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Full text of "Practical physics"

PRACTICAL PHYSICS 



MILLIKAN AND GALE 



GIFT OF 
Agriculture education 




PEACTICAL PHYSICS 



BY 

EGBERT ANDREWS MILLIKAN, PH.D., Sc.D. 

DIRECTOR OF THE NORMAN BRIDGE LABORATORY OF 
PHYSICS, PASADENA, CALIFORNIA 

AND 

HENRY GORDON GALE, PH.D. 

PROFESSOR OF PHYSICS IN THE UNIVERSITY OF CHICAGO 



BEING A REVISION OF THE AUTHORS' "A FIRST COURSE IN 
PHYSICS" DONE IN COLLABORATION WITH 

WILLARD R. PYLE, B.S. 

HEAD OF THE DEPARTMENT OF PHYSICS, MORRIS HIGH SCHOOL 
NEW YORK CITY 




GTNN AND COMPANY 

BOSTON NEW YORK CHICAGO LONDON 
ATLANTA DALLAS COLUMBUS SAN FRANCISCO 



COPYRIGHT, 1906, 1913, BY ROBERT A. MILLIKAN 
AND HENRY G. GALE 



COPYRIGHT, 1920, 1922, BY GINN AND COMPANY 

ENTERED AT STATIONERS' HALL 

ALL RIGHTS RESERVED 

B424.1 tflfb 






A6RIO, OFPT. 









, 






GINN AND COMPANY PRO 
PRIETORS BOSTON U.S.A. 



PREFACE 

The chief aim of this book in all of its editions has been to 
present elementary physics in such a way as to stimulate the 
pupil to do some thinking on his own account about the hows 
and whys of the physical world in which he lives. To this end 
such subjects, and only such subjects, have been included as 
touch most closely the everyday life of the average pupil. In 
a word, the endeavor has been to make this book represent 
the practical, everyday physics which the average person 
needs to help him to adjust himself to his surroundings and 
to interpret his own experiences correctly. 

But the conditions of modern life are changing at an aston- 
ishing rate and calling for the continuous revision of any text 
which would keep pace with them. For example, within the 
past ten years the internal-combustion engine has not only 
taken its place as an agent of equal importance with the 
steam engine in the world's industries but, what is more im- 
portant, it has also come more fully into the daily life of the 
average man and woman than even the dynamo and motor 
have ever begun to do. The automobile is accordingly given 
fuller treatment in this new book than it has ever received 
before in any elementary physics text. 

Again, man's conquest of the air, after centuries of failure, 
is not only the most significant advance, on the practical side, 
of the twentieth century, but the airplane now attracts the 
attention and excites the interest of almost every man, 
woman, and child. Accordingly, the principles underlying 
this advance, and the methods by which it was brought 
about,, find as full treatment in this volume as is consistent 

iii 

55752S 



iv PKEFACE 

with the simplicity and clearness demanded in a beginning 
course in physics. The book may be used, if desired, even 
in the second year of the high school. 

Further, the World War was responsible not only for 
extraordinary developments in physics but also for demon- 
strating, both to the American youth and to the leader of 
American industry, the necessity of the more intensive cul- 
tivation of physical science. These developments and these 
new demands, with which the authors came into the closest 
touch because of their service in the army both in this 
country and in France, have been fully reflected in this 
book, the emphasis, however, being placed upon develop- 
ments which make for peace rather than for war. 

As in preceding editions, the full-page inserts, though a very 
vital part of the book, are not a necessary and integral part 
of the course. They have been inserted, in more than double 
their former number, in order to add human and historic in- 
terest and to stimulate the pupil to look farther into a sub- 
ject than his immediate assignment requires him to do. It is 
thought that they will be found to be an invaluable adjunct 
to the course. 

Both the order and the treatment are in many places 
markedly different from those of preceding editions, and 
reflect the experience of the tens of thousands of teachers 
who have used this course, many of whom have assisted the 
authors with their suggestions. Especially in the problems 
have important improvements been made. 

For the sake of indicating in what directions omissions 
may be made, if necessary, without interfering with con- 
tinuity, paragraphs have here and there, as in former editions, 
been thrown into fine print. These paragraphs will be easily 
distinguished from the classroom experiments, which are in 
the same type. They are for the most part descriptions of 
physical appliances. 



PREFACE v 

The authors are under great obligation to all of their 
friends who have assisted them in this work, particularly to 
their collaborator, Mr. W. R. Pyle ; also to Mr. J. R. Towne 
of East High School, Minneapolis, Mr. C. F. Button, of the 
West High School of Commerce, Cleveland, Mr. E. Waite 
Elder, of the Eastside High School, Denver, Mr. C. E. Harris, 
of the East High School, Rochester, N. Y., Mr. Walter L. 
Barnum and Mr. Robert E. Hughes, of the Evanston High 
School, Evanston, 111., and Dr. George de Bothezat, aeronaut- 
ical expert of the Advisory Commission for Aeronautics. 

R. A. MILLIKAN 
H. G. GALE 



CONTENTS 

CHAPTER PAGE 

I. MEASUREMENT 1 

Fundamental Units. Density 
II. PRESSURE IN LIQUIDS 11 

Liquid Pressure beneath a Free Surface. Pascal's Law. The 
Principle of Archimedes 

III. PRESSURE IN AIR 26 

Barometric Phenomena. Compressibility and Expansibility 
of Air. Pneumatic Appliances 

IV. MOLECULAR MOTIONS 49 

Kinetic Theory of Gases. Molecular Motions in Liquids. 
Molecular Motions in Solids 

V. FORCE AND MOTION 57 

Definition and Measurement of Force. Composition and Reso- 
lution of Forces. Gravitation. Falling Bodies. Newton's Laws 

VI. MOLECULAR FORCES 90 

Elasticity. Capillary Phenomena. Absorption of Gases 
VII. WORK AND MECHANICAL ENERGY 105 

Definition and Measurement of Work. Work and the Pulley. 
Work and the Lever. The Principle of Work. Power and 
Energy 

VIII. THERMOMETRY ; EXPANSION COEFFICIENTS .... 128 
Thermometry. Expansion Coefficient of Gases. Expansion 
of Liquids and Solids. Applications of Expansion 

IX. WORK AND HEAT ENERGY 144 

Friction. Efficiency. Mechanical Equivalent of Heat. Specific 
Heat 

X. CHANGE OF STATE 161 

Fusion. Properties of Vapors. Hygrometry. Boiling. Artifi- 
cial Cooling. Industrial Applications 
vii 



viii CONTENTS 

CHAPTER PAGE 

XI. THE TRANSFERENCE OF HEAT 203 

Conduction. Convection. Radiation. Heating and Ventilating 
XII. MAGNETISM 214 

General Properties of Magnets. Terrestrial Magnetism 

XIII. STATIC ELECTRICITY 225 

General Facts of Electrification. Distribution of Charge. 
Potential and Capacity 

XIV. ELECTRICITY IN MOTION 244 

Detection of Electric Currents. Chemical Effects. Magnetic 
Effects. Measurement of Currents. Electric Bell and Tele- 
graph. Resistance and Electromotive Force. Primary Cells. 
Secondary Cells. Heating Effects 

XV. INDUCED CURRENTS 290 

The Principle of the Dynamo and Motor. Dynamos. The 
Principle of the Induction Coil and Transformer 

XVI. NATURE AND TRANSMISSION OF SOUND 319 

Speed and Nature. Reflection, Reenf orcement, and Interfer- 
ence 

XVII. PROPERTIES OF MUSICAL SOUNDS 337 

Musical Scales. Vibrating Strings. Fundamentals and 
Overtones. Wind Instruments 

XVIII. NATURE AND PROPAGATION OF LIGHT 357 

Transmission of Light. The Nature of Light 

XIX. IMAGE FORMATION 378 

Images formed by Lenses. Images in Mirrors. Optical 
Instruments 

XX. COLOR PHENOMENA 402 

Color and Wave Length. Spectra 

XXI. INVISIBLE RADIATIONS 417 

Radiation from a Hot Body. Electrical Radiations. Cathode 
and Rontgen Rays. Radioactivity 

APPENDIX 447 

INDEX . 465 



PORTRAITS OF PHYSICISTS AND ILLUSTRATIONS 
OF RECENT ACHIEVEMENTS IN PHYSICS 

PAGE 

1. The Navy-Curtiss Hydroplane, NC-4 (In colors) . . . Frontispiece 

2. Archimedes 22 

3. The Details of a Submarine . . . 23 

4. Otto von Guericke 32 

5. The Mercury-Diffusion Air Pump 33 

6. British Dirigible Airship R-34 Arriving in America 44 

7. The United States Army Observation Balloon 45 

8. Galileo 72 

9. French 340-mm. Gun in Action 73 

10. Sir Isaac Newton 84 

11. The Cream Separator 85 

12. James Clerk-Maxwell 102 

13. Heinrich Rudolph Hertz 102 

14. A Gas Mask 103 

15. James Prescott Joule 122 

16. James Watt 122 

17. The Rocket and the Virginian Mallet 123 

18. Lord Kelvin (Sir William Thomson) 134 

19. The Clermont and the Leviathan 135 

20. A United States Dreadnaught in the Panama Canal 152 

21. The Vickers-Vimy Airplane 153 

22. A Tank 190 

23. The Liberty Motor 191 

24. Section of a Modern Automobile 198 

25. The Carburetor and an Ignition System 199 

26. William Gilbert 222 

27. The Sperry Gyrocompass 223 

28. Benjamin Franklin < 230 

29. Franklin's Kite Experiment 231 

30. Count Alessandro Volta 240 

31. A Modern High-Tension Tower 241 

32. Hans Christian Oersted 246 

33. Joseph Henry 246 

34. Electromagnets 247 

ix 



X LIST OF ILLUSTRATIONS 

PAGE 

35. Andre" Marie Ampere 256 

36. Huge Rotor 257 

37. Samuel F. B. Morse 260 

38. Diagrams of Morse Telegraph 261 

39. Georg Simon Ohm 268 

40. The Electric Iron and Fuses 269 

41. Michael Faraday 290 

42. Induction Motor 291 

43. Alexander Graham Bell 316 

44. Thomas A. Edison 316 

45. Guglielmo Marconi 316 

46. Orville Wright 316 

47. The Original Wright Glider and the First Power-Driven Airplane 317 

48. Sound Waves of Spoken Words . 346 

49. Sound Ranging Record of the End of the War 347 

50. A. A. Michelson 358 

51. Lord Rayleigh (John William Strutt) 358 

52. Henry A. Rowland .358 

53. Sir William Crookes 358 

54. X-Ray Picture of the Human Thorax 359 

55. Christian Huygens 364 

56. The Great Telescope of the Yerkes Observatory 365 

57. Section of a " Movie " Film ' 386 

58. Arthur L. Foley's Sound-Wave Photographs 387 

59. Three-Color Printing (In colors) 408 

60. The Wireless Telephone utilized in Aviation 424 

61. Cinematograph Film of a Bullet fired through a Soap Bubble . . 425 

62. Alexanderson High-Frequency Alternator 428 

63. Interior of Radio Broadcasting Station 429 

64. Sir Joseph Thomson 440 

65. Amplifier, and Diagram of Receiving and Amplifying Set .... 441 

66. William Conrad Rontgen 446 

67. Antoine Henri Becquerel 446 

68. Madame Curie 446 

69. E. Rutherford 446 

70. X-Ray Spectra 447 



PRACTICAL PHYSICS 

CHAPTER I 

MEASUREMENT 
FUNDAMENTAL UNITS 

1. Introductory. A certain amount of knowledge about 
familiar things comes to us all very early in life. We learn 
almost unconsciously, for example, that stones fall and bal- 
loons rise, that the teakettle stops boiling when removed 
from the fire, that telephone messages travel by electric cur- 
rents, etc. The aim of the study of physics is to set us to 
thinking about how and why such things happen, and, to a less 
degree, to acquaint us with other happenings which we may 
not have noticed or heard of previously. 

Most of our accurate knowledge about natural phenomena 
has been acquired through careful measurements. We can 
measure three fundamentally different kinds of quantities, 
length, mass, and time, and we shall find that all other 
measurements may be reduced to these three. Our first prob- 
lem in physics is, then, to learn something about the units in 
terms of which all our physical knowledge is expressed. 

2. The historic standard of length. Nearly all civilized 
nations have at some time employed a unit of length the 
name of which bore the same significance as does foot in 
English. There can scarcely be any doubt, therefore, that in 
each country this unit has been derived from the length of 

l 



2 MEASUREMENT 

the human foot. It is probable that in England, after the yard 
(a unit which is supposed to have represented the length of 
the arm of King Henry I) became established as a standard, 
the foot was arbitrarily chosen as one third of this standard 
yard. In view of such an origin it will be clear why no agree- 
ment existed among the units in use in different countries. 

3. Relations between different units of length. It has also 
been true, in general, that in a given country the different 
units of length in common use (such, for example, as the 
inch, the hand, the foot, the fathom, the rod, the mile, etc.) 
have been derived either from the lengths of different mem- 
bers of the human body or from equally unrelated magni- 
tudes, and in consequence have been connected with one 
another by different, and often by very awkward, multipliers. 
Thus, there are 12 inches in a foot, 3 feet in a yard, 5J yards 
in a rod, 1760 yards in a mile, etc. 

4. Relations between units of length, area, volume, and 
mass. A similar and even worse complexity exists in the rela- 
tions of the units of length to those of area, capacity, and mass. 
Thus, there are 272| square feet in a square rod ; 57| cubic 
inches in a quart, and 31J gallons in a barrel. Again, the 
pound, instead of being the mass of a cubic inch or a cubic 
foot of water, or of some other common substance, is the mass 
of a cylinder of platinum, of inconvenient dimensions, which 
is preserved in London. 

5. Origin of the metric system. At the time of the French 
Revolution the extreme inconvenience of existing weights and 
measures, together with the confusion arising from the use of 
different standards in different localities, led the National 
Assembly of France to appoint a commission to devise a more 
logical system. The result of the labors of this commission 
was the present metric system, which was introduced in France 
in 1793 and has since been adopted by the governments of 
most civilized nations except those of Great Britain and the 



FUNDAMENTAL UNITS 3 

United States ; and even in these countries its use in scientific 
work is practically universal. The World War has done much 
to speed its adoption in these countries. 

6. The standard meter. The standard length in the metric 
system is called the meter. It is the distance, at the freezing 
temperature, between two transverse parallel lines ruled on 
a bar of platmum-iridium (Fig. 1), which is kept at the 
International Bureau of Weights and Measures at Sevres, 
near Paris. This distance is 39.37 inches. 

In order that this standard length might be reproduced if 
lost, the commission attempted to make it one ten-millionth 



Exact size of 
the cross section 




FIG. 1. The standard meter 

of the distance from the equator to the north pole, measured 
on the meridian of Paris. But since later measurements have 
thrown some doubt upon the exactness of the commission's 
determination of this distance, we now define the meter, not 
as any particular fraction of the earth's quadrant, but simply 
as the distance between the scratches on the bar mentioned 
above. On account of its more convenient size, the centi- 
meter, one one-hundredth of a meter, is universally used, for 
scientific purposes, as the fundamental unit of length. 

7. Metric standard capacity. The standard unit of capacity 
is called the liter. It is the volume of a cube which is one tenth 
of a meter (about 4 inches) on a side. The liter is therefore 



4 MEASUKEMEXT 

equal to 1000 cubic centimeters (cc.). It is equivalent to 1.057 
quarts. A liter and a quart are therefore roughly equivalent 
measures. 

8. The metric standard of mass. In order to establish a 
connection between the unit of length and the unit of mass, 
the commission directed a committee of the French Academy 
to prepare a cylinder of platinum which should have the same 
weight as a liter of water at its temperature of greatest density, 
namely, 4 Centigrade (39 Fahrenheit). An exact equivalent 
of this cylinder, made of platinum-iridium and kept at Sevres 
with the standard meter, now represents the standard of mass 
in the metric system. It is called the standard kilogram and 
is equivalent to about 2.2 pounds. One one-thousandth of this 
mass was adopted as the fundamental unit of mass and was 
named the gram. For practical purposes, therefore, the gram 
may be taken as equal to the mass of one cubic centimeter of water, 

9. The other metric units. The three standard units of the 
metric system the meter, the liter, and the gram have 
decimal multiples and submultiples, so that every unit of 
length, volume, or mass is connected with the unit of next 
higher denomination by an invariable multiplier, namely, ten. 

The names of the multiples are obtained by adding the 
Greek prefixes, deka (ten), hecto (hundred), kilo (thousand) ; 
while the submultiples are formed by adding the Latin prefixes, 
deci (tenth), centi (hundredth), and milli (thousandth). Thus : 

1 dekameter = 10 meters 1 decimeter = J_. meter 

1 hectometer = 100 meters 1 centimeter = -j-L meter 

1 kilometer = 1000 meters 1 millimeter = 10 1 00 meter 

The most common of these units, with the abbreviations 
which will henceforth be used for them, are the following: 

meter (m.) millimeter (mm.) gram (g.) 

kilometer (km.) liter (1.) kilogram (kg.) 

centimeter (cm.) cubic centimeter (cc.) milligram (mg.) 



FUNDAMENTAL UNITS 5 

10. Relations between the English and metric units. The 

following table, which is inserted for reference, gives the 
relation between the most common English and metric units. 

1 inch (in.) = 2.54 cm. 1 cm. = .3937 in. 

1 foot (ft.) = 30.48 cm. 1 m, = 1.094 yd. = 39.37 in. 

1 mile (mi.) = 1.609 km. 1 km. = .6214 mi. 

1 grain = 64.8 mg. 1 g. = 15.44 grains 

1 oz. av. = 28.35 g. 1 g. = .0353 oz. 

1 Ib. av. = .4536 kg. 1 kg. = 2.204 Ib. 

The relations 1 in. = 2.54 cm., 1 m. = 39.37 in., 1 kilo 
(kg.) = 2.2 Ib., 1 km. = .62 mi. should be memorized. 
Portions of a centimeter and of an inch scale are shown 
together in Fig. 2. 

11. The standard unit of time. The second is taken among 
all civilized nations as the standard unit of time. It is 
86400 part of the time from noon to noon. 

12. The three fundamental units. It is evident that meas- 
urements of both area and volume may be reduced simply 



CENTIMETER 

0123456 



UUU 



I llll IIJllJU 




1 1] 1 1 I) I I PI 1 1 1 I] I] If] I IT 

INCH 1 2 

FIG. 2. Centimeter and inch scales 

to measurements of length; for an area is expressed as the 
product of two lengths, and a volume as the product of 
three lengths. For these reasons the units of area and 
volume are looked upon as derived units, depending on one 
fundamental unit, the unit of length. 

Now it is found that just as measurements of area and 
of volume can be reduced to measurements of length, so 
the determination of any measurable quantities, such as the 
pressure in a steam boiler, the velocity of a moving train. 



6 MEASUREMENT 

the amount of electricity consumed by an electric lamp, the 
amount of magnetism in a magnet, etc., can be reduced 
simply to measurements of length, mass, and time. Hence 
the centimeter, the gram, and the second are considered the three 
fundamental units. Whenever any measurement has been 
reduced to its equivalent in terms of centimeters, grams, 
and seconds, it is said, for short, to be expressed in C.G.S. 
(Centimeter-Gram-Second) units. 

13. Measurement of length. Measuring the length of a 
body consists simply in comparing its length with that of 
the standard meter bar kept at the International Bureau. In 
order that this may be done conveniently, great numbers of 
rods of the same length as this standard meter bar have been 
made and scattered all over the world. They are our common 
meter sticks. They are divided into 10, 100, or 1000 equal 
parts, great care being taken to have all the parts of exactly 
the same length. The method of making a measurement with 
such a bar is more or less familiar to everyone. 

14. Measurement of mass. Similarly, measuring the mass 
of a body consists in comparing its mass with that of the 
standard kilogram. In order that this might be done con- 
veniently, it was first necessary to construct bodies of the 
same mass as this kilogram, and then to make a whole series 
of bodies whose masses were |, -j^-, y^-, 10 1 00 , etc. of the 
mass of this kilogram; in other words, to construct a set of 
standard masses commonly called a set of weights. 

With the aid of such a set of standard masses the deter- 
mination of the mass of any unknown body is made by first 
placing the body upon the pan A (Fig. 3) and counterpoising 
with shot, paper, etc., then replacing the unknown body by 
as many of the standard masses as are required to bring the 
pointer back to again. The mass of the body is equal to 
the sum of these standard masses. This rigorously correct 
method of weighing is called the method of substitution. 



FUNDAMENTAL UNITS 



If a balance is well constructed, however, a weighing may 
usually be made with sufficient accuracy by simply placing 
the unknown body upon one 
pan and finding the sum of 
the standard masses which 
must then be placed upon 
the other pan to bring the 
pointer again to 0. This is 
the usual method of weighing. 
It gives correct results, how- 
ever, only when the knife-edge 
is exactly midway between 
the points of support m and 
n of the two pans. The method of substitution, on the other 
hand, is independent of the position of the knife-edge. It is 
customary to consider that the mass of a body determined as here 
indicated is a measure of the quantity of matter which it contains. 




FIG. 3. The simple balance 



QUESTIONS AND PROBLEMS 

1. The 200-meter run at the Olympic games corresponds to the 220- 
yard run in our local games. Which is the longer and how much ? 

2. The French 75-mm. guns have what diameter in inches ? 

3. The Twentieth Century Limited runs from New York to Chicago 
(967 mi.) in 20 hr. Find its average speed in miles per hour. 

4. Name as many advantages as you can which the metric system 
has over the English system. Can you think of any disadvantages ? 

5. What must you do to find the capacity in liters of a box when 
its length, breadth, and depth are given in meters ? to find the capacity 
in quarts when its dimensions are given in feet? 

6. Find the number of millimeters in 6 km. Find the number of 
inches in 4 mi. Which is the easier? 

7. With a Vickers-Vimy biplane Captain Alcock and Lieutenant 
Brown completed, on June 15, 1919, the first nonstop transatlantic flight 
of 1890 miles frojn Newfoundland to Ireland in 15 hr. 57 min. How 
many miles per hour? How many kilometers per hour? 

8. Find the capacity in liters of a box .5 m. long, 20 cm. wide, and 
100 mm. deep. 



8 MEASUREMENT 

DENSITY 

15. Definition of density. When equal volumes of different 
substances, such as lead, wood, iron, etc., are weighed in the 
manner described above, they are found to have widely differ- 
ent masses. The term " density " is used to denote the mass, 
or quantity of matter, per unit volume. 

Thus, for example, in the English system the cubic foot is 
the unit of volume and the pound the unit of mass. Since 1 cubic 
foot of water is found to weigh 62.4 pounds, we say that in the 
English system the density of water is 62.4 pounds per cubic foot. 

In the C.G.S. system the cubic centimeter is taken as the 
unit of volume and the gram as the unit of mass. Hence we 
say that in this system the density of water is 1 gram per 
cubic centimeter, for it will be remembered that the gram was 
taken as the mass of 1 cubic centimeter of water. Unless 
otherwise expressly stated, density is now universally under- 
stood to mean density in C.G.S. units; that is, the density of a 
substance is the mass in grams of 1 cubic centimeter of that sub- 
stance. For example, if a block of cast iron 3 cm. wide, 8 cm. 
long, and 1 cm. thick weighs 177.6 g., then, since there are 
24 cc. in the block, the mass of 1 cc., that is, the density, is 
equal to |^-, or 7.4 g. per cubic centimeter. 

The density of some of the most common substances is given 
in the following table : 

DENSITIES OF SOLIDS 

(In grams per cubic centimeter) 

Aluminium 2.58 Nickel 8.9 

Brass 8.5 Oak 8 

Copper 8.9 Pine 5 

Cork 24 Platinum 21.4 

Glass 2.6 Silver 10.5 

Gold 19.3 Tin 7.3 

Iron (cast) 7.4 Tungsten 19.6 

Lead . 11.3 Zinc . 7.1 



DENSITY 9 

DENSITIES OF LIQUIDS 

(In grams per cubic centimeter) 

Alcohol 79 Hydrochloric acid . . 1.27 

Carbon bisulphide . . . 1.29 Mercury 13.6 

Glycerin ..'.'. 1.26 Gasoline 75 

16. Relation between mass, volume, and density. Since the 
mass of a body is equal to the total number of grams which 
it contains, and since its volume is the number of cubic centi- 
meters which it occupies, the mass of 1 cubic centimeter is 
evidently equal to the total mass divided by the volume. Thus, 
if the mass of 100 cubic centimeters of iron is 740 grams, the 
density of iron must equal 740 -f-100 = 7.4 grams to the cubic 
centimeter. To express this relation in the form of an equa- 
tion, let M represent the mass of a body, that is, its total 
number of grams ; V its volume, that is, its total number of 
cubic centimeters ; and D its density, that is, the number of 
grams in 1 cubic centimeter; then 

-f m 

This equation merely states the definition of density in 
algebraic form. 

17. Distinction between density and specific gravity. The 
term " specific gravity " is used to denote the ratio between the 
weight of a body and the weight of an equal volume of water.* 

Thus, if a certain piece of iron weighs 7.4 times as much 
as an equal volume of water, its specific gravity is 7.4. But 
since the density of water in C.G.S. units is 1 gram per cubic 
centimeter, the density of iron in that system is 7.4 grams 
per cubic centimeter. It is clear, then, that density in 0. G-.S. 
units is numerically the same as specific gravity. 

* For the present purpose the terms "weight" and "mass" may be used 
interchangeably. They are in general numerically equal, although an impor- 
tant distinction between them will be developed in 73. Weight is in reality 
a force rather than a quantity of matter. 



10 MEASUREMENT 

Specific gravity is the same in all systems, since it simply 
expresses how many times as heavy as an equal volume of water 
a body is. Density, however, which we have defined as the 
mass per unit volume, is different in different systems. Thus, 
in the English system the density of iron is 462 pounds per 
cubic foot (7.4 x 62.4), since we have found that water weighs 

62.4 pounds per cubic foot and that iron weighs 7.4 times as 
much as an equal volume of water.* 

QUESTIONS AND PROBLEMS t 

1. A liter of milk weighs 1032 grams. What is its density and its 
specific gravity ? 

2. A ball of yarn was squeezed into of its original bulk. What 
effect did this produce upon its mass, its volume, and its density ? 

3. If a wooden beam is 30 X 20 x 500 cm. and has a mass of 150 kg., 
what is the density of wood ? 

4. Would you attempt to carry home a block of gold the size of a 
peck measure? (Consider a peck equal to 8 1. See table, p. 8.) 

5. What is the mass of a liter of alcohol? 

6. How many cubic centimeters in a block of brass weighing 34 g.? 

7. What is the weight in metric tons of a cube of lead 2 m. on an 
edge ? (A metric ton is 1000 kilos, or about 2200 Ib.) 

8. Find the volume in liters of a block of platinum weighing 

45.5 kilos. 

9. One kilogram of alcohol is poured into a cylindrical vessel and 
fills it to a depth of 8 cm. Find the cross section of the cylinder. 

10. Find the length of a lead rod 1 cm. in diameter and weighing 1 kg. 

* Laboratory exercises on length, mass, and density measurements should 
accompany or follow this chapter. See, for example, Experiments 1, 2, and 3 
of the authors' Manual. 

t Questions and problems to supplement this chapter and all following 
chapters are given in the Appendix, page 447. 






CHAPTER II 

PRESSURE IN LIQUIDS 

LIQUID PRESSURE BEKEATH A FREE SURFACE 

18. Force beneath the surface of a liquid. We are all 

conscious of the fact that in order to lift a kilogram of mass 
we must exert an upward pull. Experience has taught us 
that the greater the mass, the greater the force which we 
must exert. The force is commonly taken as numerically 
equal to the mass lifted. This is called the weight measure of 
a force. A. push or pull which is equal to that required to sup- 
port a gram of mass is called a gram of force. Thus, five grams 
of force are needed to lift a new five-cent piece. 

To investigate the nature of the forces beneath the free surface of a 
liquid we shall use a pressure gauge of the form shown in Fig. 4. If 
the rubber diaphragm which is stretched across the mouth of a thistle 
tube A is pressed in lightly with the finger, the drop of ink B will be 
observed to move forward in the tube T, but it will return again to its 
first position as soon as the finger is removed. If the pressure of the 
finger is increased, the drop will move forward a greater distance than 
before. We may therefore take the amount of motion of the drop as a 
measure of the force acting on the diaphragm. 

Now let A be pushed down first 2 cm., then 4 cm., then 8 cm. below 
the surface of the water *(Fig. 4). The motion of the index B will show 
that the upward force continually increases as the depth increases. 

Careful measurements made in the laboratory will show 
that the force is directly proportional to the depth.* 

* It is recommended that quantitative laboratory work on the law of 
depths and on the use of manometers accompany this discussion. See, for 
example, Experiments 4 and 5 of the authors' Manual. 

11 




12 PKESSUKE IN LIQUIDS 

Let the diaphragm A (Fig. 4) be pushed down to some convenient 
depth (for example, 10 centimeters) and the position of the index noted. 
Then let it be turned sidewise so that its plane is vertical (see a, Fig. 4), 
and adjusted in position until its center is exactly 10 centimeters beneath 
the surface, that is, until the 
average depth of the diaphragm 
is the same as before. The 
position of the index will show 
that the force is also exactly Fm 4 Qauge for measuri liquid 
the same as before. pressure 

Let the diaphragm then be 

turned to the position Z>, so that the gauge measures the downward force 
at a depth of 10 centimeters. The index will show that this force is 
again the same. 

We conclude, therefore, that at a given depth a liquid 
presses up and down and sidewise on a given surface with 
exactly the same force. 

19. Magnitude of the force. If a vessel like that shown 
in Fig. 5 is filled with a liquid, the force against the bottom 
is obviously equal to the weight of the column of 
liquid resting upon the bottom. Thus, if F repre- 
sents this force in grams, A the area in square centi- 
meters, h the depth in centimeters, and d the density 
in grams per cubic centimeter, we shall have 

F=Ahd. (1) FIG. 5 

Since, as was shown by the experiment of the preceding 
section, the force is the same in all directions at a given 
depth, we have the following general rule : 

Tlie force which a liquid exerts against any surface is equal 
to the area of the surface times its average depth times the density 
of the liquid. 

It is important to remember that " average depth " means 
the vertical distance from the level of the free surface to the 
center of the area in question. 




PRESSURE BENEATH A FREE SURFACE 



13 



20. Pressure in liquids. Thus far attention has been con- 
fined to the total force exerted by a liquid against the whole 
of a given surface. It is often more convenient to imagine 
the surface divided into square centimeters or square inches, 
and then to consider the force on one of these units of area. 
In physics the word " pressure " is used exclusively to denote 
the force per unit area. Pressure is thus a measure of the 
intensity of the force acting on a surface, and does not de- 
pend at all on the area of the surface. Since, by 19, F= Ahd, 
and since by definition the pressure p is equal to the force 
per unit area, we have 

(2) 



~ 



Therefore the pressure at a depth of h centimeters below the 
surface of a liquid of density d is hd grams per square centimeter. 

If the height is given in feet and the density in pounds per 
cubic foot, then the product hd gives pressure in pounds 
per square foot. Dividing by 144 gives the result in pounds 
per square inch. 

21. Levels of liquids in connecting vessels. It is a perfectly 
familiar fact that when water is poured into a teapot it stands 
at exactly the same level in 
the spout as in the body of 
the teapot ; or if it is poured 
into a number of connected 
vessels like those shown in 
Fig. 6, the surfaces of the 
liquid in the various vessels 
lie in the same horizontal 
plane. Now the pressure at 
c (Fig. 7) was shown by the 
experiment of 18 to be 
equal to the density of the liquid times the depth eg. The 
pressure at o in the opposite direction must be equal to 




FIG. 6. Water level in communi- 
cating vessels 



14 



PBESSUKE IN LIQUIDS 



that at c, since the liquid does not tend to move in either 
direction. Hence the pressure at o must be ks times the density. 

If water is poured in at s so that the 
height Jcs is increased, the pressure to 
the left at o becomes greater than the 
pressure to the right at <?, and a flow of 
water takes place to the left until the 
heights are again equal. 

It follows from these observations 
on the level of water in connected 




FIG. 7. Why water seeks 
its level 



vessels that the pressure beneath the 

surface of a liquid depends simply on the vertical depth beneath 

the free surface, and not at all on the size or shape of the vessel. 



QUESTIONS AND PROBLEMS 

1. Soundings at sea are made by lowering some kind of pressure 
gauge. When this gauge reads 1.3 kg. per square centimeter, what is 
the depth? (Density of sea water=1.026.) 

2. Kerosene is 0.8 as heavy as water (1 cu. ft. of water=62.4 lb.). 
Find the pressure of the kerosene per square foot and per square inch 
on the bottom of an oil tank filled to a depth of 30 ft. 

3. What pressure per square inch is required to force water to the 
top of the Woolworth building in New York City, 780 ft. high ? 

4. A swimming tank 50 ft. square is filled with water to a depth of 
5 ft. Find the force of the water on the bottom ; on one side. 

5. If the areas of the surfaces AB in 
Fig. 8, (1) and (#), are the same, and if 
water is poured into each vessel at D till 
it stands at the same height above AB, 
how will the downward force on A B in 
Fig. 8, (#), compare with that in Fig. 8, 
(1)? Test your answer, if possible, by 

making AB a piece of cardboard and FIG. 8. Illustrating hydro- 
pouring water in at D, in each case, static paradox 
until the cardboard is forced off. 

6. If the vessel shown in Fig. 10, (.?) (p. 15), has a base of 200 sq. cm. 
and if the water stands 100 cm. deep, what is the total force on the 
bottom ? 




PASCAL'S LAW 



15 



7. If the weight of the empty vessel in Fig. 10, (I), is small compared 
with the weight of the contained water, will the force required to lift 
the vessel and water be greater or less than the force 

exerted by the water against the bottom ? Explain. 

8. A whale when struck with a harpoon will often 
dive straight down as much as 400 fathoms (2400 ft.). 
If the body has an area of 1000 sq. ft., what is the total 
force to which it is subjected ? 

9. A hole 5 cm. square is made in a ship's bottom 
7 m. below the water line. What force in kilograms is 
required to hold a board above the hole? 

10. Thirty years ago standpipes were generally 
straight cylinders. To-day they are more commonly 
of the form shown in Fig. 9. What are the advantages 
of each form ? 



PASCAL'S LAW 




FIG. 9. A water 
reservoir 



22. Transmission of pressure by liquids. 

From the fact that pressure within a free liquid 
depends simply upon the depth and density of 'the liquid, it 
is possible to deduce a very surprising conclusion, which was 
first stated by the famous French scientist, mathematician, and 
philosopher, Pascal (1623-1662). 
Let us imagine a vessel of the 
shape shown in Fig. 10, (J), to be 
filled with water up to the level 
db. For simplicity let the upper 
portion be assumed to be 1 square 
centimeter in cross section. Since 
the density of water is 1, the force 
with which it presses against any 
square centimeter of the interior 
surface which is li centimeters 
beneath the level ab is h grams. 
Now let 1 gram of water (that is, 1 cubic centimeter) be 
poured into the tube. Since each square centimeter of sur- 
face, which before was h centimeters beneath the level of the 











A 




a 





* 


a 


= 


^ 


(1) 


f 




<*) 


5 






_s 


i^^. 


p 




^ 


l-C-= 


i 






i 


s 



FIG. 10. Proof of Pascal's law 



16, PEESSUEE IN LIQUIDS 

water in the tube, is now A+l centimeters beneath this level, 
the new pressure which the water exerts against it is 7i-fl 
grams ; that is, applying 1 gram of force to the square cen- 
timeter of surface ab has added 1 gram to the force exerted 
by the liquid against each square centimeter of the interior 
of the vessel. Obviously it can make no difference whether 
the pressure which was applied to the surface ab was due 
to a weight of water or to a piston carrying a load, as in 
Fig. 10, (^), or to any other cause whatever. We thus arrive 
at Pascal's conclusion that pressure applied anywhere to a l>ody 
of confined liquid is transmitted undiminished to every portion 
of the surface of the containing vessel. 

23. Multiplication of force by the transmission of pressure 
by liquids. Pascal himself pointed out that with the aid of 
the principle stated above we ought to be able to transform 
a very small force into one of un- 1 J^2M 
limited magnitude. Thus, if the !? . 

area of the cylinder ab (Fig. 11) a w> 

is 1 sq. cm., while that of the cylin- F- 

der AB is 1000 sq. cm., a force of FIG. 11. Multiplication of 

1 kg. applied to ab would be trans- force by transmission of 

, , pressure 

mitted by the liquid so as to act with 

a force of 1 kg. on each square centimeter of the surface AB. 
Hence the total upward force exerted against the piston AB 
by the 1 kg. applied at ab would be 1000 kg. Pascal's own 
words are as follows : " A vessel full of water is a new prin- 
ciple in mechanics, and a new machine for the multiplication 
of force to any required extent, since one man will by this 
means be able to move any given weight." 

24, The hydraulic press. The experimental proof of the correctness 
of the conclusions of the preceding paragraph is furnished by the 
hydraulic press, an instrument now in common use for subjecting to 
enormous pressures paper, cotton, etc. and for punching holes through 
iron plates, testing the strength of iron beams, extracting oil from 



PASCAL'S LAW 



17 



seeds, making dies, embossing metal, etc. Hydraulic presses of great 
power have been designed for use in steel works to replace huge steam 
hammers. Compressing forces of 10,000 tons or more are thus obtained. 
Much cold steel, as well as hot, is now pressed instead of hammered. 
Such a press is represented in section in Fig. 12. As the small piston 
p is raised, water from the cistern C enters the piston chamber through 
the valve v. As soon 
as the downstroke 
begins, the valve v 
closes, the valve v' 
opens, and the pres- 
sure applied on the 
piston p is trans- 
mitted through the 
tube K to the large 
reservoir, where it 
acts on the large 
cylinder P. 

The force exerted 
upon P is as many 
times that applied 
to p as the area of 
P is times the area 
OJ P- FIG. 12. Diagram of a hydraulic press 

25. No gain in the product of force times distance. It should 
be noticed that, while the force acting on AB (Fig. 11) is 
1000 times as great as the force acting on ab, the distance 
through which the piston AB is pushed up in a given time is 
but YoVo ^ the distance through which the piston ab moves 
down. For forcing ab down a distance of 1 centimeter crowds 
but 1 cubic centimeter of water over into the large cylinder, and 
this additional cubic centimeter can raise the level of the water 
there but 10 1 00 centimeter. We see, therefore, that the product 
of the force acting by the distance moved is precisely the same 
at both ends of the machine. This important conclusion will 
be found in our future study to apply to all machines. 




18 



PEESSUEE IN LIQUIDS 



26. The hydraulic elevator. Another very common application of 
the principle of transformation of pressure by liquids is found in the 
hydraulic elevator. The simplest form of such an elevator is shown in 
Fig. 13. The cage A is borne on the top of a long piston P which runs 
in a cylindrical pit C of the same depth as the height to which the 
carriage must ascend. 
Water enters the pit 
either directly from 
the water mains, m, 
of the city's supply or, 
if this does not fur- 
nish sufficient pres- 
sure, from a special 
reservoir on top of 
the building. When 
the elevator boy pulls 
up on the cord cc, the 
valve v opens so as 
to make connection 
from m into C. The 
elevator then ascends. 
When cc is pulled 
down, v turns so as to 
permit the water in 
C to escape into the 
sewer. The elevator 
then descends. 

Where speed is re- 
quired the motion of 
the piston is com- 
municated indirectly 
to the cage by a sys- 
tem of pulleys like 
that shown in Fig. 14. 
With this arrangement a foot of upward motion of the piston P 
causes the counterpoise D of the cage to descend 2 feet, for it is clear 
from the figure that when the piston goes up 1 foot, enough rope must 
be pulled over the fixed pulley p to lengthen each of the two strands a 
and b 1 foot. Similarly, when the counterpoise descends 2 feet, the cage 
ascends 4 feet. Hence the cage moves four times as fast and four times 




FIG. 14 

Diagrams of hydraulic elevators 



PASCAL'S LAW 



19 



as far as the piston. The elevators in the Eiffel Tower in Paiis are 
of this sort. They have a total travel of 420 feet and are capable of 
lifting 50 people 400 feet per minute. The cylinder C and piston P are 
often not in a pit but lie in a horizontal position. Most modern eleva- 
tors are electric rather than hydraulic. 

27. City water supply. Fig. 15 illustrates the method by 
which a city is often supplied with water from a distant source. 
The aqueduct from the lake a passes under a road r, a brook 
^ and a hill //, and into a reservoir e, from which it is forced 
by the pump p into the standpipe P, whence it is distributed 
to the houses of the city. If a static condition prevailed in 




FIG. 15. City water supply from lake 

the whole system, then the water level in e would of neces- 
sity be the same as that in a, and the level in the pipes of 
the building B would be the same as that in the standpipe P. 
But when the water is flowing, the friction of the mains 
causes the level in e to be somewhat less than that in a, and 
that in B less than that in P. It is on account of the friction 
both of the air and of the pipes that the fountain / does not 
rise nearly as high as the ideal limit shown in the figure. 

QUESTIONS AND PROBLEMS 

1. A jug full of water may often be burst by striking a blow on 
the cork. If the surface of the jug is 200 sq. in. and the cross section of 
the cork 1 sq. in., what total force acts on the interior of the jug when 
a 10-lb. blow is struck on the cork? 

2. How does your city get its water? How is the pressure in the 
pipes maintained? 



20 PRESSUEE IN LIQUIDS 

3. If the water pressure in the city mains is 70 Ib. to the square inch, 
how high above the town is the top of the water in the standpipe ? 

4. The cross-sectional areas of the pistons of a hydraulic press were 
3 sq. in. and 60 sq. in. How great a weight would the large piston 
sustain if 75 Ib. were applied to the small one ? 

5. The diameters of the pistons of a hydraulic press were 2 in. and 
20 in. What force would be produced upon the large piston by 50 Ib. 
on the small one ? 

6. The water pressure in the city mains is 80 Ib. to the square inch. 
The diameter of the piston of a hydraulic elevator of the type shown 
in Fig. 13 is 10 in. If friction could be disregarded, how heavy a load 
could the elevator lift? If 30% of the ideal value must be allowed for 
frictional loss, what load will the elevator lift? 

7. Suppose a tube 5 mm. square and 200 cm. long is inserted into the 
top of a box 20 cm. on a side and filled with water ; what will be the 
total force on the bottom of the box ? on the top ? 



THE PRINCIPLE OF ARCHIMEDES* 

28. Apparent loss of weight of a body in a liquid. The 
preceding experiments have shown that an upward force acts 
against the bottom of any body immersed in a liquid. If 
the body is a boat, cork, piece of wood, or any body which 
floats, it is clear that, since it is in equilibrium, this upward 
force must be equal to the weight of the body. Even if the 
body does not float, everyday observation shows that it still 
loses a portion of its natural weight, for it is well known 
that it is easier to lift a stone under water than in air, or, 
again, that a man in a bathtub can support his whole weight 
by pressing lightly against the bottom with his fingers. It 
was indeed this very observation which first led the old 
Greek philosopher Archimedes (287-212 B.C.) (see opposite 
page 22) to the discovery of the exact law which governs 
the loss of weight of a body in a liquid. 

* A laboratory exercise on the experimental proof of Archimedes' princi- 
ple should either precede or accompany this discussion. See, foi example, 
Experiment 6 of the authors 1 Manual. 



THE PRINCIPLE OF ARCHIMEDES 21 

Hiero, the tyrant of Syracuse, had ordered a gold crown 
made, but suspected that the artisan had fraudulently used 
silver as well as gold in its construction. He ordered Archi- 
medes to discover whether or not this were true. How to do 
so without destroying the crown was at first a puzzle to the 
old philosopher. While in his daily bath, noticing the loss of 
weight of his own body, it suddenly occurred to him that 
any body immersed in a liquid must apparently lose a loeight 
equal to the weight of the displaced liquid. He is said to have 
jumped at once to his feet and rushed through the streets 
of Syracuse crying, " Eureka ! Eureka ! " (I have found it ! I 
have found it!) 

29. Theoretical proof of Archimedes* principle. It is prob- 
able that Archimedes, with that faculty which is so common 
among men of great genius, saw the truth of his conclusion 
without going . through any logical process 
of proof. Such a proof, however, can easily 
be given. Thus, since the upward force on 
the bottom of the block abed (Fig. 16) is 
equal to the weight of the column of liquid 
obce, and since the downward force on the 
top of this block is equal to the weight of 

the column of liquid oade, it is clear that FlG : 16 ' Proof that 

an immersed body 
the upward force must exceed the down- j s buoyed up by a 

ward force by the weight of the column force equal to the 
of liquid abed. Archimedes' principle may wei ht of the dis - 

J placed liquid 

be stated thus: 

The buoyant force exerted by a liquid is exactly equal to the 
weight of the displaced liquid. 

The reasoning is exactly the same, no matter what may be 
the nature of the liquid in which the body is immersed, nor 
how far the body may be beneath the surface. Further, if the 
body weighs more than the liquid which it displaces, it must 




22 



PKESSUKE IN LIQUIDS 




sink, for it is urged down with the force of its own weight, 
and up with the lesser force of the weight of the displaced 
liquid. But if it weighs less than the dis- 
placed liquid, then the upward force due to 
the displaced liquid is greater than its own 
weight, and consequently it must rise to the 
surface. When it reaches the surface, the 
downward force on the top of the block,, 
due to the liquid, becomes zero. The body 
must, however, continue 
to rise until the upward 
force on its bottom is equal 
to its own weight. But 
this upward force is al- 




FIG. 17. Proof that 
a floating body is 
buoyed up by a 
force equal to the 
weight of the dis- 
placed liquid 



ways equal to the weight of the displaced 
liquid, that is, to the weight of the column 
of liquid mbcn (Fig. 17). Hence 

A floating body must displace its own weight 
of the liquid in which it floats. 

This statement is embraced in the state- 
ment of Archimedes' principle, for a body 
which floats has lost its whole weight. 

30. Specific gravity of a heavy solid. The specific gravity 
of a body is by definition the ratio of its weight to the weight 
of an equal volume of water ( 17). Since a submerged body 
displaces a volume of water equal to its own volume, how- 
ever irregular it may be, 

o -a --L t, i Weight of body 

Specific gravity of body TTT . 1 ^- - 

Weight of water displaced 

Making application of Archimedes' principle, we have 

i. j Weight of body 

Specific gravity of body = -- 

Loss of weight in water 

Fig. 18 shows a common method of weighing under water. 



FIG. 18. Method of 

weighing a body 

under water 




ARCHIMEDES (287-212 B.C.) 
(Bust in Naples Museum) 

The celebrated geometrician of antiquity; lived at Syracuse, 
Sicily; first made a determination of IT and computed the area 
of the circle ; discovered the laws of the lever and was author of 
the famous saying, " Give me where I may stand and I will move 
the world"; discovered the laws of flotation; invented various 
devices for repelling the attacks of the Romans in the siege of 
Syracuse ; on the capture of the city, while in the act of drawing 
geometrical figures in a dish of sand, he was killed by a Roman 
soldier to whom he cried out, " Don't spoil my circle " 




THE DETAILS OF A SUBMARINE 

The submarine, one of the newest of marine inventions, is a simple application of 
the principle of Archimedes, one of the oldest principles of physics. In order to 
submerge, the submarine allows water to enter her ballast tanks until the total 
weight of the boat and contents becomes nearly as great as that of the water she 
is able to displace. The boat is then almost submerged. When she is under head- 
way in this condition, a proper use of the horizontal, or diving, rudders sends her 
beneath the surface, or, if submerged, brings her to the surface, so that she can 
scan the horizon with her periscope. The whole operation takes but a few seconds. 
When the submarine wishes to come to the surface for recharging her batteries 
or for other purposes, she blows compressed air into her ballast tanks, thus driv- 
ing the water out of them. Submarines are propelled on the surface by Diesel oil 
engines ; underneath the surface, by storage batteries and electric motors 



THE PRINCIPLE OF ARCHIMEDES 



23 




FIG. 19. Method of finding specific 
gravity of a light solid 



31. Specific gravity of a solid lighter than water. If the 

body is too light to sink of itself, we may still obtain the 

weight of the equal volume 

of water by forcing it beneath 

the surface with a sinker. 

Thus, suppose u\ represents 

the weight on the right pan 

of the balance when the body 

is in air and the sinker in 

water, as in Fig. 19, while w z 

is the weight on the right pan 

when both body and sinker 

are under water. Then w^ w 2 

is obviously the buoyant effect 

of the water on the body alone 

and is therefore equal to the weight of the displaced water. 

32. Specific gravity of liquids by the hydrometer method. 
The commercial hydrometer such as is now in common use 
for testing the specific gravity of alcohol, milk, 

acids, sugar solutions, etc. is of the form shown 
in Fig. 20. The stem is calibrated by trial so 
that the specific gravity of any liquid may be 
read upon it directly. The principle involved is 
that a floating body sinks until it displaces its 
own weight. By making the stem very slender 
the sensitiveness of the instrument may be made 
very great. Why ? 

33. Specific gravity of liquids by "loss of 
weight " method. If any suitable solid be 
weighed, first in air, then in water, and then in 
a liquid of unknown specific gravity, by the 
principle of Archimedes the loss of weight in 

the liquid is equal to the weight of the liquid displaced, 
and the loss in water is equal to the weight of the water 



FIG. 20. Con- 
stant-weight 
hydrometer 



24 



PRESSURE IN LIQUIDS 



displaced. If we divide the loss of weight in the liquid by 
the loss of weight in water, we are dividing the weight of a 
given volume of liquid by the weight of an equal volume of 
water. Therefore^ 

To find the specific gravity of a liquid, divide the loss of 
weight of some solid in it by the loss of weight of the same body 
in water.* 

QUESTIONS AND PROBLEMS 

1. Let a vessel of water, together with an object heavier than water, 
be counterpoised as in Fig. 21 (position a). Now if the object be placed 
inside the vessel of water (position 6), will the scales remain balanced? 
Predict the result and then 

try the experiment. 

2. Does the weight ap- 
parently lost by a submerged 
body depend upon its volume 
or its weight ? Explain. 

3. A brick lost 1 Ib. when 
submerged 1 ft. deep; how 
much would it lose if sus- 
pended 3 ft. deep ? 

4. Will a boat rise or sink 
deeper in the water as it passes 
from a river to the ocean ? 

5. A fish lies perfectly FIG. 21 
motionless near the center 

of an aquarium. What is the average density of the fish? Explain. 

6. Where do the larger numbers appear on hydrometers, toward 
the bottom or toward the top of the stem ? Explain. 

7. A 150-lb. man can just float. What is his volume? 

8. Describe fully how you would proceed to find the specific gravity 
of an irregular solid heavier than water, showing in every case why you 
proceed as you do. 

9. A body loses 25 g. in water, 23 g. in oil, and 20 g. in alcohol. Find 
the specific gravity of the oil and of the alcohol. 

* Laboratory experiments on the determination of the densities of solids 
and liquids should follow or accompany the discussion of this chapter. See, 
for example, Experiments 7 and 8 of the authors' Manual. 




THE PRINCIPLE OF ARCHIMEDES 25 

10. A platinum ball weighs 330 g. in air, 315 g. in water, and 303 g. 
in sulphuric acid. Find the volume of the ball and the specific gravity 
of the platinum and of the acid. 

11. A piece of paraffin weighed 178 g. in air, and a sinker weighed 
30 g. in water. Both together weighed 8 g. in water. Find the specific 
gravity of the paraffin. 

12. A cube of iron 10 cm. on a side weighs 7500 g. What will it 
weigh in alcohol of density .82 ? 

13. What fraction of the volume of a block of wood will float above 
water if its density is .5 ? if its density is .6 ? if its density is .9 ? State 
in general what fraction of the volume of a floating body is under water. 

14. If a rectangular iceberg rises 100 ft. above water, how far does 
it extend below water? (Assume the density of the ice to be .9 that 
of sea water.) 

15. A barge 30 it. by 15 ft. sank 4 in. when an elephant was taken 
aboard. What was the elephant's weight ? 

16. A cubic foot of stone weighed 110 Ib. in water. Find its specific 
gravity. 

17. Steel is three times as heavy as aluminum. When equal volumes 
of each are submerged in water, how do their apparent losses of weight 
compare ? 

18. The density of cork is .25 g. per cubic centimeter. What force 
is required to push a cubic centimeter of cork beneath the surface 
of water? 

19. A block of wood 15 cm. by 10 cm. by 4 cm. floats in water with 
1 cm. in the air. Find the weight of the wood and its specific gravity. 

20. The specific gravity of milk is 1.032. How is its specific gravity 
affected by removing part of the cream ? by adding water ? May these 
two changes be made so as not to alter its specific gravity at all? 

21. A piece of sandstone having a specific gravity of 2.6 weighs 
480 g. in water. Find its weight in air. 

22. The density of stone is about 2.5. If a boy can lift 120 Ib., how 
heavy a stone can he lift to the surface of a pond ? 

23. The hull of a modern battleship is made almost entirely of steel, 
its walls being of steel plates from 6 to 18 in. thick. Explain how it 
can float. 



CHAPTER III 





PRESSURE IN AIR 

BAROMETRIC PHENOMENA 

34. The weight of air. To ordinary observation air is scarcely 
perceptible. It appears to have no weight and to offer no resist- 
ance to bodies passing through it. But if a bulb is balanced as 
in Fig. 22, and then removed and 
filled with air under pressure by a 
few strokes of a bicycle pump, it 
will be found, when placed on the 
balance again, to be heavier than it 
was before. On the other hand, if 
the bulb is connected with an air 
pump and exhausted, it will be 
found to have lost weight.* Evi- 
dently, then, air can be put into and 
taken out of a vessel, weighed, and 
handled, just like a liquid or a solid. 

We are accustomed to say that bodies are "as light as air "; 
yet careful measurement shows that it takes but 12 cubic feet 
of air to weigh a pound, so that a single large room contains 
more air than an ordinary man can lift. Thus, the air in a 
room 60 feet by 30 feet by 15 feet weighs more than .a ton. 
The exact weight of air at the freezing temperature and un- 
der normal atmospheric conditions is .001298 gram per cubic 
centimeter, that is, 1.293 grams per liter. A given volume of 
air therefore weighs y^- as much as an equal volume of water. 

* Another experiment is to weigh an electric-light bulb, then puncture it 
with a blowpipe and weigh again. 

26 



FIG. 22. Proof that air 
has weight 



BAROMETRIC PHENOMENA 



27 



35. Proof that air exerts pressure. Since air has weight, 
it is to be inferred that air, like a liquid, exerts force against 
any surface immersed in it. The following experiments 
prove this. 

Let a rubber membrane be stretched over a glass vessel, as in Fig. '23. 
As the air is exhausted from beneath the membrane the latter will be 
observed to be more and more depressed until it will finally burst under 
the pressure of the air above. 

Again, let a tin can be partly filled with water and the water boiled. 
The air will be expelled by the escaping steam. While the boiling is 




FIG. 23. Rubber mem- 
brane stretched by weight 
of air 




FIG. 24. Gallon can crushed by 
atmospheric pressure 



still going on, let the can be tightly corked, then placed in a sink or 
tray and cold water poured over it. The steam will be condensed and 
the weight of the air outside will crush the can (see Fig. 24). 

36. Cause of the rise of liquids in exhausted tubes. If the 

lower end of a long tube be dipped into water and the air 
exhausted from the upper end, water will rise in the tube. We 
prove the truth of this statement every time we draw lemonade 
through a straw. The old Greeks and Romans explained such 
phenomena by saying that " nature abhors a vacuum," and 
this explanation was still in vogue in Galileo's time. But in 
1640 the Duke of Tuscany had a deep well dug near Florence, 
and found to his surprise that no water pump which could 
be obtained would raise the water higher than about 32 feet 
above the level in the well. When he applied to the aged 



28 



PRESSURE 



AIR 



(1) 





Galileo (see opposite p. 72) for an explanation, the latter 
replied that evidently " nature's horror of a vacuum did not 
extend beyond 32 feet." It is quite likely that Galileo sus- 
pected that the pressure of the air was responsible for the 
phenomenon, for he had himself proved before that air had 
weight; and, furthermore, he at once devised another experi- 
ment to test, as he said, the " power of a vacuum." He died 
in 1642 before the experiment was performed, but suggested 
to his pupil Torricelli that he con- 
tinue the investigation. 

37. Torricelli's experiment. Tor- 
ricelli argued that if water would 
rise 32 feet, then mercury, which 
is about 13 times as heavy as water, 
ought to rise but -^ as high. To 
test this inference he performed, 
in 1643, the following famous 
experiment : 

Let a tube about 4 ft. long, which is 
sealed at one end, be completely filled 
with mercury, as in Fig. 25, (J), then 
closed with the thumb and inverted, and 
the bottom immersed in a dish of mer- 
cury, as in Fig. 25, (2). When the thumb 
is removed from the bottom of the tube, 
the mercury will fall away from the 
upper end of the tube, in spite of the 

fact that in so doing it will leave a vacuum above it; and its upper 
surface will, in fact, stand about ^ of 32 ft., that is, between 29 and 
30 in., above the mercury in the dish. 

Torricelli concluded from this experiment that the rise 
of liquids in exhausted tubes is due to an outside pressure 
exerted by the atmosphere on the surface of the liquid, 
and not to any mysterious sucking power created by the 
vacuum as is popularly believed even to-day. 





FIG. 25. Torricelli's 
experiment 



BAKOMETKIC PHENOMENA 



29 




FIG. 26. Barometer 
falls when air pres- 
sure on the mercury 
surface is reduced 



38. Further decisive tests. An unanswerable argument in 
favor of this conclusion will be furnished if the mercury in 
the tube falls as soon as the air is removed from above the 

surface of the mercury in the dish. 

To test this point, let the dish and tube be 

placed on the table of an air pump, as in Fig. 26, 

the tube passing through a 

tightly fitting rubber stop- 
per A in the bell jar. As 

soon as the pump is started 

the mercury in the tube will, 

in fact, be seen to fall. As 

the pumping is continued it 

will fall nearer and nearer 

to the level in the dish, 

although it will not usually 

reach it, for the reason that 

an ordinary vacuum pump 

is not capable of producing 

as good a vacuum as that which exists in the 
top of the tube. As the air is allowed to return 
to the bell jar the mercury will rise in the tube CJIil * mid 

to its former level. 

39. Amount of the atmospheric pressure. 
Torricelli's experiment shows exactly how 
great the atmospheric pressure is, since 
this pressure is able to balance a column 
of mercury of definite length. As the pres- 
sures along the same level ac (Fig. 27) are 
equal, the downward pressure exerted by 
the atmosphere on the surface of the 
mercury at c is equal to the downward 
pressure of the column of mercury at a. 

But the downward pressure at this point within the tube is 
equal to hd, where d is the density of mercury and li is the 
depth below the surface b. Since the average height of this 



FIG. 27. Air column 

to top of atmosphere 

balances the mercury 

column ab 



30 PRESSURE IN AIR 

column at sea level is found to be 76 centimeters, and since 
the density of mercury is 13.6 grams per cubic centimeter, the 
downward pressure inside the tube at a is equal to 76 times 
13.6 grams, or 1033.6 grams per square centimeter. Hence 
the atmospheric pressure acting on the surface of the mercury 
at c is 1033.6 grams, or, roughly, 1 kilogram per square 
centimeter. The pressure of one atmosphere is, then, about 
15 pounds per square inch. 

40. Pascal's experiment. Pascal thought of another way 
of testing whether or not it were indeed the weight of the 
outside air which sustains the column of mercury in an 
exhausted tube. He reasoned that, since the pressure in a 
liquid diminishes on ascending toward the surface, atmos- 
pheric pressure ought also to diminish on passing from sea 
level to a mountain top. As there was no mountain near Paris, 
he carried Torricelli's apparatus to the top of a high tower 
and found, indeed, a slight fall in the height of the column 
of mercury. He then wrote to his brother-in-law, Perrier, who 
lived near Puy de DOme, a mountain in the south of France, 
and asked him to try the experiment on a larger scale. 
Perrier wrote back that he was " ravished with admiration 
and astonishment" when he found that on ascending 1000 
meters the mercury sank about 8 centimeters in the tube. 
This was in 1648, five years after Torricelli's discovery. 

At the present clay geological parties actually ascertain dif- 
ferences in altitude by observing the change in the barometric 
pressure as they ascend or descend. A fall of 1 millimeter 
in the barometric height corresponds to an ascent of about 
12 meters. 

41. The barometer. The modern barometer (Fig. 28) is 
essentially nothing more nor less than Torricelli's tube. Tak- 
ing a barometer reading consists simply in accurately measur- 
ing the height of the mercury column. This height varies from 
73 to 76.5 centimeters in localities which are not far above 



BAROMETKIC PHENOMENA 



31 



sea level, the reason being that disturbances in the atmosphere 
affect the pressure at the earth's surface in the same way in 
which eddies and high waves in a tank of water would affect 
the liquid pressure at the bottom of the tank. 
The barometer does not directly foretell 
the weather, but it has been found that a 
low or rapidly falling pressure is usually 
accompanied, or soon followed, by stormy 
conditions. Hence the barometer, although 
not an infallible weather prophet, is never- 
theless of considerable assistance in fore- 
casting weather conditions some hours 
ahead. Further, by comparing at a central 
station the telegraphic reports of barometer 
readings made every few hours at stations 
all over the country, it is possible to deter- 
mine in what direction the atmospheric 
eddies which cause barometer changes and 
stormy conditions are traveling and hence 
to forecast the weather even a day or two 
in advance. 

42. The first barometers. Torricelli actually 
constructed a barometer not essentially different 
from that shown in Fig. 28 and used it for 
observing changes in the atmospheric pressure; 
but perhaps the most interesting of the early 
barometers was that set up about 1650 by Otto 
von Guericke of Magdeburg (1602-1686) (see 
opposite p. 32). He used for his barometer a 
water column the top of which passed through 
the roof of his house. A wooden image which 

floated on the upper surface of the water appeared above the housetop 
in fair weather but retired from sight in foul, a circumstance which 
led his neighbors to charge him with being in league with Satan. 

43. The aneroid barometer. Since the mercurial barometer is some- 
what long and inconvenient to carry, geological and surveying parties 



FIG. 28. The Fortin 
barometer 



32 PRESSURE IN AIR 

commonly use an instrument called the aneroid barometer. It consists 
essentially of an air-tight cylindrical box the top of which is a metallic 
diaphragm which bends slightly under the influence of change in the 
atmospheric pressure. This motion of the top of the box is multiplied 
by a delicate system of levers and communicated to a hand which moves 
over a dial whose readings are made to correspond to the readings of a 
mercury barometer. These instruments are made so sensitive as to 




TIG. 29. The aneroid barometer 

indicate a change in pressure when they are moved no farther than from 
a table to the floor. In the self-recording aneroid barometer, or baro- 
graph, used by the United States Weather Bureau (Fig. 29), several of the 
air-tight boxes are superposed for greater sensitiveness, and the pressures 
are recorded in ink upon paper wound about a drum. Clockwork inside 
the drum makes it revolve once a week. A somewhat different form of 
the instrument is used by aviators to record altitude. 

QUESTIONS AND PROBLEMS 

1. Why does not the ink run out of a pneumatic inkstand like that 
shown in Fig. 30 ? 

2. If a tumbler is filled, or partly filled, with water, and a piece of 
writing paper is placed over the top, it may be inverted, as in Fig. 31, . 
without spilling the water. Explain. What is the function of the paper ? 




OTTO VON GUERICKE (1602-1686) 

German physicist, astronomer, and man of affairs ; mayor of Mag- 
deburg; invented the air pump in 1650, and performed many 
new experiments with liquids and gases ; discovered electrostatic 
repulsion ; constructed the famous Magdeburg hemispheres which 
four teams of horses could not pull apart (see p. 33) 



Water^Outlet 




THE MERCURY-DIFFUSION AIR PUMP 

The latest development of the air pump is shown in the accompanying diagram. 
It is over a million times more effective than an air pump of the mechanical 
kind invented by Von Guericke. The principle is as follows: The jet of water 
pouring out through J^ from an ordinary water tap T entrains the air in the 
chamber C and thus pulls the pressure in C" down to from 10 to 15 mm. of mer- 
cury. Next, the mercury jet ,7 2 > produced by boiling violently the mercury above 
the electric furnace F, entrains the air in the chamber (J" and thus lowers the 
pressure in this chamber to, say, .01 mm. of mercury. Again, the stream of mer- 
cury vapor pouring out of </ 3 , under the influence of the furnace F', carries with it 
the molecules of air coming out of C'". Finally, the liquid-air trap freezes out the 
mercury vapor, some of which would otherwise find its way through C'" into the 
high-vacuum chamber. So little air is finally left in this high-vacuum chamber 
that the pressure there may be as low as a hundred-millionth of a millimeter of 
mercury. Pumps of this sort are now used for exhausting audion bulbs and high- 
vacuum rectifiers, which are becoming of very great commercial value. The credit 
for the invention of this form of pump belongs primarily to a fellow countryman 
of Von Guericke, Professor Gaede, of Freiburg, Germany. Improvements of his 
design, however, have been made quite independently and along somewhat 
different lines by several Americans: namely, Irving Langmuir of the General 
Electric Company, Schenectady ; O. E. Buckley of the Western Electric Company, 
New York ; and W. W. Crawford of the Victor Electric Company, Chicago. The 
particular design shown in the diagram is due to Dr. J. E. Shrader of the 
Westinghouse Research Laboratory, Pittsburgh 



COMPRESSIBILITY OF AIR 



33 




3. If a small quantity of air should get into the space at the top of 
the mercury column of a barometer, how would it affect the readings ? 
Why? 

4. Would the pressure of the atmosphere hold mer- 
cury as high in a tube as large as your wrist as in one 
having the diameter of your finger ? Explain. 

5. Give three reasons why mercury is better than 

water for use in barometers. FlG - 

6. Calculate the number of tons atmospheric force on the roof of 
an apartment house 50 ft. x 100 ft. Why does the roof not cave in? 

7. Measure the dimensions of your classroom in 
feet and calculate the number of pounds of air in 
the room. 

8. Magdeburg hemispheres (Fig. 32) are so 
called because they were invented by Otto von 
Guericke, who was mayor of Magdeburg. When 
the lips of the hemispheres are placed in contact 
and the air exhausted from between them, it is 
found very difficult to pull them apart. Why? 

9. Von Guericke's original hemispheres are 
still preserved in the museum at Berlin. Their 

interior diameter is 22 in. On the cover of the book which describes 

his experiments is a picture which represents four teams of horses on 

each side of the hemispheres, trying to separate them. The experiment 

was actually performed in this way before 

the German emperor Ferdinand III. If the 

air was all removed from the interior of 

the hemispheres, what force in pounds was 

in fact required to pull them apart? (Find 

the atmospheric force on a circle of 11 in. 

radius.) 




FIG. 31 




FIG. 32. Magdeburg 
hemispheres 



COMPRESSIBILITY AND EXPANSIBILITY OF AIR 

44. Incompressibility of liquids. Thus far we have found 
very striking resemblances between the conditions which exist 
at the bottom of a body of liquid and those which exist at the 
bottom of the great ocean of air in which we live. We now 
come to a most important difference. It is well known that 
if 2 liters of water be poured into a tall cylindrical vessel, the 
water will stand exactly twice as high as if the vessel contained 



34 PRESSURE IN AIR 

but 1 liter; or if 10 liters be poured in, the water will stand 
10 times as high as if there were but 1 liter. This means that 
the lowest liter in the vessel is not measurably compressed 
by the weight of the water above it. 

It has been found by carefully devised experiments that 
compressing weights enormously greater than these may be 
used without producing a marked effect ; for example, when a 
cubic centimeter of water is subjected to the stupendous pres- 
sure of 3,000,000 grams, its volume is reduced to but .90 cubic 
centimeter. Hence we say that water, and liquids generally, 
are practically incompressible. Had it not been for this fact 
we should not have been justified in taking the pressure at 
any depth below the surface of the sea as the simple product 
of the depth by the density at the surface. 

The depth bomb, so successful in the destruction of sub- 
marines, is effective because of the practical incompressibility 
of water. If the bomb explodes within a hundred feet of 
the submarine and is far enough down so that the force of the 
explosion is not lost through expansion at the surface, the 
effect is likely to be disastrous. 

45. Compressibility of air. When we study the effects of 
pressure on air, we find a wholly different behavior from that 
described above for water. It is very easy to compress a body 
of air to one half, one fifth, or one tenth of its normal volume, 
as we prove every time we inflate a pneumatic, tire or cushion of 
any sort. Further, the expansibility of air (that is, its tendency 
to spring back to a larger volume as soon as the pressure 
is relieved) is proved every time a tennis ball or a football 
bounds, or the air rushes out from a punctured tire. 

But it is not only air which has been crowded into a pneu- 
matic cushion by some sort of pressure pump which is in 
this state of readiness to expand as soon as the pressure is 
diminished; the ordinary air of the room will expand in the 
same way if the pressure to which it is subjected is relieved. 



COMPRESSIBILITY OF AIR 



Thus, let a liter beaker with a sheet of rubber dam tied tightly over 
the top be placed under the receiver of an air pump. As soon as the 
pump is set into operation the 
inside air will expand with suffi- 
cient force to burst the rubber 
or greatly distend it, as shown 
in Fig. 33. 

Again, let two bottles be ar- 
ranged as in Fig. 34, one being 




FIG. 33 FIG. 34 

Illustrations of the expansibility of air- 



stoppered air-tight, while the 

other is uncorked. As soon as 

the two are placed under the 

receiver of an air pump and the air exhausted, the water in A will pass. 

over into B. When the air is readmitted to the receiver, the water will 

flow back. Explain. 

46. Why hollow bodies are not crushed by atmospheric, 
pressure. The preceding experiments show why the walls 
of hollow bodies are not crushed in by the enormous forces 
which the weight of the atmosphere exerts against them. 
For the air inside such bodies presses their walls out with 
as much force as the outside air presses them in. In the 
experiment of 35 the inside air was removed by the es- 
caping steam. When this steam was condensed by the cold 
water, the inside pressure became very small and the out- 
side pressure then crushed the can. In the experiment shown 
in Fig. 33 it was the outside pressure which was removed 
by the air pump, and the pressure of the inside air then 
burst the rubber. 

47. Boyle's law. The first man to investigate the exact- 
relation between the change in the pressure exerted by a con- 
fined body of gas and its change in volume was an Irishman, 
Robert Boyle (1627-1691). We shall repeat a modified form 
of his experiment much more carefully in the laboratory, but 
the following will illustrate the method by which he discov- 
ered one of the most important laws of physics, a law which 
is now known by his name. 



36 



PRESSURE 



AIR 



Let mercury be poured into a bent glass tube until it stands at the 
same level, in the closed arm A C as in the open arm ED (Fig. 35). 
There is now confined in A C a certain volume of air under the pressure 
of one atmosphere. Call this pressure P r Let the length A C be meas- 
ured and called V r Then let mercury be poured into the long arm 
until the level in this arm is as many centimeters 
above the level in the short arm as there are centi- 
meters in the barometer height. The confined air 
is now under a pressure of two atmospheres. Call it 
P 2 . Let the new volume A^C(= F 2 ) be measured. 
It will be found to be just half its former value. 

Hence we learn that doubling the pressure 
exerted upon a body of gas halves its volume. 
If we had tripled the pressure, we should have 
found the volume reduced to one third its 
initial value, etc. That is, the pressure which 
a given quantity of gas at constant temperature 
exerts against the walls of the containing vessel 
is inversely proportional to the volume occupied. 
This is algebraically stated thus: 




or 



FIG. 35. Method 

of demonstrating 

Boyle's law 

(i) 



This is Boyle's law. It may also be stated in slightly 
different form. Doubling, tripling, or quadrupling the pres- 
sure must double, triple, or quadruple the density, since the 
volume is made only one half, one third, or one fourth as 
much, while the mass remains unchanged. Hence the pres- 
sure which a gas exerts is directly proportional to its density, 
or, algebraically, # 

&sad=4. (<r\ 

^ D* 

48. Extent and character of the earth's atmosphere. From 
the facts of compressibility and expansibility of air we may 

* A laboratory experiment on Boyle's law should follow this discussion. 
See, for example, Experiment 9 of the authors' Manual. 



COMPKESSIBILITY OF AIR 



37 



know that the air, unlike the sea, must become less and less 
dense as we ascend from the bottom toward the top. Thus, 
at the top of Mont Blanc, an altitude of about three miles, 
where the barometer height is but 38 centimeters, or one half 
of its value at sea level, the density also must, by Boyle's 
law, be just one half as much as at sea level. 



Heights 

in miles 



Barometer 
keif/his in 




Air 

densities 



FIG. 36. Extent and character of atmosphere 

No one has ever ascended higher than 7 miles, which was 
approximately the height attained in 1862 by the two daring 
English aeronauts Glaisher and Cox we 11. At this altitude the 
barometric height is but about 7 inches, and the temperature 
about 60 F. Both aeronauts lost the use of their limbs, 
and Mr. Glaisher became unconscious. Mr. Coxwell barely 
succeeded in grasping with his teeth the rope which opened a 
valve and caused the balloon to descend. Again, on July 31, 
1901, the French aeronaut M. Berson rose without injury to 



38 PKESSUEE IN AIR 

a height of about 7 miles (35,420 feet), his success being 
due to the artificial inhalation of oxygen. The American 
aviator Lieutenant John A. Macready of the United States 
Army, on September 28, 1921, ascended in an airplane to a 
height of 34,563 feet. He found the temperature 58 F. 

By sending up self-registering thermometers and barome- 
ters in balloons which burst at great altitudes, the instruments 
being protected by parachutes from the dangers of rapid fall, 
the atmosphere has been explored to a height of 35,080 
meters (21.8 miles), this being the height attained on Decem- 
ber 7, 1911, by a little balloon which was sent up at Pavia, 
Italy. These extreme heights are calculated from the indi- 
cations of the self -registering barometers. 

