1 S ^ ^ < S gvwm e i i WL_ I I I 3 f? 3 s s ^ t g y. ^-^ ' "5. > ^^ ^ rc GINN & COMPANY PRO- . PRIETORS BOSTON U.S.A. ac-35 INTRODUCTION Although laboratory work is now generally recognized as an indispensable part of any adequate course in elementary physics,' it is nevertheless a lamentable fact that there are still some schools in which it is not attempted at all, while there are others in which, despite the most expensive equipment, the laboratory fails, on the whole, either to interest or instruct. Both of these conditions are probably attributable to one and the same cause. In our modern glorification of the laboratory, method, particularly of exact, quantitative measurements, and in our haste to get away from the superficial, descriptive physics of thirty years ago, some of us have undoubtedly gone so far as to defeat our own aims. We have made the laboratory an impos- sibility in schools which are financially weak, because we have made its expense prohibitive ; and we have made it a disap- pointment in other schools which are financially strong, because in our eagerness to show our students exactly how much we have neglected to show them how and why. In short, the gravest danger which threatens the efficiency of the high-school labora- tory to-day is the danger which arises from the creeping over of the methods and the instruments of research and specialization from the university into the high school, where they have abso- lutely no place, the danger that principles shall be lost sight of in the bewildering details of refined methods and refined instruments. The primary aims of the authors in the development of this course have been : (1) to make it a continuous and inspiring laboratory study of physical phenomena, and as far as possible iv INTRODUCTION removed from a mere drill in physical manipulation ; and (2) to reduce apparatus to its simplest possible terms and yet to present a thorough course in laboratory physics. Such success as has been attained in the accomplishment of these ends has been due not merely to a large amount of labor and experimentation on the part of the authors, but also to sug- gestions which have come in from the score of schools in which this course has been given a thorough trial during the past three years, and especially to the expert assistance of the instrument maker, Mr. William Gaertner, who has so simplified the design of the apparatus herewith presented that a large part of it can now be made at home if desired. Even if it is all purchased, it need not cost more than fifty dollars for a complete set, and six such sets have been used most satisfactorily at the University of Chicago in conducting laboratory sections of twenty pupils. The authors recommend, however, that wherever conditions will permit, all of the pupils of a section be kept working upon the same experi- ment at the same time. This arrangement requires about half as many sets as there are pupils. With instructions as complete as those here given, the experience of a number of schools has shown that with fifteen sets one instructor can successfully con- duct a class of as many as thirty pupils. Great care has been taken to incorporate only such experiments as experience has shown to be workable with large classes and with a minimum tax upon the teacher's time outside of laboratory hours. Another feature of the course is that the experiments do not presuppose either any previous study of the subject involved, or any antecedent knowledge of physics. The laboratory work may be kept in advance of the class-room discussion throughout the entire course if desired. Indeed, in their own elementary work the authors prefer to let more than half of the experiments constitute the student's first introduction to the subject treated. Furthermore, students are neither instructed nor advised to study INTRODUCTION v their experiments before entering the laboratory, for each experi- ment has been arranged to carry with it its own introduction. As was to have been expected from the statement of the aims of the course, it has been made a thorough mixture of qualitative and quantitative work. Indeed, the endeavor to make an ele- mentary laboratory course either wholly qualitative or wholly quantitative seems to the authors to result inevitably in artifi- cial and irrational distinctions, and to be perhaps the most fruitful cause of the failure of laboratory work. The most approved and most satisfactory division of time between the class room and the laboratory is three single periods per week in the former and two double periods in the latter. Abundant experience in schools quite variously situated has shown that the work herein outlined can be easily completed in two such eighty- or ninety-minute periods per week for thirty- six weeks, even when all the notebook work is done in class. The length of the experiments has not, however, been adjusted so as to fit, in all cases, one school period ; first, because the lengths of school periods are so different in different schools, and second, because the authors have not wished to sacrifice the logical development of a subject to a consideration which is after all wholly artificial and mechanical. The division into ex- periments is made on the basis of subject-matter rather than of time. A considerable number of the experiments will be found to require two periods, while in a few instances two experiments can be performed in a single period. This arrangement has not been found to be at all objectionable where all of the pupils work simultaneously upon the same experiment, and even in courses which are conducted with but a few sets of apparatus the difficulties arising from this source have been found to be trifling. In case individual teachers find it desirable to shorten or modify the course, the subdivisions of each experiment make vi INTRODUCTION omissions easy and simple. It has been an especial aim of the authors to make both this course and the class-room text which it is designed to accompany sufficiently flexible to give full play to the individuality of the teacher. Both books have there- fore been made complete enough to allow of a considerable range of choice. The two books together constitute a one-year course in high-school physics. The laboratory portion has, however, been made completely independent of the other portion, and in a number of instances has been given as a short course by itself with very satisfactory results. It is the firm conviction of the authors, based upon a considerable experience, that in schools in which only a short course in physics can be offered, a course of this sort with laboratory work for its backbone is much more satisfactory than one based upon an abridgment of a class-room text. With respect to the notebook the authors can express but little sympathy with any rigid, mechanical form of arrangement to which all experiments must be forced to conform, and they are convinced that in some schools the real study of physics has been sacrificed to the study of notebook form. Their directions to their own pupils are, "Fill out your notebook as you proceed with your work in the laboratory, and let it be merely a brief running record of what you do, of what results you obtain, and of what conclusions you draw." Blank books of coordinate paper are required, and left-hand pages are used for scratch- book purposes, i.e. they contain preliminary observations and computations, while right-hand pages contain the orderly out- line of the work, including the title and subheads of each experiment as found in the manual, a very brief statement of what is done under each, an orderly statement of results (copied in some instances from the left-hand page), and conclu- sions. Outline drawings are encouraged whenever the idea can be expressed more quickly and clearly in a drawing than in INTKODUCTION vii words. In order to place especial insistence upon the conclu- sions, questions have been freely scattered through the text, the answers to which generally involve the conclusions which are to be drawn. In schools in which double laboratory periods cannot be obtained time may be gained, without sacrificing the real study of physics, by having the orderly part of the notebook work done at home. If still further time must be gained, the authors prefer to save it at the expense of the writ- ten work rather than at that of the experiments, oral answers and discussion in the laboratory replacing some of the written work called for. For the benefit of those who use both this book and the authors' class-room text a suggested time schedule for a thirty- six weeks' school year is inserted in Appendix A. Whether this particular schedule is followed or not, it seems to the authors a matter of great importance that each teacher begin his year with some well-considered time schedule before him, and that he plan each lesson and make his omissions and addi- tions with this schedule in mind. Otherwise it almost invariably happens that the subjects treated in the first half of the text receive a disproportionate amount of time. In Appendix C will be found a complete list of the apparatus desirable for the course. The experiments do not, however, preclude the use of the more expensive forms of instruments which are already common in the equipment of high schools, although the authors believe the simpler apparatus to be, in general, the more instructive. The form which has been given to the Boyle's Law experi- ment (page 26) was first called to the authors' attention by Mr. C. H. Perrine of the Wendell Phillips High School, Chicago, although a modification of the same method is found in the admirable laboratory manual by Nichols, Smith, and Turton." The experiment on the cooling of acetamide through its change viii INTRODUCTION of state is the authors' modification of a similar experiment on acetanilid suggested to them by Dr. C. E. Linebarger of the Lake View High School, Chicago. The experiment on the mechanical equivalent of heat (Experiment 20) is similar to one described in Edser's Heat. The remaining experiments are either so familiar as to be common property or else have been devised by the authors. The single balance, which serves all the pur- poses of the course, was designed especially for it by Mr. Gaert- ner, with a view to gaining the great advantages which the suspended-beam type of balance possesses over the trip scale, and at the same time doing away with the nuisance of small weights. The apparatus used in the study of electricity is nearly all new, and, though very inexpensive and apparently crude, has proved extremely satisfactory. 1 Among the large number of teachers who have already used the course and who have assisted in perfecting it, the authors are under especial obligation to Dr. G. M. Hobbs, Dr. C. J. Lynde, and Mr. F. H. Wescott of the University High School, Mr. George Winchester, now of Washington State University, and Mr. Harry D. Abells of Morgan Park Academy. R. A. M. II. G. G. 1 All of the apparatus for the course can be obtained of William Gaertner & Co., 5347 Lake Avenue, Chicago. CONTENTS EXPERIMENT PAGE 1. DETERMINATION OF TT * 1 2. VOLUME OF A CYLINDER 3 3. DENSITY OF STEEL SPHERES 8 4. RESULTANT OF Two FORCES 11 5. PRESSURE WITHIN A LIQUID 14 6. USE OF MANOMETERS 17 7. ARCHIMEDES' PRINCIPLE 19 8. DENSITY OF LIQUIDS 21 9. DENSITY OF A LIGHT SOLID 24 10. BOYLE'S LAW 20 11. DEW-POINT 30 12. HOOKE'S LAW .35 13. EXPANSION OF AIR . . . . . . . . . .37 14. EXPANSION OF BRASS 40 15. PRINCIPLE OF MOMENTS 44 1C. THE INCLINED PLANE 46 17. THE PEN-DILI M 48 18. THE LAW OF MIXTURES 52 19. SPECIFIC HEAT 55 20. THE MECHANICAL EQUIVALENT OF HEAT . , . . .59 21. COOLING THROUGH CHANGE OF STATE 62 22. HEAT OF FUSION OF ICE 64 23. BOILING POINT OF ALCOHOL 66 24. FREEZING AND BOILING POINTS OF WATER 68 25. MAGNETIC FIELDS . . . . . . . .70 26. MOLECULAR NAT*URE OF MAGNETISM . . . . . 71 27. STATIC ELECTRICAL EFFECTS 74 ix X CONTENTS EXPERIMENT PAGE 28. THE VOLTAIC CELL 79 29. MAGNETIC EFFECT OF A CURRENT * 82 30. MAGNETIC PROPERTIES OF COILS 85 31. ELECTROMOTIVE FORCES 87 32. OHM'S LAW 91 33. COMPARISON OF RESISTANCES 93 34. INTERNAL RESISTANCE 97 35. ELECTROLYSIS AND THE STORAGE BATTERY 99 36. INDUCED CURRENTS 102 37. ELECTRIC BELLS AND MOTORS 106 38. SPEED OF SOUND IN AIR 107 39. VIBRATION RATE OF A FORK . . . . . . . . 108 40. WAVE LENGTH OF A FORK , . .110 41. LAWS OF VIBRATING STRINGS Ill 42. PLANE MIRRORS 113 43. INDEX OF REFRACTION 114 44. CRITICAL ANGLE OF GLASS 116 45. CONCAVE MIRRORS 118 46. CONVEX LENSES 119 47. MAGNIFYING POWER OF A SIMPLE LENS 121 48. THE ASTRONOMICAL TELESCOPE 122 49. THE COMPOUND MICROSCOPE 123 60. PRISMS 124 61. PHOTOMETRY 128 APPENDIX A 129 APPENDIX B 130 ' APPENDIX C 131* INDEX . . 133 LABORATORY PHYSICS /*.*/* EXPERIMENT 1 EXPERIMENTAL DETERMINATION OF TT (The ratio of the circumference of a circle to its diameter) (a) Measurement of circumference. Measure the circumference to an accurately turned disk in the following way. Scratch a short mark A (Fig. 1) on the face of the disk perpendicu- M ( O lar to its edge. Stand the disk on edge on a meter stick so B FIG ^ that the mark A is very accu- rately above some chosen division B, e.g. the 10-cm. mark of the meter stick. Then, supporting the disk by causing the thumb and fore- finger to meet through 0, roll it very carefully along the meter stick until it has turned through one complete revolu- tion. (Don't touch circumference in rolling.) The mark A will fall on some point of the scale. If it does not fall exactly on one of the millimeter divisions, in order to retain a decimal system throughout, record the fractional part of the last divi- sion in tenths, not in halves, thirds, or quarters. 1 1 Unfamiliarity with the metric system may make it seem more natural to estimate in halves, thirds, or quarters, but it will be easy to express the result in tenths if one reflects that .4 is a little less, and .6 a little more, than 1/2;' .2 a little less and .3 a little more than 1/4; .1 a little less than .2, i.e. 1/5, etc. 1 2 LABORATORY PHYSICS Repeat the measurement and estimation four times, starting at a different point on the scale each time. Take a mean of these five readings as the most correct value of the circumfer- ence obtainable by this method. Since the separate observations were uncertain in the tenths millimeter place, the mean will surely be uncertain in the hundredths millimeter place. To reserve places beyond this, then, would not only be useless but misleading, since it would indicate that the measurement was made to a higher degree of accuracy than it really was. The best usage in recording physical observations is to record one uncertain figure, but never more, except in recording the mean of a considerable number of observations, when one more figure may be retained, especially if the difference between the individual observations is slight. If this uncertain figure hap- ii. , , . i .^.^.,1,^^^^ pens to be zero, it should be recorded like any other digit. (b) Measurement of diameter. Next measure the diameter of the ring with a meter stick held on edge as in Fig. 2. Record five observations taken along differ- ent diameters, and take the mean, estimating in each case to tenths of a millimeter. (c) Computation. From these measurements compute TT, the ratio of the circumference of a circle to its diameter. In the result save only one uncertain figure. To find the first uncertain figure in the result, divide as in 8.436 126.52 |3.143 the illustration, underlining the uncertain ~~25308~ figures throughout. 1 2120 Compare the result of your measurement 8436 with that given by mathematical theory, 36840 viz. 3.1416. Find first the amount of the 33744 error, and then compute what per cent 30960 the error is of the whole quantity, e.g. if VOLUME OF A CYLINDER 3 the result of your measurement is 3.143, then by taking the difference between this and 3.1416 we get 3.143 1% of 3.1416 = .031416 3.1416 .0014 .-. Per cent of error = = .045 .0014 = error .031 In the last division only two significant figures were used in the denominator, since it is never necessary to find the per cent of error to more than this degree of accuracy. Record measurements and computations as below : Trial Diameter Circumference 1 8.43 26.50 2 8.45 26.55 3 8.44 26.52 Circumference 4 8.43 26.50 Diameter 5 8.43 26.52 Error = .0014 Mean 8.436 26.51.8 Per cent of error = .045 State in the notebook, beneath the results tabulated as above, what per cent of error would have been introduced into the result if you had made an error of .1 mm. in measuring the diameter. (Find what per cent .1 mm. is of the whole diameter 8.436.) State, therefore, whether your error is more or less than should have" been expected from reasonably careful measure- ments. (Put your answers into the form of complete sentences.) EXPERIMENT 2 DETERMINATION OF THE VOLUME OF A CYLINDER I. By computation from linear measurement. (a) Measurements. Measure with a metric rule the inside depth of the cylindrical vessel shown in Fig. 8, in three differ- ent places, estimating as before very carefully to tenths of a millimeter. LABORATORY PHYSICS Measure the inside diameter D with a vernier caliper, 1 if this instrument is available; if not, use the method of the previous experiment, taking pains that the edge of the meter stick is held in every case exactly across a diameter. (b) Computation. Compute the volume of the cylinder from the area of the base (-^r-> or TUP, K being the radius j and the height L. Underline all uncertain figures, and save only two uncertain figures in the result. The following illustrates the method of computation : L= 8.01 fi = 2.513 cm. 2.513 A J2 = 6.315 TT = 3.142 7539 2513 12565 5026 12630 25250 6315 18945 6.315 7T.K 2 = 19.841 1984 15872 158.91 = volume in cubic centimeters 1 The vernier is a device for measuring fractional parts of a scale division. It consists of a movable scale AB arranged to slide along a fixed scale CD (Fig. 3). e f The object to be measured is placed between the jaws EF, which are so made that when they are in contact the zero of the sliding scale is opposite the zero of the fixed scale. FIG. 3 Ten divisions of the sliding scale A E are made equal to nine divisions, i.e. 9 mm., on the main scale CD; hence one vernier division is equal to .9 mm. Fig. 4 (1) shows the vernier scale and the fixed scale enlarged. Here the zero of the vernier is exactly opposite the 5-mm. mark of the fixed scale, this being the relative position of the two scales when an object 6 mm. in diameter is placed between the jaws. Since one division on VOLUME OF A CYLINDER 5 Tabulate your results in some form similar to the following : First Second Third observation observation observation Height of cylinder = 8.26 cm. 8.25 cm. 8.25 cm. 8.253 cm. Inner diameter of cylinder = 6.04 cm. 6.03 cm. 6.04 cm. 6.03J7 cm. . . R = 3 .019 .