:'i wams liWlilliiS jffji^'Hjjjf IMI^i $!$jf$l! ,|i| ; iifiifl 5HUiiuiIiH!Ji!a'iHiU^ii ii PRACTICAL PHYSICS THE MACMILLAN COMPANY NSW YORK BOSTON CHICAGO DALLAS ATLANTA SAN FRANCISCO MACMILLAN & CO., LIMITED LONDON BOMBAY CALCUTTA MELBOURNE THE MACMILLAN CO. OF CANADA, LTIX TORONTO GALILEO GALILEI. Born 1564, in Pisa, Italy. Died 1642. Often called " the father of modern science " because he was one of the first who thought it worth while to subject his ideas to the test of experiment. PRACTICAL PHYSICS FUNDAMENTAL PRINCIPLES AND APPLICATIONS TO DAILY LIFE BY N. HENRY BLACK, A.M. SCIENCE MASTER, ROXBURY LATIN SCHOOL BOSTON, MASS. AND HARVEY N. DAVIS, PH.D. ASSISTANT PROFESSOR OF PHYSICS HARVARD UNIVERSITY Neto gork THE MACMILLAN COMPANY 1917 All rights reserved COPYBIGHT, 1918, BY THE MACMILLAN COMPANY. Set up and electrotyped. Published June, 1913. Reprinted August, 1913; April, June, 1914; January, July, December, 1915; July, 1916; May, August, 1917. J. 8. Cushing Co. Berwick & Smith Co, Norwood, Mass., U.S.A. G( C I 3-- PREFACE THE most difficult problem which confronts any author of a textbook is the selection of material. This is usually a process of exclusion. One has always to keep in mind the capacities and limitations, the interests and inclinations, of the young people most directly concerned, as well as the beauty and vast extent of the subject to be taught. This is especially true of a first course in physics. The number of suitable topics is far greater than can be well handled in any one-year course, however substantial it may be. A good book may, therefore, be judged as well by its omissions as in any other way. In preparing this book, we have tried to select only those topics which are of vital interest to young people, whether or not they intend to continue the study of physics in a college course. In particular, we believe that the chief value of the infor- mational side of such a course lies in its applications to the machinery of daily life. Everybody needs to know some- thing about the working of electrical machinery, optical instruments, ships, automobiles, and all those labor-saving devices, such as vacuum cleaners, fireless cookers, pressure cookers, and electric irons, which are found in many modern homes. We have, therefore, drawn as much of our illus- trative material as possible from the common devices in modern life. We see no reason why this should detract in the least from the educational value of the study of physics, for one can learn to think straight just as well by thinking about an electrical generator, as by thinking about a Geissler tube. v VI PREFACE This does not mean that we have tried to make the sub- ject interesting by selecting only the easy topics. There are many parts of physics which are of great practical value, but are essentially difficult. We have tried to present these subjects very slowly and carefully, believing that if any presentation is so simple and direct that the student can understand it clearly, his very understanding begets at once the interest which is fundamental. Even after a careful exclusion of material, we have selected somewhat more than it is probably advisable for any class to undertake in a single year. This gives the teacher an oppor- tunity to adapt his instruction to the local needs of his com- munity and to the amount of time available. In particular, the chapter on the strength of materials, the discussion of momentum, the chapter on the beginnings of electricity, the chapter on alternating currents, the chapter on electric waves and X-rays, and even the chapter on sound, may well be omitted altogether, or assigned for outside reading without careful discussion, if it seems desirable. We believe that it is most important for teachers to select carefully just what material they can best use, and to teach that thoroughly, rather than try to touch upon many topics superficially. We think it of great importance that the topics in a course in physics should be arranged in the most teachable order ; that is, with the easiest and simplest topics first. Thus in mechanics, the subject of acceleration and Newton's laws is essentially hard, and so we have put it at the end of that part of the book. On the other hand, the simple machines, such as the lever and the wheel and axle, are essentially easy, and so they come first. To understand any machine clearly, the student must have clearly in mind the fundamental principles involved. Therefore, although we have tried to begin each new topic, however short, with some concrete illustration familiar to young people, we have proceeded, as rapidly as seemed wise, PREFACE Vll to a deduction of the general principle. Then, to show how to make use of this principle, we have discussed other prac- tical applications. We have tried to emphasize still further the value of principles, that is, generalizations, in science, by summarizing at the end of each chapter the principles dis- cussed in that chapter. In these summaries we have aimed to make the phrasing brief and vivid so that it may be easily remembered and easily used. The problems are the result of considerable experience in trying to find suitable numerical exercises which will empha- size and illustrate the principles involved, with a minimum of arithmetical drudgery. They, too, are arranged, within each group, as far as possible in the order of their difficulty. It should always be emphasized, however, that the study of physics does not begin and end in the classroom, but is inti- mately connected with industrial and domestic life. It is very desirable to stimulate in students thought and imagina- tion about what they see, and to get them into the habit of asking intelligent questions of the mechanics, artisans, and engineers whom they meet. We have, therefore, added at the end of each of the earlier chapters, and in many places in the later chapters, questions, which require some knowledge gained in this way from outside life. We do not expect that every student can answer even a majority of these ques- tions at first ; but after he has tried to answer them, he is in a position to learn a great deal from the subsequent discussion of them in the classroom. Our treatment of acceleration, Newton's laws, kinetic en- ergy and momentum, is essentially different from either the dyne and poundal method common in physics textbooks, or the " slug " or " wog " method of engineers, and is apparently new. It has, however, been thoroughly tried out in the classroom, and we find it simpler and more direct than the usual presentation. We feel sure that it is as precise and scientific in its logic as any other. It was first developed by Vill PREFACE Professor E. V. Huntington, of Harvard University, to whom we gladly make acknowledgment of priority. We have borrowed ideas also from the books of Mr. Frank M. Gilley, of the Chelsea High School, and Director E. Grimsehl, of Hamburg, Germany. We have received valu- able assistance in the preparation of the manuscript from Professor Frank A. Waterman, of Smith College ; Mr. Irving O. Palmer, of the Newton Technical High School; Professor J. M. Jameson and Professor J. A. Randall, of Pratt Insti- tute, and many others. To all of these gentlemen we give our hearty thanks. We are indebted to the General Electric Company, the Westinghouse Companies, the Columbia Graphophone Com- pany, Stone and Webster, and others for material for certain of the plates and illustrations. Finally, we wish especially to express our obligation to Dr. William C. Collar, lately of the Roxbury Latin School, and to Professor W. S. Franklin, of Lehigh University, but for whose initiative, encouragement, and interest, this book never would have been written. We shall be grateful for corrections or suggestions from any source. K H. B. H. N. D. CONTENTS CHAPTER I. INTRODUCTION : WEIGHTS AND MEASURES PAGB 1 II. SIMPLE MACHINES . 13 III. TV MECHANICS OF LIQUIDS . 47 . 77 XV* V. NON-PARALLEL FORCES ..... . 105 VI. ELASTICITY AND STRENGTH OF MATERIALS . . 120 VII. ACCELERATED MOTION . . . . . 133 VIII. IX. FORCE AND ACCELERATION .... . 146 . 157 X. HEAT EXPANSION AND TRANSMISSION . 170 XI. XTT WATER, ICE, AND STEAM .... . 196 . 219 WJ.JL* XIII. XIV. MAGNETISM . 238 . 248 XV. BATTERY CURRENTS . 263 XVI. MEASURING ELECTRICITY . 281 XVII. INDUCED CURRENTS . 308 XVIII. ELECTRIC POWER ...... . 318 XIX. ALTERNATING CURRENT MACHINES . 358 XX. SOUND . . . . 374 XXI. LAMPS AND REFLECTORS . 405 XXII. LENSES AND OPTICAL INSTRUMENTS . 427 XXIII. SPECTRA AND COLOR . 456 XXIV. ELECTRIC WAVES : ROENTGEN RAYS . 469 PRACTICAL PHYSICS CHAPTER I INTRODUCTION: WEIGHTS AND MEASURES Why study physics content and divisions of physics physics involves measurement as well as merely description units in English and metric systems density. 1. Why study physics ? Every one these days has had something to do with machines of one sort or another all his life. In the country we mow, reap, and thresh grain with machines ; we pump water with windmills, gas or hot-air en- gines ; and we skim milk with a machine called a separator. In the city we travel on electric cars ; we go upstairs on hydraulic or electric elevators ; we print our newspapers on presses run by electric motors ; and we distribute our mail through pneumatic tubes. In business and in commerce we are constantly using steam, gas, and electric engines, cranes and derricks, locomotives, ships, and automobiles, and per- haps, in a few years, we shall all be using flying machines. Every one has used some of these devices and almost every one has at some time wondered and perhaps discovered how each of them works. That is," almost every one has already begun to study physics, for it is one of the chief aims of physics to discover all that can be known about such ma- chines as have just been mentioned. 2. Physics a science. The sort of physics that will be found in this book differs from the sort that every one has been unconsciously studying all his life, chiefly in that it seeks to answer not only the questions "why" and "how," but also the question "how much." It is only when we B 1 2 PRACTICAL PHYSICS begin to measure things definitely that we get the kind oi information that helps us to use them to the best advantage. Thus every one knows in a vague way that an automobile goes up a hill because the gasolene which is burned in the engine makes it turn the driving wheels, and these in turn push against the road, if it is not too slippery, and thus pro- pel the automobile. The physicist, when he had thought of all this, would go on to ask himself such questions as " How much gasolene does it take, how much ought it to take under ideal conditions, and what becomes of the difference? How much force must be exerted by the brakes to hold the auto- mobile on a hill, how large a brake surface will do this, and how strong must the brake wire be?" When he can answer all these and many other questions, he is in a position to use his machine more effectively, and perhaps to improve its mechanism. 3. Divisions of physics. The object of studying physics is, then, chiefly to learn to think accurately about very familiar things. But these things are so various in kind that we shall find it convenient to divide the whole subject into five divisions : mechanics, heat, electricit}^ sound, and light. For example, suppose we wanted to make a thorough study of the automobile. Under mechanics, we should study about its cranks, gears, levers, valves, and brakes, including their movements, and the strength of the material of their construction ; under heat, the engine, its fuel and radiator ; under electricity, the spark plug, spark coil, magneto, and battery ; under sound, the horns and trumpets ; and finally, under light, the lamps and their reflectors and lenses. In a similar way it might be shown that any piece of modern machinery, whether it is an automobile or a locomotive, a motor boat or an Atlantic liner, a flying machine or a sub- marine boat, is not only an embodiment of the principles of physics, but has in very large measure been made possible by the science of physics. INTRODUCTION: WEIGHTS AND MEASURES 3 4. Physics contains some abstractions. While it is true that physics has to do chiefly with familiar things, yet in order to make its study effective we shall also have to considei some things which are not so familiar, such abstractions as density and calories and wave length and refraction and electrical resistance, which may not be interesting at first, and may seem to have little to do with our everyday life. We shall also find many problems to be solved whose answers will seem trivial and unimportant. These things should be done patiently because they pave the way for more valuable things later on. 5. Physics begins with measurements. At the very out- set we may well recall an old saying of Plato's : " If arith- metic, mensuration, and weighing be taken away from any art, that which remains will not be much." In the labora- tory the student will learn to measure many different kinds of things, not mainly for the sake of the results he gets, but rather that all through life he may know a good measure- ment when he sees one, and may be able to discuss accurately and with confidence the quantitative problems that are al- ways coming up. 6. Units of measurement. In business in the United States the value of things that are bought and sold is measured in dollars and cents. Fortunately this system of money is made on the decimal plan, that is, in multiples of ten. Our sys- tem of weights and measures, on the other hand, is not a decimal system, and is very inconvenient. Nevertheless,, since the pound, foot, quart, gallon, and bushel are still in general use in Great Britain and in the United States, we must be familiar with them. During the last century most of the other civilized nations have adopted the metric system of weights and measures, in which the relation of the units is expressed in multiples of ten. In scientific work the met- ric system is almost universally used throughout the world, because it greatly reduces the work in making computations. 4 PRACTICAL PHYSICS Therefore it is advisable for us to become proficient in the use of both the English and the metric system of weights and measures. 7. Meter and yard. The meter is the distance between two lines on a metal bar (Fig. 1) which is preserved in the vaults of the International Bureau of Weights and Measures near Paris.* Since the length of this metal bar changes a little with the tem- perature, the distance is measured at the temperature of melting ice. A very accurate copy of this bar FIG. i. -The international i s deposited in the United States Bureau of Standards in Washing- ton, D.C., and this copy is the legal meter of the United States. In the United States the yard is legally defined as |ffy of a meter. 8. Some important units of length. In the problems of physics we shall find that certain units of length are very frequently used. These are given in the following table : UNITS OF LENGTH ENGLISH. 1 foot (ft.) = 12 inches (in.). 1 yard (yd.) = 3 feet. 1 mile (mi.) = 5280 feet. * It was originally intended that the meter should be equal to one ten- millionth part of the distance from the equator to either pole of the earth, but it is impossible to reproduce an accurate copy of the meter on the basis of this definition. Later measurements have shown that the "mean polar quadrant " of the earth is about 10,002,100 meters. INTRODUCTION: WEIGHTS AND MEASURES METRIC. 1 meter (m.) = 1000 millimeters (mm.). 1 meter = 100 centimeters (cm.). 1 kilometer (km.) = 1000 meters. 1 inch = 2.540 centimeters. 1 meter = 39.37 inches. CENTIMETERS 2 1 Square Jentimete 1 Square Inch INCHES 123 FIG. 2. Relative sizes of the inch and the centimeter. 9. Ijnits of area. The unit of area which is most exten- sively used is the area of a square of which the side is of unit length. Thus the area of a city house lot is reckoned in square feet, where the unit is a square one foot on each side. In the laboratory, area is often measured in square centimeters (cm 2 ), the unit being a square one centimeter on each side. It is evident from figure 3 that one square inch is equal to about 6 square centimeters. More ac- FlG ; ^.-Relative sizes ,1 , r * r p A n. AC of the square inch curately, it is 2.54 x 2.54, or 6.45 square an d the square ceu- centimeters. timeter. The usual method of determining area is by calculation from the measured linear dimensions.- Thus the area of a rectangle or parallelo- gram is equal GO the base times the altitude (A = b x h). The area of a triangle is equal to \ the base times the altitude (A = \b x A). The area of a circle is equal to 3.14 times the square of the radius (J. = Tir 2 ). 10. Units of volume or capacity. The unit of volume that is most extensively used is the volume of a cube of which the edge is of unit length. Thus the volume of a freight car is reckoned in cubic feet, the unit being a cube one foot on each edge. In the laboratory we measure the capacity of a flask in cubic centimeters (cm 3 ). PRACTICAL PHYSICS UNITS OF VOLUME ENGLISH. 1 cubic foot (cu. ft.) = 1728 cubic inches (cu. in.). 1 cubic yard (cu. yd.) = 27 cubic feet. 1 gallon (gal.) = 4 quarts (qt.) = 231 cubic inches ' METRIC. 1 liter (1.) = 1000 cubic centimeters (cm 3 ) 1 cubic meter (m 3 ) = 1000 liters. 1 liter = 1.06 quarts. The usual method of determining the volume of a regular solid is by calculation from the measured linear dimensions. Thus to get the volume of a rectangular block of stone, or a box, we find the product, length by width by depth. In the case of a cylindrical figure we compute the area of the circu- lar base (irr 2 ), and multiply by the height. For measuring liquids, we ordinarily use a graduated ves- sel of metal or glass. Thus in the English system we have gallon and quart measures, and for small quantities, fluid ounces (sixteenths of a pint). In the metric system, we have tfiU in the laboratory graduated cylinders (Fig. 4) for measur- ing liquids in cubic centimeters. FIG. 4. A graduated cylinder. PROBLEMS 1. Change 2.55 meters- to centimeters. 2. Change 1575 cubic centimeters to liters. 3. A boy is 5 feet 6 inches tall. Express his height in centimeters. '*" 4. Express 1 kilometer as a decimal part of a mile. * 5. The Falls of Niagara on the American side are about 165 feet high. Express this in meters. ^ -6. A standard size of automobile tire is ^ inches in diameter and fits a-^-inch wheel. Express these dimensions in the metric system. 7. ^"you wanted to buy If yards of silk in Paris, what length should you ask for ? 8. A certain type of Bleriot monoplane has a wing surface of 15 square meters. Express this in square feet. 9. How many gallons in a cubic foot? 10. Milk sells in Berlin for 40 pfennigs per liter. What is its cost in cents per quart? (100 pfennigs = 1 mark = $0.238.) * : INTRODUCTION: WEIGHTS AND MEASURES 11. How many liters does a tank hold which is 3 meters long, 1.5 meters wide, and 1 meter deep? 12. A cylindrical berry box is measured and found to be 6.15 inches in diameter and 2.1 inches deep. What is its capacity in dry quarts? (In the United States it is understood that a dry quart contains 67 1 cubic inches.) 11. Units of weight.* The kilogram is the weight of a .f ' certain platinum -iridium cylinder that is preserved with the standard meter near Paris, or that of a very accurate copy of this cylinder which is deposited in the United States Bureau of Standards in Washington. It was intended that these cylinders should weigh the same as one liter of pure water, but this has turned out to be not quite true.f It is, however, nearly enough true for our present purposes. Therefore the gram, which is the one-thousandth part of a kilogram, is the weight of one cubic centimeter of water. It may be helpful to remember that our 5-cent nickel piece weighs 5 grams and our silver half-dollar weighs 12.5 grams. In the United States the pound avoirdupois is denned - *- -- '* K tiSls. 7*trt> tTklTS OF WEIGHT * '* ENGLISH. 1 pound (lb.) = 16 ounces (oz.). 1 ton (T.) = 2000 pounds. METRIC. A^Z. -2 tfi- or 7.8 grams per cubic centimeter. From the preceding examples it will be seen that the density of a body is found by dividing its weight by its volume. In other words, weight It is also evident that if we know the density of a substance, we can compute the weight of any volume of the substance. It is by this method that engineers calculate the weight of buildings and bridges which it would be impossible to weigh. For example, an engineer finds that a reenforced concrete pier contains 2500 cubic feet of material, and he knows that such material averages 150 pounds per cubic foot. Then the weight of the pier is equal to 2500 times 150, or 375,000 pounds, or about 188 tons. In other words, Weight = density x volume. If it is the volume of anything that we want to know, we have Volume =5. A density INTRODUCTION: WEIGHTS AND MEASURES 11 PROBLEMS (Use data given in table on page 9 when necessary.) 1. A block of iron is 10 centimeters by 8 centimeters by 5 centime- ters, and weighs 3 kilograms. What is its density expressed in grams per cubic centimeter? 2. A block of stone measures 4 feet by 2 feet by 15 inches, and weighs 1625 pounds. Find its density in pounds per cubic foot. 3. How many pounds does 1 cubic foot of aluminum weigh ? 4. The cork in a life preserver weighs 20 pounds. What is its vol- ume in cubic feet? 5. A flask with a capacity of 120 cubic centimeters is filled with mercury. How many kilograms of mercury does it hold? 6. A quart bottle is weighed empty and then full of milk. How many pounds should it gain in weight? 7. A cylindrical railway water tank measures on the inside 10 feet in depth and 6 feet in diameter. How many tons of water doos it hold? 8. A piece of platinum wire is 12.5 centimeters long and 0.8 milli- meter in diameter. How much would it cost if the price of platinum is $1.00 per gram? 9. If a certain copper telephone wire is 0.165 inch in diameter, what does a mile of the wire weigh ? 10. The inside diameter of a lead pipe is 1 inch, and the wall is 0.25 inch thick. How many pounds does it weigh per foot? 15. The three fundamental units. On account of its more convenient size, the centimeter, instead of the meter, is universally used in scien- tific work as the fundamental unit of length. For a similar reason, the gram, instead of the kilogram, is used as the fundamental unit of weight. The second is taken among all civilized nations as the standard unit of time. It is -^ToTr ^ tne time from noon to noon. The process of weighing some- thing on a balance is quite dis- FIG. 7. Stop watch. 12 PRACTICAL PHYSICS tinct from the measurement of a length, and the measure- ment of time is wholly different from the measurement either of length or weight. Moreover, each is done with a distinct sort of instrument. In a time measurement the instrument is a clock or watch. For short intervals of time a special type of watch is used, known as a stop watch (Fig. 7). It is found that the measurement of any quantity, such as the steam pressure in a boiler, the speed of an express train, or the loudness of a foghorn, can, in the ultimate analysis, be reduced to measurements of length, weight, and time. The units of length, weight, and time are therefore the three fundamental units of physics. SUMMARY OF PRINCIPLES IN CHAPTER I weight Density = volume QUESTIONS * 1. What is the origin of the prefixes deci, centi, and milli, used in the metric system? 2. How could you determine the volume of an irregular piece of rock by means of a graduated cylinder partly filled with water? 3. How would you measure the diameter of a steel ball ? 4. How does your local jeweler get " standard time " to set his clocks and watches correctly? 5. How can the thickness of this sheet of paper be measured? 6. What is the difference between a ship's chronometer and a dollar alarm clock ? 7. Why is it that the United States and Great Britain are the only two civilized countries that do not use the metric system commercially ? * In trying to find the answers to these questions, the student is expected to consult various reference books, such as dictionaries, encyclopedias, en- gineering handbooks, and popular science magazines.. He is also expected to keep his eyes open outside of the classroom, and to ask questions of me- chanics and tradespeople. CHAPTER II SIMPLE MACHINES Levers of various kinds principle of moments force at . the fulcrum weight of a lever center of gravity in general wheel and axle pulley systems parallel forces. Work principle of work differential pulley inclined plane wedge screw combinations of simple machines power transmission of power. Friction so-called " laws of friction " coefficient of fric- tion advantages of friction rolling friction efficiency of machines. 16. Why we use machines. A man can lift a piano up to a window on the second floor with a rope and tackle. A boy can roll a barrel of flour up into a wagon with a skid. A girl can pull a nail out of a box with a claw hammer al- though she could not move the nail at all with her fingers alone. It is obvious that we can do many things with simple machines that it would be quite impossible for us to do without them because we are A T B not strong enough. Further- more, some machines enable us to do things more quickly or more conveniently than we could without them. Most important of all, we often use machines in order to make use of forces exerted by animals, wind, water, or steam. 17. Equal-arm lever. Doubtless the simplest ma- chine is the lever with equal 13 FIG. 8. Equal-arm lever. 14 PRACTICAL PHYSICS arms, such as a seesaw, or the walking beam on a steamboat, or the scale beam on a platform balance. In this case we know that equal weights or equal forces just balance when placed at equal distances from the point of support. Thus in figure 8, when W l equals TF 2 , the distance AF must equal the distance BF. In the technical language of physics the point of support (^) of a lever is called its fulcrum. 18. Unequal-arm lever. Very often the distances of the weights from the fulcrum are not equal. For example, the distances are unequal when two persons of unequal weight are seesawing, or in the case of an ordinary pump handle. It is evident that at equal distances, the larger weight would have the greater tendency to tip the lever, and also that, with equal weights, the weight at the greater distance from the fulcrum has the greater tendency to tip the lever. There- fore in order to have two unequal weights balance, they must be so placed that the smaller weight is at the greater distance from the fulcrum. 40cm F 50 ^ 100 g 7 FIG. 9. Two unequal forces. If we balance an ordinary meter stick in the middle and suspend a 50-gram weight (W^) at A, which is 40 centimeters from the fulcrum (F), and then hang a 100-gram weight (W 2 ) on the other side at such a point as just to balance the first weight, we shall find that the point B where the 100-gram weight is hung is about 20 centimeters from F or half as far from the fulcrum as the 50-gram weight. Careful experiments show that any two unequal forces will balance only if the force on one side multiplied by the per- pendicular distance of its line of action from the fulcrum equals SIMPLE MACHINES 15 the force on the other side multiplied by the distance of its line of action from the fulcrum. For example, in figure 9, W 1 x AF= Wt x BF. This relation of the forces and distances may also be ex- pressed by a proportion W 1 : W 2 :: BF : AF, which may be stated in words as follows : the forces are inversely proportional to their distances from the fulcrum. This means that if one force is three times as great as another, then its line of action must be one third as far away from the fulcrum as the other to make the lever balance. Crowbars, shears, glove stretchers, pliers, etc., are all ex- amples of this sort of lever. 19. One-arm lever. When the fulcrum is located at one end of the lever, as in figure 10, the same principle is in- volved. There are two tendencies which must balance, the tendency of the weight to tip the lever down and the tend- ency of the pull applied to the lever to lift it up. The weight multiplied by the perpendicular distance from the fulcrum to its line of action measures its turning effect about the fulcrum; that is, its tendency to tip the lever down. This must be balanced by an equal turning effect in the opposite direction, namely, the upward pull multiplied by its distance from the fulcrum. p FIG. 10. One-arm levers. Suppose we fasten a stick (Fig. 10) by a screw (F) to an upright support, so that the stick is free to turn, and hang a weight (W), say 10 16 PRACTICAL PHYSICS pounds, at a distance of 6 inches from the fulcrum (F) Then if we pull up with a spring balance at a point (B) 12 inches from the ful- crum (F), we shall find that the pull measured W ^r^~-MB& by fche s P rin g balance is about 5 pounds. (Of course allowance has to be made for the weight of the stick.) FIG. 11. Nutcracker. m, ,. 1 he equation representing these tend- encies to turn the stick in opposite directions would be as before =Px BF. It is also evident that if the 10-pound weight ( W ) were hung 12 inches from the fulcrum FIG. 12. Crowbar. >, and the up- ward pull applied 6 inches from the fulcrum, the pull needed would be 20 pounds. In other words, the same principle applies to the one- arm lever wherever the weight and the upward pull are applied. A nut cracker (Fig. 11), a crow bar when used with one end on the ground (Fig. 12), and the forearm (Fig. 13) when it sup- ports a weight in the extended hand are examples of levers with the fulcrum at one end, or one- arm levers. 20. Lever with two weights. The ordinary wheelbarrow is a good example of a one-arm lever. . The fulcrum is located at the axle of the wheel, the weight is the w ' load carried, and the upward pull FIG. 13. Forearm. is exerted on the handles by the SIMPLE MACHINES 17 man. In practice, however, it often happens that the load consists of two weights, such as two bags of cement or two boxes or kegs, as shown in figure 14. To get the upward pull we have merely to compute the turn- FIG. 14. Wheelbarrow with two weights. ing effect of each of the weights (TP^ and W%) about the fulcrum (JF 7 ) and make the sum of these effects equal to the turning effect of the upward pull (P). That, is,. W 1 x BF+ W 2 x AF= P x OF. In general, then, we see that we can balance the turning effect of two or more weights by multiplying each weight by the perpendicular distance of its line of action from the fulcrum, and making the sum of these products equal to the product of the pull by the perpendicular distance of its line of action from the fulcrum. 21. Principle of moments. It has been seen that the turning effect of a force depends on two factors, the amount of the force and the distance of its line of action from the fulcrum. This product force times perpendicular distance to fulcrum is called the moment of the force. For a lever to be in equilibrium, the sum of the moments of the forces tending to turn it in one direction must equal the sum of the moments of the forces tending to turn it in the opposite direction. 22. Force at the fulcrum. It must not be forgotten that in examples of the lever, the fulcrum itself exerts a force, that is, a push or a pull. When the fulcrum is between the 'two weights, it evidently has to push up an amount equal to the sum of the weights ; that is (Fig. 15, top), F W 1 -f- W y \ 18 PRACTICAL PHYSICS When the fulcrum is at one end of the lever, and the pull at the other end, it is clear that the fulcrum must exert an up- ward push, which must ibe such that it and the upward pull (P) are to- 1 gether equal to the weight. That is (Fig. 15, middle), W=F+P. When the fulcrum is at one end and the weight at the other end, it will be readily seen that the fulcrum has to push down- ward and that the upward pull (P) must equal the sum of this downward push at F and the weight W. That is (Fig. 15, bottom), P = W+ F. In short, it will be seen that in all these cases the sum of the forces pulling up FIG. 15. Force exerted by fulcrum of lever, must equal the 8Um of the forces pulling down. PROBLEMS 1. Identify the fulcrum, and the direction of the two forces, in the case of a pair of shears, a glove stretcher, a pair of tongs, and a nut cracker, regarded as examples of the lever, and think of other examples. 2. What weight placed 20 inches from the fulcrum will balance 100 pounds placed 8 inches away on the opposite side? What is the pressure on the fulcrum ? 3. In figure 9 the movable weight on an old-fashioned steelyard weighs 3 pounds, and is placed at such a distance as to balance a 50-pound sack which is hung from a point 1 inch from the point of support. How far from the point of support must the sliding weight be placed ? SIMPLE MACHINES 19 4. A piece of wire, which is to be cut with shears, is placed 0.5 inch from the rivet. If a force of 25 pounds is applied on the handles 6 inches from the rivet, how much force is exerted on the wire ? 5. A plank 12 feet long is to be used as a seesaw by two boys who weigh 100 pounds and 140 pounds. How far from the lighter boy must the prop be placed ? (HINT. Let x = distance from small boy and 12 x = distance from big boy.) 6. The handles of a wheelbarrow (Fig. 10) are 4 feet 6 inches from the axle, and the load of 200 pounds can be considered as 18 inches from the axle. How much effort must be exerted to raise the handles? 23. Bent lever. Consider next a claw hammer (Fig. 16) with a 12-inch handle. If a 60-pound pull (P) at B is necessary to pull the nail at A, which is 1.5 inches from F, what is the resistance (R) which the nail offers ? The moment of P is P X BF, and the moment of R is R x AF, therefore 60 x 12 = R x 1.5, and R = 480 pounds. In this case it will be seen that the two arms of the lever are inclined to each other, but the principle of moments applies just as if it were a straight lever. The bent lever is very common as a part of a machine. A great many other objects can be regarded as bent levers. For example, suppose a door (Fig. 17) 8 feet high and 4 feet wide, weighing 60 pounds, swings on hinges placed 1 foot from the top and 1 foot from the bottom, (a) What is the vertical pressure on each hinge? If the door is properly hung, the weight will be equally divided between the two hinges, and each hinge will support 30 pounds. (6) How great is -Pi ^t J G. 1 L" x z 7 7. Doorasabeut lever. FIG. 16. Hammer as a bent lever. 20 PRACTICAL PHYSICS the horizontal pull on the upper hinge? If we consider the entire weight of the door as acting at its center, then the moment of this weight about the lower hinge will be 2 times 60, or 120. The moment of the pull exerted by the upper hinge, reckoned about the lower hinge, will be 6 times the pull. Making these two moments equal, we find that the pull is 20 pounds, (c) In a similar way, by considering the upper hinge as a fulcrum, we may compute the push exerted by the lower hinge, which also equals 20 pounds. 24. Center of gravity. So far in our study of levers we have assumed that the weight of the lever itself could be neglected, but in practice this is not always the case. It is our problem now to find how to make allowance for the weight of the lever. We have already seen that a lever carrying two weights ( Fi * 18 ) can be supported at a point in between, which we have called the fulcrum, but which we may FIG. 18. - Center of gravity of two ^ightl now cal1 the " cen ~ ter of gravity" or "center of weight." The force necessary to support this point is the same as if the whole weight were concentrated there. In the same way we could support a bar carrying three or more weights on a single fulcrum, if it is placed at the right point. That point would be the center of gravity of the weights. In general, everything has a center of grav- ity at which we can consider its whole weight concentrated. To find the position of the center of gravity, we have simply to find the point at which the object would balance on a knife edge. This may be computed, but it is usually easier to locate it experimentally. 25. How to find a center of gravity by experiment. If the shape of the object is simple and its density is everywhere the same, as in the case of a shaft or a board, we should ex- SIMPLE MACHINES 21 pect the center of gravity to be in the middle, and if we try to balance the object on some sharp edge, we find that the center of gravity is indeed located at the geometrical center. In the case of an irregularly shaped object like a baseball bat, the simplest way is to balance the bat on a knife edge. In the case of a chair, the center of gravity may be found by considering that, if the chair is hung so as to swing freely, the center of gravity will lie directly under the point of suspension. Therefore, if a chair, or any irregular object, is hung from two points successively, the point of intersec- tion of the plumb lines from these points will locate the center of gravity. To make this clear, let us take an irregular sheet of zinc and drill three holes near the edge, A, B, and C, in figure 19. Let the zinc be hung from a pin put through the, hole A and let a plumb line be also hung from the pin. Draw a line on the zinc to show where the plumb line crosses it. Then let the zinc be hung from another hole and draw another line in a similar way. The point of intersection is the center of gravity. When the zinc is hung from the third hole, the plumb line will pass through the center of grav- ity already found. FIG. 19. Finding center of gravity. In the case of a ring, or a cup, or a boat, the center of gravity will not lie in the substance itself, but in the empty space inside ; but this will not bother [us in answering questions about how such objects act. We -may, if we like, think of such a center of gravity as rigidly attached to the object by a very light, stiff framework. We shall find this idea of the center of gravity especially convenient in problems where the weight of a lever has to be considered, for we can now assume that the whole weight of the lever is concentrated and acting at its center of gravity. 22 PEACTICAL PHYSICS Suppose that an 18-ounce hammer balances 10 inches from the handle end. When a fish is, tied to the end of the handle, the whole balances .6 inches from the end. How much does the fish weigh? We may con- sider the weight of the hammer, 18 ounces, as concentrated at a point 10 inches from the end of the handle or 4 inches from the fulcrum. Let x be the weight of the fish, which is applied 6 inches from the fulcrum. Then we have 'V 6z = 4x 18, x = 12 ounces, the weight of the fish. PROBLEMS * 1. A boy has a 2-pound fish pole 10 feet long, the center of gravity of which is 3.5 feet from* the thick end. He finds the weight of his string of fish by hanging them from the thick end of the pole and then balancing .the pole J>n a^ence rail, t He findsthat it balances at a point 15 niches from th end. feow many pounds of fish has he? 2. A pole 20 feet long* weighs 120 fjoundft^. When a 30-pound bag of meal is hung q one en,d, ^hfe balancing point is 3 feet from the same end. Where is the center of gravity of the pole? 3. A 6-foot crowbar balances at a point 2.5 feet from its sharp end. If a weight of 30 pounds is hung 0.5 feet from this end, and 50 pounds is hung 1 foot from the other end, it balances at its mid-point. How heavy is the bar ? 4. A uniform beam AB, 20 feet long, weighing 600 pounds, is sup- ported by props placed under its ends. Four feet from prop A, a weight of 200 pounds is suspended. Find the pressure on each prop. (HINT. Regard as a lever, with its fulcrum at one end.) 5. A rectangular gate 3.5 feet high and 5 feet wide has its center of gravity at its geometrical center. It is hung on hinges placed 3 inches from the top and bottom. The gate weighs 100 pounds, (a) What vertical pressure should each hinge sustain ? (b) What is the horizontal pull on the upper hinge ? (c) What is the horizontal push against the lower hinge? 26. Wheel and axle. A special form of lever consists of a wheel or crank which is fastened rigidly to an axle or drum. The weight to be lifted, or the resisting force of whatever kind, is generally applied to the axle by means of a rope or chain, and the " effort," or pull, is exerted on the rim of the SIMPLE MACHINES 23 wheel, as shown in figure 20. In calculating the effort (P) needed to balance a given resistance ( TF) we have merely to take moments about the center (.F) of the wheel and axle. If we call the radius of the wheel R and that of the axle r, then, Weight x axle^ or or r-r<^^^= = effort x wheel-radius PxK, PaV, FIG. 20. Wheel and axle. 27. Uses of the wheel and axle. A windlass used in drawing water from a well (Fig. 21) by means of a rope and bucket is an application of the principle of the wheel and axle. In the windlass, a crank takes the place of a wheel, and the length of the crank is the radius of the wheel. If a wheel is used in turning the rudder of a boat, the rope attacned to the rudder is wound round the axle, and the steersman applies his effort to the handles which project from the rim of the wheel ( Fig. 22). In the derrick (Fig. 23), which is used in lifting heavy FIG. 21. Windlass for a well. FIG. 22. Steering wheel in a boat. FIG. 23. Hoisting derrick. 24 PRACTICAL PHYSICS weights, we usually have a double wheel and axle. The effort of the workmen is applied at the cranks, which are at- tached to one axle. This then drives, through a spur gear, a wheel on a second axle. 28. The pulley. The fixed pulley, shown in figure 24, con- sists of a wheel with a grooved rim, called a sheave, free to rotate on an axle which is suppor^M^a fixed block. A flexible rope or cable passes over ll Bel. Tt is evident . ////////////////////////////////////////// FIG. 24. Fixed pulley. FIG. 25. Movable pulley. that if equal weights or equal forces are applied to the ends of the rope, they just balance each other. That is, the effort P is equal to the resistance W. So there is no advantage in the fixed pulley, except that it is sometimes more convenient to exert a certain pull downwards rather than upwards. Oftentimes the block is attached to the weight to be lifted, as shown in figure 25, and then it is called a movable pulley. Here the effort P is not equal to the weight W, for it will be seen that the load IF" is supported by two ropes, and there- fore each exerts a pull equal to one half the weight. That = or SIMPLE MACHINES 25 The ratio of the weight or resistance to be overcome to the effort put forth is' called tJu- mechanical advantage of a machine. Fof^ekample, the mechanical advantage of a single fixed pulley is 1 and of a single movable pulley is 2. 29. Combinations of pulleys. In practical work it is quite common to use a fixed block witji two sheaves and a movable block with two sheaves, as shown in figure 26. One end of the rope is attached to the fixed block, and the effort is applied to the other end of the rope. Let us compute the relation between the weight to be lifted and the effort applied. From figure 26 it will be seen that the weight and the movable block are supported by four ropes, and so the pull on each rope, neglecting the weight of the block, is one fourth the weight W. It will also be seen that the pull P is equal to that in each of the ropes, since a pulley only changes the direction of the pull. There- fore p _ i jjr FIG. 26. Double blocks. and the mechanical advantage, JF/P, is 4. This means that, neglecting friction and the weight of the movable block, a pull of 100 pounds applied at P would just balance a weight of 400 pounds at W. In general, we can find the mechanical advantage of any combination of pulleys by counting the number of ropes which support the weight. 30. Parallel forces. Suppose we have a 3000-pound auto- mobile standing on a bridge in a position one fourth of the length of the bridge from one end (Fig. 28), and we wish to know how much of the weight is borne by the supports at each end of the bridge. First let us try a very simple experiment which will make clear the principles involved in this problem. 26 PRACTICAL PHYSICS I Nail FIG. 27. Parallel forces, move now. But we can now think of the stick as Hang a light stick (Fig. 27) by two or more stirrups attached to spring balances (A, B, C), and let several weights (Z>, E} be hung from it at various points. If the sup- ports do not break, the stick will remain suspended mo- tionless indefinitely. The sum of the forces pulling up is equal to the sum of the forces pulling down. Now suppose that there happen to be several holes through the stick and that a nail is care- fully driven through one of them into the wall behind. If the stick did not move before, it certainly will not lever with the nail as a fulcrum, and it is in equilibrium about that nail. This means that the sum of the moments of the forces tending to turn it in one direction equals the sum of the moments of the forces tending to turn it in the op- posite direction. Evidently this nail could have been put through a hole at any point along the stick, and the moments calculated around that point would balance. This example and section 22 show that when several paral- lel forces are in equilibrium two conditions must be fulfilled. (1) The sum of the forces pulling in one direction must equal the sum of those pulling in the opposite direction. (2) The sum of the moments tending to rotate the whole in one direction around any point whatever must equal the sum of the moments tending to rotate the whole in the opposite direction around that same point. Let us apply these principles of parallel forces to the problem of the automobile standing on the bridge. This can be represented by figure 28, where A is the weight of the . \ A 3000 Ibs. 3x FIG. 28. Bridge with automobile on it. SIMPLE MACHINES 27 automobile, and B and C are the upward forces exerted by the end sup- ports. We know one force (A = 3000 pounds), and the relative dis- tances between these forces. We are to find the magnitudes of B and C. Since B + C = 3000, C - 3000 - B. Suppose we take the position of the automobile as the point about which to compute moments ; then we have B x3x = (3000 - B) x x, B = 750 pounds, J5's load, 3000 - B = 2250 pounds, C's load. We can also solve this problem by taking moments first around one end, and then around the other. Working in this way, we do not need the first principle at all. Do this and see if you get the same answers. It should be noticed that all the machines so far considered, namely, the lever (except the bent lever), the wheel and axle, and the pulley, are simply special cases of parallel forces, and that we can discover anything we want to know about any of them, by means of one or both of the general principles mentioned just above. For the lever and the wheel and axle, the principle of moments is enough, unless we want to know the force at the fulcrum. For that we need the first principle. For the pulley we need only the first principle. PROBLEMS 1. The diameter of an axle is 1 foot, and the diameter of the circle in which a crank on the axle moves, is 3 feet. If 150 pounds is the weight to be raised, how much force must be applied to the crank ? 2. The crank on a grindstone is 9 inches long, and the diameter of the stone is 30 inches. If 50 pounds is the force applied on the crank, what force can be exerted on the rim of the stone ? 3. What must be the ratio of the diameters of a wheel and axle, in order that 150 pounds may support 1 ton ? What is the mechanical advantage? 4. Two single fixed pulleys are used to raise a barrel of flour, as shown in figure 29. If a barrel of FlG - 29 - Simple pulley system, flour weighs 200 pounds, how much does the horse have to pull? 28 PRACTICAL PHYSICS 5. The gaff of a boat is to be raised by means of a movable single block attached to it, and a fixed double block attached to the top of the inast, one end of the rope being tied to the movable block. How much resistance can be overcome by 100 pounds exerted on the rope? 6. A pair of triple blocks contain three sheaves each. The rope is attached to the upper fixed block. What force is just sufficient to bal- ance a weight of 1 ton, neglecting friction ? 7. An automobile gets stuck in the sand. In order to pull it out, a horse, a rope, and a couple of triple blocks are used. If the horse exerts a steady pull of 500 pounds on the rope, and one block is fastened to a tree and the other to the machine, how much resistance can be overcome? Find two solutions for this problem, the rope being fastened in one case to the fixed block, and in the other to the movable block. 8. Two boys, A and B, are carrying a 100-pound load slung on a pole between them. Their hands are 10 feet apart, and the load is 3 feet from A. How much does each carry? Neglect the weight of the pole. 9. A man holds a shovelful of coal, weighing 50 pounds, with his left hand at the end of the shovel, and his right hand 22 inches away. Supposing the center of gravity of the shovel and coal to be 40 inches from his left hand, how much does he push down with his left hand, and how much does he pull up with his right hand ? 10. A man and a boy carry a load of 200 pounds on a pole 8 feet long. Where must the load be placed if the boy is to bear only 45 pounds of it? 31. Work. The function of every machine is to do a certain amount of work. Now in the technical language of science, work means the overcoming of resistance. For example, we do work when we lift a box from the floor to the table, or when we push the box along the floor against friction. But we are not doing work in the scientific sense of the word, no matter how hard we push or pull, if we do not lift or move the box. In other words, work is measured by accomplish- ment, not by effort or by fatigue. If we lift one pound one foot, we are said to do one foot pound of work; if we lift 5 pounds 3 feet, we do 15 foot pounds of work ; or if we pull hard enough on a box to lift SIMPLE MACHINES 29 5 pounds and thus drag it 3 feet, we still do 15 foot pounds of work. In other words, Work (foot pounds) = force (pounds) x distance (feet). It should be remembered that the distance must be meas- ured in the same direction as that in which the force is ex- erted. Thus, if a machinist exerts upon a file a force of 10 pounds downward and 15 pounds forward, how much work will he do in 40 horizontal strokes, each 6 inches long? Evidently the total distance is 20 feet and the horizontal force is 15 pounds ; therefore the work done is 300 foot pounds. The vertical pressure does not enter into the cal- culation of work because the motion is horizontal. 32. Principle of work. In every machine a certain resist- ance is overcome by a certain effort exerted on another part of the machine. The principle of work which applies to all machines where the losses due to friction may be neglected, may be stated as follows: The work put into a machine is equal to the work got out. In short, Input = output. For example, in the wheel and axle (see Fig. 20, section 26) the output is equal to the weight times the distance it is lifted, and the input is equal to the effort times the distance through which it is exerted. For convenience, suppose the wheel makes just one turn. Then the dis- tance the weight is lifted is equal to the circumference of the axle, 2?rr, and the distance through which the effort is exerted, is the circumference of the wheel. 2-jrR. The input is 'P x 2TrR, and the output is W x 2irr. Therefore, by the principle of work, P x 2irR = Wx2irr, or P x R = W x r, which is exactly the equation got by considering the wheel and axle as a modified lever. Another example is the system of pulleys shown in figure 26 in sec- tion 29. The output is equal to the weight W times the distance it is lifted, and the input is equal to the effort P times the distance through which it is exerted. Suppose the distance the weight W is lifted is D, 30 PRACTICAL PHYSICS and the distance through which the effort P is exerted is d. The outpui is W x D and the input is P x d. Then, by the principle of work, W x D = or D But when the weight is lifted 1 foot, it is evident that each of the sup- porting ropes must be shortened by 1 foot, and therefore P must move 4 feet ; in other words, Substituting this value of d in the preceding equation, we have which is the same as the result which we got by considering the pulley as a case of parallel forces. 33. The differential pulley. In shops where heavy machin- ery is to be lifted, constant use is made of the differential pulley, shown in figure 30. This con- sists of two sheaves of different diameters in the upper block rigidly fastened together, and one sheave in the lower block. An endless chain runs over these blocks. The rims of the sheaves have projections which fit between the links and so keep the chain from slipping. Such a differential pulley has a very large mechanical FIG. 30. Differential pulley. advantage. To see just now it comes to have a large mechanical advantage, let us set up such a pulley and study it carefully. 'When the chain is pulled down as shown in the diagram, it is wound up faster on the large fixed pulley than it is unwound on the smaller pulley. In order to compute the mechanical advantage of the contrivance, let us suppose that P moves SIMPLE MACHINES 31 down far enough to turn the fixed pulley around once. If R is the radius of the large fixed pulley, then the work done by P will be P x 2 TrR. If r is the radius of the small fixed pulley, then the length of chain unwound in one revolution will be 2 TIT. The weight W will therefore be raised ^(2-n-R - 2 ?rr) or ir(R - r) and the work done will be Wx-rr(R - r). Therefore, if we neglect losses due to friction, we have W x 7r(R - r) = P x 2 7T/2, W 2R whence, ^R^r' Since the difference between the radii of the two fixed pulleys (R r) is small, it is evident that the mechanical advantage is large. The differential pulley has a second practical advantage in that there is always enough friction to keep the weight from dropping when the force P is released. PROBLEMS 1. A man carries in baskets a ton of coal up 20 steps, each 7 inches high. How much work does he do on the coal ? 2. In the metric system, work is measured in kilogram meters. How much work is done in pumping 50 liters of water 40 meters high ? 3. A man weighing 150 pounds raises himself up a mast in a sling by means of a rope passing over a fixed pulley attached to the top of the mast. If the mast is 100 feet high, how much work does he do ? How hard must he pull ? 4. If in problem 1 on page 27 the weight is raised 10 feet, how many foot pounds of work are done by the machine ? 5. If in problem 2 on page 27 the stone is turned 30 revolutions per minute, how many foot pounds of work are put into the grindstone per minute ? 6. In a certain differential pulley the large wheel is 6 inches and the small wheel 5 inches in diameter. What is the mechanical advantage? 34. Inclined plane. Barrels and casks which are too heavy to lift from the ground into a wagon are often rolled up a plank or skid. This is an example of what is called an inclined plane. Every street or road which is not level is an example of an inclined plane. Experience teaches us that 32 PEACTICAL PHYSICS FIG. 31. Inclined plane. the steeper the incline, the greater the pull required to haul the load up the grade. In order to find out just how the effort and the weight or load are related to the grade, let us try a simple experiment, where friction can be neglected. Suppose we arrange a very smooth plane, such as a piece of plate glass, at an angle, as shown in figure 31. Let the weight or load ( W) be a heavy metal cylinder which turns with very little friction. Attach to the cylinder a cord and pass it over a good pulley fastened to the top of the plane, and then hang from the other end enough weights to pull the load slowly up the inclined plane. You will find that the ratio P/Wis approximately the same as the ratio H/L, where H is the height of the incline and L is its length. From the general principle of work we can also arrive at this relation of effort and resistance to the grade. Suppose the weight W is rolled from the bottom to the top of the incline. Then it has been lifted .ZTfeet, and the work done is W (pounds) times H (feet), or WJT foot pounds. But while the weight W has been traveling up the incline whose length is L, the force or pull P has moved down L feet, and the work put in is equal to P (pounds) times L (feet), or PL foot pounds. Therefore, if we neglect friction, we have or W L 35. The grade of an incline. This ratio of the height to the length of an incline is expressed by engineers as so many feet rise per hundred feet along the incline, and is called the grade of the incline. For example, suppose a road rises SIMPLE MACHINES 33 5 feet for every 100 feet along the incline, then this road is said to have a 5 % grade. Since a 3 % grade is the steepest allowable on a really good road, it is readily seen that a small force, such as can be exerted by a horse, can move a much heavier load up a gradual incline than could be lifted directly. For this reason the highways in mountain regions are laid out as zigzags and switchbacks. If we want a flight of steps easy to climb, we make the slope gentle. Nevertheless it should be remembered that while the pull is less than the weight of the load, yet the distance the load travels is greater than when it is lifted straight up. In other words, what we gain in the amount of effort required we lose in the distance over which it must be exerted. The total work to be done is independent of the grade, except for the indirect effect of friction. 36. Wedge. If instead of pulling the load up the incline, we push the incline under the load, the inclined plane is called a wedge. Of course the smaller the angle of the wedge, the easier it is to drive it against the resistance. The fact that friction plays a very important part in its action makes it impossible to make a simple statement of the relation of the effort required to force in a wedge to the resistance to be overcome. All cutting and piercing instruments, such as the ax, the chisel, and the carpenter's plane, as well as nails, pins, and needles, act like wedges. The carpenter uses wedges to fasten the heads of hammers and axes on their handles. The woodsman uses wedges to split logs of wood. 37. Screw. When an enormous force must be exerted, as in lifting a building, such machines as the lever, pulley, and inclined plane will not do, because we cannot get enough mechanical advantage. A screw, such as the jack- screw (Fig. 32), is sometimes used for this purpose. In one complete turn of the screw, the weight is lifted the distance between two successive threads, which is called the pitch of 34 PRACTICAL PHYSICS the screw, while the effort is exerted through a distance equal to the circumference of the circle traced by the end of the bar or handle. In each complete turn the output is equal to the weight times the distance between two successive threads, and the input is equal to the effort times the distance through which it acts ; namely, the circumference of a circle. If W equals the weight to be lifted and p (pitch) equals the distance between threads, the output for one turn is TFtimes p. FIG. 32. Jackscrew. Let P equal the effort or force applied on the handle, and 2 irr equal the circumfer- ence of the circle in which it acts. Then P times 2 irr is the input. Therefore applying the principle of work to the machine, we would have, if friction could be neglected, W X P X 2 77T, p In other words, the mechanical advantage of the screw is equal to the ratio of the circumference of the circle moved over by the end of the lever, to the distance between the threads of the screw. As a matter of fact, friction consumes a large part of the work put in, and therefore the input is greater than the output. But this loss is not wholly a disadvantage, for it keeps the screw from turning backward of itself. 38. Applications of the screw. We are all fa- miliar with carpenter's wood screws (Fig. 33) and machinist's bolts (Fig. 34). Ordinarily, however, we do not think of the FIG. 33. Wood screw. FIG. 34. Bolts. SIMPLE MACHINES 35 O o FlG - 3r> - ~ Screw FIG. 36. Micrometer screw. propeller of a boat or flying machine as a screw, but it is. The propeller (Fig. 35), with its two, three, or four blades fas- tened to one end of the shaft, is driven by an en- gine at the other end. Its rotation is so rapid that the water has no time to get out of the way, and r\/-\ the propeller screws itself through the water like a O wood screw through wood. Another example of the screw is the micrometer screw (Fig. 36), which is used to make very precise measurements. It consists of an accurately turned thread of small pitch, perhaps 1 millimeter. It is evident that if such a screw is turned ^^ of a complete turn, the spindle moves along its axis just 0.01 millimeters. This is the easiest way of measuring so small a distance. In order to discover readily through just what fraction of a turn the screw is turned, the head is divided into 100 divisions. 39. Combinations of simple machines. What is called a single machine in factories and shops is usually a combination of the simple machine ele- ments described above. It is, in fact, a more or less complicated collec- tion of levers, pulleys, wheels, axles, and screws. In order to show how such a machine may be analyzed FIG. 37. Builder's crane. 36 PRACTICAL PHYSICS into its elements, let us, as it were, dissect a crane or derrick (Fig. 37) such as is used in unloading freight cars, or in hoisting building material into place. The movable pulley to which W is attached gives a mechanical advan- tage of two ; the fixed pulley at the end of the boom, merely changes the direction of the pull ; the wheel D and its axle give a mechanical advan- tage equal to the ratio of the size of the wheel to the size of the axle. A third mechanical advantage is gained in the wheel and axle, B and C, and finally there is the mechanical advantage of the crank P and the axle A. The total mechanical advantage of this compound machine is the product (not the sum) of the separate advantages gained by its separate elements. This is true of compound machines in general. PROBLEMS NOTE. Friction is to be neglected in these problems. 1. What force will be needed to pull a weight of 200 pounds slowly up a slope which rises 1 foot in 25 feet ? 2. What weight can be moved on a 10 % grade with a pull of 50 pounds ? 3. A boy, who , which are also equal. What is the mechanical advantage of the whole machine, and what force, neglecting friction, must be applied at P ? 12. The pedal of a bicycle is halfway down and is pressed down with a force of 100 pounds. The crank arm is 6 inches long and the sprocket wheel is 8 inches in diameter. Find the tension or pull on the chain. 13. In the preceding problem the sprocket wheel attached to the rear wheel is 2.5 inches in diameter and the wheel is 28 inches in diameter. How far does the bicycle go when the pedal makes one complete revolu- tion ? How much does the tire of the rear driving wheel push backward on the roadbed when the man presses 100 pounds on the pedal ? 40. Work and power. The words " work " and " power " are often confused or interchanged in colloquial use. The term "work" in physics means the overcoming of resistance. For example, if a boy carries a pail of water weighing 50 pounds up a flight of stairs 12 feet high, he does 600 foot pounds of work. The amount of work done would be the same whether he did this in one minute or one hour, but the amount of power required to do this job in one minute would be 60 times the power required to do it in one hour. The term "power" adds the notion of time. Power means the speed or rate of doing work. 41. Horse power. The earliest use of steam engines was to pump water from mines. This work had previously been done by horses ; so the power of the various engines was estimated as equal to that of so many horses. Finally, James Watt carried out some experiments to determine how many foot pounds of work a horse could do in one minute. He found that a strong dray horse working for a short time could do work at the rate of 33,000 foot pounds per minute or 38 PRACTICAL PHYSICS 550 foot pounds per second. This rate is therefore called a horse power. To get the horse power of an engine, compute the number of foot pounds of work done per minute and then divide by 33,000, or per second and divide by 550. Horse power f H P ) = nds per minute _ foot pounds per second 33000 550 Suppose an engine is used to 'pump 10,000 gallons of water per hour into a reservoir 50 feet above the supply. How much horse power is required ? One gallon of water weighs 8.34 pounds ; so 10,000 gallons of water weigh 83,400 pounds. The work done in lifting this weight 50 feet is 83,400 x 50, or 4,170,000, foot pounds. Since this is done in one hour, the work per minute is ^Vk - 00 or 69,500 foot pounds. The horse power required would be fff or 2.1 H. P. 42. Transmission of power. In any shop containing sev- eral machines one easily distinguishes two kinds the driv- ing machines, which may be steam, gas or hot-air engines, or water or electric motors, and the driven machines, sucli as lathes, drills, planers, and saws. There must always be some connecting link between a driving and a working ma- chine ; that is, some means of transmission. If these ma- chines are not far apart, the common method is to use shaft- ing, belts, chains, or cogwheels; but when the prime mover and the driven machine are widely separated, sometimes even miles apart, some form of elec- trical transmission is used. Electrical transmission will be explained later in Chapter XVIII. When a belt, rope, cable, or endless chain is used, it passes over two pulleys, as. shown in figure 40. In case a, the pulleys rotate in the same direction, FIG. 40. Transmission of power by a belt. SIMPLE MACHINES 39 while in case 5, where the belt is crossed, they rotate in op- posite directions. It is evident that the small pulley turns just as many times as fast as the large pulley, as the circum- ference (or diameter) of the small pulley is contained in the circumference (or diameter) of the large pulley. The same is true of cogwheels, and since the teeth on the perimeters of two interlocking wheels must be the same size, it follows that the number of cogs on each wheel is a measure of its circumference. The speeds of two such wheels- are in- versely proportional to the number of teeth on them. Just as in the case of two pulleys with a crossed belt, two cog- wheels rotate in opposite directions. Suppose a pulley A is driving a second pulley B by means of a belt, as shown by the arrows in figure 40 ; both sides of the belt must be under some tension in order to give the necessary pressure on the pulleys, so that the friction may keep the belt from slipping. It is the usual practice to drive with the upper side of the belt slack, so that any sagging due to the weight of the belt may increase the arc of contact. The tension, then, on the lower side (^) must be greater than the tension on the upper side (f). It is the difference in tension (Ti} of the two sides of the belt which measures the force involved in the transmission of power. The work done in one minute is equal to the difference in tension times the speed of the belt in feet per minute. Horse power = difference in tension x speed (ft. per min.) 33000 PROBLEMS 1. If it takes 22 pounds to pull a 200-pound sled along a level road covered with snow, how much work is done in dragging the sled 50 feet? 2. In the preceding problem, if the sled is drawn at the rate of 4 miles an hour, how many horse power are required? 3. How much work can a 5-horse-power engine do in 10 minutes ? 40 PRACTICAL PHYSICS 4. What is the horse power of an elevator motor, if it can raise the car with its load, 1500 pounds in all, from the bottom to the top of a 100-foot building in 10 seconds ? 5. An aeroplane with a 50 horse-power engine makes 60 miles an hour. What is the backward thrust of the propeller ? 6. A locomotive pulling a train along a level track at the rate of 25 miles an hour expends 75 horse power. Find the total resistance overcome. 7. A motor has a 4-inch pulley which is belted to a 16-inch pulley on an overhead shaft. The motor is making 1800 revolutions per minute. What is the speed of the overhead shaft ? 8. In an electric car motor a pinion or small cogwheel, attached to the armature shaft, has 20 cogs, and the gear wheel attached to the car axle has 36 cogs. If the car wheel is 33 inches in diameter, find the number of revolutions the motor makes while the car goes 100 feet. 9. If the tension T in the tight side of a belt 1 inch wide can safely be 44 pounds greater than the tension t in the slack side of the belt, how fast must the belt run to transmit 1 horse power? 10. It takes about 4 times as great a thrust to drive an aeroplane at 80 miles an hour, as to drive the same aeroplane at 40 miles an hour. Compare the horse powers required at the two speeds. i 43. Friction. In the study of machines thus far we have assumed that we were dealing with ideal or perfect machines, in which the output equals the input. But in every actual machine the output is not quite equal to the input. This loss or waste of work is due to friction. By friction we mean the resistance which opposes every effort to slide or roll one body over another. This resistance, which always opposes the mo- tion of the machine, depends on the condition of the rubbing surfaces. Great pains are therefore taken to diminish the friction as much as possible by making the surfaces which are to rub together smooth and hard, and by using various lubricants, such as soap and paraffin on wood, and grease, oil, and graphite on metal. For example, in a watch, the hardened steel axles turn in jewel bearings,' which are the hardest and smoothest bearings known, and are lubricated with a special oil made for the purpose. SIMPLE MACHINES 41 44. So-called laws of friction. The factors which control friction in any actual case are so numerous and so dependent upon the conditions, that only the most general principles may be stated positively. (1) Experience shows that starting friction is greater than sliding friction. For when we push a box across the table, we find that the force necessary to overcome the resistance of friction, which acts like a back- ward drag, is greater at the start than when the box is once in motion. (2) Friction does not much depend on velocity, but is a little greater at slow speeds. (3) Friction depends very much on the nature of the rubbing surfaces. (4) When a box is loaded, it requires much more force to pull it along than when it is empty. Careful experiments seem to show that the force needed to slide a given box over a certain floor is just about doubled when the pressure (weight of box and load) is doubled, and tripled when the pressure is tripled. That is, the force needed to overcome the friction seems to be proportional to the pressure. Experiments show that this force of friction may be a very small fraction of the pressure, such as 0.06 in the case of lubricated iron on bronze, or a large fraction of the pressure, such as 0.4 in the case of oak on oak without lubricant. 45. Coefficient of friction. This fraction, the friction divided by the pressure, is called the coefficient of friction. Coefficient of friction = force of friction pressure or weight In accordance with the statements in the last paragraph, the coefficient of friction for any particular pair of surfaces is pretty nearly constant for different loads or speeds. This is, however, only an approximation to the truth. Thus it has recently been found that the coefficient of friction of brake shoes on railroad car wheels nearly doubles when the speed drops from 60 miles an hour to 20 miles an hour. This is why an engineer or motorman lessens the pressure of his brakes as his train or car slows down. 42 PRACTICAL PHYSICS The usefulness of even roughly accurate coefficients of friction is that they give some idea of how much resistance has to be overcome in any given case. Thus in the country, farmers often haul stones and pieces of heavy machinery on low sledges without wheels, called stone boats. To calcu- late how much force is needed to drag such a stone boat, one has only to look up the coefficient of friction between wood and dirt (about 0.66) in an engineer's handbook, and multi- ply it by the weight of the boat and its load. For Force of friction = coefficient of friction x pressure. 46. Advantages of friction. In general it is true that friction reduces the amount of useful work which can be gotten out of a machine, yet it must not be forgotten that many machines depend upon friction for their operation. Without friction, belts would not cling to their pulleys, ropes could not be made, nails and screws would be useless, and even walking would be impossible, as any one can see who has experienced the difficulty of running on a polished floor or on ice. It is friction which has made possible our high-speed express trains ; first because it is the friction or traction between the driving wheels of the locomotive and the rails that enables them to move at all, and second, because it is the friction between the brakes and the car wheels that enables them to stop quickly in case of emergency. 47. Rolling friction. Every one knows that the friction which opposes drag- ging a load along can be greatly reduced by mount- FIG. 41. Rolling friction (exaggerated). J J , . ing the load on wheels, but it should be noticed that even in this case there is something equivalent to friction between the wheels and the roadbed. When a car wheel rolls over a smooth track, as shown in SIMPLE MACHINES 43 figure 41, its own weight and that of its load flatten it a little where it rests on the track, and also make a slight depression in the track. So as it rolls along it is continually forced to climb up out of the depression. Of course this depression is not easy to detect in the case of a steel track, but in the case of a soft dirt road it is very considerable. It is for this reason that the wheels of wagons which carry heavy loads are provided with wide tires so as to sink less into the roadbed ; and for just this reason the hard sur- faces of car wheels and tracks enable a locomotive to pull enormous loads. This resistance to rolling is called rolling friction. The great advantage of ball and roller bearings is that they substitute rolling for sliding friction between the axles and their bearings. But even in ball bearings there is some sliding friction where adjoining balls rub against each other. 48. Efficiency of machines. The efficiency of a machine is the ratio of output to input. It is usually expressed as a per cent; that is, the output is a certain per cent of the input delivered to the machine. !?.: output work done by machine Efficiency = = - * - input work done on machine or Output = efficiency x input. For example, suppose we have an inclined plane of 5 % grade (5 feet rise in 100 feet) and a load of one ton. If, because of friction, it takes a pull of 150 pounds to haul the load up the slope, what is the efficiency? In lifting 2000 pounds 5 feet, we do 10,000 foot pounds of work ; this is the output. But we must pull with a force of 150 pounds through 100 feet, or put in 15,000 foot pounds of work. Therefore the efficiency is , or 0.667, or 66.7%. The efficiency of a lever where the friction is very small is nearly 100 %, but in the commercial block and tackle it is sometimes less than 50%, and in the jackscrew, the friction is so large that the efficiency is often as low as 25 %. 44 PRACTICAL PHYSICS PROBLEMS 1. A tool is pressed on a grindstone with a force of 25 pounds ; the coefficient of friction is 0.3. What is the backward pull of friction? 2. The coefficient of friction between the driving wheels of a loco- motive and the rails is 0.25. How much must the locomotive weigh in order to exert a pull of 10 tons ? 3. A test shows that it takes a pull of 17 pounds to pull on ice a man weighing 150 pounds. What is the coefficient of friction ? 4. In lifting a 1250-pound block of marble to a height of 90 feet, the hoisting engine did 125,000 foot pounds of work. What was the efficiency of the hoist ? 5. What load can a pair of horses, working at the rate of 2 horse power, draw along a level highway at the rate of 3 miles an hour, if the coefficient of friction of the wagon on the road is 0.17? 6. With a certain block and tackle it is found that a force of 125 pounds is necessary to lift a weight of 500 pounds, and the force must move 6 feet in order to raise the weight 1 foot. What is the efficiency of this block and tackle? 7. A motor whose efficiency is 90% delivers 5 horse power. What must be the input ? 8. A hod carrier, weighing 160 pounds, carries 100 pounds of brick up a ladder to a height of 35 feet. How much work does he do in all? How much of it is useful work ? 9. What is the efficiency of a pump which can deliver 250 cubic feet of water per minute to a height of 20 feet, if it takes a 10 horse-power engine to run it? 10. A steam shovel driven by a 6 horse-power engine lifts 200 tons of gravel to a height of 15 feet in an hour. How much work is done against friction ? SUMMARY OF PRINCIPLES IN CHAPTER II The principle of moments: used in solving all kinds of levers, straight and bent, the wheel and axle, etc. ; Effort x lever arm = resistance x lever arm. To get force on fulcrum : or to solve a pulley system, Sum of forces up = sum of forces down. SIMPLE MACHINES 45 Laws of equilibrium: applicable to any object at rest under the action of two or more forces ; (1) Sum of forces in any direction = sum of forces in opposite direction. (2) Sum of moments clockwise around any point = sum of moments counter-clockwise around same point. The principle of work; Work (foot pounds) = force (pounds) x distance (feet). In any frictionless machine, Input = output. If there is friction, Input = output 4- work lost by friction. Power = rate of doing work. i horse power = 550 foot pounds per second, = 33,000 foot pounds per minute. Coefficient of friction = force of friction . pressure Force of friction = coefficient x pressure. Efficiency = input Output = efficiency x input. QUESTIONS 1. Make a list of a dozen applications of the simple machine ele- ments described in this chapter that you have seen outside of the class- room within a week. 2. Distinguish between the popular use of the term "work" and its technical use in physics and engineering. Give an example of " work " that is not technically "work." 3. Analyze the working of the following machines : clothes wringer, broom, ice-cream freezer, plow, grindstone, and rotary meat chopper. 46 PRACTICAL PHYSICS 4. Distinguish between the terms " mechanical advantage " and "efficiency." Illustrate by an example. 5. Is there any " mechanical advantage " in an equal arm lever ? Why is it often used in machines? 6. Why is an unequal arm lever useful? 7. Show how the principle of work applies to the lever. 8. How would you calculate the moment of the force F as applied to the grindstone in figure 42 ? 9. Why are you likely to twist off the head of a screw by using a screwdriver in a bit brace ? 10. When a machinist speaks of " an 8-32 screw/' what does he mean ? 11. What is meant by a perpetual -motion ma- chine ? 12. -What kind of lubricant is used on journals of car wheels? What kind on clocks and watches? Why the difference in kind of lubricant? 13. What determines the "angle of repose," or slope, of the rock waste, or talus, at the base of a cliff? 14. Why are the modern air brakes on cars more effective than the old-fashioned hand brakes ? FIG. 42. Crank grindstone. CHAPTER III MECHANICS OF LIQUIDS Hydraulic machines Pascal's principle of transmitted pres- sure applications in presses and elevators pressure in a liquid due to its weight levels of liquids in connecting vessels upward pressure of liquids Archimedes' principle and its applications specific gravity of solids and liquids city water works, faucets, gauges, and meters water wheels interaction between solids and liquids capillarity. 49. Hydraulic machines. As we continue our study of machines we find some machines that involve more than the simple elements, the lever, the pulley, and the screw. For instance, there are a great many machines that make use of liquids, such as the water wheel, hydraulic press, and hydraulic elevator. These are called hydraulic machines, and this chapter will be devoted to the study of them. In the course of it we shall also have to consider dams and reser- voirs, as well as all sorts of things that float or sink in water. 50. Pressure transmitted by a liquid. Suppose we fill a bottle with water and close it with a one-hole rubber stopper. Then let us fasten the stopper securely, as shown in figure 43, and force into the hole a metal rod of such a size as to fit rather tightly. The force applied to the rod will be transmitted to the inner surface of the bottle, and the bottle will burst. This experiment shows that the water FIG 43. -Water trans- mits pressure of pis- which is pressing against the bottom of ton. 47 48 PRACTICAL PHYSICS the piston is also pressing against everything else that it touches. 51. Pascal's principle. It seems reasonable to suppose that if we had a box filled with water and fitted with two equal pistons A and B, as in figure 44, the water would press equally hard on each pis- ton. It is also evident that if a third equal piston were placed in the side of the box, as at (7, the water would press sideways on it with an equal force.* In short, if a liquid is pressing against any square inch with a FIG. 44. Pascal's principle. certain force, it is pressing equally hard against every square inch of everything it touches. 52. The hydraulic press. The most useful application of this principle can be described in Pascal's (1623-1662) own words : " If a vessel full of water, closed in all parts, has two openings, of which the one is a hundred times the other, placing in each a piston which fits it, the man pushing the small piston will equal the force of a hundred men who push that which is a hundred times as large, and surpass that of ninetjr-nine. Whatever proportion these openings have, and whatever direction the pistons have, if the forces that apply on the pistons sg."*n ^^^^^^ H3 1 s in < are as the openings, they will be in equilibrium." 100 100 Ibs. uumumi 1 Ib m M^^P^^i^ ^r-_-^^-_^^- ^ =^-=~- ~E^-=: ^7^-Z^ -^I^-Z^T^EI^ FIG. 45. Diagram of hydraulic press. This refers to a mechanism like that shown in figure 45. Suppose there is a force of one pound pushing down on the small piston, and that the large piston has 100 times as great an area. Then there must be 100 pounds push- ing down on the large piston to balance it. It will be seen, however, * The effect of the weight of the liquid is here neglected. BLAISE PASCAL. French scientist and mathematician. Born 1623. Died 1662. Studied the pressures exerted by liquids and gases. Famous also for his achieve- ments in mathematics. MECHANICS OF LIQUIDS 49 that the pressure on each square inch of the large piston is one pound. In other words the pressure has been transmitted by the liquid so as to act with the same force on every square inch. 53. Applications of the hydraulic press. This device of Pascal gives us an easy way of exerting enormous forces, such as are needed in baling paper, cotton, etc., in punching holes through steel plates, and for extracting oil out of seeds. The commercial machine (Fig. 46) is exactly like that described by Pascal except that there is usually a check valve (v) between the small piston and the big one, and the small piston is arranged to work like a pump, with a valve (d) at the bottom for admit- ting more oil. Often the small piston is forced down by a lever. The method of operation is sim- ple. On the upstroke of the pump piston, the valve at the FIG. 46. Hydraulic press. bottom of the pump opens and oil flows in from the reser- voir. On the downstroke of the pump piston, the oil is forced over through the connecting pipe past the valve, and pushes the large working piston up very slightly. If the large piston is 100 times as large in cross section as the small piston (i.e. diameters as 10 : 1), the large piston is lifted only -^^ the distance the pump piston is pushed down each stroke. But since the force exerted by the large piston is, neglecting friction, 100 times that applied to the small piston, it follows that the work done on the machine is equal to the work done by the machine. If we consider the work done against friction, the equation becomes, Input = output + work done against friction. 54. Working model of a hydraulic press. Let us try to appreciate the tremendous forces which are obtainable with the hydraulic press by 50 PRACTICAL PHYSICS operating a model press, such as is shown in figure 47, to break a stick of wood. By measuring the diameters of the pistons, and the lengths of the lever arms, we may calculate the total mechanical advantage of the machine. FIG. 47. Working model of FIG. 48. Hydrostatic hydraulic press. bellows. Another striking experiment is to let a boy bal- ance his own weight against a column of water by means of the hydrostatic bellows (Fig. 48). By cal- culating the actual areas involved and the force acting on each square inch, we may compute the height of water that should be required and compare this with the actual height. 55. Hydraulic elevators. Pascal's prin- ciple is also used in hydraulic elevators, which are commonly employed where heavy machinery is to be lifted. A simple form is shown in figure 49. At the bottom of the elevator well is a pit as deep as the building is high. In the pit is a cylinder ( (7) and in this C}^linder is a plunger (P), to the top of which the elevator cage (^4) is firmly fastened. When water under pressure (often simply the pressure of the water mains) is admitted through the valve (v) into the cylinder, the plunger rises and forces up the elevator. The weight of the elevator is partly counter- FIG. 49. Hydraulic elevator. MECHANICS OF LIQUIDS 51 balanced by a weight (IF). When the operator, by pulling the cord, turns the valve so as to connect the cylinder in the pit with the sewer pipe, the elevator comes down. When speed is demanded, as in high office buildings, the motion of the hydraulic plunger is communicated to the cage by a cable passing over a series of pulleys, so that the cage moves four times as far and four times as fast as the plunger. 56. Pressure and force. It is necessary to distinguish be- tween the terms pressure and force. Force means a push or a pull, and is usually expressed in terms of the push or pull necessary to hold up a given weight, such as a pound or a kilogram. Pressure means the push or pull per unit area of surf ace. Pressure may be expressed in various ways, for example, as so many grams per square centimeter or so many pounds per square inch. The real advantage of the hydraulic press is that, although the pressure on the large piston is exactly the same as that on the small piston, the force exerted by the large piston is many times greater. PROBLEMS 1. If the diameters of two pistons in a hydraulic press are 1 inch and 10 inches, what are their areas of cross section ? 2. If the small piston in problem 1 is subjected to a pressure of 10 pounds per square inch, what pressure, neglecting friction, must be applied to the large piston to hold it in place ? 3. If a total force of 10 pounds is applied to the small piston in prob- lem 1, what total force must be applied to the large piston to hold it in place ? 4. The diameters of the pistons in a hydraulic press are 20 inches and 1 inch. What must be the force on the small piston if a force of 5 tons is to be exerted by the large piston? 5. In problem 4, suppose the small piston to move 1 foot. How far does the large piston move ? 6. If the water pressure in a city water main is 50 pounds per square inch and the diameter of the plunger of an elevator is 10 inches, how heavy a load can the elevator lift ? If the friction loss is 25 %, what load can be lifted ? 52 PRACTICAL PHYSICS 57. Pressure in a liquid due to its weight. Not only does a liquid transmit pressure when it is in a closed vessel, but a liquid in an open vessel, such as water in a tin pail, exerts a pressure on the bottom of the vessel because the liquid is it- self heavy. This bottom pressure, that is, the force on each square inch, evidently depends on the depth of the liquid, and also on its density. For example, suppose we have a box with a bottom 10 centimeters by 20 centimeters and 15 centimeters deep, filled with water. Then on each square centimeter of the bottom of the box there rests a column of water 15 centimeters tall, weighing 15 grams, and so the pressure on the bottom is 15 grams per square centimeter. The total downward force of the water against the bottom would be 200 x 15, or 3000 grams, for Total force = area x pressure. If the box were filled with mercury instead of water, the pressure on the bottom would be the weight of a column of mercury 15 centimeters high and 1 square centimeter at the base; that is, the weight of 15 cubic centimeters of mercury. Since 1 cubic centimeter of mercury weighs 13.6 grams, 15 cubic centimeters would weigh 15 x 13.6, or 204 grams. The total force of the mercury pushing down on the bottom of the box would be 200 x 204, or 40,800 grams, or 40.8 kilograms. 58. Bottom pressure and shape of vessel. So far we have considered vessels with vertical sides such as A in figure 50. d C FIG. 50. Vessels with (A) vertical, (B) flaring, and (C) conical sides. In the ordinary pail, however, the sides are not vertical, but flare outward as shown in B in figure 50. Perhaps one might expect that the pressure on each square centimeter of the bottom would be greater than in case J., because there is so much more water in the vessel. This, however, is not the case. Each square centimeter of the bottom has to hold MECHANICS OF LIQUIDS 53 up only the little column of water above it just as it did in case A. The extra water above the slanting sides is held up by those sides and not by the bottom. If the area of the base and depth of liquid is the same in both A and B, then the total downward push of the liquid on the bottom will be the same even though B holds more liquid than A. In case (7, the depth of liquid and area of base are the same as in cases A and J9, but the top is smaller than the base. It is easy to see that the pressure on that portion of the base ab directly under the top would be the same as in the other vessels, but it might at first seem that the pressure would gradually decrease as we go from a to c and from I to d. There is an interesting experiment devised to settle this question. 59 Experiments with Pascal's vases. The apparatus (Fig. 51) consists of three glass vessels of shapes to correspond roughly to A, B, and C in figure 50. The bottom of each vessel is made the same size and screws into a short cyl- inder, across the bottom of which is tied a disk of sheet rubber. The pointer below is a lever with its short arm pressing against the center of the rubber disk, and the long arm moves up and down across a scale. With this apparatus it is possible to show that (a) the downward pressure of a liquid is proportional to the depth, (b) the downward pressure of a liquid is proportional to its density, and (c) the downward pressure in a liquid is inde- pendent of the shape of the vessel. It seems impossible that unequal quantities of water should exert an equal downward push against the bottom. But if we recall that when the sides slope outward, the sides FIG. 51. Pascal's vases. 