At a height of 35 miles the density of the atmosphere is 
estimated to be but 30 Q 00 of its value at sea level. By calcu- 
lating how far below the horizon the sun must be when the 
last traces of color disappear from the sky, we find that at a 
height as great as 45 miles there must be air enough to reflect 
some light. How far beyond this an extremely rarified atmos- 
phere may extend, no one knows. It has been estimated at 
all the way from 100 to 500 miles. These estimates are based 
on observations of the height at which meteors first become 
visible, on the height of the aurora borealis, and on the dark- 
ening of the surface of the moon just before it is eclipsed by 
the shadow of the solid earth. 

QUESTIONS AND PROBLEMS 

1. The deepest sounding in the ocean is about 6 mi. Find the 
pressure in tons per square inch at this depth. (Specific gravity of 
ocean water = 1.026.) Will a pebble thrown overboard reach the 
bottom ? Explain. 

2. What sort of a change in volume do the bubbles of air which 
escape from a diver's suit experience as they ascend to the surface ? 

3. With the aid of the experiment in which the rubber dam was 
burst under the exhausted receiver of an air pump explain why high 



COMPRESSIBILITY OF AIE 



39 



mountain climbing ofieii causes pain and bleeding in the ears and nose. 
Why does deep diving produce similar effects? 

4. Blow as hard as possible into the tube of the bottle shown in 
Fig. 37. Then withdraw the mouth and explain all of the effects 
observed. 

5. If a bottle or cylinder is filled with water and inverted in a dish 
of water, with its mouth beneath the surface (see Fig. 38), the water 
will not run out. Why ? 

6. If a bent rubber tube is inserted beneath the cylinder 
and air blown in at o (Fig. 38), it will rise to the top and 
displace the water. This is the method regularly used in col- 
lecting gases. Explain what forces the gas up into it, and 
what causes the water to descend in the tube as the gas rises. 

7. Why must the bung be removed from a cider barrel in 
order to secure a proper flow from the faucet ? 

8. When a bottle full of water is inverted, the water will FIG. 37 
gurgle out instead of issuing in a steady stream. Why? 

9. If 100 cu. ft. of hydrogen gas at normal pressure are forced into 
a steel tank having a capacity of 5 cu. ft., what is the gas pressure in 
pounds per square inch ? 

10. An automobile tire having a capacity of 1500 cu. in. is inflated 
to a pressure of 90 pounds per square inch. What is the density of the 
air within the tire? To what volume would the air 

expand if there should be a " blow-out " ? 

11. Under ordinary conditions a gram of air occu- 
pies about 800 cc. Find what volume a gram will occupy 
at the top of Mont Blanc (altitude 15,781 ft.), where the 
barometer indicates that the pressure is only about one 
half what it is at sea level. 

12. The mean density of the air at sea level is about 

.0012. What is its density at the top of Mont Blanc? FIG. 38. 

What fractional part of the earth's atmosphere has 

one left beneath him when he ascends to the top of this mountain ?' 

13. If Glaisher and Coxwell rose in their balloon until the barometric 
height was only 18 cm., how many inhalations were they obliged to- 
il lake in order to obtain the same amount of air which they could 
obtain at the surface in one inhalation ? 

14. 1 cc. of air at the earth's surface weighs .00129 g. If this, 
were the density all the way up, to what height would the atmos- 
phere extend? 




40 



PRESSURE IX AIR 



PNEUMATIC APPLIANCES 

49. The siphon. Let a rubber or glass tube be filled with water and 
then placed in the position shown in Fig. 39. Water will be found to 
flow through the tube from vessel A into vessel B. If then B be raised 
until the water in it is at a higher level than 
that in A, the direction of flow will be reversed. 
This instrument, which is called the siphon, is 
very useful for removing liquids from vessels 
which cannot be overturned, or for drawing off 
the upper layers of a liquid without disturbing 
the lower layers. Many commercial applications 
of it are found in various siphon flushing systems. 



f 1 



i 



The explanation of the siphon's action p IG . 39. The siphon 
is readily seen from Fig. 39. Since the 
tube acb is full of water, water must evidently flow through 
it if the force which pushes it one way is greater than that 
which pushes it the other way. Now the upward pressure at 
a is equal to atmospheric pressure minus the downward pres- 
sure due to the water column ad, while the upward pres- 
sure at b is the atmospheric pressure minus the downward 
pressure due to the water column be. 
Hence the pressure at a exceeds the pres- 
sure at b by the pressure due to the water 
column fb. The siphon will evidently 
cease to act when the water is at the same 
level in the two vessels, since then/5 = 
and the forces acting at the two ends of 
the tube are therefore equal and opposite. 
It will also cease to act when the bend c 
is more than 34 feet above the surface of the water in A, 
since then a vacuum will form at the top, atmospheric 
pressure being unable to raise water to a height greater than 
this in either tube. 

Would a siphon flow in a vacuum ? 




FIG. 40. Intermittent 
siphon 



PNEUMATIC APPLIANCES 



41 



50. The intermittent siphon. Fig. 40 represents an intermittent 
siphon. If the vessel is at first empty, to what level must it be filled 
before the water will flow out at o ? To what level will the water then 
fall before the flow will cease ? 

51. The air pump. The air pump was invented in 1650 
by Otto von Guericke, mayor of Magdeburg, Germany, who 

deserves the greater credit since he 
was apparently altogether without 
knowledge of the discoveries which 
Galileo, Torricelli, and Pascal had 
made a few 
years earlier 
regarding the 
character of the 
earth's atmos- 




FIG. 41. A simple air pump 



phere. A simple form of such a pump 
is shown in Fig. 41. When the piston 
is raised, the air from the receiver R 
expands into the cylinder B through the 
valve A. When the piston descends, it 
compresses this air and thus closes 
the valve A and opens the exhaust 
valve C. Thus, with each double stroke 
a certain fraction of the air in the 
receiver is transferred from R through 
the cylinder to the outside. 

In many pumps the valve C is in the 
piston itself. 

52. The compression pump. A com- 
pression pump is used for compressing 

a gas into a container. If the pump shown in Fig. 41 be 
detached from the receiver plate and the vessel to receive 
the gas be attached at (7, we have a compression pump. 
Fig. 42 shows a common form of compression pump used for 



FIG. 42. Automobile 
compression pump 



PRESSURE IK AIR 



inflating automobile tires. Cup valves are shown at c and <?'. 
They are leather disks a little larger than the barrel of the 
pump, attached to a loosely fitting metal piston. 

When the pistons are forced down, the valve c spreads 
tightly against the wall, forcing the air past the valves c 
and v. On the upstroke the valve c' spreads and forces the 
compressed air in the small barrel past v, while at the same 
time air passes by c, again filling the two barrels, v prevents 
any air from reentering the small barrel from the hose h. 
The greater compressing power of the two-barreled pump 
is due to the fact that c f on the upstroke compresses air that 
has already been compressed by c on the 
downstroke. 

Compressed air finds so many applications 
in such machines as air drills (used in min- 
ing), air brakes, air motors, etc. that the 
compression pump must be looked upon as 
of much greater importance industrially than 
the exhaust pump. 

53. The lift pump. The common water 
pump, shown in Fig. 43, has been in use at 
least since the time of Aristotle (fourth cen- 
tury B. c.). It will be seen from the figure 
that it is nothing more nor less than a 
simplified form of air pump. In fact, in the earlier strokes 
we are simply exhausting air from the pipe below the valve b. 
Water could never be obtained at S, even with a perfect 
pump, if the valve b were not within 34 feet of the surface 
of the water in W. Why ? On account of mechanical im- 
perfections this limit is usually about 28 feet instead of 34. 
Let the student analyze, stroke by stroke, the operation of 
pumping water from a well with the pump of Fig. 43. Why 
will pouring in a little water at the top, that is, " priming," 
often assist greatly in starting such a pump ? 




FIG. 43. The lift 
pump 



PNEUMATIC APPLIANCES 




54. The force pump. Fig. 44 illustrates the construction of 
the force pump, a device commonly used whe;i it is desired 
to deliver water at a point higher than the position at which 
it is convenient to place the pump 

itself. Let the student analyze the 
action of the pump from a study of 
the diagram. 

In order to make the flow of water 
in the pipe HS continue during the 
upstroke, an air chamber is always 
inserted between the valve a and the 
discharge point. As the water is 
forced violently into this chamber by 
the downward motion of the piston 
it compresses the confined air. It is, 
then, the reaction of this compressed 
air which is immediately responsible for the flow in the dis- 
charge tube ; and as this reaction is continuous, the flow is 
also continuous. 

55. The Cartesian diver. Descartes 
(1596-1650), the great French philoso- 
pher, invented an odd device which illus- 
trates at the same time the principle of 
the transmission of pressure by liquids, 
the principle of Archimedes, and the 
compressibility of gases. A hollow glass 
image in human shape (Fig. 45, (1)) 
has an opening in the lower end. It is 
filled partly with water and partly with 

air, so that it will just float. By pressing on the rubber dia- 
phragm at the top of the vessel it may be made to sink or 
rise at will. Explain. If the diver is not available, a small 
bottle or test tube (Fig. 45, (2)) may be used instead ; it 
works equally well and brings out the principle even better. 



FIG. 44. The force pump 



(2) 




FIG. 45. 



The Cartesian 
diver 



44 



PRESSURE IN AIR 



The modern submarine (see opposite page 23) is essentially 
nothing but a. huge Cartesian diver which is propelled above 
water by oil or steam engines, and when submerged, by electric 
motors driven by storage batteries. The volume of the air in 
its chambers is changed by forcing water in or out, and it dives 
by a combined use of the propeller and horizontal rudders. 

56. The balloon. A reference to the proof of Archimedes' principle 
( 29, p. 21) will show that it must apply as well to gases as to liquids. 
Hence any body immersed in air is buoyed up l>y a force which is equal 
to the weight of the displaced air. The body 
will therefore rise if its own weight is less 
than the weight of the air which it displaces. 

A balloon is a large silk bag (see opposite 
page 45) impregnated with rubber and filled 
either with hydrogen or with common illumi- 
nating gas. The former gas weighs about .09 
kilogram per cubic meter, and common illumi- 
nating gas weighs about .75 kilogram per cubic 
meter. It will be remembered that ordinary air 
weighs about 1.20 kilograms per cubic meter. 
It will be seen, therefore, that the lifting force 
of hydrogen per cubic meter namely, 1.20 
.09 = 1.11, is more than twice the lifting force 
of illuminating gas, 1.20 .75 = .45. 

Ordinarily a balloon is not completely filled 

at the start ; for if it were, since the outside pressure is continually 
diminishing as it ascends, the pressure of the inside gas would subject 
the bag to enormous strain and would surely burst it before it reached 
any considerable altitude. But if it is but partially inflated at the start, 
it can increase in volume as it ascends by simply inflating to a greater 
extent. Thus, a balloon which ascends until the pressure is but 7 centi- 
meters of mercury should be only about one fourth inflated when it is 
at the surface. 

The parachute (Fig. 46) is a huge, umbrella-like affair with which 
the aeronaut may descend in safety to the earth. After opening, it 
descends very slowly on account of the enormous surface exposed to the 
air. A hole in the top allows air to escape slowly, and thus keeps the 
parachute upright. 




FIG. 40. The parachute 



PNEUMATIC APPLIANCES 



45 




57. Helium balloons. One of the striking results of the World War 
was the development of the helium balloon. Helium is a noninflam- 
mable gas twice as dense as hydrogen and having a lifting power .92 as 
great. It is so rare an element that before the war not over 100 cu. ft. 
had been collected by anyone. Its pre-war price was $1700 per cu. ft. 
At the close of the war 147,000 cu. ft., extracted at a cost of ten cents 
a cubic foot from the gas wells of Texas and Okla- 
homa, were ready for shipment to France, and plans 

were under way for producing it at the rate of 50,000 
cu. ft. per day. The production of a balloon gas that 
assures safety from fire opens up a new era for the 
dirigible balloon (see opposite page 44). 

58. The diving bell. The diving bell (Fig. 47) 
is a heavy, bell-shaped body with rigid walls, 

which sinks of its own weight. Formerly the workmen who 
went down in the bell had at their disposal only the amount of 
air confined within it, and 
the water rose to a certain 
height within the bell on 
account of the compression 
of the air. But in modern 
practice the air is forced in 
from the surface through a 
connecting tube a (Fig. 48) 
by means of a force pump h. 
This arrangement, in addi- 
tion to furnishing a con- 
tinual supply of fresh air, 
makes it possible to force 
the water down to the 

level of the bottom of the 

i n T ,. . . FIG. 48. Laying foundations of piers 

bell. In practice a contm- with the diving bell 

ual stream of bubbles is 

kept flowing out from the lower edge .of the bell, as shown 

in Fig. 48, which illustrates subaqueous construction. 




46 



PRESSURE IN AIR, 



The pressure of the air within the bell must, of course, be 
the pressure existing within the water at the depth of the 
level of the water inside the bell; that is, in Fig. 47 at the 
depth AC. Thus, at a depth of 34 feet the pressure is 2 
atmospheres. Diving bells are used for putting in the founda- 
tions of bridge piers, doing subaqueous excavating, etc. The 
so-called caisson, much used in bridge building, is simply a 
huge stationary diving bell, which the workmen enter through 
compartments provided with air-tight doors. Air is pumped 
into it precisely as in Fig. 48. 

59. The diving suit. For most purposes except those of heavy engi- 
neering the diving suit (Fig. 49) has now replaced the diving bell. This 
suit is made of rubber and has a metal helmet. The diver is sometimes 
connected with the surface by a tube through which 

air is forced down to him. It passes out into the 
water through the valve V in his suit. But more 
commonly the diver is entirely independent of the 
surface, carrying air under a pressure of about 40 at- 
mospheres in a tank on his back. This air is allowed 
to escape gradually through the suit and out into the 
water through the valve V as fast as the diver needs 
it. When he wishes to rise to the surface, he simply 
admits enough air to his suit to make him float. 

In all cases the diver is subjected to the pressure ex- 
isting at the depth at which the suit or bell commu- 
nicates with the outside water. Divers seldom work 
at depths greater than 60 feet, and 80 feet is usually 
considered the limit of safety. But Chief Gunner's 
Mate Frank Crilley, investigating the sunken U. S. 
submarine f-4 at Honolulu in 1915, descended to a 
depth of 304 feet. 

The diver experiences pain in the ears and above 

the eyes when he is ascending or descending, but not when at rest. This 
is because it requires some time for the air to penetrate into the interior 
cavities of the body and establish equal pressure in both directions. 

60. The gas meter. Gas from tjie city supply enters the meter through 
P (Fig. 50) and passes through the openings o and o x into the compart- 
ments B and B l of the meter. Here its pressure forces in the diaphragms 




FIG. 49. The div- 
ing suit 



PNEUMATIC APPLIANCES 



47 



d and d r The gas already contained in A and A 1 is therefore pushed 
out to the burners through the openings o f and o^ and the pipe P r As 
soon as the diaphragm d has moved as far as it can to the right, a lever 
which is worked by the movement of d causes the slide valve u to move 
to the left, thus closing o and shutting off con- 
nection between P and B, but at the same time 
opening o' and allowing the gas from P to enter 
compartment A through o'. A quarter of a cycle 
later u^ moves to the right and connects A l 
with P and B l with P r If u and u^ were set 
so as to work exactly together, there would 
fye slight fluctuations in the gas pressure at P r 
The movement of the diaphragms is recorded 
by a clockwork device, the dials of which in- 
dicate the number of cubic feet of gas which 
have passed through the meter. FIG. 50. The gas meter 




QUESTIONS AND PROBLEMS 

1. A water tank 8 ft. deep, standing some distance above the ground, 
closed everywhere except at the top, is to be emptied. The only means 
of emptying it is a flexible tube, (a) What is the most convenient way 
of using the tube, and how could it be set into operation ? (b) How 
long must the tube be to empty the tan.fc completely? 

2. Kerosene has a specific gravity of .8. Over what height can it be 
siphoned at normal pressure ? 

3. Let a siphon of the form shown in Fig. 51 be made by filling a 
flask one third full of water, closing it with a cork through 

which pass two pieces of glass tubing, as in the figure, 
and then inverting so that the lower end of the straight 
tube is in a dish of water. If the bent arm is of consid- 
erable length, the fountain will play forcibly and continu- 
ously until the dish is emptied. Explain. 

4. Diagram a lift pump on upstroke. What causes 
the water to rise in the suction pipe ? What happens on 
downstroke ? 

5. Diagram a force pump with air dome on down- 
stroke. What happens on upstroke ? FIG. 51 

6. If the cylinder of an air pump is of the same 

size as the receiver, what fractional part of the air is removed by 
one complete stroke? What fractional part is left after 3 strokes? 
after 10 strokes ? 




48 



PRESSURE IN AIR 



CUBIC 



FEET 




CUBIC 



FEET 



7. If the cylinder of an air pump is one third the size of the receiver, 
what fractional part of the original air will be left after 5 strokes? 
What will be the reading of a barometer within the receiver, the outside 
pressure being 76 ? 

8. Theoretically, can a vessel ever be completely exhausted by an 
air pump, even if mechanically perfect ? 

9. Explain by reference to atmospheric pressure why a balloon rises. 

10. How many of the laws of liquids and gases do you find illustrated 
in the experiment of the Cartesian 

diver? 

11. Pneumatic dispatch tubes 
are now used in many large stores 
for the transmission of small pack- 
ages. An exhaust pump is attached 
to one end of the tube in which a 
tightly fitting carriage moves, and 
a compression pump to the other. 
If the air is half exhausted on one 
side of the carriage and has twice 
its normal density on the other, 
find the propelling force acting on 
the carriage when the area of its 
cross section is 50 sq. cm. 

12. What determines how far a 
balloon will ascend? Under what 
conditions will it begin to descend ? 
Explain these phenomena by the 
principle of Archimedes. 

13. If a diving bell (Fig. 47) is sunk until the level of the water within 
it is 1033 cm. beneath the surface, to what fraction of its initial volume 
has the inclosed air been reduced ? (1033 g. per sq. cm. = 1 atmosphere.) 

14. If a diver's tank has a volume of 2 cu. ft. and contains air under 
a pressure of 40 atmospheres, to what volume will the air expand when 
it is released at a depth of 34 ft. under water ? 

15. A submarine weighs 1800 tons when its submerging tanks are 
empty, and in that condition 10 per cent by volume of the submarine 
is above water. What weight of water must be let into the tanks to 
just submerge the boat? 

16. (a) The upper figure shows a reading of 84,600 cu. ft. of gas. 
The lower figure shows the reading of the meter a month later. What 
was the amount of the bill for the month at $.80 per 1000 cu. ft. ? 
(b) Diagram the meter dials to represent 49,200 cu. ft. 




FIG. 52. The dials of a gas meter 



CHAPTER IV 

MOLECULAR MOTIONS 
KINETIC THEORY OF GASES 

61. Molecular constitution of matter. In order to account 
for some of the simplest facts in nature for example, the 
fact that two substances often apparently occupy the same 
space at the same time, as when two gases are crowded together 
in the same vessel or when sugar is dissolved in water it 
is now universally assumed that all substances are composed 
of very minute particles called molecules. Spaces are supposed 
to exist between these molecules, so that when one gas enters 
a vessel which is already full of another gas the molecules 
of the one scatter themselves about among the molecules of 
the other. Since molecules cannot be seen with the most 
powerful microscopes, it is evident that they must be very 
minute. The number of them contained in a cubic centi- 
meter of air is 27 billion billion (27 x 10 18 ). It would take 
as many as a thousand molecules laid side by side to make 
a speck long enough to be seen with the best microscopes. 

62. Evidence for molecular motions in gases. Certain very 
simple observations lead us to the conclusion that the mole- 
cules of gases, even in a still room, must be in continual and 
quite rapid motion. Thus, if a little chlorine, or ammonia, 
or any gas of powerful odor is introduced into a room, in a 
very short time it will have become perceptible in all parts of 
the room. This shows clearly that enough of the molecules 
of the gas to affect the olfactory nerves must have found 
their way across the room. 

49 



50 



MOLECULAR MOTIONS 




FIG. 53. Illustrat- 
ing the diffusion 
of gases 



Again, chemists tell us that if two globes, one containing 
hydrogen and the other carbon dioxide gas, be connected as 
in Fig. 53, and the stopcock between them opened, after a 
few hours chemical analysis will show that each of the globes 
contains the two gases in exactly the same 
proportions, a result which is at first sight 
very surprising, since carbon dioxide gas is 
about twenty-two times as heavy as hydrogen. 
This mixing of gases in apparent violation of 
the laws of weight is called diffusion. 

We see, then, that such simple facts as 
the transference of odors and the diffusion 
of gases furnish very convincing evidence 
that the molecules of a gas are not at rest 
but are continually moving about. 

63. Molecular motions and the indefinite 
expansibility of a gas. Perhaps the most 

striking property which we have found gases to possess is the 
property of indefinite or unlimited expansibility. The exist- 
ence of this property was demonstrated by the fact that we 
were able to attain a high degree of exhaustion by means of 
an air pump. No matter how much air was removed from the 
bell jar, the remainder at once expanded and filled the entire 
vessel. The motions of the molecules furnish a thoroughly 
satisfactory explanation of the phenomenon. 

The fact that, however rapidly the piston of the air pump 
is drawn up, gas always appears to follow it instantly, leads 
us to the conclusion that the natural velocity possessed by 
the molecules of gas must be very great. 

64. Molecular motions and gas pressures. How are we to 
account for the fact that gases exert such pressures as they 
do against the walls of the vessels which contain them? 
We have found that in an ordinary room the air presses 
against the walls with a force of 15 pounds to the square 



KINETIC THEORY OF GASES 51 

inch. Within an automobile tire this pressure may amount 
to as much as 100 pounds, and the steam pressure within the 
boiler of an engine is often as high as 240 pounds per square 
inch. Yet in all these cases we may be certain that the mole- 
cules of the gas are separated from each other by distances 
which are large in comparison with the diameters of the mole- 
cules ; for when we reduce steam to water, it shrinks to 16 1 00 
of its original volume, and when we reduce air to the liquid 
form, it shrinks to about -g-i-^ of its ordinary volume. 

The explanation is at once apparent when we reflect upon 
the motions of the molecules. For just as a stream of water 
particles from a hose exerts a continuous force against a wall 
on which it strikes, so the blows which the innumerable 
molecules of a gas strike against the walls of the containing 
vessel must constitute a continuous force tending to push 
out these walls. In this way we account for the fact that 
vessels containing only gas do not collapse under the enor- 
mous external pressures to which we know them to be 
subjected. A soap bubble 6i inches in diameter is, at normal 
atmospheric pressure, under a total crushing force of one ton. 

65. Explanation of Boyle's law. It will be remembered 
that it was discovered in the last chapter that when the den- 
sity of a gas is doubled, the temperature remaining constant, 
the pressure is found to double also ; when the density was 
trebled, the pressure was trebled ; etc. This, in fact, was the 
assertion of Boyle's law. Now this is exactly what would be 
expected if the pressure which a gas exerts against a given 
surface is due to blows struck by an enormous number of 
swiftly moving molecules ; for doubling the number of mole- 
cules in the given space, that is, doubling the density, would 
simply double the number of blows struck per second against 
that surface, and hence would double the pressure. The 
kinetic theory of gases which is here presented accounts in 
this simple way for Boyle's law. 



52 MOLECULAR MOTIONS 

66. Brownian movements and molecular motions. It has recently 
been found possible to demonstrate the existence of molecular motions 
in gases in a very direct and striking way. It is found that very minute 
oil drops suspended in perfectly stagnant air, instead of being them- 
selves at rest, are ceaselessly dancing about just as though they were 
endowed with life. In 1913 it was definitely proved that these mo- 
tions, which are known as the Brownian movements, are the direct 
result of the bombardment which the droplets receive from the flying 
molecules of the gas with which they are surrounded; for at a given 
instant this bombardment is not the same on all sides, and hence 
the suspended particle, if it is minute enough, is pushed hither and 
thither according as the bombardment is more intense first in one 
direction, then in another. There can be no doubt that what the oil 
drops are here seen to be doing, the molecules themselves are also doing, 
only in a much more lively way. 

67. Molecular velocities. From the known weight of a cubic centi- 
meter of air under normal conditions, and the known force which it 
exerts per square centimeter (namely, 1033 grams), it is possible to 
calculate the velocity which its molecules must possess in order that 
they may produce by their collisions against the walls this amount 
of force. The result of the calculation gives to the air molecules under 
normal conditions a velocity of about 445 meters per second, while it 
assigns to the hydrogen molecules the enormous speed of 1700 meters 
(a mile) per second. The speed of a projectile is seldom greater than 
800 meters (2500 feet) per second. It is easy to see, then, since the 
molecules of gases are endowed with such speeds, why air, for example, 
expands instantly into the space left behind by the rising piston of the 
air pump, and why any gas always fills completely the vessel which 
contains it (see mercury-diffusion air pump, opposite page 33). 

68. Diffusion of gases through porous walls. Strong evi- 
dence for the correctness of the above views is furnished by 
the following experiment : 

Let a porous cup of unglazed earthenware be closed with a rubber 
stopper through which a glass tube passes, as in Fig. 54. Let the tube 
be dipped into a dish of colored water, and a jar containing hydrogen 
placed over the porous cup ; or let the jar simply be held in the position 
shown in the figure, and let illuminating gas be passed into it by means 
of a rubber tube connected with a gas jet. The rapid passage of bubbles 
out through the water will show that the gaseous pressure inside the 



MOLECULAR MOTIONS IN LIQUIDS 



53 




cup is rapidly increasing. Now let the bell jar be lifted, so that the 
hydrogen is removed from the outside. Water will at once begin to rise 
in the tube, showing that the inside pressure is now rapidly decreasing- 

The explanation is as follows : We have 
learned that the molecules of hydrogen have 
about four times the velocity of the mole- 
cules of air. Hence, if there are as many 
hydrogen molecules per cubic centimeter 
outside the cup as there are air molecules 
per cubic centimeter inside, the hydrogen 
molecules will strike the outside of the wall 
four times as frequently as the air molecules 
will strike the inside. Hence, in a given 
time the number of hydrogen molecules 
which pass into the interior of the cup 
through the little holes in the porous mate- 
rial is four times as great as the num- 
ber of air particles which pass out ; hence 
the pressure within increases. When the bell jar is removed, 
the hydrogen which has passed inside begins to pass out faster 
than the outside air passes in, and hence the inside pressure is 
diminished. 

MOLECULAR MOTIONS IN LIQUIDS 

69. Molecular motions in liquids and evaporation. Evidence 
that the molecules of liquids as well as those of gases are in a 
state of perpetual motion is found, first, in the familiar facts 
of evaporation. 

We know that the molecules of a liquid in an open vessel 
are continually passing off into the space above, for it is only 
a matter of time when the liquid completely disappears and the 
vessel becomes dry. Now it is hard to imagine a way in which 
the molecules of a liquid thus pass out of the liquid into the 
space above, unless these molecules, while in the liquid condition, 



FIG. 54. Diffusion 

of hydrogen through 

porous cup 



54 MOLECULAR MOTIONS 

are in motion. As soon, however, as such a motion is assumed, 
the facts of evaporation become perfectly intelligible. For it is 
to be expected that in the jostlings and collisions of rapidly 
moving liquid molecules an occasional molecule will acquire a 
velocity much greater than the average. This molecule may 
then, because of the unusual speed of its motion, break away 
from the attraction of its neighbors and fly off into the space 
above. This is indeed the mechanism by which we now believe 
that the process of evaporation goes on from the surface of 
any liquid. 

70. Molecular motions and the diffusion of liquids. One of 
the most convincing arguments for the motions of molecules 
in gases was found in the fact of diffusion. 
But precisely the same sort of phenomena are 
observable in liquids. 

Let a few lumps of blue litmus be pulverized and 
dissolved in water. Let a tall glass cylinder be half 
filled with this water anc|, a few drops of ammonia 
added. Let the remainder of the litmus solution be 
turned red by the addition of one or two cubic centi- 
meters of nitric acid. Then let this acidulated water 
be introduced into the bottom of the jar through a FIG. 55. Diffusion 
thistle tube (Fig. 55). In a few minutes the line of of liquids 

separation between the acidulated water and the blue 
solution will be fairly sharp ; but in the course of a few hours, even 
though the jar is kept perfectly quiet, the red color will be found to have 
spread considerably toward the top, showing that the acid molecules have 
gradually found their way up. 

Certainly, then, the molecules of a liquid must be endowed 
with the power of independent motion. Indeed, every one of 
the arguments for molecular motions in gases applies with 
equal force to liquids. Even the Brownian movements can 
be seen in liquids, though they are here so small that high- 
power microscopes must be used to make them apparent. 




MOLECULAR MOTIONS IN SOLIDS 55 

MOLECULAR MOTIONS IN SOLIDS 

71. Molecular motions and the diffusion of solids. It has 
recently been demonstrated that if a layer of lead is placed 
upon a layer of gold, molecules of gold may in time be de- 
tected throughout the whole mass of the lead. This diffusion 
of solids into one another at ordinary temperature has been 
shown only for these two metals, but at higher temperatures 
(for example, 500 C.) all of the metals show the same char- 
acteristics to quite a surprising degree. 

The evidence for the existence of molecular motions in 
solids is, then, no less strong than in the case of liquids. 

72. The three states of matter. Although it has been 
shown that, in accordance with current belief, the molecules of 
all substances are in very rapid motion, yet differences exist 
in the kind of motion which the molecules in the three states 
possess. Thus, in the solid state it is probable that the mole- 
cules oscillate with great rapidity about certain fixed points, 
always being held by the attractions of their neighbors, that 
is, by the cohesive forces (see 112), in very nearly the same 
positions with reference to other molecules in the body. In 
rare instances, however, as the facts of diffusion show, a 
molecule breaks away from its constraints. In liquids, on 
the other hand, while the molecules are, in general, as close 
together as in solids, they slip about with perfect ease over 
one another and thus have no fixed positions. This assump- 
tion is necessitated by the fact that liquids adjust themselves 
readily to the shape of the. containing vessel. In gases the 
molecules are comparatively far apart, as is evident from the 
fact that a cubic centimeter of water occupies about 1600 
cubic centimeters when it is transformed into steam ; and, 
furthermore, they exert almost no cohesive force upon one 
another, as is shown by the indefinite expansibility of gases. 



56 MOLECULAK MOTIONS 



QUESTIONS AND PROBLEMS 

1. If a vessel with a small leak is filled with hydrogen at a pressure 
of 2 atmospheres, the pressure falls to 1 atmosphere about four times 
as fast as when the same experiment is tried with air. Can you see a 
reason for this? 

2. What is the density of the air within an automobile tire that is 
inflated to a pressure of 80 Ib. per square inch ? (1 atmosphere = 14.7 Ib. 
per sq. in.) 

3. A liter of air at a pressure of 76 cm. is compressed so as to occupy 
400 cc. What is the pressure against the walls of the containing vessel? 

4. If an open vessel contains 250 g. of air when the barometric height 
is 750 mm., what weight will the same vessel contain at the same tem- 
perature when the barometric height is 740 mm.? 

5. Find the pressure to which the diver was subjected who descended 
to a depth of 304 ft. Find the density of the air in his suit, the density 
at the surface being .00128 g. per cubic centimeter and the temperature 
being assumed to remain constant. Take the pressure at the surface 
as 30 in. 

6. A bubble of air which escaped from this diver's suit would increase 
to how many times its volume on reaching the surface? 

7. Salt is heavier than water. Why does not all the salt in a mixture 
of salt and water settle to the bottom? 



CHAPTER V 

FORCE AND MOTION 
DEFINITION AND MEASUREMENT OF FORCE 

73. Distinction between a gram of mass and a gram of force. 
If a gram of mass is held in the outstretched hand, a down- 
ward pull upon the hand is felt. If the mass is 50,000 g. in- 
stead of 1, this pull is so great that the hand cannot be held 
in place. The cause of this pull we assume to be an attractive 
force which the earth exerts on the matter held in the hand, 
and we define the gram of force as the amount of the earths pull 
at its surface upon one gram of mass. 

Unfortunately, in ordinary conversation we often fail alto- 
gether to distinguish between the idea of mass and the idea 
of force, and use the same word " gram " to mean sometimes 
a certain amount of matter and at other times the pull of the 
earth upon this amount of matter. That the two ideas are, how- 
ever, wholly distinct is evident from the consideration that 
the amount of matter in a body is always the same, no matter 
where the body is in the universe, while the pull of the earth 
upon that amount of matter decreases as we recede from the 
earth's surface. It will help to avoid confusion if we reserve 
the simple term " gram " to denote exclusively an amount of 
matter (that is, a mass) and use the full expression " gram of 
force " wherever we have in mind the pull of the earth upon 
this mass. 

74. Method of measuring forces. When we wish to com- 
pare accurately the pulls exerted by the earth upon different 
masses, we find such sensations as those described in the 

57 



58 



FORCE AND MOTION 




preceding paragraph very untrustworthy guides. An accurate 
method, however, of comparing these pulls is that furnished 
by the stretch produced in a spiral spring. Thus, the pull of 
the earth upon a gram of mass at its sur- 
face will stretch a given spring a given 
distance, ab (Fig. 56) ; the pull of the earth 
upon 2 grams of mass is found to stretch the 
spring a larger distance, ac\ upon 3 grams, a 
still larger distance, ad; etc. In order to 
graduate a spring balance (Fig. 57) so that 
it will thenceforth measure the values of any 
pulls exerted upon it, no matter how these 
pulls may arise, we have only to place a fixed -p IG 55 Method of 
surface behind the pointer and make lines measuring forces 
upon it corresponding to the points to which 
it is stretched by the pull of the earth upon different masses. 
Thus, if a man stretch the spring so that the pointer is opposite 
the mark corresponding to the pull of the earth 
upon 2 grams of mass, we say that he exerts 
2 grams of force ; if he stretch it the distance 
corresponding to the pull of the earth upon 3 
grams of mass, he exerts 3 grams of force ; etc. 
The spring balance thus becomes an instrument 
for measuring forces. 

75. The gram of force varies slightly in differ- 
ent localities. With the spring balance it is easy 
to verify the statement made above, that the 
force of the earth's pull decreases as we recede 
from the earth's surface ; for upon a high moun- 
tain the stretch produced by a given mass is indeed found 
to be slightly less than at sea level. Furthermore, if the 
balance is simply carried from point to point over the earth's 
surface, the stretch is still found to vary slightly. For ex- 
ample, at Chicago it is about one part in 1000 less than it 



FIG. 57. The 

spring balance 



COMPOSITION AND RESOLUTION OF FORCES 59 

is at Paris, and near the equator it is five parts in 1000 less 
than it is near the pole. This is due in part to the earth's 
rotation and in part to the fact that the earth is not a perfect 
sphere and that in going from the equator toward the pole 
we are coming nearer and nearer to the center of the earth. 
We see, therefore, that the weight of one gram of mass is not an 
absolutely definite unit of force. One gram of force is, strictly 
speaking, the weight of one gram of mass in latitude 45 at 
sea level. 

COMPOSITION AND RESOLUTION or FORCES 

76. Graphic representation of force. A force is completely 
described when its magnitude, its direction, and the point at 
which it is applied are given. Since the three characteristics of 
a straight line are its length, its direction, and the point at 
which it starts, it is obviously possible to 

represent forces by means of straight lines. A ^ 

Thus, if we wish to represent the fact that FlG - 58< Gra P hic 
r f. -. . . , representation of 

a force ot 8 pounds, acting in an easterly a gingle force 

direction, is applied at the point A (Fig. 58), 
we draw a line 8 units long, beginning at the point A and 
extending to the right. The length of this line then repre- 
sents the magnitude of the force ; the direction of the line, 
the direction of the force ; and the starting point of the line, 
the point at which the force is applied. 

77. Resultant of two forces acting in the same line. The 
resultant of two forces is defined as that single force which will 
produce the same effect upon a body as is produced by the joint 
action of the two forces. 

If two spring balances are attached to a small ring and 
pulled in the same direction until one registers 10 g. of force 
and the other 5, it will be found that a third spring balance 
attached to the same point and pulled in the opposite direc- 
tion will register exactly 15 g. when there is equilibrium ; 



60 



FORCE AND MOTION 




that is, the resultant of two parallel forces acting in the same 
direction is equal to the sum of the two forces. 

Similarly, the resultant of two oppositely directed forces applied 
at the same point is equal to the difference between them, and its 
direction is that of the greater force. 

78. Equilibrant. In the last experiment the pull in the 
spring balance which registered 15 g. was not the resultant 
of the 5 g. and 10 g. forces ; it was rather a force equal and 
opposite to that resultant. Such a force is called an equilibrant. 
The equilibrant of a force or forces is that 

single force ivhich will just prevent the motion 
which the given forces tend to produce. It is 
equal and opposite to the resultant and has 
the same point of application. 2~" 

79. The resultant of forces acting at an FI G . 59. Direction 
angle (concurrent forces). If a body at A of resultant of two 
is pulled toward the east with a force of equal f ^ g at ' 

10 Ib. (represented in Fig. 59 by the line 

AC) and toward the north with a force of 10 Ib. (repre- 

sented in the figure by the line AIT), the effect upon the 

motion of the body must, of course, be the same as though 

some single force acted somewhere 

between AC and AB. If the body 

moves under the action of the two 

equal forces, it may be seen from 

symmetry that it must move along 

a line midway between AC and AB, 

that is, along the line AR. This line, 

therefore, indicates the direction as well as the point of appli- 

cation of the resultant of the forces AC and AB. 

If the two forces are not equal, as in Fig. 60, then the 
resultant will lie nearer the larger force. The following 
experiment will show the relation between the two forces 
and their resultant, 




6Q The resultant Iies 
nearer the larer force 



COMPOSITION AND RESOLUTION OF FORCES 61 




FIG. 61. Experimental proof 
of parallelogram law 



Let the rings of two spring balances be hung over nails B and C in 
the rail at the top of the blackboard (Fig. 61), and let a weight W be 
tied near the middle of the string joining the hooks of the two balances. 
The weight W is not supported by the 
pull of the balance E or by that of 
F; it is supported by their resultant, 
which evidently must act vertically up- 
ward, since the only single force capable 
of supporting the weight W is one that 
is equal and opposite to W. Let the lines 
OA and OD be drawn upon the black- 
board behind the string, and upon these 
lines lay off the distances Oa and Ob, 
which contain as many units of length 
as there are units of force indicated by 
the balances E and F respectively. Simi- 
larly, on a vertical line from lay off the 
exact distance OR required to represent 

the force that supports the weight. This, as noted above, represents the 
resultant. Now let a parallelogram be constructed upon Oa and Ob as 
sides. The line OR already drawn will be the diagonal. 

Hence, to find graphically the resultant of two concurrent 
forces, (.?) represent the concurrent forces, (2) construct upon them 
as sides a parallelogram, and (3) draw a diagonal from the point 
of application. This diagonal represents the point of application, 
direction, and magnitude of the resultant. 

80. Component of a force. When- 
ever a force acts upon a body in some 
direction other than that in which the 
body is free to move, it is clear that 
the full effect of the force cannot be 
spent in producing motion. For ex- 
ample, suppose that a force is applied 

in the direction OR (Fig. 62) to a car on an elevated track. 
Evidently OR produces two distinct effects upon the car : on 
the one hand, it moves the car along the track; and, on the 
other, it presses it down against the rails. These two effects 



R 



FIG. 62. Component of 
a force 



62 



FORCE AND MOTION 



might be produced just as well by two separate forces acting 
in the directions OA and OB respectively. The value of the 
single force which, acting in the direction OA, will produce 
the same motion of the car on the track as is produced by 
OR, is called the component of OR in the direction OA. Simi- 
larly, the value of the single force which, acting in the direc- 
tion OB, will produce the same pressure against the rails as 
is produced by the force OR, is called the component of OR 
in the direction OB. In a word, the component of a force in a 
given direction is the effective value of the force in that direction. 
81. Magnitude of the component of a force in a given direc- 
tion. Since, from the definition of component just given, 
the two forces, one to be applied in the direction OA and 
the other in the direction OB, are together to be exactly 
equivalent to OR in their effect on the car, their magnitudes 
must be represented 
by the sides of a par- 
allelogram of which 
OR is the diagonal. 
For in 79 it was 
shown that if any one 
force is to have the 
same effect upon a 
body as two forces acting simultaneously, it must be repre- 
sented by the diagonal of a parallelogram the sides of which 
represent the two forces. Hence, conversely, if two forces are 
to be equivalent in their joint effect to a single force, they 
must be sides of the parallelogram of which the single force 
is the diagonal. Hence the following rule : To find the com- 
ponent of a force in any given direction, represent the force by 
a line; then, using the line as a diagonal, construct upon it a 
rectangle the sides of which are respectively parallel and perpen- 
dicular to the direction of the required component. The length of 
the side which is parallel to the given direction represents the 




FIG. 63. Horizontal component of pull on a sled 



COMPOSITION AND RESOLUTION OF FORCES 63 

magnitude of the component which is sought. Thus, in Fig. 62 
the line Om completely represents the component of OR in 
the direction OA, and the line On represents the component 
of OR in the direction OB. 

Again, when a boy pulls on a sled with a force of 10 Ib. 
in the direction OR (Fig. 63), the force with which the sled 
is urged forward is represented by the length of Om, which 
is seen to be but 9.3 Ib. instead of 10 Ib. The component 
which tends to lift the sled is represented by On. 

To apply the test of experiment to the conclusions of the preceding 
paragraph, let a wagon be placed upon an inclined plane (Fig. 64), the 
height of which, be, is equal to one half its length ab. In this case 
the force acting on the wagon is the weight of the wagon, and its 
direction is downward. Let this force be represented by the line OR. 
Then, by the construction of the preceding paragraph, the line Om will 
represent the value of the force which is pulling the carriage down the 
plane, and the line On the value of the 
force which is producing pressure against 
the plane. Now, since the triangle ROm is 
similar to the triangle abc (for ZmOR = 
Z abc, Z RmO = Z acb, and Z ORm = 
we have 

Om _ bc^ 
OR ~ ab' 

FIG. 64. Component of 

that is, in this case, since be is equal to one weight parallel to an in- 
half of ab, Om is one half of OR. Therefore clined plane 
the force which is necessary to prevent the 

wagon from sliding down the plane should be equal to one half its weight. 
To test this conclusion let the wagon be weighed on the spring balance 
and then placed on the plane in the manner shown in the figure. The 
pull indicated by the balance will, indeed, be found to be one half the 
weight of the wagon. 

The equation Om/OR = bc/ab gives us the following rule for finding 
the force necessary to prevent a body from moving down an inclined 
plane, namely, the force which must be applied to a body to hold it in place 
upon an inclined plane bears the same ratio to the weight of the body as the 
height of the plane bears to its length. 




64 



FORCE A]S T D MOTION 



82. Component of gravity effective in producing the motion 
of the pendulum. When a pendulum is drawn aside from its 
position of rest (Fig. 65), the force acting on the bob is its 
weight, and the direction of this force is vertical. Let it be 
represented by the line OR. The 
component of this force in the 
direction in which the bob is free 
to move is On, and the component 
at right angles to this direction is 
Om. The second component Om 
simply produces stretch in the 
string and pressure upon the point 
of suspension. The first compo- 
nent On is alone responsible for 
the motion of the bob. A consid- 
eration of the figure shows that 
this component becomes larger 
and larger the greater the dis- 
placement of the bob. When the 
bob is directly beneath the point of support, the component 
producing motion is zero. Hence a pendulum can be per- 
manently at rest only when its bob is directly beneath the 
point of suspension.* 




FIG. 65. Force acting on dis- 
placed pendulum 



QUESTIONS AND PROBLEMS 

1. The engines of a steamer can drive it 12 mi. per hour. How fast 
can it go up a stream in which the current is 3 mi. per hour ? How fast 
can it come down the same stream ? 

2. The wind drives a steamer east with a force which would carry it 
12 mi. per hour, and its propeller is driving it south with a force which 
would carry it 15 mi. per hour. What distance will it actually travel in 
an hour ? Draw a diagram to represent the exact path. 

* It is recommended that the study of the laws of the pendulum be intro- 
duced into the laboratory work at about this point (see Experiment 12, 
authors' Manual). 



COMPOSITION AND RESOLUTION OF FORCES 65 




3. A barge is anchored in a river during a storm. If the wind acts 
eastward on it with a force of 3000 lb. and the tide northward with a 
force of 4000 lb., what is the direction and magnitude of the equilibrant ; 
that is, the pull of the anchor cable upon the barge? 

4. A picture weighing 20 lb. hangs upon a cord whose parts make 
an. angle of 120 with each other. Find the tension (pull) upon each 
part of the cord. 

5. If the barrel of Fig. 66 
weighs 200 lb., with what 
force must a man push par- 
allel to the skid to keep the 
barrel in place if the skid is 
9 ft. long and the platform 
3 ft. high? 

6. A cake of ice weighing 
200 lb. is held at rest upon an 

inclined plane 12 ft. long and F IG> 66. Force necessary to prevent a bar- 
3 ft. high. By the resolution- re l from rolling down an inclined plane 
and-proportion method find 

the component of its weight that tends to make the ice slide down the 
incline. With what force must one push to keep the ice at rest ? How 
great is the component that tends to break the incline ? 

7. A tight-rope 20 ft. long is depressed 1 ft. at the center when 
a man weighing 120 lb. stands upon it. Determine graphically the 
tension in the rope. 

8. The anchor rope of a kite balloon makes an angle of 60 with 
the surface of the earth. If the lifting power of the balloon is 1000 lb., 
find the pull of the balloon on the rope and the horizontal force of 
the wind against the balloon. 

9. A canal boat and the engine towing it move in parallel paths 
which are 50 ft. apart. The tow rope is 130 ft. long, and the force 
(effort) applied to 

the end of the rope 
is 1300 lb. Find what 
component of the 
loOOlb. acts parallel 
to the path of the 
boat. 

10. In Fig. 6 7 the 
line on represents F IG . 67. Forces acting on a kite 

the pull of gravity 

on a kite, and the line om represents the pull of the boy on the string. 
What is the name given to the force represented by the line oRI 




FORCE AND MOTION 




FIG. 68. Forces acting on an aeroplane 
in flight 



11. If the force of the wind against the kite is represented by the 
line AB, and it is considered to be applied at o, what must be the relation 
between the force oR and the 

component of AB parallel to n s 

,, , ., . . .,., Direction of Flight 

oR when the kite is in equilib- 
rium under the action of the 
existing forces? 

12. If the wind increases, 
why does the kite rise higher ? 

13. Show from Fig. 68 what 
force supports an aeroplane in 
flight. (Remember that oR, the 
component of the wind pressure 
AB perpendicular to the plane, 

is the only acting force out of which a support for the aeroplane 
can be derived.) (See frontispiece and opposite pp. 153, 316, and 317.) 

GBAVITATION 

83. Newton's law of universal gravitation. In order to ac- 
count for the fact that the earth pulls bodies toward itself, 
and at the same time to account for the fact that the moon and 
planets are held in their respective orbits about the earth and 
the sun, Sir Isaac Newton (16421727) (see opposite p. 84) 
first announced the law which is now known as the law of 
universal gravitation. This law asserts first that every body in 
the universe attracts every other body with a force which varies 
inversely as the square of the distance between the two bodies. 
This means that if the distance between the two bodies con- 
sidered is doubled, the force will become only one fourth as 
great; if the distance is made three, four, or five times as 
great, the force will be reduced to one ninth, one sixteenth, 
or one twenty-fifth of its original value ; etc. 

The law further asserts that if the distance between two 
bodies remains the same, the force with which one body attracts 
the other is proportional to the product of the masses of the two 
bodies. Thus we know that the earth attracts 3 cubic centi- 
meters of water with three times as much force as it attracts 



GRAVITATION 67 

1, that is, with a force of 3 grams. We know also, from the 
facts of astronomy, that if the mass of the earth were doubled, 
its diameter remaining the same, it would attract 3 cubic cen- 
timeters of water with twice as much force as it does at pres- 
ent, that is, with a force of 6 grams (multiplying the mass 
of one of the attracting bodies by 3 and that of the other by 
2 multiplies the forces of attraction by 3 x 2, or 6). In brief, 
then, Newton's law of universal gravitation is as follows : Any 
two bodies in the universe attract each other with a force which 
is directly proportional to the product of the masses and inversely 
proportional to the square of the distance between them. 

Two masses of 1 gram each at a distance apart of 1 cm. 
attract each other with a force of about 1 6 , 00,000.000 g ram - 
The masses of the sun and the earth are so great that even 
though 93,000,000 miles apart, they attract each other with 
a force of about 4,000,000,000,000,000,000 tons. A body 
weighing 100 pounds on the earth would weigh about 2700 
pounds on the sun. A freely falling body on the earth drops 
16 feet the first second, while on the sun it would fall 27 
times that far in the first second, or 432 feet. On the moon 
we should weigh 1 of what we do on the earth; we could 
jump 6 times as high and should fall i as fast. 

84. Variation of the force of gravity with distance above the 
earth's surface. If a body is spherical in shape and of uniform 
density, it attracts external bodies with the same force as 
though its mass were concentrated at its center. Since, there- 
fore, the distance from the surface to the center of the earth 
is about 4000 miles, we learn from Newton's law that the 
earth's pull upon a body 4000 miles above its surface is but 
one fourth as much as it would be at the surface. 

It will be seen, then,. that if a body be raised but a few feet 
or even a few miles above the earth's surface, the decrease in 
its weight must be a very small quantity, for the reason that 
a few feet or a few miles is a small distance compared with 



68 FORCE AND MOTION 

4000 miles. As a matter of fact, at the top of a mountain 
4 miles high 1000 grams of mass is attracted by the earth 
with 998 grams instead of 1000 grams of force. 

85. Center of gravity. From the law of universal gravita- 
tion it follows that every particle of a body upon the earth's 
surface is pulled toward the earth. It is evident that the sum 
of all these little pulls on the particles of which the body is 
composed must be equal to the total pull of the earth upon 
the body. Now it is always possible to find one single point 
in a body at which a single force, equal in magnitude to the 
weight of the body and directed upward, can be applied so 
that the body will remain at rest in whatever position it is 
placed. This point is called the center of gravity of the body. 
Since this force counteracts entirely the earth's pull upon the 
body, it must be equal and opposite to the resultant of all 
the small forces which gravity is exerting upon the different 
particles of the body. Hence the center of gravity may be de- 
fined as the point of application of the resultant of all the little 
downward forces of gravity acting upon 

the parts of the body ; that is, the center of 

gravity of a body is the point at which the 

entire weight of the body may be considered 

an concentrated. The earth's attraction for 

a body is therefore always considered not 

as a multitude of little forces but as one 

single force F (Fig. 69) equal to the pull FIG. 69. Center of 

of gravity upon the body and applied at its 

center of gravity G. It is evident, then, that 

under the influence of the earths pull, every body tends to assume 

the position in which its center of gravity is as low as possible. 

86. Method of finding center of gravity experimentally. 
From the above definition it will be seen that the most direct 
way of finding the center of gravity of any flat body, like that 
shown in Fig. 70, is to find the point upon which it will balance. 




GRAVITATION 



69 



Let an irregular sheet of zinc be thus balanced on the point of a 
pencil or the head of a pin. Let a small hole be punched through 
the zinc at the point of balance, and let a needle be thrust through this 
hole. When the needle is held hor- 
izontally, the zinc will be found to 
remain at rest, no matter in what 
position it is turned. 

To illustrate another method of 
finding the center of gravity of 
the zinc, let it be supported from 
a pin stuck through a hole near 
its edge, that is, b (Fig. 70). Let 
a plumb line be hung from the 
pin, and let a line' In be drawn 
through 1} on the surface of the 

zinc parallel to and directly behind the plumb line. Let the zinc be hung 
from another point a, and let another line am be drawn in a similar way. 




FIG. 70. Locating center of gravity 




Since the attraction of the earth for a body may be con- 
sidered as a single force applied at the center of gravity, a 
suspended body (for example, the sheet of zinc) can remain 
at rest only when the center of gravity is directly beneath the 
point of support (see 85). It must therefore lie somewhere 
on the line am. For the same 
reason it must lie on the line bn. 
But the only point which lies on 
both of these 
lines is their 
point of inter- 
section G. The 
point of inter- 
section, then, of 

any two vertical lines dropped through two different points of 
suspension locates the center of gravity of a body. 

87. Stable equilibrium. A body is said to be in stable equi- 
librium if it tends to return to its original position when very 
slightly tipped, or rotated, out of that position. A pendulum, 






A B c D 

FIG. 71. Illustration of varying degrees of stability 



70 



FOKCE AND MOTION 



a chair, a cube resting on its side, a cone resting on its base, 
a boat floating quietly in still water, are all illustrations. 

In general, a body is in stable equilibrium whenever tip- 
ping it slightly tends to raise its center of gravity. Thus, in 
Fig. 71 all of the bodies A, B, (7, Z>, are in stable equilibrium, 
for in order to overturn any one of them its center of gravity 




FIG. 72. Quebec bridge 

G must be raised through the height ai. If the weights are 
all alike, that one will be most stable for which ai is greatest. 
In building cantilever bridges such as the large one over the 
St. Lawrence River at Quebec (Fig. 72) the engineers build 
out the cantilever arms equally in opposite directions, so as to 
keep their centers of gravity constantly 
over the piers until the parts either meet 
at the center or are close enough to receive 
the central span, which is hoisted to place. 




The condition of stable equilibrium for bod- 
ies which rest upon a horizontal plane is that a 
vertical line through the center of gravity shall 
fall within the base, the base being defined as 
the polygon formed by connecting the points at 
which the body touches the plane, as ABC 
(Fig. 73) ; for it is clear that in such a case a 
slight displacement must raise the center of 

gravity along the arc of which OG is the radius. If the vertical line 
drawn through the center of gravity fall outside the base, as in Fig. 74, 
the body must always fall. 



B 



FIG. 73. Body in stable 
equilibrium 




GRAVITATION 71 

The condition of stable equilibrium for bodies supported from a single 
point, as in the case of a pendulum, is that the point of support be above 
the center of gravity. For example, the beam of a balance cannot be in 
stable equilibrium, so that it will return to the 
horizontal position when slightly displaced, un- 
less its center of gravity g (Fig. 3, p. 7) is below 
the knife-edge C. (The pans are not to be con- 
sidered, since they are not rigidly connected to 
the beam.) 

88. Neutral and unstable equilibrium. 

, . -i ^ i 7 -TT - FIG 74. Body not in 

A body is said to be in neutral equilibrium equilibrium 

when, after a slight displacement, it tends 
neither to return to its original position nor to move farther 
from it. Examples of neutral equilibrium are a spherical ball 
lying on a smooth plane, a cone lying on its side, a wheel free 
to rotate about a fixed axis through its center, or any body 
supported at its center of gravity. In general, a body is in 
neutral equilibrium when a slight displacement neither raises 
nor lowers its center of gravity. 

A body is in unstable equilibrium when, after a slight tip- 
ping, it tends to move farther from its original position. A 
cone balanced on its point or an egg on its end are examples. 
In all such cases a slight tipping lowers the center of gravity, 
and the motion then continues until the center of gravity is as 
low as circumstances will permit. The condition for unstable 
equilibrium in the case of a body supported by a point is that 
the center of gravity shall be above the point of support. 

QUESTIONS AND PROBLEMS 

1. Explain why the toy shown in Fig. 75 will not lie upon its side, 
but rises to the vertical position. Does the center of gravity rise? 

2. Where is the center of gravity of a hoop? of a cubical box? Is 
the latter more stable when empty or when full ? Why ? 

3. Where must the center of gravity of the beam of a balance be 
with reference to the supporting knife-edge C? (Fig. 3, p. 7.) Why? 
Could you make a weighing if C and g coincided? Why? 



72 



FORCE AND MOTION 




4. What is the object of ballast in a ship? 

5. What is the most stable position of a brick? the least stable? Why? 

6. In what state of equilibrium is a pendulum at rest? Why? 

7. What purpose is served by the tail of a kite? 

8. Do you get more sugar to the pound in ; \ 
Calcutta than in Aberdeen when using a beam *>j.( 
balance? when using a spring balance? Explain. 

9. What change would there be in your 
weight if your mass were to become four times 
as great and that of the earth three times, the 
radius of the earth remaining the same ? 

10. The pull of the earth on a body at its sur- 
face is 100 kg. Find the pull on the same body 4000 mi. above the surface ; 
1000 mi. above the surface ; 3 mi. above 'the surface. (Take the earth's 
radius as 4000 mi.) 

FALLING BODIES 

89. Galileo's early experiments. Many of the familiar and 
important experiences of our lives have to do with falling 
bodies. Yet when we ask ourselves the 
simplest question which involves quan- 
titative knowledge about gravity, such 
as, for example, Would a stone and a 
piece of lead dropped from the same 
point reach the ground at the same time 
or at different times ? most of us are 
uncertain as to the answer. In fact, it 
was the asking and the answering of 
this very question by Galileo, about 
1590, which may be considered as the 
starting point of modern science. 

Ordinary observation teaches that 
light bodies like feathers fall slowly and 
heavy bodies like stones fall rapidly, 
and up to Galileo's time it was taught 
in the schools that bodies fall with " velocities proportional to 
their weights." Not content with book knowledge, however, 




FIG. 76. Leaning tower 
of Pisa, from which were 
performed some of Gali- 
leo's famous experiments 
on falling bodies 




GALILEO (1564-1642) 

Great Italian physicist, astronomer, and mathematician; "founder of experi- 
mental science"; was son of an impoverished nobleman of Pisa; studied medi- 
cine in early youth, but forsook it for mathematics and science ; was professor 
of mathematics at Pisa and at Padua ; discovered the laws of falling bodies and 
the laws of the pendulum ; was the creator of the science of dynamics ; constructed 
the first thermometer; first used the telescope for astronomical observations; 
discovered Jupiter's satellites and the spots on the sun. Modern physics begins 

with Galileo 



FALLING BODIES 



73 



Galileo tried it himself. In the presence of the professors 

and students of the University of Pisa he dropped balls of 

different sizes and materials from the top of 

the tower of Pisa (Fig. 76), 180 feet high, 

and found that they fell in practically the 

same time. He showed that even very light 

bodies like paper fell with velocities which 

approached more and more nearly those of 

heavy bodies the more compactly they were 

wadded together. From these experiments 

he inferred that all bodies, even the lightest, 

would fall at the same rate if it were not for 

the resistance of the air. 

That the air resistance is indeed the chief factor 
in the slowness of fall of feathers and other light 
objects can be shown by pumping the air out of a 
tube containing a feather (or some small pieces of 
tissue paper) and a coin (Fig. 77). The more com- 
plete the exhaustion the more nearly do the feather 
and the coin fall side by side when the tube is inverted. The air pump, 
however, was not invented until sixty years after Galileo's time. 

90. Exact proof of Galileo's conclusion. We can demon- 
strate the correctness of Galileo's conclusion in still another 
way, one which he himself used. 

Let balls of iron and wood, for example, be started together down the 
inclined plane of Fig. 78. They will be found to keep together all the 



C I 

FIG 77. Feather 
and coin fall to- 
gether in a vacuum 




FIG. 78. Spaces traversed and velocities acquired by falling bodies in one, 
two, three, etc. seconds 



way down. (If they roll in a groove, they should have the same diame- 
ter ; otherwise, size is immaterial.) The experiment differs from that 



74 FORCE AND MOTION 

of the freely falling bodies only in that the resistance of the air is here 
more nearly negligible because the balls are moving more slowly. In 
order to make them move still more slowly and at the same time to 
eliminate completely all possible effects due to the friction of the plane, 
let us follow Galileo and suspend the different balls as the bobs of pen- 
dulums of exactly the same length, two meters long at least, and start 
them swinging through equal arcs. Since now the bobs, as they pass 
through any given position, are merely moving very slowly down identi- 
cal inclined planes (Fig. 65), it is clear that this is only a refinement of 
the last experiment. We shall find that the times of fall, that is, the 
periods, of the pendulums are exactly the same. 

From the above experiment we conclude with Galileo and 
with Newton, who performed it with the utmost care a hundred 
years later, that in a vacuum the velocity acquired per second 
by a freely falling body is exactly the same for all bodies. 

91. Relation between distance and time of fall. Having 
found that, barring air resistance, all bodies fall in exactly 
the same way, we shall next try to find what relation exists 
between distance and time of fall ; and since a freely falling 
body falls so rapidly as to make direct measurements upon 
it difficult, we shall adopt Galileo's plan of studying the 
laws of falling bodies through observing the motions of a 
ball rolling down an inclined plane. 

Let a grooved board 17 or 18 ft. long be supported as in Fig. 78, one 
end being about a foot above the other. Let the side of the board be 
divided into feet, and let the block B be set just 16 ft. from the start- 
ing point of the ball A. Let a metronome or a clock beating seconds be 
started, and let the marble be released at the instant of one click of the 
metronome. If the marble does not hit the block so that the click pro- 
duced by the impact of the ball coincides exactly with the fifth click of 
the metronome, alter the inclination until this is the case. (This adjust- 
ment may well be made by the teacher before class.) Now start the 
marble again at some click of the metronome, and note that it crosses 
the 1-ft. mark exactly at the end of the first second, the 4-ft. mark at 
the end of the second second, the 9-ft. mark at the end of the third 
second, and hits B at the 16-ft. mark at the end of the fourth second. 
This can be tested more accurately by placing B successively at the 



FALLING BODIES 75 

9-ft., the 4-ft., and the 1-ft. mark and noting that the click produced by 
the impact coincides exactly with the proper click of the metronome. 

We conclude, then, with Galileo, that, the, distance traversed 
by a falling body in any number of seconds is the distance 
traversed the first second times the square of the number of 
seconds ; that is, if D represents the distance traversed the first 
second, S the total space, and t the number of seconds, S = Dt*. 

92. Relation between velocity and time of fall. In the last 
paragraph we investigated the distances traversed in one, two, 
three, etc. seconds. Let us now investigate the velocities acquired 
on the same inclined plane in one, two, three, etc. seconds. 

Let a second grooved board Jlf be placed at the bottom of the incline, 
in the manner shown in Fig. 78. To eliminate friction it should be 
given a slight slant, just sufficient to cause the ball to roll along it with 
uniform velocity. Let the ball be started at a distance D up the incline, 
D being the distance which in the last experiment it was found to roll 
during the first second. It will then just reach the bottom of the incline 
at the instant of the second click. Here it will be freed from the influ- 
ence of gravity, and will therefore move along the lower board with the 
velocity which it had at the end of the first second. It will be found 
that when the block is placed at a distance exactly equal to 2 D from 
the bottom of the incline, the ball will hit it at the exact instant of the 
third click of the metronome, that is, exactly two seconds after starting ; 
hence the velocity acquired in one second is 2 D. If the ball is started at 
a distance 4 D up the incline, it will take it two seconds to reach the 
bottom, and it will roll a distance 4 D in the next second ; that is, in 
two seconds it acquires a velocity 4 D. In three seconds it will be found 
to acquire a velocity 6 Z>, etc. 

The experiment shows, first, that the gain in velocity each 
second is the same; second, that the amount of this gain 
is numerically equal to twice the distance traversed the first 
second. Motion, like the above, in which velocity is gained at 
a constant rate is called uniformly accelerated motion. 

In uniformly accelerated motion the gain each second in the 
velocity is called the acceleration. It is numerically equal to 
twice the distance traversed the first second. 



76 



FORCE AND MOTION 



93. Formal statement of the laws of falling bodies. Put- 
ting together the results of the last two paragraphs, we obtain 
the folloAving table, in which D represents the distance trav- 
ersed the first second in any uniformly accelerated motion. 



NUMBER OF 

SECONDS (t) 


VELOCITY AT THE 
END OF EACH 
SECOND (v) 


GAIN IN VELOCITY 
EACH SECOND (a) 


TOTAL DISTANCE 
TRAVERSED (S) 


1 


2 D 


21) 


ID 


2 


4D 


2D 


4D 


3 


QD 


2D 


91) 


4 


SD 


2D 


16 D 


t 


2tD 


2D 


PD 



Since D was shown, in 92, to be equal to one half of the 
acceleration a, we have at once, by substituting J a for D 
in the last line of the table, 

v = at, (1) 

S = %aP. (2) 

These formulas are simply the algebraic statement of the facts 
brought out by our experiments, but the reasons for these facts may 
be seen as follows : 

Since in uniformly accelerated motion the acceleration a is the 
velocity in centimeters per second gained each second, it follows at 
once that when a body starts from rest, the velocity which it has at the 
end of t seconds is given by v at. This is formula (1). 

To obtain formula (2) we have only to reflect that distance traversed 
is always equal to the average velocity multiplied by the time. When 
the initial velocity is zero, as in this case, and the final velocity is at, 
average velocity = (0 + at) -s- 2 = 1 at. Hence 

5 = $ at\ 
This is formula (2). 

These are the fundamental formulas of uniformly accelerated motion, 
but it is sometimes convenient to obtain the final velocity v directly from 
the total distance of fall S, or vice versa. This may of course be done 

by simply substituting in (2) the value of t obtained from (1), namely, - 
This gives 

v = V2 a5. (3) 



FALLING BODIES 



77 



Distances 
in ft. per sec. in feet 

Ot 



To illustrate the use of these formulas, sup- 
pose we wish to know with what velocity a 
body will hit the earth if it falls from a height 
of 200 meters, or 20,000 centimeters. From (6) 
we get 



v - V2 x 980 x 20,000 = 6261 cm. per second. 

95. Height of ascent. If we wish to find the 
height S to which a body projected vertically 
upward will rise, we reflect that the time of 
ascent must be the initial velocity divided by 
the upward velocity which the body loses per 

second, that is, t = - ; and the height reached 
9 



32.16 



94. Acceleration of a freely falling body. If in the above 
experiment the slope of the plane be made steeper, the results 
will obviously be precisely the same, ex- velocities 
cept that the acceleration has a larger 
value. If the board is tilted until it be- 
comes vertical, the body becomes a freely 
falling body (Fig. 79). In this case the 
distance traversed the first second is 
found to be 490 centimeters, or 16.08 
feet. Hence the acceleration, expressed 
in centimeters, is 980 ; in feet, 32.16. 
This acceleration of free fall, called the 
acceleration of gravity, is usually denoted 
by the letter g. For freely falling bodies, 
then, the three formulas of the preceding 
paragraph become 

v = ff t, (4) 



64.32 



128.64 





(16.08) 
16.08 



> (48.24) 



64.32 



(80.40) 



144.72 



(112.56) 



257.28 



FIG. 79. A freely fall- 
ing body 



78 



FOKCE AND MOTION 



must be this multiplied by the average velocity ; that is, 



(7) 




FIG. 80. Path of a projectile 



Since (7) is the same as (6), we learn that in a vacuum the speed with 
which a body must be projected upward to rise to a given height is the 
same as the speed which it acquires in falling from the 
same height. 

96. Path of a projectile. Imagine a projectile 
to be shot along the line ab (Fig. 80). If it 
were not for gravity and the resistance of 

the air, the projectile would travel 
with uniform velocity along the 
line ab, arriving at the points 
1, 2, 3, etc. at the end 
of the successive seconds. 
Because of gravity, how- 
ever, the projectile would 
be vertically below these 
points by the distances 

16.08 ft., 64.32 ft., 144.72 ft., etc. Hence it would follow the path indi- 
cated by the dotted curve (a parabola). But because of air resistance 
the height of flight and range are diminished, and the general shape of 
the trajectory is similar to the continuous curved line. 

97. The airplane. The principles underlying stability, as 
well as those having to do with the resolution of forces, are 
well illustrated by the modern airplane, which grew out of a 
study of the laivs of air resistance and the properties of gliders. 

When a plate of area A moves in still air in a direction 
perpendicular to its plane, with a velocity V (see Fig. 81, (1)), 
the air resistance R is found by experiment to be given by 
the equation 

R = KAY*, (8) 

where R is the force in kilograms, A the area in square meters, 
V the speed in meters per second, and K a constant which has 
the value .08. Thus, when an automobile is going 40 miles 



FALLING BODIES 



79 



per hour (18 meters per second), the force of the air against 
.5 square meter of wind-shield is .08 x .5 x (18) 2 = 13 kg. 
When the plate moves so that the direction of its motion 
makes a small angle i (between and 10) (Fig. 81, (2)) 
with its plane, the air resistance R is perpendicular to the 
plate and is given by the empirical formula 

R = kAV% (9) 

where J?, A, and V have the same significance as above, i is 
the angle in degrees, and k is very near to .005. 

As i, which is called the angle of attack or of incidence, 
decreases, the center of pressure C (Fig. 81, (2)) moves 

R 



(1) 




FIG. 81. Forces acting on a glider 



toward the front edge and tends toward a certain definite 
limiting position C Q as the angle i becomes smaller and smaller. 
When a flat object like a sheet of paper is allowed to fall, 
it is acted upon by two forces, one W, acting at its center 
of gravity g, which is always vertical and equal to the 
weight, and the other R, which is due to the air resistance 
acting at the center of pressure C and perpendicular to the 
plane. If the plane is to fall without acceleration and with- 
out rotation, that is, if it is to glide, it is clear that these 
two forces must act at the same point and be equal and 
opposite. Hence any gliding plane must be horizontal and 
must move with a speed V at an angle i (see Fig. 81 (3)), 
given by the equation 

(10) 



80 



FORCE AND MOTION 




Since the plane must be horizontal, and since there is 
only one angle of attack which will bring the center of 
pressure and the center of gravity together, it will be seen 
that the gliding angle i is the 
same for all values of the weight 
W, but that the speed V will be 
proportional to the square root 
of the weight (see equation 10). FIG. 82. A stabilized glider 

The foregoing theory of gliding may be nicely illustrated with paper 
gliders thus : Fold a sheet of writing paper lengthwise, exactly along 
the middle. Refold the upper half twice on itself so as to make it \ its 
original width; then fasten it down to the lower half with paste or 
light gummed paper. The center of gravity will now be -^ of the new 
width behind the back edge of the folded 
portion. When started slowly with the 
folded edge forward, the paper will glide 
as described. Heavier paper will glide at 
the same angle but with greater speed. 
If started thin edge foremost, the forces 
at once turn the glider over, and it glides 
with the heavier edge in front. To in- 
crease the lateral stability it is sufficient 
to give the paper the shape shown in 
Fig. 82. (See opposite p. 317.) 

When the motor of an airplane 
stops, the plane glides safely to FlG> 8 3. Forces acting on an 
earth under the laws of equation airplane in flight 

10. If the airplane propeller is 

pulling forward with a horizontal force Q, and the wings are 
set back at an angle i, R and W no longer balance each other, 
but their resultant is equal and opposite to Q; that is, the 
forces R, W, and Q form, a system in equilibrium, as shown 
in Fig. 83. The plane moves forward horizontally with a 
speed V. If the angle i or the force Q is increased, the plane 
rises ; if i or Q is diminished, the plane descends. 




FALLING BODIES 81 

98. The laws of the pendulum. The first law of the pendu- 
lum was found in 90, namely, 

(1) The periods of pendulums of equal lengths swinging through 
short arcs are independent of the weight and material of the bobs. 

Let the two pendulums of 90 be set swinging through arcs of 
lengths 5 centimeters and 25 centimeters respectively. We shall thus 
find the second law of the pendulum, namely, 

(2) The period of a pendulum swinging through a short arc is 
independent of the amplitude of the arc. 

Let pendulums ^ and ^ as long as the above be swung with it. The 
long pendulum will be found to make only one vibration while the others 
are making two and three respectively. The third law of the pendulum 
is therefore 

(3) The periods of pendulums are directly proportional to the 
square roots of their lengths. 

The accurate determination of g is never made by direct measure- 
ment, for the laws of the pendulum just established make this instru- 
ment by far the most accurate one obtainable for this determination. 
It is only necessary to measure the length of a long pendulum and the 
time t between two successive passages of the bob across the mid-point, 

and then to substitute in the formula t = *\l- in order to obtain g with a 

iff 

high degree of precision. The deduction of this formula is not suitable 
for an elementary text, but the formula itself may well be used for 
checking the value of g, given in 94. 

QUESTIONS AND PROBLEMS 

1. If a body starts from rest and travels with a constant acceleration 
of 10 ft. per second each second, how fast will it be going at the close 
of the fifth second? What is its average velocity during the 5 sec., and 
how far did it go in this time? 

2. A body starting from rest and moving with uniformly accelerated 
motion acquired a velocity of 60 ft. per second in 5 sec. Find the acceler- 
ation. What distance did it traverse during the first second ? the fifth ? 

3. A body moving with uniformly accelerated motion traversed 6 ft. 
during the first second. Find the velocity at the end of the fourth second. 



82 



FORCE AND MOTION 



4. A ball thrown across the ice started with a velocity of 80 ft. 
per second. It was retarded by friction at the rate of 2 ft. per second 
each second. How long did it roll? How far did 

it roll ? 

5. A bullet was fired with a velocity of 2400 ft. per 
second from a rifle having a barrel 2 ft. long. Find 
(a) the average velocity of the bullet while moving 
the length of the barrel; (b) the time required to 
move through the barrel ; (c) the acceleration of the 
bullet while in the barrel. 

6. A ball was thrown vertically into the air with 
a velocity of 160 ft. per second. How long did it re- 
main in the air? (Take g=32 ft. per sec 2 .) 

7. A baseball was thrown upward. It remained 
in the air 6 sec. With what velocity did it leave the 
hand ? How high did it go ? 

8. A ball dropped from the top of the Woolworth 
Building in New York City, 780 ft. above Broadway, 
would require how many seconds to fall ? With what 
velocity would it strike ? (Take g = 32 ft. per sec 2 .) 

9. How high was an airplane from which a bomb 
fell to earth in 10 sec. ? 

10. W T ith what speed does a bullet strike the earth 
if it is dropped from the Eiffel Tower, 335 m. high ? 

11. If the acceleration of a marble rolling down 
an inclined plane is 20 cm. per second, what velocity 
will it have at the bottom, the plane being 7 m. long ? 

12. If a man can jump 3 ft. high on the earth, how 
high could he jump on the moon, where g isj as much? 

13. The brakes were set on a train running 60 mi. per hour, and the 
train stopped in 20 sec. Find the acceleration in feet per second each 
second and the distance the train ran after the brakes were applied. 

