of common salt. 
 2 Dry cells. 
 Connecting wires. 
 Connectors for joining wires. 
 
 In order to compare the electromotive 
 forces, or the electric pressures of cells, we 
 may compare the currents which they 
 send through a high resistance galva- 
 nometer. A very convenient galvanom- 
 eter for this purpose is the d'Arsonval 
 galvanometer (Fig. 37), which consists 
 essentially of a horseshoe steel magnet 
 with a coil of many turns of fine copper 
 wire hung between the poles. The coil 
 is suspended so that the plane of the coil 
 is parallel to the line joining the poles, 
 but when a current, even a very slight 
 current, is sent through the coil, it is 
 turned because it acts as an electro- 
 magnet and its poles are attracted and 
 repelled by the poles of the horseshoe 
 magnet. In this experiment we shall 
 connect in series with the galvanometer 
 
 JFig. 37 
 
64 
 
 LABORATORY MANUAL 
 
 a coil of small German silver wire having 
 a resistance of about 1000 ohms. Such 
 a galvanometer may be replaced by the 
 more convenient voltmeter (Fig. 38), 
 which is simply a portable d'Arsonval 
 galvanometer with a high resistance coil 
 in series. 
 
 Fig. 38 
 
 I. Effect of Size of Cell on the E. M. F. 
 
 Connect a simple cell, such as used in Exp. 29, with the gal- 
 vanometer having the high resistance in series. Note the 
 deflection of the needle which is attached to the mov- 
 able coil. Then move the plates as far apart as possible in 
 the jar and again note and record the deflection. Finally 
 lift the plates almost out of the liquids and record the 
 deflection. 
 
 What effect does the distance between the plates and the area 
 of the plates immersed seem to have on the electromotive force of 
 a cell ? 
 
 II. Effect of Using Different Metals on the E. M. F. Note 
 the direction and amount of the deflection caused by the 
 zinc-copper cell. Remove the copper plate and insert a 
 carbon plate or rod and again note the direction and amount 
 of the deflection. If the deflection is in the same direction 
 as above, it shows that the carbon is positive ( + ) with 
 respect to zinc ; but if it is in the opposite direction, then 
 the zinc is positive ( + ) with respect to the carbon. In the 
 same way test the following pairs of metals as electrodes : 
 zinc-lead, lead-copper, and lead-carbon. 
 
 Which pair gives the highest E. M. F. ? 
 
 Is there any metal among those investigated that is jyosi- 
 tive ivith respect to some metals and negative with respect to 
 others ? 
 
ELECTROMOTIVE FORGE 65 
 
 III. Effect of Different Liquids (Electrolytes) on the E. M. F. 
 
 Note again the amount and direction of the deflection when 
 zinc and copper are immersed (a) in dilute sulphuric acid ; 
 (6) in dilute hydrochloric acid (HC1) ; (#) in a solution of 
 common salt (NaCl) ; (c?) in water (H 2 0). 
 
 The plates should be thoroughly rinsed off before placing 
 them in a new liquid. 
 
 What is the effect of the different liquids used as electrolytes 
 on the F. M. F. of the cell? 
 
 IV. Effect of Series and Parallel Arrangement on the E. M. F. 
 
 Using the high resistance coil in series with the galvanometer, 
 connect two similar cells (such as dry cells) in series, that 
 is, connect the zinc of 
 one to the copper (or /^g\^^ g \ + 
 
 W V_^ 
 
 carbon) of the other as 
 
 shown in Fig. 39 and 
 
 record the deflection. FlG " 39 FlG ' 40 
 
 Then connect the same cells in parallel, that is, zinc to zinc 
 
 and copper to copper, as shown in Fig. 40, and again read 
 
 and record the deflection. 
 
 Compare these results with the deflection of a single cell. 
 
 What is the effect of the series arrangement on the F. M. F? 
 What is the effect of the parallel arrangement on the FJ. M, F? 
 
 Question. Six storage cells, 2 volts each, are connected in 
 two rows of three cells each. The three cells in each row 
 are joined in series, and two rows of cells are joined in 
 parallel. What is the E. M. F. of this arrangement ? 
 
66 LABORATORY MANUAL 
 
 EXPERIMENT 32 
 
 THE FALL OF POTENTIAL ALONG A CONDUCTOR 
 
 When a steady current is flowing along a conductor, how does 
 the fall of potential (" voltage ") between two points vary with 
 the resistance? 
 
 When the resistance remains fixed, how does the fall of potential 
 depend upon the current ? 
 
 Low resistance galvanometer Voltmeter (low range) or 
 
 or ammeter (0-5 amp.). high resistance galva- 
 
 1-meter high-resistance wire nometer. 
 
 stretched along a meter stick. Variable rheostat. 
 
 Storage battery (3 cells) or 
 other source of steady cur- 
 rent, such as Daniell cells. 
 
 I. Potential Difference across Equal Resistances. Connect 
 one meter of high resistance wire in series with a low reading 
 ammeter (A), an adjustable resistance (B), and a source of 
 steady current, such as a battery of storage or Daniell cells 
 (Fig. 41). Make the connections such that the current enters 
 
 Fig. 41 
 
 at the end marked and adjust the resistance so that the cur- 
 rent is one ampere. Touch the + terminal of a low reading 
 voltmeter (F) to the terminal of the wire and touch the 
 other terminal firmly against the wire at a point just 10 cm. 
 from the terminal. Read carefully the voltmeter and 
 record this as the potential difference or difference in electrical pres- 
 
THE FALL OF POTENTIAL ALONG A CONDUCTOR 67 
 
 sure between the ends of this 10-em. length of wire. In the 
 same way measure the fall of potential (or voltage) from 10 
 to 20, 20 to 30, etc., i.e. for each 10-cm. length along the 
 wire. Assuming the wire is of uniform cross section, how 
 do the resistances of equal lengths compare ? What conclu- 
 sion can you draw regarding the drop in potential for equal 
 resistances and the same current? 
 
 II. Potential Difference across Varying Resistances. Con- 
 nect the + terminal of the voltmeter to the end of the wire 
 and place the other terminal successively at 10, 20, 30 cm., 
 etc., and record the voltage for each case. How does the 
 resistance of 20 cm. of wire compare with the resistance of 
 10 cm.? How does the drop in potential (or voltage) across 
 20 cm. of wire compare with that across 10 cm.? Compare 
 the resistances and voltages for 40 cm. and 80 cm. lengths 
 in the same way. 
 
 When the current is constant in a conductor, hoiv does the 
 drop in potential depend on the resistance ? 
 
 III. Effect of Varying Current on Potential Difference. 
 
 Measure the voltage across 50 cm. of wire when the current 
 is 0.5 ampere and then 1.0, 1.5, 2.0, 2.5, and 3.0 amperes. 
 
 How does the fall of potential in any given conductor vary 
 with the current flowing ? 
 
 Upon what does the drop in potential across any given con- 
 ductor depend? 
 
 Note. The terms "drop in potential" and "potential difference' ' as 
 used in this experiment mean the same thing — " voltage." 
 
 Problem. A generator is sending 7.5 amperes through 
 two resistances, 8 ohms and 10 ohms in series. What is the 
 voltage across the 8-ohm resistance ? What is the voltage 
 across the 10- ohm resistance ? What is the voltage across 
 both resistances ? 
 
68 LABORATORY MANUAL 
 
 EXPERIMENT 33 
 
 DETERMINATION OF RESISTANCE BY USE OF AMMETER 
 AND VOLTMETER 
 
 How should the ammeter be used to measure current (a) in two 
 
 coils in series, (b) in two coils in parallel ? 
 How should the voltmeter be used to measure the voltage (a) 
 
 across two coils in series, (b) across two coils in parallel ? 
 How can we compute the resistance of (a) each of the two coils 
 
 and (b) of the two coils in parallel ? 
 
 110-volt direct current line or Fuses. 
 
 storage battery. Voltmeter (0-150). 
 
 Two resistance coils of manga- Ammeter (0-15). 
 
 nin wire, or la la wire. 
 
 I. Measurement of Current. Join the two coils in series 
 and connect with the 110-volt D.C. service or other supply 
 of steady current. Place the ammeter (a) between coil 1 
 and the power, (5) between coil 1 and coil 2, (c) between 
 coil 2 and the power. Record the average reading of the 
 ammeter in each position. What do you conclude about the 
 current in a series circuit ? Where should the ammeter be 
 placed in a series circuit ? 
 
 Join the two coils in parallel and measure the current 
 with the ammeter (&) in the line between the coils and the 
 power, (J) in the circuit of No. 1 alone, and (#) in the circuit 
 of No. 2 alone. Compare the sum of currents in (V) and (c) 
 with the current in (a). Where must the ammeter be placed 
 to measure the current in a branch circuit ? 
 
 II. Measurement of Voltage. With the coils in series, 
 measure the voltage across (a) the two coils together and 
 (6) each coil alone. Take the average reading of the volt- 
 
DETERMINATION OF RESISTANCE 69 
 
 meter. Compare the sum in (6) with the reading in (a). 
 What is the effect upon the current flowing through each 
 part of a series circuit, if the resistance of any unit is de- 
 creased ? 
 
 Connect the two coils in parallel and take the voltage be- 
 tween the binding posts of each coil. Compare these read- 
 ings. Assuming a constant voltage service, what will be the 
 effect upon the voltage across the group if the resistance of 
 one coil is decreased ? Upon the current flowing along that 
 coil ? Upon the current in the other coil ? In the line ? 
 
 III. Computation of Resistance. From the readings in 
 Part I and II, compute, using Ohm's Law, the resistance of 
 each coil and the joint resistance of the two coils in paral- 
 lel. Compare this latter result with that obtained by com- 
 puting the joint resistance from the separate resistances. 
 In recording the data of this experiment, make careful dia- 
 grams to show the connections. 
 
 Problem. A circuit has two branches, one of 2 ohms, the 
 other of 12 ohms. The current in the 2-ohm branch is 5 
 amperes. What difference of potential is maintained between 
 the terminals of the circuit ? What current flows in the 
 second branch ? 
 
70 LABORATORY MANUAL 
 
 EXPERIMENT 34 
 
 MEASUREMENT OF RESISTANCE BY WHEATSTONE 
 
 BRIDGE 
 
 How can resistances be compared by a Wheatstone bridge ? 
 What is the resistance of 50 ft. of No. 30 copper wire? 
 
 2 dry cells. D'Arsonval galvanometer. 
 
 Key. Resistance box or known resistance coils. 
 
 Wheatstone bridge. 50-f t. coil of No. 30 copper wire. 
 
 The Wheatstone bridge consists essentially of a loop of 
 four resistances, indicated in Fig. 42 as R, X, w, and n. 
 
 When the key, if, is closed, the 
 current from the cells flows into 
 the loop at A, and there divides 
 so that part (ij) goes through 
 AC and part (Jg) through AD. 
 A sensitive galvanometer (6r) is 
 connected between O and D. 
 Then the resistances R, X, ra, 
 
 Fig 42 
 
 and n are so adjusted that no 
 current flows through the galvanometer, which means that 
 all of I x has to go on through CB and all of I 2 through DJS, 
 and also that C and D are " equipotential " points. When this 
 adjustment has been made, 
 
 the voltage drop across A O = I X R, 
 
 and the voltage drop across AD = I 2 m. 
 
 But since and D are at the same potential, these voltage 
 drops are equal, and j j> _. j r-\\ 
 
 For similar reasons I X X = I 2 n. (2) 
 
MEASUREMENT OF RESISTANCE 71 
 
 Dividing equation (1) by equation (2), we have 
 
 R_m 
 X~~n' 
 
 From this fundamental equation of the Wheatstone bridge, 
 if we know i?, ra, and n, we can compute X. 
 
 In the form of this appa- R 
 
 ratus shown in Fig. 43, the 
 resistance ABB consists of 
 
 a wire of uniform cross sec- ^r u * j 
 
 tion and one meter long. 
 
 Since the resistances m and 
 
 n are then directly proportional to the distances AB and 
 
 BB, the equation becomes 
 
 R ___ Distance AD 
 X~ Distance DB' 
 
 where R is a known resistance such as a resistance box, and 
 the distances AB and BB are read off on a meter stick. It 
 will be helpful to remember that 
 
 Left Resistance __ Left Distance 
 Right Resistance Right Distance m 
 
 Connect the apparatus, as shown in Fig. 43, using a 
 50-ft. coil of No. 30 copper wire in position marked X. 
 When the key in the battery circuit is closed, the current 
 comes to A where it divides, part going through the known 
 resistance J2, along the bar of the bridge (whose resistance 
 is negligible), and through the unknown coil X to B\ 
 the other part going by way of the German silver wire ABB 
 to B. If the known resistance is made in the form of a 
 resistance box, we may remove the 10-ohm plug, place the 
 slider B connected to the galvanometer in the middle of 
 the German silver wire, and make contact for an instant 
 
72 LABORATORY MANUAL 
 
 only. If the galvanometer needle moves, it shows that the 
 two points and D are at different potentials. First try 
 another value for R, say 1 ohm, and if the galvanometer 
 needle swings the other way when contact is made at D, it 
 shows that X, the unknown resistance, lies between 1 and 10 
 ohms. By trial just as in weighing make a balance between 
 R and X. When it is approximately balanced, make the 
 fine adjustment by sliding D back and forth along the wire 
 until the galvanometer shows no current flowing when the 
 contact is made at D. From the above equation compute the 
 resistance of 50 ft. of No. 30 copper wire. 
 
 Repeat the experiment twice, using slightly different 
 values for i?, the known resistance. Find the average or 
 mean value of these three results and compute from this the 
 resistance of 1000 feet of No. 30 copper wire. Compare this 
 with the result given in the Wire Tables in the Appendix. 
 
 Problem. In testing a certain Wheatstone bridge, a 
 standard 5-ohm coil is placed at R and a standard 4-ohm 
 coil at X. What is the correct position of D, i.e. what are 
 the correct values for m and n ? 
 
INTERNAL RESISTANCE OF A BATTERY 73 
 
 EXPERIMENT 35 
 
 INTERNAL RESISTANCE OF A BATTERY 
 
 What is the effect on the current of decreasing the size of the 
 plates of a cell and the distance between them ? 
 
 When the external resistance is small, what effect does it have 
 on the current to arrange cells (a) in series and (b) in 
 parallel? 
 
 How can we measure the internal resistance of a cell? 
 
 Daniell cell. Two dry cells. 
 
 Ammeter or low resistance gal- High resistance wire such as 
 
 vanometer. No. 36 G. S. wire. 
 
 In this experiment we shall consider only cases where the 
 external resistance is small. To measure the current we 
 shall use an ammeter or galvanometer with low resistance. 
 
 I. Effect of Internal Resistance on Current Furnished by a 
 Cell. Connect a Daniell cell to an ammeter and observe the 
 effect of bringing the zinc and copper plates (a) near together 
 and (b) far apart. What effect on the internal resistance of 
 a cell does it have to increase the distance between the 
 plates ? 
 
 Gradually lift the plates out of the liquid and record the 
 effect on the current. What effect on the internal resistance 
 of a cell does it have to diminish the area plates immersed ? 
 
 II. When the External Resistance is Small, what Combina- 
 tion of Cells gives the Greatest Current ? (a) Connect two 
 similar cells in series with an ammeter and record the cur- 
 rent. Compare this with the current furnished by one cell. 
 How do the results of this experiment compare with results 
 of testing the E. M. F. of two cells in series (Exp. 31) ? 
 