-. Volume = 236.2 cc. Write in your notebook answers to the following questions, using complete sentences as in Experiment 1. If the diameter of a circle is measured as 10.1 cm. when it is actually 10 cm., by what per cent will the square of the diameter as measured differ from the square of the true diameter? (If in doubt, work it out.) Hence what per cent of error will be intro- duced into the computed value of the area of a circle, if there is an error of 0.3 per cent in the measurement of the diameter? AB is equal to only .9 mm., while one division on CD is equal to a whole milli- meter, it follows that the mark 1 of the sliding scale AB is .1 mm. behind the mark 6 of the fixed scale; 2 on AB is .2 mm. behind 7 on CD; 3 is .3 mm. behind 8 ; 7 is .7 mm. behind 12, etc. Therefore, if the sliding scale were moved up so as to bring its mark 1 opposite the mark 6 on the fixed scale, its zero mark would move up .1 mm. beyond 5. If the vernier had moved up until its 5 mark were opposite 10 on CD, the zero mark would have moved .5 mm. beyond 5, etc. In general, then, it is only necessary to observe which mark on the sliding scale (1) (2) Co I i 3 5 6 7 8 9 10 II It !3 l .5 It 17 D C I 8 . J 5 > '0 n * .13 D 1 1 1 1 1 1 1 1 1 1 III I 1 1 ^\ } \\\ FIG. 4 AB is directly opposite a mark on CD, in order to know how many tenths of a millimeter the zero mark of AB has moved beyond the last division passed on CD. Thus the reading in Fig. 4 (2) is 3.7 mm. (.37 cm.), since the zero mark of the vernier has passed the 3-mm. mark on the fixed scale CD, and the 7 mark on the vernier is directly opposite some mark of CD. In order that the interior as well as exterior dimensions of hollow objects may be readily determined, the jaws ef (Fig. 3) are added in many vernier calipers. These jaws are inserted just inside the walls and the reading taken as described. LABORATORY PHYSICS If you misread the diameter of your cylinder by 0.1 mm., what per cent of error did you thus introduce into the diameter? into the computed area of the base of the cylinder? into the computed volume of the cylinder? II. By weighing the cylinder first when empty and then when filled with water. (a) Weighing cylinder by method of substitution. Place the empty cylinder with its ground-glass cover on the pan 11 (Fig. 5) of the balance, and add to the other pan any convenient objects, such as pieces of iron, shot, and bits of paper, until the pointer stands opposite the middle mark at , the rider R being at zero. Then replace the cylinder and cover by weights from the set in the following way. Find by trial the largest weight which is not too large, and place it on pan B. Add the equal weight, or, if there is no equal, the next smaller one, if it is not too heavy; add again the equal or next smaller weight, and so on, always working down from weights which are too large. This saves the delay and annoyance caused by adding a large number of small weights and at last rinding that their sum is still too small. When a balance has been obtained to within 10 g., slide the rider R along the graduated beam until the pointer stands opposite the middle mark at s. The weight of the body is then the sum of the weights on the pan plus the reading of the left edge of the index R on the graduated beam. Since each division of the scale on the beam represents one tenth of a gram, by estimating to fractional parts of a division we can obtain the weight by this method to hundredths of a gram. FIG. 5 VOLUME OF A CYLINDER 7 The preceding is the rigorously correct method of making a weighing. It is called the method of substitution. (b) Weighing cylinder by usual method. Next weigh the same object by the following simpler and quicker method. Empty the pans, move R to its zero point, and bring the pointer to the middle mark by altering if necessary the nut n (Fig. 5). Then place the object on pan A and find what weights must be added to pan B in order to bring the pointer to the middle mark again, the adjustment for weights smaller than 10 g. being made as above with the rider. Unless the difference in the two weigh- ings is larger than one or two tenths of a gram, you may hence- forth use the second method for all ordinary weighings ; for the imperfections in inexpensive commercial weights, such as we are using, are likely to amount to as much as a tenth of a gram. Hence we are taking needless pains and adding nothing to the accuracy of the result by using the rigorous method. 1 ( 3 , where V represents the volume and I) the diameter. Here, and henceforth, instead of underscoring all uncertain figures as heretofore, you may simply retain in any product or quotient the same number of significant figures as there are figures in the least accurate factor which enters into the product or quo- tient. and turning h through one fiftieth of a revolution changes the distance between aJI) by -^ x \ .01 mm. If, then, there are fifty divisions upon the circumference of d, each division represents a motion of .01 mm. at b. To make a measurement, turn up the milled head h (Fig. 7) until the jaws ab are in contact, i.e. until the milled head, held with light pressure between the thumb and finger, will slip between the fingers instead of rotating further. FIG. 7 Never crowd the threads. The zero of the graduated circle should now coincide with the line ec on the scale. If this is not the case, have the instructor adjust the stop a. Insert the object to be measured between the jaws ab and again turn up the milled head until it slips between the fingers when held with the same pressure as that used to test the zero reading. Read the whole number of millimeters and half millimeters of separation of the jaws upon the scale ec and add the num-* ber of hundredths millimeters registered upon d. This is the thickness of the object. 10 LABORATORY PHYSICS The following illustrates the method of computation : D = 2.534 cm. IP = 6.421 D 3 = 16.27 2.534 D = 2.534 TT = 3.142 10136 25 684 3 254 7602 19263 6508 1 267 3 210 5 1 62 7 5 068 12 842 48 81 D2 = 6.421 Z>3=16.27 irD 8 = 51.12 6|51.12 8.520 cc. = i Tr/) 3 = Volume (b) Weight of balls. Weigh ten or twelve balls all at once on the balances. From the total weight, the number of balls, and the volume of a single ball find the density of steel, i.e. the number of grams in 1 cc. Record thus : First Second Third Fourth Fifth ball ball ball ball ball Diameters: 19.053 19.050 19.048 19.047 19.050 19.050mm. .-. Volume of 1 ball = 3.6216 cc. Weight of 12 balls = 341.0 g. .-. Weight of 1 ball = 28.42 g. .-. Density of steel = 7.846 II. From weight of spheres and weight of water which they displace. Fill a cylindrical vessel, holding about 150 cc., with water and cover with a ground-glass plate (Fig. 8), carefully excluding all air bubbles. Dry the outside and place on the left pan of the bal- ance. Place on the same pan, beside the vessel of water, the same number of balls used in I, and find the weight of the whole load. Remove the vessel of water, lift off the cover, and drop the balls into the water. Replace the cover, dry the outside of the cylinder, replace it on the balance pan, and weigh again. From the two weighings find the weight of the water displaced by the balls. Since 1 cc. of water weighs 1 g., this last weight is, of course, the volume in cubic centimeters RESULTANT OF TWO FORCES 11 of the displaced water, and this is, of course, the same as the volume of the balls. Find the weight of the balls alone and thence compute the density of steel. Find the per cent of dif- ference between this value and that obtained in I. Record thus : Weight of 12 balls plus cylinder full of water = 668.4 g. Weight of 12 balls in cylinder full of water = 625.0 g. Weight of water displaced by balls = 43.4 g. Weight of 12 balls alone (from I) = 341.0 g. .-. Density of- steel = 7.85 Per cent of difference between results of I and II = .2 State in your notebook which of the above methods of finding the density of steel you consider the more accurate, giving the reason for your opinion. EXPERIMENT 4 RESULTANT OF TWO FORCES I. Parallel forces. Support two spring balances from nails, pegs, or tripod rods, as in Fig. 9, and so choose the distance FIG. 9 between the supports that the meter stick ab is supported at, say, the 10-cm. and 90-cm. divisions. Record the readings of the balances 1 and 2 (see figure). 12 LABOR ATOKY PHYSICS Hang from the 50-cm. mark a mass JF which you have already weighed on one of the spring balances, and which is large enough to stretch it nearly to its limit. Read the balances 1 and 2 and call the differences between these readings and the initial readings F l and Z\ respectively. Then move W successively to the 40-cm., the 30-cm., and the 20-cm. marks, and repeat the readings for each position. Let Zj and / 2 represent in each case the distance in decimeters from the point from which W is hung to 1 and 2 respectively. Record as indicated below : Reading of 1 : without W ; at 30 cm. ; at 20 cm. Reading of 2 : without W ; at 30 cm ; at 20 cm. IF at 50 cm. at 40 cm. Wat 50 cm. at 40 cm. />', State in your notebook what you learn from your results regarding, first, the magnitude of the resultant of two parallel forces ; and second, the product of either of the two forces by its distance from the resultant. II. Concurrent forces. Fasten three spring balances to a small ring a by cords about 8 in. long, and slip the rings of the bal- ances over wooden pegs or nails in a board AB about 3 ft. square (Fig. 10). Choose such holes for the pegs that each balance is stretched to at least one half of its full range. RESULTANT OF TWO FORCES 13 FIG. 10 Slip a page of your notebook beneath the central ring, fasten it down with thumb tacks or weights, and with a sharp-pointed pencil make a dot on the paper just at the center of the ring. Displace the ring and see that A its center comes back exactly to the same position as at first. If this is not the case, the cause probably lies in the friction which exists between the balances and the table top, a difficulty which may be remedied by raising the rings slightly on the pegs. Make a dot exactly beneath each string and as far from a as possible ; then take the three balance readings. Unhook each balance from its peg and note the reading of the pointer as the balance lies flat on the table. If this reading is less than zero, add the suitable correction to the balance reading recorded on the paper; if it is more than zero, subtract the appropriate amount. Remove the paper and with great care draw a fine line from the central point through each of the three outside points. The direction of each line will represent the direction of the corre- sponding force. Measure off a distance on each line which shall be propor- tional to the corresponding force, choosing any convenient scale; e.g. if the forces are 700, 1000, and 1200 g., they may be conveniently represented by lines 7, 10, and 12 cm. long. With any two of these lines as sides complete a parallelogram, using a ruler and compasses to get the sides exactly parallel. Draw the diagonal of this parallelogram from the central point a, measure its length, and find the magnitude of the force which 14 LABORATORY PHYSICS it represents. Thus, if the diagonal has a length of 134 mm., it would represent in the foregoing illustration a force of 1340 g. Compare with the reading of the third balance. Tabulate thus : Reading of balance 1 = Correction = .-. F^ = Reading of balance 2 = Correction = Reading of balance 3 = Correction = Length of line 1 = of line 2 = - Length of diagonal = - .-. Resultant = % error = State in your notebook what you have proved to be true regarding the magnitude and direction of the resultant of two forces which meet at an angle. EXPERIMENT 5 PRESSURE BENEATH THE FREE SURFACE OF A LIQUID I. Verification of the law of depths and densities. (a) Measurements in water. Immerse the manometer Mot Fig. 11 to the greatest depth possible in the long glass vessel V filled with water. 1 A length of at least 1 m. is desirable (see tube of Experiment 40). Measure the distance from the surface of the water to the top of the mercury in the short arm, and record this distance as the first depth. Measure the distance be- tween the two levels of the mercury in the two arms of the manometer, and record this difference as the first FIG. 11 pressure. (It is often convenient to express pressures in this way, in millimeters of mercury instead of in grams.) Raise the manometer about 5 cm. and make similar measure- ments. Continue in this way, diminishing the depth about 5 cm. at a time, until the surface is reached. 1 A piece of glass tubing about 1 m. long, 4 or 5 cm. in diameter, and closed at the bottom with a rubber stopper answers the purpose admirably. PEESSUBE WITHIN A LIQUID 15 (b) Measurements in gasoline. Fill the vessel V with gasoline instead of water, and make another set of similar observations. Tabulate results as follows : WATER Depth Pressure Pressure cm. mm. cm. mm. cm. mm. etc. etc. etc. etc. II. Graphical representation of a direct proportion. When two quantities are related in the way in which the pressure P and the depth D are seen to be related above, i.e. when making one quantity two, three, or four times as great makes the other two, three, or four times as great, the one quantity is said to be directly proportional to the other, or to vary directly with the other. It will be seen, from the third and sixth columns above, that the ratio between the two quantities D and P, which are related in this way, is always constant. Hence, if P v P 2 , P 3 , etc., repre- sent the pressures at depths D v Z> 2 , Z> 3 , etc., then I), P, D, P. D, !) !> - = - > * = - l ' etc., or - = = etc., D P 7) P P P P ^2 *! ^3 ^3 *1 ^2 ^3 or, more simply, = constant. This is the analytic or algebraic way of expressing the fact that D and P are directly proportional to each other. A third way of expressing the relationship between two quan- tities one of which depends for its value upon the value of the other, is to plot them in a " graph," or curve. To find the nature of the curve which represents the direct proportionality of this experiment, proceed as follows : Draw two straight lines OX and OF on a piece of squared ' (coordinate) paper (Fig. 12). Represent pressures by distances 16 LABORATORY PHYSICS 130 S 25 2 B | 20 S = 15 1,0 above OX, and depths by distances to the right of OF; e.g. let one space above OX represent a pressure of 1 mm. of mercury, Y M an( l one space to the right of OF represent a depth of 2 cm. below the surface of the liquid. Any point on the line AB will therefore rep- resent a pressure of 18.5 rnm. of mercury, since it is 18.5 spaces aboveOX; and any point on CD will represent a depth of 25 cm., since this line is 12.5 spaces to the right of Y. The point b at the intersec- tion of these lines there- fore represents a pressure of 18.5 mm. and a depth of 25 cm. Similarly, if the table shows that the pressure is 29.6 mm. when the depth is 40 cm., this fact will be represented by the point Z, which is 29.6 spaces above OX and 20 spaces to the right of OF, since we have chosen to let one space in the direction OX stand for 2 cm. Find in this way the point corresponding to each depth and its corresponding pressure for the measurements taken in water. These points will be found to lie almost exactly on a straight line ON. With a sharp pencil and a ruler draw through the straight line which passes as close as possible to all of the plotted points. In a similar way plot for the readings in gasoline, using the same axes, OX and OF, and the same "scale"; i.e. let one space above OX represent a pressure of 1 mm. of mercury, and 10 20 C 30 40 50 Depths in centimeters FIG. 12 60 70 MEASUREMENT OF PRESSURE 17 one space to the right of OY represent a depth of 2 cm. 1 These points will be found to lie almost exactly on the straight line ON. We learn, therefore, that the geometrical or graphical inter- pretation of a direct proportionality is a straight line. Divide the pressure Cg, which your graph shows to exist at a given depth in gasoline, by the pressure Cb at the same depth in water. The density of gasoline is about .71. What do you get by this division? Summarize in the notebook the results of the experiment, stating first in words the law which expresses the relation between pressure and depth, as proved in the experiment; stating, second, what is the analytic expression of this law; and, third, what is its graphical expression. State also why dividing Cg by Cb in Fig. 12 gave us the density of gasoline. EXPERIMENT 6 MEASUREMENT OF PRESSURES BY MANOMETERS I. Determination of the densities of the liquids used in the manometers. Weigh a glass-stoppered bottle having a capacity of at least 200 cc., first when empty, then when filled with water, and again when filled with gasoline. Subtract the weight of the empty bottle and stopper from each of the last two weights. This gives the weight of equal volumes of water and of gasoline. From these two weights find the specific gravity of gasoline, i.e. the ratio between the weights of equal volumes of gasoline and water. This is numerically equal to the density 1 The scale should always be so chosen that the curve will cover nearly the entire page. Any number of spaces, however, or any fractional part of a space might be used vertically or horizontally to represent a millimeter of pressure or a centimeter of depth. 18 LABORATORY PHYSICS of gasoline, i.e. the number of grams in 1 cc., since 1 cc. of water weighs 1 g. Record thus : Weight of bottle = g. Weight of bottle and water = g. Weight of bottle and gasoline = g. .-. Weight of water = g. .-. Weight of gasoline g. .-. Density of gasoline II. Determination of the pressure within the bottle B. Arrange two pressure gauges, or manometers, as in Fig. 13, gauge 1 being filled with water, and gauge 2 with gasoline. Force air through into the bottle B until the gasoline column is near the top. Then close with the pinch- cock K the rubber tube which connects the bottle with the outside air. As soon as the levels of the gauges are stationary measure with a meter stick the height of the liquid surfaces above the table at a, d, 5, and e, measuring in each case to the lowest part of the curved liquid surface. Let h l represent the difference in level in centimeters between the points a and d, and let 7i 2 represent the difference between the points b and e. Let d 1 and d. 2 represent the densities of the liquids in 1 and 2 respec- tively. From each of the relations p li^d^ and p = A 2 c? 2 , compute the pressure jo, in grams per square centimeter, existing within the bottle, and see how well the two results agree. This will be a check on the correctness of the density determination which you made in I. It need scarcely be said that the pressure acting upon each manometer is necessarily the same, since it is simply the pressure existing within the bottle. FIG. ARCHIMEDES' PRINCIPLE DENSITY OF SOLIDS 19 Record the results of your measurements in the following form : From table to a = From table to d .