14. How far will a body fall from rest during the first half second ? 

15. With what velocity must a ball be shot upward to rise to the 
height of the Washington Monument (555 ft.)? How long before it 
will return ? 

16. Fig. 84 represents the pendulum and escapement of a clock. 
The escapement wheel D is urged in the direction of the arrow by the 
clock weights or spring. The slight pushes communicated by the teeth 
of the wheel keep the pendulum from dying down. Show how the 
length of the pendulum controls the rate of the clock. 

17. What force supports an airplane in flight? What is "gliding"? 




FIG. 84 



NEWTON'S LAWS OF MOTION 83 

18. A pendulum that makes a single swing per second in New 
York City is 99.3 cm., or 39.1 in., long. Account for the fact that a 
seconds pendulum at the equator is 39 in. long, while at the poles it is 
39.2 in. long. 

19. How long is a pendulum whose period is 3 sec.? 2 sec.? \ sec.? 
sec.? 

20. A man was let down over a cliff on a rope to a depth of 500 ft. 
What was his period as a pendulum ? 



NEWTON'S LAWS OF MOTION 

99. First law inertia. It is a matter of everyday observa- 
tion that bodies in a moving train tend to move toward the 
forward end when the train stops and toward the rear end 
when the train starts ; that is, bodies in motion seem to want 
to keep on moving, and bodies at rest to remain at rest. 

Again, a block will go farther when driven with a given 
blow along a surface of glare ice than when knocked along 
an asphalt pavement. The reason which everyone will assign 
for this is that there is more friction between the block and 
the asphalt than between the block and the ice. But when 
would the body stop if there were no friction at all? 

Astronomical observations furnish the most convincing 
answer to this question^ for we cannot detect any retardation 
at all in the motions of the planets as they swing around the 
sun through empty space. 

Furthermore, since mud flies off tangentially from a rotating 
carriage wheel, or water from a whirling grindstone, and since, 
too, we have to lean inward to prevent ourselves from falling 
outward in going around a curve, it appears that bodies in 
motion tend to maintain not only the amount but also the 
direction of their motion (see gyrocompass opposite p. 223). 

In view of observations of this sort Sir Isaac Newton, in 
1686, formulated the following statement and called it the 
first law of motion. 






84 FOKCE AND MOTION 

Every body continues in its state of rest or uniform motion in a 
straight line unless impelled by external force to change that state. 

This property, which all matter possesses, of resisting any at- 
tempt to start it if at rest, to stop it if in motion, or in any way to 
change either the direction or amount of its motion, is called inertia. 

100. Centrifugal force. It is inertia alone Xyhich prevents 
the planets from falling into the sun, which causes a rotating 
sling to pull hard on the hand until the stone is released, 
and which then causes the stone to fly off tangentially. It 
is inertia which makes rotating 

liquids move out as far as possi- 
ble from the axis of rotation 
(Fig. 85), which makes flywheels 
sometimes burst, which makes 
the equatorial diameter of the 
earth greater than the polar, 

which makes the heavier milk 

, ,. , ! ,, ,, ,. , . FIG. 85. Illustrating centrifugal 

move out farther than the lighter f orce 

cream in the dairy separator (see 

opposite p. 85), etc. Inertia manifesting itself in this tendency 
of the, parts of rotating systems to move away from the center of 
rotation is called centrifugal force. 

101. Momentum. The quantity of motion possessed by a 
moving body is defined as the product of the mass and the 
velocity of the body. It is commonly called momentum. Thus, 
a 10-gram bullet moving 50,000 centimeters per second has 
500,000 units of momentum ; a 1000-kg. pile driver moving 
1000 centimeters per second has 1,000,000,000 units of mo- 
mentum ; etc. We shall always express momentum hi C.G.S. 
units, that is, as a product of grams by centimeters per second. 

102. Second law. Since a 2-gram mass is pulled toward 
the earth with twice as much force as is a 1-gram mass, and 
since both, when allowed to fall, acquire the same velo'city in 





SIR ISAAC NEWTON (1642-1727) 

English mathematician and physicist, "prince of philosophers" ; 
professor of mathematics at Cambridge University; formulated 
the law of gravitation ; discovered the binomial theorem ; invented 
the method of the calculus ; announced the three laws of motion 
which have become the basis of the science of mechanics ; made 
important discoveries in light; is the author of the celebrated 
" Principia " (Principles of Natural Philosophy) , published in 1687 



Skim-milk Outlet 



Cream Outlet 
Skim-milk Outlet 








THE CREAM SEPARATOR (2) 

The milk is poured into a central tube (see 1, a) at the top of a nest of disks (see 
1 and 4} situated within a steel bowl. The milk passes to the bottom of the cen- 
tral tube, then rises through three series of holes (see 1, b, b, b, etc.) in the nest 
of disks, and spreads outward into thin sheets between the slightly separated 
disks. By means of a system of gears (see 3) the disks and bowl are made to 
revolve from 6000 to 8000 revolutions per minute. The separation of cream from 
skim-milk is quickly effected in these thin sheets ; the heavier skim-milk (water, 
casein, and sugar) is thrown outward by centrifugal force against the under sur- 
faces of the bowl disks (see 5), then passes downward and outward along these 
under surfaces to the periphery of the bowl (see 1, d, d, d, etc.), and finally rises 
to the skim-milk outlet. The lighter cream is thereby at the same time displaced 
inward and upward along the upper surfaces of the bowl disks (see 5), then passes 
over the inner edges of the disks to slots (see 1, c, c, c, etc.) on the outside of the 
central tube, finally rising to the cream outlet, which is above the outlet for the 
skim-milk (see 1 and 2) 



NEWTON'S LA\VS OF MOTION 85 

a second, it follows that in this case the momentums produced 
in the two bodies by the two forces are exactly proportional to 
the forces themselves. In all cases in which forces simply over- 
come inertias this rule is found to hold. Thus, a 3000-pound 
pull on an automobile on a level road, where friction may be 
neglected, imparts in a second just twice as much velocity as 
does a 1500-pound pull. In view of this relation Newton's 
second law of motion was stated thus: Rate of change of 
momentum is proportional to the force acting, and the change 
takes place in the direction in which the force acts. 

103. The third law. When a man jumps from a boat to 
the shore, we all know that the boat experiences a backward 
thrust ; when a bullet is shot from a gun, the gun recoils, or 
" kicks " ; when a billiard ball strikes another, it loses speed, 
that is, is pushed back while the second 
ball is pushed forward. The following 
experiment will show how effects of 
this sort may be studied quantitatively. 

Let a sceel ball A (Fig. 80) be allowed 
to fall from a position C against another 
exactly similar ball B. In the impact A will 
lose practically all of its velocity, and B will ^ ^ 

move to a position D, which is at the same FIG. 86. Illustration of 
height as C. Hence the velocity acquired third law 

by B is almost exactly equal to that which 

A had before impact. These velocities would be exactly equal if the 
balls were perfectly elastic. It is found to be true experimentally that 
the momentum acquired by B plus that retained by A is exactly equal 
to the momentum which A had before the impact. The momentum 
acquired by B is therefore exactly equal to that lost by A. Since, by the 
second law, change in momentum is proportional to the force acting, 
this experiment shows that A pushed forward on B with precisely the 
same force with which B pushed back on A. 

Now the essence of Newton's third law is the assertion 
that in the case of the man jumping from the boat the mass 




86 FORCE AND MOTION 

of the man times his velocity is equal to the mass of the 
boat times its velocity, and that in the case of the bullet and 
gun the mass of the bullet times its velocity is equal to the 
mass of the gun times its velocity. The truth of this assertion 
has been established by a great variety of experiments. 

Newton stated his third law thus: To every action there is 
an equal and opposite reaction. 

Since force is measured by the rate at which momentum 
changes, this is only another way of saying that whenever a 
body acquires momentum some other body acquires an equal and 
opposite momentum. 

It is not always easy to see at first that setting one body 
into motion involves imparting an equal and opposite momen- 
tum to another body. For example, when a gun is held 
against the earth and a bullet shot upward, we are conscious 
only of the motion of the bullet; the other body is in this 
case the earth, and its momentum is the same as that of the 
bullet. On account of the greatness of the earth's mass, 
however, its velocity is infinitesimal. 

104. The dyne. Since the gram of force varies somewhat with locality, 
it has been found convenient for scientific purposes to take the second 
law as the basis for the definition of a new unit of force. It is called an 
absolute, or C.G.S., unit because it is based upon the fundamental units 
of length, mass, and time, and is therefore independent of gravity. It 
is named the dyne and is defined as the force which, acting for one second 
upon any mass, imparts to it one unit of momentum ; or the force which, act- 
ing for one second upon a one-gram mass, produces a change in its velocity 
of one centimeter per second. 

105. A gram of force equivalent to 980 dynes. A gram of force was 
defined as the pull of the earth upon 1 gram of mass. Since this pull is 
capable of imparting to this mass in 1 second a velocity of 980 centi- 
meters per second, that is, 980 units of momentum, and since a dyne 
is the force required to impart in 1 second 1 unit of momentum, it is 
clear that the gram of force is equivalent to 980 dynes of force. The 
dyne is therefore a very small unit, about equal to the force with which 
the earth attracts a cubic millimeter of water. 



NEWTON'S LAWS OF MOTION 87 

106. Algebraic statement of the second law. If a force F acts for t 
seconds on a mass of m grams, and in so doing increases its velocity 
v- centimeters per second, then, since the total momentum imparted in 

a time t is mv, the momentum imparted per second is ; and since 
force in dynes is equal to momentum imparted per second, we have 



But since - is the velocity gained per second, it is equal to the acceler- 
ation a. Equation (8) may therefore be written 

F = ma. (9) 

This is merely stating in the form of an equation that force is 
measured by rate of change of momentum. Thus, if ap engine, after pull- 
ing for 30 sec. on a train having a mass of 2,000,000 kg., has given it a 
velocity of 60 cm. per second, the force of the pull is 2,000,000,000 x | = 
4,000,000,000 dynes. To reduce this force to grams we' divide by 980, 
and to reduce it to kilos we divide further by 1000. Hence the pull 
exerted by the engine on the train = 4 ' Sgo t ggo 000 = 4081 k S'-> or 4 - 08 l 
metric tons. 

QUESTIONS AND PROBLEMS 

1. What principle is applied when one tightens the head of a 
hammer by pounding on the handle? 

2. Why does not the car C of Fig. 87 fall? What carries it from BtoDl 

3. Why does a flywheel cause machinery to run more steadily? 

4. Balance a calling card on the finger and place a coin upon it. 
Snap out the card, leaving the 

coin balanced on the finger. 
What principle is illustrated? 

5. Is it any easier to walk 
toward the rear than toward 

the front of a rapidly moving B 

train? Why? Fl( . 87 A very anc i en t loop the loops 

6. Suspend a weight by a 

string. Attach a piece of the same string to the bottom of the weight. 
If the lower string is pulled with a sudden jerk, it breaks ; but if the 
pull is steady, the upper string will break. Explain. 

7. Where does a body weigh the more, at the poles or at the equator ? 
Give two reasons. 




88 



FORCE AND MOTION 



8. If the trains A, B, and C (Fig. 88) are all running 60 mi. 
per hour, what is the velocity of A with reference to 5? to C? 

9. If a weight is dropped from the roof to the floor of a moving- 
car, will it strike the point on the floor which was di- 
rectly beneath its starting point? 

10. Why is a running track banked at the turns? C< 

11. If the earth were to cease rotating, would bodies p IG- g8 
on the equator weigh more or less than now ? Why ? 

12. How is the third law involved in rotary lawn sprinklers? 

13. The modern way of drying clothes is to place them in a large 
cylinder with holes iu the sides, and then to 

set it in rapid rotation. Explain. 

14. Explain how reaction pushes the ocean 
liner and the airplane forward. 

15. If one ball is thrown horizontally from 
the top of a tower and another dropped at the 
same instant, which will strike the earth first ? 
(Remember that the acceleration produced by 
a force is in the direction in which the force 
acts and proportional to it, whether the body 
is at rest or in motion. See second law.) If 

possible, try the experiment with an arrangement like that of Fig. 89- 

16. If a rifle bullet were fired horizontally from a tower 19.6 m. high 
with a speed of 300 m., how far from the base of the tower would it 
strike the earth if there were no air resistance ? 




\ 



FIG. 89. Illustrating New- 
ton's second law 




FIG. 90. Hydraulic ram 

17. The hydraulic ram (Fig. 90) is a practical illustration of the 
principle of inertia. With its aid water from a pond P can be raised 



NEWTON'S LAWS OF MOTION 




FIG. 91 



into a tank that stands at a higher level than the pond. With the aid 
of Fig. 91 explain how it works, remembering that the valve V will not 
close until the stream of water 
flowing around it acquires suffi- 
cient speed. 

18. If two men were together 
in the middle of a perfectly smooth 
(frictionless) pond of ice, how 
could they get off? Could one 
man get off if he were there 
alone ? 

19. If a 10-g. bullet is shot from a 5-kg. gun with a speed of 400 m. 
per second, what is the backward speed of the gun ? 

20. If a team of horses pulls 500 Ib. in drawing a wagon, with what 
force does the wagon pull backward upon the team ? ^hy do the wheels 
turn before the hoofs of the horses slide ? 

21. Why does a falling mass, on striking, exert a force in excess of 
its weight? 

22. A pull of a dyne acts for 3 sec. on a mass of 1 g. What velocity 
does it impart ? 

23. How long must a force of 100 dynes act on a mass of 20 g. to 
impart to it a velocity of 40 cm. per second? 

24. A force of 1 dyne acts on 1 g. for 1 sec. How far has the gram 
been moved at the end of the second ? 

A laboratory exercise on the composition of forces should be performed 
during the study of this chapter, See, for example, Experiment 11 of the 
authors' Manual. 



CHAPTER VI 

MOLECULAR FORCES* 
MOLECULAR FORCES IN SOLIDS. ELASTICITY 

107. That the molecules of solids cling together with forces 
of great magnitude is proved by some of the simplest facts of 
nature ; for solids not only do not expand indefinitely 
like gases, but it often requires enormous forces to 
pull their molecules apart. Thus, a rod of cast steel 
1 centimeter in diameter may be loaded with a weight 
of 7.8 tons before it will be pulled in two. 

The following are the weights in kilograms necessary 
to break drawn wires of different materials, 1 square 
millimeter in cross section, the so-called relative 
tenacities of the wires. 

Lead, 2.6 Platinum, 43 Iron, 77 

Silver, 37 Copper, 51 Steel, 91 

108. Elasticity. We can obtain additional infor- 
mation about the molecular forces existing in different 
substances by studying what 
happens when the weights ap- 
plied are not large enough to 
break the wires. 



Thus, let a long steel wire (for ex- 
P ample, No. 26 piano wire) be suspended 

FIG. 92. Elasticity of a steel wire from a hook in the ceiling, and let the 

* This chapter should be preceded by a laboratory experiment in which 
Hooke's law is discovered by the pupil for certain kinds of deformation 
easily measured in the laboratory. See, for example, Experiment 13 of the 
authors' Manual. 

90 



MOLECULAR FORCES IN SOLIDS 91 

lower end be wrapped tightly about one end of a meter stick, as in 
Fig. 92. Let a fulcrum c be placed in a notch in the stick at a distance 
of about 5 cm. from the point of attachment to the wire, and let the 
other end of the stick be provided with a knitting needle, one end of 
which is opposite the vertical mirror scale S. Let enough weights be 
applied to the pan P to place the wire under slight tension ; then let 
the reading of the pointer p on the scale S be taken. Let three or four 
kilogram weights be added successively to the pan and the correspond- 
ing positions of the pointer read. Then let the readings be taken again as 
the weights are successively removed. In this last operation the pointer 
will probably be found to come back exactly to its first position. 

This characteristic which the steel has shown in this experi- 
ment, of returning to its original length when the stretching 
weights are removed, is an illustration of a property possessed 
to a greater or less extent by all solid bodies. It is called 
elasticity. 

109. Limits of perfect elasticity. If a sufficiently large 
weight is applied to the end of the wire of Fig. 92, it will be 
found that the pointer does not return exactly to its original 
position when the weight is removed. We say, therefore, 
that steel is perfectly elastic only so long as the distorting 
forces are kept within certain limits, and that as soon as 
these limits are overstepped it no longer shows perfect 
elasticity. Different substances differ very greatly in the 
amount of distortion which they can sustain before they 
show this failure to return completely to the original shape. 

110. Hooke's law. If we examine the stretches produced by 
the successive addition of kilogram weights in the experiment 
of 108, Fig. 92, we shall find that these stretches are all 
equal, at least within the limits of observational error. Very 
carefully conducted experiments have shown that this law, 
namely, that the successive application of equal forces pro- 
duces a succession of equal stretches, holds very exactly for 
all sorts of elastic displacements so long, and only so long, 
as the limits of perfect elasticity are not overstepped. This 



92 MOLECULAR FORCES 

law is known as Hooke's law, after the Englishman Robert 
Hooke (1635-1703). Another way of stating this law is the 
folloAving : Within the limits of perfect elasticity elastic deforma- 
tions of any sort, be they twists or bends or stretches, are directly 
proportional to the forces producing them. The common spring 
balance (Fig. 57) is an application of Hooke's law. 

111. Cohesion and adhesion. The preceding experiments 
have brought out the fact that, in the solid condition at least, 
molecules of the same kind exert attractive forces upon one 
another. That molecules of unlike substances also exert 
mutually attractive forces is equally true, as is proved by 
the fact that glue sticks to wood with tremendous tenacity, 
mortar to bricks, nickel plating to iron, etc. 

The forces which bind like kinds of molecules together are 
commonly called cohesive forces ; those which bind together 
molecules of. unlike kind are called adhesive forces. Thus, we 
say that mucilage sticks to wood because of adhesion, while 
wood itself holds together because of cohesion. Again, adhe- 
sion holds the chalk to the blackboard, while cohesion holds 
together the particles of the crayon. 

112. Properties of solids depending on cohesion. Many of the 
physical properties in which solid substances differ from one 
another depend on differences in the cohesive forces existing 
between their molecules. Thus, we are accustomed to classify 
solids with relation to their hardness, brittleness, ductility, 
malleability, tenacity, elasticity, etc. The last two of these 
terms have been sufficiently explained in the preceding para- 
graphs; but since confusion sometimes arises from failure 
to understand the first four, the tests for these properties 
are here given. 

We test the relative hardness of two bodies by seeing 
which will scratch the other. Thus, the diamond is the 
hardest of all substances, since it scratches all others and 
is scratched by none of them. 



MOLECULAR FORCES IN LIQUIDS 93 

We test the relative brittleness of two substances by 
seeing which will break the more easily under a blow from a 
hammer. Thus, glass and ice are very brittle substances ; 
lead and copper are not. 

We test the relative ductility of two bodies by seeing 
which can be drawn into the thinner wire. Platinum is the 
most ductile of all substances. It has been drawn into 
wires only .00003 inch in diameter. Glass is also very 
ductile when sufficiently hot, as may be readily shown by 
heating it to softness in a Bunsen flame, when it may be 
drawn into threads which are so fine as to be almost invisible. 

We test the relative malleability of two substances by 
seeing which can be hammered into the thinner sheet. Gold, 
the most malleable of all substances, has been hammered 
into sheets 3 0*0 o o mcn ni thickness. 

QUESTIONS AND PROBLEMS 

1. Tell how you may, by use of Hooke's law and a 20-lb. weight, make 
the scale for a 32-lb. spring balance. 

2. A broken piece of wrought iron or steel may be welded by heating 
the broken ends white hot and pounding them together. Gold foil is 
welded cold in the process of filling a tooth. Explain welding. 

3. A piece of broken wood may be mended with glue. What does 
the glue do? 

4. Why are springs made of steel rather than of copper? 

5. If a given weight is required to break a given wire, how much 
force is required to break two such wires hanging side by side ? to break 
one wire of twice the diameter ? 

MOLECULAR FORCES IN LIQUIDS. CAPILLARY PHENOMENA 

113. Proof of the existence of molecular forces in liquids. 
The facility with which liquids change their shape might lead 
us to suspect that the molecules of such substances exert 
almost no force upon one another, but a simple experiment 
will show that this is far from true. 



94 



MOLECULAR FORCES 




FIG. 93. Illustrating 
cohesion of water 



By means of sealing wax and string let a glass plate be suspended 
horizontally from one arm of a balance, as in Fig. 93. After equilibrium 
is obtained, let a surface of water be placed 
just beneath the plate and the beam pushed 
down until contact is made. It will be found 
necessary to add a considerable weight to the 
opposite pan in order to pull the plate away 
from the water. Since a layer of water will be 
found to cling to the glass, it is evident that 
the added force applied to the pan has been 
expended in pulling water molecules away 
from water molecules, not in pulling glass 
away from water. Similar experiments may 
be performed with all liquids. In the case of % 

mercury the glass will not be found to be wet, showing that the co- 
hesion of mercury is greater than the adhesion of glass and mercury. 

114. Shape assumed by a free liquid. Since, then, every 
molecule of a liquid is pulling on every other molecule, any 
body of liquid which is free to take its natural shape, that is, 
which is acted on only by its own cohesive forces, must draw 
itself together until it has the smallest possible surface com- 
patible with its volume ; for, since every molecule in the surface 
is drawn toward the interior by the attraction of the molecules 
within, it is clear that molecules must continually move toward 
the center of the mass until the whole has reached the most 
compact form possible. Now the geometrical figure which has 
the smallest area for a given volume is a sphere. We conclude, 
therefore, that if we could relieve a body of liquid from the 
action of gravity and other outside forces, it would at once 
take the form of a perfect sphere. This conclusion may be 
easily verified by the following experiment: 

Let alcohol be added to water until a solution is obtained in which 
a drop of common lubricating oil will float at any depth. Then with a 
pipette insert a large globule of oil beneath the surface. The oil will be 
seen to float as a perfect sphere within the body of the liquid (Fig. 94). 
(Unless the drop is viewed from above, the vessel should have flat rather 



MOLECULAR FORCES IN LIQUIDS 



95 



FIG. 94. Spherical 
globule of oil, freed 
from action of gravity 



than cylindrical sides, otherwise the curved surface of the water will 
act like a lens and make the drop appear flattened.) 

The reason that liquids are not more commonly observed 
to take the spherical form is that ordinarily the force of gravity 

is so large as to be more influential in deter- _ = 

mining their shape than are the cohesive 
forces. As verification of this statement we 
have only to observe that as a body of 
liquid becomes smaller and smaller that 
is, as the gravitational forces upon it be- 
come less and less it does indeed tend 
more and more to take the spherical form. Thus, very small 
globules of mercury on a table will be found to be almost 
perfect spheres, and raindrops or minute floating particles of 
all liquids are quite accurately spherical. 

115. Contractility of liquid films; surf ace tension. The tend- 
ency of liquids to assume the smallest possible surface fur- 
nishes a simple explanation of the contractility of liquid films. 

Let a soap bubble 2 or 3 inches in diameter be blown on the bowl 
of a pipe and then allowed to stand. It will at once begin to shrink 
in size and in a few minutes will disappear within the bowl of the pipe. 






FIG. 95 'FiG. 96 FIG. 97 

Illustrating the contractility of soap films 

The liquid of the bubble is simply obeying the tendency to reduce its 
surface to a minimum, a tendency which is due only to the mutual at- 
tractions which its molecules exert upon one another. A candle flame 



96 



MOLECULAE FORCES 



held opposite the opening in the stem of the pipe will be deflected by 
the current of air which the contracting bubble is forcing out through 
the stem. 

Again, let a loop of fine thread be tied to a wire ring, as in Fig. 95. 
Let the ring be dipped into a soap solution so as to form a film across 
it, and then let a hot wire be thrust through the film inside the loop. 
The tendency of the film outside the loop to contract will instantly snap 
out the thread into a perfect circle (Fig. 96). The reason that the thread 
takes the circular form is that, since the film outside the loop is striving 
to assume the smallest possible surface, the area inside the loop must 
of course become as large as possible. The circle is the figure which 
has the largest possible area for a given perimeter. 

Let a soap film be formed across the mouth of a clean 2-inch funnel, 
as in Fig. 97. The tendency of the film to contract will be sufficient 
to lift its weight against the force of gravity. 

The tendency of a liquid to reduce its exposed surface to a 
minimum, that is, the tendency of any liquid surface to act like 




Fig. 98. Some of the stages through which a slowly forming drop passes 

a stretched elastic membrane, is called surface tension. The elas- 
tic nature of a film is illustrated in Fig. 98, which is from a 
motion-picture record of some of the stages through which 
a slowly forming drop passes. 

116. Ascension and depression of liquids in capillary tubes. 
It was shown in Chapter II that, in general, a liquid stands 
at the same level in any number of communicating vessels. 
The following experiments will show that this rule ceases to 
hold in the case of tubes of small diameter. 



MOLECULAR FORCES IN LIQUIDS 



9T 




Let a series of capillary tubes of diameter varying from 2 mm. to 
.1 inm. be arranged as in Fig. 99. 

When water or ink is poured into the vessel it will be found to rise 
higher in the tubes than in the vessel, and it will be seen that the 
smaller the tube the greater the height to which it 
rises. If the water is replaced by mercury, however, 
the effects will be found to be just inverted. The 
mercury is depressed in all the tubes, the depression 
being greater in proportion as the tube is smaller 
(Fig. 100, (1)). This depression is most easily ob- 
served with a U-tube like that shown in Fig. 100, (2). 

Experiments of this sort have established 
the following laws: 

1. Liquids rise in capillary tubes when they FlG - " Rise of 

7 7 />,,, 7 T -i liquids in capillary 

are capable oj wetting them, but are depressed tubes 

in tubes which they do not wet. 

2. The elevation in the one case and the depression in the 
oilier are inversely proportional to the diameters of the tubes. 

It will be noticed, too, that when a liquid rises, its surface 
within the tube is concave upward, and when it is depressed 
its surface is convex upward. 

117. Cause of curvature of 
a liquid surface in a capillary 
tube. All of the effects pre- 
sented in the last paragraph 
can be explained by a consider- 
ation of cohesive and adhesive 
forces. However, throughout 
the explanation we must keep 
in mind two familiar facts : first, that the surface of a body 
of water at rest, for example a pond, is at right angles to the 
resultant force, that is, gravity, which acts upon it; and, second, 
that the force of gravity acting on a minute amount of liquid is 
negligible in comparison with its own cohesive force (see 114). 




FIG. 100. Depression of mercury in 
capillary tubes 



98 



MOLECULAR FORCES 



Consider, then, a very small body of liquid close to the 
point o (Fig. 101), where water is in contact with the glass 
wall of the tube. Let the quantity of liquid considered be 
so minute that the 
force of gravity act- 
ing upon it may 
be disregarded. The 
force of adhesion si 
the wall will pull 
the liquid particles 





FIG. 101 FIG. 102 

Condition for elevation of a liquid near a wall 



at o in the direction 
oE. The force of 
cohesion of the liquid 
will pull these same particles in the direction oF. The resul- 
tant of these two pulls on the liquid at o will then be repre- 
sented by oR (Fig. 101), in accordance with the parallelogram 
law of Chapter V. If, then, the resultant oR of the adhesive 
force oE and the cohesive force oF lies to the left of the 
vertical om (Fig. 102), since the surface of a liquid always 
assumes a position at right angles to 
the resultant force, the liquid must rise 
up against the wall as water does 
against glass (Fig. 102). 

If the cohesive force 0^(Fig. 103) is 
strong in comparison with the adhesive 
force oE, the resultant oR will fall to 
the right of the vertical, in which case 
the liquid must be depressed about o. 

Whether, then, a liquid will rise 

against a solid wall or be depressed by it will depend only 
on the relative strengths of the adhesion of the wall for the 
liquid and the cohesion of the liquid for itself. Since mercury 
does not wet glass, we know that cohesion is here relatively 
strong, and we should expect, therefore, that the mercury 




F 

FIG. 103. Condition for 

the depression of a liquid 

near a wall 



MOLECULAR FORCES IN LIQUIDS 



99 



would be depressed, as indeed we find it to be. The fact 
that water will wet glass indicates that in this case adhesion 
is relatively strong, and hence we should expect water to rise 
against the walls of the containing vessel, as in fact it does. 

It is clear that a liquid which is depressed near the edge 
of a vertical solid wall must assume within a tube a surface 
which is convex upward, while a liquid which rises against a 
wall must within such a tube be concave upward. 

118. Explanation of ascension and depression in capillary 
tubes. As soon as the curvatures just mentioned are pro- 
duced, the concave surface aob (Fig. 104) tends, by virtue of 



FIG. 104 FIG. 105 

A concave meniscus causes a rise 
in a capillary tube 



FIG. 106 



FIG. 107 



A convex meniscus causes 
a fall 



surface tension, to straighten out into the flat surface ao'b. 
But it no sooner thus begins to straighten out than adhesion 
again elevates it at the edges. It will be seen, therefore, 
that the liquid must continue to rise in the tube until the 
weight of the volume of liquid lifted, namely amnb (Fig. 105), 
balances the tendency of the surface aob to flatten out. That 
the liquid will rise higher in a small tube than in a large 
one is to be expected, since the weight of the column of 
liquid to be supported in the small tube is less. 

The convex mercury surface aob (Fig. 106) falls until the 
upward pressure at 0, due to the depth h of mercury (Fig. 107), 
balances the tendency of the surface aob to flatten. 



100 



MOLECULAK FOBCES 



119. Capillary phenomena in everyday life. Capillary phe- 
nomena play a very important part in the processes of nature 
and of everyday life. Thus the rise of oil in wicks of lamps, 
the complete wetting of a towel when one end of it is allowed 
to stand in a basin of water, the rapid absorption of liquid by 
a lump of sugar when one corner of it only is immersed, the 
taking up of ink by blotting paper, are all illustrations of pre- 
cisely the same phenomena which we observe in the capillary 
tubes of Fig. 99. 

120. Floating of Small Objects On water. Let a needle be laid 
very carefully on the surface of a dish of water. In spite of the fact 
that it is nearly eight times as dense as water it will 

be found to float. If the needle has been previously 
magnetized, it may be made to move about in any 
direction over the surface in obedience to the pull of 
a magnet held, for example, underneath the table. FIG. 108. Cross 

section of a 
To discover the cause ot this apparently floating needle 

impossible phenomenon, examine closely the 

surface of the water in the immediate neighborhood of the 

needle. It will be found to be depressed in the manner shown 

in Fig. 108. This furnishes at once the explanation. So long 

as the needle is so small that its own weight is no greater than 

the upward force exerted upon it by 

the tendency of the depressed (and 

therefore concave) liquid surface to 

straighten out into a flat surface, the 

needle cannot sink in the liquid, no 

matter how great its density. If the 

water had wet the needle, that is, if it had risen about the 

needle instead of being depressed, the tendency of the liquid 

surface to flatten out would have pulled it down into the 

liquid instead of forcing it upward. Any body about which 

a liquid is depressed will therefore float on the surface of 

the liquid if its mass is not too great. Even if the liquid 




FIG. 109. Insect walking 
on the surface of water 



MOLECULAK FORCES IN LIQUIDS 101 

tends to rise about a body when it is perfectly clean, an im- 
perceptible film of oil upon the body will cause it to depress 
the liquid, and hence to float. 

The above experiment explains the familiar phenomenon of 
insects walking and running on the surface of water (Fig. 109) 
in apparent contradiction to the law of Archimedes, in ac- 
cordance with which they should sink until they displace their 
own weight of the liquid. 

QUESTIONS AND PROBLEMS 

1. Explain how capillary attraction comes usefully into play in the 
steel pen, camel's-hair brushes, lamp wicks, and sponges. 

2. Candle grease may be removed from clothing by covering it with 
blotting paper and then passing a hot flatiron over the paper. Explain. 

3. Why will a piece of sharp-cornered glass become rounded when 
heated to redness in a Bunsen flame ? 

4. The leads for pencils are made by subjecting powdered graphite 
to enormous pressures produced by hydraulic machines. Explain how 
the pressure changes the powder to a coherent mass. 

5. Float two matches an inch apart. Touch the water between them 
with a hot wire. The matches will spring apart. What does this show 
about the effect of temperature on surface tension ? 

6. Repeat the experiment, touching the water with a wire moistened 
with alcohol. What do you infer as to the relative surface tensions of 
alcohol and water? 

7. Fasten a bit of gum camphor to one end of half a toothpick and 
lay it upon the surface of a large vessel of clean still water. Explain the 
motion. 

8. Shot are made by pouring molten lead through a sieve on top 
of a tall tower and catching it in water at the bottom. Why are the 
shot spherical? 

9. Explain how capillary attraction makes an irrigation system 
successful. 

10. In building a macadam road coarse stones are placed at the 
bottom, on top of them smaller stones, and finally little granules tightly 
rolled together by means of a steam roller. Explain how this arrange- 
ment of material keeps the road dry. 

11. What force is mainly responsible for the return of the water 
that has gravitated into the soil? Would the looseness of the soil make 
any difference (dry farming) ? 



102 



MOLECULAR FORCES 




ABSORPTION OF GASES BY SOLIDS AND LIQUIDS 

121 . Absorption Of gases by solids. Let a large test tube be filled 
with ammonia gas by heating aqua ammonia and causing the evolved 
gas to displace mercury in the tube, as in Fig. 110. Let a piece of 
charcoal an inch long and nearly 
as wide as the tube be heated 
to redness and then plunged be- 
neath the mercury. When it is 
cool, let it be slipped underneath 
the mouth of the test tube and 
allowed to rise into the gas. The 
mercury will be seen to rise in 
the tube, as in Fig. 111. Why? FIG. 110. Filling tube with ammonia 

This property of absorbing gases is possessed to a notable 
degree by porous substances, especially coconut and peach-pit 
charcoal. It is not improbable that all solids hold, closely 
adhering to their surfaces, thin layers of the gases with which 
they are in contact, and that the prominence 
of the phenomena of absorption in porous 
substances is due to the great extent of sur- 
face possessed by such substances. 

That the same substance exerts widely 
different attractions upon the molecules of 
different gases is shown by the fact that char- 
coal will absorb 90 times its own volume of 
ammonia gas, 35 times its volume of carbon 
dioxide, and only 1.7 times its volume of 
hydrogen. The usefulness of charcoal as a 
deodorizer is due to its enormous ability to absorb certain 
kinds of gases. This property made it available for use in gas 
masks (see opposite p. 103) during the World War. If a 
little spongy platinum is suspended in a vessel above wood 
alcohol, it will glow brightly because of the absorption into 
the platinum of both vapor of alcohol and oxygen. The rapid 




FIG. 111. Absorp- 
tion of ammonia 
gas by charcoal 




JAMES CLERK-MAXWELL 

(1831-1879) 

One of the greatest of mathemati- 
cal physicists ; born in Edinburgh, 
Scotland ; professor of natural 
philosophy at Marischal College, 
Aberdeen, in 1856, of physics and 
astronomy in Kings College, Lon- 
don, in I860, and of experimental 
physics in Cambi'idge University 
from 1871 to 1879 ; one of the most 
prominent figures in the develop- 
ment of the kinetic theory of 
gases and the mechanical theory 
of heat ; author of the electro- 
magnetic theory of light a the- 
ory which has become the basis of 
nearly all modern theoretical work 
in electricity and optics (see p. 426) 




HEINRICH RUDOLPH HERTZ 

(1857-1894) 

One of the most brilliant of Ger- 
man physicists, who, in spite of his 
early death at the age of thirty- 
seven, made notable contributions 
to theoretical physics, and left be- 
hind the epoch-making experimen- 
tal discovery of the electromagnetic 
waves predicted by Maxwell. Wire- 
less telegraphy is but an applica- 
tion of this discovery of so-called 
" Hertzian " waves (see p. 422). The 
capital discovery that ultra-violet 
light discharges negatively electri- 
fied bodies is also due to Hertz 




A GAS MASK 



U. S. Official 



A great variety of poisonous gases having a density greater than air were set free 
and carried by the wind against the Allied armies in the World War. and others 
were fired in explosive shells. Until gas masks were devised these gases, settling 
into the trenches, wrought frightful havoc among the troops. The absorptive power 
of charcoal, especially when impregnated with certain chemicals, proved an effec- 
tive barrier against the deadly fumes, since all of the air entering the lungs of 
the soldiers had to be inhaled through the charcoal within a canister carried in 
the bag designed to hold the gas mask. The illustration shows an American gas 
mask adjusted to the head of an American soldier 




MOLECULAR FORCES IX LIQUIDS 103 

rise in temperature is due to the increased rate of oxidation 
of the alcohol brought about by this more intimate mixture. 
This property of platinum is utilized in the platinum-alcohol 
cigar lighter (Fig. 112). 

122. Absorption of gases in liquids. 

Let a beaker containing cold water be slowly 

heated. Small bubbles of air will be seen to Sponau 

collect in great numbers upon the walls and Platinum^ 

to rise through the liquid to the surface. Platinun 

That they are indeed bubbles of air and not Wick 

of steam is proved, first, by the fact that they WoodAlcohqi 

appear when the temperature is far below inCotton 
boiling, and, second, by the fact that they do 

not condense as they rise into the higher and 

FIG. 112. The platinum- 
cooler layers of the water. alcohol dgar Hghter 

The experiment shows two things : 

first, that water ordinarily contains considerable quantities of 
air dissolved in it ; and, second, that the amount of air which 
water can hold decreases as the temperature rises. The first 
point is also proved by the existence of fish life ; for fishes 
obtain the oxygen which they need to support life from air 
which is dissolved in the water. 

The amount of gas which will be absorbed by water varies 
greatly with the nature of the gas. At C. and a pressure of 
76 centimeters 1 cubic centimeter of water will absorb 1050 
cubic centimeters of ammonia, 1.8 cubic centimeters of carbon 
dioxide, and only .04 cubic centimeter of oxygen. Commercial 
aqua ammonia is simply ammonia gas dissolved in water. 

The following experiment illustrates the absorption of 
ammonia by water : 

Let the flask F (Fig. 113) and tube b be filled with ammonia by passing 
a current of the gas in at a and out through b. Then let a be corked 
up and b thrust into G, a flask nearly filled with water which has been 
colored slightly red by the addition of litmus and a drop or two of acid. 
As the ammonia is absorbed the water will slowly rise in b, and as soon 



104 



MOLECULAR FORCES 




FIG. 113. Absorp- 
tion of ammonia 
by water 



as it reaches F it will rush up very rapidly until the upper flask is 
nearly full. At the same time the color will change from red to blue 
because of the action of the ammonia upon the litmus. 

Experiment shows that in every case of ab- 
sorption of a gas by a liquid or a solid the 
quantity of gas absorbed decreases with an in- 
crease in temperature, a result which was 
to have been expected from the kinetic 
theory, since increasing the molecular veloc- 
ity must of course increase the difficulty 
which the adhesive forces have in retaining 
the gaseous molecules. 

123. Effect of pressure upon absorption. 
Soda water is ordinary water which has been 
made to absorb large quantities of carbon 
dioxide gas. This impregnation is accom- 
plished by bringing the water into contact 
with the gas under high pressure. As soon as the pressure is 
relieved, the gas passes rapidly out of solution. This is the 
cause of the characteristic effervescence of soda water. These 
facts show clearly that the amount of carbon dioxide which can 
be absorbed by water is greater for high pressures than for low. 
As a matter of fact, careful experiments have shown that the 
amount of any gas absorbed is directly proportional to the pres- 
sure, so that if carbon dioxide under a pressure of 10 atmos- 
pheres is brought into contact with water, ten times as much 
of the gas is absorbed as if it had been under a pressure of 
1 atmosphere. This is known as Henry's law. 

QUESTIONS AND PROBLEMS 

1. Why do fishes in an aquarium die if the w r ater is not frequently 
renewed ? 

2. Explain the apparent generation of ammonia gas when aqua 
ammonia is heated. 

3. Why, in the experiment illustrated in Fig. 113, was the flow so 
much more rapid after the water began to run over into -F? 



CHAPTER VII 

WORK AND MECHANICAL ENERGY* 
DEFINITION AND MEASUREMENT OF 



124. Definition of work. Whenever a force moves a body 
on which it acts, it is said to do work upon that body, and 
the amount of the work accomplished is measured by the 
product of the force acting and the distance through which 
it moves the body. Thus, if i gram of mass is lifted 1 centi- 
meter in a vertical direction, 1 gram of force has acted, and 
the distance through which it has moved the body is 1 centi- 
meter. We say, therefore, that the lifting force has accom- 
plished 1 gram centimeter of work. If the gram of force had 
lifted the body upon which it acted through 2 centimeters, 
the work done would have been 2 gram centimeters. If a 
force of 3 grams had acted and the body had been lifted 
through 3 centimeters, the work done would have been 9 gram 
centimeters, etc. Or, in general, if W represent the work 
accomplished, F the value of the acting force, and s the dis- 
tance through which its point of application moves, then the 
definition of work is given by the equation 

W=Fxs. (1) 

In the scientific sense no work is ever done unless the 
force succeeds in producing motion in the body on which it 

* It is recommended that this chapter be preceded by an experiment in 
which the student discovers for himself the law of the lever, that is, the 
principle of moments (see, for example, Experiment 16, authors' Manual), 
and that it be accompanied by a study of the principle of work as exempli- 
fied in at least one of the other simple machines (see, for example, Experi- 
ment 17, authors' Manual). 

105 



106 WORK AND MECHANICAL ENERGY 

acts. A pillar supporting a building does 110 work ; a man 
tugging at a stone, but failing to move it, does no work. 
In the popular sense we sometimes say that we are doing work 
when we are simply holding a weight or doing anything else 
which results in fatigue; but in physics the word "work" is 
used to describe not the effort put forth but the effect ac- 

A tA/ 

complished, as represented in equation (1). 

125. Units of work. There are two common units of work 
in the metric system, the gram centimeter and the kilogram 
meter. As the names imply, the gram centimeter is the work 
done by a force of 1 gram when it moves the point on which 
it acts 1 centimeter. The kilogram meter is the work done 
by a kilogram of force -./hen it moves the point on which it 
acts 1 meter. The gram meter also is sometimes used. 

Corresponding to the English unit o^ force, the pound, is 
the unit of work, the foot pound. It is the work done by a 
" pound of force " when it moves the point on which it acts 
1 foot. Thus, it takes a foot pound of work to lift a pound 
of mass 1 foot high. 

In the absolute system of units the dyne is the unit of force, and the 
dyne centimeter, or erg, is the corresponding unit of work. The erg is 
the amount of work done by a force of 1 dyne when it moves the point 
on which it acts 1 centimeter. To raise 1 liter of water from the floor 
to a table 1 meter high would require 1000 x 980 X 100 = 98,^00,000 ergs 
of work. It will be seen, therefore, that the erg is an exceedingly small 
unit. For this reason it is customary to employ a unit which is equal 
to 10,000,000 ergs. It is called a joule, in honor of the great English 
physicist James Prescott Joule (1818-1889). The work done in lifting 
a liter of water 1 meter is therefore 9.8 joules. 

QUESTIONS AND PROBLEMS 

1. To drag a trunk weighing 120 Ib. required a force of 40 Ib. How 
much work would be required to drag this trunk 2 yd. ? to lift it 2 yd. 
vertically ? 

2. A carpenter pushed 5 Ib. on his plane while taking off a shaving 
4 ft. long. How much work was done? 



WOEK AND THE PULLEY 10T 

3. How many foot pounds of work does a 150-lb. man do in climbing 
to the top of Mt. Washington, which is 6300 ft. high ? 

4. A horse pulls a metric ton of coal to the top of a hill 30 m. high. 
Express the work accomplished in kilogram meters (a metric ton = 
1000 kg.). 

5. If the 20,000 inhabitants of a city use an average of 20 liters of 
water per capita per day, how many kilogram meters of work must the 
engines do per day if the water has to be raised to a height of 75 m. ? 

WORK EXPENDED UPON AND ACCOMPLISHED BY SYSTEMS 

OF PULLEYS 

126. The single fixed pulley. Let the force of the earth's attrac- 
tion upon a mass R be overcome by pulling upon a spring balance S, 
in the manner shown in Fig. 114, until R moves slowly upward. If R 
is 100 grams, the spring balance will also be found to t f 

register a force of 100 grams. /HFT 

Experiment therefore shows that in the use 
of the single fixed pulley the acting force, or 
effort, E, which is producing the motion, is equal 
to the resisting force, or resistance, JK, which is 
opposing the motion. 

Again, since the length of the string is always \ A 
constant, the distance s through which the point E 
A, at which E is applied, must move is always FIG. 114. The 
equal to the distance s' through which the weight sm s le fixed 
R is lifted. Hence, if we consider the work put 
into the system at A, namely, E x , and the work accomplished 
by the system at R, namely, R x s', we find, obviously, since 
R = E and s = *', that 

Exs = fixs'; (2) 

that is, in the case of the single fixed pulley, the work done 
by the acting force E (the effort) is equal to the work done 
against the resisting force R (the resistance), or the work put 
into the machine at A is equal to the work accomplished by 
the machine at R. 



108 



WOBK AND MECHANICAL ENEKGY 



127. The single movable pulley. Now let the force of the earth's 
attraction upon the mass R be overcome by a single movable pulley, as 
shown in Fig. 115. Since the weight of R (R repre- 
senting in this case the weight of both the pulley and 
the suspended mass) is now supported half by the strand 
C and half by the strand B, the force E which must act 
at A to hold the weight in place, or to move it slowly 
upward if there is no friction, should be only one half 
of R. A reading of the balance will show that this is 
indeed the case. 

Experiment thus shows that in the case of the 
single movable pulley the effort E is just one half 
as great as the resistance R. 

But when we again consider the work which 
the force E must clo to lift the weight R a dis- 




tance *', we see that A must move upward 2 



FIG. 115. The 

single movable 
pulley 

inches in order to raise R 1 inch; for when 

R moves up 1 inch, both of the strands B and C must be 

shortened 1 inch. As before, therefore, since R = 2 E and 



that is, in the case of the single movable pulley, as in the 
case of the fixed pulley, the work put into the machine by the 
effort E is equal to the work accomplished by the machine against 

the resistance R. 



128. Combinations of pulleys. Let a weight R be lifted by means 
of such a system of pulleys as is shown in Fig. 116, either (1) or (2). 
Here, since R is supported by 6 strands of the cord, it is clear that the 
force which must be applied at A in order to hold R in place, or to 
make it move slowly upward if there is no friction, should be but i of R. 

The experiment will show this to be the case if the effects 
of friction, which are often very considerable, are eliminated 
'by taking the mean of the forces which must be applied at E 
to cause it to move first slowly upward and then slowly down- 
ward. The law of any combination of movable pulleys may 



WORK AND THE PULLEY 



109 



then be stated thus : If n represents the number of strands 
between which the weight is divided, 

E = R/n. (3) 

But when we again consider the work which the force E 
must do in order to lift the weight R through a distance *', 
we see that, in order that the weight 
R may be moved up through 1 inch, 
each of the strands must be short- 
ened 1 inch, and hence the point A 
must move through n inches ; that 
is, s' = s/n. Hence, ignoring friction, 
in this case also we have 



(i) 



E X s = R x s f ; 

that is, although the effort E is only 
- of the resistance R, the work put 



n 




FIG. 116. Combinations 
of pulleys 



into the machine by the effort E is 
equal to the work accomplished by the 
machine against the resistance R. 

129. Mechanical advantage. The 
above experiments show that it is 

sometimes possible by applying a small force E to overcome 
a much larger resisting force R. The ratio of the resistance R 
to the effort E (ignoring friction) is called the mechanical advan- 
tage of the machine. Thus, the mechanical advantage of the 
single fixed pulley is 1, that of the single movable pulley is 
2, that of the system of pulleys shown in Fig. 116 is 6, etc. 

If the acting force is applied at R instead of at E the me- 
chanical advantage of the systems of pulleys of Fig. 116 is i ; 
for it requires an application of 6 pounds at R to lift 1 pound 
at E. But it will be observed that the resisting force at jE'now 
moves six times as fast and six times as far as the acting force 
at R. We can thus either sacrifice speed to gain force, or 



110 WOEK AND MECHANICAL ENERGY 

sacrifice force to gain speed ; but in every case, whatever we 
gain in the one we lose in the other. Thus in the hydraulic 
elevator shown in Fig. 13, p. 18, the cage moves only as fast 
as the piston ; but in that shown in Fig. 14 it moves four times 
as fast. Hence the force applied to the piston in the latter 
case must be four times as great as in the former if the same 
load is to be lifted. This means that the diameter of the latter 
cylinder must be twice as great. 

QUESTIONS AND PROBLEMS 

1. Although the mechanical advantage of the fixed pulley is only 1, 
it is extensively used in connection with clothes lines, awnings, open 
wells, and flags. Explain. 

2. If the hydraulic elevator of Fig. 14, p. 18, is to carry a total load 
of 20,000 lb., what force must be applied to the piston? If the water 
pressure is 70 lb. per square inch, what must be the area of the piston? 

3. Draw a diagram of a set of pulleys by which a force of 50 lb. can 
support a load of 200 lb. 

4. Draw a diagram of a set of pulleys by which a force of 50 lb. can 
support 250 lb. What would be the mechanical advantage of this 
arrangement ? 

5. Two men, pulling 50 lb. each, lifted 300 lb. by a system of pulleys. 
Assuming no friction, how many feet of rope did they pull down in 
raising the weight 20 f t. ? 

WORK AND THE LEVER 

130. The law of the lever. The lever is a rigid rod free 
to turn about some point P called the fulcrum (Fig. 117). 

First let a meter 
stick be balanced as 
in the figure, and 
then let a mass of, 
say, 300 g. be hung 

by a thread from a ' ' 

point 15 cm. from FIG. 117. The simple lever 

the fulcrum. Then 

let a point be found on the other side of the fulcrum at which a weight 

of 100 g. will just support the 300 g. This point will be found to be 



I L__L 



J I 1 I J 




WORK AND THE LEVER 111 

45 cm. from the fulcrum. Jt will be seen at once that the product of 
300 x 15 is equal to the product of 100 x 45. 

Next let the point be found at which 150 g. just balance the 300 g. 
This will be found to be 30 cm. from the fulcrum. Again, the products 
300 x 15 and 150 x 30 are equal. 

No matter where the weights are placed, or what weights 
are used on either side of the fulcrum, the product of the 
effort E by its distance I A p B 

from the fulcrum (Fig. 118) 
will be found to be equal 
to the product of the re- 
sistance R by its distance I' s 
from the fulcrum. Now the ^IG. 118. Illustrating the law of moments, 

namely, El=Rl' 
perpendicular distances I 

and I' from the fulcrum to the line of action of the forces are 
called the lever arms of the forces E and R, and the product of 
a force by its lever arm is called the moment of that force. The 
above experiments on the lever may then be generalized in 
the following law : The moment of the effort is equal to the 
moment of the resistance. Algebraically stated, it is 

El = Rl'. (4) 

It will be seen that the mechanical advantage of the lever, 
namely R/E, is equal to l/l' ; that is, to the lever arm of the 
effort divided by the lever arm of the resistance. 

131. General laws of the lever. If parallel forces are applied 
at several points on a lever, as in Figs. 119 and 120, it will be 
found, in the particular cases illustrated, that for equilibrium 

. 200 x 30 - 100 x 20 + 100 x 40 
and 300 x 20 + 50 x 40 = 100 x 15 + 200 x 32.5 ; 

that is, the sum of all the moments which are tending to turn 
the beam in one direction is equal to the sum of all the moments 
tending to turn it in the opposite direction. 



112 



WORK AND MECHANICAL ENERGY 



If, further, we support the levers of Figs. 119 and 120 
by spring balances attached at P, we shall find, after allowing 
for the weight of the stick, that the two forces indicated by 
the balances are respectively 200 + 100 + 100 = 400 Q 
and 300 + 100 + 200 50 = 550 ; that is, the sum of 
all the forces acting in one direction on the lever is equal to 
the sum of all the forces act' 
ing in the opposite direction. 




200 



FIG. 119 FIG. 120 

Condition of equilibrium of a bar acted upon by several forces 

These two laws may be combined as follows : If we think 
of the force exerted by the spring balance as the equilibrant 
of all the other forces acting on the lever, then we find that the 
resultant of any number of parallel forces is their algebraic sum, 
and its point of application is the point about which the algebraic 
sum of the moments is zero. 

132. The couple. There is one case, however, in which paral- 
lel forces can have no single force as fheir resultant, namely, 
the case represented in Fig. 121. Such a pair of equal F 
and opposite forces acting at different points on a lever is 

called a couple and can be neutralized * g 

only by another couple tending to 

produce rotation in the opposite 

direction. The moment of such a * FlG ' 12L The cou P le 

couple is evidently F 1 X oa + F 2 x ob F l X ab ; that is, it is 

one of the forces times the total distance between them. The 

forces applied to the steering wheel of an automobile illustrate 

the couple. 




WORK AND THE LEVEE 113 

133. Work expended upon and accomplished by the lever. 
We have just seen that when the lever is in equilibrium 
that is, when it is at rest or is moving uniformly the relation 
between the effort E and the resistance R is expressed in the 
equation of moments, namely El = Rl f . Let us now suppose, 
precisely as in the case of 

the pulleys, that the force E 
raises the weight R through 
a small distance s f . To ac- 
complish this, the point A to E 

which E is attached must 

,, , ,. , FIG. 122. Showing that the equation 

move through a distance 8 O f moments, 1W = r, is equivalent to 
(Fig. 122). From the simi- Es = Ks' 

larity of the triangles APn 

and BPm it will be seen that l/l' is equal to s/s'. Hence 
equation (4), which represents the law of the lever, and which 
may be written E/ R = I' /I, may also be written in the form 

E/R = *'/, or Es *= Rs 1 . 

Now Es represents the work done by the effort E, and Rs 1 
tlie work done against the resistance R. Hence the law of 
u. moments, which has just been found by experiment to be the 
law of the lever, is equivalent to the statement that whenever 
work is accomplished l>y the use of the lever, the work expended 
upon the lever by the effort E is equal to the work accomplished 
by the lever against the resistance R. 

134. The three classes of levers. Although the law stated 
in 133 applies to all forms of the lever, it is customary to 
divide them into three classes, as follows : 

1. In levers of the first class the fulcrum P is between the 
acting force E and the resisting force R (Fig. 123). The 
mechanical advantage of levers of this class is greater or less 
than unity according as the lever arm I of the effort is greater 
or less than the lever arm V of the resistance. 



114 



WORK AND MECHANICAL ENERGY 



2. In levers of the second class the resistance R is between 
the effort E and the fulcrum P (Fig. 124). Here the level- 
arm of the effort, that is, the distance from E to P, is neces- 
sarily greater than the lever arm of the resistance, that is, the 



I ' S7 




(1) 





(2) 




FIG. 123. Levers of 
first class 



FIG. 124. Levers of 
second class 



FIG. 125. Levers of 
third class 



distance from R to P. Hence the mechanical advantage of 
levers of the second class is always greater than 1. 

3. In levers of the third class the acting force is between the 
resisting force and the fulcrum (Fig. 125). The mechanical 
advantage is then obviously less than 1, that is. in this type 
of lever force is always sacrificed for the sake of gaining speed. 

QUESTIONS AND PROBLEMS 

1. In which of the three classes of levers does the wheelbarrow 
belong? grocer's scales? pliers? sugar tongs? a claw hammer? a 
pump handle ? 

2. Explain the principle of weighing by the steelyards (Fig. 126). 
What must be the weight of the bob P if at a distance of 40 cm. from 
the fulcrum it balances a weight of 10 kg. placed at a distance of 
2 cm. from ? 

3. If you knew your own weight, how could you determine the 
weight of a companion if you had only a teeter board and a foot rule ? 

4. How would you arrange a crowbar to use it as a lever of the first 
class in overturning a heavy object? as a lever of the second'class ? 

5. Why do tinners' shears have long handles and short blades and 
tailors' shears just the opposite ? 



WORK AND THE LEVER 



115 




FIG. 126. Steelyards 



6. By reference to moments explain (a) why a door can be closed 
more easily by pushing- at the knob than at a point close to the hinges ; 
(b) why a heavier load can be lifted on a wheelbarrow having long- 
handles than on one with short han- 
dles; (c) why a long-handled shovel 

generally has a smaller blade than 
one with a shorter handle. 

7. Two boys carry a load of 60 Ib. 
on a pole between them. If the load 
is 4 ft. from one boy and 6 ft. from 
the other, how many pounds does each 
boy carry? (Consider the force ex- 
erted by one of the boys as the effort, 
the load as the resistance, and the 
second boy as the fulcrum.) 

8. Where must a load of 100 Ib. be placed on a stick 10 ft. long if 
the man who holds one end is to support 30 Ib. while the man at the 
other end supports 70 Ib. ? 

9. One end of a piano must be raised to remove a broken caster. 
The force required is 240 Ib. Make a diagram to show how a 6-foot 
steel bar may be used as a second-class lever to raise the piano with an 
effort of 40 Ib. 

10. When a load is carried on a stick over the shoulder, why does 
the pressure on the shoulder become greater as the load is moved farther 
out on the stick? 

11. A safety valve and weight are arranged as in Fig. 127. If ab is 
1 in. and be 101 in., what effective steam pressure per square inch is 
required on the valve to unseat it, if the area of the valve is \ sq. in. 
and the weight of the ball 4 Ib. ? 

12. The diameters of the piston and 
cylinder of a hydraulic press are re- 
spectively 3 in. and 30 in. The piston 
rod is attached 2 ft. from the fulcrum 
of a lever 12 ft. long (Fig. 12, p. 17). 
What force must be applied at the end 
of the lever to make the press exert a 
force of 5000 Ib. ? 

13. Three boys sit on a seesaw as follows : A (= 75 Ib.), 4 ft. to the 
right of the fulcrum; B (= 100 Ib.), 7 ft. to the right of the fulcrum; 
C (= x Ib.), 7 ft. to the left of the fulcrum. Equilibrium is produced 
by a man, 12 ft. to the right of the fulcrum, pushing up with a force of 
25 Ib. Find C's weight. 



FIG. 127 



116 WOEK AND MECHANICAL ENERGY 

THE PRINCIPLE OF WORK 

135. Statement of the principle of work. The study of 
pulleys led us to the conclusion that in all cases where such 
machines are used the work done by the effort is equal to 
the work done against the resistance, provided always that 
friction may be neglected and that the motions are uniform 
so that none of the force exerted is used in overcoming 
inertia. The study of levers led to precisely the same result. 
In Chapter II the study of the hydraulic press showed that 
the same law applied in this case also, for it was shown that 
the force on the small piston times the distance through 
which it moved was equal to the force on the large piston 
times the distance through which it moved. Similar experi- 
ments upon all sorts of machines have shown that the follow- 
ing is an absolutely general law : In all mechanical devices of 
whatever sort, in all cases where friction may ~be neglected, the 
work expended upon the machine is equal to the work accom- 
plished by it. 

This important generalization, called " the principle of 
work," was first stated by Newton in 1687. It has proved 
to be one of the most fruitful principles ever put forward 
in the history of physics. By its application it is easy to 
deduce the relation between the force applied and the force 
overcome in any sort of machine, provided only that friction 
is negligible and that the motions take place slowly. It is 
only necessary to produce, or imagine, a displacement at one 
end of the machine, and then to measure or calculate the 
corresponding displacement at the other end. The ratio of 
the second displacement to the first is the ratio of the force 
acting to the force overcome. 

136. The wheel and axle. Let us apply the work principle to 
discover the law of the wheel and axle (Fig. 128). When the 
large wheel has made one revolution, the point A on the rope 



THE PRINCIPLE OF WORK 



117 



moves down a distance equal to the circumference of the wheel. 
During this time the weight R is lifted a distance equal to 
the circumference of the axle. Hence the equa- 
tion Es Rs J becomes E x 2 7rR w = R X 2wr a , 
where R w and r a are the radii of the wheel and 
axle respectively. This equation may be writ- 
ten in the form 

Rjr a ', (5) 



s as 




FIG. 128. The 
wheel and axle 




that is, the weight lifted on the axle 

many times the force applied to the wheel as the 

radius of the wheel is times the radius of the axle. 

Otherwise stated, 
the mechanical advantage of the wheel 
and axle is equal to the radius of 
the ivheel divided Iry the radius of 
the axle. 

The capstan (Fig. 129) is a spe- 
cial case of the wheel and axle, the 
length of the lever arm taking the 
place of the radius of the wheel, 
and the radius of the barrel corre- 
sponding to the radius of the axle. 
137. The work principle applied to the inclined plane. The 

work done against gravity in lifting a weight R (Fig. 130) 

from the bottom to the top of a 

plane is evidently equal to R times 

the height h of the plane. But the 

work done by the acting force E 

while the carriage of weight R is 

being pulled from the bottom tp 

the top of the plane is equal to 

E times the length I of the plane. Hence the principle of 

work gives m = R j^ or R / E = 



FIG. 129. The capstan 




FlG m The indined pljme 



118 



WORK AND MECHANICAL ENERGY 




FIG. 131. The 

jackscrew 



that is, the mechanical advantage of the inclined plane, or the 
ratio of the weight lifted to the force acting parallel to the plane, 
is the ratio of the length of the plane to the 
height of the plane. This is precisely the con- 
clusion at which we arrived in another way 
in Chapter V, p. 63. 

138. The screw. The screw (Fig. 131) is 
a combination of the inclined plane and the 
lever. Its law is easily obtained from the prin- 
ciple of work. When the force which acts 
on the end of the lever has moved this point 
through one complete revolution, the weight 

R, which rests on top of the screw, has evidently been lifted 
through a vertical distance equal to the distance between two 
adjoining threads. This distance d is 
called the pitch of the screw. Hence, if 
we represent by / the length of the lever, 
the work principle gives 

that is, the mechanical advantage of the 
screw, or the ratio of the-iveight lifted to FIG. 132. The letter press 
the force applied, 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. In actual practice 
the friction in such an arrangement is always 
very great, so that the effort exerted must 
always be considerably greater than that given 
by equation 7. The common jackscrew just 
described (and used chiefly for raising build- 
ings), the letter press (Fig. 132), and the vise FIG. 133. The vise 
(Fig. 133) are all familiar forms of the screw. 

139. A train of gear wheels. A form of machine capable of very high 
mechanical advantage is the train of gear wheels shown in Fig. 134. 





THE PRINCIPLE OF WORK 



119 



Let the student show from the principle of work, namely Es = Rs', that 
the mechanical advantage, that is, -^, of such a device is 



circum. of a no. cogs in d no. cogs in / 
circum. of e no. cogs in c no. cogs in b 



(8) 



140. The worm wheel.* Another device of high mechanical advantage 
is the worm wheel (Fig. 135). Show that if I is the length of the crank 
arm C, n the number of 
teeth in the cogwheel / 

W, and r the radius of 
the axle, the mechanical 
advantage is given by 



2-Trln _ I 
2 TIT r 



(9) 




FIG. 134. Train of gear 
wheels 



FIG. 135. The worm 
gear 



This device is used 
most frequently when 
the primary object is to 
decrease speed rather than to multiply force. It will be seen that the 
crank handle must make n turns while the cogwheel is making one. The 
worm-gear " drive " is generally used in the rear axles of auto trucks. 

141. The differential pulley. In the differential pulley (Fig. 136) an 
endless chain passes first over the fixed pulley A, then down and 
around the movable pulley C, 
then up again over the fixed pul- 
ley B, which is rigidly attached 
to A, but differs slightly from it 
in diameter. On the circumfer- 
ence of all the pulleys are projec- 
tions which fit between the links, 
and thus keep the chains from slip- 
ping. When the chain is pulled 
down at E, as in Fig. 136, (2), 
until the upper rigid system of 
pulleys has made one complete 
revolution, the chain between the 
upper and lower pulleys has been 
shortened by the difference be- 
tween the circumferences of the FIG. 136. The differential pulley 




120 



WORK AND MECHANICAL ENERGY 



pulleys A and B, for the chain has been pulled up a distance equal to the 
circumference of the larger pulley and let down a distance equal to the 
circumference of the smaller pulley. Hence the load R has been lifted by 
half the difference between the circumferences of A and B. The mechan- 
ical advantage is therefore equal to the circumference of A divided by 
one half the difference between the circumferences of A and B. 




QUESTIONS AND PROBLEMS 

1. A 1500-pound safe must be raised 5 ft. The force which can be 
applied is 250 Ib. What is the shortest inclined plane which can 
be used for the purpose? 

2. A 300-pound barrel was rolled up a plank 
12 ft. long into a doorway 3 ft. high. What force 
was applied parallel to the plank ? 

3. A force of 80 kg. on a wheel whose diameter 
is 3 m. balances a weight of 150 kg. on the axle. 
Find the diameter of the axle. 

4. If the capstan of a ship is 12 in. in diameter 
and the levers are 6 ft. long, what force must be 
exerted by each of 4 men in order to raise an anchor 
weighing 2000 Ib. ? 

5. If, in the compound lever of Fig. 137, 

AC = 6 ft., BC=l ft., DF = 4 ft., FG = 8 in., HJ = 5 ft., and.// = 2 ft., 
what force applied at E will support a weight of 2000 Ib. at R ? 



B 



I H 

R E 

FIG. 137. The com- 
pound lever 





FIG. 138. Hay scales 



FIG. 139. Windlass with gears 



6. The hay scales shown in Fig. 138 consist of a compound lever with 
fulcrums at F, F', F", F'". If Fo and F'o' are lengths of 6 in., FE and 
F'E 5 ft., F"n 1 ft., F"m 6 ft., rF'" 2 in., and F'"S 20 in., how many 
pounds at W will be required to balance a weight of a ton on the platform? 



POWER AND ENERGY 



121 




7. In the windlass of Fig. 139 the crank handle has a length of 
2 ft., and the barrel a diameter of 8 in. There are 20 cogs in the small 
cogwheel and 60 in the large one. What is the mechanical advantage 
of the arrangement? 

8. If in the crane of Fig. 140 the crank arm has a length of J m., 
and the gear wheels A, B, C, and D have- respectively 12, 48, 12, and 60 
cogs, while the axle over 

which the chain runs has 
a radius of 10 cm., what is 
the mechanical advantage 
of the crane ? 

9. If a worm wheel 
(Fig. 135) has 30 teeth, 
and the crank is 25 cm. 
long, while the radius of 
the axle is 3 cm., what is 
the mechanical advantage 
of the arrangement? 

10. A small jackscrew 
has 20 threads to the inch. 
Using a lever 3^ in. long 

will give what mechanical FIG. 140. The crane 

advantage? (Use 3.1416.) 

11. The screw of a letter press has 5 threads to the inch, and the 
diameter of the wheel is 12 in. If there were no friction, what pres- 
sure would result from a rotating force of 20 Ib. applied to the wheel ? 

12. Eight jackscrews, each of which has a pitch of in. and a lever 
arm of 18 in., are being worked simultaneously to raise a building weigh- 
ing 100,000 Ib. What force would have to be exerted at the end of each 
lever if there were no friction ? What if 75 % were wasted in friction ? 

13. What is gained by using a machine whose mechanical advantage 
is -^ ? Name two or three household appliances whose mechanical advan- 
tage is less than 1. 

POWER AXD ENERGY 

142. Definition of power. When a given load has been 
raised a given distance a given amount of work has been 
done, whether the time consumed in doing it is small or great. 
Time is therefore not a factor which enters into the deter- 
mination of work ; but it is often as important to know the 
rate at which work is done as to know the amount of work 



122 WORK AND MECHANICAL ENERGY 

accomplished. The rate of doing work is called power, or activity. 
Thus, if P represent power, W the work done, and t the time 
required to do it, 

P = -^- (10) 

{/ 

143. Horse power. James Watt (1736-1819), the inventor 
of the steam engine, considered that an average horse could do 
33,000 foot pounds of work per minute, or 550 foot pounds per 
second. The metric equivalent is 76.05 kilogram meters per 
second. This number is probabty considerably too high, but 
it has been taken ever since, in English-speaking countries, 
as the unit of power, and named the horse power (H.P.). 
The power of steam engines has usually been rated in horse 
power. The horse power of an ordinary railroad locomotive is 
from 500 to 1000. Stationary engines and steamboat engines 
of the largest size often run from 5000 to 20,000 H.P. The 
power of an average horse is about -| H.P., and that of an 
ordinary man about ^ H.P. 

144. The kilowatt. In the metric system the erg has been 
taken as the absolute unit of work. The corresponding unit of 
power is an erg per second. This is, however, so small that it 
is customary to take as the practical unit 10,000,000 ergs per 
second ; that is, one joule per second (see 125, p. 106). This 
unit is called the watt, in honor of James Watt. The power 
of dynamos and electric motors is almost always expressed in 
kilowatts, a kilowatt representing 1000 watts ; and in modern 
practice even steam engines are being increasingly rated in 
kilowatts rather than in horse pow r er. A horse power is equiva- 
lent to 746 watts, or about | of a kilowatt. A kilowatt is 
almost exactly equal to 102 kilogram meters per second. 

145. Definition of energy. The energy of a body is denned 
as its capacity for doing work. In general, inanimate bodies 
possess energy only because of work which has been done upon 
them at some previous time. Thus, suppose a kilogram weight 




JAMES PRESCOTT JOULE 
(1818-1889) 

English physicist, born at Man- 
chester ; most prominent figure in 
the establishment of the doctrine 
of the conservation of energy ; 
studied chemistry as a boy under 
John Dalton, and became so inter- 
ested that his father, a prosperous 
Manchester brewer, fitted out a 
laboratory for him at home ; con- 
ducted mostof his researches either 
in a basement of his own house or 
in a yard adjoining his brewery ; 
discovered the law of heating a 
conductor by an electric current ; 
carried out, in connection with 
Lord Kelvin, epoch-making re- 
searches upon the thermal prop- 
erties of gases; did important work 
in magnetism; first proved experi- 
mentally the identity of various 
forms of energy 




JAMES WATT (1736-1819) 

The Scotch instrument maker at 
the University of Glasgow, who 
may properly be considered the 
inventor of the steam engine ; for, 
although a crude and inefficient 
type of steam engine was known 
before his time, he left it in essen- 
tially its present form. The mod- 
ern industrial era may be said to 
begin with Watt 




= |j a I 

If 83 II 

<D ^ - <M 35 

^ 1 1 S 2 

O ^ r- C -H 



r c 
^ o 



2 n3 <D "S 

C tf M 



' trffr? 



^ i a * I 

S g 6^-5 5 
,5 2 g -e 5 o 



SB * M - 



P 111 

1 



p^ 

^j O> O rfl 
U ^ "C '^ *O 



r^ -4-> d K 

I s 



H S < S 



POWER AXD ENERGY 



123 




FIG. 141. 
tion of 



Illustra- 

potential 



energy 



is lifted from the first position in Fig. 141 through a height 
of 1 m. and placed upon the hook H at the end of a cord 
which passes over a frictionless pulley p and is attached at 
the other end to a-second kilogram weight B. The operation 
of lifting A from position 1 to position 2 has 
required an expenditure upon it of 1 kg. m. 
(100,000 g. cm., or 98,000,000 ergs) of work. 
But in position 2, A is itself possessed of a 
certain capacity for doing work which it did 
not have before ; for if it is now started down- 
ward by the application of the slightest con- 
ceivable force, it will, of its own accord, return 
to position 1, and will in so doing raise the 
kilogram \veight B through a height of 1 m. 
In other words, it will do upon B exactly the 
same amount of work that was originally 
done upon it. 

146. Potential and kinetic energy. A body may have a 
capacity for doing work not only because it has been given an 
elevated position but also because it has in some way acquired 
velocity ; for example, a heavy flywheel will keep machinery 
running for some time after the power has been shut off, and 
a bullet shot upward will lift itself a great distance against 
gravity because of the velocity which has been imparted to it. 
Similarly, any body which is in motion is able to rise against 
gravity, or to set other bodies in motion by colliding with them, 
or to overcome resistances of any conceivable sort. Hence, in 
order to distinguish between the energy which a body may 
have because of an advantageous position, and the energy which 
it may have because it is in motion, the two terms "potential 
energy" and "kinetic energy" are used. Potential energy 
includes the energy of lifted weights, of coiled or stretched 
springs, of bent bows, etc., in a word, potential energy is 
energy of position, while kinetic energy is energy of motion. 



124 WORK AND MECHANICAL ENERGY 

147. Transformations of potential and kinetic energy. The 
swinging of a pendulum and the oscillation of a weight 
attached to a spring illustrate well the way in which energy 
which has once been put into a body may be transformed 
back and forth between the potential and kinetic varieties. 
When the pendulum bob is at rest at the bottom of its arc, 
it possesses no energy of either type, since, on the one hand, 
it is as low as it can be, and, on the other, it has no velocity. 
When we pull it up the arc to the posi- 
tion A (Fig. 142), we do an amount 

of work upon it which is equal in gram 
centimeters to its weight in grams 
times the distance AD in centimeters ; 
that is, we store up in it this amount 
of potential energy. As now the bob 
falls to C this potential energy is com- 
pletely transformed into kinetic en- 
ergy. That this kinetic energy at C is 
exactly equal to the potential energy FIG. 142. Transformation 

at A is proved by the fact that if f ric- of P tential aild kinetic 

GiiGr*v 
tion is completely eliminated, the bob 

rises to a point B such that BE is equal to AD. We see, 
therefore, that at the ends of its swing the energy of the 
pendulum is all potential, while in the middle of the swing 
its energy is all kinetic. In intermediate positions the energy 
is part potential and part kinetic, but the sum of the two is 
equal to the original potential energy. 