74 LABORATOBY MANUAL 
 
 (5) Join two cells in parallel and observe the current. 
 Compare this with the current strength of one cell. How 
 do these results compare with the E. M. F. test of two 
 cells in parallel ? How do you explain this difference ? 
 
 III. Measurement of Internal Resistance. Connect a 
 Daniell cell with an ammeter and record the current. In- 
 troduce into the circuit some high resistance wire, such as 
 No. 36 German silver wire, sufficient to reduce the current 
 to just one half its former value. Measure the length of 
 the German silver wire used and calculate from the specific 
 resistance of the wire the resistance thus introduced. As- 
 suming the E. M. F. of the cell to have remained constant, 
 in order to reduce the current to one half, the resistance 
 must have been doubled. This means that the internal 
 resistance of the cell is equal to the resistance of the Ger- 
 man silver wire which has been inserted. 
 
 The internal resistance of cells arranged in series or in 
 parallel can be computed just like the resistance of several 
 wires in series or in parallel ; that is, the series arrange- 
 ment multiplies the internal resistance and the parallel 
 arrangement divides the internal resistance of one cell by 
 the number of cells. 
 
 How should cells be connected to get a large current when 
 the external resistance is small ? When the external resistance 
 is large ? 
 
 Problem. A telegraph sounder has a resistance of 70 ohms 
 and requires 0.2 ampere to work it. How many gravity 
 cells, each of 1.1 volts and 3.0 ohms, will be required? 
 
MEASUREMENT OF CURRENT 
 
 75 
 
 EXPERIMENT 36 
 
 MEASUREMENT OF CURRENT BY A COPPER 
 COULOMBMETER 
 
 How may an ammeter be cheeked by the weight of copper de- 
 posited in a certain time ? 
 
 Copper coulombmeter. 
 
 Copper sulphate (CuS0 4 ) 
 solution with a little sul- 
 phuric acid and alcohol. 
 
 Ammeter. 
 
 Adjustable resistance. 
 
 Watch or clock with second 
 
 hand. 
 Beam balance and weights. 
 Storage battery or supply of 
 
 steady current. 
 
 The copper coulombmeter consists of a glass jar with two 
 anode plates (J., A) and one cathode ( (7) or gain plate placed 
 between them (Fig. 44). About 50 
 cm. 2 of cathode surface is allowed 
 for each ampere of current, and the 
 liquid is a solution of copper sulphate 
 (CuS0 4 ), slightly acidulated with sul- 
 phuric acid (H 2 S0 4 ) and containing 
 a little alcohol. The gain plate (cath- 
 ode) is first made perfectly clean by 
 rubbing with fine emery until bright, 
 and then wiping with a clean dry 
 cloth. After it is cleaned, the part 
 which is to be immersed must not be 
 touched by the fingers. 
 
 Weigh this clean cathode as accu- 
 rately as you can and set it aside. 
 
 Connect the ammeter to be checked 
 with an adjustable resistance in circuit with the coulomb- 
 meter and some supply of steady current such as a storage 
 
 —J Cathode [ 
 
 Fig. 44 
 
Cs 
 
 76 LABORATORY MANUAL 
 
 battery. Insert in the coulombmeter a trial cathode plate, 
 not the clean one, but the same size as the one to be used. 
 The current must be made to enter at the outside plates 
 (anodes) and emerge at the middle or gain plate (cathode) 
 (Fig. 45). Close the circuit and adjust 
 
 1 J I u I q the resistance to give the desired current 
 
 (from 1 to 2 amperes). 
 
 Open the circuit and replace the trial 
 cathode by the clean weighed cathode 
 and again close the circuit, noting ex- 
 actly the time (hr. min. sec). Record 
 the ammeter reading every ten minutes 
 and keep the current constant. After 
 30 or 40 minutes, break the circuit and at once remove the 
 gain plate. Note the deposit of copper. Rinse off in clean 
 water and then in alcohol and dry quickly. Reweigh and 
 determine the gain as precisely as possible. 
 
 Compute the gain in weight per hour. 
 
 Assuming that 1.186 g. of copper is deposited by one 
 ampere in one hour, compute the average current. 
 
 Compare this value of the current with the average reading 
 of the ammeter. 
 
 Problem. How many ounces of copper would be deposited 
 from a solution of copper sulphate in 10 hours by a current 
 of 2.5 amperes? 
 
INDUCED CURRENTS 77 
 
 EXPERIMENT 37 
 
 INDUCED CURRENTS 
 
 How may currents be induced by means of a magnet? 
 How may currents be induced by an electromagnet ? 
 How may a conductor be moved in a magnetic field to generate 
 a current? 
 
 D'Arsonval galvanometer. Bar magnet. 
 
 2 dry cells. Soft iron core. 
 
 2 coils of about 800 turns No. Reversing switch. 
 
 28 copper wire. U-shaped steel magnet. 
 
 I. Induction by a Magnet. To see which way the needle 
 of the d'Arsonval galvanometer turns when the current 
 enters at the right-hand binding post, we may short-circuit 
 the instrument with a stout copper wire and connect with a 
 simple cell so that the current enters at the right terminal 
 of the galvanometer. Place a piece of paper near the in- 
 strument and record the direction of the deflection with an 
 arrow when the right terminal is made positive ( + ). Con- 
 nect to the galvanometer (now without any shunt) a coil of 
 many turns (say 800 turns of No. 28 
 copper wire). 
 
 (a) Now move the coil downward 
 quickly over the N-pole of the bar 
 magnet (Fig. 46), and record the 
 direction and amount of the deflec- 
 tion. From this deflection, deter- 
 mine the direction of the current 
 induced in the coil. While this current was flowing in the 
 coil, it made the coil a temporary magnet. What was the 
 polarity of the side of the coil approaching the N-pole of 
 the magnet ? 
 
 Fig. 46 
 
78 LABORATORY MANUAL 
 
 (h) Quickly remove the coil from the magnet and record 
 the direction and amount of the deflection. Compare the 
 direction and amount of the current thus induced with that 
 in part (a). What is the polarity of the end of the coil 
 that last leaves the magnet's N-pole ? 
 
 (tf) Repeat (a) and (5) using the S-pole of the magnet 
 and in each case determine the direction of the current in- 
 duced in the coil. Is the direction of the induced current such 
 as to oppose or to assist the motion of the coil ? 
 
 II. Induction by an Electromagnet. Insert an iron rod 
 in a coil S which is connected to the galvanometer. Con- 
 nect through a commutator one or two dry cells to a similar 
 coil P which is placed on the iron rod beside coil S. 
 
 (a) Now close the circuit by the commutator or switch 
 and record the deflection of the galvanometer. From this 
 determine the direction of the current induced in the coil S. 
 Was this current induced in coil S (called the secondary) 
 in the same direction as the current in coil P (called the 
 primary) ? Explain how this might be expected from the 
 experiment in Part I. 
 
 (5) Break the circuit at the commutator and note direc- 
 tion and amount of the deflection. Compare this with that 
 induced when the circuit is closed. 
 
 Is the induced current in the same or in the opposite direc- 
 tion to that which is flowing in the primary coil ? Note that 
 the current is induced by the changes in the magnetism of 
 the electromagnet. Is the direction of the induced current 
 such as to oppose or assist the changes in the magnetism of the 
 iron core ? 
 
 III. A Current Generated by Moving a Conductor across a 
 Magnetic Field. Hold the coil S which is connected to the 
 galvanometer between the poles of a horseshoe magnet in 
 
EFFICIENCY OF AN ELECTBIC MOTOR 
 
 79 
 
 Galv. 
 
 K\ 
 
 x 
 
 such a way that the plane of the coil is at right angles to 
 the line joining the poles (Fig. 47). Quickly turn the coil 
 a quarter turn so that the plane of the 
 coil is parallel to the magnetic field. 
 Observe the direction of the induced 
 current. After the galvanometer has 
 come back to zero, rotate the coil an- 
 other quarter turn and note the di- 
 rection of the induced current. In a 
 similar manner continue to rotate the 
 coil one quarter turn at a time. In 
 what position is the coil when the in- 
 duced current is reversed? Fig. 47 
 
 Note. In this experiment it will be helpful to record the results in the 
 form of very simple sketches showing the direction of the motion and induced 
 current and polarity of the magnet. 
 
 Question. A coil is rotated in a magnetic field in such a 
 way that no current is induced. What is the direction of 
 its axis of rotation ? 
 
 EXPERIMENT 38 
 
 EFFICIENCY OF AN ELECTRIC MOTOR 
 
 What is the ratio of the mechanical output of an electric motor 
 to the electrical input ? 
 
 0.25 horse power motor. 
 110- volt direct current 
 line or storage battery. 
 Ammeter. 
 Voltmeter. 
 
 Two spring balances and sup- 
 port. 
 Cord or strap for brake. 
 Speed counter. 
 Watch. 
 
 Connect a small D. C. motor to some supply of electric 
 current. Insert an ammeter in the line to measure the in- 
 
80 
 
 LABORATORY MANUAL 
 
 Fig. 48 
 
 tensity of the current /and put a voltmeter across the brushes 
 (Fig. 48) to get the electrical pressure E. From these two 
 
 factors we may eas- 
 ily compute the input 
 in watts which is 
 equal to the 'product 
 of volts times am- 
 peres. 
 
 To get the mechanical output we may make a brake test. 
 A very simple form of brake consists of a belt or cord 
 attached to two spring balances and passing under a pulley 
 on the motor shaft, as shown in Fig. 49. If the motor ro- 
 tates clockwise, as indicated, it is 
 evident that the spring balance A 
 will have to exert more force than 
 balance B because of the friction of 
 the pulley on the cord. The amount 
 of this friction is equal to the differ- 
 ence between the readings of A and 
 B, and it is exerted each minute 
 through a distance equal to the cir- 
 cumference of the pulley times the 
 revolutions per minute. The work 
 done in one minute is equal to the 
 friction times the distance per minute. 
 First determine the circumference 
 of the pulley by measuring the length of fine wire required 
 to make one turn around the pulley. To determine the 
 number of revolutions per minute, hold a speed counter 
 (Fig. 50) against the end of the motor shaft (S) for just 
 one minute. 
 
 When all the apparatus is assembled, start the motor by 
 closing the switch. Throw on the load by increasing the 
 
 Fig. 49 
 
EFFICIENCY OF AN ELECTRIC MOTOR 
 
 81 
 
 tension on the brake cord so as to slow down the 
 motor a little. Keeping this pull steady, we get 
 the speed of the motor and at the same time read 
 the spring balances, ammeter and voltmeter. Then 
 repeat this experiment, putting more load on the 
 motor by pulling more strongly on the balances. 
 Finally, make a third trial with still more load on 
 the motor. 
 
 It will be convenient to record the data and 
 results in tabular form, somewhat as follows : 
 
 Fig. 50 
 
 
 First Trial 
 
 Second Trial 
 
 Third Trial 
 
 Voltmeter reading 
 
 Ammeter reading 
 
 
 
 
 Watts put in motor 
 
 Number of revolutions per minute . 
 Distance meters per minute . . . 
 Balance A reading (kg.) .... 
 Balance B reading (kg.) .... 
 
 
 
 
 Friction (A - B) (kg.) .... 
 Work got out of motor (watts) . . 
 Efficiency % 
 
 
 
 
 It will be helpful to know that 1 watt = 6.12 kilogram- 
 meters per minute. 
 
 Does the efficiency of the motor change when the load is 
 changed? Why does the amount of current supplied to the 
 motor change as the brake load increases? 
 
 Problem. At 10 cts. per K.W.-hour, how much will it cost 
 per week of 54 hrs. to run a motor, having an average load 
 of 10 H.P., and an average efficiency of 90 % ? 
 
82 
 
 LABORATORY MANUAL 
 
 EXPERIMENT 39 
 
 HEATING EFFECT OF AN ELECTRIC CURRENT 
 
 How many joules of electrical energy are equivalent to one 
 calorie of heat ? 
 
 Calorimeter and stirrer. 
 32 c.p. lamp and socket. 
 Platform scales and weights. 
 Thermometer. 
 Connecting wires. 
 
 Ammeter. 
 
 Voltmeter. 
 
 Source of current, 110 volt service 
 
 or storage battery. 
 Watch or clock with second hand. 
 
 Weigh a calorimeter with its stirrer. Then pour in 
 enough water at about 10° C. below the room temperature to 
 cover the bulb of a 32 candle power lamp and weigh the 
 
 beaker again to get the weight of 
 the water. Insert the lamp bulb 
 and a thermometer in the calorim- 
 eter ((7) and connect an ammeter 
 (J.) in series with the lamp (_L) and a volt- 
 meter ( F) in shunt with the lamp as shown 
 in the Fig. 51. Stir the water and note its 
 temperature and then turn on the current at 
 S) noting precisely the time of doing so. 
 
 Allow the water to be heated about as 
 much above the room temperature as it 
 started below, stirring continually. In the 
 meantime read the voltmeter and ammeter 
 every two minutes. When the current is 
 cut off, note the time and the highest temperature to which 
 the water rises. 
 
 Record the data and results in tabular form as follows : 
 
 Fig. 51 
 
HEATING EFFECT OF AN ELECTRIC CURRENT 
 
 83 
 
 Observations 
 
 Weight of beaker and stirrer . . 
 Weight of beaker, stirrer, and water 
 Temperature of water at start . 
 Time of start (hr. min. sec.) 
 Temperature of water at finish 
 Time of finish (hr. min. sec.) . 
 
 Volts Amperes 
 
 g- 
 g- 
 
 °C. 
 
 Calculated Results 
 
 Weight of water -f water equivalent of calorimeter 
 
 Rise in temperature 
 
 Calories of heat absorbed 
 
 Time of run in seconds 
 
 Average volts 
 
 Average amperes 
 
 Joules (watt-seconds) delivered to lamp . . . . 
 Number of joules per calorie 
 
 Problem. Assuming that one joule (watt-second) is 
 equivalent to 0.24 calorie, compute the price per calorie for 
 the heat generated in an electric iron using 3.5 amperes at 
 110 volts. The cost of electricity is 10 cts. per K. W.-hour. 
 
84 
 
 LABOBATOBT MANUAL 
 
 EXPERIMENT 40 
 
 FREQUENCY OF A TUNING FORK 
 
 How many vibrations does a tuning fork make in one second? 
 
 Bristles or stiff paper points. 
 
 Wax. 
 
 Releasing clamp for tuning 
 
 fork. 
 Thin shellac. 
 
 Tuning fork. 
 
 Recording apparatus (Fig. 52). 
 Glass plates. 
 Stop watch. 
 
 Alcohol lamp filled with tur- 
 pentine and alcohol. 
 
 a tuning fork (-F), 
 with a fine wire 
 or paper point at- 
 tached to one prong, 
 and a short pen- 
 Fig. 52 ^ dulum (M)i which 
 
 rrMsasssss 
 
 hne beneath the Pom » vibrations, so as to 
 
 at right angles to the ,<b rectton ^^ ^ 
 
 make a wa.y curve , on the glass, ana 
 
 '„ nl 'we can easilv connt on the «ff&£ nl^ 
 of vibrations of the fork ~ndu« * Z Zber of 
 
 swings of the pendulum, and thus compu 
 vibrations of the fork per second. 
 
