UC-NRLF SB EM2 PHYSICAL LABORATORY GUIDE FREDERICK C. REEVE GIFT OF PHYSICAL LABORATORY GUIDE BY FREDERICK C. REEVE, E.E. MASTER IN PHYSICS, NEWARK ACADEMY, NEWARK, NEW JERSEY *** J V **"*'**>* *"> NEW YORK : CINCINNATI : CHICAGO AMERICAN BOOK COMPANY (Vt COPYRIGHT, 1912, BY FREDERICK C. REEVE. COPYRIGHT, 1912, IN GREAT BRITAIN. REEVE S PHYSICAL LABORATORY GUIDE. w. P. i ' / I- * PREFACE I HAVE endeavored to prepare a book which shall inspire in the pupil the spirit of inquiry and comparison towards his laboratory work. This appeals to me as the sanest and most rapid way by which to lead the beginner in sci- ence to a knowledge of its fundamental principles. The experiments chosen for this book are almost en- tirely quantitative. Twelve years' experience has taught me to use quantitative experiments in the laboratory and those of a purely qualitative nature in demonstrations in the class room, as far as possible. Again, the working directions in this manual are un- usually full. The delusion of giving the pupil only a hint about the experiment and then expecting him to work it out for himself always results in confusion on the part of the pupil and an impossible situation for the teacher. The pupil must have directions as to the main steps in the ex- periment. It is simpler to print these than to expect the teacher to give them over and over to each pupil. Attention is also called to the large number of questions scattered through the text. If the teacher will insist that the pupil's record contains the pupil's answers to these questions, they will be a great help in enabling him to un- derstand and remember the fundamental principles which each experiment teaches. Another feature of this manual is the reference notes. These include important fundamental laws and definitions iii 251955 iv PREFACE referred to in the text. Pupils always forget and should be taught to refresh their minds constantly by the use of works of reference. The tables of numerical data are full and carefully pre- pared and will be found useful. A few pieces of home-made apparatus are also described. These are inexpensive and require very little skill to make. Finally, this manual covers all the requirements of the " College Entrance " and other Examination Boards. Its wide range of subjects makes it possible to prepare from its pages courses to suit any requirement. I wish to acknowledge the helpful suggestions and criti- cisms of my associates and particularly the services ren- dered by my brother, Henry M. Reeve, A.B., in reading the proof. FREDERICK C. REEVE. HINTS FOR THE LABORATORY RECORD IT will be well to have the pupils familiarize themselves with the following plan before starting the laboratory work. The record of each experiment should have the following parts : 1. The Date. 2. The Experiment Number. 3. The Object. 4. The Numerical Data. 5. The Description. 6. The Conclusion. It will be found convenient to use a notebook bound on the side in such a manner that the pages of the open book will lie flat upon the table. Begin your record on the left-hand page by placing the date (day, month, and year) in the upper right-hand corner. Place the experiment number in the center of the page about an inch below the top. Copy the object given by \\\Q guide directly below the number, heading it Object, in the margin. Place the table for numerical data just a little below the object. This should be accurately laid out with a ruler and made large enough to hold the pupil's, handwriting without crowding. Mark this table Data, in the margin. Under the heading Description, also in the margin, write a complete record of everything you did of importance in connection with the experiment. A simple rule to follow is to put down the various steps in the experiment in the exact order in which you did them. vi HINTS FOR THE LABORATORY RECORD Remember that your readers will not have the Laboratory Manual or any other guide at hand when they read your record ; it should therefore be complete by itself. Finally write the conclusion, placing its heading in the margin. This should include your result in concise form, together with a clear and careful statement of any funda- mental laws or principles to which the experiment may lead. It is well to write upon but one side of the leaves. This will enable you to remove a leaf without disturbing a previously completed record. Remember that the original record made in the labora- tory is the one to be preserved. Therefore take pains to have it accurate, neat, and well laid out. When time permits, one laboratory period a month should be devoted to an informal discussion of the experiments per- formed that month. If several of the pupils' records are read and then criticized, first by the other pupils and then by the instructor, a valuable review of the work will be made, and, in addition, interest and friendly rivalry will be gained, which will greatly improve the pupils' records. The experiment to be performed each laboratory period should be assigned in advance, and the pupil required to study carefully the record of that experiment given in this guide. This will effect a great saving in time, and the pupil will go about his work much more intelligently. In performing the experiment and in writing the record, never lose sight of the real objects of your work in the laboratory : 1. To increase your knowledge of physics. 2. To train your hands for the delicate manipulation of various kinds of apparatus and many other things. 3. To form the habit of careful and accurate observation. 4. To gain the ability to record the results of your work in clear and logical fashion. CONTENTS CHAPTER I FUNDAMENTAL MEASUREMENTS EXPERIMENT J'AGK 1. To find the volume of a rectangular block i 2. To test the right-angled triangle relation .... 3 3. The use of the micrometer caliper ..... 4 4. A lesson on the use of a scalepan balance .... 5 5. The use of the graph in recording results .... 7 6. To calibrate a spring balance. The graph applied . . 9 CHAPTER II DENSITY AND SPECIFIC GRAVITY 7. To test Archimedes 1 principle . . . . . .n 8. To test the law of flotation . . . . . . .12 9. To find the volume of an irregular solid . . . .13 10. Density of a solid heavier than water . . . . .14 11. Density of a solid lighter than water 15 12. Density of a solid soluble in water ..... 16 13. Density of a liquid. Bottle method . . . . . 17 14. Density of a liquid. Fahrenheit hydrometer 18 15. Density of a liquid. Displacement method .... 20 16. Density of a liquid. Balancing columns .... 21 CHAPTER III MAGNETISM 17. Field about a bar magnet. Compass method . * . -23 18. Plotting several fields with iron filings 24 viii CONTENTS EXPERIMENT PAGE 19. Magnetic field about a single conductor .... 25 20. Magnetic field about a galvanoscope 28 CHAPTER IV VOLTAIC CELLS AND THERMOCURRENTS 21. Study of a simple voltaic cell ...... 30 22. Study of a Daniell cell. (Method i) 32 Study of a Daniell cell. (Method 2) . . . . 33 23. Thermocurrents from iron and copper 34 CHAPTER V ELECTRICAL TESTING 24. Method of handling a galvanometer. (Parti) 37 Relation between resistance and deflection. (Part 2) . -39 25. Resistance of a conductor. Substitution method . . 40 26. The e.m.f. of a cell. Equal deflection method ... 42 27. Resistance of a conductor. Wheatstone bridge ... 44 28. Resistance of a cell. Method of opposition . ... 47 29. Resistance of a cell. Mance's method 48 30. Resistance of a cell. Half-current method .... 50 31. Testing the laws of resistance . 52 32. The temperature coefficient of copper . ... . -53 33. Counter e.m.f. of a motor. Resistance: Fall of potential , method . . . . . . . . . -55 34. Construction and control of a motor 56 35. A study of the direct current dynamo 58 CHAPTER VI MECHANICS OF SOLIDS 36. The laws of beams. (Parti) 60 Plotting curves to show these laws. (Part 2) . .62 37. To test the parallelogram law . . . . . .63 38. To test the laws of parallel forces . . . . . 65 39. Center of gravity and weight of a lever . , . . .67 CONTENTS ix EXPERIMENT 40. To test the laws of vibration of a pendulum .... PAGE 69 41. To find the breaking strength of a wire .... 70 42. The elastic limit and " modulus of elasticity " of steel . 73 AT.. 7C T-J 44- To plot the path of a projectile on section paper . / } 7 6 45- To test Boyle's law V' . . 78 CHAPTER VII HEAT 46. Freezing point and boiling point of a thermometer . . 80 47- Variation of boiling point with pressure .... 82 48. The coefficient of linear expansion of brass . 83 49- Measurement of quantity of heat. " Method of Mixtures " . 85 50. The specific heat of a solid . . . . . ... , .,. 86 5 1 - The latent heat of fusion of ice . 88 52. The latent heat of vaporization of steam . 90 53- Dew point and per cent of humidity . . . . . 91 CHAPTER VIII LIGHT 54- The candle power of a lamp. Rumford photometer 94 55- The candle power of a lamp. Bunsen photometer 95 56. Position and kind of image in a plane mirror 96 57- The index of refraction from air to glass .... 98 58. The index of refraction from air to water .... 99 en. IOI jy 60. The lens formula = + Conjugate foci . F Do Di 102 61. The spectroscope . . . . . ' . . . 103 i CHAPTER IX SOUND 62. To plot several wave motions on section paper I0 5 63- To measure the vibrations of a tuning fork .... 107 X CONTENTS EXPERIMENT PAGE 64. Resonating air columns. Their relation to wave lengths . 109 65. To test the law of strings no 66. To find the velocity of sound in air 113 CHAPTER X NOTES ON THE EXPERIMENTS FVNDAMENTAL MEASUREMENTS (CHAPTER I) . . . .115 DENSITY AND SPECIFIC GRAVITY (CHAPTER II) . .^ . 119 VOLTAIC CELLS AND THERMOCURRENTS ; ELECTRICAL TESTING (CHAPTERS IV AND V) 123 THE MECHANICS OF SOLIDS (CHAPTER VI) . . . 131 HEAT (CHAPTER VII) . 140 LIGHT (CHAPTER VIII) r 142 SOUND (CHAPTER IX) 144 CHAPTER XI TABLES OF PHYSICAL CONSTANTS 147 CHAPTER XII APPARATUS REQUIRED FOR THIS BOOK AND SOME USEFUL HOME-MADE APPARATUS -175 PHYSICAL LABORATORY GUIDE CHAPTER I FUNDAMENTAL MEASUREMENTS EXPERIMENT 1 Object. To find the volume of a rectangular block. Apparatus. A weighted rectangular block, a 2O-cm. scale, a 5oo-c.c. graduate, and a piece of thread. Data. METHOD i. (By CALCULATION) OBSERVATIONS TRIAL i TRIAL 2 AVERAGE Length Width Thickness ..... Volume METHOD 2. (By DISPLACEMENT) OBSERVATIONS TRIAL i TRIAL 2 AVERAGE Volume of water Volume of water and block Volume of block Directions, Method i. To measure the length of the block, place the metric scale parallel with one of its edges LABORATORY GUIDE and in such a position that the graduations are in contact with the block. One end of the block should coincide with some convenient mark on the scale. The zero mark should be avoided if the divisions near it are worn. Now count the centimeters contained in the length of the block, also the additional tenths of centimeters (millimeters) and esti- mate the tenths of millimeters, writing these as hundredth parts of a centimeter. You will now have the length of the block in centimeters, accurate to the one hundredth part of a centimeter if the work has been carefully done. Record this in the table. For Trial 2, measure the length of the block on the opposite side, using a different part of your scale. This will average any irregularities in either the block or the scale and increase the accuracy of your work. Measure the width and thickness of the block in the same manner. Find the average length, width, and thickness, and from these calculate the volume of the block. Directions, Method 2. Fill the graduate about half full of water and read its volume, estimating tenths of the smallest divisions. It will be observed that capillary action causes the water to be drawn upward against the sides of the glass, giving the water the appearance of having two surfaces ; the lower of the two is evidently the true surface. Its position against the scale of the graduate is the one that should be measured. Now lower the block into the graduate by means of the thread and again read the 'position of the surface of the water. For Trial 2, start with a different quantity of water in the graduate and proceed as before. From these readings calculate the volume of the block. FUNDAMENTAL MEASUREMENTS 3 The Pupil's Aim. In this experiment particular effort should be made to gain proficiency in estimating tenths of the smallest divisions of the scales used. Keep in mind that the smallest part of a space which you can read may be called one tenth ; a scant quarter, two tenths ; a big quarter, three tenths ; a small half, four tenths ; etc. This process of estimating tenths will be used in all sub- sequent work. Its importance cannot be overestimated. Conclusion. i. Explain any difference in results given by the two methods. 2. How would you find the volume of an irregular solid ? EXPERIMENT 2 Object. To test the relation between the arms and the hypotenuse of a right-angled triangle. Apparatus. A small draughtsman's triangle and a 2O-cm. scale. Data. LENGTH OF ARM i ARM 2 HYPOTENUSE Trial I Trial 2 Average (Average) 2 Error Directions. Measure the three sides of the triangle in centimeters. Follow the directions for measuring given in Experiment i. As this experiment is a test of your ability to estimate tenths of millimeters, special attention should 4 PHYSICAL LABORATORY GUIDE be given to this point. Average the lengths found in Trials I and 2 and square the results. Add the square of arm I to the square of arm 2 and compare this sum with the square of the Hypotenuse. Conclusion. State the true relation between the arms and the hypotenuse of any right-angled triangle. What is the probable cause of your error ? EXPERIMENT 3 Object. To measure several small objects with a mi- crometer caliper. Apparatus. A micrometer caliper, pieces of wire and sheet metal, and a ruler. Data. OBJECT TO BE MEASURED TRIAL i TRIAL 2 AVERAGE Directions. The micrometer caliper applies the prin- ciple of the screw, one of the six simple machines. The pitch of the screw is made some convenient size, such as .025 of an inch. If the' scale on the movable sleeve is divided into twenty-five parts, the instrument reads thou- sandths of an inch directly, and ten-thousandths may be obtained, with a fair degree of accuracy, by estimating tenths of these smallest divisions. FUNDAMENTAL MEASUREMENTS 5 The smallest spaces on the fixed scale are each one revolution, and consequently have a value of twenty- five one-thousandths of an inch. A group of four of these will therefore have a value of one tenth of an inch. To make a measurement, close the instrument upon the object, using the greatest care to insure that the jaws of the caliper touch the object lightly and no more. The use of any pressure would change the size of the object, or injure the micrometer, or possibly both, besides giving an incorrect measurement. Read the whole spaces on the stationary scale, and the whole divisions on the movable sleeve and estimate the value of a fractional part of one of these spaces to the nearest tenth. The sum of these readings with their proper values assigned is the required size of the object. Make two or more trials for each object measured and record these trials and the average value obtained from them. Conclusion. Give two reasons why several trials are desirable. If you have just used a micrometer reading in the English system, suggest a convenient pitch and arrangement of scales for such an instrument to read in the Metric system, or vice versa. EXPERIMENT 4 Object. To make a weighing with a scalepan balance. Apparatus. A scalepan balance, a set of weights, 500 gm. to 10 mg., several small objects of various weights. PHYSICAL LABORATORY GUIDE Data. NAME OF OBJECT SUM OF GRAM WEIGHTS SUM OF MILLIGRAM WEIGHTS COMPLETE WEIGHT Directions. (i) Be sure that the balance is true before using it. This is easily determined by allowing it to swing through a small arc. If true, the vertical index will swing through equal arcs on either side of its vertical position. Make any necessary adjustment. If no other means is provided, add a small piece of paper to the light scalepan, adjusting its size until the balance is perfectly true. (2) Never handle any weights with your fingers. Use the tweezers provided for the purpose. Contact with the moisture of the hand corrodes the weights. (3) Try all the weights in order, beginning with the heaviest one which you think will be required. Following this simple rule will give rapid and accurate results. (4) There are only two places for the weights while making a weighing: (a) in the scalepan of the balance; (^)'on the block provided for the purpose. After adjust- ing the balance with the object in one of the scalepans, count the weights in the other pan, adding the whole gram and milligram weights separately. Record these results. Now divide the milligrams by one thousand, to reduce them to grams. Record the complete weight in the last column of the table. FUNDAMENTAL MEASUREMENTS The most common source of error in weighing is in summing up the weights. After adding the weights on the balance, obtain the sum of the vacant spaces in the block, assigning to each space the value of the weight it holds when it is in place. Compare these results. Conclusion. Write a brief statement of the directions given above. This should be carefully followed in all sub- sequent weighing. What is double weighing ? Look this subject up if you do not know. What trouble with an imperfect balance does it overcome ? EXPERIMENT 5 Object. To study the curve as a method of showing the relation between two quantities. Apparatus. Millimeter section paper and a straightedge. Data. CURVE i CURVE 2 CURVE 3 SCALE 2 MM. SCALE i MM. SC. I CM. SC. I MM. Abscissae Ordinates Abscissas Ordinates Abscissae Ordinates O 10 O 10 10 30 20 4 4 20 20 60 30 8 16 30 30 9 40 12 36 40 40 120 50 16 64 5 50 150 60 20 100 60 60 I 80 70 Directions. About 2 cm. from the edge of the paper and coinciding with one of the ruled centimeter lines, PHYS. LAB. GUIDE 2 8 PHYSICAL LABORATORY GUIDE draw a horizontal line lengthwise on a sheet of section paper. Mark this line axis of X. About 2 cm. from the left-hand edge of the paper and also coinciding with a ruled centimeter line, draw a line at right angles to the axis of X and mark this the axis of Y. The intersection of these axes is called the origin. Mark the origin o. The origin should be in the lower left-hand corner of the paper. Distances measured along the axis of X are called abscissae; distances measured along the axis of Fare called ordinates. Now lay off the distances called for in the table for curve number one on the axes of Jf and F Let each unit be equal to 2 mm. in this curve. Since the smallest values of both the abscissae and ordinates are zero, the curve begins at the origin o. To locate the next point of the curve, find where the vertical line passing through abscissa 10 intersects the horizontal line passing through ordinate 10. In like man- ner determine the other points of the curve and connect them with a line. Plot Curves 2 and 3 on the same paper, using the same s axes as in Curve i. File these curves in your notebook with the record of this experiment. Conclusion. What determines the scale to be used in plotting a curve ? Why are two of these curves straight lines ? Does this show any relation between the quantities involved ? The third curve is known as a parabola. A projectile fired horizontally has a path like this third curve. Explain the advantages of the Curve in recording data. FUNDAMENTAL MEASUREMENTS EXPERIMENT 6 9 Object. To calibrate a spring balance and show its errors- by a curve. Apparatus. A spring balance (0250 gm.), a set of weights, a piece of thread, millimeter section paper, and a 30-cm. scale. Data. LOAD BALANCE READING ERROR LOAD BALANCE READING ERROR Directions. Attach the thread to the balance, using a short piece. Its weight may be disregarded. Note whether the balance reads zero before weights are attached. Using a slipknot to hold the weights, attach 25, 50, 75 gm., etc., and read the balance each time. If the balance reads more than the value of the weights attached, the error is positive ; if less, negative. On section paper draw axes of X and Y as directed in Experiment 5, page 7. On the axis of X plot the loads in grams attached to the balance (scale I mm. equals I gm.). On the axis of Fplot the corresponding errors (scale I cm. equals I gm.). Positive errors should be plotted above axis of X, and negative values below. Axis of X should pass through center of paper. Connect the points thus deter- mined with a broken line. 10 PHYSICAL LABORATORY GUIDE Compare your curve with those plotted by your class- mates, and decide who has the best balance. Measure the balance scale with the metric rule and determine whether or not its divisions are perfectly uniform. Conclusion. Write Hooke's law. State whether you think the balance errors are due to a failure upon its part to follow Hooke's law, or whether its failure is caused by an unevenly divided scale. Base your opinion on your ob- servations and measurements in this experiment. Can you think of any other source of error ? CHAPTER II DENSITY AND SPECIFIC GRAVITY EXPERIMENT 7 Object. To test Archimedes' principle. Apparatus. A balance, a set of weights, a solid heavier than water, an overflow can, a catch bucket, a piece of thread, and a jar of water. Data. OBSERVATIONS GRAMS \Veisjht of solid in air \V6i r ht of solid in water XVcio'ht of empty catch bucket Weight of catch bucket and displaced water . . Loss of wei"ht of solid in water . ... \Vei r ht of the displaced water ... Directions. Suspend the solid fom the hook on the under side of the scalepan of the balance by means of the piece of thread. Adjust the length of the thread so that the solid shall be in the center of the jar of water when the scale beam is horizontal. Weigh in air and in water. Weigh the empty catch bucket. Cover the spout of the overflow can with your finger and fill it with water. Place it on a level table and release your finger, catching the 12 PHYSICAL LABORATORY GUIDE surplus water in the overflow can. Discard this water. By means of the thread lower the solid into the can and catch the displaced water. Weigh this. Calculate the loss of weight of solid in water and the weight of the dis- placed water. Compare these results. Conclusion. State Archimedes' principle. Does your error disprove the principle, or can you account for it? What is the most probable source of error ? EXPERIMENT 8 Object. To test the law of flotation. Apparatus. A cylinder weighted to float upright in water, an overflow can, a catch bucket, a balance, and a set of weights. Data. OBSERVATIONS GRAMS \Veijjht of cylinder in air Weight of catch bucket and displaced water . . . Weight of the displaced water Error Directions. Make the weighings called for in the table. Follow the directions given in Experiment 7 for using the overflow can and catch bucket. One end of the cylinder is weighted to make the block float upright in water. When the block is floated in the overflow can, this weighted end should be immersed first. Compare the weight of the cylinder in air with the DENSITY AND SPECIFIC GRAVITY 13 weight of the water displaced by it. What relation exists between these quantities ? Conclusion. Write the law of flotation. Will this law hold true for other liquids than water ? EXPERIMENT 9 Object. To find the volume of an irregular solid. Apparatus. The irregular body, a balance, a set of weights, a jar of water, a loo-c.c. graduate, and a piece of thread. Data. OBSERVATIONS Weight of body in air . ' \Veight of body in water . Loss of weight of body in water Volume of water in graduate Volume of water and body in graduate . . . '. Volume of the body, using a graduate . . . . Volume of the body, using a balance Directions. Suspend the irregular body from the bal- ance as directed in Experiment 5 and weigh it in air and in water. Calculate its loss of weight in water. Pour some water into the graduate and read its volume. Im- merse the irregular solid and read the combined volume of solid and water. Remember to estimate tenths of the smallest divisions. Calculate the volume of the irregular solid. Compare this volume with the loss of weight of the solid in water. Explain why the loss of weight of a solid 14 PHYSICAL LABORATORY GUIDE in water in grams is equal to its volume in cubic centi- meters. Remember that one cubic centimeter of water weighs one gram. Also consult Archimedes' principle. Conclusion. Which method is more likely to give accurate results ? Give your reasons. Could this method of using the balance for finding the volume of a solid be used conveniently with English units ? Give your reasons. EXPERIMENT 10 Object. To find the density of a solid that will sink in water. Apparatus. A balance, a set of weights, a jar of water, a piece of thread, and a heavy solid. Data. OBSERVATIONS Weight of solid in air Weight of solid in water Loss of weight of solid in water Volume of this solid Density of this solid Directions. Place the solid in one of the scalepans of the balance, and weigh. Now suspend the solid by the thread, and weigh in water. A correction should be made for the weight of the thread, by counterbalancing the thread with paper just before weighing the body in water, or better still by weighing the thread and deducting its weight. Calculate the loss of weight in water and from this the volume of the solid. DENSITY AND SPECIFIC GRAVITY 15 Dividing the weight of the solid in air by its volume gives the density. Why ? Conclusion. Define density. State the value you find for the given substance together with the true value ob- tained from your instructor or the tables in Chapter XL EXPERIMENT 11 Object. To find the density of a solid lighter than water. Apparatus. A balance, a set of weights, a jar of water, a sinker, a piece of thread, and a piece of cork. Data. OBSERVATIONS \Vei r ht of sinker in water ..... \V6i r ht of cork and. sinker in water . . Loss of weight of cork and sinker in water Loss of weight of sinker alone in water .... Loss of weight of cork alone in water Density of the cork Directions. Make the four weighings called for in the table, allowing for the weight of the thread. If a small loop that will not slip is tied in one end of the thread and the free end is passed through it, a slipknot which is readily untied is formed. By this means the sinker and cork may be fastened close together. Now make a slipknot in "the free end of the thread. This affords a convenient way of 16 PHYSICAL LABORATORY GUIDE attaching the sinker and cork to the balance and at the same time the means for adjusting the height of the objects under water. Find what the cork and sinker together weigh in air. Subtract what they together weigh in water to find the loss of weight of both in water. The loss of weight of sinker alone is readily found. Knowing how much weight both sinker and cork lose in water, find what cork alone loses in water. This will be the volume of the cork. Why ? Divide the weight of cork in air by its volume to find its density. Why ? Conclusion. Define density and compare your result with the true density of cork. Is the density of cork always the same ? Why ? EXPERIMENT 12 Object. To find the density of a solid that is soluble in water. Apparatus. A balance, a set of weights, a jar of alco- hol, a piece of copper sulphate, and a piece of thread. Data. OBSERVATIONS Weight of copper sulphate in alcohol Density of alcohol (from table of densities) . Loss of weight in alcohol . . . ^^^eight of the displaced alcohol . . Volume of the copper sulphate Density of the copper sulphate DENSITY AND SPECIFIC GRAVITY 17 Directions. Make the two weighings called for in the table. Allow for the weight of the thread. Now look up the density of alcohol in the table and calculate the loss of weight of copper sulphate in alcohol. What relation exists between this quantity and the weight of the displaced alcohol ? The density of alcohol is the weight of one cubic centi- meter of it. Knowing this, how will you find the volume of the displaced alcohol ? The volume of the copper sul- phate ? The density of the copper sulphate ? Conclusion. State the density you find for copper sul- phate and compare it with the true value obtained from your instructor. Account for any difference. EXPERIMENT 13 Object. To find the density of a liquid, using the density bottle. Apparatus. A wide-mouthed bottle with accurately fit- ting glass stopper, a balance, a set of weights, and some alcohol. Data. OBSERVATIONS Weight of empty bottle and stopper . . . . . Weight of bottle filled with alcohol Weight of bottle filled with water Weight of alcohol contained in bottle Weight of water contained in bottle Volume of the alcohol used 1 8 PHYSICAL LABORATORY GUIDE Directions. Weigh the empty bottle and be sure that it is clean and dry. Pour alcohol into the bottle until the neck is half full. Now put the stopper firmly in place, allowing it to displace a small quantity of the liquid. Care should be taken not to inclose air bubbles, as the bottle should be completely filled with liquid. Make all observa- tions required in the table. In finding the volume of the alcohol, remember that one cubic centimeter of water weighs one gram, and also that you know the weight of the water which the bottle will hold. Knowing the weight and volume of the alcohol used, its density is easily found. Conclusion. State the density you find for alcohol and compare it with the true value. Why should not a cork or a rubber stopper be satisfactory for a density bottle? Knowing the density of alcohol, what would its specific gravity be ? Why ? Define specific gravity. EXPERIMENT 14 Object. To find the density of a liquid, using a Fahren- heit hydrometer. Apparatus. A Fahrenheit hydrometer, an ordinary hydrometer of constant mass, some alcohol, two hydrom- eter jars, a set of weights, and a balance. Description. The Fahrenheit hydrometer consists of a cylindrical shell weighted at the bottom. This enables it to float upright in the liquid used. At the top is a long stem carrying a scalepan to which weights may be added. A mark on the stem indicates the depth to which this in- strument should be immersed. DENSITY AND SPECIFIC GRAVITY Data. OBSERVATIONS Weight of Fahrenheit hydrometer Additional weight required to sink hydrometer in alcohol Additional weight required to sink hydrometer in water Total weight (hydrometer and load) floating in alcohol v . Total weight (hydrometer and load) floating in water Weight of alcohol displaced . Weight of water displaced . Volume of the alcohol . Density of the alcohol (Fahrenheit hydrometer) Density of the alcohol (ordinary hydrometer) . . Directions. Weigh the Fahrenheit hydrometer. Place it in the jar of alcohol and add weights to its scalepan until it just sinks to the mark on the stem. Make the same adjustment with the hydrometer floating in water. Find the total weight of the floating body in each case. What relation exists between these values and the weights of alcohol and water displaced ? Consult Experi- ment 10. Find the volume of the displaced alcohol. Note that the displaced alcohol and water have the same volume. Why? Calculate the density of alcohol. Immerse the hydrom- eter of constant mass (ordinary commercial form) in the alcohol and read its density. Conclusion. Compare the densities found by the two hydrometers. Which is more accurate ? Why ? Has the 20 PHYSICAL LABORATORY GUIDE other any good qualities ? State the law upon which the action of these hydrometers depends. The terms constant volume hydrometer and constant mass hydrometer are sometimes applied to these instruments. Why ? What is the specific gravity of this liquid ? Why ? EXPERIMENT 15 Object. To find the density of a liquid by weighing a solid in the liquid and in water. Apparatus. A large glass stopper or other insoluble solid, a balance, a set of weights, a jar of alcohol, a jar of water, and a piece of thread. Data. OBSERVATIONS \Veififht of water displaced ... Volume of the displaced alcohol Density of the alcohol . ... Directions. Attach the solid to the balance by the thread before any weighings are made. Now make the weighings as shown in the table. Note the suggestions for doing this in Experiment 8. This will eliminate the weight of the thread from the final result. Why ? Find the remaining quantities in the table by calculation as in the preceding experiments. DENSITY AND SPECIFIC GRAVITY 21 Conclusion. Compare your result with the true density of alcohol. What law does this experiment apply ? What is the specific gravity of alcohol ? Why ? Does this rule always hold true ? EXPERIMENT 16 Object. To find the density of a liquid by balancing columns. Apparatus. Two pieces of glass tube about a meter long, one piece of glass tube about 30 cm. long, a Y tube, rubber tubing for connecting apparatus as shown in Figure I, pinch cock, meter stick, half- meter stick, bottles of water and of alco- hol. Data. FIG. i. OBSERVATIONS Distance from table to alcohol surface in tube . . Distance from table to alcohol surface in bottle . . Length of effective alcohol column . Distance from table to water surface in tube . Distance from table to water surface in bottle . . Length of effective water column Density of alcohol Directions. Set up the apparatus as shown in Figure i. Partially exhaust the air from the apparatus until the alco- hol is nearly up to the top of the vertical tube. Close the 22 PHYSICAL LABORATORY GUIDE pinch cock. Do not move the short glass tube, as this would probably change the heights of the liquids in the tubes slightly. Why ? Be sure that the apparatus is per- fectly tight. The smallest leak would cause the liquid columns to drop slowly. The effective lengths of alcohol and water columns are the distances from the surfaces of the liquids in the bottles to the surfaces of the liquids in the tubes. It is difficult to measure these lengths directly. It is better to calculate their values from the measurements called for in the table. Dividing the effective length of water column by the effec- tive length of alcohol column gives the density of alcohol, for these columns are of equal weight. Why ? Also their volumes are proportional to their lengths. Therefore, remembering that the density of water is one gram, we can make an inverse proposition between the two densities and the two column lengths, or, which amounts to the same thing, divide the water by the alcohol column as given above. Conclusion. Compare all the methods you have used for finding the density of a liquid. Which is most accu- rate ? Which is of greatest value commercially ? CHAPTER III MAGNETISM EXPERIMENT 17 Object. To plot the field about a bar magnet by means of a small compass. Apparatus. A sheet of paper 30 x 50 cm., a bar mag- net, and a compass. Directions. Place the sheet of paper upon the table with the magnet in the center of the paper, the north-seek- ing end of the magnet pointing north. Draw the outline of the magnet. (It is possible to find the magnetic merid- ian and also to determine the north-seeking end of the bar magnet with the apparatus given. How ?) Now place the compass near one corner of the magnet. With your pencil place a dot on the paper to show the position of the end of the needle farthest from the magnet. Move the compass until the end of the needle nearest the mag- net coincides with the dpt. Indicate the new position of the other end by a second dot. Proceed in this way until you reach the other pole of the magnet or the edge of the paper. Carefully draw a curved line through the dots, in- dicating the direction in which the north-seeking end of the compass points along this line by an arrow. In the same manner draw other lines, starting from different points on the sides and ends of the magnet. PHYS. LAB. GUIDE 3 23 24 PHYSICAL LABORATORY GUIDE When you have drawn a sufficient number of lines to show the direction of the field on all parts of the paper, place the compass on the bar magnet and move it back and forth, noting the direction in which the needle points. What does this indicate regarding the direction of the magnetic force within the magnet ? Using dotted lines to show the direction of the magnetic force within the mag- net, complete the drawing. Mark the poles of the mag- net N and S. Fold the completed drawing to a convenient size and file in your notebook. Conclusion. Where do the lines of force begin and end ? Do any two lines intersect ? What is the direction of the magnetic force within the magnet ? Why do the lines drawn represent the direction of magnetic force in the field about the bar magnet ? EXPERIMENT 18 Object. To plot several magnetic fields by means of iron filings. Apparatus. Two bar magnets, iron filings, a wire- gauze sieve, thumb tacks, blue-print paper (6" X 8"), a large jar of water, a board 8" x 14" with slot i" wide and \" deep running lengthwise through the center, to hold magnets. Directions. Place one of the magnets in the slot of the board and cover it with a sheet of blue-print paper, placing the sensitive side up. Be careful to have the mag- net in the center of the paper. Fasten the paper in posi- tion with thumb tacks. Write your name in a corner of MAGNETISM 25 the paper. Now sprinkle filings evenly over the paper, holding the sieve about a foot above it and tapping the sieve gently to release the filings. Avoid using too many. A light covering will show the details of the field best. Now expose the apparatus as arranged to direct sunlight for five minutes. Then remove the filings and immerse the blue print in water, washing it thoroughly. Place the print face down on a clean pane of glass to dry. Then file it in your notebook. Make prints also : (a) of the field about two unlike poles ; (b) about two like poles. Use separate magnets with the poles about 3 cm. apart. Conclusion. State what each print shows as to the direction and arrangement of the magnetic field. Why do the filings show the directions of the lines of force ? State the principle involved. NOTE. If sunlight is not available, excellent results may be obtained by using an arc light and placing the paper to be printed not more than i| feet away from the arc and under it. The time required under these conditions will not exceed ten minutes with a 2o-ampere arc. Unless the sun^ rays are nearly vertical, the filings will cast shadows which are very different in size and shape from the filings themselves. This is a serious objection, and the arc-light, although slower, is much to be preferred. EXPERIMENT 19 Object. To investigate the magnetic field surrounding a single conductor carrying an electric current. Apparatus. About a meter of insulated copper wire (20 B. & S. gauge), some source of direct current (about 2 or 3 amperes), a small magnetic compass with graduated scale, a small wooden block, and a ruler. 