148. General statement of the law of frictionless machines. 
In our development of the law of machines, which led us to the 
conclusion that the work of the acting force is always equal to 
the work of the resisting force, we were careful to make two 
important assumptions : first, that friction was negligible ; 
second, that the motions were all either uniform or so slow 
that no appreciable velocities were imparted. In other words, 




POWER AND ENERGY 125 

we assumed that the work of the acting force was expended 
simply in lifting weights or compressing springs, that is, 
in storing up potential energy. If now we drop the second 
assumption, a very simple experiment will show that our con- 
clusion must be somewhat modified. Suppose, for instance, 
that instead of lifting a 500-gram weight slowly by means of a 
balance, we jerk it up suddenly. We shall now find that the 
initial pull indicated by the balance, instead of being 500 g., 
will be considerably more, perhaps as much as several thou- 
sand grams if the pull is sufficiently sudden. This is obviously 
because the acting force is now overcoming not merely the 
500 g. which represents the resistance of gravity, but also the 
inertia of the body, since velocity is being imparted to it. Now 
work done in imparting velocity to a body, that is, in over- 
coming its inertia, always appears as kinetic energy, while work 
done in overcoming gravity appears as the potential energy of 
a lifted weight. Hence, whether the motions produced by 
machines are slow or fast, if friction is negligible the law for 
all devices for transforming work may be stated thus: The 
work of the acting force is equal to the sum of the potential and 
kinetic energies stored up in the mass acted upon. In machines 
which work against gravity the body usually starts from rest 
and is left at rest, so that the kinetic energy resulting from the 
whole operation is zero. Hence in such cases the work done is 
the weight lifted times the height through which it is lifted, 
whether the motion is slow or fast. The kinetic energy im- 
parted to the body in starting is all given up by it in stopping. 
149. The measure of potential energy. The measure of the 
potential energy of any lifted body, such as a lifted pile 
driver, is equal to the work which has been spent in lifting 
the body. Thus, if h is the height in centimeters and M the 
weight in grams, then the potential energy P.E. of the 
lifted mass is 

P.E. = Mh gram centimeters. 



126 WORK AND MECHANICAL ENERGY 

Similarly, if h is the height in feet, and M the weight in 
pounds, p E = m foot pounds . 

150. The measure of kinetic energy. Since the force of the earth's 
attraction for M grams is Mg dynes, if we wish to express the potential 
energy in ergs instead of in gram centimeters, we have 

P.E, = Mffh ergs. (12) 

Since this energy is all transformed into kinetic energy when the mass 
falls the distance h, the product Mgh also represents the number of ergs 
of kinetic energy which the moving weight has when it strikes the pile. 

If we wish to express this kinetic energy in terms of the velocity with 
which the weight strikes the pile, instead of the height from which it 
has fallen, we have only to substitute for h its value in terms of g and 
the velocity acquired (see equation (3), p. 76), namely h = i? 2 /2 g. This 
gives the kinetic energy K.E. in the form 

K.E. = -i J/y 2 ergs. (13) 

Since it makes no difference how a body has acquired its velocity, 
this represents the general formula for the kinetic energy in ergs of any 
moving body, in terms of its mass and its velocity. 

Thus, the kinetic energy of a 100-gram bullet moving with a velocity 
of 10,000 cm. per second is 

K.E. = x 100 x (10,000) 2 = 5,000,000,000 ergs. 

Since 1 g. cm. is equivalent to 980 ergs, the energy of this bullet is 
5 ' oo y 8 ' 000 = 5,102,000 g. cm., or 51.02 kg. m. 

We know, therefore, that the powder pushing on the bullet as it 
moved through the rifle barrel did 51.02 kg. m. of work upon the bullet 
in giving it the velocity of 100 m. per second. 

In general terms, if M is in grams and v in centimeters per second, 

K.E. = ^ - j^jr. g. cm. ; if M is in pounds and v in feet per second, 




QUESTIONS AND PROBLEMS 

1. A stick of dynamite has great capacity for doing work. Before 
the explosion occurs, is the energy in the potential or the kinetic form ? 

2. Explain the use of the sand blast in cleaning castings, making 
frosted glass, cutting figures on glassware, cleaning off the walls of 
stone buildings, etc. 



POWER AND ENERGY 127 

3. How much work is required to lift the 500-pound weight of a pile 
driver 30 ft.? How much potential energy is then stored in it? How 
much work does it do when it falls ? If the falling mass drives the pile 
into the earth i ft., what is its average force upon the pile ? 

4. A man weighing 198 Ib. walked to the top of the stairway of the 
Washington Monument (500 ft. high) in 10 min. At what horse-power 
rate did he work? 

5. A farm tractor drew a gang plow at the rate of 2^ mi. per hour, 
maintaining an average drawbar pull of 1500 Ib. At what average H.P. 
was the tractor working ? 

6. In the course of a stream there is a waterfall 22 ft. high. It is 
shown by measurement that 450 cu. ft. of water per second pours over 
it. How many foot pounds of energy per second could be obtained from 
it? What horse power? 

7. How many gallons of water (8 Ib. each) could a 10-horse-power 
engine raise in one hour to a height of 60 f t. ? 

8. A certain airplane using three 400-horse-power motors flew 80 mi. 
per hour. With how many pounds backward force did the propellers 
push against the air ? 

9. If a rifle bullet can just pass through a plank, how many planks 
will it pass through if its speed is doubled ? 

10. A steel ball dropped into a pail of moist clay from a height of a 
meter sinks to a depth of 2 cm. How far will it sink if dropped 4 in. ? 

11. Neglecting friction, find how much force a boy would have to 
exert to pull a 100-pound wagon up an incline which rises 5 ft. for 
every 100 ft. of length traversed on the incline. In addition to giving 
the numerical solution of the problem, state why you solve it as you do 
and how you know that your solution is correct. 



CHAPTER VIII 

THERMOMETRY ; EXPANSION COEFFICIENTS* 
THERMOMETBY 

151. Meaning of temperature. When a body feels hot to the 
touch we are accustomed to say that it has a high temperature, 
and when it feels cold that it has a low temperature. Thus the 
word " temperature " is used to denote the condition of hot- 
ness or coldness of the body whose state is being described. 

152. Measurement of temperature. So far as we know, up 
to the time of Galileo no one had ever used any special instru- 
ment for the measurement of temperature. People knew how 
hot or how cold it was from their feelings only. But under 
some conditions this temperature sense is a very unreliable 
guide. For example, if the hand has been in hot water, 
tepid water will feel cold; while if it has been in cold 
water, the same tepid water will feel warm ; a room may feel 
hot to one who has been running, while it will feel cool to 
one who has been sitting still. 

Difficulties of this sort have led to the introduction in 
modern times of mechanical devices, called thermometers, for 
measuring temperature. These instruments depend for their 
operation upon the fact that almost all bodies expand as 
they grow hot. 

153. Galileo's thermometer. It was in 1592 that Galileo, 
at the University of Padua in Italy, constructed the first 

* It is recommended that this chapter be preceded by laboratory measure- 
ments on the expansions of a gas and a solid. See, for example, Experiments 
14 and 15 of the authors' Manual. 

128 



THERMOMETRY 



129 



thermometer. He was familiar with the faots of expansion 
of solids, liquids, and gases ; and since gases expand more 
than solids or liquids, he chose a gas as his expanding 
substance. His device was that shown in Fig. 143. 

Let a bulb of air B be connected with a water manometer m, as in 
Fig. 143. If the bulb is warmed by holding a Bunsen burner beneath 
it, or even by placing the hand upon it, the water 
at m will at once begin to descend, showing that 
the pressure exerted by the air contained in the 
bulb has been increased by the increase in its 
temperature. If B is cooled with ice or ether, the 
water will rise at m. 




FIG. 143. Expansion 

of air by heat 



154. Significance of temperature from the 
standpoint of the kinetic theory. Now if, as 
was stated in 64, gas pressure is due to 
the bombardment of the walls by the mole- 
cules of the gas, since the number of mole- 
cules in the bulb can scarcely have been 
changed by slightly heating it we are forced 
to conclude that the increase in pressure 

is due to an increase in the velocity of the molecules which are 
already there. From the standpoint of the kinetic theory the 
pressure exerted by a given number of molecules of a gas is 
determined by the kinetic energy of bombardment of these 
molecules against the containing walls. To increase the tem- 
perature is to increase the average kinetic energy of the mole- 
cules, and to diminish the temperature is to diminish this 
average kinetic energy. The kinetic theory thus furnishes a 
very simple and natural explanation of the fact of the expan- 
sion of gases with a rise in temperature. 

155. The construction of a centigrade mercury thermometer. 
It was not until about 1700 that mercury thermometers 
were invented. On account of their extreme convenience 
these have now replaced all others for practical purposes. 



130 THERMOMETRY; EXPANSION COEFFICIENTS 



The meaning of a degree of temperature change as measured 
by a mercury thermometer is best understood from a descrip- 
tion of the method of making and graduating the thermometer. 

A bulb is blown at one end of a piece of thick-walled 
glass tubing of small, uniform bore. Bulb and tube are 
filled with mercury, at a temperature slightly above the 
highest temperature for which the thermom- 
eter is to be used, and the tube is sealed 
off in a hot flame. As the 
mercury cools, it contracts 
and falls away from the 
top of the tube, leaving a 
vacuum above it. 

The bulb is next sur- 
rounded with melting snow 
or ice, as in Fig. 144, and 
the point at which the mer- 

cury stands in the tube is 
marked 0. Then the bulb 
and tube are placed in the 
steam rising from boiling FlG 144< Method 
water under a pressure of of finding the 

76 cm., as in Fig. 145, and P oint in calibrat - 
. . ing a thermometer 

the new position or the 

mercury is marked 100. The space between these two 
marks 011 the stem is then divided into 100 equal parts, and 
divisions of the same length are extended above the 100 
mark and below the mark. 

One degree of change in temperature, measured on such a 
thermometer, means, then, such a temperature change as 
will cause the mercury in the stem to move over one of 
these divisions ; that is, it is such a temperature change as 
will cause mercury contained in a glass bulb to expand y^ of 
the amount which it expands in passing from the temperature 




FIG. 145. Method 
of finding the 100 
point in calibrat- 
ing a thermometer 



THERMOMETRY 



131 



of melting ice to that of steam under a pressure of 76 cm. 
A thermometer in which the scale is divided in this way is 
called a centigrade thermometer. 

Thermometers graduated on the centigrade scale are used 
almost exclusively in scientific work, and also for ordinary 
purposes in most countries which have adopted the metric 
system. This scale was first devised in 1742 by Celsius, of 
Upsala, Sweden. For this reason it is sometimes called the 
Celsius instead of the centigrade scale. 

According to the kinetic theory an increase in temperature in 
a liquid, as in a gas, means an increase in the mean kinetic 
energy of the molecules ; and, conversely, a decrease in tem- 
perature means a decrease in this average kinetic energy. 

156. Fahrenheit thermometers. The com- 
mon household thermometer in England and 
the United States differs from the centigrade 
only in the manner of its graduation. In its 
construction the temperature of melting ice 
is marked 32 instead of 0, and that of boil- 
ing water 212 instead of 100. The inter- 
vening stem is then divided into 180 parts. 
The zero of this scale is the temperature ob- 
tained by mixing equal weights of sal ammo- 
niac (ammonium chloride) and snow. In 
1714, when Fahrenheit devised this scale, he 
chose this zero because he thought it repre- 
sented the lowest possible temperature that 
could be obtained in the laboratory. 

157. Comparison of centigrade and Fah- 
renheit thermometers. From the methods of 
graduation of the Fahrenheit and centigrade 
thermometers it will be seen that 100 on 

the centigrade scale denotes the same difference of temper- 
ature as 180 on the Fahrenheit scale (Fig. 146). Hence five 




FIG. 146. The cen- 
tigrade and Fahren- 
heit scales 



132 THEEMOMETRY; EXPANSION COEFFICIENTS 



centigrade degrees are equal to nine Fahrenheit degrees. In 

Fig. 147, C represents the number of degrees in the centigrade 

reading, while F represents the number in the Fahrenheit 

reading. Since five centigrade degrees cover 

the same space on the stem as nine of the 

smaller Fahrenheit degrees, it is evident that iooHllh2i2 

C ^5 

T^T GO Q 

By this expression of the relation of the two 
scales it is very easy to reduce the readings 
of one thermometer to the scale of the other. 
For example, to find what Fahrenheit 
reading corresponds to 20 C. we have 




FIG. 147. Compari- 

158. The range of the mercury thermom- son of centigrade and 

C1 . OAO _ Fahrenheit scales 

eter. Since mercury freezes at 39 C., 
temperatures lower than this are very often measured by 
means of alcohol thermometers, for the freezing point of alcohol 
is 130 C. Similarly, since the boiling point of mercury is 
about 360 C., mercury thermometers cannot be used for 
measuring very high temperatures. For both very high and 
very low temperatures in fact, for all temperatures a gas 
thermometer is the standard instrument. 

159. The standard hydrogen thermometer. The modern gas 
thermometer (Fig. 148) is, however, widely different from that 
devised by Galileo (Fig. 143). It is not usually the increase 
in the volume of a gas kept under constant pressure which is 
taken as the measure of temperature change, but rather the in- 
crease in pressure which the molecules of a confined gas exert 
against the walls of a vessel whose volume is kept constant. 
The essential features of the method of calibration and use 



THERMOMETRY 



133 



100C 



oc 



P373A 



D273A 



of the standard hydrogen thermometer at the International 
Bureau of Weights and Measures at Paris are as follows: 

The bulb B (Fig. 148) is first filled with hydrogen and the space 
above the mercury in the tube a made as nearly a perfect vacuum as 
possible. B is then surrounded with melting ice 
(as in Fig. 144) and the tube a raised or lowered 
until the mercury in the arm b stands exactly 
opposite the fixed mark c on the tube. Now, 
since the space above D is a vacuum, the pressure 
exerted by the hydrogen in B against the mercury 
surface at c just supports the mercury column 
ED. The point D is marked on a strip of metal 
behind the tube a. The bulb B is then placed in 
a steam bath like that shown in Fig. 145. The 
increased pressure of the gas in B at once begins 
to force the mercury down at c and up at D. 
But by raising the arm a the mercury in b is 
forced back again to c, the increased pressure of 
the gas on the surface of the mercury at c being 
balanced by the increased height of the mercury 
column supported, which is now EF instead of 
ED. When the gas in B is thoroughly heated to 
the temperature of the steam, the arm a is very 
carefully adjusted so that the mercury in b stands 
very exactly at c, its original level. A second 
mark is then placed on the metal strip exactly 
opposite the new level of the mercury, that is, at F. 
Then D is marked C., and F is marked 100 C. 
The vertical distance between these marks is di- 
vided into 100 exactly equal parts. Divisions of 
exactly the same length are carried above the 

100 mark and below 'the mark. One degree of change in tempera- 
ture is then defined as any change in temperature which will cause the 
pressure of the gas in B to change by the amount represented by the 
distance between any two of these divisions. This distance is found to 
be 2^ of the height ED. 




-K O'Aor 



FIG. 148. The stand- 
ard gas thermometer 



In other words, one degree of change in temperature on the 
centigrade scale is such a temperature change as ivill cause the 



134 XHEBMOMETBY; EXPANSION COEFFICIENTS 

pressure exerted by a confined volume of hydrogen to change ly 
~-$ of its pressure at the temperature of melting ice (0 C.). 

160. Absolute temperature. Since, then, cooling the hydro- 
gen through 1 C., as denned above, reduces the pressure -^-^ 
of its value at C/, it is clear that cooling it 278 below C. 
would reduce its pressure to zero. But from the stand- 
point of the kinetic theory this would be the temperature at 
which all motions of the hydrogen molecules would cease. 
This temperature is called the absolute zero, and the temper- 
ature measured from this zero is called absolute temperature. 
Thus, if A is used to denote the absolute scale, we have 
C. - 273 A., 100 C. = 373 A., 15 C. = 288 A., etc. It 
is customary to indicate temperatures on the centigrade scale 
by , and on the absolute scale by T. We have, then, 

T= + 273. (1) 

161. Comparison of gas and mercury thermometers. Since an inter- 
national committee has chosen the hydrogen thermometer described in 
159 as the standard of temperature measurement, it is important to 
know whether mercury thermometers, graduated in the manner described 
in 155, agree with gas thermometers at temperatures other than and 
100 (where, of course, they must agree, since these temperatures are in 
each case the starting points of the graduation). A careful comparison 
has shown that although they do not agree exactly, yet fortunately the 
disagreements at ordinary temperatures are small, not amounting to more 
than .2 anywhere between and 100. At 300 C., however, the differ- 
ence amounts to about 4. (Mercury thermometers are actually used for 
measuring temperatures above the boiling point of mercury, 360C. They 
are then filled with nitrogen, the pressure of which prevents boiling.) 

Hence for all ordinary purposes mercury thermometers are sufficiently 
accurate, and no special standardization of them is necessary. But in 
all scientific work, if mercury thermometers are used at all, they must 
first be compared with a gas thermometer and a table of corrections 
obtained. The errors of an alcohol thermometer are considerably larger 
than those of a mercury thermometer. 

162. Low temperatures. The absolute zero of temperature 
can, of course, never be attained, but in recent years rapid 




SIR WILLIAM THOMSON, LORD KELVIN (1824-1907) 

One of the best known and most prolific of nineteenth-century physicists ; born 
in Belfast, Ireland ; professor of physics in Glasgow University, Scotland, for 
more than fifty years ; especially renowned for his investigations in heat and 
electricity ; originator of the absolute thermodynamic scale of temperature ; 
formulator of the second law of thermodynamics; inventor of the electrometer! 
the mirror galvanometer, and many other important electrical devices 



THERMOMETRY 135 

strides have been made toward it. Forty years ago the low- 
est temperature which had ever been measured was 110 C., 
the temperature attained by Faraday in 1845 by causing a 
mixture of ether and solid carbon dioxide to evaporate in a 
vacuum. But in 1880 air was first liquefied and found, by 
means of a gas thermometer, to have a temperature of 
-190C. When liquid air evaporates into a space which 
is kept exhausted by means of an air pump, its temperature 
falls to about 220 C. Recently hydrogen has been lique- 
fied and found to have a temperature at atmospheric pressure 
of 243 C. All of these temperatures have been measured 
by means of hydrogen thermometers. By allowing liquid 
hydrogen to evaporate into a space kept exhausted by an 
air pump, Dewar in 1900 attained a temperature of 260. 
In 1911 Kamerlingh Onnes liquefied helium and attained a 
temperature of 271.3 C., only 1.7 above absolute zero 
(see 217). 

QUESTIONS AND PROBLEMS 

1. Define 0C. and 100 C. What is 1C.? 1F.? 

2. From a study of the behavior of gases we conclude that there is a 
temperature at which the molecules are at rest and at which bodies there- 
fore contain no heat. Give the reasoning that leads to this conclusion. 

3. Normal room temperature is 68 F. What is it centigrade? 

4. The normal temperature of the human body is 98. 6 F. What 
is it centigrade ? 

5. What temperature centigrade corresponds to 0F. ? 

6. Mercury freezes at about 40 F. What is this centigrade ? 

7. The temperature of liquid air is 190 C. What is it Fahrenheit ? 

8. The lowest temperature attainable by evaporating liquid helium 
is - 271.3 C. What is it Fahrenheit ? 

9. What is the absolute zero of temperature on the Fahrenheit scale ? 

10. Why is a fever thermometer made with a very long cylindrical 
bulb instead of a spherical one ? 

11. When the bulb of a thermometer is placed in hot water, it at 
first falls a trifle and then rises. Why ? 

12. How does the distance between the mark and the 100 mark 
vary with the size of the bore, the size of the bulb remaining the same ? 

13. What is meant by the absolute zero of temperature? 



136 THEEMOMETRY; EXPANSION COEFFICIENTS 

14. Why is the temperature of liquid air lowered if it is placed under 
the receiver of an air pump and the air exhausted ? 

15. Two thermometers have bulbs of equal size. The bore of one 
has a diameter twice that of the other. What are the relative lengths 
of the stems between and 100 ? 

EXPANSION COEFFICIENTS 

163. The laws of Charles and Gay-Lussac. When, as in the 
experiment described in 159, we keep the volume of a gas 
constant and observe the rate at which the pressure increases 
with the rise in temperature, we obtain the pressure coefficient of 
expansion, which is denned as the ratio between the increase in 
pressure per degree and the value of the pressure at C. This 
was first done for different gases by a Frenchman, Charles, 
in 1787, who found that the pressure coefficients of expansion of 
all gases are the same. This is known as the law of Charles. 

When we arrange the experiment so that the gas can expand 
as the temperature rises, the pressure remaining constant, we 
obtain the volume coefficient of expansion, which is defined as the 
ratio between the increase in volume per degree and the total vol- 
ume of the gas at C. This was first done for different gases in 
1802 by another Frenchman, Gay-Lussac, who found that all 
gases have the same volume coefficient of expansion, this coefficient 
being the same as the pressure coefficient, namely, 1/273. This 
is known as the law of G-ay-Lussac. 

From the definition of absolute temperature and from 
Charles's law we learn that, for all gases at constant volume, 
pressure is proportional to absolute temperature ; that is, 

P T 

=^ = ' (2) 

^ 2 T , 

Also, from Gay-Lussac's law we learn that, for all gases at 
constant pressure, volume is proportional to absolute temperature ; 
that is, 



EXPANSION COEFFICIENTS 137 

If pressure, temperature, and volume all vary,* we have 

P V T 

fili-fi. (4) 

P V T 

a 2 2 

Any one of these six quantities may be found if the other 
five are known. 

If the volume remains constant, that is, if V 1 = V$ equation 
(4) reduces to (2), that is, to Charles's law. If the pressure 
remains constant, P I = P 2 and equation (4) reduces to (3), that 
is, to Gay-Lussac's law. If the temperature does not change, 
T^ = T 2 and equation (4) reduces to P^V^ = P 2 V 2 <> that is, to 

Boyle's law. If the ratio of densities instead of volumes is 

y j) 

sought, it is only necessary to replace in (3) and (4) by J . 

QUESTIONS AND PROBLEMS 

1. Why is it unsafe to let a pneumatic inkstand like that of Fig. 30, 
p. 33, remain in the sun ? 

2. To what temperature must a cubic foot of gas initially at C. 
be raised in order to double its volume, the pressure remaining constant? 

3. If the volume of a quantity of air at 30 C. is 200 cc., at what 
temperature will its volume be 300 cc., the pressure remaining the same? 

4. If the air within a bicycle tire is under a pressure of 2 atmospheres, 
that is, 152 cm. of mercury, when the temperature is 10 C., what pressure 
will exist within the tube when the temperature changes to 35 C.? 

5. If the pressure to which 15 cc. of air is subjected changes from 
76 cm. to 40 cm., the temperature remaining constant, what does its 
volume become ? (See Boyle's law, p. 36.) If, then, the temperature of 
the same gas changes from 15 C. to 100 C., the pressure remaining 
constant, what will be the final volume ? 

6. The air within a half-inflated balloon occupies a volume of 
100,000 1. The temperature is 15 C. and the barometric height 75 cm. 
What will be its volume after the balloon has risen to the height of 
Mt. Blanc, where the pressure is 37 cm. and the temperature 10 C.? 

* If this is not clear to the student, let him recall that if the speeds of two 
runners are the same, then their distances are proportional to their times, 
that is, -Dj/Da = t^/t z ; but if their times are the same and the speeds different, 
Dj/D-j = Sj/Sg. If now one runs both twice as fast and twice as long, he evi- 
dently goes 4 times as far; that is, if time and speed both vary, D^D^ t 



138 THERMOMETRY; EXPANSION COEFFICIENTS 



EXPANSION OF LIQUIDS AND SOLIDS 

164. The expansion of liquids. The expansion of liquids 
differs from that of gases in that 

1. The coefficients of expansion of liquids are all consider- 
ably smaller than those of gases. 

2. Different liquids expand at wholly different rates ; for 
example, the coefficient of alcohol between and 10 C. is 
.0011 ; of ether it is .0015 ; of petroleum, .0009 ; of mercury, 
.000181. 

3. The same liquid often has different coefficients at dif- 
ferent temperatures ; that is, the expansion is irregular. 
Thus, if the coefficient of alcohol is obtained between and 
60 C., instead of between and 10 C., it is .0013 instead 
of .0011. 

The coefficient of mercury, however, is very nearly constant 
through a wide range of temperature, which indeed might 
have been inferred from the fact that mercury thermometers 
agree so well with gas thermometers. 

165. Method of measuring the expansion coeffi- 
cients of liquids. One of the most convenient 
and common methods of measuring the coeffi- 
cients of liquids is to place them in bulbs of 
known volume, provided with capillary necks 
of known diameter, like that shown in Fig. 149, 
and then to watch the rise of the liquid in the 
neck for a given rise in temperature. A certain 
allowance must be made for the expansion of 
the bulb, but this can readily be done if the 
coefficient of expansion of the substance of 
which the bulb is made is known. 

166. Maximum density of water. When 

water is treated in the way described in the preceding para- 
graph, it reaches its lowest position in the stem at 4 C. As 



FIG. 149. Bulb 
for investigat- 
ing expansions 
of liquids 



EXPANSION OF LIQUIDS AND SOLIDS 139 

the temperature falls from that point down to C., water 
exhibits the peculiar property of expanding with a decrease in 
temperature. 

We learn, therefore, that water has its maximum density at 
a temperature of 4 C. 

167. The cooling of a lake in winter. The preceding para- 
graph makes it easy to understand the cooling of any large 
body of water with the approach of winter. The surface 
layers are first cooled and contract. Hence, being then 
heavier than the lower layers, they sink and are replaced 
by the warmer water from beneath. This process of cooling 
at the surface, and sinking, goes on until the whole body of 
water has reached a temperature of 4 C. After this condi- 
tion has been reached, further cooling of the surface layers 
makes them lighter than the water beneath, and they now 
remain on top until they freeze. Thus, before any ice what- 
ever can form on the surface of a lake, the T^hole mass of 
water to the very bottom must be cooled to 4 C. This 
is why it requires a much longer and more severe period 
of cold to freeze deep bodies of water than shallow ones. 
Further, since the circulation described above ceases at 
4 C., practically all of the unfrozen water will be at 4 C. 
even in the coldest .weather. Only the water which is in 
the immediate neighborhood of the ice will be lower than 
4 C. This fact is of vital importance in the preservation of 
aquatic life. 

168. Expansion of solids. The proofs of expansion of solids 
with an increase in temperature may be seen on every side. 
Railroad rails are laid with spaces between their ends so that 
they may expand during the heat of summer without crowd- 
ing each other out of place. Wagon tires are made smaller 1 
than the wheels which they are to fit. They are then heated 
until they become large enough to be driven on, and in 
cooling they shrink again and thus grip the wheels with 



140 THERMOMETRY; EXPANSION COEFFICIENTS 

immense force. A common lecture-room demonstration of 
expansion is the following: 

Lei the ball B, which when cool just slips through the ring 7?, be 
heated in a Bunsen flame. It will now be found too large to pass 
through the ring ; but if the ring is heated, or if 
the ball is again cooled, it will pass through easily 
(see Fig. 150). 

If the expansion of gases and liquids is due 
to the increase in the average kinetic energy 

., ,. .-, . i -, ,-, . FIG. 150. Expansion 

of agitation of their molecules, the foregoing of so]icls 

experiments with solids must clearly be 
given a similar interpretation. In a word, then, the temperature 
of a given substance, be it solid, liquid, or gas, is determined 
by the average kinetic energy of agitation of its molecules. 

169. Linear coefficients of expansion of solids. It is often 
more convenient to measure the increase in length of one 
edge of an Expanding solid than to measure its increase in 
volume. The ratio between the increase in length per degree rise 
in temperature and the total length is called the linear coeffi- 
cient of expansion of the solid. Thus, if l l represent the length 
of a bar at ^, and 1 2 its length at 2 , the equation which 
defines the linear coefficient k is 



L - 1 

L-l 




_2 



',(,-*,) 



(5) 



The linear coefficients of a few common substances are 
given in the following table : 

Aluminium . .000023 Gold 000014 Silver . . . .000019 

Brass . . . .000019 Iron 000012 Steel 000013 

Copper . . . .000017 Lead 000029 Tin 000023 

Glass . .000009 Platinum . . .000009 Zinc 000030 



APPLICATIONS OF EXPANSION 



141 



APPLICATIONS OF EXPANSION 

170. Compensated pendulum. Since a long pendulum vi- 
brates more slowly than a short' one, the expansion of the 
rod which carries the pendulum bob causes an ordinary 
clock to run too slowly in summer, and 

its contraction causes it to run too fast 
in winter. For this reason very accurate 
clocks are provided with compensated pen- 
dulums, which are so constructed that the 
distance of the bob beneath the point of 
support is independent of the temperature. 
This is accomplished by suspending the bob, 
by means of two sets of rods of different 
material, in such a way that the expansion 
of one set raises the bob, while the expan- 
sion of the other set lowers it. Such a 
pendulum is shown in Fig. 151. The ex- FlG 
pansion of the iron rods 6, c?, e, and i tends pensated pendulum 
to lower the bob, while that of the copper 
rods c tends to. raise it. In order to produce complete com- 
pensation it is only necessary to make the total lengths of 
iron and copper rods inversely proportional to the coefficients 
of expansion of iron and copper. 

171. Compensated balance wheel. In 
the balance wheel of an accurate watch 
(Fig. 152) another application of the 
unequal expansion of metals is made. 
Increase in temperature both increases 

the radius of the wheel and weakens _, 

FIG. 152. The compen- 

the elasticity of the spring which con- sated balance wheel 
trols it. Both of these effects tend to 
make the watch lose time. This tendency may be counter- 
acted by bringing the mass of the rotating parts in toward 




The com _ 




142 THEBMOMETRY; EXPANSION COEFFICIENTS 

the center of the wheel. This is accomplished by making the 
arcs be of metals of different expansion coefficients, the inner 



FIG. 153 FIG. 154 

Unequal expansion of metals 

metal, shown in black in the figure, having the smaller coeffi- 
cient. The free ends of the arcs are then sufficiently pulled 

in by a rise in temperature to counteract the 

retarding effects. 

The principle is precisely the same as that which 
finds simple illustration in the compound bar shown 
in Fig. 153. This bar consists of two strips, 
one of brass and one of iron, riveted to- 
gether. When the bar is placed edgewise 
in a Bunsen flame, so that both metals are 
heated equally, it will be found to bend in 
such a way that the more expansible metal, 
namely, the brass, is on the outside of the 
curve, as shown in Fig. 154. When it is 
cooled with snow or ice, it bends in the 
opposite direction. 

The common thermostat (Fig. 155) is 
precisely such a bar, which is arranged so 
as to open the drafts by closing an electri- 
cal circuit at a when it is too cold, and to close the drafts 
by making contact at b when it is too warm. 




FIG. 155. The 

thermostat 




QUESTIONS AND PROBLEMS 



FIG. 156 



1. Why is the water at the bottom of a lake usually colder than that 
at the top ? Why is the water at the bottom of very deep mountain lakes 
in some instances observed to be at 4 C. the whole year round, while 
that at the top varies from C. to quite warm ? 

2. Give three reasons why mercury is a better liquid to use in ther- 
mometers than water. 

3. Why is a thick tumbler more likely to break when hot water is 
poured into it than a thin one ? 




APPLICATIONS OF EXPANSION 143 

4. Pendulums are often compensated by using cylinders of mercury, 
as in Fig. 156. Explain. 

5. The steel cable from which Brooklyn Bridge hangs is more than 
a mile long. By how many feet does a mile of its length vary between 
a winter day when the temperature is 20 C. and 

a summer day when it is 30 C. ? 

6. If a surveyor's steel tape is exactly 100 ft. 
long at 20 C., how much too short would it be 
at C. ? 

7. A certain glass flask is graduated to hold 
1000 cc. at 15 C. How many cubic centimeters 
will the same flask hold at 40 C., the coefficient 
of cubical expansion of glass being .000025 ? 

8. The dial thermometer is a compound bar (Fig. 157) with iron on 
the outside and brass on the inside. A thread t is wound about the 
central cylinder c. Explain the action. 

9. Why may a glass stopper sometimes be loosened by pouring hot 
water on the neck of a bottle ? 

10. A metal rod 230 cm. long expanded 2.75 mm. in being raised 
from 0C. to 100C. Find its coefficient of linear expansion. 

11. The changes in temperature to which long lines of steam pipes 
are subjected make it necessary to introduce "expansion joints." These 
joints consist of brass collars fitted tightly by means of packing over 
the separated ends of two adjacent lengths of pipe. If the pipe is of 
iron, and such a joint is inserted every 200 ft., and if the range of tem- 
perature which must be allowed for is from 30 C. to 125 C., what is 
the minimum play which must be allowed for at each expansion joint ? 

12. Show from equation 5, p. 140, that linear coefficient of expansion 
may be defined as increase in length per unit length per degree. 



CHAPTER IX 

WORK AND HEAT ENERGY 
FRICTION 

172. Friction always results in wasted work. All of the 
experiments mentioned in Chapter VII were so arranged 
that friction could be neglected or eliminated. So long as 
this condition was fulfilled it was found that the result of 
universal experience could be stated thus : The work done by 
the acting force is equal to the sum of the kinetic and potential 
energies stored up. 

But wherever friction is present this law is found to be 
inexact, for the work of the acting force is then always 
somewhat greater than the sum of the kinetic and potential 
energies stored up. If, for example, a block is pulled over 
the horizontal surface of a table, at the end of the motion 
no velocity has been imparted to the block, and hence no 
kinetic energy has been stored up. Further, the block has 
not been lifted nor put into a condition of elastic strain, 
and hence no potential energy has been communicated to it. 
We cannot in any way obtain from the block more work 
after the motion than we could have obtained before it was 
moved. It is clear, therefore, that all of the work which 
was done in moving the block against the friction of the 
table was wasted work. Experience shows that, in general, 
where work is done against friction it can never be regained. 
Before considering what becomes of this wasted work we 
shall consider some of the factors on which friction depends 
and some of the laws which are found by experiment to 
hold in cases in which friction occurs. 

144 



FRICTION 



145 



173. Coefficient of friction. It is found that if F represents 
the force parallel to a plane which is necessary to maintain 
uniform motion in a body which is pressed against the plane 
with a force F', then, for small F=300 

velocities, the ratio depends 

only on the nature of the surfaces 

in contact, and not at all on the FIG. 158. The ratio of FtoF' is 

area or on the velocity of the the coefficient of friction 

77T 

motion. The ratio is called the coefficient of friction for 
F 

the given materials. Thus (Fig. 158), if F is 300 g. and F' 

goo ' The coeffi- 



is 800 g., the coefficient of friction is MS = -375. 



cient of iron on iron is about .2 ; of oak on oak, about .4. 

174. Rolling friction. The chief cause of sliding friction is the inter- 
locking of minute projections. When a round solid rolls over a smooth 
surface, the frictional resistance is generally much less than when it 
slides ; for example, the coefficient of friction of cast-iron wheels rolling 
on iron rails may be as low as .002, that is, y^ of the sliding friction 

(1) (2) 





FIG. 159. Friction in bearings 
(1) Common bearing ; (2) ball bearing 

of iron on iron. This means that a pull of 1 pound will keep a 500- 
pound car in motion. Sliding friction is not, however, entirely dis- 
pensed with in ordinary wheels, for although the rim of the wheel rolls 
on the track, the axle slides continuously at some point c (Fig. 159, 
(1)) upon the surface of the journal. Journals are frequently lined with 
brass or Babbitt metal, since this still further lowers the coefficient. 

The great advantage of the ball bearing (Fig. 159, (2)) is that the 
sliding friction in the hub is almost completely replaced by rolling 
friction. The manner in which ball bearings are used in a bicycle 



146 



WORK AND HEAT ENERGY 



pedal is illustrated in Fig. 160. The free-wheel ratchet ia shown in 
Fig. 161. The pawls a and b enable the pedals and chain wheel W to 
stop while the rear axle continues to revolve. Roller bearings are showD 
in Fig. 162. Oils and greases prevent rapid 
wear of bearings by lessening friction. 




FIG. 160. The bicycle pedal 



FIG. 161. Free-wheel ratchet 



175. Fluid friction. When a solid moves through a fluid, as when a 
bullet moves through the air or a ship through the water, the resistance 
encountered is not at all independent of velocity, as in the case of solid 
friction, but increases for slow speeds nearly as 
the square of the velocity, and for high speeds at 
a rate considerably greater. This explains why 
it is so expensive to run a fast train ; for the re- 
sistance of the air, which is a small part of the 
total resistance so long as the train is moving 
slowly, becomes the predominant factor at high 
speeds. The resistance offered to steamboats 
running at high speeds is usually considered to 
increase as the cube of the velocity. Thus, the 
Cedric, of the White Star Line, having a speed of 
17 knots, has a horse power of 14,000 and a total 
weight, when loaded, of about 38,000 tons, while 
the Mauretania, of the Cunard Line, having a 
speed of 25 knots, has engines of 70,000 horse 
power, although the total weight when loaded is 
only 32,500 tons. 

QUESTIONS AND PROBLEMS 

1. Mention three ways of lessening friction in machinery. 

2. In what respects is friction an advantage, and in what a disadvan- 
tage, in everyday life ? Could we get along without it ? 

3. Why is a stream swifter at the center than at the banks ? 

4. Why does a team have to keep pulling after a load is started? 




FIG. 162. Roller bear- 
ings of automobile front 
wheel 



EFFICIENCY 147 

5. Why is sand often placed on a track in starting a heavy train ? 

6. In what way is friction an advantage in lifting buildings with a 
jackscrew ? In what way is it a disadvantage ? 

7. A smooth block is 10 x 8 x 3 in. Compare the distances which it 
will slide when given a certain initial velocity on smooth ice if resting 
first, on a 10 x 8 face ; second, on a 10 x 3 face ; third, on an 8 x 3 face. 

8. What is the coefficient of friction of brass on brass if a force of 
25 Ib. is required to maintain uniform motion in a brass block weighing 
200 Ib. when it slides horizontally on a brass bed ? 

9. The coefficient of friction between a block and a table is .3. What 
force will be required to keep a 500-gram block in uniform motion ? 

EFFICIENCY 

176. Definition of efficiency. Since it is only in an ideal 
machine that there is no friction, in all actual machines the 
work clone by the acting force always exceeds, by the amount 
of the work done against friction, the amount of potential 
and kinetic energy stored up. We have seen that the former 
is wasted work in the sense that it can never be regained. 
Since the energy stored up represents work which can be 
regained, it is termed useful work. In most machines an effort 
is made to have the useful work as large a fraction of 
the total work expended as possible. The ratio of the useful 
work to the total work done by the acting force is called the 
EFFICIENCY of the machine. Thus 

Useful work accomplished 

Efficiency = - r- ^n C 1 ) 

lotal work expended 

Thus, if in the system of pulleys shown in Fig. 116 it is necessary to 
add a weight of 50 g. at E in order to pull up slowly an added weight of 
240 g. at 7t, the work done by the 50 g. while E is moving over 1 cm. 
will be 50 x 1 g. cm. The useful work accomplished in the same time 

1 240 x 1 4 

is 240 x g. cm. Hence the efficiency is equal to * = = 80%. 

o 50 x 1 o 

177. Efficiencies of some simple machines. In simple levers 
the friction is generally so small as to be negligible ; hence the 
efficiency of such machines is approximately 100%. When 



148 



WORK AND HEAT ENERGY 



inclined planes are used as machines, the friction is also small, 
so that the efficiency generally lies between 90% and 100%. 
The efficiency of the commercial block and tackle (Fig. 116), 
with several movable pulleys, is usually considerably less, 
varying between 40% and 60%. In the jackscrew there is 
necessarily a very large amount of friction, so that although 
the mechanical advantage is enormous, the efficiency is often 
as low as 25%. The differential pulley of Fig. 136 has also a 
very high mechanical advantage with a very small efficiency. 
Gear wheels such as those shown in Fig. 134, or chain gears 
such as those used in bicycles, are machines of comparatively 
high efficiency, often utilizing between 90% and 100% of 
the energy expended upon them. 

178. Efficiency of overshot water wheels. The overshot water wheel 
(Fig. 163) utilizes chiefly the potential energy of the water at S, for 
the wheel is turned by the weight of the 

water in the buckets. The work expended 

on the wheel per second, in foot pounds or 

gram centimeters, is the product of the 

weight of the water which passes over it 

per second by the distance through which 

it falls. The efficiency is the work which 

the wheel can accomplish in a second 

divided by this quantity. Such wheels 

are very common in mountainous regions, 

where it is easy to obtain considerable fall 

but where the streams carry a small volume 

of water. The efficiency is high, being often 

between 80 % and 90 %. The loss is due not 

only to the friction in the bearings and 

gears (see C) but also to the fact that some 

of the water is spilled from the buckets or passes over without entering 

them at all. This may still be regarded as a frictional loss, since the 

energy disappears in internal friction when the water strikes the ground. 

179. Efficiency of undershot water wheels. The old-style undershot 
wheel (Fig. 164) so common in flat countries, where there is little fall 
but an abundance of water utilizes only the kinetic energy of the water 




FIG. 163. Overshot water 
wheel 



EFFICIENCY 



149 




FIG. 164. The undershot 
wheel 



running through the race from ,-1. It seldom transforms into useful 
work more than 25% or 30% of the potential energy of the water above 
the dam. There are, however, certain mod- 
ern forms of undershot wheel. which are 
extremely efficient. For example, the Pelton 
icheel (Fig. 165), developed since 1880 and 
now very commonly used for small-power 
purposes in cities supplied with waterworks, 
sometimes has an efficiency as high as 83 %. 
The water is delivered from a nozzle 
against cup-shaped buckets arranged as in 
the figure. At the Big Creek development 

in California, Pelton wheels 94 inches in diameter are driven by water 
coming with a velocity of 350 feet per second (how many miles per 
hour?) through nozzles 6 inches in diameter. The head of water is 
here 1900 ft. 

180. Efficiency of water turbines. The 
turbine wheel was invented in France in 
1833 and is now used more than any 
other form of w r ater wheel. It stands 
completely under water in a case at the 
bottom of a turbine pit, rotating in a hori- 
zontal plane. Fig. 166 shows the method 
of installing a turbine at Niagara. C is 
the outer case into which the water enters 
from the penstock p. Fig. 167, (1), shows 
the outer case with contained turbine ; 
Fig. 167, (2), is the inner case, in which 
are the fixed guides G, which direct the 

water at the most advantageous angle against the blades of the wheel 
inside ; Fig. 167, (3), is the wheel itself ; and Fig. 167, (4), is a section 
of wheel and inner case, showing how the water enters through the 
guides and impinges upon the blades W. The spent water simply 
falls down from the blades into the tailrace T (Fig. 166). The amount 
of water which passes through the turbine can be controlled by means 
of the rod P (Fig. 167, (1)), which can be turned so as to increase or 
decrease the size of the openings between the guides G (Fig. 167, (2)). 
The energy expended upon the turbine per second is the product of 
the mass of water which passes through it by the height of the turbine 
pit. Efficiencies as high as 90 % have been attained with such wheels. 




FIG. 165. The Pelton water 
wheel 



150 



WORK AND HEAT ENERGY 



One of the largest turbines in existence is operated by the Puget Sound 
Power Co. It develops 25,000 horse power under a 440-foot head of water. 










FIG. 166. A turbine 
installed 



FIG. 167. The turbine wheel 

(1) Outer case ; (2) inner case ; (3) rotating 
part ; (4) section 



QUESTIONS AND PROBLEMS 

1 . Why is the efficiency of the jackscrew low and that of the lever high ? 

2. Find the efficiency of a machine in which an effort of 12 Ib. 
moving 5 ft. raises a weight of 25 Ib. 2 ft. 

3. What amount of work was done on a block and tackle having an 
efficiency of 60 % when by means of it a weight of 750 Ib. was raised 50 ft. ? 

4. A force pump driven by a 1-horse-power engine lifted 4 cu. ft. of 
water per minute to a height of 100 ft. What was the efficiency of the 
pump? 

5. If it is necessary to pull on a block and tackle with a force of 
100 Ib. in order to lift a weight of 300 Ib., and if the force must move 
6 ft. to raise the weight 1 ft., what is the efficiency of the system ? 



MECHANICAL EQUIVALENT OF HEAT 151 

6. If the efficiency had been 65%, what force would have been 
necessary in the preceding problem ? 

7. The Niagara turbine pits are 136 ft. deep, and their average horse 
power is 5000. Their efficiency is 85%. How much water does each 
turbine discharge per minute? 

MECHANICAL EQUIVALENT OF HEAT * 

181. What becomes of wasted work ? In all the devices for 
transforming work which, we have considered we have found 
that on account of frictional resistances a certain per cent of 
the work expended upon the machine is wasted. The question 
which at once suggests itself is, What becomes of this wasted 
work ? The following familiar facts suggest an answer. When 
two sticks are vigorously rubbed together, they become hot ;. 
augers and drills often become too hot to hold ; matches are 
ignited by friction ; if a strip of lead is struck a few sharp 
blows with a hammer, it is appreciably warmed. Now, since 
we learned in Chapter VIII that, according to modern notions, 
increasing the temperature of a body means simply increasing 
the average velocity of its molecules, and therefore their average 
kinetic energy, the above facts point strongly to the conclu- 
sion that in each case the mechanical energy expended has been 
simply transformed into the energy of molecular motion. This 
view was first brought into prominence in 1798 by Benjamin 
Thompson, Count Rumford, an American by birth, who was 
led to it by observing that in the boring of cannon heat was 
continuously developed. It was first carefully tested by the 
English physicist James Prescott Joule (see opposite p. 122) 
(1818-1889) in a series of epoch-making experiments extend- 
ing from 1842 to 1870. In order to understand these experi- 
ments we must first learn how heat quantities are measured. 

* This subject should be preceded by a laboratory experiment upon the 
"law of mixtures," and either preceded or accompanied by experiments 
upon specific heat and mechanical equivalent. See authors' Manual, Exper- 
iments 18, 19, and 20. 



152 WORK AND HEAT ENERGY 

182. Units of heat ; the calorie and the British thermal 
unit. The calorie is the amount of heat that is required to 
raise the temperature of 1 gram of water through 1 (,"'., and 
the British thermal unit {B. T. Z7.) is the amount of heat that 
is required to raise the temperature of 1 pound of water 
through 1 F. (One B.T.U. = 252 cal.) Thus, when a hun- 
dred grams of water has its temperature raised 4 C. we say 
that four hundred calories of heat have entered the water. 
Similarly, when a hundred grams of water has its temperature 
lowered 10 C. we say that a thousand calories have passed out 
of the water. If, then, we wish to measure, for instance, the 
amount of heat developed in a lead bullet when it strikes 
against a target, we have only to let the spent bullet fall into 
a known weight of water and to measure the number of 
degrees through which the temperature of the w^ater rises. 
The product of the number of grams of w r ater by its rise in 
temperature is, then, by definition, the number of calories of 
heat which have passed into the water. 

It will be noticed that in the above definition we maive 
no assumption whatever as to what heat is. Previous to the 
nineteenth century physicists generally held it to be an 
invisible, weightless fluid, the passage of which into or out 
of a body caused it to grow hot or cold. This view accounts 
well enough for the heating which a body experiences when 
it is held in contact with a flame or other hot body, but it 
has difficulty in explaining the heating produced by rubbing 
or pounding. Rumford's view accounts easily for this, as we 
have seen, while it accounts no less easily for the heating of 
cold bodies by contact with hot ones; for we have only to 
think of the hotter and therefore more energetic molecules 
of the hot body as communicating their energy to the mole- 
cules of the colder body in much the same way in which a 
rapidly moving billiard ball transfers part of its kinetic energy 
to a more slowly moving ball against which it strikes. 




Underwood & Underwood 

THE ViCKERS-ViMY AIRPLANE 

The first nonstop transatlantic airplane flight was made on June 14, 1919, from 
St. John's, Newfoundland, to Clifden, Ireland, a distance of 1890 miles. This 
historic flight the longest ever made was accomplished in fifteen hours and 
fifty-seven minutes, through fog and sleet, at an average speed of 118.5 miles per 
hour, a feat which won the $50,000 prize which had been offered for nearly five 
years by the London Daily Mail. The plane was driven by two 360-horse-power 
Rolls-Royce motors and carried 865 gallons of gasoline. It was piloted by Capt. 
John Alcock and navigated by Lieut. Arthur W. Brown. This airplane had a 
wing spread of 67 feet and a length of 42 feet 8 inches 



MECHANICAL EQUIVALENT OF HEAT 153 



183. Joule's experiment on the heat developed by friction. 

Joule argued that if the heat produced by friction etc. is 
indeed merely mechanical energy which has been transferred 
to the molecules of the heated body, then the same number 
of calories must always be produced by the disappearance of 
a given amount of mechanical energy. And this must be 
true, no matter whether the work is expended in overcoming 
the friction of wood 011 wood, of iron on iron, in percussion, 
in compression, or in any other conceivable way. To see 
whether or not this was so he caused mechanical energy 
to disappear in as many ways as possible and measured in 
every case the amount of heat developed. 

In his first experiment he caused paddle wheels to rotate in a vessel 
of water by means of falling weights W (Fig. 168). The amount of 
work done by gravity upon the weights in causing them to descend 
through any distance d was equal 
to their weight W times this dis- 
tance. If the weights descended 
slowly and uniformly, this work 
was all expended in overcoming 
the resistance of the water to 
the motion of the paddle wheels 
through it ; that is, it was wasted 
in eddy currents in the water. 
Joule measured the rise in the 
temperature of the water and 
found that the mean of his three FlG . 168> Jou i e > s first experiment on 
best trials gave 427 gram meters the mechanical equivalent of heat 
as the amount of work required 

to develop enough heat to raise a gram of water one degree. This value, 
confirmed by modern experiments, is now generally accepted as correct. 
He then repeated the experiment, substituting mercury for water, and 
obtained 425 gram meters as the work necessary to produce a calorie of 
heat. The difference between these numbers is less than was to have 
been expected from the unavoidable errors in the observations. He 
then devised an arrangement in which the heat was developed by the 
friction of iron on iron, and again obtained 425. 




154 WORK AND HEAT ENERGY 

x/ 

184. Heat produced by collision. A Frenchman named 
Hirn was the first to make a careful determination of the 
relation between the heat developed by collision and the kinetic 
energy which disappears. He allowed a steel cylinder to fall 
through a known height and crush a lead ball by its impact 
upon it. The amount of heat developed in the lead was meas- 
ured by observing the rise in temperature of a small amount of 
water into which the lead was quickly plunged. As the mean 
of a large number of trials he also found that 425 gram meters 
of energy disappeared for each calorie of heat that appeared. 

185. Heat produced by the compression of a gas. Another way 
in which Joule measured the relation between heat and work 
was by compressing a gas and comparing the amount of work 
done in the compression with the amount of heat developed. 

Every bicyclist is aware of the fact that when he inflates his 
tires the pump grows hot. This is due partly to the friction of 
the piston against the walls, but chiefly to the fact that the 
downward motion of the piston is transferred to the molecules 
which come in contact with it, so that the velocity of these 
molecules is increased. The principle is precisely the same 
as that involved in the velocity communicated to a ball by a 
bat. If the bat is held rigidly fixed and a ball thrown against 
it, the ball rebounds with a certain velocity ; but if the bat 
is moving rapidly forward to meet the ball, the latter rebounds 
with a much greater velocity. So the molecules which in their 
natural motions collide with an advancing piston rebound 
with greater velocity than they would if they had impinged 
upon a fixed wall. This increase in the molecular velocity 
of a gas on compression is so great that when a mass of gas 
at C. is compressed to one half its volume, the temperature 
rises to 87 C. 

The effect may be strikingly illustrated by the fire syringe (Fig. 169). 
Let a few drops of carbon bisulphide be placed on a small bit of cotton, 
dropped to the bottom of the tube A, and then removed; then let the 



MECHANICAL EQUIVALENT OF HEAT 155 



FIG. 169. The 
fire syringe 



piston B be inserted and very suddenly depressed. Sufficient heat will 
be developed to ignite the vapor, and a flash will result. (If the flash 
does not result from the first stroke, withdraw the piston 
completely, then reinsert, and compress again.) 

To measure the heat of compression Joule 
surrounded a small compression purnp with 
water, took 300 strokes on the pump, and meas- 
ured the rise in temperature of the water. As 
the result of these measurements he obtained 
444 gram meters as the mechanical equivalent 
of the calorie. The experiment, however, could 
not be performed with great exactness. 

Joule also measured the converse effect, 
namely, the cooling produced in a gas which 
is pushing forward a piston and thus doing work. 
He obtained 437 grain meters. 

186. Significance of Joule's experiments. Joule made three 
other determinations of the relation between heat and work 
by methods involving electrical measurements. He published 
as the mean of all his determinations 426.4 gram meters as 
the mechanical equivalent of the calorie. But the value of 
his experiments does not lie primarily in the accuracy of the 
final results, but rather in the proof which they for the first 
time furnished that whenever a given amount of work is tvasted, 
no matter in what particular way this waste occurs, the same 
definite amount of heat always appears. 

The most accurate determination of the mechanical equiva- 
lent of heat was made by Rowland (see opposite p. 358) (1848- 
1901) in 1880. He obtained 427 gram meters (4.19 x 10 7 ergs). 
We shall generally take it as 42,000,000 ergs. The mechan- 
ical equivalent of 1 B. T. U. is 778 foot pounds. 

187. The conservation of energy. We are now in a position 
to state the law of all machines in its most general form, that 
is, in such a way as to include even the cases where friction 



156 WORK AND HEAT ENERGY 

is present. It is : The work done by the acting force is equal to 
the sum of the kinetic and potential energies stored up plus the 
mechanical equivalent of the heat developed. 

In other words, whenever energy is expended on a machine or 
device of any kind, an exactly equal amount of energy always 
appears either as useful work or as heat. The useful work may 
be represented in the potential energy of a lifted mass, as 
when water is pumped up to a reservoir; or in the kinetic 
energy of a moving mass, as when a stone is thrown from a 
sling; or in the potential energies of molecules whose posi- 
tions with reference to one another have been changed, as 
when a spring has been bent; or in the molecular potential 
energy of chemically separated atoms, as when an electric 
current separates a compound substance. The ivasted work 
always appears in the form of increased molecular motion, 
that is, in the form of heat. This important generalization 
has received the name of the Principle of the Conservation of 
Energy. It may be stated thus: Energy may be transformed, 
but it can never be created or destroyed. 

188. Perpetual motion. In all ages there have been men 
who have spent their lives in trying to invent a machine out 
of which work could be continually obtained, without the ex- 
penditure of an equivalent amount of work upon it. Such 
devices are called perpetual-motion machines. The possibility 
of the existence of such a device is absolutely denied by the 
statement of the principle of the conservation of energy. For 
only in case there is no heat developed, that is, in case there 
are no frictional losses, can the w r ork taken out be equal to 
the work put in, and in no case can it be greater. Since, in 
fact, there are always some frictional losses, the principle of the 
conservation of energy asserts that it is impossible to make a 
machine which will keep itself running forever, even though it 
does no useful work ; for no matter how much kinetic or poten- 
tial energy is imparted to the machine to begin with, there 



MECHANICAL EQUIVALENT OF HEAT 157 

must always be a continual drain upon this energy to overcome 
frictional resistances, so that as soon as the wasted work has 
become equal to the initial energy, the machine must stop. 

The principle of the conservation of energy has now 
gained universal recognition and has taken its place as the 
corner stone of all physical science. 

189. Transformations of energy in a power plant. The transforma- 
tions of energy which take place in any power plant, such as that at 
Niagara, are as follows : The energy first exists as the potential energy 
of the water at the top of the falls. This is transformed in the turbine 
pits into the kinetic energy of the rotating wheels. These turbines 
drive dynamos in which there is a transformation into the energy of 
electric currents. These currents travel on wires as far as Syracuse, 
150 miles away, where they run street cars and other forms of motors. 
The principle of conservation of energy asserts that the work which 
gravity did upon the water in causing it to descend from the top to the 
bottom of the turbine pits is exactly equal to the work done by all the 
motors, plus the heat developed in all the wires and bearings and in 
the eddy currents in the water. 

Let us next consider where the water at the top of the falls obtained 
its potential energy. Water is being continually evaporated at the sur- 
face of the ocean by the sun's heat. This heat imparts sufficient kinetic 
energy to the molecules to enable them to break away from the attrac- 
tions of their fellows and to rise above the surface in the form of vapor- 
The lifted vapor is carried by winds over the continents and precipitated 
in the form of rain or snow. Thus the potential energy of the water 
above the falls at Niagara is simply transformed heat energy of the 
sun. If in this way we analyze any available source of energy at man's 
disposal, we find in almost every case that it is directly traceable 
to the sun's heat as its source. Thus, the energy contained in coal is 
simply the energy of separation of the oxygen and carbon which were 
separated in the processes of growth. This separation was effected by 
the sun's rays. 

The earth is continually receiving energy from the sun at the rate of 
342,000,000,000,000 horse power, or about a quarter of a million horse 
power per inhabitant. We can form some conception of the enormous 
amount of energy that the sun radiates in the form of heat by reflecting 
that the amount received by the earth is not more than 



,0 0,0 



158 WORK AND HEAT ENERGY 

of the total given out. Of the amount received by the earth not more 
than 1 1 OQ part is stored up in animal and vegetable life and lifted water. 
This is practically all of the energy which is available on the earth for 
man's use. 

QUESTIONS AND PROBLEMS 

1. Show that the energy of a waterfall is merely transformed solar 
energy. 

2. Analyze the transformations of energy which occur when a bullet 
is fired vertically upward. 

3. Meteorites are small, cold bodies moving about in space. Why do 
they become luminous when they enter the earth's atmosphere ? 

4. The Niagara Falls are 1GO ft. high. How much warmer is the 
water at the bottom of the falls than at the top? 

5. How many B. T. U. are required to warm 10 Ib. of water from 
freezing to boiling ? 

6. Two and a half gallons of water ( = 20 Ib.) were warmed from, 
68F. to 212F. If the heat energy put into the water could all have beei* 
made to do useful work, how high could 10 tons of coal have been 
hoisted ? 

SPECIFIC HEAT 

190. Definition of specific heat. When we experiment upon 
different substances, we find that it requires wholly different 
amounts of heat energy to produce in one gram of mass one 
degree of change in temperature. 

Let 100 g. of lead shot be placed in one test tube, 100 g. of bits of 
iron wire in another, and 100 g. of aluminium wire in a third. Let 
them all be placed in a pail of boiling water for ten or fifteen minutes, 
care being taken not to allow any of the water to enter any of the tubes. 
Let three small vessels be provided, each Of which contains 100 g. oi: 
water at the temperature of the room. Let the heated shot be poured 
into the first beaker, and after thorough stirring let the rise in the 
temperature of the water be noted. Let the same be done with the 
other metals. The aluminium will be found to raise the temperature 
about twice as much as the iron, and the iron about three times as 
much as the lead. Hence, since the three metals have cooled through 
approximately the same number of degrees, we must conclude that 
about six times as much heat has passed out of the aluminium as out 
of the lead; that is; each' gram of aluminium in cooling 1C. gives out 
about six times as many calories as a gram of lead. 



SPECIFIC HEAT 159 

The number of calories taken up by 1 gram of a substance 
when its temperature rises through 1 (7., or given up when it 
falls through 1 (7., is called the specific heat of that substance. 

It will be seen from this definition, and the definition of 
the calorie, that the specific heat of water is 1. 

191. Determination of specific heat by the method of mix- 
tures. The preceding experiments illustrate a method for 
measuring accurately the specific heats of different substances ; 
for, in accordance with the principle of the conservation of 
energy, when hot and cold bodies are mixed, as in these ex- 
periments, so that heat energy passes from one to the other, 
the gain in the heat energy of one must be just equal to the loss 
in the heat energy of the other. 

This method is by far the most common one for determin- 
ing the specific heats of substances. It is known as the method 
of mixtures. 

Suppose, to take an actual case, that the initial temperature of the 
shot used in 190 was 95 C. and that of the water 19.7, and that, after 
mixing, the temperature of the water and shot was 22. Then, since 
100 g. of water has had its temperature raised through 22 19.7 = 2.3, 
we know that 230 calories of heat have entered the water. Since the 
temperature of the shot fell through 95 22 = 73, the number of 
calories given up by the 100 g. of shot in falling 1 was ^f- = 3.15. 
Hence the specific heat of lead, that is, the number of calories of heat given 

Q -| T 

up by 1 gram of lead when its temperature falls 1C., is - = .0315. 

Or, again, we may work out the problem algebraically as follows : 
Let x equal the specific heat of lead. Then the number of calories which 
come out of the shot is its mass times its specific heat times its change in 
temperature,ihat is, 100 X a: x (95 22) ; and, similarly, the number which 
enter the water is the same, namely, 100 x 1 x (22 19.7). Hence we have 

100 (95 - 22) x = 100 (22 - 19.7), or x = .0315. 

By experiments of this sort the specific heats of some of 
the common substances have been found to be as follows: 



160 WOEK AND HEAT ENEKGY 

TABLE OF SPECIFIC HEATS 

Aluminium 218 Iron 113 

Brass 094 Lead 0315 

Copper 095 Mercury 0333 

Glass 2 Platinum 032 

Gold 0316 Silver 0568 

Ice . .504 Zinc .0935 



QUESTIONS AND PROBLEMS 

1. A barrelful of tepid water, when poured into a snowdrift, melts 
much more snow than a cupful of boiling water does. Which has the 
greater quantity of heat ? 

2. Why is a liter of hot water a better foot warmer than an equal 
volume of any substance in the preceding table ? 

3. The specific heat of water is much greater than that of any other 
liquid or of any solid. Explain how this accounts for the fact that an 
island in mid-ocean undergoes less extremes of temperature than an 
inland region. 

4. How many calories are required to heat a laundry iron weighing 
3 kg. from 20 C. to 130 C.? 

5. How many B. T. U. are required to warm a 6-pound laundry 
iron from 75 F. to 250 F. ? 

6. If 100 g. of mercury at 95 C. are mixed with 100 g. of water at 
15 C., and if the resulting temperature is 17.6 C., what is the specific 
heat of mercury? 

7. Tf 200 g. of water at 80 C. are mixed with 100 g. of water at 
10 C., what will be the temperature of the mixture? (Let x equal the 
final temperature ; then 100 (x 10) calories are gained by the cold 
water, while 200 (80 a:) calories are lost by the hot water.) 

8. What temperature will result if 400 g. of aluminium at 100 C. 
are placed in 500 g. of water at 20 C. ? 

9. Eight pounds of water were placed in a copper kettle weighing 
2.5 Ib. How many B. T. U. are required to heat the water and the kettle 
from 70 F. to 212 F.? If 4.3 cu. ft. of gas was used to do this, and if 
each cubic foot of gas on being burned yields 625 B. T. U., what is the 
efficiency of the heating apparatus? 

10. If a solid steel projectile were shot with a velocity of 1000 m. 
(3048 ft.) per second against an impenetrable steel target, and all the heat 
generated were to go toward raising the temperature of the projectile, 
what would be the amount of the increase ? 



CHAPTER X 

CHANGE OF STATE 

FUSION * 

192. Heat Of fusion. If on a cold day in winter a quantity of snow 
is brought in from out of doors, where the temperature is below 0C. 
and placed over a source of heat, a thermometer plunged into the snow 
will be found to rise slowly until the temperature reaches 0C., when 
it will become stationary and remain so during all the time the snow 
is melting, provided only that the contents of the vessel are continu- 
ously and vigorously stirred. As soon as the snow is all melted, the 
temperature will begin to rise again. 

Since the temperature of ice at C. is the same as the 
temperature of water at C., it is evident from this experiment 
that when ice is being changed to water, the entrance of heat 
energy into it does not produce any change in the average 
kinetic energy of its molecules. This energy must therefore 
all be expended in pulling apart the molecules of the crystals 
of which the ice is composed, and thus reducing it to a form 
in which the molecules are held together less intimately, that 
is, to the liquid form. In other words, the energy which existed 
in the flame as the kinetic energy of molecular motion has 
been transformed, upon passage into the melting solid, into 
the potential energy of molecules which have been pulled 
apart against the force of their mutual attraction. The number 

*This subject should be preceded by a laboratory exercise on the curve 
of cooling through the point of fusion, and followed by a determination of 
the heat of fusion of- ice. See, for example, Experiments 21 and 22 of the 
authors 1 Manual. 

161 



162 CHANGE OF STATE 

of calories of heat energy required to melt one gram of any 
substance without producing any change in its temperature is 
called the heat of fusion of that substance. 

193. Numerical value of heat of fusion of ice. Since it is 
found to require about 80 times as long for a given flame to 
melt a quantity of snow as to raise the melted snow through 
1 C., we conclude that it requires about 80 calories of heat 
to melt 1 g. of snow or ice. This constant is, however, much 
more accurately determined by the method of mixtures. Thus, 
suppose that a piece of ice weighing 131 g. is dropped into 
500 g. of water at 40 C., and suppose that after the ice is all 
melted the temperature of the mixture is found to bo 15 C. 
The number of calories which have come out of the water is 
500 x (40 - 15) = 12,500. But 131 x 15 = 1965 calories of 
this heat must have been used in raising the ice from C. 
to 15 C. after the ice, by melting, became water at 0. The 
remainder of the heat, namely, 12,500 1965 = 10,535, must 
have been used in melting the 131 g. of ice. Hence the 
number of calories required to melt 1 g. of ice is 1 " j \ 5 = 80.4. 

To state the problem algebraically, let x = the heat of fusion 
of ice. Then we have 

131 x + 1965 - 12,500 ; that is, x = 80.4. 

According to the most careful determinations the heat of fusion 
of ice is 80.0 calories. 

194. Energy transformation in fusion. The heat energy 
that goes into a body to change it from the solid state to the 
liquid state no longer exists as heat within the liquid. It has 
ceased to exist as heat energy at all, having been transformed 
into molecular potential energy ; that is, the heat which disap- 
pears represents the work that was done in effecting the change 
of state ) and it is, therefore, the exact equivalent of the 
potential energy gained by the rearranged molecules. This is 
strictly in accord with the law of conservation of energy. 



FUSION 



163 



195. Heat given out when water freezes. Let snow and salt be 
added to a beaker of water until the temperature of the liquid mixture 
is as low as 10 C. or 12 C. Then let a test tube containing a ther- 
mometer and a quantity of pure water be thrust into the cold solution. 
If the thermometer is kept very quiet, the temperature of the water in the 
test tube will fall four or five or even ten degrees below C. without 
producing solidification. But as soon as the thermometer is stirred, or a 
small crystal of ice is dropped into the neck of the tube, the ice crystals 
will form with great suddenness, and at the same time the thermometer 
will rise to C., where it will remain until all the water is frozen. 

The experiment shows in a very striking way that the proc- 
ess of freezing is a heat-evolving process. This was to have 
been expected from the principle of the conservation of energy ; 
for since it takes 80 calories of heat energy to turn a gram of ice 
at C. into water at (7., this amount of energy must reappear 
when the water turns back to ice. 

196. Use made of energy transformations in melting and 
freezing. A refrigerator (Fig. 170) is a box constructed with 
double walls so as to make it difficult for heat to pass in from 
the outside. Ice is kept in the upper 

part of one compartment so as to cool 
the air at the top, which, because of 
its greater density when cool, settles 
and causes a circulation as indicated 
by the arrows. To melt each gram of 
ice 80 calories must be taken from 
the air and food within the refrigera- 
tor. If the ice did not melt, it would 
be worthless for use in refrigerators. 
The heat given off by the freezing 
of water is often turned to practical 
account ; for example, tubs of water are sometimes placed in 
vegetable cellars to prevent the vegetables from freezing. 
The effectiveness of this procedure is due to the fact that 
the temperature at which the vegetables freeze is slightly 




FIG. 170. A refrigerator 



164 CHANGE OF STATE 

lower than C. As the temperature of the cellar falls the 
water therefore begins to freeze first, and in so doing evolves 
enough heat to prevent the temperature of the room from 
falling as far below C. as it otherwise would. 

It is partly because of the heat evolved by the freezing of 
large bodies of water that the temperature never falls so low 
in the vicinity of large lakes as it does in inland localities. 
, 197. Melting points of crystalline substances. If a piece of 
ice is placed in a vessel of boiling water for an instant and 
then removed and wiped, it will not be found to be in the 
slightest degree warmer than a piece of ice which has not been 
exposed to the heat of the warm water. The melting point of 
ice is therefore a perfectly fixed, definite temperature, above 
which the ice can never be raised so long as it remains ice, 
no matter how fast heat is applied to it. All crystalline sub- 
stances are found to behave exactly like ice in this respect, 
each substance of this class having its characteristic melting 
point. The following table gives the melting points of some 
of the commoner crystalline substances : 



Mercury . 
Ice . 
Benzine . 


-39C. 
0C. 

7C. 


Sulphur . . 
Tin . . . 
Lead . 


114 C. 
233C. 
330C. 


Silver . . 
Copper 
Cast iron . 


. 954C. 
. 1100C. 
. 1200 C. 


Acetic acid . 


17C. 


Zinc . . . 


433C. 


Platinum . 


. 1775C. 


Paraffin . . 


54C. 


Aluminium . 


650C. 


Iridium . 


. 1950C. 



We may summarize the experiments upon melting points of 
crystalline substances in the two following laws : 

1. The temperatures of solidification and fusion are the same. 

2. The temperature of the melting or solidifying substance 
remains constant from the moment at which melting or solidi- 
fication begins until the process is completed. 

198. Fusion of noncrystalline, or amorphous, substances. Let 
the end of a glass rod be held in a Bunsen flame. Instead of changing 
suddenly from the solid to the liquid state, it will gradually grow softer 



FUSION 165 

and softer until, if the rod is not too thick and the flame is sufficiently 
hot, a drop of molten glass will finally fall from the end of the rod. 

If the temperature of the rod had been measured during 
this process, it would have been found to be continually rising. 
This behavior, so completely unlike that of crystalline sub- 
stances, is characteristic of tar, wax, resin, glue, gutta-percha, 
alcohol, carbon, and in general of all amorphous substances. 
Such substances cannot be said to have any definite melting 
points at all, for they pass through all stages of viscosity both 
in melting and in solidifying. It is in virtue of this property 
that glass and other similar substances can be heated to soft- 
ness and then molded or rolled into any desired shape. 

199. Change of volume on solidifying. One has only to 
reflect that ice floats, or that bottles or crocks of water burst 
when they freeze, in order to know that water expands upon 
solidifying. In fact, 1 cubic foot of water becomes 1.09 cubic 
feet of ice, thus expanding more than one twelfth of its initial 
volume when it freezes. This may seem strange in view of 
the fact that the molecules are certainly more closely knit 
together in the solid than in the liquid state ; but the strange- 
ness disappears when we reflect that the molecules of water in 
freezing group themselves into crystals, and that this operation 
presumably leaves comparatively large free spaces between 
different crystals, so that, although groups of individual mole- 
cules are more closely joined than before, the total volume 
occupied by the whole assemblage of molecules is greater. 

But the great majority of crystalline substances contract 
upon solidifying and expand upon liquefying. Water, anti- 
mony, bismuth, cast iron, and a few alloys containing antimony 
or bismuth are the chief exceptions. It is only from substances 
which expand, or which change in volume very little on solidi- 
fying, that sharp castings can be made ; for it is clear that 
contracting substances cannot retain the shape of the mold. 
It is for this reason that gold and silver coins must be stamped 



166 CHANGE OF STATE 

rather than cast. Any metal from which type is to be cast 
must be one which expands upon solidifying, for it need 
scarcely be said that perfectly sharp outlines are indispensable 
to good type. Ordinary type metal is an alloy of lead, anti- 
mony, and copper, which fulfills these requirements. 

200. Effect of the expansion which water undergoes on 
freezing. If water were not unlike most substances in that it 
expands on freezing, many, if not all, of the forms of life which 
now exist on the earth would be impossible ; for in winter 
the ice would sink in ponds and lakes as fast as it froze, and 
soon our rivers, lakes, and perhaps our oceans also would 
become solid ice. 

The force exerted by the expansion of freezing water is very 
great. Steel bombs have been burst by filling them with water 
and exposing them on cold winter nights. One of the chief 
agents in the disintegration of rocks is the freezing and conse- 
quent expansion of water which has percolated into them. 

201. Pressure lowers the melting point of substances which 
expand on solidifying. Since the outside pressure acting on 
the surface of a body tends to prevent its expansion, we should 
expect that any increase in the outside pressure would tend 
to prevent the solidification of substances which expand upon 
freezing. It ought therefore to require a lower temperature 
to freeze ice under a pressure of two atmospheres than under 
a pressure of one. Careful experiments have verified this 
conclusion and have shown that the melting point of ice is 
lowered .0075 C. for an increase of one atmosphere in the 
outside pressure. Although this lowering is so small a quantity, 
its existence may be shown as follows : 

Let two pieces of ice be pressed firmly together beneath the surface 
of a vessel full of warm water. When taken out they will be found to 
be frozen together, in spite of the fact that they have been immersed 
in a medium much warmer than the freezing point of water. The 
explanation is as follows : 




FUSION 167 

At the points of contact the pressure reduces the freezing point of 
the ice below C., and hence it rnelts and gives rise to a thin film of 
water the temperature of which is slightly below C. When this 
pressure is released, the film of water at once freezes, for its tempera- 
ture is below the freezing point corresponding to ordinary atmospheric 
pressure. The same phenomenon may be even more strikingly illus- 
trated by the following experiment : 

Let two weights of from 5 to 10 kg. be hung by a wire over a block 
of ice as in Fig. 171. In half an hour or less the wire will be found to 
have cut completely through the block, 
leaving the ice, however, as solid as at 
first. The explanation is as follows : 
Just below the wire the ice melts be- 
cause of the pressure ; as the wire sinks 
through the layer of water thus formed, 
the pressure on the water is relieved 
and it immediately freezes again above 
the wire. 

Geologists believe that the con- 
tinuous flow of glaciers is partly ElG> 171> Reg elation 
due to the fact that the ice melts 

at points where the pressures become large, and freezes again 
when these pressures are relieved. This process of melting 
under pressure and freezing again as soon as the pressure is 
relieved is known as regelation. 

Substances ivhich expand on solidifying have their melting 
points lowered by pressure, and those which contract on solidify- 
ing have their melting points raised by pressure. 

QUESTIONS AND PROBLEMS 

1. What is the meaning of the statement that the heat of fusion of 
mercury is 2.8 ? 

2. Explain how the presence of ice keeps the interior of a refrig- 
erator from becoming warm. 

3. How many times as much heat is required to melt any piece of 
ice as to warm the resulting water 1 C. ? 1 F. ? How many B. T. U. are 
required to melt 1 Ib. of ice? How many foot pounds of energy are 
required to do the work of melting 1 Ib. of ice ? 