FREQUENCY OF A TUNING FORK 85 
 
 Clamp the tuning fork so that its tracing point is only a 
 few millimeters from the point of the pendulum. The line 
 of these two tracing points should be parallel to the direction 
 in which the glass is to move. The tracing points must rest 
 lightly on the smoked » ss surface and yet hard enough to 
 scratch away the coating. To test this, set the fork and 
 pendulum in vibration with the glass at rest. A good way 
 to set the fork vibrating is to squeeze the prongs together 
 with a little U-shaped metal clamp and then quickly pull the 
 clamp off. 
 
 When the apparatus is properly adjusted, start the pendu- 
 lum swinging and set the fork vibrating and then draw the 
 glass along the track at such a rate as to have at least one 
 complete swing of the pendulum recorded on the glass. 
 Several sets of tracings may be recorded on the same plate 
 by moving it a little sideways, and so bringing a fresh sur- 
 face under the tracing points. 
 
 To get the rate of the pendulum, set it swinging and count 
 its vibrations for one minute. Compute the number of 
 vibrations of the pendulum per second. 
 
 Next count the number of vibrations of the fork correspond- 
 ing to a full vibration of the pendulum, i.e. the number of 
 
 fc £> x 
 
 Fig. 53 
 
 vibrations traced by the fork between the points A and C 
 (Fig. 53) or between B and D, estimating in every case to 
 tenths of a vibration. 
 
 Compute the number of full vibrations made by the fork 
 per second. 
 
 Question. In this experiment what is the effect on the 
 curve traced if we move the smoked plate more rapidly ? 
 
86 
 
 LABOBATORY MANUAL 
 
 Note. If the tracings are made on smoked paper, they may easily be 
 " fixed " by pouring over the smoked surface a very thin solution of shellac. 
 After a few minutes the paper is dry and may be pasted in the notebook as 
 a part of the record of the experiment. 
 
 Since smoked glass is always more or less dirty, the glass is sometimes 
 covered with a thin coat of whiting in alcohol. 
 
 EXPERIMENT 41 
 
 WAVE-LENGTH OF SOUND 
 
 Sow long is the sound ivave in air emitted by a vibrating tuning 
 
 fork? 
 How fast does the sound wave travel in the air of the room ? 
 
 Tuning fork (n = 512). 
 Hydrometer jar of water. 
 Resonating tube. 
 
 Large flat cork. 
 Meter stick. 
 Rubber bands. 
 
 Place the resonating tube in the hydrometer jar and pour 
 in water so as nearly to fill the jar. Strike one prong of the 
 tuning fork on a large cork stopper and 
 j i hold the vibrating fork over the open 
 end of the tube (Fig. 54). By raising 
 the tube slowly out of the water, a point will 
 be found where the air-column is of just the 
 right length to reinforce the fork. Mark with a 
 rubber band around the tube the position of the 
 water where the sound was loudest. Then set 
 the fork in vibration again and by raising and 
 lowering the tube and listening intently, deter- 
 mine again as precisely as you can the point 
 where the air-column gives the greatest reinforce- 
 ment. Measure the length of the air-column. 
 In a similar manner find a second position of the water 
 surface nearer the bottom of the tube, which also gives rein- 
 
 Fig. 54 
 
WAVE-LENGTH OF SOUND 87 
 
 forcement to the sound. Measure the length of this air- 
 column and record the temperature of the air. 
 
 The length of the short air-column (plus about 0.3 the 
 internal diameter of the tube) is equal to one fourth the wave- 
 length of the tone of the fork in air. The difference between 
 the length of the short and long air-columns is equal to one 
 half a wave-length. 
 
 Compute this difference in length between the two air- 
 columns and the length of a wave emitted by the fork used. 
 
 Given the frequency of the fork, i.e. the number of vibra- 
 tions per second, compute the velocity of sound at the tem- 
 perature of the room, using the wave-length just deter- 
 mined. 
 
 It is usually stated that the velocity of sound in air is 1087 
 feet per second at 0° C. and that it increases about 2 feet per 
 second for each degree C. rise. Compare this value with 
 the result of your experiment and compute the percentage 
 error. 
 
 Problem. What is the pitch of a closed organ pipe 62 cm. 
 long on a day when the temperature is 20° C? 
 
88 LABORATORY MANUAL 
 
 EXPERIMENT 42 
 
 BUNSEN PHOTOMETER 
 
 What is the candle power of a given electric lamp bulb in terms 
 
 of a standard lamp ? 
 What is the intensity of a Tungsten lamp ? 
 What is the effect on the downward intensity of an electric lamp 
 
 of adding a shade ? 
 
 Bunsen photometer in a dark room or Voltmeter. 
 
 in a light-tight box. Ammeter. 
 
 Three incandescent lamps (one Tung- Shade for electric bulb. 
 
 sten lamp, and one of known candle 
 
 power). 
 
 Set up a Bunsen photometer in a darkened room, as shown 
 in Fig. 55. Use a standard 16 candle power bulb (#) 
 as a basis for comparison. Insert a rheostat in the power 
 
 * K^l * 
 
 3 B cm- 
 
 I I 
 
 I Eyes \ 
 
 —A cm © 
 
 I I I 
 
 I Eyes \ 
 Fig. 55 
 
 circuit so as to bring the standard lamp to its required 
 voltage. At the other end of the photometer, about 200 cm. 
 from the first lamp, set up another electric lamp (X) which 
 is to be tested. Between these two lamps place the sight 
 box or screen (6r) with the grease spot. This screen is to 
 be moved back and forth between the lights until a position 
 is found such that the screen is equally illuminated on both 
 sides, that is, such that the central spot or disk and the sur- 
 rounding rim of paper are of the same brightness. Since it 
 
BUNSEN PHOTOMETER 89 
 
 is difficult to set this sight box or screen precisely, several 
 trials should be made and the average position taken. 
 
 Suppose that the lamp X to be tested is found to be A cm. 
 from the screen and the standard lamp S equally illuminates 
 the screen when B cm. away. If the distances A and B are 
 equal, then the candle powers of the two lamps are the same; 
 but if these distances are not equal, the lamp which is farther 
 from the screen has the greater candle power. Further- 
 more, since the intensity of illumination decreases as the 
 square of the distance, the candle powers of the two lamps are 
 directly proportional to the squares of their distances from the 
 screen. That is, jr 42 
 
 In this way, knowing S and measuring A and i?, we can 
 compute X. Find the candle power of an ordinary electric 
 lamp bulb; that is, the mean horizontal candle power. From the 
 readings of the voltmeter and ammeter in the lamp circuit, 
 compute the cost of maintaining such a lamp for one hour 
 and the cost per candle power. 
 
 Similarly, find the candle power of a 50-watt Tungsten 
 lamp. 
 
 Finally, turn an incandescent lamp into such a position as 
 to measure its candle power downward both with and with- 
 out a shade. 
 
 Problem. If a 16 candle power lamp is 85 cm. from a 
 Bunsen photometer screen, how far must a 20 candle power 
 lamp be on the other side, when the screen is properly 
 adjusted ? 
 
90 LABORATORY MANUAL 
 
 EXPERIMENT 43 
 
 IMAGE IN A PLANE MIRROR 
 
 How does the angle of incidence compare with the angle of 
 
 reflection ? 
 How does the image in a plane mirror compare with the object 
 
 in respect to size, distance, and form? 
 
 Plane mirror. Protractor. 
 
 Block for holding mirror with Ruler. 
 
 rubber bands. Block with vertical black line on 
 
 Paper. one face. 
 
 I. Reflection in a Plane Mirror. Draw a straight line 
 across a sheet of paper and label this the Mirror Line. Set 
 up the mirror so that its reflecting surface is exactly over 
 this line. At a distance of 10-15 cm. in front of the mirror, 
 make a dot and label it 0. Place the small block with its 
 vertical black line standing directly over this dot. To locate 
 the image of this line lay a ruler on the paper so that its 
 edge points directly at the image. Care should be taken to 
 sight with one eye only along the edge of the ruler and 
 then draw a clean sharp line along the edge that points 
 toward the image. To make sure that the ruler has not 
 slipped in this process, remove the ruler and look along the 
 surface of the paper and see if the line does really point at 
 the image. If not, erase the line and try again. 
 
 Place the ruler on the other side of the small block and 
 make another sight line just as before, making sure that the 
 mirror still has its reflecting surface just on the mirror line. 
 
 Remove the mirror and block and continue each of the 
 sight lines as solid lines up to the mirror line and then con- 
 tinue them as dotted lines behind the mirror until they meet. 
 
IMAGE IN A PLANE MIRROR 
 
 91 
 
 Mark this point of intersection, J, the image-point. The 
 solid sight lines represent reflected rays. From the object- 
 point, (9, draw lines to the intersection of each of these sight 
 lines with the mirror line. These lines from to the mirror 
 represent the incident rays. Connect the object-point, 0, with 
 the image-point, J, making it solid in front of the mirror and 
 dotted behind the mirror. Indicate the direction in which 
 light travels along the lines by arrows, as in Fig. 56. 
 
 At one of the points of reflection erect a normal, that is, a 
 perpendicular to the mirror, and label the angle between the 
 incident ray and this normal the angle of incidence, and the 
 angle between the reflected ray and the normal the angle of 
 reflection. 
 
 Distance of object from mirror cm. 
 
 Distance of image from mirror cm. 
 
 Angle betv^een 01 and the mirror line ° 
 
 Angle of incidence ° 
 
 Angle of reflection . . ° 
 
 II. Image in a Plane Mirror. On another sheet of paper 
 draw a line across the middle and set up the mirror as be- 
 
 A 
 
 B 
 
 > ! 
 
 
 ,'' 
 
 
 Mirror 
 
 
 
 Line 
 
 Fig. 56 
 
 (&) 
 
 fore. Draw an arrow about 5 cm. long and label it AB, as 
 shown in Fig. 56. Locate as in I the image-points of A and 
 B and label these points A f and 5'.. Construct with a 
 
92 LABOBATOBY MANUAL 
 
 dotted line the image of AB. Measure the length of A'B f . 
 Prolong the lines AB and A! B f until they intersect. Where 
 does this point of intersection lie ? The mirror line is called 
 in mathematics the axis of symmetry. If the paper is folded 
 along the mirror line and if the work has been carefully 
 done, the image will be found, when the paper is held to the 
 light, to coincide with the object. 
 
 Compare the object with its image in a plane mirror with 
 respect to size, distance, and form. 
 
 Question. What is the difference between the image that 
 one sees of himself in a plane mirror and the appearance one 
 presents to other people ? 
 
 EXPERIMENT 44 
 
 IMAGES IN CYLINDRICAL MIRRORS 
 
 I. What is the position, size, and shape of an image formed 
 in a convex mirror ? 
 
 II. What is the position, size, and shape of an image formed 
 in a concave mirror? 
 
 Convex-concave cylindrical mirror. Ruler. 
 
 Paper. Pins. 
 
 I. Convex Mirror. Place on a sheet of paper a convex 
 cylindrical mirror so that its straight lines are vertical, and 
 then trace on the paper the position of its convex surface. 
 About 5 cm. in front of the mirror draw as object an arrow 
 4 cm. long and label it A, B, 0, as shown in the Fig. 57 a. 
 To locate the position of the image of A, place a pin at point 
 A so that it stands erect and then draw two sight lines along 
 the edge of a ruler (one on each side of the pin) pointing at 
 
IMAGES IN CYLINDRICAL MIRROBS 
 
 93 
 
 the image of the pin. Label each of these lines A. Then 
 stand the pin at B and draw, as before, two sight lines 
 toward the image. In the same way draw sight lines to 
 locate the image of C. 
 
 A- 
 F 
 -B 
 
 c 
 
 > Concave 
 Mirror 
 
 , Object 
 
 I 
 
 -D 
 
 (a) 
 
 Fig 57 
 
 (&) 
 
 Remove the mirror and pin and continue each pair of sight 
 lines until they intersect. In this way locate the image- 
 points of A, B, and O and label these points A ', B', C. 
 Draw a line from A' through B ! to r with an arrow at A! . 
 Label this arrow the Image. 
 
 Compare the object and its image in a convex mirror as to 
 position, size, and shape. 
 
 II. Concave Mirror. Stand the mirror a little above the 
 middle of a sheet of paper and draw a sharp line along its 
 concave edge. Remove the mirror and draw a dotted line 
 connecting the ends of the arc. Draw a perpendicular at 
 the mid-point of this chord and label it axis. Assuming that 
 the radius of curvature is 5 cm., mark the center of curvature 
 with the letter (7. Mark the focus F, which is halfway 
 between the center of curvature and the mirror M, as 
 shown in Fig. 576. In order to locate the images of objects 
 
94 LABORATORY MANUAL 
 
 at varying positions along the axis, draw a short arrow 
 between F and M and label it A, another between F and O 
 and label it B, and a third beyond and label it D, some- 
 what as shown in the figure. 
 
 Replace the mirror on its line and observe the direction, 
 curvature, and relative length of the images of A and B. In 
 order to see these images more distinctly, it will be useful to 
 draw an arrow on a small strip of paper and fold up one end 
 so that the arrow is on the vertical part as shown in Fig. 58, 
 
 and then place this strip of paper 
 over A and B. Do the images of 
 A and B point in the same direc- 
 tion as the objects ? 
 
 To locate the position of the 
 image of A, stand a pin upright at the mid-point of A 
 and draw two sight lines directly at its image. Label these 
 lines A, A. Locate the images of B and Q in the same 
 way. 
 
 When an image seems to be back of a mirror, it is said to 
 be virtual, because the rays of light do not actually come 
 from the image-point but simply look as if they had come 
 from it. On the other hand, when as in some cases with a 
 concave mirror the image is found in front of the mirror, it 
 is said to be a real image because the rays actually do pass 
 through the image-point. 
 
 State where the object must be placed in order to get a virtual 
 image and where to get a real image. 
 
 State where the object must be placed in order to get an image 
 pointing in the same direction as the object and where to get a 
 reversed image. 
 
 State where the object must be placed in order to get an image 
 which is smaller than the object and where to get a larger 
 image. 
 
INDEX OF REFBACTION OF GLASS 
 
 95 
 
 Question. What would one observe if he stood at first 
 close in front of a concave mirror and then gradually moved 
 away from it ? 
 
 EXPERIMENT 45 
 
 INDEX OF REFRACTION OF GLASS 
 
 What is the relation between the speed of light in air and in 
 
 glass f 
 
 Rectangular glass plate. 
 
 Paper. 
 
 Ruler. 
 
 Protractor. 
 
 Pins. 
 
 Millimeter paper scale. 
 
 Lay a rectangular glass plate on a sheet of paper in the 
 position shown in Fig. 59 and trace with a sharp pencil the 
 edge of the glass. Stand a pin upright at A, touching the 
 edge of the glass. 
 
 Fig. 59 
 
 If one places one's eye on a level with the paper and looks 
 into the edge DE, the portion of the pin A seen through the 
 glass seems to be in line with the part seen over the glass 
 only when the eye looks into the glass in the direction FD, 
 perpendicular to the edge DJE. 
 