6 PHYSICAL LABORATORY GUIDE Data. POSITION OF WIRE DIRECTION OF CURRENT DIRECTION OF DEFLECTION MAGNITUDE OF DEFLECTION Directions. Draw two perpendicular lines about 10 cm. long each and intersecting in the center of your notebook page. Place your compass so that its center and the intersection of the lines just drawn coincide. Trace the outline of the compass. Using the letters N, S, etc., etc., indicate the points of the compass on the ends of the intersecting lines. These should give the true directions of the four chief points of the compass when the notebook is before you in the usual convenient position for use. Place compass in the circle and have the north and south lines of the diagram and the compass scale coincide with the direction of the magnetic needle. All three will now be in the magnetic meridian. Place the conductor parallel to the north and south line of the diagram, with the current flowing from south to north. Note the direction and mag- nitude of the deflection and record in the table. Reverse the current and again test and record. In like manner, test with the conductor below the needle. Reverse the current and test again. Now place the conductor along the east and west line both above and below the needle, and in both cases try the current first in one direction and then in the other. Record all results. MAGNETISM 27 Place the compass on the block and hold the wire in a vertical position near the compass and on its north side. Test with the current in both directions. Also hold the wire just south of the compass and try the deflection with current flowing up and then down through the wire. You will now have made twelve different tests. Conclusion. State the relative position of the conductor and the lines of force as shown by this experiment. Test the following rules by applying them to the results you have just obtained; then include them in your con- clusion : 1. Place the right hand in such a position that the palm faces the compass and the conductor is between the com- pass and your hand. Then if the outstretched fingers point in the direction in which the current is flowing, the extended thumb will show the direction in which the north- seeking end of the needle will deflect. 2. If an ordinary right-handed, wood screw is turned by means of a screw driver, and if its forward motion into the wood is made to represent the direction in which a current is flowing along a conductor, then the direction of circular motion of the handle of the screw driver will show the direction of the lines of magnetic force surround- ing it. 3. Looking at the end of a conductor in which an electric current is flowing, state whether the lines of force are clockwise or counterclockwise when the current flows toward you, and vice versa. NOTE. The pupil should make a special effort to gain a very clear idea of the relative positions of the current and the lines of magnetic force from this experiment. The rules just given are secondary to this. 28 PHYSICAL LABORATORY GUIDE EXPERIMENT 20 Object. To map out the lines of magnetic force about a galvanoscope. Apparatus. A galvanoscope, a compass, a ruler, and a source of direct current. Directions. Draw a diagram in your notebook like the one shown in Figure 2. This will represent roughly a section of the galvanoscope as it would appear if seen from FIG. 2. above with the upper half of the coil removed. The small circles show the wires of the coil. Use a plus sign to mark those wires in which the current is flowing toward you. Use a minus sign to indicate those wires in which the current is flowing away from you. Now place the gal- vanoscope so that its coil is in the magnetic meridian, and pass a current of about five amperes through it in the direction indicated. Hold the compass in position a and draw an arrow to indicate the direction in which the north- seeking end of the needle points. In like manner test the direction of the magnetic field at points b, c, d and a', b', c { ', and 2-*i)*i Conclusion. Show that the formula given is correct for temperature coefficient. Compare your result with the temperature coefficient of copper given in the Appendix. ELECTRICAL TESTING EXPERIMENT 33 55 Object. To measure the counter e. m. f. of an electric motor. Apparatus. A small 10- volt shunt-wound electric motor (see Chap. XII), a voltmeter ammeter, sufficient batteries to give 10 volts, or a 5-ampere lamp bank with resistance coils in series giving 10 volts when used as a potentiometer (see Chap. XII). This is more satisfactory than the bat- teries if street direct current is available. Data. OBSERVATIONS Fall of potential across the field . . . Current through the field * Calculated resistance of the field ''.' Fall of potential across armature ...... Current through armature Calculated resistance of armature . . . '.'-.-. " : Combined resistance of field and armature , . . !.; Impressed e m f. motor runnin^ . ^ Current drawn by motor while running . Counter e m. f of motor ' Directions. Measure the resistance of the field and the armature separately by the fall of potential method as follows : Connect the voltmeter in parallel with the field and the ammeter in series with it and observe the readings carefully. Substitute the values just obtained in Ohm's law and calculate the resistance of the field. Find the resist- ance of the armature in the same manner. Now find the combined resistance of field and armature by calculation (see Chap. XI, page 170). With the armature and field con- PHYS. LAB. GUIDE 5 56 PHYSICAL LABORATORY GUIDE nected in shunt, measure the current taken and the e. m. f. impressed upon the motor while it is running. Substitute the values just found in the formula r E~ e ~~ where C = current taken to run motor. E = impressed e. m. f. e = counter e. m. f. R = combined resistance of both field and arma- ture in parallel, and solve for e. Conclusion. Explain the cause and use of the counter e. m. f. in a motor. EXPERIMENT 34 Object. To study the construction and control of a shunt-wound electric motor. Apparatus. A small ic-volt shunt-wound electric motor (see Chap. XII), a voltmeter, batteries to give 10 volts or special lamp bank (see Chap. XII) if street direct current is available, a compass (magnetic), a resistance box, and a small screw driver. Directions. Remove the pulley from the armature shaft, unscrew the bearing, and withdraw the armature carefully. Pass a small current through the field coil and test the po- larity of the magnet. Make a diagram of the motor in your notebook and mark the poles just tested. In like manner test the armature for poles with the compass. The current should pass into the armature through diametrically oppo- site points on the commutator. Mark the armature poles on the diagram, also. ELECTRICAL TESTING 57 Now carefully reassemble the motor and start it running as slowly as possible. Regulate its speed by using the smallest number of batteries or lamps on the lamp bank, which will give voltage enough to operate the motor. Meas- ure this pressure with a voltmeter. Now gradually increase the speed of the motor by putting more batteries or lamps in circuit. Note the readings of the voltmeter for each change of the speed of the motor. Connect a resistance box in series with the armature of the motor only, and while it is running remove the I, 2, 3, 5, and 10 ohms plugs in succession, noting carefully the change produced each time in the speed of the motor. Next connect the resistance box in series with the field of the motor only and remove the I, 2, 3, 5, and 10 ohms plugs in succession, noting again the effect upon its speed. Arrange the connections so that the motor runs in the reverse direction. Conclusion. Explain why the armature of an electric motor revolves. State the effect produced upon the speed of the motor and the reason for it in each of the following cases : I. When the voltage is changed. II. When resistance is put in series with the armature. III. When resistance is placed in series with the field. Does reversing the potential on a shunt-wound motor cause it to run v backwards ? Why ? If you have previously performed Experiment 33, then explain the relation of the counter e. m. f. of the motor to each of the cases I, II, and III just considered. What are the relative advantages of high and low speed motors of the same power ? PHYSICAL LABORATORY GUIDE EXPERIMENT 35 Object. To study the direct current dynamo. Apparatus. Two small shunt-wound direct current motors (see Chap. XII), a voltmeter, an ammeter, a rubber band or very small leather belt, a lo-volt battery or a potentiometer lamp bank (see Chap. XII), and a resist- ance box. Data. OBSERVATIONS SELF EXCITED SEPARATELY EXCITED E. M. F. used upon the motor . . . Amperes drawn by motor Watts consumed by motor .... E. M. F. generated by dynamo . . . Current drawn from dynamo .... Watts output of dynamo Efficiency of the transformation Directions. Belt the motor and dynamo together. Use as high an e. m. f. as possible on the motor and measure the volts and amperes consumed by motor and generated by the dynamo. Do this with the dynamo, exciting its own field and also with its field separately excited. Record both sets of data. Use the resistance box as a load for the dynamo, ad- justing the plugs until the dynamo gives its greatest output. Calculate the watts used by the motor and generated by dynamo in both cases. Account for the difference in results. ELECTRICAL TESTING 59 The watts drawn from the dynamo divided by the watts put into the motor gives the efficiency. Express this in percentage form. Conclusion. State the principle upon which a dynamo works. Name the principal parts of a dynamo and state briefly the function of each part. If the energy put into and taken out of the motor and dynamo, respectively, is not equal, account for this apparent loss of energy. CHAPTER VI THE MECHANICS OF SOLIDS EXPERIMENT 36. PART 1 Object. To find how the bending of a beam varies (a) with the load, (&) with the length. Apparatus. A wooden strip 1.5 x 1.5 cm. cross section and 100 cm. long, means for supporting one end firmly, a vertical scale, a scalepan, and a set of weights. Data. LENGTH OF BEAM LOAD IN GRAMS SCALE READING WITHOUT LOAD SCALE READING WITH LOAD DEFLECTION , Directions. Arrange the apparatus as shown in Fig- ure ii. Using a beam 75 cm. long (from support to scale- pan) read the position of the upper edge of beam against the vertical scale. Place 100 gm. in the scalepan and again read the scale. Subtract the first from this second reading to find the deflection. In like manner make read- ings every 100 gm. until a load of 500 gm. is reached. 60 THE MECHANICS OF SOLIDS 6l Next, using a constant load of 500 gm., find the de- flection when the beam is 15, 30, 45, 60, and 75 cm. long. e e e e e FIG. ii. Record all numerical data in a table, as shown. Now look the data over -carefully and decide how the bending varies with the load and with the length. It is obvious that increasing either of these quantities increases the deflection ; hence the deflection varies directly both with the load and with the length. However, it may vary 62 PHYSICAL LABORATORY GUIDE as the square or cube or fourth power of the length. To settle this point, note the deflection when the beam is 30 cm. long and again when it is twice this length (60 cm.). Is the deflection twice as much when the length is doubled ? Is it four times as much (2 2 = 4) ? Or is it eight or sixteen times as much (2 3 = 8 and 2 4 = 16) ? Conclusion. Write the two laws for the bending of beams. Does your data agree exactly with these laws ? Why ? State Hooke's law. Compare it with your first law for beams. What are some of the probable sources of error in your work ? Suggestion. - If time permits, this experiment may be made to cover the third and fourth laws of beams, as fol- lows : Using a length of 75 cm. and a load of 500 gm., place two precisely similar beams side by side and with the scalepan resting on both. Note the deflection. Compare this with a single beam under the same conditions and state how the deflection varies with the width of beam. Next, place the two beams in the support, one below the other, and again load with 500 gm., using a length of 75 cm. Comparing this result with the corresponding one for a single beam will enable you to state the fourth law, i.e. how the deflection of a beam varies with the depth. The two beams are readily held together with rubber bands. EXPERIMENT 36. PART 2 Object. To plot two curves on one sheet of section paper to show the laws of beams. Directions. Use the data obtained in Part I. Draw axes of X and Y with origin in the lower left-hand corner THE MECHANICS OF SOLIDS 63 of the paper. Plot the weights and the lengths of beam used in the two cases along the axis of X and the corre- sponding deflections produced along the axis of Y. Use any convenient scale of such a size that the curves when drawn will almost fill the paper. The scale is easily decided upon by dividing the total number to be plotted along a given axis by the number of units of length of that axis, or vice versa. This quotient will probably be a fractional number. Choose the whole number nearest to this as the scale. It is better to plot and draw one curve completely before attempting the second. Consult Experiment 5 (" To study the curve as a method," etc.), if further details of the method of plotting curves are required. Conclusion. If two quantities are directly proportional, will their graph be a straight line or a curved line ? Is this always so ? Why are very long spans for bridges difficult to construct ? Suggestion. If Part 2 is used, it may well be recorded as a separate experiment. Two laboratory periods of the usual length will be necessary to complete both parts. EXPERIMENT 37 Object. To test the parallelogram law for two con- current forces. Apparatus. Three spring balances (0-250 gm.) with holders for use in a horizontal position, drawing com- passes, a 3O-cm. metric scale, a piece of thread and some pins, and a rectangular wooden block. 64 PHYSICAL LABORATORY GUIDE Directions. Cut the thread into three pieces of equal length. Fasten together three of the ends one- end of each piece. Make loops in the free ends and attach a balance to each. Arrange two of the balances to act as components and the third as an equilibrant. Put tension on all three and do not have any reading less than 100 gm. Hold the balances in position either with clamps and cords from the edge of the table, or by driving pins into the table. Care should be taken that the draw bar of the balance does not touch either side of the slot through which the index runs, as this would introduce a serious friction error. The draw bar and thread should be in the same straight line. Why ? Place a sheet of notebook paper under the threads and in such a position that the point of application of the three forces comes near one corner of the paper. Place two dots under each thread to indicate the directions of the forces. This is best done by placing one edge of the rectangular wooden block parallel to one of the strings and as near as possible to it without touching it. While in this position draw a short line along the edge of the block. This will be directly under the thread if the work is carefully done. If this is done at both ends of each thread, their directions will be accurately recorded. Read the balances and record the results in each case, between the dots just drawn. Remove the tension from the balances and note whether they read correctly or not at zero. If there is an error, add or subtract this, as the case may be, to the readings under tension. Using any convenient scale, such as one millimeter equals one gram, construct a parallelogram upon these components as sides, drawing the lines showing their directions through the points just found. Measure its THE MECHANICS OF SOLIDS concurrent diagonal and compare its value in grams with the equilibrant force. Conclusion. State the parallelogram law. What re- lation should exist between the resultant found above and the reading of the equilibrant balance ? What relation does exist in your result ? Does this prove or disprove the law ? EXPERIMENT 38 Object. To test the laws of parallel forces. Apparatus. Two spring balances (0-250 gm.), a meter stick, a 2OO-gm. weight, a 3O-cm. rule, and some thread. Data. u FORCE MAGNITUDE OF FORCE POINT OF APPLICATION 1 DIRECTION MOMENT OF FORCE Observed Corrected Symbol Position Arm Fulcrum Value h- 1 Component I Component II Equilibrant H Component I Component II Equilibrant S Component I Component II Equilibrant Directions. Hang the balances to the crossbar of tho table, just 96 cm. apart. Attach a meter stick to the bal- 66 PHYSICAL LABORATORY GUIDE ances by means of threads, with slipknots for adjustment. The threads should be just 2 cm. from the ends of the stick. By means of another thread fasten the 2OO-gm. weight to the stick, using rather a large hoop. For Case I place the weight at the middle point of the bar. The bar should be made horizontal by adjusting the threads. In Case 2 hang the weight from the 34-cm. mark. In Case 3 it should be suspended 74 cm. from the end of the bar. The bar should be horizontal before any observations are made. Take the observations called for by the table, making all measurements of position from the zero end of the meter stick. Remember that the arms of the forces are the perpendicular distances from the lines of action of the forces to the axis about which moments are taken. Remove the 2OO-gm. weight and note the balance readings under the weight of the meter stick alone. De- duct these values in each case from the observed balance readings to obtain the corrected readings. These values are then the components of the 2OO-gm. equilibrant. In Case I take moments about the 5 Number of degrees water is heated Number of degrees shot cools Specific heat of shot . ' Directions. Place about 300 gm. of shot in the calorimeter. Heat this in the boiler, stirring from time to time with a thermometer to secure even heating. This thermometer should be kept in the shot. While the shot is heating, adjust the balance. Weigh the empty calorimeter and then the same calorimeter con- taining about 100 c.c. of cold water. When the shot attains a constant temperature, take the temperature of the cold water. Quickly pour the shot into this water. Stir thoroughly, reading the thermometer at frequent inter- vals. When the temperature remains constant for two or three of these observations, record it as the temperature of the mixture. Again weigh the calorimeter and its contents. Calculate the remaining quantities in the table. In finding the specific heat of the shot, remember that there are two principles involved : i. That the heat lost by the hot substances in cooling is equal to the heat gained by the cold substances in warm- ing. Why ? PHYS. LAB. GUIDE 88 PHYSICAL LABORATORY GUIDE 2. That the heat lost or gained by any substance through a change of temperature is always equal to (spe- cific heat) x (mass) x (change of temperature). Apply these principles, letting x equal the specific heat of shot. Indicate the operations by an algebraic equation. Then solve for x. Conclusion. Define specific heat of a substance. Com- pare your result with the known value. What in your opinion are the most probable sources of error ? State the two principles given above. NOTE. Obtain specific heat of calorimeter from your instructor. The calorimeter is one of the bodies warmed. EXPERIMENT 51 Object. To determine the latent heat of fusion of ice. Apparatus. A boiler, a burner, a calorimeter, a ther- mometer, a balance, a set of weights, a blotter, and ice in lumps about the size of hickory nuts. Data. OBSERVATIONS Weight of empty calorimeter Weight of calorimeter and hot water Weight of calorimeter, water and melted ice . \Vei a ht of hot water . . . ^^eight of ice added Temperature of water before adding ice ... . Temperature of the mixture Number of degrees hot water cools . . . . ' Number of degrees melted ice is warmed . . . , Latent heat of fusion of ice . ...... HEAT 89 Directions. Fill the boiler about half full of water and heat it to 60 approximately. Weigh the calorimeter empty and also when it contains about 150 c.c. of the hot water. Prepare enough lumps of ice the size of a hickory nut to weight approximately 40 gm. Bend a blotter lengthwise through the center to form a V-shaped trough. Place the ice on this and dry each lump just as you drop it into the hot water. Special care should be exercised at this point, as adding water with the ice would cause a serious error. Why? The temperature of the hot water should be taken just before adding the ice and the temperature of the mixture just as soon as the ice is all melted and the water thor- oughly stirred. Weigh the mixture to find the exact weight of ice added. Apply the following principles to calculate the latent heat of fusion of ice : 1. The heat lost by the hot substances in cooling is equal to the heat gained by the cold substances in warming. Why? 2. The heat lost or gained by any substance through a change of temperature equals (specific heat) X (mass) x (change of temperature). 