168 CHANGE OF STATE 

4. If the heat of fusion of ice were 40 instead of 80, how would this 
affect the quantity of ice that would have to be bought for the refriger- 
ator during the summer? 

5. Five pounds of ice melted in 1 hr. in an unopened refrigerator. 
How many B. T. U. caine through the walls of the refrigerator in 
the hour? 

6. Just what will occur if 1000 calories be applied to 20 g. of ice at 
0C.? 

7. How many grains of ice must be put into 200 g. of water at 40 C. 
to lower the temperature 10 C. ? 

8. How many grams of ice must be put into 500 g. of water at 50 C. 
to lower the temperature to 10 C.? 

9. Why will snow pack into a snowball if the snow is melting, 
but not if it is much below C. ? 



EVAPORATION AND THE PROPERTIES OF VAPORS 

202. Evaporation and temperature. If it is true that in- 
crease in temperature means increase in the mean velocity 
of molecular motion, then the number of molecules which 
chance in a given time to acquire the velocity necessary to 
carry them into the space above the liquid ought to increase 
as the temperature increases ; that is, evaporation ought to 
take place more rapidly at high temperatures than at low. 
Common observation teaches that this is true. Damp clothes 
become dry under a hot flatiron but not under a cold one ; 
the sidewalk dries more readily in the sun than in the shade ; 
we put wet objects near a hot stove or radiator when we 
wish them to dry quickly. 

203. Evaporation of solids, sublimation. That the mole- 
cules of a solid substance are found in a vaporous condition 
above the surface of the solid, as well as above that of a 
liquid, is proved by the often-observed fact that ice and 
snow evaporate even though they are kept constantly below 
the freezing point. Thus, wet clothes dry in winter after 
freezing. An even better proof is the fact that the odor of 
camphor can be detected many feet away from the camphor 



EVAPORATION 169 

crystals. The evaporation of solids may be rendered visible 
by the following striking experiment: 

Let a few crystals of iodine be placed on a watch glass and heated 
gently with a Bunsen flame. The visible vapor of iodine will appear 
above the crystals, though none of the liquid is formed. 

A great many substances at high temperatures pass from 
the solid to the gaseous condition without passing through 
the liquid state. The vaporization of a solid is called sublimation. 

204. Saturated vapor. If a liquid is placed in an open vessel, 
there ought to be no limit to the number of molecules which 
can be lost by evaporation, for as fast as the molecules emerge 
from the liquid they are carried away by air currents. As a 
matter of fact, experience teaches that water left in an open 
dish does waste away until the dish is completely dry. 

But suppose that the liquid is evaporating into a closed 
space, such as that shown in Fig. 172. Since the molecules 
which leave the liquid cannot escape from the 
space S, it is clear that as time goes on the 
number of molecules which have passed off 
from the liquid into this space must contin- 
ually increase ; in other words, the density of 
the vapor in S must grow greater and greater. 
But there is an absolutely definite limit to 
the density which the vapor can attain ; for 
as soon as it reaches a certain value, depending on the tem- 
perature and on the nature of the liquid, the number of 
molecules returning per second to the liquid surface will be 
exactly equal to the number escaping. The vapor is then 
said to be saturated. 

If the density of the vapor is lessened temporarily by in- 
creasing the size of the vessel S, more molecules will escape 
from the liquid per second than return to it, until the density 
of the vapor has regained its original value. 




170 



CHANGE OF STATE 



If, on the other hand, the density of the vapor has been 
increased by compressing it, more molecules return to the 
liquid per second than escape, and the density of the vapor 
falls quickly to its saturated value. We learn, then, that the 
density of the saturated vapor of a liquid depends on the tem- 
perature alone and cannot be affected by changes in volume. 

205. Pressure of a saturated vapor. Just as a gas exerts a 
pressure against the walls of the containing vessel by the 
blows of its moving molecules, so also does a confined vapor. 
But at any given temperature the density of a saturated vapor 
can have only a definite value ; that is, there can be only a 
definite number of molecules per cubic centimeter. It fol- 
lows, therefore, that just as at any temperature the saturated 
vapor can have only one density, so 
also it can have only one pressure. 
This pressure is called the pressure 
of the saturated vapor correspond- 
ing to the given temperature. 

Let two Torricelli tubes be set up as 
in Fig. 173, and with the aid of a curved 
pipette (Fig. 173) let a drop of ether be 
introduced into the bottom of tube 1. 
This drop will at once rise to the top, 
and a portion of it will evaporate into 
the vacuum which exists above the mer- 
cury. The pressure of this vapor will 
push down the mercury column, and the 
number of centimeters of this depres- 
sion will of course be a measure of the 
pressure of the vapor. It will be observed 
that the mercury will fall almost in- 
stantly to the lowest level which it will ever reach, a fact which indi- 
cates that it takes but a very short time for the condition of saturation 
to be attained. 

The pressure of the saturated ether vapor at the temperature 
of the room will be found to be as much as 40 centimeters. 




FIG. 173. Vapor pressure of 
a saturated vapor 



EVAPORATION 



1T1 



Let a Bunsen flame be passed quickly across the tubes of Fig. 173^ 
near the upper level of the mercury. The vapor pressure will increase 
rapidly in tube 1, as shown by the fall of the mercury column. 

The experiment proves that both the pressure and the 
density of a saturated vapor increase rapidly with the tem- 
perature. This was to have been expected from our theory, 
for increasing the temperature of the liquid increases the 
mean velocity of its molecules and hence increases the num- 
ber which attain each second the velocity necessary for escape. 
How rapidly the density and pressure of saturated water 
vapor increase with temperature may be seen from the fol- 
lowing table: 

TABLE OF CONSTANTS OF SATURATED ABATER VAPOR 

The table shows the pressure P, in millimeters of mercury, and the 
density D of aqueous vapor saturated at temperatures t C. 



t. 


P. 


D. 


t. 


P. 


D. 


t. 


P. 


D. 


- 10 


2.2 


.0000023 


4 


6.1 


.0000064 


18 


15.3 


.0000152 


- 9 


2.3 


.0000025 


5 


6.5 


.0000068 


19 


16.3 


.0000162 


- 8 


2.5 


.0000027 


6 


7.0 


.0000073 


20 


17.4 


.0000172 


- 7 


2.7 


.0000029 


7 


7.5 


.0000077 


21 


18.5 


.0000182 


- 6 


2.9 


.0000032 


8 


8.0 


.0000082 


22 


19.6 


.0000193 


- 5 


3.2 


.0000034 


9 


8.5 


.0000087 


23 


20.9 


.0000204 


40 


3.4 


.0000037 


10 


9.1 


.0000093 


24 


22.2 


.0000216 


- 3 


3.7 


,0000040 


11 


9.8 


.0000100 


25 


23.5 


.0000229 


- 2 


3.9 


.0000042 


12 


10.4 


.0000106 


26 


25.0 


.0000242 


JO 


4.2 


.0000045 


13 


11.1 


.0000112 


27 


26.5 


.0000256 





4.6 


.0000049 


14 


11.9 


.0000120 


28 


28.1 


.0000270 


1 


4.9 


.0000052 


15 


12.7 


.0000128 


30 


31.5 


.0000301 


2 


5.3 


.0000056 


16 


13.5 


.0000135 


35 


41.8 


.0000393 


3 


5.7 


.0000060 


17 


14.4 


.0000144 


40 


54.9 


.0000509 



206. The influence of air on evaporation. We observed that 
when ether was inserted into a Torricelli tube the mercury 
fell very suddenly to its final position, showing that in a 
vacuum the condition of saturation is reached almost instantly. 



172 CHANGE OF STATE 

This was to have been expected from the great velocities 
which we found the molecules of gases and vapors to possess. 

Let air be introduced into tube 2 (Fig. 173) until the mercury col- 
umn stands at a height of from 45 to 55 cm. Measure the height of 
the mercury column. In order to see what effect the presence of air 
has upon evaporation, let a drop of ether be introduced into the tube. 
The mercury will not be found to sink instantly to its final level as 
it did before ; but although it will fall rapidly at first, it will continue 
to fall slowly for several hours. At the end of a day, if the temperature 
has remained constant, it will show a depression which indicates a 
vapor pressure of the ether just as great as that existing in a tube 
which contains no air. 

The experiment leads, then, to the rather remarkable con- 
clusion that just as much liquid will evaporate into a space 
which is already full of air as into a vacuum. The air has 
no effect except to retard greatly the rate of evaporation. 

207. Explanation of the retarding influence of air on evapo- 
ration. This retarding influence of air on evaporation is easily 
explained by the kinetic theory ; for while in a vacuum the 
molecules which emerge from the surface fly at once to the 
top of the vessel, when air is present the escaping molecules 
collide with the air molecules before they have gone any 
appreciable distance away from the surface (probably less 
than .00001 centimeter), and only work their way up to the 
top after an almost infinite number of collisions. Thus, while 
the space immediately above the liquid may become saturated 
very quickly, it requires a long time for this condition of 
saturation to reach the top of the vessel. 

QUESTIONS AND PROBLEMS 

1. Account for the evaporation of naphthaline moth balls at ordi- 
nary room temperatures. 

2. Why do clothes dry more quickly on a windy day than on a quiet 
day? 

3. If the inside of a barometer tube is wet when it is filled with mer- 
cury, will the height of the mercury be the same as in a dry tube ? 



HYGROMETRY 173 

4. How many grams of water will evaporate at 20 C. into a closed 
room 18 x 20 x 4 m. ? (See table, p. 171.) 

5. At a temperature of 15 C. what will be the error in the baro- 
metric height indicated by a barometer which contains moisture? 

6. At 20 C. how great was the error in reading due to the presence 
of water vapor in Otto von Guericke's barometer ? 

HYGROMETRY, OR THE STUDY OF MOISTURE CONDITIONS 
IN THE ATMOSPHERE * 

208. Condensation of water vapor from the air. Were it not 
for the retarding influence of air upon evaporation we should 
be obliged to live in an atmosphere which would be always 
completely saturated with water vapor, for the evaporation 
from oceans, lakes, and rivers would almost instantly saturate 
all the regions of the earth. This condition one in which 
moist clothes would never dry, and in which all objects would 
be perpetually soaked in moisture would be exceedingly 
uncomfortable if not altogether unendurable. 

But on account of the slowness with which, as the last ex- 
periment showed, evaporation into air takes place, the water 
vapor which always exists in the atmosphere is usually far 
from saturated, even in the immediate neighborhood of lakes 
and rivers. Since, however, the amount of vapor which is 
necessary to produce saturation rapidly decreases with a fall 
in temperature, if the temperature decreases continually in 
some unsaturated locality it is clear that a point must soon 
be reached at which the amount of vapor already existing in a 
cubic centimeter of the atmosphere is the amount correspond- 
ing to saturation. Then, if the temperature still continues to 
fall, the vapor must begin to condense. Whether it condenses 
as dew or cloud or fog or rain will depend upon how and 
where the cooling takes place. 

* It is recommended that this subject be preceded by a laboratory deter- 
mination of dew point, humidity, etc. See, for example, Experiment 10 of 
the authors' Manual. 



174 CHANGE OF STATE 

209. The formation of dew and frost. If the cooling is due 
to the natural radiation of heat from the earth at night after 
the sun's warmth is withdrawn, the atmosphere itself does not 
fall in temperature nearly as rapidly as do solid objects on the 
earth, such as blades of grass, trees, stones, etc. The layers of 
air which come into immediate contact with these cooled bodies 
are themselves cooled, and as they thus reach a temperature 
at which the amount of moisture which they already contain 
is in a saturated condition, they begin to deposit this mois- 
ture, in the form of dew or frost, upon the cold objects. The 
drops of moisture which collect on an ice pitcher in summer 
illustrate perfectly the formation of dew. If condensation 
takes place upon a surface colder than the freezing temper- 
ature, frost is formed, as is observed, for instance, on grass 
and on windowpanes. 

210. The formation of fog. If the cooling at night is so 
great as not only to bring the grass and trees below the tem- 
perature at which the vapor in the air in contact with them is 
in a state of saturation, but also to lower the whole body of 
air near the earth below this temperature, then the condensa- 
tion takes place not only on the solid objects but also on dust 
particles suspended in the atmosphere. This constitutes a fog. 

211. The formation of clouds, rain, sleet, hail, and snow. 
When the cooling of the atmosphere takes place at some dis- 
tance above the earth's surface, as when a warm current of 
air enters a cold region, if the resultant temperature is below 
that at which the amount of moisture already in the air is 
sufficient to produce saturation, this excessive moisture im- 
mediately condenses about floating dust particles and forms a 
cloud. If the cooling is sufficient to free a considerable amount 
of moisture, the drops become large and fall as rain. If this 
falling rain freezes before it reaches the ground, it is called 
sleet. If the temperature at which condensation begins is be- 
low freezing, the condensing moisture forms into snouflakes. 



HYGROMETRY 



175 




When the violent air currents . which accompany thunder- 
storms cany the condensed moisture up and down several 
times through alternate regions of snow and rain, hailstones 
are formed. 

212. The dew point. The temperature to which the atmosphere 
must be cooled in order that condensation of the water vapor 
within it may begin is called the dew point." This 
temperature may be found by partly filling with 

water a brightly polished vessel of 200 or 300 
cubic centimeters capacity and dropping into it 
little pieces of ice, stirring thoroughly at the 
same time with a thermometer. 
The dew point is the temperature 
indicated by the thermometer at 
the instant a film of moisture ap- 
pears upon the polished surface. 
In winter the dew point is usually 
below freezing, and it will there- 
fore be necessary to add salt to the 

ice and water in order to make the film appear. The experi- 
ment may be performed equally well by bubbling a current of 
air through ether contained in a polished tube (Fig. 174). 

213. Humidity of the atmosphere. From the dew point and 
table given in 205, p. 171, we can easily find what is com- 
monly known as the relative humidity or the degree of satura- 
tion of the atmosphere. Relative humidity is defined as the 
ratio between the amount of moisture per cubic centimeter actu- 
ally present in the air and the amount which ivould be present if 
the air were completely saturated. This is precisely the same 
as the ratio between the pressure which the water vapor pres- 
ent in the air exerts and the pressure which it would exert 
if it were present in sufficient quantity to be in the saturated 
condition. An example will make clear the method of find- 
ing the relative humidity. 



FIG. 174. Apparatus for deter- 
mining dew point 



176 CHANGE OF STATE 

Suppose that the dew point were found to lye 15 C. on a day on whicli 
the temperature of the room was 25 C. The amount of moisture actu- 
ally present in the air then saturates it at 15 C. We see from the P 
column in the table that the pressure of saturated vapor at 15 C. is 
12.7 millimeters. This is, then, the pressure exerted by the vapor in the 
air at the time of our experiment. Running down the table, we see that 
the amount of moisture required to produce saturation at the tempera- 
ture of the room, that is, at 25, would exert a pressure of 23.5 millimeters. 
Hence at the time of the experiment the air contains 12.7/23.5, or .54, 
as much water vapor as it might hold. AVe say, therefore, that the air 
is 54% saturated, or that the relative humidity is 54%. 

214. Practical value of humidity determinations. From hu- 
midity determinations it is possible to obtain much information 
regarding the likelihood of rain or frost. Such observations 
are continually made for this purpose at all meteorological 
stations. They are also made in greenhouses, to see that the 
air does not become too dry for the welfare of the plants, 
and in hospitals and public buildings and even in private 
dwellings, in order to insure the maintenance of hygienic liv- 
ing conditions. For the most healthful conditions the relative 
humidity should be kept at from 50% to 60%. 

Low relative humidity in the home causes discomfort and 
colds, and leads to waste of fuel estimated at from 10% to 
25%. The average home heated to 72 F. by steam or hot 
water is estimated by health authorities to have a relative hu- 
midity of 30%, and even as little as 25% with hot-air heat- 
ing. This is less than the average humidity of extensive 
desert regions. Higher humidity in the home would diminish 
the cooling effect due to rapid evaporation of the perspiration 
from the body, and would make us feel comfortable if a lower 
temperature were maintained (see 215). 

215. Cooling effect of evaporation. Let three shallow dishes be 
partly filled, the first with water, the second with alcohol, and the third 
with ether, the bottles from which these liquids are obtained having stood 
in the room long enough to acquire its temperature. Let three students 



HYGKOMETKY 177 

carefully read as maiiy thermometers, first before their bulbs have been 
immersed in the respective liquids and then after. In every case the 
temperature of the liquid in the shallow vessel will be found to be 
somewhat lower than the temperature of the air, the difference being 
greatest in the case of ether and least in the case of water. 

It appears from this experiment that an evaporating liquid 
assumes a temperature somewhat lower than its surroundings, 
and that the substances which evaporate the most readily 
assume the lowest temperatures. 

In dry, hot climates where ice is not readily obtained drink- 
ing water is frequently kept in canvas bags or unglazed earth- 
enware. The slow evaporation of the water from the outside 
of the porous container keeps the water within quite cool. 

Another way of establishing the same truth is to place a few drops 
of each of the above liquids in succession on the bulb of the arrange- 
ment shown in Fig. 143 and observe the rise of water in the stem ; or, 
more simply still, to place a few drops of each liquid on the back of 
the hand and notice that the order in which they evaporate namely, 
ether, alcohol, water is the order of greatest cooling. 

In twenty-four hours a healthy person perspires from a pint 
to a quart, while one who exercises violently may perspire a 
gallon in that time. 

216. Explanation of the cooling effect of evaporation. The 
kinetic theory furnishes a simple explanation of the cooling 
effect of evaporation. We saw that, in accordance with this 
theory, evaporation means an escape from the surface of 
those molecules which have acquired velocities considerably 
above the average. But such a continual loss of the most 
rapidly moving molecules involves, of course, a continual 
diminution of the average velocity of the molecules left behind, 
and this means a decrease in the temperature of the liquid. 

Again, we should expect the amount of cooling to be pro- 
portional to the rate at which the liquid is losing molecules. 
Hence, of the three liquids studied, ether should cool most 
rapidly, since it evaporates most rapidly. 



178 CHANGE OF STATE 

217. Freezing by evaporation. In 206 it was shown that 
a liquid will evaporate much more quickly into a vacuum 
than into a space containing air. Hence, if we place a liquid 
under the receiver of an air pump and exhaust rapidly, we 
ought to expect a much greater fall in temperature than 
when the liquid evaporates into air. This conclusion may 
be strikingly verified as follows: 

Let a thin watch glass be filled with ether and placed upon a drop 
of cold water, preferably ice water, which rests upon a thin glass plate. 
Let the whole arrangement be placed underneath the receiver of an air 
pump and the air rapidly exhausted. After a few minutes of pumping 
the watch glass will be found frozen to the plate. 

By evaporating liquid helium in this way Professor Kara- 
erlingh Onnes of Leyden, in 1911, attained the lowest tem- 
perature that had ever been reached, namely, 271.3 C. 
( - 456.3 F.), less than 2 C. above absolute zero. 

218. Effect of air currents upon evaporation. Let four ther- 
mometer bulbs, the first of which is dry, the second wetted with water, 
the third with alcohol, and the fourth with ether, be rapidly fanned and 
their respective temperatures observed. The results will show that in 
all of the wetted thermometers the fanning will considerably augment 
the cooling, but the dry thermometer will be wholly unaffected. 

The reason why fanning thus facilitates evaporation, and 
therefore cooling, is that it removes the saturated layers of 
vapor which are in immediate contact with the liquid and re- 
places them by unsaturated layers into which new evaporation 
may at once take place. From the behavior of the dry-bulb 
thermometer, however, it will be seen that fanning produces 
cooling only when it can thus hasten evaporation. A dry body 
at the temperature of the room is not cooled in the slightest 
degree by blowing a current of air across it. 

219. The wet- and dry-bulb hygrometer. In the wet- 
and dry-bulb hygrometer (Fig. 175) the principle of cooling 
by evaporation finds a very useful application. This instrument 



HYGKOMETRY 



179 








consists of two thermometers, the bulb of one of which is dry, 
while that of the other is kept continually moist by a wick 
dipping into a vessel of water. Unless the air is saturated 
the wet bulb indicates a lower tempera- 
ture than the dry one, for the reason that 
evaporation is continually taking place 
from its surface. How much lower will 
depend on how rapidly the evaporation 
proceeds, and this in turn will depend 
upon the relative humidity of the atmos- 
phere. Thus, in a completely saturated 
atmosphere no evaporation whatever takes 
place at the wet bulb, and it consequently 
indicates the same temperature as the dry 
one. By comparing the indications of this 
instrument with those of the dew-point 
hygrometer (Fig. 1 74) tables have been 
constructed which enable one to deter- 
mine at once from the readings of the 
two thermometers both the relative humidity and the dew 
point. On account of their convenience instruments of this 
sort are used almost exclusively in practical work. They are 
not very reliable unless the air is made to 
circulate about the wet bulb before the 
reading is taken. In scientific work this is 
always done. 

220. Effect of increased surface upon evap- 
oration. Let a small test tube containing a few 
drops of water be dipped into a larger tube or a 
small glass containing ether, as in Fig. 176, and 
let a current of air be forced rapidly through the 
ether with an aspirator in the manner shown. The water within the 
tube will be frozen in a few minutes, if the aspirator is operated vigor- 
ously. The experiment works most successfully if the walls of the test 
tube are quite thin and the walls of the outer vessel fairly thick. Why ? 



FIG. 175. Wet- and dry- 
bulb hygrometer 




FIG. 176. Freezing 
water by the evap- 
oration of ether 



180 CHANGE OF STATE 

The effect of passing bubbles through the ether is simply 
to increase enormously the evaporating surface, for the ether 
molecules which could before escape only at the upper sur- 
face can now escape into the air bubbles as well. 

221. Factors affecting evaporation. The above results may 
be summarized as follows: The rate of evaporation depends 
(1) on the nature of the evaporating liquid ; (2) on the 
temperature of the evaporating liquid ; (3) on the degree of 
saturation of the space into which the evaporation takes place 
(4) on the density of the air or other gas above the evaporating 
surface ; (5) on the rapidity of the circulation of the air above 
the evaporating surface ; (6) on the extent of the exposed 
surface of the liquid. 

QUESTIONS AND PROBLEMS 

1. Why do spectacle lenses become coated with mist on entering a 
warm house on a cold winter day? 

2. Does dew "fall"? 

3. Why are icebergs frequently surrounded with fog? 

4. Dew will not usually collect on a pitcher of ice water standing 
in a warm room on a cold winter day. Explain. 

5. The dew point in a room was found to be 8 C. What was the 
relative humidity if the temperature of the air was 10 C.? 20 C.? 
30 C. ? (Consult table, p. 171.) 

6. What weight of water is contained in a room 5x5x3 m. if the 
relative humidity is 60% and the temperature 20 C. ? (See table, p. 171.) 

7. If a glass beaker and a porous earthenware vessel are filled with 
equal amounts of water at the same temperature, in the course of a few 
minutes a noticeable difference of temperature will exist between the 
two vessels. Which will be the cooler, and why ? Will the difference in 
temperature between the two vessels be greater in a dry or in a moist 
atmosphere ? 

8. Why will an open, narrow-necked bottle containing ether not 
show as low a temperature as an open shallow dish containing the 
same amount of ether? 

9. Why is the heat so oppressive on a very damp day in summer? 
10. A morning fog generally disappears before noon. Explain the 

reason for its disappearance. 



BOILING 181 

11. What becomes of the cloud which you see about a blowing loco- 
motive whistle ? Is it steam ? 

12. Explain why it is necessary in winter to add moisture to the air 
of our homes to maintain proper relative humidity, but not necessary in 
the summer. 

13. What factors affecting evaporation are illustrated by the follow- 
ing : (1) a wet handkerchief dries faster if spread out, (2) clothes dry 
best on a windy day, (3) clothes do not dry rapidly on a cold day, (4) 
clothes dry slowly on humid days ? Explain each fact. 

BOILING * 

222. Heat of vaporization defined. The experiments per- 
formed in Chapter IV, Molecular Motions, led us to the 
conclusion that, at the free surface of any liquid, molecules 
frequently acquire velocities sufficiently high to enable them 
to lift themselves beyond the range of attraction of the mole- 
cules of the liquid and to pass off as free gaseous molecules 
into the space above. They taught us, further, that since it is 
only such molecules as have unusually high velocities which 
are able thus to escape, the average kinetic energy of the mole- 
cules left behind is continually diminished by this loss from 
the liquid of the most rapidly moving molecules, and conse- 
quently the temperature of an evaporating liquid constantly 
falls until the rate at which it is losing heat is equal to the 
rate at which it receives heat from outside sources. Evapora- 
tion, therefore, always takes place at the expense of the heat 
energy of the liquid. The number of calories of heat which dis- 
appear in the formation of one gram of vapor is called the heat 
of vaporization of the liquid. 

223. Heat due to condensation. When molecules pass off 
from the surface of a liquid, they rise against the downward 

* It is recommended that this subject be accompanied by a laboratory 
determination of the boiling point of alcohol by the direct method and by 
the vapor-pressure method, and that it be followed by an experiment upon 
the fixed points of a thermometer and the change of boiling point with 
pressure. See, for example, Experiments 23 and 24 of the authors 1 Manual. 



182 



CHANGE OF STATE 



forces exerted upon them by the liquid, and in so doing ex 
change a part of their kinetic energy for the potential energy 
of separated molecules in precisely the same way in which a 
ball thrown upward from the earth exchanges its kinetic 
energy in rising for the potential energy which is represented 
by the separation of the ball from the earth. Similarly, just 
as when the ball falls back it regains in the descent all of 
the kinetic energy lost in the ascent, so when the molecules 
of the vapor reenter the liquid they must regain all of the 
kinetic energy which they lost when they passed out of the 
liquid. We may expect, therefore, that every gram of steam 
which condenses will generate in this process the same number 
of calories as was required to vaporize it. This is the prin- 
ciple of the steam heating of buildings, by which the heat 
energy that disappears in converting the water in the boilers 
into steam is generated again when the steam condenses to 
water within the radiators. 

224. Measurement of heat of vaporization. To find accurately 

the number of calories expended in the vaporization, or released in the 
condensation, of a gram of water at 100 C., we pass steam rapidly for 
two or three minutes from an arrangement 
like that shown in Fig. 177 into a vessel 
containing, say, 500 g. of water. We ob- 
serve the initial and final temperatures and 
the initial and final weights of the water. 
If, for example, the gain in weight of the 
water is 16.5 g., we know that 16.5 g. of 
steam have been condensed. If the rise in 
temperature of the water is from 10 C. to 
30 C., we know that 500 x (30- 10) = 10,000 
calories of heat have entered the water. If 
x represents the number of calories given 
up by 1 g. of steam in condensing, then the 
total heat imparted to the water by the con- 
densation of the steam is 16.5 x calories. This condensed steam is at 
first water at 100 C., which is then cooled to 30 C. In this cooling 




FIG. 177. Heat of vaporiza- 
tion of water 



BOILING 183 

process it gives up 16.5 x (100 30) = 1155 calories. Therefore, equat- 
ing the heat gained by the water to the heat lost by the steam, we have 

10,000 = 16.5 x + 1155, or x = 536. 

This is the method usually employed for finding the heat of 
vaporization. The now accepted value of this constant is 536. 

225. Boiling temperature defined. If a liquid is heated by 
means of a flame, it will be found that there is a certain tem- 
perature above which it cannot be raised, no matter how rapidly 
the heat is applied. This is the temperature which exists when 
bubbles of vapor form at the bottom of the vessel and rise to 
the surface, growing larger as they rise. This temperature is 
commonly called the boiling temperature. 

But a second and more exact definition of the boiling point 
may be given. It is clear that a bubble of vapor can exist 
within the liquid only when the pressure exerted by the vapor 
within the bubble is at least equal to the atmospheric pressure 
pushing down on the surface of the liquid; for if the pres- 
sure within the bubble were less than the outside pressure, 
the bubble would immediately collapse. Therefore the boiling 
point is the temperature at which the pressure of the saturated 
vapor first becomes equal to the pressure existing outside. 

226. Variation of the boiling point with pressure. Since the 
pressure of a saturated vapor varies rapidly with the temper- 
ature, and since the boiling point has been defined as the 
temperature at which the pressure of the saturated vapor is 
equal to the outside pressure, it follows that the boiling point 
must vary as the outside pressure varies. 

Thus let a round-bottomed flask be half filled with water and boiled. 
After the boiling has continued for a few minutes, so that the steam 
has driven out most of the air from the flask, let a rubber stopper be 
inserted and the flask removed from the flame and inverted as shown 
in Fig. 178. The temperature will fall rapidly below the boiling point ; 
but if cold water is poured over the flask, the water will again begin to 
boil vigorously, for the cold water, by condensing the steam, lowers the 



184 



CHANGE OF STATE 




FIG. 178. Lowering the 
boiling point by dimin- 
ishing the pressure 



pressure within the flask, and thus enables the water to boil at a temper- 
ature lower than 100 C. The boiling will cease, howe^ 7 er, as soon as 
enough vapor is formed to restore the pressure. 
The operation may be repeated many times 

without reheating. 

<* 

At the city of Quito, Ecuador, water 
boils at 90 C. ; on the top of Mt. Blanc 
it boils at 84 C. ; and on Pikes Peak, 
at 89 C. On the other hand, in the 
boiler of a locomotive on which the 
gauge records a pressure of 250 pounds, 
as is frequently the case, the boiling point 
of the water is 208 C. (406 F.). 

Closed boilers provided with safety valves (see (7, Fig. 179) 
and known as digesters are used for more rapid cooking in 
mountainous regions. Indeed, a temperature only a few de- 
grees above 100 C. causes starch grains to burst open much 
more rapidly than does a temperature of 
100 C. Large digesters are used in ex- 
tracting gelatin from bones and in reclaim- 
ing valuable fatty substances at garbage 
plants. In the cold-pack method of pre- 
serving fruits and vegetables the final 
sterilizing is done by placing the jars or 
cans in closed boilers known as steam- 




FIG. 179. A closed 
boiler for family use 



pressure canners.* 

227. Evaporation and boiling. The only 
essential difference between evaporation 
and boiling is that the former consists in the passage of 
molecules into the vaporous condition from the free surface 
only, while the latter consists in the passage of the molecules 
into the vaporous condition both at the free surface and at 



* Farmers' 1 Bulletin No. 839, on steam-pressure canning, may be obtained 
from the United States Department of Agriculture, Washington, D. C. 



BOILING 



185 



the surface of bubbles which exist within the body of the 
liquid. The only reason why vaporization takes place so much 
more rapidly at the boiling temperature than just below it 
is that the evaporating surface is enormously increased as 
soon as the bubbles form. The reason why the temperature 
cannot be raised above the boiling point is that the surface 
always increases, on account of the bubbles, to just such an 
extent that the loss of heat because of evaporation is exactly 
equal to the heat received from the fire. 

228. Distillation. Let water holding in solution some aniline dye 
be boiled in B (Fig. 180). The vapor of the liquid will pass into the 
tube T, where it will be condensed 

by the cold water which is kept in 
continual circulation through the 
jacket /. The condensed water col- 
lected in P will be seen to be free 
from all traces of the color of the 
dissolved aniline. 

We learn, then, that when 
solids are dissolved in liquids, the 
vapor which rises from the solu- 
tion contains none of the dissolved 

substance. Sometimes it is the pure liquid in P which is 
desired, as in the manufacture of alcohol, and sometimes 
the solid which remains in B, as in the manufacture of 
sugar. In the white-sugar industry it is necessary that the 
evaporation take place at a low temperature, so that the 
sugar may not be scorched. Hence the boiler is kept par- 
tially exhausted by means of an air pump, thus enabling 
the solution to boil at considerably reduced temperatures. 

229. Fractional distillation. When bo'th of the constituents 
of a solution are volatile, as in the case of a mixture of alcohol 
and water, the vapor of both will rise from the liquid. But 
the one which has the lower boiling point, that is, the higher 




FIG. 180. Distillation 



186 CHANGE OF STATE 

vapor pressure, will predominate. Hence, if we have in B 
(Fig. 180) a solution consisting of 50% alcohol and 50% 
water, it is clear that we can obtain in P, by evaporating 
and condensing, a solution containing .a much larger percent- 
age of alcohol. By repeating this operation a number of times 
we can increase the purity of the alcohol. This process is 
called fractional distillation. The boiling point of the mixture 
lies between the boiling points of alcohol and water, being 
higher the greater the percentage of water in the solution. 
Gasoline and kerosene are separated from crude oil, and 
different grades of gasoline are separated from each other by 
fractional distillation. 

QUESTIONS AND PROBLEMS 

1. A fall of 1 C. in the boiling point is caused by rising 960 ft. 
How hot is boiling water at Denver, 5000 ft. above sea level? 

2. How may we obtain pure drinking water from sea water ? 

3. After water has been brought to a boil, will eggs become hard 
any quicker when the flame is high than when it is low ? 

4.. The hot water which leaves a steam radiator may be as hot as 
the steam which entered it. How, then, has the room been warmed ? 

5. In a vessel of water which is being heated fine bubbles rise long 
before the boiling point is reached. Why is this so ? How can you dis- 
tinguish between this phenomenon and boiling ? 

6. When water is boiled in a deep vessel, it will be noticed that the 
bubbles rapidly increase in size as they approach the surface. Give two 
reasons for this. 

7. Why are burns caused by steam so much more severe than burns 
caused by hot water of the same temperature ? 

8. How many times as much heat is required to convert any body 
of boiling water into steam as to warm an equal weight of water 1 C.? 

9. How many B. T. U. are liberated within a radiator when 10 Ib. 
of steam condense there ? 

10. In a certain radiator 2 kg. of steam at 100 C. condensed to water 
in 1 hr. and the water left the radiator at 90 C. How many calories 
were given to the room during the hour? 

11. How many calories are given up by 30 g. of steam at 100 C. in 
condensing and then cooling to 20 C. ? How much water will this steam 
raise from 10 C. to 20 C.? 



ARTIFICIAL COOLING 187 

ARTIFICIAL COOLING 

230. Cooling by solution. Let a handful of common salt be placed 
in a small beaker of water at the temperature of the room and stirred 
with a thermometer. The temperature will fall several degrees. If equal 
weights of ammonium nitrate and water at 15 C. are mixed, the tem- 
perature will fall as low as 10 C. If the water is nearly at C. when 
the ammonium nitrate is added, and if the stirring is done with a test 
tube partly filled with ice-cold water, the water in the tube will be frozen. 

These experiments show that the breaking up of the crystals 
of a solid requires an expenditure of heat energy, as well when 
this operation is effected by solution as by fusion. The reason 
for this will appear at once if we consider the analogy between 
solution and evaporation ; for just as the molecules of a liquid 
tend to escape from its surface into the air, so the molecules at 
the surface of the salt are tending, because of their velocities, 
to pass off, and are only held back by the attractions of the 
other molecules in the crystal to which they belong. If, how- 
ever, the salt is placed in water, the attraction of the water 
molecules for the salt molecules aids the natural velocities of 
the latter to carry them beyond the attraction of their fellows. 
As the molecules escape from the salt crystals two forces are 
acting on them, the attraction of the water molecules tending 
to increase their velocities, and the attraction of the remaining 
salt molecules tending to diminish these velocities. If the 
latter force has a greater resultant effect than the former, the 
mean velocity of the molecules after they have escaped will 
be diminished and the solution will be cooled. But if the 
attraction of the water molecules amounts to more than the 
backward pull of the dissolving molecules, as when caustic 
potash or sulphuric acid is dissolved, the mean molecular 
velocity is increased and the solution is heated. 

231. Freezing points of solutions. If a solution of one part 
of common salt to ten of water is placed in a test tube and 
immersed in a " freezing mixture " of water, ice, and salt, the 



188 CHANGE OF STATE 

temperature indicated by a thermometer in the tube will not be 
zero when ice begins to form, but several degrees below zero. 
The ice which does form, however, will be found, like the vapor 
which rises above a salt solution, to be free from salt, and it is 
this fact which furnishes a key to the explanation of why the 
freezing point of the salt solution is lower than that of pure 
water. For cooling a substance to its freezing point simply 
means reducing its temperature, and therefore the mean ve- 
locity of its molecules, sufficiently to enable the cohesive forces 
of the liquid to pull the molecules together into the crystalline 
form. Since in the freezing of a salt solution the cohesive 
forces of the water are obliged to overcome the attractions 
of the salt molecules as well as the molecular motions, the 
motions must be rendered less, that is, the temperature must 
be made lower, than in the case of pure water in order that 
crystallization may occur. From this reasoning we should ex- 
pect that the larger the amount of salt in solution the lower 
would be the freezing point. This is indeed the case. The 
lowest freezing point obtainable with common salt in water is 
22 C., or 7.6 F. This is the freezing point of a saturated 
solution. 

232. Freezing mixtures. If snow or ice is placed in a vessel 
of water, the water melts it, and in so doing its temperature is 
reduced to the freezing point of pure water. Similarly, if ice 
is placed in salt water, it melts and reduces the temperature of 
the salt water to the freezing point of the solution. This may 
be one, or two, or twenty-two degrees below zero, according 
to the concentration of the solution. Therefore, whether we 
put the ice in pure water or in salt water, enough of it always 
melts to reduce the whole mass to the freezing point of the 
liquid, and each gram of ice which melts uses up 80 calories 
of heat. The efficiency of a mixture of salt and ice in producing 
cold is therefore due simply to the fact that the freezing point of 
a salt solution is lower than that of pure water. 



INDUSTRIAL APPLICATIONS 189 

The best proportions are three parts of snow or finely 
shaved ice to one part of common salt. If three parts of 
calcium chloride are mixed with two parts of snow, a tem- 
perature of 55 C. may be produced. This is low enough 
to freeze mercury. 

QUESTIONS AND PROBLEMS 

1. When salt water freezes, the ice formed is free from salt. What 
effect, then, does freezing have on the concentration of a salt solution ? 

2. A partially concentrated salt solution which has a freezing point of 
5 C. is placed in a room which is kept at 10 C. Will it all freeze ? 

3. Explain why salt is thrown on icy sidewalks on cold winter days. 

4. Give two reasons why the ocean freezes less easily than the lakes. 

5. Why does pouring H 2 SO 4 into water produce heat, while pouring 
the same substance upon ice produces cold? 

6. Why will a liquid which is unable to dissolve a solid at a low 
temperature often do so at a higher temperature ? (See 230.) 

7. When the salt in an ice-cream freezer unites with the ice to form 
brine, about how many calories of heat are used for each gram of ice 
melted ? Where does it come from ? If the freezing point of the salt 
solution were the same as that of the cream, would the cream freeze ? 

INDUSTRIAL APPLICATIONS 

233. The modern steam engine. Thus far in our study of 
the transformations of energy we have considered only cases 
in which mechanical energy was transformed into heat energy. 
In all heat engines we have examples of exactly the reverse 
operation, namely, the transformation of heat energy back into 
mechanical energy. 'How this is done may best be understood 
from a study of various modern forms of heat engines. The 
invention of the form of the steam engine which is now in use 
is due to James Watt, who, at the time of the invention (1768), 
was an instrument maker in the University of Glasgow. 

The operation of such a machine can best be understood 
from the ideal diagram shown in Fig. 181. Steam generated 
in the boiler B by the fire F passes through the pipe S into 



190 



CHANGE OF STATE 



the steam chest V, and thence through the passage N into the 
cylinder (7, where its pressure forces the piston P to the left. 
It will be seen from the figure that as the driving rod R 
moves toward the left the so-called eccentric rod R', which 
controls the valve P 7 , moves toward the right. Hence, when 
the piston has reached the left end of its stroke, the passage 




FIG. 181. Ideal diagram of a steam engine 

N will have been closed, while the passage M will have been 
opened, thus throwing the pressure from the right to the left 
side of the piston, and at the same time putting the right end of 
the cylinder, which is full of spent steam, into connection with 
the exhaust pipe E. This operation goes on continually, the rod 
R' opening and closing the passages M and ^Vat just the proper 
moments to keep the piston moving back and forth through- 
out the length of the cylinder. The shaft carries a heavy 
flywheel W, the great inertia of which insures constancy in 
speed. The motion of the shaft is communicated to any 




i! ill 




THE LIBERTY MOTOR 

This 400-horse-power motor, one of America's important contributions to the World 
War, was developed for use on the larger types of bombing airplanes. It makes 
1700 revolutions per minute and has twelve cylinders, which are water-cooled. 
It weighs 806 pounds, or about 2 pounds per horse power. The NC-4, which made 
the first transatlantic flight, was equipped with three of these motors 



INDUSTEIAL APPLICATIONS 



191 



desired machinery by means of a belt which passes over the 
pulley W. Within the boiler the steam is at high pressure 
and high temperature ( 226). The steam falls in temperature 
within the cylinder while doing the work of pushing the piston. 
A steam engine is a mechanical device ivhich accomplishes useful 
work by transforming heat energy into mechanical energy. 

234. Condensing and noncondensing engines. In most sta- 
tionary engines the exhaust E leads to a condenser which 
consists of a chamber Q, into which plays a jet of cold water 
T, and in which a partial vacuum is maintained by means of 
an air pump. In the best engines the pressure within Q is 
not more than from 3 to 5 centimeters of mercury, that is, 
not more than a pound to the square inch. Hence the con- 
denser reduces the back pressure against that end of the 
piston which is open to the atmosphere from 15 pounds 
down to 1 pound, and thus increases the effective pressure 
which the steam on the other side of the piston can exert. 

235. The eccentric. In practice the valve rod R' is not attached as in 
the ideal engine indicated in Fig. 181, but motion is communicated to 
it by a so-called ec- 
centric. This consists 

of a circular disk K 

(Fig. 182) rigidly at- 

tached to the axle but 

so set that its center 

does not coincide with 

the center of the axle 

A. The disk # rotates 

inside the collar C and 

thus communicates to FTG> 182 . The eccentric 

the eccentric rod R' a 

back-and-forth motion which operates the valve V in such a way as 

to admit steam alternately through M and N at the proper time. 

236. The boiler. When an engine is at work, steam is being removed 
very rapidly from the boiler ; for example, a railway locomotive consumes 
from 3 to fi tons of water per hour. Tt is therefore necessary to have 




192 



CHANGE OF STATE 



the fire in contact with as large a surface as possible. In the tubular 
boiler this end is accomplished by causing the flames to pass through 
a large number of metal tubes immersed in water. The arrangement 




FIG. 183. Diagram of locomotive 

of the furnace and the boiler may be seen from the diagram of a loco- 
motive shown in Fig. 183. (See early and modern types opposite p. 123.) 

237. The draft. In order to force the flames through the tubes B of 
the boiler a powerful draft is required. In locomotives this is obtained 
by running the exhaust steam from the cylinder C (Fig. 183) into the 
smokestack E through the blower F. The strong 

current through F draws with it a portion of the 
air from the smoke box Z), thus producing within 
D a partial vacuum into which a powerful draft 
rushes from the furnace through the tubes B. The 
coal consumption of an ordinary locomotive is from 
one-fourth ton to one ton per hour. 

In stationary engines a draft is obtained by mak- 
ing the smokestack very high. Since in this case 
the pressure which is forcing the air through the 
furnace is equal to the difference in the weights of 
columns of air of unit cross section inside and outside the chimney, it 
is evident that this pressure will be greater the greater the height of 
the smokestack. This is the reason for the immense heights given to 
chimneys in large power plants. 

238. The governor. Fig. 184 shows an ingenious device of Watt's, 
called a governor, for automatically regulating the speed with which a 
stationary engine runs. If it runs too fast, the heavy rotating balls B 




FIG. 184. The 
governor 



INDUSTRIAL APPLICATIONS 



193 



move apart and upward and in so doing operate a valve which reduces 
the speed by partially shutting off the supply of steam from the cylinder. 
239. Compound engines. In an engine which has but a single cylin- 
der the full force of the steam has not been spent when the cylinder 
is opened to the exhaust. The waste of energy which this entails is 
obviated in the compound engine 
(see Fig. 311) by allowing the 
partially spent steam to pass 
into a second cylinder of larger 
area than the first. The most 
efficient of modern engines have 
three and sometimes four cylin- 
ders of this sort, and the en- 
gines are accordingly called triple 
or quadruple expansion engines. 




FIG. 185. Cross-compound engine 
cylinders 



Fig. 185 shows the relation be- 
tween any two successive cylin- 
ders of a cross-compound engine. 
By automatic devices not differing in principle from the eccentric, valves 
C 1 , D 2 , and E 2 open simultaneously and thus permit steam from the 
boiler to enter the small cylinder A, while the partially spent steam in 
the other end of the same cylinder passes through D 2 into B, and the 
more fully exhausted steam in the upper end of B passes out through 
E 2 . At the upper end of the stroke of the pistons P and P', C 1 , D 2 , and 
E 2 automatically close, while C 2 , D\ and E 1 simultaneously open and 
thus reverse the direction of motion of both pistons. These pistons are 
attached to the same shaft. 

240. Efficiency of a steam engine. We have seen that it is 
possible to transform completely a given amount of mechani- 
cal energy into heat energy. This is done whenever a moving 
body is brought to rest by means of a frictional resistance. 
But the inverse operation, namely, that of transforming heat 
energy into mechanical energy, differs in this respect, that it 
is only a comparatively small fraction of the heat developed 
by combustion which can be transformed into work. For it is 
not difficult to see that in every steam engine at least a part 
of the heat must of necessity pass over with the exhaust steam 
into the condenser or out into the atmosphere. This loss is so 



194 



CHANGE OF STATE 




great that even in an ideal engine not more than about 23% 
of the heat of combustion could be transformed into work. In 
practice the very best condensing engines of the quadruple- 
expansion type transform into mechanical work not more than 
17% of the heat of combustion. Ordinary locomotives utilize 
at most not more than 8%. The efficiency of a heat engine is 
defined as the ratio between the heat utilized, or transformed into 
work, and the total heat expended. The efficiency of the best 
steam engines is therefore about -|^, or 75%, of that of an 
ideal heat engine, while that of the ordinary locomotive is 
only about ^-, or 26%, of the ideal limit. 

241. Principle of the internal-combustion engine. Let two 

iron or steel wires be pushed through a cork stopper and their ends * 
brought near together (1/32 inch will do) 
(Fig. 186). With an atomizer spray into the 
bottle a small amount of benzine or gasoline 
(the amount to use can be determined by 
trial), insert the stopper, and bring the tips 
of the heavily insulated wires leading from an 
induction coil to the underside of the wires 
a, b. A spark will pass at s ; and, if the mix- 
ture is not too " rich " or too " lean," a violent 
explosion will occur, throwing the stopper as 
high as the ceiling. (A heavy round bottle must 
be used for safety. Wrap it well in wire gauze.) 

Within the last two decades gas 

engines have become quite as important a factor in modern 
life as steam engines. (See opposite pp. 190, 191, and 198.) 
Such engines are driven by properly timed explosions of a 
mixture of gas and air occurring within the cylinder. 

Fig. 187 is a diagram illustrating the four stages into 
which it is convenient to divide the complete cycle of opera- 
tions which goes on within such an engine. Suppose that 
the heavy flywheel W has already been set in motion. As the 
piston p moves down in the first stroke (see 1) the valve D 



FIG. 186. A mixture of 

gasoline vapor and air 

will explode 



INDUSTRIAL APPLICATIONS 



195 





FIG. 187. Principle of the gas engine 



opens and an explosive mixture of gas and air is drawn into the 

cylinder through D. As the piston rises (see 2) valve D closes, 

and the mixture of gas and 

air is compressed into a 

small space in the upper 

end of the cylinder. An 

electric spark ignites the 

explosive mixture, and the 

force of the explosion drives 

the piston violently down 

(see 3}. At the besrirmintj 

\ y o o 

of the return stroke (see 4) 

the exhaust valve E opens, ; \ w } \w j \ w 
and as the piston moves 
up, the spent gaseous prod- 
ucts of the explosion are forced out of the cylinder. The initial 
condition is thus restored and the cycle begins over again. 

Since it is only during the third stroke that the engine is 
receiving energy from the exploding gas, the flywheel is 
always made very heavy so that the energy stored up in it 
in the third stroke may keep the machine running with little 
loss of speed during the other three parts of the cycle. 

The efficiency of the gas engine is often as high as 25%, or nearly 
double that of the best steam engines. Furthermore, it is free from 
smoke, is very compact, and may be started at a moment's notice. On 
the other hand, the fuel (gas or gasoline) is comparatively expensive. 
Most automobiles are run by gasoline engines, chiefly because the 
lightness of the engine and of the fuel to be carried are here considera- 
tions of great importance. 

It has been the development of the light and efficient gas engine 
which has made possible man's recent conquest of the air through the 
use of the airplane and airship. 

242. The automobile. The plate opposite page 198 shows 
the principal mechanical features of the automobile in their 
relation to one another. It will be seen that the cylinders 



196 



CHANGE OF STATE 



of the engine are surrounded 
by water jackets which form 
part of a circulating system. 
The heat of the engine is car- 
ried by convection currents in 
this water to the radiator, 
where it is lost to the atmos- 
phere through the air currents 
produced in part by a revolving 
fan (10). Unless some means 
were provided for cooling a gas 
engine, it would become so over- 
heated that the pistons would 
stick fast. The power of the 
engine is transmitted to the rear 
axle through the clutch (11), 
the transmission (12), and the 
differential gearing. 

243. The clutch and the transmis- 
sion. Since a gas engine develops 
its power by a series of violent ex- 
plosions within the cylinders, it is 
clear that it cannot start with a load 
as does the steam engine. In start- 
ing an automobile it is first necessary 
that the engine acquire a reasonable 
speed and that the power be applied 
gradually to the rear axle by the use 
of a friction clutch (11); otherwise 
the engine will stall. The shaft of 
the engine has upon its rear .end a 
flywheel which, in the cone clutch, is 
turned to a conical shape inside. 
Close to this but attached to the 
transmission shaft is the clutch plate, 
a heavy disk faced with leather, which 




Rear 
(Transmission Shaft] l|f 



Countershaft 



Neutral 




Firxt (Low Speed) 2 




Second (Intermediate Speed) 





FIG. 188. Automobile transmission 



INDUSTRIAL APPLICATIONS 



197 



fits the inside of the flywheel and is pressed into it by a spring suffi- 
ciently strong to prevent any slipping when the clutch is engaged. 
The driver throws out the clutch by depressing a lever with his foot. 
In the disk clutch the bearing surfaces are two series of disks, one 
revolving with the engine shaft, the other with the transmission. 

The amount of work done by a gas engine in a minute depends upon 
the work done by each explosion multiplied by the number of explosions 
per minute. Therefore it can develop its full power only while revolving 
rapidly. In hill climbing, for example, the speed of the engine must be 
great while that of the car is comparatively small. To meet this require- 
ment a system of reduction gears called the transmission (12) is used 
to make the number of revolutions of the driving shaft less than that 
of the crank shaft (4) of the engine. In Fig. 188, (1), the gears are in 
neutral, gears 1 and # being always in mesh. By use of the gear-shift 
lever (14) gears 3 and 5 (Fig. 188) are made to slide upon a square 
shaft. Before shifting the gears the clutch is released to disconnect the 
power of the motor from the driving shaft ; and, to avoid a clash when 
meshing the gears on the transmission shaft with those on the counter- 
shaft, care should be taken that they revolve at about the same speed. 
Fig. 188, (2), shows the low-speed connection. In shifting to second speed 
(Fig. 188, (#)) the clutch is released, gear 5 is thrown into neutral, and 
finally gear 3 is meshed with 4, after which 
the clutch is allowed to grip. In going 
to high speed (Fig. 188, (4)) gear 3 is 
shifted through neutral to engagement 
with gear 1. This connects the crank shaft 
of the engine directly to the driving shaft 
so that the two revolve at the same speed. 
For the reverse (Fig. 188, (5)) an eighth 
gear is thrown up from beneath so as 
simultaneously to engage 5 and 7. Such 
an interposition of a third gear wheel 
between 5 and 7 obviously reverses the 
direction of rotation of the driving shaft. 
244. The differential. An automobile 
is driven by .power applied to the rear 
axle. This requires the axle to be in two 

parts with a differential between, so that in turning corners the outer 
wheel may revolve faster than the inner. It will be seen from the 
large drawing opposite page 198, and from Fig. 189, that the pinion 




FIG. 189. The differential 



198 CHANGE OF STATE 

attached to the driving shaft rotates the main bevel gear B, to which 
are rigidly attached the differential gears 1 and 2. The left axle is 
directly connected to gear 3, and only indirectly connected to the main 
bevel gear B through gears 1 and 2. In running straight both rear 
wheels revolve at the same rate; therefore, while gears 3 and 4 and 
the main bevel gear are revolving at the same speed they carry around 
with them pinions 1 and 2, which are now, however, not revolving on 
their bearings. When the car is turning a corner, gears 3 and 4 are 
turning at different rates ; hence pinions 1 and 2 are not only carried 
around by the main bevel gear but at the same time are revolved in 
opposite directions on their bearings. 

245. The carburetor. The carburetor is a device for converting 
liquid gasoline, kerosene, etc. into -vapor and mixing it with air in 
proper proportions for complete combustion. ,The simple principle of 
carburetion is shown in the upper diagram opposite page 199. Liquid 
gasoline comes through the supply pipe and enters the float chamber 
through the valve V. By acting on the levers L the float closes the valve 
V when the gasoline reaches a certain level. From the float chamber 
the gasoline is drawn to the spray nozzle O. While the engine is running, 
the downward movement of the pistons in stroke 1 (Fig. 187) sucks 
air violently past the spray nozzle into the region called the venturi, 
where the jet of gasoline is emerging from 0. The spray of fuel thus 
formed intermingles with air in the mixing chamber and passes by the 
throttle to the engine as a highly explosive mixture. 

246. The ignition. The lower diagram opposite page 199 illustrates 
the principle of high-tension magneto ignition which is widely used on 
automobiles. A rolling contact R is mounted on the cam shaft, which 
revolves at half crank-shaft speed and is carried around the interior of 
the stationary fiber ring D. When the switch S is closed and the roller 
R passes across the metal segment G, a current of electricity passes from 
the magneto through the rolling contact to the central shaft C, and from 
there through the iron work of the car to the magneto by way of the 
primary coil of the induction coil. While the roller is in contact with 
the segment G the induction coil produces a shower of sparks between 
the points P of the spark plug, thus igniting the explosive mixture 
in the cylinder of the engine. Since the power stroke of the piston 
occurs but once in two revolutions of the crank shaft, it is necessary 
that the crank shaft revolve twice while the contact revolves but once. 
This, as shown in the diagram, is accomplished by having the crank 
shaft geared to the cam shaft in a velocity ratio of 2 to 1. 



To Engine 




Throttle 
-Mixing chamber 

Venturi 
-Spray nozzle 



Needle valve 



Gasoline supply 



THE C A 11 B u RBTO R 




Insulating 
Fibre Ring 





Magneto 


ro0s"i 


/ . \ 



SmtchAS 



Cam Sraft Gear 
(42 Teeth) 



Lever Jor moving ring D 
-Metal Segment 
Rolling Contact 



^-Crank Shaft Gear 
3 (ZITeeth) 



'rank Handle 



Ax IGNITION SYSTEM 



INDUSTRIAL APPLICATIONS 



199 



The explosive mixture requires a very short but measurable time for 
combustion ; hence the full force of the explosion occurs a short time 
after the spark ignites the mixture. Therefore, at high speed the spark 
should occur a little earlier with reference to the position of the piston 
than at low speed. The spark is advanced or retarded by a spark lever 
L which changes the position of the segment G by pulling around 
slightly the movable fiber ring to which it is attached. 

The diagram applies to a one-cylinder engine. In case the engine has 
four cylinders, three additional segments must be added, as indicated 
by the clear spaces, together 
with three additional induction 
coils and spark plugs.* 

247. The steam turbine. The r 

steam turbine represents the M : W 

latest development of the heat 
engine. In principle it is very 
much like the common wind- 
mill, the chief difference being 
that it is steam instead of air 
which is driven at a high veloc- 
ity against a series of blades 
arranged radially about the cir- 
cumference of the wheel that 
is set into rotation. The steam, 
however, unlike the wind, is FlG 190< The principle of the 

always directed by nozzles at steam turbine 

the angle of greatest efficiency 

against the blades (see Fig. 190). Furthermore, since the energy of the 
steam is far from spent after it has passed through one set of blades 
(such as that shown in Fig. 190), it is in practice always passed through 
a whole series of such sets (Fig. 191), every alternate row of which is 
rigidly attached to the rotating shaft, while the intermediate rows are 
fastened to the immovable outer jacket of the engine and only serve as 
guides to redirect the steam at the most favorable angle against the 
next row of movable blades. In this way the steam is kept alternately 
bounding from fixed to movable blades until its energy is expended. The 
number of rows of blades is often as high as sixteen. 

* The pupil may well consult the more extended treatises for actual details 
of the many different systems of ignition used on automobile and airplane 
engines. 




200 



CHANGE OF STATE 



Turbines are at present coming rapidly into use, chiefly for large- 
power purposes. Their advantages over the reciprocating steam engine 
lie first in the fact that they run with almost no jarring, and therefore 
require much lighter and less expensive foundations, and second in the 
fact that they occupy less than one tenth the floor space of ordinary 
engines of the same capacity. Their efficiency is fully as high as that 

Exhaust 



Revolving 



Stationary 



Revolving 



Nozzle 




FIG. 191. Path of steam in Curtis's turbine 



of the best reciprocating engines. The highest speeds attained by ves- 
sels at sea, namely, about 40 miles per hour, have been made with the 
aid of steam turbines. One of the largest vessels which have thus far 
been launched, the Berengaria, 919 feet long, 98 feet wide, 100 feet high 
(from the keel to the top of her ninth deck), having a total displace- 
ment of 57,000 tons and a speed of 221 knots, is driven by four steam 
turbines having a total horse power of 61,000. One of the immense 
rotors contains 50,000 blades and develops 22,000 horse power. The 
United States Shipping Board, on July 24, 1919, announced plans for 



INDUSTRIAL APPLICATIONS 



201 



building two gigantic ocean liners swifter and larger than any afloat. 
They are to be 1000 feet long and are to have a horse power of 110,000 
and a speed of 30 knots. (See opposite p. 135.) 

248. Manufactured ice. In the great majority of modern ice plants 
the low temperature required for the manufacture of the ice is produced 
by the rapid evaporation of liquid ammonia. At ordinary temperatures 
ammonia is a gas, but it may be liquefied by pressure alone. At 80 F. 
a pressure of 155 pounds per square inch, or about 10 atmospheres, is 
required to produce its liquefaction. Fig. 192 shows the essential parts 
of an ice plant. The compressor, which is usually run by a steam engine, 



Low Pressure 
Gau 



HighPressure 
Gauge 




FIG. 192. Compression system of ice manufacture 



forces the gaseous ammonia under a pressure of 155 pounds into the con- 
denser coils shown on the right, and there liquefies it. The heat of con- 
densation of the ammonia is carried off by the running water which 
constantly circulates about the condenser coils. From the condenser 
the liquid ammonia is allowed to pass very slowly through the regulat- 
ing valve V into the coils of the evaporator, from which the evaporated 
ammonia is pumped out so rapidly that the pressure within the coils 
does not rise above 34 pounds. It will be noted from the figure that 
the same pump which is there labeled the compressor exhausts the 
ammonia from the evaporating coils and compresses it in the condensing 
coils, for the valves are so arranged that the pump acts as an exhaust 
pump on one side and as a compression pump on the other. The rapid 
evaporation of the liquid ammonia under the reduced pressure existing 



202 CHANGE OF STATE 

within the evaporator cools these coils to a temperature of about 5 F. 
The brine with which these coils are surrounded has its temperature 
thus reduced to about 16 or 18 F. This brine is made to circulate 
about the cans containing the water to be frozen. The heat of vapori- 
zation of ammonia at 5 F. is 314 calories. 

Many thousands of feet of circulating saltwater pipe are laid horizon- 
tally and covered with water to be frozen for large indoor skating rinks. 

249. Cold storage. The artificial cooling of factories and cold-storage 
rooms is accomplished in a manner exactly similar to that employed 
in the manufacture of ice. The brine is cooled precisely as described 
above, and is then pumped through coils placed in the rooms to be 
cooled. In some systems carbon dioxide is used instead of ammonia, 
but the principle is in no way altered. Sometimes, too, the brine is 
dispensed with, and the air of the rooms to be cooled is forced by means 
of fans directly over the cold coils containing the evaporating ammonia 
or carbon dioxide. It is in this way that theaters and hotels are cooled. 

QUESTIONS AND PROBLEMS 

1. Why is a gas engine called an internal-combustion engine ? 

2. Why do gasoline engines have flywheels ? Why is a one-cylinder 
engine of the four-cycle type especially in need of a flywheel ? 

3. How does the temperature of the steam within a locomotive boiler 
compare with its temperature at the moment of exhaust ? Explain. 

4. On the drive wheels of locomotives there is a mass of iron op- 
posite the point of attachment of the drive shaft. Why is this necessary ? 

5. Why does not the water in a locomotive boil at 100 C. ? 

6. If liquid oxygen is placed in an open vessel, its temperature will 
not rise above 182 C. Why not? Suggest a way in which its tem- 
perature could be made to rise above 182 C., and a way in which it 
could be made to fall below that temperature. 

7. How many foot pounds of energy are there in 1 Ib. of coal con- 
taining 14,000 B. T. U. per pound ? How many pounds of iron must be 
held at a height of 150 ft. to have as much energy as this pound of coal? 

8. The average locomotive has an efficiency of abdut 6%. What 
horse power does it develop when it is consuming 1 ton of coal per 
hour? (See Problem 7, above.) 

9. What amount of useful work did a gasoline engine working at 
an efficiency of 25% do in using 100 Ib. of gasoline containing 18,000 
B.T.U. per pound? 

10. What pull does a 1000 H.P. locomotive exert when it is running 
at 25 mi. per hour and exerting its full horse power? 



CHAPTER XI 



THE TRANSFERENCE OF HEAT 

CONDUCTION 

250. Conduction in solids. If one end of a short metal bar is 
held in the fire, the other end soon becomes too hot to hold ; but if the 
metal rod is replaced by one of wood or glass, the end away from the 
flame is not appreciably heated. 

This experiment and others like it show that nonmetallic 
substances possess much less ability to conduct heat than 
do metallic substances. But although 
all metals are good conductors as 
compared with nonmetals, they differ 
widely among themselves in their con- 
ducting powers. 

Let copper, iron, and German-silver wires 
50 cm. long and about 3 mm. in diameter be 
twisted together at one end as in Fig. 193, 
and let a Bunsen flame be applied to the 
twisted ends. Let a match be slid slowly 
from the cool end of each wire toward the 

hot end, until the heat from the wire ignites it. The .copper will be 
found to be the best conductor and the German silver the poorest. 

In the following table some common substances are arranged 
in the order of their heat conductivities. The measurements 
have been made by a method not differing in principle from 
that just described. For convenience, silver is taken as 100. 




FIG. 193. Differences in 

the heat conductivities of 

metals 



Silver . . . 


. 100 


Tin . 


. 


15 


Mercury . 


1.5 


Copper . . 
Aluminium . 


74 

. 48 


Iron . 
Lead . 


. . . 


12 

8.5 


Ice .... 

Glass .... 


.21 
.15 


Brass . 


. 27 


German 


silver . 


6.3 


Hard rubber . 


.04 








203 









204 



THE TRANSFERENCE OF HEAT 




FIG. 194. Water a nonconductor 



251. Conduction in liquids and gases. Let a small piece of ice 
be held by means of a glass rod in the bottom of a test tube full of ice 
water. Let the upper part of the 

tube be heated with a Bunsen 
burner as in Fig. 194. The upper 
part of the water may be boiled for 
some time without melting the ice. 
Water is evidently, then, a very poor 
conductor of heat. The same thing 
may be shown more strikingly as 
follows : The bulb of an air ther- 
mometer is placed only a few milli- 
meters beneath the surface of water 
contained in a large funnel arranged 
as in Fig. 195. If now a spoonful 

of ether is poured on the water and set on fire, the index of the air 
thermometer will show scarcely any change, in spite of the fact that 
the air thermometer is a very sensitive indicator of 
changes in temperature. 

Careful measurements of the conductivity 
of water show that it is only about 12 1 QO of 
that of silver. The conductivity of gases is 
even less, not amounting on the average to 
more than ^ that of water. 

252. Conductivity and sensation. It is a 
fact of common observation that on a cold 
day in winter a piece of metal feels much 
colder to the hand than a piece of wood, 
notwithstanding the fact that the tempera- 
ture of the wood must be the same as that 
of the metal. On the other hand, if the same 
two bodies had been lying in the hot sun in 
midsummer, the wood might be handled without discomfort, 
but the metal would be uncomfortably hot. The explanation 
of these phenomena is found in the fact that the iron,|being 
a much better conductor than the wood, removes heaF from 




FIG. 195. Burning 
ether on the water 
does not affect the 
air thermometer 



CONDUCTION 205 

the hand much more rapidly in winter, and imparts heat 
to the hand much more rapidly in summer, than does the 
wood. In general, the better a conductor the hotter it will 
feel to a hand colder than itself, and the colder to a hand 
hotter than itself. Thus, in a cold room oilcloth, a fairly 
good conductor, feels much colder to the touch than a carpet, 
a comparatively poor conductor. For the same reason linen 
clothing feels cooler to the touch in winter than woolen goods. 

253. The role of air in nonconductors. Feathers, fur, felt, 
etc. make very warm coverings, because they are very poor 
conductors of heat and thus prevent the escape of heat from 
the body. Their poor conductivity is due in large measure to 
the fact that they are full of minute spaces containing air, 
and gases are the best nonconductors of heat. It is for this 
reason that freshly fallen snow is such an efficient prqtection 
to vegetation. Farmers always fear for their fruit trees and 
vines when there is a severe cold snap in winter, unless there 
is a coating of snow on the ground to prevent a deep freezing. 

254. The Davy safety lamp. Let a piece of wire gauze be held 
above an open gas jet and a match applied above the gauze. The flame 
will be found to burn above the gauze 

as in Fig. 196, (1), but it will not 
pass through to the lower side. If 
it is ignited below the gauze, the 
flame will not pass through to the 
upper side but will burn as shown 
in Fig. 196, (2). 

The explanation is found in 
, T r> ,T ,i T FIG. 196. A flame will not pass 

the fact that the gauze conducts through wire gauze 

the heat away from the flame so 

rapidly that the gas on the other side is not raised to the 
temperature of ignition. Safety lamps used by miners are 
completely incased in gauze, so that if the mine is full of 
inflammable gases, they are not ignited outside of the gauze 
by the lamp. 




206 



THE TKANSFERENCE OF HEAT 




FIG. 197. A lireless cooker 



QUESTIONS AND PROBLEMS 

1. With the aid of Fig. 197, which represents a fireless cooker, ex- 
plain the principle on which fireless, cooking is done. 

2. Why do firemen wear flannel shirts in summer to keep cool and 
in winter to keep warm ? 

3. If a package of ice cream is 
put inside a paper bag, it will not 
melt so fast on a hot day. Explain. 

4. If the ice in a refrigerator is 
wrapped up in blankets, what is the 
effect on the ice ? on the refrigerator ? 

5. If a piece of paper is wrapped 
tightly around a metal rod and held 
for an instant in a Bunsen flame, it 
will not be scorched. If held in a 
flame when wrapped around a wooden 
rod, it will be scorched at once. 
Explain. 

6. If one touches the pan contain- 
ing a loaf of bread in a hot oven, he receives a much more severe burn 
than if he touches the bread itself, although the two are at the same 
temperature. Explain. 

7. Why are plants often covered with paper on a night when frost 
is expected? 

8. Why will a moistened finger or the tongue freeze instantly to a 
piece of iron on a cold winter's day, but not to a piece of wood ? 

9. Does clothing ever afford us heat in winter? How, then, does it 
keep us warm ? 

10. Why is the outer pail of an ice-cream freezer made of thick wood 
and the inner can of thin metal ? 

CONVECTION 

255. Convection in liquids. Although the conducting power 
of liquids is so small, as was shown in the experiment of 251, 
they are yet able, under certain circumstances, to transmit 
heat much more effectively than solids. Thus, if the ice in the 
experiment of Fig. 194 had been placed at the top and the 
flame at the bottom, the ice would have been melted very 
quickly. This shows that heat is transferred very much 



CONVECTION 



207 



more readily from the bottom of the tube toward the top 
than from the top toward the bottom. The mechanism of 
this heat transference will be evident from the following 
experiment : 

Let a round-bottomed flask (Fig. 198) be half filled with water and 
a few crystals of magenta dropped into it. Then let the bottom of the 
flask be heated with a Bunsen burner. The magenta 
will reveal the fact that the heat sets up currents 
the direction of which is upward in the region im- 
mediately above the flame but downward at the sides 
of the vessel. It will not be long before the whole 
of the water is uniformly colored. This shows how 
thorough is the mixing accomplished by the heating. 

The explanation of the phenomenon is as 
follows: The water nearest the flame be- 
came heated and expanded. It was thus ren- 
dered less dense than the surrounding water, 
and was accordingly forced to the top by 
the pressure transmitted from the colder 
and therefore denser water at the sides 
which then came in to take its place. 

It is obvious that this method of heat transfer' is applicable 
only to fluids. The essential difference between it and con- 
duction is that the heat is not transferred from molecule to 
molecule throughout the whole mass, but is rather transferred 
by the bodily movement of comparatively large masses of 
the heated liquid from one point to another. This method 
of heat transference is known as convection. 

256. Winds and ocean currents. Winds are convection cur- 
rents in the atmosphere caused by unequal heating of the 
earth by the sun. Let us consider, for example, the land and 
sea breezes so familiar to all dwellers near the coasts of large 
bodies of water. During the daytime the land is heated more 
rapidly than the sea, because the specific heat of water is 
much greater than that of earth. Hence the hot air over the 




FIG. 198. Convec- 
tion currents 



208 THE TRANSFERENCE OF HEAT 

land expands and is forced up by the colder and denser air 
over the sea which moves in to take its place. This con- 
stitutes the sea breeze, which blows during the daytime, 
usually reaching its maximum strength in the late afternoon. 
At night the earth cools more rapidly than the sea and hence 
the direction of the wind is reversed. The effect of these 
breezes is seldom felt more than twenty-five miles from shore. 
Ocean currents are caused partly by the unequal heating 
of the sea and partly by the direction of the prevailing 
winds. In general, both winds and currents are so modified 
by the configuration of the continents that it is only over 
broad expanses of the ocean that the direction of either can 
be predicted from simple considerations. 

RADIATION 

257. A third method of heat transference. There are certain 
phenomena in connection with the transfer of heat for which 
conduction and convection are wholly unable to account, 
For example, if one sits in front of a hot grate fire, the 
heat which he feels cannot come from the fire by convection, 
because the Currents of air are moving toward the fire rather 
than away from it. It cannot be due to conduction, because 
the conductivity of ah- is extremely small and the colder 
currents of air moving toward the fire would more than 
neutralize any transfer outward due to conduction. There 
must therefore be some way in which heat travels across the 
intervening space other than by conduction or convection. 

It is still more evident that there must be a third method 
of heat transfer when we consider the heat which comes to 
us from the sun. Conduction and convection take place only 
through the agency of matter; but we know that the space 
between the earth and the sun is not filled with ordinary 
matter, or else the earth would be retarded . in its motion 
through space. Radiation is the name given to this third 



RADIATION 209 

method by which heat travels from one place to another, 
and which is illustrated in the passing of heat from a grate 
fire to a body in front of it, or from the sun to the earth. 

258. The nature of radiation. The nature of radiation will 
be discussed more fully in Chapter XXI. It will be sufficient 
here to call attention to the following differences between 
conduction, convection, and radiation. 

First, while conduction and convection are comparatively 
slow processes, the transfer of heat by radiation takes place 
with the enormous speed with which light travels, namely 
186,000 miles per second. That the two speeds are the same 
is evident from the fact that at the time of an eclipse of the 
sun the shutting off of heat from the earth is observed to take 
place at the same time as the shutting off of light. 

Second, radiant heat travels in straight lines, while conducted 
or convected heat may follow the most circuitous routes. The 
proof of this statement is found in the familiar fact that ra- 
diation may be cut off by means of a screen placed directly 
between a source and the body to be protected. 

Third, radiant heat may pass through a medium without 
heating it. This is shown by the fact that the upper regions 
of the atmosphere are very cold, even in the hottest days in 
summer, or that a hothouse may be much warmer than the 
glass through which the sun's rays enter it. 

259. The Dewar flask and the thermos bottle. For the 
retention of extremely cold liquids, such, for example, as 
liquefied air, whose boiling point is -190 C. (=- 310 F.), 
Dewar invented a double-walled vessel. The space between 
the walls is a. vacuum, and the inner surface of the outer 
vessel and the outer surface of the inner vessel are silvered. 
There are three ways in which heat may pass inward through 
the double wall conduction, convection, and radiation. The 
vacuum prevents almost entirely the first two, while the silver- 
ing eliminates passage of heat by radiation. The well-known 



210 



THE TRANSFERENCE OF HEAT 



glass part of the thermos bottle (Fig. 199) is simply a 
cylindrical Dewar flask for keeping liquids either hot or 
cold, since it is as difficult for heat to pass outward through 
the walls as to pass inward. The glass flask is provided with 
a cork stopper, and a strong outside metal 
case for its protection. Hot liquids, as well as /) 

those that are cold, may be kept for several 
hours in a thermos bottle with only a few 
degrees change in temperature. 

THE HEATING AND VENTILATING OF 
BUILDINGS 



260. The principle of ventilation. The heating 
and ventilating of buildings are accomplished 
chiefly through the agency of convection. 



FIG. 199. The in- 
ner glass flask of 
a thermos bottle 



To illustrate the principle of ventilation let a candle be lighted and 
placed in a vessel containing a layer of water (Fig. 200). When a lamp 
chimney is placed over the candle so that the 
bottom of the chimney is under the water, the 
flame will slowly die down and will finally 
be extinguished. This is because the oxygen, 
which is essential to combustion, is gradually used up 
and no fresh supply is possible with the arrangement 
described. If the chimney is raised even a very little 
above the water, the dying flame will at once brighten. 
Why? If a metal or cardboard. partition is inserted in 
the chimney, as in Fig. 200, the flame will burn con- 
tinuously, even when the bottom of the chimney is 
under water. The reason will be clear if a piece of 
burning touch paper (blotting paper soaked in a solu- 
tion of potassium nitrate and dried) is held over the 
chimney. The smoke will show the direction of the 
air currents. If the chimney is a large one, in order 
that the first part of the above experiment may succeed, 
it may be necessary to use two candles ; for too small 
a heated area permits the formation of downward currents at the sides. 