 In order to show just how much a ray of light is bent in 
 passing from glass to air, place a second pin B close to the 
 
96 LABORATORY MANUAL 
 
 edge BE as shown in the figure. Now move the head 
 slowly to the left until the pin B just covers the image of 
 pin A seen through the glass* Place a ruler so that one edge 
 points directly at B and the image of A seen through the 
 glass, and then draw the sight line G. 
 
 Remove the glass, and connect the points A and B, which 
 line represents the direction of a ray of light through the 
 glass. Prolong the sight line until it strikes the point B. 
 This sight line shows the direction of the ray AB after leav- 
 ing the glass. 
 
 The refraction of light in passing from glass into air de- 
 pends on the relative speeds of light in glass and air. If we 
 erect a normal MN at B perpendicular to DE, we find that 
 the angle in air is greater than the angle in glass. It has also 
 been found that the speed of light in air is to the speed in glass 
 as the sine of the angle in air is to the sine of the angle in glass. 
 To get this ratio of the sines of these angles, lay off on AB and 
 BO equal distances (the longer the better), such as BE and 
 BGr, and draw FH and GK perpendicular to the normal MN. 
 The sine of angle a is GK/B G and the sine of angle b is 
 EH I BE, but since BF=BG, 
 
 sine Aa __ GK 
 sine Z.b~~ ~EH 
 
 In short, to get the index of refraction of the glass used in 
 this experiment, i.e. ratio of speed of light in air to speed of 
 light in glass, we have merely to divide the length of GK 
 (measured to tenths of a millimeter) by the length of EH. 
 
 To make a second trial, move the position of pin A to a 
 new point A! along the edge of the glass and repeat the 
 experiment. 
 
 Question. The index of refraction of water is 1.33. Does 
 this mean that water refracts light more or less than glass ? 
 
FOCAL LENGTH AND CONJUGATE FOCI 97 
 
 EXPERIMENT 46 
 
 FOCAL LENGTH AND CONJUGATE FOCI OF A CONVERG- 
 ING LENS 
 
 How far is the picture of a distant object from a convex lens? 
 What relation exists between the object-distance and the image- 
 distance when the object is near a convex lens? 
 
 Optical bench (Fig. 60) White cardboard screen. 
 
 (meter stick and supports). Holders for lens and screen. 
 
 Screen with wire netting. Electric or gas lamp. 
 Double convex lens (f. 10-15 cm.). 
 
 I. Focal Length. An object which is 100 feet or more 
 away sends to a lens rays that are practically parallel, i.e. 
 rays from any distant object-point to different parts of the 
 lens are very nearly parallel. These parallel rays converge 
 at a point called the principal focus and the distance between 
 the lens and the principal focus is called the focal length. 
 
 Set the double convex lens and the cardboard screen on a 
 simple optical bench (Fig. 60) and hold the bench in the 
 
 o ' ; ' ' ' 40 ' ! ! 'so 60 " : . ' jo ■ : = j^ ' ; 106] 
 
 ' ^ *-unuJ 
 
 Fig. 60 
 
 back part of the room but pointing at some distant object 
 out of the window. Having placed the lens on one of the 
 main divisions of the meter stick, move the screen toward 
 and away from the lens until the most distant bright object 
 which can be seen through the window is sharply focused 
 on the screen, i.e. forms a clear picture. Read and record 
 the positions of lens and screen. 
 
98 
 
 LABORATORY MANUAL 
 
 Move the lens to a new position on the stick, and again 
 make a new setting of the screen in the same way as before. 
 After making a third trial, find the average of the three 
 focal lengths and record this as the focal length of the lens. 
 
 II. Relations of Object and Image. Set up the optical 
 bench as shown in Fig. 60, so that the object (an illuminated 
 wire netting) is away from the window. Place the card- 
 board screen at the opposite end and darken the room. Slide 
 the lens back and forth between this screen and the object 
 until a position is found where the picture of the netting 
 appears on the screen as sharp as possible. 
 
 Is the image larger or smaller than the object ? 
 
 Cover one part of the object and see if the image is erect or 
 inverted. 
 
 Without moving the object or the screen, try to find 
 another position of the lens that will give a sharp image. 
 
 Is it smaller or larger than the object, erect or inverted? 
 
 When the image is smaller than the object, which is nearer 
 the lens, the object or the image ? 
 
 When the image is larger than the object, which is nearer the 
 lens, the object or the image ? 
 
 Read the position of the object, lens, and image on the 
 meter stick as accurately as possible, and record in tabular 
 form as follows : 
 
 
 Positions 
 
 Object- 
 distance 
 
 Image- 
 distance 
 
 1 , 1 
 
 1 
 
 Object 
 
 Lens 
 
 Image 
 
 Obj.-dist. "*" Im.-dist. 
 
 Focal Length 
 
 
 
 
 
 
 
 
SIZE AND SHAPE OF A REAL IMAGE 99 
 
 Move the screen up nearer the object and again find two 
 positions where the lens forms a sharp image. 
 
 Continue to move the screen up closer to the object until 
 it is possible to get only one distinct image. What is the 
 shortest distance between object and screen, at which the lens 
 will form a distinct image ? How many times the focal length 
 of the lens is this minimum distance between object and image ? 
 
 Compare the sum of the reciprocals of the image- and object- 
 distances with the reciprocal of the focal length. 
 
 Problem. What is the focal length of a lens if the image 
 of an object 10 ft. away is 5 in. from the lens ? 
 
 EXPERIMENT 47 
 
 SIZE AND SHAPE OF A REAL IMAGE 
 
 Is the real image of a straight line formed by a convex lens 
 straight or curved ; and if curved, does its center bend toward 
 or away from the lens? 
 
 How are the image- distance, object-distance, length of image, 
 and length of object related ? 
 
 Strip of paper (about 20 x 75 cm.) . Block with vertical line. 
 
 Meter stick. Block with bent wire. 
 
 Double convex lens and holder. 
 
 Lay a strip of paper on the table so that the long side 
 extends toward the window. Draw a line down the middle 
 of the paper and near the end farthest from the window, 
 draw an arrow about 10 cm. long. Divide the arrow into 
 four equal parts and mark the points of division 1, 2, 3, 4, 
 and 5 as shown in Fig. 61. On the long line, mark the 
 position of the lens, which should be distant from point 3 of 
 
100 LABORATORY MANUAL 
 
 the arrow from one and a half to two times the focal length 
 of the lens ; that is, if the lens has a focal length of 12 cm., 
 place it from 18 to 24 cm. from the center of the arrow. 
 
 it— 
 
 Fig. 61 % 
 
 Place the lens so that its center is directly over this point 
 and its plane at right angles to the line. To locate the 
 image-points corresponding to each of the five points of the 
 object, stand the vertical line of the wooden block directly 
 over point 3, and using one eye only, look into the lens from 
 the other end of the paper so as to see the image of the ver- 
 tical line. Move the block carrying the bent wire until the 
 vertical part of the wire just covers the image. To see the 
 wire and image distinctly, the eye should be about 30 cm. 
 away from the wire. Move the wire to and from the lens 
 until a position is found where, as the head moves slowly 
 from side to side, the wire and the image keep exactly to- 
 gether, showing that each is at the same distance from the 
 eye. As soon as this position is sharply determined, mark 
 a dot directly under the point of the wire and label it 3'. 
 
 Move the vertical line along to 4 and locate in the same 
 way the position of its image 4'. In this manner determine 
 the position of the image of each of the five points of the 
 object arrow. In locating these points it is quite essential 
 that the observer should not let any preconceived notion as to 
 the proper position of the image-points affect his judgment 
 as to where each image-point really is. 
 
 Connect the image-points l'and 2' and 3', etc., with straight 
 lines to get a rough idea of the shape of the whole image. 
 Draw a straight line from each object-point to its corre- 
 sponding image-point. Where do these lines intersect? 
 
SIZE AND SHAPE OF A EEAL IMAGE 101 
 
 Connect the ends of the image arrow by a straight line, 
 measure its length, and call it L { . Measure the distance of 
 the lens from the center of the object and the distance of 
 the lens from the point where the straight line joining the 
 ends of the image crosses the axis, and call these distances 
 D and D t respectively. 
 
 Call the length of the object X , compute the value of the 
 
 ratio — £ which is called the magnifying power of the lens. 
 
 D 
 
 Also compute the value of the ratio —± and compare this 
 
 result with the magnifying power. (Express the ratio to 
 three significant figures.) 
 
 Does the center of the image bend toward the lens or aivay 
 from it? 
 
 To explain this curvature of the image consider D for 
 point 1 and D for point 3. Then, if the lens formula 
 
 ( — + — = -] holds true, and / is a constant for the lens, 
 
 what would be expected of Di for point 1 and D { for 
 point 3? 
 
 Sow is this defect in a lens corrected so as to give what the 
 photographers call a "flat image " ? 
 
 Problem. A lantern slide picture 3 inches long is to be 
 projected on a screen 30 feet away so as to form a picture 
 6 feet long. What must be the focal length of the lens ? 
 How far from the slide must the lens be placed? 
 
102 LABORATORY MANUAL 
 
 EXPERIMENT 48 
 
 MAGNIFYING POWER OF A SIMPLE LENS 
 
 How many diameters does a converging lens seem to magnify an 
 
 object ? 
 
 Meter stick. Paper millimeter scale. 
 
 Double convex lens (f. 2.5-7.5 cm.) Black cardboard with square 
 and holder. hole and holder. 
 
 In many optical instruments a double convex lens is used 
 as a simple microscope or magnifying glass. For the aver- 
 age person the distance of most distinct vision is about 
 25 cm. (10 in.), but with a magnifying glass, the distance 
 between the lens and the object is made a little less than 
 the focal length and so adjusted that an erect enlarged 
 virtual image is formed about 25 cm. away. To get the 
 magnifying power of a simple microscope we have to find 
 the ratio of the size of the image to the size of the object. 
 This is, however, equal to the distance of the image divided 
 by the distance of the object, that is, 25 /D where D is the 
 object-distance in centimeters. 
 
 First find the focal length of the lens by holding a meter 
 stick horizontally with one end against a piece of white card- 
 board and with the other end pointing at some distant object 
 outside the window. Hold the lens in the hand and move 
 it slowly away from the screen until it forms a clear picture. 
 This distance between the lens and the screen is the focal 
 length of the lens. Record the focal length and number of 
 the lens. 
 
 Place a paper millimeter scale on the table and stand a 
 meter stick upright on it. At a distance of 25 cm. fasten a 
 short focus lens to the meter stick. Then just under the 
 
MAGNIFYING POWER OF A SIMPLE LENS 
 
 103 
 
 \Lens 
 
 Screen 
 
 I 
 
 lens set a black cardboard screen with 
 a square opening (1 cm. 2 ) at a distance a 
 little less than the focal length of the 
 lens, as shown in Fig. 62. Bring the head 
 down so that the right eye is directly over 
 the lens and adjust the screen so as to 
 get a sharp image of its surface. Keep- 
 ing both eyes open, count the number of 
 millimeters which the image of the open- 
 ing in the cardboard, as seen by the right 
 eye through the lens, seems to correspond 
 to on the millimeter scale as seen by the 
 unaided left eye. Divide this number by 
 the width (10 mm.) of the opening in the 
 cardboard and the quotient gives how 
 many times the object seems to be mag- 
 nified when seen through the lens as 
 compared to what it seems to be when 
 seen with the naked eye at the distance 
 of most distinct vision (25 cm.). 
 
 Measure the distance of the opening in 
 the cardboard from the center of the lens 
 and call it D . Then since the distance 
 of the image (2)^) is 25 cm., the magnify- 
 ing power of the lens can also be computed as the ratio 25/Z) . 
 
 Since the lens formula is 1 = .-, and, for this virtual 
 
 Do I>i f 
 
 Scale 
 
 Fig. 62 
 
 ±_ 
 
 image, _Z), = — 25 cm., one gets the expression — — — . = - 
 
 1^ 
 25 
 
 and the magnifying power is 
 
 25 
 
 = 1 + 
 
 25 
 
 1 
 
 Do 25 /' 
 
 Compute the 
 
 OV f 
 
 magnifying power of the lens also by means of this equa- 
 tion, using the value of/ found in the first part of this ex- 
 
104 LABORATORY MANUAL 
 
 periment. Record these three values of the magnifying 
 power. 
 
 Draw carefully a diagram to show the relative positions of 
 the eyes, the lens, the opening in the cardboard, and the 
 paper scale. 
 
 If time permits, repeat the experiment with another lens 
 of slightly different focal length. 
 
 Problem. What is the magnifying power of a 3-inch 
 lens used as a simple magnifier? 
 
 EXPERIMENT 49 
 
 TELESCOPE AND COMPOUND MICROSCOPE 
 
 How may two convex lenses be arranged to act like a telescope ? 
 How may two convex lenses be arranged to act like a compound 
 microscope ? 
 
 Two short focus lenses (f . 2.5-7.5 cm.). Cardboard screen and holder. 
 
 Long focus lens (f. 25 cm.). Two lens holders. 
 
 Optical bench. Cardboard screen with wire 
 Electric or gas lamp. netting and holder. 
 
 I. Astronomical Telescope. Find the focal length of each 
 lens, as in Exp. 48. 
 
 Mount a short focus lens near one end of the meter stick 
 and set up a cardboard screen at such a distance beyond 
 that its surface is seen distinctly when the eye is held close 
 to the lens. On the other side of the screen mount the long 
 focus lens at such a distance from the screen that it shows a 
 sharp image of some distant object. Measure and record on 
 a diagram the distance of the screen from each lens. With- 
 out disturbing the lenses, remove the screen and look through 
 the short focus lens, or eye-piece, and observe that the image 
 formed by the other lens, or objective, can be distinctly seen. 
 
TELESCOPE AND COMPOUND MICROSCOPE 
 
 105 
 
 These two lenses thus arranged constitute the essential parts 
 of a very crude astronomical telescope. Measure the dis- 
 tance between the lenses and compare this distance with the 
 sum of the focal lengths. 
 
 To measure the magnifying power of the telescope, fasten 
 on the opposite wall of the room a strip of white paper with 
 a series of thick black lines drawn across it at 
 regular intervals of about one inch. Be sure 
 this paper scale is about on a level with the 
 axis of the telescope and that the lenses are so 
 adjusted as to give a sharp image. Then look 
 through the telescope with one eye and at the 
 same time look at the scale directly with the 
 other eye. Adjust the telescope so that object 
 and image appear about as shown in Fig. 63, 
 and so that one mark of the image exactly 
 coincides with one mark of the object. Count 
 the number of spaces between two successive 
 marks of the image. This gives the magnify- 
 ing power of the telescope. Compare this value 
 with the ratio of the focal length of the ob- 
 jective to the focal length of the eye-piece. 
 
 II. Compound Microscope. Measure the focal 
 length of each of two short focus lenses. Set up 
 the eye-piece lens and the cardboard screen just as in Part I. 
 Place the other short focus lens, the objective, about 25 cm. be- 
 yond the screen. Then place the screen (Exp. 46) with the 
 aperture covered with wire netting, illuminated by some kind 
 of lamp, at such a distance beyond the objective that a sharp 
 picture of the wire netting will be formed on the translucent 
 screen. 
 
 Measure and record on a diagram the distances between 
 the screen and lenses. 
 
 Fig. 63 
 
106 LABORATORY MANUAL 
 
 Take away the translucent screen and observe the image 
 of the wire netting through the eye-piece. 
 