3. The heat lost or gained by any substance through a change of form equals (latent heat) X (mass). Notice (a) that both the hot water and the calorimeter lose heat by cooling, (b) that the ice takes in heat first in melting, second to heat the resulting water to the temper- ature of the mixture. Conclusion. Define latent heat of fusion. Compare your result with the known value. What are the most 90 PHYSICAL LABORATORY GUIDE probable sources of error ? State the principles involved in this experiment. NOTE. Obtain specific heat of calorimeter from your instructor. The calorimeter is one of the bodies cooled. EXPERIMENT 62 Object. To determine the latent heat of vaporization of steam. Apparatus. A boiler and cover, a burner, a calorimeter, a thermometer, a balance, a set of weights, and a steam trap. Data. OBSERVATIONS Weight of empty calorimeter Weight of calorimeter and cold water Weight of calorimeter, water and condensed steam. Weight of cold water Weight of steam added Temperature of water before adding steam Temperature of the mixture Number of degrees water is heated Number of degrees condensed steam cools . . . Latent heat of vaporization of steam Directions. Weigh the calorimeter empty and when it contains 200 gm. of cold water. Take the temperature of this water and immediately pass steam into it from the boiler. The delivery tube should dip about 2 cm. under the water, and the steam trap should be 3 or 4 cm. above the water. A paper pad or other non-conducting HEAT 91 substance should be placed between the boiler and the calorimeter. This will prevent the absorption of heat by radiation. Continue the heating of the water by the steam, stirring the mixture continually until the temperature reaches about 40 C. Remove the calorimeter quickly from the steam supply. Stir the mixture thoroughly, and record its exact temperature. Weigh the calorimeter and its contents and calculate the weights of water and steam used. To find the latent heat of steam apply the three prin- ciples stated in the last experiment, remembering (a) that the steam loses heat in condensing and also by the cooling of the water it forms, (b) that both the cold water and the calorimeter are raised in temperature and therefore absorb the heat given out by the steam. Conclusion. Define latent heat of vaporization. Com- pare your result with the known value. State the most probable sources of error. NOTE. Obtain temperature of steam from the barometer. See Experiment 43 for directions necessary to make this calculation. s^ EXPERIMENT 63 Object. To determine the dew point and per cent of humidity of the air in the laboratory. Apparatus. A polished calorimeter, a thermometer, finely cracked ice, either sal ammoniac or common salt, and a teaspoon. A sling psychrometer (desirable but not essential). This instrument depends upon the change in rate of evaporation with a change in the humidity. 92 PHYSICAL LABORATORY GUIDE Data. OBSERVATIONS Temperature of the laboratory Temperature when the dew first appears .... Temperature when the dew begins to disappear . . Water vapor in one kilogram of air to-day . . . Water vapor to saturate one kilogram of air to-day. Calculated dew point Calculated per cent of relative humidity .... Directions. Pour cold water into the calorimeter to a depth of about 3 cm. Stir the water with the thermome- ter and note its temperature. Add the cracked ice, very little at a time, with a teaspoon, stirring constantly. The temperature should drop about one half of one degree each time the ice is added. Continue in this way until dew begins to form on the outside of the calorimeter. Note carefully the temperature at which this occurs. Allow the calorimeter to warm gradually, stirring from time to time. Note the temperature when the dew begins to dis- appear. The average of these temperatures is the dew point. If the dew point is below o C., it will be necessary to add sal ammoniac or salt with the ice. Avoid letting moisture from the hand or breath come in contact with the calorimeter. From the table in the Appendix find the weight of water vapor necessary to saturate one kilogram of air at the dew point. This will be the actual weight of water vapor in one kilogram of the air in the laboratory at the time of the experiment. From the same table find the weight of water vapor necessary to saturate the same weight of air at the temperature of the laboratory. The ratio be- HEAT 93 tween these weights just found reduced to decimal form will give the per cent of relative humidity at the time of the experiment. Conclusion. Define dew point and per cent of humidity. Would the dew point be the same if you performed the experiment outdoors ? Would the per cent of humidity be the same ? Why ? What two things cause the per cent of humidity to change from time to time ? Why does a high humidity make a hot summer's day so much more uncomfortable ? Why will ice and salt lower the tempera- ture of the water in the calorimeter below o C., while ice alone will not ? NOTE. If a sling psychrometer is available, obtain the readings of its wet and dry-bulb thermometers after whirling it about gently for a few moments. From the depression of the mercury in the wet-bulb thermometer and the meteorological tables given in Chapter XI find the dew point and per cent of humidity. Compare these values with those obtained by the calorimeter method. CHAPTER VIII LIGHT EXPERIMENT 54 Object. To measure the candle power of a gas flame or incandescent lamp by means of a Rumford photometer. Apparatus. A large candle, a gas flame or an incan- descent lamp, an opaque rod and support, a piece of red glass, a meter stick, a white cardboard screen and support. Directions. Set up the vertical screen and place the opaque rod in front of it and about 3 cm. away. Arrange the candle and light to be measured about 50 cm. from the screen and in such positions that the two shadows cast by the rod are close together. Notice that the shadows are of unequal intensity. Move the lights toward or away from the screen until the shadows are equally dark. View them through a piece of red glass. This will do away with difference in color and make the comparison easier. Now measure the distance from the center of each light to the shadow which it illuminates. Remembering that the candle powers of lights vary directly as the squares of their distances from a screen which they illuminate equally, calculate the candle power of the gas flame or the incandescent lamp. 94 LIGHT 95 Make at least three trials, using different distances. Record the measurements and calculated results in tabular form. The arrangement of this table is left to the pupil. Care should be taken to keep the candle burning with a normal flame without smoking. This is accomplished by gradually cutting the wick shorter a very little at a time. Conclusion. Compare the law given for candle power under the conditions of this experiment with the law of inverse squares for the intensity of illumination. EXPERIMENT 56 Object. To measure the candle power of a gas flame or an incandescent lamp by means of a Bunsen pho- tometer. Apparatus. A large candle, a gas flame or an incan- descent lamp, a Bunsen photometer, and a meter stick. Directions. Set up the photometer in a darkened room with the candle on one side of the screen and the light to be measured on the other. Adjust the position of the screen, moving it toward or away from the candle until its translucent and opaque surfaces appear equally illu- minated. When this position is correctly found, measure the distances from the candle and the lamp to the screen. Remembering that the candle powers of lights vary directly as the squares of their distances from a screen which they illuminate equally, calculate the candle power of the gas flame or the incandescent lamp. Make at least three trials. Record the measurements and calculated results in tabular form. The arrangement of this table is left to the pupil. 96 PHYSICAL LABORATORY GUIDE Care should be taken to keep the candle burning with a normal flame without smoking. This is accomplished by cutting the wick off a very little at a time. Explanation. When the apparatus is correctly ad- justed, view the screen from the candle side and note that the light which reaches your eye from the opaque portion of the screen is reflected light from the candle, whereas the light which comes to your eye from the translucent spot is direct light from the lamp on the other side of the screen. Therefore when all parts of the screen are equally illuminated, the lamp and the candle are giving the same intensity of illumination at their respective distances from the screen. Hence their candle powers are directly proportional to the squares of their distances from the screen. In some forms of Bunsen photometer mirrors are provided for viewing both sides of the translucent spot at once. This is a decided advantage. Conclusion. State some of the difficulties connected with accurate photometric work. A standard candle should burn 120 gr. of the wax per hour. In the light of this statement, suggest how, if time permitted, you might increase the accuracy of your work still further. State the law of intensity of illumination and the law of candle powers. Compare them. EXPERIMENT 56 Object. To find the position and size of an image as seen in a plane mirror. Apparatus. A plane mirror, supporting block, and rubber band, a small block with a vertical black mark, a LIGHT 97 pair of drawing compasses, and a sheet of white paper about 12 x 20 in. Directions. Draw a straight line on the sheet of paper connecting the middle points of the long sides. Attach the mirror to the block with a rubber band. Place the reflecting surface of the mirror over the line just drawn, The middle point of the mirror should bisect this line, and the surface of the mirror should be exactly vertical. Draw an equilateral triangle in front of the mirror with its base parallel to the short edge of the paper and about 3 cm. from this edge. Use the compasses for this purpose and make each edge 8 cm. long. Number the vertices of this triangle I, 2, and 3. Place the small block so that the foot of the vertical mark coincides exactly with vertex I of the triangle. Place the ruler in such a position that a line drawn along its edge, if produced, would appear to pass through the image of vertex I. From the opposite side of the paper sight another line to pass through the same point. Make the angle between these lines as great as possible. Number each of these lines I. Next place the vertical line over vertex 2 and locate its image. Find the image of vertex 3 in the same manner. Remove the mirror and produce the lines just sighted until lines (i) (i), (2) (2), and (3) (3) intersect. Connect these points by dotted lines to form the image of the triangle. Number these vertices i r , 2', and 3'. Now draw dotted lines connecting points i and i', 2 and 2', also 3 and 3'. Conclusion. What kind of an image is formed by a plane mirror ? How do you know this ? Is this image erect or inverted or reversed ? How does its size compare 98 PHYSICAL LABORATORY GUIDE with that of the object ? Compare the distance of points I and i', 2 and 2', etc., from the mirror. What angles do lines i-i', 2-2', and 3-3' make with the reflecting surface of the mirror ? NOTE. Great care should be exercised in making the drawing in this experiment, and also in a number of the experiments on Light, as any inaccuracy will give misleading results. EXPERIMENT 57 Object. To determine the index of refraction from air to glass. Apparatus. A piece of plate glass, a straightedge, a scale, pins, a sheet of notebook paper, and drawing com- passes. Directions. Through the center of the sheet of paper draw a straight line parallel to one of its shorter edges. Place the piece of glass on the side of this line farthest from you so that one of its polished edges coincides with the line. Stick a pin against the glass perpendicular to the paper and at its center. If the glass has been prop- erly placed, this pin will now be at a point distant one third of the length of the glass plate from the end of the plate. On the opposite side of the glass place another pin distant one third of the length of the glass plate from the other end of the plate. Now sight with the straightedge until a line drawn along it would pass through the nearest pin and appear to pass through the image of the opposite pin as seen through the glass. Draw this line and then remove both pins and the glass. Draw a second line through these two pinholes to meet the first. The first line is the path of a ray in the air along which the observer looks ; the second, its path through the glass. Why ? LIGHT 99 Great care should be exercised in sighting this ray, as any inaccuracy here will seriously affect the final result. Through the point where the ray enters the glass draw a perpendicular to this edge of the glass. Next, lay off equal distances from this point on the rays in the air and in the glass. From these points draw normals to the per- pendicular. Measure the lengths of these normals accu- rately. The ratio of their lengths will be the required index of refraction. In laying off the equal distances referred to above, it is well to make them as great as is practicable. Why ? Conclusion. The pin seen over the glass and the same pin seen through the glass do not coincide. Explain this. Can you find any position from which you could view this pin and have the pin seen above and through the glass coincide ? Why ? Does the distance you choose to lay off on the two rays affect the value of the index ? Try it. Does the angle of incidence chosen affect the index value? Try an angle different from the one first drawn and com- pare the results. This point should be settled carefully, as it is of great importance. What do you conclude would affect the value of the index of refraction ? Compare your results with the correct value given in the table (see Chap. XI). Is the value you have found the index from air to glass or from glass to air ? Find the value for the other. EXPERIMENT 68 Object. To find the index of refraction from air to water. Apparatus. A glass jar, a metal bridge to fit the jar, a metal index to slide upon the edge of the jar, a 3O-cm. rule, a pair of drawing compasses. 