-. A = - cm.. cm. cm. From table to b = From table to e = cm. cm. Mean p, in grams per square centimeter, Per cent of difference between pressure by 1 and '2 = - III. Measurement of pressure in city gas mains. Attach K to the gas cock and see how good an agreement you can obtain between the two different measurements of the gas pressure furnished by the two manometers. Record III exactly as you recorded II. Answer in your notebook the following questions : If the manometer tubes had had different diameters, would the results have been different? State reasons. - Can you see in II a ready means of comparing the densities of any two liquids? From your results compare the densities of water and gasoline by this method and see how well the result agrees with that found in I. EXPERIMENT 7 ARCHIMEDES' PRINCIPLE AND THE DENSITY OF A SOLID I. To test Archimedes' prin- ciple for immersed bodies. Re- move the left pan from the balance and replace it by the counterpoise c (Fig. 14) which is made as nearly as possible of the same weight as the pan. Adjust the balance by means of the nut n until the pointer stands at FIG. 14 20 LABORATORY PHYSICS the middle mark. Suspend an aluminum cylinder, or any regu- lar solid body of volume 50 cc.- or more, from the left arm of the balance and counterpoise accurately with weights in the opposite pan. Record this weight. Immerse the cylinder in water, as in Fig. 14. Carefully remove all air bubbles and weigh again. From these observations find the loss of weight which the body experiences when immersed in water. Measure the dimensions of the cylinder with the microm- eter or vernier calipers or simply by wrapping a fine silk thread about it say thirty times and measuring the length of the thread. Then compute the volume in cubic centimeters. Compare the loss of weight obtained above with the weight of the liquid displaced by the body (i.e. the volume of the body times the density of the liquid, which is in this case 1). Weigh the cylinder when it is immersed in a beaker of gaso- line and compare the loss of weight with the weight of the dis- placed liquid, taking the density of gasoline from the results of Experiment 6 (I). Record thus : Mean Weight of cylinder in air = g. Diameters cm. Weight of cylinder in water = g. Length = cm. .-.Vol. = cc. Loss of weight in water = g. Weight of displaced water = g. Per cent of difference Weight in gasoline = g. Weight of displaced gasoline = g. Loss of weight in gasoline = g. Per cent of difference State in your notebook in your own words the principle which your experiment has shown to be true. II. To find the density of a solid heavier than water by loss of weight method. Since density is defined as it is volume obvious that the most direct way of determining the density of any regular solid is to find its mass by a weighing and its vol- ume by direct measurement. But it would evidently be quite ARCHIMEDES' PRINCIPLE DENSITY OF LIQUIDS 21 impossible to find in this way the density of an irregular body, like a lump of coal, because of the difficulty of measuring its volume. The principle discovered in I, however, furnishes a very simple way of finding this volume, since it is only neces- sary to find the loss of weight which the body experiences in water, in order to find the weight of an equal volume of water, and this is the same as the volume of the body, since the density of water is 1. We have, then, weight in air Density = , & . , : loss of weight in water Without making any additional measurements, find the den- sity of the body used in I, (a) by dividing the weight in air by the volume as there computed from its dimensions, and (b) by dividing the weight in air by the volume of the cylinder as found from the loss of weight in water. Find in the latter way the density of some irregular body, for example, a brass weight. Record thus : (a) Density of aluminum = mass -=- volume from dimensions = (fi) Density of aluminum = mass -f- volume from loss of weight = Per cent of difference = Weight of brass body in air = g. ; weight in water = .-. Density of brass = Accepted value =8.4 EXPERIMENT 8 ARCHIMEDES' PRINCIPLE AND THE DENSITY OF A LIQUID I. To test Archimedes' principle for floating bodies. Place in a deep vessel of water (see Fig. 11, p. 14) a piece of thin- walled, cylindrical glass tubing about three quarters of an inch in diam- eter, twenty-four inches long, and loaded with shot at the lower 22 LABORATORY PHYSICS end (Fig. 15). (For the sake of convenience in II it is best to load the tube first in a vessel of gasoline until it sinks to within say 2 cm. of the top and then to transfer it with- out change in the load to the vessel of wate,r.) Place a rubber band about the tube at the exact point to which it sinks. Remove the tube from the water, wipe it dry, and then weigh it with the contained shot. Measure the diameter of the tube in four or five different places, and the distance from the rubber band to the bottom. From these two measurements compute the volume, and therefore the weight, of the water displaced by the float- ing body. Record thus : First diam. = cm. Length immersed = cm. Second diam. = cm. Area of cross section = sq.cm. Third diam. = cm. Weight of displaced water = g. Fourth diam. = cm. Weight of tube and shot = g. Mean diam. = cm. Per cent of difference = Infer from your results the general law of flotation and state it in your notebook. Fio lfi II. Density of a liquid by the principle of flotation. (a) Constant-weight hydrometer. Immerse the* tube with its contents in a vessel of gasoline. Since the tube will float only when the weight of the displaced liquid is equal to the weight of the floating body, and since gasoline is less dense than water, the tube must sink to a greater depth in the lighter liquid than it did in water, e.g. to some point C. Place a rubber band at this point, and then remove and measure the length immersed. If Zj is the length of the tube immersed in water and l z the length immersed in gasoline, then the density of gasoline must be Zj/Zj times the density of water ; for if A represents the area of the cross section of the tube, the weight of the water dis- placed by the tube is Al-^ ; and if d is the density of gasoline, ARCHIMEDES' PRINCIPLE DENSITY OF LIQUIDS 23 the weight of the displaced gasoline is Al^d\ and since these weights are equal, being both equal to the weight of the float- ing body, we have Al 2 d = Al v i.e. d = l^ / l^. Test the correctness of your result by means of a commercial constant-weight hydrometer (see Fig. 16). (b) Constant-volume hydrometer. Drop shot into a test tube which has been drawn out to the shape shown in Fig. 17 until, when immersed in gasoline, it sinks to the mark a on the narrow part of the stem. Remove the tube, dry, and weigh with the con- tained shot. Immerse in water, add more shot until the tube sinks to the same mark, remove, dry, and weigh again. The volume of the liquid displaced is the same in the two cases, and the weight of this volume is equal to the weight of the tube and its contents. The specific grav- ity or density of the gasoline may therefore be 1 found at once, since the data are available for FIG. !<>-. . FlG - !' finding the weight of a given volume of gaso- line and the weight of an equal volume of water. Compare the results with those obtained in (). Record as follows : () (6) Length in water cm. Weight in water = g. Length in gasoline cm. Weight in gasoline = g. Density of gasoline Density of gasoline By hydrometer of Fig. 16= Diff . between (a) and (It) = Per cent of difference = Per cent of error State in your notebook what two general methods }*ou have discovered for finding the densities of liquids. Can you see any reason why a constant-weight hydrometer made with a narrow stem (Fig. 16) is a much more accurate instrument for determining the densities of liquids than a cylin-" drical constant-weight hydrometer like that shown in Fig. 15 ? 24 LABORATORY PHYSICS If any convenient solid is weighed first in air, then in water, and then in some other liquid, e.g. gasoline, the three weighings will furnish data for determining the density of gasoline. Write an explanation of this in your notebook, and compute the density of gasoline from the weighings of this sort which you made in Experiment 7. EXPERIMENT 9 DENSITY OF A SOLID LIGHTER THAN WATER I. By weighing first in air and then when immersed in water with the aid of a sinker. If a body is lighter than water, the weight of an equal volume of water may be obtained with the aid of a sinker. Use a wooden block E (Fig. 18) which has been paraffined so as to prevent the ab- sorption of water. Weigh the block in air and then with the sinker attached, the block being in air and the sinker S in water, as shown in the figure. Lastly, weigh when the block and sinker are both under water. The difference between the second and third weighings is evidently the buoyant effect of the water on the block alone, i.e. it is the weight of the water displaced by the block, and hence it is also the volume of the block. From this difference and the weight of the block in air obtain the density of the wood. Record thus : Weight of block alone in air g. Weight when block is in air and sinker in water g. Weight when both block and sinker are in water = g. .-. Density of wood FIG. 18 DENSITY OF A SOLID LIGHTER THAN WATEK 25 Explain in your notebook how you calculated the density of wood and why your method of procedure gives this density. II. From weight, length, breadth, and thickness of block. Measure the three dimensions of the block with a meter stick held on edge, as in Fig. 2. From these measurements and the weight of the block, obtained in I, compute the density of the wood. Record thus : Length of block = Height of block Thickness of block = cm. .-. Volume = cm. .-. Density = % of difference in I and II = III. From the depth to which the block sinks in water. Wax a pin to the end of a metric rule ai, arranged as in Fig. 19, and take the reading of the point on this rule at which it meets the straight edge CD when the pin point just touches the corner m of the floating block. Then take the reading on ab when the pin point just touches the surface of the water, say 1 cm. away from the edge of the block. The difference between these two read- ings subtracted from the thickness of the block would give the distance which the block sinks in the liquid, if the surface of the block were accurately horizontal. In order to obtain as accurate a value as possible for this distance, repeat the measurements at each corner of the block, and take a mean of these four differ- ences. From this mean difference find the distance h' which the block sinks in water. Then, from h' and the thickness h of the block, compute its density d from the relation FIG. 19 26 LABORATORY PHYSICS Record the results of your observations thus : First Second Third Fourth corner corner corner corner Reading with pin touching water = cm. cm. cm. cm. Reading with pin touching block = cm. cm. cm. cm. Differences cm. cm. cm. cm. Mean difference = It = .-. It' - .-. d Prove in your notebook that the above equation for the 7 I density of the block, namely d = , follows at once from the statement of Archimedes' principle as applied to floating bodies, viz. " The weight of the floating body is equal to the weight of the liquid which it displaces." (Remember that weight = vol- ume X density ; so that, if A represent the area of the top of the block, the weight of the block is Ahd, while the weight of the displaced liquid is Ah'd', d' in this case being 1.) Can you see from your analysis any general relation which must always exist between the density of a body floating on water, the volume of the body, and the fraction of the volume which is beneath the surface? EXPERIMENT 10 THE RELATION BETWEEN THE PRESSURE AND VOLUME OF A GIVEN MASS OF GAS AT CONSTANT TEMPERATURE I. Verification of Boyle's law. The object of this experiment is to vary the volume of a small quantity of air AD (Fig. 20, 1), confined in a barometer tube, by varying the pressure to which it is subjected, and to find how this volume changes as we double, treble, quadruple, etc., the pressure. First read the barometer and record its height in centimeters ; then, by means of a clamp (7, hold in the position 1 (Fig. 20) a BOYLE'S LAW 27 barometer tube which is closed at the upper end and open at the lower end, and which contains a mercury column AS and the thread of air AD. 1 Measure carefully the length AD of the confined body of air. Since the cross section of the tube is everywhere the same, the volume of the confined air will always be proportional to its length ; hence we shall call the length AD volume 1, and shall denote it by l\. 1 To construct tubes of this sort pieces of barometer tubing should be chosen which are from 1 mm. to 1.5 mm. in bore and 110 cm. long. They should be cleaned by pouring through them a hot solution of potassium bichromate in 28 LABORATORY PHYSICS Next measure the length of the mercury column AB in centi- meters. The barometric height minus this length AB is obvi- ously the pressure, measured in centimeters of mercury, to which the air Fj is subjected. Call this pressure P r Incline the tube slowly until the volume T 2 (see Fig. 20, 2) of the inclosed air is one half of the original volume F r Now meas- ure the heights of the points A and B above the table and sub- tract the difference AB' from the barometric height, thus getting P 2 , the pressure corresponding to the volume F 2 . (The reason for this procedure will be clear when it is remembered that pressure in liquids depends simply upon difference in horizontal levels. 1 } Place the tube successively in positions 3, 4, 5 (see Fig. 20) such that the volume of the inclosed air shall be 1/3, 1/4, 1/5, and, if possible, 1/6 of the original volume. Measure in each case the heights of the ends A and B of the mercury column from the table top and compute the pressures corresponding to each volume. (Remember that the pressure on the confined air is less than the barometric pressure if the open end of the tube is lower than the closed end, and greater than the barometric pressure if the open end is above the closed end.) strong sulphuric acid. They should then be rinsed first with distilled water, then with clean alcohol, and finally dried with a current of air from a bellows. These tubes may be filled by sinking them in a larger tube containing perfectly clean mercury until the mercury rises in the capillary bore to within 12 or 15 cm. of the top, and then sealing the top with hard wax and withdrawing ; or, again, the tube may be laid horizontally and a piece of gum tubing attached to one end and clean mercury poured into this tubing until it approaches to within 5 or 6 cm. of the other end, when the sealing should be done. J The proof that this is indeed the case is found in the familiar fact that water will stand at the same level in two vessels connecting at the bottom and consist- ing, the one of a long inclined tube, the other of a short vertical one. If the pressure at the bottom of the longer tube were the greater, the water would, of course, have to stand higher in the shorter tube. BOYLE'S LAW 29 Record as follows : POSI- TION VOLUME OF CON- FIXED Am HEIGHT OF A ABOVE TABLE HEIGHT OF B ABOVE TABLE DIFFER- ENCE BARO- METRIC; HEIGHT PRES- SURE PRES- SURE TIMES VOLUME DIFFER- ENCE FROM MEAN rv 1 2 3 4 5 II. Graphical representation of an inverse proportion. When two quantities are related in the way in which P and V are found to be related above, i.e. when making P two, three, or four times as great makes V 1/2, 1/3, or 1/4 as great, one quantity is said to be inversely proportional to the other, or to vary inversely with the other. It will be seen from the next to the last column that the product of two quantities which vary in this way is always constant. Hence, if P v P 2 , P 3 , etc., represent the pressures corresponding to the volumes V v F 2 , F 3 , etc., then p z v \ A v i or, more simply, PF = constant. This is the analytic or algebraic way of expressing the fact that P and V are inversely proportional to each other. To find the graph or curve which represents an inverse pro- portion, plot on a sheet of coordinate paper, precisely as in 30 LABORATORY PHYSICS Experiment 5, the pressures in the table above as horizontal distances and the corresponding volumes as vertical distances. Utilizing the law discovered experimentally above, compute the pressures which would correspond to two, three, and four times the original volume, and the volumes corresponding to two, three, and four times the greatest pressure, and plot as part of the same curve not only the points corresponding to the observed values but also those corresponding to these computed values of the pressure and volume. Select your scale so that the curve will just nicely fill a sheet of coordinate paper. This curve is an hyperbola. Its two arms approach nearer and nearer to the axes OX and OF, but the curve can never touch these arms, for no matter how great the pressure may become, the volume will never become zero, and no matter how great the volume may become, the pressure will never be quite zero. The lines which an hyperbola approaches indefinitely, without ever exactly reaching, are called the asymptotes of the hyperbola. In this case the asymptotes are the coordinate axes OT and OY. Summarize in the notebook the results of the experiment, stating first in words the relation which has been found to exist between pressure and volume, then expressing this rela- tion in the form of an equation, and then stating what sort of curve the experiment has shown to be the graph of this type of relationship. EXPERIMENT 11 COOLING BY EVAPORATION; SATURATION; DEW-POINT; FREEZING BY EVAPORATION I. Cooling by evaporation. Let three 4-oz. bottles, one half full of ether, one half full of alcohol, and one half full of water, be provided. The bottles should be closed with small corks and HYGROMETRY 31 should have been standing in the room long enough to acquire room temperature. Holding a thermometer by a string attached to the upper end, swing it back and forth through the air until its reading is con- stant. Record this reading as the room temperature. Insert the thermometer in the ether bottle, pushing the bulb down beneath the surface of the liquid. After half a minute record the reading as the temperature of the ether in the closed bottle. In the same way take the temperatures of the alcohol and water. Pour into small porcelain evaporating dishes enough of each liquid to cover the bulb of the thermometer. Pour about the same amount of ether into an open test tube (or the metal tube of Fig. 21), and set it aside in a beaker or other convenient support. Place the thermometer in the evaporating dish which contains the ether, and, keeping the stem inclined so that the bulb is always covered, watch the temperature until it ceases to change, and then record. Take in succession the temperatures of the alcohol and of the water in the evaporating dishes, and of the