 Make a simple diagram to show the relative positions of 
 the eye, the two lenses, and the object. 
 
 Problem. A telescope has an objective of 30 ft. focal 
 length and an eye-piece of 1 in. focal length. What is its 
 magnifying power ? 
 
 EXPERIMENT 50 
 
 DISPERSION OF LIGHT BY A PRISM 
 
 How may white light be separated into the primary colors by a 
 
 prism ? 
 
 Triangular 60° prism. Gas flame or incandescent lamp filament. 
 
 Black cardboard. Pins. 
 
 Rnler. 
 
 To show how a beam of light is refracted by a triangular 
 prism, place a prism on a sheet of paper and draw a sharp 
 line around its edge. Then set up two pins D and E about 
 
 10 cm. apart and located as 
 shown in Fig. 64. Now look 
 with one eye into the face AC 
 of the prism in such a way that 
 the images of D and E seem to 
 be in line. Lay a ruler on the 
 paper so that its edge EG- and 
 the images of D and E, all seem 
 to be in the same line. Remove 
 the prism and draw straight lines through D and E and F 
 and Gr. Also draw the path of the ray in the prism HK. 
 The broken line DHK shows how a ray of light is refracted 
 by a prism. 
 
DISPERSION OF LIGHT BY A PRISM 107 
 
 Hold the prism in direct sunlight so as to refract the rays 
 of light upon some shaded part of the floor. Place between 
 the sun and the prism a sheet of black cardboard which has 
 a horizontal slit 2 or 3 mm. wide. What colors can be 
 recognized now on the floor ? What color is refracted most, 
 that is, tvhich color lies farthest from the refracting angle A 
 of the prism? Which color is refracted least, that is, which 
 lies nearest to the angle ? Compare the width of the slit with 
 the width of the band of color or spectrum. 
 
 In another sheet of black cardboard cut two slits 2 mm. 
 in width and about 2 mm. apart. Keeping one slit covered, 
 observe the spectrum and then note the effect in the middle 
 of the spectrum when it is uncovered. The middle of the 
 colored band is where the two spectra overlap. Does this 
 show that certain colors of the spectrum may unite to produce 
 white ? Now remove the cardboard screen with the slits and 
 observe that only the edges of the band of light are colored 
 and not the middle. Why ? 
 
 Arrange a fish-tail gas flame so that the narrow edge is 
 turned toward the eye. Holding the prism in front, of the 
 right eye with the refracting angle toward the nose, observe 
 this flame (or better an electric light filament) at a distance 
 of 2 or 3 m. How must one turn in order to observe 
 the image of the flame ? What color is the image ? What 
 color lies farthest toward the right and which farthest to the 
 left ? What are the intervening colors ? 
 
 Make a careful sketch to show just how the prism was 
 held and what colors were seen. 
 
 Question. If one pastes a strip of white paper upon a 
 black card and, holding it in the sunlight, examines it by 
 looking through a prism, he will see that the edges of the 
 paper give the spectrum colors. But if one examines in the 
 same way strips of red and blue paper, he will see only the 
 color which the paper reflects. Explain. 
 
APPENDIX 
 
 I. Rules for Computation 
 Area of triangle = base x altitude 
 
 Circumference of circle = ttD 
 Area of circle = ttR 2 
 Surface of sphere = ^ttR 2 
 4tt£ 3 
 
 Volume of sphere 
 
 Volume of prism 
 Volume of cylinder 
 
 area of base x altitude 
 
 7T = 31 or 3.14 
 
 II. Table of Equivalents 
 
 1 centimeter = 0.394 inch 
 1 kilometer = 0.621 mile 
 1 kilogram = 2.20 pounds 
 1 liter = 1.06 quarts 
 
 1 cm. 3 water weighs 1 gram 
 
 1 inch = 2.54 centimeters 
 1 foot = 30.5 centimeters 
 1 ounce = 28.4 grams 
 1 pound = 454 grams 
 1 cu. ft. water weighs 62.4 pounds 
 
 Alcohol, 95 % 
 Aluminum 
 Brass . . . 
 Coal, anthracite 
 Copper . . 
 Gasolene . . 
 Glass (Flint) 
 Glass (Crow^n) 
 Gold . . . 
 Ice .... 
 Iron . . . 
 
 III. Table of Densities 
 
 (In grams per cubic centimeter) 
 
 0.807 Lead 11.4 
 
 2.65 Marble 2.5-2.8 
 
 8.4-8.7 Mercury 13.6 
 
 1.4-1.8 Platinum 21.5 
 
 8.93 Silver 10.5 
 
 0.68-0.72 Tin 7.3 
 
 3.0-3.6 Sea Water 1.03 
 
 2.5-2.7 Wood — Ebony ... 1.2 
 
 19.3 Oak .... 0.7-0.9 
 
 0.918 Pine .... 0.4-0.6 
 
 7.1-7.9 Zinc . : 7.1 
 
 109 
 
110 
 
 APPENDIX 
 
 IV. Density of Dry Air at Different Temperatures and 
 Pressures (Grams per Liter) 
 
 
 
 
 Pressure in 
 
 Millimeters 
 
 
 
 rp 
 
 
 
 
 
 
 
 
 
 
 710 
 
 720 
 
 730 
 
 740 
 
 750 
 
 760 
 
 770 
 
 780 
 
 o°c. 
 
 1.208 
 
 1.225 
 
 1.242 
 
 1.259 
 
 1.276 
 
 1.293 
 
 1.310 
 
 1.327 
 
 2 
 
 1.199 
 
 1.216 
 
 1.233 
 
 1.250 
 
 1.267 
 
 1.284 
 
 1.300 
 
 1.317 
 
 4 
 
 1.190 
 
 1.207 
 
 1.224 
 
 1.241 
 
 1.258 
 
 1.274 
 
 1.291 
 
 1.308 
 
 6 
 
 1.182 
 
 1.199 
 
 1.215 
 
 1.232 
 
 1.248 
 
 1.265 
 
 1.282 
 
 1.298 
 
 8 
 
 1.173 
 
 1.190 
 
 1.207 
 
 1.223 
 
 1.240 
 
 1.256 
 
 1.273 
 
 1.289 
 
 10 
 
 1.165 
 
 1.182 
 
 1.198 
 
 1.214 
 
 1.231 
 
 1.247 
 
 1.264 
 
 1.280 
 
 12 
 
 1.157 
 
 1.173 
 
 1.190 
 
 1.206 
 
 1.222 
 
 1.238 
 
 1.255 
 
 1.271 
 
 14 
 
 1.149 
 
 1.165 
 
 1.181 
 
 1.197 
 
 1.214 
 
 1.230 
 
 1.246 
 
 1.262 
 
 16 
 
 - 1.141 
 
 1.157 
 
 1.173 
 
 1.189 
 
 1.205 
 
 1.221 
 
 1.237 
 
 1.253 
 
 18 
 
 1.133 
 
 1.149 
 
 1.165 
 
 1.181 
 
 1.197 
 
 1.213. 
 
 1.229 
 
 1.245 
 
 20 
 
 1.125 
 
 1.141 
 
 1.157 
 
 1.173 
 
 1.189 
 
 1.205 
 
 1.220 
 
 1.236 
 
 22 
 
 1.118 
 
 1.133 
 
 1.149 
 
 1.165 
 
 1.181 
 
 1.196 
 
 1.212 
 
 1.228 
 
 24 
 
 1.110 
 
 1.126 
 
 1.141 
 
 1.157 
 
 1.173 
 
 1.188 
 
 1.204 
 
 1.220 
 
 26 
 
 1.103 
 
 1.118 
 
 1.134 
 
 1.149 
 
 1.165 
 
 1.180 
 
 1.196 
 
 1.211 
 
 28 
 
 1.095 
 
 1.111 
 
 1.126 
 
 1.142 
 
 1.157 
 
 1.173 
 
 1.188 
 
 1.203 
 
 30 
 
 1.088 
 
 1.103 
 
 1.119 
 
 1.134 
 
 1.149 
 
 1.165 
 
 1.180 
 
 1.195 
 
 V. Tensile Strength of Wires 
 
 (Kilograms per square millimeter) 
 
 Aluminum 17-20 
 
 Brass 31-39 
 
 Copper, hard drawn 40-46 
 
 Copper, annealed 28-31 
 
 German Silver 46 
 
 Iron, hard drawn 54-62 
 
 Iron, annealed about 46 
 
 Steel, ordinary about 110 
 
 Steel, piano ..,,,,,...,,,,... 186-233 
 
APPENDIX 
 
 111 
 
 VI. Coefficients of Linear Expansion of Solids 
 
 Aluminum .... 0.0000231 
 Brass ...... 0.0000189 
 
 Copper 0.0000167 
 
 Glass (soft) .... 0.0000085 
 
 " Invar " (Nickel steel) 0.0000009 
 
 Quartz (fused) . . . 0.0000005 
 
 Steel 0.000011 
 
 Zinc 0.000026 
 
 VII. Specific Heats of Various Substances 
 
 Aluminum . . . . . 0.22 
 
 Brass 0.090 
 
 Copper 0.094 
 
 Iron 0.12 
 
 Lead . . . . ... 0.031 
 
 Mercury 0.033 
 
 Tin 0.055 
 
 Zinc 0.093 
 
 VIII. Electromotive Forces of Cells 
 
 Volts 
 
 Daniel! cell 1.1 
 
 Gravity cell • . .1.1 
 
 Sal-ammoniac cell 1.5 
 
 Volts 
 
 Dry cell 1.5 
 
 Lead storage cell . . . . . 2.0 
 Edison storage cell , . . .1.2 
 
 IX. Specific Resistance and Temperature Coefficient 
 (From Timbie's " Elements of Electricity ") 
 
 Material (Commercial) 
 
 Specific Resistance 
 
 Ohms per Mil-Foot 
 
 at 20° C. 
 
 Temperature 
 
 Coefficient = 
 
 Increase per degree C. 
 
 Resistance at 0° C. 
 
 Aluminum 
 
 
 17.4 
 
 10.4 
 
 10.65 
 
 90. 
 
 64. 
 
 114 to 275 
 
 250 to 450 
 
 283 
 
 300 
 
 294 
 
 0.00435 
 
 Copper, annealed . 
 
 
 
 0.0042 
 
 Copper, hard drawn . . 
 Iron, annealed .... 
 
 
 0.005 
 
 Iron, E. B. B. (Roebling) 
 German Silver .... 
 
 
 0.0046 
 0.00025 
 
 Manganin 
 
 
 0.00001 
 
 la la (Boker) , soft . . 
 la la (Boker), hard . . 
 Advance (Driver-Harris) 
 
 
 0.000005 
 
 0.00001 
 
 0.00000 
 
112 
 
 APPENDIX 
 
 X. Resistance of Annealed Copper Wire 
 
 B. &S. 
 Gauge 
 
 Diameter in 
 Millimeters 
 
 Diameter in 
 Mils 
 
 Area in 
 Circular Mils 
 
 Ohms per 1000 
 Ft. at 20° C. 
 
 Feet per Lb., 
 
 Double Cotton 
 
 Covered 
 
 10 
 
 2.59 
 
 101.9 
 
 10,380. 
 
 1.00 
 
 30.9 
 
 11 
 
 2.31 
 
 90.7 
 
 8,234. 
 
 1.26 
 
 38.9 
 
 12 
 
 2.05 
 
 80.8 
 
 6,530. 
 
 1.59 
 
 48.8 
 
 13 
 
 1.83 
 
 72.0 
 
 5,178. 
 
 2.00 
 
 61.5 
 
 14 
 
 1.63 
 
 64.1 
 
 4,107. 
 
 2.52 
 
 77.4 
 
 15 
 
 1.45 
 
 57.1 
 
 3,257. 
 
 3.18 
 
 97.2 
 
 16 
 
 1.29 
 
 50.8 
 
 2,583. 
 
 4.01 
 
 122. 
 
 17 
 
 1.15 
 
 45.3 
 
 2,048. 
 
 5.06 
 
 153. 
 
 18 
 
 1.02 
 
 40.3 
 
 1,624. 
 
 6.37 
 
 192. 
 
 19 
 
 .90 
 
 35.4 
 
 1,288. 
 
 8.04 
 
 247. 
 
 20 
 
 .81 
 
 32.0 
 
 1,022. 
 
 10.1 
 
 298. 
 
 21 
 
 .72 
 
 28.5 
 
 810. 
 
 12.8 
 
 375. 
 
 22 
 
 .64 
 
 25.3 
 
 643. 
 
 16.1 
 
 472. 
 
 23 
 
 .57 
 
 22.6 
 
 509. 
 
 20.3 
 
 585. 
 
 24 
 
 .51 
 
 20.1 
 
 404. 
 
 25.6 
 
 730. 
 
 25 
 
 .46 
 
 17.90 
 
 320. 
 
 32.3 
 
 901. 
 
 26 
 
 .41 
 
 15.94 
 
 254. 
 
 40.8 
 
 1123. 
 
 27 
 
 .36 
 
 14.20 
 
 202. 
 
 51.4 
 
 1389. 
 
 28 
 
 .32 
 
 12.64 
 
 159.8 
 
 64.8 
 
 1695. 
 
 29 
 
 .29 
 
 11.26 
 
 126.7 
 
 81.7 
 
 2127. 
 
 30 
 
 .26 
 
 10.02 
 
 100.5 
 
 103. 
 
 2564. 
 
 31 
 
 .23 
 
 8.93 
 
 79.7 
 
 130. 
 
 
 32 
 
 .20 
 
 7.95 
 
 63.2 
 
 164. 
 
 
 33 
 
 .18 
 
 7.08 
 
 50.1 
 
 207. 
 
 
 34 
 
 .16 
 
 6.30 
 
 39.7 
 
 261. 
 
 
 35 
 
 .14 
 
 5.61 
 
 31.5 
 
 328. 
 
 
 36 
 
 .13 
 
 5.00 
 
 25.0 
 
 414. 
 
 
 It will be noticed in the table above that #13 wire is about half the size 
 of # 10 wire, and so has twice as much resistance. In the same way # 16 wire 
 is half the size of # 13, and has double the resistance.] 
 