100 PHYSICAL LABORATORY GUIDE Directions. Put the bridge in position. Care should be taken to have the bridge perpendicular to the surface of the water, which should come as close as possible to its lower edge without touching it. Now looking along the diameter of the jar, which is perpendicular to the plane of the bridge, sight the appara- tus until the inner edge of the jar, the lower edge of the bridge, and the point of the index appear to be in line. Are they ? It will be necessary to raise or lower the index until its correct position is found. Make a drawing of the jar (full size). Use the inside diameter of the jar and carefully locate the position of the bridge, index, and water surface, etc. This is best done by talking all vertical measurements from the table up. Draw a line from this point of the index to the lower surface of the bridge and another from this last point to the edge of the jar along which you sighted. These lines represent the path of the ray, along which you looked, in the water and in the air, respectively. Are the three points on the same straight line ? Why ? Draw a normal to the surface of the water at the point where the ray enters it. Lay off from this point equal distances on the rays in the water and in the air. Make these distances as large as practicable. From the points thus found, draw perpendiculars to the normal. These lines are the sines of the angles of incidence and refraction. Measure their lengths accurately. The ratio of these lengths gives the index of refraction. Conclusion. Define incident and refracted ray. Sup- pose you had arranged the apparatus so that the angle of incidence was different ; would this have changed the value of angle of refraction ? Would it have changed the value LIGHT : , i>a tijj ioi of their sines ? Would it give a different value for the index of refraction ? Compare your result with the known value. EXPERIMENT 59 Object. To find the focal length of a double convex lens. Two methods : (a) by throwing the image of a dis- tant object on a screen ; () by the method of parallax. Apparatus. A meter stick, a screen, a double convex lens, a pin mounted on a sliding block, a 3O-cm. scale. Directions. (a) Darken the laboratory by drawing the shades. Have one window open from the bottom. Take your position on the side of the room opposite this open window. Place the lens and screen upon the meter stick, mounted in such a way that either will slide on the stick. Focus the lens until a sharp image of some distant object out of doors is formed upon the screen. A tall chimney, flagstaff, or steeple will answer well. The object should be at least one eighth of a mile away. Why ? What rays intersect only at the principal focus of a double convex lens ? Now measure the distance from the optical center of the lens to the center of the image. This will give the focal length of the lens. Why? Make several trials, using different objects and resetting the lens each time. (b) Replace the screen with the pin mounted vertically on the sliding block. Raise all the shades. Rest the meter stick on any convenient support. Look through the lens at one of the distant objects used in part (a). A real, inverted image will be seen. Place the pin where you think this real image is. Now, while looking at this image and the pin, move your head from side to side and 102 PHYSICAL -LABORATORY GUIDE note whether they remain the same distance apart. They should. If they do not, try other positions until you find the correct one. The distance from the pin to the optical center of the lens is its focal length. Why ? Try the same principle, using two pencils held upright. Note how the distance between them seems to vary except when they are side by side. Record the results of both parts in one table. Average the trials made with each method. Average these results, if they are not alike, and take this as the true focal length of the lens. Conclusion. Which method is more accurate in your opinion ? Why ? What is meant by the term parallax ? Use the dictionary if necessary. Define focal length of a lens. Also define optical center of a lens. EXPERIMENT 60 Object. To test the formula = + -^-. for a double F Do Dt convex lens : a study of conjugate foci. Apparatus. A candle, a double convex lens and holder, a paper screen and support, and a meter stick. Directions. With the room darkened and the lens between the candle and the screen, adjust the apparatus until a clear image of the candle is formed. In focusing the image, attention should be directed to the candle wick or some other detail in order to obtain the best results. If the room is not very dark, the screen should be so placed that direct light from the windows cannot strike it. Now measure the distances from the optical center of the LIGHT 103 lens to the image on the screen (image distance, Di) and the distances to the candle (object distance, Do). At least three trials should be made, using a different object dis- tance each time. Substitute these values in the lens formula = *H , F Do Dz and solve for F the focal length of the lens. Average the values thus found and compare the result obtained with the known focal length of the lens as determined in Ex- periment 56. Record the data in tabular form. Conclusion. Define conjugate foci. Are these foci interchangeable ? Test this point first by focusing image of candle on the screen, marking positions of candle and screen in some way, and second by changing these objects about. Is the image formed still in good focus ? Suggest some practical optical problems for whose solution this lens formula would be valuable. EXPERIMENT 61 Object. To study the spectroscope and the three kinds of spectra. Apparatus. A spectroscope, a spectrum chart, a Bun- sen burner, a small platinum wire mounted, solutions of salts of the alkaline earth metals, pieces of red, green, and blue glass, solution (dilute) of chlorophyll in a bottle with flat sides (soda mint bottle). Directions. I. Remove the cover from the circular box at the top 'of the vertical support. Note carefully the position of the prism. Unscrew the telescope from the support and note the number and position of its lenses. PHYS. LAB. GUIDE 8 104 PHYSICAL LABORATORY GUIDE Look through it at objects across the street. Remove the draw tube from the collimator and note position of adjus- table slit and lens. Now make a careful diagram of the instrument, looking down from above, showing position of prism, -telescope, collimator tubes, and all lenses. Explain the use of the various parts. II. With the spectroscope properly assembled, now point the collimator toward the sky and adjust slit and telescope until the more prominent Fraunhofer lines are clearly seen. Compare these with the picture of the solar spectrum given, and decide which lines you have seen. What is the name of this class of spectra, and what other sources of light would give the same result ? Darken the room and adjust the spectroscope again, using a luminous gas flame as the source of light. Does this spectrum show any dark lines ? Name this class of spectra. Under what conditions is this kind of spectrum always obtained ? Use the non-luminous Bunsen flame and dip a platinum wire into one of the solutions given. Compare this spec- trum carefully with the chart given, and decide what mate- rial is in the solution. Test the other solutions in the same way. Name this third class of spectra. III. Using the luminous gas flame as a source of light, hold the different colored pieces of glass successively between the source of light and the slit. Account for the results. Hold the bottle of chlorophyll solution between the light and the slit, and note the result. Conclusion. Name and explain the practical applica- tions of the spectroscope based on the experiments you have just performed. CHAPTER IX SOUND EXPERIMENT 62 Object. To plot several wave motions on section paper and to find the resultant wave in each case. Apparatus. Section paper ruled to inches, half inches, and tenths of inches, or section paper ruled to centimeters and millimeters, a pair of drawing compasses, and a blue pencil. NOTE. If metric paper is provided, use centimeters to replace half inches. Directions. CASE i. Draw a straight line lengthwise through the middle of a sheet of section paper. This line should coincide with one of the half-inch (centimeter) ruled lines on the paper. Near the left-hand end of this line draw a circle of i^-inch radius. The center of this circle should be on the line just drawn and should coincide with an intersection of the half-inch lines. Divide this circle into twelve equal parts. Do this with the compasses, using points on the circumference 90 apart as centers and drawing arcs to intersect the circle. The radius used is the radius of the circle. Now locate the successive positions of the vibrating par- ticles causing the wave motion, as follows : Suppose the first particle to be on the first vertical half-inch line to the I0 5 106 PHYSICAL LABORATORY GUIDE right of the circle and to coincide with the horizontal axis, the second particle to be on the second half-inch vertical line and above the axis. Its position may be found by projecting the second division on the circle upon this ver- tical line. Continue in this manner, advancing one divi- sion on the circle and one half-inch along the axis to the right until the points are plotted for one complete wave consisting of a crest and trough. Draw a solid pencil line through these points to complete the wave. Beginning at the same points on axis and curve, but advancing along the circle in the opposite direction, locate the points for another complete wave. Draw a dotted pencil line through these points. Counting distance above the horizontal axis plus-dis- placement, and distance below, minus-displacement, locate the points of the wave motion resulting from the combina- tion of the two waves just drawn. Draw a blue line through these points. What is the amplitude of these waves ? What is their length ? Are they in like or opposite phase ? What phe- nomenon in sound does this drawing illustrate ? Mark it so. CASE 2. In like manner make another drawing on a separate sheet of paper showing these waves in like phase. Find the resultant wave. What phenomenon does this drawing illustrate ? Mark it so. CASE 3. On a third sheet of paper draw two waves the first to be precisely like those drawn in Cases I and 2, and the second to have one half the wave length an'd two thirds the amplitude of the first. Find the resultant curve. This drawing shows a fundamental tone and its first harmonic sounded together. What musical interval exists between the notes ? Why ? SOUND 107 Conclusion. How is a simple harmonic motion plotted ? What kind of motion does a particle vibrating in a medium transmitting sound have? Of what kind is the onward motion of the wave itself ? EXPERIMENT 63 Object. To find the number of vibrations made in one second by a tuning fork. Apparatus. A tuning fork apparatus (consisting of a large heavy fork, and a quarter-seconds pendulum with needle point, several pieces of glass, a carrier and carrier track), gum camphor, matches, bristles and wax for attach- ing them to a prong of the fork, a bass viol bow, a watch, and crucible tongs or a pair of tweezers. Data. OBSERVATIONS Vibrations of fork per one pendulum vibration . . Vibrations of fork in one second (calculated) . ' , -. Vibrations of fork in one second (stamped) . . ;. ' Directions. By means of a piece of burning camphor held in the tongs, smoke several of the glass slides on one side. The film of smoke should be as light as possible and still completely cover the glass. Attach a bristle to one prong of the fork. This is best done by warming one end of the fork in a flame until it will just melt the wax. Attach the bristle, using as little wax as possible. Why ? Next set up the apparatus and adjust the stylus on the pendulum and the bristle o'n the fork until they are as 108 PHYSICAL LABORATORY GUIDE close together as possible without touching. Each should just graze the smoked glass. Set the fork and pendulum in vibration at the same time and quickly draw the glass plate along the track under the fork. If the work is carefully timed, you will now have a record of two or three swings of the pendu- lum together with the more rapid vibration of the fork traced on the glass. Some patience and practice are necessary to obtain a good record. When two or more clear records are obtained, count the number of vibrations of the fork to each pendulum vibra- tion. Average these values and record the result. Find the time of one vibration of the pendulum by counting it for a minute. Several trials should be made to secure its exact rate. Make this test with the stylus touching the smoked-glass plate. Why ? Calculate the number of vibrations made by the fork per second from your data. Compare your result with the value stamped on the fork by its maker. Conclusion. What might cause a disagreement between the known vibration- rate of the fork and the value you have obtained ? Is it possible to change the vibration rate of a fork without permanently injuring it ? What kind of motion did you give the glass ? What kind of motion have the pendulum and fork ? The curves you traced are called sine curves. Compare those on the smoked glass with the curves plotted in Experiment 58. Are they also sine curves ? How do you know ? NOTE. As it is nearly impossible to have the fork stylus and the pendulum stylus coincide, it is well to count the fork vibrations made during two vibrations of the pendulum and divide by two. This elim- inates a possible source of error. Why ? SOUND 109 EXPERIMENT 64 Object. To calculate the wave lengths of the sounds emitted by several tuning forks at the temperature of the laboratory and to compare these wave lengths with the lengths of the columns of air which reenforce them. Apparatus. A set of heavy tuning forks (C = 256, E = 320, G = 384, and C' = 512), a glass cylinder about 2.5" x 1 8", a thermometer, a small pitcher of water, and a medi- cine dropper. Data. - OBSERVATIONS C E G C' Vibration frequency of fork Observed length of resonating air column . Correction for diameter of the jar True length of resonating air column Temperature of the air in jar Velocity of sound in air at this temperature Wave length of sound from V = LN . . Wave length divided by resonating column Directions. Pour or drop water into the cylindrical jar until it reenforces the sound of tuning fork C = 256 most loudly. Hold the fork close to the mouth of the jar with as great a length of the vibrating prong over the jar as possible. Care should also be taken to strike the fork against a book or other soft object, always with the same blow, in order that it may have the same amplitude of vibra- tion each time. If this is not done, the true length of the vibrating column may not be determined. Why ? In the 110 PHYSICAL LABORATORY GUIDE same way find the lengths of the columns that best ree'n- force the other forks. Measure the internal diameter of the jar carefully and add half of this (its radius) to the observed lengths, to obtain the true lengths of the vibrating air columns. Take the temperature of the air in the room. If the precaution has been taken of letting the water used stand in the room long enough to assume the room temperature, a possible source of error will be eliminated. Look up the velocity of sound in air at o C. and the amount this velocity is increased for each degree Centi- grade above zero, and calculate its value in centimeters per second for the temperature of the laboratory. Next, find the wave length for each fork, using the fun- damental relation that velocity = wave length x vibration frequency, or v = In. Finally, find the ratio of the wave length to the length of resonating column for each fork. Conclusion. What is your average value for the wave length divided by the length of resonating column ? What should its value be ? Make a diagram of the vibrating fork and its resonating air column. Referring to this drawing, prove that your answer to the last question is correct. You have noted the increase in the velocity of sound in air with a rise in temperature. Is its velocity affected by changes in the amount of the barometric pressure ? Give reasons for your answer. EXPERIMENT 65 Object. To test the laws for the vibration of strings. Apparatus. A sonometer, weights and two wooden prisms for bridges, piano wire, sizes 22 and 28, a catgut SOUND III violin string the same diameter as the 22 piano wire, a set of tuning forks (C 256 , E, G, and C'), a meter stick, a micrometer caliper. Data. VIBRATIONS PER SECOND CALCULATED VIBRATIONS PER SECOND BY THE FORK LENGTH OF STRING DIAMETER OF STRING TENSION ON STRING SQ. ROOT OF TENSION Directions. (a) Using the 28 piano wire, Adjust the tension until the open string vibrates nearly in unison with fork C 266 . The tone of the string should be a little lower than the fork. By means of the bridge shorten the string, a very little at a time, until it and the fork vibrate in uni- son. When the adjustment is nearly right, the beats may be counted. Continue the adjustment until the beats dis- appear. Measure the length, diameter, etc., of the string and record in the table. Without changing the tension, move the bridge until the length of the string is just half what it was before. Com- pare the tone it emits under these conditions with the tone of the C' 512 fork. If time permits, find the lengths of the string which will vibrate in unison with forks E and G. From the known vibration rate of the C 256 fork and the observed lengths of the strings with which you have ex- 112 PHYSICAL LABORATORY GUIDE perimented, calculate the vibration rates of the last three strings used. Do this by an inverse proportion. Com- pare these vibration rates with the vibration rates of the forks which vibrate in unison with them. (b) Adjust the tension and length as in (a) of the 22 piano wire until it is in unison with fork C 256 . Adjust the 28 wire to exactly the same length and tension. With which fork is this string now in unison ? What kind of a proportion exists between the diameters and vibration rates of these strings ? (c) Using some whole number of pounds tension, adjust the length of the 28 piano wire until unison is established between it and fork C 256 . Keeping the length the same, apply four times the tension. With which fork is the string now in unison ? Did multiplying the tension by four also increase the vibration rate to four times its original v^lue ? (d) Adjust the tension and length of the 22 piano wire until it vibrates in unison with fork C 256 . Also adjust the gut string to the same length and tension. Which gives the higher tone ? Approximately, how much is one higher than the other ? Find which fork is more nearly in unison with the second string. Which string has the greater density ? Which has the greater vibration rate? By reference to the tables in Chapter XI, find the ratio of the densities of steel and gut. Also find the square root of this ratio. Conclusion. State the known laws for the vibration of strings. Compare your data with these laws. State how closely you have proved the laws, and mention some of the difficulties to be overcome if the actual data is to follow the laws exactly. In doing this consider sections a, b, c, and d separately. SOUND 113 EXPERIMENT 66 Object. To find the velocity of sound in air. Apparatus. Two revolvers and blank cartridges (a small cannon is better than the revolvers), two stop watches, a loo-ft. tape, and two thermometers. Directions. This experiment should be performed on some level ground out in the country where it is quiet. Select two stations about two or three thousand feet apart. Measure the distance between them accurately. Divide the class into two squads, and let one squad take up its position at each station. Each station is provided with one stop watch and one revolver. Let one of the members of Squad i fire his revolver and one member of Squad 2 take the elapsed time between the appearance of the smoke and the time when the sound reaches his ear. Next let a member of Squad 2 fire his revolver and a member of Squad I time the sound. Continue signaling back and forth in this way until each member of the class has timed the sound at least once. It will be well to appoint one member of each squad to act as recorder and keep a record of the results. If time permits, continue the experimenting, using a different distance between the stations. The temperature of the air at the time of the experiment should be carefully observed by each station. Also, the direction of the wind with respect to the direction of the line joining the two stations should be recorded Record all results in tabular form. Conclusion. Calculate the velocity of sound in air from each observation made. Find the average velocity in each direction. One of these will probably be larger and the 114 PHYSICAL LABORATORY GUIDE other smaller than the true value. Why ? Add these average velocities in each direction together and divide by two. Using this result as the velocity of sound in air at the temperature of the experiment, calculate the velocity for sound in air at o C. Compare this value with the known velocity of sound in air at o C. as given in your textbook. NOTE. A Saturday morning or afternoon spent by teacher and class in performing this experiment will be found to well repay the effort not only for the sake of the experiment itself, but because of the interest it will awaken in scientific research in general on account of the historic interest of this particular experiment. CHAPTER X NOTES ON THE EXPERIMENTS FUNDAMENTAL MEASUREMENTS (Chapter I) I. The Law of Conservation of Matter and Energy. Matter and energy cannot be created or destroyed. Careful measurements extending over long periods of time, and dealing with many different substances and with all the known forms of matter or energy, show that the dis- appearance of a given quantity of either is always followed by the formation of an exactly equivalent quantity of some new form. Thus oxygen and hydrogen, two gases, unite chemically to form water. Kinetic energy may be transformed into heat or electrical energy. In every case, however, noth- ing is lost. The sum of the quantities involved before any transformation, either of matter or energy, is always exactly equal to the sum of the products formed. An appeal to this law frequently sheds important light upon the investi- gation of many phenomena. II. The Laws of Capillary Action. 