MILLIKAN - GALE - BISHOP EDUCATION DEPT. A FIRST COURSE IN ;; ; LABORATORY PHYSICS FOR SECONDARY SCHOOLS BY ROBERT ANDREWS MILLIKAN, PH.D., Sc.D. DIRECTOR OF THE NORMAN BRIDGE LABORATORY OF PHYSICS, PASADENA, CALIFORNIA HENRY GORDON GALE, PH.D. EDWIN SHERWOOD BISHOP, PH.D. FORMERLY INSTRUCTOR OF PHYSICS IN THE SCHOOL OF EDUCATION AT THE UNIVERSITY OF CHICAGO G1NN AND COMPANY BOSTON NEW YORK CHICAGO LONDON ATLANTA DALLAS COLUMBUS SAN FRANCISCO .->' : ; ;..;* , , "r -;\* , ,f i .ic N* * 8 *; ;:^s,".' acs? COPYRIGHT, 1914, BY EGBERT A. MILLIKAN, HENRY G. GALE AND EDWIN S. BISHOP ALL RIGHTS RESERVED 523.9 Qt EDUCATION gtbtnatum GINN AND COMPANY PRO- PRIETORS BOSTON U.S.*. PREFACE This course of about fifty laboratory exercises represents an endeavor to bring beginning students of physics into direct first-hand contact with the most significant of the principles of the subject and with their applications to daily life. Since the precise method of accomplishing this end will depend upon the sort of laboratory equip- ment which is available, the course has been given considerable flexibility by introducing alternative experiments. Thus, if gas is not accessible the student will omit Exp. 5, but will get exactly the same principle through performing Exp. 5 A. Or, if the laboratory is not equipped with commercial ammeters and voltmeters, Exp. 31 will be omitted and Exp. 31 A performed. Similar choices will be found indicated throughout the text. Another feature of the course is that the experiments do not presuppose any previous study of the subject involved, or any antecedent knowledge of physics. The laboratory work may be kept in advance of the classroom 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 their experiments before entering the laboratory, for each experiment has been arranged to carry with it its own introduction. Problems on the practical transformations of energy have been given the important place in this course which they merit, and it is hoped that an advance has been made in the way in which they are treated. Thus, in comparing the efficiencies of two different appliances which accomplish the same result, as, for example, an electric stove and a gas stove, the f^ct has often been overlooked that in daily life people are interested in efficiency only as it affects cost of operation. The emphasis has here been thrown, therefore, on the real test of efficiency from the consumer's standpoint, namely the relative cost of a given output rather than on the mere ratio of energy output to energy input. In order to instil in the pupil the habit of orderliness and to teach him to collect and organize related data in such a way as to draw conclusions from it, a form of record has been placed at the end of most of the experiments. This procedure also enables the teacher to check up the experiments with a minimum expenditure of tune and energy. In the- t case of qualitative work the Record of Experiment has, as a rule, been omitted. For the benefit of those who use both this book and the classroom text entitled " A First Course in Physics," 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 impor- tance 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 additions with this schedule in mind. Otherwise it almost invariably happens that the subjects treated in the first half of the text receive a dispropor- tionate amount of time. The initial cost of equipment for satisfactorily conducting this course with classes of say twelve pupils need not exceed two or three hundred dollars. If commercial electrical instruments are employed, however, the cost may of course reach a much higher figure. R. A. M. H. G. G. E. S. B. [iii] fiK ,,:, CONTENTS EXPERIMENT DATE ASSIGNED DATE APPROVED 1. Determination of TT 2. Volume of a Cylinder 3. Density of Steel Spheres .... 4. Pressure within a Liquid .... 5. Pressure in Gas Mains 5 A. Lung-Pressure 6. Archimedes' Principle 7. Density of Liquids 8. Density of a Solid Lighter than Water 9. Boyle's Law 9 A. Weight of Air 10. Molecular Constitution of Matter . . 10 A. Evaporation and Dew-Point . . . 11. Resultant of Two Forces 12. The Pendulum 13. Hooke's Law 14. Charles's Law 14 A. Gay-Lussac's Law 15. Expansion of Brass 16. Principle of Moments 17. The Inclined Plane 17 A. The Use of Pulleys 18. Heat of Combustion of Gas .... 18 A. Efficiency of a Gas Stove .... 19. Specific Heat 20. The Mechanical Equivalent of Heat . 21. Cooling through Change of State . 22. Heat of Fusion of Ice 23. Boiling Point of Alcohol 24. Effect of Pressure on the Boiling Point 25. Magnetic Fields EXPERIMENT DATE ASSIGNED DATE APPROVED 26. Molecular Nature of Magnetism 27. Static Electrical Effects 28. The Voltaic Cell 28 A. The Voltaic Cell 29. Magnetic Effect of a Current 30. Properties and Applications of the Electromagnet 31. Electromotive Forces 31 A. Electromotive Forces 32. Laws of Resistance 32 A. Wheatstone's Bridge 33. Internal Resistance 34. Efficiency of Lamps 34 A. Heating Effects of the Electric Current 35. Electrolysis and the Storage Battery 36. Induced Currents 37. Power and Efficiency of Motors 37 A. Principles of the Motor and the Dynamo 38. Speed of Sound in Air 39. Frequency of a Tuning Fork 40. Wave Length of a Note 41. Laws of Vibrating Strings 42. Plane Mirrors 43. Index of Refraction 44. Critical Angle of Glass 45. Concave Mirrors 46. Convex Lenses 47. Magnifying Power of a Convex Lens 48. The Astronomical Telescope 49. The Compound Microscope 50. Prisms and Spectra 51. Photometry 51 A. Photometry Appendix A ' Appendix B [vi] LABORATORY PHYSICS EXPERIMENT 1 FIG. 1 TO DETERMINE H, THE RATIO OF THE CIRCUMFERENCE OF A CIRCLE TO ITS DIAMETER I. Measurements, (a) Measurement of circumference. Scratch a fine line A along a radius of an accurately turned disk. Place A accurately above some division B on the meter stick (Fig. 1), and roll the disk between the thumb and finger until A is again in contact with the meter stick. Record the positions of A in centimeters, by noting first the whole number of centimeters, then the number of millimeters in the tenths place, and lastly the estimated tenths of a millimeter in the hundredths place.* The circumference is the difference between this reading and the start- ing point. Starting at different marks on the scale, repeat four times and take the average of the five trials as the circumference. (6) Measurement of diameter. Lay the disk flat on the table. Place the meter stick on edge (Fig. 2) so that the centimeter face is along a diameter and so that some centimeter division coincides with one edge of the disk. Record the diameter, estimating tenths of a millimeter. Repeat four times, measuring different diameters, and take the average of the five trials as the diameter. II. Computation, (a) The last figure of each measurement was estimated and therefore uncertain. (5) Retain one more uncertain figure in the average than in the in- dividual measurements. (c) After every multiplication or division retain the same number of significant figures in the product or quotient that there are in that factor which has the smallest number of significant figures. The numbers 583, .409, 1.03, .00110 hare three significant figures each. Thus, ciphers before a number in a decimal fraction less than one are not significant figures. (rf) Keeping in mind what has been said about significant figures, compute TT from your mean values of the circumference and the diameter. * Unf amiliarity 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 .5, or 1/2 ; .2 a little less and .3 a little more than .25, or 1/4 ; .1 a little less than .2, or 1/5, etc. [1] Correct method of using meter stick FIG. 2 Incorrect method of using meter stick EXPERIMENT 1 (Continued) III. Per cent of error. The per cent of error in any product or quotient can best be illustrated by an example. If in the measurements - rr-r =2000 an error of were made in the 200, 202 x 1005 4- .5% in the 1000, and - .5% in the 100, the result would be -- ^-= -- = 2040 +. Thus we see that yy.o the result 2040 is 40, or 2%, larger than the true value 2000. We also see that in this case the errors 1%, .5%, and .5% added together produce a total error of 2%. Thus, to find the error of any experimental result which is obtained by taking the product or quotient of several physical measurements, add the per cents of error in each of the factors entering into such product or quotient, and the sum of these will be the per cent of error allowable in the final result. To find the per cent of error in any one of the factors, find what per cent the probable error in measuring that quantity is of the quantity itself. Answer in your notebook the questions which appear at the end of the experiment. Questions, a. What per cent of error would have been introduced into the diameter by an error of .01 cm. ? b. What per cent of error would have been introduced into the circumference by an error of .02 cm. ? c. Your value of TT might reasonably be in error by the sum of these two errors. State, therefore, whether your result is as accurate as reasonably careful measurements would give. RECORD OF EXPERIMENT TRIAL DlAMKTEB IN CM. CIRCUMFERENCE IN CM. 1 2 3 4 5 Mean = Mean = circumference diameter Correct value = 3.1416 Difference, or error = f*rrf Per cent of error = a 1% error .0314 [2] EXPERIMENT 2 HOW TO FIND THE VOLUME OF A CYLINDER I. By computation from linear measurements, (a) Measurements. With a meter stick measure to tenths of a millimeter three different depths of the cylindrical vessel shown in Fig. 8. Measure the inside diameter D as in Exp. 1 (see Fig. 2). Take the above measurements with a vernier caliper,* if available. 2 (5) Computation. Volume of cylinder = area of base x depth, or volume = L = irR^L where R is the radius and L is the depth. Before computing read carefully Exp. 1, II. In this experiment make all computations a part of the final record. Questions, a. If the measured diameter of a circle is 10.1 cm., and the true diameter is 10 cm., what will be the per cent of error in the area of the circle ? b. What per cent of error will be introduced 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 ? c. Allowing .01 cm. error in the mean values of D and L, find the per cent of error in the volume. II. By weight of water contained by cylinder, (a) Weighing cylinder by method of substitution. Place the empty cylinder with its ground-glass cover on the pan B (Fig. 3) of the balance and add to pan A any convenient objects, such as pieces of iron, shot, and bits of paper, until the pointer stands opposite the middle mark at s, the rider R being at zero. Then replace the cylinder and its 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 finding 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 8. 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 tenths of a division we can obtain the weight by this method to hundredths of a gram. * 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. 4). The object to be measured is placed between the jaws EF, e f which are so made that when they are in con- tact the zero of the sliding scale is opposite the zero of the fixed scale. Ten divisions of the slid- ing scale AB are made equal to nine divisions, that is, 9 mm., on the main scale CD ; hence one vernier division is equal to .9 mm. Fig. 5 (1) shows the vernier scale and the fixed scale enlarged. Here the zero of the vernier is ex- actly opposite the 5-mm. mark of the fixed scale, this being the relative position of the two scales when an object 5 mm. in diameter is placed between the jaws. Since one division on AB is equal to only .9mm., while one divi- sion on CD is equal to a whole millimeter, 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. be- hind 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, [3] FIG. 3 EXPERIMENT 2 (Continued) This method of substitution is the rigorously correct method of making a weighing. (6) Weighing cylinder by usual method. Remove the weights from pan J5, keeping all of these weights together for this weighing also. Empty pan A, move R to its zero point, and bring the pointer to the middle mark by altering, if necessary, the nut n (Fig. 3). Then place the object on pan A and the weights used in (a) on pan B and again bring the pointer to the middle mark by using the rider R as before. Unless the difference in the two weighings is larger than one or two tenths of a gram, you may henceforth use the second, or usual,* method of weighing ; for the imperfections in inexpen- sive commercial weights, such as we are using, are likely to amount to as much as a tenth of a gram. It was for this reason that precisely the same weights were used in both (a) and (5). (c) Weighing cylinder full of water. Next fill the cylinder with water and place the cover over it, taking care that no air bubbles are left inside. Carefully wipe all moisture from the outside and weigh. Refill the cylinder and repeat this last weighing in order to see how closely two observations can be made to agree. From the mean of these two weighings and the mean of the weighings of the empty cylinder and cover find the weight of the water. Since 1 cc. of water weighs 1 g., volume in cubic centimeters equals weight of contained water in grams. Questions, a. What per cent of error would an error of .2 g. in the weight of the water alone introduce into your last measurement of the volume ? b. Is your per cent of difference in I and II greater or less than the sum of the errors mentioned in I, Question c, and in II, Question a? c. Do your results in I and II agree as well as they should ? RECORD OF EXPERIMENT First Observation Second Observation Third Observation Mean I. Depth of cylinder =..... cm cm cm cm. Inner diameter of cylinder = cm cm cm cm. Volume = ^ L = TrR*L = cc. By Substitution By Usual Method Mean II. Weight of empty cylinder and cover = g. g. g. Weight of cylinder + water, first trial = g. Weight of cylinder + water, second trial = g. g. Weight of water alone = g. .