54 PRACTICAL PHYSICS hold up the excess of water, we can see that when the sides slope inward, they push down enough to make up for the deficit in water. 60. Liquids also exert pressure sidewise. We all know that if a hole is bored in the side of a tank or barrel of water, the water will spurt out. This means that before the hole was bored the liquid must have been pressing against that bit of the side of the barrel. Liquids, then, exert a sidewise pressure due to their weight, as well as a downward pressure. We can investigate how this sidewise pres- sure varies with the depth and .the direction by means of the gauge shown in figure 52. The apparatus consists of a rubber diaphragm, which may be turned about a horizontal axis, and is connected by a rubber tube to a hori- zontal glass tube containing a globule of some colored liquid. As we lower the pressure gauge into the jar of water, we observe that the globule moves to the right showing a gradual increase of pressure with increase of depth. If we repeat this with the diaphragm facing in another direc- FIG. 52. -Pressure gauge tion> we get the same resulL If we hold the to show pressure equal frame ftt gome fixed d th and rotate the dia _ in all directions. ' phragrn around a horizontal axis, we find the globule remains practically stationary, showing that the pressure is the same in all directions. The sidewise pressure of a liquid increases with the depth and density of the liquid. At a given depth a liquid presses down- ward and sidewise with exactly the same force. 61. Calculation of sidewise pressure. ' To calculate the sidewise push of water against a dike or dam, we have to remember that both the downward and sidewise pressure increase gradually from zero at the surface to their value at the bottom. We have already seen that this bottom pressure is equal to the weight of a column of water with a base one unit square and with a height equal to the depth. The MECHANICS OF LIQUIDS 55 average side wise pressure is equal to the pressure halfway down, or is one half the bottom pressure. The total side- wise push of the water against the dam is then equal to the area times the average pressure. For example, suppose we have a box 10 centimeters wide, 20 centi- meters long, and 15 centimeters deep filled with water. What is the total force tending to push out the end of the box ? The pressure at a point halfway down the side would be 7.5 grams per square centimeter. There are in the end 10 x 15, or 150 square centimeters. Therefore the total force against the end is 150 x 7.5, or 1125 grams. Again, suppose the box were a large tank full of water, and the di- mensions, expressed in feet, were 10 by 20 by 15. What is the end thrust? The pressure halfway down would be the weight of a column of water with FIG. 15 cm 20 cm 53. Sidewise push of water against end of box. 1 square foot for its base and 7.5 feet high, i.e. 7.5 x 62.4, or 468 pounds per square foot. Since there are 10 x 15, or 150 square feet, in the end of the tank, the total end thrust is 150 x 468, or 70,200 pounds, or about 35 tons. 62. Levels of liquids in connecting vessels. Probably every one has observed that water stands at the same level in the spout of a teakettle as in the kettle itself (Fig. 54). In other words, liquids seek their own level, or the same liquid in any number of connecting vessels will have its free surface at the same level in each. This is to be expected from the fact that the pressure in a liquid depends upon the depth FIG. M. -water seeks its own below the free surface. Thus if level in a teakettle. .-..! any point in the connecting por- tion between the two vessels were unequally far below the two surfaces, the pressures in either direction would not 56 PRACTICAL PHYSICS balance, and the liquid would flow from one vessel to the other until the levels were equalized. The water gauge on a steam boiler (Fig. 55) is a good application of this principle. The gauge consists of a thick-walled glass tube which connects at the top with the steam space, and at the bottom with the water in the boiler. The valves A. and B are closed when the glass tube is to be replaced. The valve C is opened oc- casionally to test the gauge to see that it reads correctly and has not clogged up. 63. Upward pressure of liquids. If one tries to push a pail under water bottom downward, he finds he must overcome considerable resistance because FIG ' "'"iblriter gauge n of the upward push of the water on the pail. In order to see just how much this upward push of the water is, let us try the following experiment. Let a glass cylinder, which has its bottom edge ground off smooth, be closed with a glass plate or piece of cardboard, held in place by a thread, as shown in figure 56. When we push this cylinder into a jar of water, we can let go the thread and yet the glass bottom will not fall off. It is evident that there is an upward pressure due to the water, and the next question is, how much? If we pour colored water into the cylinder until the bottom drops off, we shall have to fill the cylinder until the levels inside and outside are the same. In general we may say that the upward pressure exerted by a liquid at any depth is equal to the down- (j> Upward pressure oi water. MECHANICS OF LIQUIDS 57 ward pressure which would be exerted by the same liquid at the same depth. PROBLEMS 1. The water in a standpipe is 10 meters deep. What is the pres- sure on one square centimeter of the bottom ? 2. The water in a standpipe is 40 feet deep. What is the pressure on one square inch of the bottom ? 3. If the diameter of the tank in problem 2 is 10 feet, what is the total force which the bottom of the tank must sustain ? 4. A diver goes down into sea water (density 1.03 grams per cubic centimeter) to a depth of 10 meters. What is the pressure on him in kilograms per square centimeter? 5. The hydraulic engineer speaks of pressure as "head of water," which means the pressure due to the weight of column of water as high as the " head of water." Express in pounds per square inch a " head of 50 feet." 6. What is the pressure, near the keel, on a vessel drawing 6 meters? 7. Figure 57 is a cylindrical tank 10 x 12 centi- meters ; out of the top rises a tube 20 centimeters long. The box and tube are filled with water. (a) Find the pressure in grams per square centimeter at the bottom of the tank. (6) Does the size of the tube affect the pressure on the bottom ? (c) Find the pressure halfway up the side of the tank. (d) Find the pressure at the top of the tank. 8. A rectangular tank is 5 feet wide, 10 feet long, and 4 feet deep. Calculate the total force exerted on the end when the tank is full of water. < 12 cm. 9. Assuming that a cubic inch of mercury weighs FIG. 57. Box 0.49 pounds, find the pressure on the bottom of a turn- and tube full bier in which the mercury stands 4 inches deep. of water. 10. How high a column of water could be supported by a pressure of one kilogram per square centimeter? 11. If the density of mercury is 13.6 grams per cubic centimeter, what is the pressure exerted at the base of a column 76 centimeters high ? 12. A dam is 50 feet long and 6 feet high, and the water just reaches the top. What is the total force against the dam ? 13. A hole 6 inches square is cut in the bottom of a ship drawing 18 feet of water. What force must be exerted to hold a board tightly against the inside of the hole ? 58 PRACTICAL PHYSICS 14. How much " head of water " is needed to give a pressure of 1 pound per square inch? 15. What must be the difference in height between a fire hydrant and the surface of the water in a city res- ervoir to give a pressure of 50 pounds per square inch at the hydrant ? 16. In figure 58, the U-tube is partly filled (BAC) with mercury whose density is 13.6 grams per cubic centimeter, and partly (CD) with a liquid of unknown density. If the length of the column BA is 5 centi- meters and that of the column CD is 75 centimeters, what is the density of the liquid ? 64. Buoyant effect of liquids. When swim- FJG. 58. u-tube ming in deep water, we find that our bodies are and 'another vej T nearly floated. When we pick up a stone liquid. under water, we find it much heavier if we lift it above the surface. Things seem to be lighter under water ; in other words, water buoys up anything placed in it. In order to find how much lighter anything is under water than it is out of water let us try the following experiment. We have a hollow metal cylindrical cup (7, and a cylindrical block B, which has been nicely turned to fit inside the cup C. We hang both from a beam balance, as shown in figure 59, and counterbalance with a weight W on the other scalepan. Then we bring a glass of water up under the block B, so that it is entirely under water. The left-hand side of the balances rises, which shows the upward push of the water upon B. But we can restore the equilibrium again by pouring water into the cup C until it is just filled., This shows that B loses in apparent weight the weight of its own bulk of water. If we try the experiment, using kerosene instead of water, we find that exactly the same thing is true. FIG, 59. Buoyant effect of liquids. MECHANICS OF LIQUIDS 59 65. Archimedes' principle. The principle proved by this experiment may be stated as follows : The loss of weight of a body submerged in a liquid is the weight of the displaced liquid. It is supposed that this principle about the loss of weight of a body in a liquid was discovered by the old Greek phi- losopher Archimedes (287-212 B.C.). Hiero, king of Syra- cuse, suspected a goldsmith who had made a crown for him, and ordered Archimedes to find out if any silver had been mixed with the gold in the crown. To do this without destroying the crown seemed a puzzle at first, but one day, while Archimedes was in the public bath, he noticed that his body was buoyed up by the water in which it was sub- merged. Seeing in this effect the solution of his problem, he leaped from the bath and rushed home shouting, " Eureka ! Eureka ! " (I have found it ! I have found it !). 66. Explanation of Archimedes' principle. This principle will be readily understood from the following example. Suppose we place a rectangular block in ajar of water, as shown in figure 60. Let the block be 10 x 6 x 4 centimeters and let the top be 5 centimeters below the surface of the water, and the bottom 15 centimeters beneath the surface. Then the pressure on top, that is, the down- ward push on each square centimeter, is 5 grams and the pressure on the bottom, that is, the upward push on each square centi- meter, is 15 grams. Since the top and bottom each have an area of 6x4, or 24 square centimeters, the whole upward push on the bottom is 24 x 15, or 360 grams, while the whole downward push on the top is only 24 x 5, or 120 grams. This leaves a net upward force or buoyancy of 240 grams. But this is exactly the weight of the displaced water, for the volume of the displaced water is 10 x 6 x 4 = 240 cubic centimeters,. and we have seen in section 11 that this much water weighs 240 grains. FIG. 60. Lifting effect of water on submerged block. 60 PRACTICAL PHYSICS The same sort of reasoning would hold at any depth and for any liquid other than water and with any irregular- shaped body. So it may be said that in any liquid of any density a body seems lighter by the weight of the displaced volume of that liquid. 67. Floating bodies. Let us think what will happen if this upward force, or buoyant force, is more than the weight of the body submerged. Evidently the body will rise and will continue to rise as long as the upward push remains greater than the downward pull of gravity. But as soon as any of the body projects above the surface, less water is dis- placed and the upward push is less. When enough of the body projects to reduce the buoyant force to equality with the weight, the body stops rising and floats. In this case we see that the loss of weight is the whole weight itself. A floating body displaces its own weight of the liquid it is floating in. The following experiment will help to make this principle of Archi- medes, as applied to floating bodies, seem more real. Suppose we balance an overflow can on a platform scale, as shown in figure 61. The can is filled with water so that it just over- flows and is balanced by the weight on the other platform. We will place a dish to catch the overflowing water, and then put a block of wood gently in the can. After the water has stopped overflowing, it will be seen '" -> balance. This means the weight of water which flowed over was just equal to the weight of the block. This can be veri- fied in another way by weighing the water displaced by the block. 68. Applications of Archimedes' principle. If we know the total weight of a ship and its equipment, we can tell at once what weight of water it will displace, and so it is possible to compute how deep it must sink to displace its own weight MECHANICS OF LIQUIDS 61 of water. It is also evident that a boat must sink a little deeper in fresh water than in salt water, and will sink deeper when loaded than when empty. A submarine boat is so constructed that it is only slightly lighter than water. It can then be submerged by letting water into certain tanks and can be made to rise by pumping the water out of the tanks. This same idea is made use of in the floating dry- dock shown in figure 62. When the tanks T, T, T are full of water, the dock sinks until the water level is at LL. The ship to be re- paired is then floated into the dock and the water is pumped out of the tanks w - T, T, T. As the com- partments are emptied of water, the dock rises until the water level is at the line TPJ W, lifting the ship out of water. The ship and dry-dock still displace their own weight of water, but the displacement is in a different place. PROBLEMS 1. A piece of stone weighing 235 grams in air and 128 grams in water is put into a dish just full of water. How much water runs over? 2. A rowboat weighs 200 pounds. How many cubic feet of water does it displace ? 3. A barge is 30 feet long and 16 feet wideband has vertical sides. When a large elephant is driven on board, it sinks 4 inches farther in the water. How many tons does the elephant weigh ? 4. What is the volume of a 125-pound boy, if he can float entirely submerged except his nose ? 5. A rectangular block is 22 centimeters long, 6 centimeters wide, and 4 centimeters high, and floats in water with 1 centimeter of its height above water. How much does it weigh? 6. A cube 5 centimeters on an edge- weighs 600 grams in air. How much does it weigh in water ? 7. How much will a cubic foot of brass (density 8.4 grams per cubic centimeter) weigh in gasolene (density 0.79 grams per cubic centimeter) ? 62 PRACTICAL PHYSICS ' 8. A rectangular solid 10 x 8 x 6 centimeters is submerged in water, so that the top, whose dimensions are 10 x 8 centimeters, is horizontal and 12 centimeters below the water surface. (a) Find the total force pressing down on the top. (b) Find the total force pushing up on the bottom. (c) Find the loss of weight of the solid. 69. Specific gravity and density. Archimedes' principle furnishes us with a convenient method of comparing the weight of a substance with the weight of an equal bulk of water. The ratio of these weights is called the specific gravity of the body. In other words, weight of body Specific gravity = . . . . . , J ^ weight of equal bulk of water For example, a piece of marble weighs 100 grams and an equal bulk of water weighs 40 grams, then the marble is 100/40 or 2.5 times as heavy as the water. The specific gravity of marble, then, is 2.5. The term specific gravity does not mean quite the same thing as density. The specific gravity of a substance is an abstract number ; for example, the specific gravity of mercury is 13.6. But the density of a substance is a concrete number ; for example, the density of mercury is 13.6 grams per cubic centimeter, or 850 pounds per cubic foot. In the metric system, the density of water is one gram per cubic centimeter, and therefore Density (g. per cm. 3 ) =. (numerically) specific gravity. In the English system, the density of water is 62.4 pounds per cubic foot, and therefore Density (Ibs. per cu. ft.) = (numerically) 62.4 x specific gravity. 70. Methods of determining specific gravity of solids. GENERAL RULE. First weigh the object. Next find by some indirect method the weight of an equal bulk of water. Finally divide the weight of the object by the weight of the equal bulk of water. MECHANICS OF LIQUIDS 63 This general statement covers all the various processes for finding the specific gravity either of solids or of liquids. The different procedures vary only in the method of finding the weight of an equal bulk of water. . 1st Method. If the object is a regular geometrical solid, you can measure its dimensions and calculate its volume, and from that get the weight of an equal bulk of water. 2d Method. If the object is a solid that will sink in water, and will not dissolve, you can determine its loss of apparent weight in water. This is the weight of an equal bulk of water. That is, weight of body Specific gravity = loss of weight in water For example, suppose a piece of copper weighs 178 grams in air and 158 grams in water. The loss, 20 grams, is the weight of an equal bulk of water. Therefore the specific gravity of copper = 178/20 = 8.9. 3d Method. If the object is lighter than water, and does "not dissolve, select a suffi- ciently large sinker and suspend it below the object, as shown in figure 63. Then bring a jar of water up under the whole thing until the water level is between the sinker and the object, and weigh. Then raise the jar still farther until the water level is above the object, and weigh again. This weight will be less than the first because in this case the water buoys up the object, while in the first case it does not. The difference between the two weights is equal to the weight of the water displaced by the object. FIG. 63. Specific gravity with sinker. Specific eravit - weight of body ^ ~ lifting effect of water on body only* 64 PRACTICAL PHYSICS It will be noticed that in this case the loss of weight or lifting effect of the water on the body is larger than the whole weight. This is why the body floats. For example, suppose a piece of wood weighs 120 grams in air, and that, with a suitable sinker, it weighs 270 grams when the sinker is under water, and 90 grams when both are under water. Then the lifting effect of the water on the wood is 270 90, or 180 grams. Therefore the spe- cific gravity of the wood is 120/180 = 0.667. 71. Specific gravity of liquids. 1st Method. Weigh a bottle empty, then full of the liquid, and then full of water. Subtract the weight of the empty bottle in each case, and then compare the weight of the liquid with the weight of an equal volume of water. . . weight of liquid Specie gravity = weight of equal volume of . water " Bottles, called specific gravity flasks (Fig. 64), are made for the purpose of determining the specific gravity of liquids with great accuracy and facility. They are usually made to contain a definite quantity of pure water at a specified temperature ; for example, 250 grams. 2d Method. Weigh a piece of glass in air, then in the liquid, and then in water. Find the loss of weight in the liquid and the loss of weight in water. This loss of weight in the liquid is the weight of the liquid displaced, and the loss of weight in water is the weight FIG. 64. Specific & _, gravity flask. of an equal volume of water. Then loss of weight in liquid Specific gravity = loss of weight in water For example, suppose the glass weighs 330 grams in air, 150 grams in sulphuric acid, and 230 grams in water. The glass loses 180 grams in acid and 100 grams in water. Since these are the weights of equal volumes of acid and water, the specific gravity of the acid 180/100 = 1.8. MECHANICS OF LIQUIDS 65 3d Method. * The most common way of determining the spe- cific gravity of liquids is by the hydrometer. This is usually made of glass, and consists of a cylindrical stem and a bulb weighted with mercury or shot to make it float upright (Fig. 65). The liquid is poured into a tall jar, and the hy- drometer is gently lowered into the liquid until it floats freely. The point where the surface of the liquid touches the stem of the hydrometer is noted. There is usually a paper scale inclosed inside the stem, so made that the specific gravity (or density in grams per cubic centimeter) can be read off directly. In light liquids, like kero- sene, gasolene, and alcohol, the hydrometer must sink deeper to displace its weight of liquid than in heavy liquids like brine, milk, and acids. In fact it is usual to have two separate instruments, one for heavy liquids, on which the mark 1.000 for water is near the top, and one for light liquids, on which the mark 1.000 is near the bottom of the FIG. 65. Stem. Hydrometer. 72. Commercial uses of the hydrometer. Since the com- mercial value of many liquids, such as sugar solutions, sul- phuric acid, alcohol, and the like, depends directly on the specific gravity, there is extensive use for hydrometers. Perhaps the best-known form of hydrometer is the kind used in testing milk, called a lactometer. The specific gravity of cow's milk varies from 1.027 to 1.035. Since only the last two figures are important, the scale of a lactometer is made to run from 20 to 40, which means from 1.020 to 1.040. The specific gravity of milk does not give us a conclusive test as to its worth. Milk contains besides the water * There is another method, using balancing columns, which will be de- scribed in the Laboratory Manual. To understand it one must have read Chapter IV. F 66 PRACTICAL PHYSICS (which is about 87 %) some substances which are heavier than water, such as albumen, sugar, and salt, and others that are lighter than water, such as butter fat. Besides the specific gravity, one needs to determine the amount of fat, and, if possible, the other solids in the milk, in order to know its richness. Of course the very important question as to the cleanliness of milk must be left to the bacteriologist. PROBLEMS 1. A piece of ore weighs 42 grams in air and 25 grams in water. Calculate its specific gravity. 2. A stone weighs 15 pounds in air and 9 pounds in water. (a) Find its specific gravity. (b) Find its density in the metric system. (c) Find its density in the English system. 3. A body has a specific gravity of 3.5. What is its density in (a) the metric system, and (b) the English system? 4. If the specific gravity of lead is 11.4, how many cubic centimeters of lead does it take tojnake a kilogram weight? 5. If the specific gravity of cork is 0.25, how many cubic feet of cork are there in 1 pound of cork ? 6. A block of wood, 15 x 10 x 8 centimeters, floats with one of its largest sides 2 centimeters out of water. (a) Find its weight. (b) Find its specific gravity. 7. A plank 8 centimeters thick floats with 5 centimeters under water. Find its specific gravity. 8. A block of wood weighs 150 grams ; a sinker is suspended from it, and when the sinker is under water and the block is in air, the combina- tion weighs 350 grams. When the wood and the sinker are both under water, they weigh 100 grams. Find (a) the volume of the block of wood, and () its specific gravity. 9. A cube of iron 10 centimeters on an edge (specific gravity 7.5) floats in mercury (specific gravity 13.6). How many cubic centimeters are above the mercury? 10. A can weighs 190 grams when empty, 600 grams when full of water, and 613 grams when full of milk. (a) What is the capacity of the can in cubic centimeters? (6) What is the specific gravity of the milk ? 11. How much does 1 cubic centimeter of lead (specific gravity 11.4) weigh in kerosene (specific gravitv 0.79) ? MECHANICS OF LIQUIDS 67 12. A bottle weighs 80 grams empty, 280 grains when filled with water, and 250 grains when filled with a medicine. What is the specific gravity of the medicine? 13. An empty bottle weighs 50 grams ; the same bottle full of water weighs 200 grams. Some sand is put into the empty bottle and it then weighs 320 grams. Finally the bottle is filled with water, and the bottle, sand, and water weigh 370 grams. (a) Find the capacity of the bottle. (6) Find the volume of the sand. (c) Find the specific gravity of the sand. 14. If one buys 10 pounds of mercury (specific gravity 13.6), how many cubic inches should one get? 15. If the inside of an ice chest measures 24 x 18 x 12 inches, how many pounds of ice (specific gravity 0.92) will it hold ? 16. How many pounds of sulphuric acid (specific gravity 1.84) does a 5-gallon carboy contain ? 73. City waterworks. Every city has to face the problem of providing a plentiful supply of pure water for household use, for industrial purposes, and for fire protection. Not only must there be enough water, but it must be furnished at sufficient pressure to force it to the tops of high buildings. If the city is located near the mountains, as are Denver and Los Angeles, it is an easy matter to conduct the water from an elevated reservoir in large pipes or mains to the houses. Since the water tends to seek its own level, it will rise in the buildings to the height of the reservoir. But in most cities, such as New York, Philadelphia, and Boston, the gravity system of waterworks is impossible and a pumping system must be employed. The operation of the big steam pumps that are used will be explained later (section 100). 74. Hydrants and faucets. The only parts of this great system of water pipes which we ordinarily see are the hydrants on the edge of our sidewalks, and the taps or faucets at our sinks and bathtubs. These are merely valves for opening and closing the pipes, The internal construction of the or- dinary tap is shown in figure 66. The handle operates a screw which forces a disk, faced with a fiber washer, against 68 PRACTICAL PHYSICS a circular opening or seat, and so shuts off the water. If the handle is turned the other way, the disk is raised, leav- ing an opening. This sort of valve may get out of order in two ways : the fiber washer may wear out and the packing about the handle rod may get loose. FIG. 66. Cross section Both of these can be easily replaced, of common faucet. The packing consists of cotton twine wrapped around the valve stem, and is held in place by what is called a gland. 75. How we measure water pressure. Doubt- less we have all found that water flows slowly from a faucet on an upper floor. This is because the water pressure is low there. To measure it, we use some form of pressure gauge, and for as small a pressure as this would be, an open mercury manometer would be the most accurate form of pressure gauge. It consists of a U-shaped tube filled with mercury, as shown in figure 67. Suppose the water pressure is enough to balance a FIG. 67. Mer- mercury column 4 feet high. How much is the pressure cury pressure in pounds per square inch? A column of mercury 4 gauge, ieet high and 1 square inch at the base would contain 48 cubic inches, and \vould weigh 23.5 pounds. Therefore the pres- sure of the water would be 23.5 pounds per square inch. With such a gauge it is easy to show that the water pressure is less on the top floor than in the basement. A mercury gauge is so cumbersome and expensive that a Bourdon spring gauge is generally used. It consists of a brass tube of elliptical section, bent into a nearly complete ring, and closed at one end, as shown in figure 68. The flatter sides of the tube form the inner and outer sides of the ring. The open end of the tube is connected with the pipe MECHANICS OF LIQUIDS 69 through which the liquid under pressure is admitted. The closed end of the tube is free to move. As the pressure in- creases the tube tends to straighten out, moving a pointer to which it is connected by levers and small chains. These spring gauges have the scale so graduated that FIG. 68. Bourdon gauge. they read directly in pounds per square inch. 76. Fluctuations in water pressure. Not only does one find a decrease of water pressure in going from the basement to the attic of a house, but if the gauge is attached at one point and watched closely, it will be seen to fluctuate according as much or little water is being drawn elsewhere in the building. The following experiment shows the same thing on a smaller scale. The tank or reservoir R in figure 69 is connected with a supply pipe AB. The pressure along the pipe is indicated by the height of the water in the tubes C, A and E. When the pipe is closed at B, the level is the same in R, C, Z>, and E ; this is called the static condition. But when the jp^ga^ stopper is removed from B, g N^\\ and water flows out, the FIG. 69. -Pressure falls with flow. "* Psure is no longer the same at all points along the pipe, but falls off as the distance from the reservoir R increases. Tli is drop in pressure is due to friction against the walls of the pipe through which the water has to run. From this experiment* we see that, when a number of faucets are open and the water is flowing, the pressure in the 70 PRACTICAL PHYSICS neighborhood becomes small. *Bo. equalize these changes in water pressure and also to pro\de fsome flexibility in the system, it is quite common to havefci fltandpipe in the water system nearer the houses than the main reservoir. This also serves as an auxiliary reservoir in case of emergency. 77. Water meter. It is common now to measure the quantity of water which is used by each house. This is done by an instrument called a water meter. There are several types of these meters; one of the sim- plest is shown in figure 70, and its action is shown in the four diagrams in figure 71. The water enters through the left- hand kidney-shaped opening, shown by dotted lines, and leaves through the simi- lar opening at the right. The moving part, shown by the heavy line, has a hub (tlie black circle) that travels around in the little circular track provided for it, the moving part meanwhile oscillating to and fro without turning completely around. This makes the various annular spaces enlarge as long as they are in connection with the inlet (watch, FIG. 70. Water meter. FIG. 71. Diagrams to show operation of water meter. for example, the space marked a in the diagrams) and con- tract when they are in connection with the outlet (watch, for example, the space marked 5). In this way each space measures out its appropriate quantity of water and delivers it to the outlet pipe. The number of revolutions of the hub MECHANICS OF LIQUIDS 71 FIG. 72. Meter dials. is registered on a series of dials (see figure 72) which indicate the number Df cubic feet that have passed through the meter. Thus the dials in figure 72 indicate 94,450 cubic feet. The official of the water department reads these dials periodically, and by sub- tracting can easily compute the water consumed during the period, and so fix the charge in proportion. 78. Water motors. In cities where water is supplied under considerable pressure, it may be used to run sewing machines, small polishers, grinders, lathes, etc., by means of a water motor. A simple form is shown in figure 73. The stream of water is made to pass through a small open- ing at high velocity and to strike against some blades or buckets on the rim of a wheel. The wheel is inclosed in a metal case, from which the water flows away to the drain- pipe. The impact of the water against the blades turns the shaft, to which the machines to be driven are connected either directly or by belts. 79. Water wheels. Just as a small stream of water may be used to turn small machinery, so it is possible to make large streams of water turn large machines, which saw wood, grind corn, and furnish electric lights for streets and houses. Any community possessing a waterfall or a rapid in a river has a valuable source of power. The older types of water wheels were the overshot, where the weight of the water slowly turns the wheel, and the undershot, where the wheel is let down into a swiftly flowing current. The modern forms of water wheels are the Pelton wheel and the turbine. The little water motor described above is a typical form of Pelton FIG. 73. Water motor. 72 PRACTICAL PHYSICS wheel, the parts of a commercial wheel being the same, but much larger (see plate facing page 72). The efficiency of this type of wheel is much greater than that of the undershot wheel, and sometimes runs as high as 83 %. By far the most important type of water wheel to-day is the turbine. This is somewhat like a windmill. The water is conducted from the reservoir above the dam through a cylindrical tube to a " penstock" which surrounds the case of the wheel (Fig. 74). This case stands on the floor of the penstock and is submerged in water to a depth equal to the " head " or height of water supply. The water is not let into the case about the wheel at one opening, but. through many inlets or passages, which are so curved as to direct the Stationary water against the blades of the wheel in the most favorable direc- tion to produce rotation, as shown in figure 75. The wheel is attached to a shaft which transmits the power to the machinery above. A small shaft controls the size of the inlet openings in the case. When the water has done its work, it falls from the bottom of the wheel case into the "tail race" below the penstock. These turbines some- times have an efficiency of 90 %. Pelton wheels are used in general where the fall is high and the quantity of water small, turbines where the fall is low and the quantity of water great. Stationary FIG. 75. Stationary and moving blades of water turbine. Pelton water wheel, to be installed at Rjnkan, in Norway, where it will develop 7500 horse power. The wheels of small water motors are similar in shape. MECHANICS OF LIQUIDS 73 PROBLEMS 1. The water level in a tank on top of a building is 100 feet above the ground. What is the pressure in pounds per square inch at a faucet 10 feet above the ground ? 2. If 200 cubic feet of water flow each second over a dam 25 feet high, what is the available power? 3. If the efficiency of the water wheel used at the dam described in problem 2 is 65 %, how many horse power can it supply ? 4. How many cubic feet of water must be supplied every second to an overshot wheel which is 20 feet in diameter and delivers 40 horse power at an efficiency of 85%? 5. The Niagara turbine pits are 136 feet deep, and the average horse power of the turbines is 5000. Their efficiency is 85%. How many cubic feet of water does each turbine handle per minute ? 80. Molecular attractions. When a drop of water falls through the air, it draws itself into an almost perfect sphere. Similarly, lead shot are made by letting molten lead fall from a sieve at the top of a tower into a pool of water at the bottom. In general, a liquid when left to itself tends to get into the shape which has the smallest possible surface, as if it were composed of little particles which had great attraction for one another. It is also observed that there is a great attraction between many pairs of substances if they are brought very close together, as between wood and glue, stone and cement, paint and wood. When this attraction is between particles of the same kind, it is called cohesion, and when between particles of different kinds, it is called adhesion. In soap bubbles, it is the cohesion of the little particles of soapsuds which makes the thin film act like an elastic mem- brane. It is this same property of liquids which makes it possible to lay a somewhat greasy needle on the surface of water and have it float, although steel is eight times as dense as water. 81. Capillarity. Suppose we have two U- tubes (Fig. 76) with their side tubes 30 mm. and 1 mm. in diameter. If we pour water colored with ink into the first tube, and mercury into the second tube, we observe 74 PRACTICAL PHYSICS that in each case the surfaces in the two sides of the U-tube are not at the same level. The water wets the surface of the glass and is attracted by it, i.e. the adhesion is great. The mercury does not wet the glass, and the cohesion of particles of mercury for each other makes it appear as if there were repul- sion between glass and mercury. The FIG. 76. - Capillarity in surface of the merC ury is convex, and small tubes. J it stands at a lower level in the nar- row tube than in the wide one. In the case of water, each tube is drawing the liquid up into itself against the pull of gravity. The narrower the tube, the higher the liquid is raised. Since these small tubes have haiiiike dimensions, they are called capillary tubes (from Latin capillus, a hair), and this phenomenon is called capillarity. In this way liquids rise in wicks, in filter paper, and in the soil. SUMMARY OF PRINCIPLES IN CHAPTER III force Pressure = area Force = pressure x area. For liquids under pressure (weight of liquid negligible in com- parison) : Pressure everywhere the same. Force varies as area. For liquids with a free surface (weight of liquid the only thing that counts) : Pressure proportional to depth, independent of direction, Proportional to density of liquid, Equal to weight of a column of liquid with a base one unit square and a height equal to the depth. Average pressure on a surface = pressure at center of surface. Total force on a surface = average pressure x area. MECHANICS OF LIQUIDS 75 Archimedes' principle : The loss of weight of a body either partly or wholly submerged in a liquid is equal to the weight of the displaced liquid. If the body just floats, this loss of weight is also equal to the weight of the body. Density = weight of body ^ volume of body Specific gravity = - weight of body weight of equal volume of water In the metric system, since 1 cu. cm of water weighs 1 gram, Density (g. per cm. 3 ) = (numerically) specific gravity. In the English system, since 1 cu. ft. of water weighs 62.4 Ibs., Density (Ib. per ft. 3 ) = (numerically) 62.4 x specific gravity. To get specific gravity : Find weight of body. Find weight of equal volume of water. Divide. To get weight of equal volume of water : 1. Compute volume. Weight of water = volume x density of water. 2. Loss of weight of body when wholly submerged weight of equal volume of water. (May have to use sinker.) 3. Weigh equal volumes of liquid and of water in a bottle. 4. Find loss of weight of a solid in the liquid and in water. (May use either sinker or float, i.e. hydrometer.) 5. Use balancing columns (see laboratory manual). QUESTIONS 1. What advantages has the hydraulic press in testing steam boilers? 2. What device is used to prevent the oil or water from leaking out around the pistons of a hydraulic press ? 3. How is Archimedes supposed to have done his famous experiment with the crown? 76 PRACTICAL PHYSICS 4. When a ship passes from a river, where the water is fresh, into the ocean, does it rise or sink in the water? 5. If you have a table of densities in the metric system, how could you make a table of specific gravities? 6. How could you determine the specific gravity of a solid soluble in water, but insoluble in kerosene ? 7. What is the water pressure in your laboratory? 8. Why has skimmed milk a greater density than normal milk? 9. Two faucets in a town show the same pressure on the gauge and are the same size. If one is one mile from the reservoir, and the other is two miles away, will each faucet deliver the same quantity of water per minute when opened wide ? 10. Sometimes when a faucet is opened, especially on an upper floor, the water comes with a rush at first and much more slowly after it has been running a few seconds. Explain. 11. Why does one need to take temperature into account in using the lactometer? 12. What metals float in mercury? 13. How can one pour a liquid out of a glass with the aid of a spoon or glass rod, so that it will not run down the side of the glass ? 14. Explain the action of a towel ; of a sponge. 15. Explain the process of " fire-polishing " the broken end of a glass tube. 16. If you know the displacement of a battleship, how could you find its weight? 17. Why does one use snowshoes in walking over deep snow? 18. Why is it easier to float when swimming in the ocean than in a river ? 19. Why should life preservers be filled with cork instead of hay? 20. A schoolboy in Holland is said to have saved his country from a flood by thrusting his arm into a hole in the dike 150 centimeters below the surface of the sea. Could a small boy hold back the whole North Sea? CHAPTER IV MECHANICS OF GASES Liquids and gases differ in compressibility air compressors uses Boyle's law vacuum pumps uses weight of the air atmospheric pressure measured by Torricelli's experi- ment barometer and its uses pressure gauges lifting effect of air uses in balloons and pumps for liquids other proper- ties of gases absorption and diffusion molecular theory. COMPRESSED AIR 82. Pneumatic machines. Just as hydraulic machines make use of the properties of liquids, so pneumatic machines make use of the properties of gases. Nowadays we often clean our houses with vacuum pumps ; we stop our express trains with air brakes ; we drive the drills and hammers in our shops with compressed air; and we have begun to travel through the air with dirigible balloons and flying machines. To understand the operations of all these machines, we must study the properties of gases. 83. Liquids and gases alike in some respects. Liquids and gases are called fluids, because they have no definite shape, but adapt themselves to the shape of the vessel containing them. A liquid, however, has a definite volume under ordi- nary conditions, filling the lower part of a containing vessel, and being bounded by a free surface above. A gas, on the other hand, has no fixed volume and no free surface, but fills the whole of its containing vessel at once if the vessel is closed, and escapes if the vessel is open at the top. So the little particles of a gas have much more mobility than those of a liquid. 77 78 PRACTICAL ^HYSICS Gases and liquids are alike in that each, when under pres sure, distributes that pressure undiminished in all directions in accordance with the principle of Pascal. The gauges which are used to measure gas pressure are often the same gauges that would be used to measure the pressure exerted by a liquid (see section 75). 84. Air is very compressible. In one respect gases are very different from liquids, namely, in compressibility. This striking difference can be shown in the fol- lowing experiment. When a brass tube, with a closely fitting steel rod (Fig. 77), is filled with air, the steel plunger can be easily pushed down by hand, and when the plunger is released, it springs back nearly to its initial position. If it does not come quite back to its initial position, it means that some of the air has leaked out. The en- trapped air acts like a spring. But when .the tube is filled with water, or any other liquid, it is quite impos- sible to push the plunger down, to any perceptible ex- tent, by hand, and when the end of the plunger is struck with a hammer, the effect is as if the entire tube were a solid steel column, because the liquid is so nearly incom- pressible. FIG. 77. Com- pressibility of fluids. 85. Air compressors. The simplest form of air com- pressor is the ordinary bicycle pump, such as is used to in- nate the tires on bicycles and automobiles. Figure 78 shows a sectional view of such a pump attached to a tire. It consists of a cylinder O and piston P. On the down stroke some air is entrapped below the piston and com- pressed, its pressure rising until it becomes equal to that of the air already in the tire. Then the valve S opens, and FIG. 78. Air compressor. MECHANICS OF GASES 79 during the rest of the down stroke the air is forced into the tire. When the up stroke starts, this valve closes and the leather washer on the piston bends down and allows air to flow past the piston into the cylinder below. Then on the next down stroke this air, entrapped by the spreading of the leather flange, is compressed and forced over into the tire. There is only one valve, and that is in the stem of the tire. Large air compressors driven by steam engines or electric motors are much used in steel plants, shops, and quarries to furnish a supply of compressed air. This is delivered as a forced draft to blast furnaces, or stored in steel tanks and used to drive all sorts of pneumatic machinery. 86. Uses of compressed air. There are many tools which are driven by compressed air, such as riveting hammers for forming the riveted heads on steel work, and the pneumatic tools used in stone cutting, iron chipping, drilling, etc. These are in general lighter and simpler than other portable tools, and there is less danger of fire. When such tools are used in mines, the waste air which they discharge helps to furnish ventilation, and this is often an important advantage. Rock drills, and sand blasts for clean- ing metal and stone surfaces, are other common applications. But perhaps the most interesting ap- plication is the air brake. The essential parts of the Westing- house air brake are shown in figure 79. P is the train pipe leading from a large reservoir on the engine, in which the air is maintained at a pressure of about 75 p IG< 79 _ Westinghouse air pounds per square inch. As long as this brake. 80 PRACTICAL PHYSICS pressure is applied to the automatic valve V there is maintained a com munication between P and an auxiliary tank R under each car, and at the same time air is cut off from the brake cylinder C. But whenever the pressure in P drops, either by the moving of a lever in the engine cab or by the accidental parting of a hose coupling, the valve V shuts off P and connects the reservoir R with the cylinder C. This pressure on the piston in C forces the brakes against the wheels. As soon as the pressure in the pipe is restored, the valve V reestablishes the connection between P and R, and at the same time the air in C escapes. The spring S then releases the brakes by pushing up the piston. 87. How volume of air changes with pressure Boyle's law. In studying about compressed air we are soon con- fronted with the question as to how much the volume of a given quantity of air changes as the pressure changes. This was first investigated for the case where the temperature of the air does not change during compression, by an Irishman, Robert Boyle (1626-1691), and a few years later by a Frenchman, Mariotte. The results of their ex- periments showed that if we start FIG. 80. Compression of with a given volume of air V, subjected to a certain pressure P (Fig. 80), and double the pressure, the volume of air will be reduced to one half. If the pressure be made three times as great, the volume of the air will be reduced to one third, provided the temperature of the air is kept constant. This principle is known as Boyle's law and applies to all gases. It may be stated as follows : The volume of a gas at constant temperature varies inversely as the pressure. This may also be expressed in symbols as P : P 1 : : V : V (notice the inverse proportion), or PV=P'V, where P and P r are the pressures, and V and V the cor- responding volumes of a given quantity of gas, kept at some fixed temperature. MECHANICS OF GASES 81 At very low temperatures or at very high pressures, this law of Boyle and Mariotte does not hold exactly. It should be noticed, however, that the air in a bicycle pump does not stay at the same temperature when com- pressed rapidly, but becomes considerably warmer. The effect of this heating will be discussed in Chapter X. It will then appear that when the air is allowed to get hot, more work has to be done on the pump to produce the same useful result on the tire. The same is true of large com- pressors, and so it is customary to keep the air in them as cool as possible during compression by circulating water through a jacket around the cylinder, or by spraying water into the cylinder. The ideal case is compression at constant temperature, in accordance with Boyle's law, and large com- pressors should come as near to this as is practicable. PROBLEMS NOTE. Assume constant temperature in these problems. 1. One hundred cubic feet of air under a pressure of 15 pounds per square inch is compressed to 300 pounds per square inch. What does the volume become ? 2. The volume of a tank is 2 cubic feet, and it is filled with com- pressed air until the pressure is 2000 pounds per square inch. How many cubic feet of air under a normal pressure of 15 pounds per square inch were forced into the tank ? 3. What is the total force applied to a brake piston 10 inches in diameter, when the pressure is 80 pounds per square inch? 4. One hundred cubic feet of air at a pressure of 15 pounds per square inch are compressed to 36 cubic feet. What is the pressure then? 5. Oxygen is sold in steel tanks under a pressure of 150 pounds per square inch. As the gas is used, the pressure drops. When it has dropped to 50 pounds, what fractional part of the original gas remains? Give your reasoning. 88. Vacuum pumps. We have seen how a bicycle pump can be used to force more air into a given space, and now we shall see how a slight change in the valves will enable us to PRACTICAL PHYSICS suck the air out of a vessel. The first of these so-called " air pumps " was made as long ago as 1650 by a German. Otto von Guericke, then mayor of Magdeburg, who per- formed numerous experiments. For example, he found that a clock in a vacuum cannot be heard to strike; a flame dies out in it ; a bird opens its bill wide, gasps for air, and dies ; fish perish ; and yet grapes can be preserved six months in vacuo. Vacuum pumps used to be found only in physical laboratories, but now they are used so extensively in vacuum cleaners, and in making in- candescent lamps and X-ray bulbs, that they are of great commercial importance. A simple form of mechan- ical vacuum pump is shown in figure 81. It consists of a metal cylinder O fitted with a piston, and having at the lower end two short tubes, A and jB, within which are self- acting conical valves, so arranged that the air enters at A and leaves through B. When the piston is raised, the air in the vessel R, which is to be exhausted, expands into the cylinder O through the valve A. When the piston is pushed down, it compresses this air, closing the valve A and opening the outlet valve B. Thus with each double stroke a certain fraction of the air in the vessel R is removed. It will be seen that even with a mechanically perfect pump we never take out quite all the air ; for by each stroke we remove only a certain fraction of the air, and the remainder expands to fill the vessel. In practice, no pump is perfect because of leakage. To reduce this, it is common, in "high vacuum" pumps, to cover the piston arid the valves with oil, and in some forms made of glass the piston is replaced by a column of mercury. FIG. 81. Vacuum pump. MECHANICS OF GASES 83 89. Applications of the vacuum pump. Vacuum cleaning (Fig. 82) is an application of the force of suction, created by a vacuum, to the cleansing of buildings and their furnishings. Some vacuum cleaners are portable and some are stationary, some are operated by hand and some by an electric motor, some tend to produce a vacuum by a pump and some by a rotating fan, but the general prin- ciple is the same in all. The problem of getting the air out of incandescent lamp bulbs is quite dif- ferent from that of vacuum cleaning, in that we have a very limited space to be exhausted and this must be very completely pumped out. Usually less than one millionth part of the air is left in the bulb. For this purpose two mechanical pumps are worked in tandem, one to take air directly from the bulb, and the other to take it from the cylinder of the first pump. After these have done their work, the air remaining is still further reduced by burning phosphorus or some other com- bustible in the bulb. X-ray tubes are made in much the same way, except that the process must be continued longer so as to produce a still more rarified condition of the air. WEIGHT OF THE AIR 90. Density of air. We are so accustomed to having air about us that we do not ordinarily think of it as having either volume or weight. We speak of an " empty " bottle when we usually mean a bottle filled with air. Yet when we try to fill a narrow-necked bottle with a liquid, we find that we can make the liquid run in only as fast as the air gets out. If we push a glass tumbler mouth down into a FIG. 82. Vacuum cleaner. 84 PRACTICAL PHYSICS pail of water, it is not filled with water, because it is filled with air. Air occupies space just as does any other fluid. Furthermore, air and other gases have weight, although we seldom realize this fact. In order to make it evident that air has weight, let us try the follow- ing experiments. Suppose we care- fully counterbalance on the scales (Fig. 83) a hollow metal vessel (a tin can with a bicycle valve soldered into the top will serve). Then if we pump more air into the vessel and FIG. 83. Proof that air has weight, put it on the scales again, we find that it has gained in weight. If we repeat the process, we find that it weighs a little more after each pumping. In the same way if we take a vessel from which the air has already been exhausted, such as an electric light bulb, carefully counterbalance it, and then let the air in by filing off the tip, we find that the scalepan containing the bulb and the broken pieces goes down, showing that the air which has entered has weight. Careful experiments show that under ordinary conditions a liter of air weighs about 1.3 grams, or 1 cubic foot weighs about 1.3 ounces. Since gases have both volume and weight, we may express their densities in the usual way, as so many grams per cubic centimeter or so many^ pounds per cubic foot. For example, the density of ordinary air is about 0.0013 grains per cubic centimeter, or 0.08 pounds per cubic foot. Many gases have densities even smaller than that of air. Thus the density of hydrogen under standard conditions is only 0.000090 grams per cubic centimeter. Evidently if the pressure on a certain volume of air is doubled, the volume is halved, and the air becomes twice as dense. In other words, the density of air or of any gas, varies directly as the pressure at constant temperature. MECHANICS OF GASES 85 PROBLEMS 1. If a liter of air weighs 1.3 grams, how much does the air in a room weigh, if the room is 3 meters high, 10 meters long, and 8 meters wide? 2. If the pressure in a compressed-air tank is 150 pounds per square inch, what does 1 cubic foot of this compressed air weigh ? (1 cubic foot under a pressure of 15 pounds weighs 1.3 ounces.) 3. A spherical balloon 10 meters in diameter is filled with hydrogen. Find the weight of the hydrogen. 4. A bicycle tire has about the same volume as a cylinder 85 inches long and 1 inch in diameter. If you pump your tires up from 15 pounds to 75 pounds per square inch, how much more will the bicycle weigh than before? 5. A compression pump, whose capacity is 500 cubic centimeters, is used to force air into a can whose volume is 1 liter. What is the density of the air after 3 complete strokes? 6. A vacuum pump, whose capacity is 500 cubic centimeters, is used to exhaust the air from a liter flask. What is the density of the air left in the flask after 3 complete strokes? 91. Pressure of the atmosphere. Since we are living at the bottom of an ocean of air, and this air is a fluid which has weight, it is natural to expect that it exerts a pressure. Ordinarily we are not aware of this pressure because it pushes up on the bottoms of objects almost as much as it pushes down on the tops of them. If we could get rid of this upward pressure underneath, we would see how great the downward pressure on top really is. . This can be done with a vacuum pump, or in part even with the lungs. Let us fasten a piece of sheet rub- ber over the end of a thistle tube, as shown in figure 84. If we suck the air out of the bulb with the mouth, the rubber is forced downward be- FlG 84._ RemoviDg the upward cause of the atmospheric pressure. pressure of the air. This experiment is even more strik- ing when performed with a larger membrane and with a vacuum pump. If we tie a piece of rubber over the mouth of the glass vessel shown in 86 PRACTICAL PHYSICS figure 85, and gradually pump out the air, the rubber will be pushed down more and more by the pressure of the air above it, until it finally bursts. If a piece of bladder is used instead of rubber, it will break with a loud report. FIG. 85. Air pressure breaking a membrane. FIG. 86. Fountain in vacuo, If we pump the air out of a tall glass vessel provided with a stopcock and jet tube, and then place the mouth of the jet tube under water and open the stopcock, we see the water rushing up into the vacuum like a fountain. How can we determine how much air was removed ? One of the most interesting of Otto von Guericke's experi- ments was that with his famous "Magdeburg hemispheres." These were two hollow "hemispheres a little over a foot in diameter which fitted together so well that the air could be pumped out from between them. The pressure of the sur- rounding atmosphere then held them together firmly. In a test before the Reichstag and the Emperor, it required six- teen horses, four pairs on each hemisphere, to pull them apart. 92. "Nature abhors a vacuum." The ancients tried to explain many phenomena by saying that "nature abhors a vacuum," but when the great Italian philosopher, Galileo (1564-1642), found that a suction pump would not raise MECHANICS OF GASES 87 water more than 33 feet, he remarked that nature's horror of a vacuum was a curious emotion if it stopped suddenly at 33 feet. He already knew both that air has weight and that the " resistance to a vacuum " was measured by a column of water about 33 feet high, yet he left it to his friend and successor, Torricelli (1608-1647), to unite these two ideas. 93. Torricelli's experiment. Torricelli devised a means of measuring this 4 ' resistance" which nature "offers to a vacuum" by a column of mercury in a glass tube instead of a column of water. We may repeat this experiment if we take a stout glass tube about 3 feet long, closed at one end, and fill it completely with mercury. If we close the opening with the finger, invert the tube, and put its open end into a tumbler of mer- cury, we observe that, when the finger is removed, the mercury in the tube (Fig. 87) sinks to a level about 30 inches above the mercury surface in the tumbler. If we incline the tube to one side, the metal fills the entire tube and hits the top of the glass with a sharp click. The space above the mercury is empty except for a minute quan- tity of mercury vapor. It is, indeed, the most perfect vacuum that we know how to make. FIG. 87. Torricelli's experiment. The column of mercury in the tube just balances the pressure of the atmos- phere on the mercury in the larger vessel at the bottom. In other words, liquids rise in exhausted tubes because of the pressure exerted by the atmosphere on the surface of the liquid outside, and not because of any mysterious sucking power created by the vacuum. 94. How to calculate the pressure of the atmosphere. From the law that pressure in a heavy liquid is everywhere the same at the same depth, we know that the pressure on the mercury in the dish (Fig. 88) is the same at a as outside. 88 PRACTICAL PHYSICS Vacuum FIG. 88. Mercury column supported by air. Outside this pressure is exerted by the atmosphere. At a it is exerted by the column of mercury ab. Under standard conditions, the pressure at a, that is, the force per square centimeter, is evidently equal to the weight of a column of mer- cury 76 centimeters high and 1 square cen- timeter in cross section. This is the weight of 76 cubic centimeters of mercury, or 76 times 13.6 grams, or 1034 grams. In the English system it is the weight of a column of mercury about 30 inches high and 1 square inch in cross section ; that is, 30 x 0.49, or 14.7 pounds. Roughly, then, one " atmosphere " is about 1 kilogram per square, centimeter or about 15 pounds per square inch. 95. Pascal's experiments. Pascal reasoned that if the mercury column was held up simply by the pressure of the air, the column ought to be shorter at a high altitude. So he carried a Torricelli tube to the top of a high tower in Paris, and found a slight fall in the height of the mercury column. Desiring more de- cisive results, he wrote to his brother-in-law to try the experiment on the Puy de Ddme, a high mountain in southern France. In an ascent of 1000 meters, the mercury sank about 8 centimeters, which greatly delighted and as- tonished them both. Pascal also tried Torricelli's experiment, using red wine and a glass tube 46 feet long, and found that with a lighter liquid a much higher column was sustained by the pressure of the air. These experiments were carried out in 1648, five years after Torricelli's discovery. 96. The barometer. The arrangement constructed by Torricelli may be set up permanently as a means of measur- ing the pressure of the atmosphere. It is then called a MECHANICS OF GASES 89 barometer. To " read the barometer " means simply to meas- ure accurately the height of the mercury column above the surface of the liquid in the reservoir. In the form of barometer shown in figure 89 this reservoir has a flexible bottom which may be raised or lowered so as to bring the surface of the mercury to the zero point of the scale which is at the tip of a point pro- jecting into the reservoir. The height of the mercury is then read by observing the position of the liquid in the tube. A more convenient form to carry about is the aneroid or metallic barometer (Fig. 90). As the name indicates, it is "without liquid" and consists essentially of a disk- shaped metal box, which has a thin corru- gated metal top. When the air has been pumped out of the box, it is sealed up, its top being supported by a stout spring to prevent its collapsing. As the pressure of the air changes, the top of the box moves up or down, and the small motion is greatly magnified by means of levers and a delicate chain, and is communicated to a pointer which moves over a scale. A hairspring serves to take up the slack of the chain. The scale is grad- uated to corre- spond to the read- ings of a standard mercurial barom- eter. Aneroid barometers are made in various sizes. Some are even as small as FIG. 90. - Aneroid barometer. Ordinary watches. FIG. 89. Mercu- rial barometer. 90 PRACTICAL PHYSICS 97. Uses of the barometer. The barometer indicates changes in atmospheric pressure. These changes may be due to fluc- tuations in the atmosphere itself or to changes in the elevation of the observer. If a barometer, kept always at the same eleva- tion, is frequently observed, or if it makes a continuous record, as does a barograph (Fig. 91), it is found to FIG. 91. Barograph, or self-recording ;; barometer. fluctuate according to the weather. Experience shows that a " falling barometer," that is, a sudden decrease of atmospheric pressure, precedes a storm ; and a " rising barometer," that is, an increasing atmos- pheric pressure, indi- cates the approach of fair weather; while a steady " high barom- eter" means settled fair weather. The Weather Bureau has barometric readings taken simultaneously at many different places, and the results are tele- graphed to central sta- tions, where weather maps are prepared. On these maps it is observed FIG. 92. Portion of a weather map. that there are certain broad areas where the pressure is low, other sections where the pressure is high. The areas of MECHANICS OF GASES 91 low barometric pressure are usually storm centers, which move in a general easterly direction. If we know where these low pressure areas are located and their probable movement, we may predict the weather. Figure 92 shows a portion of a government weather map. The curved lines, showing the places where the barometric pressure is equal, are called isobars. The direction of the wind at places of observation is indicated by an arrow, and it will be noticed that these arrows usually point from a u high" to a "low." A careful study of these phenomena (which is called mete- orology) shows that these " lows " are really great eddies of air slowly moving in a counterclockwise direction about the center of the low. Another important use of the barometer is to measure the difference in altitude of two places. If a surveyor or explorer carries a barometer up a mountain, he notices that it indi- cates a decrease in atmospheric pressure as he ascends. For places not far above sea level this decrease is about 1 milli- meter for every 11 meters of elevation or 0.1 of an inch for every 90 feet of ascent. Aneroid barometers graduated in feet or meters are always carried by balloonists and aviators to tell how high they are. 98. Pressure gauges. Besides barometers, which are really pressure gauges designed for pressures of one atmosphere or less, we need gauges for higher pressures such as those in a steam boiler, or a compressed-air tank, and gauges for very low pressures, such as those in the condenser of a steam engine or a vacuum pump. To measure slight diff erences in pressure, the open manometer, described in section 75, is used, usually with some liquid lighter than mercury as the indicating fluid. If we bend a piece of glass tubing as shown in figure 93, and partly fill the tube with colored water, we have a suitable gauge to measure the pressure of ordinary illuminating gas, which will usually cause a differ- ence in levels, A, B, of about 2 inches. 92 PRACTICAL PHYSICS For high pressures this form of gauge, even when filled with mercury, becomes too cumbersome, so a closed manometer, like that shown in figure 94, is used. The mercury stands at the same level in both arms, when the pressure is one atmosphere. If the pressure is greater than this, the mercury is forced into the closed arm, com- pressing the confined air according to Boyle's law. The scale may be made to read in atmospheres. For practical work, the Bourdon spring gauge, described in section 75, is used. Such gauges are usually graduated so as to read zero when the pressure is really one atmos- phere ; that is, they indicate the difference between the given pressure and atmos- pheric pressure. Therefore when an engi- FIG. 93. Open ma- neer speaks of a pressure of 100 pounds " by the gauge," he means 100 pounds per square inch above one atmosphere ; when he means the total pressure above a vacuum, he usually says " 100 pounds absolute." When pressures less than one atmos- phere are to be measured, such as the vacuum in the condenser of a steam en- gine (section 219), a barometer of the ordinary form would be inconvenient because the whole reservoir or cup at the bottom would have to be exposed to the pressure to be measured. The gauge is, therefore, arranged so as to admit the low pressure to be measured to the top of the barometer tube. The height of the mercury then indicates the difference between the small pressure and that of the atmosphere. The better FIG. 94. Closed* manom- eter. MECHANICS OF GASES 93 the vacuum, the higher such a gauge reads. Thus engi- neers usually speak of a 26 or a 28 inch vacuum, meaning a pressure less than the standard 30 inch atmosphere, by 26 or 28 inches of mercury. The best vacuums now obtained steam turbine condensers are from 29 to 29.5 inches. in Since these mercury gauges would be inconvenient in engine houses, Bourdon gauges are used. They are graduated to read in inches like the mercury gauges which they replace. PROBLEMS To how Kerosene 1. A diver works 51 feet below the surface of the water, many atmospheres of pressure is he subjected ? 2. When the barometer reads 74.5 centimeters, how many inches does it read? 3. When a mercury barometer reads 76 centimeters, what would a glycerine barometer read ? (The density of ^ ^ glycerine is 1.26 grams per cubic centimeter.) 4. When the barometer reads 75 centi- meters, what is the atmospheric pressure in grams per square centimeter? 5. During a storm the barometer "dropped" 1.5 inches. How far would a water barometer have fallen ? 6. If a certain pressure is 75 pounds per square inch, how many kilograms per square centimeter is it ? 7. During a mountain climb the barom- eter falls 1.75 inches. What is the net height climbed (in feet) ? 8. Two glass tubes are arranged verti- cally (Fig. 95) so that their lower ends dip into water and kerosene, respectively, while their upper ends are joined to a mouthpiece. When some of the air in the tubes is sucked out, the water rises 26 centimeters and the kerosene 33 centimeters. Find the specific gravity of the kerosene. (This is a common way of getting specific gravity.) 9. How much force is exerted against an 8-inch piston of an ah brake when the pressure is 90 pounds " by the gauge " ? Water FIG. 95. Specific gravity by balanced columns. 94 PRACTICAL PHYSICS 10. The original Magdeburg hemispheres are' preserved in a mu- seum at Munich. They are about 1.2 feet in diameter inside. When the air was exhausted, it is said to have required 8 horses on each half to separate them. Assuming that the pressure of the atmosphere was 15 pounds per square inch, find the force exerted by each set of horses. (Reckon pressure on circle 1.2 feet in diameter. Why?) 99. The lifting effect of air. We have seen that when one climbs a mountain, the pressure of the air decreases. A sen- sitive barometer will indicate this decrease of pressure even when it is lifted from the floor to a table. Therefore the up- ward pressure of the air on the bottom of any object is slightly more than the downward pressure of the air on the top. In other words, just as in the case of liquids, there is a lifting effect on everything surrounded- by air, and this lifting effect is equal to the weight of the air which is displaced. To make this principle of the buoy- ancy of the air seem more real, let us balance a hollow brass globe against a solid piece of brass under the receiver of a vacuum pump (Fig. 96). When the air is pumped out, the globe seems to be heavier than the solid brass weight, be- cause the support of the air around it has been withdrawn. If the air is re- admitted rapidly, the rise of the globe FIG. 96. Lifting effect of air. will be very apparent. Most things are so heavy in comparison with the amount of air they displace that this loss in weight, due to the buoyancy of the air, is not taken into account. For example, a barrel of flour would weigh about 8 ounces more in vacua than in air. But if the volume of air displaced is very large and the weight small, as in the case of a balloon, the object is lifted just as a piece of wood is lifted when immersed in water. A balloon is usually made of cloth which is treated with a special varnish to make it as nearly gas-tight as possible, MECHANICS OF GASES 95 FIG. 97. A dirigible balloon. and is surrounded by a network of ropes and cords to hold up the car and its load. The bag is filled with hydrogen, which, volume for volume, is only one fourteenth as heavy as air. Sometimes, for short trips, illuminating gas, or even hot air is used. Of course a large part of the lifting force is used in raising the car, the rigging of the balloon, and the silk of which the bag is made. The rest is available for lifting passengers and ballast. To compute the lifting force of a balloon we have only to get the difference between the weight of the air dis- placed and the weight of the hydrogen, gas, or hot air. The dirigible balloon (Fig. 97) is provided with propellers driven by gas engines, and rudders to steer with. But the bag has to be made so large to support the weight of all this machinery, that the balloon is much at the mercy of the wind. 100. Pumps for liquids. The ancients used pumps to lift water from wells, even though they did not know why a pump works ; they thought it was because " na- ture abhors a vacuum." We know now that the underlying principle is the same as in a mercurial barometer : it is the pressure of the atmosphere on the surface of the water in the well that pushes the water up into the pump. For example, let us consider the ordi- nary suction pump shown in figure 98. This consists of a cylinder (7, which is connected with the well or cistern by a pipe T. At the bottom of the cylinder is FIG. 98. A suction J pump. a clapper valve o, opening up. A piston 96 PRACTICAL PHYSICS P can be worked up and down in the cylinder by means of a handle. This piston also contains a valve opening up. On the up stroke of the piston P, the valve V remains closed because of its weight and the pressure of the air upon it. Between the piston and the bottom of the cylinder there would be a partial vacuum if the valve S remained closed. But the pressure of the air on the water in the well forces some water up through the pipe T, past the valve S into the cylinder (7. On the down stroke of the piston the valve S closes, the valve V opens, and the water gets above the piston. On the next up stroke it is lifted out through the spout. The valve S must never be more than 34 feet above the water in the well, and in practice this distance is seldom more than 30 feet. Why? Another kind of pump, shown in figure 99, is called a force pump. The suction pipe T with its valve S are exactly like the correspond- ing parts of the house pump just described, but the piston has no opening through it, and the outlet pipe and a second valve are at the bottom of the cylinder. Rais- ing the piston fills the cylinder with water ; pushing it down again forces the water out through the second pipe. If enough force is exerted on the piston, the water can be pushed up to a considerable height. The pump can therefore be located near the bottom of a well or mine shaft. Since the water is forced up only on the down stroke, it comes in jerks. To reduce the jar and shock, an air chamber FIG. 99, A force pump. MECHANICS OF GASES 97 ivery A is connected with the delivery pipe, so that the air may act as a cushion or spring. Power pumps, such as are used on fire engines, or in city waterworks, are " double acting " (Fig. 100), which gives a still steadier stream. When a large volume of water is to be lifted a short distance, a cen- trifugal pump (Fig. 101) is used. This is something like a water wheel worked backwards. As the wheel in- side (Fig. 102) is turned, the water, which enters near the hub, gets caught between the blades and is hurled outward into the delivery space around the wheel, even against some pressure there. Similar ma- chines, called " blowers," are used to FlG - m '~ A double-acting . ,, , , .,, force pump. force a current of air through a build- ing for ventilation, or to make " f 6rced draft," for furnaces. Often several of these pumps are used in series to give higher pressures. Large tur- bine pumps of this sort, driven by steam turbines, have recently begun to revolutionize blast furnace practice in the United States, FIG. 101. -Centrifugal pump. because of the extremely steady rate at which they furnish the air needed for combustion. Another form of pump is the " air-lift " pump (Fig. 103). Its action depends upon the formation of a column of . \ , 7.1.1 i. FlG - 102 - Section of cen* mixed water and aw which, because of trifugai pump. 98 PRACTICAL PHYSICS JVatcr its lesser specific gravity, is raised by a shorter column of water. Such a pump will lift water mixed with air as much compressed as 40 feet above the level of the water. It con- sists of two tubes, the smaller of which is centered within the larger. The smaller pipe conveys compressed air down into the water to be lifted. The mixture of water and air rises through the outer tube. This sort of pump is cheap to make, is simple in its operation, and has no wearing parts ; but its efficiency is low. It would be especially useful in an artesian or oil well if the water or oil naturally stands too far below the surface to be reached by a suction pump and if the well is so small that a force pump cannot be put down into- it. 101. Siphon. The siphon is a bent tube with unequal arms. It is used to empty bottles and tanks which cannot be overturned, or to draw off the liquid from a vessel without disturbing the sedi- ment at the bottom. If the tube is filled and placed in the position shown in figure 104, the liquid will flow out of the vessel A and be discharged at a lower level D. The force which makes it flow is the weight of the column of water <7Z), which is between the water level A A' and the water level DD f . If the water level DD f is raised to AA 1 ', this moving force becomes nothing and the water ceases to flow ; if the level DD f is lifted above AA' , the liquid flows back into the vessel A. A siphon works, then, as long as the free surface of the liquid in one vessel is lower than the free surface of FIG. 103. Air- lift pump. FIG. 104. A siphon. MECHANICS OF GASES 99 the liquid in the other vessel. A water siphon will not work if the top of the bend B is more than 34 feet above the level^'. Why? Siphons are often used on a large scale in engineering. For instance, in power plants the water used to condense the steam is often taken from the ocean, raised 10 or 15 feet to the condenser, and carried back to the ocean, through a pipe that is everywhere air-tight and acts like a siphon. The only work that the pumps have to do is to keep the water moving against the friction in the pipe. A large inverted siphon is used at Storm King on the Hudson River, to carry the water supply of New York City under the river, some 700 feet below its surface. The lifting of the water on one side is done by the water descending from a slightly greater height on the other. Siphons on a smaller scale are used in every aqueduct to carry water over hills or across valleys. In such cases air bubbles carried along in the water tend to collect at the top of every hill, and so small air pumps have to be installed to keep the pipes full of water. PROBLEMS 1. How many feet could water be lifted with a perfect suction pump (a) at sea level, and (6) in Denver, Col. (altitude about 5000 ft.) ? 2. How many feet could crude oil (density 0.89 grams per cubic centi- meter) be lifted out of an oil well by a perfect suction pump at sea level ? 3. How much work is needed to lift 100 gallons of water 25 feet with a perfect pump ? 4. How much power is needed to raise 100 gallons of water per minute 25 feet with a perfect pump? 5. A force pump is to deliver water at a point 20 feet above the level of its barrel. How great is the water pressure in the barrel when the piston is descending ? 6. The piston of a fire-engine force pump is 4 inches in diameter, and the total force exerted on it by the engine is 600 pounds. If the pump acts perfectly, at how great a height will it deliver water ? 7. A siphon is to be used to transfer mercury from one bottle to another. How far above the level of the mercury in the higher bottle can the top of the siphon tube be? 100 PRACTICAL PHYSICS OTHER LESS IMPORTANT PROPERTIES OF GASES 102. Absorption of gases in liquids. If we slowly heat a beakei containing cold water, small bubbles of air will be seen to collect in great numbers upon the walls (Fig. 105) and to rise through the liquid to the surface. It might seem at first that these are bubbles of steam, but they must be bubbles of air, first because they are formed at a temperature below the boiling point of water, and second because they do not condense .as they come to the cooler layers of water above. This simple experiment shows that ordinary water contains dissolved air, and that the amount of air which water can hold decreases FIG. 105. Bub- as th e temperature rises. It is the oxygen of bies of air in the air that is dissolved in water which sup- ports the life of fish. The amount of gas ab- sorbed by a liquid depends on the pressure of the gas above the liquid. Thus soda water is oidinary water which has been made to absorb large quantities of carbon dioxide gas by pressure. When the pressure is relieved, the gas escapes in bubbles, causing effervescence. Careful experi- ments show that the amount of gas absorbed is proportional to the pressure. The amount of gas which will be absorbed by water varies greatly with the nature of the gas. For example, at C. and at a gas pressure of 76 centimeters of mercury, 1 cubic centimeter of water will absorb 0.049 cubic centimeters of oxygen, 1.71 cubic centimeters of carbon di- oxide, and 1300 cubic centimeters of ammonia gas. The ordinary commercial aqua ammonia is simply ammonia gas dissolved in water. 103. Absorption of gases in solids. Certain porous solids, such as charcoal, meerschaum, silk, etc., have a great capacity for absorbing gases. For example, charcoal will absorb 90 times its volume of ammonia gas and 35 volumes of carbon dioxide. It is this property of charcoal which makes it use- MECHANICS OF GASES 101 ful as a deodorizer. This absorption seems to be due to the condensation of a layer of gas on the surface of the body or of the pores within the body. Platinum in a spongy state absorbs hydrogen gas so powerfully that if a small piece is placed in an escaping jet of hydrogen, the heat developed by the condensation is enough to ignite the jet. This has been made use of in self-lighting Welsbach mantles. A familiar example of the absorption of gases by liquids and solids is the contamination of milk and butter by onions, fish, or other kinds of food, if they are kept in the same com- partment of a refrigerator. Onions, for instance, give off a small quantity of gas which we can easily detect by our sense of smell, or by the watering of our eyes. This gas, when absorbed by milk or butter, affects its taste. 104. Diffusion of gases. One of the difficulties in the suc- cessful construction of balloons is due to the diffusion of the gas through the bag. The diffusion of hydrogen through a porous cup is shown in the following experiment. If we set up a porous cup with a stopper and glass tube, as shown in figure 106, and allow hydrogen (or illuminating gas) to fill the jar which surrounds the porous cup, we observe bubbles rising from the end of the glass tube, which dips underwater. This means that the gas is going through the porous walls of the cup and forcing the air out at the bottom. If we now shut off the gas and remove the jar, we presently see the water slowly rising in the tube, which shows that the gas inside the cup is going out. FIG. 106. Diffusion of hydrogen through porous cup. The fact that a little ammonia (or any other gas with a powerful odor) introduced into a room is soon perceptible in every part of the room shows that the gas particles travel quickly across the room. Moreover, this mixing of gases goes on whatever 102 PRACTICAL PHYSICS the relative densities of the gases, so that a heavy gas like carbon dioxide and a light gas like hydrogen will not re- main in layers like mercury and water, but will quickly diffuse and become a homogeneous mixture. Experiments show that the smaller the density of the gas, the greater the velocity of its diffusion. 105. Molecular theory of gases. To explain the pressure of gases and their diffusion, it is now generally supposed that all substances are made of very minute particles called molecules. These molecules are so minute that we cannot see them even with the most powerful microscopes. In one cubic centimeter of a gas there are probably not less than 10 19 (that is, 1 followed by nineteen ciphers) molecules. The spaces between these molecules are supposed to be much larger than the molecules themselves. This explains why gases are so easily compressed and diffuse so quickly. Then, too, these little particles are supposed to be flying about in all directions with great velocity. They are sup- posed to travel in straight lines except when they hit each other and bounce off. Gas molecules seem to have no inher- ent tendency to stay in one place, as do the molecules of solids. This explains why gases fill the whole interior of a contain- ing vessel. This also explains gas pressures, for the blows which the innumerable molecules of a gas strike against the surrounding walls constitute a continuous force tending to push out these walls. When a gas is compressed to half its volume, the pressure is doubled, because doubling the density doubles the number of blows struck per second against the walls. It has even been possible to calculate the molecular velocity necessary to produce this outward pressure. It ap- pears that the molecules of gases under ordinary conditions are traveling at speeds between 1 and 7 miles per second. The speed of a cannon ball is seldom greater than one half a mile per second. This, in brief, is the so-called kinetic theory of gases. MECHANICS OF GASES 103 SUMMARY OF PRINCIPLES IN CHAPTER IV Pascal's Law of Transmission of Pressure : For gases under pressure, the pressure is everywhere the same ; the force varies as the area. Boyle's Law : Volume of gas at constant temperature varies inversely as pressure. Density of a gas varies directly as pressure. Lifting effect of air is equal to weight of air displaced. Atmospheric pressure equal to about 30 inches of mercury, 34 feet of water, 15 pounds per square inch, 1 kilogram per square centimeter. QUESTIONS 1. Why can Torricelli's experiment be performed as well indoors as outdoors ? 2. How and why can a glass of water be inverted with the aid of a card without spilling the water ? 3. Why does a rubber tube often collapse when connected with a vacuum pump? Why does not a rubber tube always collapse when con- nected with a vacuum pump? 4. Why must a mercurial barometer be hung in a vertical position ? 5. What would be the result of putting a mercurial barometer under a tall bell glass on an air pump ? 6. Would a siphon work in a vacuum ? 7. What would be the effect of lengthening the long arm of a si- phon ? 8. A boat lying on a beach is full of water. How could you empty it with the help of a suitable length of rubber hose ? Could you use the same method to get the bilge water out. of a boat floating in the water ? 9. Why are not barometers filled with water ? 10. What advantage has a pneumatic automobile tire over a solid tire of the same size ? 104 PRACTICAL PHYSICS 11. How can a balloon be made to sink or rise ? 12. Why does a man under water in a diving suit have to be sup- plied with compressed air? 13. Explain why the liquid does not run out of a medicine dropper. 14. Explain the action of a so-called "pneu- matic " inkstand (Fig. 107), or of a drinking foun- tain (Fig. 108), or of a poultry fountain (Fig. 109). 15. A man finds that cider does not flow out of a barrel until he removes the bung. Explain. 16. A vessel 1 meter deep is filled with mercury. Can it be entirely emptied by means of a siphon? 17. Why does a chemist usually reduce the vol- umes of gases to standard pressure, that is, 76 centimeters? 18. What advantages has compressed air over electricity for the transmission of power? 19. If the area of a man's body is 20 square feet, what is the total force exerted on him by the atmosphere? Why is he not crushed by this force ? 20. What facts indicate that the atmosphere be- comes rarer and rarer as one rises above sea level ? 21. In building tunnels workmen usually have to work in chambers filled with compressed air. Why is this necessary ? 22. Get the dimensions and weights of some of the large balloons used in international races, and compute their lifting power. Estimate the amount of ballast that can be carried in addition to the weight of the balloon, car, and passengers. 23. How does a gas meter work ? 24. Would it make any difference in the gas bill if the meter were in the attic instead of in the cellar? In apartment houses with separate meters for each apartment, do the people on the top floor get more or less gas for their money? FIG. 108. Drinking fountain. FIG. 109. Poultry foun- tain. CHAPTER V NON-PARALLEL FORCES Representation of forces by arrows the parallelogram of forces composition and resolution of forces application to roof truss, friction, sailboat, and aeroplane. 106. Three forces acting at a point. In machines and other contrivances it often happens that forces which are not par- allel balance each other and are thus in equilibrium. For example, suppose a street lamp is suspended over a A street by a wire stretched between two posts, as shown in figure 110. We have here three non- parallel forces in equilib- rium first, the verti- cal pull OW due to the weight of the lamp; sec- ond, the pull exerted by one of the ropes ; arid third, the pull exerted by the other rope. We are to find what relation must exist between the magnitude and direction of any three such forces, if they are to produce equilibrium. 107. Representation of forces by arrows. It will help us to form a mental picture of these three forces if we represent them by three arrows. The direction of each force will be indicated by the direction of the arrow, the point of applica- tion by the tail of the arrow, and the magnitude of the force by the length of the arrow, drawn to some convenient scale. 105 FIG. 110. Three non-parallel forces. 106 PRACTICAL PHYSICS Thus in figure 111 we have an arrow 5 units long, and if we assume that each unit represents 10 pounds, the arrow AB , , . , , v shows a force of 50 pounds applied at A, acting due east. Figure 112 represents FIG. 111.- A force of 50 t f QA f 3Q poundg ti pounds acting east. due east applied at 0, and the other OB of 40 pounds, acting due north, applied at the same point 0. If these two forces act simultaneously upon the body at 0, the result will be the same as if a single force were applied, acting somewhere between OA and OB, but nearer the greater force OB. This single force, which produces the same result as two forces, OB and OA, is called their resultant. 108. Principle of parallelogram of forces. If a parallelogram is constructed on OA and OB, the diagonal 00 represents the resultant, as can be proved by the following experi- ment. Suppose we hang two spring balances A and B from two nails in the molding at the top of the blackboard, as shown in figure 113, and tie some known weight W near the middle of a string joining the hooks of the two balances. If we draw lines on the blackboard behind each of the three strings, we shall have represented the direction of each of the three forces. Then, if we note the tension in each string as shown by the amount of the weight W and the readings of the spring balances A and B, we may remove the apparatus and FIG. 113. Experiment to illustrate paral- complete the diagram. Choos- lelogram law. ing some convenient scale, we NON-PARALLEL FORCES 107 measure off on OA a distance corresponding to the tension in OA, and place an arrowhead at X , and in the same way we locate Y on OB. Then we construct a parallelogram on OX and OF by drawing XR parallel to OF and YR parallel to OX. It will be evident that the diagonal OR is the resultant of OX and OF, for if we measure OR and determine its magnitude from our scale of force, we find that this resultant OR is almost exactly. equal and opposite to the third force OW. That is, either OR, or OX and OF, balances OW. The force necessary to balance or hold in equilibrium two forces is called the equilibrant. Thus in the case just de- scribed, the force OWis the equilibrant of the two forces OX and OY. The resultant of two forces acting at any angle may be rep- resented by the diagonal of a parallelogram constructed on two arrows representing the two forces. When three forces are in equilibrium, the resultant of any two of the forces is equal and opposite to the third, which can be regarded as their equilibrant. 