ether in the test tube. Record thus : Temperature in room Temperature in bottle of ether Temperature in bottle of alcohol Temperature in bottle of water Temperature of ether in evaporating dish = - Temperature of alcohol in evaporating dish = Temperature of water in evaporating dish = Temperature of ether in test tube State in your notebook what effect your experiments have shown evaporation to have upon the temperature of the evapo- rating body. Explain, if you can, why the temperature of the ether in the test tube was different from that in the evaporating dish. Put a drop of ether, of alcohol, and of water upon the hand and notice the order in which they disappear. Explain 32 LABORATORY PHYSICS with the aid of this experiment and the answer to the first ques- tion why the ether in the evaporating dish had a lower temper- ature than the alcohol, and the alcohol a lower temperature than the water. When a body is below room temperature it is continually receiving heat from the room. When the liquids in the evapo- rating dishes had reached a constant temperature, what relation existed between the amount of heat which they lost per second by evaporation and the amount which they received per second from the room? ' II. Saturation. From the above readings of the room tem- perature and the temperature of the liquids in the closed bottles, can you draw any inference as to whether or not any evapora- tion was going on from the surfaces of the liquids in the closed bottles? A space in which evaporation will no longer take place from the surface of a given liquid placed within the space is said to be saturated with the vapor of the liquid. This means simply that the space already contains as much of the vapor of the liquid as it is capable of holding at the given temperature. Cover the bulb of the thermometer with a bit of absorbent cotton, dip it into the bottle of ether, and then lift it so that the bulb and cotton are above the surface of the ether, but still in the bottle. Watch the temperature for a minute or two, and then record. Transfer the covered bulb from the bottle to the test tube and hold it there above the surface. After a minute or two record the temperature. Lift the covered bulb out into the air and record the temperature after it has become constant. What do you learn from this experiment regarding the temperature which a thermometer surrounded with a cloth soaked in a liquid will maintain in a space which is saturated with the vapor of the liquid? in a space which is partially saturated? in a space which is free from this vapor, i.e. which is dry? HYGEOMETRY 33 Wrap some fresh cotton about the bulb of the thermometer, and dip it into the bottle of water ; then remove the thermom- eter and swing it in the room until its reading becomes con- stant. Record. Would this reading be any different if there were no water vapor already in the room ? What would it be if the air were already saturated with water vapor? Can you see, then, how the difference between the readings of a ther- mometer whose bulb is kept dry and one whose bulb is kept moist gives us some information regarding the dryness of the atmosphere ? III. Dew-point. The amount of vapor which a given space can hold is found to decrease rapidly as the temperature decreases. Hence, if we lower the temperature of a space which is already saturated with any vapor, a part of it condenses. If we lower the temperature of a space which is not saturated, but which contains some vapor, nothing happens until the temperature is reached at which the amount of vapor which already exists in the space is the amount Fi which saturates it. Then condensa- tion begins. The temperature at which water vapor begins to con- dense out of the atmosphere as the temperature is lowered, is called the dew-point. It varies of course from day to day, depending upon how much water vapor exists in the atmosphere. Fill the polished metal tube l of Fig. 21 two thirds full of ether, and force air very gently through it by squeezing the bulb. 1 This experiment can be performed with almost as good success by simply dropping bits of ice slowly into water contained in a polished vessel, and noting the temperature at which, with continual stirring, the cloud appears on the out- side. If the dew-point is below zero, salt should be added bit by bit to the iced water until the cloud appears. 34 LABORATOBY PHYSICS This process facilitates cooling, since it increa'ses enormously the evaporating surface, every bubble having a large surface into which evaporation can take place. The temperature exist- ing within the tube when the first cloudiness begins to appear upon the polished surface is the dew-point, for it is the tem- perature at which the layers of air in contact with the tube become saturated and begin to deposit their moisture. As soon as this cloudiness is noticed take the reading of the thermometer, re. P rc. P tc. P -10 2.2 6.5 19 16.3 - 9 2.3 6 7.0 20 17.4 - 8 2.5 7 7.5 21 18.5 - 7 2.7 8 8.0 22 19.6 - 6 2.9 9 8.5 23 20.9 - 5 3.2 10 9.1 24 22.2 - 4 3.4 11 9.8 25 23.5 - 3 3.7 12 10.4 26 25.0 - 2 3.9 13 11.1 27 26.5 - 1 4.2 14 11.9 28 28.1 4.6 15 12.7 29 29.7 1 4.9 16 13.5 30 31.5 2 6.3 17 14.4 35 41.8 3 5.7 18 15.3 40 54.9 4 6.1 45 71.4 1 and then stop the current and notice the temperature at which the cloudiness disappears. Take pains in these experiments not to breathe upon the polished surface. Repeat the whole opera- tion until the temperatures of appearance and disappearance do not differ by more than 1. Take the mean of the two tem- peratures as the dew-point. From the dew-point and the accompanying table find the humidity of the atmosphere. This is the ratio between the amount of moisture in the atmosphere at the time of the ex- periment and the total amount which it is capable of holding HOOKE'S LAW 35 at the temperature of the room. It is found by dividing the pressure of saturated water vapor at the temperature of the dew-point by the pressure of saturated water vapor at the tem- perature of the room (see table on page 34 ). 1 IV. Freezing by evaporation. Place a few drops of water upon the table and set the polished metal tube containing ether upon it. Force air through the ether rapidly and see if you can freeze the tube to the table. EXPERIMENT 12 RELATION BETWEEN FORCE ACTING UPON AN ELASTIC BODY AND THE DISPLACEMENT PRODUCED (If yoke's law) I. Stretching. Set up a steel spring S and mirror scale M, in the manner shown in Fig. 22. Take the reading of the index upon the scale when only the weight holder hangs from the spring. In so doing place the eye so that "the image of the tip of the pointer p, as seen in the mirror, is exactly in line with the tip of the pointer itself. Record the position at which the line of sight crosses the mirror scale, reading to the nearest tenth millimeter (this tenth millimeter place being, of course, an estimate). Increase the weight upon the pan 100 g. at a time until it has reached a total of 400 g., and take the reading on the scale after each addition. Then remove the weights 100 g. at a time and take the corresponding readings. Tabulate results as indicated on page 36. 1 The table shows the pressure P, in millimeters of mercury, of water vapor saturated at temperature t C. FIG. 22 36 LABORATORY PHYSICS II. Bending. Set up the mirror scale behind the middle of a thin wooden or steel rod supported as in Fig. 23, and take FIG. 23 again a set of readings like those in I, the index being now the point of a pin stuck with wax to the middle of the rod. Tabulate results of all observations as follows : Spring Differences Rod Differences Pan reading = 100-g. reading = 200-g. reading = 300-g. reading = 400-g. reading = 300-g. reading = 200-g. reading = 100-g. reading = Pan reading State in your own words in the notebook the law which the above study of two different sorts of elastic displacement has shown to exist between the distorting force F and the displace- ment D which this force produces. State this result in the form of an equation. Finally, put the results of each experiment into graphical form, letting one space in the direction OY (see Fig. 12) rep- resent 15 mm. of displacement from the "pan reading," and one space in the direction OX, 10 g. of weight added to the COEFFICIENT OF EXPANSION OF AIR 37 pan. For each set of observations draw with a ruler straight lines which shall come as near as possible to touching all the points located. EXPERIMENT 13 COEFFICIENT OF EXPANSION OF AIR A and B in this experiment are intended as alternatives, the choice depending upon equipment. It is interesting, however, to have a part of the class perform A and a part B, and then to let them compare results. A. Pressure coefficient of expansion. When a body of gas is heated in a closed vessel the volume of which is kept constant, the pressure which the gas exerts against the walls of the vessel increases as the temperature rises. The ratio between the increase in pressure per degree and the pressure which the gas exerts at 0C. is called the pressure coefficient of expansion of the gas. For example, if P t represents the pressure at a temperature of tC. and P the pressure at 0C., then the increase in pressure has been P t P , the increase per degree has been 9 , and the pressure coefficient c is this increase divided by P Q . Thus, FIG. 24 To find this coefficient experimentally, first read the barometer. Then, before attaching the bulb B, adjust the arms a and b (Fig. 24) until the mercury in each stands, say, 5 cm. above the bottom of the scale S, the distance from the bottom of S to the point of attachment of the rubber tub- ing to the arm b being at least 30 cm., and the distance from 38 LABORATORY PHYSICS the mercury surface in a to the scratch m on the tube a being about 4 cm. See that a few drops of concentrated sulphuric acid are inserted in B in order to keep the inclosed air perfectly dry ; then attach B as in the figure, with a bit of thick-walled gum- rubber tubing, and pack wet snow or crushed ice about it in a vessel V until B is completely covered. Raise the arm b until the mercury in a is just opposite the scratch ?n, tapping a gently with a pencil to prevent sticking of the mercury. Wait two or three minutes to make sure that the air in B has reached the temperature of the ice, and then adjust again to the scratch m and read on the scale S the levels in both a and b. Put the bulb into the steam generator shown in Fig. 25, and boil the water. Adjust the arm b until the level in a is again at m ; tap and again read the level of the mercury in b. Immediately after this reading loiver the arm b to its first position, so that the mercury may not be drawn over into B as the bulb cooh. The difference between the two readings in b represents the increase in the pressure exerted by the gas in B as the tempera- ture was raised from 0C. to 100C.; i.e. this difference is P t - P Q of our equation, t being in this case 100. The pressure in B at 0C., namely P , is simply the barometric height less the differ- ence between the mercury levels in a and b at zero. Record your results in systematic form, including a statement of the per cent by which your result differs from the accepted value of this constant, namely .00367, or 1/273. State in your own way in your notebook exactly what this quantity is which you have found above, and which you call the " pressure coefficient of expansion." What per cent of error would have been introduced into your numerator, JP 100 JP , and therefore into your result by an error of half a millimeter in reading either of the levels in b ? COEFFICIENT OF EXPANSION OF AIE 39 If the boiling point of water on the day of your experiment were 99.5, instead of 100, what per cent of error would you have introduced into your result by calling it 100? On the whole, is your result as accurate as you could have expected in view of such sources of error as you can see ? B. Volume coefficient of expansion. When a confined body of gas is kept under constant pressure and heated, it follows, from Boyle's law, that its volume must increase at the same rate at which its pressure would increase if the volume were kept constant. The ratio between the increase in volume per degree and the volume at 0C. is called the volume coefficient of expansion; i.e. if F 100 and F represent the volumes at 100C. and 0C. respectively, then the volume coefficient c is given by the equation This coefficient may be defined as the expansion at 0C. per cubic centimeter per degree. It should be the same as the pres- sure coefficient discussed above. To find it experimentally let a thread of dry air about 23 cm. long be confined by a mercury index 2 cm. or 3 cm. long in a piece of barometer tubing which is sealed at one end and is about 40 cm. long. 1 First measure carefully and record the length of the index and the total length of the bore, allowing as best you can for the fact that the bore is not quite uniform very near the closed end. 1 To make such tubes take barometer tubing of 1.5-mm. bore, clean it with hot aqua regia, or a hot solution of potassium bichromate in strong sulphuric acid, then rinse with distilled water, and dry by gently heating while a current of air passes first through a calcium chloride drying tube, and then through the barometer tube. By sucking through the drying apparatus draw a thread of mercury about 2 cm. long into one end of the tube, shake it to within 23 cm. of the other end, and then detach from the drying apparatus and quickly seal this latter end in a Bunsen flame. 40 LABORATORY PHYSICS Then stand the tube upright, closed end down, in a battery jar, and pack wet snow about it up to the index. Tap the tube with a pencil, and then measure from the top of the tube to the top of the index. Remove the tube and push it through the hole in the cork which closes the steam generator of Figs. 25 and 36. After the steam has been issuing from the upper vent for a minute or two, adjust the height of the tube in the cork so that the upper end of the index is just on a level with the top of the cork, and then measure from the top of the tube to the top of the cork. Since the tube is of approximately uniform bore, you may take the difference between the last two measurements as F 100 FQ. From the first three readings find the length of the thread of air at 0C. and call it V Q . The following are typical observations made by a student. Length of index = 18.0mm. Length of bore = 476.5 mm. From top to index at C. = 251.0 mm. From top to index at 100C. = 174.5 mm. ' FIOO - V o = ( 251 - - 1 74.5) = 76.5 mm, F = 476.5 - (251. + 18) = 207.5 mm. .-. c ^ = .00369. Per cent of departure from accepted value (.00367) = .6. Is your error larger than would be accounted for by an error of, say, 1 mm. in measuring ( F 100 V ) ? If so, it is probable either that the bore is not uniform, or else that the confined air is not thoroughly dry. EXPERIMENT 14 COEFFICIENT OF EXPANSION OF BRASS The coefficient of expansion of a solid is equal to that frac- tional part of its length which it increases when heated 1, i.e. it is the expansion per centimeter per degree. Thus, if f 3 COEFFICIENT OF EXPANSION OF BRASS 41 represent the length at a temperature 2 , and ^ at a temperature t v the coefficient k is given by It may be determined experimentally by the apparatus shown in Fig. 25. A shallow transverse groove is filed at some point c (Fig. 25) near one end of a piece of brass tubing about a meter long and a centimeter in diameter. Place the tube upon two wooden blocks A and B, so that the groove rests upon a sharp metal edge attached to A, while the FIG. 25 other end is supported by a piece of glass or brass tubing b about 6 mm. in diameter, which in turn rests upon a smooth glass plate waxed to the top of B. To one end of the glass rod b is attached by means of sealing wax a pointer p about 20 cm. long. When the brass rod is heated its expansion causes b to roll forward, and this produces a motion of the end of the pointer p over the mirror scale s. Attach the tube, as in the figure, to a steam boiler containing at first only cold water. Then insert a thermometer into the open end o of the brass tube. Give the thermometer three or four minutes to take up the temperature of the tube ; then read, record, and replace it 42 LABOKATORY PHYSICS Record the position of the tip of the pointer upon the mirror scale, estimating very carefully to tenths of a millimeter. In taking this reading sight (as always) across the image of the pointer and the pointer itself. Apply heat to the boiler until steam passes rapidly through the tube. If the current of steam is sufficiently strong, the brass tube will not need a nonconducting covering. Neverthe- less it is generally advisable before beginning the ex- periment to roll up a paper tube about \\ cm. in diameter, and to slip it over the tube between c and I in order to minimize heat losses. After steam has been issuing from o for one or two minutes, take again the reading of the pointer p upon the scale . Take the reading of the thermometer as it lies in the tube surrounded by the steam escaping from o. Measure with a meter stick the distance between the knife- edge c and the middle of the rod b. Measure also with the meter stick the length of the pointer p from its tip to the middle of b. Measure with the micrometer caliper the diameter of 6, taking readings upon at least three different diameters. This measure- ment should be made to within a hundredth of a millimeter at the least. If the calipers are not available, wrap a fine linen thread ten or twenty times around 5, measure the length of the thread, and from this compute the diameter. To find the amount of expansion of the brass tube, divide the difference in the pointer readings on s by the ratio of the length of the pointer to the diameter of the glass rod. The reason for this can be seen from Fig. 26. At any given instant the rod is rotating about its lowest point d. The line ef represents the COEFFICIENT OF EXPANSION OF BKASS 43 distance through which the end of the pointer moves while the top of the rod is moving through a distance ab ; but from similar triangles ab ef . , , de . =-f, i.e. ab = ef+ . ad de ad From the expansion of the brass tube, its length between c and b, and its change in temperature, compute the coefficient of expansion of the tube, i.e. the fractional part of its own length by which that part of the tube between c and b expands when heated 1C. If time permit, take out the brass tube, cool it with tap water to about the temperature of the room, and repeat the experiment. Take the mean of the two trials as the value of k. In calculating be sure that you express all length measure- ments in the same units, i.e. all in centimeters, or all in milli- meters ; not part in centimeters and part in millimeters. Tabulate as follows : First Second ^ Prnv>l i Trial tempera- tempera- Differ- r , Differ- Length Diarne- Coeffi- turc of tureof ence on g y on s ence f cb terofb cient rod rod j Mean value of k = Accepted value = .0000187 Per cent of error =. - Express in words the equation on page 41. What per cent of error did you introduce into the measure- ment of the motion of the pointer over the scale, if you made a mistake of 0.2 mm. in estimating either position of the pointer? What per cent is introduced into the result if the mean tem- perature of the tube is 1 lower than that of the steam? Are these errors greater or less than the observed error? 