-. volume of cylinder = cc. Per cent of difference between I and II = difference _ 1% of either result its zero mark would move up .1 mm. beyond 6. 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 AB is directly opposite a mark on CD, in order to know how many tenths of a mil- (1) (2) limeter the zero mark of AB has moved beyond Co i t 3 5 ? a 9 K> n a * a it D Co _> t > * s ? g 9 .0 .. <; n D the last division passed on CD. Thus the reading I I I I JJ I I I 1. 1. 1. 1. I 1 1 1 1 1 in Fig. 5 (2) is 3.7 mm. (.37 cm.), since the zero f , _, mark of the vernier has passed the 3-mm. mark " on the fixed scale CD, and the 7 mark on the ^ IG ' 5 vernier is directly opposite some mark of CD. * The usual method would be as correct as the method of substitution, provided we could know that the two balance arms are of exactly the same length (see Principle of Moments, p. 41). If, therefore, you get different results by this method and the method of substitution, you may know that the instrument maker did not succeed in getting the balance arms quite equal in length. Errors due to this cause are, however, usually very slight. [4] EXPERIMENT 3 FIG. 6 HOW TO FIND THE DENSITY OF STEEL SPHERES I. From weights and diameters of spheres, (a) Diameters of spheres. Measure the diameters of several steel spheres with the micrometer caliper,* if this instrument is available. If not, the diameters may be obtained by placing the balls between two blocks, as in- dicated in Fig. 6, and measuring the distance between the blocks. If this method is used, however, it will be better to place six or eight balls in a row between two meter sticks, set the blocks at the ends of the row, and divide the distance between the blocks by the number of balls. It will be best to use balls about 2 cm. in diameter. Take the mean of five or, better, ten diameter measurements. Compute the volume of a sphere from the relation V \ 7rJ> 8 , where V represents the volume and D the diameter. Remember that you are to 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 quotient. The following illustrates the method of computation : D = 1.9053 cm. JD? = 3.6302 7) 8 = 6.9166 1.9053 57159 95265 171477 19053 D^ 3.6302 /. volume = 3.6215 cc. 1.9053 108906 181510 326718 36302 = 6.9166 5= .5236 D 414996 207498 138332 345830 3.6215 () Weight of balls. Weigh together on the balances all the balls measured. Compute the density of steel ; that is, the number of grams in 1 cc. 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 balance. 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. * In the micrometer caliper (Fig. 7) the divisions upon the scale c correspond to the distance between the threads of the screw s. This distance is usually a half millimeter. Hence turning the milled head h through one complete revolution changes the distance between the jaws ab by exactly one-half millimeter, and turning h through one fiftieth of a revolution changes the distance between 06 by ^ x \ - = .01 mm. If, then, there are fifty divisions upon the circumference of d, each divi- . . sion represents a separation of .01 mm. of 6 from a. * To make a measurement, turn up the milled head h (Fig. 7) until the jaws 06 are in contact, that is, until the milled head, held with light pressure between the thumb and finger, will slip between the fingers instead of rotat- ing further. 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 number of hundredths of a millimeter registered upon d. This is the thickness of the object. [5] FIG. 7 EXPERIMENT 3 (Continued) 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 of the displaced water, and this is, of course, the same as the volume of the balls. Take the weight of the balls alone from I and compute the density of steel. Find the per cent of difference between this value and that obtained in I. Questions. An error of .005 mm. in the mean diameter of the balls (see illustration in I) would introduce an error into the diameter of '-r^ %, or .026%, and into the volume (^lA of 3 x .026%, or .078%. FIG. 8 An error of .2 g. in the weight of the water displaced by ten balls would introduce an error into the 2 weight of the displaced water, and therefore into the determination of their volume of -^ %, or .56%. .00 a. Using your own data and allowing the same errors as above, compute the per cent of error in deter- mining the volume of the balls by both methods. Which method is the more accurate ? b. How could you find the volume of the ten balls with a graduate ? c. Would this method (by use of the graduate) be as accurate as the method of displacement of water in II ? Give reason for your answer. RECORD OF EXPERIMENT I. BALL DIAMETER IN MM. BALL DIAMETER IN MM. 1 6 2 7 3 8 4 9 5 10 Volume of 1 ball = \ *D S = cc. Weight of 10 balls = g. .-. weight of 1 ball = g. .. density of steel = g. per cc. Mean Diameter = mm. = cm. II. Weight of 10 balls + cylinder full of water Weight of 10 balls in cylinder full of water Weight of water displaced by balls .-. volume of 10 balls Weight of 10 balls alone from I .-. density of steel Per cent of difference between two values of density given above = difference 1% of either value g- g- cc. g- . g. per cc. [6] EXPERIMENT 4 HOW PRESSURE BENEATH THE FREE SURFACE OF A LIQUID VARIES WITH DEPTH I. Verification of the law of depths and densities, (a) Measurements in water. Immerse the manom- eter M of Fig. 9 to the greatest depth possible in the long glass vessel V filled with water.* A length of at least 1 m. is desirable (see tube of Exp. 40). Record the surface reading where the level of the liquid touches the meter stick. (Read where the level strikes the meter stick and not the point up to which the water laps upon the K ~ meter stick.) Then record the level of the mercury both in the open arm of the manometer and in the arm against which the liquid pressure acts. (In the last two readings be careful to hold the eye so that the line of sight is at right angles to the meter stick, then take the reading at the top of the curved mercury meniscus, estimating the reading to tenths of a milli- meter.) Evidently the depth is the difference between the first and third readings, and the pressure in centimeters of mercury is the difference between the second and third readings. Raise the manometer about 10 cm. and make similar measurements. Continue in this way, raising the manometer about 10 cm. at a time, until a depth of 10 or 15 cm. is reached. (6) Measurements in gasoline. Fill the vessel V with gasoline instead of with water and make a similar set of observations for gasoline. II. Algebraic or analytic representation of a direct proportion. From your data it will be seen that within the experimental error the result obtained, for any liquid, by dividing the depth H by the pressure P is always the same, or, stated algebraically, rr etc., or = constant. FIG. 9 H Hence in the equation = constant, if // is made 2, 3, 4, etc. times as great, P will also be 2, 3, 4. H v " etc. times as large, since their ratio remains unchanged. Whenever two quantities, such as H and P above, vary in such a way that doubling one doubles the other, trebling one trebles the other, etc., the one is said to be directly propor- tional to the other, or to vary directly with the other. The first equation for a direct proportion may also be stated -p TT T> TT by = - = - etc., or again by P oc H, where oc is read P 2 H 2 P S H S " is proportional to." III. Graphical representation of a direct proportion. That 10 the pressure in any liquid is directly proportional to the depth g is shown graphically by Fig. 10. The curve, or " graph," for a direct proportion is seen to be a straight line. On a sheet of coordinate paper plot your own data. Choose a scale along OX, that is, to the right of the origin 0, so that the greatest depth will come near the right side of the page. (For example, the greatest depth plotted in Fig. 10 was 60 cm. in gasoline.) Choose a different scale along Y, that is, above the origin, so that the greatest pressure will come at least halfway to * A piece of glass tubing about 1 m. long and 4 or 5 cm. in diameter, closed at the bottom with a rubber stopper, answers the purpose admirably. Use ^-in. tubing for manometer. Support at 10 cm. intervals with knitting needle K. m aao tH O 22.5 | 2 - 1 A o a 1.5 10 20 C 30 40 50 Depths in centimeters FIG. 10 60 70 EXPERIMENT 4 (Continued) the top of the sheet of paper. In general, choose the scale in each case so that the greatest distance along OX (abscissa) and the greatest distance along Y (ordinate) are roughly of the same magnitude. Then a single point will represent a set of readings for a given depth, the distance the point is to the right of representing the depth, and the distance it is above representing the pressure. Having plotted all of these points for the set of data on water, with a sharp pencil and straightedge draw a line through which passes as close as possible to all of the plotted points, leaving half the points on either side of the line in case the line does not pass through all of them. This is a graphical way of averaging. Questions, a. Why must the straight line be drawn through 0, the origin ? b. Using the same scale, plot the readings for gasoline on the same sheet of coordinate paper, and draw the graph showing the relation between depth and pressure in gasoline. c. From your graph find (a) the pressure in centimeters of mercury at a depth of 40 or 50 cm. in gaso- line, (&) at the same depth in water. Divide the pressure thus obtained for gasoline by that for water at the same depth. This result gives the density of gasoline, which is about .74. Why ? d. The density of mercury is 13.6. How would the pressure in mercury compare with the pressure in water at the same depth ? e. How would the height of a column of water compare with the height of a column of mercury which produced the same pressure ? /. How would the height of a column cf gasoline compare with the height of a column of mercury which produced the same pressure ? g. Compare your answers to the last two questions with the results obtained by dividing depth by pres- sure in both cases. (See data.) h. How does the pressure at the water taps vary on going from the basement to the second floor of your house ? i. Which of these locations would be the better for the installation of a water motor ? RECORD OF EXPERIMENT (Record the readings in centimeters, estimating tenths of a millimeter) WATER SURFACE READING OPEN AKM OF MANOMETER LOWER ABM OF MANOMETER DEPTH PRESSURE IN CM. OF MERCURY DEPTH PRESSURE GASOLINE [8] EXPERIMENT 5 WHAT IS THE PRESSURE OF THE GAS IN YOUR CITY GAS MAINS ? A D About 50 or 60 cm, About 20cm, v FIG. 11 I. Density of gasoline used in manometer, (a) By specific-gravity bottle. Weigh any glass-stoppered bottle of about 200 cc. capacity (or, instead, a specific-gravity bottle). Fill with water and weigh. Rinse with a little gasoline, then fill with gasoline and weigh. Divide the weight of the gasoline alone by the weight of the water alone to get the specific gravity of gasoline ; that is, the ratio of the weight of gasoline to the weight of an equal volume of water. This is numerically equal to the density of gasoline in grams per cubic centimeter, since 1 cc. of water weighs 1 g. (b) By balancing columns. Bend a piece of glass tubing from 5 to 10 mm. in diameter and about 2 m. long, as shown in Fig. 11. Pour gasoline into the left arm to a depth of 10 or 15 cm. Then pour water into the right arm until the level at C is 3 or 4 cm. below the bend at E. Then pour gasoline again into the left arm until the level at B is 3 or 4 cm. below the bend at K Repeat these operations until the left tube is nearly filled with gasoline. (It is unnecessary to have any two of the surfaces at the same level when ready for use.) The pressure on the confined air in the bend E is equal to the pressure due to the column of gasoline AB + atmospheric pressure and is also equal to the pressure due to the column of watei* CD -f- atmospheric pressure. Hence the pressure due to the column AB equals the pressure due to the column (7D, or AB . d g = CD d u = CD . 1 where d g and d w refer to the densities of gasoline and water respectively. With a meter stick measure AB and CD and compute the density of gasoline. II. Measurement of pressure in gas mains. With a Y or T connector attach the manometers of Fig. 12 to a gas cock. Open the gas cock, and with a meter stick measure the height of A, , C, and D above the table. Then, as before, p = AB.d g =CD.d w where p is the pressure in grams per square centimeter in the gas mains in excess of atmospheric pressure. Using the average of the density of gasoline as found in I, (a) and I, (5), compute the pressure in the gas mains as given by each manometer. Questions, a. If, in the apparatus of Fig. 11, mercury were used in the left-hand arm in place of gaso- line, how would the vertical distance DC compare with the vertical distance AB ? b. If the manometer tubes of Fig. 12 had had different diameters, would the result have been different ? State reasons. c. Gas plants use water manometers at distributing stations, and in this country the pressure is usually read in inches of water. What is meant then by a gas pressure of 7 in. ? FIG. 12 EXPERIMENT 5 (Continued) RECORD OF EXPERIMENT I. Density of gasoline (a) Weight of bottle Weight of bottle + water Weight of bottle + gasoline .. weight of water alone .-. weight of gasoline alone .-. density of gasoline (&) From table to A From table to B From table to C From table to D .