FIG. 200. Con- 
vection currents 
in air 



HEATING AND VENTILATING 



211 



261. Ventilation of houses. In order to secure satisfactory 
ventilation it is estimated that a room should be supplied with 

2000 cubic feet of fresh air per hour for each occupant 
(a gas burner is equivalent in oxygen consumption to 

four persons). A 
current of air mov- 
ing with a speed 
great enough to be 
just perceptible has 
a velocity of about 
3 feet per second. 
Hence the area of 
opening required for 
each person when 
fresh air is entering 
at this speed is 
about 25 or 30 
square inches. The 
manner of supply- 
ing this requisite 

amount of fresh air in dwelling houses depends upon the 

particular method of heating employed. 
If a house is heated by stoves or fireplaces, 

no special provision for ventilation is needed. 

The foul air is drawn up the chimney with 

the smoke, and the fresh air which replaces 

it finds entrance through cracks about the 

doors and windows and through the walls. 

262. Hot-air heating. In houses heated by hot-air 
furnaces an air duct ought always to be supplied for 
the entrance of fresh cold air, in the manner shown 
in Fig. 201 (see " cold-air inlet "). This cold air from 

out of doors is heated by passing in a circuitous way, FIG. 202. Princi- 
as shown by the arrows, over the outer jacket of iron p] e o f hot-water 
which covers the fire box. It is then delivered to the heating 




FIG. 201. Ho^-air heating 




212 



THE TRANSFERENCE OF HEAT 



rooms. Here a part of it escapes through windows and doors, and the 
rest returns through the cold-air register to be reheated, after being 
mixed with a fresh supply from out of doors. 

When the fire is first started, in order to gain a strong draft the 
damper C is opened so that the smoke 
may pass directly up the chimney. 
After the fire is under way the damper 
C is closed so that the smoke and hot 



Cold water 




Copper 

heating 

coils 




FIG. 203. A gas heating coil 



FIG. 204. Hot-water heater 



gases from the furnace must pass, as indicated by the dotted arrows, 
over a roundabout path, in the course of which they give up the major 
part of their heat to the steel walls of the jacket, which in turn pass 
it on to the air which is on its way to the- living rooms. 

263. Hot-water heating. To illustrate the principle of hot-water 
heating let the arrangement shown in Fig. 202 be set up, the upper 
vessel being filled with colored water, and then let a flame be applied 
to the lower vessel. The colored water will show that the current moves 
in the direction of the arrows. 



HEATING AND VENTILATING 213 

This same principle is involved in the gas heating coil used in 
connection with the kitchen boiler (Fig. 203). Heat from the flame 
passes through the copper coil to the water, and convection begins as 
indicated by the arrows. When hot water is drawn from the top of the 
boiler, cold water enters near the bottom so as not to mingle with the 
hot water that is being used. The principle is still further illustrated 
by the cooling systems used for keeping automobile engines from 
becoming overheated. Heat passes from the engine into the water, 
which loses heat in circulating through the coils of the radiator. 

The actual arrangement of boiler and radiators in one system of hot- 
water heating is shown in Fig. 204. The water heated in the furnace 
rises directly through the pipe A to a radiator R, and returns again to 
the bottom of the furnace through the pipes B and D. The circulation 
is maintained because the column of water in A is hotter and therefore 
lighter than the water in the return pipe B. 

By eliminating the expansion tank and partly filling the boiler with 
water the system could be converted into a steam-heating plant. 

QUESTIONS AND PROBLEMS 

1. If we attempt to start a fire in the kitchen range when the chimney 
is cold and damp, the range " smokes." Explain. 

2. Why is a hollow wall filled with sawdust a better nonconductor 
of heat than the same wall filled with air alone ? 

3. In a system of hot-water heating why does the return pipe always 
connect at the bottom of the boiler, while the outgoing pipe connects 
with the top ? 

4. Which is thermally more efficient, a cook stove or a grate? Why? 

5. When a room is heated by a fireplace, which of the three methods 
of heat transference plays the most important role ? 

6. Why do you blow on your hands to, warm them in winter and 
fan yourself for coolness in summer? 

7. If you open a door between a warm and a cold room, in what 
direction will a candle flame be blown which is placed at the top of the 
door? Explain. 

8. Why is felt a better conductor of heat when it is very firmly 
packed than when loosely packed? 

9. If 2 metric tons of coal are burned per month in your house, and 
if your furnace allows one third of the heat to go up the chimney, 
how many calories remain to be used per day ? (Take 1 g. as yielding 
6000 calories. A metric ton = 1000 kg.) 



CHAPTER XII 

MAGNETISM* 
GENERAL PROPERTIES OF MAGNETS 

264. Magnets. It has been known for many centuries that 
some specimens of the ore known as magnetite (Fe 3 O 4 ) have 
the property of attracting small bits of iron and steel. This 
ore probably received its name from the fact that it was 
first observed in the province of Magnesia, in Thessaly. 
Pieces of this ore which exhibit this attractive property are 
known as natural magnets. 

It was also known to the ancients that artificial magnets 
may be made by stroking pieces of steel with natural magnets, 
but it was not until about the twelfth century that the dis- 
covery was made that ta suspended magnet tvill assume a north- 
and-south position. Because of this latter property natural 
magnets became known as lodestones (leading stones), and 
magnets, either artificial or natural, began to be used for deter- 
mining directions. The first mention of the use of the compass 
in Europe is in 1190. It is thought to have been introduced 
from China. (See opposite p. 223 for the gyrocompass.) 

Magnets are now made either by stroking bars of steel in 
one direction with a magnet, or by passing electric currents 
about the bars in a manner to be described later. The form 
shown in Fig. 205 is called a bar magnet, that shown in 
Eig. 206 a horseshoe magnet. The latter form is the more 
common, and is the better form for lifting. 

*Tliis chapter should be either accompanied or preceded by laboratory 
experiments on magnetic fields and on the molecular nature ef magnetism. 
See, for example, Experiments 25 and 26 of the authors' Manual. 

214 



GENERAL PROPERTIES OF MAGNETS 



215 




FIG. 206. A horseshoe 
magnet 



If a magnet is dipped into iron filings, the filings will be 
seen to cling in tufts near the ends. but scarcely at all near 
the middle (Fig. 207). These places 
near the ends of a magnet at which its 
strength seems to be concentrated are 
called the poles of the magnet. The end of a freely swing- 
ing magnet which points to the north is designated as the 
north-seeking pole, or simply the north 
pole (jV) ; and the other end as the 
south-seeking pole, or the south pole ($) 
The direction in ivhich a compass needle 
points is called the magnetic meridian. 

265. The laws of magnetic attraction and repulsion. In the 
experiment with the iron filings no particular difference was 
observed between the action of the 
two poles. That there is a difference, 
however, may be shown by experi- 
menting with two magnets, either 
of which may be suspended (see 

Fig. 208). If two N poles are brought near one another, they 
are found to repel each other. The S poles likewise are found 
to repel each other. But the N pole of 
one magnet is found to be attracted by the 
S pole of another. The results of these 
experiments may be summarized in a 
general law: Magnet poles of like kind repel 
each other, while poles of unlike kind attract. 

The force which any two poles exert 
upon each other in air is equal to the 
product of the pole strengths divided by 

the square of the distance between them. FlG - 208 ' Ma S netic at - 
, . 7.-I/.T 17.7 tractions and repulsions 

A unit pole is defined as a pole which, 

when placed at a distance of 1 centimeter from an exactly 
similar pole, in air, repels it with a force of 1 dyne. 



FIG. 207. Iron filings cling- 
ing to a bar magnet 




216 



MAGNETISM 




266. Magnetic materials. Iron and steel are the only 
substances which exhibit magnetic properties to any marked 
degree. Nickel and cobalt are also attracted appreciably by 
strong magnets. Bismuth, antimony, and a number of other 
substances are actually repelled instead of attracted, but the 
effect is very small. It has recently been found possible to 
make quite strongly magnetic alloys out of certain nonmag- 
netic materials. For example, a mixture of 65% copper, 27% 
manganese, and 8% aluminium is quite strongly magnetic. 
These are called Heusler alloys. For practical purposes, how- 
ever, iron and steel may be considered as 

the only magnetic materials. 

267. Magnetic induction. If a small un- 
magnetized nail is suspended from one end 
of a bar magnet, it is found that a second 
nail may be suspended from this first nail, 
which itself acts like a magnet, a third from 
the second, etc., as shown in Fig. 209. But 
if the bar magnet is carefully pulled away 

from the first nail, the others will instantly fall away from 
each other, thus showing that the nails were strong magnets 
only so long as they were in contact with the 
bar magnet. Any piece of soft iron may 
be thus magnetized temporarily by holding 
it in contact with a permanent magnet. In- 
deed, it is not necessary that there be actual 
contact, for if a nail is simply brought near 
to the permanent magnet it is found to 
become a magnet. This may be proved by 
presenting some iron filings to one end of 
a nail held near a magnet in the manner 
shown in Fig. 210. Even inserting a plate of glass, or of 
copper, or of any other material except iron between S and N 
will not change appreciably the number of filings which cling 



FIG. 209. Magnetism 
induced by contact 



FIG. 210. Magnet- 
ism induced with- 
out contact 



GENERAL PROPERTIES OF MAGNETS 217 

to the end of $', a fact which shows that nonmagnetic mate- 
rials are transparent to magnetic forces. But as soon as the 
permanent magnet is removed, most of the filings will fall. 
Magnetism produced by the mere presence of adjacent magnets, 
unth or without contact, is called induced magnetism. If the 
induced magnetism of the nail in Fig. 210 is tested with a 
compass needle, it is found that the remote induced pole is 
of the same kind as the inducing pole, while the near pole 
is of unlike kind. This is the general law of magnetic 
induction. 

Magnetic induction explains the fact that a magnet attracts 
an unmagnetized piece of iron, for it first magnetizes it by 
induction, so that the near pole is unlike the inducing pole, 
and the remote pole like the inducing pole ; and then, since 
the two unlike poles are closer together than the like poles, 
the attraction overbalances the repulsion and the iron is 
drawn toward the magnet. Magnetic induction also explains 
the formation of the tufts of iron filings shown in Fig. 207, 
each little filing becoming a temporary magnet such that 
the end which points toward the inducing pole is unlike 
this pole, and the end which points away from it is like this 
pole. The bushlike appearance is due to the repulsive action 
which the outside free poles exert upon each other. 

268. Retentivity and permeability. A piece of soft iron 
will very easily become a strong temporary magnet, but when 
removed from the influence of the magnet it loses practically 
all of its magnetism. On the other hand, a piece of steel 
will not be so strongly magnetized as the soft iron, but it 
will retain a much larger fraction of its magnetism after it 
is removed from the influence of the permanent magnet. 
This quality of resisting either magnetization or demagnetiza- 
tion is called retentivity. Thus steel has a much greater reten- 
tivity than wrought iron, and, in general, the harder the steel 
the greater its retentivity. 



218 



MAGNETISM 




A substance which has the property of becoming strongly 
magnetic under the influence of a permanent magnet, whether 
it has a high retentivity or not, is said to possess permeability in 
large degree. Thus iron is much more permeable than nickel. 

269. Magnetic lines of force. If we could separate the N 
and S poles of a small magnet so as to get an independent 
N pole, and were to place this 
N pole near the N pole of a bar 
magnet, it would move over to 
the S pole along some curved 
path similar to that shown in 

Fig. 211. The reason it would FlG " 21 ^ A line of force set up 

by the magnet AB 
move in a curved path is that it 

would be simultaneously repelled by the N pole of the bar 
magnet and attracted by its S pole, and the relative strengths 
of these two forces would continually change as the relative 
distances of the moving pole from these two poles changed. 

To verify this conclusion let a strongly magnetized sewing needle be 
floated in a small cork in a shallow dish of water, and let a bar or 
horseshoe magnet be placed just 
above or just beneath the dish (see 
Fig. 212). The cork and needle will 
then move as would an independent 
pole, since the remote pole of the 
needle is so much farther from the 
magnet than the near pole that its 
influence on the motion is very small. 
The cork will actually be found to move in a curved path from N to S. 

Any path which an independent N pole would take in 
going from N to S is called a line of force. The simplest way 
of finding the direction of this path at any point near a 
magnet is to hold a short compass needle at the point con- 
sidered. The needle sets itself along the line in which its 
poles would move if independent, that is, along the line of 
force which passes through the given point (see C, Fig. 211). 







FIG. 212. Showing direction of 

motion of an isolated pole near 

a magnet 



GENERAL PROPERTIES OF MAGNETS 



219 



270. Fields of force. The region about a magnet in which 
its magnetic forces can be detected is called its field of force. 
The easiest way of gaining an idea of the way in which the 




\ ! / /V""^,\ UN \ '. ' 
/ // ,.-* , N \\ \ \ \ \ i / , 

x^^ \\ (( 'iff' ''" ~^ N \\V< : \$M& 




FIG. 213. Arrangement of iron 
filings about a bar magnet 



FIG. 214. Ideal diagram of field 
of a bar magnet 



lines of force are arranged in the magnetic field about any 
magnet is to sift iron filings upon a piece of paper placed 
immediately over the magnet. Each little filing becomes a 
temporary magnet by induction, and therefore, like the com- 
pass needle, sets itself in the direction of the line of force at 
the point where it is. Fig. 213 
shows how the filings arrange 
themselves about a bar magnet. 
Fig. 214 is the corresponding 
ideal diagram showing the lines 
of force emerging from the JV" 
pole and passing about in curved 
paths to the S pole. It is custom- 
ary to imagine these lines as re- 
turning through the magnet from 
S to N in the manner shown, so 
that each line is thought of as a closed curve. This conven- 
tion was introduced by Faraday, and has been found of 
great assistance in correlating the facts of magnetism. 

A magnetic field of unit strength is defined as a field in which 
a unit magnet pole experiences 1 dyne of force. It is customary 




FIG. 215. The strength of a mag- 
netic field is represented by the 
number of lines of force per 
square centimeter 



220 MAGNETISM 

to represent graphically such a field by drawing one line per 
square centimeter through a surface such as ABCD (Fig. 215) 
taken at right angles to the lines of force. If a unit N pole be- 
tween N and S (Fig. 215) were pushed toward S with a force 
of 1000 dynes, the strength of the field would be 1000 units and 
it would be represented by 1000 lines per square centimeter. 

271. Molecular nature of magnetism. If a small test tube 
full of iron filings be stroked from end to end with a magnet, 
it will be found to have become itself a magnet ; but it will 
lose its magnetism as soon as the filings are shaken up. If a 
magnetized knitting needle is heated red-hot, it will be found 
to have lost its magnetism completely. Again, if such a needle 
is jarred, or hammered, or twisted, the strength of its poles, 
as measured by their ability to pick up tacks or iron filings, 
will be found to be greatly diminished. 

These facts point to the conclusion that magnetism has 
something to do with the arrangement ~of the molecules, since 
causes which violently dis- 
turb the molecules of a mag- 



net weaken its magnetism. Jf Jja ff 



Again, if a magnetized needle & I % $ 4 

is broken, each part will be FIG. 210. Effect of breaking a magnet 

found to be a complete mag- 

net; that is, two new poles will appear at the point of breaking. 
a new N pole on the part which has the original S pole, and 
a new S pole on the part which has the original N pole. The 
subdivision may be continued indefinitely, but always with 
the same result, as indicated in Fig. 216. This suggests that 
the molecules of a magnetized bar may themselves be little 
magnets arranged in rows with their opposite poles in contact. 
If an unmagnetized piece of hard steel is pounded vigorously 
while it lies between the poles of a magnet, or if it is heated 
to redness and then allowed to cool in this position, it will 
be found to have become magnetized. This suggests that the 




GENEEAL PKOPERTIES OF MAGNETS 221 

molecules of the steel are magnets even when the bar as a 
whole is not magnetized, and that magnetization may consist 
in causing them to arrange themselves in rows, end to end, 
just as the magnetization of the tube of iron filings mentioned 
above was due to a special arrangement of the filings. 

272. Theory of magnetism. In an unmagnetized bar of iron 
or steel it is probable, then, that the molecules themselves are 
tiny magnets which are 
arranged either haphaz- 
ard or in little closed 
groups or chains, as in 
Fig. 217, SO that, 011 the FlG - 21L Arrangement of molecules in an 

unmagnetized iron bar 
whole, opposite poles 

neutralize each other throughout the bar. But when the bar 
is brought near a magnet, the molecules are swung around 
by the outside magnetic force into an arrangement somewhat 
like the one shown in 
Fig. 218, where the op- 
posite poles completely 
neutralize each other 
only in the middle of FIG 21g Arrangement of molec ules in a 
the bar. According to magnetized iron bar 

this view, heating and 

jarring weaken the magnet because they tend to shake the 
molecules out of alignment. On the other hand, heating and 
jarring facilitate magnetization when the bar is between the 
poles of a magnet because they assist the magnetizing force 
in breaking up the molecular groups and chains and getting 
the molecules into alignment. Soft iron has higher permea- 
bility than hard steel, because the molecules of the former 
substance are much easier to swing into alignment than those 
of the latter substance. Steel has a very much greater re- 
tentivity than soft iron, because its molecules are not so easily 
moved out of position when once they have been aligned. 



\ 



222 MAUNETISM 

273. Saturation. Strong evidence for the correctness of 
the above view is found in the fact that a piece of iron or 
steel cannot be magnet- 
ized beyond a certain 
limit, no matter how 
strong the magnetizing 



cm CM cm cm cm cm CM CM cm cm cm am cm annum ami an 

as an am an am am cm am cm an cm nm cm cannon am 

aicmizmcMcnaBCMcraca 

cm en an ami OB an cm cm ami a" rm OB axemen am cm I 



force is. This limit ,, 

FIG. 219. Arrangement of molecules m a 

probably corresponds to saturated magnet 

the condition in which 

the axes of all the molecules are brought into parallelism, 

as in Fig. 219. The magnet is then said to be saturated, 

since it is as strong as it is possible to make it. 

TERRESTRIAL MAGNETISM 

274. The earth's magnetism. The fact that a compass needle 
always points north and south, or approximately so, indicates 
that the earth itself is a great magnet having an 8 pole near 
the geographic north pole and an N pole near the geographic 
south pole ; for the magnetic pole of the earth which is near 
the geographic north pole must of course be unlike the pole 
of a suspended magnet which points toward it, and the pole 
of the suspended magnet which points toward the north is the 
one which, by convention, it has been decided to call the JVpole. 
The magnetic pole of the earth which is near the north geo- 
graphic pole was found in 1831 by Sir James Ross in 
Boothia Felix, Canada, latitude 70 30' N., longitude 95 W. 
It was located again in 190.5 by Captain Amundsen (the dis- 
coverer of the geographic south pole, 1912) at a point a 
little farther west. Its approximate location is 70 5' N. and 
96 46' W. It is probable that it shifts its position slowly. 

275. Declination. The earliest users of the compass were 
aware that it did not point exactly north; but it was Columbus 
who, on his first voyage to America, made the discovery, much 
to the alarm of his sailors, that the direction of the compass 




WILLIAM GILBERT (1540-1603) 

English physician and physicist; first Englishman to appreciate 
fully the value of experimental observations; first to discover 
through careful experimentation that the compass points to the 
north not because of some influence of the stars, but because the 
earth is itself a great magnet ; first to use the word " electricity " ; 
first to discover that electrification can be produced by rub- 
bing a great many different kinds of substances ; author of the 
epoch-making book entitled "De Magnete, etc.," published in 
London in 1600 




TEKKESTRIAL MAGNETISM 223 

needle changes as one moves about over the earth's surface. 
The chief reason for this variation is found in the fact that the 
magnetic poles do not coincide with the geographic poles ; 
but there are also other causes, such as the existence of large 
deposits of iron ore, which produce local effects upon the 
needle. The number of degrees by which at a given point on 
the earth the needle varies from a true north-and-south line is 
called its declination at that point. Lines drawn over the earth 
through points of equal declination are called isogonic lines. 

276. The dipping needle. Let an umnagnetized knitting needle a 
(Fig. 220) be thrust through a cork, and let a second needle b be passed 
through the cork at right angles to a and as 

close to it as possible. Let a pin c be adjusted 

until the system is in neutral equilibrium 

about b as an axis, when a is pointing east and 

west. Then let a be carefully magnetized by 

stroking one end of it, from the middle out, FJG 22Q Arrangement 

with the N pole of a strong magnet, and the for s } low i n g dip 

other end, from the middle out, with the S 

pole of the same magnet. If now the needle is replaced on its supports 

and turned into a north-and-south position, its N pole will be found 

to dip so as to cause the needle to make an angle of from 60 to 70 

with the horizontal. 

The experiment shows that in this latitude the earth's mag- 
netic lines make a large angle with the horizontal. This angle 
between the earth's surface and the direction of the magnetic 
lines is called the dip, or inclination, of the needle. At Wash- 
ington it is 71 5' and at Chicago 72 50V At the magnetic 
pole it is of course 90, and at the so-called magnetic equator, 
which is an irregular curved line near the geographic equator, 
the dip is 0. 

277. The earth's inductive action. That the earth acts like a 
great magnet may be very strikingly shown in the following way : 

Hold a steel rod (for example, a tripod rod) parallel to the earth's 
magnetic lines (the north end slanting down at an angle of about 70 
or 75) and strike it a few sharp blows with a hammer. The rod will 



224 MAGNETISM 

be found to have become a magnet with its upper end an S pole, like 
the north pole of the earth, and its lower end an N pole. If the rod is 
reversed and tapped again with the hammer, its magnetism will be re- 
versed. If held in an east-and-west position and tapped, it will become 
demagnetized, as will be shown by the fact that either end of it will 
attract either end of a compass needle. In some respects a soft-iron rod 
is more satisfactory for this experiment than a steel rod, on account of 
the smaller retentivity. 

QUESTIONS AND PROBLEMS 

1. Make a diagram to show the general shape of the lines of force 
between unlike poles of two bar magnets ; between like poles. 

2. Devise an experiment which will show that a piece of iron attracts 
a magnet just as truly as the magnet attracts the iron. 

3. In testing a needle with a magnet to see if the needle is magnet 
ized why must you get repulsion before you can be sure it is magnetized? 

4. A nail lies with its head near the N pole of a bar magnet. 
Diagram the nail and magnet, and draw from the N pole through the 
nail a closed curve to represent one line of force. 

5. Explain, on the basis of induced magnetization, the process by 
which a magnet attracts a piece of soft iron. 

6. Do the facts of induction suggest to you any reason why a horse- 
shoe magnet retains its magnetism better when a bar of soft iron (a 
keeper, or armature) is placed across its poles than when it is not so 
treated? (See Fig. 218.) 

7. Why should the needle used in the experiment of 276 be placed 
east and west, when adjusting for neutral equilibrium, before it is 
magnetized ? 

8. How would an ordinary compass needle act if placed over one of 
the earth's magnetic poles ? How would a dipping needle act at these 
points ? 

9. Why are the tops of steam radiators magnetic poles, as proved 
by their invariable repulsion of the 5 pole of a compass ? 

10. Give two proofs that the earth is a magnet. 

11. A magnetic pole of 80 units' strength is 20 cm. distant from a 
similar pole of 30 units' strength. Find the force between them. 



CHAPTER XIII 

STATIC ELECTRICITY 

GENERAL FACTS OF ELECTRIFICATION 

278. Electrification by friction. If a piece of hard rubber or 
a stick of sealing wax is rubbed with flannel or cat's fur and 
then brought near some dry pith balls, bits of paper, or other 
light bodies, these bodies are found to jump toward the rod. 
This sort of attraction, so familiar to us from the behavior of 
our hair in winter when we comb it with a rubber comb, was 
observed as early as 600 B. c., when Thales of Greece com- 
mented upon the fact that rubbed amber draws to itself threads 
and other light objects. It was not, however, until A. D. 1600 
that Dr. William Gilbert, physician to Queen Elizabeth, and 
sometimes called the father of the modern science of electricity 
and magnetism, discovered that the effect could be produced 
by rubbing together a great variety of other substances besides 
amber and silk, such, for example, as glass and silk, sealing 
wax and flannel, hard rubber and cat's fur, etc. 

Gilbert (see opposite p. 222) named the effect which was 
produced upon these various substances by friction electrifi- 
cation, after the Greek name electron, meaning " amber." Thus, 
a body ivhich, like rubbed amber, has been endowed with the 
property of attracting light bodies is said to have been electrified, 
or to have been given a charge of electricity. In this statement 
nothing whatever is said about the nature of electricity. We 
simply define an electrically charged body as one which has 
been put into the condition in which it acts toward light 
bodies like the rubbed amber or the rubbed sealing wax. To 

225 




226 STATIC ELECTRICITY 

this day we do not know with certainty what the nature of 
electricity is, but we are fairly familiar with the laws which 
govern its action. The following sections deal with these laws. 

279. Positive and negative electricity. Let a pith ball suspended 
by a silk thread, as in Fig. 221, be touched to a glass rod which has been 
rubbed with silk ; the ball will thus be put into the condition in which 
it is strongly repelled by this rod. 
Next let a stick of sealing wax or an 
ebonite rod which has been rubbed 
with cat's fur or flannel be brought 
near the charged ball. It will be 
found that it is not repelled but, on 
the contrary, is very strongly at- 
tracted. Similarly, if the pith ball 
has touched the sealing wax so that 
it is repelled by it, it is found to be FIG. 221. Pith-ball electroscope 
strongly attracted by the glass rod. 

Again, two pith balls both of which have been in contact with the 
glass rod are found to repel each other, while pith balls one of which 
has been in contact with the glass rod and the other with the sealing 
wax attract each other. 

Evidently, then, the electrifications which are imparted to 
glass by rubbing it with silk and to sealing wax by rubbing 
it with flannel are opposite in the sense that an electrified 
body that is attracted by one is repelled by the other. We 
say, therefore, that there are two kinds of electrification, and 
we arbitrarily call one positive and the other negative. Thus, a 
positively electrified body is one which acts with respect to other 
electrified bodies like a glass rod which has been rubbed with 
silk, and a negatively electrified body is one which acts like a 
piece of sealing wax which has been rubbed with flannel. These 
facts and definitions may be stated in the following general 
law: Electrical charges of like kind repel each other, while 
charges of unlike kind attract each other. The forces of attrac- 
tion or repulsion are found, like those of gravitation and 
magnetism, to decrease as the square of the distance increases. 



GENERAL FACTS OF ELECTRIFICATION 227 




280. Measurement of electrical quantities. The fact of attraction and 
repulsion is taken as the basis for the definition and measurement of 
so-called quantities of electricity. Thus, a small charged body is said to 
contain 1 unit of electricity when it will repel an exactly equal and 
similar charge placed 1 centimeter away with a force of 1 dyne. The 
number of units of electricity on any charged body is then measured 
by the force which it exerts upon a unit charge placed at a given distance 
from it; for example, a charge w r hich at a distance of 10 centimeters 
repels a unit charge with a force of 1 dyne contains 100 units of elec- 
tricity, for this means that at a distance of 1 centimeter it would repel 
the unit charge w r ith a force of 100 dynes (see 279). 

281. Conductors and nonconductors. Let an electroscope E 

(Fig. 222), consisting of a pair of gold leaves a and ft, suspended from 

an insulated metal rod r and protected from air currents by a case /, 

be connected with the metal ball 

B by means of a wire. Now let 

an ebonite rod be electrified and 

rubbed over B. The immediate 

divergence of the gold leaves will 

show that a portion of the electric 

charge placed upon B has been 

carried by the wire to the gold 

leaves, where it causes them to 

diverge in accordance with the 

law that bodies charged with the 

same kind of electricity repel FIG. 222. Illustrating conduction 

each other. 

Let the experiment be repeated when E and B are connected with a 
thread of silk or a long rod of wood instead of the metal wire. No 
divergence of the leaves will be observed. If a moistened thread con- 
nects E and B, the leaves will be seen to diverge slowly when the ball B 
is charged, showing that a charge is carried slowly by the moist thread. 

These experiments .make it clear that while electric charges 
pass with perfect readiness from one point to another in a wire, 
they are quite unable to pass along dry silk or wood, and pass 
with difficulty along moist silk. We are therefore accustomed 
to divide substances into two classes, conductors and noncon- 
ductors, or insulators, according to their ability to transmit 



A 



228 



STATIC ELECTRICITY 



electrical charges from point to point. Thus, metals and 
solutions of salts and acids in water are all conductors of 
electricity, while glass, porcelain, rubber, mica, shellac, wood, 
silk, vaseline, turpentine, paraffin, and oils are insulators. No 
hard-aid-fast line, however, can be drawn between conduc- 
tors and nonconductors, since all so-called insulators conduct 
to some slight extent, while the so-called conductors differ 
greatly in the facility with which they transmit charges. 

The fact of conduction brings out sharply one of the most 
essential distinctions between electricity and magnetism. Mag- 
netic poles exist only in iron and steel, while electrical charges 
may be communicated to any body whatever, provided it is 
insulated. These charges pass over conductors and can be 
transferred by contact from one 
body to any other, while mag- 
netic poles remain fixed in posi- 
tion and are wholly uninfluenced 
by contact with other bodies, 
unless these bodies themselves 
are magnets. 




FIG. 223. Illustrating induction 



282. Electrostatic induction. 

Let the ebonite rod be electrified by 

friction and slowly brought toward 

the knob of the gold-leaf electroscope (Fig. 223). The leaves will be 

seen to diverge, even though the rod does not approach to within a foot 

of the electroscope. 

This makes it clear that the mere influence which an electric 
eharge exerts upon a conductor placed in its neighborhood is 
able to produce electrification in that conductor. This method 
of producing electrification is called electrostatic induction. 

As soon as the charged rod is removed, the leaves will be 
seen to collapse completely. This shows that this form of elec- 
trification is only a temporary phenomenon which is due simply 
to the presence of the charged body in the neighborhood. 



GENEKAL FACTS OF ELECTRIFICATION 229 
283. Nature of electrification produced by induction. Let a 

metal ball A (Fig. 224) be strongly charged by rubbing it with a charged 
rod, and let it then be brought near an insulated* metal body B which 
is provided with pith balls or strips of paper a, b, c, as shown. The di- 
vergence of a and c will show that the ends of B have received electrical 
charges because of the presence of 
A, while the failure of b to diverge /" "N o. 



. _ _ 

will show that the middle of is ( + ) Cl _ ? _ t) 
uncharged. Further, the rod which 

charged A will be found to repel c FIG. 224. Nature of induced 
but to attract a. charges 

We conclude, therefore, that when a conductor is brought 
near a charged body, the end away from the inducing charge 
is electrified with the same kind of electricity as that on the in- 
ducing body, while the end toward the inducing body receives 
electricity of the opposite kind. 

284. The electron theory of electricity. The atoms of all 
substances are now known to contain as constituents both 
positive and negative electricity, the latter existing in the form 
of minute corpuscles, or electrons, each of which has a mass 
1 8 * of that of the hydrogen atom. These electrons are 
probably grouped in some way about the positive electricity 
as a nucleus. The sum of the negative charges of these elec- 
trons is supposed to be just equal to the positive charge of 
the nucleus, so that in its normal condition the whole atom is 
neutral, or uncharged. But in conductors electrons are con- 
tinually getting loose from the atoms and reentering other 
atoms, so that at any given instant there are in every con- 
ductor a number of free negative electrons and a correspond- 
ing number of atoms which have lost electrons and which 
are therefore positively charged. Such a conductor would, as a- 
whole, show no charge of either positive or negative electricity. 

* Sulphur is practically a perfect insulator in all weathers, wet or dry. 
Metal conductors of almost any shape resting upon pieces of sulphur will 
serve the purposes of this experiment in summer or winter. 



230 STATIC ELECTRICITY 

But as soon as a body charged, for example, positively 
(Fig. 224) is brought near su^h a conductor, the negatively 
charged electrons are attracted to the near end, leaving behind 
them the positively charged atoms, which are not free to move 
from their positions. On the other hand, if a negatively charged 
body is brought near the conductor, the negative electrons 
stream away and the near end is left with the immovable plus 
atoms. As soon as the inducing charge is removed, the con- 
ductor becomes neutral again, because the little negative cor- 
puscles return to their former positions under the influence of 
the attraction of the positive atoms. This is the present-day 
picture of the mechanism of electrification by induction. 

The charge of one electron is called the elementary electrical 
charge. Its value has recently been accurately measured. 
There are 2.095 billion of them in one of the units denned in 
280. Every electrical charge consists of an exact number of 
these ultimate electrical atoms. 

285 . Charging by induction. Let two metal balls or two eggshells, 
A and B, which have been gilded or covered with tin foil be suspended 
by silk threads and touched together, as in Fig. 225. Let a positively 
charged body C be brought near them. 
As described above, A and B will at once 
exhibit evidences of electrification ; that 
is, A will repel a positively charged pith 
ball, while B will attract it. If C is re- 
moved while A and B are still in contact, 
the separated charges reunite and A and 

B cease to exhibit electrification. But if 

FIG. 22o. Obtaining a 
A and B are separated from each other plug ftnd a mmug chftrge 

while C is in place, A will be found to bv i n( j uc ti O n 

remain positively charged and B nega- 
tively charged. This may be proved either by the attractions and repul- 
sions which they show for charged rods brought near them or by the 
effects which they produce upon a charged electroscope brought into 
their vicinity, the leaves of the latter falling together when it is brought 
near one and spreading farther apart when brought near the other. 





BENJAMIN FRANKLIN (1706-1790) 

Celebrated American statesman, philosopher, and scientist; born 
at Boston, the sixteenth child of poor parents ; printer and pub- 
lisher by occupation; pursued scientific studies in electricity as 
a diversion rather than as a profession ; first proved that the two 
coats of a Leyden jar are oppositely charged; introduced the 
terms positive and negative electricity; proved the identity of 
lightning and frictional electricity by flying a kite in a thunder- 
storm and drawing sparks from the insulated lower end of the 
kite string ; invented the lightning rod ; originated the one-fluid 
theory of electricity which regarded a positive charge as indi- 
cating an excess, a negative charge a deficiency, in a certain 
normal amount of an all-pervading electrical fluid 




FRANKLIN'S KITE EXPERIMENT 

In June, 1752, Franklin demonstrated the identity of the electric spark and light- 
ning. To prevent his kite from being torn in the rain he made it of a silk handker- 
chief. The lower end of the kite string and a silk ribbon were tied to the ring of a 
key, and, to prevent any charge that might appear upon the string and the key from 
escaping through his body to the earth, he held the kite by grasping the insulating 
silk ribbon. Standing under a shed to keep the ribbon dry, Franklin, by presenting 
his knuckle to the key, obtained sparks similar to those produced by his electric 
machine. With these sparks he charged his Leyden jar and used it to give a shock. 
Indeed, he performed with lightning all the experiments which he had previously 
performed with sparks from his frictional machine. The experiment is dangerous 
and should not be attempted by inexperienced persons 




GENERAL FACTS OF ELECTRIFICATION 231 

We see, therefore, that if tve cut in two, or separate into 
two parts, a conductor while it is under the influence of an 
electric charge, ive obtain two permanently charged bodies, the 
remoter part having a charge of the same sign as that of the 
inducing charge, and the near part having a charge of unlike 
sign. Under the influence of the positive charge on C the 
negative electrons moved out of A into B, which act made A 
positive and B negative. 

Let the conductor R (Fig. 226) be touched at a by -the finger while a 
charged rod C is near it. Then let the finger be removed and after it 
the rod C. If now a negatively charged pith ball is brought near B, it 
will be repelled, showing that B 

has become negatively charged. In (+ B -a) 

this experiment the body of the 
experimenter corresponds to the 

egg A of the preceding experiment^ ^ m A fe d 

and removing the finger from B ti(m hag ft charge Qf ^ Qpposite 
corresponds to separating the two that of the inducing charge 

eggshells. Let the last experi- 
ment be repeated with only this modification, that B is touched at 
b rather than at a. When B is again tested with the pith ball, it will 
still be found to have a negative charge, exactly as when the finger 
was touched at a. 

We conclude, therefore, that no matter where the body 
B is touched, the sign of the charge left upon it is always 
opposite to that of the inducing charge. This is because the 
negative electricity, that is, the electrons, can under no 
circumstances escape from b so long as C is present, for 
they are bound by the attraction of the positive charge 
on C. Indeed, the final negative charge on B is due merely 
to the fact that the positive charge on C pulls electrons into 
B from the finger, no matter where B is touched. In the 
same way, if C had been negative, it would have pushed 
electrons off from B through the finger and thus have left 
B positively charged. 



232 STATIC ELECTRICITY 

286. Charging the electroscope by induction. Let an ebonite 

rod which has been rubbed with catskin be brought near the knob of 
the electroscope (Fig. 223). The leaves at once diverge. (Make a dia- 
gram of the electroscope with the negatively charged ebonite rod near 
the knob. By use of + and signs explain the electrical condition of 
both the knob and the leaves.) Let the knob be touched with the finger 
while the rod is held in place. The leaves will fall together. (Explain 
by a diagram as before.) Let the finger be removed and then the rod. 
The leaves will fly apart again. (By a diagram explain the final elec- 
trical condition of both the knob and the leaves.) 

The electroscope has been charged by induction, and since 
the charge on the ebonite rod was negative, the charge on 
the electroscope must be positive. If this conclusion is tested 
by bringing the charged ebonite rod near the electroscope, 
the leaves will fall together as the rod approaches the knob. 
How does this prove that the charge on the electroscope is 
positive ? If the empty neutral hand approaches the knob, 
the leaves diverge less. Explain. 

287. Plus and minus electricities always appear simultane- 
ously and in equal amounts. Let an ebonite rod be completely 
discharged by passing it quickly through a Bunsen flame. Let a flannel 
cap having a silk thread attached be slipped over 

the rod, as in Fig. 227, and twisted rapidly around 
a immber of times. When rod and cap together 
are held near a charged electroscope, no effect will 
be observed ; but if the cap is pulled off, it will be 
found to be positively charged, while the rod will 

be found to have a negative charge. 

FIG. 22 7. Plus and 

Since the two together produce no effect, minus electricities 
the experiment shows that the plus and alwavs developed 

in equal amounts 
minus charges were equal in amount. This 

experiment confirms the view already brought forward in 
connection with induction, that electrification always consists 
in a separation of plus and minus charges which already exist 
in equal amounts within the bodies in which the electrification 
is developed. 





DISTRIBUTION OF CHARGE 233 



QUESTIONS AND PROBLEMS 

1. If pith balls, or any light figures, are placed between two plates 
(Fig. 228), one of which is connected to earth and the other to one knob 
of an electrical machine in operation, the figures will bound back and 
forth between the two plates as long as the machine is operated. Explain. 

2. Given a gold-leaf electroscope, a glass rod, and a 
piece of silk, how, in general, would you proceed to test 
the sign of the electrification of an unknown charge? 

3. Charge a gold-leaf electroscope by induction from 
a glass rod. Warm a piece of paper and stroke it on 
the clothing. Hold it over the charged electroscope. 
If the divergence of the gold leaves is increased, is the 
charge on the paper + or ? If the divergence is 
decreased, what is the sign of the charge on the paper ? 

4. If you are given a positively charged insulated 

sphere, how could you charge two other spheres, one positively and the 
other negatively, without diminishing the charge on the first sphere? 

5. If you bring a positively charged glass rod near the knob of an 
electroscope and then touch the knob, why do you not remove the nega- 
tive electricity which is on the knob ? 

6. In charging an electroscope by induction, why must the finger 
be removed before the removal of the charged body? 

7. If you hold a brass rod in the hand and rub it with silk, the rod 
will show no sign of electrification ; but if you hold the brass rod with 
a piece of sheet rubber and then rub it with silk, you will find it elec- 
trified. Explain. 

8. State as many differences as you can between the phenomena of 
magnetism and those of electricity. 

9. If an electrified rod is brought near to a pith ball siispended by 
a silk thread, the ball is first attracted to the rod and then repelled 
from it. Explain this. 

DISTRIBUTION OF ELECTRIC CHARGE UPON CONDUCTORS 

288. Electric charges reside only upon the outside surface of 
conductors. Let a deep tin cup (Fig. 229) be placed upon an insulating 
stand and charged as strongly as possible either from an ebonite rod 
or from an electrical machine. If now a smooth metal ball suspended by a 
silk thread is touched to the outside of the charged cup and then brought 
near the knob of a charged electroscope, it will show a strong charge ; 
but if it is touched to the inside of the cup, it will show no charge at all. 



234 



STATIC ELECTRICITY 



These experiments show that an electric charge resides 
entirely on the outside surface of a conductor. This is a result 
which might have been inferred from 
the fact that all the little electrical 
charges of which the total charge is 
made up repel each other and there- 
fore move through the conductor 
until they are, on the average, as 
far apart as possible. 

289. Density of charge greatest 
where curvature of surface is greatest. 
Since all of the parts of an electric charge tend, because of 
their mutual repulsions, to get as far apart as possible, we 
should infer that if a charge of either sign is placed upon an 
oblong conductor like that of Fig. 230, (1), it will distribute 
itself so that the electrification at the ends will be stronger 
than that at the middle. 




FIG. 229. Proof that charge 
resides on surface 



(1) 




To test this inference let a proof plane a flat metal disk (for example, 
a cent) provided with an insulating handle be touched to one end of 
such a charged body, the charge conveyed 
to a gold-leaf electroscope, and the amount 
of separation of the leaves noted. Then let 
the experiment be repeated when the proof 
plane touches the middle of the body. The 
separation of the leaves in the latter case 
will be found to be very much less than in 
the former. If we should test the distribu- 
tion on a pear-shaped body (Fig. 230, (2)) in 
the same way, we should find the density of 
electrification considerably greater on the 

small end than on the large one. By density of electrification is meant 
the quantity of electricity on unit area of the surface. 

290. Discharging effect of points. The above experiments 
indicate that if one end of a pear-shaped body is made more 
and more pointed, then, when the body is charged, the electric 



FIG. 230. Distribution of 
charge over oblong bodies 






DISTRIBUTION OF CHARGE 235 

density on this end will become greater and greater. The fol- 
lowing experiment will show what happens when the conductor 
is provided with a sharp point. 

Let a very sharp needle be attached to any smooth insulated metal 
body provided with paper or pith-ball indicators, as in Fig. 224, p. 229. 
If the body is now charged either with a rubbed rod or with an electric 
machine, as soon as the supply of electricity is stopped the paper indi- 
cators will immediately fall, showing that the body is losing its charge. 
To show that this is certainly due to the effect of the point, remove the 
needle and repeat. The indicators will fall very slowly if at all. 

The experiment shows that the electrical density upon the 
point is so great that the charge escapes from it into the air. 
This is because the intense charge on the point causes many 
of the adjacent molecules of the air to lose an electron. This 
leaves these molecules positively charged. The free electrons 
attach themselves to neutral molecules, thus charging them 
negatively. One set of these electrically charged molecules 
(called ions) is attracted to the point and the other repelled 
from it. The former set move to the conductor, give up 
their charges to it, and thus neutralize the charge upon it. 

The effect of points may be shown equally well by charging the gold- 
leaf electroscope and holding a needle in the hand within a few inches 
of the knob. The leaves will fall together rap- 
idly. In this case the needle point becomes elec- 
trified by induction and discharges to the knob 
electricity of the opposite kind to that on the 
knob, thus neutralizing its charge. An entertain- 
ing variation of the last experiment is to attach 
a tassel of tissue paper to an insulated conductor j, 031 Dischare 1 
and electrify it strongly. The paper streamers i ng effect of points 
under their mutual repulsions will stand out in all 

directions, but as soon as a needle point is held in the hand near them, 
they will fall together (Fig. 231), being discharged as described above. 

291 . The electric whirl. Let an electric whirl (Fig. 232) be bal- 
anced upon a pin point and attached to one knob of an electric machine. 
As soon as the machine is started, the whirl will rotate rapidly in the 
direction of the arrows. 




236 



STATIC ELECTRICITY 





FIG. 232. The 
electric whirl 



FIG. 233. The elec- 
tric wind 



The explanation is as follows : The air close to each point 
is ionized, as explained in 290. The ions of sign unlike 
that of the charge on the point are drawn to the point and 
discharged. The other set 
of ions is repelled. But 
since this repulsion is mu- 
tual, the point is pushed 
back with the same force 
with which these ions are 
pushed forward ; hence the 
rotation. The repelled ions 
in their turn drag the air with them in their forward motions 
and thus produce the " electric wind," which may be detected 
easily by the hand or by a candle flame (Fig. 233). 

292. Lightning and lightning rods. It was in 1752 that 
Franklin (see opposite p. 230), during a thunderstorm, sent 
up his historic kite (see opposite p. 231). This kite was pro- 
vided with a pointed wire at the top. As soon as the hempen 
kite-string had become wet he succeeded in drawing ordinary 
electric sparks from a key attached to the lower end. This 
experiment demonstrated for the first time that thunderclouds 
carry ordinary electrical charges which may be drawn from 
them by points, just as the charge was drawn from the tassel 
in the experiment of 290. It also showed that lightning is 
nothing but a huge electric spark. Franklin applied this dis- 
covery in the invention of the lightning rod. The way in which 
the rod discharges the cloud and protects the building is as 
follows : As the charged cloud approaches the building it 
induces an opposite charge in the rod. This induced charge 
escapes rapidly and quietly from the sharp point in the manner 
explained above and thus neutralizes the charge of the cloud. 

To illustrate, let a metal plate C (Fig. 234) be supported above a 
metal ball E, and let C and E be attached to the two knobs of an electri- 
cal machine. When the machine is started, sparks will pass from C to E. 



POTENTIAL AND CAPACITY 



237 



But if a point p is connected to E, the sparking will cease ; that is, the 
point will protect E from the discharges, even though the distance Cp 
be considerably greater than CE. 

The lower end of a lightning rod should be buried deep 
enough so that it will always be surrounded by moist earth, 
since dry earth is a poor conductor. It will be seen, therefore, 
that lightning rods protect 
buildings not because they 
conduct the lightning to earth, 
but because they prevent the 
formation of powerful charges 
in the neighborhood of the 
buildings on which they are 
placed. 

Flashes of lightning over a 
mile long have frequently been observed. Thunder is due to 
the violent expansion of heated air along the path of discharge. 
The roll of thunder is due to reflections from clouds, hills, etc.* 




FIG. 234. Illustrating the action of 
a lightning rod 






POTENTIAL AND CAPACITY 

293. Potential difference. There is a very instructive anal- 
ogy between the use of the word " potential " in electricity 
and " pressure " in hydrostatics. For ex- 
ample, if water will flow from tank A to 
tank B through the connecting pipe R 
(Fig. 235), we infer that the hydrostatic 
pressure at a must be greater than that 
at J, and we attribute the flow directly 
to this difference in pressure. In exactly 
the same way, if, when two bodies A and B (Fig. 236) are 
connected by a conducting wire r, a charge of -f- electricity 



R 



* A laboratory exercise on static electrical effects should follow the discus- 
sion of this section. See, for example, Experiment 27 of the authors' Manual. 



238 STATIC ELECTRICITY 

is found to pass from A to B (that is, if electrons are found 
to pass from B to A) we say that the electrical potential is 
higher at A than at B, and we assign this difference of poten- 
tial as the cause of the flow.* Thus, just as water tends to 
flow from points of higher hydrostatic pressure to points of 
lower hydrostatic pressure, so elec- ^_^ ^_^ 

tricity tends to flow from points of ( <O ( B j 

higher electrical pressure, or poten- 

, . & , . , f , , . , FIG. 236. Illustrating electri- 

tial, to points of lower electrical cal pressure 

pressure, or potential. 

Again, if water is not continuously supplied to one of the 
tanks A or B of Fig. 235, we know that the pressures at 
a and b must soon become the same. Similarly, if no elec- 
tricity is supplied to the bodies A and B of Fig. 236, their 
potentials very quickly become the same. In other words, 
all points on a system of connected conductors in which the 
electricity is in a stationary, or static, condition are at the same 
potential. This result follows at once from the fact of mobility 
of electric charges through conductors. 

But if water is continuously poured into A and removed 
from B (Fig. 235), the pressure at a will remain permanently 
above the pressure at b, and a continuous flow of water will 
take place through R. So, if A (Fig. 236) is connected with an 
electrical machine and B to earth, a permanent potential differ- 
ence will exist between A and B, and a continuous current of 
electricity will flow through r. Difference in potential is 
commonly denoted simply by the letters P. D. (Potential 
Difference). 

* Franklin thought that it was the positive electricity which moved through 
a conductor, while he conceived the negative as inseparably associated with 
the atoms. Hence it became a universally recognized convention to regard 
electricity as moving through a conductor in the direction in which a -f charge 
would have to move in order to produce the observed effect. It is not de- 
sirable to attempt to change this convention now, even though the electron 
theory has exactly inverted the roles of the + and charges. 



POTENTIAL AND CAPACITY 



239 



294. Some methods of measuring potentials. The simplest 
and most direct way of measuring the potential difference be- 
tween two bodies is to connect one to the knob, the other to 
the conducting case,* of an electroscope. The amount of 
separation of the gold leaves is a measure of the P.D. between 
the bodies. The unit in which P.D. is usually expressed is 
called the volt. It will be accurately denned in 334. It will 
be sufficient here to say that it is approximately equal to the 
electrical pressure between the ends of copper and zinc strips 
when dipped in dilute sulphuric acid 
or to two thirds of the electrical pres- 
sure between the zinc and carbon 
terminals of the familiar dry cell. 

Since the earth is, on the whole, 
a good conductor, its potential is 
everywhere the same ( 293) ; hence 
it makes a convenient standard of 
reference in potential measurements. 
To find the potential of a body rela- 
tive to that of the earth, we connect 
the outer case of the electroscope to 
the earth by means of a wire, and 
connect the body to the knob. If the 
electroscope is calibrated in volts, 
its reading gives the P.D. between 
the body and the earth. Such cali- 
brated electroscopes are called electrostatic voltmeters. They 
are the simplest and in many respects the most satisfactory 
forms of voltmeters to be had. Their use, both in laboratories 




FIG. 237. Electrostatic 
voltmeter 



* If the case is of glass, it should always be made conducting by pasting 
tin-foil strips on the inside of the jar opposite the leaves and extending these 
strips over the edge of the jar and down on the outside to the conducting 
support on which the electroscope rests. The object of this is to maintain 
the walls always at the potential of the earth. 



240 



STATIC ELECTRICITY 



and in electrical power plants, is rapidly increasing. They 
can be made to measure a P.D. as small as l * QQ volt and as 
large as 200,000 volts. Fig. 237 shows one of the simpler 
forms. The outer case is of metal and is connected to earth 
at the point a. The body whose potential is sought is con- 
nected to the knob b. This is in metallic contact with the 
light aluminium vane c, which takes the place of the gold leaf. 
A very convenient way of measuring a large P.D. without 
a voltmeter is to measure the length of the spark which will 
pass between the two bodies whose P.D. is sought. The P.D. 
is roughly proportional to spark length, each centimeter of 
spark length representing a P.D. of about 30,000 volts if the 
electrodes are large compared to their distance apart. 

295. Condensers. Let a metal plate A be mounted on an insulating 
base and connected with an electroscope, as in Fig. 238. Let a second 
plate B be simi- A R 

larly mounted and 
connected to the 
earth by a conduct- 
ing wire. Let A be 
charged and the 
deflection of the 
gold leaves noted. 
If now we push B 
toward A, we shall observe that, as it comes near, the leaves begin to 
fall together, showing that the potential of A is diminished by the 
presence of B, although the quantity of electricity on A has remained 
unchanged. If we convey additional charges to A with the aid of a 
proof plane, we shall find that many times the original amount of elec- 
tricity may now be put on A before the leaves return to their original 
divergence, that is, before the body regains its original potential. 

We say, therefore, that the capacity of A for holding elec- 
tricity has been very greatly increased by bringing near it 
another conductor which is connected to earth. It is evident 
from this statement that we measure the capacity of a body by 
the amount of electricity which must be put upon it to raise it to 




FIG. 238. The principle of the condenser 




COUNT ALESSANDRO VOLTA (1745-1827) 

Great Italian physicist, professor at Como and at Pavia ; inventor 
of the electroscope, the electrophorus, the condenser, and the 
yoltaic pile (a form of galvanic cell) ; first measured the potential 
differences arising from the contact of dissimilar substances; 
ennobled by Napoleon for his scientific services; the volt, the 
practical unit of potential difference, is named in Ms honor 




A MODERN HIGH-TENSION TOWER ON THE SOUTHERN CALIFORNIA EDISON 
COMPANY'S BIG CREEK LINE 

These wires carry an alternating current having a potential of 150,000 volts. The 
current is generated hy four 17,500-kilowatt dynamos driven hy 8 Pelton water- 
wheels operating under a head of 1900 feet and developing a horse power of 100,000. 
Even in wet weather the under surfaces of the series of nine petticoat insulators 
from which each wire is hung remain sufficiently dry to prevent large leakage 
losses. The wires are spaced 16 feet apart 



POTENTIAL AND CAPACITY 241 

a given potential. The explanation of the increase in capacity 
in this case is obvious. As soon as B was brought near to A 
it became charged, by induction, with electricity of opposite 
sign to J, the electricity of like sign to A being driven off to 
earth through the connecting wire. The attraction between 
these opposite charges on A and B drew the electricity on A 
to the face nearest to B and removed it from the more remote 
parts of A, so that it became possible to put a very much 
larger charge on A before the tendency of the electricity on A 
to pass over to the electroscope became as great as it was at 
first, that is, before the potential of A rose to its initial value. 
In such a condition the electricity on A is said to be bound 
by the opposite electricity on B. 

An arrangement of this sort consisting of two conductors sepa- 
rated by a nonconductor is called a condenser. If the conducting 
plates are very close together and one of them grounded, the 
capacity of the system may be thou- 
sands of times as great as that of one 
of the plates alone. 

296. The Leyden jar. The most com- 
mon form of condenser is a glass jar 
coated part way to the top inside and 
outside with tin foil (Fig. 239). The 

inside coating- is connected by a chain to 

* J . FIG. 239. The Leyden jar 

the knob, while the outside coating is 

connected to earth. Condensers of this sort first came into 
use in Leyden, Holland, in 1745. Hence they are now called 
Leyden jars. 

To charge a Leyden jar the outer coating is held in the hand while 
the knob is brought into contact with one terminal of an electrical 
machine, for example, the negative. As fast as electrons pass to the 
knob they spread to the inner coat of the jar, where they repel electrons 
from the outer coat to the earth, thus leaving it positively charged. If 
the inner and outer coatings are now connected by a discharging rod, 




242 



STATIC ELECTRICITY 



as in Fig. 239, a powerful spark will be produced. This spark is due to 
the rush of electrons from the coat to the + coat. Let a charged 
jar be placed on a glass plate so as to insulate the outer coat. Let the 
knob be touched with the finger; no appreciable discharge will be 
noticed. Let the outer coat be in turn touched with the finger ; again 
no appreciable discharge will appear. But if the inner and outer coatings 
are connected with the discharger, a powerful spark will pass. 

The experiment shows that it is impossible to discharge 
one side of the jar alone, for practically all of the charge is 
bound by the opposite charge on the other coat. The full 
discharge can therefore occur only when the inner and outer 
coats are connected. 

Leyden jars and other forms of condensers are of great 
practical use. They are used, for instance, in certain systems 
of telephony and telegraphy, in wireless 
communication, and in electrostatic ma- 
chines and induction coils. 




FIG. 240. The elec- 
trophorus 



297. The electrophorus. The electrophorus 

is a simple electrical generator which illustrates 
well the principle underlying the action of all 
electrostatic machines. All such machines gen- 
erate electricity primarily by induction, not by 
friction. B (Fig. 240) is a hard-rubber plate 
which is first charged by rubbing it with fur or 
flannel. A is a metal plate provided with an insulating handle. When 
the plate A is placed upon B, touched with the finger, and then removed, 
it is found possible to draw a spark from it, which in dry weather may 
be a quarter of an inch or more in length. The process may be repeated 
an indefinite number of times without producing any diminution in the 
size of the spark which may be drawn from A. 

If the sign of the charge on A is tested by means of an 
electroscope, it will be found to be positive. This proves 
that A has been charged by induction, not by contact with B, 
for it is to be remembered that the latter is charged nega- 
tively. The reason for this is that even when A rests upon 
B it is in reality separated from it, at all but a very few 



POTENTIAL AND CAPACITY 243 

points, by an insulating layer of air ; and since B is a non- 
conductor, its charge cannot pass off appreciably through 
these few points of contact. It simply repels negative elec- 
trons to the top side of the metal plate A, and thus charges 
positively the lower side. The electrons pass off to earth 
when the plate is touched with the finger. Hence, when the 
finger is removed and A lifted, it possesses a strong positive 
charge. Every commercial electrostatic machine is simply a 
continuously acting electrophorus which generates electricity 
by induction, not by friction. 

QUESTIONS AND PROBLEMS 

1. If you set a charged Ley den jar on a cake of paraffin, why can 
you not discharge it by touching one of the coatings ? 

2. Will a solid sphere hold a larger charge of electricity than a 
hollow one of the same diameter? 

3. Why cannot a Leyden jar be appreciably charged if the outer coat 
is insulated ? 

4. With a stick of sealing wax and a piece of flannel, in what two 
ways could you give a positive charge to an insulated body? 

5. Explain, using a set of drawings, the charging of the cover of an 
electrophorus. 

6. Represent by a drawing the electrical condition of a tower just 
before it is struck by lightning, assuming the cloud at this particular 
time to be powerfully charged with + electricity. 

7. When a negatively electrified cloud passes over a house provided 
with a lightning rod, the rod discharges positive electricity into the 
cloud. Explain. 



CHAPTER XIV 



ELECTRICITY IN MOTION * 
DETECTION OF ELECTRIC CURRENTS 
298. Electricity in motion produces a magnetic effect. Let a 

powerfully charged Leyden jar be discharged through a coil which sur- 
rounds an unmagnetized knitting needle, insulated by a glass tube, in 
the manner shown in Fig. 241, the compass needle being at rest in the 
position shown. After the discharge the knitting 
needle will be found to be distinctly magnetized. 
If the sign of the charge on the jar is reversed, 
the direction of deflection and 
the poles will in general be 
reversed. 

The experiment shows 
that there is a definite 
connection between elec- 
tricity and magnetism. 
Just what this connection is we do not yet know with cer- 
tainty, but we do know that magnetic effects are always ob- 
servable near the path of a moving electrical charge, while 
no such effects can ever be observed near a charge at rest. 

To prove that a charge at rest does not produce a magnetic effect, 
let a charged body be brought near a compass needle. It will attract 
either end of the needle with equal readiness. While the needle is 
deflected, insert between it and the charge a sheet of zinc, aluminium, 
brass, or copper. This will act as an electric screen and will therefore 
cut off all effect of the charge. The compass needle will at once swing 
to its north-and-south position. 




FIG. 241. Magnetic effect of an electric 
current produced from a static charge 



* This chapter should be accompanied or, better, preceded by laboratory 
experiments on the simple cell and on the magnetic effects of a current. See, 
for example, Experiments 28, 29, and 30 of the authors' Manual. 

244 



DETECTION OF ELECTRIC CURRENTS 245 

Let the compass needle be deflected by a bar magnet, and let the 
screen be inserted again The sheet of metal does not cut off the 
magnetic forces in the slightest degree. 

The fact that an electric charge exerts no magnetic force is shown, 
then, both by the fact that it attracts either end of the compass needle 
with equal readiness and by the fact that the screen cuts off its action 
completely, while the same screen does not have any effect in cutting 
off the magnetic force. 

An electrical charge in motion is called an electric current, 
and its presence is most commonly detected by the magnetic 
effect which it produces. A current of electricity is now con- 
sidered to be a stream of negative electrons (see 293). 

299. The galvanic cell. When a Leyden jar is discharged, 
only a very small quantity of electricity passes through the 
connecting wires, since the current lasts for but a small frac- 
tion of a second. If we could keep a current flowing continu- 
ously through the wire, we should expect the magnetic effect 
to be much more pronounced. It was in 1786 
that Galvani, an Italian anatomist at the Uni- 
versity of Bologna, accidentally discovered that 
there is a chemical method for producing such 
a continuous current. His discovery was not 
understood, however, until Volta (see opposite 

p. 240X while endeavoring* to throw liofht upon FIG. 242. Sim - 

ple voltaic cell 
it, in 1800 invented an arrangement which is 

now known sometimes as the voltaic and sometimes as the 
galvanic cell. This consists, in its simplest form, of a strip of 
copper and a strip of zinc immersed in dilute sulphuric acid 
(Fig. 242). 

Let the terminals of such a cell be connected for a few seconds to the 
ends of the coil of Fig. 241 when an unmagnetized needle lies within 
the glass tube. The needle will be found to have become magnetized 
much more strongly than before. Again, let the wire which connects 
the terminals of the cell be held above a magnetic needle, as in Fig. 243 ; 
the needle will be strongly deflected 





246 ELECTRICITY IN MOTION 

Evidently, then, the wire which connects the terminals of a 
galvanic cell carries a current of electricity. Historically the 
second of these experiments, per- 
formed by the Danish physicist 
Oersted (see on opposite page) 
in 1820, preceded the discovery 
of the magnetizing effects of cur- 
rents upon needles. It created a FlG 243 oersted's experiment 
great deal of excitement at the 

time, because it was the first clue which had been found 
to a relationship between electricity and magnetism. 

300. Plates of a galvanic cell are electrically charged. Since 
an electric current flows through a wire as soon as it is touched 
to the zinc and copper strips of a galvanic cell, we at once 
infer that the terminals of such a cell are electrically charged 
before they are connected. That this is indeed the case may 
be shown as follows : 

Let a metal plate A (Fig. 244), covered with shellac on its lower side 
and provided with an insulating handle, be placed upon a similar plate 
B which is in contact with the knob of an electroscope. Let the copper 
plate of a galvanic cell be connected with A and the zinc plate with B f 
as in Fig. 244. Then let the connecting wires be removed and the 
plate A lifted away from B. The opposite electrical charges which were 
bound by their mutual attractions to the adjacent faces of A and B, so- 
long, as these faces were separated only by the thin coat of shellac, are 
freed as soon as A is lifted, and hence part of the charge on B passes 
to the leaves of the electroscope. These leaves will indeed be seen to 
diverge. If an ebonite rod which has been rubbed with flannel or cat's fur 
is brought near the electroscope, the leaves will diverge still farther, thus 
showing that the zinc plate of the galvanic cell is negatively charged.* If 
the experiment is repeated with the copper plate in contact with B and the 
zinc in contact with A, the leaves will be found to be positively charged. 

* If the deflection of the gold leaves is too small for purposes of demon- 
stration, let a battery of from five to ten cells be used instead of the single 
cell. If, however, the plates A and B are three or four inches in diameter, 
and if their surfaces are very flat, a single cell is sufficient. 




HANS CHRISTIAN OERSTED 

(1777-1851) 

The discoverer of the connection 
'between electricity and magnetism 
was a Dane and a professor at the 
University of Copenhagen. His 
famous experiment made in 1820 
stimulated the researches which 
led to the modern industrial devel- 
opments of electricity 




JOSEPH HENRY (1797-1878) 

Born in Albany, New York ; taught 
physics and mathematics in Albany 
Academy and Princeton College. 
He invented the electromagnet 
(1828), discovered the oscillatory 
nature of the electric spark (1842) 
by magnetizing needles in the 
manner described on page 244, and 
made the first experiments in self- 
induction (1832). He was the first 
secretary of the Smithsonian Insti- 
tution, and the organizer of the 
Weather Bureau 




ELECTROMAGNETS 

This page shows in the upper right-hand corner a photograph of the first electro- 
magnet. It was constructed at Princeton in 1828 by Henry. He wound the arms 
of a U-shaped piece of iron with several layers of wire insulated by wrapping 
around it strips of silk. The main illustration is a huge modern lifting magnet 
which itself weighs 8720 pounds, is 5 feet 2 inches in diameter, and can lift a 
single flat piece of iron weighing 70,000 pounds. It has 118,000 ampere turns, and 
carries 84 amperes at 220 volts. The coil is built up of several pancakes of cop- 
per straps, the turns of strap being insulated from one another by asbestos ribbon 
wound between them. The magnet is loading a freight car with pig iron, of which 
its average lift is 4000 pounds 




DETECTION OF ELECTRIC CURRENTS 247 

The terminals of a galvanic cell therefore carry positive 
and negative charges just as do the terminals of an electrical 
machine in operation. The + charge is 
always found upon the copper and the - 
charge upon the zinc. The source of 
these charges is the chemical action 
which takes place within the cell. When 
these terminals are connected by a con- 
ductor, a current flows through the latter 

just as in the case of the electrical ma- FlG - 244 - Showing 
, . , .. . ., . charges on plates of 

chine; and it is the universal custom to a voltaic cell 

consider that it flows from positive to neg- 
ative (see 293 and footnote), that is, from copper to zinc. 

301. Comparison of a galvanic cell and a static machine. If 
one of the terminals of a galvanic cell is touched directly to 
the knob of a gold-leaf electroscope, without the use of the 
condenser plates A and B of Fig. 244, no divergence of the 
leaves will be detected ; but if one knob of a static machine 
in operation were so touched, the leaves would probably be 
torn apart by the violence of the divergence. Since we have 
seen in 294 that the divergence of the gold leaves is a meas- 
ure of the potential of the body to which they are connected, 
we learn from this experiment that the chemical actions in the 
galvanic cell are able to produce between its terminals but a 
very small potential difference in comparison with that pro- 
duced by the static machine between its terminals. As a matter 
of fact the potential difference between the terminals of the 
cell is about one volt, while that between the knobs of the 
electrical machine may be as much as 200,000 volts. 

But if the knobs of the static machine are connected to the 
ends of the wire of Fig. 243, and the machine operated, the cur- 
rent sent through the wire will not be large enough to produce 
any appreciable effect upon the needle. Since under these same 
circumstances the galvanic cell produced a very large effect 



248 ELECTKICITY IN MOTION 

upon the needle, we learn that although the cell develops a very 
small P.D. between its terminals, it nevertheless sends through 
the connecting wire very much more electricity per second 
than the static machine is able to send. This is because the 
chemical action of the cell is able to recharge the plates to 
their small P.D. practically as fast as they are discharged 
through the wire, whereas the static machine requires a rela- 
tively long time to recharge its terminals to their high P. D. 
after they have once been discharged. 

QUESTIONS AND PROBLEMS 

1. Under what conditions will an electric charge produce a magnetic 
effect? 

2. How can you test whether or not a current is flowing in a wire ? 

3. How does the current delivered by a cell differ from that delivered 
by a static machine ? 

4. Mention three respects in which the behavior of magnets is similar 
to that of electric charges ; two respects in which it is different. 

CHEMICAL EFFECTS OF THE CURRENT ; ELECTROLYSIS * 

302. Electrolysis. Let two platinum electrodes be dipped into a 
solution of dilute sulphuric acid, and let the terminals of a battery 
producing a pressure of 10 volts or more be applied to these electrodes. 
Oxygen gas is found to be given off at the electrode at which the cur- 
rent enters the solution, called the anode, while hydrogen is given off 
at the electrode at which the current leaves the solution, called the 
cathode. These gases may be collected in test tubes in the manner 
shown in Fig. 245. 

In accordance with the theory now in vogue among physi- 
cists and chemists, when sulphuric acid is mixed with water 
so as to form a dilute solution, the H 2 SO 4 molecules split 
up into three electrically charged parts, called ions, the two 

* This subject should be accompanied or followed by a laboratory experi- 
ment on electrolysis and the principle of the storage battery. See, four 
example, Experiment 35 of the authors' Manual. 



CHEMICAL EFFECTS; ELECTROLYSIS 



249 




FIG. 245. Electrolysis 
of water 



hydrogen ions each carrying a positive charge and the SO 4 ion 
a double negative charge (Fig. 246). This phenomenon is 
known as dissociation. The solution as 
a whole is neutral ; that is, it is un- 
charged, because it contains just as many 
positive as negative charges. 

As soon as an electrical field is estab- 
lished in the solution by connecting the 
electrodes to the positive and negative 
terminals of a battery, the hydrogen ions 
begin to migrate toward the negative elec- 
trode (that is, the cathode) and there, after giving up their 
charges, unite to form molecules of hydrogen gas (Fig. 245). 
On the other hand, the negative 
SO 4 ions migrate to the positive 
electrode (that is, the anode), 
where they give up their charges 
to it, and then act upon the 
water (H 2 O), thus forming 
H 2 SO 4 and liberating oxygen. 

If the volumes of Iwdrogen 

J & FIG. 246. Showing dissociation of 

and of oxygen are measured, sulphuric-acid molecules in water 
the hydrogen is found to occupy 

in every case just twice the volume occupied by the oxygen. 
This is, indeed, one of the reasons for believing that a molecule 
of water consists of two atoms of hydrogen and one of oxygen. 
303. Electroplating. If the solution, instead of being sul- 
phuric acid, had been one of copper sulphate (CuSO 4 ), the 
results would have been precisely the same in every respect, 
except that, since the hydrogen ions in the solution are now 
replaced by copper ions, the substance deposited on the cathode 
is pure copper instead of hydrogen. This is the principle 
involved in electroplating of all kinds. In commercial work 
the positive plate, that is, the plate at which the current 







250 



ELECTRICITY IN MOTION 



X 



FIG. 247. A simple electro- 
plating bath 



enters the bath, is always made from the same metal as that 
which is to be deposited from the solution, for in this case 
the SO 4 or other negative ions dissolve this plate as fast as 
the metal ions are deposited upon 
the other. The strength of the solu- 
tion, therefore, remains unchanged. 
In effect, the metal is simply taken 
from one plate and deposited on the 
other. Fig. 247 represents a simple 
form of silver-plating bath. The 
anode A is of pure silver. The 
spoon to be plated is the cathode K. In practice the articles to 
be plated are often suspended from a central rod (Fig. 248). 
while on both sides about the articles are the suspended 
anodes. This arrangement gives 
a more even deposit of metal. 
In silver plating the solution 
consists of 500 grams of potas- 
sium cyanide and 250 grams of 
silver cyanide in 10 liters of 
water. 




FIG. 248. Electroplating bath 



304. Electrotyping. In the process of electrotyping, the page 
is first set up in the form of common type. A mold is then 
taken in wax or gutta-percha. This mold is then coated with 
powdered graphite to render it a conductor, after which it is 
ready to be suspended as the cathode in a copper-plating bath, 
the anode being a plate of pure copper and the liquid a solu- 
tion of copper sulphate. When a sheet of copper as thick as 
a visiting card has been deposited on the mold, the latter is 
removed and the wax replaced by a type-metal backing, to 
give rigidity to the copper films. From such a plate as many 
as a hundred thousand impressions may be made. Nearly 
all books which run through large editions are printed from 
such electrotypes. 



CHEMICAL EFFECTS; ELECTEOLYSIS 251 

305. Legal units of current and quantity. In 1834 Faraday 
(see opposite p. 290) found that a given current of elec- 
tricity flowing for a given time always deposits the same 
amount of a given element from a solution, whatever be the 
nature of the solution which contains the element. For ex- 
ample, one ampere, the unit of current, always deposits in an 
hour 4.025 grams of silver, whether the electrolyte is silver 
nitrate, silver cyanide, or any other silver compound. Simi- 
larly, an ampere will deposit in an hour 1.181 grams of copper, 
1.203 grams of zinc, etc. Faraday further found that the 
amount of metal deposited in a given cell depended solely 
on the product of the current strength by the time, that is, on 
the quantity of electricity which had passed through the cell. 
These facts are made the basis of the legal definitions of 
current and quantity, thus : 

The unit of quantity, called the coulomb, is the quantity of 
electricity required to deposit .001118 gram of silver. 

The unit of current, the ampere, is the current which will 
deposit .001118 gram of silver in one second. 

QUESTIONS AND PROBLEMS 

1. What was the strength of a current that deposited 11.84 g. of 
copper in 30 min. ? 

2. How long will it take a current of 1 ampere to deposit 1 g. of 
silver from a solution of silver nitrate ? 

3. If the same current used in Problem 2 were led through a solution 
containing a zinc salt, how much zinc would be deposited in the same time? 

4. How could a silver cup be given a gold lining by use of the 
electric current? 

5. If the terminals of a battery are immersed in a glass of acidulated 
water, how can you tell from the rate of evolution of the gases at the 
two electrodes which is positive and which is negative ? 

6. The coulomb ( 305) is 3 billion times as large as the electrostatic 
unit of quantity denned in 280. How many electrons pass per second 
by a given point on a lamp filament which is carrying 1 ampere of 
current (see 284) ? 



252 



ELECTRICITY IN MOTION 



MAGNETIC EFFECTS OF THE CURRENT ; PROPERTIES 
OF COILS 

306. Shape of the magnetic field about a current. If we place 
the wire which connects the plates of a galvanic cell in a vertical posi- 
tion (Fig. 249) and explore with a compass needle the shape of the 
magnetic field about the current, we find that the magnetic lines are 
concentric circles lying in a plane perpendicular to the wire and having 




FIG. 249 FIG. 250 

Magnetic field about a current 

the wire as their common center. We find, moreover, that reversing the 
current reverses the direction of the needle. If the current is very strong 
(say 40 amperes), this shape of the field can be shown by scattering iron 
filings on a plate through which the current passes (Fig. 249). If the cur- 
rent is weak, the experiment should be performed as indicated in Fig. 250. 

The relation between the 
direction in which the current 
flows and the direction in which 
the N pole of the needle points 
(this is, by definition, the direc- 
tion of the magnetic field) is given in the following conven- 
ient rule, known as Ampere's Rule : If the right hand grasps 
the wire as in Fig. 251, so that the thumb points in the direction 
in which the current is flowing, then the magnetic lines encircle 
the wire in the same direction as do the fingers of the hand. 