1. Liquids rise in tubes when they wet them, and their surface is concave ; they are depressed in tubes when they do not ivet them, and their surface is convex. 2. The rise or depression of the liquid varies inversely as the diameter of the tube. "5 Il6 PHYSICAL LABORATORY GUIDE 3. Increasing the temperattire of a liquid diminishes its capillarity, and vice versa. Capillary phenomena will be understood when the forces involved are considered. These forces are three in number, as follows : (a) Adhesion, a molecular force of attraction acting be- tween unlike molecules and causing an upward force tend- ing to lift the column of liquid in the tube. () Cohesion, a molecular force acting between like molecules and tending to draw any mass of liquid into the form of a sphere. It is evident that this force opposes the force of adhesion in capillary tubes. (c) Gravity is the mutual attraction between any body and the earth. This force, according to the laws of gravity pressure in fluids, tends to keep the liquid surfaces, within and outside of the tube, at the same level. (See laws of fluid pressures in your textbook.) Evidently- this force also opposes the rise of liquids in capillary tubes. Liquids will rise then under the force of adhesion until this force is balanced by the combined action of cohesion and gravity, when the liquid column will remain stationary. Since the weight of the liquid column varies with the square of its radius while its surface in contact with the tube varies only as the first power, liquids will not rise so high in tubes of large diameter. Furthermore, a rise in temperature increases the spaces between the molecules, and this cuts down the intensity of the molecular forces while gravity remains practically unchanged. Thus an increase of temperature in a liquid necessarily decreases the amount of capillarity. What appears to be a double surface of most liquids where they come in contact with the containing vessel is NOTES ON THE EXPERIMENTS 117 due to capillary action. Capillary action explains the working of lamp wicks, blotters, etc. III. To read a Fortin Barometer. The barometer must hang vertically. Read the temperature at once, for otherwise the presence of the body of the observer may vitiate the observation. Tap the barometer gently near the upper level of the mercury. This enables the menis- cus to assume its proper shape. Adjust the level of the mercury in the cistern. To do this, if necessary, lower and then raise the cistern screw until the level of the mercurial surface just touches the tip of the ivory pointer. This will be indicated by a slight depression and irregularity of the surface. If the surface is bright and clean, the image of the pointer will be seen in this surface by reflection. Next set the vernier. The bottom of the vernier must be brought so as to be an apparent tangent to the convex surface of the meniscus. To avoid parallax, advantage must be taken of the movable tube on which the vernier is graduated. The back, lower edge of this ought to coin- cide with the front, lower edge when viewed from the proper position. When thus set, if the eye be moved slightly up and down, no line of light should appear in the middle. We are thus sure that the line of sight is hori- zontal. The reading may now be observed from the fixed scale and from the coincident lines on the vernier. For very accurate work a number of corrections should be applied to the observed barometric height as follows : (a) Correction for temperature, (<) correction for capil- larity, (c) correction for errors in the scale graduations, (d) correction for unequal intensity of gravity, (e) reduc- tion to sea level. Il8 PHYSICAL LABORATORY GUIDE For ordinary labratory wdrk the first and second of these only need be considered. Tables giving corrections will be found in Chapter XL If the barometer is graduated in English measure, its temperature correction may be calculated from the follow- ing formula : H=N--^- (.09 /- 2.56 1000 where H = corrected barometric height, N observed barometric height, / = the temperature of the barometer. Use tables in Chapter XI to correct a metric barometer. IV. The Atmospheric Pressure. Galileo (1564-1642) suspected the existence of an atmospheric pressure, but died before proving it. His pupil, Torricelli, not only proved the existence of an atmospheric pressure, but also measured its amount by means of the familiar barometer tube and bowl of mercury. The amount of this pressure is constantly varying, but under standard conditions, that is, a mercury column 760 mm. (29.92 in.) high, it amounts to 1033.3 g m - per square centimeter (14.7 Ib. per square inch). The temperature of the mercury under standard conditions must be o C. A liquid boils when its vapor tension (the pressure of the vapor) is equal to or slightly exceeds the atmospheric pressure. Its vapor tension depends upon the energy of its molecules, and hence upon its temperature. It is evident, then, that the boiling point of a liquid is not a constant temperature, but depends directly upon the amount of the atmospheric pressure. Scientists have agreed to call the temperature of the NOTES ON THE EXPERIMENTS 119 steam from water boiling under standard conditions 100 C. Experiment shows that a rise or fall of I cm. in the baro- metric reading changes the boiling point .37 C. (One inch changes it .945 C.) The variation is direct, a rising barometer increasing the boiling point, and vice versa. By noting how much the barometer reads above or below standard, the boiling point corresponding to this pressure is easily calculated from the data just given. For an accurate determination of the boiling point from the observed height of the barometer several corrections must be applied to this barometer reading. (See Section III on the Barometer; also the tables for barometric cor- rection in Chapter XL) DENSITY AND SPECIFIC GRAVITY (Chapter I) V. Archimedes' Principle. A body immersed in a fluid is buoyed up by a force equal to the weight of the fluid it displaces ; or, The loss of weight of a body immersed in a fluid is equal to the weight of the displaced fluid, which has the same volume as the body. This law discovered by Archimecfes (287-212 B.C.) is particularly interesting, both on account of its early dis- covery and because of its wide application. Most of the methods used for specific gravity determinations depend upon it. In fact, Archimedes was trying to find the amount of pure gold in his king's crown when he discov- ered it. The ascension of balloons likewise is governed by this principle. VI. The Law of Flotation. A floating body displaces its own iveight of the liquid in which it floats. This law is only a special case of Archimedes' principle, PHYS. LAB. GUIDE 9 120 PHYSICAL LABORATORY GUIDE in which the body is able to displace a volume of the liquid which weighs as much as the body itself. The construc- tion of boats and of hydrometers depends on this law. VII. Pascal's Law. Pressure exerted upon any given area of a liquid inclosed in a vessel is transmitted undimin- ished to every equal area. The laws of gravity pressure : (a) The pressure is directly proportional to the depth of the liquid. (b) The pressure is directly proportional to the density of the liquid. (c) The intensity of pressure at any point in a liquid is the same in all directions. VIII. Density and Specific Gravity. Density is the mass per unit of volume of a substance. The usual unit of mass is the gram, and the unit of volume is the cubic centimeter. Density then is the mass (or weight) of one cubic centi- meter of a substance measured in grams. The density of water is one gram. Specific gravity is the weight of a given quantity of a substance compared with tJie weight of tJie same volume of water. Hence, the specific gravity of water must be one. It is evident that the density and the specific gravity of any substance must be numerically equal. For since the weights of any equal volumes of the substance and water when compared give the specific gravity of the substance, we can choose the weights of one cubic centimeter of each material. But the weight of one cubic centimeter of water is one gram. Dividing the density of a substance by one does not alter its magnitude. Thus, the density and the specific gravity of any substance are numerically equal, al- NOTES ON THE EXPERIMEiNTS 121 though the meaning of these numbers is quite different. The same argument would apply to equal volumes con- taining many cubic centimeters. In determining density with a balance, five important cases must be considered. In the formulae that follow, the symbols used have the following meanings : W = the weight of the substance in air. W^ = the weight of the substance in water. W a = the weight of the substance in a liquid whose density is s. S = the density of the liquid used in place of water. W where / = the time of one vibration, / = the length of the pendulum, g the acceleration due to gravity. 140 PHYSICAL LABORATORY GUIDE XXIV. The Laws of Sliding Friction. - 1 . Sliding friction is very nearly independent of the speed. 2. Sliding friction is independent of the area of the sur- faces in contact, unless this area is so small that one surface cuts into the other. 3. Sliding friction is directly proportional to the amount of pressure between the surfaces in contact. 4. Sliding friction depends upon the kinds of surfaces in contact. Friction is an opposing force. When this force is moved through space, work is done. This is seldom, if ever, useful work, but is transformed into heat and wasted. The use of roller and ball bearings in machinery, and the application of lubricating oils which really constitute molecular rollers, will greatly reduce the energy losses due to friction. The amount of this force of friction for any two sliding surfaces is measured by their coefficient of friction. This coefficient is equal to the friction divided by the pressure. By the third law the coefficient is a constant quantity for the same two surfaces, since the friction and the pressure are directly proportional. HEAT (Chapter VII) XXV. Heat. Some important definitions : (a) Heat is a form of energy. According to the kinetic theory the molecules of every body are constantly in mo- tion. This motion may be of a simple vibratory nature, or it may be exceedingly complex and irregular. Any in- crease in the energy of these molecular motions increases the temperature of the body. (b) Temperature is the thermal condition which deter- NOTES ON THE EXPERIMENTS 141 mines the direction and rate of transfer of heat energy from one body to another. It is analogous to the pressures in liquids and gases or the potential difference of various parts of an electric circuit. (<:) The linear coefficient of expansion of a solid is the amount one unit of its length increases in length when heated i Centigrade. (d) Just as the degree Fahrenheit or the degree Centi- grade is the unit of temperature or heat intensity, just so the calorie measures the quantity of heat energy. The calorie is the amount of heat necessary to raise I gram of water i centigrade in temperature. (e) Specific heat of any substance is the number of calo- ries of heat necessary to raise the temperature of I gram of the substance i centigrade. (/) The thermal capacity of any body is the total amount of heat in calories necessary to raise the temperature of the entire body i centigrade. It is calculated by multi- plying the mass of the body in grams by its specific heat in calories. This product is sometimes called the water equivalent of the body, because it not only is the amount of heat necessary to raise the body i centigrade, but it is also the weight of water which would require the same amount of heat to raise its temperature i centigrade that the body requires. (g) The latent heat of fusion of a substance is the num- ber of calories of heat required to change I gram of the substance from the solid to the liquid state without change of temperature. (/z) The latent heat of vaporization of a substance is the number of calories of heat required to change I gram of the substance from the liquid to the gaseous state without change of temperature. 142 PHYSICAL LABORATORY GUIDE (i) The dew point is that temperature at which the aqueous (water) vapor present in the atmosphere is just sufficient to saturate it. It is that temperature to which if the air were cooled its relative humidity would become 100 per cent. (/ ) Relative humidity is the ratio of the weight of water vapor in a given quantity of air to the greatest weight of water vapor which the same quantity of air could hold. Since the capacity of the air to hold water vapor increases with the temperature, it is evident that relative humidity depends both upon the actual quantity of aqueous vapor present and upon the temperature. LIGHT (Chapter VIII) XXVI. Light. Important laws and definitions : (a) Laws of intensity. The intensity of light upon any area of the surface : 1. Varies directly as the illuminating power of the source. 2. Varies inversely as the square of the distance from the area to the source. 3. Diminishes as the inclination of the surface to the rays of light increases. () The law of candle power. The illuminating powers of two sources are directly proportional to the squares of their distances from a surface which they illuminate with equal intensity. (c) The law of reflection. The angle of reflection is equal to the angle of incidence, and the two angles are in the same plane. (d) The laws of refraction. I. The angles of incidence and refraction lie in one plane. NOTES ON THE EXPERIMENTS 143 2. The angle of refraction is smaller or larger than the angle of 'incidence -, according as the light passes from a rarer to a denser medium, or the reverse. 3. The index of refraction has a constant value for the same two media. (e) Some definitions : I . The index of refraction is the ratio of the sine of the angle of incidence to the sine of the angle of refraction. 2. The optical center of a lens is a point through which a ray passes without any appreciable change in direction. It is frequently the geometrical center of the lens as well. 3. The principal focus of a lens is the point of intersec- tion of the rays parallel to the principal axis after they pass through the lens. 4. The focal length of a lens is the distance from its optical center to its principal focus. 5. A real image is formed by the actual intersection of the light rays and may be received upon a screen. 6. A virtual image is formed by the apparent intersec- tion of the light rays produced in such a direction as to cause them to intersect. Such an image has no real exist- ence outside of the eye. 7. Conjugate foci are two points so related to a lens or mirror that if a luminous point is placed at one of these points its image will be formed at the other. It is imma- terial at which point the object is placed; its image will appear at the other. 8. A simple relation connecting the focal length and the distance from the conjugate foci to the optical center of a lens or mirror is as follows : where F = the focal length of the lens, 144 PHYSICAL LABORATORY GUIDE d = the distance of the object from the optical center of the lens, di the distance from the image to the optical center of the lens. NOTE. In the formula just given, the sign of F is positive for a converging lens and negative when the lens is diverging. SOUND (Chapter IX) XXVII. Sound. (a) Simple harmonic motion, two definitions : 1. It is a vibration in a straight line, the motion being such that the vibrating point has an acceleration which is toward the center of its path and proportional to its dis- tance from the center. 2. When a body vibrates to and fro in a straight line, in such a manner that its position at any moment is the same as the projection on that line of a point moving uniformly in a circle whose diameter is the length of the straight line, it moves with what is known as a simple harmonic motion. (b) Waves. All bodies emitting sound are in a state of vibration and have a simple harmonic motion. Such a body will impart its motion to any elastic material medium surrounding it, and hence will produce waves in that medium. Air is the common medium for the transmission of sound waves. A wave is the combination of at least two motions ; namely, the simple, harmonic motion of the vibrating par- ticles, and the onward uniform motion of the disturbance through the medium. When these two motions are at right angles, the waves are called transverse. Longitudi- NOTES ON THE EXPERIMENTS 145 nal waves are produced when both motions are in the same straight line. Sound waves are of this kind and consist of alternate condensations and rarefactions in the medium. Each complete vibration of the sounding body, that is, a motion twice over its path, once in each direction, produces one wave. Hence the length of one wave multi- plied by the number of complete vibrations made per second must give the distance traveled by the sound in one second, or its velocity. In algebraic form this relation is expressed thus : V=LN when V the velocity of sound, L = the wave length, N = the number of vibrations per second. Experiment proves that sounds of different vibration rates, hence different pitches, all have the same velocity. For this reason equation (i) shows that the wave length depends upon the vibration rate. The greater the vibra- tion rate, the shorter the wave length, and vice versa. (c) The sine curve. The various vibrating parts of a medium at different distances from the source of the dis- turbance are not in the same phase ; that is, they do not all reach any particular point in their path, such as the middle point, at the same time, but each is just a little behind its predecessor. Now, if the different positions of these particles in their paths at the same instant are plotted as ordinates and the regular, even distance between the paths as abscissae, the resulting wavelike form connecting these points is called a sine curve. Although these curves do not show the true form of a sound wave which, as stated above, is a longitudinal and not a transverse vibration, still they throw much light upon such quantities as wave length, amplitude, period of vibra- 146 PHYSICAL LABORATORY GUIDE tion, resonance, interference, and harmonic overtones, and therefore are a valuable part of the student's work in sound. (d} Some definitions : Resonance is the increase in the intensity of a sound due to two or 'more waves coming together in like phase, and therefore producing a wave of greater amplitude, and hence greater intensity. Interference is the decrease in the intensity of a sound due to two or more waves coming together in opposite phase, and hence producing a wave of amplitude equal to the dif- ference between the amplitudes of the component waves. Sometimes the interference is complete, and silence results. Beats. Two trains of sound waves of slightly different length coming together in the same medium will cause alternate resonance and interference to take place. The uneven volume of sound, or surging, as it is sometimes called, thus produced, is known as beating. Harmonic overtones are tones of higher pitch, whose vibration rates are 2, 3, 4, 5, etc., times as great as the fundamental tone. Some of these are usually present in sounding bodies, and are due to the vibration of the body in parts at the same time that it vibrates as a whole. The quality of a sound depends upon the number and relative intensity of these harmonic overtones. (e) The laws of vibrating strings. 