44 LABORATORY PHYSICS EXPERIMENT 15 THE PRINCIPLE OF MOMENTS Slip the meter bar AB through the sliding knife-edge sup- port C (Fig. 27) until it will rest exactly horizontally when the knife-edge rests upon the glass surfaces of the wooden frame/. See that C is clamped firmly to the bar, read the posi- tion of the knife-edge on the bar, and then proceed as follows. (a) By means of thread hang a 100-g. weight W^ from a point near one end of the beam and find the point at which a 200-g. FIG. 27 weight W z must be hung on the other side in order that the bar may rest again exactly horizontally. Take the product of each weight by its distance from the fulcrum. What relation do you discover between these two jnoments ? (The product of a force by the lever arm on which it acts is called the "moment" of the force.) (b) Change one of the weights and again compare the moments. (e) Hang two weights, say a 100-g. weight 1J\ and a 50-g. weight JF 2 , at different points on the left side of the fulcrum and not too close to it, and then balance the lever by hanging a 200-g. weight JF 3 at the proper point on the other side. Com- pare the sum of the moments of the first two forces with the moment of the second. THE PBINCIPLE OF MOMENTS 45 (d ) Hang some unknown weight X from a point near the left end at a distance I from the fulcrum, and balance it by a known weight W hung at the proper point on the other side. By apply- ing the principle of moments, which you learned in (a), (6), and (c), find the value of X. Weigh it on the balance and compare the two results. (e) Hang from different points on the right side an unknown weight X and a known weight W v and balance by two known weights Jr 3 and JF 4 placed at different points on the other side. Let I represent the distance of X from the fulcrum. Com- pute the weight of the unknown body and compare with the result of a direct weighing. (/) Slip the knife-edge C to some point and clamp. Slip a known weight, say 200 g., along between and B until the beam rests horizontally when placed in the support. Then by applying the principle of moments find the weight of the beam on the assumption that the whole effect of the earth's attrac- tion on the beam is equivalent to one single force equal to the whole weight of the beam and applied at the first position of the knife-edge, i.e. at (7, the center of gravity of the beam. If W represents the weight of the beam, the principle of moments then gives: W X distance CO = known weight X its distance from O. Compare the result with a direct weighing of the beam. Tabulate as follows : () w i =- its lever arm = its moment = ~| per cent of its lever arm = its moment = ) ' error= its lever arm = its moment- = \ per cent of its lever arm = its moment = J ' error = its lever arm = its moment = "1 f- ; sum = its lever arm = its moment J its lever arm = its moment = . 1 per cent of its lever arm = L error = its moment = . . Y . by direct weighing A' 46 LABORATORY PHYSICS (e) W 3 = ; its lever arm = ; its moment = W 4 = ; its lever arm ; its moment = W l = ; its lever arm = ; its moment = . / = ; .-. X = ; by direct weighing A' . (/) Reading of knife-edge atC = ; reading at O .-. Lever arm OC = ; known weight ; its lever arm = .;. Weight of bar = ; by direct weighing = ; per cent of error = . State what general conclusion you are able to draw from (a), (5), and ( .0815 It will be noticed that the weight W of the shot cancels out ; hence it need not be taken. In the above directions the attempt is made to eliminate radiation and conduction losses by making the initial tempera- ture of the shot about as far below the temperature of the room as the final temperature is to be above it. This is the usual way of eliminating radiation, when, as in this case, the change in temperature between the readings of the initial and final temperatures takes place rapidly and at a uniform rate. Repeat the experiment several times if time permits. Record the results thus : First Second Third trial trial trial Temperature of room = 18.5C. 18.5 C. 18.5C. Mean value Initial temperature = 16.0 C. 17.1C. 16.7 C. = 437 g. m. Final temperature = 21.7C. 22. 6 C. 21.0C. Accepted value Number of reversals = 100 100 80 = 427 g. m. Height of fall (A) .76 rn. .70 m. .70 m. Mechanical equivalent = 423 g. m. 439 g. m. 449 g. m. % of error = 2.4 What conclusions do you draw from your experiment? The chief source of error in the experiment arises from the fact that the thermometer requires considerable time to come to the temperature of the shot. During all this time the shot is gain- ing or losing heat by conduction and radiation, so that the temperature indicated may not be quite the mean temperature of the shot. This source of error is unavoidable. 62 LABORATORY PHYSICS Why did we attempt to have the initial temperature as far below the temperature of the room as the final temperature was above it? EXPERIMENT 21 COOLING THROUGH CHANGE OF STATE I. Solidification a heat-evolving process. The object of this experiment is to show that just as it requires an expenditure of heat energy to melt ice or any other crystalline substance, so when water or any liquid freezes, i.e.. changes back to the crys- talline form, heat energy is given up to the surroundings. Support vertically in a burette holder or other clamp a test tube in which has been placed enough loose crystals of acetamide to fill it about a third full. Then heat gently with a Bunsen burner until the crystals are all melted. 1 Slowly insert a ther- mometer into the liquid, but watch the thread all the time, and if it rises to within half an inch of the top of the bore, instantly remove the bulb from the liquid. The thermometer will burst under the force of expansion of the mercury if the thread reaches the top of the bore. If there is an expansion chamber at the top, this danger is of course avoided. If there is no expansion chamber, it will be safer to melt the acetamide by dipping the tube into boiling water rather than by applying the flame directly. As soon as the liquid acetamide has cooled down to about 100 C., insert the thermometer in it permanently, and without touching further either the tube or the thermometer, watch carefully both the liquid and the thread of mercury as cooling takes place. The temperature may fall as low as 60 C. before crystallization begins. As soon as crystals begin to form, what sort of a temperature change do you observe ? What conclusion do you draw from this observation ? Watch the temperature for 1 If the acetamide has absorbed much moisture, boil it. COOLING THROUGH CHANGE OF STATE 63 two or three more minutes and decide whether or not the temper- ature of a solidifying liquid remains constant during the process of solidification. Since it is giving up heat rapidly all this time, it must get it from some source. What must this source be? II. The curve of cooling. Again raise the temperature to 100C, taking the precautions mentioned above against breaking the thermometer. Record the temperature every half minute as the 11-15 17 13 21 23 25 27 29 31 33 35 3? 39 41 41 FIG. 34 substance cools from about 100 C. to 45 C. Plot these obser- vations in the manner shown in Fig. 34, temperatures being represented by vertical distances and times by horizontal dis- tances. Thus the observations plotted in the figure began at 11:15 A.M. and continued to 11:45 A.M. The curve shows that between 11:15 and ll:19.5 the temperature fell rapidly from 100 to 71.8, that it then rose suddenly to 79, remained there five minutes, then fell slowly during the next twenty minutes from 79 to 43.5. 64 LABORATORY PHYSICS Write in your notebook a similar explanation of your own curve. Almost any substance, if kept very quiet and cooled through its freezing point, will show the phenomenon of under- cooling exhibited here by the acetamide, i.e. its temperatures will fall a little below the freezing points before the crystalliza- tion gets started. It will then rise suddenly to the freezing point and remain there until the crystallization is practically complete. If time permits, dip a test tube containing a little distilled water into a freezing mixture of salt water and ice, the tem- perature of which is say 8 C., and see if water too will not show the same behavior. (The tube must be kept very quiet.) If you get the temperature down to 2 or 3, lift the test tube, stir, and observe the instant formation of the crystals of ice. If you wish to try a substance which does not undercool, treat a little naphthaline l precisely as you treated the acetamide. EXPERIMENT 22 THE HEAT OF FUSION OF ICE The heat of fusion of ice, i.e. the number of calories of heat required to change a gram of ice at C. into water at C., or the number given up when a gram of water changes to ice, may be determined experimentally as follows. Weigh the inner vessel of a calorimeter of about 300 cc. capacity first when empty, and then after it has been filled about two thirds full of water. 2 Heat this water to a temperature of about 25 C. above that of the room ; then replace the inner vessel in its jacket (Fig. 31). 1 Naphthaline can be obtained at any drug store. Acetamide will have to be purchased at a chemical supply house. 2 If you use the small cylinders of Experiment 3 for the calorimeters, take just half of the amounts of ice and water indicated. THE HEAT OF FUSION OF ICE 65 Prepare a lump of clear ice of about the size of a hen's egg, and perform the following operations in quick succession. While one student is drying the ice upon a towel let another stir the water in the calorimeter thoroughly. If its tempera- ture is less than 15 C. above that of the room, heat it up again until it is between 15 C. and 25 C. above. Again check the weight, for the loss by evaporation may not have been inappre- ciable. Stir vigorously; then quickly take a careful reading of the temperature, keeping the thermometer bulb all the time immersed, and not more than a second or two after the reading let the first student drop the dry ice into the water, being very careful not to spill a drop. The splash may often be avoided by letting the ice slide along the thermometer into the water. Stir continuously while the ice is melting and read the tem- perature of the water just after the ice has all disappeared. This temperature should be from 2 C. to!0 C. below the tempera- ture of the room. If it should happen to be above the room temperature, try again \vith a slightly larger piece of ice. The limits here given are chosen so as to make it legitimate to assume that the heat exchanges which take place between the calorimeter and the room are, on the whole, negligible. Again weigh the inner vessel of the calorimeter, with its contained water, and take the difference between this weighing and the last as the weight of the ice. Let x represent the heat of fusion of ice and w the weight in grams of the ice melted. Then the number of calories expended in melting the ice is ivx. After the ice is melted it becomes iv grams of water at C. This water is then raised to the final temperature t of the mixture. The number of calories required for this operation is wt. All of this heat has come from the cooling of the water and the calorimeter. If the weight of the water cooled is W and its initial temperature t v while the water equivalent of the calorimeter is e, then the 66 LABORATORY PHYSICS total number of calories given up by the water and calorimeter is (W+e) (ti~t). Hence, by equating "heat lost" and "heat gained," it is easy to obtain x, the only unknown quantity of the equation. Tabulate as follows : Weight of calorimeter Weight of calorimeter + water .-. Weight of water Temperature of room Initial temperature of water Final temperature of water = .-. Fall in temperature of water Weight of calorimeter + water + ice .-. Weight of ice Water equivalent of calorimeter (Experiment 18) = .-. Heat of fusion of ice Accepted value is 80. .-. Per cent of error State in your notebook the meaning of the " latent heat of water," the quantity which has been found above. 1 EXPERIMENT 23 THE BOILING POINT OF ALCOHOL The boiling point of a liquid is denned as the temperature at which the pressure of its saturated vapor becomes equal to the atmospheric pressure. There are, therefore, two ways in which the boiling point of alcohol may be obtained, and these 1 A further experiment on latent heat, which may be introduced for the benefit of those who have time and inclination for extra work, is the following. To find the heat of condensation of steam. Pass dry steam into say 250 g. of cold water, the temperature of which is 10 C. below that of the room, until the temperature is 10 above that of the room. Weigh again to find the weight of the steam, and then calculate as above how many calories of heat have been given up by each gram of steam in condensing. THE BOILING POINT OF ALCOHOL 67 two ways should give identical results. The first is to confine the liquid and its vapor alone in a closed vessel, and then to meas- ure the pressure exerted by the vapor at different temperatures. That temperature at which the pressure becomes equal to atmos- pheric pressure will then be the boiling temperature. The sec- ond and more direct way consists in simply boiling the liquid in an open vessel and observing the temperature indicated by a thermometer held in the vapor rising from the liquid. I. Temperature at which pressure of saturated vapor becomes equal to atmospheric pressure. A glass tube A (Fig. 35) is closed at one end, and is then bent into the U-shape and par- tially filled with mercury. Some alcohol is then poured in, which by careful tilting is worked around into the closed arm, while the air is altogether worked out of this arm. With this arrangement proceed as follows. Immerse the tube and a thermometer together in a vessel of water, and, keeping the short arm completely immersed, heat slowly, stirring continually. As the ' temperature increases a point is reached at which alcohol vapor begins to form in the closed tube. Still further increase in tem- perature causes the mercury to sink farther and farther in the closed end. When the levels of the mercury in the two arms are the same, it is clear that the pressure of the alcohol vapor is just equal to the atmospheric pressure. Raise the temperature of the water gradually and stir thor- oughly until this condition is reached ; then read and record the temperature. Continue heating until the level in the short arm is 5 cm. lower than that in the long one. Then again read the ther- mometer and compute how much the boiling point of alcohol increases per centimeter increase in the barometric pressure. II. Temperature of vapor rising from boiling liquid. Place a little alcohol in a large test tube ; put a few tacks in the bottom 68 LABORATORY PHYSICS of the tube in order to assure smooth boiling; then immerse the lower end of the tube in a vessel of water and heat the water until the alcohol boils vigorously. Hold the bulb of a thermome- ter in the tube a little distance above the surface of the boiling liquid. As soon as the thermometer reading becomes station- ary, take the temperature and compare with that obtained in I. Record thus : I. Temperature at which alcohol vapor exerts pressure of 1 atmosphere Temperature at which alcohol vapor exerts pressure of 1 atmosphere + 5 cm. of mercury = C. Rise in boiling point of alcohol per cm. increase in pressure = C. II. Temperature of vapor rising from boiling alcohol = - C. Difference between results of I and II = State in your notebook what you consider to have been proved in this experiment. EXPERIMENT 24 TO TEST THE FIXED POINTS OF A THERMOMETER, AND TO FIND THE CHANGE IN THE BOILING POINT OF WATER PER CENTIMETER CHANGE IN THE BARO- METRIC PRESSURE Fill the boiler of Fig. 36 half full of water, and thrust the thermometer through a tightly fitting cork in the top until the 100 point is only 2 mm. or 3 mm. above the cork. Attach an open-arm manometer u (Fig. 36) to the exit o, and then boil, regulating the flame until the mercury stands at the same height in both arms of the manometer. After the water has been boiling steadily for two or three minutes, read the thermometer very carefully. Then take the barometer reading. Next place a piece of tightly fitting rubber tubing over the escape tube e and partly close the free end of it with a pinchcock until the difference in the levels in the FREEZING AND BOILING POINTS OF WATER 69 FIG. 36 manometer arms, due to the partial closing of the vent for the steam, amounts to 2 cm. or 3 cm. Read the thermometer and (with a meter stick) the difference in the levels in the manometer arms. Close the pinchcock still further, until the difference in level amounts to 4 cm. or 5 cm. ; then read again. Continue thus, taking readings at intervals of about 2 cm., until the difference in level amounts to 8 cm. or 10 cm. It may be necessary to use several burners in order to obtain the last readings, for the steam must be generated very rapidly in order to compensate for the inevitable leakage. From each of these readings calculate the changes produced in the boiling point by a change of 1 mm. in the barometric height. Take a mean of all these calculations as the correct value of this quantity. From this result and the barometer reading calculate what your thermometer would read under a pressure of 76 cm. The error in the graduation of the thermometer is the difference between this result and 100. Test the zero point of the same thermometer by sinking it up to the zero mark in a funnel filled with melting snow or finely chopped ice over which a little water has been poured, and allowing it to remain there until the thread is stationary. Tabulate results thus : First Difference in levels in gauge Corresponding boiling-point readings = Change in boiling point per millimeter = Mean change per millimeter .-. Reading of thermometer at 76 cm. = .