109. Resultant depends on the angle between components. To determine the resultant of two or more forces, we must know not only the magnitude of the " components," but also the angle between them. This will be made clear by study- ing the same two forces at different angles, as in figure 114. It will be seen that the resultant OR gradually increases as O 4. " O (c) (d) (e) FIG. 114. Two forces at varying angles. the angle between the components OA and OB decreases. For example, if the angle is 180 (case (a)), the forces OA and OB are opposite and the resultant is the difference be- tween the forces, 4 3, or 1, and acts in the direction of the greater force, i.e. toward the right. As the angle gradually decreases the resultant OR increases, until, when the angle is 108 PBACTICAL PHYSICS (case (e)), the forces OA and OB are acting in the same straight line and in the same direction, and the resultant is the sum of the two forces, 4 + 3, or 7. When the forces are at right angles (case (bythe "fatigue" of metals (see encyclopedia). 10. What advantages has reenforced concrete over ordinary concrete for building purposes? 11. How are the walls of high office buildings supported, and why V , , CHAPTER VII ACCELERATED MOTION Speed and acceleration laws of motion at constant accel- eration falling is motion at constant acceleration value of acceleration of gravity. 129. Average speed. If a man walks 12 miles in 3 hours, we say that he averages 4 miles an hour. To be sure, at any particular point on his journey he may have been going faster or slower, but his average speed or velocity is 4 miles an hour. If we know that the average speed of a steamer is 22 miles an hour, we can find a day's run by multiplying the average speed by the number of hours in a day; thus 22 x 24 = 528 miles. In general, Distance = average speed x time. Speed is expressed in various ways; for example, we say that an automobile travels at the rate of 25 miles an hour, a steamer does 18 knots or 18 nautical miles an hour, a sprinter runs 100 yards in 10 seconds, and a rifle ball goes 2000 feet per second. For purposes of comparison it is convenient to have some uniform way of expressing speed, and so engineers and other scientific men have come to use feet per second (ft. /sec.) or centimeters (or meters) per second (cm. /sec. or m./sec.). The following table gives some average speeds: TABLE OF SPEEDS Soldiers marching 4.3 ft./sec. = 1.4 m./sec. Horse galloping 16 ft./sec. = 5.2 m./sec. Ocean steamer 40 ft./sec. = 12.2 m./sec. Express train 82 ft./sec. = 26.9 m./sec. Wind in hurricane 165 ft./sec. = 54.2 m./sec. Sound 1120 ft./sec. = 386 m./sec. Rifle hall 1500 to 2000 ft./sec. = 493 to 657 m./sec. 133 134 PRACTICAL PHYSICS QUESTIONS AND PROBLEMS 1. Sixty miles an hour equals how many feet per second ? You would do well to remember this number. 2. With the help of a time-table, compute the average speed of an express train, and of a local. 3. If the distance across the Atlantic Ocean is about 3000 miles, how many days will it take a steamer to cross, at the speed given in the table above ? 4. An officer on horseback starts on the gallop to overtake his regiment a mile away, which is marching ahead. If they travel at the speeds given in the table, how long will it take him? 5. How long will it take an express train to cover 50 miles, going at the rate given in the table ? 6. A rifle is fired at a target half a mile away. How long after it is fired does the sound it makes against the target reach the man with the rifle? 7. There is a common rule that if any one in a train counts for 19 seconds the number of .clicks as the car passes over the ends of the rails, the number he gets will be the speed of the train in miles per hour. What must be the length of the rails to make this rule work ? 130. Variable speed. When a train is starting out from a station, it is gaining speed, and when it is approaching a station where it must stop, it is losing speed. So we see that on account of stops and differences in grade, the speed of a train is not uniform or constant, but is changing or variable. When a loaded sled starts at the top of a long hill, it gains in speed as it descends the hill ; but when it reaches the bottom, it is retarded and loses speed until it stops. Its speed or velocity, starting at zero, has increased to a maxi- mum and then has decreased to zero again. Similarly, the speed of a projectile from a big gun or of the piston of an en- gine is not uniform but variable. If we wished to determine the speed of an automobile at any instant or point, we would measure off some convenient distance near the point and then get the time which elapsed while the automobile traveled the fixed distance. For ex- ample, if the measured distance, sometimes called a " trap," ACCELERATED MOTION 135 was a quarter of a mile and the time was 20 seconds, the speed was three quarters of a mile per minute or 45 miles per hour, But if the driver of the automobile was aware of the trap and was driving at a dangerously high speed at the beginning of the trap, he would slow down so that his average speed over the measured distance would be within the limit. To catch such a driver, that is, to get his speed more accurately at any point, we take as short a distance as is consistent with an accurate measurement of the time. 131. Acceleration. It is unpleasant to be on a street car when it starts or stops too suddenly. This suggests the problem of measuring a rate of change of speed, which is called acceleration. It has been found that a city street car standing at rest can safely gain speed, so that at the end of 10 seconds it is going 15 miles per hour. Assuming that this gain in speed is made at a constant rate (only constant accelerations will be discussed in this book), the speed of the car increased 1.5 miles-per-hour every second. In other words, the accel- eration was 1.5 miles-per-hour per second. Or, since 15 miles an hour is 22 feet per second, we can say that the gain in speed each second is 2.2 feet per second. In general, Acceleration = gain in speed per unit time, and acceleration is always to be expressed as so many speed units per time unit. Since there are many different speed units, such as miles-per-hour, kilometers-per-hour, feet-per- second, and centimeters-per-second, there are many ways of expressing the same acceleration. Thus the acceleration of the electric car just mentioned is VELOCITY UNIT TIME UNIT 1.5 miles-per-hour per second, or 2.4 kilometers-per-hour per second, or 2.2 feet-per-second per second, or 67.0 centimeters-per-second per second. 136 PRACTICAL PHYSICS All these statements mean exactly the same thing. En- gineers use the first two expressions for acceleration, while other scientific men more commonly use the last. two. It is convenient to abbreviate " feet-per-second per second " as ft. /sec. 2 and " centimeters-per-second per second " as cm. /sec. 2 , but each of these abbreviated expressions means simply so many velocity units gained per second. The accelerating rates of cars vary according to service and equipment, but the following rates are common in prac- tical operation : Steam locomotive, freight service, 0.1-0.2 miles-per-hr. per sec. Steam locomotive, passenger service, 0.2-0.5 miles-per-hr. per sec. Electric locomotive, passenger service, 0.3-0.6 miles-per-hr. per sec. Electric car, interurban service, 0.8-1.3 miles-per-hr. per sec. Electric car, city service, 1.5 miles-per-hr. per sec. Electric car, rapid transit service, 1.5-2.0 miles-per-hr. per sec. 132. Positive and negative acceleration. When the speed is increasing, the acceleration is said to be positive, and when the speed is decreasing, the acceleration is negative. Thus when a baseball is dropped from a tower, it goes faster and faster ; it has positive acceleration. When, however, it is thrown upward, it goes more and more slowly ; it has nega- tive acceleration or retardation. 133. Relation of speed to time at constant acceleration. If we know the acceleration of any body, we can easily com- pute its speed at any time after it started. For example, if the rate of acceleration of a train is 0.2 miles-per-hour per second, how fast is it moving one minute after it starts? One minute equals 60 seconds. If the train gains 0.2 miles-per-hour every second, then its speed, 60 seconds after starting, would be 60 times 0.2, or 12 miles per hour. LAW I. If the acceleration is constant, the speed acquired is directly proportional to the time. Final velocity = acceleration x time. v = at (I) ACCELERATED MOTION 137 PROBLEMS (Assume constant acceleration.) 1. Express 32 feet-per-second per second in miles-per-hour per second. 2. A body has a speed of 16 feet per second at a certain instant, and 3 seconds later it has a speed of 112 feet per second. What is its acceleration ? 3. A train starting from rest has, after 33 seconds, a speed of 15 miles an hour. What is the average acceleration, (a) In miles-per-hour per second? (b) In feet-per-second per second? 4. If a locomotive can give a train an acceleration of 5 feet-per-second per second, how long will it take, after slowing down for a crossing, to increase the speed of the train from 22 feet per second to 82 feet per second ? 5. What is the acceleration of a train if the initial speed is 45 feet per second, and after 5 seconds the speed is 15 feet per second ? 6. The negative acceleration (retardation) in stopping electric trains is seldom greater than 4 feet-per-second per second. How long does it take to stop a train from 60 miles an hour? 7. Which of the following accelerations is the largest: (a) One foot-per-second per five seconds, (6) One foot-per-five-seconds per second, (c) One fifth of a foot-per-second per second ? 134. Relation of distance to time at constant acceleration. Suppose a sled gains speed at a constant rate as it goes down a hill. If its acceleration is 3 feet-per-second per second, how far will it go in the first five seconds after starting from rest? We have already seen that its velocity at the end of five seconds will be 5 x 3, or 15 feet per second. Now it started from rest, that is, its initial velocity was zero, and gradually its speed increased until its final velocity, at the end of 5 seconds, is 15 feet per second. Therefore its average velocity is one half the sum of its initial and final velocities, or 7.5 feet per second. Average velocity = initial velocity + final velocity^ 2 138 PRACTICAL PHYSICS We have already learned (section 129) that the distance traversed is the product of the average velocity arid the time. So in this case the sled has gone 7.5 x 5, or 37.5 feet. In general, for a body starting from rest, the average veloc- ity is one half the final velocity; Average velocity = 2 But we already know that the final velocity is v = at ; then, Average velocity = - Therefore the distance is =f" = !* (M./SEC.) 1 16.1 32.2 4.9 9.8 2 ? ? ? v 144 PRACTICAL PHYSICS 2. A stone is dropped from the top of a cliff and strikes at the base in 5 seconds, (a) What velocity did it acquire ? (b) How high is the cliff? 3. If a falling body has acquired a velocity of 150 feet per second, how long has it been falling ? How far ? 4. How many centimeters does a stone fall in 0.5 seconds ? 5. How many centimeters does a stone fall during the fifth second? 6. A rifle is fired straight up (for speed, see table in section 129). How long before the bullet comes down again ? How high will it go ? (Assume that air resistance is negligible, which is far from true.) 7. A baseball is thrown up in the air and reaches the ground after 4 seconds. How high did it rise ? 8. The weight of a pile driver drops 5 feet at first and later 15 feet. How much faster is it moving when it strikes in the latter case than in the first case ? 9. A body is thrown vertically upward with a velocity of 50 meters per second. With what velocity will it pass a point 100 meters from the ground ? (HiNT. How high does the body rise ?) 10. How long would it take a bomb to fall 1000 feet from an aero- plane? During the fall the bomb would continue to move sidewise with the same velocity as the aeroplane, and so would always be directly under it. If the speed of the aeroplane is 60 miles an hour, how far will the bomb move sidewise while it is falling? Speed = SUMMARY OF PRINCIPLES IN CHAPTER VII distance time Acceleration = gain in speed , time Laws of motion at constant acceleration : I.. v=at, m. i^ = 2 as. Value of acceleration of gravity : 0= 32.2 ft/sec. 2 = 980 cm./sec. 2 . ACCELERATED MOTION 145 QUESTIONS 1. If you take two sheets of paper of the same size, and roll one of them into a ball, and let both the ball and the sheet of paper fall at the same instant from the same height, what is the result? Why? 2. How mtfst the pendulum bob be moved on a clock which is run- ning too fast ? 3. What takes the place of a pendulum in a watch ? CHAPTER VIII FORCE AND ACCELERATION Inertia the fundamental proportion action and reaction mass. 141. Newton's laws of motion. We are studying motion, and so far we have considered how bodies move ; that is, we have been describing different motions, such as motion at constant speed and motion at constant acceleration. Now we shall begin to study why bodies move ; we shall try to explain different motions by studying the forces that cause them. Practically all that we know about this part of physics dates back to Sir Isaac Newton (1642-1727), who wrote a treatise on the principles (Principia) of natural philosophy or physics. His whole book, and indeed all mechanics since his day, is based on three very simple laws, called Newton's laws. The first of them is the law of inertia, the second the law of acceleration, and the third the law of interaction. These will now be discussed in turn. 142. First law Inertia. It is a familiar fact that nothing in nature will either start or stop moving of itself. Some force from outside is always required. For example, a horse when starting a wagon, even on an excellent road, has to pull very hard at first ; once the wagon is going, the horse can keep it moving with very little effort ; but if he tries to stop it to avoid running over some one, he has to push back hard. So also when a moving ship collides with another ship or a dock, it requires an enormous retarding force to stop her. In 1908 the Florida rammed the Republic, and her bow was crumpled back 30 feet before the force stopped her. 146 SIR ISAAC NEWTON. Born in England, in 1612. Died in 1727, and is buried in Westminster Abbey. Founded the science of mechanics, and made many im- portant discoveries in light. Famous also for his achievements in mathe- matics and astronomy. FORCE AND ACCELERATION 147 This inability of matter to change its state of motion (or of rest), except it be influenced from outside, is called inertia. We may illustrate this property of inertia by bal- ancing a card on a finger with a coin on top. Then we may snap the card out, leaving the coin on the finger. The coin moves only a little because there is only a small force due to friction to get it started. This may also be done with the apparatus shown in figure 135. Another interesting experiment is to try to pick up a flatiron by means of a linen thread tied to it (Fig. 136). If we pull slowly, we may be able to do this, but if we pull with a jerk, the string always breaks, because so much extra force is required to set the flat- iron in motion quickly. Fia. 135. Inertia keeps the ball from moving. I FIG. 136. Inertia holds the weight still. This familiar fact that bodies act as if disinclined to change their state, whether of rest or motion, was expressed by Newton in the following way: LAW I. Every body persists in a state of rest, or of uniform motion in a straight line, unless compelled by external forces to change that state. QUESTION If you roll a ball along the ground, it does not keep going indefinitely. An automobile can start by itself. Do these facts controvert Newton's First Law? 143. Applications of inertia. A nail can easily be driven into a heavy piece of wood, even when the wood does not lie on a firm foundation, because the quick blow of a hammer does not set the heavy piece of wood in motion to any great 148 PRACTICAL PHYSICS FIG. 137. Inertia of sledge hammer. extent. It is very difficult, however, to drive a nail through a light stick unless the stick is placed upon a solid foundation, or unless the stick is steadied by the inertia of a heavy sledge hammer, as shown in figure 137. When the head of a hammer comes off, the best way to drive it on again is to hit the other end of the handle, rather than the head, against some solid foundation or with an- ^ other hammer. (Why ?) 144. Inertia in curved motion. This tendency of a body to continue to move in a straight line is very evident when it is desirable to make the body move in a circle. In this common case, a force is required to pull the body in toward the center of the circle, so that it may not fly off on a tangent. Such a force is called a centripetal force, mean- ing a force directed toward the center. When an athlete swings a 16-pound hammer around his head before throwing it, he has to pull it inward because of its inertia. When he stops pulling inward, it flies off on a tangent. So all he has to do to throw it is to let go. FIQ. 138. Mud flies off on a tangent. Emery wheels revolve very rapidly. Sometimes one bursts because the cohesion between its parts is not enough to supply the centripetal force_ necessary to keep these various parts moving in their respective circles. The mud on a bicycle wheel stays on the wheel only if the FORCE AND ACCELERATION 149 adhesion between it and the tire is great enough to pull it around with the tire ; otherwise it flies off on a tangent. In a cream separator the denser part of the milk gets out- side and crowds the lighter cream inward. This is because the greater inertia of the milk (that is, its greater tendency to move along a tangent) prevails over that of the cream. When a train goes around a curve, the flanges of the wheels are pressed inward by the outer rail ; if the rail is not strong enough to exert the necessary force inward, the train is wrecked on the outside of the roadbed. This is made clear in figure 139. The weight of the train is balanced by the upward push A of the tracks, the centripetal force B is ex- erted inward by the rails against the flanges, and there- fore the resultant R is in- Clined. Consequently the FIG. 139. -Banking rail, on a carve. track should be tilted toward the center, that is, " banked," so as to be at right angles to R. This equalizes the pressure on both sides and relieves the pressure on the outside flanges, thus making them less likely to break. 145. Second law Acceleration. We have been discussing what happens to a body when forces do not act on it. Let us now consider what happens when forces do act on it. Whenever an " unbalanced " force is acting on a body, the body has an acceleration in the direction in which the force acts, and the acceleration is proportional to the force. By an unbalanced force we mean more push or pull in one direction than in the other. For example, a locomotive is pulling a train at a constant speed of 50 miles an hour. The engine is certainly exerting a force on the train, but there are other forces, due to friction and air resistance, acting in the opposite direction, and these just balance the pull of the 150 PRACTICAL PHYSICS engine. The net force forward is zero ; if it was not zero\ the train would not only be going forward but accelerating forward ; it would be gaining speed. It is important to keep in mind that it is net force and acceleration which always go together, and not net force and motion. The above example shows that we can have motion without net force if the speed is not changing. . LAW II. The acceleration of a given body is proportional to the force causing it. That is, if any given body is acted on at one time by a force F v and at another time by another force jP 2 , then where a l and a 2 -are the accelerations produced by F^ and F 2 . In other words, if we pull a body with a certain force, and at another time pull it twice as hard, it will have twice as much acceleration the second time as the first. One way to cause a force to act on a body is to let the body fall. In this case the force acting is known, namely, the weight TFof the body. The acceleration is also known, namely, #, which is 32.2 feet-per-second per second, or 980 centimeters-per-second per second. So the weight of the body and its acceleration when falling can always be used as two of the numbers in a proportion. That is, -*.f. This enables us to compute the force needed to give a certain body any desired acceleration. For example, a freight train weighs 1000 tons. How great a force is necessary to give it an acceleration of half a foot-per-second per second 1 F _ 0.5 1000 ~ 32.2' 1000 x 0.5 32.2 ^ FORCE AND ACCELERATION 151 146, Units. In the equation F/W=a/g, it makes no difference in what unit F and W are expressed, provided only that both are expressed in the same unit. Both can be expressed in pounds, or in ounces, or in tons, or in kilograms, or in grams, or in a less familiar unit called a " dyne." The dyne is a very small unit of force much used in scientific work, especially electrical measurements. It can be defined as 1/980 of a gram weight.* It is about the weight of a milli- gram. If a force is given in terms of any one of these units, it can be expressed in terms of any other of them with the help of the following table: - 1 gram = 980 dynes. 1 dyne = 0.00102 grams. 1 pound = 454 grams. 1 gram = 0.00220 pounds. 1 pound = 445,000 dynes. 1 dyne = 0.00000225 pounds. Similarly a and g may be in any units, provided only that both are in the same unit. If both are to be in feet-per-second per second, the numerical value of g is 32.2 ; if both are to be in centimeters-per-second per second, the numerical value of g is 980. PROBLEMS 1. Express 110 grams in pounds. 2. Express 110 grains in dynes. 3. Express 8,000,000 dynes in pounds. 4. What acceleration will a force of 5 pounds produce in a body weighing 16.1 pounds? 5. What acceleration will a force of 1 gram produce in a body weigh- ing 327 grams ? 6. What acceleration will a force of 1 pound produce in a body weighing 1 pound ? 7. What acceleration will a force of 1 dyne produce in a body weigh- ing 1 gram ? (NOTE. The answer to this problem is often regarded as the definition of a dyne.) 8. State accurately in words the definition of a dyne that is referred to in the last problem. * See also problems 7 and 8 below. 152 PRACTICAL PHYSICS 9. A body weighing 10 pounds is observed to have an acceleration of 2 feet-per-secoud per second. .What force is acting? 10. A force of 1 kilogram is observed to produce an acceleration of 9.8 centime*ters-per-secoud per second in a certain body. How much does the body weigh? 11. A force of 1000 dynes is observed to produce an acceleration of 9.8 centimeters-per-second per second in a certain body. How many grains does the body weigh? 12. An automobile weighing 2 tons is started from rest with an acceleration of 4 feet-per-second per second. How hard is the road push- ing the bottoms of the rear tires forward ? 13. An elevator weighing 980 kilograms is pulled upward by a force great enough to hold up the weight and give 200 kilograms of net force besides. What is the acceleration of the elevator? 14. What pressure will a 150-pound man exert on the floor of an elevator which is going up with an acceleration of 4 feet-per-second per second ? 15. A train starting from rest with a constant acceleration takes 44 seconds to get up to a speed of 30 miles an hour. If the train consists of 4 all-steel cars, each weighing with its load 62. 5 tons, what pull is exerted by the engine? (HINT. Compute acceleration and then find force.) 147. Third law Interaction. Newton's third law is based on two familiar facts. One way of stating the first of these facts is that there can never be a force acting in nature unless two bodies are involved, one exerting it and one on which it is exerted. Thus, when a railroad train is pulled, there is an engine that does the pulling ; and on the other hand, the engine cannot exert a 'pull or a push without something to be pvlled or pushed. An electric car or an automobile seems, perhaps, to push itself along, but really the track or the road under the wheels is exerting a force on the wheels and pushing the car along. We have all seen what happens when the car track is so icy or the road so muddy that it cannot push on the wheels. The motor is going just as hard as ever, but the car does not move. In order to make this idea seem more real to us, let us try the experi- ment on a small scale, as shown in figure 140. If we wind up the little toy engine, and place it on the circular track, which is so mounted as to turn FORCE AND ACCELERATION 153 easily, we find that the track turns around and the rails under the wheels go backwards. If we hold the track fast, the engine goes ahead twice as fast as at first, and if we hold the engine fast, the track turns around backwards twice as fast as at first. Another case is that of any heavy object : there is a force called its weight (force of gravity) pulling it down ; but we know that it is the earth that exerts this force. FIG. 140. Track pushes the engine forward. This, then, is the first fact : whenever there is a force in nature there must be two bodies, one to exert it and one to receive it. But we can go farther than this. We can say that when- ever there is a force in nature, there must be not only two bodies involved, but another force. That is, forces never exist singly, but always in pairs. If the first force was exerted by a locomotive on a train, the second will be exerted by the train on the locomotive. The train will pull back on the locomotive just as hard as the locomotive pulls forward on the train. If a road is pushing forward on the wheels of the automobile, the wheels must be pushing back on the road. If, instead of the road, we substitute great rollers, we may measure this backward push. This is the method sometimes used in testing labora- tories in making power tests of automobiles and locomotives. 154 PRACTICAL PHYSICS Finally, when any heavy object is pulled downward by the earth, the heavy object must be pulling the earth up with an equal force. This does not seem very likely at first, but this is simply because the force is so small and the earth so large that the force has an imperceptible effect on the earth. If the heavy body which we are thinking of is the moon, the whole thing becomes reasonable at once, for the earth and the moon are actually rotating about a point (Fig. 141), which is not ex- actly at the center of the earth. So the moon must continually pull the earth to make MOON ^s center of grav- ity move in its circle. EARTH This fact that FIG. 141. Rotation of the moon about the earth. f , forces always occur in pairs, one of the pair being equal and opposite to the other, was expressed by Newton in the following form : - LAW III. With every action (or force) there is an equal and opposite reaction. 148. Mass vs. weight. " Mass " and " weight " are con- stantly confused in ordinary conversation. While we have preferred not to use the term "mass" in studying Newton's second" law, yet it is well to know its precise meaning that we may read intelligently the books which make use of it. Mass means quantity of matter. It is the answer to the question, " How much matter is there in a given body ? " Weight means the pull of gravity on the body. The weight of a body is & force acting on the body, not a descrip- tion of what it contains. The unit of mass is the quantity of matter contained in a certain piece of platinum (the standard kilogram, Fig. 142). FORCE AND ACCELERATION 155 The unit of weight is the pull of the earth on that same piece of platinum, when it is near sea level and at latitude 45. Since a kilogram mass weighs a kilogram under these standard conditions, the mass and the " standard weight " of a body are numerically equal. But if we carry a kilogram mass to the top of a high mountain, and weigh it on a very sensitive spring balance, it will weigh less than a kilo- gram, because it is farther from the center of the earth, and so the earth pulls less hard on it. The reading of the spring balance might be called its "local weight." Since all bodies on the mountain top would weigh less in the same proportion, we can get the standard weight of anything without de- scending the mountain by weighing it on an equal-arm bal- ance against a set of "standard weights." This is what we always do in the laboratory and in the outside world when we want to know weights accurately. So when we speak of the weight of a body we almost always mean its " standard weight." W Since F = a, and since the standard weight W and the 9 mass M are numerically equal, we shall get the same value for F if we write (when using grams, centimeters, and seconds) FIG. 142. Standard kilogram. 980' or 156 PRACTICAL PHYSICS Here F is in grams; if we choose, however, to express the force as F' dynes, instead of as F grams, then F and F' will be different numbers, and F 1 = 980 F, so F' (dynes) = M (grams) x a (cm. /sec. 2 ). This is a common way of expressing Newton's second law. SUMMARY OF PRINCIPLES IN CHAPTER VIII Newton's laws and the fundamental proportion : I. Every body continues in a state of rest or of uniform motion in a straight line, unless compelled by external forces to change that state. II. The acceleration of a given body is proportional to the force causing it. = - W~ g III. With every action (or force) there is an equal and opposite reaction. Distinction between mass and weight QUESTIONS 1. How is the water quickly removed from wet clothes in a steam laundry? 2. Why does a train continue to move after the steam is shut off ? 3. Why do automobiles " skid" in rounding corners rapidly? 4. What does an aviator have to do to round a corner safely, and why? 5. Why can small emery wheels be safely driven at a greater speed, that is, at more revolutions per minute, than larger ones ? 6. Why does a wheel, or any revolving part of a machine, sometimes shake or hammer in its bearings? 7. Explain how a locomotive engineer can tell, when he starts up his train, if one of the cars has been uncoupled from the train. 8. Explain why lawn sprinklers rotate. Would such a sprinkler ro- tate in a vacuum ? CHAPTER IX ENERGY AND MOMENTUM Kinetic energy the law of energy potential energy the conservation of energy momentum and its law. 149. Kinetic energy. We have already seen (section 31) that in physics work involves not only force but also dis- placement. Whenever a force moves anything in its own direction, the force does work on the thing, and when- ever anything moves against a force, the thing does work against the force. The energy of anything may be defined as its capacity for doing work. Thus a heavy flywheel will keep machinery running for some time after the power has been shut off. Therefore, a heavy flywheel in motion can do work; it has energy. The energy of any body which is due to its motion is called kinetic energy. Let us consider more carefully the case of a heavy flywheel on an engine. At first the engine has to push and pull on the crank shaft to get the flywheel started and to bring it up to speed; the engine has to do work on the flywheel. When once the flywheel is up to speed, however, the engine does not have to push or pull any longer to keep the flywheel going (except for friction, which we will neglect for the moment). From this time on all the work that the engine does goes into the driven machinery attached to the shaft. Suppose now that the pressure of the steam on the engine suddenly drops, or that an extra load is thrown on the shaft. The shaft does not stop turning suddenly, or drop instantly to a lower speed. It slows down gradually, pulling back on 157 158 PRACTICAL PHYSICS the flywheel as it does so, and taking work out of the fly- wheel, that is, making the flywheel do work instead of absorbing it. This continues until the engine picks up the load again, or until the flywheel stops. In other words, the flywheel, as long as it is moving, can do work on the shaft if necessary, and the faster it is moving, the more work it can do before it comes to rest. In physics we describe this very familiar fact by saying that the fly- wheel has energy, and since its energy depends upon its being in motion, we call it kinetic energy, or energy of motion. Every body in motion has kinetic energy; that is, it will do a certain amount of work against a resisting force before it will stop. Furthermore the kinetic energy of a body will be greater the heavier it is and the faster it is moving. 150. How to measure kinetic energy. It will be easier to do this for a body moving straight ahead rather than in a circle. We will consider first how much work it takes to get a heavy body up to a given speed, and then how much work it will do before it stops. By definition this latter is its kinetic energy. The force necessary to get a body started with a given acceleration a is, by the fundamental proportion (section 145), W W n J1 = a. 9 If the distance which the body moves before it gets up to a given speed is called s, the work done is the product of the force by the distance, namely, Jk-JTi. 9 But it will be seen that the product as can be expressed in terms of the speed acquired, v, by means of the third law of accelerated motion (section 135). Thus, v 2 = 2 as, ENERGY AND MOMENTUM 159 I So the work done is Fs= ^ Thus we see that the work required to bring a heavy body from rest up to a given speed does not depend on the acceleration, or on the distance covered while coming up to speed, but only on the weight of the body and the speed itself. Now, how much work will the body do against a retarding force before it comes to rest? We have already seen that the easiest way to think of a retardation problem is as an acceleration problem reversed. That is, a body will stop under a given retarding force in the same distance that it would need to get up speed under an equal accelerating force, and it will do the same work against the retarding force that an equal accelerating force would have to do on it to get it started. So the formula above gives not only the work necessary to start it, but also the work it will do when it stops. Therefore, Kinetic energy = . 151. The energy equation. The equation just found, namely, is called the energy equation. It applies, as we have just seen, either to accelerating or to retarding bodies, if they start from or come to rest. It can be stated in words as follows : If the body is gaining speed, Gain of kinetic energy = accelerating force x distance = work done by force on body. 160 PRACTICAL PHYSICS If the body is losing speed, Loss of kinetic energy = retarding force x distance = work done by body against force. 152. Units. In using this equation we must be consistent in our units. Thus .Fand TFare both forces and both must be expressed in the same unit in any one application of the equation. In one problem we may choose tons and in an- other dynes, but in any single problem all forces must be in tons if we have chosen tons, and in dynes if we have chosen dynes. In the same way, s, v, and g must all involve the same unit of length. In one problem we may choose centimeters and in another feet, but once we have started the problem we must stick to our choice. In expressing the velocity, v, and the acceleration, g, it is customary always to use the second as the unit of time. Therefore g will always be either 32.2 ft. /sec. 2 or 980 cm. /sec. 2 according as we have chosen feet or centimeters as the unit of length. The left-hand side of the equation, Fs, is force times dis- tance, or work, and so the right-hand member, which is equal to it, will come out expressed in work units. There are several work units in common use, such as the foot pound (ft. lb.), foot ton (ft. T.), gram centimeter (g. cm.), kilogram meter (kg. m.), and dyne centimeter ("erg"). Since each of these work units is a force unit times a dis- tance unit, we can always tell what unit the kinetic energy will come out in, if we notice what force unit and what dis- tance unit we started with. For example, if W is in pounds, v in feet per second, and g in feet-per- second per second (# = 32.2 ft./sec. 2 ), the kinetic energy (Wv*/2 g} will ENERGY AND MOMENTUM 161 be in foot pounds. But if W is expressed in dynes, v in centimeters pet second, and g in centimeters-per-second per second (g = 980 cm. /sec. 2 ), the kinetic energy (Wo*/'2g') will be hi dyne centimeters. There is a shorter name for a " dyne centimeter " ; it is usually called an erg. Since the erg is a very small unit of work, the joule = 10 7 ergs is often used. 153. Applications of the energy equation. The energy equa- tion will help us to solve many useful problems about moving things which involve the question "how far," or the idea of distance in general. For example, consider again the problem of the engineer and the child (section 136). Suppose that the train is going 50 miles an hour, but that we do not know its rate of retardation. If the retarding force is equal to one eighth of the weight of the train, how far will the train run before coming to a standstill? We can compute the rate of retardation from the fundamental pro- portion, and then proceed as before, but it will be easier to use the energy equation as follows : The speed 50 miles an hour = 73.3 ft./sec. So the kinetic energy is 2 x 32.2 The retarding force is W/S Ibs. Therefore, Z x s = 8 - 2 x 32.2 and since the Ws cancel out, this can be solved for s, giving s = 667 feet = 222 yards. So in this case also, the engineer could not stop in time. Again, suppose a car weighing 10 tons is going 36 miles an hour. What force is required to stop it within a space of 100 feet? The velocity must be expressed in feet per second since we ordinarily do not use g in miles/hour 2 . v = 36 miles/hour = 52.8 ft./sec. But W and F can be left in tons. The kinetic energy is 10 x ' = 433 ft. T. So F x 100 = 433, or F = 4.33 tons. 162 PRACTICAL PHYSICS Finally, suppose that the flywheel mentioned in section 149 has a 10 ton rim, and that we can neglect the effect of the thin spokes. Suppose also that it is 16 feet in diameter and making 15 revolutions per minute (r. p. m.). How much kinetic energy has it? Each part of the rim is making 15 turns per minute and therefore moving with a velocity of 15 x 2 TIT = 15 x 2 x 3.14 x 8 = 754 ft./min., which is equal to 12.5 ft./sec. Therefore, the kinetic energy of the whole rim is 10 x (12.5) 2 , o f 2x32.2 = This is the same as 48,600 foot pounds. It is the amount of work which the flywheel could do before stopping. PROBLEMS (State the unit in which each answer is expressed.) 1. What is the kinetic energy of a baseball weighing one third of a pound if its velocity is 64.4 feet per second? 2. What is the kinetic energy of an 80-ton locomotive going 60 miles an hour ? 3. What is the kinetic energy of a 9.8-kilogram weight which has been falling long enough to have a velocity of 12 meters per second? 4. What is the kinetic energy of a 16.1-gram bullet whose velocity is 600 meters per second? 5. Find the kinetic energy in ergs of a stone weighing 20 grams when it is thrown with a velocity of 800 centimeters per second. 6. The 14-inch guns on some of the United States warships fire a projectile weighing 1400 pounds and' are said to give it a " muzzle energy " of 65,600 foot tons. What is the velocity of the projectile as it leaves the gun ? 7. What resistance is necessary to stop a body whose kinetic energy is 90,000 ergs, in a distance of 3 meters ? 8. A boy weighing 100 pounds starts to slide on ice at a speed of 20 feet per second. What is his initial kinetic energy ? If the retarding force due to friction is 40 pounds, how far will he go before stopping? 9. How great a force in excess of that required to overcome friction is necessary to bring a 3220-pound automobile up to a speed of 30 miles an hour in a distance of 242 feet ? 154. Potential energy. Some things have a capacity for doing work even when they are not in motion. Thus when a clock spring is wound up, it can drive the clock as it un- ENERGY AND MOMENTUM 163 coils, because of the elastic strain in it, due to its change of shape. If the clock has a weight instead of a spring, the weight can drive the clock because of its elevated position. Such energy, due to strain or to position, is called potential energy. Just as the kinetic energy of a moving weight can be measured either by the work required to get it up to speed or by the work it will do while stopping, so the potential energy* of a raised weight or of a coiled spring can be meas- ured either by the work required to raise or coil it, or by the work it will do when it falls or unwinds. In a later chapter we shall see that when a lump of coal burns, it gives out energy in another form called heat, some of which can be used to drive a steam engine. Thus the unburned coal has in it capacity to do work, that is, energy, and since this energy is not due to any motion of the lump of coal, it must also be potential. This kind of potential energy is usually called chemical energy. 155. Transformation of energy. In nature the various forms of energy, kinetic or potential, are continually changing into one another. For example, when a pen- dulum bob (Fig. 143) is at the highest part of its swing A, it has potential energy because of its height. As it swings down this potential energy disappears, but the bob gains speed and kinetic energy. As the bob swings up again on the other side, C, its velocity and kinetic energy decrease, but its potential energy increases. FIG. 143. Transformation of energy in pendulum. 164 PRACTICAL PHYSICS Similarly when coal is burned, its chemical energy changes into heat. Some of this heat may be changed into potential energy in the form of steam under pressure. A steam engine could then change some of this into kinetic energy in a flywheel, or into some other form of mechanical energy in a driven machine, or into electrical energy in a dynamo. Some of this latter might be changed into light in a lamp, while the rest would turn back to heat. In all these cases we may think of energy as flowing about from one place to another, passing through the various ma- chines and having its outward appearance changed by them, almost like water flowing from a reservoir through a dye- house, where it is used for many purposes, only finally to be dumped into a stream or sewer, changed in appearance, but unmistakablythe same kind of thing that went in. 156. The conservation of energy. After its use in the dye- house some of the water might never get through to the stream, having been used up in some chemical process, so that it is no longer water. But in the case of energy this cannot happen. Energy is never made from anything that is not energy, or turned into anything that is not energy. The total quantity of energy in the universe is always the same and is changed 'only in form and distribution. In any given machine there may be leaks of energy because of fric- tion, radiation, etc., just as there may be leaks in the pipes in the dyehouse, but the energy that leaks away is not destroyed, but is given as heat to the surroundings of the machine, where it is of no more use than water spilled on the floor. Thus in the pendulum (Fig. 143) the sum of the kinetic and potential energies is the same wherever it is in its swing, unless there is friction. If there is friction, some energy disappears as heat and less is left in the pendulum, but the total quantity, counting in the heat, is unchanged. This fact, that energy can never be manufactured or de- stroyed, but only transformed, and directed in its flow, was first stated (although not very clearly) by a German, Robert ENERGY AND MOMENTUM 165 Mayer, in 1842. It is called the law of the conservation of energy. It has become the most important generalization in all physics, and its value will be more and more evident as we study the subject. 157. " Perpetual motion " machines. One of the most interesting applications of this principle is that it assures us that "perpetual motion " machines are impossible. Such a machine would be one that runs of it- self, without being driven by an engine, and without burning any fuel, and does something useful without cost. Such a machine, if it could be built, would be of extraordinary value to its inventor and to the world, and for hundreds of years people have been trying to invent one. But the principle of the conservation of energy shows that no such machine can possibly be made, because it would be manufacturing energy out of nothing. 158. Momentum and energy. In the colloquial use of these words there is a great deal of confusion. When a per- son is thinking of something which a body does because it is moving, he is likely to talk about either its " momentum " or its " energy," whichever word first occurs to him. It is therefore worth while to take a little trouble to understand clearly the difference between momentum and energy. We have seen that when a force acts on a moving body through a long distance, it accomplishes more than when the distance is short. The work done is greater. It is also evi- dent that when a force acts on a moving body for a long time, it accomplishes more than when the time is short. In the technioal language of physics we say that the impulse of the force is greater. Impulse may be defined as the force multiplied by the length of time it acts. Thus, Work = force x distance, Impulse = force x time. We shall find that momentum has the same relation to impulse that kinetic energy has to work. The idea of mo- mentum will help us to solve problems involving "how long?" just as the idea of kinetic energy helps us to solve 166 PRACTICAL PHYSICS problems involving " how far ? " To show this we will print again the proof of the energy equation side by side with the corresponding proof of a momentum equation. PROOF OF ENERGY EQUATION But v 2 = 2 as or = as. 2 So Wv* 2<7 PROOF OF MOMENTUM EQUATION 9 But v at. So g The expression - - is called the momentum of a moving body. & Both kinetic energy and momentum are proportional to the weight of the moving body ; thus a railroad train has both more momentum and more energy than a motor cycle running at the same speed. In the second place both the momentum and the energy of a moving body increase when its speed increases, but not ac- cording to the same law. The energy is proportional to the square of the speed. That is, doubling the speed of a train makes its kinetic energy four times as large. But the momen- tum is proportional only to the first power of the speed. That is, doubling the speed of a train merely doubles its momentum. Finally, we must not forget that there is a two (2) in the denominator of the expression for energy, but not in the expression for momentum. 159. The momentum equation. The equation -** 9 is called the momentum equation. It holds either for accel- erating or retarding bodies, and can be expressed in words as follows : ENERGY AND MOMENTUM 167 If the body is gaining speed, Gain of momentum = accelerating force x time = impulse received from force. If the body is losing speed, Loss of momentum = retarding force x time = impulse lost to force. 160. Units of momentum. In using the momentum equa- tion, as in using the energy equation, we must be consistent in our units. That is, _Fand IT must be in the same unit of force, and v and g must involve the same unit of length. Furthermore, v, g, and t must all be expressed in terms of seconds, because it is not worth while to remember any other way of expressing g than 32.2 ft. /sec. 2 or 980 cm. /sec. 2 . The momentum equation shows that a momentum Wv/g is equal to a force times a time, and so the unit of momentum will be a force unit times a time unit. Thus, momentum may be expressed as pound seconds, or ton seconds, or gram seconds, or kilogram seconds, or dyne seconds, according to the force and time units used in the equation. The dyne second as a unit of momentum corresponds to the dyne centi- meter or erg as a unit of energy, but curiously no one has ever thought it worth while to give it a name of its own corresponding to " erg." 161. Applications of the momentum equation. The momen- tum equation will help us to solve many problems about moving things which involve the question "how long?" or the idea of time in general. For example, a certain engine can exert a " drawbar " pull on its train equal to ^ of the weight of the train. How long will it take to bring the train up to a speed of 50 miles an hour, starting from rest? v 50 miles/hour = 73.3 ft./sec. W \, f - Wx 7 40 X ' ~ 32.2 168 PRACTICAL PHYSICS and since the W's cancel out, t = 91 seconds. Again, an electric car weighing 12 tons, running 15 miles an hour, can stop in 7 seconds. What is the retarding force? v = 15 miles hour = 22 ft. /sec. F x 7 = 12 x 22 ton seconds. 32.2 F=l.l7 tons. Again, a steamboat weighing 20,000 tons is being pulled by a tug- boat, which exerts, a force great enough to overcome the friction of the water and to give a net force of 2 tons besides. What speed will the boat acquire in 4 minutes, starting from rest? v = 0.773 ft. /sec. Another application, which is important in studying^ steam turbines, windmills, and aeroplanes, is the case of a steady stream of fluid strik- ing against a solid surface. For this purpose we may write the equation F-Sx'i, * , g . and W/t is then the weight of fluid striking the surface per second. One of the useful applications of the momentum equation is in studying a blow, such as a bat gives a ball, or a collision, as between two billiard balls. We naturally speak of the forces acting in such cases as " impulses," and this explains why the product F x , which was first used in solving such problems, is called "impulse." PROBLEMS (State the unit in which each answer is expressed.) 1. What is the momentum of a 180-pound football player running at a speed of 20 feet per second? 2. What is the momentum of a 66,000-ton ship when it is going 24 miles an hour (about 21 knots) ? 3. How fast must a 1000-kilogram automobile be going to have 3000 kilogram seconds of momentum ? 4. A car weighing 12 tons, moving 5 feet per second, is stopped by a bumper in 0.2 seconds. What is the average force of the blow? ENERGY AND MOMENTUM 169 5. An 8000-ton ship moving 4 miles an hour is stopped in 2 min- utes. Find the average force. 6. A 5-pound hammer moving 40 feet per second strikes a nail. If the average resistance of the wood to the nail is 1240 pounds, what fraction of a second was required to bring the hammer to rest? 7. A fire engine throws a 2-inch stream of water horizontally against a brick wall with a velocity of 150 feet per second. What is the force exerted on the wall? 8. A gun delivers 100 bullets per minute, each weighing one ounce, with a horizontal velocity of 1500 feet per second. What is the average force exerted by the gun? SUMMARY OF PRINCIPLES IN CHAPTER IX The law of energy ("How far?"). Work = force x distance. Wv~ Kinetic energy = Work done on body = gain of kinetic energy. Work done by body = loss of kinetic energy. The conservation of energy : Energy can never be manufactured or destroyed, but only transformed or directed in its flow. The law of momentum ("How long?"). Impulse = force x time. Wv Momentum = 9 Impulse given to body = gain of momentum. Impulse given by body = loss of momentum. QUESTIONS 1. The pendulum of a clock would die down because of the friction of the air around it if energy were not continually supplied to it. How is this done ? 2. Look up "perpetual motion" machines in an encyclopedia and try to see for yourself why some of them cannot work. 3. A certain rifle was once described in the headline of a maga- zine advertisement as striking " a blow of 2038 pounds." Farther down in the advertisement it appeared that the bullet weighed ^ of a pound, and that its velocity was 2142 feet per second. What did the headline mean ? CHAPTER X HEAT EXPANSION AND TRANSMISSION Thermometer scales linear and volumetric expansion of solids expansion of liquids maximum density of water expansion of gases pressure coefficient of gases the gas thermometer and the absolute scale gas formula hot-air engine convection currents heat transfer by convection heating and ventilation systems conduction radiation molecular theory. EXPANSION BY HEAT 162. Sources of heat. Our most important source of heat is the sun. The sun's rays give more heat, the more nearly vertical they are. This explains why we receive more heat at noon than in the morning or evening, and more heat in summer than in winter. The interior of the earth also is hot. In mine shafts sunk into the earth the temperature rises about one degree for every hundred feet of depth. Hot springs and volcanoes also lead us to think that the inside of the earth is hot. To warm our houses and run our engines, we do not as yet depend directly on the sun or on the heat in the earth, but on the heat produced in burning wood, coal, oil, or gas. The heat thus obtained comes indirectly from the sun, having been stored as chemical energy in plants in past ages. "We have already learned in our study of machines and in our everyday experience that friction produces heat. For example, in scratching a match, in using drills, saws, and files, indeed, whenever mechanical energy is apparently lost, we find that heat appears. 170 HEAT EXPANSION AND TRANSMISSION 171 John Tyndall (1820-1893) in his lectures on " Heat con- sidered as a mode of motion " used to perform a striking ex- periment to show that friction produces heat. Let us try the same experiment by putting a little water in a metal tube (Fig. 144). If we close the tube with a stopper and rotate it either by hand or with a motor, we shall find that the friction between the rotating tube and the wooden clamp will gener- ate in a few minutes enough heat to boil the water and blow the stopper out. 163. The thermometer. A FIG. 144. Boiling water by friction. deep cellar seems cold in sum- mer and warm in winter, even though it remains at nearly the same temperature. A room often seems hot after we have been out in the cold, although it seems chilly after we have been in it awhile. Our sensations about the temperature of things are therefore very unreliable and depend on our own condition at the moment. So it is necessary to have some kind of instrument to indicate accu- rately how hot or cold things are, that is, a thermometer. The usual form of thermometer is based on the fact that most liquids, such as mercury and alcohol, expand when being heated and contract again on cooling. 164. Making a mercury thermometer. A spherical or cylindrical bulb is blown on one end of a piece of glass tub- ing with a very fine uniform bore, and the bulb and part of the stem are filled with mercury. When the mercury is warmed, it expands and rises in the stem until it overflows. Then the top of the tube is closed by melting the glass. When the mercury cools again, it leaves a vacuum in the top of the tube. If the bulb is now placed in the steam from boiling water, the mercury rises to a definite point on the 172 PRACTICAL PHYSICS 100- -212- stem, which is marked with a scratch. This point is called the boiling point. If the thermometer is then put in melting ice, the mercury goes back down the stem and stops at a definite point. This point is called the freezing point. In thermometers that are used for scientific work the distance on the stem between these two fixed points is di- vided into 100 equal spaces, called degrees. In this thermometer, which is called a Centi- grade thermometer, the freezing point is marked zero and the boiling point is marked one hun- dred. When these divisions extend below the zero point, they are called degrees below zero or minus degrees. 165. Centigrade and Fahrenheit scales. In England and in North America a scale de- vised by Fahrenheit is in common use. On this scale the freezing point is marked 32 de- grees (32) and the boiling point 212, so that the space between the freezing and boil- ing points is divided into 180 divisions (Fig. 145). Since 100 divisions on the Centigrade scale are equivalent to 180 divisions on the Fahrenheit scale, one division Centigrade is equivalent to -| divisions Fahrenheit. To change a temperature expressed on the Cen- tigrade scale to the Fahrenheit scale, we have FIG. 145. Centi- only to multiply by -| and add 32. For ex- grade and Fah- am pl e : renheit scales. 30 C = (f x 30) -f 32 = 86 F. To change a temperature expressed on the Fahrenheit scale to the Centigrade scale, we must first subtract 32 and then multiply by |. For example : 98.6 F = (98.6 - 32)f = 37 C. -17.8 \32 ( HEAT EXPANSION AND TRANSMISSION 173 FIG. 146. Minimum and maximum thermometers. Inasmuch as mercury freezes at 39 C, the thermometers used for very low temperatures contain alcohol, which is usually colored red or blue. 166. Special thermometers. In Weather Bureau stations the lowest temperature during the night and the highest temperature during the day are auto- matically recorded by special thermom- eters called mini- mum and maximum thermometers. These are usually mounted as shown in figure 146. The upper one is the minimum and the lower the maxi- mum thermometer. In the maximum thermometer, the bore is constricted just above the bulb, so that the mercury passes through with some difficulty when the tempera- ture rises and does not run back again when the temperature falls. The minimum thermometer is filled with alcohol, and contains within its tube a small black index rod, which is shaped like a double-headed pin. As the temperature falls, the index is drawn down toward the bulb by the surface of the alcohol, and when the tem- perature rises, the index is left behind. Another kind of thermometer, which is used by doctors and nurses to detect fever, is the clin- ical thermometer (Fig.. 147). This is a maxi- mum thermometer on the Fahrenheit scale, and the range is from 92 F to 110 F, each degree being divided into fifths. The normal tempera- ture of the human body is 98.6 F or 37 C. FIG. 147. Clinical ther- mometer. QUESTIONS AND PROBLEMS 1. Change to Centigrade : 70 F, 150 F, 0F, -10F. 2. Change to Fahrenheit: 15 C, 500 C, -26 C, - 190 C. 174 PRACTICAL PHYSICS 3. What would a rise in temperature of 80 on the Centigrade scale be in Fahrenheit divisions? 4. The temperature of the air on a certain day was 90 F at noon and 45 F late the next night. What was the " drop " in Centigrade degrees? 5. At what temperature do a Centigrade and a Fahrenheit ther- mometer read the same ? 6. How do primitive people start a fire ? 7. Why do sparks fly from car wheels when the brakes are quickly applied ? 8. Why must a tool be kept wet with cold water when being sharp- ened on a grindstone ? 9. After violent physical exercise one feels very hot . Is the body temperature higher than normal? 10. If one wants the division marks far apart on the stem of a ther- mometer, what must be the relative size of bulb and stem ? 167. Expansion by heat Solids. When a railroad track is built, a gap is usually left between the ends of the rails, to allow for the expansion of the steel in summer. Iron rims are placed on wheels while hot, because they are then bigger and can be easily slipped on. When they cool, they Fig. 148. Force exerted by expansion and contraction of metal bar. contract and hold fast to the wheel. An ordinary wall clock loses time in summer because its pendulum expands a little, and so swings more slowly. Almost all solids expand more or less when heated, but this expansion is so very small that one must take special pains to see it. When solids expand and contract, they may exert enor- mous forces. We can show in a striking way the power exerted by the expanding and contracting of a metal bar in the following experiment. First, let us show that a metal bar does expand when heated. In the apparatus shown in figure 148, there is a metal bar which is heated by a HEAT EXPANSION AND TRANSMISSION 175 series of little flames below. The expansion, although very slight, is shown by the bent lever at the end, so that as the bar gets hot, the pointer rises. Second, let us show the great force exerted by this process. If we put a steel rod in the slot at right angles to the bar near the lever, when we heat the metal bar, the steel rod suddenly breaks and the pointer is thrown violently up. If we put another steel rod through a hole in the bar, and allow the bar to contract, the steel rod suddenly snaps and the pointer is thrown violently down. Careful experiments show that different metals expand at different rates. Platinum, for example, expands less and zinc more than other common metals. If we made a platinum meter rod correct at 0C, it would be 0.9 millimeters too long at 100 C. Similarly a steel meter rod would be 1.3 millimeters too long, and a zinc meter rod would be 2.9 millimeters too long. If two different metal strips, such as iron and brass, are riveted together (Fig. 149), forming a compound bar, the bar when heated will bend or curl, because of the unequal expansion of the metals. ^ G 149. Effect *of Which metal will be on the inner side heating a compound of the arc? Such compound bars are often used to regulate the temperature of chicken incubators. 168. Measurement of expansion. In considering how much a given object such as a steel rail will expand, it is necessary to know three things about it, namely, its length, and the rise in temperature and the rate of expansion of the particular substance used. For example, if we know that a steel rail is 33 feet long and each foot of it expands 0.000013 feet per degree Centigrade, we can compute how much it will expand from winter to summer, a range of perhaps 50 C. The expansion is equal to the expansion per degree for one foot, multiplied by the length in feet and by the rise in temperature. That is, Expansion = 0.000013 x 33 x 50 = 0.0214 feet = 0.257 inches. 176 PRACTICAL PHYSICS We can express this in the form of an equation, thus, where e = expansion, k = expansion per degree, per unit length, I = length, t' = temperature when hot, t = temperature when cold. The factor k is called the coefficient of linear expansion. It is a very small fraction, and it varies with different substances. It should be remembered that no matter in what unit I is expressed, e will come out in the same unit. Usually k is given per degree Centigrade, but the coefficient for the Fahrenheit scale can be computed by multiplying by -|. Why? The coefficients per degree Centigrade of some common substances are given in the following table : Zinc 0.000029 Steel 0.000013 Lead 0.000029 Cast iron 0.000011 Aluminum 0.000023 Platinum 0.000009 Tin 0.000022 Glass 0.000009 Silver 0.000019 "Invar" (nickel Brass 0.000018 steel) 0.0000009 Copper 0.000017 169. Some illustrations. In the .construction of a steel bridge allowance has to be made for the expansion of the steel. For example, in the great bridge over the Firth of Forth in Scotland, which is over a mile and a half long, the total expansion amounts to 6 feet. In steam plants, long pipes are provided with sliding or " expansion " joints, unless the bends in the pipe are such as to yield enough for the expansion. When a lamp chimney is hot, the glass expands. If a HEAT EXPANSION AND TRANSMISSION 111 drop of water strikes it, the glass in the immediate vicinity cools rapidly and pulls away from the rest, cracking the chimney. Quartz is made into crucibles and other ob- jects that are as clear as glass, but have so small a coefficient of expansion (0.0000005) that a red-hot crucible may be suddenly thrust into water without cracking. The pendulum rod of a clock is often made of dry wood, which expands very little. It is, however, affected by moisture ; so for the most accurate clocks some kind of a compensated me- tallic pendulum is used. One form of compen- sated pendulum is that commonly seen in the so-called French clocks. It consists of a glass tube or tubes filled with mercury (Fig. 150), suspended by a steel rod. When properly ad- justed, the raising of the center of gravity of the mercury, due to its expansion, is equal to the lowering of the whole reservoir of mercury due to the expansion of the steel rod, so that the ef- F IO . 150. Com- fective length of the pendulum remains constant, pensated mer- In a watch, the balance wheel if uncompen- ^[ peD sated will run slower in hot weather because the hairspring has less elasticity at a higher temperature, and also because the expansion of the radius of the wheel carries the rim farther from the center, and so slows dow,n its rotation. The rim is therefore made of two strips of metal, brass on the outer edge and steel on the inner, fastened with screws as shown in figure 151. FIG. 151. Balance When the temperature rises, the free ends wheel of a watch. o |- ne r j m cur i i nw ard, thus bringing part of the rim nearer the axis. This compensates for the expan- sion of the crossbar and the weakening of the hairspring. 178 PRACTICAL PHYSICS PROBLEMS 1. A brass meter bar is correct at 15 C. What will be the error ai 20 C? 2. A steel rail 30 feet long is found to expand 0.235 inches when heated from -17 F to 100 F. What is the coefficient of linear expan- sion on the Fahrenheit scale, and also on the Centigrade scale? 3. The steel cables of a suspension bridge are 2000 feet long. How much do they change in length between the temperatures 20 F and 97 F? 4. A steel shaft is heated to 65 C while being shaped in a lathe, and its diameter at that temperature is made just 5 centimeters. What will its diameter be at room temperature (15 C) ? 5. A steel wire, 150 centimeters long at 15 C, becomes 151.3 centi- meters long when an electric current is sent through it. How hot does it get ? 170. Cubical expansion of solids. A metal bar when heated expands, not only in length, but also in breadth and thick- ness ; in short, its volume increases. This expansion in vol- ume is called cubical expansion. Suppose we have a cube 1 centimeter on an edge at C and raise its temperature to 1 C; each edge of the cube will become (1 + &) centi- meters, k being the coefficient of linear expansion. The original volume, 1 cubic centimeter, will become (1 -f &) 3 cubic centimeters. Now (1 + &) 3 equals 1 + 3 k -f 3 & 2 + jfc 8 ; but since k is a very small fraction, the value of 3 k 2 and & will be so small that they may be neglected without appre- ciable error. The volume of the cube is, then, 1 -f- 3 k ; hence the volume expansion per cubic centimeter per degree is 3 k cubic centimeters and the coefficient of cubical expansion is three times the coefficient of linear expansion. For example, the coefficient of linear expansion of glass is 0.000009, and the coefficient of cubical expansion is 3 times 0.000009 or 0.000027. A flask which held just a liter at C would hold 1002.7 cubic centi- meters at 100 C. 171. Expansion Of liquids. Let us fill a small round-bottomed flask with water colored with ink and insert a stopper with a glass tube HEAT EXPANSION AND TRANSMISSION 179 FIG. 152. Expansion of a liquid. and paper scale (Fig. 152). Then let us put the flask into a jar of ice water and mark on the scale the position of the liquid in the tube. If we then put the flask into a basin of boiling water, we shall note at first a sudden drop of the liquid in the tube (why?) and then a rapid rise. Evidently the liquid expands more than the glass. In general it is found that liquids expand much more than solids. For example, when a liter of water is heated from to 100 C, it increases in volume about 40 cubic centimeters, whereas a block of steel of the same volume would expand only 3.9 cubic centimeters. Alcohol, oils, and especially kerosene expand even more than water. Liquids, like solids, expand with almost irresist- ible force when heated, and exert enormous pres- sures if expansion is prevented by their surround- ings. In the case of liquids and gases, cubical expansion rather than linear is what is always measured. Since, however, the vessel which contains the liquid expands as well as the liquid, we observe only the appar- ent expansion. In a mer- cury thermometer the ap- parent expansion is only about | of the real expan- sion of the mercury. The coefficient of cubical expan- sion of alcohol is 0.00104, of mercury 0.000181, and of water from 0.000053 to 0.00059 according to the temperature. water. We have just seen 1.00125 1.00025 5 10 15 20 TEMPERATURES, FIG. 153. Maximum density of water. 172. Abnormal behavior of that solids, liquids, and gases expand as a rule when heated ; water does the same except near its freezing point. 180 PRACTICAL PHYSICS If we fill a tall glass jar nearly full of cracked ice (Fig. 153) and let it stand for a while, the temperature of the water near the top comes to C and remains so, while the temperature at the bottom will be about 4 C. Since the heaviest liquid stays at the bottom, this means that water at 4 C is denser than water at 0. Very precise measurements show that water is most dense at 4 C. When water at 4 is either warmed or cooled, it expands and becomes lighter, as shown by the curve in figure 153. This fact has many important conse- quences. For example, if it were not for this, the water in lakes would freeze in winter, not merely at the surface, but solidly from top to bottom, thus destroying all aquatic life. 173. Expansion of gases. We may easily show the great expansion of a gas when heated, with the apparatus shown in figure 154. Even the heat of the hand on the flask causes bub- bles of air to be expelled from the tube and to FIG. 154. Ex pan- rise through the water. If the heat of a flame sion of gas. j s applied to the flask, the bubbles rise rap- idly. If after a time the flame is removed and the flask allowed to cool, water rises into the flask to take the place of the escaped air. From the volume of water thus drawn up into the flask, it is evident that a considera- ble fraction of the air was expelled during the expan- sion. 100 c The expansion of gases, such as air, illumi- nating gas, or acetylene, is remarkable for two reasons: first, because it is so large being about nine times as much as for water, and second, because it is nearly the same for all oc The coefficient of expansion of a gas can be meas- " * _. , j_ i .c J; IG J.OO. ured as follows. Suppose we have a tube or umtorm sion of a gag un _ bore (Fig. 155), which is closed at one end and has der constant pres- a little pellet of mercury to separate the inclosed gas sure. HEAT EXPANSION AND TRANSMISSION 181 from the atmosphere. (Dry air is a good gas to experiment with.) li we put the tube in a freezing mixture at C, the gas in the tube will contract, and we can measure the length, which we will suppose is 273 millimeters. If we put the tube in steam at 100 C, the gas will expand, and we can measure the length again. We shall find that it is about 373 millimeters. From this it is evident that the gas has ex- panded 1 millimeter for each degree rise in temperature (the expansion of the glass can be neglected). That is, it has expanded ^ or 0.00366 of its volume at C for each degree rise in temperature. study found Gay-Lussac (1778-1850) was one of the first to the expansion of gases under constant pressure. He that different gases have nearly the same coefficients of expansion, namely 2 {3 or 0.00366. 174. Pressure coefficient of gases. Since the volume of a gas increases as the temperature rises, it is reason- able to expect that if a certain quan- tity of gas were heated and yet con- fined in the same space, the pressure would increase. The following ex- periment shows that this is true. Let us start with a gas like dry air, con- fined in a bulb C, which is connected with an open manometer AB, as shown in figure 156. At first we will surround the bulb by melting ice, so that the gas is at C, and have the mercury at the same level in each arm of the manometer, so that the gas is at atmospheric pressure. Then we will surround the bulb with boiling water at 100 C, and keep the gas from expanding by pouring mercury into the manometer arm B, thus increasing the pressure. This increase of pressure is measured by the difference in levels B' and A. From this we may calculate the increase per degree rise in temperature, and finally what fraction it is of the pressure at C. The result is called the pressure coefficient of the gas. FIG. 156. Pressure of gas, heated at fixed volume, in- 182 PRACTICAL PHYSICS Very careful experiments of this sort were first carried out by a Frenchman, Regnault (1810-1878), who found that the pressure of a gas kept at constant volume increases for each degree very nearly ^yg- or 0.00366 of the pressure at 0, no matter what the gas is. It will be noticed that this is the same fraction which we found for the increase of volume. To sum up I. Different gases have nearly the same coefficients of ex- pansion; II. Different gases have nearly the same pressure coeffi- cients; III. The pressure coefficient of any gas is numerically about the same as its coefficient of expansion; each is about ^y^ or 0.00366. 175. Gas thermometers. It is evident that by measuring the increase of volume of a gas under constant pressure or the increase of pressure of a gas kept at constant volume, we have a means of measuring temperature changes. Such a thermometer, filled with hydrogen, is used as the world's standard thermometer at the International Bureau of Weights and Measures near Paris. Since the hydrogen thermometer has been chosen as the standard, it is important to know just how closely a good mercury thermometer agrees with it. Of course they agree exactly at the two fixed points and 100 C, and a careful comparison shows that between and 100 the difference is not over 0.12 at any point. 176. Absolute temperature scale. In the experiment de- scribed in section 178, we started with an air column 273 millimeters in length at C; if we had cooled the gas from to 1 C, the length AB would have been shortened a millimeter, and if we had cooled it to 10 C, the length of the air column would have become 263 millimeters. If, then, the air column continued to contract at the same rate if cooled indefinitely, the volume of the air at 273 C would be zero. HEAT EXPANSION AND TRANSMISSION 183 As a matter of fact, we can never get a gas to so low a tem- perature as 273 C, for every known gas, before that temperature is reached, becomes a liquid. This temperature - 273 C is, however, one of unusual interest in the study of gases. It is called the absolute zero, and temperatures meas- ured from this point as zero are called absolute temperatures. Absolute temperatures may be designated by the letter A. Thus, C is 273 A, 50 C is 323 A, and 100 C is 373 A. To change any temperature from the Centigrade to the absolute scale, we have merely to add 273 de- grees (Fig. 157). From the above discussion of absolute temperature it will be 100 s Cent. Absolute Scale Scale 273- -T 37 3* water boils 273 ice melts absolute zero seen that the volume of any gas FIG- 157. Absolute and Centi- is doubled when its temperature grade scales, is raised from 273 A (0 C) to 2 x 273, or 546 A (273 C). In general, the volume of a gas is very nearly proportional to its absolute temperature when the pressure is kept constant. Now since, by section 174, the coefficient of expansion of a gas at constant pressure is the same as the pressure coeffi- cient at constant volume, when the volume is kept constant, the pressure of a gas is proportional to the absolute temperature. 177. Gas formula. The relation between the volume arid the temperature of a gas can be very concisely expressed algebraically, thus, V_ = T_ v T' (i) where V and V represent the .volumes of a certain gas at the same pressure, but at different absolute temperatures T to T' '. If t is the temperature on the Centigrade scale when the volume is V, then T= 273 + t ; similarly T' = 273 + t' . The relation between the volume and pressure of a gas at 184 PRACTICAL PHYSICS constant temperature may be concisely expressed by Boyle's law (see section 87), PV=P'V, (II) where J^is the volume of a given quantity of gas under a pressure P, and V 1 is the volume of the same gas under a pressure P 1 ', the temperature in the two cases being the same. The relation of the volume to both pressure and tempera- ture can be expressed by the equation, (Ill) for it is readily seen that this equation reduces to equation (II), if T=T r , and that if P=P', the equation becomes Y/T= V /T 1 , which is another form of equation (I). Equa- tion (III) is called the gas formula. A problem will make clear the use of the gas formula. Suppose we wish to find the volume of a certain quantity of gas under standard con- ditions, that is, at C, and 760 millimeters pressure, when it is known to occupy 120 cubic centimeters at 15 C and under a pressure of 740 millimeters. Substituting in equation (III), we have 120 x 740 V x 760 273 + 15 ~~ 273 + ' whence V = 111 cubic centimeters. PROBLEMS 1. At what temperature on the Centigrade scale will a liter of air at expand to occiipy 2 liters, the pressure being held constant ? 2. A certain quantity of gas occupies 350 cubic centimeters at 27 C. What will be its volume at C, the pressure being held constant? 3. A" steel tank full of air at 15 C under atmospheric pressure was sealed and thrust into a furnace, where it was heated to 1000 C. How many atmospheres of pressure did the air then exert? Neglect the thermal expansion of the steel. 4. A liter of air at 0C and atmospheric pressure weighs 1.293 grams. What is the density of air at 100 C and atmospheric pressure ? HEAT EXPANSION AND TRANSMISSION 185 5. A student in a chemical laboratory generates 50 liters of hydrogen at 10 C, and at a pressure of 700 millimeters. Find the volume of the gas under standard conditions; that is, at C and at 760 millimeters. 6. At the beginning of the so-called " compression stroke " in an automobile engine, its cylinder contains 42 cubic inches of gas and air at atmospheric pressure, and at a temperature of 40 C. At the end of the compression the volume is 6 cubic inches and the pressure is 15 atmos- pheres. What is the temperature ? 178. Low temperatures. The investigations of Lord Kel- vin (1824-1907) and of other scientific men all point to the conclusion that the temperature 273 C is really an absolute zero in the same sense that it is the lowest possible temperature in the universe. Although no one has as yet succeeded in cooling a body to absolute zero, temperatures within a very few degrees of this point have been attained by the evapora- tion of liquefied gases. With liquid air, temperatures as low as 200 C may be obtained, and with liquid hydrogen - 258 C. In 1908 Professor Chines, at the University of Leyden in Holland, found that the boiling point of liquid helium is 268.6 C, or only about 4.5 above the absolute zero, and he has since cooled liquid helium to within 2 of the absolute zero. At these low temper- atures rubber and steel become as brittle as glass, and metals become much better con- ductors of electricity than at ordinary tem- peratures. 179. Hot-air engine. An interesting ap- plication of the expansion of gases is the hot-air engine. Its operation can be best understood by studying figure 158. A loosely fitting plunger A moves up and down and thus shifts the air back and forth in the cylinder (7, which is heated at the bottom and kept cool at the top. The working cylinder O f has a nicely fitting piston $. FIG. 158. Diagram of hot-air engine. 186 PRACTICAL PHYSICS When the plunger A moves down, the hot air below is transferred to the top, where it is cooled. This makes it con- tract. The piston 13 is then forced down by the external pressure of the atmosphere. As soon as the piston B is near the bottom of its stroke, the plunger A is raised, caus- ing the air to flow back under A, where it is heated by the fire. This makes it ex- pand and forces the piston B up again, and so the cycle is repeated. These engines are commonly used for pumping water on a small scale at isolated places, for they do not require expert at- tendants, and they use any kind of fuel. In general they cannot compete with gas engines on account of their bulk and the rapid wearing out of the heating surfaces. 180. Convection currents. All systems of heating and ventilation depend upon what are called convection currents, which in turn depend upon the expan- sion of liquids and gases. To make these clear, let us try two simple experiments. We cut off the bottom of a bottle and bend a glass tube (Fig. 159) so that the ends can be slipped through a stopper which fits the neck of the bottle. If we invert the bottle and fill it with water containing a little sawdust, we can see a circulation of the water when a flame is waved back and forth from A to B. We note that the direction is from A to B. Why? A box (Fig. 160) has a glass front, and two holes in the top, which are covered with glass chimneys. If we put a candle FlG> m _ Convection current under one chimney, convection currents of air. FIG. 159. Convection current of water. HEAT EXPANSION AND TRANSMISSION 187 of air go down the cool chimney and up the warm one. A. bit of lighted touch paper held near the top of the cool chimney makes the convection currents more evident. The draft in a lamp, stove, fireplace, or power-house chimney is a convection current* The explanation of the movement of convection currents is that any gas or liquid expands when heated, so that a given quantity of fluid increases in volume and consequently decreases in density. In a convection current, the lighter fluid is pushed up by the heavier surrounding fluid, just as a block of wood under water is pushed up by the surround- ing water. TRANSMISSION OF HEAT 181. Heat transfer by convection. Since the up-going part of a convec- tion current is warmer than the re- turning part, there is a transfer of heat from the flame or other source of heat at the bottom, to the cooler parts of the circuit at the top. This process of transporting heat by carry- ing hot bodies or hot portions of a fluid from one place to another is called con- vection. It is the basis of almost all systems for heating buildings. 182. Hot-water heating. The ar- rangement for heating water in the kitchen range for general use in laundry FlG - 161 -Hot-water heater, and bathroom is shown in figure 161. The cold water en- ters the tank through a pipe which reaches nearly to the bottom. From the bottom of the tank the water is led to a heating coil along the side of the fire box in the range. When the water becomes hot, it is pushed up and goes back into the 188 PRACTICAL PHYSICS tank at a point nearer the top. Thus a circulation is set up which continues until practically all the water in the tank has passed through the stove and the whole tankful is hot. The hot-water system of heating houses depends on this same principle of convection. Water is heated nearly to the boil- ing point in a furnace in the basement. The hot water is led from the top of the furnace through pipes to iron radia- tors in the various rooms of the building. On account of the large exposed surface in each radiator, heat is rapidly given out by the hot water to the surrounding air. The cooled water is then carried from the radiators through return pipes to the base of the furnace. To prevent ra- diation from the pipes, a thick non-conducting coating of as- bestos is often provided. 153. Hot-air system of heat- ing and ventilating. The hot- air furnace in the basement (Fig*. 162) is simply a big stove, surrounded by a shell or jacket of galvanized sheet iron. The air between the stove and outer shell is heated, and is then pushed up into the flues by the heavier cold air which comes in from out of doors through the cold-air inlet flue. The smoke, of course, goes up the chimney. The warm air which enters the rooms finds an outlet around the doors and windows. In the hot-water system of heating there is no provision whatever for changing the air in the room ; that is, for venti- lation. In the hot-air system, a small quantity of fresh air is continually flowing into the rooms. This is enough for a private house. But in schools, churches, and other public buildings, large quantities of clean, fresh, warm air have to FIG. 162. The hot-air furnace. HEAT EXPANSION AND TRANSMISSION 189 be continually supplied by other means. For the proper ventilation of a room it is estimated that each person in it requires about 50 cubic feet of fresh air every minute. In large modern school buildings the air is drawn in from out of doors by powerful fans, filtered through cloth, warmed by passing around steam pipes, and then distributed in ducts throughout the building. The vitiated air in each room is forced out through ducts near the floor. This indirect system of heating, while expensive, furnishes excellent ventilation. 184. Conduction in solids. Besides transporting heat from one place to another by carrying hot bodies about, or making hot fluids flow through pipes, we can transmit heat from one place to another, without moving any material thing, by either of two methods called conduction and radiation. Every one knows that the handle of a silver spoon gets hot when its bowl is in a cup of hot tea or coffee. If one end of an iron poker is put in the fire, the other end gets un- comfortably hot and must be provided with a wooden handle. Yet if a wooden rod is plunged into a fire, it is hard to feel any warmth at the other end. So we conclude that silver and iron conduct heat better than wood. In general, metals are good conductors of heat. There are some substances, such as stone, glass, wood, wool, fur, and ashes, which are poor conductors of heat and are therefore called heat insulators. The metals, such as silver, copper, brass, iron, lead, etc., are good conductors as compared with the non-metals. Careful study shows that even the metals vary in their power to conduct heat, that is, in con- ductivity. |\ V This can be shown by the following ex- periment. Let us fasten with sealing wax a number of steel balls at regular FIG. 163. Relative conductivity of copper and iron. 190 PRACTICAL PHYSICS intervals on the under side of two rods, one of copper and the other of iron. If we heat one end of each rod in a flame (Fig. 163), the balls on the copper rod soon begin to drop off, beginning near the flame. Later the balls on the iron rod begin to drop off. Often half the balls will haye dropped from the copper rod before the first one drops from the iron rod. 185. Conduction in liquids and gases. Liquids and gases -, ft are much poorer conductors than metals. This can be shown by the following ex- periments. FIG. 164. Water a non-conductor. Let us take a test tube full of water and place in it a few pieces of ice which are held in the bottom by a wire, as shown in figure 164. Then we may boil the water at the top of the tube for some time with- out melting the ice in the bottom. Another more striking experiment to show the poor conductivity of water is shown in figure 165. The bulb of the air thermometer is placed only half an inch below the surface of the water in the funnel. When a spoonful of ether is poured on the surface of the water and lighted, the liquid in the tube of the air thermometer will re- main practically stationary, in spite of the fact that the air thermometer is very sensitive to changes in temperature. Experiments to measure conductivity show that iron conducts 100 times as well as water, and that water conducts 25 times as well as air. In general, it may be said that liquids and gases are very poor con- ductors of heat. It is an interesting fact that substances which are good conductors of heat are good conductors of electricity as well. 186. Applications. These differences in FIG. 165. Burning conductivity explain why teapots have ther on tla * water \ IT, i , does not affect the wooden or insulated handles ; why steam a i r thermometer HEAT EXPANSION AND TRANSMISSION 191 pipes are covered with wool, magnesia, or asbestos ; why double windows are used in cold climates ; why a vacuum bottle (Fig. 166) keeps things hot or cold; and why we wear woolen clothing in winter. Woolen clothing of loose texture, furs and feathers, or eiderdown quilts are effective as heat insulators be- cause so much air is inclosed in their pores. Differences in conductivity also account for many of our curious sensations of heat and cold. Thus in a cool room some things feel much colder than others. Metallic objects, which are good conductors, take FIQ. 166. Section of heat rapidly from the hand, and so give vaTuTm^a^ver* the sensation of cold. While other ob- poor conductor of jects, such as wood and paper, do not heat ' carry off the heat of the hand and so do not feel cold. Sim- ilarly a piece of metal lying in the hot sun feels much warmer than a piece of wood beside it. 187. Radiation. If an iron ball is heated and hung up in the room, the heat can be felt when the hand is held under the ball. This cannot be due to convection, because the hot- air currents would rise from the ball. It cannot be due to conduction because gases are very poor conductors. Simi- larly a lighted electric light bulb feels hot if the hand is held near it, but when the light is turned off, the sensation stops very quickly. The glass of the bulb is a very poor conductor and there is practically no air left inside the bulb, so that the sensation of heat can be due neither to convection nor to conduction. Furthermore, an enormous quantity of heat comes to us from the sun. Yet men who make ascents in balloons and aeroplanes find that the air becomes less and less dense, so that it seems reasonable to suppose that the earth's atmosphere forms a coating only a few miles thick 192 PRACTICAL PHYSICS and that the space beyond is absolutely empty. So the sun's heat cannot come by convection or conduction. Scientists, to explain these phenomena, have imagined a weightless, elastic fluid called the ether which fills all space and transmits heat and light by a process called radiation. When a body not in contact with conducting bodies cools, it is said to radiate heat, or to cool by radiation. If one places a screen, such as a book, -between a lighted lamp and his face, he no longer feels the heat. So we think that heat rays, like light rays, travel in straight lines. Experiments also show that heat rays, like light rays, can be reflected by a mirror, or brought to a focus by a burning glass. Some substances, such as glass and air, let the sun's heat rays pass through almost unimpeded and are warmed but little by this radiant heat ; that is, they are " transparent-to- heat." Other substances, such as water, do not let heat pass through and are warmed by any radiant heat rays that strike them ; they are "opaque-to-heat." A mirror, or any highly polished surface, is a good heat reflector, and yet itself remains cold. Fresh snow melts slowly in the sun's rays, but snow covered with soot or black dirt melts rapidly. In general, reflecting or white objects do not easily absorb radiant heat, while rough or black objects absorb heat readily. It has also been found that reflecting and bright-colored objects, when hot, cool by radiation more slowly than rough and dark objects. For example, a brightly polished silver cup radiates heat twenty times more slowly than a sooty black cup. In general, good absorbers are good radiators, and poor absorbers are poor radiators. 