-. density of gasoline .-. average density in (a) and (b) = II. Pressure in gas mains Gasoline Manometer From table to A = cm. From table to B = cm. .-. AB = cm. .-. p = AB = ...cc L at atmospheric pressure J (c?) Length of laboratory = m., width = m., height = in. .-. volume = cu. m. (e) Temperature of room = C., or F., barometer reading = cm. Weight of 1 cc. of air (density) = , weight of 1 liter of air = g. Weight of 1 cu. m. of air = kg. Weight of air in laboratory = kg. = Ib. From question b density = g. per cc. Per cent of difference = From question c density = g. per cc. * On account of the very considerable work involved in preparing a large number of air-tight bottles for this experiment and drying them after use before they are in readiness for another section, unless an ample number of spheres with good stopcocks are available, the authors would suggest that this experiment be performed but once, by the teacher and class together, rather than by each pupil. t A hollow metal sphere with stopcock may be used without the tubing. All joints in either case should be made air- tight with vaseline, and the volume of the bottle or sphere should have been previously determined and marked upon it. [21] EXPERIMENT 10 THE MOLECULAR CONSTITUTION OF MATTER (a) Fill a long, narrow test tube or, better, the hydrometer tube of Fig. 15 about half full of water. (5) Then, to prevent mixing, incline the tube as much as possible while you carefully pour in alcohol till the tube is filled. If the alcohol has been poured into the tube with sufficient care, you should be able to observe a distinct surface of demarcation separating the two liquids. ( ~ P = = J . Accepted value = .00367 = ,| ff . Per cent of error = [36] EXPERIMENT 14 A THE VOLUME COEFFICIENT OF EXPANSION OF A GAS (GAY-LUSSAC'S LAW) Gay-Lussac found that when a confined body of gas is kept under constant pressure and heated, its volume increased at the same rate at which its pressure increased when the volume was kept constant (see Exp. 14). 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 C. is called the volume coefficient of expansion ; that is, if V and V represent the volumes at 100 C. and C. respectively, then the volume coefficient c is given by the equation c = V I ' 100 r 100 v This coefficient may be defined as the expansion at 0. per cubic centimeter per degree. It should be the same as the pressure coefficient discussed above. To find it experimentally, let a thread of dry air about 20-25 cm. long be con- fined by a mercury index 2 or 3 cm. long in a piece of barometer tubing which is sealed at one end and is about 40 cm. long.* (See Fig. 30.) First measure carefully and record the length BC of the mercury index and the total length AD of the bore, allowing as best you can for the fact that the bore is not quite uniform very near the closed end. 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, when the index remains constant, measure from A to the top B of the index. Remove the tube and push it through the hole in the cork which closes the steam generator of Figs. 31 and 41. 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 A 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 V Q . From the first three readings find the length of the thread of air at C. and call it V Q . Compute c from your data. Questions, a. Is your error larger than would be accounted for by an error of, say, .5 mm. in measuring V m F ? If so, it is probable either that the bore is not uniform or that the confined air is not thoroughly dry. b. Show from the results of this experiment that when a gas is heated at constant pressure the volume is directly proportional to the absolute temperature ; that is, F! fj 4- 273 7\ FIG. 30 c. If Exp. 9 (Boyle's law) was performed at 20 C., what would have been the value of the constant PV had the experiment been performed at 25 C.? * To make such tubes, take barometer tubing of about 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. Seal one end quickly in a Bun- sen burner, and with a capillary funnel introduce the thread of mercury BC. Attach the cotton- and calcium chloride-tube to keep the inside of the tube dry, and the tube should work satisfactorily for months. If the drying tube is not used, moisture will work past the mercury thread as it moves back and forth. [37] EXPERIMENT 14 A (Continued) RECORD OF EXPERIMENT Length of index, EC = cm. Length of bore, AD cm. From A to index at 0C., AB = cm. From A to index at 100 C., ^4-B 100 = ... % cm. ^100 ~ 1 r o = AB AB 100 = cm. F = AD - (AB + BC) = cm. C = v> ~ T = ... ... = . Accepted value = .00367 = ,.1*. Per cent of error = 100 V n *' J [38] EXPERIMENT 15 COEFFICIENT OF EXPANSION OF BKASS The linear coefficient of expansion of a solid is equal to that fractional part of its length which it increases when heated 1 C. The coefficient of expansion of brass is .0000187; this means that a foot of brass rod will increase .0000187 ft. in length when heated 1 C., or that 1 cm. will increase .0000187 cm. in length when heated 1 C., etc. Thus, if / 2 represents the length at a temperature t^ and ^ at a temperature t f the increase in length per degree is > and the fractional part which this is of the length is the linear coefficient of 2~ 1 expansion k. Thus, 7. __ A shallow transverse groove is filed at some point c (Fig. 31) near one end of a piece of brass tubing oc about a meter long and a centimeter in diameter. Place this tube upon two wooden blocks A and B so that the groove rests upon a sharp metal edge attached to A while the 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 a pointer p about 20 cm. long is attached by means of seal- ing wax. When the brass tube oe 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 oc, as in the fig- FlG 31 ure, to a steam boiler containing at first only cold water. Then insert a thermometer into the open end o of the brass tube oc. Give the thermometer three or four minutes to take up the temperature of the tube ; then read and record, and replace it in o. Measure with a meter stick the distance between the knife-edge c and the middle of the rod b. all this length 7^ Record the position of the tip of the pointer upon the mirror scale , estimating very carefully to nths of a millimeter. Call this reading S^ 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. Nevertheless it is generally advisable before beginning the experiment to roll up a paper tube about 1 cm. in diameter, and to slip it over the tube between c and b 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 s. Call this reading S 2 . Take the reading of the thermometer as it lies in the tube surrounded by the steam escaping from - 38 their temperatures become about 95 C. to 100 C. (/) Let each student now read the temperature, on the same thermometer, of the cold water pre- pared by A, when it is about 9 C. or 10 C. below room temperature, see that all dew on the inner calorimeter, if any formed, is wiped off, record the temperature ot the cold water and that of the shot, estimating tenths of a degree, and quickly pour the lead shot from the dipper into his calorimeter. Stir the mixture two minutes and record the temperature of the mixture, carefully estimating tenths of a degree. (<7) In the same way as in (/) the three students should take the data with the materials prepared by B and C, in each of these cases as before having the cold water 9 C. or 10 C. below room tempera- ture just before pouring the hot metal into the calorimeter. Now spread out the metals used on cloths to dry. (A) If we let S m represent the number of calories of heat given up by 1 g. of metal in cooling 1 C., that is, its specific heat, then in cooling from the temperature of the metal, m , to the tempera- ture of the mixture, ? mix , 1 g. of the metal would give up (t m t mix ) S m calories ; and the total mass of the metal, Jf TO , would give up M m (t m t mix ) S m calories. This must equal the heat received by the water and calorimeter according to the law of mixtures. (Heat lost by the body or bodies cooled = heat gained by the body or bodies warmed.) We nave Calories out of Metal Calories into Water Calories into Calorimeter* JC O, - *.i*) ^m = M* On* -<)! + M c (t^ - Q .095, where the subscript m refers to the metal used, " mix " to mixture, c to calorimeter, and w to water alone. (f) Write out the numerical equation for each metal used and solve it for S m . Explain what each part of the equation represents. State in your notebook what you understand to be represented by the quantity S m which you have found, t * Take the specific heat of the calorimeter as .095. t A further very interesting experiment which may be inserted for the benefit of those who have time and inclination for extra work is the following : To find the temperature of a white-hot body. By means of a thin copper wire suspend from a support placed from 50 cm. to [51] EXPERIMENT 19 (Continued) When the shot and the water were mixed, the changes in the temperature of each took place very rapidly at first, but very slowly as the temperature of each approached the final value. Can you see a reason, therefore, why it was advisable to choose the conditions so that the final temperature should be close to the temperature of the room ? Remember in your answer that it was necessary to wait two or three minutes for the mixture to reach its final temperature, and that a body which is hotter than the room is always losing heat to the room, while one which is colder than the room is always gaining heat from it. It is these losses of heat by radiation which constitute the greatest difficulty in the way of accurate measurements by the method of mixtures. RECORD OF EXPERIMENT METAL WEIGHT OF METAL Mm TEMPERA- TURE OF METAL tm WEIGHT OF WATER Mm TEMPERA- TURE OF WATER (. TEMPERA- TURE OF MIXTURE tmil WEIGHT OF CALO- RIMETER M c EXPERI- MENTAL VALUE OF S m ACCEPTED VALUE OF Sm PER CENT OF ERROR Lead Iron Aluminum Equation for lead : Equation for iron : Equation for aluminum : 100 cm. above the table a piece of copper rod about 2 cm. long and 12 mm. in diameter. Adjust the length of the suspension BO that the copper hangs in the hottest part of a Bunsen flame (just above the inner cone). Weigh a calorimeter of 300 cc. capacity ; then fill it about half full of water whose temperature has been reduced 12 C. or 16 C. below that of the room, and weigh again. Then replace it in its jacket. After the copper has been heating for about ten minutes take the temperature of the water veiy carefully (it should now be from 8 to 10 below the temperature of the room) ; then, all in the same second, remove the flame and lift the calorimeter so as to bring the white-hot copper to the bottom of the vessel of water. Stir the water thoroughly for one or two minutes ; then take the final temperature. Weigh the copper rod and with it as much of the copper wire as was immersed. Assuming that 0.95 calories (the specific heat of copper) came out of each gram of copper for each degree of fall in its temperature, calculate what was the temperature of the white-hot copper. Duplicate conditions as nearly as possible and see how closely two observations will agree. [52] EXPERIMENT 20 FIG. 39 THE MECHANICAL EQUIVALENT OF HEAT The object of this experiment is to show that when a falling body strikes the earth, the kinetic energy of the moving mass is transformed into the energy of molecular vibrations, that is, into heat, and to find how many gram meters of mechanical energy must disappear in order to produce 1 calorie of heat. This quantity is called the mechanical equivalent of heat. It is obtained by finding the rise in the temperature of shot when it falls through a known height. Pour about 2 kg. of dry shot into a metal vessel and set it in a cool place, for example, in a bath of ice water, until its temperature is 5 C. or 6 C. below that of the room. Pour this shot into a paper tube (Fig. 39) about a meter long and 5 or 6 cm. in diameter, made by rolling up a large number of turns of heavy brown paper and then securing them with glue and string. The tube should be closed with two tightly fitting corks. Mix the shot very thoroughly by shaking the tube and by slowly inclining it so that the shot will run from end to end. In so doing, however, grasp the tube near the middle rather than at the ends, for it is desirable that the temperature of the ends be not influenced by the heat of the hands* After inverting the tube in this way from five to ten times, remove the upper cork A and insert cork C (Fig. 39), through which passes a thermometer ; then gradually incline the tube until all the shot has run down to the thermometer end and there completely surrounds the bulb. Holding the tube inclined as in the figure, twist the thermometer around in the shot for about two minutes and then take the temperature. If this is more than 2 C. or 3 C. below the temperature of the room, continue the shaking and rolling of the shot from one end to the other until its temperature has risen to within about 3 C. of that of the room. Record this temperature, quickly replace cork C by cork A, hold the tube upright, as in the figure, and turn it end for end, say, seventy times in rapid succession, placing the lower end on the table at each reversal, so that the falling shot may not force out the corks. At each reversal the potential energy acquired by the shot in being lifted the length of the tube is converted into kinetic energy in the descent, and this kinetic energy is all transformed into heat energy at the bottom. On account of the poor conductivity of cork and paper practically all of this heat goes into the shot and but an insignificant portion of it into the corks and the tube. After the seventy reversals very quickly replace cork A by cork C and take as before the final temperature of the shot. Remove cork (7, set the tube on end, and measure the distance from the top of the shot to the position which was occupied by the bottom of cork A. This is the mean height through which the shot has fallen at each reversal. The total number of gram meters of work which have been transformed into heat is the weight W of the shot X the height h of fall (expressed in meters) X 70. The number of calories of heat developed is the weight of the shot W x its specific heat (.0315) X the rise in temperature (t z t^). Hence, if J represents the number of gram meters of energy in a calorie, we have J- Wx ( 2 -Q X. 0315 = 70 W- h. 70 h T53] EXPERIMENT 20 (Continued) 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 mak- ing the initial temperature 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. 