-. Reading of thermometer at cm. = Second Third Barometer height = Error Error = 70 LABORATORY PHYSICS State in your own words the conclusion which you draw from this experiment regarding the effect of pressure upon the boiling point. EXPERIMENT 25 MAGNETIC FIELDS I. The magnetic field about a bar magnet, (a) Lay a bar mag- net in a groove in a board (Fig. 37). Pin a sheet of blueprint paper over the magnet ; from a sifter containing iron filings sift the filings evenly, but not too thickly, over the paper from a \ height of a foot or two. Tap \. the paper gently with a ^-^ i pencil. The 'filings will be \. found to have arranged thern- \ selves in lines running in symmetrical curves from one pole around to the other. (5) Hold a short compass needle in a number of positions over the board, and observe whether or not there is any connection between the direction of the curved lines and the direction taken by the needle. These lines simply indicate the direction of the magnetic force. They are called magnetic lines of force. (c) Carefully place the board in strong sunlight without jarring the filings, and wait until the uncovered parts of the paper have turned brown. Return the filings to the box and put the blueprint paper to soak in water for about five minutes. Place the paper flat against a pane of glass to dry, and when it is dry fasten it in your notebook. If blueprint paper is not provided, or if the sun is not bright enough to make satisfactory prints, simply draw in your notebook a copy of the curves shown by the filings. In these MOLECULAR NATURE OF MAGNETISM 71 drawings and also on the blueprints indicate the N and S poles of the magnets and furnish the lines with arrows point- ing in the direction in which an N pole tends to move. (An N pole is one which, when the magnet is suspended freely, points toward the north.) II. The magnetic fields about certain combinations of horse- shoe magnets. By sprinkling iron filings upon a sheet of card- board or glass placed over various combinations of magnets, as indicated in the accompanying figures (Fig. 38), determine the nature of the magnetic field in each case, and indicate by a drawing in the notebook. EXPERIMENT 26 MOLECULAR NATURE OF MAGXETISM I. Making a permanent magnet. Mark one end of a knit- ting needle with a file for the sake of identification. (a) Stroke it once from end to end with the N pole of a horseshoe or bar magnet. Place the needle on the table in the east-and-west line which passes through the middle of a com- pass needle resting upon the table, and slide the knitting needle up toward the compass until it produces in it a deflection of 10; then mark the positions of the two ends of the knitting needle on the table. Does the near end of the knitting needle repel or attract the north-seeking end of the compass needle? Is it an N or an S pole? (If in doubt, suspend the needle in the middle by a thread and wire stirrup and see which end points north.) 72 LABORATORY PHYSICS (b) Reverse the knitting needle so that the second end occu- pies exactly the position originally occupied by the first. Com- pare the strengths and signs of the two poles. (c) Stroke the needle once more with the magnet precisely as at first, and again bring it to precisely the same position. Is the deflection increased? How much? (d) Continue to stroke the magnet in the same way until it is saturated, i.e. until further stroking produces no more change in the effect upon the compass. II. Effect of jars on a saturated magnet, (a) - Drop the needle on the floor and again test its strength exactly as before. Record the change. (b) Strike the needle a number of sharp blows against the table and test again. (c) If magnetization consists in a particular arrangement of the molecules of the needle, what effect would you expect vio-' lent jars like the above to have upon it? III. Effect of breaking a magnetized needle, (a) Magnetize a long darning needle and note which end is A r and which S. Then dip the whole needle into a box of iron filings and note whether or not it possesses any appreciable magnetism in the middle. (b) Break it in two and test the two freshly broken ends first by means of the compass and then by means of the iron filings. Test also the old ends. (c) Break one of the halves again if possible and repeat as above. (d) Summarize the results of these experiments and explain the observed effects on the assumption that a magnet consists of rows of molecular magnets arranged end to end. IV. Effects of heating a magnet, (a) Note how much deflec- tion is produced when one of the small magnets, say an inch long, obtained by breaking the darning needle, is placed at a given distance from the compass ; then make a stirrup out of copper wire, place the needle in it, heat it to redness in the MOLECULAK NATURE OF MAGNETISM 73 Bunsen flame, and again test it by means of the compass. Record the effect. (b) Heat again to redness, and then transfer it quickly to a position between the poles of a horseshoe magnet. Let it remain there until cool and test again with the compass. (c) Explain both of the effects on the assumption that mag- netization consists in a particular arrangement of the molecular magnets. (Remember that the molecules of the needle are set into violent agitation when the needle is heated to redness.) V. Making a magnet by induction, (a) Hold a short piece of unmagnetized knitting needle or a small steel nail between the poles of a horseshoe magnet and tap it vigorously with some heavy object without allowing it to touch the magnet. Remove it and test its poles with the' compass needle. (b) Turn it end for end, replace it between the poles of the horseshoe magnet, and tap again. Record the change which you observe in its poles. (c) Remove the steel rod from a tripod or take one of the small steel rods used for bending in Experiment 12. Hold it nearly vertical in a north-and-south plane, the upper end being tilted 20 or 30 toward the south. Strike the upper end three or four sharp blows with a hammer and then test the two ends of the rod for magnetism. Note which end is an N pole. (d) Repeat with the ends of the rod reversed. Which end is now an jVpole? Explain on the assumption that the molecules are permanent magnets and that magnetization consists in an alignment of these molecules. From all of the above experiments, what picture do you make to yourself regarding the operations which go on within a bar of iron when it is magnetized? Draw a diagram to represent the probable arrangement of the molecular magnets in a mag- netized bar, and another to represent some possible arrangement in an unmagnetized bar. 74 LABORATORY PHYSICS EXPERIMENT 27 STATIC ELECTRICAL EFFECTS To make an electroscope bend a piece of No. 18 copper wire into the form shown in Fig. 39, thrust it through a rubber stopper, 1 hang a piece of aluminum foil about 2 in. long over .the horizontal part of the wire, and insert in a glass flask as shown. 2 I. Conductors and nonconductors, (a) Attach one of the steel balls of Experiment 3 to a silk thread by means of sealing wax, or simply stick I ~ a penny to the end of a glass rod with the aid of sealing wax. Such an arrangement is called a proof plane. Charge this proof plane by letting it rub along a stick of sealing wax which has been electrified by being rubbed with flannel; then touch it to the wire of the electroscope. What does the instant divergence of the leaves show regarding the ease with which a charge of electricity passes through this metal wire ? What does the fact that the leaves stand apart show regarding the nature of the force which the two parts of the same charge going to the two leaves exert upon each other? (b) Touch the wire of the electroscope for an instant with a piece of sealing wax which has not been electrified. Touch it with a wooden ruler. Touch it with your finger. Which of the three conducts off the charge most readily ? 1 If the rubber stopper has not a hole through it already, you can easily make one with a hot knitting needle. If it already has a hole which is too large, cover the wire with sulphur or sealing wax. This will not only make it fit, but it will also improve the insulation. 2 An electroscope so made will hold its charge for hours, even in summer. To cut the foil blow it out flat on a sheet of paper, lay another sheet on top of it, leaving one edge uncovered, and then cut off a strip with a sharp knife or razor. A saw stroke will work best. STATIC; ELECTRICAL EFFECTS 75 (c) Charge the proof plane or steel ball, again touch it with the finger, and then try to charge the electroscope with it. Explain why the rubbed sealing wax holds its charge when it is held in the hand, while the proof plane or steel ball loses its charge as soon as it is touched with the finger. II. Positive and negative electricity, (a) Charge the electro- scope as above, then bring the charged sealing wax toward it. Record the effect produced on the divergence of the leaves. Explain this effect in view of the fact that the charge on the wire of the electroscope is a part of the charge which was originally on the sealing wax (see I (a)). (b) Rub a glass rod with silk, then bring it slowly toward the charged electroscope. Record the first effect observed. (If you bring the rod too close, the effect will be reversed.) In order to account for this effect, what sort of a force must we now assume the charge on the glass rod to exert upon the charge on the electroscope ? A charge of electricity which acts as does the charge on a glass rod which has been rubbed with silk is arbitrarily called a positive (+) charge. A charge which acts like the charge on the sealing wax when it has been rubbed with flannel is called a negative (- ) charge. (c) Discharge the electroscope, then charge it with the aid of the proof plane and glass rod, precisely as you first charged it with the aid of the proof plane and sealing wax. Note and record the behavior of the leaves when you now bring, first the glass rod, and then the charged sealing wax toward the electroscope.. In view of all these observations, state how, in general, like and unlike charges of electricity act upon one another. (d) Charge the electroscope either positively or negatively ; then rub a piece of paper on the coat sleeve and determine by bringing the paper near the electroscope whether it has received 76 LABORATORY PHYSIOS a + or a charge. Flick your handkerchief across the sus- pended steel ball and see whether it has received a + or a charge. III. To charge two bodies simultaneously by induction. Hold two suspended steel balls in contact. Bring a piece of electri- fied sealing wax to within an inch of the balls, holding it in the line joining their centers. While it is in this position separate the two balls, then bring each over a negatively charged electro- scope. Has the ball which was nearest the sealing wax received a + or a charge ? Record the sign of the charge on the other ball. If an uncharged body contains equal amounts of both positive and negative electricity which, under ordinary circum- stances, are so uniformly distributed that they completely neutralize each other, and if one or both of these electricities is free to move through the body under the influence of an outside charge, can you account for the effects which you have observed ? IV. To charge the electroscope by induction. Bring the charged sealing wax near enough to the electroscope to produce a large divergence. Remove the sealing wax. Why, on the above assumptions, do the leaves again collapse ? Again produce the divergence, but now touch the finger to the electroscope before removing the wax. Why do the leaves collapse? Re- move the finger, then remove the wax. Why do the leaves now diverge? With the charged sealing wax find whether in charg- ing an electroscope by induction as above the charge imparted to the electroscope is like or unlike that of the charging body. Repeat with the glass rod, and state a general rule for the sign of the charge of an electroscope which has been charged by in- duction. State the rule for charging by conduction (see I). V. To show that a charge is on the surface of a conductor only. Place the inner vessel of the calorimeter of Experiment 18 on two sticks of sealing wax which rest upon the table, then STATIC ELECTRICAL EFFECTS 77 charge this vessel by rubbing over it a charged rod of any kind. Bring one of the suspended steel balls into contact with the out- side of the metal vessel, then cause the ball to approach the electroscope. Has the ball received a charge ? Discharge the ball with the finger, then lower it carefully into the metal vessel till it rests on the bottom. Remove it and see whether it is now charged. Record your conclusion. Why was it neces- sary to place the metal vessel on the sticks of sealing wax ? VI. To prove that + and electricities appear in equal amount, (a) Charge a steel ball negatively and bring it care- fully inside of vessel A (Fig. 40), which is connected by a wire to the electroscope. The divergence of the leaves will measure the charge induced on the outside of A. Touch the ball to the inner wall of the vessel. / -ZJU- \ The divergence of the t- ' leaves is now a measure of the charge which was originally on the ball, for by V this charge has all passed to the outside. Did the divergence change at all when the ball touched the wall? What conclusion do you draw regarding the minus charge on the ball and the minus charge induced by it on the outside of the vessel ? (b) Recharge the ball and again hold it inside of A, without touching the wall, and note the divergence of the leaves. Touch the outside of A with the finger. Remove the finger, then remove the ball, but do not discharge it. Is the deflection the same as before? Test the sign of the charge on the leaves. Reinsert the ball and touch it to the vessel. Does the electro-' scope show any charge? What conclusion, then, do you draw regarding the charge on the ball and the + charge which was induced on the inside of A ? 78 LABORATORY PHYSICS VII. The principle of the condenser, (a) By means of a wire connect the electroscope with a vertical metal sheet A (Fig. 41), about 4 in. square, which is nailed to a piece of wood as shown. Support this on two pieces of sealing wax. Charge plate A by giving it a single stroke with a small piece of electrified sealing wax. If the electroscope shows any leak, rub the sealing-wax supports on a cloth until they are warm. Now move a second plate B, which you keep in contact with your hand, up to within about 1 mm. or 2 mm. of A. What effect do you find that this /-^ has on the potential of A ? V / x. (Consider potential to be / 1-\ x^ A B measured by the diver- gence of the leaves of the electroscope.) (b) Electrify the sealing wax again, as nearly as pos- sible in the way you did at first, and give A another stroke. Repeat until the original diver- gence is reestablished. From the number of these strokes estimate roughly how many times the electrical capacity of A has been increased by the presence of J5, i.e. how many times the original amount of electricity is now required to bring it to the same potential which it had at first. In view of the fact that the charge on A repelled negative electricity to the earth through your finger, and thus induced a + charge on B, can you see why, when B is near by, it takes a larger charge on A to produce a given divergence than when B is remote ? (c) Slip a 5 in. x 5 in. glass plate between A and B and watch the electroscope. Does this increase or decrease the potential of A? Hence does it increase or decrease the capacity of the condenser ? Push the plates together until each is in contact with the glass plate. Remove the glass without changing the distance THE VOLTAIC CELL 79 between the plates, and charge A to a given divergence. Insert the glass and find how many more approximately equal charges may now be put on A before bringing the leaves to about the same divergence. The ratio of the charge on A when the glass was in to the charge when the glass was out is called the specific inductive capacity of glass. EXPERIMENT 28 THE VOLTAIC CELL I. Action of dilute sulphuric acid on copper and zinc strips. (a) Open circuit. Fill a tumbler two thirds full of water and add about one sixtieth as much sulphuric acid. Introduce a strip of zinc about a centimeter wide into the acid, and observe and record what effect, if any, is produced by the acid. (The bubbles are hydrogen.) Repeat the experiment with a similar strip of copper. Next place both the zinc and copper in the acid at the same time, but take care that they do not touch each other at any point. Observe and record the action at each plate. (b) Closed circuit. Press the tops of the strips firmly together and notice what change, if any, takes place at the surface of each metal. Record results. II. Effect of amalgamation. Dip the zinc plate into a dish containing a little mercury and rub the mercury over the wet portion of the zinc until it is covered with a smooth, even coat of mercury. Dip the amalgamated zinc into the sulphuric-acid solution again, and repeat the observations of I, recording what differences, if any, are observed in the action. III. Effects observable about the wire connecting the strips. (a) For convenience in handling, place strips of copper and of amalgamated zinc in clamps such as those shown in Fig. 42, 80 LABORATORY PHYSICS and connect these clamps by means of, say, No. 24 copper wire to the binding posts of the 25-turn coil of No. 22 wire on the galvanoscope, after placing the latter with the plane of its coils north and south. Dip the metals in the acid and observe the effect on the needle. (b) Disconnect the wires from the galvanoscope and touch them to the tongue. What evidence do you obtain of some action going on when the plates are in the acid, but which disappears as soon as they are lifted from it? IV. Polarization. Take a fresh and dry copper plate, or else dry the old one by heating it in a Bunsen flame until it is much too hot to hold, and then letting it cool. Insert the zinc and copper in the clamps and connect as before to the 25-turn coil of the galvanoscope, but this time insert into the circuit about a meter of No. 36 German silver wire. 1 (No. 30 will do, but No. 36 is better.) Turn the compass until the needle points to ; then immerse the plates in the acid, and as soon as the needle stops swinging violently read the deflection. (If this deflection is more than 40 or 50, slide the compass along in the 1 For the sake of avoiding loose German silver wire, it is best to insert the meter of No. 36 wire between the binding posts ac of Fig. 52, and then to con- nect the zinc plate of the cell to a, the copper plate to one terminal of the gal- vanoscope, and the other terminal of the galvanoscope to c. THE VOLTAIC CELL 81 frame away from the 25-turn coil, until the deflection is reduced to 50 or less.) Watch the needle for a minute and record what you observe. In II you found that if the zinc is well amalga- mated, hydrogen appears only at the copper plate. Short-circuit the cell for half a minute by holding a short strip of copper in contact with both the copper and the zinc plates. This simply enables the hydrogen to be generated in greater abundance. It brings the deflection nearly to o because most of the current now goes through the copper strip. Remove the copper strip. Does the deflection return quite to its old value ? From these experiments, what effect do you conclude that the accumula- tion of hydrogen upon the copper plate has upon the strength of the current which the cell can furnish ? This is technically called the polarization of the cell, and a cell in which this effect occurs is called a polarizing cell. V. A nonpolarizing cell. Replace the simple cell by a Daniell cell, or construct what is essentially a Daniell cell as follows. First dry the copper plate in the Bunsen flame, then replace it in its clamp. Fill the tumbler half full of a saturated solu- tion of copper sulphate, and pour zinc sulphate into a small porous cup, which is then to be placed inside the tumbler. Now immerse the plates in the liquids, the zinc going into the zinc sulphate in the porous cup and the copper into the copper sulphate. (The porous cup is simply to keep the two liquids separated. The electric current can pass through it with ease.) Watch the needle and record its behavior. Short-circuit the cell and see if there- after the deflection returns to its old value. Is, then, a Daniell cell a polarizing or a nonpolarizing cell ? Does the fact that the element which is deposited on the copper plate when it is im- mersed in copper sulphate is copper itself suggest to you any reason why in this case the current is not changed, as was found to be the case when the deposit was hydrogen ? In which case is the character of the surface of the plate changed by the deposit ? 