FIG. 251. The right-hand rule 



MAGNETIC EFFECTS OF THE CURRENT 253 



\\ 



307. Loop of wire carrying a current equivalent to a magnet 
disk. Let a single loop of wire be suspended from a thread'in the 
manner shown in Fig. 252, so that its ends dip into two mercury cups. 
Then let the current from three or four dry cells 
be sent through the loop. The latter will be found 
to slowly set itself so that the face of the loop from 
which the magnetic lines emerge, as given by the 
right-hand rule (see 306 and also Fig. 253), is 
toward the north. Let a bar magnet be brought 
near the loop. The latter will be found to behave 
toward the magnet in all respects as though it 

were a flat magnetic 

disk whose boundary 

is the wire, the face 

which turns toward 

the north being an N 

pole and the other an 

S pole. 





FIG. 252. A loop 

equivalent to a flat 

magnetic disk 



FIG. 253. North pole of disk 
is face from which magnetic 
lines emerge ; south pole is 
face into which they enter 




The experiment shows what posi- 
tion a loop bearing a current will 
always tend to assume in a magnetic 
field ; for, since a 
magnet will always 
tend to set itself 

so that the line connecting its poles is par- 
allel to the direction of the magnetic lines 
of the field in which it is placed, a loop 
must set itself so that a line connecting its 
magnetic poles is parallel to the lines of the 
magnetic field, that is, so that the plane of 
the loop is perpendicular to the field (see 
Fig. 254); or, to state the same thing in 
slightly different form, if a loop of wire, 
free to turn, is carrying a current in a mag- 
netic field, the loop will set itself so as to include as many as 
possible of the lines of force of the field. 




FIG. 254. Position 
assumed by a loop 
carrying a current 
in a magnetic field 



254 



ELECTRICITY IN MOTION 



308. Helix carrying a current equivalent to a bar magnet. 

Let a wire bearing a current be wound in the form of a helix and held 
near a suspended magnet, as in Fig. 255. It will be found to act in 
every respect like a magnet, with an TV 
pole at one end and an pole at the other. 




FIG. 255. Magnetic effect 
of a helix 




This result might have been pre- 
dicted from the fact that a single 
loop is equivalent to a flat-disk 
magnet ; for when a series of such 
disks is placed side by side, as in the 
helix, the result must be the same as placing a series of disk 
magnets in a row, the N pole of one being directly in contact 
with the S pole of the next, etc. These poles would therefore 
all neutralize each other except 
at the two ends. We therefore 
get a magnetic field of the shape 
shown in Fig. 256, the direction of 
the arrows representing as usual 
the direction in which an N pole 
tends to move. 

The right-hand rule as given 
in 306 is sufficient in every case to determine which is the JV 
and which the S pole of a helix, that is, from which end the 
lines of magnetic force emerge from the helix and at which 
end they enter it. But it is found con- 
venient, in the consideration of coils, 
to restate the right-hand rule in a 
slightly different way, thus : If the coil 
is grasped in the right hand in such a 
way that the fingers point in the direc- 
tion in which the current is flowing in 
the wires, the thumb will point in the direction of the north pole 
of the helix (see Fig. 257). Similarly, if the sign of the poles 
is known, but the direction of the current unknown, it may 



FIG. 256. Magnetic field of helix 




FIG. 257. Rule for poles 
of helix 



MAGNETIC EFFECTS OF THE CURRENT 255 



be determined as follows : If the right hand is placed against 
the coil with the thumb pointing in the direction of the lines of 
force (that is, toward the north pole 
of the helix), the fingers will pass 
around the coil in the direction in 
which the current is flowing. 




FIG. 258. The bar electro- 
magnet 



309. The electromagnet. Let a 

core of soft iron be inserted in the helix 
(Fig. 258). The poles will be found to be 
enormously stronger than before. This 
is because the core is magnetized by induction from the field of the 
helix in precisely the same way in which it w 7 ould be magnetized by 
induction if placed in the field of a perma- 
nent magnet. The new field strength about 
*the coil is now the sum of the fields due 
to the core and that due to the coil. If the 
current is broken, the core will at once 
lose the greater part of its magnetism. If 
the current is reversed, the polarity of the 
core will be reversed. Such a coil with a 
soft-iron core is called an electromagnet. 




FIG. 259. The horseshoe 
electromagnet 



The strength of an electromagnet 
can be very greatly increased by giving it such form that 
the magnetic lines can remain in iron throughout their entire 
length instead of emerging into air, as they 
do in Fig. 258. For this reason electro- 
magnets are usually built in the horseshoe 
form and provided with an armature A 
(Fig. 259), through which a complete iron 
path for the lines of force is established, as 



shown in Fig. 260. The strength of such a FIG. 260. Themag- 
, T T n . n ,1 i netic circuit of an 

magnet depends chiefly upon the number of electromagnet 

ampere turns which encircle it, the expres- 
sion " ampere turns " denoting the product of the number of 
turns of wire about the magnet by the number of amperes 



256 ELECTRICITY IN MOTION 

flowing in each turn. Thus, a current of -^ ampere flowing 
1000 times around a core will make an electromagnet of 
precisely the same strength as a current of 1 ampere flowing 
10 times about the core. (See modern lifting magnet opposite 
p. 247.) 

QUESTIONS AND PROBLEMS 

1. Describe the magnetic condition of the space about a trolley wire 
carrying a direct current. 

2. In what direction will the north pole of a magnetic needle be 
deflected if it is held above a current flowing from north to south ? 

3. A man stands beneath a north-and-south trolley line and finds 
that a magnetic needle in his hand has its north pole deflected toward 
the east. What is the direction of the current flowing in the wire? 

4. A loop of wire lying on the table carries a current which flows 
around it in a clockwise direction. Would a north magnetic pole at the 
center of the loop tend to move up or down? 

5. If one looks down on the ends of a U-shaped electromagnet, does 
the current encircle the two coils in the same or in opposite directions ? 
Does it run clockwise or counterclockwise about the N pole ? 

MEASUREMENT OF ELECTRIC CURRENTS 

310. The galvanometer. Electric currents are, in general, 
measured by the strength of the magnetic effect which they 
are able to produce 
under specific condi- 
tions. Thus, if the wire 
carrying a current is 
wound into circular 
form, as in Fig. 261, the 
right-hand rule shows 

us that the shape of 

,, n i ! FIG. 261. Magnetic field about a circular coil 

the magnetic field at arrying a current 

the center of the coil 

is similar to that shown in the figure. If, then, the coil is 

placed in a north-and-south plane and a compass needle is 





ANDRE MARIE AMPERE (1775-1836) 

French physicist and mathematician; son of one of the victims 
of the guillotine in 1793 ; professor at the Polytechnic School in 
Paris 'and later at the College of France; hegan his experiments 
on electromagnetism in 1820, very soon after Oersted's discovery ; 
published his great memoir on the magnetic effects of currents 
in 1823 ; first stated the rule for the relation between the direction 
of a current in a wire and the direction of the magnetic field 
about it. The ampere, the practical unit of current, is named 
in his honor 




HUGE ROTOR 

The figure shows, in process of construction, one of the most recent types of huge 
generator of electricity, which are the outgrowth of the discovery of the relation 
between magnetism and electricity to which Ampere contributed so much. The 
figure shows in place one of the rotating electromagnets, which, as they swing 
past the huge coils of the stator surrounding them, at a peripheral speed of a mile 
and a half a minute, generate a current of 2700 amperes at 12,000 volts. This is 
one of the three 32,500-kilowatt machines built for installation at Niagara Falls 



MEASUREMENT OF ELECTRIC CURRENTS 257 




262. Simple 
suspended-coil gal- 
vanometer 



placed at the center, the passage of the current through the 
coil tends to deflect the needle so as to make it point east 
and west. The amount of deflection under these conditions 
is taken as the measure of current strength. 
The unit of current, the ampere, is in fact 
approximately the same as the current which, 
flowing through a circular coil of three 
turns and 10 centimeters radius, set in a 
north-and-south plane, will produce a deflec- 
tion of 45 degrees at Washington in a small 
compass needle placed at its center. The 
legal definition of the ampere is, however, 
based on the chemical effect of a current. 
It was given in 305. 

Nearly all current-measuring instruments consist essentially 
either of a small compass needle at the center of a fixed coil, as 
in Fig. 261, or of a movable coil sus- 
pended between the poles of a fixed 
magnet in the manner illustrated 
roughly in Fig. 262. The passage 
of the current through the coil pro- 
duces a deflection, in the first case, 
of the magnetic needle with ref- 
erence to the fixed coil, and, in the 
second case, of the coil with refer- 
ence to the fixed magnet. If the 
instrument has been calibrated to 
give the strength of the current 
directly in amperes, it is called an 
ammeter:, otherwise, a galvanometer 
(Fig. 263). 

311. The commercial ammeter. Fig. 264 shows the con- 
struction of the usual form of commercial ammeter. The 
coil c is pivoted on jewel bearings and is held at its zero 




FIG. 263. A lecture-table 
galvanometer 



258 



ELECTRICITY IN MOTION 



position by a spiral spring p. When a current flows through 
the instrument, if it were not for the spring p the coil would 
turn through about 120, or 
until its N pole came oppo- 
site the S pole of the magnet 
(see Fig. 264). This zero 
position of the coil is chosen 
because it enables the scale 
divisions to be nearly equal. 
The conductor z, called a 
shunt, carries nearly all the 
current that enters the in- 
strument at B, only an exceed- 
ingly small portion of it going 
through the moving coil c. 
The shunt is usually placed 
inside the instrument unless 
interchangeable shunts are 
desired. 




FIG. 264. Construction of a 
commercial ammeter 



QUESTIONS AND PROBLEMS 

1. What is the principle involved in the chemical method of measur- 
ing the strength of an electric current ? in the magnetic method ? 

2. How could you test whether or not the strength of an electric 
current is the same in all parts of a circuit? Try it. 

3. Explain from the diagram of the commercial ammeter the principle 
of the suspended-coil, or d'Arsonval, type of galvanometer. 

4. In calibrating an ammeter the current which produces a certain 
deflection is found to deposit J g. of silver in 50 min. What is the 
strength of the current? 

5. When a compass needle is placed, as in Fig. 261, at the middle of 
a coil of wire which lies in a north-and-south plane, the deflection pro- 
duced in the needle by a current sent through the coil is approximately 
proportional to the strength of the current, provided the deflection is 
small, not more, for example, than 20 or 25 ; but when the deflection 
becomes large, say 60 or 70, it increases very much more slowly 
than does the current which produces it. Can you see any reason why 
this should be so ? 



ELECTEIC BELL AND TELEGRAPH 



259 



ELECTRIC BELL AND TELEGRAPH 

312 The electric bell. The electric bell (Fig. 265) is one of the 
simplest applications of the electromagnet. When the button P is 
pressed (Figs. 265 and 266), the electric circuit of the battery is closed, 

and a current flows in at A, through the 
coils of the magnet, over the closed 
contact c, and out again at B. But 
as soon as this current is established, 
the electromagnet E pulls over the 
armature , and in so doing breaks 
the contact at c. This stops the cur- 
rent and demagnetizes the magnet E. 
The armature is then thrown back 
against c by the elasticity of the 
spring s which supports it. No sooner 
is the contact made at c than the cur- 
rent again begins to flow and the 
former operation is repeated. Thus 
the circuit is automatically made and 
broken at c, and the hammer H is 
in consequence set into rapid vibration 
against the rim of the bell. 

313. The telegraph. The electric 
telegraph is another simple appli- 




FIG. 265.,, The electric bell 



cation of the 
principle is illus- 
trated in Fig. 
267. As soon 
as the key K, 

at Chicago for example, is closed, the current 
flows over the line to, we will say, New York. 
There it passes through the electromagnet m, 
and thence back to Chicago through the earth. 
The armature b is held down by the electro- 
magnet m as long as the key K is kept closed. 
As soon as the circuit is broken at K the arma- 
ture is pulled up by the spring d. By means of 
a clockwork device the tape c is drawn along at 
a un-if orm rate beneath the pencil or pen carried 



electromagnet. 



The 




FIG. 266. Cross section 
of electric push button 



260 



ELECTRICITY IN MOTION 



by the armature b. A very short time of closing of K produces a dot upon 
the tape ; a longer time, a dash. As the Morse, or telegraphic, alphabet 
consists of certain combinations of dots and dashes, any desired mes- 
sage may be sent from Chicago and recorded in New York. In modern 



Chicago 




FIG. 267. Principle of the telegraph 



practice the message is not ordinarily recorded on a tape, for operators 
have learned to read messages by ear, a very short interval between two 
clicks being interpreted as a dot, a longer interval as a dash. 

The first commercial telegraph line was built by S. F. B. Morse (see 
on opposite page) between Baltimore and Washington. It was opened 
on May 24, 1844, with the now famous message, "What hath God 
wrought ! " 

314. The relay and sounder. Since the current that comes over a 
long telegraph line is of small amperage, the armature of the electro- 
magnet of the receiving instrument must be made very light to respond 
to the action of the cur- 
rent. The electromagnet Armaturet 
of this instrument is made 
of many thousand turns 
of fine wire, to secure the 
requisite number of am- 
pere turns ( 309) to work 
the armature. The clicks 
of such an armature are 
not sufficiently loud to be 
read easily by an operator. 
Hence at each station 

there is introduced a local circuit, which contains a local battery and a 
second and heavier electromagnet, which is called a sounder. The elec- 
tromagnet on the main line is then called the relay (see Fig. 268 and 
the drawings opposite p. 261). The sounder has a very heavy armature 



Etectrotnagnef 



Points 

Spring 
Adjusting Screw 




FIG. 268. The relay 




SAMUEL F. B. MORSE (1791-1872) 

The inventor of the electromagnetic recording telegraph and of the 
dot-and-dash alphabet known by his name, was born at Charles- 
town, Massachusetts, graduated at Yale College in 1810, invented 
the commercial telegraph in 1832, and struggled for twelve years 
in great poverty to perfect it and secure its proper presentation 
to the public. The first public exhibition of the completed instru- 
ment was made in 1837 at New York University, signals being 
sent through 1700 feet of copper wire. It was with the aid of a 
$30,000 grant from Congress that the first commercial line was 
constructed in 1844 between Washington and Baltimore 



w t 








ELECTKIC BELL AND TELEGRAPH 261 

(Fig. 269, A), which is so arranged that it clicks both when it is drawn 

down by its electromagnet against the stop S and when it is pushed 

up again by its spring, on breaking the current, against the stop L 

The interval which elapses between these 

two clicks indicates to the operator whether a 

dot or a dash is sent. The small current in the 

main line simply serves to close and open the 

circuit in the local battery which operates 

the sounder (see drawings on opposite page). 

The electromagnets of the relay and the 

sounder differ in that the latter consists of a 

few hundred turns of coarse wire and carries FlG> 269 ' The sounder 

a comparatively large current. 

315. Plan of a telegraphic system. The actual arrangement of the 
various parts of a telegraphic system is shown in the drawings on the 
opposite page. When an operator at Chicago wishes to send a message 
to New York, he first opens the switch which is connected to his key, 
and which is always kept closed except when he is sending a message. 
He then begins to operate his key, thus controlling the clicks of both 
his own sounder and that at New York. When the Chicago switch is 
closed and the one at New York open, the New York operator is able to 
send a message back over the same line. In practice a message is not 
usually sent as far as from Chicago to New York over a single line, 
save in the case of transoceanic cables. Instead it is automatically 
transferred, say at Cleveland, to a second line, which carries it on to 
Buffalo, where it is again transferred to a third line, which carries 
it on to New York. The transfer is made in precisely the same way 
as the transfer from the main circuit to the sounder circuit. If, for 
example, the sounder circuit at Cleveland is lengthened so as to extend 
to Buffalo,. and if the sounder itself is replaced by a relay (called in 
this case a repeater), and the local battery by a line battery, then the 
sounder circuit has been transformed into a repeater circuit, and all the 
conditions are met for an automatic transfer of the message at Cleveland. 

QUESTIONS AND PROBLEMS 

1. Draw a diagram showing how an electric bell works. 

2. Draw a diagram of a short two-station telegraph line which has 
only one instrument at each station. 

3. Draw a diagram showing how the relay and sounder operate in a 
telegraphic circuit. Why is a relay used? 



262 . ELECTRICITY IN MOTION 

RESISTANCE AND ELECTROMOTIVE FORCE 

316. Electrical resistance.* Let the circuit of a galvanic cell be 
connected through a lecture-table ammeter, or any low-resistance gal- 
vanometer, and, for example, 20 feet of No. 30 copper wire, and let the 
deflection of the needle be noted. Then let the copper wire be replaced 
by an equal length of No. 30 German-silver wire. The deflection will 
be found to be a very small fraction of what it was at first. 

A cell, therefore, which is capable of developing a certain 
fixed electrical pressure is able to force very much more 
current through a given wire of copper than through an 
exactly similar wire of German silver. We say, therefore, 
that German silver offers a higher resistance to the passage 
of electricity than does copper. Similarly, every particular 
substance has its own characteristic power of transmitting 
electrical currents. Since silver is the best conductor known, 
resistances of different substances are commonly referred to 
it as a standard, and the ratio between the resistance of a. 
given wire of any substance and the resistance of an exactly 
similar silver wire is called the specific resistance of that sub- 
stance. The specific resistances of some of the commoner 
metals in terms of silver are given below: 

Silver . . . 1.00 Soft iron . . G.OO German silver 18.1 
Copper . . . 1.11 Platinum . . 7.20 Mercury. . . 63.1 
Aluminium. . 1.87 Hard steel . . 13.5 Nichrome . . 66.6 

The resistance of any conductor is directly proportional to 
its length and inversely proportional to the area of its cross 
section or to the square of its diameter. 

The unit of resistance is the ohm, named after Georg Ohm 
(see opposite p. 268). A length of 9.35 feet of No. 30 copper 

* This subject should be accompanied and followed by laboratory experi- 
ments on Ohm's law, on the comparison of wire resistances, and on the 
measurement of internal resistances. See, for example, Experiments 32, 33, 
and 34 of the authors' Manual. 



RESISTANCE AND ELECTROMOTIVE FORCE 263 

wire, or 6.2 inches of No. 30 German-silver wire, has a 
resistance of about one ohm. The legal definition of the ohm 
is a resistance equal to that of a column of mercury 106.3 
centimeters long and 1 square millimeter in cross section, at 0. 

317. Resistance and temperature. Let the circuit of a galvanic 
cell be closed through a galvanometer of very low resistance and about 
10 feet of No. 30 iron wire wrapped about a strip of asbestos. Let the 
deflection of the galvanometer be observed as the wire is heated in a 
Bunsen flame. As the temperature rises higher and higher the current 
will be found to fall continually. 

The experiment shows that the resistance of iron increases 
with rising temperature. This is a general law which holds for 
all metals. In the case of liquid conductors, on the other hand, 
the resistance usually decreases with increasing temperature. 
Carbon and a few other solids show a similar behavior, the 
filament in the early form of incandescent electric lamp 
having only about half the resistance when hot which it has 
when cold. 

318. Electromotive force and its measurement.* The poten- 
tial difference which a galvanic cell or any other generator of 
electricity is able to maintain between its terminals when 
these terminals are not connected by a wire that is, the total 
electrical pressure which the generator is capable of exerting 
is commonly called its electromotive force, usually abbreviated 
to E.M.F. TJie E.M.F. of an electrical generator may be de- 
fined as its capacity for producing electrical pressure, or P.D. 
This P.D. might be measured, as in 294, by the deflection 
produced in an electroscope when one terminal is connected 
to the case of the electroscope and the other terminal to the 
knob. Potential differences are, in fact, measured in this way 
in all so-called electrostatic voltmeters. 

* This subject should be preceded or accompanied by laboratory work on 
E.M.F. See, for example, Experiment 31 of the authors' Manual. 



264 



ELECTKICITY IN MOTION 



#1- 



FIG. 270. Hydrostatic 

analogy of the action 

of a galvanic cell 



The more common type of potential-difference measurer 
consists, however, of an instrument made like a galvanometer 
(Fig. 268), except that the coil of wire is made of very many 
turns of extremely fine wire, so that it 
carries a very small current. The amount 
of current which it does carry, however, 
is proportional to the difference in elec- 
trical pressure existing between its ends 
when these are touched to the two points 
whose P.D. is sought. The principle un- 
derlying this type of voltmeter will be 
better understood from a consideration 
of the following water analogy. If the 
stopcock K (Fig. 270) in the pipe con- 
necting the water tanks C and D is closed, 
and if the water wheel A is set in motion 
by applying a weight IF, the wheel will turn until it creates 
such a difference in the water levels between C and D that 
the back pressure against the left face of the wheel stops it 
and brings the weight Wto rest. In precisely 
the same way the chemical action within the 
galvanic cell whose terminals are not joined 
(Fig. 271) develops positive and negative 
charges upon these terminals ; that is, creates 
a P.D. between them until the back electrical 
pressure through the cell due to this P.D. is 
sufficient to put a stop to further chemical 
action. The seat of the E.M.F. is at the sur- 
faces of contact of the metals with the acid, 
where the chemical actions take place. 

Now, if the water reservoirs (Fig. 270) are 
put in communication by opening the stopcock K, the differ- 
ence in level between C and D will begin to fall, and the 
wheel will begin to build it up again. But if the carrying 




FIG. 271. Meas- 
urement of P.D. 
between the ter- 
minals of a gal- 
vanic cell 



RESISTANCE AND ELECTROMOTIVE FORCE 265 

capacity of the pipe ab is small in comparison with the capac- 
ity of the wheel to remove water from D and supply it to (7, 
then the difference of level which permanently exists between 
C and D when K is open will not be appreciably smaller than 
when it is closed. In this case the current which flows through 
ab may obviously be taken as a measure of the difference 
in pressure which the pump is able to maintain between C 
and D when K is closed. 

In precisely the same way, if the terminals C and D of 
the cell (Fig. 271) are connected by attaching to them the 
terminals a and b of any conductor, they at once begin to 
discharge through this conductor, and their P.D. therefore 
begins to fall. But if the chemical action in the cell is able 
to recharge C and D very rapidly in comparison with the 
ability of the wire to discharge them, then the P.D. between 
C and D will not be appreciably lowered 
by the presence of the connecting conductor. 
In this case the current which flows through 
the conducting coil, and therefore the deflec- 
tion of the needle at its center, may be 
taken as a measure of the electrical pres- 
sure developed by the cell, that is, of the 

P.D. between its unconnected terminals. 

FIG. 272. Lecture- 
Ihe common voltmeter (Fig. 272) is, table voltmeter 

then, exactly like an ammeter, save that it 
offers so high a resistance to the passage of electricity through 
it that it does not appreciably reduce the P.D. between the 
points to which it is connected. 

319. The commercial voltmeter. Fig. 273 shows the con- 
struction of the common form of commercial voltmeter. It dif- 
fers from the ammeter (Fig. 264) in that the shunt is omitted, 
and a high-resistance coil R is put in series with the moving 
coil c. The resistance of a voltmeter may be many thousand 
ohms. The current that passes through it is very small. 




266 



ELECTRICITY IN MOTION 



320. The electromotive forces of galvanic cells. Let a voltmeter 
of any sort be connected to the terminals of a simple galvanic cell, like 
that of Fig. 242. Then let the distance between the plates and the 
amount of their immersion be 
changed through wide limits. It 
will be found that the deflection 
produced is altogether independent 
of the shape or size . of the plates 
or their distance apart. But if the 
nature of the plates is changed, 
the deflection changes. Thus, while 
copper and zinc in dilute sulphuric 
acid have an E.M.F. of one volt, 
carbon and zinc show an E.M.F. 
of at least 1.5 volts, while carbon 
and copper will show an E.M.F. of 
very much less than a volt. Sim- 
ilarly, by changing the nature of 
the liquid in which the plates are 
immersed, we can produce changes 
in the deflection of the voltmeter.* 




FIG. 273. Principle of commercial 
voltmeter 



We learn, therefore, that the E.M.F. of a galvanic cell depends 
simply upon the materials of which the cell is composed, and not 
at all upon the shape, size, or distance apart of the plates. 

321. Fall of potential along a conductor carrying a current. 
Not only does a P.D. exist between the terminals of a cell on 
open circuit, but also between any two points on a conductor 
through which a current is passing. For example, in the 
electrical circuit shown in Fig. 274 the potential at the point 
a is higher than that at m, that at m higher than that at n, 
etc., just as, in the water circuit shown in Fig. 275, the 



* A vertical lecture-table voltmeter (Fig. 272) and a similar ammeter are 
desirable for this and some of the following experiments, but homemade 
high- and low-resistance galvanometers, like those described in the authors' 
Manual, are thoroughly satisfactory, save for the fact that one student must 
take the readings for the class. 



RESISTANCE AND ELECTROMOTIVE FORCE 26T 





FIG. 274. Showing method of 
connecting voltmeter to find 
P.D. between any two points 
m and n on an electrical circuit 



hydrostatic pressure at a is greater 
than that at m, that at m greater 
than that at n, etc. The fall in the 
water pressure between m and n 
(Fig. 275) is measured by the water 
head n's. If we wish to measure the 
fall in electrical potential between 
m and n (Fig. 274), we touch the 
terminals of a voltmeter to these 
points in the manner shown in the 
figure. Its reading gives us at once 
the P.D. between m and n in volts, 
provided always that its own current- 
carrying capacity is so small that it 
does not appreciably lower the P.D. between the points m 
and n by being touched across them ; that is, provided the 
current which flows through it is neg- 
ligible in comparison with that which 
flows through the conductor which 
already joins the points m and n. 

322. Ohm's law. In 1826 Ohm 
announced the discovery that the 
currents furnished ly different gal- 
vanic cells, or combinations of cells, 
are alivays directly proportional to 
the E.M.FSs existing in the circuits in 
which the currents flow, and inversely 
proportional to the total resistances of 
these circuits ; that is, if / represents 
the current in amperes, E the E.M.F. 
in volts, and R the resistance of the 
circuit in ohms, then Ohm's law as applied to the complete cir- 



m 



R 



rt 




FIG. 275. Hydrostatic anal- 
ogy of fall of potential in an 
electrical circuit 



cuit is 



TT 

/= ; that is, current = 



electromotive force 
resistance 



268 ELECTRICITY IN MOTION 

As applied to any portion of an electrical circuit, Ohm's 
law is 

J= . that is , curren t = Potential difference ^ 
R resistance 

where P.D. represents the difference of potential in volts be- 
tween any two points in the circuit, and R the resistance in 
ohms of the conductor connecting these two points. This is 
one of the most important laws in physics. 

Both of the above statements of Ohm's law are included 

in the equation 

volts , ON 

amperes = (3) 

ohms 

323. Internal resistance of a galvanic cell. Let the zinc and 
copper plates of a simple galvanic cell be connected to an ammeter, and 
the distance between the plates then increased. The deflection of the 
needle will be found to decrease, or if the amount of immersion is 
decreased, the current also will decrease. 

Now, since the E.M.F. of a cell was shown in 320 to be 
wholly independent of the area of the plates immersed or of 
the distance between them, it will be seen from Ohm's law 
that the change in the current in these cases must be due to 
some change in the total resistance of the circuit. Since the 
wire which constitutes the outside portion of the circuit has 
remained the same, we must conclude that the liquid within 
the cell, as well as the external wire, offers resistance to the pas- 
sage of the current. This internal resistance of the liquid is 
directly proportional to the distance between the plates, and 
inversely proportional to the area of the immersed portion of 
the plates. If, then, we represent the external resistance of the 
circuit of a galvanic cell by R e and the internal by R^ Ohm's 
law as applied to the entire circuit takes the form 

(4) 




GEORG SIMON OHM (1787-1854) 

German physicist and discoverer of the famous law in physics 
which bears his name. He was born and educated at Erlangen. 
It was in 1826, while he was teaching mathematics at a gym- 
nasium in Cologne, that he published his famous paper on the 
experimental proof of his law. At the time of his death he was 
professor of experimental physics in the university at Munich. 
The ohm, the practical unit of resistance, is named in his honor 



<c 

ll 



r 




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- 5 .2 5 ~ 



r- G ~ w a 
"a, S 3 * 3 == 5 
o g J- '5 >-. o 

"*"* O gj "^ ^ "^ 5 

bx) .c "^ *c B 

I a &1? |1 

o t o & 5 * 

'o ^ c t . ^ 
< c -^ * M 



^ O O 

PH 

Q QJ ,_! 

^ 0^ 

si 

rt 05 T5 



^ p 



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w w ^ 

G S % 

o>^ 2^ e 

C ,- 



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G U 



S o 5 fi " 

g g -C g .2 1 



sme^i 

<D bJC .S G o O) e3 

S " rt O w 
a ca ,C S O en 

O CJ 1/2 "^ 

| ^ i SJ*| 

II 



RESISTANCE AND ELECTROMOTIVE FORCE 269 

Thus, if a simple cell has an internal resistance of 2 ohms and an 
E.M.F. of 1 volt, the current which will flow through the circuit when 
its terminals are connected by 9.35 ft. of No. 30 copper wire (1 ohm) is 

= .33 ampere. 

324. Measurement of internal resistance. A simple and direct method 
of finding a length of wire which has a resistance equivalent to the 
internal resistance of a cell is to connect the cell first to an ammeter 
or any galvanometer of negligible resistance* and then to introduce 
enough German-silver wire into the circuit to reduce the galvanometer 
reading to half its original value. The internal resistance of the cell is 
then equal to that of the German-silver wire. Why ? A still easier method 
in case both an ammeter and a voltmeter are available is to divide the 
E.M.F. of the cell as given by the voltmeter by the current which the cell 
is able to send through the ammeter when connected directly to its 
terminals; for in this case R e of equation (4) is negligibly small; 

therefore R { = . This gives the internal resistance directly in ohms. 

325. Measurement of any resistance by ammeter- voltmeter 
method. The simplest way of measuring the resistance of a 
wire, or, in general, of any conductor, is to connect it into the 
circuit of a galvanic cell in the manner 

shown in Fig. 276. The ammeter A is 
inserted to measure the current, and the 
voltmeter Fto measure the P. D. between 
the ends a and b of the wire r, the resist- 
ance of which is sought. The resistance 

of r in ohms is obtained at once from the 

., FIG. 276. Ammeter-volt- 

ammeter and voltmeter readings with mete r method of meas- 

the aid of the law / = , from which uring resistance 

JLk/ 

P.D. 

it follows that R = - Thus, if the voltmeter indicates a 

P.D. of .4 volt and the ammeter a current of .5 ampere, the 
4 

resistance of r is '-- = .8 ohm.t 
.o 

*A lecture-table ammeter is best, but see note on page 266. 

t See Experiment 33 of the authors' Manual for Wheatstone's bridge method. 




270 



ELECTRICITY IX MOTION 



326. Joint resistance of conductors connected in series and in 
parallel. When resistances are connected as in Fig. 277, so 

that the same current flows 

lOtim 3Ohms 50tims 

o^'YTJr'Try?rffir>/TBTr^ 



FIG. 277. Series connections 




through each of them in 

succession, they are said to 

be connected in series. The 

total resistance of a number 

of conductors so connected is the sum of the several resistances. 

Thus, in the case shown in the figure the total resistance 

between a and b is 10 ohms. 

When n exactly similar conductors are joined in the manner 
shown in Fig. 278, that is, in parallel or multiple, the total 
resistance between a and b is \/n of the 
resistance of one of them ; for obviously, 
with a given P.D. between the points 
a and b, four conductors will carry four 
times as much current as one, and n 
conductors will carry n times as much 
current as one. Therefore the resistance, 
which is inversely proportional to the 
carrying capacity (see 322), is \/n as much as that of one. 

327. Shunts. A wire connected in parallel with another 
wire is said to be a shunt to that wire. Thus, the conductor 
X (Fig. 279) is said to be shunted across 
the resistance R. Under such conditions 
the currents carried by R and X will be 
inversely proportional to their resistances, 
so that if X is 1 ohm and R is 10 ohms, R 
will carry -^ as much current as X, or -i. 
of the whole current. In other words, since the carrying 
power, or conductance, of X is ten times that of R, ten times 
as much current will flow through X as through R, or -j-^- of 
the whole current will pass through the shunt. The ammeter 
(Fig. 264) uses a shunt of exceedingly small resistance. 



FIG. 278. Parallel con- 
nections 




FIG. 279. A shunt 



RESISTANCE AND ELECTKOMOTIVE FORCE 271 



QUESTIONS AND PROBLEMS 

1. How can you prove that the E.M.F. of a cell does not depend 
upon the size or nearness of the plates ? 

2. How can you prove that the internal resistance of a cell becomes 
smaller when the plates are made larger ? when placed closer together ? 

3. If the potential difference between the terminals of a cell on open 
circuit is to be measured by means of a galvanometer, why must the 
galvanometer have a high resistance ? 

4. Why are iron wires used on telegraph lines but copper wires on 
trolley systems? 

5. A voltmeter which has a resistance of 2000 ohms is shunted 
across the terminals A and B of a wire which has a resistance of 1 ohm. 
What fraction of the total current flowing from A to B will be carried 
by the voltmeter ? 

6. In a given circuit the P.D. across the terminals of a resistance 
of 19 ohms is found to be 3 volts. What is the P.D. across the termi- 
nals of a 3-ohm wire in the same circuit ? 

7. The resistance of a certain piece of German-silver wire is 1 ohm. 
What will be the resistance of another piece of the same length but of 
twice the diameter ? 

8. How much current will flow between two points whose P.D. is 
2 volts, if they are connected by a wire having a resistance of 12 ohms ? 

9. What P.D. exists between the ends of a wire whose resistance is 
100 ohms when the wire is carrying a current of .3 ampere ? 

10. If a voltmeter attached across the terminals of an incandescent 
lamp shows a P.D. of 110 volts, while an ammeter connected in series 
with the lamp indicates a current of .5 ampere, what is the resistance 
of the incandescent filament ? 

11. A certain storage cell having an E.M.F. of 2 volts is found to 
furnish a current of 20 amperes through an ammeter whose resistance 
is .05 ohm. Find the internal resistance of the cell. 

12. The E.M.F. of a certain battery is 10 volts and the strength of 
the current obtained through an external resistance of 4 ohms is 1.25 
amperes. What is the internal resistance of the battery ? 

13. Consider the diameter of No. 20 wire to be three times that of 
No. 30. A certain No. 30 wire 1 meter long has a resistance of 6 ohms. 
What would be the resistance of 4 meters of No. 20 wire made of the 
same metal? 

14. Three wires, each having a resistance of 15 ohms, were joined 
in parallel and a current of 3 amperes sent through them. How much 
was the E.M.F. of the current? 



272 



ELECTRICITY IN MOTION 



r-*H 




FIG. 280. Chemical 
actions in the vol- 
taic cell 



PRIMARY CELLS 

328. Study of the action of a simple cell. If the simple cell 
already described, that is, zinc and copper strips in dilute sulphuric acid, 
is carefully observed, it will be seen that, so long as the plates are not 
connected by a conductor, fine bubbles of gas are 

slowly formed at the zinc plate, but none at the 
copper plate. As soon, however, as the two strips 
are put into metallic connection, bubbles appear in 
great numbers about the copper plate (Fig. 280), 
and at the same time a current manifests itself in 
the connecting wire. These are bubbles of hydro- 
gen. Their appearance on the zinc may be pre- 
vented either by using a plate of chemically pure 
zinc or by amalgamating impure zinc, that is, by 
coating it over with a thin film of mercury. But 
the bubbles on the copper cannot be thus disposed 
of. They are an invariable accompaniment of the 

current in the circuit. If the current is allowed to run for a considerable 
time, it will be found that the zinc wastes away, even though it has been 
amalgamated, but that the copper plate does not undergo any change. 

We learn, therefore, that the electrical current in the simple 
cell is accompanied by the eating up of the zinc plate by 
the liquid, and by the evolution of hydrogen bubbles at the 
copper plate. In every type of galvanic cell, actions similar 
to these two are always found ; that is, one of the plates is 
always eaten up, and upon the other plate some element is deposited. 
The zinc, which is eaten, is the one which we found to be 
negatively charged when tested ( 300), so that when the 
terminals are connected through a wire, the negative electrons 
flow through this wire from the zinc plate to the copper plate. 
This means, in accordance with the convention mentioned in 
the footnote to 293, that the direction of the current thrmtgh 
the external circuit is always from the uneaten to the eaten plate. 

329. Local action and amalgamation. The cause of the 
appearance of the hydrogen bubbles at the surface of im- 
pure zinc when dipped in dilute sulphuric acid is that little 



PEIMARY CELLS 



273 



electrical circuits are set up between the zinc and the small 
impurities in it (carbon or iron particles) in the manner 
indicated in Fig. 281. If the zinc is pure, 
these little local currents cannot, of course, be 
set up, and consequently no hydrogen bubbles 
appear. Amalgamation stops this so-called 
local action, because the mercury dissolves the 
zinc, while it does not dissolve the carbon, 
iron, or other impurities. The zinc-mercury 
amalgam formed is a homogeneous substance which spreads 
over the whole surface and covers up the impurities. It is 
important, therefore, to amalgamate the zinc in a battery, in 
order to prevent the consumption of the zinc when the cell 
is on open circuit. The zinc is under all circumstances eaten 
up when the current is flowing, amalgamation serving only 
to prevent its consumption when the circuit is open. 



FIG. 281. Local 
action 



330. Theory of the action of a simple cell. A simple cell may be 
made of any two dissimilar metals immersed in a solution of any acid 
or salt. For simplicity let us examine the action of a cell cbmposed of 
plates of zinc and copper immersed in a dilute solution of hydrochloric 
acid. The chemical formula for hydrochloric 
acid is HC1. This means that each molecule 
of the acid consists of one atom of hydrogen 
combined with one atom of chlorine. As 
was explained under electrolysis ( 302), the 
acid dissociates into positively and negatively 
charged ions (Fig. 282). 

When a zinc plate is placed in such a solu- 
tion, the acid attacks it and pulls zinc atoms 
into solution. Now, whenever a metal dis- 
solves in an acid, its atoms, for some unknown 
reason, go into solution bearing little positive 

charges. The corresponding negative charges must be left on the zinc plate 
in precisely the same way in which a negative charge is left on silk 
when positive electrification is produced on a glass rod by rubbing it 
the silk. It is in this way, then, that we account for the negative 




FIG. 282. Showing disso- 
ciation of hydrochloric- 
acid molecules in water 



274 ELECTRICITY IN MOTION 

charge which we found upon the zinc plate in the experiment which 
was performed with the galvanic cell and the electroscope (see 300). 

The passage of positively charged zinc ions into solution gives a posi- 
tive charge to the solution about the zinc plate, so that the hydrogen 
ions tend to be repelled away from this plate. When these repelled 
hydrogen ions reach the copper plate, some of them give up their charges 
to it and then collect as bubbles of hydrogen gas. It is in this way 
that we account for the positive charge which we found on the copper 
plate in the experiment of 300. 

If the zinc and copper plates are not connected by an outside con- 
ductor, this passage of positively charged zinc ions into solution con- 
tinues but a very short time, for the zinc soon becomes so strongly charged 
negatively that it pulls back on the + zinc ions with as much force as 
the acid is pulling them into solution. In precisely the same way the 
copper plate soon ceases to take up any more positive electricity from 
the hydrogen ions, since it soon acquires a large enough + charge to 
repel them from itself with a force equal to that with which they are 
being driven out of solution by the positively charged zinc ions. It is 
in this way that we account for the fact that on open circuit no chemi- 
cal action goes on in the simple galvanic cell, the zinc and copper plates 
simply becoming charged to a definite difference of potential which is 
called the E.M.F. of the cell. 

When, however, the copper and zinc plates are connected by a wire, 
a current at once flows from the copper to the zinc, and the plates thus 
begin to lose their charges. This allows the acid to pull more zinc into 
solution at the zinc plate, and allows more hydrogen to go out of solution 
at the copper plate. These processes, therefore, go on continuously so 
long as the plates are connected. Hence a continuous current flows 
through the connecting wire until the zinc is all eaten up or the 
hydrogen ions have all been driven out of the solution, that is, until 
either the plate or the acid has become exhausted. 

331. Polarization. If the simple galvanic cell described is con- 
nected to a lecture-table ammeter through two or three feet of No. 30 
German-silver wire, the deflection of the needle will decrease slowly ; 
but if the hydrogen is removed from the copper plate (this can be done 
completely only by removing and thoroughly drying the plate), the 
deflection will be found to return to its first value. 

The experiment shows clearly that the observed falling off 
in current was due to the collection of hydrogen about the 



PKIMAKY CELLS 275 

copper plate. This phenomenon of the weakening of the cur- 
rent from a galvanic cell is called the polarization of the celL 

332. Causes of polarization. The presence of the hydrogen 
bubbles on the positive plate causes a diminution in the 
strength of the current for two reasons : first, since hydrogen 
is a nonconductor, by collecting on the plate it diminishes the 
effective area of the plate and therefore increases the internal 
resistance of the cell; second, the collection of the hydrogen 
about the copper plate lowers the E.M.F. of the cell, because 
it virtually substitutes a hydrogen plate for the copper plate, 
and we have already seen ( 320) that a change in any of 
the materials of which a cell is composed changes its E.M.F. 
That there is a real fall in E.M.F. as well as a rise in internal 
resistance when a cell polarizes may be directly proved in 
the following way: 

Let the deflection of a lecture-table voltmeter whose terminals are 
attached to the freshly cleaned plates of a simple cell be noted. Then 
let the cell's terminals be short-circuited through a coarse wire for half 
a minute. As soon as the wire is removed, the E.M.F., indicated by the 
voltmeter, will be found to be much lower than at first. It will, however, 
gradually creep back toward its old value as the hydrogen disappears- 
from the plate, but a thorough cleaning and drying of the plate will be 
necessary to restore completely the original E.M.F. 

The different forms of galvanic cells in common use differ 
chiefly in different devices employed either for disposing of 
the hydrogen bubbles or for preventing their formation. 
The most common types of such cells are described in the 
following sections. 

333. The Daniell cell. The Daniell cell consists of a zinc plate 
immersed in zinc sulphate and a copper plate immersed in copper sul- 
phate, the two liquids being kept apart either by means of an unglazed 
earthen cup, as in the type shown in Fig. 283,* or else by gravity. 

* To set up, fill the battery jar with a saturated solution of copper sul- 
phate. Fill the porous cup with water and add a handful of zinc sulphate 
crystals. 



276 



ELECTEICITY IK MOTION 




FIG. 283. The Daniell cell 



In this cell polarization is almost entirely avoided, for the reason that 
no opportunity is given for the formation of hydrogen bubbles; for, 
just as the hydrochloric acid solution described in 330 consists of 
positive hydrogen ions and negative chlorine ions in water, so the zinc 
sulphate (ZnSO 4 ) solution consists of positive zinc 
ions and negative SO 4 ions, and the copper sulphate 
solution of positive copper ions 
and negative SO 4 ions. Now the 
zinc of the zinc plate goes into 
solution in the zinc sulphate in 
precisely the same way that it 
goes into solution in the hydro- 
chloric acid of the simple cell 
described in 330. This gives a 
positive charge to the solution 
about the zinc plate, and causes 
a movement of the positive ions 
between the two plates from the 

zinc toward the copper, and of negative ions in the opposite direction, 
both the Zn and the SO 4 ions being able to pass through the porous 
cup. Since the positive ions about the copper plate consist of atoms of 
copper, it will be seen that the material which is driven out of solution 
at the copper plate, instead of being hydrogen, as in the simple cell, is 
metallic copper. Since, then, the element which is deposited on the 
copper plate is the same as that of which it already consists, it is clear 
that neither the E.M.F. nor the resistance of the cell can be changed 
because of this deposit; that is, the cause of the polarization of the 
simple cell has been removed. 

The great advantage of the Daniell cell lies in the relatively high 
degree of constancy in its E.M.F. (1.08 volts). It has a comparatively 
high internal resistance (one to six ohms) and is therefore incapable of 
producing very large currents, about one ampere at most. It will fur- 
nish a very constant current, however, for a great length of time, in fact, 
until all of the copper is driven out of the copper sulphate solution. In 
order to keep a constant supply of the copper ions in the solution, copper- 
sulphate crystals are kept in the compartment S of the cell of Fig. 283 
or in the bottom of the gravity cell. These dissolve as fast as the solution 
loses its strength through the deposition of copper on the copper plate. 

The Daniell is a so-called " closed-circuit " cell ; that is, its circuit 
should be left closed (through a resistance of thirty or forty ohms) 



PRIMARY CELLS 



277 




FIG. 284. The Western 
normal cell 



whenever the cell is not in use. If it is left on open circuit, the copper 
sulphate diffuses through the porous cup, and a brownish muddy deposit 
of copper or copper oxide is formed upon the zinc. Pure copper is also 
deposited in the pores of the porous cup. Both of these actions damage 
the cell. When the circuit is closed, however, since the electrical forces 
always keep the copper ions moving toward the 
copper plate, these damaging effects are to a 
large extent avoided. 

334. The Western normal cell ; the volt. 

This cell consists of a positive electrode 
of mercury in a paste of mercurous sul- 
phate, and a negative electrode of cad- 
mium amalgam in a saturated solution of 
cadmium sulphate (Fig. 284). It is so 
easily and exactly reproducible and has an 
E.M.F. of such extraordinary constancy 
that it has been taken by international agreement as the 
standard in terms of which all E.M.F.'s and P.D.'s are rated. 
Thus the E.M.F. of a Weston normal cell at 20 C. is taken as 
1.0183 volts. The legal definition of the volt is then " an electrical 
pressure equal to 1 * 8 3 of that produced by a Weston normal celV 

335. The Leclanche cell. The Leclanche 
cell (Fig. 285) consists of a zinc rod in a 
solution of ammonium chloride (150 grams to 
a liter of water) and a carbon plate placed 
inside of a porous cup which is packed full of 
manganese dioxide and powdered graphite or 
carbon. As in the simple cell, the zinc dis- 
solves in the liquid, and hydrogen is liberated 
at the carbon, or positive, plate. Here it is 
slowly attacked by the manganese dioxide. 

This chemical action is, however, not quick enough to prevent 
rapid polarization when large currents are taken from the cell. 
The cell slowly recovers when allowed to stand for a while 




FIG. 285. The 
Leclanche" cell 



278 



ELECTRICITY IN MOTION 



on open circuit. The E.M.F. of a Leclanche cell is about 1.5 
volts, and its initial internal resistance is somewhat less than 
an ohm. It therefore furnishes a momentary current of from 
one to three amperes. 

The immense advantage of this type of cell lies in the 
fact that the zinc is not at all eaten by the ammonium chlo- 
ride when the circuit is open, and that therefore, unlike the 
Daniell cell, it can be left for an indefinite time on open 
circuit without deterioration. Leclanche cells are used almost 
exclusively where momentary currents only are needed, as, 
for example, on doorbell circuits. 
The cell requires no attention for 
years at a time, other than the oc- 
casional addition of water to replace 
loss by evaporation, and the occa- 
sional addition of ammonium chlo- 
ride (NH 4 C1) to keep positive NH 4 
and negative Cl ions in the solution. 

336. The dry cell. The dry cell 
(Fig. 286) is a modified form of 
Leclanche cell. It is not really 
dry, since the mixture within is a 
moist paste. The ordinary dry cell 

contains approximately 100 grams of water. The zinc plate 
is in the form of a cylindrical can and holds the moist black 
mixture in which the carbon plate is embedded. This mixture 
consists of ammonium chloride, black oxide of manganese, 
zinc chloride, powdered petroleum coke, and a small amount 
of graphite. As in the Leclanche cell, it is the action of the 
ammonium chloride upon the zinc which produces the current. 
The manganese dioxide overcomes the polarization due to 
hydrogen. The function of the ZnCl. 2 is to overcome the polar- 
ization due to ammonia. The graphite diminishes internal 
resistance, which, in a fresh cell of ordinary size, may be less 




- Pitch 
Sand 

?-$( Carbon rod 

Moist Hack 

mixture 

Pulp board 

lining 

Zinc plate 



FIG. 286. The dry cell 



PEIMAKY CELLS 



279 




FIG. 287. Cells con- 
nected in series 



than ^o of an ohm. Because of the low internal resistance 
these cells will deliver 30 or more amperes on momentary 
short circuit, and on account of their great convenience they are 
manufactured by the million annually, one 
firm alone making as high as 30,000 a day. 
337. Combinations of cells. There are two 
ways in which cells may be combined : first, 
in series-, and, second, in parallel. When 
they are connected in series, the zinc of one 
cell is joined to the copper of the second, the zinc of the second 
to the copper of the third, etc., the copper of the first and the 
zinc of the last being joined to the ends of the external resist- 
ance (see Fig. 287). The E.M.F. of such a combination is the 
sum of the E.M.F.'s of the single cells. 
The internal resistance of the combina- 
tion is also the sum of the internal resist- 
ances of the single cells. Hence, if the 
external resistances are very small, the 
current furnished by the combination will 
be no larger than that furnished by a single 
cell, since the total resistance of the circuit 
has been increased in the same ratio as the 
total E.M.F. But if the external resist- 
ance is large, the current produced by the 
combination will be very much greater 
than that produced by a single cell. Just 
how much greater can always be deter- 
mined by applying Ohm's law ; for if there are n cells in series, 
and E is the E.M.F. of each cell, the total E.M.F. of the cir- 
cuit is nE. Hence, if R e is the external resistance and R { the 
internal resistance of a single cell, then Ohm's law gives 




ll 


>. . . ^ 


I 


R i 

3 






b 


e 

. 

]' 













m 

FIG. 288. Water anal- 
ogy of cells in series 



T 



nE 



280 



ELECTEICITY IN MOTION 






FIG. 289. Cells 
in parallel 



FIG. 290. Water analogy 
of cells in parallel 



If the n cells are connected in parallel, that is, if all the 
coppers are connected together and all the zincs, as in Fig. 289, 
the E.M.F. of the combination is only the E.M.F. of a single 
cell, while the internal resistance is 1/n of that of a single 
cell, since connecting the cells in this way is simply equivalent 
to multiplying the area of the plates n times. The current 
furnished by such a 
combination will be 
given by the formula 



/= 



If, therefore, R e is 
negligibly small, as in 
the case of a heavy 
copper wire, the current flowing through it will be n times as 
great as that which could be made to flow through it by a 
single cell. Figs. 288 and 290 show by means of the water 
analogy why the E.M.F. of cells in series is the sum of the 
several E.M.F.'s, and why the E.M.F. of cells in parallel is no 
greater than that of a single cell. These considerations show 
that the rules which should govern the combination of cells are 
as follows : Connect in series when R e is large in comparison with 
jft . ; connect in parallel when R { is large in comparison with R e . 

QUESTIONS AND PROBLEMS 

1. A certain dry cell having an E. M. F. of 1.5 volts delivered a 
current of 30 amperes through an ammeter having a negligible resist- 
ance. Find the internal resistance of the cell. 

2. Why is a Leclanche" cell better than a Daniell cell for ringing 
doorbells ? 

3. Diagram three wires in series and three cells in series. If each 
wire has a resistance of .1 ohm, what is the resistance of the series ? If 
each cell has a resistance of .1 ohm, what is the internal resistance of 
the series? 



SECONDARY CELLS 281 

4. Diagram three wires in parallel or multiple, and three cells in 
multiple. If each wire has a resistance of 6 ohms, what is the joint 
resistance of the three ? If each cell has an internal resistance of 6 ohms, 
what is the resistance of the group ? 

5. With the aid of Figs. 288 and 290 discuss the water analogies 
of the rules at the end of 337. 

6. If the internal resistance of a Daniell cell of the gravity type is 
4 ohms, and its E.M. F. 1.08 volts, how much current will 40 cells in 
series send through a telegraph line having a resistance of 500 ohms ? 
What current will 40 cells joined in parallel send through the same 
circuit? What current will one such cell send through the same circuit? 

7. W r hat current will the. 40 cells in parallel send through an am- 
meter which has a resistance of .1 ohm ? What current would the 40 
cells in series send through the same ammeter? What current would a 
single cell send through the same ammeter ? 

8. Under what conditions \vill a small cell give practically the same 
current as a large one of the same type ? 

9. How many cells, each of E.M.F. 1.5 volts and internal resistance 
.2 ohm, will be needed to send a current of at least 1 ampere through 
an external resistance of 40 ohms ? 

10. Why is it desirable that a galvanometer which is to be used for 
measuring currents have as low a resistance as possible? 

11. Ordinary No. 9 telegraph wire has a resistance of 20 ohms to the 
mile. What current will 100 Daniell cells in series, each of E.M.F. of 
1 volt, send through 100 miles of such wire, if the two relays have a 
resistance of 150 ohms each and the cells an internal resistance of 4 
ohms each? 

12. If the relays of the preceding problem had each 10,000 turns of 
wire in their coils, how many ampere turns were effective in magnetizing 
their electromagnets ? 

13. If, on the above telegraph line, sounders having a resistance of 
3 ohms each and 500 turns were to be put in the place of the relays, 
how many ampere turns would be effective in magnetizing their cores ? 
Why, then, does the electromagnet of the relay have a high resistance ? 

SECONDARY CELLS 
338. Lead storage batteries. Let two 6 by 8 inch lead plates be 

screwed to a half-inch strip of some insulating material, as in Fig. 291, 
and immersed in a solution consisting of one part of sulphuric acid to 
ten parts of water. Let a current from two storage or three dry cells in 
series, C, be sent through this arrangement, an ammeter A or any 




282 ELECTEICITY IX MOTION 

low-resistance galvanometer being inserted in the circuit. As the current 
flows, hydrogen bubbles will be seen to rise from the cathode (the plate 
at which the current leaves the solution), while the positive plate, or 
anode, will begin to turn dark brown. 
At the same time the reading of the 
ammeter will be found to decrease rap- 
idly. The brown coating is a compound 
of lead and oxygen, called lead peroxide 
(PbO 2 ), which is formed by the action 
upon the plate of the oxygen which is ^ ^ The Q Q 

liberated, precisely as .in the experiment the gtorage battery 

on the electrolysis of water ( 302). Now 

let the batteries be removed from the circuit by opening the key K v 
and let an electric bell B be inserted in their place by closing the key 
K 2 . The bell will ring and the ammeter A will indicate a current flowing 
in a direction opposite to that of the original current. This current will 
decrease rapidly as the energy which was stored in the cell by the original 
current is expended in ringing the bell. 

This experiment illustrates the principle of the storage bat- 
tery. Properly speaking, there has been no storage of electricity, 
but only a storage of chemical energy. 

Two similar lead plates have been changed by the action of 
the current into two dissimilar plates, one of lead and one of 
lead peroxide ; in other words, an ordinary galvanic cell has 
been formed, for any two dissimilar metals in an electrolyte 
constitute a primary galvanic cell. In this case the lead per- 
oxide plate corresponds to the copper of an ordinary cell, and 
the lead plate to the zinc. This cell tends to create a current 
opposite in direction to that of the charging current ; that is, 
its E.M.F. pushes back against the E.M.F. of the charging 
cells. It was for this reason that the ammeter reading fell. 
When the charging current is removed, this cell acts exactly 
like a primary galvanic cell and furnishes a current until the 
thin coating of peroxide is used up. The only important differ- 
ence between a commercial storage cell (Fig. 292) and the 
one which we have here used is that the former is provided in 



SECONDARY CELLS 



283 




Fig. 292. Lead-plate 
storage cell 



the making with a. much thicker coat of the " active material " 

(lead peroxide on the positive plate and a porous, spongy 

lead on the negative) than can be formed by a single charging 

such as we used. This material is pressed 

into interstices in the plates, as shown 

in Fig. 292. The E.M.F. of the lead 

storage cell is about 2 volts. Since the 

plates are always very close together 

and may be given any desired size, the 

internal resistance is usually small, so 

that the currents furnished may be very 

large. 

The usual efficiency of the lead stor- 
age cell is about 75% ; that is, only 
about ^ as much electrical energy can 
be obtained from it as is put into it. 

339. Nickel-iron storage batteries. Thomas A. Edison (see 
opposite p. 316) developed and perfected the nickel-iron 
caustic-potash storage cell. The electrolyte is a 21% solu- 
tion of caustic potash in water. The negative plates contain 
iron powder securely retained in perforated flat rectangular 
capsules, while the positive plates contain oxide of nickel in 
perforated cylindrical containers. For equal capacities the 
Edison cell weighs about half as much as the lead cell, and 
it will stand a remarkable amount of electrical and mechan- 
ical abuse. The E.M.F. is about 1.2 volts. In efficiency it 
is a little below the lead cell. Caustic potash is now replaced 
by caustic soda. 

QUESTIONS AND PROBLEMS 

1. In charging a storage battery is it better to say that the current 
passes into the cell or through it ? What is " stored " ? 

2. The lead peroxide plate and the nickel oxide plate are both called 
" the positives." What is the relation of the charging current to these 
plates ? 



284 ELECTRICITY IN MOTION 

HEATING EFFECTS OF THE ELECTRIC CURRENT 

340. Heat developed in a wire by an electric current. Let the 
terminals of two or three dry cells in series be touched to a piece of 
No. 40 iron or German-silver wire and the length of wire between these 
terminals shortened to -^ inch or less. The wire will be heated to incan- 
descence and probably melted. 

The experiment shows that in the passage of the current 
through the wire the energy of the electric current is trans- 
formed into heat energy. The electrical energy expended 
when a current flows between points of given P.D. may be 
spent in a variety of ways. For example, it may be spent 
in producing chemical separation, as in the charging of a 
storage cell; it may be spent in doing mechanical work, as 
is the case when the current flows through an electric motor ; 
or it may be spent wholly in heating the wire, as was the 
case in the experiment. It will always be expended in this 
last way when no chemical or mechanical changes are pro- 
duced by it. (See drawings opposite p. 269 for uses made 
of heating effects.) 

341. Energy relations of the electric current. We found 
in Chapter IX that energy expended on a water turbine is 
equal to the quantity of water passing through it times the 
difference in level through which the water falls ; or, that 
the power (rate of doing work) is the product of the fall in 
level and the current strength. In just the same way it is 
found that when a current of electricity passes through a 
conductor, the power, or rate of doing work, is equal to the 
fall in potential between the ends of 'the conductor times the 
strength of the electric current. If the P.D. is expressed in 
volts and the current in amperes, the power is given in watts, 
and we have yoltg x ampereg = wattg _ 

The energy of the electric current is usually measured in 
kilowatt hours. 



HEATING EFFECTS 



285 



A kilowatt hour is the quantity of energy furnished in one 
hour ly a current ivhose rate of expenditure of energy is a 
kilowatt. 

342. Incandescent lamps. The ordinary incandescent lamp 
(Fig. 293) consists of a tungsten filament heated to incan- 
descence by an electric current. 

Since the filament would burn up in a few seconds in air, 
it is placed in a highly exhausted bulb. When in use it 
slowly vaporizes, depositing a dark, mirror- 
like coating of metal upon the inner surface 
of the bulb. The lead-in wires are sold- 
ered one to the base A of the socket and 
the other to its rim J5, these being the elec- 
trodes through which the current enters and 
leaves the lamp. The wires ^#, w, sealed into 
the w^alls of the bulb, must have the same 
coefficient of expansion as the glass to 
prevent leakage of air. 

Incandescent lamps are usually grouped 
in parallel or multiple, on a circuit that 
maintains a potential of something over 100 volts between 
the terminals of the lamps (Fig. 318). The rate of consump- 
tion of energy is about 1.25 watts per candle power for the 
ordinary sizes. Tungsten filaments, being operated at a much 
higher temperature than is possible with the now almost 
obsolete carbon filament, have an efficiency nearly three times 
as great. 

A customer usually pays for his light by the kilowatt 
hour ( 341). The rate at which energy is consumed by 
a lamp carrying ^ ampere at 100 volts is 25 watts. Two 
such lamps running for 4 hours would, therefore, consume 
2 x 4 x 25 = 200 watt hours = .200 kilowatt hour. The 
energy is measured and recorded on a recording watt-hour 
meter (Fig. 321). 




FIG. 293. The tung- 
sten vacuum lamp 



286 



ELECTRICITY IX MOTION 



By filling the bulb with nitrogen a very efficient form of 
the tungsten lamp is obtained. The long filament is wound 
into an exceedingly fine spiral to minimize heat radiation. 
As we have already learned ( 207), the presence of gas 
retards evaporation; hence, because of the nitrogen the fila- 
ment may be raised to a higher temperature than is permis- 
sible in a vacuum. A greatly increased candle power results 
from the slight increase in current. Moreover, the convection 
currents in the gas-filled lamp cause the mir- 
ror due to vaporization to form near the top 
of the globe, where it does not obscure the 
intensity of the light. The larger sizes of 
gas-filled lamps consume only .6 watt per 
candle power. 

343. The arc light. When two carbon rods are 
placed end to end in the circuit of a powerful elec- 
tric generator,, the carbon about the point of contact 
is heated red-hot. If, then, the ends of the carbon 
rods are separated one-fourth inch or so, the current 
will still continue to flow, for a conducting layer of 
incandescent vapor, called an electric arc, is produced 
between the poles. The appearance of the arc is 
shown in Fig. 294. At the + pole a hollow, or crater, 
is formed in the carbon, while the carbon becomes 
cone-shaped, as in the figure. The carbons are con- 
sumed at the rate of about an inch an hour, the + carbon wasting away 
about twice as fast as the one. The light comes chiefly from the + 
crater, where the temperature is about 3800 C., the highest attainable 
by man. All known substances are volatilized in the electric arc. 

The open arc requires a current of 10 amperes and a P.D. between its 
terminals of about 50 volts. Such a lamp produces about 500 * candle 
power, and therefore consumes energy at the rate of about 1 watt per 
candle power. The light of the arc lamp is due to the intense heat 
developed on account of resistance, not to actual combustion, or burning. 
Nevertheless, in the open arc the oxygen of the air unites so rapidly with 

* This is the so-called "mean spherical" candle power. The candle 
power in the direction of maximum illumination is from 1000 to 1200. 




FIG. 294. The arc 
light 



HEATING EFFECTS 



287 



the carbon at the hot tips that in a few hours the rods are consumed. 
To overcome this difficulty the inclosed arc (Fig. 295) is used. Shortly 
after the arc is " struck " the oxygen in the inner globe is used up and 
then the hot carbon tips are surrounded by an 
atmosphere of carbon dioxide and nitrogen. 
Under these conditions the carbons last 130 to 
150 hours. The inclosed arc is much longer than 
the open arc, and therefore in this lamp the P.D. 
between the tips is greater, usually about 80 volts, 
while the rest of the P.D. of the line is taken up 
in the resistance coils of the lamp. 

The recently invented flaming arc, produced 
between carbons which have a composite core con- 
sisting chiefly of carbon and fluoride of calcium, 
sometimes reaches an efficiency as high as .27 watt 
per candle power. It gives 
an excellent yellow light, 
which penetrates fog well. 
344. The arc light auto- 
matic feed. Since the two 
carbons of the arc gradually 
waste away, they would soon 
become so far separated that 
the arc could no longer be 
maintained were it not for 
an automatic feeding device 
which keeps the distance be- 
tween the carbon tips very 

nearly constant. Fig. 296 shows the essential fea- 
tures of one form of this device. When no current 
flows through the lamp, gravity holds the carbon 
tips at e together; but as soon as the current is 
thrown on, it energizes the magnet coils m, m, which 
draw up the U-shaped iron core, thus striking the 
arc at e. As the carbons slowly waste away, the arc 
becomes longer, the resistance greater, and the cur- 
rent less; hence the upward magnetic pull weakens and the upper 
carbon descends, and vice versa. From time to time the upper carbon 
slips down through the friction clutch c. It is clear, therefore, that this 
automatic device will maintain that particular length of arc for which 




FIG. 295. Mechanism 
of a direct-current in- 
closed arc lamp 




FIG. 296. Feeding 
device for arc lamp 



288 



ELECTRICITY IN MOTION 



equilibrium exists between the effect of gravity pulling down and mag- 
netism pulling up. A dashpot d, containing a stationary piston, prevents 
the magnetic pull from suddenly drawing the tips at e too far apart. 

345. The Cooper-Hewitt mercury lamp. The Cooper-Hewitt mercury 
lamp (Fig. 297) differs from the arc lamp in that the incandescent body 
is a long column of mercury vapor instead of an incandescent solid. 
The lamp consists of 
an exhausted tube 
three or four feet long, 
the positive electrode 
at the top consi sting of 
a plate of iron, while 
the negative electrode 
at the bottom is a 
small quantity of mer- 
cury. Under a suf- 
ficient difference of 
potential between these terminals a long mercury-vapor arc is formed, 
which stretches from terminal to terminal in the tube. This arc emits 
a very brilliant light, but it is almost entirely wanting in red rays. The 
strength of its actinic rays makes it especially valuable in photography. 
Its commercial efficiency is about .6 watt per candle power. Cooper- 
Hewitt lamps having quartz tubes are used for sterilizing purposes 
because of the powerful ultra-violet rays which the quartz transmits. 




FIG. 297. The Cooper-Hewitt mercury-vapor 
arc lamp 



QUESTIONS AND PROBLEMS 

1. What is meant by a 104-volt lamp? What would happen to such 
a lamp if the P.D. at its terminals amounted to 500 volts? Trolley cars 
are usually furnished with current at about 500 volts ; how would you use 
100-volt lamps on such a circuit? 

2. A very common electric 
lamp used in our homes is 
marked 25 watts and carries 
about ^ ampere. One fresh dry 
cell on short circuit will deliver 
30 or more amperes. Will the 
cell light the lamp? 

3. A 50-vol6 carbon lamp carrying 1 ampere has about the same 
candle power as a 100-volt carbon lamp carrying ampere. Explain 
why. 




I 



FIG. 298 



HEATING EFFECTS 289 

4. If a storage cell has an E.M.F. of 2 volts and furnishes a cur- 
rent of 5 amperes, what is its rate of expenditure of energy in watts? 

5. Fig. 298 shows the connections for a lamp L which can be 
turned on or off at two different points a or b. Explain how it works. 

6. How many 100-volt lamps each carrying ^ ampere may be main- 
tained on a circuit where the total power may not exceed 600 watts ? 

7. What will it cost to use an electric laundry iron for 6 hours if it 
takes 3.5 amperes on a 104-volt circuit, the cost of current being $.09 
per kilowatt hour ? 

8. A certain electric toaster takes 5 amperes at 110 volts. It will 
make two pieces of toast at once in 3 minutes. At what horse-power 
rate does the toaster convert electrical energy into heat energy? At 
$.08 per kilowatt hour what does it cost to make 12 pieces of toast? 

9. How many lamps, each of resistance 20 ohms and requiring a 
current of .8 ampere, can be lighted by a dynamo that has an output 
of 4000 watts? 

10. If one of the wire loops in a tungsten lamp is short-circuited, 
what effect will this have on the amount of current flowing through 
the lamp? on the brightness of the filament? 

11. How many cells working as in problem 4 would be equivalent 
to 1 H.P. ? (See 144, p. 122.) 

12. Since one calorie is equal to 42,000,000 ergs, 1 watt (10,000,000 
ergs per second) develops in one second .24 calories. Therefore the 
number of calories, H, developed in t seconds by a current of / amperes 
between two points whose P.D. is V volts is expressed by the equation 

H = I x V x t x .24. 

How many calories per minute are given out by the electric toaster of 
problem 8? 

13. From the equation of problem 12 show that 

H = PR x t x .24. 

14. How many minutes are required to heat 600 g. of water from 
15 C. to 100 C. by passing 5 amperes through a 20-ohm coil immersed 
in the water? 

15. Why is it possible to get a much larger current from a storage 
cell than from a Daniell cell ? 

16. If an automobile is equipped with 6-volt lamps, how many lead 
storage cells must be on the car? Are these cells in series or multiple? 

17. A small arc lamp requires a current of 5 amperes and a difference 
of potential between its terminals of 45 volts. What resistance must be 
connected in series with it in order to use it on a 110-volt circuit? 




CHAPTER XY 

INDUCED CURRENTS 
THE PRINCIPLE OF THE DYNAMO AND MOTOR 

346. Current induced by a magnet. Let 400 or 500 turns of 
No. 22 copper wire be wound into a coil C (Fig. 299) about two and a 
half inches in diameter. Let this coil be connected into circuit with 
a lecture-table galvanometer (Fig. 263), or even a simple detector made 
by suspending in a box, 
with No. 40 copper wire, 
a coil of 200 turns of No. 
30 copper wire (see Fig. 
299). Let the coil C be S[ 
thrust suddenly over the 
N pole of a strong horse- 
shoe magnet. The deflec- FlG 299 Induction of electric currents 
tion of the pointer p of by ma gnets 

the galvanometer will in- 
dicate a momentary current flowing through the coil. Let the coil be 
held stationary over the magnet. The pointer will be found to come to 
rest in its natural position. Now let the coil be removed suddenly from 
the pole. The pointer will move in a direction opposite to that of its 
first deflection, showing that a reverse current is now being generated 
in the coil. 

We learn, therefore, that a current of electricity may be 
induced in a conductor by causing the latter to move through a 
magnetic field, while a magnet has no such influence upon a 
conductor which is at rest with respect to the field. This dis- 
covery, one of the most important in the history of science, 
was announced by the great Faraday in 1831. From it have 
sprung directly most of the modern industrial developments 
of electricity. 

290 




MICHAEL FARADAY (1791-1867) 

Famous English physicist and chemist ; one of the most gifted of experimenters 
son of a poor blacksmith ; apprenticed at the age of thirteen to a London book- 
binder, with whom he worked nine years ; applied for a position in Sir Humphry 
Davy's laboratory at the Royal Institution in 1813 ; became director of this labo- 
ratory in 1825; discovered electromagnetic induction in 1831; made the first 
dynamo; discovered in 1833 the laws of electrolysis, now known as Faraday's 
laws ; the farad, the practical unit of electrical capacity, is named in his honor 





INDUCTION MOTOR 

One of the most familiar of the more recent applications of the great principle of 
induction discovered by Faraday is the induction motor, which has come into 
extensive use in both large and small sizes. The particular one here shown is 
known as the squirrel-cage form, in which there is no electrical connection 
between the stator (the stationary part) and the rotor (the revolving part) . The 
stator is wound on a laminated core like the stator of a dynamo, while the rotor 
consists of copper bars laid in a slotted laminated core, their ends being joined to 
copper rings, one at each end. The bars are therefore in parallel. The alternating 
current applied to the stator windings develops a magnetic field which rotates 
around the iron ring of the stator. This is equivalent to a set of magnetic poles 
mechanically rotated around the rotor. The magnetic lines of force which there- 
fore cut across the copper bars of the rotor generate in them an E.M.F. which 
causes a current to flow in the copper system of the rotor. The rotating field 
reacts with the field produced by the current in the conductors of the rotor so as 
to cause the rotor to be dragged around after the rotating field 



PRINCIPLE OF THE DYNAMO AND MOTOR 291 



347. Direction of induced current. Lenz's law. In order to 

find the direction of the induced current, let a very small P.D. from a 
galvanic cell be applied to the terminals A and B (Fig. 299), and note 
the direction in which the pointer moves when the current enters, say, 
at A. This will at once show in what direction the current was flow- 
ing in the coil C when it was being thrust over the N pole. By a simple 
application to C of the right-hand rule ( 308) we can then tell which 
was the N and which the face of the coil when the induced current 
was flowing through it. In this way it will be found that if the coil w T as 
being moved past the N pole of the magnet, the current induced in it 
was in such a direction as to make the lower face of the coil an N pole 
during the downward motion and an S pole during the upward motion. 
In the first case the repulsion of the N pole of the magnet and the N 
pole of the coil tended to oppose the motion of the coil while it was 
moving from a to b, and the attraction of the N pole of the magnet and 
the S pole of the coil tended to oppose the motion while it was moving 
from b to c. In the second case the repulsion of the two N poles tended 
to oppose the motion between b and c, and the attraction between the 
N pole of the magnet and the S pole of the coil tended to oppose the 
upward motion from b to a. In every case, therefore) the motion is made 
against an opposing force. 

From these experiments, and others like them, we arrive at 
the following law : Wfenever a current is induced by the rela- 
tive motion of a magnetic field and a conductor, the direction of 
the induced current is always such as to set up a magnetic field 
which opposes the motion. This is Lenz's law. 
This law might have been predicted at once 
from the principle of the conservation of 
energy ; for this principle tells us that since 
an electric current possesses energy, such 
a current can appear only through the ex- 
penditure of mechanical work or of some F IG . 300. 
other form of energy. 

348. Condition necessary for an induced 
E.M.F. Let the coil be held in the position 

shown in Fig. 300, and moved back and forth parallel to the magnetic 
field, that is, parallel to the line NS. No current will be induced. 




Currents 
induced only when 
conductor cuts lines 
of force 



292 



INDUCED CURRENTS 




FIG. 301. E.M.F. 
induced when a 
straight conductor 
cuts magnetic lines 



By experiments of this sort it is found that an E.M.F. is 
induced in a coil only when the motion takes place in such a way 
as to change the total number of magnetic lines 
of force which are inclosed by the coil. Or, to 
state this rule in more general form, an 
E.M.F. is induced in any element of a con- 
ductor when, and only when, that element is 
moving in such a way as to cut magnetic 
lines of force.* 

It will be noticed that the first statement 
of the rule is included in the second, for 
whenever the number of lines of force which 
pass through a coil changes, some lines of force must cut 
across the coil from the inside to the outside, or vice versa. 

349. The principle of the electric motor. 
Let a vertical wire ab be rigidly attached to a 
horizontal wire gh, and let the latter be supported 
by a ring or other metallic support, in the manner 
shown in Fig. 302, so that ab is free to oscillate 
about gh as an axis. Let the lower end of ab dip 
into a trough of mercury. When a magnet is held 
in the position shown and a current from a dry cell 
is sent down through the wire, the wire will in- 
stantly move in the direction indicated by the 
arrow f, namely, at right angles to the direction of 
the lines of magnetic force. Let the direction of 
the current in the wire be reversed. The direction 
of the force acting on the wire will be found to be 
reversed also. 