188. Theory as to what heat is. There are many reasons for thinking that heat is a rapid vibratory motion of the molecules of substances or of the ether which fills the spaces between the molecules. We imagine that the molecules in a hot flatiron are vibrating more rapidly than when it was HEAT EXPANSION AND TRANSMISSION 193 cold, and that this molecular vibration extends to the sur- rounding ether and so is sent out in straight lines in all di- rections as radiant heat. At a temperature of about 550 C iron becomes " red hot," and at 1300 C it gets " white hot." We imagine that the iron, before it begins to glow, is sending out dark heat rays, but that, when red hot or white hot, it is sending out visible heat rays, that is, light rays. We think that these heat rays and light rays differ only in the rapidity of the vibratory motion, and in their effect on man's organs of sense. If the vibrations are under 400 trillion per second, we recognize them as heat; but if the vibrations are between 400 and 800 trillion per second, the nerves of the eye recognize them as light. Heat and light are both forms of radiant energy. This radiant energy travels at the enormous speed of 187,000 miles per second, which means that radiant energy could circle the earth seven times in one second. On this theory, the expansion of bodies when heated is due to the more violent vibration of their molecules, which require more room to move about in. At a certain tem- perature this motion becomes so violent that the molecules break away froni their former position and the body changes its state ; that is, it melts or boils. SUMMARY OF PRINCIPLES IN CHAPTER X 100 Centigrade degrees = 180 Fahrenheit degrees. Temp. Fahr. = (f Temp. Cent.) + 32. Temp. Cent. == f (Temp. Fahr. 32). Coefficient of linear expansion = expansion per degree for unit length _ total expansion total length x rise in temperature Total expansion = coefficient x length x rise in temperature, o 194 PRACTICAL PHYSICS Coefficient of volume expansion = expansion per degree for unit volume, total expansion total volume x rise in temperature Total expansion = coefficient x volume x rise in temperature. For solids, volume coefficient = 3 x linear coefficient. Pressure coefficient of gases = total pressure rise pressure x rise in temperature Total pressure rise = coefficient x pressure x rise in temperature, 1 Volume coefficient of all gases nearly the same. Pressure coefficient of all gases nearly the same. Value Volume and pressure coefficients nearly equal. Gas law: QUESTIONS 1. Is friction ever a source of useful heat? 2. Are the sun's rays ever used practically as a direct source of heat for engines? 3. Why does spring water seem warm in winter and cool in summer? 4. Why does the water seem much colder before a bath than after- wards ? 5. Why can a platinum wire be sealed or melted into glass while a copper wire cannot ? 6. Why do glass bottles crack when placed on a hot stove ? 7. Why do apples and pieces of green wood swell when heated ? 8. Why is there a cold indraft of air at the bottom of an open window? 9. Is there any other reason than convenience for putting furnaces in cellars rather than in attics ? 10. How is the water which is standing in the hot-water pipes in a house kept hot ? 11. Does a hot body cool more rapidly if placed on metal than if placed on wood ? Why ? HEAT EXPANSION AND TRANSMISSION 195 12. Why does a glowing coal die out quickly on a metal shovel, and yet glow for a long time in ashes? 13. How does a fire less cooker work ? 14. Look up Davy's lamp for miners in an encyclopedia. What is its advantage ? Why is it that a flame will not strike through the fine-net wire gauze ? 15. Why are the walls of ice houses often packed with sawdust? 16. Why should an air space be left in building the walls of brick and cement houses? 17. Does woolen ctothing supply any heat to maintain the body's temperature ? 18. Why do people prefer to wear white clothes in summer and in hot countries? 19. Why should the surface of a teakettle be brightly polished and the bottom blackened ? 20. Is it advisable to put any sort of aluminum or gold paint on a radiator that is to heat a room ? 21. Describe carefully the "dampers" of some stove or furnace you have seen, and explain how they accomplish the desired results. CHAPTER XI WATER, ICE, AND STEAM Measurement of heat B. t. u. and calorie specific heat freezing point change of volume in freezing latent heat, ice to water boiling point under various pressures dis- tillation latent heat, water to steam humidity fog, rain, and snow artificial ice. 189. How we measure heat. If a man buys a ton of coal, what does he get for his money ? One answer would be, about 2000 pounds of material, of which, perhaps, 40 pounds is water, 320 pounds is ash, and the rest mostly carbon and hydrogen. What the man is really interested in, however, is not the sort of material, but the amount of heat he has bought. Since heat is not a substance, but a form of energy, we cannot measure it directly in pounds or quarts, but must measure it by the effect it caii produce. For example, if one pound of hard coal could be completely burned, and if all the heat generated in this process could be used to heat water, it would be found that about 7 tons of water could be raised 1 F in temperature. Engineers reckon the heat value of fuel in units sucli that each represents the heat required to raise one pound of water one degree Fahrenheit. This heat unit is called the " British thermal unit," and is written B. t. u. For example, the heat value of a pound of coal varies from 11,000 to 16,000 B. t. u. ; a pound of petroleum gives about 25,000 B. t. u., a pound of gasolene about 19,000 B. t. u., and a pound of dry wood about 5000 B. t. u. The heat unit employed in Europe, and in all physical and chemical laboratories, is a metric unit called the calorie. The calorie is the heat required to raise the temperature of a gram of water one degree Centigrade. 196 WATER, ICE, AND STEAM 197 190. Heat absorbed by different substances. It is well known that a kettle of water on a stove gets warm much less quickly than a flatiron of the same weight. For example, the heat required to warm a kilogram of water 1 degree will warm the same weight of copper 10 degrees, of silver or tin 20 degrees, and of lead or mercury 30 degrees. In fact experiments show that water requires more heat per unit weight per degree rise of temperature than any other common substance. Since one calorie is required to raise the temperature of one gram of water one degree, only one tenth of a calorie would be needed to raise the temperature of one gram of copper a degree, one twentieth of a calorie to raise a gram of silver one degree, and one thirtieth of a calorie to raise a gram of lead one degree. The number of calories required to raise the temperature of a gram of a substance one degree Centigrade is called its specific heat. Thus the specific heat of water is 1, of copper about 0.1, etc. The following experiment of Tyndall's illustrates how much substances differ in their specific heats. We may heat a number of balls of the same weight but of different metals, such as iron ; zinc, copper, lead, and tin, to about 150 C in oil. Then if we place them all at the same time on a thin cake of paraffin wax which is held on a ring, as shown in figure 167, they will melt the wax and sink into it, but at different rates. The iron works its way most vigorously into the wax, and even through the cake. The zinc and copper balls come next, while the lead ball makes but little headway. The metal with the largest specific heat, iron, gives out the largest amount of heat in cooling and so melts JT IG 167 _ Metals differ the most paraffin. in specific heat. 191 How specific heat is determined. When a' hot sub- stance, such as hot mercury, is poured into cold water, the 198 PRACTICAL PHYSICS water and mercury soon come to the same temperature. The heat given up by the cooling mercury is used in warming the water. If no heat is lost in the process, the heat units given out by the hot body are equal to the heat units gained by the cold body. This method of mixtures is accurate only when no heat is lost during the transfer. This is rather difficult to manage in practice. Nevertheless, this method is the one generally used in laboratories to determine the specific heat of substances. For example, suppose that 300 grams of mercury are heated to 100 C and then quickly poured into 100 grams of water at 10 C, and that, after stirring, the temperature of the water and mercury is 18.2 C. If we let x be the specific heat of the mercury, the mercury gives out 300(100 - 18.2)z calories. Since the specific heat of water is 1, the water absorbs 100(18.2 10)1 calories. Therefore we may make the equation 300(100 - 18.2)* = 100(18.2 - 10)1, whence x = 0.033 calories. By very careful experiments of this sort the specific heats of some of the common substances have been found to be as follows : TABLE OF SPECIFIC HEATS Water 1.00 Pine wood 0.65 Alcohol 0.60 Ice 0.50 Aluminum 0.22 Sand 0.19 Iron 0.12 Copper 0.094 Zinc 0.093 Mercury 0.033 It is remarkable that of all ordinary substances water has the greatest specific heat. Thus it takes about four times as much heat to raise a pound of water one degree as to raise a pound of solid earth one degree, and so the ocean acts as a great moderator of temperatures. In summer the water absorbs a vast amount of heat which it slowly gives up in winter to the land and air. This explains why the tempera- ture on some ocean islands does not vary more than 10 F during the whole year. WATER, ICE, AND STEAM 199 PROBLEMS 1. How many calories of heat are needed to raise the temperature of 10 grams of water 5 C ? 2. How many calories are required to heat 15 grams of iron 20 C ? 3. Compute the calories given out by a kilogram of copper in cool- 'ngfrora 110 C to!5C. 4. How many B. t. u. are necessary to heat a 2-pound flatiron from 70 F to 350 F ? 5. If the heat value of coal is 14,000 B. t. u. per pound, how many tons of water can be heated from 32 to 212 F by the combustion of one ton of coal in a boiler whose efficiency is 75 % ? 6. If 400 grams of water at 100 C are mixed with 100 grams of water at 20 C, what will be the temperature of the mixture? 7. It' 500 grams of copper at 100 C, when plunged into 300 grams of water at 10 C, raise the temperature to 22 C, what is the specific heat of copper? 8. A piece of iron weighing 150 grams is warmed 1 C. How many grams of water could be warmed 1 by the same amount of heat ? (The answer is called the water equivalent of the piece of iron.) 9. A 50-pound iron ball is to be cooled from 1000 F to 80 F, by putting it in a tank of water at 32 F. How many pounds of water must there be in the tank? 10. A platinum ball weighing 100 grams is heated in a furnace for some time, and then dropped into 400 grams of water at C, which is raised to 10 C. How hot was the furnace? (Sp. heat = 0.04.) 192. Melting and freezing. If one brings in from out of doors on a cold winter day a pailful of snow or ice and sets it on a stove, he finds that its temperature is at first below C and slowly rises to that point. It then remains stationary, or nearly so, until all the snow is melted. Then the temperature of the water gradually rises. This stationary temperature, where the ice (snow) changed to water, is called the melting point of ice, and is C or 32 F. We may also determine the freezing point of water by making a freezing mixture of cracked ice and salt and placing in it a test tube containing some pure water. The tempera- ture of the water will be observed to fall slowly until the water begins to freeze. Then the temperature remains con- 200 PRACTICAL PHYSICS stant until all the water is frozen. This stationary tempera- ture at which water changes into ice is called the freezing point of water, and is C or 32 F. Substances which are crystalline, such as ice and many metals, change into liquids at a definite temperature, and the melting point of such a substance is the same as its freez- ing point. TABLE OF MELTING OR FREEZING POINTS Platinum Steel Glass Copper Gold Silver Lead above 1700 C 1300 to 1400 C 1000 to 1400 C 1083 C 1062 C 960 C 327 C Tin 232 C Sulphur 115 C Naphthalene (moth balls) 80 C Paraffin about 54 C Ice C Mercury - 39 C Alcohol about - 112 C Non-crystalline substances, such as iron, glass, and paraffin, pass through a soft, pasty stage as the melting point is ap- proached. In the case of some substances, such as the fats, the melting point is not the same as the freezing point. Thus butter will melt between 28 and 33 C and yet solidi- fies between 20 and 23 C. There are several alloys of metals which melt at a much lower temperature than any of the metals of which they are made. " Wood's metal " (2 tin + 4 lead + 7 bismuth + 1 cadmium by weight) melts at 70 C, although the lowest melting point of any of its constituents is that of tin (232 C). Wood's metal will melt even in hot water. Such alloys are used to seal tin cans and automatic fire sprinklers. Other similar alloys are used for fusible plugs for boilers. 193. Expansion in freezing. When a liquid freezes, we would naturally expect it to contract, because it would seem that the molecules would be more closely knit together in the solid than in the liquid state. This is generally true. But when we recall that ice floats and pitchers of water are often cracked by freezing, we see that water expands on freezing. WATER, ICE, AND STEAM 201 In fact a cubic foot of water becomes 1.09 cubic feet of ice. Cast iron is another substance that expands a little in solidifying, and it is therefore adapted to making castings, for in this way every detail of the mold is sharply re- produced. In making good type we must have a metal which expands a little on solidifying, and so an alloy of lead, antimony, and copper, which has this property, is used. That the expansive force of water in freezing is enormous can be seen from the following experiment. Let us fill a cast-iron bomb with water, close the hole with a screw plug (Fig. 168), and put the bomb in a pail of ice and salt. When the water in the bomb freezes, the pressure inside increases more and more, and the bomb eventually explodes. This shows why water pipes burst on nights cold enough to freeze the water in them. A similar process is active every winter in breaking the rocks of mountains to pieces. Water percolates into the crev- FlG - 168 -~ Ex P an - , sive force exerted ices, freezes, and expands. by freezing water. 194. Effect of pressure on melting ice. If we suspend a weight of 40 or 50 pounds by a wire loop over a block of ice (Fig. 169), the wire will cut slowly through the ice. The pressure causes the ice to inelt under the wire ; but the water flowing around the wire freezes again above it, and leaves the block as solid as be- fore. This experiment shows that pressure causes ice to melt by lowering the freez- ing point. This might be expected, for pressure on any body tends to prevent its expansion, and since water does ex- pand on freezing, pressure will tend to prevent freezing ; that is, it lowers the It requires, however a . 169. -Wire cutting through a block of ice. pressure of almost a ton (1850 pounds) 202 PRACTICAL PHYSICS per square inch to lower the freezing point one degree Cen- tigrade. In skating, the pressure of the edge of the skate blade melts the ice and so forms a film of water which is very slip- pery. This also explains how snowballs can be made by pressing the snow between the hands. The pressure at the points of contact between the flakes of snow melts them and then the film of water that is formed freezes again when the pressure is released. The flow of glaciers of solid ice around corners is explained in the same way. 195. Latent heat : ice to water. If a dish of ice and water at C is kept in a room where everything else is at 0, the ice will not melt and the water will not freeze. But if the dish is surrounded by a freezing mixture, such as salt and ice, the water will freeze, or if the dish is brought into a warm room, the ice will melt. In either case, however, the temper- ature of the mixture will remain steady at until either all the ice is melted or all the water is frozen. It seems evident, then, that when ice melts, heat energy, called latent heat, is absorbed, which does not show itself in a rise of temperature. 196. How much heat to melt 1 gram of ice ? In solving this problem we may apply the method of mixtures which was used in determining the specific heat of a metal. If we put 200 grains of ice at 0C into 300 grams of water at 70 C and stir them thoroughly, the temperature of the water, after the ice is all melted, will be 10 C. Let x no. of calories required to melt 1 g. of ice. Then 200 x = no. of calories required to melt 200 g. of ice. Also 200 x 10 = no. of calories required to raise melted ice from to 10, and 300 (70 - 10) = no. of calories given out by the water in cooling. Then 200 x + 200 x 10 = 300 (70 - 10), whence x = 80 calories. WATER, ICE, AND STEAM 203 The best experiments that have been made show that the latent heat of melting ice is just about 80 calories, which means that 80 calories are absorbed in changing 1 gram of ice at C into water at C. 197. Heat given out when water freezes. We have just seen that heat energy is required to pull apart the molecules of the solid ice and change it into the liquid state, where we believe the molecules are held together less intimately. Now we want to show that in the reverse process, that is, in freezing, this energy ap- pears again as heat. We may show that freezing is a heat-evolving process in the following experiment. If we repeat the experiment described in section 192, except that we keep the water, thermometer, and test tube (Fig. 170) very quiet, we shall be surprised to find that the water will cool several degrees below C before the freezing begins. When once started by stirring or dropping in a crystal of ice, the crystals of ice form rapidly, but the temperature jumps to C and remains stationary until all the water is frozen, even though the freezing mixture in the jar outside the test tube is as cool as 10 C. People sometimes make use of the heat given out by water when it freezes, by putting pails or tubs of water in a green- house or a cellar to prevent the freezing of the plants or vegetables. As the water begins to freeze first, the heat evolved in the process prevents the temperature from falling much below C. When a large lake freezes, the heat evolved helps to keep the temperature in its vicinity from falling as low as it does farther away. PROBLEMS 1. How many calories of heat are required to melt 20 grams of ice at 0C? 2. How much heat is evolved in cooling and freezing 12 grams of water originally at 10 C ? 17Q _ F reez j ng water evolves heat. 204 PRACTICAL PHYSICS 3. How many B. t. u. are required to melt one pound of ice at C ? 4. How much water at 100 C will be needed to melt 300 grams of snow at C, and raise its temperature to 20 C ? 5. If a 500-gram iron weight is heated to 250 C and placed on a block of ice, how many grams of the ice will be melted ? 198. Process of boiling water. Let us fill a round-bottomed flask (Fig. 171) half full of water and put through the stopper a thermometer, an open manometer, and an outlet tube for the steam. At first, as the water is heated, the air, which is dissolved in the water, rises to the surface in little bubbles. Then bubbles of steam form at the bottom, but these col- lapse when they strike the upper, cooler layers of water, and disappear, causing the rattling noise known as "singing" or "simmering." When the bubbles of steam begin to reach the surface, the water is said to "boil." It will be noticed that the steam in the flask is as clear as air, but as it leaves the outlet tube it condenses and forms a white cloud or mist. As soon as boiling begins, the thermometer, which has been rising rapidly, reaches 100 C and remains stationary. ~/~~^ 4^1_^S^'^^fl If we partly close the outlet valve, the manometer will show an increase of pressure, while the thermometer will show a rise in the temperature of the boiling water. FIG. 171. Boiling water. Finally if we remove the burner, and let the water cool a bit, we may connect the outlet tube with an aspirator, which will reduce the pressure and make the water boil again. The process of boiling consists in the formation in a liquid of bubbles of vapor, which rise to the surface and es- cape. The temperature at which this takes place is the boiling point of the liquid. There is a second and more exact definition of the boiling point. It is evident that a bubble of water vapor can exist within the liquid only when the pressure exerted outward by the vapor within the bubble is at least equal to the atmos- pheric pressure pushing down on the surface of the liqui.d. WATER, ICE, AND STEAM 205 For if the pressure within the bubble were less than the outside pressure, the bubble would immediately collapse. Now the pressure that would exist inside a bubble, if it could form at all, would be different at different temperatures. It is called the vapor pressure, or vapor tension, of the liquid, and we shall soon see how to determine its values at different temperatures. The boiling point of a liquid may therefore be defined as the temperature at which its vapor pressure is one atmosphere. 199. Effect of changing pressure. We have just seen in the experiment about boiling that if the pressure on the surface of the liquid is increased, the temperature has to be raised before the liquid will boil. If the pressure is de- creased, the liquid will boil at a lower temperature. We can understand this if we recall that ordinarily the atmos- phere is exerting a pressure of about 15 pounds per square inch on the surface of the liquid. If we reduce this pressure, it is easier for the bubbles of vapor to form ; if the pressure is increased, it is more difficult for the bubbles to form. In any case, they will form only when the temperature is high enough so that, when they have formed, the pressure in them is equal to the pressure on the surface of the liquid. So by observing the temperatures at which a liquid boils under different pressures, we can determine how the vapor pressure of the liquid changes with temperature. Experi- ments have shown that, near 100 C, the vapor pressure of water increases by about 27 millimeters of mercury for each Centigrade degree rise of temperature. Benjamin Franklin devised the following interesting ex- periment to show water boiling under reduced pressure. Let a flask half full of water, which is boiling vigorously, be removed from the flame and instantly corked air-tight with a rubber stopper. We may then invert the flask, as shown in figure 172, and cool the top by pouring on cold water. The water in the flask immediately begins to boil again. This is because the steam in the top of the flask is condensed and so the pressure on the surface of the liquid is much reduced. 206 PRACTICAL PHYSICS Sometimes it is very desirable to boil liquids at as low a temperature as possible. For example, the water is boiled away from sirup and from milk in what are called vacuum pans, which are merely closed kettles with part of the air pumped out. The water boils away at about 70 C and leaves the granulated sugar or milk condensed, but not cooked. On the tops of high mountains the temper- ature of boiling water is so low that eggs cannot be cooked. In Cripple Creek, Col., about 10,000 feet above sea level, it takes about twice as long to cook potatoes as in Boston. In some high altitudes closed ves- FIG. 172. Boiling sels provided with safety valves, called water under re- "digesters" or "pressure cookers" (Fiff. 173), duced pressure. , , nave to be used in cooking. Digesters are also used for extracting gelatine from bones. The effect of the increased pressure in a digester or pressure cooker is the same as in a boiler. The water in a boiler whose gauge reads 100 pounds is boil- ing, not at 100 C, but at 170 C or 338 F. Since we have denned the 100 point on the Centigrade scale as the tempera- ture of boiling water, and since the tem- perature at which water boils is so much affected by changes in pressure, it is necessary to fix on some standard pressure at which thermometers are to be " cali- FlG - 173 - Pressure brated" or marked. By common agree- ment, this standard pressure is the pressure exerted by a column of mercury 760 millimeters high, the temperature of the mercury being C. The temperature at which water boils under this pressure is, by definition, 100 C. WATER, ICE, AND STEAM 207 200. Summary. What has been said about the process of boiling can be summarized as follows : (1) A liquid will boil only when its temperature is such that its vapor pressure is equal to the pressure on its surface. (2) What is called " the boiling point " of a liquid is the temperature at which it will boil under atmospheric pressure ; that is, the temperature at which its vapor pressure is one atmosphere, or 760 millimeters of mercury. (3) Every liquid has its own boiling point. The boiling point of water is by definition 100 O. (4) The rule about boiling under other pressures than one atmosphere is, the higher the pressure, the higher the tempera- ture required to make the liquid boil. TABLE OF BOILING POINTS (At a pressure of 760 millimeters ) Zinc 918 C Sulphur 445 C Mercury 357 C Saturated salt solution 108 C Water 100 C Alcohol Ether Ammonia Oxygen Hydrogen 78 C 35 C - 34 C - 183 C - 253 C 201. Distillation. In many localities the only way to be sure of getting pure water is by what is called distillation. Let us set up a boiler B and a condenser C as shown in figure 174, and color the water in the boiler with blue vitriol (copper sulphate). When the solution is boiled, the vapor or steam given off is con- densed, by the continual cir- culation of cold water through the jacket, as a colorless, taste- Fm 174 ._ Purification of water by distillation, less liquid, pure or distilled water. The non-volatile impurities, including the vitriol, are left behind in the boiler. 208 PRACTICAL PHYSICS The process of distillation consists of boiling a liquid and condensing its vapor. In commercial work this is usually done in a "worm con- denser." This consists of a pipe coiled into a spiral and surrounded by circulating cold water (Fig 175). In this way a large condens- ing surface is obtained in a small space. When a mixture of two liquids is distilled, the liquid with the lower boiling point vaporizes and is con- densed first. It can thus be sepa- rated from the one with the higher boiling point. Thus alcohol is Fia. 175. Worm condenser, distilled from fermented liquors by this process of fractional distillation. It is in this way that gasolene and kerosene are got from crude petroleum. PROBLEMS AND QUESTIONS 1. How is the temperature of boiling water affected by taking the water to the bottom of a deep mine ? 2. If water boils at 99 C, what is the atmospheric pressure ? 3. If water boils at 208 F, what does the barometer read ? 4. An elevation of 900 feet makes a difference of about 1 inch in the barometer. At what temperature would water boil 1500 feet above the sea? 5. What effect does salt or sugar have oh the boiling point of water ? Try it. 6. In distilling a mixture of alcohol and water, which liquid begins to distill over first ? 7. How could you obtain fresh water from sea water? 8. Mark Twain in his " Tramp Abroad " tells of stopping on his way up a mountain to " boil his thermometer." What did he do, and why? WATER, ICE, AND STEAM 209 202. Latent heat : water to steam. When a kettle of water is put on a stove, it gets hotter and hotter until it boils. Then no matter how much heat we apply to the kettle, if there is a free outlet for the steam to escape, the temperature remains constant at 100 C or 212 F. The heat energy which seems to disappear in boiling the water is called the latent heat of steam or the latent heat of vaporization. When steam flows from a steam pipe into a radiator in a room, some of it condenses and gives back the heat which apparently disappeared when the water changed into steam. This latent (or hidden) heat is now understood to represent the energy needed to pull the molecules of water away from each other and set them free as steam. 203. How much heat is needed to make a gram of steam? When we want to determine the amount of heat needed to change a gram of water at 100 C into steam at 100 C, we usually apply the method of mixtures. In practice we generally try to determine the heat evolved in condensing a gram of steam by running dry steam into a given quantity of water at a known temperature for some time. We meas- ure the rise in temperature and the increase in weight, which is the weight of the condensed steam. Then we make an equation in which the number of calories received by the water in being warmed is put equal to the calories given out by the steam in condensing to water at 100 C and by this hot water in cooling from 100 C to the temperature of the mixture. Suppose we take 400 grams of water at 5 C and run in 20 grams of steam at 100 C, which raises the temperature of the water to 35 C. What is the number of calories of heat given out by 1 gram of steam in condensing to water at 100 C ? Let x = latent heat of steam. Since 400 (35 5) = heat absorbed by cold water, and 20 x heat given out by condensing of steam, and 20(100-35) = heat given out by water in cooling from 100 to 35 C, then 400(35 - 5) = 20 x + 20(100-35), and x = 535 calories. 210 PRACTICAL PHYSICS Recent experiments have shown that the latent heat oi steam is about 540 calories. In other words, it takes more than five times as much heat to change any quantity of water into steam as to raise the same quantity of water from the freez- ing to the boiling point. In English units it requires 540 x 1. 8 or 972 B. t. u. to change a pound of water at 212 F into steam at 212 F. PROBLEMS 1. Find the number of calories required to change 15 grams of water at 100 C into steam. 2. Compute the heat evolved by condensing 10 grams of steam at 100 C and cooling it down to 50 C. 3. How much heat will be required to convert 1 kilogram of ice at C into steam at 100 C? 4. How much steam at 100 C must be run into 500 grams of water at 10 to raise it to 40 V 5. In the illustrative example in section 203, the latent heat came out 535, which is a little too low. This shows that the temperature of the mixture (35 C) was not acccurately observed. What should it have been ? 6. How many pounds of coal will be needed in a boiler whose efficiency is 65%, to convert 100 pounds of water at 50 F into steam at 212 F? Assume that the heat value of the coal is 14,500 B. t. u. per pound. 204. Evaporation. Everybody is familiar with the fact that water left in an open dish gradually disappears or evaporates. Evaporation is different from boiling, in that evap- oration takes place at any temperature but only at the surface of a liquid, while boiling goes on inside the liquid but only at a fixed or definite temperature. Evaporation goes on more rapidly the warmer and drier the surrounding air is. For example, wet clothes dry more quickly on a hot day than on a cold, foggy day. 205. Cooling by evaporation. If one pours a few drops of alcohol or ether on his hand, the liquid quickly evaporates, causing a markecj. sensation of cold. Whenever a liquid evaporates, it must get heat from somewhere, and so the WATER, ICE, AND STEAM 211 temperature of the liquid itself and of anything near it drops. That is to say, heat is absorbed in the process of evaporation. It is always more comfortable on a hot day to ride in a car than to sit still, because the rapid circulation of the air makes the moisture of the skin evaporate more rapidly. This is why one can tell the direction of the wind by lifting a moistened finger; the wind blows from the side which feels cool. 206. Moisture in the air. In the summer time a pitcher of ice water is usually covered with little drops of water or "sweat." It might at first be thought that these were due to the water oozing through the pores in the side of the pitcher ; but the microscope does not show any pores in glazed porcelain or glass, so we must conclude that the drops come from the surrounding air. The air is cooled by coming in contact with the cold pitcher and deposits some of its mois- ture. If we put a little water in a bottle and cork it tightly, the water does not evaporate because the air above the water quickly becomes "saturated" with moisture. Thus we see that air can take up only a definite quantity of moisture, depending on the temperature. This can be better under- stood from the following experiment. Let us place a little water in a thin -walled flask and cork it. If we place tne cask in a warm place until it becomes warm, and then cool it, its walls become dim, due to the drops of water. The warm saturated air becomes " supersaturated " on cooling. Careful experiments show that a cubic meter of saturated air contains at different temperatures the following amounts of water vapor: 2 grams at - 10 C. 5 grams at C. 9 grams at 10 C. 17 grams at 20 C. 30 grams at 30 C. 597 grams at 100 C. 212 PRACTICAL PHYSICS From this table it will be seen that air, which is saturated at one temperature, can, at a higher temperature, take up still more water vapor before becoming saturated , but if cooled, it must deposit some of the water vapor which it already has. 207. Relative humidity. Usually the air does not contain all the moisture which it can hold ; that is, it is not saturated. If, however, the temperature suddenly drops, the same ac- tual amount of moisture will saturate the air. For example, if the water in a polished nickel-plated cup is cooled with ice below the temperature of the room, a mist will appear on the outside of the beaker. The temperature of the water when this occurs is the " dew point." The dew point is the temperature at which the water vapor in the air begins to condense. If the air is cooled below the dew point, some of its vapor condenses, and dew collects on objects. Thus we see that the words " dry " or "moist," as applied to the atmosphere, have a purely rel- ative significance. They involve a comparison between the amount of water vapor actually present, and that which the air could hold if saturated at the same temperature. The ratio of these two quantities is called the relative humidity. For example, we may read in the newspaper that the relative humidity is 75%. This means that the amount of water vapor actually present in the air is 75 % of what the air might have contained at the given tempera- ture if it had been saturated. 208. Wet and dry bulb thermometers. Let two thermometers be arranged as shown in figure 176. The bulb of the thermometer at the left is dry, while the other ther- mometer has its bulb wrapped with cotton cloth which is kept moist by a cup of water. If we keep the air around the thermometers circulating by an electric fan, after a ra 1 g s i s I. I a s j -^ jj 1 nr 7>r2/ JFe< FIG. 176; Wet and dry bulb thermometers. WATER, ICE, AND STEAM 213 little while the wet-bulb thermometer will indicate a lower temperature than the dry-bulb thermometer. This is because of the cooling caused by the evaporation from the cotton cloth. The drier the surrounding air, the more rapid will be the evaporation, and so the greater will be the difference between the wet and dry bulb thermometers. With the aid of tables furnished by the Weather Bureau, we may determine from these thermometer readings the so-called " relative humidity " of the air. 209. Practical importance of determining humidity. It is well known that a hot day in Boston is much more uncomfortable than an equally hot day in Denver. This is because a city near the ocean, like Boston, has a higher relative humidity than a city which is inland and a mile above sea level, like Denver. When the relative humidity is high, we feel " sticky " because the perspiration of the skin does not evap- orate readily. On the other hand, too little humidity is in- jurious. Special precautions are taken to keep the air in schools, hospitals, and private houses from getting too dry in winter, and the air in greenhouses must be kept quite damp for the growth of plants. In cotton mills it has been found that the air must be rather moist to make the spinning of yarn suc- cessful. Since the occurrence of frost in the late spring or early fall is injurious to many crops, it is often highly important that farmers should know in the afternoon whether freezing weather during the night is to be expected. The tempera- ture of the dew point gives a ready means of predicting how low the temperature at night will drop ; for when the dew point is reached, further cooling is retarded. So if the dew point is above 40 F, it is seldom that the temperature will fall to freezing in the night. 210. Dew, fog, rain, and snow. On clear, still nights the ground radiates the heat that it has received during the daytime. The grass and leaves, which can radiate heat freely, cool rapidly and soon bring the air near them below its dew point. Then moisture condenses, as dew or at lower tern- 214 PRACTICAL PHYSICS peratures as frozen dew or frost. This phenomenon is exactly like the formation of drops of water on a pitcher of ice water, or on one's spectacles when he conies from the cold out- doors into a warm room. Clouds covering the sky hinder the formation of dew because they restrict radiation. If the condensation of the moisture of the air is not brought about by contact with cold solid objects at the surface of the earth, but by great masses of cold air high above the earth, clouds are formed and rain may result. Fog is merely clouds very near the earth. Clouds at very high altitudes may be composed of bits of ice, but, in general, clouds are made up of minute drops of water. Like particles of fine dust, very small drops of water tend to fall, but can do so only very slowly. Sometimes they fall into warm and not yet saturated layers of air, and then they change back again into vapor. Sometimes they are carried up by ascending currents of air faster than they can fall through them, and so seem to float. For example, the cloud of steam above a locomotive stack is com- posed of minute drops of water and yet rises with the warm air. Clouds are not durable. They simply mark the place in the atmosphere where the process of condensation of water vapor is going on. In rain clouds the little particles of water come together and form FIG. 177. Snow crystals. drops which easily over- WATER, ICE, AND STEAM 215 come the resistance of the air and fall to the ground. If the temperature of the cloud is below 32 F, the particles of water unite to form little delicately fashioned hexagonal snow crystals (Fig. 177). Snow and rain together make what the " weather man " calls "precipitation." Thus in New York there are about 150 days of rain or snow each year, and the total precipitation in a year, if it did not dry up, would cover the earth to a depth of about 3 feet. QUESTIONS AND PROBLEMS 1. A room is 3 meters high, 10 meters long, and 6 meters wide. How many grams of water will be required to saturate the air at 20 C ? 2. An experiment showed that on a certain day, when the tempera- ture was 30 C, the air contained 12 grams of water per cubic meter. What was the relative humidity? 3. How do undue dryness and undue dampness affect wooden furni- ture? 4. What change in the thermometer usually goes with a rising ba- rometer ? 5. What happens when a moist wind from the ocean strikes a mountain range ? 6. In some hot countries the people cool their drinking water by setting it in jars of porous earthenware, in a shady place, where there is a current of air. Explain. 7. Milk used to be set away in shallow pans for the cream to rise. Now they use cylindrical tanks of small area and quite deep. Which is the better, and why? 8. Why do clothes dry best on a windy day ? 9. Why does sprinkling the street on a hot day cool the air? 211. Freezing by boiling. The fact that a large quantity of heat is needed to vaporize a substance is often made use of in getting low temperatures. If a cylinder of liquefied carbon dioxide is tilted, as shown in figure 178, and the valve is opened, the liquid released from pressure vaporizes so rapidly as to cool everything, including the rest of the liquid, and so 216 PRACTICAL PHYSICS some of it is frozen. After the valve has been open a short time, the bag is tilled with a white solid, frozen carbon dioxide. This solid evap- orates very readily, and gives a temperature as low as 80 C. If the solid is put in a beaker and mixed with ether, the mixture will freeze a test tube of mercury. The ether serves to carry the heat quickly from the test tube to the solid. FIG. 178. Liquid carbon dioxide be- ing frozen. 212. Artificial ice. In the manufacture of artificial ice and in refrigerating plants (Fig. 179), gaseous ammonia is compressed by a pump and then cooled until it liquefies. During this process of com- pression and of condensation, heat is evolved, which is removed by passing the ammonia through a pipe covered with running water. The liquefied ammonia is then piped to the ice tank or cold- storage room, and allowed to expand through a valve with a small opening. This checks the flow, and so enables the pump to maintain enough pres- sure to keep the am- monia in liquid form on its way to the valve ; while beyond the valve the pressure is very small, so that the am- monia expands and evaporates rapidly. While doing so, it absorbs heat from the refrigerating room. It is then ready to be compressed again. In ths manufacture of ice, the expansion pipes pass through a brine tank in which are smaller tanks of pure water. When the water in these tanks is frozen, the tanks are pulled up and the ice removed and stored. The ammonia is used I, To sewer FIG. 179. Diagram of cold-storage plant. WATER, ICE, AND STEAM 217 over and over again, but power must be constantly supplied to keep the compressor working. SUMMARY OF PRINCIPLES IN CHAPTER XI Heat units : 1 B. t. u. = heat to raise 1 Ib. of water 1 F. 1 calorie = heat to raise 1 gram of water 1 C. Specific heat = calories to raise 1 gram of substance 1 C. Specific heat of water = 1. Method of mixtures : Heat given up by hot bodies = heat absorbed by cold bodies. Pressure : Lowers freezing point of water 0.0072 C per atmosphere. Raises boiling point of water 0.037 C per millimeter of mercury. Latent heat of melting = heat absorbed during melting, = heat yielded during freezing. Value for water, 80 calories. Latent heat of vaporization = heat absorbed during evaporation, = heat yielded during condensation. Value for water, 640 calories. Relative humidity actual moisture in air moisture sufficient to saturate air at same temp. QUESTIONS 1. If you know the dew point to be 10 C, how could you find the rel- ative humidity at 20 C ? 2. Human hair when treated with ether is very sensitive to mois- ture. When it is moist it contracts, and when it dries it elongates. Explain how a moisture gauge or "hygrometer" could be made with a hair. 218 PEACTICAL PHYSICS 3. Why do they not cast gold money instead of stamping it with a die? 4. Why is a burn from live steam so severe ? 5. Why does one sometimes " catch cold " by sitting in a draft of cool air after taking violent exercise ? 6. How low may the temperature fall during a rain? 7. Why can mercury mixed with zinc and tin be purified by distilla tion? 8. Why is it difficult to make snowballs out of dry snow? CHAPTER XII HEAT ENGINES The invention of the steam engine boilers slide-valve and Corliss engines expansion compounding condensers efficiency steam turbines 2-cycle and 4-cycle gas engines balance sheets of engines mechanical equivalent of heat. 213. The invention of the steam engine. In our age no other machine is of such importance as the steam engine. It furnishes the driving power for running a countless number of machines in our shops and factories, as well as for trans- portation on land and sea. Up to about two hundred years ago steam had been used only in various devices, called steam fountains, for raising water. In 1705 the first suc- cessful attempt to combine the ideas of these devices into an economical and convenient ma- chine was made by Thomas New- comen (1663-1729), a blacksmith of Dartmouth, England. This machine was called an " atmos- pheric steam engine" (Fig. 180). It consisted of a boiler A, in which the steam was generated, and a cylinder J5, in which a piston moved. When the- valve V was opened, the steam pushed up the piston P. At the top of the stroke, the valve 219 FIG. 180. Newcomen's steam engine. 220 PRACTICAL PHYSICS V was closed, the valve V was opened, and a jet of cold water from the tank was injected into the cylinder, thus condensing the steam and reducing the pressure under the piston. The atmospheric pressure above then pushed the piston down again. This machine was used to pump water from mines. It consumed a great deal of fuel, because the cold water cooled the cylinder walls so much that when the steam was turned in, much steam condensed before the piston was raised. The next great step in the development of the steam en- gine came through a Scotch in- strument maker, James Watt (1736-1819). He arranged a separate vessel for condensing the steam, as shown in figure 181. This condenser, (7, was connected with the cylinder through a valve V . When the piston had reached the top of the FIG. 181. -Watt added a separate cylinder, the valve Fwas closed condenser. t -m and V was opened. Then the steam rushed from the cylinder into the condenser, which was kept cold and under less than atmospheric pressure. At first these valves V and V had to be operated by hand, but later, it is said, a boy named Potter, whose job it was to turn these valves, connected the valve handles by cords to the beam ED in such a way that the machine became automatic. In all these crude machines the steam simply furnished the vacuum, and atmospheric pressure did the work. Later, Watt made a machine with a closed cylinder and a piston that was pushed down as well as up by steam. By the use HEAT ENGINES 221 of a connecting rod and crank shaft, ho contrived to change the back-and-forth motion of the piston to a rotary motion, and so made the steam engine available for many new uses. Within a few years the development of the steam engine revolutionized most lines of industry. 214. A modern steam plant. In a modern steam plant the steam is made in a boiler, is used in a steam engine, and is got rid of in an exhaust or condenser. We will discuss these in turn. 215. Steam boilers. A fire-tube boiler consists of a steel cyl- inder which sometimes stands on end, as in the small " donkey engines " used with derricks, but generally is set on its side, FIG. 182. Section of a locomotive boiler. as in locomotives (Fig. 182). Running through this cyl- inder are tubes, three or four inches in diameter, through which the fire and smoke pass. The water and steam fill the rest of the cylinder outside the tubes. These tubes give the boiler a much greater heating surface, so that it makes more steam per hour. Such boilers are called fire-tube boilers. In an- other type, called a water-tube boiler (Fig. 183), the water is inside the tubes and the fire is outside. Such a boiler consists of a large number of tubes, inclined at an angle and fastened at euch end into vertical "headers": these headers communi- 222 PRACTICAL PHYSICS Steam FIG. 183. Section of water-tube boiler. cate with a drum above, which is half full of water, the re mainder of the drum forming a space for steam. The watei descends by the back headers, rises through the inclined tubes, and passes up the front headers, thus maintaining a very good circu- lation. The fire is placed under the front end of V the tubes ; the gases are de- flected by brick walls, so that they pass completely over and under the whole length of the tubes. In some water-tube boilers the fire grate is sloping and arranged like a flight of steps. The coal is automati- cally fed through a chute from the coal loft above to the grate. The principal advantages of this type of boiler are its great freedom from risk of explosion and its ability to make steam quickly. A modified form of this boiler is generally used in marine work. Not only is it desirable to get the greatest quantity of steam with the least expenditure of fuel, but it is also essen- tial to keep the steam pressure constant and to prevent an explosion which may have frightful consequences. There- fore every boiler is equipped with a steam gauge, which is merely a Bourdon pressure gauge (section 75), and a water gauge (section 62), which enable the engineer in charge to watch the pressure and water level in the boiler. If the water level is too low, there is danger of burning the tubes HEAT ENGINES 223 and plates and perhaps of wrecking the boiler ; if it is too high, water is liable to be carried along with the steam and so damage the engine. Besides these devices, every boiler must have a safety valve, which auto- matically lets the steam blow off when the pressure exceeds a certain limit. A simple form , ,, , . , . FIG. 184. -Safety valve. ot satety valve is shown m ng- ure 184. In some forms a spring is set so as to release the steam if the steam pressure becomes too great inside the boiler. In order to make steam rapidly, the fire must burn fiercely, which requires a -good draft. To get this, tall chimneys are sometimes used, and at other times a forced draft is made by a big fan. On battleships a forced draft is often obtained by making the whole fireroom, within which the stokers work, air-tight, and keeping it full of air under pressure, supplied by blowers or pumps as fast as it can escape through the fires. One pound of coal, whose heat value is 14,000 B. t. u., could change 14.4 pounds of water at 212 F into steam at 212 F if no heat were wasted. In actual practice, one pound of coal evaporates between 8 and 10 pounds of water " from and at 212 F," which means an efficiency of from 55 to 70%. One great source of loss of heat is the flue gases. Smoke pouring from the chimney means that just so much unconsumed fuel is going to waste, and, what is worse, is adding to the dirty atmosphere of the neighborhood. To-day steam engi- neers are able to design boilers which, when properly stoked, produce no smoke. 216. Steam engine. The type of engine most commonly used for small plants and for locomotives is the slide-valve engine (Fig. 185). Steam comes from the boiler into a box or steam chest, and then into the working end of the cylinder 224 PRACTICAL PHYSICS FIG. 185. Slide-valve steatn engine. through a passage shown by the arrows at the right of the picture. At the same time the spent steam in the other end of the cylinder is escap- ing through the hollow interior of the valve, to the exhaust passage. It then escapes to the air, or to the condenser, through a pipe at the back, which does not show in the figure. At the end of the stroke the valve is pulled far enough to the right to admit live steam to the left-hand end of the cylinder, while the spent steam in the right-hand end es- capes into the exhaust. In large steam engines Corliss valves are more often used. A Corliss valve (Fig. 186) opens and closes by turning a little in its seat. In a Corliss engine there are four such valves two at each end of the cylinder. Two of them, A and J5, are for admitting the steam, and two, O and 2>, for letting the steam out. When valve B is open to admit steam, valve D is also open to let steam out of the other end of the cylinder, / FIG. 186. Corliss steam engine. while A and C are closed ; on the reverse stroke, A and are open, while B and D are closed. These valves are automatically opened and closed at the proper time by the engine itself. The fact HEAT ENGINES 225 that the time at which each valve opens can be accurately adjusted independently of the other valves makes Corliss engines more efficient than slide-valve engines, and has led to their extensive use in large installations. 217. Expanding steam. If live steam from the boiler is allowed to push the piston through its entire stroke, and is then thrown away, that is, al- lowed to pass into the atmos- phere or into a condenser, it is T evident that much energy is wasted. To get more work out of the steam, the valve is closed after the piston has made about siroke 1 or Of its Stroke, and the FIG. 187. - Pressure m cylinder of steam is allowed to expand through the rest of the stroke. The pressure continues to drop after the " cut-off," as shown in figure 187, where the pressure P is represented vertically and the stroke horizon- tally. Such pressure diagrams can be made automatically by the engine itself while in actual operation, and enable those in charge to adjust the valves properly. 218. Compound engine. Another device for getting more work out of the steam is to use the steam at high pressure in one cylinder, then allow it to pass into a second, larger cylinder, where it expands some more, and sometimes into a third and a fourth cylinder. These are called compound, triple and quadruple expansion engines. When the expansion and consequent cooling of the steam take place in steps, there is no large drop in temperature in any one cylinder. So the walls of a cylinder never get much cooler than the incoming steam, and there is little condensation in the cylinders. In a simple engine, the initial steam pressure varies from 80 to 100 pounds, while in compound engines the initial pressure is usually higher, from 100 to 175 pounds. A simple engine requires from 17 to 35 pounds of steam an hour for each 226 PRACTICAL PHYSICS horse power developed, while a compound engine may need as little as 11.2 pounds of steam per horse-power hour. Triple-expansion engines are usually used in marine work. 219. Condenser. When its exhaust pipe opens directly into the atmosphere, an engine is called a non-condensing engine. The power depends on the excess of the steam pressure in the boiler above that of the atmosphere outside. Ordinary locomotives and most small engines are of this type. In fact the locomotive depends on the escaping steam to furnish a draft for the boiler. Greater economy is obtained by sending the exhaust steam to a vacuum chamber, or condenser. In one type the steam coming from the engine is condensed by a jet of cold water, and in another type it is condensed in tubes surrounded by cold water. A small pump is used to pump out the condensed steam as well as any air which may have leaked in. Such engines are known as condensing engines. Marine engines are always condensing engines. 220. Efficiency of a steam plant. We have already seen that the modern steam boiler has an efficiency of about 70%, but there are still larger losses in the engine itself. The escaping steam from an engine always carries away a large amount of unutilized heat energy. It can indeed be proved that the greatest efficiency possible for a steam engine is represented by the fraction where T^ is temperature (Absolute) of the steam supplied and T z is temperature (Absolute) of the steam rejected. For example, an engine running at 163 pounds boiler pressure takes in steam at about 185 C, and T^ is 458. If the temperature of the exhaust steam is 100 C, T 2 is 373. Such an engine cannot possibly have an efficiency greater than 468^-878 HEAT ENGINES 227 For this reason steam engineers try to use high-pressure steam, because of its high temperature, so as to make (2\ T 2 ) as large as possible. The temperature T^ is sometimes still further increased by passing the steam through pipes (Fig. 183) in the furnace to " superheat " it. It must be remembered that this 18.5% is the efficiency of the engine alone, so that the efficiency of the engine and boiler would be 18.5 % of 70 %, or only about 13 %. This means that about 87 % of the energy of the coal would not be converted into mechanical energy. By using very high temperatures, the latest style of quadruple expansion and condensing engine has been made to utilize about 20% of the energy originally in the coal. The ordinary locomotive, however, does not utilize more than 8 %. PROBLEMS 1. The area of the piston of a steam engine is 120 square inches and its stroke is 2 feet. If the " mean effective pressure " of the steam is 50 pounds per square inch, what is the total force exerted on the piston ? 2. In problem 1, how many foot pounds of work are done in one revolution of the shaft (two strokes) ? 3. If the engine in problem 1 is making 150 revolutions per minute, what is its " indicated horse power " ; that is, what is the rate in H. P. at which the steam does work on the piston ? 4. A locomotive with cylinders 18 inches in diameter and a stroke of 2 feet is provided with driving wheels 6 feet in diameter. It the mean effective pressure of the steam in the cylinder is 60 pounds per square inch, and the engine is making 50 miles an hour, what is the indicated horse power ? 5. How much mean effective steam pressure will be needed to get 10 horse power from a "donkey engine " running at 200 revolutions per minute ? (Assume area of piston to be 50 square inches, and stroke 1 foot.) 221. Steam turbine. Thus far we have been describing reciprocating engines, in which the back-and-forth motion of the piston rod is turned into rotary motion by means of a crank and connecting rod. Since the piston must come to a standstill at the end of each stroke, this means in high- 228 PRACTICAL PHYSICS speed engines very frequent starting and stopping, which causes so much shaking as to require big and expensive foundations. On steamships the continual jarring causes a disagreeable vibration. A new and distinctly different type of engine called a steam turbine has been developed in recent years in which there is no reciprocating motion. 222. Curtis turbine. Steam turbines can be divided into two main classes, of which the Parsons and the Curtis tur- bines are typical representatives. The Curtis turbine is, in principle, like the Pelton water wheel (sec- tions 78 and 79). Steam is de- livered to the machine through nozzles in which it expands and gains a high velocity. It then strikes against blades fastened to the edge of a revolving disk and gives up its kinetic energy to them. In some forms of turbine FIG. 188. -steam turbine with one ^ig. 188) there is only one set set of nozzles. J of nozzles, and the steam expands in one step from the boiler pressure to the condenser vacuum. Under such conditions the speed of the steam as it strikes the blades is so great, often more than 4000 feet per second or 2700 miles per hour, that it is difficult to handle it effi- ciently. Curtis turbines are therefore built in from three to six sections, each section be- ing a complete turbine with its nozzles and wheel, and the steam is run through the sections in succession, as in a compound r . FIG. 189. Moving and stationary or multiple-expansion engine. blades in a Curtis turbine, A Curtis turbine (at the right) with the upper half of its casing removed. There are three wheels and two rows of blades on each wheel. It is used to drive the generator at the left. A Westinghouse turbine with the upper half of its casing lifted. There are a great many rows of moving blades. The balancing dummies are at the near end. The generator is at the other end, and is cooled by air drawn in through the duct. " 11 ft- s -M o o o sM 1l! rt ^ 3 s3 2 2^ HEAT ENGINES 229 In order to reduce still further the speed at which the blade wheels have to run, they are so designed that each jet has two or three chances at a given blade wheel before losing all its velocity. As it escapes at reduced speed from each set of moving blades, it is caught by guides attached to the surrounding casing and turned around so as to strike another set of moving blades on the same wheel, as shown in figures 189 and 190. 223 Parsons turbine. The Parsons turbine is somewhat like a succession of windmills set in line behind each other. The steam flows along the turbine from one end to the other in the annular space between the cylindrical drum or rotor and a slightly larger cylindrical casing, and acts on the wind- mill-like blades fastened to the drum. In passing through these rows of moving vanes, the steam would quickly get to spinning with the rotor and would then fail to act effectively on the later vanes, if it were not for the rows of stationary guide blades attached to the casing. These project between the rows of moving blades, catch the steam as it comes through, and direct it against the next row of moving blades at the proper angle. Thus the steam goes zigzagging down the annular space, striking first a row of fixed blades, then a row of moving blades, then another row of fixed blades, and so on. As the steam flows along, its pressure decreases and it expands ; so the space between the rotor or drum and the outer case has to increase gradually as the low-pressure end is approached, to give the steam the extra space it requires. This is done by making the blades short at the inlet end and long at the outlet end, and by occasionally increasing the diameter of both rotoi and casing, as shown in figure 191. Ss/sncing Dummies RotaHnybladts FIG. 191. Section of a Parsons turbine. 230 PRACTICAL PHYSICS 224. Advantages of turbines. Turbine engines always run at high speed, so a large amount of power can be de- livered by a small machine. This makes them especially valuable in city power stations where land is expensive. Furthermore, their lightness and steadiness make smaller and cheaper foundations sufficient. They have been installed also on large, high-speed passenger vessels and on torpedo boats and destroyers. To be operated most efficiently they should work through a wide range of temperature, corresponding to a boiler pressure of from 200 to 250 pounds, and a very per- fect condenser vacuum (often better than 29 inches). A large supply of cool condensing water is therefore desirable, and turbines are especially adapted for power stations on rivers, lakes, or the ocean. Under such conditions, when working at their maximum capacity, they are slightly more efficient than even the best reciprocating engines. 225. Gas engine. The essential difference between a steam engine and a gas engine is that in the steam engine the fuel is burned under a boiler and the working substance, steam, is conducted to the engine in pipes, while in the gas engine the fuel is burned in the cylinder of the engine and the hot products of combustion are themselves the working substance. In othar words, the gas engine is an internal com- bustion engine. The fuel, gasolene, is a liquid which is con- verted into a gas in what is called a carbureter. The liquid fuel is sprayed into the carbureter, vaporizes, and is mixed with the proper amount of air. This mixture of gas and air is compressed in the cylinder of the engine and then exploded by an electric spark, which causes the exceedingly rapid burning of the gas. This results in an enormous in- crease in pressure, which pushes out the piston. Then the exploded gases are forced out of the cylinder and a new charge of gas and air are taken in. Inasmuch as the cylinder has to be a furnace as well as a cylinder, it would get dangerously hot if it were not cooled HEAT ENGINES 231 from the outside. It may be water-cooled by surrounding it with a jacket or outer case, in which water is circulated ; or it may be air-cooled by giving it a corrugated outer surface which radiates heat rapidly, and forcing a stream of air against this surface. 226. Two-cycle engine. In the two-cycle gas engine, we have one explosion for every two strokes or for each revolution of the crank shaft. A simple form, such as is used on motor boats, is shown in figure 192. The explosive mix- ture is taken into an air- tight crank case and slightly compressed on the outward or down stroke of the piston. As the piston nears the bot- tom of its stroke, it un- covers first the outlet port, E, letting part of the spent gases in the cylin- der blow off, and then the inlet port B. The slightly compressed charge in the crank case then rushes into the cylinder, sweeping out the rest of the exploded gases before it. On the upstroke of the piston the ports are covered and the fresh charge is considerably compressed. As the piston passes its upper dead center (or soon afterward) the charge is exploded, and expands at a much higher average pressure than during the compres- sion, giving back the work of compression and considerably more besides. Such an engine is called single acting, meaning that work is done only on one side of the piston. If the spark does not come at the upper dead center, but part way down the expansion stroke, the power yielded is much less. This is done to make a boat run slowly. Adjusting the electrical connections so as to bring the time of explosion FIG. 192. Two-cycle engine. 232 PRACTICAL PHYSICS (1) nearer the upper dead center is called " advancing the spark." Running on a " retarded spark " wastes gasolene, because the amount used per stroke is the same as at full power. The only true valve in this engine is a light clap valve, where the fresh gases enter the crank case. The disadvantage of this style of engine is that some of the fresh gas is lost with the spent gases through the exhaust, so that it uses more gasolene than some other styles. But, on the other hand, it is very simple and gives a push every revolution. 227. Four-cycle engine. In the four-cycle engine, we get a push or thrust only once in every two revolutions or every four strokes of the piston. Four-cycle engines, like two-cycle engines, are usually single acting. The four-cycle type is the one most commonly used for automobiles and for stationary work. The four strokes of the piston, corresponding to two revolutions of the shaft, are shown in figure 193. It will be noticed that whereas the two- cycle type has no valves in the cylinder, the four-cycle has two valves, one for the intake of gas and air and another for the ex- haust of the spent gases. These valves are operated mechani- cally by cams on a small half-time shaft, which is driven through gears at half the speed of the main shaft. In figure 193, (1), the intake valve is open, and the piston is going down, thus drawing in the explosive mixture. In (2) the return or back stroke of the piston compresses the mixture. In (3) the mixture has been ignited by an electric spark or flame, and power is obtained from the thrust of the expanding gas on the outward stroke. This is the working stroke. In (4) the exhaust valve is open and the spent gases are being pushed out of the cylinder by the returning piston. Then FIG. 193. Four cycles of a gas engine. HEAT ENGINES 233 the whole cycle is repeated again. Since power is obtained only on every alternate outward stroke, a heavy flywheel is used to keep the engine going during the other three strokes, or, as in automobiles, four such engines may act on the same shaft, so arranged that the explosions in the several cylinders take place successively, one for every half revolution of the shaft. 228. Disadvantages of the gas engine. Although the internal combustion engine has been immensely improved in the last decade, it is still a very sensitive machine. The spark must come at just the right time, and must come every time. The method for producing the spark will be described in Chapter XVII. The steam engine is more easily varied in speed than the gas engine. To be sure, it is possible to vary the speed of a gas engine somewhat by advancing or retarding the spark, and by controlling the supply of gas ; nevertheless, automobiles have to use gears to get a sufficient variety of speeds at full power. Then, too, a steam locomotive will run either way by simply shifting the slide valve, while the gasolene auto- mobile has to use a reversing gear. Finally a gas engine is not always free from noise and smell. 229. Advantages of the gas engine. On account of light- ness and compactness, and the small space occupied by the fuel, there has been a phenomenal development in the manu- facture of gasolene engines for small pumping stations, shops, and factories, as well as for automobiles, launches, and ae'ro- planes. The gas engine does not require any stoking of a boiler or constant care to keep up the right pressure of steam. In fact, once started it requires very little attention. It can be started at a moment's notice, while if a steam engine and its boiler have been " shut down," it takes a good while to get up steam. Furthermore, no fuel is wasted when a gas engine is shut down at night or between periods of use. In efficiency the modern gas engine ranks much higher than the steam engine. 234 PRACTICAL PHYSICS 230. Balance sheet of heat engines. When an engine is tested, a heat balance sheet is usually made up. This is somewhat like a cash account, in that it accounts for all the energy delivered to the engine by the fuel. These heat bal- ance sheets vary somewhat for different engines even of good design, but the following are fairly typical for large and efficient engines of the two types : STEAM ENGINE Useful work 15% Friction 5 % Exhaust 45 % Up the chimney 35% 100% GAS ENGINE Useful work Friction, etc. Exhaust Jacket 25% 10% 30% 35% 100% 231. Mechanical equivalent of heat. We have been con- sidering the efficiency of engines without stopping to de- scribe how it is measured. Evidently we must have some way of comparing the output, which would naturally be measured in foot pounds or kilogram meters, with the input, which would naturally be measured in B. t. u. or calories. This involves finding a definite relation between a foot pound and a B. t. u., or between a kilogram meter and a calorie. This problem was not solved until about the middle of the last century, when an Englishman, Joule (1818-1889), did his famous experiment of churning water. He arranged a paddle wheel in a box of water FIG. 194. Joule's machine to find me- (Fig. 194). The paddles chanical equivalent of heat. were ^^ ^ y weigh ts which descended and thus unwound cords on the spindle of the wheel. The water was kept from following the rotat- HEAT ENGINES 235 ing paddles by fixed paddles which projected from the sides of the box. In this experiment the mechanical work put in could be measured by multiplying the weights by the distance through which they fell ; and the heat produced could be measured by multiplying the weight of the water by the rise in tem- perature. Great care was taken to prevent any loss of heat. The result of this and many other experiments of a similar nature led Joule to announce this principle: The number of units of work put in is always proportional to the number of units of heat produced. As a result of Joule's experiments and also of the more accurate experiments of Rowland (1848-1901) and of many others, we believe that 778 foot pounds of work are equivalent to the heat required to raise one pound of water one degree Fahrenheit, or that the energy required to heat one kilogram of water one degree Centigrade is equal to the work done in rais- ing one kilogram to a height of 427 meters. 1 B. t. u. = 778 foot pounds of work. 1 kilogram calorie = 427 kilogram meters of work. To compute the efficiency of an engine we have, therefore, to divide the work done by the heat put in, expressing both in the same units by means of the above relationships. This work of Joule's was a clinching argument in favor of the principle of the conservation of energy, for it meant that heat and work are but different forms of energy. PROBLEMS 1. If a horse power is equal to 33,000 foot pounds of work per minute, how many foot pounds are there in a horse power hour; that is, in the total amount of work produced by a 1 H. P. engine working for 1 hour? 2. A pound of average coal yields 14,500 B. t.u. when burned. To how many foot pounds is this heat equivalent ? 3. From the results of problems 1 and 2, calculate the horse power hours per pound of coal. 236 PRACTICAL PHYSICS 4. A test of a certain steam engine showed that 1 pound of coal generated 1 horse power hour; from the three preceding problems com- pute the efficiency. 5. Calculate the efficiency of a gasolene engine from the following data: 16 cubic feet of gas were used per horsepower hour; 1 cubic foot of gas yields 700 JB. t. u. SUMMARY OF PRINCIPLES IN CHAPTER XII The mechanical equivalent of heat is the value in foot pounds of one B. t. u. or in kilogram meters of one calorie. 1 B. t. u. = 778 ft. Ib. 1 kg. cal. = 427 kg. meters. Efficiency = 2^'. input Both must be expressed in same unit by means of above relations. The conservation of energy in engines requires that all energy supplied as heat of combustion of the fuel be accounted for as useful output or specified waste ("making up the heat balance sheet of the engine "). QUESTIONS 1. Why does the steam jacket increase tne efficiency of a steam engine ? 2. Does the water jacket increase the efficiency of a gasolene engine? 3. What did Count Rumford learn about heat while boring cannon for the Bavarian government? 4. How are the cylinders of engines lubricated? 5. How does a ship equipped with steam turbines reverse its pro- pellers?* 6. Describe the reversing mechanism of a locomotive. 7. Is an ordinary gas engine self-starting? How are automobile engines made self-starting? 8. When you see steam coming from the exhaust pipe of a steam engine in puffs, do you know whether it is a condensing or non-condens- ing engine ? 9. Why are condensers not used on locomotives? HEAT ENGINES 237 10. What advantages has oil as a fuel for locomotives and steam- ships ? 11. Why are marine engines always condensing engines? 12. How would you compute the efficiency of a gun regarded as a heat engine ? 13. What makes the water circulate in a water-tube boiler? 14. Why does a high-speed turbine give more power than a low= speed reciprocating engine of about the same size ? 15. What is the use of the radiator on an automobile ? CHAPTER XIII MAGNETISM The lodestone magnetic poles attraction and repulsion the compass and magnetism of the earth magnetic field induced magnetism permeability theory of magnetism. 232. The lodestone. For many centuries it has been known that a certain kind of rock, called the lodestone, has the power of attracting iron filings and small fragments of the same rock. Its abundance near Magnesia in Asia Minor led the Greeks to call it " magnetite " or " magnetic " iron ore. Let us take a piece of magnetite (Fe 3 O 4 ) and show that it picks up pieces of iron (Fig. 195), but does not pick up copper or zinc. We may magnetize a knitting needle by stroking it with a piece of magnetite. This kind of iron ore occurs in many places in this country as well as in Norway and FIG. 195. Lode- Sweden. When a steel bar is rubbed with stone attracts such a natural magnet, the steel itself becomes magnetic and is then called an artificial mag- net. In a later chapter we shall learn how to make magnets by using an electric current. 233. Magnetic poles. It was a good many years before any one in Europe noticed that the magnetic proper.ty of a lodestone was concentrated more or less definitely in two or more spots, and that if a somewhat elongated lodestone with only two of these spots, and those near its ends, is hung by a thread, it will set itself with one spot toward the north and the other toward the south. We now use magnetized 238 MAGNETISM 239 needles instead of lodes tones, and call such an arrangement a compass, and we all know how valuable it is to mariners and explorers. Probably the Chinese had compasses many years before Europeans reinvented them. The two spots which point one to the north and one to the south are called the poles of the magnet ; one is called the north-seeking pole (N) and the other the south-seeking pole (#). 234. Magnetic repulsion. It was many centuries after people had known that magnets would at- tract things before they learned that mag- nets sometimes repel things. If we bring the north-seeking or JV-pole of a magnet near the ^V-pole of a suspended magnet, the poles repel each other (Fig. 196). If we bring the two S-poles together, they also repel each other. FIG. 1^96. Magnetic But if we bring an N-po\e toward the S-pole of the repulsion, moving magnet, or an S-pole to the jV-pole, they attract each other. That is, Like poles repel each other, Unlike poles attract each other. Experiment shows that these attractive or repulsive forces vary inversely as the square of the distance between the poles. 235. Declination and dip. Soon after the compass was invented, it was noticed that it did not point true north and south. For a long time it was supposed that this de- viation or declination was everywhere the same, until Colum- bus, on his way to America in 1492, discovered near the Azores a place of no declination. Evidently an exact knowledge of the declination at different places is of the greatest impor- tance to mariners and surveyors, and so careful maps are published by the different governments giving lines of equal declination. Figure 197 shows such a map. From this map it will be observed that in the extreme eastern section of the 240 PRACTICAL PHYSICS United States the declination is as much as 20 W. This decreases to zero at a place near Cincinnati, O., and becomes an easterly declination amounting to 20 E. in the northwest. FIG. 197. Map showing declination of the compass in the United States. It was nearly a hundred years after Columbus' time before it was discovered that if a compass needle is perfectly balanced so that it can swing up and down as well as sidewise, its north-seeking pole will dip down at a considerable angle (Fig/ 198). This angle increases as one goes farther north, and decreases as one goes south. Along a line near the equator there is no dip. In the southern hemisphere the north-seeking pole of a needle points up in the air, and re- cently Shackleton's South Polar Expedition FJG. 198. Com- found a point on the great Antarctic conti- pass needle to nent w ^ ere a neec Qe would hang vertically show magnetic . , ., , -, . -, dip with its north-seeking pole on top. MAGNETISM 241 236. The earth a magnet. An Englishman, Gilbert, in the sixteenth century was the first to explain these curious magnetic phenomena. He had ground a little lodestone into the shape of a globe, and noticed that when tiny compass needles were brought near it, they acted just, like compasses on the surface of the earth. So he called his lodestone globe the "ter- rella " or " little earth " (Fig. 199), and came to believe that it gave a true representation of the earth itself. The earth is, then, simply a huge magnet, much thicker in proportion to its length than FlG 199 _Qiibert's the magnets with which we are familiar in labo- terreiia or little ratories, but otherwise exactly like them. earth - It has a north-seeking and a south-seeking pole like any other magnet, but from the laws of attraction and repulsion we see that, curiously enough, its south-seeking pole must be at Peary's end, and its north-seeking pole at Amundsen's end. These magnetic poles are not exactly at the geographical poles. One of them is in North America near Hudson's Bay and the other is nearly opposite. Since the lines of equal declination and of equal dip are not true circles, the magnetization of the earth must be somewhat irregular. Furthermore, the positions of its mag- netic poles are known to be changing slowly from year to year. Why these things are so, and, for that matter, why the earth is magnetized at all, is not yet known. QUESTIONS 1. Does a magnet ever have more than two poles ? 2. In what direction did Peary's compass point when he reached the North pole ? 3. How far is the magnetic pole from the geographical North pole ? 4. How can you tell whether or not a steel rod is a permanent magnet ? 5. Why are knives, files, and scissors sometimes found to be magnetized? 242 PRACTICAL PHYSICS 6. Will a magnet attract a tin can ? Explain. 7. Would a -magnet floating on a cork in a dish of water float toward the north, as well as turn north and south ? 8. What advantage is there in making a magnet in the shape of a horseshoe ? 237. The field around a magnet. Michael Faraday (1791- 1867) was the first to see that a true understanding of the action of magnets could be had only by studying the empty space around them, as well as the magnets themselves. One way to do this is to lay a stiff piece of paper over a magnet and sprinkle iron filings on it (Fig. 200). When the paper is tapped lightly so as to shake the filings about a little, they arrange themselves in regular lines leading from one pole to the other. This is because each Fia. 200. Magnetic lines of force around a bar magnet. filing gets slightly magnetized by the influence of the original magnet, and sets itself in the direction in which a tiny compass needle would lie if it were at the same place. This can be verified by actually using a small compass instead of the filings. The lines can be mapped in this way, but it is not as quickly done. In this way, Faraday drew what he called lines of force around a magnet. A line of force may be defined as a line MAGNETISM 243 which indicates at its every point the direction in which a north- seeking pole is urged by the attractions and repul- sions of all the poles in the neighborhood. When lines of force are thought of in this way, they should have little arrowheads on them, pointing in the direction of their journey from a north-seeking pole to a south-seeking pole. We shall find this conception of lines of magnetic force or magnetic flux a convenient way of remembering how a magnet will affect other magnets in its vicinity. 238. Lines of force like elastic fibers. Faraday himself thought of these lines of force as having a much more real meaning than this. He thought of them as actually existing throughout the space around every magnet, even when there are no filings to show them. He believed that they repre- sent a real state of strain in the ether (see section 187), in which all material bodies are immersed. Even now we know very little about what the ether really is. We know simply that it is not a kind of matter, but something much more subtle and fundamental. At any rate, these lines of force of Faraday's act as if they were stretched fibers in the ether which are con- tinually trying to contract and are thus pulling on the poles at their ends. They also act as if they were trying to swell up sidewise as they contract, and thus seem to crowd each other *x \ / ^'"""^^ \ / apart. It is not easy to -~~-^X s see why lines of force ---_:--_;: have these properties, C... (* but once the properties 7^ : :-i-- '>V :: are assumed (as rules of " ,.-'' > \\^' '''/'I \ \ ~~~ the game), it is easy to *** / \ ^ / \ reason out from them / \ what will happen in many . FIG. 201. Lines of force between two unlike practical cases. poles> 244 PRACTICAL PHYSICS For example, if two magnets are placed with their unlike poles to- gether and their lines of force traced with iron filings, the result will be as shown in figure 201. If we \ / N , assume that the lines of force / \ i / tend to contract, it is easy to poles Like FIG. 202. Lines of force between two like poles. an easy way of seeing what will happen, and it will be useful later on see that two unlike must attract each other, poles, however, would show a field of force as shown in figure 202, and if we assume that lines of force squeeze against each other sidewise, and tend to separate, evi- dently two like poles must repel each other. This is not an explanation of why these things happen ; it is, however, 239. Induced magnetism. If we plunge one end of a piece of unmagnetized soft iron into some iron filings, it does not attract them, but if we bring near it a permanent magnet, as shown in figure 203, the soft iron becomes a magnet and attracts the filings. When the per- manent magnet is removed, the soft iron loses its magnetism, and drops the filings. A piece of iron which is magnetized by being near a magnet is said to be magnet- ized by induction. If the pole of the mag- net, which was brought near the iron, was a north-seeking pole, the induced magnet can be shown by a compass to have a ^V-pole away from the magnet and a $-pole near the magnet. Experiments show that very soft iron quickly becomes magnetized by induction FlG and quickly loses its magnetism when re- moved from the field. Hardened steel, however, is magnet- ized with difficulty, but retains its magnetism well. For MAGNETISM 245 this reason the magnets used in telephones and magnetos are made of hardened steel. 240. Permeability. Although a magnet will act through a vacuum or through glass or wood, yet the magnetic flux seems to prefer soft iron to any other medium. We can show this by the following experiment. We will take a horseshoe magnet and lay across its poles a sheet of stiff paper, and then bring up a mass of iron filings under the paper. The iron filings will cling under the poles as shown in figure 204. If we slip a plate of glass between the paper and the poles at A A, most of the filings still stick, but when we substitute an iron plate for the glass, most of the filings drop off immediately. This shows that an iron plate screens the region beyond from the magnetic action. FIG. 204. iron is more P ermeable than Lord Kelvin has called the ease with which lines of force may be established in any medium as compared with a- vacuum, the permeability of the medium. Thus iron has a permeability several hundred times greater than air. When a watch is brought near a powerful magnet, its balance wheel is often magnetized. This disturbs its working. To protect it from such magnetic disturbances a good watch is often inclosed in a soft iron case. 241. Theory of magnetism. Our present theory of magnet- ism was suggested by the following experiment. Let us harden a knitting needle or a piece of watch spring by first heating it red hot, and then plunging it into cold water. Then let us magnetize it and mark the AT-pole. If we now break it near the middle Fia. 205. A broken magnet shows poles at the break. where it does not show any magnetism, we shall find, by bringing the broken ends near a compass needle, that we have an ^V-pole arid an S-pole as indicated in figure 205. If we repeat the process, we shall 246 PRACTICAL PHYSICS find that each time the magnet is broken, new poles are formed at the break. A magnet can be broken into a great number of little magnets. A glass tube full of iron filings can be magnetized, but when shaken, it loses its magnetism. Any magnet loses a part or all of its power if it is heated red hot, jarred, hammered, or twisted. All these facts point to a molecular theory of magnetism, which was suggested by a Frenchman, Ampere, and elaborated by a German, Weber, and an Englishman, Ewing. Every molecule of a bar of iron is supposed to be itself a tiny permanent magnet why, no one yet knows. Ordinarily, ________________________ these molecular magnets are turned helter-skelter throughout the bar (Fig. 206), and have no cumu- FIG. 206. Unmagnetized bar. lative effect that can be noticed outside the bar. When the bar is magnetized, how- ever, they get lined up more or less parallel (Fig. 207), like soldiers, all facing the same way. Near the middle of the bar the front ends of one row are neutralized by the back ends of the row in front; but at the ends of the bar a lot of unneutralized poles are exposed, north-seeking at one end and south-seek- ing at the other. These .. c , , FIG. 207. Magnetized bar. free poles make up the ac- tive spots which we have called the poles of the magnet. On this theory it is easy to see that when a magnet is broken in two without disturbing the alignment of the molecular magnets, the new poles which appear at the break are simply collections of molecular poles that have been there all the time, but are now for the first time in an independent, recognizable position. It will also be evident that, if this theory is true, there cmcmcmca MAGNETISM 247 is a perfectly definite limit to the amount of magnetism a given piece of iron can have. For when all the molecular magnets are lined up in perfect order, there is nothing more that can be done, no matter how strong the magnetizing force may be. Such a magnet is said to be saturated. SUMMARY OF PRINCIPLES IN CHAPTER XIII Like poles repel each other. Unlike poles attract each other. The earth is a magnet with its " south-seeking " pole at Peary's end. Lines of force tend to contract and swell sidewise ; that is, there is tension along them, and compression at right angles to them. QUESTIONS 1. If two bar magnets are to be kept side by side in a box, how should they be arranged ? Why ? 2. If a magnetic needle is attracted by a certain body, does that prove that the body is a permanent magnet? 3. What is meant by the " aging " of magnets ? 4. How must a ship's compass box be supported so as to remain steady during the rolling of the ship ? 5. A long soft iron bar is standing upright. Why does its lower end repel the north pole of a compass needle ? 6. Does hammering the bar while it is in the position described in problem 5 increase or decrease the effect ? Why ? 7. Why are the hulls of most iron ships permanently magnetized? What determines the direction in which they are magnetized? 8. How can the compass on an iron ship be " compensated " for the induced magnetism in the ship? 9. The Carnegie Institute has a special ship built almost without iron. What kind of a survey of the world do you suppose it is made for ? What is the advantage of such a ship for this purpose ? 10. How does a jeweler demagnetize a watch? 11. What effect does the angle of dip have on the horizontal intensity of the earth's magnetism at any point ? CHAPTER XIY THE BEGINNINGS OF ELECTRICITY Frictional electricity conductors and insulators positive and negative charges electroscope frictional electric machine the lightning rod induction Leyden jar electrophorus theories as to nature of electricity. 242. Electricity by friction. As far back as 600 B.C., Thales of Miletus, one of the " seven wise men," knew that the yellow resinous substance called amber, of which pipe- stems and jewelry are now often made, would, when rubbed, attract bits of paper or other light objects. We now know that many other substances, such as rubber, glass, and sul- phur, have the same property. Any one can observe this on a cold, dry morning after combing his hair vigorously with a hard rubber comb. The comb will then support long chains of bits of paper. Another way to show this is to scuff one's feet on a carpet, or to rub a cat's back. In either case, if the knuckle is brought near a gas fixture, tiny sparks will pass. Since amber, in common with gold and certain bright alloys, was called " electron," by the Greeks, these phenomena were many years later named by Gilbert " electric," that is, " amberous," phenomena. 243. Electric vs. magnetic attraction. These electric at- tractions are in many ways so much like magnetic attractions that it was not until the sixteenth century that it was clearly seen that two very different kinds of phenomena are involved. Magnetization can be produced only in three metals, iron, nickel, and cobalt, and in one or two uncommon alloys, while electrification can be produced by rubbing almost any sub- 248 THE BEGINNINGS OF ELECTRICITY 249 stance, especially non-metals. A magnetized body always has at least two poles where its magnetism is more or less concentrated, and these poles are unlike, for if one of them attracts the north-seeking end of a compass, the other will always repel it. A metallic body electrified by friction will ordinarily not have its properties concentrated in spots, and all parts of it will act very much alike in their attracting power. Nevertheless, we shall presently see that there are two kinds of electricity, just as there are two kinds of magnetic poles. 