APPENDIX 
 
 113 
 
 XI. Natural Sines and Tangents 
 
 Angle 
 
 Sine 
 
 Tangent 
 
 Angle 
 
 Sine 
 
 Tangent 
 
 Angle 
 
 Sjne 
 
 Tangent 
 
 
 
 0.000 
 
 0.000 
 
 31 
 
 0.515 
 
 0.601 
 
 62 
 
 0.883 
 
 1.881 
 
 1 
 
 0.017 
 
 0.017 
 
 32 
 
 0.530 
 
 0.625 
 
 63 
 
 0.891 
 
 1.963 
 
 2 
 
 0.035 
 
 0.035 
 
 33 
 
 0.545 
 
 0.649 
 
 64 
 
 0.899 
 
 2.050 
 
 3 
 
 0.052 
 
 0.052 
 
 34 
 
 0.559 
 
 0.675 
 
 66 
 
 0.906 
 
 2.145 
 
 4 
 
 0.070 
 
 0.070 
 
 35 
 
 0.574 
 
 0.700 
 
 66 
 
 0.914 
 
 2.246 
 
 5 
 
 0.087 
 
 0.087 
 
 36 
 
 0.588 
 
 0.727 
 
 67 
 
 0.921 
 
 2.356 
 
 6 
 
 0.105 
 
 0.105 
 
 37 
 
 0.602 
 
 0.754 
 
 68 
 
 0.927 
 
 2.475 
 
 7 
 
 0.122 
 
 0.123 
 
 38 
 
 0.616 
 
 0.781 
 
 69 
 
 0.934 
 
 2.605 
 
 8 
 
 0.139 
 
 0.141 
 
 39 
 
 0.629 
 
 0.810 
 
 70 
 
 0.940 
 
 2.747 
 
 9 
 
 0.156 
 
 0.158 
 
 40 
 
 0.643 
 
 0.839 
 
 71 
 
 0.946 
 
 2.904 
 
 10 
 
 0.174 
 
 0.176 
 
 41 
 
 0.656 
 
 0.869 
 
 72 
 
 0.951 
 
 3.078 
 
 11 
 
 0.191 
 
 0.194 
 
 42 
 
 0.669 
 
 0.900 
 
 73 
 
 0.956 
 
 3.271 
 
 12 
 
 0.208 
 
 0.213 
 
 43 
 
 0.682 
 
 0.933 
 
 74 
 
 0.961 
 
 3.487 
 
 13 
 
 0.225 
 
 0.231 
 
 44 
 
 0.695 
 
 0.966 
 
 75 
 
 0.966 
 
 3.732 
 
 14 
 
 0.242 
 
 0.249 
 
 45 
 
 0.707 
 
 1.000 
 
 76 
 
 0.970 
 
 4.011 
 
 15 
 
 0.259 
 
 0.268 
 
 46 
 
 0.719 
 
 1.036 
 
 77 
 
 0.974 
 
 4.331 
 
 16 
 
 0.276 
 
 0.287 
 
 47 
 
 0.731 
 
 1.072 
 
 78 
 
 0.978 
 
 4.705 
 
 17 
 
 0.292 
 
 0.306 
 
 48 
 
 0.743 
 
 1.111 
 
 79 
 
 0.982 
 
 5.145 
 
 18 
 
 0.309 
 
 0.325 
 
 49 
 
 0.755 
 
 1.150 
 
 80 
 
 0.985 
 
 5.671 
 
 19 
 
 0.326 
 
 0.344 
 
 50 
 
 0.766 
 
 1.192 
 
 81 
 
 0.988 
 
 6.314 
 
 20 
 
 0.342 
 
 0.364 
 
 51 
 
 0.777 
 
 1.235 
 
 82 
 
 0.990 
 
 7.115 
 
 21 
 
 0.358 
 
 0.384 
 
 52 
 
 0.788 
 
 1.280 
 
 83 
 
 0.993 
 
 8.144 
 
 22 
 
 0.375 
 
 0.404 
 
 53 
 
 0.799 
 
 1.327 
 
 84 
 
 0.995 
 
 9.514 
 
 23 
 
 0.391 
 
 0.424 
 
 54 
 
 0.809 
 
 1.376 
 
 85 
 
 0.996 
 
 11.43 
 
 24 
 
 0.407 
 
 0.445 
 
 55 
 
 0.819 
 
 1.428 
 
 86 
 
 0.998 
 
 14.30 
 
 25 
 
 0.423 
 
 0.466 
 
 56 
 
 0.829 
 
 1.483 
 
 87 
 
 0.999 
 
 19.08 
 
 26 
 
 0.438 
 
 0.488 
 
 57 
 
 0.839 
 
 1.540 
 
 88 
 
 0.999 
 
 28.64 
 
 27 
 
 0.454 
 
 0.510 
 
 58 
 
 0.848 
 
 1.600 
 
 89 
 
 1.000 
 
 57.29 
 
 28 
 
 0.469 
 
 0.532 
 
 59 
 
 0.857 
 
 1.664 
 
 90 
 
 1.000 
 
 Infinity 
 
 29 
 
 0.485 
 
 0.554 
 
 60 
 
 0.866 
 
 1.732 
 
 
 - 
 
 
 30 
 
 0.500 
 
 0.577 
 
 61 
 
 0.875 
 
 1.804 
 
 
 
 
114 
 
 APPENDIX 
 XII. Four-Figure Logarithms 
 
 N 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789 
 
 IO 
 II 
 12 
 13 
 14 
 
 15 
 16 
 
 17 
 18 
 19 
 
 0000 
 0414 
 0792 
 
 1139 
 1461 
 
 1761 
 2041 
 2304 
 2553 
 2788 
 
 0043 
 0453 
 0828 
 ii73 
 1492 
 
 1790 
 2068 
 2330 
 2577 
 2810 
 
 0086 
 0492 
 0864 
 1206 
 1523 
 
 1818 
 2095 
 2355 
 2601 
 
 2833 
 
 0128 
 0531 
 0899 
 1239 
 1553 
 
 1847 
 2122 
 2380 
 2625 
 2856 
 
 0170 
 0569 
 
 0934 
 1271 
 
 1584 
 
 1875 
 2148 
 2405 
 2648 
 2878 
 
 0212 
 0607 
 0969 
 1303 
 1614 
 
 1903 
 
 2175 
 2430 
 2672 
 2900 
 
 0253 
 0645 
 1004 
 1335 
 1644 
 
 1931 
 2201 
 
 2455 
 2695 
 2923 
 
 0294 
 0682 
 1038 
 1367 
 1673 
 
 1959 
 
 2227 
 2480 
 2718 
 2945 
 
 ^334 
 3719 
 1072 
 
 1399 
 1703 
 
 1987 
 2253 
 2504 
 2742 
 2967 
 
 0374 
 0755 
 1 106 
 1430 
 1732 
 
 2014 
 2279 
 
 2529 
 2765 
 2989 
 
 4 8 12 17 
 4 8 11 15 
 3 7 10 14 
 3 6 10 13 
 3 6 9 12 
 
 3 6 8 11 
 3 5 8 11 
 2 5 7 10 
 2 5 7 9 
 
 2 4 7 9 
 
 21 
 19 
 17 
 16 
 
 15 
 
 14 
 13 
 12 
 12 
 11 
 
 25 29 33 37 
 23 26 30 34 
 21 24 28 31 
 19 23 26 29 
 18 21 24 27 
 
 17 20 22 25 
 16 18 21 24 
 15 17 20 22 
 14 16 19 21 
 13 16 18 20 
 
 20 
 21 
 22 
 
 23 
 24 
 
 25 
 26 
 
 27 
 28 
 29 
 
 30 
 31 
 
 32 
 
 33 
 34 
 
 35 
 36 
 37 
 38 
 39 
 
 3010 
 3222 
 
 3424 
 3617 
 3802 
 
 3979 
 4150 
 4314 
 4472 
 4624 
 
 477i 
 4914 
 5051 
 5185 
 5315 
 
 544i 
 5563 
 5682 
 5798 
 59ii 
 
 3032 
 3243 
 3444 
 3636 
 3820 
 
 3997 
 4166 
 4330 
 4487 
 2639 
 
 4786 
 4928 
 5065 
 5198 
 5328 
 
 5453 
 5575 
 5694 
 5809 
 5922 
 
 3054 
 3263 
 3464 
 3655 
 3838 
 
 4014 
 4183 
 4346 
 4502 
 4654 
 
 4800 
 4942 
 5079 
 5211 
 5340 
 
 5465 
 5587 
 5705 
 5821 
 
 5933 
 
 3075 
 3284 
 3483 
 3674 
 3856 
 
 4031 
 
 4200 
 4362 
 45i8 
 4669 
 
 4814 
 
 4955 
 5092 
 5224 
 5353 
 
 5478 
 5599 
 5717 
 5832 
 5944 
 
 3096 
 3304 
 3502 
 3692 
 3874 
 
 4048 
 4216 
 4378 
 4533 
 4683 
 
 4829 
 4969 
 5105 
 5237 
 5366 
 
 5490 
 5611 
 5729 
 5843 
 5955 
 
 3118 
 3324 
 3522 
 3711 
 3892 
 
 4065 
 4232 
 4393 
 4548 
 4698 
 
 3i39 
 3345 
 3541 
 3729 
 3909 
 
 4082 
 
 4249 
 4409 
 
 4564 
 4713 
 
 3160 
 3365 
 356o 
 3747 
 3927 
 
 4099 
 4265 
 4425 
 4579 
 4728 
 
 3181 
 3385 
 3579 
 3766 
 
 3945 
 
 4116 
 4281 
 4440 
 4594 
 4742 
 
 3201 
 3404 
 3598 
 3784 
 3962 
 
 4i33 
 4298 
 4456 
 4609 
 4757 
 
 2468 
 2468 
 2468 
 2467 
 2 4 5 7 
 
 2 3 5 7 
 2 3 5 7 
 2356 
 2356 
 1346 
 
 11 
 10 
 
 10 
 9 
 9 
 
 9 
 
 8 
 8 
 8 
 7 
 
 13 15 17 19 
 12 14 16 18 
 12 14 15 17 
 
 11 13 15 17 
 11 12 14 16 
 
 10 12 14 15 
 
 10 11 13 15 
 
 9 11 13 14 
 
 9 11 12 14 
 
 9 10 12 13 
 
 4843 
 4983 
 5ii9 
 5250 
 5378 
 
 5502 
 5623 
 5740 
 5855 
 5966 
 
 4857 
 4997 
 5132 
 5263 
 5391 
 
 5514 
 5635 
 5752 
 5866 
 5977 
 
 4871 
 5011 
 5145 
 5276 
 
 5403 
 
 5527 
 5647 
 5763 
 5877 
 5988 
 
 4886 
 5024 
 5159 
 5289 
 54i6 
 
 5539 
 5658 
 5775 
 5888 
 5999 
 
 4900 
 5038 
 5172 
 5302 
 5428 
 
 555i 
 5670 
 5786 
 5899 
 6010 
 
 13 4 6 
 1346 
 13 4 5 
 13 4 5 
 13 4 5 
 
 1245 
 1245 
 1235 
 1235 
 1234 
 
 7 
 7 
 7 
 6 
 6 
 
 6 
 6 
 
 6 
 6 
 
 5 
 
 9 10 11 13 
 8 10 11 12 
 8 9 11 12 
 8 9 10 12 
 8 9 10 11 
 
 7 9 10 11 
 7 8 10 11 
 7 8 9 10 
 7 8 9 10 
 7 8 9 10 
 
 40 
 4i 
 42 
 43 
 
 44 
 
 45 
 46 
 47 
 48 
 49 
 
 6021 
 6128 
 6232 
 6335 
 6435 
 
 6532 
 6628 
 6721 
 6812 
 6902 
 
 6031 
 6138 
 6243 
 
 6345 
 6444 
 
 6542 
 6637 
 6730 
 6821 
 6911 
 
 6042 
 6149 
 6253 
 6355 
 6454 
 
 6551 
 6646 
 6739 
 6830 
 6920 
 
 6053 
 6160 
 6263 
 
 6365 
 6464 
 
 6561 
 6656 
 6749 
 6839 
 6928 
 
 6064 
 6170 
 6274 
 6375 
 6474 
 
 6571 
 6665 
 6758 
 6848 
 6937 
 
 6075 
 6180 
 6284 
 6385 
 6484 
 
 6580 
 6675 
 6767 
 6857 
 6946 
 
 6085 
 6191 
 6294 
 6395 
 6493 
 
 6590 
 6684 
 6776 
 6866 
 6955 
 
 6096 
 6201 
 6304 
 6405 
 6503 
 
 6599 
 6693 
 6785 
 6875 
 6964 
 
 6107 
 6212 
 6314 
 6415 
 6513 
 
 6609 
 6702 
 
 6794 
 6884 
 6972 
 
 6117 
 6222 
 
 6325 
 6425 
 6522 
 
 6618 
 6712 
 6803 
 
 6893 
 6981 
 
 1234 
 1234 
 1234 
 1234 
 1234 
 
 1234 
 1234 
 1234 
 1234 
 1234 
 
 5 
 5 
 5 
 5 
 5 
 
 5 
 
 5 
 5 
 4 
 4 
 
 6 8 9 10 
 6789 
 6789 
 6789 
 6789 
 
 6789 
 6778 
 5678 
 5678 
 5678 
 
 50 
 5i 
 52 
 53 
 54 
 
 6990 
 7076 
 7160 
 7243 
 7324 
 
 
 
 6998 
 7084 
 7168 
 7251 
 7332 
 
 I 
 
 7007 
 7093 
 7177 
 7259 
 7340 
 
 2 
 
 7016 
 7101 
 7185 
 7267 
 7348 
 
 3 
 
 7024 
 7110 
 7193 
 
 7275 
 7356 
 
 4 
 
 7033 
 7118 
 7202 
 7284 
 7364 
 
 5 
 
 7042 
 7126 
 7210 
 7292 
 7372 
 
 6 
 
 7050 
 
 7135 
 7218 
 7300 
 738o 
 
 7 
 
 7059 
 7143 
 7226 
 73o8 
 7388 
 
 8 
 
 7067 
 7152 
 7235 
 73i6 
 7396 
 
 1233 
 1233 
 1223 
 1223 
 1223 
 
 4 
 
 4 
 4 
 4 
 4 
 
 5678 
 5678 
 5677 
 5667 
 5667 
 
 9 
 
 12 3 4 
 
 5 
 
 6789 
 
APPENDIX 
 
 115 
 
 
 
 
 XII. FouR-FiGi 
 
 [JRE 
 
 Logarithms - 
 
 — Continm 
 
 3d 
 
 
 N 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 7474 
 755i 
 7627 
 7701 
 7774 
 
 7846 
 7917 
 7987 
 8055 
 8122 
 
 8189 
 8254 
 8319 
 8382 
 
 8445 
 
 8506 
 
 8567 
 8627 
 8686 
 8745 
 
 8802 
 8859 
 8915 
 8971 
 9025 
 
 9079 
 9133 
 9186 
 9238 
 9289 
 
 9340 
 9390 
 9440 
 9489 
 9538 
 
 1234 
 
 5 
 
 6789 
 
 55 
 56 
 57 
 58 
 59 
 
 60 
 61 
 62 
 63 
 64 
 
 65 
 66 
 
 67 
 68 
 69 
 
 70 
 
 7i 
 72 
 
 73 
 74 
 
 75 
 76 
 77 
 78 
 79 
 
 80 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 90 
 91 
 
 92 
 
 93 
 94 
 
 95 
 96 
 97 
 98 
 99 
 
 7404 
 7482 
 7559 
 7634 
 7709 
 
 7782 
 7853 
 7924 
 7993 
 8062 
 
 8129 
 8i95 
 8261 
 
 8325 
 8388 
 
 8451 
 8513 
 8573 
 8633 
 8692 
 
 8751 
 8808 
 8865 
 8921 
 8976 
 
 9031 
 9085 
 9138 
 9191 
 9243 
 
 9294 
 9345 
 9395 
 9445 
 9494 
 
 9542 
 9590 
 9638 
 9685 
 9731 
 
 9777 
 9823 
 9868 
 9912 
 9956 
 
 
 