1 . The vibration rate of a string varies inversely as the length. 2. The vibration rate of a string varies inversely as the diameter. 3. The vibration rate of a string varies directly as the square root of the tension. 4. The vibration rate of a string varies inversely as the square root of the density of the material of which it is made. CHAPTER XI TABLES OF PHYSICAL CONSTANTS I. MENSURATION Circle: radius = R; circumference = 2 irR; area = Sphere : radius = R ; surface = 4 TrR 2 ; volume = f ?rR 3 . II. ENGLISH AND METRIC EQUIVALENTS LENGTH i inch I centimeter 2.54 centimeters .3937 inch I mile I kilometer I pound I ounce MASS 1.61 kilometers .6214 mile 453-59 grams 28.35 g rams III. BAROMETRIC CORRECTIONS (a) CORRECTION FOR TEMPERATURE Mercury Brass scale correct at o C. TEMPERATURE 73 74 75 76 77 78 79 Degrees C. 15 0.178 0.181 0.183 0.186 o.i 88 0.191 0.193 16 0.190 0.193 0.196 0.198 O.2OI 0.203 0.206 17 O.2O2 o 205 0.208 O 2IO 0.213 0.216 0.218 18 O.2i4 0.217 0.220 0.223 0.226 0.229 0.231 19 O.220 0.229 0.232 0- 2 35 0.238 0.241 0.244 20 0.238 0.241 0.244 0.247 0.251 0.254 0.257 21 0.250 0.253 0.256 0.260 0.263 0:267 0.270 22 O.26I 0.265 0.269 0.272 0.276 0.279 0.283 23 0.273 0.277 0.281 0.284 0.288 0.292 0.296 24 0.285 0.289 0.293 0.297 0.301 0.305 0.309 Corrections are to be subtracted from observed readings viz. if reading at 19 is 76 centimeters, the "corrected" reading is 76-0.235 = 75.765 centimeters, 148 PHYSICAL LABORATORY GUIDE (b} CORRECTION FOR VARIATION IN g. LATITUDE 73 74 75 76 77 78 79 35 or 55 0.065 0.066 0.066 0.067 0.068 0.069 0.070 40 or 50 0.032 0.033 0.033 0.034 0-035 0.035 o-35 45 5 o o o o (c) CAPILLARY DEPRESSION OF MERCURY IN GLASS Height of Meniscus in Millimeters 0.4 0.6 0.8 I 1.2 1.4 1.6 1.8 Corrections to be Added Diameter mm. 4 5 6 7 8 9 10 11 12 13 mm. 0.83 0.47 0.27 0.18 mm. 1.22 0.65 0.41 0.28 O.2O 0.15 mm. 0.86 0.56 0.40 0.29 O.2I O.I 5 0.10 0.07 0.04 mm. 1.98 I.IO 0.78 0-53 0.38 0.28 0.20 O.I4 O.IO 0.07 mm. 2 -37 145 0.98 0.67 0.46 -33 0.25 0.18 0.13 O.IO mm. mm. mm. 1.80 1. 21 0.82 0.56 0.40 0.29 0.21 O.I 5 O.I 2 143 0.97 0.65 0.46 o-33 0.24 0.18 0.13 M3 0.77 0.52 o.37 0.27 0.19 0.14 ( 'J 2.6 3.2 165200 Oak . . 60 90 37 ^5 o/ 0^ TABLES OF PHYSICAL CONSTANTS DENSITIES MISCELLANEOUS. Continued GRAMS PER CUBIC CENTIMETER POUNDS PER CUBIC FOOT Paper . . 0. 7 1 . 1 C 44 72 Paraffin .87- .01 C4- ry Peat ... .84 C2 1.82 1 14 Pitch 1.07 67 Porcelain ... . 2.1 2.S ' 14-1-1 e6 Pyrites 4.Q -5.2 '106324 37 .QO 2v;6 Quartz 'ji *y 2.6* 03" i6c Resin . 1.07 J 67 Rock salt 2.28-2.41 142150 Sal ammoniac . I.e -1.6 Q4 IOO Saltpeter . 1.95-2.08 I22-I3O 1.40 i. 6c 87IO3 Sand damp . I QO 2 OS 1 19128 Sandstone . .... 2.2 -2.5 137 1<\6 Shale 2.6 l62 2.O -2.<: 125-156 Slate 2.6 2.7 162-168 Snow, loose .I2C 7.8 Starch Suffar 1.53 i 61 95 IOO Talc . 2.7 1 68 Tallow .01 .Q7 H P 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 105 11.0 11.5 12.0 19 -25 19 20 -19 -32 20 21 -15 -24 -47 21 22 ii -19 -3i 22 23 - 8 -4 -24 45 23 24 - 5 10 -18 -3 24 25 2 7 -13 -42 25 26 O 4 - 9 -17 -28 26 27 - 3 i - 6 12 20 -37 27 28 5 i - 3 - 8 -15 -25 -54 28 29 7 4 A 10 -18 -32 29 30 9 6 2 2 - 6 -'3 22 -43 30 31 ii 8 5 I - 3 - 8 -15 -27 31 32 *3 10 7 4 4 10 -18 33 32 33 M 12 9 6 - 3 i 6 12 22 -44 33 34 16 14 ii 8 6 2 2 - 8 15 27 34 35 18 15 U 10 8 5 i 4 9 18 -32 35 36 19 '7 15 12 10 8 4 r 12 20 -42 36 37 21 19 *7 14 12 9 6 - 3 _ 2 - 6 14 -25 p 2 37 38 22 20 19 16 14 ii 9 6 2 2 - 8 16 29 38 39 24 22 20 18 16 H ii 8 C I - 4 10 -18 39 40 2 5 23 22 20 18 16 13 ii 8 4 - 5 12 40 41 26 25 23 21 20 1 7 15 13 10 7 - 4 i 6 41 42 27 26 24 2 3 21 19 18 15 1 2 10 7 - 3 2 42 43 29 27 26 24 23 21 19 17 14 12 9 6 2 43 44 3 28 27 26 24 22 20 18 26 14 12 9 6 44 45 3 1 3 28 27 2 5 24 22 20 18 16 13 ii 8 45 46 32 3i 3 28 27 2 5 24 22 20 18 16 13 ii 46 47 33 32 3i 29 28 26 2 5 23 22 20 18 15 13 47 48 35 33 3 2 3 29 28 26 2 5 23 21 20 17 15 48 49 36 34 33 32 31 29 28 26 25 23 21 19 17 49 t 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10 5 Ii 11.0 11.5 12.0 t TABLES OF PHYSICAL CONSTANTS 159 X. TEMPERATURE OF THE DEW POINT, IN DEGREES FAHRENHEIT. - Continued (I DIFFERENCE BETWEEN THE DRY AND WET THERMOMETERS (/-/') jjj 01 c 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 Q 50 37 35 34 33 32 31 29 28 26 24 23 21 19 50 51 38 37 36 34 33 32 31 29 28 26 24 22 21 51 52 40 38 37 36 34 33 32 -30 29 28 26 24 23 52 53 39 38 37 36 34 33 32 3 29 28 26 24 53 54 42 41 40 39 37 36 34 33 32 30 29 27 26 54 55 43 42 4i 40 39 37 36 34 33 32 30 29 28 55 56 44 43 42 41 40 39 37 36 34 33 32 30 29 56 57 46 45 44 42 40 39 37 36 35 33 32 30 57 58 47 46 45 44 42 41 40 39 37 36 35 33 32 58 59 48 47 46 45 44 43 4i 40 39 38 3 6 35 33 59 60 49 48 47 46 45 44 43 4i 40 39 38 36 35 60 61 5 49 48 47 46 45 44 43 42 39 38 36 61 62 52 5 1 50 49 48 47 45 43 42 41 41 39 38 62 63 53 5 2 5 49 48 47 45 44 43 42 39 63 64 54 53 52 50 49 48 47 46 45 43 42 4i 64 65 66 55 56 54 55 53 54 52 53 51 52 50 49 50 48 49 s 46 47 45 46 43 45 42 44 65 66 67 57 56 55 55 54 53 52 51 5 48 47 46 45 67 68 58 57 57 56 55 54 53 52 50 49 47 46 68 69 59 58 58 57 56 55 54 53 52 5 49 48 69 70 61 60 59 58 57 56 55 54 53 52 5 1 5 49 70 71 62 61 60 59 58 57 56 55 55 54 53 52 71 72 73 63 64 62 63 61 62 60 62 59 61 8 58 59 56 57 55 5 6 54 55 53 54 52 53 72 73 74 65 64 63 63 62 61 60 59 58 57 56 55 54 74 75 76 66 67 65 66 64 65 64 65 63 64 62 63 61 62 60 61 59 61 c 57 56 58 56 57 75 76 77 68 67 67 66 65 64 63 62 62 61 60 59 58 77 78 69 68 68 67 66 66 65 64 63 62 61 60 59 78 79 70 69 69 68 67 67 67 65 64 63 62 61 61 79 80 72 71 7 69 68 68 67 66 65 64 63 62 62 80 t 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 t i6o PHYSICAL LABORATORY GUIDE X. TEMPERATURE OF THE DEW POINT, IN DEGREES FAHRENHEIT. Continued ft M > (2 DIFFERENCE BETWEEN THE DRY AND WET THERMOMETERS (t-f) J 1 12.0 12.5 13.0 135 14.0 14.5 150 155 U 16.0 16.5 17.0 17.5 18.0 40 12 22 -44 40 41 - 6 13 -25 41 42 2 - 7 -15 -28 42 43 2 - 3 - 8 -17 -33 43 44 6 i - 4 10 -19 -40 44 45 8 5 o 4 ii 22 -48 45 46 ii 8 _ 4 O 5 -13 -24 46 47 13 10 7 - 3 -27 47 48 15 12 10 6 2 2 - 8 -16 -3 48 49 17 14 12 9 6 2 - 3 - 9 -18 -25 49 50 19 16 14 12 9 S i - 4 10 20 -42 50 51 21 18 17 14 ii 8 5 o - 5 12 22 -52 51 52 23 21 19 16 14 ii 8 - 4 o - 6 13 -25 52 53 24 22 2O 18 16 14 ii 8 - 4 i - 6 -14 -28 53 54 ' 26 24 22 20 18 16 13 10 7 - 3 2 - 8 -16 54 55 28 26 24 22 20 18 16 13 10 7 - 3 2 - 8 55 56 2 9 2 7 26 2 4 22 20 18 15 13 10 6 2 2 56 57 30 29 28 26 24 22 20 18 15 13 10 6 2 57 58 32 3 2 9 27 26 24 22 20 18 15 1 2 9 6 58 59 33 3 2 31 2 9 27 26 24 22 20 18 15 12 9 59 60 35 33 32 30 2 9 27 26 24 22 20 18 15 12 60 61 36 35 33 32 31 2 9 28 26 24 22 20 l8 15 61 62 38 37 35 34 3 2 3 1 29 28 26 24 22 2O 18 62 63 39 38 37 35 34 32 31 2 9 28 26 24 22 20 63 64 4 1 39 38 37 35 34 3 2 31 29 28 26 24 22 64 65 42 4i 40 38 37 35 34 3 2 3 1 29 28 26 24 65 66 44 43 4 1 40 38 37 35 34 32 31 30 28 26 66 67 68 45 46 44 45 43 44 43 40 4 2 39 40 37 39 36 38 It 32 34 3 1 33 30 3 1 28 3 67 68 69 48 47 46 45 43 42 40 39 38 36 34 33 32 69 70 71 49 48 49 % 46 47 45 46 43 45 42 43 42 39 4 1 38 39 36 38 11 33 35 70 71 72 52 5 1 5 49 47 46 45 44 43 40 38 37 72 73 53 52 51 50 49 48 46 45 44 43 4 1 40 38 73 74 54 53 5 2 5 49 48 47 45 44 43 40 74 75 56 55 54 53 52 So 49 48 47 45 44 43 42 75 76 57 56 55 54 53 52 So 49 48 47 46 45 43 76 77 58 57 56 55 54 53 52 51 5 49 48 46 45 77 78 59 58 57 56 55 53 52 5 1 50 49 48 78 79 61 60 59 58 57 56 55 54 53 S 2 49 48 79 80 62 61 60 59 58 57 56 55 5* 53 52 51 So 80 t 12.0 12.5 13.0 13.5 140 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 t TABLES OF PHYSICAL CONSTANTS 161 X. TEMPERATURE OF THE DEW POINT, IN DEGREES FAHRENHEIT. Continued ft m & > K P DlFEERENCE BETWEEN THE DRY AND WET THERMOMETERS (t-t') g J 1 180 19.0 20.0 21.0 MtO 23.0 S!40 9150 II 1 26.0 27.0 28.0 290 300 55 - 8 56 -19 57 2 10 -48 58 6 3 22 58 59 9 i 12 59 60 12 5 - 5 -25 60 61 15 9 14 61 62 18 12 - 6 -28 62 63 20 15 9 o 63 64 22 18 12 - 4 - 6 -32 64 65 2 4 20 15 9 o -16 65 66 26 22 l8 12 - 4 - 7 -34 66 67 28 2 4 20 15 9 I -16 67 68 3 26 2 3 18 12 - 4 - 7 -37 68 69 32 28 2 5 20 *5 8 o -!7 69 70 33 3 2 7 23 ^9 12 - 5 - 7 -39 70 71 35 32 29 25 21 16 9 o -17 71 72 37 33 31 27 23 18 13 - 5 6 -39 72 73 38 35 32 29 25 21 16 10 -16 73 74 40 37 34 3i 28 24 19 13 - 6 6 -37 74 75 42 39 36 32 30 26 22 16 10 -16 75 76 43 41 38 34 32 28 24 20 H - 6 - 6 -34 76 77 45 42 40 36 33 30 26 22 i'7 ii i -14 77 78 47 44 4i 38 35 32 28 24 20 14 7 - 4 -3 78 79 48 46 43 40 37 34 31 27 23 18 ii 2 ij 79 80 5 47 45 42 39 36 32 29 25 21 15 8 3 80 t 18.0 19.0 20.0 21.0 22.0 230 240 25.0 26.0 27.0 28.0 29.0 30.0 t 1 62 PHYSICAL LABORATORY GUIDE XI. RELATIVE HUMIDITY, PER CENT i ^& DIFFERENCE BETWEEN THE DRY AND WET THERMOMETERS (/-/') 8 ~ 1 05 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 >< M Q 20 92 85 77 70 63 56 48 4i 34 27 20 13 20 21 93 85 78 7 1 64 57 50 43 36 29 23 16 21 22 93 86 79 72 65 58 5 1 45 38 32 2 5 19 22 23 93 86 80 73 66 60 53 46 40 34 2 7 21 23 24 93 87 So 74 67 61 54 48 42 36 30 24 24 25 94 87 81 74 68 62 56 5 44 38 32 26 25 26 94 88 81 75 69 63 57 5i 45 40 34 28 26 27 94 88 82 76 7 64 59 53 47 42 42 36 27 28 94 88 82 77 7i 65 60 54 49 43 38 33 28 29 94 89 83 77 72 66 61 56 50 45 40 35 29 30 94 89 84 78 73 67 62 57 5 2 47 41 36 30 31 95 89 84 79 74 68 63 58 53 48 43 38 31 32 95 9 84 79 74 69 64 59 54 5 45 40 32 33 34 95 95 90 9i 3 80 81 75 75 7 72 65 67 60 62 56 57 5i 53 47 48 42 44 33 34 35 95 9i 86 82 76 73 69 65 59 54 5 45 35 36 96 9i 86 82 77 73 70 66 61 56 5 1 47 36 37 96 9i 87 82 78 74 7 66 62 57 5 2 48 37 38 96 92 87 83 79 75 7i 67 63 58 54 5 38 39 96 92 88 83 79 75 72 68 63 59 55 5 2 39 40 96 92 88 84 80 76 72 68 64 60 56 53 40 41 96 92 88 84 80 76 72 69 65 61 57 54 41 42 43 96 96 92 92 88 88 84 85 81 81 77 77 73 74 69 70 s 62 63 58 59 55 56 42 43 44 96 92 88 85 81 78 74 70 67 63 60 57 44 45 96 92 89 85 82 78 75 7 1 67 64 61 58 45 46 47 96 96 93 93 89 89 85 86 82 83 79 79 9 72 72 68 69 Si 61 62 58 59 46 47 48 96 93 89 86 83 79 7 6 73 69 66 63 60 48 49 97 93 80 86 83 80 7 6 73 70 67 63 60 49 50 97 93 90 87 83 80 77 74 70 67 64 61 50 51 97 93 90 87 84 81 77 74 7 1 68 65 62 51 52 97 94 90 8 7 84 81 78 75 72 69 66 63 52 53 97 94 9i 87 84 81 78 75 72 69 66 63 53 54 97 94 9i 88 85 82 79 76 73 7 67 64 54 t 0.5 1.0 1.5 20 2.5 3.0 3.5 40 4.5 5.0 5.5 60 t TABLES OF PHYSICAL CONSTANTS 163 XI. RELATIVE HUMIDITY, PER CENT. Continued % DIFFERENCE BETWEEN THE DRY AND WET THERMOMETERS (t - 1') | Q 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 Q 55 97 94 91 88 85 82 79 76 73 70 68 65 55 56 97 94 91 88 85 82 80 77 74 71 68 65 56 57 97 94 91 88 86 83 80 77 74 7 1 69 66 57 58 97 94 91 89 86 83 80 78 75 72 69 67 58 59 97 94 91 89 86 83 81 78 75 72 70 67 59 60 97 94 92 89 86 84 81 78 75 73 70 68 60 61 97 94 92 89 87 84 81 78 7.6 73 7 1 68 61 62 97 95 92 89 87 84 81 79 76 74 7 1 69 62 63 97 95 92 89 87 84 82 79 77 74 72 69 63 64 97 95 92 90 87 85 82 79 77 74 72 70 64 65 97 95 92 90 87 85 82 80 77 75 72 7 65 66 97 95 92 90 87 85 82 80 78 73 66 67 98 95 93 90 88 85 83 80 78 76 73 7 1 67 68 98 95 93 90 88 85 83 81 78 76 74 7 1 68 69 98 95 93 90 88 86 83 81 78 76 74 72 69 70 98 95 93 90 88 86 83 81 79 77 74 72 70 71 98 95 93 88 86 84 81 79 77 75 .72 71 72 98 95 93 91 88 86 84 82 79 77 75 73 72 73 98 95 93 91 88 86 84 82 80 78 75 73 73 74 98 95 93 9i 88 86 84 82 80 78 76 74 74 75 98 95 93 9i 89 87 84 82 80 78 76 74 75 76 98 95 93 91 89 87 85 82 80 78 76 74 76 77 98 95 93 91 89 87 85 83 80 78 76 74 77 78 98 96 93 91 89 87 85 83 81 79 77 75 78 79 98 96 94 9i 8 9 87 85 83 81 79 77 75 79 80 98 96 94 92 89 87 85 83 81 79 77 75 80 t 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 t 1 64 PHYSICAL LABORATORY GUIDE XI. RELATIVE HUMIDITY, PER CENT. Continued I M P . DIFFERENCE BETWEEN THE DRY AND WET THERMOMETERS (tt'} g M P 6.0 6.5 7.0 7.5 80 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 19 10 19 20 r 3 6 20 21 16 9 2 21 22 1 9 12 6 22 23 21 15 9 2 23 24 24 I7 ii 6 24 25 26 2O J 4 8 3 25 26 28 23 17 ii 6 26 27 3 2 5 19 14 9 3 27 28 33 27 22 17 ii 6 I 28 29 35 29 24 19 H 9 4 29 30 36 3 1 26 22 12 7 2 30 31 38 33 29 24 19 14 10 5 31 32 40 35 31 26 21 17 12 8 3 32 33 42 37 33 28 24 19 J 5 10 6 2 33 34 44 39 35 30 26 21 17 13 9 4 34 35 45 37 3 2 28 2 4 19 15 12 7 3 35 36 47 43 38 34 3 26 22 18 14 10 6 2 36 37 48 44 40 36 32 28 2 4 20 16 12 8 5 I 37 38 5 46 42 38 34 30 26 22 18 15 ii 7 3 38 39 5 2 48 44 40 36 32 28 24 20 17 13 9 6 39 40 53 49 45 38 34 30 26 22 19 16 12 8 40 41 54 5 46 43 39 36 32 29 2 4 21 18 *4 10 41 42 55 51 48 44 40 37 34 30 27 23 20 16 '3 42 43 56 S 2 49 46 42 38 35 32 2 9 2 5 22 19 15 43 44 57 53 5 47 43 40 37 33 30 27 24 21 17 44 45 58 54 48 44 38 32 29 25 22 19 45 46 58 55 52 49 46 42 39 36 33 30 27 23 21 46 47 59 5 6 53 5 47 44 40 38 34 31 28 25 22 47 48 60 56 53 5 1 48 45 42 39 36 33 3 27 24 48 49 60 57 54 52 49 46 43 40 37 34 31 29 26 49 t 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 '10.5 11.0 11.5 12.0 t TABLES OF PHYSICAL CONSTANTS 165 XI. RELATIVE HUMIDITY, PER CENT. Continued D *S Q DIFFERENCE BETWEEN THE DRY AND WET THERMOMETERS (/-/') | ~ >H M q 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 50 61 58 55 5 2 5 47 44 41 38 36 33 3 27 50 51 62 59 56 53 5 48 45 42 39 37 34 3i 28 51 52 63 60 57 54 5i 48 46 43 40 38 35 33 30 52 53 63 6l 58 55 5 2 49 47 44 42 39 36 34 31 53 54 64 61 59 5 6 53 50 48 45 43 40 38 35 32 54 55 65 62 59 57 54 51 49 46 43 4i 39 36 34 55 56 65 63 60 57 55 5 2 5 47 44 42 40 37 35 56 57 66 64 61 58 55 53 5 48 45 43 40 38 36 57 58 67 64 61 59 56 53 5 1 49 46 44 42 39 37 58 59 67 65 62 60 57 54 5 2 49 47 45 43 40 38 59 60 69 65 63 60 58 55 53 5 48 46 44 4i 39 60 61 68 66 63 61 58 56 54 5 1 49 47 44 42 40 61 62 69 66 64 61 59 57 54 5 2 5 47 45 43 4i 62 63 69 67 64 62 60 57 55 53 5 1 48 46 44 42 63 64 70 67 65 62 60 58 56 53 5i 49 47 45 43 64 65 70 68 65 63 61 59 56 54 S 2 50 48 46 44 65 66 7 1 68 66 63 61 59 57 55 53 5 1 49 47 45 66 67 7i 69 66 64 62 60 58 55 53 5 1 49 47 45 67 68 7i 69 67 65 63 60 58 56 54 5 2 50 48 46 68 69 72 7 6 7 65 63 61 59 57 55 53 5 1 49 47 69 70 72 70 68 66 64 62 60 57 55 53 5 2 5 48 70 71 72 70 68 66 64 62 60 58 56 54 52 50 48 71 72 73 7 1 69 67 65 63 61 59 57 55 53 5 1 49 72 73 73 7i 69 67 6 5 63 61 59 57 55 53 5 2 5 73 74 74 72 70 68 66 64 62 60 58 56 54 5 2 50 74 75 74 72 70 68 66 64 62 60 58 56 55 53 5i 75 76 74 72 70 68 66 64 63 61 59 57 55 53 52 76 77 74 73 7 1 69 67 65 63 61 59 57 56 54 5 2 77 78 75 73 7 1 69 67 65 63 62 60 58 56 54 53 78 79 75 73 7i 70 68 66 64 62 60 58 57 55 53 79 80 75 73 72 7 68 66 64 63 61 59 57 55 54 80 t 6.0 65 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 t 1 66 PHYSICAL LABORATORY GUIDE XI. RELATIVE HUMIDITY, PER CENT. Continued pi jjj DIFFERENCE BETWEEN THE DRY AND WET THERMOMETERS (t t') jjj 1 120 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0" Q 40 8 5 i 40 4i 10 7 4 41 4. 13 10 6 3 42 4 > IS 12 9 5 2 43 44 17 14 ii 8 5 i 44 45 Ig 16 13 10 7 4 i 45 46 21 18 15 12 9 6 3 46 47 22 20 16 M ii 8 5 3 47 48 24 21 19 16 13 10 7 5 2 48 49 26 23 20 17 IS 12 9 7 4 i 49 50 27 2 4 22 19 16 H n 9 6 4 i 50 51 28 26 23 21 18 16 13 10 8 5 3 51 52 53 3 31 2 7 2 9 Ii 22 24 20 21 17 19 11 12 14 10 12 7 9 5 7 4 2 52 53 54 32 30 28 25 23 20 18 15 13 ii 8 6 4 54 55 34 31 29 26 2 4 22 19 17 15 12 10 8 6 55 56 35 33 30 28 25 23 21 19 16 14 12 10 8 56 57 3 6 34 29 2 7 24 22 20 18 16 13 ii 9 57 58 37 35 33 30 28 26 24 21 19 7 15 13 ii 58 59 38 36 34 31 2 9 27 25 23 21 18 16 12 59 60 39 37 34 32 30 28 26 24 22 20 18 16 M 60 61 62 40 38 39 35 37 33 34 32 32 29 30 3 3 23 21 22 20 18 15 16 61 62 63 64 42 43 40 i H 33 34 31 32 29 30 28 29 27 24 25 22 23 20 21 18 19 63 64 65 44 42 39 37 35 33 3' 29 28 26 2 4 22 20 65 66 67 68 45 45 46 42 43 44 40 42 38 39 40 36 37 38 34 H 32 33 34 30 32 33 29 30 2 29 11 27 23 25 26 22 23 24 66 67 68 69 47 45 43 39 37 35 33 32 3 28 26 25 69 70 48 46 44 4 2 40 38 36 34 33 3i 2 9 27 26 70 71 48 46 45 43 41 39 37 35 34 3 2 30 28 2 7 71 72 49 47 45 43 42 40 38 36 35 33 3 1 3 28 72 73 74 5 5 48 48 46 47 44 45 42 43 4 1 39 40 Ii 9 34 35 32 33 30 3 1 29 3 73 74 75 51 49 47 46 44 42 40 39 37 35 34 32 31 75 76 52 50 48 46 45 43 4 1 39 38 36 35 33 31 76 77 5 2 5 49 47 45 44 42 40 39 37 35 34 32 77 78 53 49 48 46 44 43 39 38 36 35 33 78 79 53 52 50 48 47 45 43 42 40 39 37 36 34 79 80 54 52 51 49 47 45 44 42 4i 39 38 36 35 80 t 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 175= 18.0 t TABLES OF PHYSICAL CONSTANTS 167 XL RELATIVE HUMIDITY, PER CENT. Continued 'j. M J 5 g DIFFERENCE BETWEEN THE DRY AND WET THERMOMETERS (/-*') Q 18.0 19.0 20.0 21.0 22.0 23.0 24.0 25.0 26.D 27.0 28.0 29.0^ 30.0 re 6 j 55 56 8 3 56 57 9 5 57 53 ii 7 2 58 59 12 8 4 59 60 14 10 6 2 60 61 15 ii 7 3 61 62 16 13 9 5 62 63 18 H 10 7 3 63 64 19 15 12 8 5 I 64 65 20 17 13 10 6 3 65 66 22 18 14 ii 8 4 i 66 67 2 3 19 16 12 9 6 2 67 68 24 20 J 7 14 10 7 4 i 68 69 2 5 22 18 15 12 8 5 2 69 70 26 23 19 16 13 10 7 4 I 70 71 2 7 24 20 17 14 ii 8 5 2 71 72 28 24 22 18 15 12 9 6 3 I 72 73 29 22 19 16 13 10 8 2 73 74 30 26 23 20 18 15 12 9 6 3 I 74 75 31 27 24 21 19 16 13 10 7 5 2 75 76 31 28 2 5 22 20 17 14 ii 8 6 3 I 76 77 32 2 9 26 23 20 18 15 12 10 7 4 2 77 78 79 33 34 30 3 1 3 24 25 21 22 19 19 17 13 14 ii 12 9 6 7 3 4 I 2 78 79 80 35 32 29 26 23 20 18 15 13 10 8 6 3 80 t 18.0 19.0 20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.029.0 30.0 t 1 Ii 1 FHYS. LAB. GUIDE 12 1 68 PHYSICAL LABORATORY GUIDE XII. INDICES OF REFRACTION Air . . I 000294 Ice .31 Alcohol 1.36 Iceland spar, ordinary ray . .65 Canada balsam . . . 1.54 i 68 Iceland spar, extraordinary rav .48 2 A 7 to 2 7^ \Vater .336 Ether 1.36 The eye : Glass, crown . . . Glass, flint .... Glycerine .... 1.53 to 1.56 1.58 to 1.64 1.47 Aqueous humor . . Vitreous humor Crystalline lens . . 337 339 3^4 XIII. SPECIFIC HEATS Acetic acid 0.6589 Acetone -53 Alcohol, ethyl (o-5O) . .0.615 Air 0.2374 Alcohol, methyl (o-6i) . 0.613 Aluminum (i5-97) . . 0.2122 Antimony (o-ioo) . . . 0.0507 Beeswax 0.64 Benzene (n-8i) . . . 0.45 Bismuth (9-iO2) . . . 0.0298 Brass, hard (o-ioo) . . 0.0858 Carbon disulphide (34-6o) 0.2206 Copper (o-ioo) .... 