244. Conductors and insulators. Some substances will con- duct electricity, while others will not. Thus a metal sphere can be charged with electricity by touching it with some electrified substance, such as a stick of sealing wax which has been rubbed with a cat's skin, if the sphere is suspended by a dry silk thread, but not if suspended by a wire. In the latter case just as much electricity gets into the sphere as in the former, but it all runs out again through the wire. So we distinguish between conductors, the best of which are the metals, and non-conductors or insulators, such as dry silk, glass, hard rubber, sulphur, porcelain, paraffin, and resin. It is to prevent the leakage of the electricity in the conductor that electric light, telephone, and telegraph wires are supported on glass or porcelain knobs called " insulators." There is no sharp line between conductors and insulators ; most substances conduct a little, and even the good con- ductors vary greatly in conductivity. In the following table a few common substances are ar- ranged according to their insulating powers. INSULATORS POOR CONDUCTORS GOOD CONDUCTORS Amber Dry wood Metals Sulphur Paper Gas carbon Glass Alcohol Graphite Hard rubber Kerosene Water solutions of Dry air Pure water salts and acids 250 PRACTICAL PHYSICS It will be noticed that the substances which can be easily electrified by friction are all insulators. One reason for this is that when electricity is generated at any point on a body by rubbing, it stays there and makes its presence known, if the body is an insulator ; but if it were a conduc- tor, the electricity would leak away at once. It will also be noticed that those substances which are good conductors of electricity are also good conductors of heat. This curious fact, long not understood, seems to be due to the fact that both heat and electricity are carried through metals by a swarm of tiny particles, called elec- trons, which drift about between the much larger molecules of metal like wind through a forest. 245. Positive and negative electricity. If we hang up in a stirrup, suspended by a silk thread, a glass rod which has been rubbed with silk, and then bring near one end of it another glass rod which has also been rubbed, they repel each other (Fig. 208). In a simi- lar way two hard rubber rods or sticks of seal- ing wax repel each other. But when we bring a rubbed stick of sealing wax near a rubbed glass rod in the stirrup, they attract each other. FIG. 208. Two electrified From such experiments as these rods repel each other. 1 -, . , . -11 we have come to distinguish be- tween two states of electrification. We call one kind " vitreous " (glass) electricity or positive electricity, and the other " resinous " electricity or negative electricity. Bodies charged with the same kind of electricity repel each other, and bodies charged with different kinds of electricity attract each other. That is, Like charges repel and unlike charges attract. 246. How to detect electricity. To test the electrical con- dition of a body we use an electroscope. A simple form of THE BEGINNINGS OF ELECTRICITY 251 electroscope consists of a pith ball hung by a silk thread from a glass support (Fig. 209). If an uncharged body is brought near the pith ball, nothing happens. If a positively charged body is brought near the pith ball, the latter is attracted, becomes itself positively charged, and is then repelled. Then if a negatively charged body is brought near, the positively charged pith ball is attracted, but when it touches, it becomes negatively charged and flies back. If we now bring a negatively charged body near, the negatively charged pith ball is repelled. If, then, we know what the nature of the charge on the pith ball is, and find that a body repels it, we know the body must be charged the same way. If there is attraction, we cannot be sure whether the body is uncharged or oppositely charged. FJG. 209.- Pith-ball electroscope. A more reliable form of electroscope is the so-called " gold- leaf " electroscope, although nowadays they are quite commonly made of two aluminum leaves hung from a brass rod. These are usually mounted in some sort of a glass case, as shown in figure 210. When one brings near the top of the brass rod a charged glass rod, the aluminum leaves separate and hang like an inverted V. If the rod is removed, the leaves come together again. If, however, one actually touches the charged rod to the electroscope, the leaves separate and stay apart. The electroscope is then said to be charged. If we bring near a positively charged electro- scope a positively charged body, the leaves will fly farther apart ; but if the body brought near has a negative charge, the leaves will fall toward each other. In either case they will return to their origi- nal charged position when the outside charged body is taken away. So with an electroscope one can tell the electrical condition of a body. FIG. 210. The aluminum- leal electroscope. 252 PRACTICAL PHYSICS With such an electroscope it is possible to learn much about electrified bodies. For example, when an insulated conductor is rubbed, it becomes charged with electricity ; so we conclude that all bodies become electrified by friction. If we stand on an insulated stool, while we rub a glass rod, our body becomes negatively charged ; and by rubbing seal- ing wax with cat's fur, we become positively charged. In general, whenever two different substances are rubbed on one another, one becomes positively charged with electricity, while at the same time the other is negatively charged. 247. Frictional electric machine. All the early forms of electrical machines were frictional, and such machines are still used for demonstration purposes. A circular glass plate is mounted firmly on an axle, so that it can be turned between two silk-covered cushions, which are pressed against the glass by springs. The charge on the glass is drawn off by a metal comb which is supported on a glass rod. When the plate is rotated, it becomes positively charged and this charges the metal comb positively; at the same time the rubbers be- come negatively charged and should be connected with the ground by a wire or chain, that is, grounded, so that the negative charges can escape. 248. Distribution of electricity on a conductor. Let us place a metal can, such as is used for heat measure- ments, on a glass plate as shown in fig- ure 211, and connect it with an electrical machine by a wire. After we have charged the can as much as possible, we may test it at various points by means of a little metal disk or ball mounted FIG. 211. -Charging a metal can. on an insulating handle and known as a proof plane. If we touch it to the outside surface of the charged can and bring it near the knob of THE BEGINNINGS OF ELECTRICITY 253 a charged electroscope, and then repeat the test, touching it to the inside surface, we find that there is a strong charge on the outside but none on the inside. Such experiments show that the charge is entirely on the outer surface of a conductor and that its greatest density is at the corners and projecting points. In fact the density of the charge at sharp points is so great that the charge will escape into the air easily at such points. If we attach a tassel of tissue paper to the insulated conductor of the electric machine and charge it, the little paper streamers repel each other and stand out in all directions, but if a needle point is held near them, they fall together at once. We may fasten to a friction machine an " electric whirl," balanced on a pin point. When the machine is started, the whirl turns as shown in figure 212. If a bent point is attached to the machine, and a candle flame is held near the point, the so-called " elec- tric wind " may blow the candle flame aside. It is not, however, the electricity itself that blows the candle, but the surrounding air which is in some way set in motion by the discharge. Such experiments show that a conductor can be charged or discharged more easily at a sharp ^ ric wh i rlt point than at a rounded surface. 249. Lightning and lightning rods. For a long time people supposed that thunder and lightning were caused by the com- bustion of some kind of gas in the clouds. But when elec- tricity began to be studied, it occurred to some philosophers that lightning might be an electrical phenomenon. Thus we find Benjamin Franklin in his notebook, under the date of November 7, 1749, making a list of the respects in which lightning resembled electric sparks, such as "giving light, color of the light, crooked direction, swift motion, being con- ducted by metals, crack or noise in exploding, rending bodies it passes through, destroying animals, heating metals and kindling inflammable substances, and its sulphurous smell" 254 PRACTICAL PHYSICS (now known to be due to ozone). He then wondered ii lightning, like electricity, could be drawn off by points. " Since they agree in all the particulars wherein we can already compare them, is it not probable that they agree like- wise in this? Let the experiment be made." But this was not easy. Franklin thought he would require a tower or steeple high, enough to reach into the clouds themselves, and his friends set about raising the money to build one by giving popular lectures on electricity all over the country. In the meantime two Frenchmen were bold enough to try the experiment with insulated pointed rods less than a hundred feet high, and were successful in drawing off sparks from the lower ends of the rods during thunder showers. But Franklin was not satisfied, because the rods did not reach into the thunder clouds, and might have been electrified some other way. Suddenly in 1752 a new idea flashed into his mind, and he set about making his famous kite. The result is known to every one. Almost the most wonderful part of it was that Franklin was not killed at once. Within a year one Richman was killed while making a similar experiment in St. Petersburg. So Franklin invented the lightning rod to conduct elec- tricity safely from the clouds to the earth. Nowadays in cities where the houses are built in blocks with frameworks, tops, and cornices of metal, the lightning rod is not much used. But tall chimneys, church steeples, and isolated houses are often provided with lightning rods. It should be remembered that unless a lightning rod is put up with considerable care, it is a menace rather than a protection. In particular, its lower end must be well " grounded," as by soldering to large copper plates buried in damp soil, and no part of the rod should turn a sharp corner. If these precautions are not observed, a lightning rod will often discharge into the house itself, rather than into the ground, the electricity which it has attracted. THE BEGINNINGS OF ELECTRICITY 255 QUESTIONS 1. Compare the behavior of a magnetic pole with the behavior of an electrically charged body. 2. Does a freely swinging charged body take a definite direction ? 3. What becomes of the mechanical energy exerted in rubbing a glass rod to electrify it ? 4. What kind of electricity is generated by rubbing a fountain pen on woolen cloth ? 5. Why do experiments with friction al electricity work better on a cold, dry winter day V 6. Does one remove magnetism from a magnet by touching it with iron? 7. Faraday built a large box and lined it with tin foil. He then took his most sensitive electroscope into the box and found that even when the outside of the tin foil was so charged that it sent forth long sparks, he could not observe any electrical effects inside. Explain. 8. What evidence have you that the human body is a good conductor ? 250. Charging by induction. If one brings a positively electrified ball near an insulated conductor, such as a metal cylinder on a glass support, and then removes it again, the cylinder is not electrified. But if, while the electrified body is near, one touches the cylinder with his finger or a grounded wire for an instant, the cylinder is found to be negatively charged after the charged body has been removed. If one repeats this experiment using a negatively charged ball, the metal cylinder becomes positively charged. Since the electricity is not diminished in the ball, we must look to the cylinder for the electricity. Charges produced in a conductor by virtue of its proximity to a charged body are called induced charges. This process of charging by induction may be explained as follows. When the posi- tively charged ball is brought near the cylinder, the positive and negative electricity in the FlG - 213 - - Charging by induction, cylinder are distributed as shown in figure 213. When one touches the cylinder, the positive electricity, 256 PRACTICAL PHYSICS which is repelled, finds its way to the ground through the body, but the negative electricity remains bound (Fig. 214). It does not flow off when the conductor is touched, but is held by the presence of the charged body. This helps us to FIG. 214. Bound charge. O Fia. 215. Charging an electro- scope by induction. understand the gold-leaf electroscope. When a charged body is brought near the knob of the electroscope, the leaves separate because they are charged by induction with the same kind of electricity as the charged body (Fig. 215). If the electroscope is charged by contact positively and a posi- tively charged body is brought near, it repels more of the posi- tive electricity into the leaves and so they diverge more widely. On the other hand if a negatively charged body is brought near, it draws some of the positive electricity up into the knob, and the leaves come together more or less according to the amount of the charge. 251. Condenser. In many practical applications of elec- tricity, it is necessary to increase the capac- ity of a conductor for holding electricity. A This is done in what / \ is called a condenser. t TO earth FIG. 216. Action of a condenser. Let us arrange a metal plate on an insulating base and connect the plate by a wire to an electroscope, as shown in figure 216. If we charge the plate A, we see the leaves of the electroscope diverge. We will now THE BEGINNINGS OF ELECTRICITY 257 bring up a second metal plate B similar to plate A, but connected with the ground. As we bring the plate B near plate A, the electroscope leaves begin to fall together, but if we remove plate B again, the leaves separate as before. Let us now bring the plate B back to a position near plate A, and charge plate A until it shows the same deflection as before. It will be evident that the capacity of plate A for holding electricity is much in- creased by being close to a similar grounded plate B. We may also show the influence of the insulating material between the conducting plates, by introducing a pane of glass. The leaves of the electroscope fall nearer together, but rise again when the glass is removed. This shows that the capacity of the condenser is increased by the glass plate. A combination of conducting plates separated by an insu- lajbor is called a condenser. The capacity of a condenser for holding electricity is proportional to the size of the plates and increases as the distance between them decreases. It also depends on the nature of the insulator, or dielectric, as it is called. Mica and paraffin paper are much used in com- mercial work. 252. Leyden jar. At the University of Leyden in Hol- land, as early as 1745, they used a condenser in the form of a wide jar or bottle (Fig. 217), coated inside and out with tin foil. Inside the jar, and connected at the bottom to the inside coating, is a rod with a knob on top. If one allows a charge of positive electricity to jump to the knob the positive electricity on the inner lin- ing attracts through the glass the negative elec- tricity of the outer coating, while at the same time the compensating positive electricity origi- nally in the outer coating is repelled and escapes through its support or the hand which holds it. It is possible to make a great number of sparks jump to the knob before it ceases to receive them. Then the jar is charged. If one connects the outer coating and the knob by a metal wire, the elec- FIG. 217. Ley den jar. 258 PRACTICAL PHYSICS FIG. 218. Hydraulic analogy of a condenser. trical strain or pressure is released with a bright crackling spark. If the jar is discharged through a piece of paper, the spark makes a hole in the paper. If one makes the connec- tion through his own body, he feels a lively sensation, known as a shock. 253. Hydraulic analogy of a condenser. We may illustrate a condenser by two standpipes filled to different levels with water, as shown in figure 218. The coatings of the condenser correspond to the standpipes. The pipe A, with the water standing at a higher level, rep- resents the positively charged plate or coating, while the other pipe B is the negatively charged plate. The connect- ing pipe at the bottom of the tanks corresponds to the wire connecting the coatings. When the connection is made, the water rushes through the pipe and equalizes its levels very quickly. This represents the discharge of the con- denser. When the valve V in the pipe is first opened, the water rushes through so fast that it usually overdoes things, and rises to a higher level in B than in A. Then it flows back again and so on, oscillating back and forth until the motion dies out because of friction in the pipe. In much the same way, when a condenser is short-circuited, the dis- charge of electricity goes too far and charges up the condenser the other way. Then it discharges back again, arid so the electric charges oscillate very quickly back and forth until the motion of the electricity dies out because of something akin to friction, called the electrical resistance of the wire. The technical way of describing this is to say that the dis- charge of a condenser is oscillatory. THE BEGINNINGS OF ELECTRICITY 259 254. Induction machines for producing electricity. The simplest machine . for producing electricity by induction is the electrophorus. It ^ consists of a hard rubber disk and an- other somewhat smaller , fe: Nr- A .(+ + + TD. metal disk, which is provided with an in- sulating handle (Fig. 219). If we rub the hard rubber plate of an electrophorus with cat's fur, we find it (I / Sit FIG. 219. Electrophorus. is charged negatively. Then we place the metal disk on the plate and touch the finger to the metal disk so as to " ground " it. When we lift up the disk and bring it near the knuckle, or the knob of a Leyden jar, a spark jumps across the gap. We may charge a Leyden jar with an electrophorus by repeating this process again and again. When the rubber plate is electrified, it becomes negatively charged. When the metal disk is placed upon it, a positive charge is attracted to the lower surface of the disk next to the plate, while the negative electricity is repelled. When we touch the metal disk, this negative electricity escapes through the hand to the ground. In this process the disk becomes charged positively throughout. After the rubber plate is once charged, any number of charges can be obtained from the electro- phorus, without producing any appreciable change in the charge on the plate. This is because the energy comes from the agent who lifts the disk. 255. Toepler-Holtz ma- FIG. 220. Toepler-Holtz machine. Chine. Among the ma- 260 PRACTICAL PHYSICS chines which make use of this principle of induction to pro- duce electricity is the so-called Toepler-Holfcz machine, shown in figure 220. The details of construction are so many, and the explanation of its operation is so complex, that it is left to the special books on electricity. If one of these machines is in working order, many entertaining experiments can be done with it. 256. Theories as to the nature of electricity. To explain these electrical phenomena, du Fay, a Frenchman, assumed that there were in all bodies two fluids, namely vitreous electricity and resinous electricity. When these are present in equal quantities, they neutralize each other. If a glass rod is rubbed by silk, the silk, which has a greater " affinity " for the resinous fluid than the glass, absorbs some of it from the glass, and at the same time the glass, having a greater affinity for the vitreous fluid than the silk, absorbs some from the silk. So each body gets an excess of its preferred fluid and becomes charged. Later Franklin suggested that there was only one kind of fluid, namely, vitreous electricity, of which a certain amount " belonged " in every body. If it had an excess, it was what had been called vitreously charged. If it had less than enough, it was resinously charged. This led to the terms " positive " and " negative " charge, which are still in use. Lately, we have come back to something nearer du Fay's idea. We do not think of electricity as a kind of matter, as the word "fluid" indicates, but we believe that there are two kinds, a negative or resinous kind occurring in very small lumps which we now call corpuscles or electrons, and a positive kind of a different nature, not yet understood. Even in the modern electron theory, however, there are some who prefer to believe with Franklin that there is only one kind of electricity, namely electrons, which may be present either in excess or in defect. If this turns out to be true, THE BEGINNINGS OF ELECTRICITY 261 Franklin's only mistake was that he hit on the wrong kind of electricity as positive. It makes very little difference whether we talk and think in terms of the one-fluid or the two-fluid theory, inasmuch as everything we know can be expressed either way, and we do not yet know which is right. 257. Conclusion. Practically all that people knew about electricity up to the beginning of the nineteenth century has been briefly outlined in this chapter in very much the order in which it was discovered. Few discoveries were made, and they dealt only with electricity at rest (electrostatics). Almost the only useful electrical invention was the lightning rod, and its usefulness has been much overestimated. The most useful instrument which had been devised was the condenser. Nevertheless, the people of the eighteenth century were fas- cinated by electricity. It was the most exciting topic with which scientific men dealt; it was lectured about and shown off to large audiences, and was as much talked about by everybody as radium or wireless telegraphy have been recently. But it was merely a plaything in labora- tories. In the last half of the nineteenth century, as we shall see in the following chapters, electricity suddenly leaped into a commanding position in the arts and engineering. Probably no more spectacular service has ever been rendered to the welfare of mankind by what practical men like to call " pure science." The story of this development is a most convinc- ing answer to those who, even now, distrust "pure science" as " impractical " and " useless." SUMMARY OF PRINCIPLES IN CHAPTER XIV All bodies can be electrified by friction, becoming charged either positively (vitreously) or negatively (resinously). 262 PRACTICAL PHYSICS Like charges repel each other. Unlike charges attract each other. All conductors can be electrified by induction, showing both a positive and a negative charge in different places. Of these one is bound by the inducing charge, but the other is free. QUESTIONS 1. Why cannot a Leyden jar be appreciably charged if the jar stands on a glass plate ? 2. If a charged Leyden jar is placed on a glass plate, why does one not get a shock if he touches the knob ? 3. How would you arrange four Leyden jars to get increased capacity ? 4. How would you arrange four Leyden jars to get as long a spark as possible ? 5. If an insulated metal globe is negatively charged, how can any number of other insulated globes be positively charged ? 6. If an insulated metal globe is negatively charged, how can any number of other insulated rnetal globes be negatively charged? 7. In the experiment shown in figure 214, why must the finger be removed before the removal of the charged body? CHAPTER XV BATTERY CURRENTS The voltaic cell action in a cell hydraulic analogy de- fects of simple cell commercial cells. Magnetic field around a current, and around a coil electro- magnet electric bell telegraph. BATTERIES 258. Beginnings of the electric battery. For nearly two thousand years friction and induction were the only meth- ods known for producing electricity. But, in 1786, an unexpected observation of an Italian anatomist, Galvani, in Bologna, started a series of most important discoveries and inventions. He observed that the legs of frogs which he had been dissecting twitched every time there was a discharge from his electric machine. Later he found that if strips of two different metals, such as copper and zinc, were fastened together like an inverted V, and their free ends applied to frogs' legs, there were the same nervous twitchings as followed the discharge of electricity. There- fore he concluded that he had found a new way of producing electricity. He thought the elec- tricity was formed at the contact of the dissimi- lar metals. While -investigating this question, Volta invented a chemical method of producing elec- tricity continuously, called an electric battery. 259, Voltaic battery. A glass tumbler, with a strip of zinc and a strip of copper dipping into dilute sul- phuric acid (Fig. 221), is one form of voltaic cell, and when several cells are combined, they constitute a battery. 263 Dilute Sul- phuric Acid FIG. 221. Vol- taic cell. 264 PRACTICAL PHYSICS FIG. 222. To show charges on plates of voltaic cell. To show that the copper and zinc strips are each charged with electric- ity, we will connect six such cells in series as shown in figure 222. To detect the feeble charge we will put a 3-inch disk on the top of the brass rod of the aluminum- leaf electroscope. Then we will take another similar disk which is provided with an insulating handle and has a thin coating of shellac on the bottom, and place this disk on top of the other. This forms a condensing electroscope. If we touch the wires leading from the zinc and copper strips of the battery to the lower and upper disks of the con- Zn denser, as shown in figure 222, and then remove the wires and lift off the upper disk, we find that the leaves of the electroscope diverge. If we bring a charged stick of sealing wax near the electroscope, the leaves spread still farther apart, which shows that the electroscope and the zinc are negatively charged. If we repeat the experiment with the wires reversed, we can show that the copper is positively charged. The copper (or the carbon which often replaces it) is called the positive electrode ojM- pole, while the zinc is called the negative electrode or_ jx>le. The solution in the cell is called the electrolyte. When the poles of a cell are joined by a conductor, we have an electric path or circuit con- sisting of the electrodes, the electrolyte, and the metallic conductor joining the poles. If a bell or lamp is to be oper- ated by an electric battery, it is so connected that the elec- tricity passes through it as a part of the circuit. When this circuit is broken at any point by a switch, key, or push button, so that no electricity jumps the gap, the circuit is said to be open. When the switch or key is closed so as to make a continuous path, the circuit is said to be closed or made. 260. Action of an electric cell. We have already seen that when a Leyden jar is discharged, or any two charged bodies are connected by a wire, there is what we call a flow of electricity ; that is, an electric current. By convention we say that the electricity in the connecting wire flows from the positive to the negative conductor. In a single electric cell we shall speak, BATTERY CURRENTS 265 therefore, of the electricity as flowing through the outside circuit from the copper or carbon electrode (-hpole) to the zinc electrode ( pole). Inside the cell the electricity must evidently flow " uphill " through the solution or electrolyte back to the copper electrode. We shall see presently why it is able to flow uphill inside the cell. To understand a little better just what is happening inside the cell, let us dip a strip of ordinary zinc into very dilute sulphuric acid. We shall see bubbles rising from the zinc and coming to the surface of the acid. These bubbles are a gas called hydrogen. If we leave the zinc in the acid, it gradually dissolves, leaving behirioTonly a few insoluble impurities. If we repeat the experiment, using a copper strip, we shall find no action ; but if we put both the zinc and the copper strips into the acid and connect them with copper wires to some instrument that indicates a current of electricity (a galvanometer), we see that a current is produced, and that bubbles are coming from both the copper and the zinc strips. Next we will remove the zinc strip and rub a little mercury on it. The mercury clings to the zinc and can be spread over its surface. Such a union of a metal with mercury is called amalgamation. If this amalga- mated zinc is used in the cell, no bubbles are formed on it. When the circuit is closed, bubbles rise from the copper plate, and when the circuit is broken or open, these bubbles stop. A galvanometer in the circuit shows a current as before, but now the amalgamated zinc is consumed only when the circuit is closed. The copper is not consumed by the acid at all. In general it can be said that the electric current depends on the difference in the chemical action of the acid on the two metals used as electrodes. The metal which is dissolved or acted upon by the acid is the negative electrode ; the metal which is apparently unchanged and from which the hydrogen bubbles rise while the circuit is closed is the posi- tive electrode. 261. The chemistry of the cell. In chemistry we learn that sulphuric acid is made up of two parts hydrogen, one part sulphur, and four parts oxygen, as expressed by the symbol H 2 SO 4 . When sulphuric acid is dissolved in water, some of it breaks up into two parts, H 2 and SO 4 . These 266 PRACTICAL PHYSICS two parts, called ions, carry opposite kinds of electricity. + + The H 2 is positively charged and the SO 4 is negatively charged. When zinc (Zn) is placed in the acid, a little of it dis- + + solves, becoming zinc ions (Zn), which unite with the SO 4 ions to form zinc sulphate (ZnSO 4 ). The displaced hydro- + + gen (H 2 ) goes to the copper plate, gives up its charge to the plate, and then rises as bubbles of gas. It is important to remember that the positively charged part of the electrolyte (H 2 ) goes with the current through the cell. The electric current will flow through the wire from the copper to the zinc as long as the chemical action is maintained. Thus we see that it is the energy of the chemical action which forces the electricity to run uphill inside the cell. In this way chemical energy is transformed into electrical energy. In a good commercial cell the chemical action takes place only when the cell is delivering electrical energy. The rate at which this energy is delivered by the cell determines the rate at which the zinc is used up ; just as the rate at which steam energy is delivered by a boiler determines the rate of coal consumption. Zinc is, then, the fuel of the electric cell. 262. Electric currents and water currents. Although it must not be supposed that electricity is a material flowing through the circuit as water flows through a pipe, yet it will greatly help us to form a mental pic- ture of the situation if we compare electric currents with water currents. FIG. 223,-Water at different In figure 2 23 we have two tall open vessels containing water. These are connected by a pipe which contains a pump driven by the weight W. The water will evidently be pumped from A to J9 ? w BATTERY CURRENTS 267 FIG. 224. Water iu circu- lation. until the back pressure on the pump due to the higher level of the water in B is enough to balance the weight W. This difference in level does not depend on the size of the vessels. Suppose now that the vessels are connected by a second pipe, as shown in figure 224. Then the difference in levels will cause the water to flow from B to A. The water level in B drops a little and that in A rises, so that the difference in levels between A and B becomes less. When the back pressure against the wheel of the pump is thus reduced, the weight drops and drives the water around the circuit. This will continue as long as the weight can move downward. The difference in level in A and B, in figure 223, repre- sents the difference in the electrical condition of the two electrodes, copper and zinc. This is called the difference of potential between the positive and negative poles of the cell. The pump represents the chemical action of the acid on the zinc, which produces this difference of potential. Figure 223 is, then, analogous to the cell with its circuit open. The cell with its circuit closed is represented by figure 224. The tube connecting A and B represents the outside circuit between the copper and the zinc. The circulation of the water represents the flow of electricity. The rate at which the water circulates depends on the difference in level which the pump can maintain ; that is, on the power of the pump. Similarly the rate of flow of electricity depends on the electromotive force which the chemical action of the acid and zinc can maintain. Furthermore, the rate of flow of the water depends on the friction in the connecting pipes, and similarly, the rate of flow of the electricity depends on the electrical friction or resistance of the circuit. Finally, just 268 PRACTICAL PHYSICS as the energy needed to circulate the water comes from the action of gravity on the weight, so the energy needed to drive the electric current is supplied by the chemical changes which take place at the electrodes. 263. Two defects in a simple cell. Volta's simple cell, which has been described, was soon found to have two defects, local action and polarization. When ordinary zinc is used, bubbles of hydrogen are formed at the surface of the zinc strip even before it is connected with the copper. This means a wearing away of the zinc to no purpose, and is called local action. It is due to impurities, such as iron or carbon, embedded in the zinc. These impurities form with the zinc a minute voltaic cell, as shown in figure 225. The local current flows from the iron or carbon directly to the zinc and then back through the acid to the iron again. In this process, the zinc is eaten away near FIG. 225. Local ac- the impurity, and hydrogen is set free. To tion in a cell. avoid this useless wasting away of the zinc, it is necessary to use strictly pure zinc or else to amalgamate the zinc electrode with mercury to cover up the impurities. The second defect is the fact that, when the poles of a simple cell are connected by a wire, the current does not remain constant, but rapidly gets weaker. This polarization, as it is called, is caused by the hydrogen bubbles which col- lect on the copper strip and thus form a gaseous coating. This layer of hydrogen is a poor conductor of electricity and therefore weakens the current. Furthermore the hydrogen layer has a slight battery action of its own, tending to send a current in a direction opposite to that desired, and this also weakens the current delivered by the cell. Let us set up a zinc-sulphuric-acid-copper cell, connect it to a high resistance galvanometer, and observe the deflection. If we then short- ?U| Zi ~ Carbon 80$ j 1 1 BATTERY CURRENTS 269 circuit the poles of the cell by a short wire, which polarizes the cell quickly, we shall observe, on removing the wire, that the deflection is less than before. We may restore the cell by lifting the copper plate out of the acid for a moment or by brushing off the hydrogen bubbles. We may also show polarization in a carbon-zinc cell in a similar way, but we can easily restore the cell by pouring into the acid a solution of potassium dichromate, a substance rich in oxygen. This increases the current because the hydrogen is taken up chemically by the oxydizing agent. If we now " short-circuit " the cell, that is, connect the terminals with a low-resistance conductor, the cell recovers quickly when the short circuit is removed. Such a substance as the potassium dichromate is called a depolarizer. 264. Commercial cells. There is a two-fluid cell, called the Daniell cell, which is free from polarization. In this cell the copper plate (Cu) stands in a solution of copper sulphate or blue vitriol (CuSO 4 ) and the zinc (Zn) in a solution of zinc sulphate (ZnSO 4 ). Both the copper sulphate and the zinc sulphate break up into ions. When the circuit is closed, both copper and zinc ions carry the current toward the copper electrode. The zinc ions, however, do not reach the copper plate, because zinc in copper sulphate replaces copper, forming zinc sulphate. The result is that the zinc goes into a solution form- ing zinc sulphate, and metallic copper is deposited on the copper electrode. One form of this cell, much used in teleg- raphy, is called a gravity cell (Fig. 226) because the two liquids are separated by gravity. The dilute solution of zinc sul- phate is lighter and therefore floats on the saturated solution of copper sulphate. The copper plate in the bottom of the jar is surrounded by crystals of copper sul- FIG. 226. Gravity phate to keep the solution saturated. In the dilute zinc-sulphate solution above is a heavy piece of zinc in the shape of a " crowfoot." 270 PRACTICAL PHYSICS If the gravity cell is allowed to stand with its circuit open, the liquids mix slowly, and copper is deposited on the zinc in long festoons which cause local action, and sometimes grow long enough to short-circuit the cell. To prevent this, the external circuit must be kept closed. The cell is therefore well adapted for telegraphy, where a small, constant current is needed, but is not good for ringing doorbells or other intermittent work. In another form of Daniell cell, the solutions are sep- arated by a cup of porous earthen- ware. For open-circuit work, such as ring- ing doorbells, the sal-ammoniac cell (Fig. 227) is used. The electrodes are zinc and carbon, and the electrolyte is a solution of sal- ammoniac (ammonium chloride, NH 4 C1). To reduce the polarization as much as possible, the carbon electrode is made with a large surface, and the cell often contains, as a depolar- izer, a mixture of carbon and manganese dioxide. Since this depolarizer is slow in its action, the cell is adapted only to open-circuit work. It gives off no fumes, has very little local action, and so, when once set up, requires very little attention. Occasionally the water which has evaporated must be replaced and the zinc renewed. The type of cell now most used for small intermittent work is the dry cell. This differs from the sal-ammoniac cell just described only in that the electrolyte is in the form of a paste instead of being a liquid. The negative electrode is the zinc can which contains the carbon and paste FIG. 227. Sal-ammoniac cell. BATTERY CURRENTS 271 (Fig. 228). The zinc is protected on the inside by several layers of blotting paper, and the space around the carbon is filled with a mixture of carbon, man- ganese dioxide, and sawdust, saturated with a solution of sal-ammoniac. The top is sealed with wax, and the whole cell is slipped into a pasteboard box. The dry cell is much used for ringing doorbells, running clocks, and operating the spark coils used to ignite gas engines on boats and automobiles. It requires no attendance, but must not be left on closed circuit. Sometimes the life of U FIG. .228. Dry cell. an exhausted dry cell can be extended slightly by punching a hole in the top and pouring in water, but usually exhausted cells are thrown away. QUESTIONS 1. What are the points which a good cell should possess? 2. Why would you not use a gravity cell for ringing a doorbell ? 3. What is the " fuel " in the dry cell ? 4. Why are the small motors for fans, sewing machines, etc., never run by batteries if any other source of power is available ? 5. If a person touches the poles of a cell, why does he not get a " shock " ? 6. If you touch the two wires from a dry cell to the tip of your tongue, do you taste anything, and if so, why? MAGNETIC EFFECT OF ELECTRIC CURRENT 265. Oersted's discovery. In 1819 a Danish physicist, Oersted, made a discovery which aroused the greatest inter- est because it was the first evidence of a connection between magnetism and electricity. He found that if a wire connect- ing the poles of a voltaic cell was held over a compass needle, the north pole of the needle was deflected toward the west 272 PRACTICAL PHYSICS Wire above Wire under Prmf j n pr nr needle needle [CtOr ' when the current flowed from south to north, as shown in figure 229, while a wire placed under the compass needle caused the north end of the needle to be deflected toward the east. 266. Magnetic field around a current. Inasmuch as the compass needle indi- cates the direction of magnetic lines of force, it is evident from Oersted's ex- periment that a current must set up a magnetic field at right angles to the To make this clear, the FIG. 229. Deflection of student may perform the following ex- magnetic needle by periment. electric current. We will send a strong current down a vertical wire which passes through a horizontal piece of cardboard. To indicate the magnetic lines of force, we will sprinkle iron filings on the cardboard and tap it gently while the current is Jfy f ^\ on. The filings ar- "^ range themselves in concentric rings about the wire. By placing a small com- pass at various posi- tions on the board, we see that the di- rection of these lines of force is as shown in figure 230. A convenient rule for remembering the direction of the magnetic flux around a straight wire carrying a current is the so-called thumb rule. If one grasps the wire with the right hand (Fig. 231) so that the FIG. 231. Thumb rule for mag- thumb points in the direction of netic field around a wire. , 7 .7 /; -77 '* the current, the fingers will point in the direction of the magnetic field. Fia 2 30. Magnetic lines of force around a current. BATTERY CURRENTS 273 If we know the direction of the magnetic field near a con- ductor, we can, by applying this rule, find the direction of the current. Figure 232 shows the field around the wire with the current going in and figure 233, with the current coming out. FIG. 232. Current going in, clock- wise field. Fio. 233. Current coming out, anti- clockwise field. 267. Magnetic field around a coil. If a wire carrying a cur- rent is bent into a loop, all the lines of force enter the loop at one face and come out at the other face. If several loops are put together to form a coil, practically all the lines will thread the whole coil and return to the other end outside the coil. (1) We may thread a loose coil of copper wire through a board or sheet of celluloid in such a way that when iron filings are evenly scattered over the smooth surface of the board, while a strong current is sent through the wire, they will indicate the lines of magnetic force (Fig. L'34). By tapping the board gently and using a small com- pass, we can see the general di- rection of th<* lines of magnetic flux. It will be noticed that there are a few circular lines around each wire, arid that these lines go out between the loops. They are called the " leakage flux " of the coil. FIG. 234. Magnetic flux around a coil. 274 PRACTICAL PHYSICS (2) tf we send a current through a close-wound coil of insulated copper wire, and bring it near a compass needle, we find that it behaves like a bar magnet. If the current is reversed, the poles of the coil are reversed. (3) If we put a soft iron core inside the coil when the current is on, the iron exerts a very strong pull on bits of iron ; but when the current is off, the iron loses this magnetism almost at once. (4) If we use a large horseshoe electromagnet, or a model of a mag- netic hoist, and considerable current, we may show that a tremendous force can be exerted by an electromagnet. An iron core in a coil of wire is so much more permeable than air that the same current in the same coil produces several thousand times as many lines of forces in the iron core as it would in air alone. 268. Electromagnet. An iron core, surrounded by a coil of wire, is called an electromagnet. It owes its great utility not so^ much to the fact of its great strength, as to the fact that, if it is made of soft iron, its magnetism can be controlled at will. Such an electromagnet is a magnet only when cur- rent flows through its coil. When the current is stopped, the iron core returns almost to its natural state. This loss of magnetism is, however, not absolutely complete ; a very little residual magnetism remains for a longer or shorter time. An electromagnet is a part of nearly every electrical machine, including the electric bell, telegraph, telephone, dynamo, and motor. To determine its polarity, we shall find it convenient to ex- press the thumb rule as usd for a straight wire, in another way, as follows : - THUMB RULE FOR A COIL. Grrasp the coil with the right hand so that the fingers point in the di- rection of the current in the coil, FIG. 235. Rule for polarity of and the thumb will point to the coil carrying current. mrth poU Q j ^ ^ ( Fig> 235)> The strength of an electromagnet depends on the strength of the current and on the number of loops or turns of wire, MICHAEL FARADAY. Born in London, in 1791, the son of a blacksmith. Died in 1867. A chemist who made many wonderful discoveries in elec- tricity and magnetism. JOSEPH HENRY. Born in Albany, N.Y., in 1799. Died in 1878. Was for six years a schoolmaster at Albany Academy, for fourteen years a professor at Princeton, and for the rest of his life the head of the Smithsonian Institution in Washington. Made the first careful study of the electromagnet, and shares with Faraday the honor of discovering the laws of electromagnetic induction. BATTERY CURRENTS 275 It is the practice, in order to make use of both poles of an elec- tromagnet, to bend the iron core and the coil into the shape of a horseshoe, as shown in figure 236. Practical electromagnets were made in 1831 by Joseph Henry, a famous American schoolmaster and scientist, then teaching in the academy at Albany, N.Y., and by Faraday in England. Henry's magnet was capable of supporting fifty times its own weight, which was considered very remarkable at the time. Magnetic hoists are now built p FIG. 236. Electromagnet. FIG. 237. Electric-bell circuit. so powerful that when the face of the iron cores is brought in contact with iron or steel castings and the current is turned on, the magnets will lift from 100 to 200 pounds of iron per square inch of pole face, and yet re- lease the load of iron the moment the current is cut off. APPLICATIONS OF THE ELECTRO- MAGNET 269. Electric bell. An electric-bell circuit usually includes a battery of two or more cells, a push button, and connecting wires, besides the bell itself (Fig. 237). When the circuit is closed by pushing the button P, the current flows through the electric magnet (rn) .and attracts the armature -4). As 276 PRACTICAL PHYSICS the armature swings to the left, it pulls the spring (#) away from the screw contact (J5) and breaks the circuit. This stops the current, and the electromagnet releases the armature. It then springs back again and closes the circuit at the screw, and the whole process is re- peated. The swinging of the armature, which carries a hammer, causes a series of rapid strokes against the bell as long as the button is pushed. It does not mat- ter in which direction the current flows. The construction of the push button P is FIG. 238.-Push button. , figure 270. What to do when the bell won't ring. First make sure that the connecting wires at the bell, push button, and battery are firmly screwed into the binding posts. Next inspect the battery. The liquid should fill the jar within an inch of the top. The zinc should be clean and free from crystals and should dip into the solution, but should not touch the carbon. If the battery consists of dry cells, you will do well to get a pocket ammeter and try each cell. A new cell will indicate about 20 amperes. If a cell has dropped much below 5 amperes, it is dead. Next test the push button by removing the cover and holding a a piece of metal across the terminal wires. If the bell rings, it shows that the trouble is a poor connection in the button. Brighten up the contact points with sandpaper. Finally look over the bell itself carefully, especially the point where the make and break occurs. Sometimes the screw with the platinum point gets loose or gets worn off and needs readjustment. 271. Telegraph. The word " telegraph " means an instru- ment which " writes at a distance," for the early forms in- vented by Samuel F. B. Morse, in 1844, were designed to make dots and dashes on a moving strip of paper, Nowa- days the receiving instrument, called the sounder, makes a series of clicks separated by short or long intervals of time to represent the dots and dashes. BATTERY CURRENTS 277 The telegraph consists essentially of a battery, a key, and a sounder, as shown in figure 239. Gravity cells are used in .Key Sounder Sounder 'itch fain Hi Earth Earth,. FIG. 239. Simple telegraph circuit. practical work, but for experimental purposes any kind of battery will serve. The key (Fig. 240) is a device, something like a push button, for making and breaking the circuit. The sounder (Fig. 241) consists of an electromagnet with a soft iron armature which is fastened to a brass bar. This ADJUSTING SCREWS CONTACT- BUTTON LEGJI FIG. 240. Telegraph key. bar is pivoted so as to move up and down. When a cur- rent flows through the elec- tromagnet, the armature is pulled down ; when the circuit is broken, a spring pulls the bar up again. Two set screws above and below the bar limit its motion and make the clicks. As the clicks made by the bar hitting these two set screws are different, the ear recog- nizes the time between these FIG. 241. -Telegraph sounder. two c li c k s as a dot Or a dash according as the key is depressed a short or a long time. When the telegraph came into commercial use, it was found that the resistance of the connecting wires, called the 278 PRACTICAL PHYSICS line, was so great that the current was too feeble to operate the sounder, even when many cells were connected in series. A relay (Fig. 242) is there- fore employed to open and close the circuit . of a local battery which operates the sounder. This relay contains an electromagnet whose coil has many turns of very small FIG. 242. Telegraph relay. T f t ,,. copper wire. In front of this magnet is a light iron lever which is held away from the electromagnet by a very delicate spring. The connections are shown in figure 243. When the key in the main circuit is closed, the weak current excites the relay magnet enough to pull the armature against a set screw, thus closing the local circuit which sends a strong current through the sounder. In ordinary telegraphy it is custom- Local ary to use a single wire of galvanized iron or hard-drawn copper, and to use the earth as a return circuit. At each Earth ==- station along the line there is a local FlG - - 43 -- Dia ^am of r* & lay telegraph circuit. circuit consisting of battery and sounder, which is closed by a relay. The relay is in another circuit containing a key and the main-line battery or gen- erator. Each key is provided with a switch so that the main circuit is kept closed everywhere except at the station where the operator is sending a message. 272. Other forms of telegraphs. Through the inventions of Edison and others we are now able to send two messages simultaneously in each direction. In other words, we can send four messages over a single wire all at the same time. This is called quadruplex telegraphy. BATTERY CURRENTS 279 Submarine telegraphy began as early as 1837, but it was not till 1866 that a really successful Atlantic cable was laid. Such a cable contains a central conducting core of copper wires twisted together. This is surrounded by a thick in- sulating coating of rubber and outside of this is a protective covering of hemp and steel wires. The copper core and the steel sheath act like the coatings of an immense Leyden jar. The effect of this is to make the sending of messages very slow. The impulses received at the other end are also very weak. It was only when an exceedingly delicate receiving instrument had been devised by Lord Kelvin, that the first Atlantic cable could be used at all. SUMMARY OF PRINCIPLES IN CHAPTER XV Current flows downhill, from 4- to , in outside circuit. Current is pumped uphill, from to -f-, inside of cell. Energy is supplied by chemical action of acid on zinc. Zinc is fuel of cell. Current carried through cell by charged ions (pieces of molecules). Lines of magnetic force around a straight current are concentric circles. Thumb rule for straight wire: Use right hand. Thumb points with current. Fingers curl with field. Lines of force around a coil mostly go through inside and come back outside. Thumb rule for coil: Use right hand. Thumb points with field toward AT-pole. Fingers curl with current. QUESTIONS 1. An electromagnet is found to be too weak for the purpose intended. How may its strength be increased? 2. In looking at the TV end of an electromagnet, in which direction does the current go around the core, clockwise or anticlockwise ? 280 PRACTICAL PHYSICS 3. If you find that the JV-pole of a compass held under a north and south trolley wire points toward the east, what is the direction of the current in the wire? 4. In a certain factory, steel was once used by mistake instead of soft iron to make the cores of the electromagnets for some bells. What would be the matter with the bells? 5. What would be the effect of winding an electromagnet with bare copper wire instead of insulated? 6. What sort of material is used to insulate copper wire which is to be used () to wind electromagnets, (6) to wire electric doorbell circuits, and (c) for electric lights? 7. What is the difference between a relay and a sounder that makes it possible for a weak current to work one and not the other? CHAPTER XVI MEASURING ELECTRICITY Galvanometers the ampere ammeters the ohm in- ternal and external resistance the volt voltmeters. Ohm's law for whole circuit and for part of circuit resist- ances in series and in parallel cells in series and in parallel. Specific resistance and the circular mil effect of tempera- ture on resistance resistance boxes measurement of resis^t- ance by voltmeter-ammeter method, and by Wheatstone bridge. 273. Necessity for a unit of current strength. In the con- struction, study, and use of electrical machinery, we are con- stantly dealing with electric currents. We say a current is strong or weak, just as we speak in a rough way of things being fast or slow, hot or cold. When, however, we go a step farther and ask how strong this current is or how weak that current is, we are forced to have some unit of current strength, and some means of measuring currents in terms of it. 274. Galvanometers. We can get an idea of the relative strength of two currents by means of a galvanometer. There are two kinds of galvanometers in common use, the older of which is the moving-magnet galvanometer (Fig. 244). This consists of a compass needle pivoted or hung at the center of a large wooden frame on which are wound one or more turns of wire. This coil is set facing east and west so that the compass needle lies parallel to its plane. When a cur- rent is sent through the wire, an east and west magnetic field is set up at the center of the coil and the compass is deflected more or less according as the current is stronger or weaker. 281 282 PRACTICAL. PHYSICS In the type of galvanometer just described, the coil is large and is fastened firmly to the base, while the magnet is FIG. 244. Moving-magnet galvanometer and diagram of essential parts. small and movable. In the moving-coil type (Fig. 245), the magnet is large and is fastened firmly to the base, while the coil is small and movable. The magnet, NS, is usually made in the shape of a horseshoe so that it may be as strong as possible. The coil is wound on a very light rectangular frame and hangs between the jaws of the magnet. Usually there is a cylinder, I, of soft iron in the space inside the moving frame to still further increase the field. The bottom of the coil is con- nected with a binding post, B, by a spiral of very fine wire which carries the current into the coil without disturbing its freedom to rotate ; the current leaves the coil through the fine suspension wire, AC. The top of this wire is twisted until the coil hangs in the plane of the poles N FIG. 245. Moving-coil galva- nometer and diagram of essen- tial parts. MEASURING ELECTRICITY 283 and S when no current is passing through it. If there is a current, the coil acts like a tiny magnet with poles pointing to the front and rear, and tries to turn itself so that these poles may get as near possible to the .2V and S poles of the magnet. The amount by which it is able to twist the sus- pension wire measures the current. The moving-coil type is much more convenient for ordi- nary work, but the moving-magnet type can be made much more sensitive, and is used when very small currents have to be detected or measured. 275. The ampere. Having learned how to compare cur- rents by means of a galvanometer, let us consider what the unit is, in terms of which currents can be measured. When we open the faucet at a sink, a current of water flows through the pipe. The rate of this flow can be easily measured in cubic feet (or gallons) of water per minute (or per second). Thus we speak of water as flowing at the rate of 1 gallon per second or 5 gallons per second. In much the same way we speak of electricity as flowing along a wire at the rate of 1 coulomb per second or 5 coulombs per second. The coulomb is the unit quantity of electricity, just as the gallon is the unit quantity of water. We have to consider the rate of flow of electricity so often that we have a special name for the unit rate of flow, 1 coulomb per second. We call it an ampere. Thus 5 amperes means 5 coulombs per second. It is possible to define the ampere in terms of the magnetic effect of an electric current, but, as a matter of fact, electrical engineers have agreed to define the ampere in terms of its chemical effect. If two silver (Ag) plates are placed, in a jar of silver nitrate solution (AgNO 3 ), and if the + and - terminals of a battery are connected, one to one plate and one to the other, it will be found that the plate where the current goes in (the anode) loses in weight because silver is dissolved, and the plate where the current comes out (the cathode) gains in weight because silver is deposited. By international agree- 284 PRACTICAL PHYSICS ment the quantity of electricity which deposits 0.001118 grams of silver is one coulomb, and the current which deposits silver at the rate of 0.001118 grams per second is one ampere. The apparatus used in the accurate measurement of current by this method is shown in figure 246. The anode is the silver disk at the left, and the cathode is the silver (or plati- num) cup at the bottom. The porous cup at the right is put between the anode and the cathode in the solution like the cup in a Daniell cell. 276. Illustrations of the ampere. When FIG. 246. - Silver coulomb- a ne w dr ^ cel1 is short-circuited with a short stout meter. wire, about 20 amperes flow through the wire. An ordinary 16 candle power carbon filament electric lamp takes a little less than half an ampere, while the arc lamps used for street lighting require from 6 to 10 amperes. A telegraph sounder operates on 0.25 amperes, and a telephone receiver on less than 0.1 am- peres, while the motor on a street car often takes as much as 40 or 50 amperes. 277. The ammeter. The legal method, described above, of defin- ing an ampere is not, of course, a convenient method of measuring current strength. The coulomb- meter is used only for standardiz- ing the ammeters which are used in everyday life to indicate cur- rent strength. The commercial ammeter (ampere- meter) is a shunted, moving coil gal- vanometer. The instrument (Fig. 247) contains a coil of fine insulated copper wire, wound on a light frame, and mounted in jeweled bearings between the FIG. 247. Ammeter. MEASURING ELECTEICITT 285 poles of a strong permanent horseshoe magnet. A fixed soft iron cylinder midway between the poles of the magnet concen- trates the field. The moving coil rotates in the gap between the core and the pole pieces. The coil is held in equilibrium bv two spiral springs, which serve also to carry the current into and out from the coil. Only a small fraction, perhaps 0.001 of the current to be measured, goes through the mov- able coil, the major part being carried past the coil by a metal strip called a shunt. Since the current through the coil is a constant fraction of the whole current, the pointer which is attached to the moving coil can be made to indicate directly on a graduated scale the number of amperes in the total current. It will be seen that the resistance of an ammeter, which is practically the resistance of the shunt, is very small, and that the whole current passes through the instrument. 278. Electrical resistance. Although we divide substances into two classes, conductors and non-conductors or insu- lators, yet even the best conductors of electricity are not perfect. This means that all conductors offer some resistance to the flow of electricity and transform a part of the energy which they carry into heat. We are already familiar with the fact that a stream of water flowing through a pipe is held back or retarded by the friction of the pipe. The amount of this friction depends on the smoothness of the inner surface, the length and the size of the pipe. So with electricity, the resistance of a conductor depends : (1) On the material used ; iron, for example, has nearly 7 times as much resistance as copper ; (2) On the length ; a wire 10 feet long has twice as much resistance as a wire 5 feet long ; (3) On the size of the wire ; a wire 0.04 inches in diameter has one fourth the resistance of a wire 0.02 inches in diameter ; (4) On the temperature ; heating a copper wire from to 100C increases its resistance about 40%. 286 PRACTICAL PHYSICS 279. Legal ohm, the unit of resistance. The legal unit of resistance, called the ohm, is the resistance at C of a column of mercury 106.3 centimeters long, with a cross section of about 1 square millimeter (more exactly, of uniform cross section and weighing 14.4521 grams). This legal definition of the ohm fixes the material, length, cross section, and tem- perature of the conductor whose resistance is taken as the standard. Since a column of mercury is not convenient to handle, we ordinarily use "standard coils" made of some high-resistance alloy, such as German silver or manganin. 280. Illustrations of the Ohm. About 157 feet of # 18 copper wire (the size ordinarily used to connect electric bells), or 26 feet of iron wire or 6 feet of manganin wire of the same size, has a resistance of 1 ohm. The resistance of a small electric bell is about 3 ohms, of a telegraph sounder 4 ohms, of a relay 200 ohms, of a telephone receiver 60 ohms, and of 16 candle power incandescent lamp 220 ohms when hot. 281. Internal and external resistance. It must not be for- gotten that there is resistance to the flow of electricity in every part of an electric circuit. In the case of the electric- bell circuit, there is the bell itself, the push button, the con- necting wires, and the battery. The resistance of the generator, whether it be a battery or a dynamo, is called the internal resistance, and that of the rest of the circuit is the external resistance. It is the gradual increase in the internal resistance of a long-used dry cell which cuts down the cur- rent it can deliver and so destroys its usefulness. 282. Electromotive force. In hydraulics we know that to get water to flow along a pipe it is essential to have some driving or motive force, such as that furnished by a pump. In much the same way, to get electricity to flow along a wire we must have an electromotive force, such as that furnished by a battery or dynamo. The unit of electromotive force is the volt. A volt may be defined as the electromotive force needed to drive a current of one ampere through a resistance of one ohm. MEASURING ELECTRICITY 287 283. Illustrations of VOlts. A common dry cell gives about 1.4 volts, and a storage cell about 2 volts. A gravity cell gives about 1.08 volts, and the so-called Weston Standard cell, used in very exact voltage measurements, gives 1.0183 volts at 20 C. The current for lighting a building is usually delivered at 110 or 220 volts, and street cars op- erate on about 550 volts. 284. Distinction between volts and amperes. The intensity of an electric current is measured in amperes, the electromotive force driving the current is measured in volts. In a given cir- cuit the greater the electromotive force is, the greater is the current. We know that we must have a certain " head " of water in order to get a given number of gallons of water to flow through a given pipe each second ; so we must have a certain electromotive force to make a given current of elec- tricity flow through a given wire. With both water and electricity we must have a motive force in order to have a current, but we may have the motive force and yet have no current. If the valve is closed in the water pipe or the switch is open in the electric circuit, we might have motive force (volts) but no current (amperes). COMPARISON OF HYDRAULIC AND ELECTRICAL UNITS UNITS WATER ELECTRICITY Quantity Gallon Coulomb Current Gallon per sec. Ampere = 1 coulomb per sec. Motive force " Feet of head " Volt Resistance Ohm 285. The voltmeter. The commercial voltmeter is simply a high-resistance galvanometer. When electromotive force is applied to a galvanometer, the current it allows to pass is proportional to the voltage, and so the scale can be gradu- ated to read the voltage directly. The instrument (Fig. 248) is usually a moving coil galvanometer, like an ammeter. Indeed the same instrument is often used for both purposes. A voltmeter does not have a shunt between its terminals, 288 PRACTICAL PHYSICS FIG. 248. Voltmeter. like an ammeter, but does have a large resistance coil inserted in se- ries, so that only a very small cur- rent passes through the instrument, but all of it goes through the mov- ing coil. In fact such a voltmeter gives correct values only when the current used is so small as not to affect appreciably the voltage to be measured. This will be understood by considering the water analogy shown in figure 249. It is evident that the current in the connecting pipe AB is a good measure of the difference in level between L and L', only when the current in AB is so small as not to change appreciably the levels whose difference is to be measured. To make voltmeters usable over dif- ferent ranges we have merely to con- nect coils of different resistance in series with the same galvanometer. Since the voltmeter is an instrument for measuring the electromotive force between the two ends of a circuit or of part of a circuit, it must have its ter- minals Connected to the two points; FIG. 249. Water analogue that is, it mut be put across the circuit, not in it. The proper connections for both ammeter and voltmeter are shown in figure 250. 286. Electromotive force of a cell. If the electromotive force of a simple cell is observed with a voltmeter, it will be found that the voltage of the cell is not changed by moving the plates near together or far apart, or by lifting them almost out of the liquid so as to change greatly their effective size. These changes affect the current sent by the cell through an ex- ternal circuit by changing the internal resistance of the cell, not its voltage. w FIG. 250. How to connect a voltmeter and ammeter. MEASURING ELECTRICITY 289 If a stick of carbon is used instead of a copper plate, the voltage of the cell will be found to be greater; if, however, hydrochloric acid is used instead of sulphuric, the voltage is less. All this shows that the voltage of a cell depends, not on its size, but on the materials of which it is made. A very large storage cell with plates several square feet in area, such as is used in power stations, gives exactly the same 2 volts that a tiny cell in a test tube would if made of the same materials. The large cell can drive more current through a given circuit than a small one because its internal resistance is so small. Of course, with constant use, the small cell would be exhausted much more quickly. 287. Ohm's law. Let a Daniell cell be connected in series with a considerable resistance, perhaps 100 ohms, and a galvanometer, and the current noted. If two cells are used in series, the current will be about twice as great. If, without changing the number of cells, we double the external resistance, the current will be about half as great. If we halve the external resistance, the current will be doubled. In general, we find that the current increases as the electromotive force increases, and that the current decreases as the resistance in the circuit increases. A German physi- cist, Ohm (1789-1854), was the first to state this relation between current, electromotive force, and resistance. The law is : The intensity of the electric current along a conductor equals the electromotive force divided by the resistance. Current = electromotive force resistance In electrical units: volts In symbols : Amperes ohms /=! 1 R' where 1= Intensity of current in amperes, E Electromotive force in volts, R = Resistance in ohms. 290 PRACTICAL PHYSICS If we know the current and resistance and want the electromotive force, we have If we know the electromotive force and current and want to calculate the resistance, we have ..*. 288, Examples using Ohm's law. 1. What is the intensity of the current sent through a resistance of 5 ohms by an electromotive force of 110 volts? / = E. = 115 = 22 amperes. R 5 2. What electromotive force is needed to send a current of 0.03 amperes through a resistance of 1000 ohms ? E = IR = 0.03 x 1000 = 30 volts. 3. Through what resistance will 110 volts send a current of 10 amperes ? fl = *? = !!? = 11 ohms. PROBLEMS 1. Find the intensity of the current which an electromotive force of 10 volts sends through a resistance (a) of 3 ohms, (b) of 40 ohms. 2. How much electromotive force is needed to send 2 amperes through (a) 2 ohms, (&) 50 ohms ? 3. What is the resistance of a circuit when the electromotive force is 110 volts and the current intensity is 2 amperes ? 4. An electric heater of 10 ohms resistance can safely carry 12 amperes. How high can the voltage run? 5. An .electromagnet draws 4 amperes from a 110-volt line. How much would it draw from a 220-volt line ? 6. A certain dry cell has an electromotive force of 1.5 volts and will give about 27 amperes when short-circuited. What is its internal resistance? What is the internal resistance of the same cell when, after much use, it will give only 9 amperes ? Button MEASURING ELECTRICITY 291 289. Application of Ohm's law to partial circuits. Not only does Ohm's law apply to an entire circuit, the current in the entire circuit being equal to the total electromotive force divided by the resistance of the entire circuit, but it also applies to any part of a circuit. That is, the current in a certain Ben part of a circuit equals the volt- age across that same part divided by the resistance of the part. For example, suppose the electromo- tive force of a battery is 3 volts, the re- sistance of the bell (Fig. 251) is 3 ohms, Battery the resistance of the wires and button is fio. 251. Bell circuit. 1.5 ohms, and the internal resistance of the battery is 0.5 ohms. To find the intensity of the current, we have -El Q I = = - = 0.6 amperes. R 3+1.5 + 0.5 The current has the same intensity throughout the circuit. To find the voltage across the bell, we have E = IR = 0.6 x 3 = 1.8 volts. To find the voltage drop within the battery, we have E = IR = 0.6 x 0.5 = 0.3 volts. Since the total electromotive force of the battery is 3 volts, and it takes 0.3 volts to send the current through the battery itself, the terminal voltage of the battery is 3 - 0.3, or 2.7 volts. Of this 1.8 volts is needed to send the current through the bell and the remainder, 0.9 volts, is used to send the current through the connecting wires and push button. If a voltmeter were connected across the battery, it would read 2.7 volts, or the terminal voltage. The total electromotive force (e. m. f.) is computed by multiplying the current in the circuit, 0.6 amperes, by the total resistance, 3 + 1.5 + 0.5 = 5 ohms. E = IR = 0.6 x 5 = 3.0 volts total e. m. f . 3.0 - 0.3 = 2.7 volts terminal voltage. 290. Terminal voltage of a cell depends on its current. Connect a voltmeter to the terminals of a dry cell, and note the e. m. f. Then connect a coil of very high resistance (1000 ohms) across the ter- 292 PRACTICAL PHYSICS minals. The terminal voltage, as indicated by the voltmeter, is very nearly the same as before. But if we connect a short, thick wire across the terminals, so as to draw a large current, we see by the volt- meter that the terminal voltage drops instantly. Thus we see that the voltage drop in a cell depends di- rectly upon the current used, and that the terminal voltage decreases when the current increases. 291. Series arrangement. Let us consider still further the electric current in apparatus arranged in series. A B c 6 ohms. 3 ohms. 1.5 ohms. 123 1 1 ll ll 0.5 0.5 0.5 Battery FIG. 252. Three cells and three resistances in series. In figure 252 we have three cells and three resistances connected in series. By this we mean that the carbon of cell 3 is joined to the zinc of cell 2, and the carbon of cell 2 is joined to the zinc of cell 1. The circuit then runs from the carbon of cell 1 through the resistances A, B, and C in succession, back to the zinc of cell 3. The laws governing series circuits are as follows: The current in every vart of a series circuit is the same. The resistance of several resistances in series is the sum of the separate resistances. The voltage across several resistances in series is equal to the sum of the voltages across the separate resistances. Moreover, since the voltage is equal to the resistance times the current (jB r =ZZ2), and since the current (/) in every part of a series circuit is the same, it follows that the voltage across any part of a series circuit is proportional to the resist- ance of that part. For example, in figure 252, if the e. m. f . of each cell is 2 volts, the e. m. f. of the three cells in series is 3 times 2, or 6 volts. MEASURING ELECTRICITY 293 If the resistance of A is 6 ohms, of B, 3 ohms, of C, 1.5 ohms, and of each cell, 0.5 ohms, the total resistance is 6 + 3 + 1.5 + (3 x 0.5) = 12 ohms. The current is T 6 2, or 0.5 amperes. The voltage across A is 6 times 0.5, or 3 volts, across B, 3 times 0.5, or 1.5 volts, and across C, 1.5 times 0.5, or 0.75 volts. The voltage " drop " in each cell is 0.5 times 0.5, or 0.25 volts, so that the terminal voltage of each cell is 2 0.25, or 1.75 volts. 292. Parallel arrangement. When the several resistances are so arranged that the current divides between them, as shown in figure 253, part going through A, part through B, and the rest through (7, they are said to be in parallel or multiple or shunt. The voltage across each 12 volts 1 amp. Y .6 amps. FIG. 253. Three resistances in parallel. / "7 ^ )' 7 1 * separate resistance of the three parallel resistances is the same. For example, if the voltage across A is 12 volts, then the voltage across B is 12 volts, and also across (7, for each resistance lies between the same two points, X and Y. The currents, however, in each of the resistances in parallel are not the same, unless the resistances are all equal. If, for example, the resistances of A, B, and are each 6 ohms, the current in each is 2 amperes. But if the resistances are unequal, the greatest current will flow through the smallest resistance. Of course the total current passing through a parallel arrangement of resistances is equal to the sum of the currents in the separate conductors. Thus if the current in A is 1 ampere, in B, 2 amperes, and in (7, 3 amperes, the total current through the combination, and through the rest of circuit, is 1 + 2 + 3, or 6 amperes. 293. Calculation of resistances in parallel. If we know the voltage and total current through a set of resistances in parallel we have merely to apply Ohm's law to compute the 294 PRACTICAL PHYSICS total resistance of the combination. Thus, if the voltage across A, B, and (7 in figure 253 is 12 volts, and the total current is 6 amperes, the total resistance is 2 ohms. In case we know only the separate resistances and want to compute their combined resistance in parallel, we may well make use of the idea of conductance. By conductance we mean the ease with which a current flows along a wire, while resistance represents the difficulty. Conductance is the reciprocal of resistance ; that is, 4 Conductance = resistance' The unit of conductance is the mho, which is the unit of resistance (ohm) spelled backwards. 4 1 mho = 1 ohm Thus a wire has a conductance of 1 mho when its resistance is 1 ohm, and a conductance of 2 mhos when the resistance is 0.5 ohms. It can be easily shown that the conductance, of a parallel arrangement is equal to the sum of the conductances of the separate parts. Thus suppose three resistances, A, B, and (7, are arranged in parallel and are 12, 6, and 4 ohms respectively. Find their combined resistance. Let R = resistance of A, B, and C in parallel. Then JTH+J + i- Whence R = 2 ohms. 294. Cells arranged in parallel. Not only may the separate external resistances be arranged in parallel, but the cells or generators themselves may be so arranged. For example, in figure 254 we have a battery of three cells arranged in parallel. MEASURING ELECTRICITY 295 The laws governing such a case are as follows : The voltage of the battery is the voltage of one cell. The internal resistance of the battery is the resistance of one cell divided by the number of cells, since three cells* R for example, have three times the conductance of one cell. The current will be the sum of the currents through each cell. * ? 2 For example, suppose that in figure 254 the t voltage of each cell is 2 volts, the resistance of e each cell is 0.6 ohms, and the external resist- ance U is 0.3 ohms, and we desire to find the FIG. 254. Three current through each cell. 8 in paraUeL The total current Jis found by Ohm's law; thus E 2 2 / = -p = - ^ 7 = -^ = 4 amperes. Then the current in each cell will be \ of 4 amperes or 1.3 amperes. 295. Best arrangement of cells of a battery. By means of a lecture table voltmeter we may show that the e. ra. f. of 6 cells in series is 6 times that of one cell, and that the e. m.f. of 6 cells in parallel is the same as that of one cell. By using an ammeter and a small external resistance, we can show that 6 cells arranged in parallel give more current than 6 cells in series; but with considerable external resistance, the series arrangement fur- nishes the greater current. In general, to make the intensity of the current as large as possible, when the external resistance is large, arrange the cells in series, but when the external resistance is small, arrange the cells in parallel. We can easily see the reason for this if we recall from the foregoing discussion that in a series battery the voltage and 296 PRACTICAL PHYSICS the internal resistance of each cell are both multiplied by the number of cells. In the parallel arrangement of cells the voltage is not increased, and the internal resistance of each cell is divided by the number of cells. From Ohm's law we have where R is the external resistance and r the internal. If R is much larger than r, it does not make much difference just how large r is, and we should make E as large as possible by arranging the cells in series. But if R is small, r becomes the important part of the denominator, and it pays to make r as small as possible by arranging the cells in parallel. In practical work the external resistance is usually large compared with the internal resistance, so the cells of a battery are generally arranged in series. PROBLEMS 1. Three resistances, A = 80 ohms, R = 60 ohms, and C = 40 ohms, are put in parallel and the voltage across the combination is 120 volts. Find the current in each, the total current, and the resistance of the combination. 2. If a battery is used to light 20 lamps arranged in parallel, and each lamp requires 0.5 amperes, how many amperes must the battery supply ? 3. What e. m. f. will be needed to force 2 amperes through a series circuit, containing a battery of resistance ohm, a line of resistance 1 ohm, and a lamp of resistance 100 ohms? 4. Three lamps of 150 ohms each are joined in series. If each lamp requires 0.5 amperes, what is the total current required ? What is the total voltage required? 5. If the three lamps of problem 4 were arranged in parallel, what would be the total current and total voltage needed? 6. Six cells, each having an e. m. f. of 2 volts and an internal resist- ance of 0.3 ohms, form a series battery to send a current through a resistance of 50 ohms. How strong is the current? 7. If the cells of problem 6 are arranged in parallel, what is the cur- rent strength ? MEASURING ELECTRICITY 297 8. Calculate the current strength sent by the six cells of problem 6, arranged in series, through an external resistance of 0.1 ohms. Also the current when the cells are in parallel. 9. If a current of 0.25 amperes is needed in a telegraph circuit, how many gravity cells in series will be required, if each has an e. m. f . of 1.08 volts and a resistance of 2 ohms, and if the line resistance is 500 ohms? 10. Six cells are arranged 3 in series and 2 in multiple (Fig. 255) to send a current through an external resistance of 4 ohms. If each cell has an e. m. f. of 1.5 volts and a resistance of 0.5 ohms, how intense will the current be ? 11. A galvanometer, whose resistance is 299 ohms, -r -r has a short stout wire of 1 ohm resistance connected _l I across the terminals. What fraction of the total cur- T rent goes through the galvanometer ? _l _J 12. A storage battery is sending current through "^ f two wires in parallel, each having a resistance of 10 ohms. If the current through the battery is 6 am- F \ h r ee 5 i 1 T 8 e r i re peres, what is the voltage drop in each wire ? two in mu i t ipi' e . 13. A wire of 4 ohms is connected in series with 2 wires joined in parallel and having resistances of 8 and 12 ohms. Find the total resistance. 14. A dry cell when tested with a voltmeter showed 1.5 volts, and when tested with an ammeter whose resistance was negligible, gave 7.5 amperes. Find the internal resistance of the cell. 15. If the voltage drop in a trolley line carrying 150 amperes is 12.5 volts, what is the resistance of the line? 296. Computation of resistance. For the measurement of voltage and of intensity of current we have direct reading voltmeters and ammeters, but as yet we have no simple instrument for measuring resistance directly in ohms. In many cases, however, we can compute the resistance of a wire, if we know its material, length, size, and temperature. Since wires are usually round, it is inconvenient to com- pute their area of cross section in square inches. Conse- quently electrical engineers call a wire, which is one thousandth of an inch in diameter, 1 mil in diameter and its area of cross section 1 circular mil. Inasmuch as the areas of circles vary as the squares of their diameters, the 298 PRACTICAL PHYSICS area of a wire expressed in circular mils is equal to the square, of its diameter expressed in mils. For example, suppose a wire is 0.015 inches in diameter. What is its cross section in circular mils? 0.015 inches = 15 mils ; area = (15) 2 = 225 circular mils. The resistance of a wire is usually computed by comparing it with the resistance of a wire of the same material and of a standard size and length. The standard usually chosen is 1 foot long and 1 circular mil in area of cross section. Such a piece of wire is called a mil foot of wire. The resistance of a mil foot of wire is sometimes called the specific resistance of the substance of which the wire is made. For example, the specific resistance of copper is about 10.4 ohms, of aluminum 17.4 ohms, and of iron 64 ohrns. Since the resistance of a conductor varies directly as its length and inversely as its area of cross section, we can readily compute the resistance of a wire when its length and diameter are given. Suppose we wish to find the resistance of 500 feet of #18 copper wire. Since the specific resistance of copper is 10.4, we know that the resist- ance of 1 mil foot of copper wire is 10.4 ohms. So that of 500 feet of copper wire 1 mil in diameter is 500 x 10.4, or 5200 ohms. But from the wire tables given on page 304, we find that #18 wire is 40.3 mils in diam- eter. Therefore its cross section is (40.3) 2 , or 1624 circular mils. There- fore the resistance will be j^V? of the resistance of a wire 1 mil in diameter, or X 520 = 3 ' 2 ohms ' As this computation has to be made very often in practical work, it is convenient to put it in the form of an equation. 7? kl R = ^ where R = resistance in ohms, k = specific resistance (ohms per mil foot), I = length in feet, d = diameter in mils. Thus fl = 10102 =3 .2 ohms. MEASURING ELECTRICITY 299 297. Effect of temperature on resistance. If we coil about 10 feet of #30 iron wire around a piece of asbestos and send a current through it, k we can observe with a lecture-table ammeter that, as we heat the jvire in a Bunsen flame, the intensity of the current is greatly reduced. If we connect an incandescent lamp in series with a coil of iron wire, as shown in figure 256, we can observe by the dimming of the lamp that the current becomes less when the iron wire is heated. Experiments show that the resistance of 1 mil foot of copper wire at 20 C or 68 F is 10.4 ohms, while at C it is 9.6 ohms. The resistance of a one-ohm coil of copper, correct at C, increases as the temperature rises, approximately 0.0042 ohms for each degree. For example, a coil which measures 10 ohms at C will at 50 C have a resistance of 10 + (0.0042 x 50 x 10) = 12.1 ohms. By carefully measuring the resistance of a wire when cold and then when hot, we have an ^ electrical method of measuring temperature. Most pure metals have nearly the same rate of increase of resistance with rise of temperature. Most alloys of metals not only have a much higher resistance than the pure metals of which they are made, but are much less affected by tem- perature changes. For example, " manganin " is an alloy of copper, nickel, and iron manganese, which has a specific resistance of from 250 to 450 ohms according to the propor- tion of the metals used, but its resistance shows scarcely any change with temperature. There are a few substances, such as carbon, glass, and porcelain, which decrease in resistance when heated. For example, the resistance of a carbon filament lamp when it is hot is about half of the resistance of the same filament when it is cold. FIG. 256. Iron wire when hot has more resistance than when cold. 300 PRACTICAL PHYSICS PROBLEMS Find the resistance of each of the wires described in problems 1 to 6 : 1. One mile, # 10 copper wire, diameter 0.102 inches. 2. Fifty feet, # 16 copper wire, diameter 0.051 inches. 3. Twenty feet, # 30 copper wive, diameter 0.010 inches. 4. Two miles, # 14 iron wire, diameter 0.064 inches. 5. Two hundred feet, # 10 iron wire, diameter 0.102 inches. 6. Five thousand feet, #6 aluminum wire, diameter 0.162 inches. 7. Find the number of feet of # 20 iron wire needed to make a resist- ance of 5 ohms. 8. Find the diameter of a copper conductor which has a resistance of 2 ohms per 1000 feet. 9. What size of copper wire must be used for a trolley wire 4 miles long, if the line resistance must not exceed 2 ohms? 10. What is the "line drop," that is, voltage drop, in a 4-mile copper wire carrying 100 amperes, if the wire is 0.325 inches in diameter? (Volt- age drop E = IR.) 298. Rheostats and resistance boxes. To control an elec- tric current, we must regulate either the voltage or the resistance. As electricity is usually supplied to us at fixed voltages, such as 110, 220, or 500 volts, we have to control the intensity of the current by a variable resistance, called a rheostat. For example, in starting a motor, for reasons which will be discussed in Chapter XVIII, the current must not be thrown on at full intensity at first, and so a rheostat (Fig. 257) is inserted. By moving a lever arm the resistance is gradually cut out as the motor comes up to speed. Rheostats are usually made of some high-resistance alloy such as German silver, or of carbon (lamps), or sometimes of water with a little salt dissolved in it. It is not enough to know the resistance of a rheostat. We must know also its carrying capacity, for the electrical energy consumed in the rheostat is converted into heat and must be radiated off as fast as it is produced. Otherwise the temper- ature will rise to a dangerous point, so that the wire melts or sets on fire things which are near it. MEASURING ELECTRICITY 301 A resistance box is also made of resistance coils, but since they are used for electrical measurements which involve only FIG. 257. Starting rheostat. small currents, they have very small carrying capacity. The coils have definite resistances, such as 1, 2, 3, 5, 10, 20 ohms, and are made of a wire which is only slightly affected by temperature changes. The resistance box corresponds for electrical measurements to a set of weights used in weighing. For convenience, the coils are usually mounted in a box, as shown in figure 258, which has an insulating hard rubber FIG. 258. Resistance box. top. On this are fastened a series of brass blocks which can be connected by brass plugs which fit between them. Inside the box are the various coils wound on spools. The ends of a coil are connected to adjoining blocks, so that each gap is 302 PRACTICAL PHYSICS Voltmeter Ammeter bridged inside by a coil. At each end of the series of blocks is a terminal binding post. When all the plugs are firmly in place, the only resistance is that of the series of blocks and of the plugs themselves, which is usually negligible; but when a cer- tain plug is removed, the resistance of that coil is introduced. 299. Measurement of resistance by voltmeter-ammeter method. As has been said, there is no simple instrument for measuring a resist- ance directly, as the voltmeter measures voltage, or an ammeter current. But there are two ways of measuring a resistance indirectly. If extreme accuracy is not required, the method shown in figure 259 is commonly used. The unknown resistance is placed in series with an ammeter, and the voltage across the resistance is obtained by a voltmeter. Then, by Ohm's law, E Battery FIG. 259. Resistance measured by a voltmeter and an am- meter. It is essential that the resistance of the voltmeter be so high that practically no current goes through it. This method also requires that both ammeter and voltmeter be accurately calibrated ; that is, compared with standard instruments and the errors noted. 