 7412 
 7490 
 7566 
 7642 
 7716 
 
 7789 
 7860 
 
 793i 
 8000 
 8069 
 
 8136 
 8202 
 8267 
 8331 
 8395 
 
 8457 
 8519 
 8579 
 8639 
 8698 
 
 8756 
 8814 
 8871 
 8927 
 8982 
 
 9036 
 9090 
 
 9143 
 9196 
 9248 
 
 9299 
 935o 
 9400 
 9450 
 9499 
 
 9547 
 9595 
 9643 
 9689 
 9736 
 
 9782 
 9827 
 9872 
 9917 
 9961 
 
 I 
 
 7419 
 7497 
 7574 
 7649 
 
 7723 
 
 7796 
 7868 
 7938 
 8007 
 8075 
 
 8142 
 8209 
 8274 
 8338 
 8401 
 
 8463 
 8525 
 8585 
 8645 
 8704 
 
 8762 
 8820 
 8876 
 8932 
 8987 
 
 9042 
 9096 
 9149 
 9201 
 9253 
 
 9304 
 9355 
 9405 
 9455 
 9504 
 
 9552 
 9600 
 9647 
 9694 
 9741 
 
 9786 
 9832 
 9877 
 9921 
 
 9965 
 
 2 
 
 7427 
 7505 
 7582 
 7657 
 773i 
 
 7803 
 7875 
 7945 
 8014 
 8082 
 
 8i49 
 8215 
 8280 
 8344 
 8407 
 
 8470 
 853i 
 8591 
 8651 
 8710 
 
 8768 
 8825 
 8882 
 8938 
 8993 
 
 9047 
 9101 
 
 9154 
 9206 
 9258 
 
 9309 
 9360 
 9410 
 9460 
 9509 
 
 7435 
 7513 
 7589 
 7664 
 7738 
 
 7810 
 7882 
 7952 
 8021 
 8089 
 
 8156 
 8222 
 8287 
 8351 
 8414 
 
 8476 
 8537 
 8597 
 8657 
 8716 
 
 8774 
 8831 
 
 8887 
 
 8943 
 8998 
 
 9053 
 9106 
 
 9159 
 9212 
 9263 
 
 9315 
 9365 
 9415 
 9465 
 9513 
 
 7443 
 7520 
 7597 
 7672 
 
 7745 
 
 7818 
 7889 
 7959 
 8028 
 8096 
 
 8162 
 8228 
 8293 
 8357 
 8420 
 
 8482 
 8543 
 8603 
 8663 
 8722 
 
 8779 
 8837 
 8893 
 8949 
 9004 
 
 9058 
 9112 
 9165 
 9217 
 9269 
 
 9320 
 9370 
 9420 
 9469 
 95i8 
 
 7451 
 7528 
 7604 
 7679 
 7752 
 
 7825 
 7896 
 
 7966 
 
 8035 
 8102 
 
 8169 
 
 8235 
 
 8299 
 
 8363 
 8426 
 
 8488 
 
 8549 
 8609 
 8669 
 8727 
 
 8785 
 
 8842 
 8899 
 8954 
 
 9009 
 
 9063 
 9117 
 9170 
 
 9222 
 
 9274 
 9325 
 
 9375 
 9425 
 9474 
 9523 
 
 7459 
 7536 
 7612 
 7686 
 7760 
 
 7832 
 7903 
 7973 
 8041 
 8109 
 
 8176 
 8241 
 8306 
 8370 
 8432 
 
 8494 
 8555 
 8615 
 8675 
 8733 
 
 8791 
 
 8848 
 8904 
 8960 
 
 9015 
 
 9069 
 9122 
 
 9175 
 9227 
 
 9279 
 
 9330 
 9380 
 9430 
 9479 
 9528 
 
 7466 
 
 7543 
 7619 
 7694 
 7767 
 
 7839 
 7910 
 7980 
 8048 
 8116 
 
 8182 
 8248 
 8312 
 8376 
 8439 
 
 8500 
 8561 
 8621 
 8681 
 8739 
 
 8797 
 8854 
 8910 
 8965 
 9020 
 
 9074 
 9128 
 9180 
 9232 
 9284 
 
 9335 
 9385 
 9435 
 9484 
 9533 
 
 1223 
 1223 
 1223 
 1 1 2 3 
 1 1 2 3 
 
 4 
 4 
 4 
 4 
 4 
 
 5567 
 5567 
 5567 
 4567 
 4567 
 
 1 1 2 3 
 1 1 2 3 
 1 1 2 3 
 1 1 2 3 
 1 1 2 3 
 
 1 1 2 3 
 1 1 2 3 
 1 1 2 3 
 1 1 .2 3 
 1 1 2 2 
 
 4 
 4 
 3 
 3 
 3 
 
 3 
 3 
 3 
 3 
 3 
 
 4566 
 4566 
 4566 
 4 5 5 6 
 4 5 5 6 
 
 4 5 5 6 
 4 5 5 6 
 4 5 5 6 
 4 4 5 6 
 4 4 5 6 
 
 1 1 2 2 
 i 1 2 2 
 1 1 2 2 
 1 1 2 2 
 1 1 2 2 
 
 1 1 2 2 
 1 1 2 2 
 
 I 1 2 2 
 
 II 22 
 1 1 2 2 
 
 3 
 3 
 3 
 3 
 3 
 
 3 
 3 
 3 
 3 
 3 
 
 4 4 5 6 
 4 4 5 5 
 4 4 5 5 
 4 4 5 5 
 4 4 5 5 
 
 3 4 5 5 
 3 4 5 5 
 3 4 4 5 
 3 4 4 5 
 3 4 4 5 
 
 1 1 2 2 
 1 1 2 2 
 1 1 2 2 
 1 1 2 2 
 1 1 2 2 
 
 1 1 2 2 
 1 1 2 2 
 1 1 2 
 1 1 2 
 1 1 2 
 
 3 
 3 
 3 
 3 
 3 
 
 3 
 3 
 2 
 2 
 
 2 
 
 3 4 4 5 
 3 4 4 5 
 3 4 4 5 
 3 4 4 5 
 3 4 4 5 
 
 3 4 4 5 
 3 4 4 5 
 3 3 4 4 
 3 3 4 4 
 3 3 4 4 
 
 9557 
 9605 
 9652 
 9699 
 9745 
 
 9791 
 9836 
 9881 
 9926 
 9969 
 
 3 
 
 9562 
 9609 
 9657 
 9703 
 9750 
 
 9795 
 9841 
 9886 
 9930 
 9974 
 
 4 
 
 9566 
 9614 
 9661 
 9708 
 9754 
 
 9800 
 
 9845 
 9890 
 
 9934 
 9978 
 
 5 
 
 9571 
 9619 
 9666 
 9713 
 9759 
 
 9805 
 9850 
 9894 
 9939 
 9983 
 
 6 
 
 9576 
 9624 
 9671 
 9717 
 9763 
 
 9809 
 9854 
 9899 
 9943 
 9987 
 
 7 
 
 958i 
 9628 
 
 9675 
 9722 
 9768 
 
 9814 
 9859 
 9903 
 9948 
 9991 
 
 8 
 
 9586 
 9633 
 9680 
 9727 
 9773 
 
 9818 
 9863 
 9908 
 9952 
 9996 
 
 9 
 
 1 1 2 
 1 1 2 
 1 1 2 
 1 1 2 
 1 1 2 
 
 1 1 2 
 1 1 2 
 i 1 2 
 1 1 2 
 1 1 2 
 
 2 
 2 
 2 
 2 
 2 
 
 2 
 2 
 
 2 
 2 
 2 
 
 3 3 4 4 
 3 3 4 4 
 3 3 4 4 
 3 3 4 4 
 3 3 4 4 
 
 3 3 4 4 
 
 3 3 4 4 
 
 ,3344 
 
 '3344 
 
 3 3 3 4 
 
 1234 
 
 5 
 
 6789 
 
116 
 
 APPENDIX 
 
 XIII. Antilogarithms 
 
 Log 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1234 
 
 5 
 
 6789 
 
 .00 
 .01 
 .02 
 .03 
 .04 
 
 •05 
 .06 
 .07 
 .08 
 .09 
 
 1000 
 1023 
 1047 
 1072 
 1096 
 
 1122 
 1 148 
 
 "75 
 
 1202 
 1230 
 
 1002 
 1026 
 1050 
 1074 
 1099 
 
 1125 
 1151 
 1178 
 1205 
 1233 
 
 1005 
 1028 
 1052 
 1076 
 1 102 
 
 1127 
 1153 
 1 180 
 1208 
 1236 
 
 1007 
 1030 
 
 1054 
 1079 
 1 104 
 
 1130 
 1156 
 "83 
 1211 
 1239 
 
 1009 
 1033 
 1057 
 1081 
 1 107 
 
 1132 
 
 "59 
 1186 
 1213 
 1242 
 
 1012 
 1035 
 1059 
 1084 
 1 109 
 
 "35 
 1161 
 1189 
 1216 
 
 1245 
 
 1014 
 1038 
 1062 
 1086 
 1112 
 
 1138 
 1164 
 1191 
 1219 
 1247 
 
 1016 
 1040 
 1064 
 1089 
 1114 
 
 1 140 
 1167 
 1 194 
 1222 
 1250 
 
 1019 
 1042 
 1067 
 1091 
 1117 
 
 1 143 
 1 169 
 1197 
 1225 
 
 1253 
 
 1021 
 
 1045 
 1069 
 1094 
 1119 
 
 1 146 
 1172 
 1199 
 
 1227 
 1256 
 
 1 1 
 1 1 
 1 1 
 1 1 
 1 1 1 
 
 1 1 1 
 1 1 1 
 
 O I I T 
 O I I I 
 O I I I 
 
 
 1222 
 1222 
 1222 
 1222 
 2222 
 
 2222 
 2222 
 2222 
 2223 
 2223 
 
 .10 
 .11 
 .12 
 
 • 13 
 .14 
 
 •15 
 .16 
 
 .17 
 .18 
 .19 
 
 1259 
 1288 
 1318 
 1349 
 1380 
 
 1413 
 1445 
 1479 
 1514 
 1549 
 
 1262 
 1291 
 1321 
 1352 
 1384 
 1416 
 1449 
 1483 
 1517 
 1552 
 
 1265 
 1294 
 1324 
 1355 
 1387 
 
 1419 
 1452 
 i486 
 1521 
 1556 
 
 1268 
 1297 
 1327 
 1358 
 1390 
 
 1422 
 
 1455 
 1489 
 
 1524 
 1560 
 
 1271 
 1300 
 1330 
 1361 
 1393 
 1426 
 1459 
 1493 
 1528 
 1563 
 
 1274 
 1303 
 1334 
 1365 
 1396 
 
 1429 
 1462 
 1496 
 1531 
 1567 
 
 1276 
 1306 
 1337 
 1368 
 1400 
 
 1432 
 1466 
 1500 
 1535 
 i57o 
 
 1279 
 1309 
 1340 
 1371 
 1403 
 
 1435 
 1469 
 1503 
 1538 
 1574 
 
 1282 
 1312 
 1343 
 1374 
 1406 
 
 1439 
 1472 
 1507 
 1542 
 1578 
 
 1285 
 1315 
 1346 
 1377 
 1409 
 
 1442 
 1476 
 1510 
 1545 
 1581 
 
 O I I I 
 O I I I 
 O I I I 
 O I I I 
 O I I I 
 
 O I I I 
 O I I I 
 O I I I 
 O I I I 
 O I I I 
 
 2 
 2 
 2 
 2 
 
 2 
 2 
 2 
 2 
 
 2 
 
 2223 
 2223 
 2223 
 2233 
 2233 
 
 2233 
 2233 
 2233 
 2233 
 2 3 3 3 
 
 .20 
 .21 
 .22 
 
 .23 
 
 .24 
 
 .25 
 .26 
 .27 
 .28 
 .29 
 
 1585 
 1622 
 1660 
 1698 
 1738 
 
 1778 
 1820 
 1862 
 1905 
 1950 
 
 1589 
 1626 
 1663 
 1702 
 1742 
 
 1782 
 1824 
 1866 
 1910 
 1954 
 
 1592 
 1629 
 1667 
 1706 
 1746 
 1786 
 1828 
 1871 
 1914 
 1959 
 
 1596 
 1633 
 1671 
 1710 
 I750 
 1791 
 1832 
 1875 
 1919 
 1963 
 
 1600 
 1637 
 1675 
 1714 
 
 1754 
 
 1795 
 1837 
 1879 
 1923 
 1968 
 
 1603 
 1641 
 1679 
 1718 
 1758 
 1799 
 1841 
 1884 
 1928 
 1972 
 
 1607 
 1644 
 1683 
 1722 
 1762 
 
 1803 
 1845 
 1888 
 1932 
 1977 
 
 1611 
 1648 
 1687 
 1726 
 1766 
 
 1807 
 1849 
 1892 
 1936 
 1982 
 
 1614 
 1652 
 1690 
 1730 
 1770 
 
 1811 
 
 1854 
 1897 
 1941 
 1986 
 
 1618 
 1656 
 1694 
 1734 
 1774 
 1816 
 1858 
 1901 
 
 1945 
 1991 
 
 O I I I 
 O I I 2 
 O I I 2 
 O I I 2 
 O I I 2 
 
 O I I 2 
 O I I 2 
 O I I 2 
 O I I 2 
 O I I 2 
 
 2 
 2 
 2 
 2 
 2 
 
 2 
 2 
 2 
 2 
 2 
 
 2 3 3 3 
 2 3 3 3 
 2 3 3 3 
 2 3 3 4 
 2 3 3 4 
 
 2 3 3 4 
 
 3 3 3 4 
 3 3 3 4 
 3 3 4 4 
 3 3 4 4 
 
 .30 
 •31 
 .32 
 •33 
 •34 
 
 •35 
 .36 
 •37 
 .38 
 •39 
 
 1995 
 2042 
 2089 
 2138 
 2188 
 
 2239 
 2291 
 2344 
 2399 
 2455 
 
 2000 
 2046 
 2094 
 2143 
 2193 
 
 2244 
 2296 
 23S0 
 2404 
 2460 
 
 2004 
 2051 
 2099 
 2148 
 2198 
 
 2249 
 2301 
 
 2355 
 2410 
 2466 
 
 2009 
 2056 
 2104 
 2153 
 2203 
 
 2254 
 2307 
 2360 
 2415 
 
 2472 
 
 2014 
 2061 
 2109 
 2158 
 2208 
 
 2259 
 2312 
 2366 
 2421 
 2477 
 
 2018 
 2065 
 2113 
 2163 
 2213 
 
 2265 
 2317 
 2371 
 2427 
 2483 
 
 2023 
 2070 
 2118 
 2168 
 2218 
 
 2270 
 2323 
 2377 
 2432 
 2489 
 
 2028 
 2075 
 2123 
 2173 
 2223 
 
 2275 
 2328 
 2382 
 2438 
 2495 
 
 2032 
 2080 
 2128 
 2178 
 2228 
 
 2280 
 
 2333 
 2388 
 2443 
 2500 
 
 2037 
 2084 
 2133 
 2183 
 2234 
 2286 
 2339 
 2393 
 2449 
 2506 
 
 O I I 2 
 O I I 2 
 O I I 2 
 
 I I 2 
 
 1 I 2 2 
 
 I I 2 2 
 I I 2 2 
 I I 2 2 
 I I 2 2 
 I I 2 2 
 
 2 
 2 
 2 
 2 
 3 
 
 3 
 3 
 3 
 3 
 3 
 
 3 3 4 4 
 3 3 4 4 
 3 3 4 4 
 3 3 4 4 
 3 4 4 5 
 
 3 4 4 5 
 3 4 4 5 
 3 4 4 5 
 3 4 4 5 
 
 3 4 5 5 
 
 .40 
 .41 
 .42 
 •43 
 .44 
 
 •45 
 .46 
 •47 
 .48 
 •49 
 
 2512 
 2570 
 2630 
 2692 
 2754 
 2818 
 2884 
 
 2951 
 3020 
 3090 
 
 2518 
 2576 
 2636 
 2698 
 2761 
 
 2825 
 2891 
 2958 
 3027 
 3097 
 
 I 
 
 2523 
 2582 
 2642 
 2704 
 2767 
 
 2831 
 2897 
 2965 
 3034 
 3I05 
 
 2 
 
 2529 
 2588 
 2649 
 2710 
 2773 
 2838 
 2904 
 2972 
 
 3041 
 3112 
 
 2535 
 2594 
 2655 
 2716 
 2780 
 
 2844 
 2911 
 2979 
 3048 
 3"9 
 
 2541 
 2600 
 2661 
 2723 
 2786 
 
 2851 
 2917 
 2985 
 3055 
 3126 
 
 2547 
 2606 
 2667 
 2729 
 2793 
 2858 
 2924 
 2992 
 3062 
 3133 
 
 2553 
 2612 
 2673 
 2735 
 2799 
 2864 
 2931 
 2999 
 3069 
 3141 
 
 2559 
 2618 
 2679 
 2742 
 2805 
 
 2871 
 2938 
 3006 
 3076 
 3148 
 
 2564 
 2624 
 2685 
 2748 
 2812 
 
 2877 
 2944 
 3013 
 3083 
 3i55 
 
 I I 2 2 
 I I 2 2 
 112 2 
 I I 2 3 
 I I 2 3 
 
 I I 2 3 
 I I 2 3 
 I I 2 3 
 I I 2 3 
 I I 2 3 
 
 3 
 3 
 3 
 3 
 3 
 
 3 
 3 
 3 
 
 4 
 4 
 
 4 4 5 5 
 4 4 5 5 
 4 4 5 
 4 4 5 
 4 4 5 6 
 
 4 5 5 6 
 4 5 5 
 4 5 5 6 
 4566 
 4566 
 
 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 12 3 4 
 
 5 
 
 6789 
 
APPENDIX 
 
 111 
 
 XIII. Antilogakithms — Continued 
 
 Log 
 
 •50 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 789 
 
 3162 
 
 3170 
 
 3177 
 
 3184 
 
 3192 
 
 3199 
 
 3206 
 
 3214 
 
 3221 
 
 3228 
 
 1 
 
 I 
 
 2 
 
 3 
 
 4 
 
 4 
 
 567 
 
 .51 
 
 3236 
 
 3243 
 
 3251 
 
 3258 
 
 3266 
 
 3273 
 
 3281 
 
 3289 
 
 3296 
 
 3304 
 
 1 
 
 2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 567 
 
 •52 
 
 33ii 
 
 3319 
 
 3327 
 
 3334 
 
 3342 
 
 3350 
 
 3357 
 
 3365 
 
 3373 
 
 338i 
 
 1 
 
 2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 567 
 
 •53 
 
 3388 
 
 3396 
 
 3404 
 
 3412 
 
 3420 
 
 3428 
 
 3436 
 
 3443 
 
 3451 
 
 3459 
 
 1 
 
 2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 6 7 
 
 •54 
 
 3467 
 
 3475 
 
 3483 
 
 3491 
 
 3499 
 
 3508 
 
 35i6 
 
 3524 
 
 3532 
 
 3540 
 
 1 
 
 2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 667 
 
 •55 
 
 3548 
 
 3556 
 
 3565 
 
 3573 
 
 358i 
 
 3589 
 
 3597 
 
 3606 
 
 3614 
 
 3622 
 
 1 
 
 2 
 
 2 
 
 3 
 
 4 
 
 5 
 
 677 
 
 .56 
 
 3631 
 
 3639 
 
 3648 3656 
 
 3664 
 
 3673 
 
 3681 
 
 3690 
 
 3698 
 
 3707 
 
 1 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 678 
 
 •57 
 
 37i5 
 
 3724 
 
 3733 3741 
 
 3750 
 
 3758 
 
 3767 
 
 3776 
 
 3784 
 
 3793 
 
 1 
 
 2 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 7 8 
 
 •58 
 
 3802 
 
 3811381913828 
 
 3837 
 
 3846 
 
 3855 
 
 3864 
 
 3873 
 
 3882 
 
 1 
 
 2 
 
 3 
 
 4 
 
 4 
 
 5 
 
 678 
 
 •59 
 
 3890 
 
 389939083917 
 
 3926 
 
 3936 
 
 3945 
 
 3954 
 
 3963 
 
 3972 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 5 
 
 6 7 8 
 
 .60 
 
 398i 
 
 3990 
 
 3999 
 
 4009 
 
 4018 
 
 4027 
 
 4036 
 
 4046 
 
 4055 
 
 4064 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 6 7 8 
 
 .61 
 
 4074 
 
 4083 
 
 4093 
 
 4102 
 
 4111 
 
 4121 
 
 4130 
 
 4140 
 
 4150 
 
 4159 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 789 
 
 .62 
 
 4169 
 
 4178 
 
 4188 
 
 4198 
 
 4207 
 
 4217 
 
 4227 
 
 4236 
 
 4246 
 
 4256 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 8 9 
 