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 gaining or losing heat by conduction and radiation, so the temperature indicated may not be quite the mean temperature of the shot. This source of error is unavoidable. Questions, a. Why did we attempt to have the initial temperature as far below the temperature of the room as the final temperature was above it ? 6. If iron shot had been used instead of lead shot, would the rise in temperature be more or less than it was with lead shot ? c. Why is lead better for this experiment than any of the other metals ? RECORD OF EXPERIMENT Illustrative data taken by a student. First Trial Second Trial Third Trial Temperature of room = 18.5 C. 18.5 C. 18.5 C. Mean value = 437 g. m. Initial temperature = 16.0 C. 17.1 C. 16.7 C. Final temperature = 21.7 C. 22.6 C. 21.0 C. Accepted value = 427 g. m. Number of reversals = 100 100 80 % Height of fall (A) = .76 m. .76 m. .76 m. Mechanical equivalent = 423 g. m. 439 g. m. 449 g. m. Per cent of error = 2.4. NOTE. The error in this experiment, even with careful work, may sometimes be as high as 10%. 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, that is, changes back to the crystalline form, heat energy is given up to the surroundings. Support vertically in a burette holder or other clamp a test tube in which enough loose crystals of acetamide have been placed to fill it about a third full. Then heat gently with a Bunsen burner until the crystals are all melted.* Slowly insert a thermometer 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 tempera- ture 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 two or three minutes more and decide whether or not the temperature 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 thermome- ter. Record the temperature every half minute as the substance cools from about 100 C. to 45 C. Plot these observations in the manner shown in Fig. 40, temperatures being represented by vertical distances and times by horizontal distances. 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 11 : 19.5 the temperature fell rapidly from 100 C. to 71.8 C., that it then rose suddenly to 79 C., remained there five minutes, and then fell slowly during the next twenty minutes from 79 C. to 43.5 C. 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 undercooling exhibited here by the acetamide ; that is, its temperature will fall a little below the freezing point before crystallization gets started. It will then rise suddenly to the freezing point and remain there until crystallization is practically complete. Why ? ins * If the acetamide has absorbed much moisture, boil it. [55] EXPERIMENT 21 (Continued) If time permits, dip a test tube containing a little distilled water into a freezing mixture of salt water and ice, the temperature 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 C. or 3 C., 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 * precisely as you treated the acetamida RECORD OF EXPERIMENT TIME TEMPERATURE Hour Minute etc. etc. etc. Naphthaline can be obtained at any drug store. Acetamide will have to be purchased at a chemical supply house. [56] EXPERIMENT 22 THE HEAT OF FUSION OF ICE The heat of fusion of ice, that is, 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.* Heat this water to a temperature of about 25 C. above that of the room ; then support the inner vessel by its ring in the outer vessel of the calorimeter. 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 temperature 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 inappreciable. 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 temperature of the water just after the ice has all disappeared. This temperature should be from 2 C. to 10 C. below the temperature of the room. If it should happen to be above the room temperature, try again with 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 wx. After the ice is melted it becomes w 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 ^, while the water equivalent of the calorimeter is e, (.095 x weight of calorimeter), then the total number of calories given up by the water and calorimeter is (W + e) (^ t). Hence, by equating " heat lost " and " heat gained," we have the equation ( W+ e) (^ f) = wx + wt, from which compute x. Questions, a. What is meant by " latent heat of ice," the quantity which you found above ? b. Explain why ice rather than ice water is used to cool lemonade. c. Explain what each part of your numerical equation represents. t * If you use the small cylinders of Exp. 3 for the calorimeters, take just half of the amounts of ice and water indicated. t 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 w of the steam condensed. Let x represent the heat of condensation of steam, that is, the number of calories of heat given up by a gram of steam in changing from steam to water at the same temperature. Then the number of calories of heat produced by the condensation of the steam is wx. The water formed by the condensation of the steam in cooling to the final temperature t of the mixture will give up w (100 t) calories. If the weight of the water heated is W and its initial temperature ^ , while the water equivalent of the calorimeter is e, then the heat exchanges are given by the equation wx + w (100 - t) = (W + e) (t - tj. [57] EXPERIMENT 22 (Continued) RECORD OF EXPERIMENT 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 = Equation .-. heat of fusion of ice, x, = caL Accepted value is 80. .. per cent of error = [58] 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 two ways should give identical results. The first is to confine the liquid and its vapor alone in a closed vessel, and then to measure 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 second 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. 41) is closed at one end, and is then bent into the U-shape and partially filled with mer- cury. 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, with constant stirring. As the temperature increases a point is reached at which alcohol vapor begins to form in the closed tube. Still further increase in temperature 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 thoroughly until this condition is reached ; then read and record y IQ> 41 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 thermometer and compute how much the boiling point of alcohol increases per centi- meter increase in the barometric pressure. II. Temperature of vapor rising from boiling liquid. Place a little alcohol in a large test tube ; put few tacks in the bottom of the tube in order to insure 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 thermometer in the tube a little distance above the surface of the boiling liquid. As soon as the thermometer reading becomes stationary, take the temperature and compare with that obtained in I. Questions, a. If the test tube of alcohol were placed under the receiver of an air pump, how would its boiling point change as the air was exhausted from the receiver ? 6. If the boiling point of alcohol was determined in a deep mine, would it be higher or lower than you found it to be in I, (#) or II, (a). (See data record.) RECORD OF EXPERIMENT I. (a) Barometer reading = cm. (6) Temperature at which alcohol vapor exerts a pressure equal to the atmospheric pressure = C. (c) Temperature at which alcohol vapor exerts a pressure equal to the atmospheric pres- sure + 5 cm. of mercury = C. (rf) Rise in boiling point of alcohol per centimeter increase in pressure = C. (e) Boiling point of alcohol at 76 cm. pressure = C. II. (a) Temperature of vapor rising from boiling alcohol = G. Difference between results of I, '(6) and II, (a) = C. [59] 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 BAROMETRIC PRESSURE Fill the boiler of Fig. 42 half full of water and thrust the thermometer through a tightly fitting cork in the top until the 100 point is only 2 or 3 mm. above the cork. Attach an open-arm manometer u (Fig. 42) to the exit 0, 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 manometer arms, due to the partial closing of the vent for the steam, amounts to 2 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 or 5 cm. ; then read again. Continue thus, taking readings at intervals of about 3 cm., until the differ- ence in level amounts to 9 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 cm. 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 ther- mometer 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 with finely chopped ice over which a little water has been poured, and allowing it to remain there until the thread is stationary. Questions, a. Why will a thermometer placed in a steam boiler often register as high a temperature as 150 C. ? b. When a steam boiler bursts, the pressure to which the steam and water was subjected almost instantly changes to what pressure ? c. How do you account for the production of a very much larger quantity of steam when a boiler explodes than was in the boiler just before the explosion ? FIG. 42 RECORD OF EXPERIMENT Trial 1 Trial 2 Trial 3 Trial 4 Difference in levels in gauge = cm cm cm Corresponding boiling-point readings = C C C Change in boiling point per cm. = C C C Mean change per cm. = C. Barometer height = cm. Boiling point at 76 cm. = C. Error .C. Freezing point (reading on thermometer) = C. Error = C. [61] FIG. 43 EXPERIMENT 25 MAGNETIC FIELDS* I. The magnetic field about a bar magnet, (a) Lay a bar magnet in the groove of the board shown in (Fig. 43, 1). Pin a sheet of blue-print 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 pencil. The filings will be found to have arranged themselves in lines run- ning 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. With a lead pencil indicate on the paper the N and S poles of the magnet. ().) From these experiments what effect do you conclude that the accumulation 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. EXPERIMENT 28 A (Continued) V. A nonpolarizing cell, (a) 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 solution 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.) As in IV, watch the ammeter reading for two minutes. Short-circuit the cell for one minute and see if thereafter the ammeter reading 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 immersed 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 ? VI. A polarizing commercial cell. Replace the Daniell cell by either a Leclanche or a dry cell. Record (a) the current when the cell is first connected to the ammeter ; (5) the current at the end of two minutes ; () Lead . . . copper . . . H 2 S0 4 (*) Copper . . . iron . . . H 2 S0 4 Lead . . . aluminum . . . H 2 S0 4 Copper . . . iron . . . (NH,) 2 S Lead . . . carbon . . . H 2 SO 4 IV. (a) Deflection for a single cell = , (ft) for 2 cells in series = , (c) for 2 cells V. Deflection for a Daniell cell = , for a Leclanch6 cell = , for a .... E.M.F. of a Daniell cell =1.08 volts, .-. of a Leclanch6 cell = volts, .-. of a [82] in parallel cell = .. cell = . . volts. EXPERIMENT 32 HOW DOES THE RESISTANCE OF ELECTRICAL CONDUCTORS DEPEND UPON THE LENGTH, DIAMETER, MATERIAL, AND METHOD OF CONNECTION? I. Length, (a) Connect two dry cells or a storage battery in series with a key, K, an ammeter, and 100 cm. of No. 30 German-silver wire (wire 1 of Fig. 63). Close the key and record the ammeter reading and the voltmeter reading when the voltmeter is connected across 50 cm. of the wire. By Ohm's law, the resistance I Ammeter] of any portion of a circuit is given by the equation potential difference Resistance = , or Ohms = current volts ,' _^--" ~-\ 6 1 / aX o 2 fen o 3 c n o 4 FIG. 63 amperes Compute and record the resist- ance of the 50 cm. of wire. (5) Take observations with the voltmeter connected across the 100 cm. of wire and compute its resistance. Call this resistance R^ (c) State the law proved by I, (a) and I, (5). II. Diameter, (a) Determine the resistance of 100 cm. of No. 24 German-silver wire (wire 2 of Fig. 63). Call this resistance R z . 1(5) See Appendix B for diameter of wires used or measure them with a micrometer caliper. (c) Compute the ratios indicated hi the data record. (d) State the law proved by these ratios. III. Material, (a) Determine the resistance of 100 cm. of No. 30 iron wire (wire 3 of Fig. 63). Call this resistance R . (b~) Find the resistance of 100 cm. of No. 30 copper wire (wire 4 of Fig. 63). Call this resistance R^ ( I r\ T> I ~v Jr/1 = Ji/JL. To prove that this is so, we have only to apply Ohm's law. For if PZ> 1 represents the potential difference between a and d, and PD Z that between d and c, then, since b and d have the same poten- tial, PJ) l will also represent the potential difference between a and b, and PD Z that between b and c. Now by Ohm's law, since the same current C l is flowing through ad and dc, we have C l = PDjP = PDJQ, or PDJPD Z = P/Q. Similarly, on the lower branch, PDjPD^ = R/X. Therefore P/Q = R/X and X= Q x R/P. (a) Stretch No. 30 German-silver wire between a and c, as in Fig. 65, 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, B say a 1-ohm coil. Between b' and c insert a 3-m. coil of No. 30 copper wire. The brass strap between b and b' has a negligible resistance, so that the whole of it may be considered as the point b of Fig. 64. Connect to the binding post at m one terminal of a D'Arsonval galvanometer G. This instrument is precisely that shown in Fig. 56, save that a slender pointer must be inserted in the place provided for it for the sake of making small deflections more easily observable. 