300. Measurement of resistance by Wheatstone bridge. A more accurate method of measuring resistance is the Wheat- stone bridge, which is a machine for balancing resistances. It consists essentially of a loop of four resistances, R, JT, w, and /&, arranged as in figure 260. When the key (jfiT) is closed, the current from the cell flows into the loop at J., and there divides so that part (Tj) goes through AC and part (Jg) through AD. A sensitive galvanometer is con- MEASURING ELECTRICITY 303 nected between (7 and D. Then the resistances R, m, and n are so adjusted that no current flows through the galvanom- eter, which means that all of Jj has to go on through CB and all of I z through DB, and also that and D are " equipo- tential " points. When this adjustment has been made, the voltage drop across AC is J^, and the voltage drop across AD -i I 2 m. But since C and D are at the same 's D 4 || 'l ^1*^2 CVH ' /fei; Cell FIG. 260. Wheatstone bridge to balance re- sistances. potential, these voltage drops are equal, and For similar reasons (2) Dividing equation (1) by equation (2), we have R_ m, X~ n From this fundamental equation of the Wheatstone bridge, if we know R, m, and w, we can compute X. In one form of this apparatus the resistance ADB consists of a wire of uniform cross section one meter long. Since the resistances m and n are then directly proportional to the distances AD and DB, the equation becomes R X Distance AD Distance DB* 304 PRACTICAL PHYSICS WIRE TABLES American or Brown and Sharp (B. and S.) Gauge GAUGE DIAMETER IN MILS AREA IN CIRCULAR MILS DIAMETER IN MILLIMETERS CARRYING CA- PACITY, KUBBER INSULATION, AMPERES 0000 460. 211,600. 11.68 210. 000 410. 167,800. 10.40 177. 00 365. 133,100. 9.27 150. 325. 105,500. 8.25 127. 1 289. 83,690. 7.35 107. 2 258. 66,370. 6.54 90. 3 229. 52,630. 5.83 76. 4 204. 41,740. 5.19 65. 6 181.9 33,100. 4.62 54. 6 162.0 26,250. 4.12 46. 7 144.3 20,820. 3.67 8 128.5 16,510. 3.26 33. 9 114.4 13,090. 2.91 . 10 101.9 10,380. 2.59 24. 11 90.7 8,234. 2.31 ' -12 80.8 6,530. 2.05 17. 13 72.0 5,178. 1.83 -14 64.1 4,107. 1.63 12. 15 57.1 3,257. 1.45 1<> 50.8 2,583. 1.29 6. 17 45.3 2,048. 1.15 18 40.3 1,624. 1.02 3. 19 35.4 1,288. .90 20 32.0 1,022. .81 21 28.5 810. .72 22 25.3 643. .64 23 22.6 509. .57 -24 20.1 404. .61 25 17.90 320. .46 -26 15.94 254. .41 27 14.20 202. - -36 __-28 12.64 159.8 .32 29 11.26 126.7 .29 -30 10.02 100.5 .26 31 8.93 79.7 .23 32 7.95 63.2 .20 33 7.08 50.1 .18 34 6.30 39.7 .16 35 5.61 31.5 .14 - 36 5.00 25.0 .13 37 4.45 19.83 .11 38 3.96 15.72 .10 39 3.5 12.47 .09 40 3.14 9.89 .08 MEASURING ELECTRICITY 305 where R is a known resistance, such as a resistance box, and the distances AD and DB are read off on a meter stick. It may help one to remember this equation to observe that Left resistance _ Left distance Right resistance Right distance For example, suppose R is 5 ohms and AD is 45.5 centimeters; then DB is 54.5 centimeters, and . 5 ^45.5 X 54.5' X = 6.05 ohms. PROBLEMS 1. Compute the resistance of a lamp through which a voltage of 113 volts sends a current of 0.4 amperes. 2. Find the resistance of a street-car heater which takes 5 amperes of current from a 550 volt line. 3. A wire 50 feet long has a drop of 2 volts across it. Find the drop across 20 feet. 4. In a slide-wire Wheatstone bridge, the known resistance is 12 ohms, and the balance is obtained when AD (Fig. 260) is 42.5 centi- meters. Compute the value of the unknown resistance. 5. In testing a Wheatstone bridge, 4 ohm and 6 ohm coils are in- serted in the loops AC and CB. Find the position which D should have on the meter wire ADB. SUMMARY OF PRINCIPLES IN CHAPTER XVI Unit of current is ampere. Corresponds to gallons per second. Unit of resistance is ohm. Corresponds to friction in pipe. Unit of e. m. f. is volt. Corresponds to " head." Ammeter low resistance put in series carries whole cur- rent. Voltmeter high resistance put across circuit diverts small current. E. M. F. of cell = total pump action in cell. Terminal voltage = potential difference between terminals. 306 PRACTICAL PHYSICS Terminal voltage less than e. m. f. by amount needed to keep current moving through internal resistance of cell. Ohm's law: Current = e ' m ' f - resistance Applies to whole circuit, or to any part of circuit. If applied to whole circuit, must take account of internal resist- ance of cell, as well as of external resistance. For resistances in series : Current everywhere the same. Resistance of combination is sum of resistances of parts. Voltage across combination is sum of voltages across parts. For resistances in parallel : Total current through combination is sum of currents through parts. Conductance of combination is sum of conductances of parts. Voltage across conductors same for all. For cells in series : E. m. f. is sum of e. m. f.'s of parts. Resistance is sum of resistances of parts. Current same in all cells as in external circuit. For cells in parallel : E. m. f. is same as e. m. f. of one cell. Resistance of n cells in parallel is - th the resistance of any one alone. Current in each cell is - th the current in external circuit. n Resistance of wire = specific resistance ( mil f t) X length (feet). square of diameter (mils) In slide-wire Wheatstone bridge : Left resistance _ left distance Right resistance . . right distance MEASURING ELECTRICITY 307 QUESTIONS 1. Why are telegraph lines usually made of iron wire, while trolley wires are made of copper ? 2. Why should the circuit of a dry cell be kept open when the cell is not in use? 3. Why should a gravity cell be left on closed circuit when not in use? 4. What would happen if an ammeter were connected across the line? (Don't try it !) 5. What would happen if a voltmeter were put in series in a line ? 6. Why is the moving-magnet type of galvanometer inconvenient? 7. What is the use of the shunt in an ammeter? 8. A copper wire and an iron wire of the same length are found to have the same resistance. Which is the larger? 9. Why do we get a more intense current by moving the plates of a cell close together? 10. What is the effect on the current strength of allowing the liquid to evaporate to half its volume in a sal-ammoniac cell, and why? 11. What instruments would we need in addition to a coulombmeter to measure the intensity of a current? 12. Why should keys be inserted in both the battery line and the galvanometer line of a Wheatstone bridge? 13. Why are electric bells usually arranged in parallel instead of in series ? CHAPTER XVII INDUCED CURRENTS Induction by permanent magnets direction of induced cur- rent induction by electromagnets induction coil jump spark ignition self-induction make and break ignition telephone. 301. Faraday's discovery. If we had to depend on bat- teries for all our electric currents, we should not be lighting our streets and houses with electric lamps or riding on electric cars. The cost of zinc as a fuel in the voltaic cell makes the battery too expensive as a source of large quantities of electricity. It is, however, possible to turn mechanical energy directly into electrical energy by means of a machine called a dy- namo, in which currents are induced by moving magnets. It ^._v=^i%?, was the discovery of the dynamo that made possible the modern age of electricity. 302. Currents induced by mag- nets. If we connect the ends of a coil of many turns of fine insulated wire to a lecture-table galvanometer, and then move the coil quickly down over one pole of a strong horseshoe magnet, as shown in figure 261, we observe a de- flection. When we raise the coil again, we observe a deflection in the opposite direction. If we lower the coil again and hold it down, we find that the galvanometer pointer conies back to zero. If we repeat the experiment, moving the coil down slowly and up slowly, we find that the deflection is less than before. 308 FIG. 261. A coil moving in a mag- netic field generates a current. INDUCED CURRENTS 309 Such experiments show that it is possible to produce momentary electric currents without a battery. An electric current produced by moving a coil in a magnetic field is called an induced current. It is evident from the experiment that the current is induced only when the wire is moving and that the direction of the current is reversed when the motion changes direction. Since an electric current is always made to flow by an electromotive force, the motion of a coil in a magnetic field must generate an induced electromotive force. Experiments have shown that this induced electromotive force varies directly as the speed of the moving coil. 303. Direction of induced currents. If we take the same apparatus (Fig. 261) and move the coil down over the ./V-pole of the magnet and then down over the S-pole, we find that the deflections are in opposite directions in the two cases. To determine in which direction the induced current is flowing in the coil, one may make a little voltaic cell by putting in his rnouth a copper wire and a zinc wire connected to the galvanometer. Since we know that the copper is the positive electrode, we can compare the direction of the galvanometer deflection caused by the cell current with that caused by the induced current, and so determine the direction of the latter. In this way we find that when the coil is moving down over the ^V-pole of the magnet, the induced current is in such a direction that the lower face of the coil is an ^-pole. In a similar way we find that when the coil is brought down over the -pole of the magnet, the induced current is in such a direction that the lower face of the coil is an *** 208. Carbou trans- brates. The other plate is fastened mitter. INDUCED CURRENTS 315 rigidly to the solid back of the case. A current from a battery flows through the diaphragm to the front plate, then back through the granules to the other plate, and then out along the telephone line to a receiver. When the diaphragm moves back a little, it compresses the granules, their resistance de- creases, and the current gets stronger and pulls the diaphragm of the receiver back also. When the transmitter diaphragm moves out, the current decreases and the receiver diaphragm moves out also. So all the motions of the transmitter diaphragm are reproduced l>y the receiver diaphragm. If one speaks into the transmitter, causing its diaphragm to move in a corresponding way, the receiver diaphragm moves in the same way and produces the same kind of waves in the surrounding air. 312. Central vs. local batteries. The system we have just described is the one in use in all large cities. The battery is a large storage battery (or a dynamo) at the central sta- tion and is used on all the lines that happen to be busy at any instant. In many country exchanges and on isolated lines another system, called the local battery system, is used because it is cheaper to install and maintain. Even in cities some- thing equivalent to this system is used in "long- distance " work. In this system (Fig. 269) each subscriber's telephone set contains a few dry cells which are connected in series with his transmitter, as already described. But the varying cur- rent produced, instead of being sent directly out on to the line, goes to the primary of a little induction coil and back to the battery. The secondary of the induction coil mean- while sends out into the line an induced current that varies ine Transmitter .. Receiver FIG. 269. Local battery telephone system. 316 PRACTICAL PHYSICS exactly like the primary current, but is at much higher volt- age. This, as we shall see in Chapter XVIII, makes the " line losses " much smaller, and so more energy gets through to the receiver than if the original current had been trans- mitted directly. This system is really better, electrically, than the central battery system (Fig. 270). It is not used in large //, L-5= cities, chiefly be- cause of the trouble Fia. 270. Telephone with central battery. involved in keep- ing so many local batteries in proper working condition. 313. Return wire necessary. Telephone circuits used to be made like telegraph circuits, with only one wire, the return being through the earth. But in cities this is imprac- tical because of the noise and confusion caused by stray cur- rents in the earth due to trolley cars and other electrical disturbances. So in cities two wires are used, and they are put close together so that no currents can be induced in them by stray magnetic fields from other circuits (which would cause " cross-talk "), or from lighting and power circuits. SUMMARY OF PRINCIPLES IN CHAPTER XVII Induced current exists only when the number of lines of force through the circuit is changing. Induced current has such a direction as to oppose the motion that causes it. Self-induction appears only when the current is changing. The effect of self-induction is always to oppose the change of the current. INDUCED CURRENTS 317 QUESTIONS 1. Why is it that the self-induction of a circuit is not apparent as long as the current is steady ? 2. Why is the lamp described in the experiment in section 307 not bright all the time that the switch is closed? 3. Why is it dangerous to touch the terminals of the secondary of a large Ruhmkorff coil ? 4. What is likely to happen to an induction coil if you short-circuit the secondary while the coil is running? 5. Why is the induced e. m. f. in the secondary of an induction coil so much greater at the break of the primary than at the make? 6. What furnishes the energy of an induced current? 7. Upon what three factors does the e. m. f. of an induced current depend? 8. In a central battery telephone system, what arrangements are made to keep the battery from sending current all the time through tele- phone lines not in use ? CHAPTER XVIII ELECTRIC POWER The generator wire cutting lines of force dynamo rule for direction of current law of induced e. m. f. revolving loop commutator Gramme ring drum armature field ex- citation. Electric power how measured the joule and watt com- mercial units. Electric heating common applications fuses computa- tion. Electric lighting the arc modern forms incandescent lamps metal filaments efficiency. The motor side push on wire carrying current motor rule for direction of motion forms of motor back e. m. f. start- ing box applications efficiency. Chemical effects electrolysis bleaching electroplating . % electrotypiug refining metals electrochemical equiva- lents storage battery. THE GENERATOR 314. The importance of the generator. ^ The most useful application of induced currents did not come until nearly forty years after Henry and Faraday made their wonderful discovery. Then the generator was developed, by means of which the enormous energy of steam engines and water wheels can be transformed into electricity. The electricity generated in this way can be transmitted many miles, and used in motors to turn all sorts of machinery, in lamps of various kinds to light our streets and homes, in heaters to warm cars and sometimes houses, to toast bread and heat flatirons, and in furnaces to melt steel in iron mills. Thus 318 ELECTRIC POWER 519 the generator has revolutionized modern industry by furnish- ing cheap electricity. 315. Wire cutting lines of magnetic force. A simple way -to get at the fundamental idea of the generator is to think, as Faraday did, of the induced e. m. f. produced in a single wire when it is moved through a magnetic field. Suppose the straight wire AB is pushed down across the magnetic field shown in figure 271. An induced e. m. f. is set up in AB, which makes B of higher potential than A, as FIG. 271. - induced e. m f. iu a wire 5 r . cutting lines of force. can be shown by connecting B and A with a galvanometer. As long as the wire remains stationary no current flows. Even if the wire does move, if it moves in a direction parallel to the lines of force, no current flows. In short, a wire, to have an e. m. f. induced in it, must move so as to cut lines of force. 316. Direction of induced e. m. f. We have just seen that when the wire AB in figure 271 is moved down, the induced current in it is from A to B. If the wire were moved up, the induced current would be from B to A. Furthermore, if the field is re- versed without changing the direction of motion of the wire, the current re- verses. It will be seen, then, that the direction of the induced e. m. f. depends upon two factors, (#) the di- rection of the motion of the wire and (j) tne direction of the flux or mag- ! i c < m i ,- t netic lines ot torce. I he relation ot these three directions may be kept in mind by Fleming's rule of three fingers, as shown in figure 272. FIG 272.-Ri g ht-hand rule for induced e. m. f. 320 PRACTICAL PHYSICS FLEMING'S RULE. Extend the thumb, forefinger, and center finger of the right hand so as to form right angles with each other. If the thumb points in the direction of the motion of the wire, and the forefinger in the direction of the magnetic flux, the center finger will point in the direction of the induced current. To remember this rule, notice the corresponding initial letters in the words "fore" and "flux," " center" and "cur- rent." 317. Amount of induced C. m. f. If we have a large electromagnet with flat-faced pole pieces (Fig. 273), we can demonstrate the various laws about induced currents in a conductor. If we move a wire down through the gap between the pole pieces, a mil- livoltmeter will show the in- duced current. If we hold the wire at rest in the gap, we ob- serve no current. If we move the wire horizontally parallel FIG. 273. Electromagnet for demonstrating to the lines of magnetic flux, induced e. m. f. we get no current. If we move the wire up. through the gap, we observe a current in the opposite direction, as predicted by Fleming's rule. If we increase the magnetic field by increasing the current through the electromagnet, we increase the induced current. If we move the wire more quickly through the gap, we increase the induced current. Finally, if we bend the wire into a loop of several turns, and move the loop down over one pole so that all the wires on one side of the loop pass through the gap, we find that the current is increased. In this experiment we see that the induced e. m. f. is in- creased by moving the wire faster across the magnetic field, by making the magnetic field stronger, and by using more turns of wire. In short, the amount of induced e. m.f. de- pends on three factors : (1) the speed ; (2) the magnetic field ' f and (3) the number of turns. Experiments show that Induced e. m. f . varies as speed x flux x turns. ELECTRIC POWER 321 318. Commercial generators. A machine for converting mechanical energy into electrical energy is called a dynamo or generator. Its essential parts are two, (1) the magnetic field, which is produced by permanent magnets, as in the magneto, or by electromagnets, as in larger generators, and (2) 'a moving coil of copper wire, called the armature, wound on a revolving iron ring or drum. The armature wires corre- spond to the moving wires in the experiments above. 319. Current in a revolving loop of wire. If we rotate a rectan- gular coil between the poles of a large horseshoe magnet, or better, of an electromagnet, we can detect an electric current in the revolving coil by connecting it with flexible leads to a galvanometer. As we turn the coil, the current is reversed every half revolution. It will help us to understand just what is happening in the revolving coil if we first consider what would happen in a single loop of wire which is rotated in a magnetic field, as shown in figure 274. If we start with the plane of the loop ver- Fl0 ' m - ~ Sin e le "Sjjjf turning in a mag ' tical and turn the handle in a clockwise direction, the wire BO moves down during the first half turn, and so, by Fleming's rule, we should expect the induced e. m. f. to tend to send the current from to B. At the same time the wire AD is moving up, and the current will tend to flow from A to D. The result is that during the first half turn the current goes around the loop in the direction AD OB. During the second half turn the current is reversed and goes around in the direction ABOD. To show that this really does happen in the loop, we can cut the wire and connect the ends to slip rings x and y, as Y 322 PRACTICAL PHYSICS shown in figure 275. The brushes B' and B", which rest on the rings, are connected to a galvanometer. In this way it can be shown that there is generated in the coil an alternating current which reverses its direction twice in every rev- olution. Moreover, it is pos- sible to show that the induced FIG. 275.- Single loop connected to e . m .f. starting at Z61'O ffOCS UD slip rings. to a maximum and then back to zero in the first half turn; then it reverses and goes to a maximum in the opposite direction and finally back to zero. The induced e. m. f . reaches its maximum when the coil is horizontal, because in this position the wires AD and BO are cutting lines of force most rapidly. This is illustrated by the curve shown in figure J- 10 276. Machines which are built to deliver alternating cur- rents are called alternators or A. C. generators. 320. Commutator. To get a direct current, that is, one which flows always in the same direction, we have to use a commutator. To under- stand how this works, let us study a very simple case. If the ends of the loop in section 319 are connected to a split ring, as shown in figure 277, B 7 * - we may set the brushes FIG. 277. Split-ring commutator. -B+ an( l B~ on opposite /* \ . s' ' \ ~ , ' 7_ , $ r -2 , 2 g" t r v \ / \ S po SIT ON OF 1 OP IN DF( ;RF FS FIG. 276. Curve to show relation of induced e.m. f. to position of loop. ELECTRIC POWER 323 sides of the ring, so that each brush will connect first with one end of the loop and then with the other. By properly adjust- ing the brushes, so that they shift sections on the commutator just when the current reverses in the loop, that is, when the loop is in a vertical position, we may get the current to flow only out at one brush B + , and only in at the other brush B . The direction of the current in the ex- ternal circuit is always the same, even though the current in the loop itself reverses twice in every revolution. The current de- livered by such a machine can be represented by the curve in figure +30 2+20 + 10 o 5J-IO 2 20 '-SO 1 "X, x ^ \, /* / y \ / / 1 5 I- f* . \ i POSITION OF LOOP IN DEGREES FIG. 278. Pulsating e. ra. f. delivered by loop fitted with commutator. 278. Although it is always in the same direction, it is pulsating. A machine with a commutator for delivering direct current is called a direct-current dynamo or D.C. generator. 321. Generators of steady currents. The e.m.f. produced by rotating a single loop in a magnetic field can be raised by using many turns of wire and by rotating the coil very fast. Nevertheless the current will be pulsating, and this is unsatisfactory for many purposes. To get a machine to deliver a steady current, a Frenchman, named Gramme, invented in 1870 the so-called Gramme ring form of arma- ture. The Gramme ring armature is now very seldom used, but it is worth studying carefully because the fundamental prin- ciples of its action can be understood from very simple dia- grams, whereas most armatures of the common or drum type, although based on exactly the same principles, cannot be represented 'by simple diagrams. A rotating soft-iron ring or hollow cylinder is mounted be- 324 PRACTICAL PHYSICS FIG. 279. Magnetic field in a Gramme ring. tween the poles of an electromagnet, as in figure 279. The ring serves to carry the flux across from one pole to the other. There are scarcely any lines of force in the space in- side the ring. A con- tinuous coil of insu- lated copper wire is wound on the ring, threading through the hole every turn. When the ring rotates, as in figure 280, the wires on the outside are cutting lines of force, but those inside are not. Furthermore, according to the right- hand rule, the outside wires on the right-hand side are moving in such a direction that the in- duced current tends to flow towards us. The wires lying on the other side of the ring are mov- ing so as to induce a cur- FIG. 280. Gramme ring rotating in a mag- netic field. rent away from us. If there were no outside connections, these two opposing e. m. f.'s would just balance, and would no current would flow. This would be like ar- ranging a lot of cells in series with an equal number turned so that they are opposed to the first group [Fig. 281 (a)] ; obviously no cur- rent would flow. FIG. 281. Batteries (a) without, and (6) with an external circuit. ELECTRIC POWER 325 But if we imagine the copper wires on the outer surface of the ring to be scraped bare, and if two metal or carbon blocks or brushes at the top and bottom rub on the wires as they pass, a current could be led out of the armature at one brush, and, after passing through an external resistance, such as a lamp, could be led back to the armature again at the other brush. In this case the armature circuit is double, con- sisting of its two halves in parallel. It is like adding an external circuit to the arrangement of cells described above. This battery analogue for a Gramme ring armature is shown in figure 281 (6). In the Gramme ring arrangement there are at every instant the same number of active con- ductors in each half of the armature circuit, and so the current delivered by the armature is not FIG. 282. Ring armature with commutator. only direct but also steady. In practice, however, it would be difficult to make a good contact directly with the wires of the armature, because the wires must be carefully insulated from each other and from the iron core, and so the various turns of wire, or groups of turns, have branch wires which lead off to the commutator segments, as in figure 282. The commutator consists of copper bars or segments which are arranged around the shaft and insulated from each other by thin plates of mica (Fig. 283). To get a satisfactorily steady FIG. 283. -Commutator current there ^ould be many segments and brush. in a commutator, so that the brushes 326 PRACTICAL PHYSICS FIG. 284. Slotted armature core, drum type. may always be connected to the armature circuit in the most favorable way. 322. Drum armature. Since very little flux passes across the air space in the center of a Gramme-ring armature, the wires on the in- ner surface of the ring do not cut lines of mag- netic force and are useless, ex- cept to connect the adjoining wires on the outer surface. Furthermore, it is very incon- venient to wind the wire on an armature of the ring form. For these reasons, most armatures are now of the drum type. In this form, the core is made with slots along the circum- ference for the wires to lie in (Fig. 284). Since the active wires in one slot are connected across the end to active wires in another slot, there are no idle wires inside the core. 323. Multipolar generators. The machines which hav-e been described are called bipolar machines. For commercial purposes, especially in large ma- chines, it is common practice to use four, six, eight, or even more poles. Such machines are called multipolar. By increasing the number of poles we can get the commercial voltages (110, 220, or 500 volts), at much slower speeds than would be neces- sary in a bipolar machine. We have already seen that the voltage depends on the rate at which the Wires Of the armature CUt the lines ?IG. 285.- Four-pole generator. of magnetic force. Bat in a four-pole machine (Fig. 285) each wire on the armature cuts a complete set of lines of ELECTRIC POWER 327 force four times in each revolution instead of twice as in a two-pole machine. For this reason the speed of a four- pole machine is one half the speed required in a two-pole machine for the same voltage. Furthermore, the multipolar machine is more economical to build because it requires less iron to carry the magnetic flux. It will be observed from the diagram (Fig. 285) that every other brush is positive and is connected to the positive terminal of the machine. QUESTIONS 1. If a person stands facing in the direction of the magnetic flux, and thrusts downward a wire which he holds in his two hands, in which direction is the induced e. m. f . ? 2. What are the three factors which determine the voltage of a dynamo? How does each affect the voltage ? 3. How many revolutions per minute (r. p. m.) would a single-coil bipolar dynamo have to make in order that the current might have 120 alternations per second ? 4. How manV revolutions per minute would an eight-pole generator have to make to have the current alternate 120 times a second? 5. Why are carbon blocks generally used instead of copper brushes ? 324. Excitation of the field of generators. In the magneto (Fig. 286) the magnetic field is supplied by permanent steel magnets. In most other generators, the magnetic field is furnished by powerful electromagnets. Some- times the current needed to excite these mag- nets is supplied by some outside source, such as a storage battery, but generally the machine itself furnishes the exciting current. There are three types of generators differing in the method of excit- ing the field coils ; (1) series-wound, in which the whole cur- rent generated passes through the field coils on its way to FIG. 286. neto has nent steel mag- nets. 328 PRACTICAL PHYSICS the external circuit ; (2) shunt-wound, in which the field is excited by diverting a small part of the main current, the field coils and the external circuit being in parallel or in shunt ; and (3) compound- wound, which has both a series coil and a shunt coil. In the series generator (Fig. 287), the field coils are wound with a few turns of FIG. 287. Series- wound lar ge wire. When the Current in the ex- generator supplying ternal circuit increases, the field is more highly magnetized, and so a higher volt- age is available to supply the current. This machine is used to furnish current for arc lamps, which operate on a constant current. When the field is shunt-wound (Fig. 288), the coils have many turns of small wire, for in this case it is desirable to di- vert as little current as possible from the main circuit, and so the resistance of the field coils should be high. Such machines FIG. 288. Shunt-wound are run at constant speed. When more generator supplying load is thrown on the machine, that is, ^candescent lamps, when more lamps are turned on, so that more current is needed, the terminal volt- age drops a little. This decreases the current in the field coils and still further reduces the terminal voltage. A shunt ma- chine, therefore, cannot be used when very constant voltage is desired. This drop in the terminal voltage of shunt generators under heavy loads can be over- ^ "^ 7, i" come by the use of the compound-wound gen- FIG. 289. Compound- _. ... f wound generator. erator (Fig. 289), which is the one most ELECTRIC POWER 329 commonly used. Here the voltage is kept constant by adding a series coil of a few turns, which tends to raise the voltage when the current increases, just as in a series generator. If the coils are carefully adjusted, the voltage remains practi- cally constant at all loads. 325. Source of energy in the dynamo.' It is important to remember that the electric generator or dynamo can not of itself make electricity, but can only transform mechanical en- ergy into electrical energy. For example, if we want to light a house with electricity, it is not enough for us to buy a dynamo, we must get also a steam engine, or a gas engine or a water wheel to drive the dynamo. We have already seen that the induced current is always in such a direction as to oppose the motion of the wire. Consequently, the greater the current in the dynamo, the greater the power needed to turn it. Large generators, such as are used in power sta- tions to furnish electricity for street railways, sometimes re- quire steam engines of 16,000 to 20,000 H. P. capacity. ELECTRIC POWER 326. How electric power is measured. To measure water power, we must know the quantity of water flowing per minute and the " head " of the water. Thus Water power = quantity of water per minute x head. H P _lb. per min. x ft. 33000 To measure electric power, we must multiply the quantity of electricity flowing per second that is, the intensity of the electric current by the voltage. Thus Electric power = intensity of current x voltage. The watt is the unit of electric power and may be defined as 330 PRACTICAL PHYSICS the power required to keep a current of one ampere flowing under a drop or " head " of one volt. Watts = amperes x volts. Since the watt is a very small unit of power, we commonly use the kilowatt (K.W.) which is 1000 watts. v -.. amperes x volts Jtv. W . =: 1000 Inasmuch as mechanical power is reckoned in horse power (H. P.), it will be convenient to know the relation of the unit of mechanical power to the unit of electrical power. Experiment shows that 1 horse power = 746 watts. 1 Kilowatt (K.W.) = 1.34 horse power (H. P.). Since we have to compute electrical power very often, we may find a formula convenient. P=IE, where P = power in watts, 1= current in amperes, E= e. m. f. in volts. For example, if a lamp draws 0.5 amperes from a 110 volt circuit, it is using power at the rate of 0.5 times 110 or 55 watts. Again, suppose a street-car heater has a resistance of 110 ohms. At what rate is it consuming electricity on a 550 volt line ? The current is |-^ or 5 amperes, and the power is 5 times 550 or 2750 watts or 2.75 K. W. 327. Commercial units of electrical work. Power means the rate of doing work. The total work done is equal to the product of the rate of doing work by the time. Thus if a steam engine is working at the rate of 15 horse power for 8 hours, it does 8 times 15 or 120 horse-power "hours of work. In a similar way, if an electric generator is delivering electricity at the rate of 15 kilowatts for 8 hours, it does 8 times 15 or 120 kilowatt hours of work. ELECTRIC POWER 331 For example, we buy electricity by the kilowatt hour. In Boston the price is about 10 cents per kilowatt hour. If a store uses 100 lamps for 3 hours, each consuming electricity at the rate of 50 watts, it will cost 100 x 3 x 50 x 0.10 1000 328. Small units of electrical work. In the laboratory we often find it convenient to use a smaller unit of work, the watt second or joule. Work (joules) = current (amperes) x e. m. f. (volts) x time (seconds). Or W = lEt, since 1 Kilowatt-hour = 3,600,000 watt seconds or joules, 1 Horse-power hour = 1,980,000 foot pounds. Therefore 1 joule = 0.74 foot-pounds. PROBLEMS 1. How much electrical power (watts) is required to light a room with 5 lamps, if each lamp draws 0.4 amperes from a 110-volt line? 2. A street railway generator is delivering current to a trolley line at the rate of 1500 amperes and at 550 volts. At what rate (kilowatts) is it furnishing power? 3. How many horse power will be required to drive the generator in problem .2, if its efficiency is 90%? 4. A 10 kilowatt generator is working at full load. If the voltmeter reads 115 volts, how much does the ammeter read? 5. How many lamps, each of 120 ohms and requiring 1.1 amperes, can be lighted by a 25 K. W. generator? 6. How much power is required by a laundry using 5 electric flat- irons of 50 ohms each on a 110-volt line? 7. How much will it cost at 10 cents per kilowatt hour, to run a 220- volt motor for 10 hours, if the motor draws 25 amperes ? 8. Would it be cheaper to buy the power needed in problem 7 at 8 cents per horse-power hour ? 9. How much energy is consumed in a line whose resistance is 0.5 ohms, and which carries a current of 150 amperes for 10 hours? 10. How many joules of energy are consumed when a 40- watt lamp burns 10 minutes ? 332 PRACTICAL PHYSICS ELECTRIC HEATING 329. Heating by electricity. We are familiar with the fact that electric cars are heated by electricity, and that an electric light bulb gets hot, and we may have used or seen electric flatirons (Fig. 290), electric ovens, or electric furnaces ; but perhaps we do not realize that every electric current, however small, gener- ates heat. This is because heat is gen- erated so slowly in an electric bell, tele- graph, or telephone, that it is radiated off without raising 1 the temperature of FIG. 290. Flatiron . . . , , . r ,, . heated by electricity, tn ^ wires appreciably. It is this heat- aud the resistance wire ing effect which limits the output of a in it shown separately. generator> for if too heavy a Clirrent is drawn from the machine, the armature and field coils get so hot that the insulation is set on fire. 330. Fuses and circuit breakers. To protect electrical machines from too much heat caused by excessive cur- rent, some sort of "electrical safety valve " has to be in- serted in the circuit. Fuses are used for the small cur- rents in house lights and small motors, and circuit breakers for larger currents in power stations. The es- sential part of a fuse is a strip of an alloy [Fig. 291 (a)], which melts at such a low temperature that the melted metal can do no . . . . FIG. 291. Fuses: (a) wire fuse; (6) car- narm. ine size 01 trie iuse tridgefuse; (c) plug fuse. ELECTRIC POWER 333 FIG. 292. Circuit breaker. is such that if by accident too heavy a current is sent through the wires, the fuse melts and breaks the circuit. At the mo- ment the fuse melts there is an arc across the gap which might set things on fire. So the fuse is commonly inclosed in an asbestos tube, as in the " cartridge fuse " [Fig. 291 (&)], or in a porcelain cup, which screws into a socket like a lamp, as in the " plug fuse " [Fig. 291 (on filament air present to support the combustion, it has to be inclosed in a glass bulb (Fig. 299) in which there is a very high vacuum. The electricity is led into and out of the filament through two short platinum wires, melted into the glass bulb at one end. These platinum wires are connected by copper wires to the brass collar and metal tip at the end of the bulb. Such lamps are usually made for 110 or 220 volts. If a lamp made for 110 volts is used on a 105 volt line, it will probably last twice as long, but will only give 80% as much light. If it is used on a 113 volt line, even though it gives about 18% more light, it will last only half as long. So it is very desirable to use lamps on the voltage for which they are intended. This means we must have good regulation on the electric lighting service ; that is, constant voltage at all loads. 335. Commercial rating of electric lights. To measure the output of light from a lamp, we need some standard lamp for comparison. As will be explained in Chapter XXI, this standard is the so-called international candle. The ordinary 338 PRACTICAL PHYSICS incandescent light is equivalent to about 16 such standard candles, and it said to be 16 candle power (16 c.p.). Since lamps do not show the same brightness on all sides, it is customary to take the average candle power in all directions in a horizontal plane. Thus incandescent lamps are often rated according to their mean horizontal candle power. The input of electrical energy is measured in watts. The commercial rating, which is also called the " efficiency" * of elec- tric lamps is the number of watts per candle power. For example, an ordinary 50 watt lamp gives 16 candle power ; so its commercial rating is -|J or 3.1 watts per candle power. By a special firing process, carbon filaments can be " metallized " The efficiency of such filaments is about 2.5 watts per candle power. 336. Metal filament lamps. Still more efficient incan- descent lamps are made with metallic filaments. The metals most used are tantalum and tungsten, both of which have melting points much higher than that of platinum. Since their specific resistance is much lower than that of carbon, a metal filament must be very much longer and thinner (about 0.02 millimeters in di- ameter) than a carbon filament to have the FIG soo Metal necessarv resistance. So long a wire can be filament lamp. put in a bulb of the ordinary size only by " winding it zigzag on star-shaped reels, as shown in figure 300. One difficulty with these metal filaments is their brittle- ness and liability to breakage. Furthermore, they soften somewhat when hot, and if a metal-filament lamp is used in a horizontal position, the filament may sag and short-circuit. Nevertheless, the extremely high efficiency of these lamps, their long life (except for breakage), and their wonderful *This is really a measure of inefficiency ; the larger the number the worse the lamp. ELECTRIC POWER 339 white light, which is the same color as daylight, have made them very popular. COMPARATIVE " EFFICIENCY " OF ELECTRIC LAMPS NAME OF LAMP WATTS PER CANDLE POWER NAME OF LAMP WATTS PER CANDLE POWER Carbon filament . . Metallized carbon Tantalum 3 to 4 2.5 20 Arc lamp Mercury arc flaming arc 0.5 to 0.8 0.6 0.4 Tungsten 1 to 1 5 QUESTIONS AND PROBLEMS 1. Why must a rheostat be used in series with the arc lamp in a pro- jection lantern ? 2. Why are the flaming arc lamps, which are used for street lighting, placed high above the street ? 3. When an incandescent light bulb gets very hot and blackens on the inside, what does it indicate? 4. What must be the voltage of an arc-lighting dynamo which is to furnish 8 amperes to 25 street lamps arranged in series, if each lamp re- quires a terminal voltage of 50 volts? 5. What would be the kilowatt output of the generator in problem 4 ? 6. How may a street car, which is operated on a 550 volt line, be lighted by 110 volt lamps? Draw a diagram of the connections. 7. In considering the proper kind of electric lamp for illumination, what other factors must be considered besides watts per candle power ? 8. How many 0.5 ampere lamps, connected in parallel, can be pro- tected by a 20-ampere fuse ? 9. How many candle power should a 50 watt tungsten lamp give, if its efficiency is 1.2 watts per candle power? 10. It was found on testing a 32 candle power lamp that it consumed 100 watts of electric power, of which 88 watts were turned into heat. What was its efficiency for heating? What was its light efficiency in the true sense? What was its commercial rating? 340 PRACTICAL PHYSICS ELECTRIC MOTOR 337. The dynamo as a motor. We have already seen that a dynamo, when driven by a steam engine, gas engine, or water wheel, may generate electricity. Now w r e shall see how this electric current can be supplied to a second machine, exactly like a dynamo, but called a motor, which may be used to drive an electric car, a printing press, a sewing machine, or any other machine requiring mechanical energy. In short, the dynamo is a reversible machine, and sometimes in shops, and often on self-starting automobiles, the same machine is driven as a generator part of the time, and used as a motor to drive another machine the rest of the time. Structurally, the motor, like the dynamo, consists of an electromagnet, an armature, and a commutator with its brushes. To understand how these, act in the motor, how- ever, we must get a clear idea of the behavior of a wire carrying an electric current in a magnetic field. 338. Side push of a magnetic field on a wire carrying a cur- rent. We will stretch a flexible conductor loosely between two binding FIG. 301. Side push on wire carrying a current. posts A and B, so that a section of the conductor lies between the poles of an electromagnet, as shown in figure 301. Let the exciting current be so connected to the electromagnet that the poles are ^and S as shown. Then, if a strong current from a storage battery is sent through the con- ductor from A to B by closing the key K, it will be seen that the wire. ELECTRIC POWER 341 with current going in. between the magnet's poles is instantly thrown upward. If the current is sent from B to A, the motion of the conductor is reversed, and it is thrown doivnward. It will help us to understand this side push exerted on a current-carrying wire in a magnetic field, if we recall that every current generates a magnetic field of its own, the lines of which are concentric circles. Figure 302 shows a wire carrying a current w, that is, at right angles to the paper and away from us. The lines of force are going around the wire in clockwise direc- tion. The magnetic field between the poles of a strong magnet is practi- cally uniform and is represented by parallel lines of force shown in figure 303. If we put the wire, with its cir- cular field, in the uniform field be- FIG. 303. "Uniform magnetic tween the N and S poles of the magnet, the lines of force are very much more crowded above the wire (Fig. 304) than below. But we have seen in section 238 that we can think of magnetic lines of force as act- ing like rubber bands which would, in this case, push the wire down. If the current in the wire is re- versed, the crowding of the lines of force comes below the wire, and it is pushed up. 339. Motor rule of three fingers. The rule for remembering which FIG. 304. Lines of force about a wire carrying current in a magnetic field. way this side push on a wire in a magnetic field will move the wire is precisely the same as that for the generator except that the left hand instead of the right is used. 342 PRACTICAL PHYSICS FIG. 305. Drum-wound motor. 340. The action of a motor. In motors, as in dynamos, the drum type of armature is almost exclusively used. It will be remembered (see section 322) that in this type the active wires lie in slots along the outside of the drum, as in figure 305, and the wiring con- nections across the ends of the armature are such that when the current is coming out on one side, say the right, it will be going in on the other side the left. Just how these wiring con- nections are made is not important for the present purpose, and in- deed there are many different ways in which they can be ar- ranged. In any case, from what has just been said, it will be clear that the wires (O) on the right side of the armature will be pushed upward, and those (0) 011 the left side of the armature will be pushed downward by the magnetic field. In other words, there will be a torque tending to rotate the armature counter-clockwise. The amount of this torque de- pends on the number and length of the active wires on the armature, on the current in the armature, and on the strength of the magnetic field. Another way of lookirfg at this action is to notice that the effect of these armature currents is such as to make the armature core a magnet, with its north pole at the bottom and its south pole at the top. The attractions and repulsions between these poles and those of the field magnet cause the armature to rotate as indicated by the arrows. The function of the commutator and brushes is, as in the generator, to reverse the current in certain coils as the armature rotates, so as to keep the current circulating, as shown in figure 305. 341. Forms of motors. D.C. generators and motors are often of identical construction. Thus we have series motors, ELECTRIC POWEE 343 such as are used on street cars and automobiles, and shunt motors, such as are used to drive machinery in shops. So also we have bipolar and multipolar motors. When it is de- sirable that a motor shall run at a slow speed, it is built with a large number of poles. 342. Back e. m. f . in a motor. Suppose we connect an incandescent lamp in series with a small motor. If we hold the armature stationary, and throw on the current from a battery, the lamp will glow with full brilliancy, but when the armature is running, the lamp grows dim. This shows that a motor uses less current when running than when the armature is held fast. The electromotive force of the battery and the resistance of the circuit are not changed by running the motor. Therefore, the current must be diminished by the development of a back electromotive force, which acts against the driving e. m. f . Since a motor has a series of armature wires cutting mag- netic lines of force, it is bound to generate an e.m. f. in these wires. That is, every motor is at the same time a dynamo. The direction of this induced e. m.f. will always be opposite to^that driving the current through the motor. Just as in the generator, when the armature revolves faster, the back e. m. f . is greater, and the difference between the impressed e. m. f. and the back e. m. f . is therefore smaller. This difference is what drives the current through the re- sistance of the armature. So a motor will draw more current when running slowly than when running fast, and much more when starting than when up to speed. For example, suppose the impressed or line voltage on a motor is 110 volts, and the back e.m. f. is 105 volts. Then the net voltage which will force current through the armature is 110 105, or 5 volts. If the arma- ture resistance is 0.50 ohms, the armature current is 5.0/0.5, or 10 am- peres. But if the whole voltage (110 volts) were thrown on the arma- ture while at rest, the current would be 110/0.5 or 220 amperes. 343. Starting a motor. When a motor starts from rest, there is, of course, no back e. m. f . at first, and if the motor 344 PRACTICAL PHYSICS is thrown directly on the line, there will be such an exces- sive current as to " burn out " the, armature. To prevent this first rush of current, a starting resistance is put into the circuit at first, and cut out step by step as the machine speeds up. The device for doing this is shown in figure 306. See also figure 257. 344. Applications of the motor. The transmission of power through shops and factories by means of shaft- ing, cables, and belts is dangerous, noisy, and un- economical. In a modern system, electric power is generated in a central power house, is transmitted to va- rious parts of the plant, and is used in electric F,G.306.-Motor with staTn'g resistance. mOt rS t() d " Ve eith <* indi - vidual machines or groups of machines. When electrical transmission is used, the danger and inconvenience of belts and shafting are avoided, the machines can be set in any position, and their speed can be easily controlled by field rheostats. In shops and factories thus equipped, shunt motors are commonly used, for constant speed motors are required, and the speed of a shunt motor under no load, or a light load, is nearly the same as at full load. Series motors are used on cranes, automobiles, and electric cars, because this type of motor has a large starting torque. The torque in a series motor is proportional to the square of the current, while in a shunt motor it is directly propor- tional to the current. The fact that the torque in a series motor is largest when the speed is slowest (because there is ELECTRIC POWER 345 little back e.m. f.) makes it just the kind of motor for crane or vehicle work. When the load on a series motor drops to zero, the motor may " race " ; that is, go faster and faster until the armature flies to pieces. For this reason, series motors are connected, either directly (on same shaft) or by cogwheels, to the machines to bs driven, so that they can never escape their load. Figure 307 shows a street- car motor with its case lifted to show the inside arrangement. The field consists of four short poles projecting from the case, which serves both to protect the motor, and as a path for the magnetic flux. The armature revolves so rapidly that its speed has to be reduced by a pair of cogwheels, the larger of which is on the axle of the driving wheels, and is not shown in the picture. These make the speed of the axle about one fourth that of the motor. Street cars are usually operated on a direct-current system. A large multipolar compound-wound generator (Fig. 308) at the power station maintains about 550 volts between the trolley or third rail and the track. A " feeder " or cable of low resistance is run parallel to the trolley wire and connected FIG. 308. General scheme of a trolley line. ^o ft a ^ inter- vals, to avoid a large voltage drop in the line when a number of cars are taking current at a distance from the power plant. The current passes down the trolley pole FIG. 307. - Street-car motor with toj of case lifted up. 346 PRACTICAL PHYSICS Armature Armature field Rail Parallel into the controller (Fig. 309). This is an ingenious ar- rangement of switches by which the motorman can start Trolley Trolley his car with both motors in series and with the starting resistance all in; then by moving a lever he gradually cuts out the starting resistance and finally throws both the motors in parallel, as shown in figure 310. Thus, when starting, each motor receives less than half the line volt- age, and when running at full power, gets full voltage. The current leaves the motors by the wheels, and goes back to the power station through the rails. 345. Efficiency of the electric motor. One reason for the extensive use of electric motors is their great efficiency, sometimes as high as 80 % or 90 %. The efficiency of a motor, just as of any machine, means the ratio of out-put to in-put. We can easily measure the number of amperes and the num- ber of volts supplied to the motor and thus compute the watts put in. To get the output of mechanical work, engineers usually make a "brake-test." One simple form of brake consists of a belt or cord attached to two spring balances and passing under a pulley on the motor shaft, as shown in figure 311. If the pulley rotates as indicated, it is evident that one spring balance will have to exert more force than the other because of the friction of the pulley on the cord, The amount Rail Series FIG. 310. Series-parallel control of electric cars. CflBUE STRuNCi ON LINE OF STflNDBRO TOWE.RS. ST-LOUIS TRRNSMISSION LINE NOV FIG. 309 (above at left). Street car controller. FIG. 324 (below at right) . Transmission line. Direct Current Motor with field coils shown above. ELECTRIC POWER 347 of friction is equal to the difference between the readings of the two balances, and it is exerted each minute through a dis- tance equal to the circumference of the pulley times the revolutions per minute. The work done in one minute is equal to the friction times the distance per min- ute. Finally, if we express the out- put and input in some common unit of power and di- FIG. 311. Measuring output of a motor by means of vide, we have the efficiency. It will be helpful to know that 1 watt = 44.3 foot pounds per min. = 6.12 kilogram meters per min. QUESTIONS AND PROBLEMS 1. Figure 812 represents a bipolar motor with the armature revolving counter-clockwise. Copy it and indicate by dots and crosses * in circles, the direction of the various currents. 2. What is the armature resistance of a motor in which the armature current is 4 am- peres, the impressed e. m.f. is 115 volts, and the back e.m.f. is 112 volts? 3. Find the back e. m. f. in a motor in which the armature resistance is 0.3 ohms, the current is 15 amperes, and the impressed voltage is 110 volts. FIG. 312 Bipolar motor. * A cross in a circle represents the feathers of an arrow sticking into the paper, and means current going in. A dot in a circle means a current com- ing out. 348 PRACTICAL PHYSICS 4. How much current will be drawn by a motor whose efficiency is 90%, when it is developing 5 H. P. and is connected to the 110 volt service ? 5. When a certain motor was tested by the brake test, it took 67 amperes at 113 volts and developed 8.5 H. P. Calculate its efficiency. CHEMICAL EFFECTS OF ELECTRIC CURRENTS 346. Conduction by solutions. When an electric current flows along a copper wire, the wire becomes warm and is surrounded by a magnetic field. When an electric curre-it flows through a solution of salt and water, the solution is warmed and is surrounded by the magnetic field, and it is at the same time decomposed or broken up. For example, under certain conditions an electric current will decom- pose brine into a metal, sodium, and a gas, chlorine, which are the two elements com- posing salt. Not all liquids conduct elec- tricity ; thus alcohol and kerosene are non- conductors. Bat all liquids which do conduct electricity are more or less decom- posed in the process. 347. Electrolysis of water. Water (made slightly acid with sulphuric acid) can be decomposed by an electric current in the apparatus shown in figure 313. The platinum electrodes are connected with a battery C'IG. 313. Water is or generator, giving at least 5 or 6 volts. The elec- into trode in tube A, which is connected to the positive hy- ( + ) pole, is called the anode, and the other electrode j n j s ^he cathode. The current passes through the solution from the anode A to the cathode B. Small bubbles of gas are seen to rise from both electrodes, and the gas collects in tube B twice as fast as in tube A. When tube B is full, we open the switch, and test the collected gases. To test the gas in tube B, we open the stopcock at the top and apply carefully a lighted match. This gas burns with a pale broken up oxygen and drogen. ELECTRIC POWER 349 blue flame which shows it to be hydrogen. If we open the stopcock in tube A and bring a glowing pine stick near, it bursts into a flame, which shows the gas to be oxygen. Thus we see that water is decomposed by electricity into its constituent elements, hydrogen and oxygen. This pro- cess of decomposing a compound by means of an electric current is called electrolysis. 348. Theory of electrolysis. The theory of this process may be stated as follows: The small quantity of sulphuric acid (H 2 SO 4 ), when put into the water, breaks up into hydrogen ions (2 H + ) and sulphate ions (SO 4 ~ -), which have positive and negative charges of electricity respectively. When the current is sent through the solution, the positive hydrogen ions (2 H + ) wander toward the cathode and the negative sulphate ions (SO 4 ~~) toward the anode. At the cathode, the hydrogen ions give up their positive charges and rise to the surface as bubbles of hydrogen. At the anode, the sulphate ions give up their negative charges of electricity and react with the water (H 2 O) to form sulphuric' acid (H 2 SO 4 ) and to set free oxygen (O 2 ). In this way the sul- phuric acid, which is added to conduct the electricity, is not used up, while the water (2 H 2 O) is broken into hydrogen (2 R 2 ) and oxygen (O 2 ). 349. Electroplating. We may illustrate the process of electroplat- ing by the following experiment. We will put two platinum electrodes in a U-tube filled with copper sulphate solu- tion (CuSO 4 ), as shown in figure 314. After the electric current has passed through the solution for a few minutes, we find the cathode is coated with metallic copper, while the anode is unchanged. If we re- verse the direction of the current, we find that copper is deposited on the clean platinum plate which is now the cathode, and the copper coating on the anode gradually disappears. FIG. 314. Electrolysis of copper sulphate. 350 PRACTICAL PHYSICS In this way one metal can be coated with another. For example, articles of brass and iron, which corrode in the air, can be coated with nickel, which does not corrode. Similarly, much cheap jewelry is gold or silver plated. Many knives, forks, and spoons are silver plated, the best being what is called "triple" or "quadruple plate." In practice the process is done in vats, as in figure 315. The objects to be plated are hung from one copper " bus " bar, and the metal to be deposited, in this case pure silver, is hung from the other bar. The vat contains a solution of the metal to be deposited. For silver plat- ing a solution of silver and potassium cyanide is used. The bar carrying the FIG. 315. Diagram of metal to be deposited is connected with electroplating vat. the + terminal of a low- voltage gener- ator and the other bar to the terminal. The silver plates at the anode dissolve as fast as the silver is deposited on the cath- ode, the strength of the solution remaining unchanged. When the coating has reached the proper thickness, a final process of buffing and polishing gives the surface the desired appearance. 350. Electrotyping. One might at first suppose tha*- this book was printed from the actual type which was set up, but that is not the case. Most books which are made in large numbers are printed from electrotype "plates." A wax im- pression of the page as set up in type is made in such a way that every letter leaves its imprint on the wax mold. Since the wax is itself a non-conductor, it has to be coated with graphite. This mold is then placed in a solution of copper sulphate and attached to the negative bus bar, so that it becomes the cathode, while a copper plate acts as the anode. After the current has deposited copper on the wax mold to the thickness of a visiting card, this shell of copper is sepa- rated from the mold and "backed up" with type metal to give it the necessary strength for printing. ELECTRIC POWER 351 351. Refining of metals. Copper as it comes from the smelting works is not pure enough for some purposes, such as making wires and cables for carrying electricity. So the copper for electrical machinery is refined by electricity. The crude copper is the anode, a thin sheet of pure copper is the cathode, and the solution is copper sulphate. The copper deposited by the electric current is remarkably pure. The anode of crude copper gradually dissolves, and the impurities drop to the bottom of the vat as mud. In this mud there is generally enough gold and silver to pay the expense of the process. Copper purified in this way is known commercially as electrolytic copper. 352. Electrochemical equivalents of metals. Experiments show that a given current always deposits the same amount of a given metal from a solution in a given time. In fact, this is so accurately true that it is the basis of the most accurate method known for calibrating standard ammeters (see section 275). The amount of metal deposited by a current depends (1) on the strength of the current, (2) on the time it flows, and (3) on the nature of the metal. The definite quantity of a substance deposited per hour by elec- trolysis when one ampere is flowing through a solution is called the electrochemical equivalent of the substance. ELECTROCHEMICAL EQUIVALENTS ELEMENT SYMBOL GRAMS PER AMPERE HOUR Aluminum Al 0.337 Copper Cu 1.186 Gold Au 3.677 Hydrogen H 0.0376 Nickel Ni 1.094 Oxygen O 0.298 Silver Ag 4.025 352 PRACTICAL PHYSICS QUESTIONS AND PROBLEMS 1. To determine which is the + and which the pole of a generator, two copper wires are sometimes connected to the terminals and the bared ends dipped in a glass of water. One will soon turn dark. How does this experiment show which is the positive terminal? 2. How many grams of silver are deposited in 8 hours from a silver nitrate solution by a current of 5 amperes? 3. How many liters of hydrogen will be generated by a current of 10 amperes in 4 hours? (A liter of hydrogen weighs 0.09 grams under standard conditions.) 4. How many amperes will be needed to deposit 1.5 pounds of copper per day of 24 hours ? 5. How long will it take a current of 200 amperes to refine a ton of copper? 6. In calibrating an ammeter the current was allowed to run 2 hours and 15 minutes, and deposited 39.5 grams of silver. What would be the reading of the ammeter, if correct? 7. Two electroplating vats are arranged in series, one for gold and the other for silver. How much gold is deposited while 1 gram of silver is being deposited ? 8. An electroplater buys his electricity by the kilowatt hour. The metal deposited in electroplating is proportional to the number of am- pere hours. Why does he use as low a voltage as possible? 9. What is meant by triple and quadruple plate ? j 353. Storage battery. Some people think a storage bat- tery is a sort of condenser where electricity is stored, but it is not that. In the storage battery, as in any other battery, the electrical energy comes from the chemical energy in the cells. The charging process consists in forming certain chemi- cal substances by passing electricity through a solution, just as hydrogen and oxygen are formed in the electrolysis of water. In the discharging process, electricity is produced by the chemical action of the substances which have been formed in the charging process. 354. Lead Storage cell. We may make a small lead storage cell by putting two sheets of ordinary lead in a glass battery jar with a very dilute solution of sulphuric acid. To charge it or " form " the plates ELECTRIC POWER 353 quickly we connect this cell and an ammeter in series with a battery of three or more cells, or better, a generator of about 6 volts {Fig. 316). While the current is passing, bubbles of gas rise from each plate. If, after a few minutes, we disconnect the generator and touch the wires of a voltmeter to the lead terminals, it shows an e. in. f. of about 2 volts. If we then connect an electric bell in series with the ammeter and the lead cell, the bell rings, which shows that a cur- rent is produced, and the ammeter shows that the current on dis- Ammeter Voltmeter Fia. 316. Forming a lead storage cell. FIG. 317. Commercial lead storage cell. charge is opposite to that used in charg- ing the cell. When the plated are lifted out of the solution after charging, plate B, the anode, is brown, due to a coating of lead per- oxide (PbO 2 ), and plate A, the cathode, is the usual gray of pure lead (Pb). In the commercial lead storage (Fig. 317) cell, the negative plates are pure spongy lead (Pb), the posi- tive are lead peroxide (PbO 2 ), and the electrolyte is dilute sulphuric acid. In the charging process, the pos- itive plate, which is dark brown, is coated with lead peroxide, and the negative, which is gray, is made into spongy lead. In the dis- charging process, both plates gradu- ally return to a condition where each is covered with lead sulphate (PbSO 4 ). This isshownin figure 318. The chemistry o'f these changes can be briefly described by the equation FIG. 318. Discharging a lead Charge -< ceil. Pb0 2 + Pb + 2 H 2 S0 4 = 2 PbS0 4 + 2 H 2 0. >- Discharge 2A 354 PRACTICAL PHYSICS It will be noticed that during the charging process the acid becomes more concentrated. So the condition of a storage cell can be determined, at least roughly, by the spe- cific gravity of the acid. The plates in the commercial lead battery are either roughened and then changed into the proper active materials, lead peroxide and lead, by a chemi- cal process, or are punched full of holes which are filled with the active material. 355. Advantages and disadvantages of the storage cell. The lead cell is heavy and expensive, and requires careful handling to get an efficiency even as high as 75%. Its principal use is not as yet for automobiles, but in three other fields. First, it is often used to carry the " peak " of the load of a power station. In certain hours of the day the demand for current is too great for the generators to carry, so a large storage battery, which has been charging while the load was light, is used to help out the generators. Second, many companies, which have to furnish electricity without interruption or pay a heavy fine, use a storage battery as a reserve supply of electrical energy. In case of accident, the storage battery can be drawn upon at a moment's notice. Third, in some small plants the load on the generators is very light for a considerable time each day or night. In such cases a storage battery is sometimes used to take care of this long-continued light load, and the engine and generators are shut down. 356. Edison storage battery. Edison has invented a stor- age cell in which the negative plate is pure iron in a steel frame, the positive plate is nickel oxide, and the solution is caustic potash. Since this cell is intended for traction work, great pains have been taken to make it light, strong, and com- pact. Instead of being placed in a glass or hard-rubber tank, it has a thin nickel-plated sheet-steel case. In a lead cell the normal voltage on discharge is 2 volts ; in the Edison cell it is 1.2 volts. For the same capacity of output, ELECTRIC POWER 355 the Edison cell is about half as heavy as the lead cell. As the internal resistance of the Edison is a little more than that of the lead cell, its efficiency is a little lower. Whether or not the Edison cell is going to be better than the lead cell depends on its " life " under commercial conditions, and this is not yet settled. QUESTIONS AND PROBLEMS 1. In a trolley system the generator maintains 565 volts on the line. How many lead storage cells, each of 2.1 volts, will be needed to help the generator carry the peak of the load ? 2. Storage cells are sold according to their "capacity" in ampere hours. What " capacity " will be required to deliver 10 amperes contin- uously for 8 hours? 3. Most manufacturers of lead cells allow about 55 ampere hours for each square foot of positive plate area. How large a plate area will be required in problem 2 ? 4. If the e. in. f. of a lead cell is 2.3 volts on open circuit, while the terminal voltage when the cell is delivering 10 amperes is only 2 volts, what is the internal resistance of the cell ? 5. A battery of 24 lead storage cells in series, each having an e.m.f. of 2.1 volts, a normal charging rate of 15 amperes, and an internal resistance of 0.005 ohms, is to be charged by a dynamo, what must be the terminal voltage Of the dynamo ? SUMMARY OF PRINCIPLES IN CHAPTER XVIII When a wire cuts lines of force, an induced e.m.f. is set up in the wire. To get direction of current, use right hand. Thumb = Motion, Forefinger = Flux, Center finger = Direction of Current. Magnitude of e. m. f. varies as speed X flux X turns. Slip rings give alternating current. Commutator gives direct current. 356 PRACTICAL PHYSICS Dynamo does not make energy; it transforms mechanical into electrical energy. Motor transforms electrical energy into mechanical energy. Power delivered to circuit = intensity of current X voltage. Watts = amperes X volts. 1 H. P. = 746 watts. Power turned into heat = current squared X resistance. Watts = (amperes) 2 X ohms. Heat in calories = 0.24 I 2 Rt. A wire carrying a current, when set at right angles to a mag- netic field, is pushed sideways by the field. To get direction of motion, use left hand. As before, Thumb = Motion, Forefinger = Flux, Center finger = Current. Every motor, when running, is acting at the same time as a dynamo. The e.m.f. of this dynamo action opposes the current driving the motor, and is the back e. m.f. Net e.m.f., which drives current through armature, equals im- pressed e. m. f. minus back e. m. f . Ohm's law applies to a motor armature only if net e. m. f. is used. Weight of a substance deposited by a current = electrochemical equivalent X current X timec QUESTIONS 1. Why cannot a lead storage cell be charged from a dry cell ? 2. Why do the lights on an electric car often grow dim when the car is crowded and going up grade ? 3. Would it be possible to drive the propellers of an ocean liner by electric motors? Why is it not commonly done? Why are some people seriously considering doing it in the near future? ELECTRIC POWER 357 4. Which will yield the more heat for warming an electric car, a 50 ohm resistance connected across a 50 volt line, or a 100 ohm resistance connected across a 100 volt line ? 5. Compare the cost per hour of running a 55 ohm electric heater on a 55 volt circuit and on a 110 volt circuit, if power costs 10 cents per kilowatt hour. 6. The "carrying capacity" of a wire is limited by the rate at which it can radiate the heat generated in it. Which will require wires of larger carrying capacity, a 1100 volt power transmission line, carrying 1000 amperes, or a 11,000 volt line, carrying 100 amperes? 7. Which of the lines in the last problem will deliver more power at the other end ? 8. Why are electric cars not more generally operated on storage cells instead of by an overhead or a third-rail system of transmission ? 9. Why are electric light bills made out in kilowatt hours instead of kilowatts ? 10. Why does it take twice as much power to keep a generator going when there are 200 incandescent lamps lighted in parallel as when there are only 100 lamps in use? 11. What methods are used to make the track of a street-car system a better conductor ? 12. If you were to charge a storage battery so incased that you could see only the two terminals which were marked + and , how would you connect it to a generator ? 13. How does the back e. m. f . of a motor vary with its speed ? 14. A belt-driven shunt dynamo is used to charge a storage battery. The belt breaks, but the dynamo keeps on running. Explain. 15. Does it make any difference which end of the field coils of a shunt-wound dynamo is connected with the positive brush ? If you have an experimental dynamo, try it. 16. The speed of a shunt-wound motor can be controlled by putting an auxiliary resistance, called a field rheostat, in series with its field coils, so as to decrease the current through them. Will this increase or de- crease its speed? Why? If you have an experimental motor, try it. 17. What is the advantage of electrotype plates over the original type in printing a book ? CHAPTER XIX ALTERNATING CURRENT MACHINES Why alternating currents are used the transformer long- distance transmission eddy currents alternators polyphase circuits A. C. motors rotating field squirrel-cage rotor A. C. power wattmeters. 357. Why alternating currents are used. For heating and lighting an alternating current is just as satisfactory as a direct current. For plating and refining an alternating cur- rent cannot be used because a unidirectional current is neces- sary to make a metal deposit. If motors are to be run by an alternating current, a special type of motor is generally used, which is quite different from the ordinary direct-current motor. The real advantage in the use of alternating currents is economy of transmission. This is made possible by a simple and efficient machine known as a transformer. 358. Induced currents in a transformer. As long ago as 1831 Faraday wound two coils of wire on a soft iron ring, as FIG. 319. Faraday's ring trans- , . ~ ^ ~ TTT1 ., former, shown in figure 319. When coil A was connected with a battery and coil B with a galvanometer, he found that the needle of the galvanometer was disturbed every time the circuit was made and every time it was broken. The modern transformer consists of two coils side by side on a common iron core not unlike Faraday's ring. When an 358 ALTERNATING CURRENT MACHINES 359 alternating current is set up in one coil, called the primary, it magnetizes the iron core, causing surges of magnetic flux, first in one direction and then in the opposite direction. Since this magnetic flux passes through the second coil, called the secondary, as well as the first, it induces an alternating current in the secondary. Since the same number of lines of force pass through both coils, the volts per turn are the same. Therefore the total voltage in the primary coil is to the~<* total voltage in the secondary coil as the number of turns in the primary is to the number of turns in the secondary. The line voltage in the street is often 2200 volts, which is too high to be safely used in private houses. It is therefore necessary to transform or " step down " to 110 volts. A primary coil of fine wire is connected to the 2200 volt circuit, and a secondary coil of coarse wire is connected with the lamp circuit of the house. The primary coil must have 20 times as many turns as the sec- ondary. The secondary coil must be made of larger wire than the primary coil, because the secondary current is about twenty times the current taken by the primary. Thus the trans- former delivers the same amount of energy which it receives, except for a small amount (from 2 % to 5 %), which is lost as heat in the transformer. The efficiency of a transformer is therefore very high, from 95 % to 98 %. 359. Commercial forms of trans- FIG. 321. Shell type of former. Transformers are built in two transformer. -, , , N ,-, ^^^. general types : (a) the core type (tig. 320), in which the coils are wound around two sides of a rectangular iron core, and (5) the shell type (Fig. 321), in FIG. 320. Core type of transformer. 360 PRACTICAL PHYSICS FIG. 322. Transformer case mounted on pole. which the iron core is built around the coils. The iron core of both types is made of sheets of mild steel. To keep the coils insulated, the transformer is put in an iron case and surrounded with oil. These iron cases (Fig. 322) are commonly attached to poles near houses wherever the alternat- ing current is used for lighting purposes. 360. Uses of transformers. In electric light stations it is common practice to use alternators to gener- ate electricity at 2200 volts. The current is transmitted at this high voltage to the various districts, where it is transformed or " stepped down" to 110 volts for use in light- ing houses. Another important use of the transformer is to furnish large currents at very low voltage for electric furnaces and electric welding. To illustrate this, we may wind a turn or two of very large copper wire around the core of a small step-down transformer (Fig. 323), and connect its primary to a 110 volt A.C. circuit (if one is available). The ends of the large wire should be at- tached to a couple of iron nails. If, when the current is on, the tips of the nails are brought together, they get red hot and can be welded. The adjoining rails of a car track are often welded together in this way. A heavy current is required for a short time, and is obtained by using a step- down transformer, in which the secondary consists of only one or two turns, made of very large copper bars. The ends FIG. 323. Step-down transformer, used for welding. ALTERNATING CURRENT MACHINES 361 of this secondary are clamped to the rails to be welded, one on each side of the junction. 381. Long distance transmission of power. By the use of alternating currents of high voltage, even up to 100,000 volts, power is now transmitted very long distances. For example, electric power is generated in hydroelectric power plants in the Sierra Nevada Mountains of California, and transmitted 200 miles to San Francisco. To understand why the economical transmission of electricity demands such high voltage, we have only to recall that the power transmitted is the product of the voltage and the current strength. Evidently, then, if we can make the voltage high, the current can be low. But a smaller current means smaller losses in transmission, for they are due to the heat- ing effect of the electric current, and we have already seen that this varies as the square of the current. It is an impressive sight to see three or six copper cables, each about | of an inch in diameter, suspended about 75 feet above the ground on steel towers (Fig. 324, opposite page 347), and to know that those wires are carrying 30,000 H. P. of electrical energy. Hydroelectric power plants are being developed all over the country. For example, at Niagara power plants are generating electricity, raising the voltage to 60,000 and transmitting some of the enormous energy available at the Falls to distant cities like Buffalo, Rochester, and Syracuse. Just outside the city limits there are sub- stations where the voltage is reduced to about 2000, and then it is distributed to factories and for general use in lighting and traction. Before the current actually enters the buildings, the voltage is again stepped down to 220 or 110 volts. 362. Eddy currents. We have seen that the cores of transformers are made of soft sheet-iron, or " mild steel," stamped out in the desired shape and then assembled. In the construction of induction coils the cores are made of 862 PRACTICAL PHYSICS Insulation FIG. 325. Laminated core of a dynamo armature. soft iron wires which are put together in a bundle. If we examine the armature of a dynamo, we find that the iron drum is made of laminae (sheets) of mild steel which are stamped out in the shape of disks with notches around the edge (Fig. 325), and then assembled on a framework called the " spider," and mounted on the shaft. .In all these cases the sheets or wires are insulated from each other by a coating of shellac, which eliminates what are sometimes called Foucault or eddy currents. We have already seen, in studying the generator, that when any conductor cuts lines of force, an induced electro- motive force tends to send a current along the conductor. In the generator copper wires are provided to carry this current; but these wires are wound on an iron core, and if this core is itself an electrical conductor, an induced e. m. f. will be set up in it as it revolves in the magnetic field. This induced e. m. f. would send electric currents through certain portions of the core. These so- called eddy currents would soon heat the core, and would also retard the mo- tion of the armature and waste power. To reduce these currents to as small a value as possible, the core is laminated in such a way that the insulation is transverse to the direction in which the eddy currents tend to flow. 363. Use of eddy currents in damping. To show that eddy currents tend to retard the motion of a conductor in a magnetic field, we may set up between the poles of a strong electro- magnet a pendulum made of thick sheet copper (Fig. 326). If the mag- net is not excited, the pendulum swings back and forth as any pendulum FIG. 326. Damping by eddy currents. ALTERNATING CURRENT MACHINES 363 does, but when we throw on the current in the magnet, the copper pendu- lum cannot swing through the magnetic field, and is instantly checked. The eddy currents set up in the copper tend to retard the motion of the pendulum, much as if "it were swinging in thick sirup. This effect is very useful in stopping the vibrations of the moving coil of a d'Arsonval galvanometer (section 274). The wire is usually wound on a light copper or aluminum frame, and the eddy currents in this metal frame check its swinging. Such a galvanometer is called "dead-beat." We shall see, in section 372, that this same principle is used to check the rotation of a wattmeter. QUESTIONS AND PROBLEMS 1. What limits the voltage which it is practicable to use on high- tension transmission lines? 2. Why are the cables for long-distance transmission sometimes made of aluminum instead of copper? 3. If a step-down transformer is to be used to change the voltage from 1100 to 220, what must be the ratio of turns of wire on the primary and secondary coils? 4. A transformer has 1000 turns on the primary and 50 turns on the secondary and the primary current is 20 amperes. About how much is the secondary current? 5. What generates the heat required to weld the nails in the experi- ment shown in figure 323 ? Why does not the copper wire S melt as well as the the tips of the nails? 364. Alternators. When a coil of wire is rotated in a magnetic field, we have seen (section 319) that the current changes its direction every half turn. That is, there are two alternations for each revolution in a bipolar machine. In a D. C. generator this alternating current is rectified by the use of a commutator. In the alternating current (A. C.) gener- ator, called an alternator, the current induced in the armature is led out through slip rings, or collecting rings, as shown in figure 275. So almost any direct-current generator can be made into an alternator by substituting slip rings for the commutator. 364 PRACTICAL PHYSICS The field magnet of an alternator is usually an electro- magnet which is excited by direct current from a small auxiliary generator called the exciter. Since it is only the relative motion of the armature wind- ings and field magnet which is essential in any generator, large alternators are usually built with a stationary arma- ture and a revolving field. The revolving projecting poles (JV, 8, N, 8, in figure 327) sweep past the armature wires which are placed in slots around the inner pe- riphery of the stationary structure A. The direct V current for exciting the field coils is led in through FIG. 327. Revolving field and stationary , , , . , , armature. brushes which rub on two insulated metal rings. The alternating current is led directly from the windings of the stationary armature through cables to the switchboard. Figures 328, 329, and 330 (opposite pages 364 and 365) show the revolving field and stationary armature of commercial machines of this type, and an assembled machine. 365. Cycles and phase of alternating currents. When a conductor is moved past a magnetic N- pole, the induced e. m. f. is in one di- rection, and when it +30 jj+20 o, 10 a o ^ "X ,** f \ / ' / , V 0- 7 / \ o 3 l a- 20 V / X, ^ PO SIT ON OF IO IP IN >FC ,RE IS FIG. 331. Alternating e. m. f. one complete cycle. moves past an $-pole, the induced e. m. f. is in the opposite direction. This can be best represented by the curved line shown in figure 331. One complete wave is produced when II | e FIG. 329 (above). Stationary armature of alternator. FIG. 330 (below). Alternator, belt driven. The long shaft allows the arma- ture to be slid to one side so that the rotor can be examined and repaired. The small "exciter " is on the end of the shaft at the right. ALTERNATING CURRENT MACHINES 365 a wire moves through a complete revolution in a bipolar machine, or from a north pole past a south pole to the next north pole in a multipolar machine, and is called a cycle. In practice it is common to use for lighting an alternating current whose frequency is 60 cycles per second, while for power purposes 25 or even currents mon. A complete wave or cycle is called 360 electrical degrees 15 cycle are com- -t-30 |f20 M-lfl 2 o h ! -10 X "X, X* "X s ^ X ' / \ '"N / / ^ 4 t -V V 1 ' 1 p. - 7 / \ \ ^ y ,.x X, j ^ X X 1 ; p ")Sl Tin N F A RM VT! RF FT, -tr-f 1 FIG. 332. Two alternating currents which differ in phase. by analogy with the complete revolution of a bipolar generator. Any point or position in the cycle is spoken of as a certain phase. When, for example, the cycle is half completed, the phase is said to be 180 degrees, and when the cycle is one fourth completed, the phase is 90 de- grees. Two alternating currents of electricity, flowing in branch circuits, may be at different phases, as represented in figure 332, where one .curve represents the current in one branch and the other curve the current in the other branch. In the case shown, one current is said to lag behind the other by 90 degrees. FIG. 333. Diagram to represent armature and -_ field coils on alternator. ^OO- Single and pOly- phase circuits. If we connect all the stationary armature coils of a generator in series, and revolve the field as shown in figure 333, a single- phase alternating current is produced whose frequency we can Circwf 366 PRACTICAL PHYSICS determine by multiplying the number of revolutions per second of the rotor by the number of pairs of poles. To make use of this current for any purpose, such as electric lighting, we have simply to cut this armature circuit at any convenient step-down transform 2300 volts 2300 volts 2300 volts FIG. 334. Alternating system three phases and six wires. point and connect the ends directly to the mains. It will be noticed that there are as many coils on the armature as there are poles in the field magnet in the single-phase machine. It has been found more economical of space to have more than one coil for each pole of the field, and so we have two-phase and three-phase machines, in which there are two or three sets of coils on the armature. In the three-phase machine, which is the type T\ /$~\ /s~\ ^~\ /^\ /-" most used to-day, the three sets of armature coils may 2 each be used separately to furnish electricity for three separate lighting circuits, as shown in figure 334. FIG. 335. Curves for three-phase current ,, . . , system. The currents in the three circuits differ in phase by 120 degrees (Fig. 335). It will be seen that the currents are such that at any instant their sum is zero. ALTERNATING CURRENT MACHINES 367 To save wire, electrical engineers have devised ways of connecting the three sets of coils so as to have only three- line wires, instead of six, as shown in figure 336. 367. Use of alternators. The revolving-armature type of alternator is generally used only in small electric lighting stations. Large alternators of the re- volving-field type are usually mounted on the same shaft (direct-connected) with the driving engine or water wheel. Alternators of very large ca- pacity are now extensively used with steam turbines. They can be com- paratively small in size because they are driven at such high speed. These alternators have a revolving field of only a few poles (sometimes only two) and a wide air gap between the ar- mature core and the field poles. Figu re 337 shows a 7500 kilowatt alternator mounted on the crank shaft of a 10,000 horse-power steam turbine, having a speed of 1800 revolutions per minute. In high-tension transmission, the three-wire three-phase sys- tem is commonly used. FIG. 336. Y and A con- nections on three-phase cir- cuit. QUESTIONS 1. How can the engineer at the power house control the frequency of an alternating current? 2. How many revolutions per minute will an 8-pole machine have to make to give a 60-cycle current ? 3. What objection is there to using a 15-cycle current for lighting purposes ? 4. Draw a diagram to show two alternating currents which differ in phase by 45 degrees. 5. How much do the two currents generated by a two-phase alternator differ in phase ? 368 PRACTICAL PHYSICS Line If 368. Alternating current motors. An A. C. generator can be run as a motor, provided it is first brought up to the exact speed of the alternator which is supplying current to it and put in step with the alternations of the current supplied. Such a machine is called a synchronous motor. Since it is not self-starting, it is not convenient for general use, but is used in substations to drive D. C. generators. An ordinary series motor, by certain modifications in its design, can be made to operate on either D. C. or A. C. systems. These so-called A. C. commutator motors or single- phase series motors are coming into use for electric cars and locomotives when an alternating current is used. They are also to be found, in very small sizes, on egg-shaking machines in drug stores, and on vacuum cleaners. They are labeled " A.C. or D.C." on the name plates. The A. C. motor most frequently used is the in- duction motor. The distinc- tive features of this motor FIG. 338. Iron ring excited by two currents are that the stationary 90 degrees apart. winding, or " stator," sets up a rotating magnetic field, and that the rotating part of the motor, or "rotor," is built on the plan of a squirrel cage.* These will be discussed in turn. 369. Rotating magnetic field. To produce a rotating field, we will suppose that we have two alternating currents of the same frequency, but differing in phase by 90 degrees, and that we connect them to two sets of coils wound on a ring, as shown in figure 338. When the current in line I is at a maximum, it will be seen from the curves (Fig. 339) that the current in line II is zero. The top of the ring is therefore a north pole, N v and ALTERNATING CURRENT MACHINES 369 the bottom is a south pole, S. One eighth of a cycle (45 degrees) later, current 1 has decreased in strength and cur- rent 2 has increased in strength. The result of both currents is to form a north pole in the position N v 45 degrees farther along. One eighth of a cycle (45 degrees) later, current I has dropped to zero and current II is at a maximum. This brings the north pole of the ring to the right side (iV 3 ). Evidently the north pole is traveling around the ring, and will make a complete circuit for each complete cycle of the current. This produces a rotating field, and would cause a magnet, such as NS, to ro- tate with the field. We should then have a little two-phase A. C. motor. Figure 340 shows a working model to demonstrate the rotating field produced by a two-phase current system. 