 .63 
 
 4266 
 
 4276 
 
 4285 
 
 4295 
 
 4305 
 
 4315 
 
 4325 
 
 4335 
 
 4345 
 
 4355 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 8 9 
 
 .64 
 
 4365 
 
 4375 
 
 4385 
 
 4395 
 
 4406 
 
 4416 
 
 4426 
 
 4436 
 
 4446 
 
 4457 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 8 9 
 
 .65 
 
 4467 
 
 4477 
 
 4487 
 
 4498 
 
 4508 
 
 4519 
 
 4529 
 
 4539 
 
 4550 
 
 456o 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 8 9 
 
 .66 
 
 457i 
 
 458i 
 
 4592 
 
 4603 
 
 4613 
 
 4624 
 
 4634 
 
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 4656 
 
 4667 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 9 10 
 
 .67 
 
 4677 
 
 4688 
 
 4699 
 
 4710 
 
 4721 
 
 4732 
 
 4742 
 
 4753 
 
 4764 
 
 4775 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 7 
 
 8 9 10 
 
 .68 
 
 4786 
 
 4797 
 
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 4819 
 
 4831 
 
 4842 
 
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 4864 
 
 4875 
 
 4887 
 
 1 
 
 2 
 
 3 
 
 4 
 
 6 
 
 7 
 
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 .69 
 
 4898 
 
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 4920 
 
 4932 
 
 4943 
 
 4955 
 
 4966 
 
 4977 
 
 4989 
 
 5000 
 
 1 
 
 2 
 
 3 
 
 5 
 
 6 
 
 7 
 
 8 9 10 
 
 .70 
 
 5012 
 
 5023 
 
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 5070 
 
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 5ii7 
 
 1 
 
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 4 
 
 5 
 
 6 
 
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 .71 
 
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 5164 
 
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 5212 
 
 5224 
 
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 1 
 
 2 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 10 11 
 
 .72 
 
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 5260 
 
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 52845297 
 
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 2 
 
 4 
 
 5 
 
 6 
 
 7 
 
 9 10 11 
 
 •73 
 
 537o 
 
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 8 
 
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 5 
 
 6 
 
 8 
 
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 1 
 
 3 
 
 4 
 
 5 
 
 7 
 
 8 
 
 9 10 12 
 
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 5821 
 
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 5 
 
 7 
 
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 7 
 
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 11 
 
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 16 18 20 
 
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 9 
 
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 16 18 20 
 
 I 
 
 2 
 
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 5 
 
 6 
 
 7 
 
 8 9 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
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 789 
 
T 
 
 HE following pages contain advertisements of a 
 few of the Macmillan books on kindred subjects 
 
Practical Physics for Secondary Schools 
 
 By N. HENRY BLACK of the Roxbury Latin School, 
 Boston, and Professor HARVEY N. DAVIS of Harvard 
 University. 
 
 Cloth, i2mo, illustrated, 488 pages. List price, $1.25 
 
 " In preparing this book," say the authors in the Preface, " we have tried to 
 select only those topics which are of vital interest to young people, whether or 
 not they intend to continue the study of physics in a college course. 
 
 " Jn particular, we believe that the chief value of the informational side of 
 such a course lies in its applications to the machinery of daily life. Everybody 
 needs to know something about the working of electrical machinery, optical 
 instruments, ships, automobiles, and all those labor-saving devices, such as 
 vacuum cleaners, tireless cookers, pressure cookers, and electric irons, which 
 are found in many American homes. We have, therefore, drawn as much of 
 our illustrative material as possible from the common devices in modern life. 
 We see no reason why this should detract in the least from the educational 
 value of the study of physics, for one can learn to think straight just as well by 
 thinking about an electrical generator, as by thinking about a Geissler tube. . . . 
 
 " To understand any machine clearly, the student must have clearly in mind 
 the fundamental principles involved. Therefore, although we have tried to 
 begin each new topic, however short, with some concrete illustration familiar 
 to young people, we have proceeded, as rapidly as seemed wise, to a deduction 
 of the general principle. Then, to show how to make use of this principle, we 
 have discussed other practical applications. We have tried to emphasize still 
 further the value of principles, that is, generalizations, in science, by summariz- 
 ing at the end of each chapter the principles discussed in that chapter. In 
 these summaries we have aimed to make the phrasing brief and vivid so that 
 it may be easily remembered and easily used." 
 
 The new and noteworthy features of the book are the admirable 
 selection of familiar material used to develop and apply the principles 
 of physical science, the exceptionally clear and forceful exposition, 
 showing the hand of the master teacher, the practical, interesting, 
 thought-provoking problems, and the superior illustrations. 
 
 THE MACMILLAN COMPANY 
 
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 Chicago New York City Dallas 
 
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Chemistry and its Relations to Daily Life 
 
 By LOUIS KAHLENBERG and EDWIN B. HART 
 
 Professors of Chemistry in the University of Wisconsin 
 
 Cloth, i2mo, illustrated, 3Q3 pages. List price, $1.2$ 
 
 If the contributions of chemical science to modern civilization 
 were suddenly swept away, what a blank there would be ! If, on 
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 of agriculture and home economics in secondary schools, its use will 
 do much to increase the efficiency of the farm and the home. In 
 the language of modern educational philosophy, it " functions in the 
 life of the pupil.'" 
 
 Useful facts rather than mere theory have been emphasized, 
 although the theory has not been neglected. The practical char- 
 acter of the work is indicated by the following selected chapter 
 headings : 
 
 IL The Composition and Uses of Water* 
 
 IV* The Air, Nitrogen* Nitric Acid* and Ammonia* 
 
 IX. Carbon and Its Compounds* 
 
 XII* Paints* Oils* and Varnishes* 
 
 XIII* Leather* Silk* Wool* Cotton* and Rubber* 
 
 XV* Commercial Fertilizers* 
 
 XVI* Farm Manure* 
 
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 XXL Poisons for Farm and Orchard Pests* 
 
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Botany for Secondary Schools 
 
 By L. H. BAILEY 
 
 Of Cornell University 
 
 Cloth, i2mo, illustrated, 460 pages. List price, $1.25 
 
 It is not essential nor desirable that everybody should become a botanist, 
 but it is inevitable that people shall be interested in the more human side 
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 The secondary school could not teach botanical science if it would ; lack of 
 time and the immaturity of the pupils forbid it. But it can encourage a 
 love of nature and an interest in plant study; indeed, it can originate these, 
 and it does. Professor Bailey's Botany has been known to do it. 
 
 In the revision of this book that has just been made, the effective simplicity 
 of the nature teacher and the genuine sympathy of the nature lover are as 
 successfully blended as they were in the former book. Bailey's Botany for 
 Secondary Schools recognizes four or five general life principles : that no 
 two natural things are alike ; that each individual has to make and main- 
 tain its place through struggle with its fellows ; that " as the twig is bent 
 the tree inclines " ; that " like produces like," and so on. From these 
 simple laws and others like them Professor Bailey proceeds to unfold a 
 wonderful story of plant individuals that have improved upon their race 
 characteristics, of plant communities that have adopted manners from 
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 plants because of changed conditions of life or surroundings. The story 
 vibrates with interest. 
 
 The book is, moreover, perfectly organized along the logical lines of 
 approach to a scientific subject. Four general divisions of material insure 
 its pedagogical success : 
 
 Part I. — The Plant Itself; 
 
 Part II. — The Plant in Its Relation to Environment and to Man; 
 
 Part III. — Histology, or the Minute Structure of Plants ; 
 
 PART IV. — The Kinds of Plants, including a Flora of 130 pages. 
 
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 Publishers 64-66 Fifth Avenue New York 
 
 BOSTON CHICAGO ATLANTA DALLAS SAN FRANCISCO 
 
Shelter and Clothing : 
 
 A TEXTBOOK OF THE HOUSEHOLD ARTS 
 
 By HELEN KINNE, Professor of Household Arts Educa- 
 tion, and ANNA M. COOLEY, Assistant Professor of House- 
 hold Arts Education, Teachers College, Columbia University. 
 Cloth, i2mo, illustrated, 37 J pages. $uo 
 
 This book and the volume, Foods and Household Management, that follows 
 it, make up a full course in domestic matters not confined to details of cooking 
 and sewing. The books treat fully, but with careful balance, every phase of 
 home-making. The authors hold that Harmony will be the keynote of the 
 home in proportion as the makers of the home regard the plan, the sanitation, 
 the decoration of the house itself, and as they exercise economy and wisdom in 
 the provision of food and clothing. 
 
 " Home Economics stands for the utilization of the resources of modern 
 science to improve home life," and to this end homemakers should be con- 
 versant with modern scientific thought on matters domestic. The best schemes 
 of heating and lighting, modern arrangements for the disposal of waste, the 
 sanitary efficiency of tinted walls, of bare floors, of furniture built on simple 
 lines, these are some ways in which modern science instructs the intelligent 
 homemaker. In the selection of textiles for clothing and domestic use, a 
 housekeeper to be efficient must be able to distinguish between fabrics of dif- 
 ferent fibers and to choose durable weaves, she must be able to detect adultera- 
 tion and the deceptive " finishing " processes. In buying ready-made garments 
 she must know how to protect herself and her family from the danger of gar- 
 ments infected by diseased operators in sweatshops. The up-to-date book on 
 home economy treats such topics and relates them to common experience. 
 
 The plan of the book is flexible. Parts may be omitted or shifted to meet 
 the necessity or the convenience of different schools. The chapter headings 
 in some measure disclose the breadth, the variety, and the practicability of the 
 book : 
 
 The Home. — Its plan and construction ; heating, ventilating, lighting, 
 water supply, and the disposal of waste ; decoration ; furnishing. Textiles. — 
 Materials and how they are made. Garment-making. — Patterns ; cutting and 
 making garments; embroidery. Dress. — History of costume; hygiene of 
 clothing; economics of dress ; care and repair of clothing; millinery. 
 
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SEP 18 1913