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 etc is uniform, the ratio of the resistances P and Q is simply the ratio of the lengths ad (= ^) and dc (= Z 2 ). Hence, or = X (6) In the same way measure the resistance of exactly 50 cm. of No. 30 iron wire, and by the law of lengths calculate from the result the resistance in ohms of such a wire 3 m. long. [85] EXPERIMENT 32 A (Continued) (c) In the same way measure the resistance of exactly 25 cm. of No. 30 German-silver wire, and compute from the result the resistance of such a wire 3 m. long. (cT) Measure, also, the resistance of exactly 50 cm. of No. 24 German-silver wire, and compute from the result the resistance of such a wire 3 m. long. Questions, a. The resistance of an iron wire is how many times that of a copper wire of the same diame- ter and length ? b. The resistance of a German-silver wire is how many times that of a copper wire of the same length ? c. The diameter of No. 24 wire is twice that of No. 30 wire (see Appendix B). How does the resistance of a wire depend upon its diameter ? RECORD OF EXPERIMENT /, IN CENTIMETERS / s IN CENTIMETERS R IN OHMS X IN OHMS ItESISTANCE OF 300 CM. () () (<0 (<0 Resistance of iron Resistance of copper /Diameter of No. 24 wire\ 2 \Diameter of No. 30 wire/ resistance of German silver resistance of copper resistance of 300 cm. of No. 30 German-silver wire ' resistance of 300 cm. of No. 24 German-silver wire [86] EXPERIMENT 33 HOW DOES THE RESISTANCE OF GALVANIC CELLS DEPEND .UPON THE AREA OF THE PLATES IMMERSED, THE DISTANCE BETWEEN THE PLATES, AND THE METHOD OF CONNECTING THEM? I. Area of plates immersed, (a) Connect an improvised Daniell cell * to the single turn of coarse copper wire of the galvanoscope or to an ammeter. Record the reading of the instrument used. (6) Lift the plates gradually out of the glass and record the effect. Since, as proved in Exp. 31, the E.M.F. is not diminished by decreasing the area of the plates immersed, what do you conclude, from Ohm's law, must have changed in the circuit as the plates were lifted ? How, then, is the internal resistance affected by the size of the plates ? For a battery circuit Ohm's law must then be = E.M.F. where R e is the resistance of the circuit external to the battery, -and R. is the internal resistance of the battery. II. Distance between plates. Dispense with the plate holder of the cell. Press the wires firmly against the plates and record the reading of the instrument used, first, when the plates of the cell are brought as close together as possible, that is, on adjacent sides of the porous cup, and second, when the plates are held as far apart as possible in the cell. How is R t affected by the distance between the plates ? III. Internal resistance of cells in series, (a) Connect a single Daniell cell to the single turn coil of the galvanoscope or to an ammeter. (In this and succeeding parts of the experiment, if the gal- vanoscope is used, the compass should be slipped along in the frame until the deflection at first is not lore than 16.) The external resistance of the circuit is now very small and, without appreciable E.M.F. jrror, may be considered equal to zero, so that under these conditions C = '- Now introduce enough German-silver wire in series with the circuit to reduce the current 'ammeter reading or deflection, depending on the instrument used) to one. half its former value, [easure the length, in centimeters, of the German-silver wire thus introduced and find its resistance in ohms. (1 cm. of No. 30 German-silver wire has a resistance of .0621 ohms.) Since the introduction of the German-silver wire halved the current, the resistance of the circuit p -\ t -p must have been doubled. Hence, by the equation C = '^ , the resistance R e of the German-silver rire introduced into the circuit must be equal to the internal resistance R t of the cell. Call this resistance (R^)^ (5) In the same way find the internal resistance of a second Daniell cell, expressed first in centi- meters of No. 30 German-silver wire and then in ohms. Call this resistance (-R,-) 2 - ( R 2 = 00 R s = 00 Rt = (a), (6), (c), and (rf), in parallel * * * R P = II. LAMP VOLTS AMPERES RESISTANCE (WHEN COLDER) (a) R^ () ,= () ,= 09 4 = (a), (6), (c), and (d), in series p t j L j. , from - = + -- + + , H K /i K /t R P , from I, (For above, use values of 7? x , J? 2 , etc., when hot.) 7? 5 , from R s =R l + R 2 + R a + R v R s , from II, = (For above, use values of R lt R z , etc., when colder.) .ohms ohtus These spaces to be left blank by the student. [91] EXPERIMENT 34 A HEATING EFFECTS OF THE ELECTEIC CURRENT The application of electric currents to heating is daily becoming of greater commercial importance. Our highest temperatures are obtained in the electric arc and the electric furnace. Electric disk stoves, teakettles, egg cookers, toasters, chafing dishes, percolators, grills, water heaters, immersion coils, flat- irons, curling irons, mangles, foot warmers, radiators, shaving mugs, milk warmers, and sterilizers are some of the household conveniences. Electric soldering pots, soldering irons, glue cookers, glue pots To Line FIG. 68 FIG. FIG 70 for cabinet makers, melting pots for lead alloys, instantaneous heaters for soda fountains, mangles, fluting irons, automobile tire vulcanizers, and electric welders are also some of the commercial applica- tions of heating by the electric current. The designer and the producer of these useful appliances are interested in increasing the percentage of the energy of the electric current which is transformed into heat available for the intended purpose. The ratio of this available heat energy (or output) to the electric energy (or input) for any of these levices is its efficiency. The consumer or user of these appliances is interested not only in their efficiency and cost of jration but also in their convenience. Heating water with the electric current. Pour 1 Ib. of cold water into the teakettle used in Jxp. 18 and place it on the electric disk heater of Fig. 68. Connect an ammeter in series with the heater and line and a voltmeter across the line, as in Fig. 71. To healer ^ Line FIG. 71 Caution. Do not turn on the current until an instructor has O.K.'d the arrangement of your apparatus Now turn on the current and simultaneously observe the exact time that it is turned on. Record the voltmeter and the ammeter readings every minute until the water boils. Then turn off the current, noting the exact time that it is turned off. f931 EXPERIMENT 34 A (Continued) From the average voltmeter and ammeter readings and from the time compute the number of kilowatt hours of electricity used. At the local price per kilowatt hour for electricity, compute the cost of heating 1 qt. of water to the boiling point. Compare this cost to the cost of heating 1 qt. of water to the boiling point with the gas stove (see Exp. 18 A). Practical efficiency of the electric heater. Pour 500 g. of water at a temperature of 12 C. or 15 C. below room temperature into the teakettle and place a thermometer in the water. Turn on the current ; stir the water continually with the thermometer ; observe the exact time when the water attains a temperature which is 10 C. below room temperature ; and again observe the time when the water attains a temperature which is 10 C. above room temperature. The practical efficiency is then the ratio of the number of calories of heat received by the water to the number of calories of heat produced by the heating effect of the electric current in the coils of the stove ; that is, , , c ^ ,. , ~? weight ot water X change in temperature Practical efficiency = .24 x watts x seconds Questions, a. If the teakettle were covered with asbestos, would the combined efficiency of the stove and teakettle be higher ? Why ? b. If the electric teakettle of Fig. 69 is used, should its efficiency be higher than that of a teakettle used with the electric disk stove of Fig. 68 ? Why ? (The teakettle of Fig. 69 has a " self-contained heating coil.") c. How would you expect the efficiency of the immersion heater shown in Fig 70 to compare with the efficiency of either of the other heaters shown ? Give reason for your answer. d. In obtaining the " theoretical efficiency " the water equivalent of the teakettle would have to be taken into account. Would the " theoretical efficiency " be higher or lower than the " practical efficiency " ? EXPERIMENT 35 ELECTROLYSIS AND THE STORAGE BATTERY I. Electrolysis of water. Bare the ends of two pieces of copper wire and wrap each about the head of a wire nail.* Connect the other ends of the wires to the terminals of two dry cells joined in series. Dip the ends of the nails into a dilute solution of sulphuric acid like that used in Exp. 28. Is the nail from which the bubbles appear first and most abundantly connected to the + or to the pole of the battery ; that is, to the carbon or to the zinc ? This gas which is given off most abun- dantly is hydrogen ; that which appears at the other nail is oxygen. In order to account for these effects we assume that when the molecules of sulphuric acid (H 2 SO 4 ) go into solution in water they split up into two electrically charged atoms, or ions, of hydrogen and one oppositely charged ion of SO 4 . It was this hydrogen which, according to this hypothesis, appeared at one nail while the SO 4 went to the other and there gave up an atom of oxygen. If this hypothesis is correct, must the hydrogen ion in solution carry a + or a charge in order to appear upon the nail upon which you observed it ? What kind of a charge must the SO 4 ion carry ? II. Electroplating. Remove the nails and attach each bare wire to some sort of improvised metal clip (ordinary paper fasteners are excellent). In each of these clips place a nickel and dip the lower half of each into a solution of copper sulphate (CuSO 4 ). About which nickel do you now see bubbles, the one connected to the + or the one connected to the pole of the battery ? (The former is called the anode, the latter the cathode.) These bubbles are oxygen. After about a minute remove the nickels and dry them with a cloth. Record what has happened. Decide from your results whether the copper ions of the copper sulphate solution carry + or charges. Interchange the nickels between the two clips and repeat the above operations. Record the results. (If you wish to restore your nickels quickly to their original condition, dip them for an instant in strong nitric acid and rub with an old cloth.) Ill (a). The storage battery, f Arrange a simple cell in the manner shown in Fig. 72, a and b nng the copper and the zinc strip to which are connected the terminals of an improvised voltmeter consisting of the 1000-ohm resistance coil E and the galvanoscope V, with the compass beneath its high-resistance coil. A is an improvised ammeter consisting of an- other galvanoscope with the compass beneath the 25-turn coil of coarse wire ; r is a resistance of about 100 ohms (use for it 4 m. of No. 36 German-silver wire, wound on a spool of insulated wire or held 0:1 the frame of Fig. G3 if bare wire) ; B is a battery of two dry cells connected in series but not joined, at first, to the ter- minals m and n of the cell circuit. Move the compass of V until the deflection is 8 or 10. This amount of deflection then rep- resents the E.M.F. of a copper-zinc sulphuric acid cell (approxi- mately 1 volt). Now replace the zinc and the copper strip by two strips of sheet lead. Does the voltmeter Fnow indicate any E.M.F. ? Explain the reason. Next connect m and n to the terminals of the dry battery #, and as soon as the needles are sufficiently quiet, record the deflections shown by both A and V\ then watch both needles carefully for about two minutes and record the readings, expressing the reading of A simply in scale divisions, but that of V in both scale divisions and volts. * Platinum electrodes are better, but they are less convenient and much more expensive. t Two sets of students are expected to work together on this experiment, and where low-reading voltmeters and ammeters are available, the method of III (b) will be found somewhat shorter than that of III (a) and just as satisfactory. [95] B ~ FIG. 72 EXPERIMENT 35 (Continued) Now short-circuit the terminals o and s of the resistance r by pressing a strip of metal against the two binding posts o and s or by connecting them with a copper wire. Watch the plates and note the hydrogen appearing in considerable quantity about the cathode, while but little oxygen appears about the anode. After the current has been running through the short circuit on r for about two minutes lift the plates from the liquid. Do you see a faint reddish deposit upon the anode where the oxygen would naturally have appeared ? If not, let the current run a little longer and observe again. This deposit is lead peroxide (PbO 2 ). Why, then, did so little oxygen gas appear about the anode ? Replace the plates in the acid, take away the shunt from os, and record the reading of V. By how many volts is it now larger than it was when m and n were first joined to j5 ? Disconnect m and n from B and observe how many volts of E.M.F. have been developed between the lead plates. Now watch the ammeter as you join m and n to each other. What is the direction of the observed cur- rent with reference to that which the battery sent through the ammeter? Watch the voltmeter and the ammeter for two minutes while the tstoraye 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.