82 LABORATORY PHYSICS VI. A polarizing commercial cell. Replace the Daniell by a Leclanche cell, if one is available (a dry cell will answer nearly as well). This consists of a zinc rod in sal ammoniac and a carbon plate inside a porous cup which is full of manganese dioxide. See first whether the current which this cell sends through the three feet of No. 36 German silver wire weakens at all in two minutes. (If the deflection is more than 45, push the compass farther away or change to the one-turn coil.) Then short-circuit the cell for half a minute and see if there- after the deflection returns to the old value. Is, then, this cell polarizing or nonpolarizing? Watch the needle for a minute after the cell has been short-circuited. Does the current gradu- ally recover part of its former strength? Break the circuit entirely and let the cell stand for a few minutes; then read the deflection. Try the same experiment with a simple cell. Record the difference in the behavior of the two cells. This difference is due to the fact that in the simple cell there is nothing to remove the film of hydrogen from the surface of the plate upon which it is deposited. In the Leclanche cell, on the other hand, the man- ganese dioxide slowly unites with and therefore removes the hydrogen from the carbon plate. This is indeed the object of its use. A Leclanche cell is, then, one which recovers on open circuit. EXPERIMENT 29 MAGNETIC EFFECT OF A CURRENT I. The right-hand rule, or Ampere's rule. Since a wire through which a current is flowing has just been found to deflect a magnetic needle held near it, the wire must be sur- rounded by magnetic lines of force. The direction in which the MAGNETIC EFFECT OF A CUBEENT 83 FIG. 43 N pole of the magnetic needle tends to move gives, by definition, the direction of these magnetic lines. The direction in which the positive electricity flows through the circuit of a zinc-copper cell is from zinc to copper inside the liquid and from copper to zinc in the connecting wire, i.e. it flows in the direction in which the hydro- gen was found to move in the last experiment. We know this be- cause a very delicate electroscope will show that on open cir- cuit the copper plate acquires a small + charge of static elec- tricity and the zinc a small charge. For this reason the copper or carbon plate of a voltaic cell is always called the plus (+) plate and the zinc the minus ( ) plate. The direction of an electric current is defined as the direction in which the positive electricity moves. By the series of experiments given below, test the following rule. If the conductor is grasped by the right hand so that the thumb points in the direction in which the current flows, then the magnetic lines of force pass in con- centric circles around the wire in the direction in which the fin- gers of the hand encircle it (Fig. 43). (a) Connect either a simple cell or a dry cell in the manner shown in Fig. 44, so that the current will flow from the copper 84 LABORATORY PHYSICS (or carbon) through the commutator C, then over the needle from south to north, and back through the commutator to the zinc. All of the connecting wires should be copper, for exam- ple No. 24, and that to the right of the commutator should be 10 ft. or 12 ft. long. Insert the top of the commutator and record the direction in which the north pole of the needle turns. (b) Turn the top of the commutator through 90, so that the mercury cup a is connected to e and b to c?, instead of a to b and e to d. This reverses the current in the wire so that it goes over the needle from north to south. Record the effect on the needle and compare with Ampere's rule. (c) Place the compass above the wire without changing the direction of the current, and compare with the rule the effect produced on the needle. Reverse the direction of the current by means of the commutator and again compare. (d) Hold the wire so that the current flows vertically down- ward just in front of the N pole of the compass ; then cause the current to flow upward past the same pole, and test the rule in each case. (e) Hold the wire so that the current flows from west to east over the middle of the needle. Does the experiment show that the lines of magnetic force lie in planes at right angles to the direction of the wire ? How ? II. To find the direction of an unknown current. Let the instructor bring a current the direction of which is unknown into the laboratory by a wire connected with a cell in a closet or in an adjoining room. Hold a compass needle near the wire and determine the direction in which the current is flowing in the wire. Record your result and then test the correctness of it by following the wire to the cell. III. The effect of loops, (a) As in I, pass a current from a cell over the compass from south to north, keeping the wire MAGNETIC PROPERTIES OF COILS 85 as close to the face of the compass as possible. Note the amount of deflection. Then cause the wire to return beneath the needle, so that a loop is formed, in the upper part of which the current flows past the needle from south to north and in the lower part from north to south. Is the deflection greater or less than at first? Why? (b) Try the effect of placing both sides of the loop above the needle, as in Fig. 45. Explain the observed effect. (c) Loop the wire several times around the compass in such a way that the plane of the coil is north and south. What change is produced in the deflection by each new turn? Explain. EXPERIMENT 30 MAGNETIC PROPERTIES OF COILS CARRYING CURRENTS I. Magnetic effect of a helix, (a) Having the circuit arranged as in Fig. 44, the current being furnished either by a simple cell or by a dry cell, form a close helix (see Fig. 46) by wrap- ping the conducting wire forty or fifty times around a lead pencil. Then with the aid of the compass see whether or not the helix is a magnet, i.e. whether one end of it attracts the north pole while the other repels it. (b) By means of the commutator reverse FlG - 46 the direction of the current through the helix and record what effect is thus produced upon the poles. (c} Test the following rule for determining the poles of a helix. If the helix is grasped in the right hand so that the fingers are pointing in the direction in which the current is flowing in the 86 LABORATOKY PHYSICS V \ 'vOOnOCYXYl coils (see Fig. 47), the thumb will point in the direction of the magnetic lines of force, i.e. the thumb will point towards the north pole of the helix. Show how this rule fol- lows from Ampere's rule. II. The principle of the electro- magnet, (a) Thrust an unmagnet- ized soft iron rod, e.g. a wire nail, into the helix and then test the nail and helix together in the same way in which the helix alone was tested in the preceding experiment. Are the poles stronger or weaker than before? (b) Reverse the current by means of the commutator and test and record the effect on the poles. (c) Bend a piece of large iron wire into the shape of a letter U and mark one end with chalk. About the ends of both arms FIG. 47 FIG. 48 of the U wind a wire carrying a current, in such a way that the "marked end of the U shall be an N magnetic pole and the other an S pole. Test by means of a compass. ELECTBOMOTIVE FORCES 87 III. Principle of the D'Arsonval galvanometer, (a) Hang a coil of about one hundred and seventy-five turns of No. 32 copper wire between the poles of a horseshoe magnet in the manner shown in Fig. 48, so that the plane of the coil is parallel to the line joining the poles. The two wires which run from the coil up to the cork support should be of No. 40 insulated copper, and one of them should be twisted about the other loosely, as in the figure. Pass a current from a cell first through a commu- tator and then through the coil. Record the effect observed in the coil. (b) Reverse the direction of the current and observe the effect produced. Explain why the coil turns as it does, remembering that it is nothing but a flat helix. (c) By rotating the cork at the top, set the coil between the poles of the magnet in such a way that its plane is perpen- dicular to the line joining these poles. Turn on the current and note the effect. (d) Reverse the current and note again the effect. Explain in each case the effect observed. EXPERIMENT 31 ELECTROMOTIVE FORCES In the present experiment we shall compare the electromotive forces, or the electric pressures, which cells of different form are able to maintain, by comparing the currents which they can force through a long piece of fine wire (a large resistance). I. Effect of size of plates and distance between them on the electromotive force of a cell. To one of the terminals of the 100-. turn coil of the galvanoscope connect a small coil R (Fig. 49) of German silver wire the resistance of which is about 1000 ohms. Then complete the circuit of the simple cell through this 88 LABORATORY PHYSICS high-resistance galvanometer in the manner shown, and read the deflection of the needle. If it is more than 20, push the com- pass farther away from the coil. Lift the plates almost out of the liquid, and read again. Disconnect the wires from the binding posts of the cell, remove the frame and plates from the tumbler, press the wires very firmly against much narrower zinc and copper strips than those used before, immerse these in the liquid, and read again. Place these strips as far apart in the tumbler as you can, and see if the deflection changes as you move them together. (In all cases in which accurate readings of deflections are to be taken it is desirable to tap the frame of the galvanometer lightly with a pencil so as to overcome any tendency which the needle may have to stick.) What conclusions do you draw in regard to the effect of the distance between the plates and the area of immersion of the plates on the electromotive force of a cell? II. Effect of different metal plates on the electromotive force of a cell, (a) Without changing anything else in the circuit, insert in the clamp of the simple cell a lead plate in place of the copper plate of the above experiment. If the needle is deflected in the same direction as before, we may know that in the external circuit the current flows from the lead to the zinc, i.e. that lead in sulphuric acid is + with respect to zinc r but ELECTROMOTIVE FORCES 89 if the needle turns in the opposite direction, then the zinc is -f with respect to the lead. Record tests with zinc-lead, zinc-car- bon, and zinc-aluminum electrodes in the following form : Zinc - Copper + Deflection 12 Zinc ? Lead ? Deflection ? Zinc ? Carbon ? Deflection ? Zinc ? Aluminum ? Deflection ? (b) Replace the zinc by a lead plate, and record tests on lead- copper, lead-aluminum, and lead-carbon thus : Lead ? Copper ? Deflection ? Lead ? Aluminum ? Deflection ? Lead ? Carbon ? Deflection ? Do you see any connection between the results in (a) and (b) which enables you to predict all the results in (b) from those in (a)? If so, arrange these five substances in a list such that each substance will be positive with respect to any substance below it in the list, but negative with respect to any substance above it. Which pair give the highest E.M.F. ? What conclusion do you draw in regard to the effect on the E.M.F. of the kind of plates used ? III. Effect of different liquids (electrolytes) on the E.M.F. Measure the deflection again, using the same galvanoscope, when zinc and copper are immersed (a) in dilute sulphuric acid (H 2 SO 4 ) ; (b) in a solution of common salt (NaCl, i.e. sodium chloride) ; ( 2 that between d and c, then, since b and d have the same potential, PD l will also represent the potential difference between a and d, and PZ> 2 that between d and c. Now, by Ohm's law, since the same current C l is flowing through ad and dc, we have C\ = PDJP = PD^/Q, or PD^PD^ = P/Q. Similarly, on the lower branch, PD l /PD 2 = R/X. Therefore, P/Q = R/X and X = P x R/Q. 96 LABORATORY PHYSICS (a) Stretch No. 30 German silver wire between a and c, as in Fig. 5(7, place a meter stick beneath it, and then connect a simple or a dry cell B to the terminals a and c. Between the binding posts a and b insert some known resistance, say a one-ohm coil. Between b' and c insert the 3-m. coil of No. 30 copper wire used in I. The brass strap between b and b' has a negli- gible resistance, so that the whole of it may be considered as the point b of Fig. 54. Connect to the binding post at m one terminal of a D'Arsonval galvanometer G. This instrument is precisely that shown in Fig. 48, save that a slender pointer must be inserted in the place provided for it (see also Fig. 57) for the sake of making small deflections more easily observable. FIG. 65 Touch the free terminal of the galvanometer at a number of points along the wire ac until you find that point at which the galvanometer shows no deflection on making contact. Since the wire ac is uniform, the ratio of the resistances P and Q is simply the ratio of the lengths ad (= IJ and dc (= / 2 ). Hence, X/R = l z /l v or X = R x yi r (b) In the same way measure the resistance of exactly 50 cm. of No. 30 iron wire, and calculate from the result the resistance in ohms of such a wire 3 m. long. By what does the value thus found for the relative resistance of iron and copper differ from that found in I ? (c) In the same way measure the resistance of exactly 25 cm. of No. 30 German silver wire, and compute from the result INTERNAL RESISTANCE OF GALVANIC CELLS 97 the resistance of such a wire 3 m. long. Record the per cent of difference between this result and that found in I. Tabulate in che form given below the final results of your measurements upon the relative resistances of the three metals, copper being taken as 1. METAL FALL OF POTENTIAL METHOD BRIDGE METHOD Copper 1 1 Iron 8.1 7.9 German silver .... 17.8 18.5 EXPERIMENT 34 INTERNAL RESISTANCE OF GALVANIC CELLS I. Currents furnished by galvanic cells when the external re- sistance is small. In the experiment on E.M.F. (Experiment 31) we found that changing the distance between the plates, or the area of the plates immersed, had no effect on the current sent through a high-resistance coil. Try the same experiment with a low-resistance coil in the following way. (a) Connect the improvised Daniell cell with the single turn of coarse copper wire which connects the middle binding posts of the galvanoscope, and observe the deflection of the compass needle. (b) Lift the zinc gradually out of the cup, and record the effect. Since, as proved in Experiment 31, the E.M.F. is not diminished by decreasing the area of plates immersed, what do you conclude, from Ohm's law, must have changed in the cir- cuit as the zinc was lifted? How, then, is the internal resist- ance affected by the size of the plates and the distance between them? 98 LABORATORY PHYSICS II. Current furnished by combinations of cells when the exter- nal resistance is small, (a) Connect a single Daniell cell with the single-turn coil of the galvanoscope. Slip the compass along until the deflection is from 6 to 10. (b) Select another Daniell cell which gives approximately the same deflection when tested in the same way. Connect the two cells in series. How does the deflection given by two Daniell cells joined in series with a small external resistance compare with that given by a single cell joined to the same ex- ternal resistance ? What difference do you notice between the effects here obtained and those produced in Experiment 31, where the external resistance was large? ( ? Disconnect m and n from 2?, and observe how many volts of E.M.F. have been developed between the lead plates. Now watch the am- meter as you join m and n to each other. What is the direction of the observed current with reference to that which the battery sent through the ammeter? Watch the voltmeter and ammeter for two minutes while the storage cell is discharging. In view of this back E.M.F. which the experiment has shown was developed in the lead cell by the deposit of lead peroxide on the anode, explain why during the charging of the storage cell the voltmeter deflection rose, while that of the ammeter fell. From your experiment, decide how many volts are required to charge a storage cell. 1 EXPERIMENT 36 INDUCED CURRENTS I. Induction of currents by magnets, (a) Set up the D' Arson val galvanometer (Fig. 57), and insert in the place provided for it a slender wire or broom-corn pointer in the manner shown in the figure. Short-circuit a simple cell by means of a few feet of copper wire ; then to the galvanometer terminals touch wires which are connected to the cell and note the direction of deflec- tion. (The object of the short-circuiting is to prevent a too vio- lent throw of the coil.) Record the terminal (right or left) of the galvanometer at which the current entered it when the deflec- tion was in a given direction (right or left). This w T ill enable 1 If you wish to repeat the experiment with the same lead plates, you should first clean them very thoroughly with sandpaper. INDUCED CURRENTS 103 you henceforth to know at which terminal any current enters your galvanometer, as soon as you observe the direction of deflec- tion. Connect to the galvanometer a 600- or 700-turn coil A of No. 27 copper wire. Take particular pains to scrape the ends of all wires which are to be joined, and to twist the scraped ends firmly together. Thrust the coil A suddenly over the north pole of the bar magnet, and note and record the direction and the approximate amount of the deflection of the end of the pointer attached to the coil. A paper scale sup- ported between the walls be- neath the pointer will enable you to estimate amounts. (6) From the direction of the deflection, determine the direction of the current in- duced in the coil of wire thrust over the pole. While this induced current was flowing did it make the end of the coil, considered as a temporary magnet (see Experiment 30), which was approaching the N pole itself an N or an S pole ? (c) Suddenly withdraw the coil from the magnet. Note and record as before the direction and amount of deflection. How does the direction and amount of the induced current now com- pare with that found in (a) ? Is the end of the coil which leaves the magnet last of the same sign as the pole of the magnet or of unlike sign? (d) Draw in your notebook four figures like those shown in Fig. 58, and insert in each the signs of the poles of the coil due to the induced current, when the coil is in the four positions indicated in the figures and moving in the directions indicated by the arrows. 