0.0949 Ether (o-33) 0.517 Glass, thermometer (o-ioo) 0.1770 Glycerine (o-ioo) . . . 0.555 Hydrogen 3.409 Ice Iron (o-ioo) . , Lead (i9-48) . Marble . . . Mercury (o-ioo) Nickel (i4-97) 0.504 0.1098 0.0315 0.2129 0-0333 0.1217 Nitrogen 0.2438 Olive oil 0.310 Oxygen 0.2175 Platinum (o-ioo) . . . 0.0355 Silver (o-ioo) .... 0.0559 Salt 0.173 Sulphur (i5-95). . . - 0.1844 Steel 0.118 Tin (o-ioo) 0.0559 Turpentine (o-ioo). . . 0.426 Zinc (o-ioo) -935 XIV. SPECIFIC RESISTANCES RESISTANCE IN OHMS RESISTANCE IN OHMS TEMPERATURE COEF- OF WIRE 100 CM. OF WIRE i FOOT FICIENT (INCREASE LONG AND i MM. LONG AND i MIL. OF RESISTANCE) OF IN DIAMETER AT DIAMETER AT i OHM FOR A RISE IN TEMPERATURE o C. TEMPERATURE o C. TEMPERATURE i C. Aluminum 0.03699 17.48 0.00388 Copper . . . O.O2O62 10.19 00388 German silver . 0.2660 181.3 0.00044 Iron .... 0.1234 61.3 0.00055 Mercury . 1.198 574-0 0.00072 Platinum . . . o.i 150 7-5 Silver .... 0.02019 9-53 0.00377 TABLES OF PHYSICAL CONSTANTS 169 XV. TABLE OF NATURAL SINES AND TANGENTS ANGLE SINE TANGENT ANGLE SINE TANGENT ANGLE SINE TANGENT Degrees Degrees Degrees o.ooo O.OOO 31 -S l S 0.601 62 0.883 I.88I 1 0.017 0.017 32 0.530 0.625 63 0.891 1.963 2 0.035 0-035 33 0-545 0.649 64 0.899 2.050 3 0.052 0.052 34 o-559 0.675 65 0.906 2.145 4 0.070 0.070 35 o-574 0.700 66 0.914 2.246 5 0.087 0.087 36 0.588 0.727 67 0.921 2.35 6 6 0.105 0.105 37 0.602 o-754 68 0.927 2 -475 7 0.122 0.123 38 0.616 0.781 69 0-934 2.605 8 0.139 0.141 39 0.629 0.810 70 0.940 2.747 9 0.156 0.158 40 0.643 0.839 71 0.946 2.904 10 0.174 0.176 41 0.656 0.869 72 0.951 3.078 11 O.I9I 0.194 42 0.669 0.900 73 0.956 3-271 12 0.208 0.213 43 0.682 0-993 74 0.961 3487 13 0.225 0.231 44 0.695 0.966 75 0.966 3-732 14 0.242 0.249 45 0.707 I.OOO 76 0.970 4.011 15 0.259 0.268 46 0.719 1.036 77 0.974 4-331 16 0.276 0.287 47 0-731 1.072 78 0.978 4-75 17 0.292 0.306 48 o-743 I. Ill 79 0.982 5-H5 18 0.309 0-325 49 0-755 1.150 80 0.985 5.67 1 19 0.326 0-344 50 0.706 1.192 81 0.988 6.314 20 0.342 0.364 51 0.777 L235 82 0.990 7-U5 21 0.358 0.384 52 0.788 1.280 83 0-993 8.144 22 -375 0.404 53 0-799 1-327 84 0-995 9-5 l 4 23 0.391 0.424 54 0.809 I.37 6 85 0.996 n-43 24 0.407 0-445 55 0.819 1.428 86 0.998 14.30 25 0.423 0.466 56 0.829 1.483 87 0.999 19.08 26 0.438 0.488 57 0.839 1.540 88 0.999 28.64 27 0.454 0.510 58 0.848 i. 600 89 I.OOO 57-29 28 0.469 0.532 59 0.857 1.664 90 I.OOO OO 29 0.485 o-554 60 0.866 I -73 2 30 0.500 -577 61 0.875 1.804 PHYSICAL LABORATORY GUIDE XVI. NUMBER, DIAMETER, WEIGHT, LENGTH, AND RESISTANCE OF PURE COPPER WIRE BROWN AND SHARPE GAUGE No. * DlAM. IN MILS CIRCULAR MILS (DR.) I MlL = .001 IN. WEIGHT, POUNDS PER IOOO FT. LENGTH, FEET PER POUND RESISTANCE OF PURE COPPER AT 75 F. Ohms per IOOO ft. Feet per Ohm Ohms per Pound oooo 460.000 211600.0 639.32 1.56 0.051 19605.69 0.0000798 000 409.640 167805.0 507.01 1.97 0.064 15547.87 0.000127 00 364.800 I33 79.2 402.09 2.49 0.081 12330.36 0.000202 324-95 105534.0 319.04 3-!3 0.102 9783.63 0.000320 I 289.300 83694.0 252.88 3.95 0.129 7754.66 0.00051 2 257.630 66373.0 200.04 4.99 0.163 6149.78 O.OOOSII 3 229.420 526334 159-03 6.29 0.205 4876.73 0.001289 4 204.310 41742.5 126.12 7-93 0.259 3867.62 0.00205 5 181.940 33 I02 -3 IOO.OI 10.00 0.326 3067.06 0.00326 6 162.020 26250.5 79-32 12.61 0.411 2432.22 0.00518 7 144.280 20817.0 62.90 15.90 0.519 1928.75 0.00824 8 128.490 16509.0 49.88 20.05 0.654 1529.69 O.OI3II 9 114.430 13094.0 39-56 25.28 0.824 1213.22 0.02083 10 101.890 10381.0 3 J -37 31.88 1.040 961.91 0.03314 it 90.742 8234.1 24.88 40.20 1.311 762.93 0.05269 12 80.808 6529.9 19-73 50.69 1.653 605.03 0.08377 13 71.961 5 I 78-4 I5-65 63.91 2.084 479.80 O.I332I *4 64.084 4106.8 12.41 80.59 2.628 380.51 0.2II8 15 57.068 3256.8 9.84 101.63 3.314 301.75 0.3368 16 50.820 2582.7 7.81 128.14 4.179 239.32 0-5355 17 45- 2 57 2048.2 6.19 161.59 5.269 189.78 0.8515 18 40-303 1624.3 4.91 203.76 6.645 150-50 1.3539 19 35.890 1288.1 3.78 264.26 8.617 116.05 2.2772 20 31.961 1021.5 3.09 324.00 10.566 94.65 3423 21 28.462 810.08 2-45 408.56 13.323 75.06 5-443 22 23 25-347 22.571 642.47 509-45 1.94 1-54 S I S- I S 649.66 16.799 21.185 59-53 47.20 8.654 13-763 24 2O.IOO 504.01 1.22 819.21 26.713 3743 21.885 17.900 320.41 0.97 1032.96 33.684 29.69 34-795 26 15.940 254.08 0.77 1302.61 42.477 23-54 55-331 27 I4- I 95 201.50 0.6 1 1642.55 53.563 18.68 87.979 28 12.641 159-79 0.48 2071.22 67.542 14.81 139.893 29 11.257 126.72 0.38 2611.82 85.170 11.74 222.449 3 10.025 100.50 0.30 3293.97 107.391 9.31 353-742 3 1 8.928 79.71 0.24 4152.22 135.402 7.39 562.221 S 2 7.950 63.20 0.19 5236.66 170.765 5.86 894.242 33 7.080 5-*3 0.15 6602.71 215.312 4-64 1421.646 34 6.304 39-74 O.I2 8328.30 27 I -583 3-68 2261.82 5.614 3 J -52 O.IO 10501.35 342.443 2.92 3596.104 36 5.000 25.00 0.08 13238.83 431.712 2.32 57I5.36 37 4-453 19.83 O.O6 16691.06 544.287 1.84 9084.71 38 3-9 6 5 15.72 O.O5 20854.65 686.511 1.46 14320.26 39 3-531 12.47 0.04 26302.23 865.046 1.16 2^752.6 40 3- J 44 9.88 0.03 33*75-94 1091.865 0.92 36223.59 TABLES OF PHYSICAL CONSTANTS XVII. ELECTRICAL RESISTANCE, DIAMETER, CROSS SEC- TION, ETC., OF COPPER WIRE, AMERICAN GAUGE, TEMPERATURE 24 C. d % J SIZE WEIGHT RESISTANCE CAPACITY IN AMPERES Diam. Inches Area Sq. In. Lb. per 1000 Ft. Feet per Pound Ohms per looo Ft. Feet per Ohm Ohms per Pound 0000 .4600 .166191 639.60 1.564 0.051 19929.7 0.0000785 312.0 000 .4096 .131790 507.22 1.971 0.063 15804.9 0.000125 262.0 00 .3648 .104590 402.25 2.486 0.080 12534.2 0.000198 22O.O .3249 .082932 319.17 3-133 O.IOI 9945-3 0.000315 185.0 1 .2893 065733 252.93 3.952 0.127 7882.8 0.000501 156.0 2 .2576 .052130 200.63 4-994 0.160 6251.4 0.000799 I3I.O 3 .2294 .041339 159.09 6.285 0.202 4957-3 0.001268 IIO.O 4 .2043 .032784 126.17 7.925 0.254 3931-6 0.002016 92.3 5 .1819 .025998 100.05 9-995 0.321 3117.8 0.003206 77-6 6 .1620 .020617 79-34 12.604 0.404 2472.4 0.005098 65-2 7 1443 .016349 62.92 I5.893 0.509 1960.6 0.008106 54-8 8 .1285 .012766 49.90 20.040 0.643 JSSS-o 0.01289 46.1 9 .1144 .010284 39.58 25-265 0.811 1233-3 0.02048 38.7 10 .1014 .008153 31-38 31.867 1.023 977.8 0.03259 32.5 11 .0907 .006467 24.89 40.176 1.289 775-5 0.05181 27-3 12 .0808 .005129 19.74 50.651 1.126 615.02 0.08237 23.0 13 .0720 .004067 *S'(>5 63.898 2.048 488.25 0.13087 19.2 14 .0641 .003147 12.41 80.580 2.585 386.80 0.20830 16.2 15 .0571 .002558 9.84 101.626 3-!77 306.74 o.33 x 33 13.6 16 .0508 .002029 7.8! 128.041 4.582 243-25 0.52638 "5 17 0453 .001609 6.19 161.551 5-183 192.91 0.83744 9-6 18 .0403 .001276 4.91 203.666 6.536 152.99 i-33 12 8.1 19 0354 .000984 3.786 264.136 8.477 117.96 2.2392 6.7 20 .0320 .000802 3.086 3 2 4.045 10.394 96.21 3.3438 57 21 .0285 .000636 2.448 408.497 13.106 76.30 5-3539 4.8 22 0253 .000505 1.942 5I4.933 16.525 60.51 8.5099 4.0 23 .0226 .000400 J -539 649773 20.842 47.98 13-334 3-4 24 .O2OI .000317 I.22I 819.001 26.284 38.05 21.524 2.8 25 .0179 .000252 0.967 1034.126 33-135 30.18 34-298 2-4 26 .0159 .000199 0.768 1302.083 41.789 23.93 54410 2.0 27 .0142 .000158 0.608 1644.737 52.687 18.98 86.657 1-7 28 .0126 .000125 0.484 2066.116 66.445 15-05 137.283 1.4 29 .0113 .OOOIOO 0.384 2604.167 83752 11.94 218.104 1.2 30 .oioo .000079 0.302 33H-258 105.641 9.466 349.805 I.O 31 .0089 .000063 0.239 4184.100 133.191 7.508 557.286 0.84 32 .0079 .000050 0.190 5263.158 168.011 5.952 884.267 0.70 33 .0071 .000039 O.I5I 6622.517 211.820 4.721 1402.78 O.6o 34 .0063 .000031 O.I2I 8264463 267.165 3.743 2207.98 0.50 35 36 .0056 .0050 .000025 .000020 0.094 0.075 10638.30 13333-33 336.81 42465 2.969 2-355 3583.12 5661.71 0.42 0-35 37 .0045 .000016 0.000 535-33 1.868 8922.20 0.27 38 .0040 .000012 0.045 22222.22 675.22 1481 15000.5 0.25 39 0035 .000010 0.038 26315.79 851.789 1.174 22415.5 0.21 40 .0031 .000008 0.030 33333-33 1074.11 0.931 35803.8 O.I 7 1 72 PHYSICAL LABORATORY GUIDE XVHI. RESISTANCES OF GERMAN SILVER WIRE AMERICAN GAUGE SIZE 18% 30% OHMS PER 1000 Fl. OHMS PER POUND OHMS PER 1000 FT. OHMS PER POUND Number 8 11.772 0.23598 17.658 0.36397 9 11.832 0-37494 17.748 0.56241 10 18.72 0.59652 28.08 0.89478 11 23-598 0.94842 35-397 1.42263 12 29.754 1.50786 44.631 2.26179 13 37-512 2.39778 56.268 3.59667 14 47.3 4 3.8124 70.956 5.7186 15 59.652 6.0624 89.478 9.0936 16 75-222 9.639 112.833 14.458 17 94.842 I5-327 142.263 22.990 18 119.61 24.3702 179.41 36.5553 19 155.106 40.9896 232.659 61.4844 20 190.188 61.614 285.282 92.421 21 239.814 97-974 359-721 146.96! 22 302.382 155-772 453-573 233.658 23 38i.33 247-734 57^99 371.601 24 480.834 393-93 721.251 590.89 25 606.312 626.31 909.468 939.46 26 764.586 995-958 1146.879 1493-937 27 964.134 1583.622 1446.201 2375-433 28 1215.756 2518.075 1823.634 3777.112 29 1533.06 4004.082 2299.59 6006.123 30 i933- 38 6368.356 2899.557 9552.354 . 31 2437.236 10119.978 3655.854 15179.967 32 3073.77 16096.356 4610.65 24144.534 33 3875.616 25589.628 5813.424 38384.442 34 4888.494 40712.76 7332-741 61069.14 35 6163.974 64729.87 9245.961 97094.80 36 7770.816 102876.482 11656.224 i543 I 4-7 2 3 37 9797.166 163524.78 14695.749 245287.17 38 12357.198 257764.68 I8535.797 386647.02 39 15570.828 409546.8 23356.242 614320.2 40 19653.57 652024.62 29480.35 978036.93 TABLES OF PHYSICAL CONSTANTS XIX. VELOCITY OF SOUND AT C. METERS METERS Air per sec. 332 Hydrogen per sec. 1269 Ash per sec. 4668 Iron per sec. 5 I2 7 Brass per sec. 3318 Lead per sec. 1228 Caoutchouc per sec. 60 Maple per sec. 4106 Carbon monoxide per sec. 337 Oak per sec. 3847 Carbon dioxide per sec. 261 Oxygen per sec. 317 Cedar per sec. 530 Pine per sec. 3322 Chlorine per sec. 206 Silver per sec. 2607 Copper per sec. 3556 Steel per sec. 5237 Elm per sec. 4120 Tallow per sec. 357 Ether per sec. "59 Turpentine at 24 per sec. J2I2 Fir per sec. 4638 Walnut per sec. 4601 Glass per sec. 5026 Water at 8.1 per sec. J 435 Gold per sec. 1743 Wax per sec. 857 CHAPTER XII (a) APPARATUS REQUIRED FOR THIS BOOK (6) SOME USEFUL HOME-MADE APPARATUS NOTE. A great saving in apparatus required may be effected : (a) By having two pupils work together. () With more advanced pupils the author has tried the plan of having five different experiments in one laboratory period and repeating these same experiments for five successive periods. With costly apparatus this is a great advantage, and also develops self-reliance in the pupil. LIST OF APPARATUS Ammeter, 1 amperes, (22), (33). (34), (35). Alcohol, (12), (13), (14), (15), (16), (43). Blue-print paper (6" x 8"), Eastman's, (18). Board (8" x 14"), with slot, (18). Bunsen burner, low form, (23), (32), and (46-52). Block, rectangular, weighted, (i), (37), (39), (43), (56). Balance scalepan, (4), (7-15), (49), (5)> (50> (52), (22). Balance spring (0-250 gm.), (6), (37), (38), (43). Balance spring (0-30 lb.), (0-15 kgm.), (41), (42). Bottle, wide-mouth, ground stopper, 4-oz., (13). Balancing column tubes, (16). Beeswax. Boyle's law tube, " J " form, (45). Barometer, mercury preferred, (45), (46). Boiler, steam, with attachments, (46), (47), (48), (49), (50-52). Beaker (or wide-mouth bottle), 8-oz., (46). Block, small, with vertical, black mark, (56). Bristles, (63). Bow, bass viol, (63 and 65). 175 176 PHYSICAL LABORATORY GUIDE Balance holders, large and small, for horizontal position, (37), (38), (43), (40, (42). Bar magnets, 2 (6" x i"), (17), (18). Compass (small pocket, scale in degrees), (17), (19), (20). Cell, simple voltaic (special form), (21) (see Chap. XII). Cell, Daniell, 2, (22), (24-26), (28), (29), (30). Cell, dry, (23), (26), (31), (32). Coil, copper, temperature coefficient, (32). Catch bucket, (7), (8). Cylinder, wood-weighted, floating, (8). Copper sulphate, (12), (22). Calorimeter to fit boiler, (49), (32). Calorimeter (use overflow can), (49), (52). Calorimeter, polished (use overflow cm), (53). Candle, large, best quality, (54), (61). Compasses, drawing, (56-58), (61). Camphor gum, (63). Crucible tongs, (63). Emery cloth, (21). Filings (iron), (18). Funnel (glass), (46). Galvanoscope, (20), (21), (22), (30). Galvanometer shunt, adjustable (spec.), (see Chap. XII), (24-26), (29). Graduate (500 c.c.), (i). Graduate (100 c.c.), (9). Glass pane (9" x 24"), (43) Gas burner, mounted, (54). Glass, piece of red, (54). Glass, piece of plate, (57). Glass jar (quart), (12), (15), (22), (24-26), (28), (29), (30), (58). Glass (four pieces), (red, yellow, 'green, blue), (61). Glass jar (gallon), (7), (9), (10), (11), (15). Hydrometer, Fahrenheit, (14). Hydrometer, ordinary, constant mass, (14). Hydrometer jar, large (2\" x 18"), (14), (64). Hydrometer jar, small, (14). Index (refraction, air and water), (58). Knife edge, wooden, (39) . Linear expansion apparatus, (48) . LIST OF APPARATUS 177 Lead shot or copper filings, (50). Lens, double convex, (59), (60). Micrometer caliper, (3), (31), (41), (42), (66). Meter stick, (16), (31), (38), (39), (42), (43), (45), (48), (54), (55), (56), (60), (64), (65). Mercury (quicksilver), (45). (Numerous experiments, small quantity.) Manometer, open end, (47). Mirror plane (3" x 8"), (56). Metal bridge to fit quart jar, (58). Overflow can, (7), (8). Pinch cock, (16), (47). Paper, tissue, for cleaning glass, (43) . Psychrometer sling, (53), (desirable, not essential). Paper, white sheets (12" x 20"), (56). Paper section, inches and tenths, (62). Pins, ordinary, (37), (59). Resistance box (i ohm-ioo ohms), (23-32), (34). Rod, opaque, supported vertically, f" diameter, (54). Rubber bands, (16), (45), (56). Resin, (63), (65). 2 Revolvers and blank cartridges, (66). Sulphuric acid, dilute (1-20 by volume), (21), (22), (24-26), (28-30). Switch, reversing (mercury contacts), (24-26), (30). Scale, metric, 2o-cm., (i), (2). Useful in many others (paper). Sinker, metal, (n). Straightedge, accurate, desirable, not essential, (56). Stopper, rubber, (46), (47). Scale, mounted vertically, (36), (47). (See Fig. n.) Steam-trap, glass, (52). Sal ammoniac, (52). Sodium chloride, (53). Screen, 6" square, mounted vertically, (54), (59), (60). Sonometer, (65). Strips, wood, hard, 1.5 x 1.5 cm. x 100 cm., (36). Scalepan, spec, (see description, Chap. XII), (36). Thumb tack, \ doz., (18). Tubing, rubber, burner size, (oo). Tubing, rubber, pure gum, i-inch, (47), (48), (52). Thermometer (- io-uo C.), (32-43), (46-53), (64). 1/8 PHYSICAL LABORATORY GUIDE Triangle, draughtsman's (3o-6o), (2). Tube, glass Y tube, (16). Thread, coarse linen. Many experiments. Tuning fork apparatus, (63). Tuning fork, large, C, 128, (63). Tuning fork, heavy set, (64), (65). Tape line, 100 ft., (66). Voltmeter (or volt ammeter), (33), (34), (35). Wire gauze sieve, (18), (or bottle covered with cheesecloth). Wire, copper (20 B. & S.), insulated, (19), (31), and for electrical con- nections. Wire, copper, bare (20 B. & S.), (23). Wire, iron, bare (20 B. & S.), (23). Wire, German silver (22 insulated), (27), (31). Wire, soft iron (28 B. & S.), (41) Wire, soft copper (28 B. & S.), (41). Wire, hard, drawn copper (28 B. & S.), (41). Wire, steel, piano (28 B. & S.), (41), (42), (65). Wire, steel, piano (22 B. & S.), (65). Catgut, same diameter as 22 wire, (65). Wheatstone bridge (special form; see Chap. XII), (27), (28), (29), (30, (32). Weights, set (500 gm. to 10 mg.), (33), (36), (40), (46), (4), (7-i?)> (47-49)- Wire-testing machine (desirable, not essential), (41). Wax, sealing, and paraffin. Watches, stop, (66) . A SIMPLE FORM OF VOLTAIC CELL This is clearly shown in Figure 14. The supporting stick should be half inch square cross section and must be of hard wood to be satis- factory. The brass screws should be of such a size and thread that the small thumb nuts taken from old dry batteries may be used for binding post connections. No dimensions are given. The apparatus may be of any size to fit the jar with which it is intended to use it. I have found 3" x 4^" a convenient size for the plates, giving an immersed surface of about 3" x 3". By the use of washers or short pieces of ^-inch brass pipe the distance between the plates may be regulated to show variation of internal resistance of the cell. LIST OF APPARATUS 179 FIG. 14. i8o PHYSICAL LABORATORY GUIDE A VARIABLE RESISTANCE GALVANOMETER SHUNT This consists of a baseboard 4" x 6" x 1" mounted on feet made of two strips of 2-inch dowel pin each 4" long. Bore holes for the 1 1 s'J*\ b^=* i i i i i ! i i t r- i i I i i i &J I I I_U_T LLJ_ FIG. 15. binding posts and mercury cups. Put all screws, washers, etc., in place and then solder in resistances and connections on the under side of the board. The resistances are best made of No. 22 cotton insulated German LIST OF APPARATUS 181 silver wire which runs nearly one ohm per foot. Relative values 1:2:4 for the resistance coils are convenient. These used singly or two or three in series will give a wide range of combinations suitable for all kinds of work. The actual resistance of these coils will of course depend upon the re- sistance and sensitiveness of the galvanometer with which it will be used. Short pieces of heavy copper wire bent to connect two adjacent mercury cups are used for short-circuiting the coils when not in use. See diagram. A WHEATSTONE BRIDGE Select apiece of -board about 8" x 15" x i". This should be well- seasoned wood. Bore holes for binding posts and mercury cups, as shown in the drawing. dx. _O FIG. 16. 182 PHYSICAL LABORATORY GUIDE The contact keys are made of strips of hard sheet brass bent as shown. For the ratio coils No. 22 double cotton insulated German silver wire will be found convenient. It is desirable to adjust these coils to exactly one and ten ohms each, but this is not essential. The author has obtained good results by simply measuring off lengths of one and ten feet accurately. The resistance of these wires will not vary greatly from the values marked, and their ratio will be very close to 10 : I, which is the essential thing. All permanent connections shown in the drawing should be carefully soldered on the under side of the bridge. A coat or two of orange shellac will make a neat finish. This apparatus used in connection with an ordinary resistance box (.1 to no ohms) will give a possible range for measurements from .01 to 1 1 oo ohms. This bridge will commend itself on account of its teaching value, since it follows the theoretical Wheatstone bridge design very closely. Another good point is its low cost. The necessary material need not cost over seventy-five cents, and the labor involved in making it is small. COPPER TEMPERATURE COIL I have made a satisfactory coil by winding fine insulated copper wire No. B. & S. (Brown & Sharpe) 34 or 36 on the cardboard cover of a thermometer case ; after winding, one end of the coil is fitted snugly with a little shellac into a hole in a flat cork 3" or 4'' in diameter. Binding posts mounted on the cork and soldered to the ends of the temperature coil will give the apparatus a neat appearance. Finish it with a coat of shellac. A HAND SCALEPAN Cut out a disk 3^" in diameter from thin sheet copper, notch the disk at diametrically opposite points. Bend the wire into the shape of a V and bend the ends under the disk and solder it. Make the whole construction as light as possible. When it is completed, weigh it accurately and stamp this weight on the disk. This apparatus is very useful in laboratory work. OALIPORNU LIBEAET IS BOOK IS DU 7o7 THElASTl)ATE STAMPED BELOW YB 66580 251955