370. The rotor of an induction motor. The rotating mag- net can, of course, be replaced by an electromagnet, which FIG. 339. Curves of two alternating currents, which differ in phase by 90 degrees. FIG. 340. Working model of two-phase rotating field. is excited by some outside source of direct current. The rotor of a commercial A.C. motor is, however, much simpler, It consists of an iron core, much like the core of a drum 2B 370 PRACTICAL PHYSICS armature, with large copper bars placed in slots around the circumference and connected at both ends to heavy copper rings. This is called a squirrel-cage rotor (Fig. 342). When it is placed in a rotating magnetic field, the con- ductors on the two sides and the rings across the ends act like a closed loop of wire, and a large current is induced, even though the rotor has no electrical connection with any outside circuit. This large induced current makes a magnet of the iron core, and the field, acting on this magnet, drags it around. The rotor can never spin quite as fast as the magnetic field. If it did, there would be no cutting of lines of force, no cur- rents would be induced, and there would be no power avail- able to drive the rotor against its load. As in the case of the Gramme ring dynamo, the ring wind- ing is riot used in practical motors. The common construc- tion is to slip coils into slots in the inner periphery of a laminated iron " stator," as shown in figure 341. A squirrel- cage rotor (Fig. 342) is simple and strong, and needs only to be kept cool. This is done by air circulated through the core by fan blades. The assembled machine (Fig. 343) is simple, strong, compact, and almost "fool-proof." For these reasons, the induction motor is finding a wide field of useful- ness in shops and factories, and even on electric locomotives. 371. A. C. power. We have seen that we can determine the power of a direct-current circuit by multiplying the volts and amperes together. With a non-inductive circuit, such as a lamp, we can do the same with alternating currents. In the case of machines which have self-induction, that is, coils of wire with iron cores, the number of volt amperes is greater than the true number of watts. Although we cannot attempt to show in this book just how the watts may be computed from the volts and amperes of an alternating cur- rent, yet we can see why it is not a simple case of multipli- cation. FIG. 337 7500 k.w. alternator driven by steam turbine. FIG. 341. Stator of an induction motor. FIG. 342. Squirrel-cage rotor of induction motor. FIG. 343. Induction motor. ALTERNATING CURRENT MACHINES 371 In the first place, we will represent the varying electro- motive force by the " pressure " curve in figure 344, and the varying current by the current curve in the same figure. It will be noticed that the current curve lags, that is, it starts after the e. m. f. curve. This is due to the self-induction of the circuit which impedes the flow of the alternating current. To get the power of such a current, we should have to mul- tiply the simultaneous values of current and pressure for a great number of points, and then get a general average of these products. Now what an A. C. ammeter (which we will not attempt to describe) re- cords, is the " effective value " of the alternating current ; that is, the value in amperes of the direct current which would produce the same heating FIG. 344. Voltage and cur- effect. It can be shown that this " effective value " of an alternating current is about 0.7 of its maximum value. The effective value of an electromotive force is said to be one volt, when it will develop an alternat- ing current of one ampere in a non-inductive resistance of one ohm. It is also about 0.7 of the maximum value of the e. m. f. Evidently it will not do to multiply these effective values of current and voltage together, because, in the averag- ing process described above, large values of the current are likely to be paired with small values of the e. m. f., and vice versa. It can be shown that the A. C. watts are equal to the volt- amperes times a factor, which is called the power factor. This factor varies according to the circuit. It is always less than 1 for an inductive circuit. 372. Wattmeters. Every user of electricity should be in- terested in the recording wattmeter, which records on dials, like those of a gas meter, the number of kilowatt hours of elec- tricity consumed. It is on the readings of this instrument. 372 PRACTICAL PHYSICS that the monthly bills are based. Figure 345 shows the Thomson form of wattmeter. It is really a little shunt motor, the armature of which turns at a speed proportional to the rate at which electrical energy is passing through it. This armature is geared to the recording dials. The field of the instrument is made by stationary field coils which are connected in series with the line. The field strength is Dials Brushes-one/ FIG. 345. Thomson's watt-hour meter. therefore proportional to the current flowing in the main line. The armature is connected across the line, and takes a current proportional to the voltage across the line. There- fore, the torque which turns the armature is proportional to the product of the current and the voltage ; that is, to the watts in the line. The inertia of such a machine would make it run too fast, or fail to stop when the current stopped, if it were not for the electric damping caused by the rotation of an aluminum disk between the poles of permanent magnets. The eddy cur- rents generated in the disk tend to retard its motion. This type of wattmeter is used for both A. C. and D. C. work. When used with alternating currents it automatically averages the products mentioned at the top of page 371. ALTERNATING CURRENT MACHINES 373 SUMMARY OF PRINCIPLES IN CHAPTER XIX In a transformer : Voltage on primary turns of primary Voltage on secondary turns of secondary In an alternator : Frequency = revolutions per second x number of pairs of poles. A. C. power = amperes x volts x power factor. Power factor usually less than one. QUESTIONS 1. The iron case of a transformer is often corrugated. Why? 2. Why must the dielectric strength of the oil used in transformers be carefully tested ? 3. In long-distance transmission of power by high-tension lines, the wires are often supported on steel towers 50 feet or more above the ground, and the company gets a right of way to a strip of land 100 feet wide over which to run its wires. W T hy these precautions ? 4. What is gained by making the armature of big alternators station- ary, and rotating the field? CHAPTER XX SOUND What makes sound what carries sound velocity of sound water waves velocity, wave length, and frequency longi- tudinal waves sound waves loudness and distance direct- ing sound reflecting sound musical tones intensity, pitch, and quality resonators- overtones beats the musical scale stringed instruments wind instruments membranes the phonograph. 373. What makes sound ? When a bell rings, we see the hammer or clapper hit the bell, and hear the sound which it makes. If we hold a pencil against the edge of the bell just after it has been struck, we find that the metal is moving to and fro very rapidly. When a guitar string is plucked, it gives forth a note which we can hear, and at the same time we can see that the string looks broader than when at rest. We con- clude that the string is vibrating or oscil- lating back and forth. When we strike a tuning fork and hold it near the ear, we hear a note, and if we touch the fork to the lips, we feel its vibratory motion. To make visible the vibration of a tuning fork let us touch it to a light glass bubble suspended on a thread (Fig. 346). The bubble is set violently in motion. Another way to show the vibratory motion of a fork is to attach a point of stiff paper to one prong. Let us set such a fork in vibration and draw it over a piece of smoked glass (Fig. 347). The curve which is traced is easily made visible by putting white paper behind the glass. ~ 374 FIG. 346. Vibration of tuning fork made visible. SOUND 375 Whenever we look for the source of a sound, we find that something has been set in motion. It may be that something has fallen, a bell has been struck, a whistle has been blown, or some one has shouted; always some- thing has been set vibrat- , . , , 3 , -, FIG. 347. Curve traced by a vibrating ing which has caused the fork sensation of sound. 374. What carries sound? Ordinarily the air$ which is everywhere about us, brings sound to our ears. To make this evident let us try the following experiment. Let us suspend an electric bell under the receiver of a good vacuum pump, as shown in figure 348. If we set the bell to ringing and then pump out the air, we find that the sounds be- come fainter and fainter. When we let the air in again, the bell sounds as loud as at first. It seems probable that the bell would become quite inaudible if we could get a perfect vacu- um, and if no sound were conducted out by the suspension wires. We know that both heat and light can traverse a vacuum, as in the case of the electric incandescent light bulb, but we see from the last experiment that sound does not traverse a vacuum. It can be shown that other gases be- sides air carry sound, and that liquids and solids are even better carriers of sound than gases. For example, if one holds his ear under water while some one hits two stones together at some dis- tance away, the sound is heard very distinctly. It is also a familiar fact that one can hear a train a long distance away by putting one's ear close to the steel rail. Loud sounds, like those of cannon, or of volcanic eruptions, can be heard at a FIG. 348. Sound is not car- ried through a vacuum. 376 PEACTICAL PHYSICS distance of several hundred miles by putting one's ear to the ground. To show that liquids transmit sound, let us put the stem of a tuning fork into a hole bored in a large cork. If we set the fork in vibration, it is hardly audible; but if we hold it with the cork resting on the sur- face of a glass of water, we hear it distinctly. The sounds seem to be coming from the table on which the tumbler of water stands. This ex- periment shows that the vibration of the tuning fork is transmitted through the cork and the water to the air in the room. To show that solids transmit sound, we may hold one end of a long wooden stick against a door, and rest a vibrating tuning fork on the other end ; the sound of the fork seems to be coming from the door. The wooden stick here serves as the sound carrier and transmits the vibration of the fork to the door. So we conclude that solids, liquids, and gases may serve as carriers of sound. 375. How fast does sound travel ? In an ordinary room one is not aware that it takes any appreciable time for sound to travel from its source to one's ears; but in a large hall, or out doors, one often hears an echo, which shows that sound does take time to travel to a reflecting surface and back. During a thunder shower we hear the roll of the thunder after we see the flash. The farther away the lightning discharge is, the longer the interval between seeing the flash and hearing the rumble. Every one has doubtless seen the steam from a dis- tant whistle, and then later heard the whistle. So there is no doubt that sound travels much more slowly than light. One way to measure how fast sound travels is to discharge a cannon on a distant hill and measure the time between see- ing the flash of the cannon and hearing its report. In one such experiment, which was performed by two Dutch scien- tists in 1823, the cannons were set up on two hills about eleven miles apart, and observations were made first from one hill and then from the other, to eliminate the error due to wind. They concluded that sound travels 1093 feet (or 333 meters) per second, which was remarkably near the truth, considering SOUND 377 the instruments they had. Since then, several men have made determinations of the velocity of sound in air, which show that at C and 76 centimeters pressure the velocity of sound is 1087 feet ( or 331 meters) per second. The speed of sound in water is about 4.5 times the speed in air, and in steel it is more than 15 times as great as in air. It has also been found that the speed of sound in air increases about 2 feet (or 0.6 meters) per second for each degree centigrade rise in temperature. For practical purposes it is enough to remember that sound travels about 1100 feet per second. PROBLEMS (Assume that the time taken by, light to travel ordinary distances is negligibly small) 1. The sound of a steam whistle is heard 2.6 seconds after the steam is seen. About how far away is the whistle ? 2. A man can see the hammer strike a bell once every 2 seconds. If the man is a mile away, w^hat is the interval between the sounds of each stroke ? 3. On a hot summer day, when the temperature is 30 C, the flash of a gun is seen 2 miles away. How long after the flash will the report of the gun be heard ? 4. A stone is dropped from the top of the Woolworth Building in New York, which is 750 feet high. How long before a man on top would hear the sound of the stone as it struck the pavement? (The time includes the time for the stone to fall and for the sound to return.) 5. If an experiment shows that sound travels in water 4814 feet per second at 14 C, how many times as fast does sound travel in water as in air at this temperature ? 376. Sensation of sound. We have been considering the transmission of " sound " through gases, liquids, and solids, although we know that it is merely a sort of motion which is transmitted. Ordinarily we find it hard to think of sound without thinking of an ear to hear it. Thus we find people asking whether a waterfall in a very remote part of the earth, never visited by any man or animal, makes any 378 PRACTICAL PHYSICS sound. Evidently there are two things which are called " sound " the vibrations, and the sensation they produce when they strike against the tympanum or eardrum. The study of what happens in the ear and brain is properly left to physiology and psychology. In physics we shall study only the vibrations in the air or other transmitting medium, and shall refer to them when we say "sound." In this sense the waterfall makes just as much sound whether there is an ear to hear it or not. 377. Sound a wave motion. Evidently nothing material (that is, weighable) travels from the source of a sound to the ear; otherwise, how did the sound of the electric bell under the bell jar get through the glass ? This and other facts point unmistakably to the conclusion that what is transmitted is merely a vibration or mode of motion, called a wave. 378. Water waves. Since sound waves are usually invisi- ble, we will start with a study of water waves. When a stone is dropped into a smooth pond, a disturbance is produced which extends over the surface of the water in circles centered at the place where the stone struck. The water is pushed down and aside by the stone, forming a circular ridge which expands into a larger circle, and is followed by a second cir- cular ridge which expands, and so on. The result is that the surface is soon covered with a series of circular swells which are separated by circular troughs, all moving away from the center of the disturbance. To study these water waves more carefully, let us pour water into a long tank with glass sides (Fig. 349) to a depth of 2 inches, set a paddle upright about 6 inches from one end of the tank, and start a wave by drawing the paddle to the end of the tank. It will be observed that the wave travels to the other end of the tank. There it is turned back or reflected, returning to the first end, undergoing another reflection, and so on. By measuring the length of the tank and observing the time of six round trips of a wave (observe the rise and fall of the water at one side) we can calculate the speed of the wave. If we pour more water into the tank until the depth is 3 inches, and SOUND 379 again time six round trips and calculate the speed of the wave motion, we shall find that waves travel faster in deep water. To study stationary water waves we place a little block on the water at one end of the tank. By raising and lowering the block periodically, FIG. 349. Tank for water waves. we may set up stationary water waves, in which the water simply " see- saws " up and down with no apparent backward and forward motion. The surface of a water wave may be represented by the curved line shown in figure 350. The stationary points, A, -B, (7, .Z), etc., are called the nodes ; the intervening spaces are called the loops, or internodes. The water between nodes oscillates up and down; when it is up, it forms a crest, and when it is down, it is a trough. A crest and trough together form a wave, as from A to C, or B to D. The length of a wave (0 is measured K ? 1 ^X^v 9 c s~^P 2J~"-P^- horizontally from any point on one wave to the corresponding point in the , P J FIG. 350. Surface of a next wave. Corresponding points are water wave< called points in the same phase. The amplitude (d) of the wave vibration is half the vertical dis- tance from trough to crest. 379. Relation between velocity, wave length, and frequency. In the case of the waves started by throwing a stone into a quiet pool, we know that while the circular waves grow larger and larger, any particular crest seems to move out radially until it reaches the bank or dies away. The dis- tance which a crest travels in one second is called its velocity. The number of crests passing a fixed point in one second is called the frequency. The time it takes one wave to pass a 380 PRACTICAL PHYSIQS given point, that is, the time between crests, is called the period of the wave motion. If n is the number of waves passing a given point in one second, that is, the frequency, and if p is the time required for one wave to pass a given point, that is, the period, then, Again, if I is the length of one wave in feet, and n is the number of waves passing any point in one second, the dis- tance traveled by a wave in one second, that is, its velocity v in feet per second, is equal to n times I ; that is, v = nl It should be remembered that it is only the wave form that travels over the surface of the water, not the water particles themselves. Thus if we float a cork or a toy boat ou a pool over whose surface waves are passing, the cork or boat merely bobs up and down as a wave passes, but is not carried along with it. 380. Transverse and longitudinal waves. An easy way of illus- trating wave motion is to fasten one end of a piece of rubber tubing about 20 feet long to a hook jmr^^* ^^^^ ^-^ in the wall. If we (11(10) - ^ ^^^^ ^Gl take the free end in FIG. 351. Waves in a rubber tube. the hand, we can, by a quick shake, send a wave along the tube (Fig. 351). If a single depression is sent along the tube to the fixed end, it is reflected and returns as an elevation ; in like manner a single elevation sent along the tube comes back as a de- pression. In the case of water waves and of the waves in a tube or cord, the particles of water or tubing oscillate up and down, while the disturbance moves horizontally. Such waves are called transverse waves. A second kind of wave motion takes place in substances such as gases and wire springs, which are elastic and com- SOUND 381 pressible. This kind of wave can be studied by letting a coil of wire represent the substance through which such waves are transmitted. Figure 352 represents a spring whose turns are large and are supported by threads. If we strike the spring at one end, we compress a few turns near that end. These move slightly and compress those just ahead, and WOK FIG. 352. Spring wave model. these in turn squeeze together the turns still farther along. Thus a pulse or wave goes along the spring. Next let one end of the spring be given a quick pull, so that the turns near by are drawn apart for an instant. Then the adjacent turns will be pulled over, one after another, until this disturbance reaches the other end. Thus it is seen that any push or pull given to the spring at one end is transmitted as a push or pull to the other end. Waves of this sort, in which the particles of the transmit- ting material move back and forth in the direction of the advance of the wave, are called compression or longitudinal waves. 381. Longitudinal vibration in solids. Not only springs, but gases and even solids like steel, transmit vibrations longi- tudinally. If we clamp a steel rod in the middle and rub it lengthwise with a cloth dusted with rosin, a clear, ringing sound may be produced. That the rod has been set in vibration longitudinally can be shown by a little 382 PRACTICAL PHYSICS FIG. 353. Ball driven from end of rod. ivory ball hung by a cord so as to rest against the end of the rod. When the rod is vibrating, the ball will swing violently out, as shown in figure 353. Another mechanical illustration of the method by which a push or pull may travel a long distance, although the individ- ual particles move only very minute distances, is shown in the following ex- periment : The apparatus shown in figure 354 consists of several glass-hard steel balls hung up in a line so that they just touch each other. If we pull aside the first ball and let it fly back and strike the line of balls, the ball it strikes does not seem to move, nor the next one. In fact none seem to be affected by the blow except the ball on the opposite end, which flies out about as far as the first ball fell. Since steel is very elastic, the impact of the first ball is handed along from ball to ball until it reaches the end one. It is as though a push were given to the first of a column of boys standing in line. It is transmitted along the line, and the last boy is pushed over. 382. Sound waves. We think of the air in sound waves as vibrating to and fro in the direction of propagation like the turns of the spring ; that is, sound waves are longi- tudinal or compression waves, made up of alternate condensations FIG. 354. Illustrating how sound travels from particle to particle. SOUND 383 rarefactions. Just as a stone thrown into a pool makes waves which spread out in ever widening concentric circles, so we think of a bell as sending out spherical waves. These are made up of alternate spherical shells of compressed and rare- fied air, traveling out in every direction through space. To form a picture of a sound wave traveling through a speaking tube, let us imagine that the spiral spring of the model (Fig. 352) is replaced by a column of air, which has a A n ffftffWtf^ FIG. 355. Diagram to show sound waves by a curve. tuning fork at one end, giving little pulses to the air column, while an eardrum at the other end receives these pulses (Fig. 355). The successive condensations and rarefactions of the air are indicated by c and r iii A. The disturbance travels from the fork to the air, but the intervening air at any point merely oscillates a very little to and fro. The curve in figure 355 is a graphical representation of these sound waves, in which the crests, 1-2,3-4, etc., represent conden- sations or compressions, and the troughs, 2-3, etc., represent rarefactions. The amplitude of the wave corresponds to the distance each particle of air moves to and fro from its origi- nal position. A sound wave includes a complete crest and trough, that is, a condensation and rarefaction, and the dis- tance between two corresponding points in any two adjacent waves is called the wave length. 384 PRACTICAL PHYSICS Since the same relation between velocity, wave length, and frequency holds for sound waves as for water waves, we can easily compute the length of a sound wave. Suppose a tuning fork is giving 256 vibrations each second, and that the velocity of sound is 1120 feet per second. Then the length of each wave is 1120 feet divided by 256, or about 4.4 feet. Or substituting in the wave equation, v= nl, 1120 = 256 I, 1 = 4.4 feet. To picture a sound wave spreading through the open air, we may imagine a great number of spiral springs radiating out from a common center at the source of the sound, all re- ceiving an impulse at the same time. PROBLEMS 1. An A tuning fork on the " international scale " makes 435 vibra- tions per second. What is the length of the sound wave given out? 2. A vibrating string gives out sound waves 2 feet long. What is the frequency of the waves? 3. The period of a sound wave is found to be 0.0025 seconds. What is the length of the wave ? 4. A bell whose frequency is 150 vibrations per second is sounded under water, in which sound travels at the rate of 4800 feet per second. Find the wave length produced by the bell. 5. If the highest tone which the ear can recognize makes 80,000 vi- brations per second, what is the shortest w-ave which the ear appreciates? 383. Intensity or loudness of sound. It must always be re- membered that when a bell is struck, the sound is heard in all directions, which means that sound waves spread out in all directions as shown in figure 356. As the distance from the source increases, the spherical waves spread out over more surface, and so the intensity of the sound decreases. For example, a bell 10 feet away will sound one fourth as loud as the same bell 5 feet away, and if 15 feet away, it sounds SOUND 385 one ninth as loud as when 5 feet away. This is because the energy of the wave must be imparted to nine times as many particles at a distance of 15 feet as at a distance of 5 feet. In general, the intensity of sound varies inversely as the square of the distance. If one ascends to a high altitude, as on a mountain top or in a balloon or aeroplane, the air becomes less dense and so not so good a carrier of sound. This makes it difficult to transmit sounds. In general, the intensity of sound depends on the density of the medium through which the sound is transmitted. 384. Speaking tubes and mega- phones. The speaking tubes used to connect rooms in buildings and ships serve to prevent the spread- ing out of sound waves in all di- rections, and SO the SOUnd is heard FIG. 356. Sound waves spread with almost its original intensity u ^ a11 directions from this at the distant point. Sharp bends in such tubes should be avoided, as they cause reflected waves, which run back. In the megaphone the sound waves which come from the mouth are not permitted by the walls of the instrument to spread out in all directions. In this way the energy of the voice is sent largely in one direction. 385. Reflection of sound. Just as any elastic body like a rubber ball bounds back when thrown against a brick wall, or a water wave is turned back by a stone enbankment, so a sound wave is turned back or reflected when it strikes against another body, such as a building, cliff, or wooded hillside, or even a cloud. The returning wave is called an echo. If the reflecting wall is near, as in a closed room, one may hear an echo almost at the same instant as the sound. This confuses 2c 386 PRACTICAL PHYSICS a hearer, and is an acoustical defect in the room. It can often be remedied by putting an absorbing material on the reflect- ing wall. When the reflecting surface is 25 or more yards dis- tant, the echo is distinct from the original sound, and excites interest and curiosity. The greater the distance, the longer is the time before the reflected wave strikes the ear, and there- fore the more distinct the echo becomes. When we have par- allel walls, as in a narrow canon, or objects at different distances, the echo is multiple or repeated, which means that the same sound is heard several times. For example, the roll of thunder results in part from the reflection of the sound from a suc- cession of mountains or clouds. The following experiment shows that sound waves, like light waves, are reflected by curved surfaces. If two large parabolic mirrors face each other, as in figure 357, a watch at the principal focus of one mirror can be distinctly heard across the room by hold- ing an ear trumpet at the focus of the other " FIG. 357. Sound of a watch reflected by mirrors. mirror. B FIG. 358. Curves to represent (A) noise and (B) music. In buildings with arched ceilings it is sometimes possible to hear a whisper at a ver}^ distant place in the room because the sound is reflected from the ceiling and concentrated at the ear of the listener. 386. Musical sounds and noises. We all recognize some sounds, such as the slamming of a door or the rumbling of a wagon over cobblestones, as noises; while we recognize the SOUND 387 sounds from a piano wire or an organ pipe as musical sounds or tones. The difference between these kinds of sounds can be best expressed by the curves in figure 358, where A is the curve of a noise, and B the curve of a musical note. It will be seen from these curves that a noise makes a very irregular and haphazard curve, while a musical note makes a uniform and regular curve. The latter produces an agree- able sensation on the ear, while the former makes a disa- greeable sensation. The great German scientist, Helmholtz, expressed this distinction by saying, " The sensation of a musical tone is due to a rapid periodic motion of a sounding body; the sensation of a noise to a non-periodic motion." 387. Three characteristics of a musical note. A musical sound or tone has intensity or loudness, pitch, and quality or timbre, and each of these characteristics depends upon some physical property of the sound wave. The intensity of a sound depends on the amplitude of the vibration; the pitch depends on the frequency of the waves; and the quality de- pends on the vibration form. 388. Intensity. We have already seen that the intensity of sound in general diminishes as the distance of the ear from the source of the sound increases and also as the density of the air diminishes. The intensity of a musical sound for a given ear and at a given distance depends on the amplitude of vibration of the waves sent out. For example, a piano string or a tuning fork gives a louder sound when struck hard than when struck gently. 389. Pitch. When we speak of a musical note as high or low, we refer to its pitch. When we strike the keys of a piano in succession, beginning at one end of the keyboard, we recognize the difference in the tones produced as a difference in pitch. By holding a card against the teeth of a rapidly revolving wheel (Fig. 359) we can show that the pitch of the note produced depends on the number of vibrations per second; that is, upon the frequency of the vibrations. 388 PRACTICAL PHYSICS We can show this very clearly by means of a siren. This is a metal disk (Fig. 360) with holes equally spaced around the edge, which can be rotated by some sort of whirling apparatus. If a current of air is directed through a tube against the holes, the regular succession of puffs produces a musical tone. As we in- crease the velocity of the wheel, the tone be- comes higher ; that is, its pitch is raised. One way to measure the frequency of vibration of a musical tone is by FIG. 359. The pitch varies means of such a rotating disk. Sup- pose the disk has 80 holes, and is at- tached to a motor making 1800 revolutions per minute. Since the disk makes 30 revolutions per second, there are 30 x 80^=2400 puffs per second. The fre- quency of the tone emitted would be 2400 vibrations per second. This would be a rather shrill note. A standard A tuning fork makes only 435 vibrations per second. 390. Limits of audibility. The lowest tone which the human ear can recognize as a musical tone has a frequency of about 16 vibrations per second. If the sound has a frequency above a certain number, the ear does not recognize it at all. This upper limit of audibility varies with differ- ent people from 20,000 to 40,000 vibrations per second. A young person can usually' Flo o caZe o 3 2. S2 ; 1 is oo *^ 2 22 ^ FIG. 371. Notes of an octave on piano keyboard. tions for middle A (second space on the treble cleff), and this makes middle C (the lower C on the treble cleff) 258.6. In physical laboratories C forks usually have a frequency of 256, to make the arithmetic easier. MUSICAL INSTRUMENTS 401. Piano. We are all familiar with the piano, or at least we have seen its keyboard, which usually has 88 keys. When we open the case, we find 88 wires of various lengths and sizes. Each key operates a little hammer which strikes a wire and thus produces a note of definite pitch. We may 398 PRACTICAL PHYSICS also notice that the notes of lower pitch are produced b^ long, large wires and the notes of higher pitch by short, thin wires. Perhaps we have watched a piano tuner loosen or tighten a wire by turning with a wrench a pin at one end. If we stretch a piece of steel wire along the table and set it vibrating, we find its tone is very weak compared to the tone of a piano. This is because the piano has a sounding board directly beneath the wires. The vibrations of the wires are transmitted through the frame to this large thin board, causing it to vibrate also. The board then sets a FIG. 372. A sonometer. larger quantity of air in vibration than the string could af- fect alone, and produces a louder tone. 402. Laws of vibrating strings. We may show by means of a so- nometer (Fig. 372), which is simply a metal wire stretched across a long wooden box, that the pitch or frequency of a wire is raised by tightening the wire. If we introduce a movable bridge or fret, the pitch is raised. The shorter we make the wire or string, the higher is the pitch. Finally we may show that a larger wire of the same length and under the same tension gives a lower note. Careful experiments of this sort have proved the following laws : (1) The vibration frequency varies inversely as the length of the vibrating string. For example, a wire under constant tension can have its pitch raised an octave by putting the movable bridge in the middle. (2) The vibration frequency varies directly as the square root of the tension. For example, if a pull of 4 pounds on a SOUND 399 string gives 100 vibrations per second, a pull of 16 pounds is required to raise the pitch an octave, or produce 200 vibrations per second. (3) The vibration frequency or pitch varies inversely as the square root of the weight per unit length of the string. For example, the wires on the piano which give the low notes are wound with wire, to get the necessary weight. 403. Other stringed instruments. The violin, mandolin, and guitar have sets of strings tuned to give certain notes, and wooden bodies to reenforce the tones of the strings. These instruments differ from the piano in that they have but few strings, and in that their strings are set in vibration by bow- ing or picking instead of by striking them with a hammer. Each string is made to give a large number of notes by pressing on it at various places and so changing its length. The particular place and manner in which the string is plucked or bowed determines the overtones and thus the quality of the tone. In this way the violin may be made to give tones with a wide range not only of pitch but also of quality. 404. Wind instruments. The simplest wind instrument is the organ pipe. Sometimes the tube is open at the upper end and is called an open pipe [Fig. 373 (J.)]; at other times the pipe is closed at the upper end and is called a closed pipe [Fig. 373 (.#)]. If we blow an open pipe, the current of air strikes against a sharp edge and is set in vibration. The tube acts as a resonator. The lowest note which such a pipe gives out is the one whose wave length is twice the length of the pipe. This note is called its fundamental. If we close the end of the tube with the hand, thus making a closed pipe, we shall find that the lowest note is an octave lower, or one whose wave length is four times the length of the pipe. This is called the fundamental note of the closed pipe. A B FIG. 373. Organ pipes: (A) open, and (B) closed. 400 PRACTICAL PHYSICS In general, then, the length of an open pipe is one half the wave length of its fundamental, and the length of a closed pipe is one quarter of a wave length of its fundamental. It will be noticed that the resonance tube in the experi- ment in section 393 is a closed pipe upside down, the tuning- fork end corresponding to the lip end of an organ pipe. When air is blown more violently into an organ pipe, overtones may be produced. The flute, clarinet, cornet, and trombone are also wind instru- ments. In the first two, the column of air is broken up by means of holes. The opening of a hole in the tube is equiva- lent to cutting the tube off at the hole. In the trombone the length of the air column can be varied by sliding a por- tion of the tube in and out. It is also possible to vary the notes by blowing harder and so getting overtones. In wind instruments of the bugle or cornet type, the vibra- tion of the air is caused by the vibrating lips of the musician. 405. Vibrating membranes. One example of this sort of musical instrument is the drum. Another is the most won- derful musical instrument of all, the human voice. It is pro- duced by the vibration of a pair of membranes on each side of the throat, called the vocal cords, and also by the vibration of the tongue and lips. By changing the muscular tension on the vocal cords one changes the pitch of his voice, and by changing the shape of the mouth, one changes the overtones, and so the quality of tone. PROBLEMS 1. An open pipe is 4 feet long. What wave length does it give? 2. What is the length of an open pipe which gives a tone an octave above that in problem 1 ? 3. A siren has 50 holes. How many revolutions per minute will it have to make to produce a tone whose frequency is 435 ? 4. A fork making 256 vibrations per second is reenforced by a tube of hydrogen 4 feet long. What is the velocity of sound in hydrogen? SOUND 401 5. Find the number of vibrations of a note three octaves below a note whose frequency is 264. 6. What is the fourth overtone of a string whose fundamental tone has a frequency of 256 ? 7. The keyboard of a piano has 7 octaves and 2 notes. If the lowest note is A 4 (27), what is the frequency of the highest note c"" ? 8. How long would an open organ pipe need to be to give the note middle A (international pitch) ? 9. How many centimeters long would the closed pipe of a whistle need to be to give middle C (international pitch) ? 406. The phonograph. The phonograph (Fig. 374), which was invented by Thomas Edison, is a remarkable machine FIG. 374. Cylinder form of phonograph and diaphragm with recording and reproducing points. for reproducing sound, especially music and speech. When the instrument is recording sound, the waves set a diaphragm vibrating, and this makes a fine metal or. sapphire point, which can move up and down, cut a spiral groove of varying depth in a wax cylinder. The bottom of this groove is a wavy line representing the condensations and rarefactions of the sound waves. To reproduce the sound a small round-ended needle is at- tached to the diaphragm and follows the groove in the wax as the cylinder turns. The varying depth of the groove moves the needle up and down and thus makes the diaphragm 2D 402 PRACTICAL PHYSICS vibrate in such a way as to reproduce the original sounds. In the machine shown in figure 374, the sharp and the round- ended points are both mounted near the center of the same diaphragm, as shown at the right. The diaphragm can be moved forward and back a little so that only one of these points touches the cylinder at any time. In another style of phonograph (Fig. 375) the wax is made in the form of a disk instead of a cylinder, and the FIG. 375. Disk form of phonograph and diaphragm. needle point vibrates from side to side instead of up and down. A phonograph does not reproduce the consonant sounds very distinctly, words being chiefly recognized by the vowel sounds which come out strong and clear. This is because the vowel sounds are more or less clearly defined musical tones, and produce regular vibrations, but the consonant sounds are noises produced by the mouth at the beginning arid end of vowel sounds. SUMMARY OF PRINCIPLES IN CHAPTER XX Sound, in physics, is a vibratory motion transmitted through air or other gases, liquids, or solids. Velocity of sound is about 1100 feet per second. SOUND 403 (Accurately it is 1087 ft./sec. at C, and it increases about 2 ft./sec. for each degree C rise.) Wave length = distance from crest to crest (or from condensation to condensation). Frequency = number of waves passing given point in one second. Velocity = frequency x wave length. Intensity or loudness depends on amplitude. Pitch (of musical tone) depends on frequency. Quality (of musical tone) depends on wave form ; i.e. on number and prominence of overtones. Pitch of a string (1) Rises when length is decreased, (2) Rises when tension is increased, (3) Is higher for small, light strings. Length of open pipe = i wave length of fundamental. Length of closed pipe = 1 wave length of fundamental. QUESTIONS 1. How can the pitch of the sound from a phonograph be raised ? 2. What causes a difference in the pitch of an organ pipe between a hot day in summer and a cold day in winter ? 3. How can a bugler produce notes of varying pitch on an instru- ment of unchanging length ? 4. Why is it better to bow a violin string near one end rather than in the middle ? 5. Is any difference in the quality of a violin tone noticeable when tne bow is moved nearer the finger board ? Why ? 6. How does the piano tuner go to work to tune a piano? 7. A distant band sounds much the same, except for loudness, as a band near by. What does this indicate about the velocity of sounds of different wave lengths ? 8. When an electric light bulb breaks, there is a loud crash. Ex- plain. 9. A man has two open organ pipes just alike. He saws off a little from the end of one. Explain what is heard when they are both sounded together. 10. How do the valves on a cornet operate to produce the different notes ? 404 PEACTICAL PHYSICS 11. There is an old saying that "if you can count three between a flash of lightning and its thunder clap, the storm is not dangerously near." According to this how far away must the thunder cloud be for safety ? 12. Explain just why the resonance experiment described in section 393 will not work if the length of the air column is half a wave length. 13. Explain how sound is produced by some form of automobile horn or signal in common use. CHAPTER XXI LIGHT: LAMPS AND REFLECTORS Illumination law of inverse squares standard lamps and " candle power " Bunsen photometer " foot candles " laws of regular reflection plane mirrors concave mirrors convex mirrors graphical construction of image size of image the mirror formula. 407. Problem of illumination. We have to do so much of our work and play by lamplight, that we ought to know something about illumination. Of course the first essential is to have enough light to see things distinctly. Further- more, experience shows that we may have enough light and yet not be able to distinguish the position and shape of objects well, because the lamps are not properly distributed to cast such shadows as we are accustomed to. Then there is the very difficult problem of getting lamplight which will give colored objects the same appearance which they have in daylight. Finally, we have to protect our eyes from the glare of the modern powerful electric and gas lamps, which are likely to give us too much light in spots. Besides these purely physical aspects of the problem of illumination, we have the economic question of its cost. 408. Some optical terms. We all know that we cannot see things in a perfectly dark room and that the something which enables us to see things is light. There are some objects, such as the sun, the stars, and lamps, which we can see because they are luminous, but almost everything that we 405 406 PRACTICAL PHYSICS see is visible because of the light which falls upon it and then comes from it to the eye. Such objects are illuminated. For example, we can see the pages of this book, if they are sufficiently illuminated, and if no obstacle is put between them and the eye. We know that light passes through some substances, like water, glass, and air, which are called transparent, and that practically no light gets through other substances, such as wood and iron, which are called opaque. Between transparent and opaque substances there is, how- ever, no sharp line ; for example, we ordinarily think of water as transparent, and yet in the depths of the ocean utter darkness prevails. On the other hand, some opaque substances transmit light if cut in thin enough sections ; for example, thin gold foil appears green when looked through. In general, light is in part turned back or reflected by sub- stances, in part transmitted, and in part absorbed. An object which absorbs all the light falling upon it is called black. 409. Light advances in straight lines. Everybody knows by experience that it is impossible to see around a corner. This is because light under ordinary cir- cumstances advances in straight lines. If we set up a screen S and a candle C, as shown in figure 376, with an opaque screen pierced by a pin hole in between, we see an inverted image of the flame. This shows that the light goes through the hole in straight lines. Simple " pinhole " cameras are sometimes made on this principle. FIG. 376. Light travels in straight lines. The precise measurement of angles by surveyors depends upon the fact that light comes from the distant object to the observer's instrument in straight lines. LIGHT: LAMPS AND REFLECTORS 407 FIG. 377. Shadow cast by the earth. Another consequence of this fact is the formation of a shadow when an opaque object obstructs the passage of light. The edge of the shadow is, however, a sharply denned tran- sition between light and dark, only when the source of light is very small. For ex- ample, the shadows cast by an arc lamp are more sharply defined than those V ^^ - Earth cast by a gas flame or a Welsbach mantle. This is also shown in the case of the shadow cast by the earth, as shown in figure 377. The region A is in the full shadow and is called the umbra, while in the region BB, on either side, the light grades off from full shadow to full illumination. This region is called the penumbra. When the moon happens to get wholly inside the umbra, we have what is called a total eclipse of the moon. When the moon is partly in the penumbra, the eclipse is partial. 410. Intensity of illumination : law of inverse squares. It scarcely needs to be stated that a book is more brilliantly illuminated when it is held near a lamp than when it is held far from the same lamp. In other words, the intensity of illumination, that is, the amount of light falling on a unit area, decreases when the distance increases. FIG. 378. Intensity decreases as the square of the distance. Let a sheet of metal which has in it a small pinhole P (Fig. 378) be set up in front of a flame, so that the source of light may be considered 408 PRACTICAL PHYSICS a point. Then, one foot away, let us put a piece of cardboard A which has a hole in it one inch square. At a distance of tivo feet from the pin- hole, we will put a screen B. It is evident that the light which passes through the inch hole in A is spread at B over a 2-inch square ; that is, over 4 square inches. If we move the screen B so that it is 3 feet from P, the light which passes through the inch hole at A is spread over a 3-inch square ; that is, over 9 square inches. The areas of these squares increase as the square of the distance. But the amount of light falling on each total area is the same. Therefore the amount on each square inch de- creases as the square of the distance. Intensity of illumination (like the intensity of sound and for the same reason) varies inversely as the square of the distance. This law assumes that the source of light is a point, and that the surface is placed at right angles to the rays of light. In all practical cases, however, the source of light is a surface or region, every point of which is giving light, and in such cases this law is only approximately true. When the receiving sur- face is inclined (Fig. 379), it FIG. 379. Surface not at right does not receive as much light per square inch as when held at right angles, and allowance has to be made for this fact. 411. Illuminating power of a lamp. In computing the amount of light received on a given area we have to con- sider not only the distance from the source, but also the illuminating power of the lamp itself. A room, for example, is much more brilliantly illuminated by a modern electric or gas lamp than by a kerosene lamp. Since there are now many different forms of lamps on the market, and every householder has to buy some kind of lamp, it is highly im- portant that we have some way of measuring the illuminat- ing power of a lamp. To do this we must have a standard lamp and some instrument for the comparison of lamps, that is, a photometer. LIGHT: LAMPS AND REFLECTORS 409 412. The standard lamp. Although many standard lamps have been proposed, none are altogether satisfactory. The oldest standard lamp, which is still used in calculation, but seldom in actual practice, is the English standard candle, which is a sperm candle made according to certain specifica- tions. The illuminating power of a horizontal beam from this candle is called a candle power. The present value of the candle power as used in the United States is that established by a set of standard incan- descent lamps maintained at the Bureau of Standards in Washington, D.C. This unit of intensity is called the international candle, and has been accepted by England and France. In Germany the legal unit of intensity is the Hefner, which is equal to 0.9 international candles. In testing gas, sperm candles are still used in routine work, although the intensity of so-called standard candles may vary by as much as 5 per cent. For more accurate work, the pentane lamp is coming into use. The Harcourt form of this lamp burns a mixture of air and pentane vapor and has an intensity of 10 candles. The ordinary open gas flame consumes from 5 cubic feet of gas per hour upward and gives from 15 to 25 candle power. In Massachusetts the legal standard for gas is that it shall give 15 candle power in a burner consuming 5 cubic feet an hour. The gas tested by the state in 1911 averaged 18.42 c. p. Welsbach lamps consume only about 3 cubic feet of gas per hour and give from 50 to 100 candle power. 413. Bunsen photometer. This is an instrument for com- paring the illuminating power of a beam from a given lamp with the illuminating power of a horizontal beam from a standard lamp. This " grease-spot " photometer was in- vented by the great German chemist, Robert Bunsen. It consists essentially of a white paper screen with a translucent spot in the center, which transmits light freely. The screen is placed between the lamps to be compared, so that one side is 410 PRACTICAL PHYSICS lighted by one lamp and one by the other. If the screen is lighted more on one side, that side appears bright with a dark spot in the center, while the other side is darker with a bright spot in the center. If the two sides are equally illu- minated, the spot disappears, or at least looks equally bright on each side. The arrangement of the Bunsen photometer T ft 1 I\ T ~T ~T~ D FIG. 380. Bunsen photometer. is shown in figure 380. The grease-spot screen is inclosed in a box, shown in figure 381, which is open at the ends A and B toward the lamps to be compared. The eye is held in front at E. Two mirrors, m 1 and m^ are placed on either side of the screen, as indicated in the figure, so that the two sides of the screen can be seen at the same time. FIG. 381. -Bunsen light box 414. Use of Bunsen photometer. The photometer must be used in a dark room or else in light-tight box. The lamp X to be tested is placed at one end of the photometer bar and the standard lamp S at the opposite end. The screen is then moved back and forth until a position is found where it is equally illuminated on both sides, and the distances A and B are measured. It is evident that if the distances A and B are equal, the candle powers of the two lamps are the same. If the dis- tances are not equal, the lamp which is farther from the screen LIGHT: LAMPS AND REFLECTORS 411 has the greater candle power. Furthermore, since the intensity of illumination decreases as the square of the distance, the candle powers of the two lamps are directly proportional to the squares of their distances from the screen. For example, and Let and Then so let 16 = candle power of lamp S, X = candle power of lamp X. 80 cm. = distance of screen from lamp S, 100 cm. distance of screen from lamp X, 16 (80) 2 X = 25 candle power. 415. Distribution of light. No lamp gives light uniformly in all directions. Thus in the ordinary kerosene lamp the burner and oil reservoir cut off the light which would be radiated downward from the flame, and if the flame is broad and thin, it will give more light broadside on than edgewise. Similarly an in- candescent lamp gives differ- ent intensities in different di- rections because of the shape of the filament. Since an incandescent lamp can be easily turr^d in any po- sition (Fig. 382), it is not dif- Fia ficult, with the Bunsen pho- tometer, to measure its candle power in various positions. If the candle power is measured for several points in a horizontal plane, and'the results of the tests averaged up, the result is called its mean horizontal candle power. Such tests show that the candle power in various directions in a horizontal plane does not vary very much. In a factory the lamp under test is rotated around a vertical axis at a speed of about 300 lamp 412 PRACTICAL PHYSICS FIG. 383. Curve to show vertical distribution. revolutions per minute, and the photometer reads directly the mean horizontal candle power of the lamp. A " 16 candle power lamp " means a lamp of which the mean horizontal intensity is 16 candles. If the lamp to be tested is tilted at various angles in a vertical plane, the results show that the lamp has very low candle power directly under the tip. The results of such tests may be best shown graphically by a diagram (Fig. 383). In this figure the inten- sity of the light in various directions in a vertical plane is indicated by the curve, which varies in its distance from the center of the concentric circles according to the intensity of the light. For example, the candle power directly under the tip of the bulb (0) is a little under 8, while horizontally (90) it is 16 candles. When it is desirable to throw as much light as pos- sible directly downward, some kind of a reflector or shade is used. Figure 384 shows the vertical distribution of light when the bulb is fitted with a special shade. From this curve it will be seen that the horizontal intensity is cut down to 6 candles, while the downward intensity runs over 50 candles. Such shades, made in a great variety of forms to give different desirable distributions, make it possible to work out scientifically the problem of lighting a given room or work shop efficiently. FIG. 384. Vertical distribution, when fitted with shade. LIGHT: LAMPS AND REFLECTORS 413 416. Measurement of intensity of illumination. We have just seen that the unit of intensity for a source of light is the international candle. The illumination which such a standard candle throws upon a surface placed one foot away and at right angles to the rays of light is called a foot candle. It is the unit of intensity of illumination. For example, a 16 candle-power lamp would illuminate a surface placed 1 foot from it with an intensity of 16 foot candles. Again if the lamp were a 32 candle power lamp and the object were 4 feet away, the intensity of illumination would be 32 divided by (4) 2 , or 2 foot candles. In these examples we have assumed that there is only one source of illumination and that the surface is perpendicular to the rays of light. In practice this is almost never the case, so that the problem of computing or measuring the in- tensity of illumination on any given surface is very difficult. One reason for this difficulty is that we have as yet no satis- factory simple instrument for measuring intensity of illu- mination directly. The amount of illumination needed to furnish " good light to see by " varies greatly with conditions. For example, drafting rooms, theater stages, and stores require about 4 foot candles ; while churches, residences, and public corridors may need but 1 foot candle. Excessive light is as undesirable as not enough. Exposed light sources of great brilliancy (more than 5 candle power per square inch) constitute a common source of eye trouble. To avoid this, electric bulbs should be frosted and distributed in small units, or covered with shades which diffuse the light, or else concealed entirely from view, in which case the illumination is obtained by light re- flected from the ceiling and walls. This indirect system of illumination gives by far the best light, especially for large rooms in public buildings, but costs more than other systems, and is to be regarded as a luxury. 414 PRACTICAL PHYSICS PROBLEMS 1. If the page of your book is sufficiently illuminated at a distance of 3 feet from an 8 candle power lamp, how many candle power will be needed when you move 2 feet farther away ? 2. If a photographic print can be made in 30 seconds when held 3 feet from a light, how long an exposure will be needed when the print is 6 feet away ? 3. A 4 candle power lamp is 120 centimeters from a screen. How far away must a 16 candle power lamp be to illuminate the screen equally? 4. In measuring the candle power of a lamp, a Hefner standard lamp (0.90 candle power) is 50 centimeters from the grease spot of a Bunsen photometer, and the lamp to be tested balances it when 150 centimeters from the grease spot. How many candle power has the lamp ? 5. Two lamps are 16 and 32 candle power respectively, and are 200 centimeters apart. Where between the lamps may a grease-spot pho- tometer screen be placed for its two sides to be equally illuminated ? 6. What is the illumination in foot candles on a surface 5 feet from an 80 candle power lamp ? 7. The necessary illumination for reading is about 2 foot candles. How far away may a 16 candle power lamp be placed? 8. If the lamp with the special shade described in section 415 were hung above a reading table, how high should it be hung ? (See curve of distribution, Fig. 384.) 9. Compare the cost of illumination with gas and electricity. A gas jet burning 5 cubic feet of gas per hour gives a flame of 18 candle power. The gas costs 85 cents per 1000 cubic feet. A 16 candle power lamp consumes 40 watts. Electricity is 10 cents per kilowatt hour. 417. Reflectors, regular and irregular. We have already said that we are able to see most objects about us by the light which they reflect to our eyes. The surface of visible objects is rough, and so the light striking the irregular surface is reflected in an irregular fashion, as shown in figure 385. This kind of reflection or turning back of the H g ht we cal1 diffused reflection. Thus the light striking a piece of paper or unvar- nished wood is scattered. If, however, light strikes a flat metallic surface so carefully polished that it is very smooth, LIGHT: LAMPS AND REFLECTORS 415 the light comes to the eye as though coming directly from a distant object, instead of from the reflecting surface. This is called regular reflection, and is illustrated in figure 386, where mm is the reflecting surface or mirror. The line OP in- dicates the direction of the light falling on the mirror and PE indicates the direction of the reflected light. 418. Law of reflection. When light comes through a small opening, the stream of light is called a beam. A narrow beam may be called a ray.* When a beam of light comes from a very distant source, such as the sun, the rays of which it is composed are parallel, and so it is called a parallel beam. In figure 386, let OP be the direction of a parallel beam striking the mirror mm obliquely, and PE that of the reflected beam. If a line nn, called the normal, is drawn perpendicular to the reflecting surface at the point P, the angle between the normal and the direction OP of the incident beam is called the angle of incidence, and the angle between the normal and the direction of the reflected beam is called the angle of reflection. Careful experiments have shown that, whatever the size of these angles, I. The incident ray, the normal, and the reflected ray lie in one plane. II. The angle of incidence is equal to the angle of reflection. 419. Images in a plane mirror. We all know that if one stands in front of a plane mirror, he sees his own image and that of the objects about him, as if FIG. 387. -Image in a plane the y were behind the irr or. In figure mirror. 387 we see that light coming from any FIG. 386. Regular re- flection from smooth surface. Object * A more accurate definition of a "ray " will be given in section 437 of the next chapter. 416 PRACTICAL PHYSICS point A of an object is reflected by the mirror to the eye as if coming from a point A' back of the mirror. Similarly, light coming from a group of points (an object AS) seems to come from a similar group of points (the image A B') back of the mirror. The group of points from which the light appears to come is called the image of the object. A line AA drawn from any point in the object to its corresponding point in the image is perpendicular to, and is bisected by, the mirror mm. In general, the image of an object in a plane mirror is the same size as the object, and as far behind the mirror as the object is in front. Indeed, such an image is so much like a real object that conjurors often make use of the illusions due to the invisibility of a well-polished mirror. It should, however, be remem- bered that the image is reversed from right to left, as is seen when a printed page is held in front of a mirror, so that in conjuror's tricks no letters or clock faces are allowed to be seen in mirrors. 420. Uses of plane mirrors. Good mirrors for household use are made of plate glass backed by a thin coating of silver or mercury. Only a very small fraction of the light is reflected from the front surface of the glass; the rest is reflected from the metal back. Large plate-glass mirrors are sometimes placed in the walls of public places to give the impres- sion of spaciousness. In scien- tific instruments a very small FIG. 388. -Sextant used to meas- mirror ften attached to a ro _ ure angles. tating part, such as the coil 01 a galvanometer. Such a mirror will turn a reflected beam of light through twice the angle through which the mirror itself is turned. A rotating mirror, M, is an essential part of the LIGHT: LAMPS AND REFLECTORS 417 sextant which the mariner uses to get the altitude of the sun. By means of a heliostat, which is simply a plane mirror turned by clockwork so as to keep up with the sun, the sun's rays may be reflected into a room, through an opening in the wall, for projection purposes. 421. Curved mirrors. A curved mirror is usually spheri- cal ; that is, it is a portion of the surface of a sphere. If it is a portion of the outer surface, it is ^ -^ called a convex mirror ; if it is a por- tion of the inner surface, it is called a f concave mirror. The center of the j sphere, of which the curved mirror \ is a portion, is called the center of cur- vature ((7 in Fig. 389). The line CM ^^_ connecting the middle of the mirror FIG. 389. Center of a curved M with the center of curvature Q is mirror, called the principal axis. Any other straight line through the center of curvature, such as OS, is called a secondary axis. It will be noted that any axis is perpendicular to the reflecting surface. 422. Principal focus. When a beam of light parallel to the principal axis strikes a concave mirror, the rays are so reflected as to pass through, or very close to, a single point (.Fin Fig. 390). This point is called the principal focus of the mirror. It may be defined as that point where all rays parallel FIG. 390. Concave mirror converges par- fo and near the principal axis allel rays. /., /, , . meet after reflection. The principal focus is located halfway between the mirror and its center of curvature. Suppose the ray QP in figure 391, parallel to the axis AB, strikes the mirror at the point P and is reflected back in the direction PF, so as to 2E 418 PRACTICAL PHYSICS make the angle of incidence i equal to the angle of reflection r. Since QP and AB are parallel lines, the angle i is equal to the angle a. There- fore the angle a must be equal to the angle r, and CF = PF. But when P is near 0, PF is nearly equal to FO, which means that F is about midway between C and 0. It can be proved that the principal focus which is very close to F is exactly halfway between C and 0. FIG. 391. Location of principal focus. A FIG. 392. Aberration in spherical concave mirror. The distance from the princi- pal focus to the mirror is called the focal length of the mirror and is one half the radius of curvature. All the rays parallel to the principal axis of a concave spherical mirror do not meet exactly at the same point after reflection. This failure of the rays to converge accu- rately at a point is called sp^ericaLaber- ration. This imperfection is slight when only a small portion of a sphere is used as a mirror. Spherical aber- ration in a large mirror is shown in figure 392, where it will be observed that only the central rays are reflected through the focus F, while the rays which strike the mirror near the edge are bent decidedly to the right of F. It is sometimes necessary, as in the case of a searchlight, to take the diver- gent rays of an arc lamp and reflect them all in one direction. This can be done roughly with a concave spherical mirror, by putting the arc at the prin- cipal focus ; for then the rays travel the same paths as above, but in the opposite FIG. 393-Paraboiic direction. To avoid spherical aberra- mirror. tion, however, a parabolic mirror (Fig. 393) \ \ A y LIGHT: LAMPS AND REFLECTORS 419 is generally used. These mirrors are also used in the head- lights of locomotives and automobiles. 423. Applications of concave mirrors. The ophthalmoscope is a concave mirror with a little hole in its center. With this instrument a physician is able to reflect light from a lamp into a patient's eye, and at the same time to look through the hole into the eye thus illuminated. . FIG. 394. Reflecting telescope. A certain type of telescope, called a reflecting telescope, con- sists of a long tube with a concave mirror mn at one end, which forms an image of a distant object. The only pur- pose of the tube is to support near its open end an eyepiece or magnifying glass, E, through which the image can be advantageously examined. In a compound microscope the light from a window or lamp is concentrated upon the small object to be examined by means of a concave mirror. We have already stated that concave mirrors are extensively used in searchlights and headlights. 424. Convex mirror. When a beam of light parallel to the principal axis strikes a convex mirror, the rays are reflected as if they came from a point behind the mirror. This is shown in figure 395, where is the center of curvature and F is the point from which the reflected rays diverge. The point F is called a virtual focus because the rays do not FIG. 395. Convex mirror and virtual focus. 420 PRACTICAL PHYSICS actually pass through it, but simply look as if they had come from it. In the case of the concave mirror the rays do ac- tually pass through the point F, as shown by the fact that a large concave mirror of short focal length causes so great a concentration of the sun's radiant energy that paper and wood may be ignited if placed at F. Such a focus is a real focus. 425. Construction of images. It is possible to learn a great deal about the position and size of images formed by mirrors, by carefully constructing dia- grams to show the paths of the rays of light. Suppose mn in figure 396 is a convex mirror, and AB an object. Let us draw A C, a ray normal to the mirror. This ray will be reflected directly back on itself. Again let us draw AL par- allel to the principal axis. This ray FIG. 396. Image in a convex mirror. . , a , , .. ., ,. will be reflected as if it came from F. The image point of A will be where these two reflected rays cross ; that is, at A f . Another ray from A that might be used in this construction is the ray through F. It would be reflected parallel to the axis and would also pass through A'. This construction shows that the image in a convex mirror always seems to be behind the mirror and smaller than the object. It is erect and is nearer the mirror than the object is. It is always a virtual image. Thus one sees a virtual image of his face in a polished ball. It is always right side up and of small size. Suppose MON (Fig. 397) is a concave mirror, of which C is the center of curvature. Let AB be an object which is placed beyond the center of curvature. To determine the position of the image, let us trace two rays from A. The point A', where they intersect after reflection, is 397> _ Construction of im in con . cave m j rror< LIGHT: LAMPS AND REFLECTORS 421 the image of A. If AN is one such ray passing through C, it will hit the mirror perpendicularly and be reflected back along the line .ZVC. If the other ray from A is AM, parallel to the axis, it will be reflected so as to pass through the focus F. Since B is on the axis, its image B' will also be on the axis ; so that the image of the arrow AB will be the arrow A'B'. Another ray from A that might be used in this construction is the ray through F. It would be reflected parallel to the axis arid would also pass through A'. It will be seen that when the object is beyond the center of curvature, the image is inverted and in front of the mirror. Since the rays of light from A really do pass through A f , the image is real. 426. image. FIG. 398. To get the size of a real image. Size of a real Let us draw the rays AO and OA' (Fig. 398). From the law of reflection, the angle of in- cidence i is equal to the angle of reflection r. Therefore, the right triangles A OB and A! OB' are similar, and their cor- responding sides are in proportion. That is, AB BO A'B 1 ~~ B' 0' flhe The size of the image is to the size ojihe object as the distance of the image from, the mirror is to the distance of the object from the mirror. ' 427. Conjugate foci. We have seen that when A is the object point, the image point is at A' . But figure 397 shows that if A! is the object point, the image point is at A ; for the rays will travel the same paths in the other direction. For example, if a candle were put at AB, an inverted smaller image would be formed on a screen placed at A B' ; also if the candle were put at AB', the image would be inverted, larger, and located at AB. 422 PRACTICAL PHYSICS FIG. 399. -Construction of virtual image in concave mirror. Two points, so situated that light from one is concentrated at the other, are called conjugate foci. For example, B and B' are two such points and therefore are conjugate foci. 428. Virtual image in a concave mirror. We have just seen that when the object is beyond the center of curvature, the image is between the principal focus F and the center of curvature C. Also when the object is between F and (7, the image is beyond C. In both these cases, the image is real ; that is, the image is always real when the ob- ject is outside the principal focus F. When, however, the ob- ject is placed inside the prin- cipal focus, that is, between F and M, as shown in figure 399, the image is behind the mirror, erect, enlarged, and virtual. To show this we may, as before, trace two rays from the point A, one parallel to the axis, which is reflected through F, and the other perpen- dicular to the mirror, which is reflected back on itself through C. They will diverge after reflection and must be produced backward to find the point of intersection A'. The image A' is a virtual image, because the light from A does not actually pass through A'. 429. Size of a virtual image. Since every ray from A (Fig. 400) is re- flected so as to seem to come from A', the ray from A to M, the middle of the mirror, will be reflected in the direction A 1 MO. Since the angles of FlG< incidence and reflection are equal, Angle AMB = angle BMC. But A' MB' and BMC are vertical angles and equal. So Angle AMB= angle A' MB' . LIGHT: LAMPS AND REFLECTORS 423 Therefore the right triangles AMB and A! MB 1 are similar, and A'B' B'M AB " BM' So in this case, as before, the size of the image is to the size of the object, as the distance of the image from the mirror is to the distance of the object from the mirror. 430. The mirror formula. Let be an object on the axis, OM any ray from meeting the mirror at M. Draw the radius CM and , T a j FIG. 401. Real image in concave mirror. construct the reflected ray MI, making angle OMG= angle OMI. Then Jis the image of 0. Since CM is the bisector of the angle OMI, it follows that IM 1C' Let TN=D l} and ON=D . When the aperture, that is, the angle MON, is small, we have the approximate relations OM=ON=D , and IM=IN=D l . Now, since FN=f, 00= ON- CN=D - 2f, IC = CN-IN=2f-D l . Substituting these values in the proportion (1), we have A 2 /- and so D l f+ D f= D D^. Dividing by D x A X/, we have JL + 1,^1 Do D, f where D Q = distance of object from mirror, D l = distance of image from mirror, f= focal length of mirror. 424 PRACTICAL PHYSICS Stated in words 1 1 Object distance Image distance Focal length This equation gives a relation between the distance of the object, the distance of the image, and the focal length. If any two of these three quantities are known, the third can be calculated. It can be proved that this equation holds as it stands for all cases of images either real or virtual, formed in a concave mirror. If the value of D L comes out negative, for certain values of D and /, as it will when D is less than /, the meaning is that the image is behind the mirror; that is, the image is virtual. It can be shown that it holds also for con- vex mirrors, if the focal length / of a convex mirror is regarded as negative. In the next chapter we shall see that the same formula holds for lenses. PROBLEMS 1. If a ray of light strikes a plane mirror so that the angle between the ray and the mirror is 25, what is the angle between the incident and reflected rays ? 2. If the mirror in problem 1 is turned 1, so that the angle between the incident ray and the mirror becomes 26, through how many degrees has the reflected ray been turned V 3. An object is placed 15 inches from a concave mirror whose radius of curvature is 12 inches. How far from the mirror is the image ? Is it real or virtual, erect or inverted? 4. If the object in problem 3 is 4.5 inches long, how long is the image ? 5. An object is placed 12 inches from a concave mirror whose focal length is 8 inches. How far from the mirror is the image ? Is it real or virtual, erect or inverted ? 6. If the object in problem 5 is 2 inches long, how long is the image? 7. An arrow 1 inch long is placed 4 inches from a concave mirror whose radius of curvature is 12 inches. Find the position, length, and nature of the image. LIGHT: LAMPS AND REFLECTORS 425 8. If the image of a candle flame, placed 10 inches from a concave mirror, is formed distinctly on a screen 30 inches from the mirror, what is the radius of curvature ? 9. How far from a concave mirror, whose focal length is 2 feet, must a man stand to see an erect image of his face twice its natural size? 10. Where must an object be placed to form, in a concave mirror whose focal length is 10 inches, a real image one half as long as the object ? SUMMARY OF PRINCIPLES IN CHAPTER XXI Intensity of illumination varies inversely as the square of the distance. Candle powers of lamps giving equal illumination are directly proportional to the squares of their distances from screen. (That is, lamp farther away is more powerful.) Unit intensity of illumination, or foot candle, is illumination due to a one candle power lamp one foot away. (Desirable intensity from 1 to 4 foot candles.) In regular reflection: I. Incident, normal, and reflected rays all in one plane. II. Angle of reflection = angle of incidence. Plane mirror: Image always behind mirror, erect, virtual, same size as object, and at same distance from mirror as object. Principal focus of curved mirror (either concave or convex), Defined as convergence point for rays parallel to axis of mirror. Located halfway between mirror and center of curvature. Concave mirror : If object is outside focus, image is also outside focus, and center of curvature is between object and image. Image is inverted and real. If object is inside focus, image is behind mirror, erect and virtual. Convex mirror : Image always behind mirror, erect and virtual. 426 PRACTICAL PHYSICS Mirror formula (holds for both concave and convex mirrors) : Object distance Image distance Focal length For concave mirror, focal length is positive. For convex mirror, focal length is negative. For real image in front of mirror, image distance comes out positive. For virtual image behind mirror, image distance comes out negative. Size rule (holds for both concave and convex mirrors) : Length of image _^ image distance (from mirror) Length of object object distance (from mirror) QUESTIONS 1. What is the difference between 16 candle power and 16 foot candles ? 2. Explain how a Welsbach gas lamp consuming only 3 cubic feet of gas per hour gives over 50 candle power, while the ordinary gas jet uses 5 er more cubic feet per hour and gives only about 18 candle power. 3. If light from a very distant object, such as the sun, falls on a concave mirror, where is the image formed? 4. How does the curve of a parabola differ from the arc of a circle? 5. How does the action of a parabolic mirror differ from that of a concave spherical mirror. 6. What is the danger in too great intensity of illumination? 7. Explain how the image of a man standing in front of a plane mirror, which is tilted so as to make an angle of 45 with the floor, appears horizontal. 8. A person looking into a mirror sees a very small image of his face upside down. What kind of mirror is it ? 9. Show by a diagram how a tailor arranges two mirrors so that a customer can see the back of his coat. 10. A room 20 feet square has plane mirrors on opposite walls. A man in the room holds a candle close to his head. Where should he stand so as to be as near as possible to the twice reflected image of the candle in the mirrors? 11. Why is an image in a plane mirror reversed from right to left, but not up and down ? CHAPTER XXII LENSES AND OPTICAL INSTRUMENTS Refraction law of refraction velocity of light wave fronts explanation of refraction index of refraction as ratio of speeds total reflection prism lens lens for- mula size rule defects of lenses. Camera projecting lantern moving pictures eye de- fects of eye magnifying glass microscope telescope erecting telescope opera glass prism binocular. 431. Optical instruments. The human eye is the most common and at the same time one of the most remarkable optical instruments known. Human eyes are often imper- fect in various ways, and have to be " corrected," or rather aided in their work; for defective eyes themselves are seldom changed by spectacles or eyeglasses. These, too, we shall study in this chapter. Even a healthy eye has its limitations, and many optical instruments have been devised to help it to see things too far away or too small for ordinary vision. And finally, there are many devices, such as cameras, stereop- ticons, and moving-picture machines, that enable us to see things far away from, or long after, their actual occurrence. All these devices for enabling us to see better, farther, or at a different time are called optical instruments. In all of them we find lenses, and in some of them also prisms. To understand how optical instruments work, we must first study the passage of light through lenses and prisms; that is, the refraction of light. 432. Refraction in water. When a stick stands obliquely in water, it appears to be broken at the surface of the water in such a way that the part under water seems to be bent 427 428 PRACTICAL PHYSICS upward (Fig. 402). The bottom of a tank of water always appears to be nearer the surface than it really is. A fish appears to be higher in the water than it actually is, so that if one wishes to spear it, he must aim under its image. All these phe- nomena are due to the re- fraction of the light as it passes from water into air. We have said that light FIG. 402. Stick partly in water appears j . . T, -,. broken, advances in straight lines, but this is only true in a single substance. In general, when light goes from one substance into another of different density, it is bent or refracted at the dividing surface. 433. Law of refraction. To measure how much a beam of light is bent in pass- ing from water into air, we may perform the following experiment. We will set a board vertically in a jar of water and fasten a wire of solder with pins along the board (Fig. 403). If we fill the jar with water, and then look down along the wire, we see that the part under water appears to be bent upward. If we bend the part that is out of water, until the whole wire seems to be straight, we have a model to show the path of the light in air and water. We may now remove the board from the water and draw the water line and the perpendicular COD (Fig. 404). From this experiment we see that a beam of light in pass- ing from water into air is bent away from the perpendicular. FIG. 403. Light is bent when leaving water obliquely. FIG. 404. Diagram of ex- periment of figure 403. LENSES AND OPTICAL INSTRUMENTS 429 It might also be shown that a beam of light in passing from air into water, in the direction BO, is bent in the direc- tion OA (Fig. 404). That is, a beam of light in passing from air into water is bent toward the perpendicular. In this case the line B represents the incident ray and the line OA the refracted ray. The angle ( COB) between the incident ray and the normal is called the angle of incidence, and the angle ( A OD) between the refracted ray and the normal is called the angle of refraction. When light passes from air into water, the angle of incidence is greater than the angle of refraction. To show the relation between the angles of incidence and refraction, we will lay off equal distances on the incident and refracted rays (AO BO), and draw perpendiculars to the normal (AD and BO). We shall find that, whatever the angle of incidence, the line BO is always a definite number of times greater than AD. For example, in this case BO might be 4 inches, while AD might be 3 inches, and then the ratio BO/ AD is | or 1.33. This ratio is called the index of refraction. Experiments show that this ratio is always the same for the same two substances, no matter what the angle of incidence may be. This ratio may also be expressed in terms of the " sines "of the angles of incidence and refraction. Sine is the name used in trigonometry for the ratio of the opposite side to the hypotenuse ; thus the sine of the angle of incidence (i) is BC /BO and the sine of the angle of refraction (r) is AD/AO. Since AO = BO by construction, S ! neof /* = E A C ' BO = * = index of refraction, sine of Zr AD/AO AD 434. Refraction of light by glass. We may also show that a beam of light is refracted in passing from air into glass. Let a block of glass of semicircular shape be attached to an optical disk, as shown in figure 405. It will be seen that part of the ray is re- flected by the glass as if it were a mirror, and part is refracted as it 430 PRACTICAL PHYSICS passes into the glass. It will also be seen that the angle of incidence is equal to the angle of reflection, but is greater than the angle of re- fraction. We may measure the perpendicular distances from the ends of the incident and refracted rays to the normal 00, and compute the index of refraction for glass and air. Ordinary crown glass bends a ray of light less that is, has a smaller index of refraction than glass made with lead, known as flint glass. The lead glass, which is denser, has an index of refrac- tion with respect to air of about 1.7, while that of crown glass and air is about 1.5. FIG. 405. Ray is partly reflected, partly refracted. In general, light is bent in passing obliquely from one substance into another, as from water to glass, diamond to air, or even from vacuum to air or from a layer of air of one density to one of another. Thus light is refracted in pass- ing through the rising column of warm air over a stove, and things seem to shimmer or dance about. The general rule is that the lesser angle is in the denser medium. 435. Some effects of refraction. An interesting case of refraction of light occurs in the atmos- phere surrounding the earth. The air extends only a few miles above the surface of the earth, thinning out as it goes, and beyond is empty space. So when a ray of sunlight (Fig. 406) comes through ths air obliquely, it is bent gradually toward the normal in passing from one layer to another; the result is that the eye at sees the sun in the direction of the dotted line in the figure, FIG. 406. Refraction by the earth's atmosphere. LENSES AND OPTICAL INSTRUMENTS 431 instead of in its real position. For this reason the heavenly bodies rise somewhat earlier and set somewhat later than they would if this were not the case. This makes the day some 7 or 8 minutes longer. 436. Speed of light through space. The reason for the refraction of light was not understood until the velocity of light in different substances had been determined. Indeed, up to 1675 it was believed that light traveled instantaneously ; that is, that light consumed no time in its passage between two points. About that time Roemer, a young Danish Ez FIG. 407. Illustrating Roemer's way of measuring speed of light. astronomer at the Paris Observatory, was observing the moons of Jupiter. With great precision he observed just when one of the satellites M (Fig. 407) passed into the shadow cast by Jupiter, J. The beginnings of these successive eclipses of Jupiter's satellite may be thought of as signals flashed at equal intervals. When the earth is traveling away from Jupiter, the interval between signals is greater than the true interval because the light from each succeed- ing signal has a greater distance to travel to reach the earth. But when we are traveling toward Jupiter, the interval between signals is less than the true interval, because the light from each succeeding signal has a shorter distance to travel to reach the earth. Thus while the earth is travel- ing from A to B, the observed times of the eclipses are delayed more and more, and when the earth has reached B, the total 432 PRACTICAL PHYSICS delay has amounted to 16 minutes and 36 seconds (about 1000 seconds). This means that it takes about 1000 seconds for the light to travel across the earth's orbit, a distance of 186,000,000 miles. Therefore the velocity of light is 186,000 miles per second (300,000 kilometers per second). In recent years the velocity of light has been directly measured on the earth's surface by several methods, and while the measurements have been made with great precision, the results agree very closely with those obtained so long ago by Roemer. This velocity is so enormous that it is not strange that the earlier experimenters could not determine it. In fact, it takes only 0.001 of a second for light to travel as far as one can see on the earth. Light travels a very little more slowly in air than in a vacuum. In denser substances, such as water and glass, light travels much more slowly. 437. Light waves. Just as we think of sound as transmitted from a source through the air by a series of waves, so we think of light as transmitted through space by a series of ether waves. When the light comes from a point source, the "crest" or wave front of a wave, as it spreads in all direc- tions with equal velocity, is spherical, and the direction of advance, being radial, is at right angles to the wave front. Figure 408 (a) represents such a series of expanding waves, in which the curved lines are the wave fronts and the lines of arrows indicate the direction of advance of a small section of the wave front. These lines of advance of light are what were called rays in the last chapter. A bundle of light rays FIG. 408. Wave fronts. LENSES AND OPTICAL INSTRUMENTS 433 is a beam. In a " parallel beam " [Fig. 408 (5)] the wave fronts are plane and the rays are parallel. By means of a lens or curved mirror a beam of light may be made to converge toward a point, called the focus. In this case the wave fronts are concave spherical surfaces which contract as they approach the focus, as shown in fig- ure 408 0). 438. Why light is refracted. When a beam of light passes from air into water, there is a change in its velocity. To see that this must cause a bending of the beam, let the parallel lines in figure 409 represent wave fronts advancing in the direction of the arrows. As soon as the edge B of a wave front enters the water, it begins to advance slowly, while the part A, which is still in the air, ad- vances with the same speed as be- fore. Consequently the direction of the wave front is changed into the position CD, and the beam is bent into a direction nearer the per- pendicular PR. This is somewhat analogous to a column of soldiers -march- ing from a smooth, hard field into a rough, plowed field, where they are slowed up. The man at B hits the rough ground before the man at A does, and so, while A travels the distance AC, B has gone a shorter distance BD. The result is that if B cannot hurry, and if A does not slow up, the column swings around from its original direction into one nearer the perpendicular PR. 439. Speed of light and index of refraction. From figure 409 it will be seen that the amount which the beam of light is refracted when passing from air into water depends upon the relation between the distances AC and BD\ that is, upon FIG. 409. Refraction of oblique waves. 434 PRACTICAL PHYSICS the relation between the speed of light in air and its speed in water. Although it is not easy to measure the speed of light in water, yet it has been done. The speed in water has thus been proved to be about three fourths that in air. This means that the speed of light in air is 1.33 times the speed in water, which is the same number that we found for the index of refraction of water and air. It can be shown that in general Index of refraction-- -?*** in air speed in other substance We may prove this as follows : Index of refraction = ?HLi (see section 433). sinr But f is equal to the angle ABC, and sin ABC = AC/BC; also r is equal to the angle BCD, and sin BCD - BD/BC. Therefore, srni = AC I EC = AC = speed in air = index of refracfcion> sin r BD/BC BD speed in water 440. Sometimes no change in direction. When a stick stands vertically in water, it does not appear to be bent, because when a beam of light leaves a substance such as water perpendicular to the surface, it suffers no refraction. The change in velocity is, of course, just the same whether the light leaves the substance normally to the surface or obliquely, but bending or refraction occurs only when the light leavas obliquely. 