104 LABOR ATOKY PHYSICS (e) Repeat the same experiments with the S pole of the mag- net, and observe in each case the direction of deflection and the direction of the current in- duced in the coil. Is the nature of the induced mag- netism of the coil A in every case such as to oppose or to assist the motion of the coil ? II. Induction of currents by electro-magnets, (a) Slip the 700-turn coil used in I over an iron bar (e.g. one of the tripod rods) and connect it through a commutator with a battery B of one or two dry cells, in the manner shown in Fig. 59. Place a second similar coil over this bar and connect it with the D'Arsonval galvanometer as shown. Now make the circuit by inserting the upper part of the commutator, and record Fiu. 5S the effect produced upon the needle. From the direction of deflection of the pointer, find the direction in which the current flowed around the iron core in the coil attached to the galva- nometer (the so-called secondary}. Was the induced current in the same or in the opposite direction to that in which the current INDUCED CURRENTS 105 from the cell is circulating around the core in the primary coil ? What connection do you find between this experiment and I? (b) Remove the commutator top and thus break the circuit in- the primary. Note the direction and amount of deflection, and compare with that observed when the current was made. Com- pare the direction of the induced current in the secondary with that which was flowing in the primary. Is the current in the secondary circuit produced by the magnetism of the electro- magnet or by changes in the magnetism of the electro-magnet ? Do -the induced currents in every case tend to assist or to oppose the changes which are taking place in the magnetism of the core? (c) Push up the base of the tripod into contact with the rod (Fig. 59), so that the magnetic lines can have a return iron path instead of a return air path. Observe the amount of the deflec- tion at make or break and com- pare with the amount when the tripod base is removed. (The dif- ference will not be large, but it will be easily observable.) III. Principles of the dynamo and motor, (a) Hold the coil A between the poles of a horseshoe magnet (Fig. 60), and in such a position that its plane is perpendicular to a line joining the poles. Rotate quickly through 90, i.e. to a position in which its plane is parallel to the lines of force. Observe the direction of deflection of the suspended coil. (b) After the pointer has come to rest rotate the coil A 90 more, and note and record the direction of deflection. (c) Similarly, rotate the coil through the next two quadrants. 106 LABORATORY PHYSICS (d) If the coil were to be rotated continuously in this way, what portions of the rotation would produce a current in one direction, and what in the opposite direction ? In what position of the coil will the induced current change from one direction to the other? (e) In a dynamo a coil is forced to rotate in the strong field of an electro-magnet and induced currents are produced. In a motor currents are sent through a coil which is in a strong magnetic field and the coil is forced to rotate. Point out the parts of the above apparatus which correspond to the dynamo, and those which correspond to the motor. EXPERIMENT 37 ELECTRIC BELLS AND MOTORS I. Study of electric bells, (d) Connect an electric bell with a dry cell, and with an inexpensive compass test the condition of the electro-magnet first when the clapper is held against the bell, then when it is held away from it. Trace the current through the instrument and, with the aid of a rough diagram, explain in your notebook why the bell rings. (5) Connect a bell, two push buttons, and a cell in such a way that pushing either button will ring the bell. II. Study of a small motor, (a) Join two dry cells in series to a small motor (Fig. 61). As soon as the motor begins to run deter- mine with a small compass needle which is the N and which the S pole of the field magnets. Trace out the winding of the field magnet, and determine from the rule of Experiment 30 which pole should be N and which S. Do the calculated and observed signs agree? SPEED OF SOUND IN AIR 107 (b) Stop the motor and trace the wires leading into one coil of the armature. Find from the rule what should be the sign of its magnetism at two or three different points in a revolu- tion. Test at each point with the compass. Notice particularly the points at which its magnetism reverses. Hence, account in your notebook for the continuous rotation and for the observed direction of rotation of the motor. (c) From a study of the windings, decide whether or not interchanging the battery terminals would reverse the direction in which the motor runs. Record the answer in your notebook, and then test the correctness of your conclusion by experiment. EXPERIMENT 38 SPEED OF SOUND IN AIR A. Let the class be divided into two sections and placed exactly a kilometer apart, the distance being measured by laying off fifty times the length of a cord 20 m. long. Each group should be provided with a pistol, blank cartridges, and at least one stop watch. Let a member of one group raise and lower a handkerchief three times as a ready signal, and simultane- ously with the last lowering let him fire a pistol. Let a mem- ber of the other group take with a stop watch the time which elapses between the flash and the report of the pistol. Then let the operations at the two stations be interchanged, in order to eliminate the effect of any wind which may be blowing. In this way take six or more observations, different members of the class timing the interval in turn. Observations which differ badly from the general average and which are evidently the result of awkward handling of the stop watch need not be included in the final mean. From this mean, compute the velocity of sound at the temperature of the air. 108 LABORATORY PHYSICS B. 1 If stop watches are not available, set up a heavy pendulum which beats seconds ; attach some white object to it ; set up a screen so that the pendulum can be seen only when it is pass- ing the middle point of its swing; let one student stationed near the pendulum pound loudly on some sonorous object at each instant at which the pendulum crosses the middle point, and let the class move away until the beats of the hammer appear again to coincide with the passages of the pendulum. The distance from the class to the pendulum is obviously nu- merically equal to the velocity of sound. EXPERIMENT 39 VIBRATION NUMBER OF A FORK 2 (a) Smoke the glass plate A (Fig. 62) by holding it in the flame of burning gum camphor or in a gas flame. 3 Keep the plate moving back and forth so that it will not become over- heated in one place and crack. Lay the plate on the board, FIG. 62 smoked side up, and adjust the two styluses by means of the clamps B and C until they touch the plate lightly, very near each other in the line in which the motion is to take place. 1 As in Experiment 13, A and B are intended as alternatives, the choice depending upon equipment. 2 One "vibration-rate apparatus" and fifteen glass plates will suffice for a class of thirty. It is recommended that the instructor make the traces, and that the students take the measurements. 8 Instead of smoking the plate the authors often mix up a paste of whiting or chalk dust in alcohol and paint the plate with it. This brings out the trace as well, and the whiting is very much cleaner than lampblack. VIBRATION NUMBER OF A FORK 109 Set the fork into vibration by striking it with a wooden mallet, or bowing with a violin bow, and as soon thereafter as possible start the bob to vibrating, and draw the plate beneath the bob with such rapidity that the trace of three or four complete vibrations of the bob will appear on the plate. (b) Count the number of vibrations of the fork corresponding to a full vibration of the bob, i.e. the number of vibrations of the fork between the points A and C (Fig. 63), then between B and '^~^^~^^\C^^~^ / ^^^ ^ J7< \ 7 E FIG. 63 I), then between C and E, then between D and F, etc., estimat- ing in every case to tenths of a vibration. Take a mean of these counts as the number of vibrations of the fork to one of the bob. ( Difference x 2 = X .-. Calculated wave length = .-. Calculated wave length = LAWS OF VIBRATING STRINGS 111 State in notebook how you have proceeded to find X. Show how this method might be used for finding the velocity of sound. Since the speed of sound is the same for notes of all pitches, what conclusion can you draw from your experiment in regard to the vibration frequencies of two notes which are an octave apart ? EXPERIMENT 41 LAWS OF VIBRATING STRINGS I. Effect of length on the vibration rate of a stretched wire. (a) Stretch a fine steel piano wire (No. 00) along the board A A FIG. 65 (Fig. 65), insert a bridge at 6, and hang a pail having a capacity of at least six quarts over the pulley p. Pour water into the pail until the note given by the wire (best ^F^| picked near the middle) is in unison with the note of the V ; lowest fork provided, viz. C. Measure carefully the length of the wire between the fixed end and b. (b) Move the bridge b until the note given by the wire is exactly in tune with a fork C', an octave higher than the first one. Measure and record the length from the fixed end to b. (c) In the same way (i.e. by moving b) tune the wire to uni- son with a third fork, e.g. G above middle C, and measure and record the corresponding length. (d) From a study of the measured lengths and of the vibra- tion numbers as marked on the forks, find and state in your notebook the law connecting the rate of a vibrating string with its length when the tension is kept constant. 112 LABORATORY PHYSICS II. Effect of tension on the vibration rate of a stretched wire. (a) Set up side by side two boards like A (Fig. 65), both of which are provided with No. 00 piano wire. Place the bridges b at the same distance, say 60 cm. from the left end of each. Produce the same tension in the two wires by hanging from each a like weight, for example a pail containing a small amount of water. The weights should be of such size as to produce in the plucked wires a low but perfectly distinct musical note. Bring the two wires into exact unison by adjusting the water in one of the pails until no beats are heard when the strings are sounded together. Find the exact tension on one of the wires by weighing the pail and water carefully with a spring balance. Produce the exact octave on the other wire by moving the bridge until the wire is only one half as long as at first. Bring the first wire into unison with it by adding water to the pail, leaving the length exactly as at first. Weigh the pail and water again, and find the ratio of the weights in the two cases. In order to double the rate, how many times has it been neces- sary to multiply the stretching force ? (b) Make the second wire just two thirds its original length, its tension still being kept constant. In what ratio will this change its vibration number? Adjust the amount of water in the pail hanging from the first wire until the two are in unison, and weigh on the spring balance again. From the law suggested in a, calculate what this last stretch- ing weight should have been, and see how well it agrees with the observed value. Tabulate results thus : I. Length of C wire = -2 k. cm. Length of C' wire = *~\ cm. Length of G wire =%&+3cm. Calculated length of C' wire = cm. Calculated length of G wire = cm. REFLECTION FROM PLA>'E MIRRORS 113 II. First stretching weight Second stretching weight = I ** Second divided by first Third stretching weight (calculated) = g. Third stretching weight (observed) = g. State in notebook the laws discovered in I and II. EXPERIMENT 42 LAWS OF REFLECTION FROM PLAXE MIRRORS I. To prove that angle of incidence equals angle of reflection. (a) Blacken one side of a strip of plate glass or a microscope slide ; attach it by means of a y . rubber band to a small wooden block, and then set it on edge so that the line AC (Fig. 66), drawn on a sheet of paper, coincides with the plane of the unblackened face. The rear face is blackened in order to prevent reflection from that face and enable one to work with the light reflected from the front face alone. Set a pin at a point B against the face of the glass. Set another pin at any point P, and then, placing the eye so as to sight along B and P", the image of P, set a third pin P' somewhere in this line of sight. Remove the glass plate and with a protractor or a pair of dividers construct a perpendicular BE to AC at the point B. Draw PB and P'B and measure the angle of incidence PBE and the angle of reflection P'BE with the protractor. If a protractor is not at hand, draw an arc with B as center, cutting the lines PB and P'B at M and 0, and measure the lines MN and ON. 114 LABORATORY PHYSICS (b) Repeat ior some other position of P. (. 37 1.75 13 1.25 1 tube for volume coefficient of 1 glass tube 110 cm. by 4 cm., air, p. 39 .15 ends annealed, rubber stopper, 1 steam generator, pp. 37, 39, 41, pp. 14, 22, 110 1.75 55,69 1.90 1 manometer bottle with inlet 1 apparatus for expansion coeffi- tube, pinchcock and manom- cient of brass, p. 41 . . . . .75 eters, p. 18 1.60 1 demonstration balance (knife- 1 aluminum cylinder, p. 19 . . .40 edge and support), p. 44 . . .65 1 constant-weight hydrometer 1 inclined plane and sonometer, tube, p 22 . . .40 pp. 47, 111 1.55 1 constant-volume hydrometer 1 carriage for inclined plane, tube, p. 23 .30 P- 47 .90 1 wooden block with sinker, pp. 1 pendulum clamp, p. 48 . . .35 24, 25 .30 1 boiling-point-of-alcohol tube . .30 131 132 LABORATORY PHYSICS 1 spun-brass calorimeter, two vessels, 300 cc. and 1000 cc., ^ pp. 52, 55, 59, 65, 67, 77 . . 82.50 1 tube for mechanical equivalent of h$at, p. 59 65" 1 high-grade compass, pp. 71, 80, 83, 88, 90, 92, 94, 98, 100 . . 1.35*" 1 small bottle acetamide, p. 63 . .50 1 bar magnet, pp. 70, 103 . . .40 1 horseshoe magnet, pp. 71, 105 .25 1 electroscope, pp. 74, 77, 78 . .50 1 galvanometer frame with three windings, pp. 80, 88, 90, 92, 93,97,100 1.60 1 simple voltaic cell (complete), pp. 80, 83, 86, 88, 90, 101 . .65 1 pordus cup for Daniell cell, pp. 81, 87, 91, 97, 100 10 1 D'Arsonval galvanometer (complete), pp. 86, 96, 103. 104, 105 2.20 1 1000-ohm resistance coil, pp. 87, 90, 101 30 1 each of carbon, aluminum, and lead electrodes, p. 89 ... .16 2 lead electrodes, p. 101 . . . $0 1 Wheatstone's bridge with po- tentiometer attachment, pp. 81, 92, 94 2.20 1 commutator, pp. 83, 86, 104 . .75 1 1-ohm resistance coil ... .40 2 dry cells, pp. 99, 104, 106 . . .45 2 coils for induction, pp. 103, 104, 105 1.00 1 electric bell, p. 106 30 2 electric push buttons, p. 106 . .25 1 electric motor, mounted, p. 106 1.25 3 tuning forks (256, 384, 512), pp. 110. Ill 3.00 1 fork-rating apparatus, p. 108 . 3.75 1 glass plate, lacquered black on back, p. 113 05 2 prisms, pp. 116, 116, 125, 126, 127 2.20 1 concave mirror, p. 118 ... .45 1 convex, mounted reading lens, pp. 119, 122 45 2 linen tester lenses, pp. 121, 123 .65 1 microscope tube, p. 124 . . .20 Total 68.00 INDEX Aluminum, 20, 55. Amalgamation, effect of, 79. Ammeter, 97, 101. Ampere's rule, 82. Archimedes' principle, 19. Balance, 6 ; spring, 11. Bar magnets, 70. Boiling point, of alcohol, 66 ; of water, 69. Boyle's law, 26. Caliper, vernier, 4 ; micrometer, 9. Calorimeter, 52. Candle power, 128. Charge on surface, 76. Combinations of cells, 90, 98. Compass, 71. Condenser, electric, 78. Conductors, 74. Convex lens, 120. Cooling, by evaporation, 30 ; through change of state, 62. Critical angle, 116. Cylinder, volume of, 3. Daniel cells, 81. Density, of steel spheres, 8 ; by loss of weight, 20 ; of liquids, 21 ; of light solids, 24. Dew-point, 33. Disk for determination of n, 1. Dispersion, 125. Dynamo, 105. Electric bells, 106. Electrolysis, 99. Electrolytes, 89. Electro-magnet, 86. Electromotive force, 87. Electroplating, 100. Electroscope, 74. Expansion, of air, 37 ; of brass, 40. Focal length of mirror, 118; of lens, 119. Freezing by evaporation, 35. Galvanometer, suspended needle form, 80 ; D'Arsonval form, 87, 103. - Gasoline, 15. Graph, of direct proportion, 16 ; of in- verse proportion, 29. Heat of fusion of ice, 64. Helix, magnetic effect of, 85. Hooke's law, for stretching, 35 ; for bending, 36. Humidity, 34. Hydrometer, constant weight, 22 ; com- mercial, 23 ; constant volume, 23. Hygrometric table, 34. Hyperbola, 30. Inclined plane, 46. Index of refraction, 114. Induction, magnetic, 73 ; electrostatic, 76 ; electro-magnetic, 102 ; coil, 104. 134 IXDEX Law of inverse squares, 128. Leclanche", 82. Magnetic fields, 70. Magnetism, molecular nature of, 71. Magnifying power, of simple lens, 121 ; of telescope, 123 ; of microscope, 124. Manometers, 17. Mechanical equivalent of heat, 59. Microscope, compound, 123. Mirror scale, 35. Mirrors, plane, 113; concave, 118. Mixtures, law of, 52. Moments, principle of, 44. Motor, 106. Naphthaline, 64. Ohm's law, 91. Parallelogram of force, 8. Pendulum, laws of, 48. Per cent of error, 2. Phoiometry, 128. Polarization of a cell, 80. Pressure, in liquids, 14 ; within a bot- tle, 18. Prisms, 128. Proportion, direct, 15 ; inverse, 29. Reflection, laws of, 113. Resistance, measurement of, 93 ; inter- nal resistance of cells, 97. Resultant, of parallel forces, 11; of concurrent forces. Saturation, 32. Solidification of acetamide, 62. Sonometer, 111. Specific heat, 55. Specific induction capacity, 79. Spectra, bright-line, 126. Speed of sound, 107. Spring balance, 11. Static electricity, 74. Steel spheres, density of, 8. Storage battery, 100. Telescope, astronomical, 122. Temperature of white-hot body, 58. Thermometer, fixed points of, 68. Total reflection, 116, 127. Tubes for Boyle's law, 27. Vernier caliper, 4. Vibrating strings, 111. Vibration of a fork, rate of, 111. Voltaic cell, 79. Voltmeter, 88, 90, 101. Wave length produced by tuning fork, 110. Weighing, method of substitution, 6; usual method, 7. Wheatstone's bridge, 94. l.f "hi \E-UNIVER% j^UIBRARYQ^ ^HIBRABY^ 5 /"~*i \ < ^ ^ajAiNdmv 5 o sr I S 5 I tf*% .AttE-raivrar/^ ft $\~r$ 27 ^AavaaiH^ %MAIfJ(MV N C, ^E-UNIVERS/A ^ I* *^p^ fe %i3wsn^^ ^\\E-UNIVER%