* Ill (&). The storage battery. Make a cell like that shown in Fig. 73, with two well-cleaned lead plates dipped into a solution made of one part sulphuric acid to ten parts water. Connect a voltmeter across the cell and see if it produces any E.M.F. To charge the cell connect it in series with a resistance of about 5 or 6 ohms (about 1 m. of No. 30 German-silver wire), a low-reading ammeter, and two dry cells. At the same instant in which the last connection of the charging circuit is made, one student should record the voltmeter reading and another the ammeter reading. Record the reading of each meter every ten or fifteen seconds for two minutes. Now increase the charging current by connecting the ends of a meter of No. 24 copper wire to the binding posts which hold the German-silver wire. Watch the plates and note the hydrogen appearing in considerable quantity about the cathode, while but little oxygen appears about the anode. After the increased charging current has been running for about two minutes lift the plates from the liquid. Do you see a faint reddish deposit upon the anode where the oxygen would naturally have appeared? If not, let the current run a little longer. This deposit is lead peroxide (PbO 2 ). Why, then, did so little oxygen appear about the anode? Replace the plates in the acid, take away the copper wire which was shunted across the German- silver wire, and record the voltmeter reading. By how many volts is it now larger than it was when m and n were first joined to If? Disconnect m and n from B and observe how many volts of E.M.F. have been developed between the lead plates. Now watch the ammeter 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 the 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. * If you wish to repeat the experiment with the same lead plates, clean them first very thoroughly with sandpaper. FIG. 73 [96] EXPERIMENT 36 INDUCED CURRENTS I. Induction of currents by magnets, (a) Set up the D'Arsonval galvanometer (Fig. 74) 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 deflection. (The object of the short-circuiting is to prevent a too violent throw of the coil.) Record the terminal (right or left) of the galvanometer at which the current entered it when the deflection was in a given direction (right or left). This will enable you henceforth to know at which terminal any current enters your galvanometer, as soon as you observe the direction of deflection. 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 supported between the walls beneath the pointer will enable you to estimate amounts. (5) From the direction of the deflection determine the direction of the current induced 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 Exp. 30) which was approaching the N pole, an jV an S pole ? (c) Suddenly withdraw the coil from the magnet. Note and record as before the direction and lount of deflection. How does the direction and amount of the induced current now compare 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 ? Us (d) Draw in your notebook four figures like those shown in Fig. 75 and insert in each the signs the poles of the coil due to the induced current, when the coil is in the four positions indicated in e figures and moving in the directions indicated by the arrows. (e) Repeat the same experiments with the S pole of the magnet and observe in each case the lirection of deflection and the direction of the current induced in the coil. Is the nature of the iduced magnetism of the coil A in every case such as to oppose or to assist the motion of the coil V [97] EXPERIMENT 36 (Continued) II. Induction of currents by electromagnets, (a) Slip the 700-turn coil used in I over an iron bar (for example, 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. 76. 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 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 galvanometer (the so-called secondary*). Was the induced current in the same or in the opposite direction to that in which the current from the cell is circulating around the core in the primary ? What connection do you find between this experiment and I ? (6) 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. Compare the direction of the induced current in the secondary with that which was flowing in the primary. Ls the current in the secondary circuit produced by the magnetism of the electromagnet or by changes in the magnetism of the electromagnet? 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. 76), so that the magnetic lines can have a return iron path instead of a return air path. Observe the amount of the deflection at make or break and compare with the amount when the tripod base is removed. (The difference will not be large, but it will be easily observable.) III. Principles of the dynamo and the motor, (a) Hold the coil A between the poles of a horseshoe magnet (Fig. 77), and in such a position that its plane is perpendicular to a line joining the poles. Rotate quickly through 90 ; that is, to a position in which its plane is parallel to the lines of force. Observe the direction of deflection of the suspended coil. (i) After the pointer has come to rest, rotate the coil A 90 mere and note and record the direc- tion of deflection. (c) Similarly, rotate the -coil through the next two quadrants. (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 electromagnet, 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. FIG. 77 [98J EXPERIMENT 37 TO DETERMINE THE POWER AND EFFICIENCY OF AN ELECTRIC MOTOR Connect the ammeter in series with the motor to measure the current through the motor, and the voltmeter in parallel with it to measure the P.D. across the motor (see Fig. 78). For measuring the output of small motors having a grooved belt wheel, use the modification of the Prony brake shown at the right in Fig. 78. Disconnect the brake belt to relieve the motor of its load. Close the switch and slowly move the lever of the starting resistance, or of the rheostat, so as to cut out the resistance in series with the motor. w Modification of Prony Brake FIG. 78 Now attach the brake belt and increase the tension on it by raising the balance support until the speed is about 100 to 200 II. P.M. (revolutions per minute). In the modified form of Prony brake this is accomplished by increasing the weight W. Let one student read the voltmeter and ammeter, another the speed indicator and. stop watch, and another the balances. The recorded voltmeter, ammeter, and balance readings should be the mean of several observa- tions made during the same time that the number of revolutions for one minute are observed. Stop the motor by opening the switch. Wrap a thread several times around the belt wheel and from the length of the thread and the number of turns determine the circumference of the wheel in feet. The circumference in feet multiplied by the pull on the belt in pounds (pull on the belt = difference in the two balance readings, or else the single balance reading minus the weight) gives the number of foot pounds of work done by the motor in one revolution. This number of foot pounds per revolution multiplied by the R.P.M. gives the output of the motor in foot pounds per minute. Express the output in horse power, remembering that 33,000 ft. Ib. per minute = 1 horse power. The input, or the rate at which energy is supplied to the motor by the electric current, expressed in watts, is equal to the number of volts P.D. across the motor multiplied by the current through the motor in amperes. Express the input also in horse power, remembering that 746 watts = 1 horse power. Calculate the efficiency of the motor ; that is, the ratio of the output to the input. Repeat the experiment, using a considerably higher speed and a smaller pull on the belt. [99] EXPERIMENT 37 (Continued} Questions, a. Is the efficiency of a motor the same for different speeds ? 6. Would its efficiency be higher if there were no atmosphere ? c. How does the heat generated in the armature and field windings (H = .24 C 2 Rt) affect the efficiency of the motor ? d. An electric automobile is run for five hours. During this time the motor delivers energy at an average rate of 2 H.P. If the motor has an efficiency of 90% and the storage batteries an efficiency of 75/ , how much does it cost to charge the storage batteries sufficiently for this trip, if the cost of the electricity used in charging the batteries is four cents per kilowatt hour. RECORD OF EXPERIMENT Output Circumference of belt wheel = ... ...ft. TRIAL READING OF BALANCE 1 READING OF BALANCE 2 PULL ON BELT IN POUNDS FOOT POUNDS PER REVOLUTION R.P.M. FOOT POUNDS PER MINUTE HORSE POWER Low speed High speed Input TRIAL P.D. IN VOLTS CURRENT IN AMPERES WATTS HORSE POWER Low speed High speed Efficiency at low speed = % Efficiency at high speed = % [lOOj EXPERIMENT 37 A A STUDY OF A SMALL MOTOR AND DYNAMO I. Adjustment of the commutator. Swing the permanent field magnets away from the armature of the motor shown in Fig. 79. Connect one dry cell to the motor. With a small compass test the polarity of each end of the armature core for a complete revolution. Note the position of the arma- ture when the polarity of its iron core changes. In what position should the armature core be when its polarity changes if the ends are to be acted upon by the field magnets in such a way as to produce continuous rotation ? Turn the toppiece which carries the brushes until the point of commutation, that is, the position where the insulating slits of the commutator pass under the brushes, is at the proper place. II. Speed of rotation, (a) Now swing the permanent field magnets close to the armature and allow the motor to come to full speed. Then gradually swing the field magnets away from the arma- ture and explain the result. (5) With the field magnets close to the armature, observe the effect on the speed of the motor of reducing the current through the armature. This may be accomplished by placing a resistance FIG. 79 FIG. 80 FIG. 81 FIG. 82 box, or rheostat, of from 4 to 40 cm. of No. 36 German-silver wire in series in the circuit. Observe the effect on the speed when this resistance is increased from 1 ohm to 10 ohms, and again when it is decreased from 10 ohms to 1 ohm. Explain. (c) The speed may also be changed by changing the point of commutation. To do this rotate the top which carries the brushes. How does this affect the speed, and why ? III. Direction of rotation, (a) Reverse the current through the armature. Observe and explain the effect observed. (6) Turn each field magnet end for end. Explain the effect which doing this has on the direction of rotation. (, then between C and E, then between D and F, etc., estimating in every case to tenths of a vibration. Take a mean of these counts as the num- :r of vibrations of the fork to one the bob. (c) Repeat the observations on two other traces and take the mean of the three means as the >rrect number of vibrations of the fork to one of the bob. (c?) Get the rate of the bob by counting, with the aid of an ordinary watch, the number of vibra- tions which it makes in one or two minutes, or, if a stop watch is available, by taking the tune of fifty vibrations of the bob. (e) Compute the number of full vibrations made by the fork per second. RECORD OF EXPERIMENT First Trace Second Trace Third Trace Number of Vibrations of Bob Vibrations between A and C = Vibrations between B and D = Vibrations between C and E = Vibrations between D and F = Means = Final mean = Number of vibrations of bob per second = .-. rate of fork = * 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. t 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 quite as well, and the whiting is very much cleaner than lampblack. [105] EXPERIMENT 40 WAVE LENGTH OF A NOTE OF A TUNING FOEK (a) Let one student strike a C' fork (that is, one which makes 512 vibrations per second) upon a block of wood, and then quickly hold it above the tube of Fig. 85 with the flat face of one prong just ve the end of the tube. (Use the tube of Fig. 9, p. 7.) Let a second student ise and lower the vessel A while the fork is sounding, and note as accurately as possible the shortest length of the air column which gives a maximum resonance. Mark this position on the tube by means of a small rubber band. Test the correct- ness of the setting by several observations. (5) Locate in the same way a second position of resonance lower in the tube, and mark with a rubber band, as above. Since the distance between two positions of maximum resonance is exactly one-half wave length, twice the distance between the rubber bands will be equal to the wave length of the note sent forth by the sounding tuning fork. Compare this value of the wave length with that computed by dividing the speed of sound at the temperature of the room by the vibration number of the fork as marked upon it. (Speed of sound in air at C. = 332 m. per second. It increases 60 cm. for each degree of rise in temperature.) (c) Find in the same way the wave length of a fork one octave lower than the first. Fie. 85 Questions, a. Explain why the distance between the rubber bands is equal to one half of the wave length of the sound wave sent forth by the sounding tuning fork. &. Show how the above experiment might be used for finding the velocity of sound. c. Sound travels about four times as fast in hydrogen as in air. What would be the first resonant length for the C' fork used above if the tube contained hydrogen ? d. 