441. Total reflection. We have seen in section 432 that when a beam of light passes obliquely from water or glass into air, the refracted ray is bent away from the perpendicu- lar. For example, in figure 410 the light coming from a point under water, in the direction oa, is refracted in the direction aa r ; the ray ob is refracted along W and oc is re- fracted along cc' . As the angle in the water increases, we come finally to a ray od which is refracted along dd f , and LENSES AND OPTICAL INSTRUMENTS 435 just grazes the surface of the water, formed between the ray od and the normal NM is called the Critical angle. For water and air ifisabout 49. If this angle is exceeded, as in the case of The angle which is the ray oe, the ray cannot leave j===5f|l the water at all, but is totally : reflected at e, just as if it had fallen on a polished metal sur- ^- - -#- face, and takes the direction ee'. FIG. 410. Total reflection of light by The critical angle is the angle in the denser medium which must not be exceeded if the ray is to get out. To illustrate total re- flection, we may hold a tumbler containing water and a spoon above the eye, and look up at the surface of the water. A very bright image of the part of the spoon in the water will be seen FIG. 411. - Refraction and reflection of light by water. bv total reflection . If the apparatus shown in figure 411 is available, the paths of various refracted and re- flected rays, including some that are totally reflected, can be studied with great ease. In optical instruments it is frequently necessary to have a very perfect reflector, and for this purpose a right-angle prism with polished sides is used. Let a ray of light A strike the side XZ of such a prism (Fig. 412) at right angles. It suffers no refrac- tion, but passes on through the glass to B FIG. 412. Total re- flection of light by right-angle prism. on the side YZ, where it makes an angle of 45 with the 436 PRACTICAL PHYSICS n normal mn. But the critical angle for crown glass is about 42 ; therefore the ray AB does not emerge from the glass, but is totally reflected in the direction BO. It then strikes the face XY perpendicularly and emerges without refraction. The result is that the ray is bent 90, as if there had been a plane mirror at TZ. 442. Refraction by plate with paral- lel sides. When a ray of light {AB, in figure 413) passes through a glass plate with parallel faces, such as a good window pane, it is refracted at B towards the normal N, and at C away from the normal M. The result is that the ray CD is parallel to the ray AB. Consequently when we look at Fia. 413. Path of ray through plate glass. any object through a glass plate, we see it slightly displaced in position, but otherwise unchanged. When the plate is thin, this change of position is too slight to attract attention. 443. Refraction by a prism. When a ray XY enters one side of a prism (yU?<7, in figure 414), it is bent in the direction YZ, and on emerging, it is again bent in the direction ZW. Thus the ray XO is bent out of its original course to X 1 W. The total change of direction is measured by the angle XOX', called the angle of de- viation. Any substance which has two plane refracting surfaces inclined to each other is a prism. The angle A is called the refracting angle of the prism. The path of a ray of light through a prism can be worked out by drawing a diagram, like figure 404, at iFand again at Z. It should be remembered that the beam is always bent toward the thicker part of a prism. B o FIG. 414. Refraction of light by a prism. LENSES AND OPTICAL INSTRUMENTS 437 PROBLEMS (The student should have a small protractor.) 1. If the angle of incidence of a ray of light passing from air into glass is 68, and the angle of refraction is 36, find by construction the index of refraction. 2. If the index of refraction for air and water is 1.33, and the larger angle is 60, find by construction the smaller angle. 3. Taking the index of refraction as 1.33, find by construction the critical angle for water. 4. If the critical angle for crown glass is 42, find by construction the index of refraction. 5. Assuming the velocity of light in air to be about 186,000 miles per second and the index of refraction of flint glass to be 1.6, compute the velocity of light in flint glass. 6. The angles of a prism are 20, 70, and 90. A ray of light enters normally the face bounded by the angles 90 and 70. The glass has a critical angle of 42. Prove that the ray will be twice reflected before it leaves the prism. 444. Lenses, convergent and divergent. A lens is a piece of glass, or other transparent substance, with polished spher^ Double Conv.ex PlcCin Convex FIG. 415. Converging lenses. ical surfaces. A straight line drawn through the centers C l and (7 2 (Fig. 415) of the two spherical surfaces is called the principal axis of the lens. Lenses are divided into two classes, converging or " thin- edged " lenses (Fig. 415), and diverging or " thick-edged " lenses (Fig. 416). A converging lens is thinner at the edge than in the center. A common type of this class is the 438 PRACTICAL PHYSICS double convex lens. A diverging lens is thicker at the edge than at the center. The double concave lens is a common Double Concave FIG. 416. Diverging lenses. Plane Concave Diverging Meniscus lens of this class. It should be remembered that when a ray of light passes through a lens, it is always bent, just as in a prism, towards the thicker part of the lens. 445. Action of converging lens. Suppose a converging lens is held so that the sunlight comes to it along its principal axis (Fig. 417). The rays of light will be so re- FIG. 417. Focus of convex leiis. fracted as to converge at a point F on the axis. If a piece of paper is held at F, a small but very bright image of the sun is formed and the paper is quickly charred.' The thicker the lens, the nearer the point F is to the lens, as shown in figure 418. The point F, where rays parallel to the principal axis converge, is called the principal focus of the lens. The dis- tance from the lens to the principal focus is called the focal length, /, of the lens. Since an incident ray and its corre- FIG. 418. Focal length of * thick and thin lenses. sponding refracted ray are reversible, it follows that a light, placed at the principal focus F, would send its rays through the lens in such a way as to come out parallel. LENSES AND OPTICAL INSTRUMENTS 439 446. How a lens is made. The surface of a lens is shaped by grinding together the glass and an iron matrix with every possible variety of sliding motion. The glass and the matrix are thus brought automatically to an almost perfect spher- ical shape. The polishing is done by using finer and finer grinding materials in succession (usually powdered emery or carborundum), ending with rouge. In the later stages the matrix is lined with a layer of stiff pitch with cross grooves cut in its surfaces to hold the rouge. 447. Conjugate foci. When the light from an object on the principal axis passes through a double convex lens, the rays, after leaving the glass, converge at a point I. Two such points, and 7, are called conjugate foci, for if the object were z) Q oo placed at J, the image FIG. 1u9.- image of distant object is at *\ would be at 0. If the point is not on the principal axis, the line joining and 1 passes through the center of the lens, called its optical center, and the line is called a secondary axis. When the lens is thin, the same formula holds as was used for mirrors (section 430). -L+l =1 i>o A / where D = distance of object from lens, Dj= distance of image from lens, f= focal length of lens. 448. Discussion of the lens formula. If the object is so far away that the rays from any point of it to different parts of the lens are practically parallel, the image is formed at F '; for D is very large, and so is nearly zero; this leads to o D I= f, as shown in figure 419. 440 PRACTICAL PHYSICS If the object is brought nearer the lens, the image moves farther away from the lens. When D = 2/, D 7 = 2/also, as shown in figure 420. -Do=2f FIG. 420. Image at same distance as object. Do=f FIG. 421. Object at F, rays emerge parallel. If the object is brought still nearer the lens, the image moves still farther away from the lens, until, when the object is at the principal focus F, the distance of the image becomes infinitely great, and the rays that go out from the lens are parallel, as shown in figure 42?1. If the object is brought even nearer the lens, the rays on the farther side diverge as if they came from a focus I behind the lens (Fig. 422). In this case, the formula shows that D/is negative. This means that the image is behind the lens. For divergent lenses r the same formula can be used, if the focal length f is regarded as negative. 449. Images formed by FlG - 422 - ~ Object inside F, image vir- lenses. The geometrical construction of images formed by lenses will indicate the size and position of these images. The method of procedure is the same as that used for spherical mirrors (section 425). If we trace two rays from any point of the object to their intersection, we have the position of the corresponding point of the image. For example, in figure 423, a ray from A parallel to the principal axis must, after refraction by the LENSES AND OPTICAL INSTRUMENTS 441 lens, pass through the principal focus F. An- other ray from A, passing through the center of lens, is undeviated. The point A 1 where these rays meet is the image point of A. Then from similar triangles it is readily seen that FIG. 423. Size of real image. Length of image _ distance of image from lens Length of object distance of object from lens The ratio of the length of the image to the length of the object is called the linear magnification. In figure 423 the object AB was beyond the principal focus of ".0,^. A' ^ ne convex lens, '^--^ Le ^ s and the image A'B 1 is inverted, real, and in this case smaller than the object. In figure 424 the object AB is between the prin- cipal focus F virtual, and larger, Lens ,--?' Virtual Image FIG. 424. Size of virtual image. and the lens. The image A'B 1 is erect, and can only be seen by looking through the lens. In figure 425 the lens is concave and the image is erect, virtual, and smaller. In all these cases it will be seen that straight lines drawn from the extremities of the object through the center of the lens pass through the extremities of the image, and FIG. 425. Virtual image formed therefore the diameters or lengths by concave lens. 442 PRACTICAL PHYSICS of object and image are to each other as their respective dis< tances from the center of the lens, as stated in the formula above. 450. Defects of images formed by lenses. In figure 423 it was assumed that the real image A' B 1 was a straight line. But it will be seen that the point A of the object is at a greater distance from the center of the lens than the point B, and, therefore, according to the lens equation, B f ought to be farther from the center of the lens than A'. In other words, the image is curved. This means that if a cam- era is equipped with a simple convex lens, and the center of the plate is sharply focused, the edges will be fuzzy, since the image does not lie in one plane. This is especially notice- able for a large object comparatively close to the lens. In the construction of figure 423 it was assumed that all the rays coming from a point in the object are accurately re- fracted by the lens to one point. But as a matter of fact the rays that strike the outer portions of a lens are refracted more strongly than the rays which fall on the central portion of the lens, and so come to a focus nearer to the lens. This lack of exact concurrence is called spherical aberration. The effects of spherical aberration are to make the image indistinct and to distort its shape. If the outer rays are cut out by means of a diaphragm or stop, the sharpness of the image is improved, but at the same time its brightness is diminished. In large lenses, such as those used in telescopes, the outer portions are so ground that their refracting power is diminished by the proper amount to insure distinct images. This whole geometrical theory of lenses applies only to very thin lenses, and to cases where the light may be assumed to pass through the lens in a direction not greatly inclined to the axis of the lens. In practice, combinations of lenses are nearly always used instead of simple lenses, and these com- binations are designed so that the imperfections of one lens are compensated or balanced by the imperfections of another lens. LENSES AND OPTICAL INSTRUMENTS 443 PROBLEMS 1. A convex lens has a focal length of 16 centimeters. Find the posi- tion and nature of the images formed when objects are placed 10 meters, 50 centimeters, and 10 centimeters respectively from the lens. 2. If an object is placed 32 centimeters from the lens described in problem 1, how far is the image from the lens? 3. A lamp placed 60 centimeters from a lens forms a distinct image on a screen 20 centimeters away on the other side. Find the focal length of the lens. OPTICAL INSTRUMENTS 451. Photographic camera. The simplest form of camera consists of a light-tight box (Fig. 426) with a converging lens at one end, so mounted as to form an image of an outside object upon a sensitive plate. This plate consists of a silver compound spread on a glass plate or celluloid sheet (film). The light is allowed to pass through the lens for a time which varies from a thousandth of a second up to several minutes, according to the lens, the brightness of the object to be photographed, and the " speed" of the sensitive plate. The image on the plate is not visible until the plate is placed in a mixture of chemicals called a "developer." To obviate the spherical aberration of a single lens a diaphragm is put in front of the lens so as to limit the size of the pencil of light. With a small opening, or " stop," we get great sharpness in the picture, but must expose it for a longer time. A " combination lens," with the diaphragm between the two lenses (Fig. 427), is used to take clear pictures FIG. 426. A simple camera. Fia. 427. Combina- tion lens for rapid work. 444 PRACTICAL PHYSICS FIG. 428. Projecting lantern. of a rapidly moving object. Since the plate on which the image is formed must be in the position which is the conjugate focus of the position occupied by the object, the camera is usually made with a bellows so that it can be " focused " on ob- jects at varying dis- tances. 452. Projecting lan- tern. The projecting lantern, or stereopticon, "si is used to throw an image of a brilliantly illuminated object or picture upon a screen. It consists essentially of a powerful source of light, such as an electric arc A (Fig. 428), the condensing lenses (7, which converge the light through the slide or transparent picture &, and the front lens or objective Z, which forms a real image of the picture on the screen S r . It will be noticed that the lantern is much like the camera except that the object and image have been interchanged. Since the screen is usually at a considerable distance, the slide $ is only a little beyond the principal focus of the objective L. It is very important to have a powerful light source which is small in size. For this purpose electric arcs, calcium lights, acetylene lights, and electric glow lamps, in which the filament is coiled into a small space, are sometimes used. Figure 429 shows the arrangement of the lantern to project opaque pictures, such as post cards. FIG. 429. Projection of opaque objects. LENSES AND OPTICAL INSTRUMENTS 445 The moving-picture machine, which is now so common, is a projecting lantern designed to show lifelike motion. A series of photographs is taken with a camera provided with a shutter which automatically opens and shuts about 12 times a second. A long narrow film moves a little while the shutter is closed, but remains stationary while it is open. Each of such a series of pictures differs slightly from the preceding one, if anything is moving in the field of the camera. Then this series of pictures is thrown on the screen at the same rate as that at which they were taken. The sensation produced by one picture re- mains until the next picture appears, so that we are not aware of any interruption be- tween the pictures. 453. The eye. The human eye (Fig- 430) is essentially a little camera, with a lens system in front, and a sensi- tive film, made of nerve fibers, . i i i FIG. 430. Section of the human eye. at the back. It has the great advantage over any other camera in that it can take a continual succession of pictures all on the same film, '" developing " them by some unknown chemical or electrical process in the nerve fibers instantaneously, and transmitting the results equally instantaneously over a " private wire " (the optic nerve) to " headquarters " (the brain). The structure of the eye is shown in figure 430. There is an outer horny membrane, the cornea, holding a watery fluid called the aqueous humor. There are also an adjustable diaphragm, or " stop,'' called the iris, and a crystalline lens. The latter is of somewhat higher index of refraction than either the aqueous humor in front or a similar fluid, the vitre- 446 PRACTICAL PHYSICS ous humor, behind. At the back is the nerve layer or retina, which acts as the sensitive film. It should be noticed that most of the converging power of the eye comes, not in the lens, but at the front surface of the cornea. This explains why we can never see objects distinctly when swimming under water. The aqueous fluid and the water outside are so much alike that there is no longer any refraction of the light as it strikes the cornea, and the lens by itself is not powerful enough to bring the light to a sharp focus on the retina. 454. Focusing the eye. If an object is moved nearer a camera, the distance between the plate and lens must be increased, or else a lens of greater convexity, that is, of shorter focus, must be substituted, if the picture is to be sharp. Of these two possibilities, the eye chooses the sec- ond. It adapts itself to varying distances, not by moving the retina, but by changing the focal length of the lens. When the muscles of the eye are relaxed, the lens is usually of such a shape as to focus clearly on the retina objects which are at a considerable distance. When one wishes to look at near objects, a ring of muscle around the crystalline lens causes the lens to become more convex, so as to form a distinct image on the retina. It is often said that objects are seen most distinctly when held about 10 inches (25 centimeters) from the eye. This simply means that 10 inches is about as near as one can usually focus an object distinctly, and since the shortest distance gives the largest image, this is where we automatically hold an object when we want to see its details. 455. Imperfections of the eye. In the short-sighted eye the image of a distant object is formed in front of the retina (at A, in figure 431). This may be due to too great con- vexity in the crystalline lens, or to the oval shape of the eye- ball. A person who is short-sighted must bring objects close to the eye to see them distinctly. LENSES AND OPTICAL INSTRUMENTS 447 In the far-sighted eye the image of an object at an ordinary distance would be formed behind the retina (at B, in figure 432). This is because the crystalline lens is too flat, or the FIG. 431. Short-sighted eye. FIG. 432. Far-sighted eye. length of the eyeball is too short. To see distinctly, such a person must hold objects at a distance. Spectacles with concave lenses are used to correct short-sighted eyes, and convex lenses are used for far-sighted eyes. Another defect of the eye is astig- matism, which occurs when the leris of the eye, or the cornea, does not have truly spherical surfaces. The effect is that a spot of light, like a star, is seen as a short, bright line. In a case of astigmatism all the lines in such a diagram as figure 433 will not appear equally distinct. Those in one direc- tion will be sharply defined, while FIG. 433. Lines to test as- those at right angles to them will ap- pear broadened and blurred. This defect is corrected by the use of cylindrical lenses. 456. Apparent distance and size. The apparent size of an object depends on the size of the image formed on the retina, and consequently on the visual angle. From figure 434 it is evident that this angle increases as the object is brought nearer the eye. FIG. 434. The visual angle. For example, when we look along a railroad track, the rails seem to come nearer together as their distance from us 448 PRACTICAL PHYSICS increases. The image of a man 100 yards away is one tenth as large as the image of the same man when he is 10 yards off. We do not actually interpret the larger image and larger visual angle as meaning a larger man, because by ex- perience we have learned to take into account the known distance of an object in estimating its size. Distant objects seen in clear mountain air often seem nearer than they really are. This is because we see the ob- jects more clearly and distinguish the details more sharply; and this often leads us to think that they are smaller than they really are. The moon, on the other hand, seems bigger when near the horizon, because we can compare it with ob- jects whose size we know. It is only by long experience that we learn to estimate the actual size and distance of objects. 457. The simple microscope or magnifying glass. We have said, in section 454, that the distance of most distinct vision is about 10 inches. If an object is placed at a greater distance than this, the image on the retina is smaller and the details of the object are not seen so distinctly. If the object is placed nearer than _... .^-"^ this, the image on the retina is blurred. When an object is examined by a magnifying glass, the distance between the lens and the object is made less than the focal length, FIG. 435. Magnifying glass. ^ -, . j , i and so adjusted that an erect enlarged virtual image is formed about 10 inches away (Fig. 435). The magnifying power of a simple microscope is the ratio of the size of the image to the size of the object. This is equal to the distance of the image divided by the dis- tance of the object, that is, 10/Z> , D being the distance of the object (in inches) from the lens. Thus if a magnifying glass can be held 1 inch from an insect, the magnification will be 10 diameters. LENSES AND OPTICAL INSTRUMENTS 449 458. Compound microscope. Very small objects are made visible by the compound microscope. It consists of two lenses or lens systems which are placed at the ends of a tube. The object AB is put just outside the principal focus of the smaller lens L (Fig. 436), called the objective, which forms an enlarged, real image CD. This real image is then ex- FIG. 436. Compound microscope. amined through the eyepiece E, which acts like a magnifying glass, giving a still larger virtual image at C'D', about 10 inches from the eye. The image CD is magnified as many times as its distance from the lens L is greater than the focal length of that lens. Usually the distance of CD from L is about 150 millimeters, and so, if the lens has a focal length of 5 millimeters, the 450 PRACTICAL PHYSICS image CD is 30 times as long as the object AB. If the eye- piece still further magnifies the image 10 times, the magni- fying power of the combination is 10 x 30, or 300 diameters. Microscopes which magnify as much as 2500 diameters are sometimes used. We are indebted to the microscope for many of our most valuable discoveries about the structure and life of plants and animals, about the smallest living things, and about the causes of disease. 459. The telescope. The telescope enables us to see clearly objects so far away that we could not otherwise see their Fia. 437. Astronomical telescope. details. The simpler sort, called the astronomical telescope, consists of two lenses or lens systems, the large objective (Fig. 437) and the eyepiece E. The inverted real image J, formed by the lens 0, is much smaller than the object, but it is brought so near to the observer that it can be exam- ined through the eyepiece E, which acts like a magnifying glass. The two lenses are mounted in an extension tube so that the eyepiece can be drawn farther from the objective when objects near at hand are to be examined. Since the magnifying glass or eyepiece (Joes not reinvert, the observer sees things upside down, just as he does in a microscope. LENSES AND OPTICAL INSTRUMENTS 451 It can be shown that the magnifying power of an astronomi- cal telescope is equal to the number of times the focal length of the eyepiece is contained in the focal length of the object glass. 460. The erecting telescope or spyglass. This instrument (Fig. 438 ) is like the astronomical telescope except that an additional converging lens or lens system L is introduced between the object glass and the eyepiece E. This lens L inverts the image T, forming another real image at I 1 ; FIG. 438. Erecting telescope or spyglass. then this erect image I' is magnified by the eyepiece, which forms an enlarged, erect, virtual image I". In the ordinary spyglass the eyepiece is a combination of two lenses, which act like a single magnifying glass. The introduction of the erecting lens L lengthens the telescope tube considerably. 461. Telescope used for sighting. A gun cannot be sighted with the greatest possible accuracy if its sights are pins or pointed projections. This is because it is impossible to focus the eye both on the sights and on a distant object at the same time. For example, the best that can be done with the naked eye at a distance of 100 yards is subject to error of one or two inches. Therefore many of the best long- range rifles are provided with telescopic sights. Similarly, surveyors make use of the telescope in their " transits " and 452 PRACTICAL PHYSICS FIG. 439. Surveyor's level. "levels." In all such cases two very fine wires or spider lines are stretched across the telescope in the plane where the image of the distant object is formed by the object glass, and the intersection of these two cross hairs is made to coincide with the image of any given point of the object. When this adjustment is made, a line drawn from the point of intersection of the cross hairs through the center of the object glass passes through the given point of the object. 462. The opera glass and field glass. The opera glass (Fig. 440) is a telescope whose eyepiece is a di- verging or concave lens. Since the eye- piece has approximately the same focal length as the eye of the observer, its effect is practipally to neutralize the lens of the eye. So we may consider that the object glass forms its image directly on the ret- ina. The field of view of the opera glass is small, and so the opera glass is usually made to magnify only three or four times. But it has the advantage of being compact and gives an erect image. Galileo made a telescope on this plan which magnified about 30 diameters and enabled him to make some exceedingly important dis- coveries. A large-sized opera glass is usually called a field glass. 463. The prism field glass or binocular. An instrument, called a binocular, has come into use in recent years which has the wide FIG. 440. Opera glass PUPIL OF EYE LENS OF EYE LENSES AND OPTICAL INSTRUMENTS 453 FIG. 441. Prism binocular. field of view of the spyglass and at the same time the com- pactness of the opera glass. This compactness is obtained by causing the light to pass back and forth between two reflect- ing prisms, as shown in figure 441. This device enables the focal length of the object glass to be three times as great as in the ordinary field glass for the same length of tube, and so the magnifying power is correspond- ingly increased. Furthermore, the reflections in the two prisms secure an erect image with- out using the erect- ing lens of the ordinary terrestrial telescope; for one double reflection tips the image right side up, and the other shifts right and left, thus restoring it completely to its natural position. PROBLEMS 1. When a camera is focused on an automobile 100 yards away, the plate is 8 inches from the lens. How much must the distance between the lens and the plate be changed when the automobile is only 10 yards away? Must the distance be shortened or lengthened? 2. A 5 inch post card is to be projected on a screen 20 feet away so as to be 5 feet long. Find the focal length of the lens required. 3. A photographer with a " 12 inch lens " wants to make a full-length picture of a 6 foot man standing 10 feet from the lens. How near the lens must the plate be placed ? 4. How long a plate must be used in problem 3 ? 5. How near to an object must a hand magnifier of 1.2 inches focal length be held to magnify it 6 diameters? 6. A reading glass of 5 inches focal length is held 4 inches from a printed page. How much does it magnify? 7. It is necessary to project a slide 3 inches wide on a wall 40 feet 454 PRACTICAL PHYSICS distant, so that the picture shall be 10 feet wide. What must be the focal length of the objective of the lantern ? 8. In a compound microscope the objective lens L (Fig. 436) has a focal length of one inch and the object AB is 1.1 inches away. How far from the lens is the image CZ>? How many times is it magnified? If the eyepiece magnifies this image 20 times, what is the magnifying power of the instrument ? 9. A telescope has an objective whose focal length is 30 feet, and an eyepiece whose focal length is 1 inch. How many diameters does it magnify ? 10. The focal length of the great lens at the Yerkes Observatory is about 60 feet and its diameter 40 inches. The eyepiece has a focal length of 0.25 inches. Calculate its magnifying power. SUMMARY OF PRINCIPLES IN CHAPTER XXII Refraction occurs when light passes obliquely from one substance to another. Smaller angle is always in denser medium. sine of larger angle Index of refraction = - > sine of smaller angle speed in rarer medium speed in denser medium Velocity of light = 186,000 miles per second, = 3 X 10 10 centimeters per second. Critical angle is smaller angle, when larger angle is 90. Prism bends light toward thick edge. Convergent (thin edged) lens bends light inward. Divergent (thick edged) lens bends light outward. Principal focus denned as convergence point for rays parallel to axis. Lens formula: Holds for both converging and diverging lenses: Object distance image distance focal length LENSES AND OPTICAL INSTRUMENTS 455 For convergent lens, focal length is positive. For divergent lens, focal length is negative. For real image, beyond lens from object, image distance comes out positive. For virtual image, on same side of lens as object, image distance comes out negative. Size rule : Holds for both converging and diverging lenses : Length of image _ image distance Length of object object distance QUESTIONS 1. Which people would be likely to become short-sighted early, those who live much out of doors or those who stay much indoors? 2. Compare the eye, part by part, with the camera. 3. How does a " wide-angle " lens differ from a long- focus lens? 4. What are the defects of a pinhole camera ? 5. What is the difference between a refracting and a reflecting telescope ? 6. Prism glass, with a section like that shown in figure 442, is often used for the upper part of shop windows and doors and for windows facing on narrow courts. Why? 7. Why is it necessary to build powerful telescopes very wide as well as very long ? 8. Why must a compound microscope be so accu- rately focused on the object? 9. Why is it best to have your light for writing or sewing come from over your left shoulder? 10. Explain how the wheels of moving vehicles in a moving picture sometimes seem to be rotating backwards. 11. What part do the condensing lenses play in the ttoaofplmteol action of a stereopticon ? prism glass. CHAPTER XXIII SPECTRA AND COLOR Prism spectrum achromatic lenses spectroscope types of spectra spectrum analysis Fraunhofer lines wave length of light colors of objects colors of thin films infra-red and ultra-violet electromagnetic theory. 464. Analysis of light by prism. If we let a beam of sunlight pass through a narrow slit into a dark room, and put a glass prism in its path (Fig. 443), the beam of light is refracted. If we put a white screen in the path of the re- fracted light, a band of colors is formed. In this band are red, yellow, green, blue, and violet, though there are no sharp lines of division between them. This colored band, which shades off gradually from red to violet, is called a spectrum. This shows that the ordinary white light of the sun is complex and contains different kinds of light. The light which is refracted least, the eye recognizes as red, and that which is most refracted, as violet. It will be shown later that the physical property of light which determines this difference in refrangibility is the wave length. To show that the prism itself did not produce the different colors, but simply separated various kinds of light already present in the beam of sunlight, Sir Isaac Newton placed a second prism in the spectrum, so that only violet light fell on it. He found that the violet light was again refracted, but that there was no further change in color. 456 FIG. 443. Light decomposed by prism. SPECTRA AND COLOR 457 He also found that when these dispersed or spread out, colored lights were brought together by a converging lens (Fig. 444), white light was the result. 465. Achromatic lenses. When sunlight passes through an ordinary double convex lens made of a single FlG ^_ Com]iinins spectral colors into piece of glass, the light is white light, refracted and converges at a point called the focus. But the light is also dispersed, just as in a prism, and the focus for red light (72, in figure 445) is at a greater distance from the lens than that for violet light (F). Such a single lens cannot give a sharp image of an object illuminated by ordinary white light, for all the lines of separation between light FIG. 445. Dispersion produced by a lens, and dark portions of the image will be colored. This defect, which is known as chromatic aberration, may be remedied by combining a lens of crown glass with a lens of flint glass, as shown in figure 446. By carefully designing the two component lenses which are in contact, it is possible to make achromatic lenses, which produce the necessary refraction without dis- persion. The two parts of small achromatic lenses are cemented to- gether with Canada balsam. 466. Spectroscope. In the spec- trum produced by a prism the different colors overlap each other to some extent. This can be remedied by using a, Converging Diverging FIG. 446. Achromatic lenses. 458 PRACTICAL PHYSICS spectroscope. There are four main parts in a spectroscope (Fig. 447): the collimator, which has a slit at one end and a convex lens at the other ; a prism, commonly of flint glass ; a telescope, which has an object glass and eyepiece, and a scale tube, which has a ruled scale at one end and a lens at the other. In the collimator the slit is at the principal focus of the lens, and so light diverging from the slit.is made parallel by the lens before it reaches the prism. Here it is refracted and dis- persed, each color going off as a parallel beam in its own FIG. 447. Spectroscope. direction. The telescope forms a sharply denned image of the spectrum. The scale tube, which is added to locate the parts of the spectrum, is so mounted that the light from the illuminated scale is reflected from the second face of the prism into the telescope along with the spectrum. 467. Kinds of spectra. The spectrum of sunlight, or solar spectrum, is frequently seen in summer time after a shower in the form of a rainbow. The sunlight is refracted and dis- persed by the raindrops. When the solar spectrum is studied carefully with a spectroscope, it is found not to be a contin- uous band of colors, but to be crossed by many vertical dark lines. Since these lines were first studied by a German astronomer, Fraunhofer, they are known as Fraunhofer lines. Not all sources of white light give these dark lines. For SPECTRA AND COLOR 459 example, an electric arc lamp, an incandescent lamp with a car- bon filament, an ordinary gas flame which contains many par- ticles of incandescent solid carbon (soot), and indeed all incandescent solids give continuous spectra. The spectrum of an incandescent vapor or gas is quite different. It is what is called a bright-line spectrum, and is characteristic of the substance used. If we dip a platinum wire or bit of asbestos into a solution of common salt (sodium chloride) and hold it in a blue Bunsen flame, we get a bright yellow flame. If we examine this flame with a spectroscope, we see a bright yellow line which occupies the position of the yellow part of the spectrum. This yellow light comes from the incandescent sodium vapor. If we repeat the experiment with a wire dipped in a chemical, called lithium chloride, we get a red flame, which gives in the spectroscope two bands, one yellow and one red. Calcium chloride also gives two bands, green and red. (The yellow band, which is likely to be seen also, is due to sodium present as an impurity.) 468. Spectrum analysis. When the spectroscope is used to examine the spectrum of other gaseous substances, it is found that each element has its own characteristic spectrum. It may be simple as in the case of sodium, or it may be com- plex as in the case of iron vapor, which has more than four hundred lines. Since a very small quantity of a substance will show its characteristic spectrum lines (for example, less than one millionth of a milligram of sodium can be detected), we have a very delicate method of analyzing substances. Spectrum analysis was first used by the chemist Bunsen in 1859. 469. Absorption spectra. Kirchhoff (1824-1887), while a professor of physics at Heidelberg, worked conjointly with Bunsen in these investigations with the spectroscope. Kirch- hoff observed that when he held an alcohol flame colored with common salt in front of the slit of the spectroscope and allowed a beam of sunlight to pass through the slit, the sodium line became especially dark and sharp, although he had expected it to be especially bright. He concluded that the 460 PRACTICAL PHYSICS sunlight had been in part absorbed by the yellow sodium flame and that the special part had been removed which the sodium flame itself ordinarily gives out. This fact was generalized by Kirchhoff in the following law : A glowing gas absorbs from the rays of a hot light-source those rays which it itself sends forth. The demonstration of Kirchhoff's law may be conveniently performed with the apparatus shown in figure 448. The source of light L is the glowing positive carbon of the electric are, whose rays are made parallel by a lens O. Two strips of asbestos board, soaked in salt water, are FIG. 448. Absorption of light by sodium vapor. heated by a wing top Bunsen burner. The light from the electric arc passes directly through the sodium flame into a "direct-vision" spectro- scope which disperses the light on the screen Sc. First we set the sodium flame burner to one side, and produce a con- tinuous pure spectrum on the screen. Then we bring the sodium flame into position, and we see in the yel low portion of the spectrum a dark line. If we cover the lens with an opaque cardboard, of course the spec- trum disappears, but in the place of the dark line we now have the bright sodium line. Finally, if we place a small white screen with a narrow slit where the dark line is located just in front of the screen Sc, the dark line on the screen Sc shows as a yellow line. This shows that the dark absorption band is not absolutely black, but is so much less intense than the direct radiation from the arc that it ap- pears black by contrast. SPECTRA AND COLOR 461 It is evident, then, that to produce Hack absorption lines the absorbing vapor must be colder than the luminous source. 470. Meaning of Fraunhofer lines. We have said in sec- tion 467 that the solar spectrum contains a large number of dark lines. Kirchhoff concluded that these dark lines were caused by the presence in the glowing solar atmosphere of those substances which themselves produce bright lines in the same positions. The core of the sun is at a very high temperature and gives forth a continuous spectrum. But this core is surrounded by a layer of gas which is cooler and absorbs those light rays which it itself would send out. On this basis he concluded that such metals as iron, magnesium, copper, zinc, and nickel exist as vapors in the solar atmos- phere. After much study he found that the bright-line spectra of all the elements on the earth correspond in position to certain Fraunhofer lines, and concluded that all the ele- ments found on the earth exist in the atmosphere of the sun. There were certain other Fraunhofer lines whose elements were not known on the earth in Kirchhoff's time. One of these new elements, helium, has since been found on the earth, and perhaps the others also will sometime be found. Kirchhoff's explanation of the Fraunhofer lines was epoch making. Helmholtz said, "It has excited the admiration and stimulated the fancy of men as hardly any other dis- covery has done, because it has permitted an insight into worlds that seemed forever veiled to us." 471. The nature of light. We have said that light is con- sidered to be a vibration of the ether. That is, light and heat are both forms of radiant energy. But we must not think that this has always been the accepted theory. To be sure, the great Dutch physicist, Huygens (1629-1695), worked out very completely the wave theory, but his rival, Sir Isaac Newton, in England, maintained the older corpuscular theory, according to which light consists of streams of very minute particles, or corpuscles, projected with enormous velocity 462 PRACTICAL PHYSICS from all luminous bodies. Newton's reputation as a scientist was so great that his unfortunate corpuscular theory con- trolled scientific thought for more than a hundred years, and it was not until the beginning of the nineteenth century that the experiments of Thomas Young in England and of Fresnel in France placed the wave theory on a firm basis. 472. Different colors due to different wave lengths. It is now possible to measure directly the length of the waves of light of different colors, and to show that the waves of red light are longest and those of violet are shortest. So in the dispersion of sunlight by a prism, it is the long waves (red) I which are refracted least, and the short waves (violet) which are refracted most. The following table gives the approxi- mate wave lengths of some of the colors. WAVE LENGTHS OF LIGHT Red, 0.000068 cm. Green, 0.000052 cm. Orange, 0.000065 cm. Blue, 0.000046 cm. Yellow, 0.000058 cm. Violet, 0.000040 cm. 473. Colors of objects. The color of any object depends (1) on the light which illuminates it, and (2) on the light it reflects or transmits to the eye. A skein of red yarn held in the red end of the spectrum appears red. But when held in the blue end of the spectrum, it appears nearly black. Similarly a skein of blue yarn appears nearly black in all parts of the spectrum except the blue, where it has its proper color. Another striking experiment is to illuminate an assortment of bril- liantly colored worsteds or paper flowers by the light from a sodium flame. This light contains but one group of wave lengths. Those wor- steds which reflect these wave lengths look bright, while those which do not reflect them look dark. They all look either yellow or dark. Thus it appears that when a piece of paper looks white in daylight, it is because it reflects all wave lengths equally, and when a piece of cloth looks red in daylight, it is because it reflects only those long waves which produce red light. If the white paper receives only waves of red light, it appears SPECTRA AND COLOR 463 red, and if the red cloth receives only waves which have no red in them, it appears dark. That is, the color of an opaque object depends on the wave length of the light it reflects. The Cooper-Hewitt mercury vapor lamp is a very efficient electric lamp, but it cannot be used in places when colors must be distinguished, for it does not furnish waves of red light. If we place a piece of red glass in the path of the light which is dispersed by a prism to form a spectrum, we see only the red portion of the spectrum. This shows that all the wave lengths except the long red ones have been absorbed. In a similar way a green glass lets the green light through, but greatly reduces the other parts of the spectrum. If we insert both the green and the red glasses, the spectrum almost completely vanishes. Thus we see that the color of a transparent object depends on the wave length of the light it transmits. Ordinary red glass, such as photographers use for their red lanterns, transmits freely only red light, and absorbs almost completely the yellow, green, blue, and violet light, which especially affect the chemical compounds used on photo- graphic plates. 474. Mixing colors and mixing pig- ments. ' There are other colors besides white which do not have a definite wave length. A mixture of several wave lengths may produce the same sensation as a single wave length. Let us rotate a disk part red and part green (Fig. 449) so rapidly that the effect on the eye is the same as though the colors came to the eye simultaneously. The revolving disk appears yel- low, much like the yellow of the spectrum. By mixing red and blue we get purple, which is not found in the spectrum. By mixing black with red or orange or yellow we get the various shades of brown. The colors of the spectrum are called pure colors and the others compound colors. If yellow light is mixed with just FIG. 449. Newton's color disk. 464 PRACTICAL PHYSICS the right tint of blue, white light is produced. Such colors are called complementary colors. Let us pulverize a piece of yellow crayon and a piece of blue crayon. If we mix the two together about half and half, the color of the resulting mixture is bright green. This shows that while mixing yellow and blue light pro- duces white, mixing yellow and blue pigments produces green. This is because the yellow pig- ment absorbs or subtracts from white light all except yellow and green, and the blue pigment sub- tracts all except blue and green, therefore the only color not ab- sorbed by one pigment or the other is green. In other words, in mixing pigments, the color of the mixture is that which escapes absorp- tion by the different ingredients. 475. Colors of thin films. The brilliant colors produced by the reflection of light from thin transparent films, like the film of a soap bubble, furnishes one of the strongest arguments for the wave theory of light. Let us bind two pieces of plate glass A and B (Fig. 450) together with rub- ber bands, in such a way that they will be separated at one end by a piece of tissue paper C. If we hold the glass strips behind a sodium flame, we see in the reflected image of the yellow flame a series of horizontal fine dark lines. To explain this effect we will draw a much-enlarged section of the glass plates with the wedge _ 2>2A ? FIG. 451. Explanation of forma- Ol air between. In ngure 451 tion of bright and dark lines. FIG. 450. Interference of light waves. Interference Re-enforcement Interference 'L Re-enforcement SPECTRA AND COLOR 465 let AB and BC be the glass plates, and let the yellow so- dium light be coming from the right as a series of trans- verse waves which we can represent by the wavy lines. We know that this light is in part transmitted and in part reflected at each glass surface. But we are interested only in what happens at the interior faces AB and BO of the plates. Let the full line DE represent the light reflected at the point D on the surface AB, and let the dotted line D' E represent the wave reflected at D r on the surface BO. If the distance from D to D 1 is such as to make one reflected wave just half a vibration behind the other in phase, they will neutralize each other or interfere. At this point we have a dark line. But at another point F the distance between the plates may be such that the wave reflected at F' coin- cides with or reenforces the wave reflected at F. At this point we see a bright yellow line. If we select any two consecutive dark lines, we know that the double path between the plates at one line must be just one wave length longer than that at the other line. This gives us a method of com- puting the length of a wave. For example, we may compute the wave length of sodium light, if we know the length of the air gap, the thickness of the paper wedge, and the distance between two dark lines. Thus suppose the length of the air wedge is 100 millimeters, the thickness of the paper is 0.03 milli- meters, and the distance between adjacent lines is 1 millimeter. Since the width of the wedge increases 0.03 millimeters in a distance of 100 millimeters, it increases 0.0003 millimeters in 1 millimeter, and the in- crease in the double path between adjacent dark lines would be 0.0006 millimeters. This is approximately the wave length of sodium light. 476. Sunlight decomposed by interference. We may sub- stitute a soap film for the wedge-shaped air film used in the preceding experiment, and illuminate it by sunlight instead of the yellow light of the sodium flame. Let us dip a clean wire ring into a soap solution and set it up so that the film is vertical. The water in the film will run down to the lower 466 PRACTICAL PHYSICS edge, and the film becomes wedge-shaped. Let a beam of sunlight, 01 the light from a projection lantern, fall on this soap film and be reflected to a white screen. Furthermore, let a convex lens be arranged, as in fig- ure 452, so as to produce a sharp image of the film F on the screen S. We shall see on the screen a series of horizontal bands of the various colors of the spectrum. The white sunlight is com- posed of different colors and so of different wave lengths. The interference of the red waves takes place at one point, and that of the yellow at a different point. Where there is interference of the red waves, the complemen- tary color, a sort of bluish- green is left ; and where there is interference of the yellow waves, the color com- plementary to yellow, namely, blue, is produced. In this way we have a series of colored bands which are complementary to all the colors of the spectrum. Many beautiful color effects are caused by the interference of light waves by very thin films. The colors of oil films on the surface of water, of the thin films of oxide on metals and on Venetian glass, of the feathers of the peacock and of changeable silk are due to the interference of light waves. 477. Infra-red and ultra-violet rays. In the last few years we have come to know that the sun is sending out not only the light waves which affect the optic nerve, but also other longer ether waves which, though invisible, yet can produce strong heating effects, and are called the infra-red rays (Fig. 453). We have also learned, by photographing the spectrum of the sun, that it is sending out rays too short to be seen, which affect a photographic plate, and are called ultra-violet rays. FIG. 452. Interference of white light in soap film. SPECTRA AND COLOR 467 478. Electromagnetic theory of light. As we have seen, Faraday was led to believe that his " lines of force " trans- mitted electricity and magnetism through some medium, probably the ether. A few years later Maxwell developed this theory of Faraday's and put it on a mathematical basis. The argument was finally clinched in 1887 by a young German, Hertz. His experiments proved that electric waves really exist, and have the same velocity as light, although Ultra- Violet A ~400 700 1000 1500 2000 FIG. 453. Chart of waves of varying lengths. they are sometimes many meters long. These electromag- netic waves are reflected and refracted like light waves. Therefore, we feel sure that light waves are electric waves. This conception, and that of the conservation of energy, are the most remarkable achievements of physics in the nineteenth century. SUMMARY OF PRINCIPLES IN CHAPTER XXIII Continuous spectrum formed by incandescent solids. Bright-line spectrum formed by incandescent gases. Dark-line spectrum formed by incandescent solid shining through an absorbing layer of cooler gas. Wave length of visible spectrum ranges from about 0.000068 cm. (red) to about 0.000040 cm. (violet). Short waves most refracted by prism. Color of an object depends on wave lengths reaching eye. Colors of thin films due to disappearance of certain wave lengths by interference. 468 PRACTICAL PHYSICS QUESTIONS 1. A clean platinum wire is held in a blue Buiisen flame and observed through a spectroscope. What sort of a spectrum would you expect to get? 2. What kind of Fraunhofer lines must one get in the light of the moon? 3. What kind of a spectrum would you get if you looked at the mantle of a Welsbach lamp through a spectroscope ? 4. The cpmplete spectrum of the sun's rays is said to consist of three parts : heat spectrum, light spectrum, and chemical spectrum. Explain the appropriateness of these terms. 5. What causes the various colored lights used in fireworks? 6. Why does a blue dress look black by the light of a kerosene lamp ? 7. Why does a reddish lampshade make a room seem more cheerful at night? 8. How are colored moving pictures produced? 9. Why do they not use glass lenses in the ultra-violet microscope? 10. What sort of waves are used in wireless telegraphy? CHAPTER XXIV ELECTRIC WAVES : ROENTGEN RAYS Discharge of condenser is oscillatory electrical resonance electric waves detectors wireless telegraphy. Discharge through gases cathode rays Roentgen rays radium. ELECTRICAL WAVES 479. Discharge of Leyden jar is oscillatory. In 1842 Joseph Henry discovered that when a Leyden jar was dis- charged through a coil of wire surrounding a steel needle, the needle was magnetized. Not only that, but he was astonished to find that sometimes one end was made the north pole and sometimes the other, even though the jar was always charged the same way. He accounted for this fact by supposing that the discharge cur- rent kept reversing back and forth, that these oscillations grad- ually died away, and that the direction in which the needle was magnetized depended on which way the last perceptible oscilla- tion happened to go. This oscillatory current is represented by the curve in figure 454. A few years later Lord Kelvin, the great English physicist and engineer, proved mathematically that the discharge must be oscillatory. Finally, in 1859, Fedclersen succeeded in photographing an electric spark by means of a rapidly rotat- 469 FIG. 454. Oscillatory electric discharge. 470 PRACTICAL PHYSICS ing mirror. Figure 455 shows such a photograph. The oscillatory discharge is drawn out into a band by the rotating mirror, and thus makes a zigzag trace on the camera plate. From this experiment it is possible to calculate the time of one oscillation. It is exceedingly short, varying from one one-thousandth to one ten-millionth of a second. 480. Electrical resonance. The frequency of the oscillatory current produced by discharging a condenser depends upon the capacity of the condenser, and upon the resistance and self-induction of the circuit through which the current surges. Now we have already seen, in studying sound waves, that two objects having the same frequency of vibration tend to vibrate in sympathy, and that this property of a vibrating body is called resonance. Mechan- ical resonance also occurs in the case of two pendulums. Let us stretch a piece of rubber tubing between two supports and suspend two weights x and y by threads of equal length, as shown in figure 456. If we set one pendulum y swinging, the other pen- dulum x soon begins to swing, and the first one dies down as energy flows across to the other. This will happen only if the pendulums are of the same length and so of the same frequency. That is, resonance is necessary for the transfer of energy. FIG. 456. Resonance in two pendulums. In a similar way, if two Leyden jar circuits have the same capacity and the same self-induction, they will have the same frequency, and one circuit will influence the other. In figure 457 let A and be two Leyden jars of the same size and thickness of wall. To the jar A is connected a rec- tangular circuit of thick wire, one end of which touches the outer coating of the jar, while the other is separated from the knob of the jar by a small spark gap. The jar B is con- nected to a similar circuit, except that the end CD of the rectangle can be slid back and forth, and there is no spark FIG. 455 (in upper comer). Oscillations of electric spark. FIG. 466. X-ray picture of a broken ankle, which had been called "sprained" by a doctor. Taken in a physics laboratory by the brother of the patient. ELECTRIC WAVES: ROENTGEN RAYS 471 gap. Finally, let the inner coating of B be connected to its outer coating by a strip of foil cut sharply across at X. If we place the two electrical cir- cuits a foot apart and parallel, and send sparks across the gap of A by means of an induction coil, we find that there is a position of the slider CD such that tiny sparks appear at the gap X in the foil strip on B. When the slider is moved a short dis- tance from this position either way, the sparks at X cease. This phenomenon is called electrical resonance. Although FIG. 457. -Resonance between elec- , . , trical circuits. there is no connection between the two circuits, yet the energy in one circuit surges over into the other, which is in tune with it, and causes a spark there. In seeking for an explanation of this experiment, and many others, we must conclude that an oscillatory dis- charge or spark sends out waves in the surrounding ether. The ether does for the electric circuits what the rubber tubing did for the pendulums. It serves as a medium for the transfer of energy. These electric waves were first detected and measured by Hertz, in 1888, and are therefore called Hertzian waves. They travel with the same velocity as light. 481. Electric wave detectors. Very sensitive means for de- tecting these electric waves have been invented. One means, invented by Branly and used by Marconi in his first wireless telegraphs, is called a coherer. It consists of a small glass tube closed at each end by metal pistons. A space of a mil- limeter or two between the pistons is filled with rather coarse filings of nickel and silver. When electric waves fall on this coherer, the mast: of filings " coheres " or sticks together and becomes a conductor. A slight tap causes the resistance of the coherer to return to its original high value. 472 PRACTICAL PHYSICS The microphone, described in section 310, is an excellent wave detector. Another form, called a crystal detector, con- sists of a piece of silicon, or of any one of several crystal- line substances, such as galena, embedded in soft metal on one side and touched on the other by a metal point. In the electrolytic detector a fine metal point just touches the sur- face of a conducting solution or electrolyte. The operation of crystal and electrolytic detectors seems to depend on some mysterious property whereby they let electricity flow through them in one direction much more easily than in the other. 482. Wireless telegraphy. Through the efforts of the Italian inventor, Marconi, and many others, electric waves are now being extensively used in wireless telegraphy. A simple sending station, such as Marconi used in his earliest experiments, is shown in figure 458. The essential part is a conductor called the aerial or antenna, extending to a con- siderable height above the ground. Powerful electrical oscillations are set up in this con- ductor, like the oscillations in the spark dis- charge shown in figure 455. These send waves out through the ether, just as a stick laid on water and shaken up and down sends out ripples over the surface of the water. One way to set up oscilla- tions in an aerial is to put a spark gap in it, and to send sparks across this gap by H: BATTERV FIG. 458. Simple sending station. means of an induction coil fed by batteries, as in figure 458. Another way is to put a condenser in parallel with the gap in the aerial, and to fill the condenser many times a second by means of a step-up transformer fed by an alternating current. ELECTRIC WAVES: ROENTGEN RAYS 473 Such a condenser will send a spark across the gap each time it fills. Another way is to put a very high frequency alter- nating current dynamo in the place of the spark gap in the antenna. The simplest kind of a receiving station is represented in figure 459. There is an aerial like that at the sending sta- tion, except that instead of a spark gap, it contains a detector of some sort. In parallel with this detector is a telephone receiver. Every time a train of waves reaches such a receiving station, some of the energy is absorbed by the aerial, and electrical oscillations are set up in it. These cannot get through the tele- phone because of its self-induction, and so they have to pass through the de- tector. But since a crystal detector lets more electricity through one way than the other, an excess of electricity accumulates in the antenna. This ex- cess then discharges through the tele- phone, and the diaphragm moves over and back once. Since this happens every time a train of waves comes in, which is many times every second, as long as the key of the sending station is closed, the telephone diaphragm is FIG. 459. A simple receiv- kept vibrating and emits a steady mg station, musical note. The duration of this note can be made shorter or longer by holding the sending key down a shorter or a longer time, and so the dots and dashes of the Morse code can be transmitted. The circuits used in commercial wireless telegraphy are much more complicated than these, because it is necessary to " tune " the sending and receiving stations accurately to the same frequency, and to make them insensitive to waves 474 PRACTICAL PHYSICS of any other frequency, so that one pair of stations may not interfere with another. For an explanation of commercial sending and receiving stations the reader may consult any of the numerous popular or technical books on wireless telegraphy. Wireless telegraphy is now used on all ocean steamships, so that they are in constant communication with other ships or with land stations. Timely aid has thus been called to ships in distress. Warships are kept in touch with the naval headquarters of their governments, which have powerful sending stations. One of the largest of these uses the Eiffel Tower in Paris as the support of its antenna, and sends out time signals to ships all over the Atlantic Ocean. Messages have been sent even as far as across the Atlantic Ocean by the Marconi stations at Wellfleet, Cape Cod, Massachusetts, and at Poldhu, England. 483. Wireless telephony. A wireless sending station ordi- narily sends out wave trains at unvarying intervals, 1000 every second, because it is fed by an alternating current of unvarying frequency, say 500 cycles per second, and emits one wave train for every loop of the current. Since the tele- phone diaphragm of the receiving station moves once for each train received, its vibration is also at a uniform rate (1000 vibrations per second in the case just mentioned) and it emits a musical note of unvarying pitch. Recently send- ing stations have been devised that emit wave trains at vary- ing intervals corresponding to the varying pitches and qual- ities of human speech. When such a succession of wave trains falls on an ordinary wireless receiving station the dia- phragm in its telephone vibrates like the diaphragm of an ordinary telephone receiver, or like the diaphragm of a phon- ograph, and emits speech. Wireless telephone messages can be picked up by any one who has a properly tuned wireless tele- graph set. Wireless telephony is alread} 7 practicable over con- siderable distances, but is not yet (1913) a commercial success. ELECTRIC WAVES: ROENTGEN BATS 475 ELECTRICAL DISCHARGE THROUGH GASES 484. Sparking voltage. The voltage needed to make a spark jump between two knobs depends on several factors, such as the size of the knobs, the distance between them, and the atmospheric pressure. It takes less voltage to cause a spark to jump between two sharp points than between two round balls. For example, the sparking voltage for two sharp points 1 centimeter apart is about 7500 volts, and for two round balls 1 centimeter in diameter and 1 centimeter apart is about 27,000 volts. The sparking voltage between two sharp points varies so nearly as the distance that this is a method used to measure very high voltage. To show the effect of atmos- pheric pressure we may connect a glass tube 2 or 3 feet long with an induction coil, as shown in figure 460. The tube is connected with a vacuum pump by a side tube. When the coil is first started, the discharge takes place between x and y, the terminals of the coil, which are only a few FIG. 460. Discharge in partial vacuum, millimeters apart, but as the air is pumped out of the tube, the discharge goes through the long tube in- stead* of across the short gap xy. This shows that the sparking voltage decreases when the pressure is diminished. 485. Discharges in partial vacua. Reducing the atmos- pheric pressure between two points makes it easier for an electric discharge to pass, until a certain point in the exhaus- tion is reached. Then it begins to be more difficult. At the very highest degree of exhaustion yet attainable it is hardly possible to make a spark pass through a vacuum tube. The changes in the appearance of such a tube as the ex- haustion proceeds are very interesting. At first the dis- charge is along narrow flickering lines, but as the pressure 476 PRACTICAL PHYSICS Fia. 461. Geissler tube, made to study spectra of hydrogen. is lowered, the lines of the discharge widen out and fill the whole tube until it glows with a steady light. With still higher exhaustion, a soft, velvety glow covers the surface of the negative electrode or cathode, while most of the tube is filled with the so-called positive column which is luminous and stratified, and reaches to the anode. The so-called Geissler tubes (Fig. 461) are little tubes of this sort which are usually made in fantastic shapes and serve as pretty toys. The color of the light from a Geissler tube depends on the gas which is in the tube, and on the kind of glass used. 486. Cathode rays. When the exhaustion of a tube is carried to a very high degree, so that the pressure is equal to about 0.0001 of a millimeter of mercury, the positive glow is very faint and the dark space around the cathode is per- vaded by a discharge. An invisible radiation streams out nearly at right angles to the cathode surface, no matter where the anode is located in the tube. This radiation from the cathode is called cathode rays and shows itself in several ways : first by a yellowish green fluorescence wherever it strikes the glass of the tube ; second, by the fact that it can be brought to a focus where it produces intense heat ; and third, by the sharply defined shadows which a metal interposed in its path produces in the fluorescence on the end of the tube. A Crookes' tube, arranged as in figure 462, shows the heating effect of the cathode rays. When an in- duction coil sends a discharge through the tube from top to bottom, the cathode rays are focused on a piece of platinum which becomes red hot. Another Crookes' tube, arranged as in figure 463, FlG 452. Heating shows that a shadow is formed on the end of the tube effect of cathode by an aluminum cross. rays. ELECTRIC WAVES; ROENTGEN BATS 477 FIG. 463. Shadow formed by cathode rays. 487. Bending of cathode rays. A Crookes' tube, made as in figure 464, sends a narrow band of cathode rays through the slit 8 in the aluminum screen mn against a fluorescent screen / slightly in- clined to them. When a strong magnet M is held near the side of this tube, it is found that the stream of cathode rays is deflected in the direction which would be expected if they were a stream of negatively charged particles. From this and other experi- ments we believe that cathode rays are nega- tively charged particles projected at very high velocity from the cathode. J. J. Thomson, the English physicist, has estimated from various experiments on cath- ode rays that the negatively charged particles, which he calls electrons, have each a mass about sixteen hundred times smaller than that of a hydrogen atom, and move with a velocity of from one tenth to one third that of light. It is supposed that each particle carries a negative charge of electricity equal to that of the hydrogen atom in electrolysis. FIG. 464. Bending 488. Roentgen rays. In 1895, while ex- of cathode rays by pe rimenting with a vac- a magnet. uum tube, Koentgen dis- covered another kind of rays which he called X-rays. When cathode rays strike against a platinum target, as shown in figure 465, Roentgen rays are sent off from this target. They affect a photo- graphic plate somewhat as sunlight does ; but, like cathode rays, they will penetrate Lai X-ray Field FIG. 465. Roentgen ray tube. 478 PRACTICAL PHYSICS many substances opaque to ordinary light, such as wood, pasteboard, and the human body. That they are not the same as cathode rays is shown by the fact that they are not deflected by a magnet. When a photographic plate, inclosed in the usual plate- holder with sides of hard rubber or pasteboard, is exposed, with a hand held over it, to Roentgen rays, a shadow pic- ture like that seen on the fluorescent screen is formed. We may demonstrate the action of Roentgen rays by operating an X-tube with an induction coil, and holding a fluorescent screen in front of the bulb. If the room is dark and the hand is interposed between the tube and the screen, the flesh, which is easily penetrated by the rays, will be seen faintly outlined, while the bones will cast a strong shadow. Figure 466 (opposite page 478) is from a photograph taken by means of X-rays, and shows how valuable they are to doctors. Roentgen rays are produced at, and sent forth from, any solid body upon which cathode rays fall. They are now known to be ether waves, just like light waves and wireless telegraph waves, but of very short wave length. 489. Radioactivity. Near the end of the nineteenth cen- tury, scientists discovered that something which resembles Roentgen rays is radiated from certain rare minerals, such as uranium, pitch-blende, and thorium. It affects a photo- graphic plate through an envelope of black paper. It has also the power of discharging electrified bodies, and so by using a very sensitive electroscope it is possible to detect and measure the intensity of this radiation. This new phe- nomenon is called radioactivity, and a new element, which is remarkably radioactive, has been discovered and called radium. , In this interesting and novel field of research many scientists are now seeking to learn the answer to the great questions " What is electricity ? " and " What is inside the atoms of substances?" INDEX (Numbers refer to pages.) Aberration, lens, 442 ; mirror, 418. Absolute, pressure, 92 ; temperature, 182; zero, 183. Absorption of gases, 100. Absorption spectra, 459. A. C., see Alternating current. Acceleration, 135, 149; of gravity, 142. Achromatic lens, 457. Adhesion, 73. Aeroplane, 115. Air, compressibility of, 78, 80 ; ex- pansion of, 180 ; weight of, 84. Air-brake, 79 ; -compressor, 78 ; -lift pump, 98. Alternating current, 322. 358 to 373; power, 370. Alternator, 322, 363. Altitude by barometer, 91. Amalgamation, 265. Ammeter, 284. Ampere, 283, 287. Amplitude, 379, 387. Aneroid barometer, 89. Anode, 283. Arc, 334; automatic feed, 335; in- closed, 336 ; naming, 336 ; mercury, 336. Archimedes' principle, 59. Armature, of bell, 275; of circuit- breaker, 333; drum, 326, 342; of generator, 321, 362 ; Gramme ring, 323, 370; of motor, 340; station- ary, 364. Astigmatism, 447. Atmosphere, moisture in, 211 ; pres- sure of, 85, 88 ; refraction in, 430. Attraction, electric, 248 ; magnetic, 238 ; molecular, 73. Audibility, limits of, 388. Back e. m. f., 343. Balance, platform, 8 ; spring, 8. Ball bearings, 43. Balloon, 95. Banking rails, 149. Barograph, 90. Barometer, 88. Battery, 263; best arrangement of, 295; Edison storage, 354; lead storage, 352. Beam, stiffness and strength of, 128. Beats, 394. Bell, Alexander Graham, 313. Bell, electric, 275. Belting, 38. Bending, 121, 123. Bicycle pump, 78. Binocular, 452. Boiler, 221. Boiling point, 172, 205 ; effect of pres- sure on, 205 ; table of, 207. Bound charge, 256. Bourdon gauge, 68, 92. Boyle's law, 80. Breaking strength, 124. Bridge, pinned, 114; riveted, 114; girder, 115; Wheatstone, 302. British thermal unit (B. t. u.), 196. Bugle, 400. Bunsen, 459 ; photometer, 409. Buoyancy, in air, 94 ; in liquids, 58. Calorie, 196. Camera, 443. Candle power, 338, 409. Capacity, 256. Capillarity, 74. Carbon, filament, 337 ; microphone, 314, 472 ; transmitter, 314. 479 480 INDEX Carbureter, 230. Cathode, 283 ; rays, 476. Cell, chemistry of, 265 ; Daniell, 269 ; dry, 270; gravity, 269; ions in, 266; local action in, 268; sal- ammoniac, 270 ; storage, 352 ; vol- taic, 263. Center, of gravity, 20; of curvature, 417. Centigrade scale, 172. Central battery system, 315. Centrifugal pump, 97. Centripetal force, 148. Chemical effects of currents, 348. Circuit, electric, 264. Circuit breaker, 333. Clarinet, 400. Clinical thermometer, 173. Clouds, 214. Coefficient, of expansion, 176, 178, 181 ; of friction, 41, 117. Coherer, 471. Cohesion, 73, 148. Cold storage, 216. Color, 462 to 466. Columbus, 239. Commercial rating of electric lights, 337. Commutator, 322, 325 ; -motor, 368. Compass, 239. Complementary colors, 464. Component, 111. Composition of forces, 108. Compound, color, 463 ; engine, 225. Compound-wound generator, 328. Compressed air, 79. Compressibility of fluids, 78. Compression, 121, 123. Compression members, 114: Compressors, air, 78. Condenser, electric, 256; steam, 220, 226. Conductance, 294. Conduction, of electricity, 249 ; of heat, 189. Conjugate foci, for lens, 439 ; for mirror, 421. Conservation of energy, 164. Controller, 346. Convection, 186. Cooper-Hewitt lamp, 336 ; color of, 463. Corliss valve, 224. Cornet, 400. Coulomb, 283. Coulombmeter, 284. Crane, 23, 35, 108, 118. Critical angle, 435. Crookes' tube, 476. Crystal detector, 472. Current, alternating, 322 ; convection, 186 ; direct, 322 ; electric, 264, 283 ; heating effect of, 333 ; induced, 309 ; magnetic field about, 272 ; water, 283. Curtis turbine, 228. Curvature, center of, 417. Cycles, 365 Damping, 362. Daniell cell, 269. Davy, 334. Declination, 239. Density, 9 ; table of, 9 ; of air, 83 ; of water, 179. Derrick, 23, 35. Detectors, 471. Dew, 213. Dew point, 212. Dielectric, 257. Diffusion, of gases, 101 ; of light, 414. Dip, 239. Direct current (D. C.), 322 ; generator, 323 ; motor, 342 ; power, 329 ; uses of, 274 to 279, 332 to 355. Discord, 395. Dispersion, 457. Distillation, 207. Double-acting pump, 97. Drum, 400. Drum armature, 323, 326, 342, 362. Dry cell, 270. Dry dock, 61. Dynamo, 318, 321 to 329 ; alternating current, 363 to 367; energy source in, 329 ; kinds of, 326, 328 ; rule, 319. Dyne, 151. Earth, as magnet, 241. Echo, 385. Eddy currents, 361. Edison, incandescent lamp, 337 *, phon- ograph, 401 ; storage battery, 354. INDEX 481 Efficiency, defined, 43 ; of air-lift pump, 98; of boiler, 223; of Edison cell, 355 ; of electric lights, 338 ; of gas engine, 233; of motor, 346; of steam engine compared with gas engine, 234 ; of steam plant, 226 ; of steam turbine, 230 ; of storage cell, 354; of transformer, 359; of water turbine, 72. Elastic limit, 124. Electric, arc, 334; attraction, 248; bell, 275 ; circuit, 264 ; current, 263 ; generator, 318, 321 to 329, 363 to 367; heating, 332; lighting, 334; machines, frictional, 252 ; machines, induction, 259 ; motor, 340 ; power, 329; waves, 471; welding, 360; whirl, 253 ; work, 330. Electricity, two kinds of, 250. Electro, -chemical equivalent, 351 ; -magnet, 274 ; -magnetic theory of light, 467; -plating, 349; -statics, 248; -typing, 350. Electrolysis, 348. Electrolytic, copper, 351 ; detector, 472. Electromotive force, 267; back, 343; of cell, 288 ; induced, 309, 319 ; unit of, 286. Electrons, 260. Electrophorus, 259. Electroscope, 250 ; condensing, 264. Energy, 157 ; chemical, 163 ; conserva- tion of, 164 ; equation, 159 ; kinetic, 157 ; potential, 162 ; transforma- tions of, 163. Engine, balance sheet of, 234; com- pound, 225; condensing, 226; Cor- liss, 224 ; 4-cycle, 232 ; hot air, 185 ; internal combustion, 230; recipro- cating, 227 ; slide valve, 223 ; single acting, 231; steam, 219; 2-cycle, 231. Equilibrant, 107. Equilibrium, conditions of, 26. Erg, 161. Ether, 192, 243, 471, 478. Evaporation, 210. Exciter, 364. Expansion, coefficient of, 176, 178, 181 ; in freezing, 200 ; of gases, 180 ; of 2l liquids, 178; of solids, 174; of steam, 225 ; of water, 179. Eye, 445 ; defects of, 446. Factor of safety, 125. Fahrenheit scale, 172. Falling bodies, 140 ; acceleration of, 142 ; laws of, 143. Faraday, electromagnet, 275, 308, 318 ; field around magnet, 242 ; properties of lines of force, 243 ; transformer, 358. Faucet, 67. Feddersen, on spark discharge, 469. Field, of generator, 321, 327, 364; magnetic, 242 ; of motor, 340,^8 ; revolving, 364 ; rotating, 368 ; side push of, 340. Field glass, 452. Filament, incandescent, 337. Fire engine pump, 97. Firth of Forth Bridge, 176. Flatiron, electric, 332. Fleming's rule, 319. Floating bodies, 60. Fluids, 77. Flute, 400. Flux, magnetic, 243, 359. Flywheel, 157. Foci, conjugate, for lens, 439 ; for mirror, 421. Focus, of lens, 438; of mirror, 417; real, 420 ; virtual, 419. Fog, 214. Foot, 4 ; -candle, 413 ; -pound, 28. Force, buoyant, 59 ; centripetal, 148 ; of expansion, 175, 201 ; of friction, 42; lines of, 242; moment of, 17; vs. pressure, 51 ; unbalanced, 149 ; unit of, 7, 155 ; useful component of, 111. Force pump, 96. Forces, composition of, 108 ; equili- brant of, 107 ; molecular, 73 ; non- parallel, 105 ; parallel, 25 ; parallelo- gram of, 106 ; represented by arrows, 105 ; resolution of, 109 ; resultant of, 106. Franklin, 205, 253, 260. Fraunhofer lines, 458; meaning of, 461. 482 INDEX Freezing, by boiling, 215 ; evolves heat, 203; -point, 172, 199, 200 (table). Frequency, of alternating current, 365 ; of sound waves, 382 ; of water waves, 379. Friction, 40 ; on incline, 116; produces electricity, 248 ; produces heat, 170 ; in water pipes, 69. Frost, 214. Fulcrum, 14 ; force at, 17. Fundamental, of string, 391 ; units, 11. Furnace, 188. Fuses, 332. Galileo, 86, 141. Galvani, 263. Galvanometers, 281. Gas, engine, 230; formula, 183; standards for, 409 ; thermometer, 181. Gases, properties of, see Air. Gauge, Bourdon, 69, 92 ; mercury, 68, 92 ; steam, 222 ; water, 56, 222. Gay-Lussac, 181. Geissler tube, 476. Generator, 318, 321 to 329; A.C., 322, 363 to 367 ; compound, 328 ; multi- polar, 326; series, 328; shunt, 328. Gilbert, 241. Girder, 115, 130. Grade, 32. Gram, weight, 7 ; mass, 154. Gramme ring, 323, 370. Gravity, acceleration of, 142 ; cell, 269 ; center of, 20 ; specific, 62. Guericke, Otto von, 82, 86. Guitar, 399. Hall-time shaft, 232. Heat, conduction of, 189 ; convection of, 186 ; generated by electric cur- rent, 333 ; latent, 202, 209 ; mechani- cal equivalent of, 234 ; molecular theory of, 192 ; radiation of, 191 sources of, 170; specific, 197; units of, 196. Heater, for hot water, 187. Heating, electric, 332; hot air, 188; hot water, 187 ; indirect, 189. Hefner, 409. Helmholtz, 387, 389; resonator, 391. Henry, Joseph, electromagnet, 275, 318 ; study of spark, 469. Hertz, 467, 471. Hooke's law, 123. Horse power, 37. Horse-power hour, 330. Hot-air, engine, 185 ; furnace, 188. Humidity, 212. Huygens, 461. Hydraulic, elevator, 50 ; machines, 47 ; press, 48. Hydraulic analogue, of condenser, 258 ; of current, 266 ; of voltmeter, 288. Hydrometer, 65. Hydrostatic bellows, 50. Hygrometer, 217. Ice, artificial, 216. Ignition, 312. Illumination, 405. Image, construction of, lens, 440, mirror, 420 ; defects of, 442 ; formed by lens, 440, by plane mirror, 415, by pinhole, 406 ; size of, lens, 441, mirror, 421; virtual, 420. Impulse, 165. Incandescent lamp, 337 ; vacuum in, 83. Incidence, angle of, 415, 429. Inclined plane, 31, 116. Index of refraction, 429, 433, 434. Induced, current, 309; e. m. f., 319; magnetism, 244. Induction, electric, 255 ; magnetic, 244. Induction coil, 310. Induction motor, 368. Inertia, 146, 312; in curved motion, 148. Infra-red, 466. Insulators, electric, 249 ; heat, 189. Interaction, 152. Interference, of light, 465 ; of sound.. 394. Ions, 266. Isobars, 91. Jackscrew, 33. Joule, 161, 331. Joule, James Prescott, 234. Jump-spark ignition, 311. INDEX 483 Kelvin, 469. Key, telegraphic, 277. Kilogram, mass, 154 ; weight, 7. Kilowatt, 330. Kilowatt hour, 330. Kinetic energy, 157. Kinetic theory, 102. Kirchhoff, 459. Koenig's manometric flame, 392. Lactometer, 65. Laminated core, 362. Lamps, illuminating power of, 408 ; kinds of, 334 to 339. Lantern, projecting, 444. Latent heat, ice to water, 202 ; water to steam, 209. Left-hand rule, 341. Length, units of, 4. Lens, achromatic, 457 ; camera, 443 ; converging, 437 to 441 ; crystalline, 445 ; cylindrical, 447 ; diverging, 438, 441 ; focal length of, 438 ; for- mula, 439 ; images formed by, 440 ; magnifying power of, 448. Levers, 13 to 21. Leyden jar, 257 ; discharge of, 469. Lifting effect, of air, 94; of water, 59. Light, analysis of, 456 ; color of, 456 to 467 ; electric, 334 ; electromag- netic theory of, 467 ; illumination by, 405 to 413 ; interference of, 465 ; nature of, 461 ; reflection of, 414 to 424; refraction of, 427 to 442; speed of, 431 ; wave length of, 462. Lightning, 253. Lines of force, 242. Liquids, buoyant effect in, 58 to 61 ; compressibility of, 78 ; conduction of electricity by, 340 ; conduction of heat by, 190 ; in connected vessels, 55 ; expansion of, 178 ; molecular attractions in, 78 ; pressure in, 52 to 57 ; pressure transmitted by, 47 to 51 ; sound transmitted by, 375. Liter, 6. Local action in cell, 268. Local battery system, 315. Locomotive boiler, 221. Lodestone, 238. Longitudinal vibrations, 381. Loudness, 384, 387. Machines, 1, 13; alternating current, 358 to 370; direct current, 318 to 329, 340 to 347 ; electrostatic, 252, 259; frictional electric, 252; hy- draulic, 47 to 51, 70 to 72 ; induction electric, 259; pneumatic, 77 to 83, 95 to 99 ; simple, 13 to 43 ; talking, 401, 402 ; for testing materials, 128 ; thermal, 185, 219 to 234. Magdeburg hemispheres, 86. Magnet, artificial, 238; broken, 245; current induced by, 308 ; earth a, 241; electro-, 274 to 278, 320; electro-, self-induction of, 312 ; field around, 242 ; by induction, 244 ; natural, 238 ; permanent, 326. Magnetic field, around coil, 273 ; around current, 272 ; around magnet, 242 ; of generator, 321 ; rotating, 368 ; side push of, 340 ; wire cutting, 319. Magnetic poles, 239. Magnetism, 238 to 247 ; induced, 244 ; molecular theory of, 246 ; residual, 274. Magnetite, 238. Magneto, 327. Magnifying glass, 448. Magnifying power, of binocular, 453 ; of lens, 448 ; of microscope, 450 ; of opera glass, 452 ; of telescope, 451. Major, scale, 396 ; triad, 396. Make-and-break ignition, 312. Mandolin, 399. Manometer, 68, 91. Manometric flame, 392. Marconi, 472. Mariotte, 80. Mass, 154. Maxwell, 467. Mayer, 165. Mechanical advantage, 25. Mechanical equivalent of heat, 234. Mechanics, Chapters II to IX, see table of contents. Medical coil, 311. Megaphone, 385. Melting point, 199, 200 (table), effect of pressure on, 201. 484 INDEX Metallized filament, 338. Meter, 4 ; water-, 70. Mho, 294. Micrometer screw, 35. Microphone, 314, 472. Microscope, 449 ; use of mirror in, 419. Mil-foot, 298. Milk, testing of, 65. Mirror, concave, 417 ; convex, 419 ; focus of, 417, 418; formula, 423; parabolic, 418 ; plane, 415. Mixtures, method of, 198. Moisture, in atmosphere, 211. Molecular forces, 73. Molecular theory, of gases, 102; of heat, 192 ; of magnetism, 245. Moments, principle of, 17. Momentum, 165 ; equation, 166 ; units of, 167. Moon, attracts earth, 154 ; eclipse of, 407. Morse, 276. Motion, laws of, 133 to 143. Motor, alternating current, 368 ; commutator, 368 ; efficiency, 346 ; electric, 340; forms of, 342; in- duction, 368 ; rule, 341 ; series, 344 ; shunt, 344; starting a, 343; syn- chronous, 368; water, 71. Moving pictures, 445. Musical, instruments, 397 to 400; scale, 396; sounds, 386. Neutral layer, 130. Newcomen, 219. Newton, corpuscular theory of light, 461 ; laws of mechanics, 146. Nodes, 379. Noise, 386. Octave, 396. Oersted, 271. Ohm, 286. Ohm's law, 289. Onnes, 185. Opera glass, 452. Optical instruments, 416, 419, 443 to 453, 458. Organ pipe, 399. Oscillations of spark, 469. Overtones, 391. Ozone, 254. Parallel, circuits, 293 ; forces, 25. Parallelogram of forces, 106. Parsons turbine, 229. Pascal, experiments with barometer, 88 ; principle, 48 ; vases, 53. Pelton wheel, 71. Pendulum, 142, 177 ; resonance of, 470. Penumbra, 407. Period, 380. Permeability, 245. Perpetual motion, 165. Phase, of alternating current, 365 ; of wave, 379. Phonograph, 401. Photometer, 409. Physics, description of, 1 ; divisions of, 2. Piano, 397. Pigments, 463. Pitch, international, 397 ; of screw, 34 ; of sound, 387. Plato, 3. Pneumatic machines, 77. Polarization, in cell, 268. Poles, of magnet, 238. Polyphase circuit, 365. Potential, difference of, 267. Potential energy, 162. Pound, mass, 154 ; weight, 7. Power, 37; alternating current, 370; electric, 329 ; electrical transmission of 361 ; factor, 371 ; horse, 37; me- chanical transmission of, 38. Precipitation, 215. Pressure, of atmosphere, 85 ; coeffi- cient of, gases, 181 ; cooker, 206 ; effect of, on boiling, 205 ; effect of, on freezing, 201 ; vs. force, 51 ; in heavy liquid, 52 ; vapor, 205. Prism, 435, 436 ; colors formed by, 456. Projecting lantern, 444. Pulley, 24, 25, 29 ; differential, 30. Pumps, 95 to 98. Quality, of sound, 388. Radiation, 191. Radio-activity, 478. INDEX 485 Radium, 478. Rain, 214. Rays, cathode, 476; infra-red and ultra-violet, 466; light, 415, 432; Roentgen, 477. Reaction, 154. Receiver, telephone, 313. Refining metals, 351. Reflection, diffused, 414; law of, 415; of light, 414 to 424 ; of sound, 385 ; total, 434. Refraction, by atmosphere, 430; ex- planation of, 433; in glass, 429; index of, 433 ; law of, 428 ; in plate, 436 ; in prism, 436 ; in water, 427. Regnault, 182. Relay, telegraphic, 278. Resistance, 258, 267 ; box, 301 ; compu- tation of, 297 ; internal and external, 286 ; measurement of, 302 ; specific (with values), 298; unit of, 286. Resolution of forces, 109. Resonance, acoustical, 390; electrical, 470 ; of pendulums, 470. Resultant, 106. Retina, 446. Rheostat, 300. Right-hand rule, 319. Rivet, 121. Roentgen rays, 477. Roller bearings, 43. Rolling friction, 42. Roof truss, 112. Rotating field, 368. Rowland, 235. Ruhmkorff coil, 311. Safety valve, 223. Sail boat, 115. Sal-ammoniac cell, 270. Scale, musical, 396. Screw, 33. Self-induction, 312. Self-lighting mantle, 101. Series, circuits, 292; generator, 328; motor, 344. Sextant, 416. Shadow, 407. Shear, 121. Shunt, circuits, 293 ; generator, 328 ; motor, 344. Sighting, 451. Siphon, 98. Siren, 388. Snow, 214. Solids, conductivity, electrical, 298; thermal, 189; density of, 9; ex- pansion of, 174 ; sound transmitted by, 375 ; specific gravity of, 62. Solutions, conduction by, 348. Sonometer, 398. Sound, 374 to 404 ; intensity of, 384, 387 ; interference of, 394 ; nature of, 378, 382 ; reflection of, 385 ; sen- sation of, 378 ; velocity of, 376. Sounder, telegraphic, 277. Sounding board, 398. Spark, oscillations of, 469. Sparking voltage, 475. Speaking tubes, 385. Specific, gravity, 62 to 66 ; heat, 197, 198 (table). Spectroscope, 457. Spectrum, 456; absorption, 459; bright line, 459 ; continuous, 459 : solar, 458. Spectrum analysis, 459. Speed, 133 (table); of electric waves, 471 ; of light, 431 ; of light in water, 434 ; of sound, 376. Spyglass, 451. Squirrel-cage rotor, 370. Standard, lamp, 409 ; weight, 155. Steam, engine, 219 ; latent heat of, 209 ; turbine, 227. Stereopticon, 444. Stiffness of beams, 128. Storage battery, 352. Strain, 122. Street-car motor, 345. Strength, of beams, 129 ; breaking, 124. Stress, 122. Strings, vibrating, 391, 398. Submarine telegraph, 278. Suction pump, 95. Surveyor's level, 452. Tables, accelerations, 136 ; accelera- tion units, 135 ; boiling points, 207 ; coefficients of expansion, 176 ; den- sities, 9 ; " efficiency " of electric lamps, 339 ; electrical conductors 486 INDEX and insulators, 249 ; electrical units, 287 ; electrochemical equivalents, 351 ; force units, 151 ; heat distri- bution in engines, 234 ; of intervals in musical scale, 397 ; length units, 4 ; melting points, 200 ; moisture in air, 211; momentum units, 167; specific heats, 198 ; specific resist- ance, 298 (in text) ; speeds, 133 ; volume units, 6 ; wave length of light, 462 ; weight units, 7 ; wire (gauge, diameter, area, carrying capacity), 304; work units, 160. Tantalum lamp, 338. Telegraph, 276 ; wireless, 472. Telephone, 313 ; wireless, 474. Telescope, astronomical, 450 ; erect- ing, 451 ; reflecting, 419. Temperature, absolute, 182 ; low, 185 ; regulator, 175. Tensile strength, 127. Tension, 121, 123 ; vapor, 205. Tension members, 114. Terminal voltage, 291. Thermometer, Centigrade, 172; clini- cal, 173 ; Fahrenheit, 172 ; gas, 181 ; maximum, 173 ; mercury, 171 ; minimum, 173 ; wet and dry bulb, 212. Thermos bottle, 191. Thomson, 477. Thumb rule, for coil, 274 ; for wire, 272. Toepler-Holtz machine, 259. Torque, 344. Torricelli, 87. Transformer, 358. Transmitter, telephone, 314. Transverse vibrations, 380. Triad, major, 396. Trombone, 400. Truss, roof, 112. Tungsten lamp, 338. Tuning fork, 374. Turbine, Curtis, 228; Parsons, 229; steam, 227 ; water, 72. Twisting, 121, 123. Tyndall, 197. Ultra-violet light, 466. Umbra, 407. Units, 3; of acceleration, 235; oi area, 5; of current, 281, 283; of density, 9 ; electrical, 287 ; of elec- trical power, 329, 347 ; of electrical work, 330, 331 ; of electromotive force, 286 ; of force, 151 ; funda- mental, 11; of heat, 196, 235; of illumination, 413 ; of kinetic energy, 160 409 167 of length, 4 ; of light intensity, of mass, 154 ; of momentum, of power, 38, 329, 347; of pressure, 51 ; of resistance, 286, 298 ; of speed or velocity, 133 ; of volume, 6 ; of weight, 7 ; of work, 28, 235, 330, 331. Unit stress and strain, 125. Vacuum, bottle, 191 ; cleaner, 83 ; discharge in, 475 ; gauge, 92 ; pan, 206 ; pumps, 81 ; sound not carried by, 375. Vapor pressure, 205. Velocity, of light, 431 ; of molecules, 102 ; of sound, 376. Ventilation, 188. Vibration, made visible, 375 ; sym- pathetic, 389. Violin, 399. Virtual image, lens, 441 ; mirror, 420. Visual angle, 447. Voice, 400. Volt, 286. Volta, 263. Voltage, sparking, 475; terminal, 291. Voltmeter, 287. Watch, balance wheel, 177 ; stop-, 12. Water, density of, 179; gauge, 56; meter, 70 ; motor, 71 ; turbine, 72 ; waves, 378 ; wheels, 71 ; works, 67, Watt, 329, 347. Watt, James, horse power, 37 ; steam engine, 220. Wattmeter, 371. Wave, front, 432; length of light, 462 ; model, 381 ; theory of light, 461. Waves, electric, 469, 471 ; light, 432 ; longitudinal, 381 ; sound, 382 ; trans- verse, 380 ; water, 378. Weather map, 90. INDEX 487 Wedge, 33. Weight, of air, 84 ; standard and local, 155 ; units of, 7. Welding, electric, 360. Wheatstone bridge, 302. Wheel and axle, 22. Wind instruments, 399. Wireless, telegraphy, 472 ; telephony, 474. Wire table, 304. Work, definition of, 28 ; electrical, 330 ; and energy, 157; and power, 37; principle of, 29 ; units of, 28, 235 330, 331. X-rays, 477. X-ray tube, vacuum in, 83. Young, 462. Zero, absolute, 183. Printed in the United States of America. Date Due NOV 7 1930 NOV 21 9 1930 1942 1930 yj j*ni -CCT- 1932 o W^ ~^4~ 1936 311 jaa SEP LIBRARY COLLEGE OF DENTISTRY UNIVERSITY OF CALIFORNIA