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 ? RECORD OF EXPERIMENT First Resonant Length ^ Second Resonant Length l t Difference x 2= I Fork No. 1 = Fork No. 2 = Number of vibrations of fork No. 1 = .-. calculated wave length = Number of vibrations of fork No. 2 = .-. calculated wave length = [107] FIG. 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 (Fig. 86), insert a bridge at 5, 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 picked near the middle) is in unison with the note of the lowest fork provided ; namely, C. Measure carefully the length of the wire between the fixed end and b. i ffl (6) 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 of the wire to 6. (c) In the same way (that is, by moving 6) tune the wire to unison with a third fork (for example, G above middle C) and measure and record the corresponding length of the wire. (d?) From a study of the measured lengths and of the vibration 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. II. Effect of tension on the vibration rate of a stretched wire, (a) Set up side by side two boards like A (Fig. 86), 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 necessary to multiply the stretching force ? (5) 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 stretching weight should have been and see how well it agrees with the observed value. Questions, a. For the high notes on a piano does the manufacturer use long or short wires ? Why ? b. State in your notebook the laws deduced from I and IL I. Effect of length Length of C wire = Length of C' wire = Length of G wire = Calculated length of C' wire = cm. Calculated length of G wire = cm. RECORD OF EXPERIMENT II. Effect of tension . cm. .cm. .cm. First stretching weight = g. Second stretching weight = g. Second divided by first = g. Third stretching weight (calculated) = g. Third stretching weight (observed) = go [109] EXPERIMENT 42 LAWS OF REFLECTION FROM PLANE MIRRORS I. To prove that the angle of incidence equals the angle of reflection, (a) Blacken one side of a strip of plate glass or a microscope slide ; attach it by means^of a rubber band to a small wooden block, and then set it on edge so that the line A C (Fig. 87), 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 reflec- tion P'BE with the protractor. If a protractor is not at hand, draw an arc with B as a center, cutting the lines PB and P'B at M and 0, and measure the lines MN and ON. (6) Repeat for some other position of P. (c) Finally, set P at such a point that it is directly in line with its own image P" and B. Draw the line PB and also construct the perpendicular to A C at B. If the angle of incidence is equal to the angle of reflection, the two lines should exactly coincide. II. To locate the image formed by a plane mirror, (a) Again set up the pin at P (Fig. 88), draw the line AC, and place the edge of the mirror upon it; then lay a straightedge on the paper in successive positions ab, cd, ef, etc., such that the image P" always appears to lie in the prolongation of the edge of the ruler. Draw the correspond- ing lines ab, cd, etc. ; then remove the glass and locate the image P" by prolonging these lines to their point of intersection. (5) Measure the perpendicular distance from P to AC and from P" to AC. Also measure the angle which PP" makes with AC. Tabulate your results neatly, and state the conclusions which you draw from I and II. P" [111] EXPERIMENT 43 TO FIND THE RATIO OF THE VELOCITIES OF LIGHT IN AIR AND GLASS (INDEX OF REFRACTION OF GLASS) Draw a straight line AC (Fig. 89) across a large sheet of paper and set one edge of the plate- glass prism mnO in exact coincidence with it. Lay a ruler on the paper in such a position that, as you/sight along its edge from some position E in the plane mnO, the apex of the prism, as seen in the face mn, appears to lie in the prolongation of the edge of the ruler. Draw a fine line ab along this edge. Then move the eye to a position E\ about as far to the right as E was to the left of the normal to mn, and draw in the same way a line cd. Mark the position of carefully by means of a pin prick. Then remove the prism, and with an accurate straightedge and a very sharp pencil or knife-edge prolong ab and cd until they meet in some point 0'. The point is then the center in the glass of the light waves by means of which you see the apex 0, while the point 0' is the center of the same waves after they have emerged into air. If, therefore, from and 0' as centers, the two arcs qrt and qr't are constructed, the arc qrt would represent the shape and position of the wave from when it has reached the points q and t, if the speed in air were the same as the speed in glass, while qr't is the actual position .of this wave in view of the fact that light travels faster in air than in glass, sr'/sr is then the ratio of these two speeds. But sr'/sr is also the ratio of the curvatures of the arcs qr't and qrt ; that is, it is the ratio of the amounts by which these curved lines depart from the straight line qst. Now if, at a given point, one arc is curving twice as rapidly as another, it is evident that its center can be but half as far away ; that is, the curvatures of two arcs are always inversely proportional to their radii. Hence the ratio sr'/sr is the same as the ratio Oq/0'q. Measure these distances as care- fully as possible with a meter stick, and record your value for the ratio of the velocities of light in air and glass. This is called the index of refraction of glass. Repeat the observations, using different positions of E and E\ and see how well the two observations agree. RECORD OF EXPERIMENT First Trial Second Trial Oq = Oq = O'q = O'q ~ Index = ... Index = ... Mean value of index Per cent of difference between first and second = [1131 EXPERIMENT 44 THE CRITICAL ANGLE OF GLASS Place the plate-glass prism ABC (Fig. 90), having three polished faces, upon a large sheet of paper in front of a window OR through which the sky is visible. If desired, OR may be a piece of ound glass behind which a white light is placed. Place the eye in a position E, so as to observe the age of the sky or ground glass as it is seen by reflection from AB. A bluish-green line will be seen dividing AB into two parts of markedly different brightness. The part to the right is brighter than the part to the left. If this line dividing the field is not seen at first, it will appear on moving the eye to the left or the right. Move the eye about until the green edge of this line is brought into exact coincidence with a small ink spot placed at s on the face AB. From the figure it will appear that the light which comes to the eye by reflection from the various points along AB must make a larger and larger angle of incidence on AB as the point considered lies farther and farther to the right of A. When this angle is equal to or greater than the critical angle, as is the case between s and B, the whole of the light incident upon AB is reflected ; when it is less than the critical angle, as is the case between A and s, part is reflected and part transmitted. The bluish-green line which separates the field into parts of unequal brightness represents the position on AB at which total reflection begins ; that is, the angle i is the critical angle for glass. To measure this angle, lay a ruler so that its edge appears to lie in the same straight line with the point * and the green edge of the line in the field, and mark with a line on the paper the position En of the straightedge. Then with a sharp pencil or a knife draw an outline ABC of the prism upon the paper, and place a pin prick at 8 just beneath the ink spot s on the face AB. Remove the prism and extend En, the line just drawn, until it meets AC at some point n. Connect this point n with the pin prick at s, erect the perpendicular upon AB at s, and measure with the protractor the angle i. This is the critical angle for glass. Extend the lines m and the perpendicular at s so as to make them from 6 in. to 1 ft. in length. Draw uv parallel to AB. Then us/uv should give the same value for the index of refraction as that obtained in the last experiment. The proof of this statement is not suitable for an elementary text, but the measurement will furnish an interesting check as to the accuracy of the results of the experiment. [-116] EXPERIMENT 45 FOCAL LENGTH OF A CONCAVE MIRROR I. Support the concave mirror in direct sunlight by means of a clamp and let the image of the sun be thrown upon a narrow strip of paper held in front of the mirror. Measure the distance from the mirror to the point at which the spot of light on the thin strip is smallest and brightest. This distance is the focal length; designate it by the letter/. II. Throw the image of a distant house on the thin strip of paper in the same way. Repeat the above measurement. III. Place a candle flame or an electric light at a distance J> , about three times the focal length from the mirror, and locate the position of the image by letting it fall on the narrow screen. Compute the focal length from the formula ^ .. .. ^ + D=f' in which D and D { are the distances of the object and image respectively from the center of the mirror. IV. Set up a pin on a block so that its head is nearly opposite the middle of the mirror. Move the pin out to about twice the focal length of the mirror. If the eye is placed in front of the mirror and as much as 8 or 10 in. farther from it than the pin, the object and image may both be seen the image inverted and the object erect, in the manner shown in another connection in Fig. 92. Shift the position of the pin or of the mirror until the image of the head of the pin is exactly in line with the head of the pin itself. Move the eye to the right and left and see whether there is any relative motion of the pin and its image. If so, it is because they are not the same distance from the eye. The one which is farther away will move to the left when the eye is moved to the left, and to the right when the eye is moved to the right, (Test the correctness of the above statement by holding two pencils in line, but at different distances from the eye, and noticing how they appear to move with reference to each other as the eye is moved from side to side.) Adjust the position of the pin until there is no relative motion between the pin and its image as the eye is moved from side to side. The image of the pin is now at the same place as the pin itself ; hence the pin must be at the centei of curvature of the mirror. Measure the distance from pin to mirror. This distance is the radius of curvature of the mirror. Find what relation exists between this distance and the focal length of the mirror. RECORD OF EXPERIMENT Focal length, by I = Focal length, by III Focal length, by II = One half of radius of mirror = 117] EXPERIMENT 46 LAWS OF IMAGE FORMATION IN CONVEX LENSES I. Set up in the positions shown in Fig. 91 a wire netting 0, a reading glass L of about 15 cm. focus, and a block B provided with a paper scale s. Set a gas flame behind to insure bright illumination. Adjust B and L until measure D , the distance from to to s. Next read on s the number of image of the netting. Then with by the same number of squares on the image of the netting is sharply outlined on . Then the middle of the lens L, and J> t ., the distance from L millimeters covered by ten or twenty squares in the another scale measure the number of millimeters covered the netting 0. These two observations give respectively FIG. 91 FIG. 92 the length L { of the image and the length L of the object. Repeat the same observations with three or four different values of D , such as 30 cm., 40 cm., 50 cm., and 60 cm., and calculate the focal length / of the lens from the formula 1+1.1. j>. -, / Also take the ratios L /L { and D /D { and tabulate as indicated in the Record of Experiment. What conclusion do you draw from the last two columns ? II. Find the focal length of the lens directly by removing and casting the image of a distant chimney or house upon s. III. As a final check on the focal length, place a plane mirror behind the lens and mount a pin in front of the lens opposite its center. Adjust the pin by the method of parallax (the method used in Exp. 45, IV), until the image of the head of the pin coincides with the head of the pin itself. The distance from the pin to the center of the lens must then be equal to the focal length of the lens, as is shown by the diagram (Fig. 92), since the waves between the lens and the mirror are plane. RECORD OF EXPERIMENT -Do -Di J), + Di / Lo Li Lo Tt D, Di Focal length (mean of co lumn 4) . cm., by II cm., by III = cm. [119] EXPERIMENT 47 MAGNIFYING POWER OF A SINGLE CONVEX LENS Fig. 93 shows a so-called linen tester a single convex lens at the focus of which is a square hole in a brass frame. Support the linen tester with a tripod and a clamp so that the lens of the linen tester is 25 cm. from the table top. Place a meter stick on the table directly below the linen tester (Fig. 93). Place the eye as close as possible to the lens and with both eyes open observe how many millimeters on the stick seen with one eye are covered by the hole seen through the lens with the other eye. Divide the number thus seen by the measured width of the hole in millimeters. This is obviously the magnifying power, expressed in diameters, of the lens, since it shows how many times as large a diameter of the object appears when seen through the lens as when viewed with the naked eye at the distance of most FlG 93 distinct vision ; namely, 25 cm. Measure as accurately as possible the focal length / of the lens (that is, the distance from the middle of the lens to the hole) and see how well the observed magnifying power agrees with the theoretical value ; namely, 25// ? . EECORD OF EXPERIMENT Number of millimeters covered by the hole on the meter stick = Width of the hole in millimeters = .-. magnifying power in diameters (experimental value) = Focal length of lens in centimeters = .-. magnifying power in diameters (theoretical value) = , [121] FIG. 94 EXPERIMENT 48 THE ASTEONOMICAL TELESCOPE ' I. To construct a telescope. With the simple magnifying glass used in the last experiment and ith an objective consisting of the reading glass of Exp. 46, construct an astronomical telescope, as Hows : Set the reading glass in some support (Fig. 94) and find, with the aid of a piece of white board, the distance F from the lens at which the image a distant building or window is formed. Then set up the linen tester behind the card at its focal length / from it. Now remove the card and view the image of the distant object through the eyepiece. Slide the eyepiece support, if necessary, until the distant object, preferably a brick wall, is very sharply seen; then measure the distance between the lenses and compare this distance with the sum of the focal lengths. Do you find any simple relation between these quantities ? Can you see any reason why there should be some such relation ? Explain. II. To measure the magnifying power of the telescope. Focus the telescope upon two heavy horizontal marks drawn, for example, on a blackboard on the opposite side of the room. Let the lines be from 3 to 6 in. apart. When the lenses have been adjusted so that a distinct image of the marks is seen with the eye which is looking through the telescope, open the other eye and direct another student to make on the board marks which shall coincide with the apparent positions on the board of the images of the two marks as seen through the telescope. It may be found difficult at first to give attention to both eyes at once, but a little practice will make it easy. Repeat several times and compute the magnifying power M from each observation. Compare this magnifying power with the theoretical value for the magnifying power of a telescope ; that is, the ratio of the focal lengths of the objective and the eyepiece. Determine these focal lengths by casting the image of a distant object on a small screen or a sheet of paper. RECORD OF EXPERIMENT I. Distance between lenses = cm.; F + f= II. M (observed) = diameters. F M (theoretical), that is, , = diameters. .cm. [123] EXPERIMENT 49 I. To construct a microscope. Place two corks which contain holes about 1 cm. in diameter in the ends of a cardboard or tin tube 4 or 5 in. long, and with the aid of a rubber band fix the lenses of two of the linen testers over the holes (Fig. 95). Support the tube vertically over the table by means of clamps, and raise or lower it until a magnified image of a millimeter scale lying on a block beneath it is in sharp focus, the distance from the table to the top of the tube being somewhat more than 25 cm. II. To determine its magnifying power, (a) Lay a meter stick on the table, as in Fig. 95, and elevate one end of it until the distance to the stick from the eye which is not looking through the microscope is exactly 25 cm. By fixing the attention simultaneously on the two scales seen, one through the microscope and the other with the unaided eye, determine how many millimeters on the meter stick * are covered by 1 mm. of the scale seen in the microscope ; that is, find the number of diameters of magnification of the microscope. (5) If ^ is the distance from the objective to the focal plane of the eyepiece, that is, the distance between the centers of the lenses minus the focal length f of the eyepiece, and if 1 2 represents the distance from the objective to the object viewed, then ljl z represents how many times the image formed by the objective is larger than the object. Since the eyepiece magnifies this image 25// times, the total magnifying power M of the compound microscope should be 25/f X ljl$ Measure l r and Z 2 and com pare the observed value of M with this calculated value. FIG. 95 RECORD OF EXPERIMENT (a) Observed magnifying power by comparing scales = ........................ diameters. cm.; cm.; 25 I f = ........................ cm. ; .. M = - * = ........................ diameters. * The distance on the meter stick which is covered by 1 mm. of the scale when viewed through the microscope may also be found by marking the projection of the two millimeter marks, as seen through the microscope, on a sheet of paper set 26 cm. from the eye, and then measuring the distance in millimeters between these two marks on the paper. The magnifying power M expressed in diameters is then obviously equal to the above-measured distance expressed in millimeters. r .125 1 EXPERIMENT 50 FIG. 96 PRISMS I. Path of a beam of light through a prism. Draw a line AC (Fig. 96) on a page of your notebook. Place the prism on the paper in the position indicated in the figure. Light coming to the prism in the direction AC will be bent both upon entering and upon leaving the prism. Place a ruler on the paper and adjust it carefully until it is exactly in line with the apparent direction of A C as seen through the prism. With a sharp pencil draw a line DE along the edge of the ruler, and trace the outline of the prism on the paper. Remove the prism and extend the lines AC and DE until they meet at / and #, the lines which represent the prism faces. Then AfgE will be the path of the light which traverses the prism. II. Dispersion, (a) With the aid of the knowledge gained in I, place the prism in direct sunlight in such a way that the beam from the sun is thrown upon some shaded portion of the floor. Place between the prism and the sun a sheet of cardboard containing a horizontal slit 2 or 3 mm. wide. Name the colors which you see upon the floor and into which the sunlight has been resolved. Which has suffered the largest bending in passing through the prism, and which the smallest? Cut two 2-mm. slits in the cardboard and leave a 2-mm. space between them. Cover one slit and note the spectrum; then uncover the slit and note the change in color in the middle of the patch where the two spectra overlap. Does this show that the spec- tral colors may be recombined into white light ? Hold the prism alone, without any slit, in the sunlight. Explain now why only the edges of the patch appear colored, while the middle appears uncolored. (5) Now place the prism immediately before the eye in such a way that you can observe through it a narrow (2-mm.) strip of white paper placed on a black back- ground, or, better still, an electric-lamp filament or the narrow edge of a gas flame. Explain why the red now appears to be on the side next the base of the prism, while the blue is nearer the apex. Substitute a broad sheet of paper for the narrow strip. When viewed through the prism, one edge will appear red, shading into yellow on the inner side, and the other will appear blue, shading into green. Explain why the paper does not appear colored in the middle, while it does appear colored at the edges. Explain further why the two edges are differently colored. III. Bright-line spectra'. Let one student hold successively in a Bunsen flame, arranged as in Fig. 97, three platinum wires or bits of asbestos, which have been dipped, one in a solution of common salt (sodium chloride), another in lithium chloride, and another in calcium chloride, taking care that the wire itself is kept below the lower edge of the slit s. Let other students look through the prisms at distances of about 10 ft., in the manner indicated in the figure, and record the character of the spectra to which the incandescent vapors of these substances give rise. IV. Path of a beam of light through a plate of glass with parallel faces, (a) Place two prisms together in the manner shown in Fig. 98, thus forming in effect a single piece of glass with the parallel edges om and pn. Draw a heavy line AB, then place a straightedge in line with the image of this line, and draw a mark A'B' along its edge, showing the direction of the light after passing through the [127] FIG. 97 FIG. 98 EXPERIMENT 50 (Continued) parallel faces om and pn. From the result obtained, state what happens to the direction of a ray of light which passes through a plate of glass with parallel faces. (5) Slide the two prisms along om until the line AB meets the first prism nearer its apex. Then slide the other prism along the common face until the perpendicular distance between the faces mo and pn is just one half as much as before, as shown in Fig. 99. With the same line AB and the face om exactly parallel to its initial position, draw again a line A'B' in the apparent prolongation of AB. (c) Slide the prisms into the position shown hi Fig. 100, being very careful to keep the face om parallel to its initial direction. The thickness of glass to be traversed will now be three times as great as in (T). Proceed precisely as in (a) and () above. (c?) Remove the prisms and prolong AB. Measure the perpendicular distances between AB arid the three prolongations of AB as seen through the three thicknesses of glass. State in what way the experiment shows that the lateral displacement of the beam varies with the thickness of the glass. (e) If the prisms are so placed that AB is perpendicular to the face om (Fig. 101), no trace of the line can be seen at A'B'. But if a drop of water is placed between the faces in contact along mp, the line AB can be seen very plainly at A'B'. Explain, remembering that the critical angle for rays of light passing from glass to air is about 42, while it is about 62 for rays passing from glass to water. If, now, A'B' is drawn as above and if AB is exactly perpendicular to om, then on removing the prisms and extending AB it will be found that AB and A'B' lie on the same straight line ; that is s there has been no lateral displacement. Why ? FIG. FIG. 100 [128] EXPERIMENT 51 TO MEASURE THE CANDLE POWER OF A WELSBACH BURNER AND OF AN ORDINARY OPEN GAS FLAME AND TO COMPARE THEIR COST OF OPERATION WITH THAT OF A TUNGSTEN LAMP I. The Welsbach burner. Place a 40 watt (34 C.P.), or a 60 watt (53 C.P.), tungsten lamp * at A, and a Welsbach burner at B (see Fig. 102). The Welsbach burner should be connected to the gas meter used in Exp. 18. FIG. 102 Slide the photometer C along the optical bench until the spot or cross in the photometer appears as nearly as possible the same on both sides. When in this position the spot is evidently illuminated equally by each light. Measure and record the distances AC and BC. If the optical bench has a graduated bar, these distances may be read directly on the bar. With a watch observe the length of time required for 1 cu. ft. of gas to pass through the burner, using the tungsten lamp for the source of known candle power. Compute the candle power of the Welsbach burner by use of the equation C.P. of source of light at A _ AC C.P. of source of light at B B(j z II. The ordinary open gas flame. Replace the Welsbach burner by an ordinary open gas flame and make a set of observations and calculations similar to those made in I. Questions, a. From your data calculate the number of cubic feet of gas consumed per hour by the Welsbach burner and also by the open gas flame. 6. At the price charged by your local gas company for gas compute the cost of operating for 500 hr. a Welsbach burner like that used above. What is the cost per candle power for the same length of time ? c. What is the cost per candle power of operating the open gas flame for 500 hr. ? d. At the price charged by your local power plant for electricity what is the cost per ca'ndle power of operating for 500 hr. the tungsten lamp used above ? e. Which of the three sources of light referred to in Questions b, c, and d has the lowest cost of opera- tion per candle power ? /. After taking into account the cost of the mantles required to operate a Welsbach lamp for 500 hr. and also the cost of the tungsten lamps which will give about the same candle power, which method of light- ing is the cheaper ? This method is approximately how many per cent cheaper than the other method ? * Accurately standardized electric lamps are unnecessary for this experiment, since the relative candle powers of the two sources at A and B does not depend upon knowing the exact candle power of the tungsten lamp. Therefore the relative cost per candle power of operating different lamps is obtained accurately by using the ordinary commercial lamp as a standard and using for its candle power the value given by the maker. [129] EXPERIMENT 51 (Continued) RECORD OF EXPERIMENT I. The Welsbach burner Candle power of tungsten lamp = , AC = , EC = .. candle power of Welsbach lamp = Time required to consume ^ cu. ft. of gas = II. The open gas flame Candle power of tungsten lamp = , AC = , BC = .-. candle power of open gas flame = Time required to consume ^ cu. ft. of gas = [130] EXPERIMENT 51 A I. Law of inverse squares, (a) Light the candle at A, and one of the group of four candles at B, in Fig. 103. Keep them trimmed so that they burn as nearly as possible alike with flames 3 cm. long. FIG. 103 Slide the photometer C along the optical bench until the spot or cross in the photometer appears as nearly as possible the same on both sides. When in this position the spot is evidently equally illuminated on both sides. Measure and record the distances AC and BC. If the optical bench has a graduated bar, these distances may be read directly on the bar. (5) Light two of the group of four candles at B. See that all three candles are burning properly, Again slide the photometer C to the position in which it is equally illuminated on both sides. Measure and record the distances AC and BC. (