We learn, therefore, that a wire carrying 
a current in a magnetic field tends to move in 

* If a strong electromagnet is available, these experiments are more instruc- 
tive if performed, not with a coil, as in Fig. 300, but with a straight rod 
(Fig. 301) to the ends of which are attached wires leading to a galvanometer. 
Whenever the rod moves parallel to the lines of magnetic force there will 
be no deflection, but whenever it moves across the lines the galvanometer 
needle will move at once. 




FIG. 302. The prin- 
ciple of the electric 
motor 



PRINCIPLE OF THE DYNAMO AND MOTOR 293 



a direction at right angles both to the direction of the field and 
to the direction of the current. This fact underlies the opera- 
tion of all electric motors. 

350. The motor and dynamo rules. A convenient rule for 
determining whether the wire ab (Fig. 302) will move forward 
or back in a given case may be obtained as follows: If the 
field of a magnet alone is represented by Fig. 303, and that 
due to the current * alone by Fig. 304, then the resultant field 
when the current-bearing wire is placed between the poles of 
the magnet is that shown in Fig. 305 ; for the strength of the 




FIG. 303. Field of 
magnet alone 



FIG. 304. Field of 
current alone 



FIG. 305. Field of magnet 
and current 



field above the wire is now the sum of the two separate fields, 
while the strength below it is their difference. Now Faraday 
thought of the lines of force as acting like stretched rubber 
bands. This would mean that the wire in Fig. 305 would be 
pushed down. Whether the lines of force are so conceived or 
not, the motor rule may be stated thus : 

A current in a magnetic field tends to move away from the 
side* on which its lines are added to those of the field. 

The dynamo rule follows at once from the motor rule and 
Lenz's law. Thus, when a wire is moved through a magnetic 
field the current induced in it must be in such a direction as 

* The cross in the conductor of Fig. 304, representing the tail of a retreat- 
ing arrow, is to indicate that the current flows away from the reader. A dot, 
representing the head of an advancing arrow, indicates a current flowing 
toward the reader. 



294 INDUCED CURRENTS 

to oppose the motion ; therefore the induced current will be 
in such a direction as to increase the number of lines on the side 
toward which it is moving. 

351. Strength of the induced E.M.F. The strength of an 
induced E.M.F. is found to depend simply upon the number of 
lines of force cut per second by the conductor, or, in the case 
of a coil, upon the rate of change in the number of lines of 
force which pass through the coil. The strength of the current 
which flows is then given by Ohm's law ; that is, it is equal to 
the induced E.M.F. divided by the resistance of the circuit. 
The number of lines of force which the conductor cuts per 
second may always be determined if we know the velocity of 
the conductor and the strength of the magnetic field through 
which it moves. For it will be remembered that, according to 
the convention of 270, a field of unit strength is said to con- 
tain one line of force per square centimeter, a field of 1000 
units strength 1000 lines per square centimeter, etc. In a 
conductor which is cutting lines at the rate of 100,000,000 
per second there is an induced E.M.F. of 1 volt. * The reason 
why we used a coil of 500 turns instead of a single turn in the 
experiment of 346 was that by thus making the conductor 
in which the current was to be induced cut the lines of force 
of the magnet 500 times instead of once, we obtained 500 
times as strong an induced E.M.F., and therefore 500 times 
as strong a current for a given resistance in the circuit. 

352. Currents induced in rotating coils. Let a 400- or 500-tum 
coil of No. 28 copper wire be made small enough to rotate between the 
poles of a horseshoe magnet, and let it be connected into the circuit of 
a galvanometer, precisely as in 346. Starting with the coil in the posi- 
tion of Fig. 306, (1), let it be rotated suddenly clockwise (looking down 
from above) through 180. A strong deflection of the galvanometer will 
be observed. Let it be rotated through the next 180 back to the starting 
point. An opposite deflection will be observed. 

* This may be considered as the scientific definition of the volt, convenience 
alone having dictated the legal definition given in 334. 



PRINCIPLE OF THE DYNAMO AND MOTOR 295 



(l) 





FIG. 306. Direction of cur- 
rents induced in a coil rotat- 
ing in a magnetic field 



The arrangement is a dynamo in miniature. During the 
first half of the revolution (see Fig. 306, (2)) the wires on 
the right side of the loop were cutting the lines of force in one 
direction, while the wires on the left 
side were cutting them in the oppo- 
site direction. A current was being 
generated down on the right side 
of the coil and up on the left side 
(see dynamo rule). It will be seen 
that both currents flow around the 
coil in the same direction. The in- 
duced current is strongest when the 
coil is in the position shown in 
Fig. 306, (2), because there the 
lines of force are being cut most rapidly. Just as the coil is 
moving into or out of the position shown in Fig. 306, (1), 
its edges are moving parallel to the lines of force, and hence 
no current is induced, since no lines of force are being cut 
As the coil moves through the last 180 of its revolution 
both sides are cutting the same lines of force as before, but 
they are cutting them in an opposite direction ; hence the 
current generated during this last half is opposite in direction 
to that of the first half.* 

QUESTIONS AND PROBLEMS 

1. Can the number of lines of force within a closed coil of wire be 
increased or decreased without the lines being cut by the wire ? Explain. 

2. Under what conditions may an electric current be produced by a, 
magnet ? 

3. How many lines of force must be cut per second to induce 10 volts? 

4. If a coil of wire is rotated about a vertical axis in the earth's field> 
an alternating current is set up in it. In what position is the coil when 
the current changes direction? 

*A laboratory experiment on the principles of induction should be 
performed at about this point. See, for example, Experiment 36 of the 
authors' Manual. 



296 



INDUCED CURRENTS 



5. State Lenz's law, and show how it follows from the principle of 
the conservation of energy. 

6. A coil is thrust over the S pole of a magnet. Is the direction of 
the induced current clockwise or counterclockwise as you look down 
upon the pole ? 

7. A ship having an iron mast is sailing east. In what direction is 
the E.M.F. induced in the mast by the earth's magnetic field? If a wire 
is brought from the top of the mast to its bottom, no current will flow 
through the circuit. Why? 

8. A current is flowing from top to bottom in a vertical wire. In 
what direction will the wire tend to move on account of the earth's 
magnetic field? 

DYNAMOS 

353. A simple alternating-current dynamo. The simplest 
form of commercial dynamo consists of a coil of wire so 
arranged as to rotate continuously between the poles of 
a powerful electromagnet 
(Fig. 307). 

In order to make the mag- 
netic field in which the con- 
ductor is moved as strong as 
possible, the coil is wound 
upon an iron core C. This 
greatly increases the total 
number of lines of magnetic 
force which pass between JV 
and S, for instead of an air 
path the core offers an iron 
path, as shown in Fig. 308. 

The rotating part, consisting of the coil with its core, is 
called the armature. One end of the coil is attached to the 
insulated metal ring R, which is attached rigidly to the shaft 
of the armature and therefore rotates with it, while the other 
end of the coil is attached to a second ring R'. The brushes 
b and V, which constitute the terminals of the external circuit, 
are always in contact with these rings. 




FIG. 307. Drum-wound armature 



DYNAMOS 



297 




As the coil rotates, an induced alternating current passes 
through the circuit. This current reverses direction as often 
as the coil passes through the 
position shown in Fig. 308, that 
is, the position in which the con- 
ductors are moving parallel to 
the lines of force ; for at this 
instant the conductors which were 
moving up begin to move down, 
and those which were moving 
down begin to move up. The cur- 
rent reaches its maximum value 
when the coils are moving through a position 90 farther on, 
for then the lines of force are being cut most rapidly by the 
conductors OR- both sides of the coil. These facts are graphi- 
cally represented by the curve of E.M.F.'s (Fig. 309). 

354. The multipolar alternator. For most commercial purposes it is 
found desirable to have 120 or more alternations of current per second. 
This could not be attained easily with two-pole machines like those 



FIG. 308. End view of drum 
armature 







90 



270 



etc. 



FIG. 309. Curve of alternating electromotive force 

sketched in Figs. 307 and 308. Hence commercial alternators are 
usually built with a large number of poles alternately N and S, arranged 
around the circumference of a circle in the manner shown in Fig. 310. 
These poles are excited by a direct current. The dotted lines represent 
the direction of the lines of force through the iron. It will be seen that 
the coils which are passing beneath N poles have induced currents set 
up in them the direction of which is opposite to that of the currents 
which are induced in the conductors which are passing beneath the S 
poles. Since, however, the direction of winding of the armature coils 
changes between each two poles, all the inductive effects of all the poles 
are added in the coil and constitute at any instant one single current 



298 



INDUCED CURRENTS 



flowing around the complete circuit in the manner indicated by the 
arrows in the diagram. This current reverses direction at the instant 
at which all the coils pass the midway points between the JV and S poles. 
The number of alternations per 
second is equal to the number of 
poles multiplied by the number of 
revolutions per second. The field 
magnets ,/Vand S of such a dynamo 
are usually excited by a direct 
current from some other source. 
Fig. 311 represents an alternating- 
current dynamo with revolving 
field and stationary armature con- 
nected directly to a tandem com- 
pound engine. Alternators of 5000- 
kilowatt capacity (nearly 7000 FIG. 310. Diagram of alternating- 
horse power) have been built to current dynamo 
run at the unusually high speed 

of 3600 revolutions per minute. Alternators of lower speed but of very 
much greater capacity are common (see huge rotor opposite p. 257). 

355. The principle of the commutator. By the use of a so- 
called commutator it is possible to transform a current which 





FK; .311. Alternating-current dynamo 

is alternating in the coils of the armature to one which always 
flows in the same direction through the external portion of 
the circuit. The simplest possible form of such a commutator 



DYNAMOS 



299 




FIG. 312. The simple commutator 



is shown in Fig. 312. It consists of a single metallic ring 

which is split into two equal insulated semicircular segments 

a and c. One end of the ro- 

tating coil is soldered to one 

of these semicircles, and the 

other end to the other semi- 

circle. Brushes b and b ! are 

set in such positions that they 

lose contact with one semicircle 

and make contact with the 

other at the instant at which 

the current changes direction in the armature. The current, 

therefore, always passes out to the external circuit through 

the same brush. While a cur- 

rent from such a coil and com- 

mutator as that shown in the 

figure would always flow in the 

same direction through the ex- 

ternal circuit, it would be of a 

pulsating rather than a steady 

character, for it would rise to a 

FIG. 313. Two-pole direct-current 

maximum and fall again to zero dynamo with ring armature 

twice during each complete revo- 

lution of the armature. This effect is avoided in the com- 
mercial direct-current dynamo by building a commutator of 
a large number of segments instead of two, and connecting 




90 180 270 360 etc. 

FIG. 314. Curve of commutated electromotive force 

each to a portion of the armature coil in the manner shown 
in Fig. 313. The result of using a simple split-ring com- 
mutator is shown graphically in Fig. 314. 



300 



INDUCED CURRENTS 




FIG. 315. The direct-current 
dynamo, drum winding 



356. The drum-armature direct-current dynamo. Fig. 315 is a diagram 
illustrating the construction of a commercial two-pole direct-current 
dynamo of the drum-armature type. 
At a given instant currents are being 
induced in the same direction in all 
the conductors on the left half of the 
armature. The cross on these conduc- 
tors, representing the tail of a retreat- 
ing arrow, is to indicate that these 
currents flow away from the reader. 
No E.M.F.'s are induced in the con- 
ductors at the top and bottom of the 
armature, where the motion is parallel 
to the magnetic lines. On the right 
half of the ring, on the other hand, the induced currents are all in the 
opposite direction, that is, toward the reader, since the conductors are 
here all moving up instead of down. The dot in the middle of these 
conductors represents the 
head of an approaching 
arrow. It will be seen, how- 
ever, in tracing out the con- 
nections 1, 1 1? 2, 2 P 3, 3 r etc., 
of Fig. 315 (the dotted lines 
representing connections at 
the back of the drum), that 
the coil is so wound about 
the drum that the currents 
in both halves are always 
flowing toward one brush b, 
from which they are led to 
the external circuit and back 
at T)'. This condition always 
exists, no matter how fast p IG 

the rotation; for it will be 
seen that as each loop ro- 
tates into the position where the direction of its current reverses, it 
passes a brush and therefore at once becomes a part of the circuit on 
the other half of the drum where the currents are all flowing in the 
opposite direction. Fig. 316 shows a typical modern four-pole generator, 
and Fig. 317 the corresponding drum-wound armature. Fig. 326 (p. 310) 




A four-pole direct-current 
generator 



DYNAMOS 



301 




Main Circuit 



illustrates nicely the method of winding such an armature, each coil 
beginning on one segment of the commutator and ending on the 
adjacent segment. 

357. Dynamo lighting circuit. The 
type of circuit generally used in 
B.C. incandescent lighting is shown 
in Fig. 318. The lamps are arranged 
in parallel between the mains. The 

field magnets are excited partly by FIG. 31 7. A modern drum armature 

a few series turns which carry the 

whole current going to the lamps, and partly by a shunt coil consisting 

of many turns of fine wire (Fig. 318). This combination of series and 

shunt winding maintains the P.D. across the 

mains constant for a great range of loads. 

Such a machine is called a compound wound 

dynamo, to distinguish it from a series wound 

machine, for example, which dispenses with 

the shunt coil. 

In all self-exciting machines there is 
enough residual magnetism left in the iron 
cores after stopping to start feeble induced 
currents when started up again. These cur- 
rents immediately increase the strength of the 
magnetic field, and so tjie machine quickly 

builds up its current until the limit of mag- FlG - 318 - The compound- 
netization is reached. wound d y namo 

358. The electric motor. In construction the electric motor 
differs in no essential respect from the dynamo. To analyze 
the operation as a motor of such a machine as that shown in 
Fig. 313, suppose a current from an outside source is 1 first sent 
around the coils of the field magnets and then into the arma- 
ture at b f . Here it will divide and flow through all the con- 
ductors on the left half of the ring in one direction, and 
through all those on the right half in the opposite direction. 
Hence, in accordance with the motor rule, all the conductors 
on the left side are urged upward by the influence of the 
field, and all those on the right side are urged downward. 
The armature will therefore begin to rotate, and this rotation 




302 



INDUCED CURRENTS 



will continue as long as the current is sent in at b r and out 
at b; for as fast as coils pass either b or b r the direction 
of the current flowing through them changes, and therefore 
the direction of the force acting on them changes. The left 
half is therefore always urged up and the right half down. 
The greater the strength of the current, the greater the force 
acting to produce rotation. 

If the armature is of the drum type (Fig. 315), the con- 
ditions are not essentially different; for, as may be seen by 
following out the windings, the current entering at b' will 
flow through all the conductors on the left half in one direction 
and through those 
on the right half in 
the opposite direc- 
tion. The commu- 
tator keeps these 
conditions always 
fulfilled. The induc- 
tion motor is pictured 
and described oppo- 




FIG. 319. Railway motor, upper field raised 



site page 291. 

The electric motor 
is a device which receives electrical energy and converts it 
into mechanical energy. The dynamo is a device which re- 
ceives mechanical energy from a steam engine, water wheel, 
or other source and converts it into electrical energy, 

359. Street-car motors. Electric street cars are nearly all operated 
by direct-current series-wound motors placed under the cars and attached 
by gears to the axles. Fig. 319 shows a typical four-pole street-car motor. 
The two upper field poles are raised with the case when the motor is 
opened for inspection, as in the figure. The current is generally supplied 
by compound-wound dynamos which maintain a constant potential of 
about 500 volts between the trolley or third rail and the track which 
is used as the return circuit. The cars are always operated in parallel, 
as shown in Fig. 320. In a few instances street cars are operated upon 



DYNAMOS 303 

alternating, instead of upon direct-current, circuits. In such cases the 
motors are essentially the same as direct-current series-wound motors ; 
for since in such a machine the current must reverse in the field magnets 
at the same time that it reverses in the armature, it will be seen that 

Trolley Wire or 3d Rail 





1 


nnnnnnnnj 1 




DDDDDI 


at Power V > 
1 Station >C 




y=m rm \ 




L) O ' 





Track 
FIG. 320. Street-car circuit 

the armature is always impelled to rotate in one direction, whether it 
is supplied with a direct or with an alternating current. Other types of 
A.C. motors are not well adapted to starting with full load. 

360. Back E.M.F. in motors. When an armature is set into 
rotation by sending a current from some outside source through 
it, its coils move through a magnetic field as truly as if the 
rotation were produced by a steam engine, as is the case in 
running a dynamo. An induced E.M.F. is therefore set up 
by this rotation. In other words, while the machine is acting 
as a motor it is also acting as a dynamo. The direction of the 
induced E.M.F. due to this dynamo effect will be seen, from 
Lenz's law or from a consideration of the dynamo and motor 
rules, to be opposite to the outside P.D., which is causing 
current to pass through the motor. The faster the motor rotates, 
the faster the lines of force are cut, and hence the greater the 
value of this so-called lack E.M.F. If the motor were doing 
no work, the speed of rotation would increase until the back 
E.M.F. reduced the current to a value simply sufficient to 
overcome friction. It will be seen, therefore, that, in general, 
the faster the motor goes, the less the current which passes 
through its armature, for this current is always due to the 
difference between the P.D. applied at the brushes 500 volts 
in the case of trolley cars and the back E.M.F. When the 



304 



INDUCED CURRENTS 



motor is starting, the back E.M.F. is zero ; and hence, if the full 
500 volts were applied to the brushes, the current sent through 
would be so large as to ruin the armature through overheating. 
To prevent this motors are furnished with a starting box, con- 
sisting of resistance coils which are thrown into series with 
the motor on starting, and thrown out again gradually as the 
speed increases and the back E.M.F. rises.* Trolley cars are 
usually run by two motors which, on starting, work in series, 
so that each supplies a part of the starting resistance for the 
other. After speed is acquired, they work in parallel. 

361. The recording watt-hour meter. The recording watt- 
hour meter (Fig. 321) is the instrument which fixes our 
electric-light bills. It is essentially 
an electric motor containing no 
iron, so that the current through 
the armature A is proportional to 
the P.D. between the mains, while 
the current through the field mag- 
nets F is the current flowing into 
the house. Therefore the force act- 
ing between A and F, or the turning 
power on A (torque), is propor- 
tional to the product of volts by 
amperes ; that is, it is proportional 

to the watts consumed. The rate of rotation is made slow by 
the magnetic drag due to the reaction between the magnets 
M and the current induced in the rotating aluminium disk D 
which rotates between the poles of the magnets. The record- 
ing dials have therefore a speed which is proportional to the 
'watts used, and their total rotation is proportional to the total 
energy, or watt hours, consumed. 

* This discussion should be followed by a laboratory experiment on the 
study of a small electric motor or dynamo. See, for example, Experiment 
No. 87 of the authors' Manual. 




FIG. 321. Interior of watt- 
hour meter 



INDUCTION COIL AND TBANSFOKMER 305 

QUESTIONS AND PROBLEMS 

1. What is the function (use) of the field magnet of a dynamo? 
Wood is cheaper than iron ; why are not the field cores made of wood? 

2. How would it affect the voltage of a dynamo to increase the speed 
of rotation of its armature ? Why ? to increase the number of turns of 
wire in the armature coils? Why? to increase the strength of the 
magnetic field? Why? 

3. When a wire is cutting lines of force at the rate of 100,000,000 
per second, there is induced in it an E.M.F. of one volt. A certain 
dynamo armature has 50 coils of 5 loops each and makes 600 revolutions 
per minute. Each wire cuts 2,000,000 lines of force twice in a revolution. 
What is the E.M.F. developed? 

4. What does the commutator of a dynamo do? What is the pur- 
pose of the commutator of a motor ? 

5. Explain the process of "building up " in a dynamo. 

6. Explain how an alternating current in the armature is trans- 
formed into a unidirectional current in the external circuit. 

7. Explain why a series-wound motor can run on either a direct or 
an alternating circuit. 

8. If a current is sent into the armature of Fig. 313 at V, and taken 
out at &, which way will the armature revolve ? 

9. Will it take more work to rotate a dynamo armature when the 
circuit is closed than when it is open ? Why ? 

10. Single dynamos often operate as many as 10,000 incandescent 
lamps at 110 volts. If these lamps are all arranged in parallel and each 
requires a current of .5 ampere, what is the total current furnished by 
the dynamo ? What is the activity of the machine in kilowatts and in 
horse power? 

11. How many 110-volt lamps like those of Problem 10 can be 
lighted by a 12,000-kilowatt generator ? 

12. Why does it take twice as much work to keep a dynamo running 
when 1000 lights are on t]ie circuit as when only 500 are turned on? 

PRINCIPLE OF THE INDUCTION COIL AND TRANSFORMER 
362. Currents induced by varying the strength of a magnetic 

field. Let about 500 turns of No. 28 copper wire be wound around one 
end of an iron core, as in Fig. 322, and connected to the circuit of a 
galvanometer G. Let about 500 more turns be wrapped about another 
portion of the core and connected into the circuit of two dry cells. When 
the key K is closed, the deflection of the galvanometer will indicate that 



306 INDUCED CUBKENTS 

a temporary current has been induced in one direction through the coil 
s ; and when it is opened, an equal but opposite deflection will indicate 
an equal current flow- 
ing in the opposite x-^ -, p ^ 

direction. V^J ^ ' '""", ,'ui\u _^ 

rrn FIG. 322. Induction of current by magnetizing 

experiment and demagnetizing an iron core 

illustrates the prin- 
ciple of the induction coil and the transformer. The coil jo, 
which is connected to the source of the current, is called the 
primary coil, and the coil s, in which the currents are induced, 
is called the secondary coil. Causing lines of force to spring 
into existence inside of s (in other words, magnetizing the 
space inside of s) has caused an induced current to flow in s ; 
and demagnetizing the space inside of s has also induced a 
current in s in accordance with the general principle stated in 
348, that any change in the number of magnetic lines of force 
which thread through a coil induces a current in the coil. We 
may think of the lines as always existing as closed loops (see 
Fig. 258, p. 255) which collapse upon demagnetization to 
mere double lines at the axis of the coil. Upon magnetization 
one of these two lines springs out, cutting the encircling 
conductors and inducing a current. 

363. Direction of the induced current. Lenz's law, which, 
it will be remembered, followed from the principle of conser- 
vation of energy, enables us to predict at once the direction 
of the induced currents in the above experiments ; and an 
observation of the deflections of the galvanometer enables us to 
verify the correctness of the predictions. Consider first the case 
in which the primary circuit is made and the core thus magnet- 
ized. According to Lenz's law the current induced in the sec- 
ondary circuit must be in such a direction as to oppose the change 
which is being produced by the primary current, that is, in such 
a direction as to tend to magnetize the core oppositely to the 
direction in which it is being magnetized by the primary. This 



INDUCTION COIL AND TRANSFORMER 307 

means, of course, that the induced current in the secondary 
must encircle the core in a direction opposite to the direction 
in which the primary current encircles it. We learn, therefore, 
that on making the current in the primary the current induced 
in the secondary is opposite in direction to that in the primary. 
When the current in the primary is broken, the magnetic 
field created by the primary tends to die out. Hence, by Lenz's 
law, the current induced in the secondary must be in such a 
direction as to tend to oppose this process of demagnetization, 
that is, in such a direction as to magnetize the core in the same 
direction in which it is magnetized by the decaying current 
in the primary. Therefore, at break the current induced in the 
secondary is in the same direction as that in the primary. 

364. E.M.F. of the secondary. If half of the 500 turns of 
the secondary s (Fig. 322) are unwrapped, the deflection will 
be found to be just half as great as before. Since the resistance 
of the circuit has not been changed, we learn from this that 
the E.M.F. of the secondary is proportional to the number of 
turns of wire upon it, a result which followed also from 
351. If, then, we wish to develop a very high E.M.F. in 
the secondary, we have only to make it of a very large number 
of turns of fine wire. 

365. Self-induction. If, in the experiment illustrated in 
Fig. 322, the coil % had been made a part of the same circuit as 
p, the E.M.F.'s induced in it by the changes in the magnetism 
of the core would of course have been just the same as above. 
In other words, when a current starts in a coil, the magnetic 
field which it itself produces tends to induce a current oppo- 
site in direction to that of the starting current, that is, tends 
to oppose the starting of the current; and when a current 
in a coil stops, the collapse of its own magnetic field tends to 
induce a current in the same direction as that of the stopping 
current, that is, tends to oppose the stopping of the current. 
This means merely that a current in a coil acts as though it had 



308 



INDUCED CURRENTS 



inertia, and opposes any attempt to start or stop it. This inertia- 
like effect of a coil upon itself is called self-induction. 

Let a few dry cells be inserted into a circuit containing a coil of a 
large number of turns of wire, the circuit being closed at some point by 
touching two bare copper wires together. Holding the bare wire in the 
fingers, break the circuit between the hands and observe the shock due 
to the current which the E. M. F. of self-induction sends through your 
body. Without the coil in circuit you will obtain no such shock, 
though the current stopped when you break the circuit will be many 
times larger. 

366. The induction coil. The induction coil, as usually 
made (Fig. 323), consists of a soft iron core C composed of 
a bundle of soft iron wires ; a primary coil p wrapped around 

this core and consisting of, say, 
200 turns of coarse copper wire 




0) 



I d 



(2) 




FIG. 323. Induction coil 

(for example, No. 16), which is connected into the circuit 
of a battery through the contact point at the end of the screw 
d\ a secondary coil s surrounding the primary in the manner 
indicated in the diagram and consisting generally of between 
30,000 and 1,000,000 turns of No. 36 copper wire, the termi- 
nals of which are the points t and t' ; and a hammer b, or 
other automatic arrangement for making and breaking the 
circuit of the primary. (See ignition system opposite p. 199.) 

Let the hammer b be held away from the opposite contact point by 
means of the finger, then touched to this point, then pulled quickly away. 
A spark will be found to pass between t and i' at break only never at make. 
This is because, on account of the opposing influence at make of self- 
induction in the primary, the magnetic field about the primary rises 



INDUCTION COIL AND TRANSFORMER 



309 



very gradually to its full strength, and hence its lines pass into the sec- 
ondary coil comparatively slowly. At break, however, by separating the 
contact points very quickly we can make the current in the primary fall 
to zero in an exceedingly short time, perhaps not more than .00001 
second ; that is, we can make all of its lines pass out of the coil in this 
time. Hence the rate at which lines thread through or cut the secondary 
is perhaps 10,000 times as great at break as at make, and therefore the 
E.M.F. is also something like 10,000 times as great. In the normal use 
of the coil the circuit of the primary is automatically made and broken 
at I by means of the magnet and the spring r, precisely as in the case of 
the electric bell. Let the student analyze this part of the coil for him- 
self. The condenser shown in the diagram, with its two sets of plates 
connected to the conductors on either side of the spark gap between r 
and d, is not an essential part of a coil, but when it is introduced it is 
found that the length of the spark which can be sent across between t 
and t' is considerably increased. The reason is as follows : When the 
circuit is broken at b, the inertia (that is, the self-induction) of the 
primary current tends to make a spark jump across 
from d to b ; and if this happens, the current con- 
tinues to flow through this spark (or arc) until the 
terminals have become separated through a con- 
siderable distance. This' makes the current die 
down gradually instead of suddenly, as it ought to 
do to produce a high E.M.F ; but when a condenser 
is inserted, as soon as b begins to leave d the current 
begins to flow into the condenser, and this gives the 
hammer time to get so far away from d that an arc cannot be formed. 
This means a sudden break and a high E. M. F. Since a spark passes 
between t and if only at break, it must always pass 
in the same direction. Coils which give 24-inch 
sparks (perhaps 500,000 volts) are not uncommon. 
Such coils usually have hundreds of miles of wire 
upon their secondaries. 

367. Laminated cores ; Foucault currents. The 
core of an induction coil should always be made of 
a bundle of soft-iron wires insulated from one an- 
other by means of shellac or varnish (see Fig. 324) ; 
for whenever a current is started or stopped in the 
primary p of a coil furnished with a solid iron core (see Fig. 325), the 
change in the magnetic field of the primary induces a current in the 




FIG. 324. Core of 
insulated iron wire 




FIG. 325. Diagram 
showing eddy cur- 
rents in solid core 



310 



INDUCED CURRENTS 




FIG. 326. Laminated drum-armature 

core with commutator, showing one 

coil wound on the core 



conducting core C, for the same reason that it induces one in the second- 
ary s. This current flows around the body of the core in the same 
direction as the induced current in the secondary, that is, in the direc- 
tion of the arrows. The only effect of these so-called eddy or Foucault 
currents is to heat the core. This is obviously a waste of energy. If 
we can prevent the appearance 
of these currents, all of the energy 
which they would waste in heat- 
ing the core may be made to 
appear in the current of the 
secondary. The core is therefore 
built of varnished iron wires, 
which run parallel to the axis of 
the coil, that is, perpendicular to 
the direction in which the cur- 
rents would be induced. The induced E.M.F. therefore finds no closed 
circuits in which to set up a current (Fig. 324). It is for the same rea- 
son that the iron cores of dynamo and motor armatures, instead of being 
solid, consist of iron disks placed side by side, as shown in Fig. 326, 
and insulated from one another by films of oxide. A core of this kind 
is called a laminated core. It will be seen that in all such cores the spaces 
or slots between the laminae must run at right angles to the direction of 
the induced E.M.F., that is, perpendicular to the conductors upon the core. 

368. The transformer. The commercial transformer is a 
modified form of the induction coil. The chief difference is 
that the core R (Fig. 327), instead of 
being straight, is bent into the form of 
a ring or is given some other shape such 
that the magnetic lines of force have a 
continuous iron path instead of being 
obliged to push out into the air, as in 
the induction coil. 

always an alternating instead of an inter- 
mittent current which is sent through the primary A. Send- 
ing such a current through A is equivalent to first magnetiz- 
ing the core in one direction, then demagnetizing it, then 
magnetizing it in the opposite direction, etc. The result of 




TT< , i , . FIG. 327. Diagram of 

Furthermore, it .s transform ' er 



INDUCTION COIL AND TRANSFORMER 



311 



Main Conductor 




FlG ' m Alternating-current light- 
ing circuit with transformers 



these changes in the magnetism of the core is of course an 
induced alternating current in the secondary B. 

369. The use of the transformer. The use of the transformer 
is to convert an alternating current from one voltage to 
another which, for some rea- 

son, is found to be more 

convenient. For example, in 

electric lighting where an al- 

ternating current is used, the 

E.M.F. generated by the dy- 

namo is usually either 1100 

or 2200 volts, a voltage too 

high to be introduced safely 

into private houses. Hence 

transformers are connected 

across the main conductors in the manner shown in Fig. 328. 

The current which passes into the houses to supply the lamps 

does not come directly from the dynamo. It is an induced 

current generated in the transformer. 

Through the use of small transformers the voltage of the 
current of the house lighting circuit is further reduced and 
made available for the ringing of doorbells. 

370. Pressure in primary and secondary. If there are a few 
turns in the primary and a large number in the secondary, the 
transformer is called a step-up transformer, because the P.D. 
produced at the terminals of the secondary is greater than that 
applied at the terminals of the primary. In electric lighting, 
transformers are mostly of the step-down type ; that is, a high 
P.D. (say, 2200 volts) is applied at the terminal of the primary, 
and a lower P.D. (say, 110 volts) is obtained at the terminals 
of the secondary. In such a transformer the primary will have 
twenty times as many turns as the secondary. In general, the 
ratio between the voltages at the terminals of the primary and 
secondary is the ratio of the number of turns of wire upon the two. 



312 



INDUCED CURRENTS 



371. Efficiency of the transformer. In a perfect transformer 
the efficiency would be unity. This means that the electrical 
power, or watts, put into the primary (that is, the volts applied 
to its terminals times the amperes flowing through it) would be 
exactly equal to the power, or watts, taken out in the secondary 
(that is, the volts generated in it times the strength of the in- 
duced current) ; and, in fact, in actual transformers the latter 
product is often more than 97% of the former (that is, there 
is less than 3% loss of energy in the transformation). This lost 
energy appears as heat in the transformer. This transfer, which 
goes on in a big transformer, of huge quantities of power 
from one circuit to another entirely independent circuit, with- 
out noise or motion of any sort and almost without loss, is one 
of the most wonderful phenomena of modern industrial life. 

372. Commercial transformers. Fig. 329 illustrates a common type of 
transformer used in electric lighting. The core is built up of sheet-iron 
laminae about ^ millimeter thick. Fig. 330 shows a section of the same 





FIG. 329. The core type 
of transformer 



FIG. 330. Cross sec- 
tion of transformer, 
showing shape of 
magnetic field 




FIG. 331. Trans- 
former case 



transformer. The closed magnetic circuit of the core is indicated by the 
dotted lines. The primaries and the secondaries are indicated by the 
letters P and S. Fig. 331 is the case in which the transformer is placed. 
Such cases may be seen, attached to poles outside of houses wherever 
alternating currents are used for electric lighting (Fig. 332). 

373. Electrical transmission of power. Since the rate of production 
of electrical energy by a dynamo is the product of the E.M.F. generated 
by the current furnished, it is evident that in order to transmit from 



INDUCTION COIL AND TRANSFORMER 313 




Transformer 



one point to another a given number of watts, say, 10,000, it is pos- 
sible to have either an E.M.F. of 100 volts and a current of 100 amperes 
or an E.M.F. of 1000 volts and a current of 10 amperes. In the two 
cases, however, the loss of energy in 
the wire which carries the current 
from the place where it is generated 
to the place where it is used will be 
widely different. For, 

watts amperes x volts ; 
but, from Ohm's law, 

volts = amperes x ohms. 
Therefore 

watts = amperes 2 x ohms = I 2 R. 

If, then, R represents the resistance 
of this transmitting wire, the so- 
called "line resistance," and / the 
current flowing through it, the heat 
developed in it will be proportional 
to I' 2 R. Hence the energy wasted 
in heating the line will be but ^-^ 
as much in the case of the 1000 volt, 

10-ampere current as in the case of the 100 volt, 100-ampere current. 
Hence for long-distance transmission, where line losses are considerable, 
it is important to use the highest possible voltages. 

On account of the difficulty of insulating the commutator segments 
from one another, voltages higher than 1200 or 1500 cannot be obtained 
with direct-current dynamos of the kind that have been described. 
With alternators, however, the difficulties of insulation are very much 
less on account of the absence .of a commutator. The large 10,000- 
horse-power alternating-current dynamos on the Canadian side of 
Niagara Falls generate directly 12,000 volts. This is the highest volt- 
age thus far produced by generators. In all cases where these high 
pressures are employed they are transformed down at the receiving end 
of the line to a safe and convenient voltage (from 50 to 500 volts) by 
means of step-down transformers. 

It will be seen from the above facts that alternating currents are 
best suited for long-distance transmission. The Big Creek plant in 
California transmits power 241 miles at a pressure of 150,000 volts. 
(See opposite p. 241.) The Southern Sierras Power Company of 



FIG. 332. Transformer on electric- 
light pole 



814 



INDUCED CURRENTS 



California sends current 830 miles across the desert. Transmission at 
220,000 volts is now under consideration for a line to extend the length 
of California, over 1100 miles. In all such cases step-up transformers, 
situated at the power house, transfer the electrical energy developed by 



2.200 volts 



22.000 volts 



22,000 



2,200 




Alternator 



m 
Transformer 




Step-down wv( 
Transformer [\uo l \o\uo 



Motcr Lamps 



Power House Distant City 

FIG. 333. High- voltage long-distance transmission line 



the generator to the line, and step-down transformers, situated at the 
receiving end, transfer it to the motors or lamps which are to be sup- 
plied (Fig. 333). The generators used on the American side of Niagara 
Falls produce a pressure of 2300 volts. For transmis- 
sion to Buffalo, 20 miles away, this is transformed up 
to 22,000 volts. At Buffalo it is transformed down to 
the voltages suitable for operating the street cars, 
lights, and factories of the city. On the Canadian side 
the generators produce currents at 12,000 volts, as 
stated, and these are transformed up, for long-distance 
transmission, to 22,000, 40,000, and 60,000 volts (see 
Fig. 166, p. 150). 

374. The tungar rectifier. Negative electrons are 
found to escape from a filament that is heated to in- 
candescence, and if this filament is then made more 
than, say, 25 volts negative with respect to a near-by 
anode any gas that surrounds the filament is found to 
be ionized (split into positively and negatively charged 
parts) by the violence of the blows which the electrons 
strike against its molecules. It is thus rendered con- 
ducting. These facts are utilized in the tungar rectifier 
of the alternating current. The bulb (Fig. 334) is filled with argon to a 
pressure of 3 to 8 cm. The anode is a small cone of graphite or tungsten, 




FIG. 334. Tun- 
gar bulb 



INDUCTION COIL AND TRANSFORMER 315 




FIG. 335. Principle of opera- 
tion of the tungar rectifier 



and the cathode is a coiled tungsten filament. When the rectifier 
is in operation, the cone and the filament are alternately + and , one 
being + while the other is . When the cone is -f and the filament , 
the negative electrons from the filament 
are forced across the space from the fila- 
ment to the cone, and the argon, which 
is thereby ionized, carries the current 
from the cone to the filament. When the 
cone is and the filament +, the nega- 
tive electrons cannot escape from the 
filament ; hence the gas does not become 
conducting. The principle of operation 
can be understood from Fig. 335. 

The rectifier is connected to the alternating-current line at C and D. 
The alternating current in the primary coil P of the transformer T 
causes an induced current in S, which keeps the filament F incandes- 
cent. Under the action of the current, A and F are alternately + and . 
When ,P is , the electrons escape and ionize -the gas, permitting the 
current to pass. When .F is + the negative electrons are driven back 
into the filament and cannot escape to ionize the gas. Hence no current 
passes. In this way a unidirectional pulsating current passes through 
the storage batteries or other load. This rectifier is used largely for 
charging storage batteries for small-power purposes. 

375. Principle of the carbon microphone. Let a dry cell, an 
ammeter, and two pieces 'of electric-arc carbon be arranged in series 
(Fig. 336). Press the carbons very gently and 
observe the reading of the. ammeter. Press 
, gradually harder, then gradually less, watch- 
ing the instrument. The current increases 
with increase in pressure, and decreases with 
decrease in pressure. 




FIG. 336. The principle 
of the carbon transmitter 



This peculiar behavior of carbon in 
offering a variable resistance with varia- 
tion in pressure is taken advantage of in constructing the 
carbon transmitter of the telephone. In the modern trans- 
mitter, however, the current is made to traverse many particles 
of granular carbon, which, lying loosely together, furnish a 
very great number of loose contacts (see Fig. 339). 



316 INDUCED CURRENTS 

376. Principle of the telephone. The telephone was invented 
in 1875 by Alexander Graham Bell of Washington (see on 
opposite page) and Elisha Gray of Chicago. The simple 
local-battery system is shown in Fig. 337. 

The current from the battery B (Fig. 337) is led first to 
the back of the diaphragm E, whence it passes through a little 
chamber C, filled with granular carbon, to the conducting 
back d of the transmitter, and thence through the primary p 
of the induction coil, and back to the battery. 

When a sound is made in front of the microphone, the 
vibrations produced by the sounding body are transmitted by 

Receiver Receiver 





B B 

FIG. 337. The telephone circuit (local-battery system) 

the air to the diaphragm, thus causing the latter to vibrate 
back and forth. These vibrations of the diaphragm vary the 
pressure upon the many contact points of the granular carbon 
through which the primary current flows. This produces con- 
siderable variation in the resistance of the primary circuit, so 
that as the diaphragm moves forward, that is, toward the carbon, 
a comparatively large current flows through p, and as it moves 
back a much smaller current. These changes in the current 
strength in the primary p produce changes in the magnetism 
of the soft-iron core of the induction coil. Currents are 
therefore induced in the secondary s of the induction coil, and 
these currents pass over the line and affect the receiver at 
the other end. A step-up induction coil is used to get 
sufficient potential to work through the high resistance of a 
long line. 











Clinedinet 

ALEXANDER GRAHAM BELL, 

WASHINGTON, D.C. 
Inventor of the telephone, 1875 



Underwood & Underwood 

THOMAS A. EDISON, ORANGE, 
NEW JERSEY 

Inventor of the phonograph, the incan- 
descent lamp, etc. 




GUGLIELMO MARCONI (ITALY) ORVILLE WRIGHT, DAYTON, OHIO 

Inventor of commercial wireless Inventor, with his brother Wilbur, of 

telegraphy the airplane 

A GROUP OF MODERN INVENTORS 



THE WRIGHT AIRPLANE 

The most significant and far-reaching of the advances of the twentieth century, 
namely, man's conquest of the air after centuries of failure, was made when the 
Wright brothers first introduced the principle upon which all successful flight by 
heavier-than-air machines now depends, namely, control of stability by the warp- 
ing of wings, or by ailerons (hinged attachments to wings), in connection with the 
use of a rudder. The ripper panel shows one of the original gliders (Wilbur 
Wright inside) with which the Wrights first mastered the art of gliding (1900- 
1903) and made more than a thousand gliding flights, some of them GOO feet long, 
following in this work the principles of gliding flight first demonstrated by 
Lilienthal and a little later, much more completely, by Chanute of Chicago (1895- 
1897) . The lower panel shows " the first successful power flight in the history of the 
world " (Orville Wright in the machine, Wilbur running beside it as it rose from 
the track) . Four such flights were made on the morning of December 17, 1903, 
the longest of which lasted 59 seconds and covered a distance of 852 feet against 

a 20-mile wind 



INDUCTION COIL AND TRANSFORMER 



317 




FIG. 338. The modern receiver 



A modern telephone receiver is shown in Fig. 338. It 
consists of a permanently magnetized U-shaped piece of steel 
in front of whose 
poles is a soft-iron 
diaphragm which 
almost touches the 
ends of the mag- 
net. Wound in 
opposite directions 
upon the two poles 
are coils of fine 
insulated wire in 
series with each other and the line wire. G- is the earpiece, 
E the diaphragm, A the U-shaped magnet, and B the coils, 
consisting of many turns of fine wire and having soft-iron 
cores. When the rapidly alternating current from the secondary 
coil s (Fig. 337) flows through the coils of the receiver, the poles 
of the permanent magnet are thereby alternately strengthened 
and weakened in synchronism with the sound waves falling 
upon the diaphragm of the transmitter. The variations in 
the magnetic pull upon the diaphragm 
of the receiver cause it to send out 
sound waves exactly like those which 
fell upon the diaphragm of the trans- 
mitter. 

Telephonic conversation can be car- 
ried on over great distances as rapidly 
as if the parties sat on opposite sides 
of the same table. An electrical im- 
pulse passes over the telephone wires 
from New York to San Francisco in 

about one fifteenth of a second. The cross section of a complete 
long-distance transmitter is shown in Fig. 339. The current 
traverses granular carbon held between solid blocks of carbon. 




FIG . 339. Cross section of 

a long-distance telephone 

transmitter 



318 INDUCED CUKKENTS 

QUESTIONS AND PROBLEMS 

1. Draw a diagram of an induction coil and explain its action. 

2. Does the spark of an induction coil occur at make or at break ? 
Why? 

3. Explain why an induction coil is able to produce such an enor- 
mous E.M.F. 

4. Why could not an armature core be made of coaxial cylinders of 
iron running the full length of the armature, instead of flat disks, as 
shown in Fig. 326 ? 

5. What relation must exist between the number of turns on the 
primary and secondary of a transformer which feeds 110-volt lamps 
from a main line whose conductors are at 1100 volts P.D.? 

6. Name two uses and two disadvantages of mechanical friction ; of 
electrical resistance. 

7. A transformer is so wound as to step the voltage of the lighting 
circuit from 2200 volts down to 110. Sketch the transformer and its 
connections, marking the primary and the secondary, and state the 
relative number of turns in each. If the house circuit uses 40 amperes, 
what current must flow in the primary ? 

8. Why does a " tungar " rectify an alternating current? 

9. The same amount of power is to be transmitted over two lines 
from a power plant to a distant city. If the heat losses in the two lines 
are to be the same, what must be the ratio of the cross sections of the 
two lines if one current is transmitted at 100 volts and the other at 
10,000 volts? (Power = IE; heat loss is proportional to 7 2 72.) 

10. In telephoning from New York to San Francisco how far do 
you think the sound goes ? What passes along the telephone wire ? 



CHAPTER XVI* 

NATURE AND TRANSMISSION OF SOUND 
SPEED AND NATURE OF SOUND 

377. Sources of sound. If a sounding tuning fork provided 
with a stylus is stroked across a smoked-glass plate, it produces 
a wavy line, as shown in Fig. 340 ; if a light suspended ball 
is brought into contact with it, the latter is thrown off with 
considerable violence. If we look 

about for the source of any sudden ^^^r ' Wr^S*~~~- 

/ ' inpitm^Q*-*' 

noise, we find that some object has FJG m Trace ma<Je by 
fallen, or some collision has occurred, vibrating fork 

or some explosion has taken place, 

in a word, that some violent motion of matter has been set 
up in some way. From these familiar facts we conclude that 
sound arises from the motions of matter. 

378. Media of transmission. Air is ordinarily the medium 
through which sound comes to our ears, yet the Indians put 
their ears to the ground to hear a distant noise, and most boys 
know how loud the clapping .of stones sounds under water. 
If the base of the sounding fork of Fig. 340 is held in a dish 
of water, the sound will be markedly transmitted by the water. 
These facts show that a gas like air is certainly no more 
effective in the transmission of sound than a liquid or a 
solid. Next let us see whether or not matter is necessary 
at all for the transmission of sound. 

* This chapter should be accompanied by laboratory experiments on the 
speed of sound in air, the vibration rate of a fork, and the determination 
of wave lengths. See, for example, Experiments 38, 39, and 40 of the authors' 
Manual. 

319 




320 NATUKE AND TRANSMISSION OF SOUND 

Let an electric bell be suspended inside the receiver of an air pump 
by means of. two fine springs which pass through a rubber stopper in 
the manner shown in Fig. 341. Let the air be exhausted from the 
receiver by means of the pump. The sound of the 
bell will be found to become less and less pro- 
nounced. Let the air be suddenly readmitted. 
The volume of sound will at once increase. 

Since the nearer we approach a vacuum, 
the less distinct becomes the sound, we infer 
that sound cannot be transferred through 
a vacuum and that therefore the transmis- 
sion of sound is effected only through the Fl G-341. Sound not 
/. 7 T , , . transmitted through 

agency oj ordinary matter. In this respect 

sound differs from heat and light, which 

evidently pass with perfect readiness through a vacuum, 

since they reach the earth from the sun and stars. 

379. Speed of transmission. The first attempt to measure 
accurately the speed of sound was made in 1738, when a com- 
mission of the French Academy of Sciences stationed two 
parties about three miles apart and observed the interval 
between the flash of a cannon and the sound of the report. 
By taking observations between the two stations, first in one 
direction and then in the other, the effect of the wind was 
eliminated. A second commission repeated these experiments 
in 1832, using a distance of 18.6 kilometers, or a little more 
than 11.5 miles. The value found was 331. 2. meters per sec- 
ond at C. The accepted value is now 331.3 meters. The 
speed in water is about 1400 meters per second, and in iron 
5100 meters. 

The speed of sound in air is found to increase with an in- 
crease in temperature. The amount of this increase is about 
60 centimeters per degree centigrade. Hence the speed at 
20 C. is about 343.3 meters per second. The above figures 
are equivalent to 1087 feet per second at 0C., or 1126 feet 
per second at 20 C. 



SPEED AND NATURE OF SOUND 321 

380. Mechanism of transmission. When a firecracker or toy 
cap explodes, the powder is suddenly changed to a gas, the 
volume of which is enormously greater than the volume of 
the powder. The air is therefore suddenly pushed back in all 
directions from the center of the explosion. This means that 
the air particles which lie about this center are given violent 
outward velocities.* When these outwardly impelled air parti- 
cles collide with other particles, they give up their outward 
motion to these second particles, and these in turn pass it on 
to others, etc. It is clear, therefore, that the motion started by 
the explosion must travel on from particle to particle to an 
indefinite distance from the center of the explosion. Further- 
more, it is also clear that, although the motion travels on to 
great distances, the individual particles do not move far from 
their original positions; for it is easy 
to show experimentally that whenever 
an elastic body in motion collides with 
another similar body at rest, the collid- 
ing body simply transfers its motion to 

the body at rest and comes itself to rest. 

FIG. 342. Illustrating the 

Let six or eight equal steel balls be hung propagation of sound from 
from cords in the manner shown in Fig. 342. particle to particle 

First let all of the balls but two adjacent 

ones be held to one side, and let one of these two be raised and allowed 
to fall against the other. The first ball will be found to lose its motion 
in the collision, and the second will be found to rise to practically the 
same height as that from which the first fell. Next let all of the balls be 
placed in line and the end one raised and allowed to fall as before. The 
motion will be transmitted from ball to ball, each giving up the whole 
of its motion practically as soon as it receives it, and the last ball will 
move on alone with the velocity which the first ball originally had. 

* These outward velocities are simply superposed upon the velocities of 
agitation which the molecules already have on account of their temperature. 
For our present purpose we may ignore entirely the existence of these latter 
velocities and treat the particles as though they were at rest, save for the 
velocities imparted by the explosion. 




322 NATURE AND TRANSMISSION OF SOUND 

The preceding experiment furnishes a very nice mechanical 
illustration of the manner in which the air particles which 
receive motions from an exploding firecracker or a vibrating 
tuning fork transmit these motions in all directions to neigh- 
boring layers of air, these in turn to the next adjoining layers, 
etc., until the motion has traveled to very great distances, 
although the individual particles themselves move only very 
minute distances. When a motion of this sort, transmitted 
by air particles, reaches the drum of the ear, it produces the 
sensation which we call sound. 

381. A train of waves ; wave length. In the preceding para- 
graphs we have confined attention to a single pulse traveling 
out from a center of explosion. Let us next consider the sort 
of disturbance which is set ABC 
up in the air by a con tin- \ / J 
uously vibrating body, like \\ VcTe'i th 

the prong of Fig. 343. Each m 

time that this prong moves 

., . , , .. -, FIG. 343. Vibrating reed sending out a 

to ihe right it sends out a train of cq ^sstant pulses 

pulse which travels through 

the air at the rate of 1100 feet per second, in exactly the 
manner described in the preceding paragraphs. Hence, if the 
prong is vibrating uniformly, we shall have a continuous 
succession of pulses following each other through the air at 
exactly equal intervals. Suppose, for example, that the prong 
makes 110 complete vibrations per second. Then at the end 
of one second the first pulse sent out will have reached a 
distance of 1100 feet. Between this point and the prong 
there will be 110 pulses distributed at equal intervals; that 
is, each two adjacent pulses will be just 10 feet apart. If 
the prong made 220 vibrations per second, the distance be- 
tween adjacent pulses Avould be 5 feet, etc. The distance, 
letiveen two adjacent pulses in such a train of waves is called 
a wave length. 



SPEED AND NATURE OF SOUND 323 

382. Relation between velocity, wave length, and number 
of vibrations per second. If n represents the number of vibra- 
tions per second of a source of sound, I the wave length, and v 
the velocity with which the sound travels through the medium, 
it is evident from the example of the preceding paragraph that 
the following relation exists between these three quantities : 

I = v/n, or v = nl ; (1) 

that is, wave length is equal to velocity divided by the number of 
vibrations per second, or velocity is equal to the number of vibra- 
tions per second times the wave length. 

383. Condensations and rarefactions. Thus far, for the sake 
of simplicity, we have considered a train of waves as a series 
of thin, detached pulses separated by equal intervals of air at 
rest. In point of fact, however, the air in front of the prong 
B (Fig. 343) is being pushed forward not at one particular 

ABC 




FIG. 344. Illustrating motions of air particles in one complete sound wave 
consisting of a condensation and a rarefaction 

instant only but during all the time that the prong is moving 
from A to (7, that is, through the time of one-half vibration of 
the fork ; and during all this time this forward motion is being 
transmitted to layers of air which are farther and farther away 
from the prong, so that when the latter reaches (7, all the air 
between C and some point c (Fig. 344) one-half wave length 
away is crowding forward and is therefore in a state of com- 
pression, or condensation. Again, as the prong moves back from 
C to A, since it tends to leave a vacuum behind it, the adja- 
cent layer of air rushes in to fill up this space, the layer next 
adjoining follows, etc., so that when the prong reaches A, all 
the air between A and c (Fig. 344) is moving backward and 

\ 



324 NATURE AND TRANSMISSION OF SOUND 




is therefore in a state of diminished density, or rarefaction. 

During this time the preceding forward motion has advanced 

one half wave length to the right, so that it now occupies the 

region between c and a (Fig. 344). Hence at the end of one 

complete vibration of the prong we may divide the air between 

it and a point one wave 

length away into two 

portions, one a region 

of condensation ac, and 

the other a region of 

rarefaction ca. The ar- "bcdefghij 

rows in Fig. 344 rep- 

resent the direction and relative magnitudes of the motions 

of the air particles in various portions of a complete wave. 

At the end of n vibrations the first disturbance will have 
reached a distance n wave lengths from the fork, and each wave 
between this point and the fork will consist of a condensation 
and a rarefaction, so that sound waves may be said to consist 
of a series of condensations and rarefactions following one 
another through the air in the manner shown in Fig. 345. 

Wave length may now be more accurately defined as the 
distance between two successive points of maximum condensation 
(b and /, Fig. 345) or of maximum rarefaction (d and h). 

384. Water-wave analogy. Condensations and rarefactions 
of sound waves are exactly analogous to the familiar crests and 
troughs of water waves. # / j 

Thus, the wave length of 
such a series of waves as 
that shown in Fig. 346 is 
defined as the distance bf 
between two crests, or the distance dh, or ae, or eg, or mn, 
between any two points which are in the same condition, or phase, 
of disturbance. The crests (that is, the shaded portions, which 
are above the natural level of the water) correspond exactly 



d h 

FIG. 346. Illustrating wave length of 
water waves 



SPEED AND NATURE OF SOUND 



325 



to the condensations of sound waves (that is, to the portions of 
air which are above the natural density). The troughs (that is, 
the dotted portions) correspond to the rarefactions of sound 
waves (that is, to the portions of air which are below the nat- 
ural density). But the analogy breaks down at one point, for 
in water waves the motion of the particles is transverse to the 
direction of propagation, while in sound waves, as shown in 
383, the particles move back and forth in the line of propaga- 
tion of the wave. Water waves are therefore called transverse 
waves, while sound waves in air are called longitudinal waves. 

385. Distinction between musical sounds and noises. Let a 

current of air from a -|-inch nozzle be directed against a row of 
forty-eight equidistant i-inch holes in a metal 
or cardboard disk, mounted as in Fig. 347 and 
set into rotation either by hand or by an elec- 
tric motor. A very distinct musical tone will 
be produced. Then let the jet of air be directed 
against a second row of forty-eight holes, which 
differs from the first only in that the holes are 
irregularly instead of regularly spaced about 
the circumference of the disk. The musical 
character of the tone will altogether disappear. 

The experiment furnishes a very 
striking illustration of the difference be- 
tween a musical sound and a noise. 
Only those sounds possess a musical qual- 
ity which come from sources capable of 
sending out pulses, or waves, at absolutely 

regular intervals. Therefore it is only sounds possessing a 
musical quality which may be said to have wave lengths. 

386. Pitch. While the apparatus of the preceding experiment is 
rotating at constant speed, let a current of air be directed first against 
the outside row of regularly spaced holes and then suddenly turned 
against the inside row, which is also regularly spaced but which contains 
a smaller number of holes. The note produced in the second case will 




FIG. 347. Regularity of 

pulses the condition for 

a musical tone 



326 NATURE AND TRANSMISSION OF SOUND 

be found to have a markedly lower pitch than the other one. Again 
let the jet of air be directed against one particular row, and let the speed 
of rotation be changed from very slow to very fast. The note produced 
will gradually rise in pitch. 

We conclude, therefore, that the pitch of a musical note de- 
pends simply upon the number of pulses which strike the ear per 
second. If the sound comes from a vibrating body, the pitch 
of the note depends upon the rate of vibration of the body. 

387. The Doppler effect. When a rapidly moving express train rushes 
past an observer, he notices a very distinct and sudden change in the 
pitch of the bell as the engine passes him, the pitch being higher as 
the engine approaches than as it recedes. The explanation is as follows : 
The bell sends out pulses at exactly equal intervals of time. As the 
train is approaching, however, the pulses reach the ear at shorter inter- 
vals than the intervals between emissions, since the train comes toward 
the observer between two successive emissions. But as the train recedes, 
the interval between the receipt of pulses by the ear is longer than the 
interval between emissions, since the train is moving away from the 
ear during the interval between emissions. Hence the pitch of the bell 
is higher during the approach of the train than during its recession. 
This phenomenon of the change in pitch of a note proceeding from an 
approaching or receding body is known as the Doppler effect. 

388. Loudness. The loudness or intensity of a sound de- 
pends upon the rate at Avhich energy is communicated by it 
to the tympanum of the ear. Loudness is therefore determined 
by the distance of the source and the amplitude of its vibration. 

If a given sound pulse is free to spread equally in all direc- 
tions, at a distance of 100 feet from the source the same energy 
must be distributed over a sphere of four times as large an 
area as at a distance of 50 feet. Hence under these ideal con- 
ditions the intensity of a sound varies inversely as the square of 
the distance from the source. But when sound is confined 
within a tube so that the energy is continually communicated 
from one layer to another of equal area, it will travel to great 
distances with little loss of intensity. This explains the effi- 
ciency of speaking tubes and megaphones. 



REFLECTION AND REENFORCEMENT 327 



QUESTIONS AND PROBLEMS 

1. A thunderclap was heard 5J sec. after the accompanying light- 
ning flash was seen. How far away did the flash occur, the temperature 
at the time being 20 C.? 

2. Why does the sound die away very gradually after a bell is struck ? 

3. Why does placing the hand back of the ear enable a partially 
deaf person to hear better? 

4. Explain the principle of the ear trumpet. 

5. The vibration rate of a fork is 256. Find the wave length of the 
note given out by it at 20 C. 

6. Since the music of an orchestra reaches a distant hearer without 
confusion of the parts, what may be inferred as to the relative velocities 
of the notes of different pitch ? 

7. What is the relation between pitch and wave length? How is 
this made evident by the fact noted in question 6 ? 

8. If we increase the .amplitude of vibration of a guitar string, what 
effect has this upon the amplitude of the wave? upon the loudness? 
upon the length of the wave ? upon the pitch ? 



REFLECTION, REENFORCEMENT, AND INTERFERENCE 

389. Echo. That a sound wave in hitting a wall suffers 
reflection is shown by the familiar phenomenon of echo. The 
roll of thunder is due to successive reflections of the original 
sound from clouds and other surfaces which are at different 
distances from the observer. 

In ordinary rooms the walls are so close that the reflected 
waves return before the effect of the original sound on the 
ear has died out. Consequently the echo blends with and 
strengthens the original sound instead of interfering with it. 
This is why, in general, a speaker may be heard so much 
better indoors than in the open air. Since the ear cannot 
appreciate successive sounds as distinct if they come at inter- 
vals shorter than a tenth of a second, it will be seen from the 
fact that sounds travel about 113 feet in a tenth of a second 
that a wall which is nearer than about 50 feet cannot possibly 
produce a perceptible echo. In rooms which are large enough 



328 NATURE AND TRANSMISSION OF SOUND 



FIG. 348. Sound foci 



to give rise to troublesome echoes it is customary to hang 
draperies of some sort, so as to break up the sound waves and 
prevent regular reflection. 

390. Sound foci. Let a watch be hung at the focus of a large con- 
cave mirror. On account of the reflection from the surface of the mirror 
a fairly well-defined beam of sound will 

be thrown out in front of the mirror, 

so that if both watch and mirror are 

hung on a single support and the whole 

turned in different directions toward a 

number of observers, the ticking will 

be distinctly heard by those directly in front of the mirror, but not by 

those at one side. If a second mirror is held in the path of this beam, 

as in Fig. 348, the sound may be again brought to a focus, so that if the 

ear is placed in the focus of this second mirror, or, better still, if a small 

funnel which is connected with the ear by a rubber tube is held in this 

focus, the ticking of the watch may sometimes be heard hundreds of feet 

away. A whispering gallery is a room so arranged c=3_ 

as to contain such sound foci. Any two opposite 

points a few feet from the walls of a dome, like 

that of St. Peter's at Rome or St. Paul's at London, 

are sufficiently near to such sound foci to make 

very low whispers on one side distinctly audible at 

the other, although at intermediate points no 

sound can be heard. There are well-known sound 

foci under the dome of the Capitol at Washington 

and in the Mormon Tabernacle at Salt Lake City. 

391. Resonance. Resonance is the reen- 
forcement or intensification of sound because 

of the union of direct and reflected waves. 

Thus, let one prong of a vibrating tuning 
fork, which makes, for example, 512 vibrations 
per second, be held over the mouth of a tube 
an inch or so in diameter, arranged as in Fig. 349, so that as the vessel 
A is raised or lowered, the height of the water in the tube may be ad- 
justed at will. It will be found that as the position of the water is 
slowly lowered from the top of the tube a very marked reenforcement 
of the sound will occur at a certain point. 




FIG. 349. Illustrating 
resonance 



REFLECTION AND REENFORCEMENT 



329 



Let other forks of different pitch be tried in the same way. It will 
be found that the lower the pitch of the fork, the lower must be the 
water in the tube in order to get the best reinforcement. This means 
that the longer the wave length of the note which the fork produces, 
the longer must be the air column in order to obtain resonance. 

We conclude, therefore, that a fixed relation exists between 
the wave length of a note and the length of the air column which 
will reenforce it. 

392. Best resonant length of a closed pipe is one-fourth wave 
length. If we calculate the wave length of the note of the 
fork by dividing the speed of sound by the vibration rate of 
the fork, we shall find that, in every case, the 
length of air column which gives the best response 
is approximately one-fourth wave Ie7igth. The 
reason for this is evident when we consider 
that the length must be such as to enable the 
reflected wave to return to the mouth just in 
time to unite with the direct wave which is at 
that instant being sent off by the prong. Thus, 
when the prong is first starting down from the 
position A (see Fig. 350), it starts the begin- 
ning of a condensation down the tube. If this 
motion is to return to the mouth just in time FlG 359 



to unite with the direct wave sent off by the nant length of a 
prong, it must get back at the instant the prong closed P l P e 
is starting up from the position C. In other 
words, the pulse must go down the tube and come back again 
while the prong is making a half vibration. This means that 
the path down and back must be a half wave length, and hence 
that the length of the tube must be a fourth of a wave length. 
From the above analysis it will appear that there should 
also be resonance if the- reflected wave does not return to the 
mouth until the fork is starting back its second time from (7, 
that is, at the end of one and a half vibrations instead of a 



330 NATUKE AND TRANSMISSION OF SOUND 

half vibration. The distance from the fork to the water and 
back would then be one and a half "wave lengths; that is, the 
water surface would be a half wave length farther down the 
tube than at first. The tube length would therefore now be 
three fourths of a wave length. 

Let the experiment be tried. A similar response will indeed be 
found, as predicted, a half wave length farther down the tube. This 
response will be somewhat weaker than before, as the wave has lost 
some of its energy in traveling a long distance through the tube. It 
may be shown in a similar way that there will be resonance where the 
tube length is f , J, or indeed any odd number of quarter wave lengths; 

393. Best resonant length of an open pipe is one-half wave 
length. Let the same tuning fork which was used in 392 be held in 
front of an open pipe (8 or 10 inches 
long) the length of which is made ad- 
justable by slipping back and forth over 
it a tightly fitting roll of writing paper ^ ^ Resonant lengtfa of an 
(Fig. 35*).. It will be found that for one Qpen pipe is ^ waw ^ ngth 
particular length this open pipe will re- 
spond quite as loudly as did the closed pipe, but the responding length 
will be found to be just twice as great as before. Other resonant lengths 
can be found when the tube is made 2, 3, etc. times as long. 

We learn, then, that the shortest resonant length of an open 
pipe is, one-half wave length, and that there is resonance at any 
multiple of a half wave length. 

The fact that the shortest resonant length of the open pipe 
is just twice that of the closed one is the experimental proof 
that a condensation, upon reaching the open end of a pipe, is 
reflected as a rarefaction. This means that when the lower 
end of the tube of Fig. 350 is open, a condensation upon 
reaching it suddenly expands. In consequence of this expan- 
sion the new pulse which begins at this instant to travel back 
through the tube is one in which the particles are moving 
down instead of up; that is, the particles are moving in a 
direction opposite to that in which the wave is traveling. 
This is always the case in a rarefaction (see Fig. 344). In 



REFLECTION AND REENFORCEMENT 331 

order then to unite with the motion of the prong this down- 
ward motion of the particles must get back to the mouth 
when the prong is just starting down from A the second time ; 
that is, after one complete vibration of the prong. This shows 
why the pipe length is one-half wave length. 

394. Resonators. If the vibrating fork at the mouth of the 
tubes in the preceding experiments is replaced by a train of 
ivaves coming from a distant source, precisely the same analysis 
leads to the conclusion that the waves reflected from the bottom 
of the tube will reenforce the oncoming waves when the length 
of the tube is any odd number of quarter wave lengths in the 
case of a closed pipe, or any number of half wave lengths in the 
case of an open pipe. It is clear, therefore, that every air cham- 
ber will act as a resonator for trains of waves of a certain wave 
length. This is why a conch shell held to the ear is always 
heard to hum with a particular note. Feeble waves which pro- 
duce no impression upon the unaided ear gain sufficient strength 
when reenforced by the shell to become audible. When the air 
chamber is of irregular form it is not usually possible to calcu- 
late to just what wave length it will respond, but it is always 
easy to determine experimentally what particular wave length 
it is capable of reenforcing. The resonators on which tuning 
forks are mounted are air chambers which are of just the right 
dimensions to respond to the note given out by the fork. 

395. Forced vibrations ; sounding boards. Let a tuning fork 

be struck and hld in the hand. The sound will be entirely inaudible 
except to those quite near. Let the base of the sounding fork be pressed 
firmly against the table. The sound will be found to be enormously 
intensified. Let another sounding fork of different pitch be held against 
the same table. Its sound will also be reenforced. In this case, then, the 
table intensifies the sound of any fork which is placed against it, while 
an air column of a certain size could intensify only a single note. 

The cause of the response in the two cases is wholly differ- 
ent. In the last case the vibrations of the fork are transmitted 



332 NATURE AND TRANSMISSION OF SOUND 

through its base to the table top and force the latter to vibrate 
in its own period. The vibrating table top, on account of its 
large surface, sets a comparatively large mass of air into motion 
and therefore sends a wave of great intensity to the ear, while 
the fork alone, with its narrow prongs, was not able to impart 
much energy to the air. Vibrations like those of the table top 
are called forced because they can be produced with any fork, 
no matter what its period. Sounding boards in pianos and 
other stringed instruments act precisely as does the table top 
in this experiment ; that is, they are set into forced vibrations 
by any note of the instrument and reenforce it accordingly. 

396. Beats. Since two sound waves are able to unite so as 
to reenforce each other, it ought also to be possible to make 
them unite so as to interfere with or destroy each other. In 
other words, under the proper conditions the union of two 
sounds ought to produce silence. 

Let two mounted tuning forks of the same pitch be set side by side, 
as in Fig. 352. Let the two forks be struck in quick succession with a 
soft mallet, for example, a rubber stopper on the end of a rod. The two 
notes will blend and produce a smooth, even tone. Then let a piece of wax 
or a small coin be stuck to a prong 
of one of the forks. This dimin- 
ishes slightly the number of vibra- 
tions which this fork makes per 
second, since it increases its mass. 




Again, let the two forks be sounded FlG ' 352 ' A int 



together. The former smooth tone 
will be replaced by a throbbing or pulsating one. This is due to the 
alternate destruction and reenforcement of the sounds produced by 
the two forks. This pulsation is called the phenomenon of beats. 

The mechanism of the alternate destruction and reenforce- 
ment may be understood from the following. Suppose that one 
fork makes 256 vibrations per second (see the dotted line AC 
in Fig. 353), while the other makes 255 (see the heavy line 
AC). If at the beginning of a given second the two forks 




REFLECTION AND KEENFORCEMENT 333 

are swinging together, so that they simultaneously send out 
condensations to the observer, these condensations will of 
course unite so as to produce a double effect upon the ear 
(see A', Fig. 353). Since now one fork gains one complete 
vibration per second over the other, at the end of the second 
considered the two forks A EC 

will again be vibrating \f\[f^^ 
together, that is, sending A> B . Q . 

out condensations which 
add their effects as before 

("see C'\ In the middle of , , 

FIG. 353. Graphical illustration of beats 

this second, however, the 

two forks are vibrating in opposite directions (see .ZT); that 
is, one is sending out rarefactions while the other sends out 
condensations. At the ear of the observer the union of the 
rarefaction (backward motion of the air particles) produced 
by one fork with the condensation (forward motion) pro- 
duced by the. other results in no motion at all, provided the 
two motions have the same energy ; that is, in the middle of the 
second the two sounds have united to produce silence (see B'). It 
will be seen from the above that the number of beats per second 
is equal to the difference in the vibration numbers of the two forks. 

To test this conclusion, let more wax or a heavier coin be added to 
the weighted prong ; the number of beats per second will be increased. 
Diminishing the weight will reduce the number of beats per second. 

In tuning a piano the double and triple strings are brought 
into unison by tuning so as to eliminate beats. 

397. Interference of sound waves by reflection. Let a thin 
cork about an inch in diameter be attached to one end of a brass rod 
from one to two meters long. Let this rod be clamped firmly in the 
middle, as in Fig. 354. Let a piece of glass tubing a meter or more 
long and from an inch to an inch and a half in diameter be slipped over 
the cork, as shown. Let the end of the rod be stroked longitudinally with 
a well-resined cloth. A loud, shrill note will be produced. 



334 NATURE AND TRANSMISSION OF SOUND 

This note is due to the fact that the slipping of the resined cloth 
over the surface of the rod sets the latter into longitudinal vibrations, 
so that its ends impart alternate condensations and rarefactions to the 
layers of air in contact with them. As soon as this note is started 




FIG. 354. Interference of advancing and retreating trains of sound waves 

the cork dust inside the tube will be seen to be intensely agitated. If the 
effect is not marked at first, a slight slipping of the glass tube forward 
or back will bring it out. Upon examination it will be seen that the 
agitation of the cork dust is not uniform, but at regular intervals 
throughout the tube there will be regions of complete rest, n A , rc 2 , n s , 
etc., separated by regions of intense motion. 

The points of rest correspond to the positions in which the 
reflected train of sound waves returning from the end of the 
tube neutralizes the effect of the advancing train passing down 
the tube from the vibrating rod. The points of rest are called 
nodes, the intermediate ^ a 3 a z % 

portions loops or anti- *==QR I I I II 

j TU/ v 4. n * n & n * n * 

nodes. 1 ne distance 

between these nodes is FlG ' 355 ' ^tance between nodes is one-half 

1. 1 1 ^ WaVG len th 

one-half wave length, for 

at the instant that the first wave front 1 (Fig. 355) reaches the 
end of the tube it is reflected and starts back toward R. Since 
at this instant the second wave front # 2 is just one wave length 
to the left of a^ the two wave fronts must meet each other at 
a point w , just one-half wave length from the end of the tube. 
The exactly equal and opposite motions of the particles in the 
two wave fronts exactly neutralize each other. Hence the point 
n^ is a point of no motion, that is, a node. Again, at the in- 
stant that the rejected wave front a^ met the advancing wave 
front # 2 at 1? the third wave front a 8 was just one wave length 
to the left of n Hence, as the first wave front a^ continues 



REFLECTION AND KEENFOKCEMENT 335 

to travel back toward R it meets a g at n^ just one-half wave 
length from n^ and produces there a second node. Similarly, 
a third node is produced at n^ one-half wave length to the 
left of n^ etc. Thus the distance between two nodes must always 
be just one lialf the wave length of the waves in the train. 

In the preceding discussion it has been tacitly assumed that the two 
oppositely moving waves are able to pass through each other without 
either of them being modified by the presence of the other. That two 
opposite motions are, in fact, transferred in just this manner through a 
medium consisting of elastic particles may be beautifully shown by the 
following experiment 
with the row of balls 
used in 380. 

Let the ball at one end FIG. 356. Nodes and loops in a cord 

of the row be raised a 

Black line denotes advancing tram ; dotted line, 
distance of, say, 2 inches reflected train 

and the ball at the other 

end raised a distance of 4 inches. Then let both balls be dropped 
simultaneously against the row. The two opposite motions will pass 
through each other in the row altogether without modification, the 
larger motion appearing at the end opposite to that at which it started, 
and the smaller likewise. 

Another and more complete analogy to the condition existing within 
the tube of Fig. 354 may be had by simply vibrating one end of a 
two- or three-meter rope, as in Fig. 356. The trains of advancing and 
reflected waves which continuously travel through each other up and 
down the rope will unite so as to form a series of nodes and loops. The 
nodes at c and e are the points at which the advancing and reflected 
waves are always urging the cord equally in opposite directions. The 
distance between them is one half the wave length of the train sent 
down the rope by the hand. 

QUESTIONS AND PROBLEMS 

1. Account for the sound produced by blowing across the mouth of 
an empty bottle. The bottle may be tuned to different pitches by add- 
ing more or less water. Explain. 

2. Explain the roaring sound heard when a sea shell, a tumbler, or 
an empty tin caa is held to the ear. 



336 NATURE AND TRANSMISSION OF SOUND 

3. Find the number of vibrations per second of a fork which produces 
resonance in a closed pipe 1 ft. long ; in an open pipe 1 ft. long*. (Take 
the speed of sound as 1120 ft. per second.) 

4. A gunner hears an echo 5^ sec. after he fires. How far away was 
the reflecting surface, the temperature of the air being 20 C.? 

5. The shortest closed air column that gave resonance with a tuning 
fork was 32 cm. Find the rate of the fork if the velocity of sound was 
340 meters per second. - 'i - 

6. A tuning fork gives strong resonance when held on its flat side or 
on its edge, but when held cornerwise over the air column the resonance 
ceases. Explain. 

7. What is meant by the phenomenon of beats in sound? How may 
it be produced, and what is its cause ? 

8. What is the length of the shortest closed tube that will act as a 
resonator to a fork whose rate is 427 per second ? (Temperature = 20 C.) 

9. A fork making 500 vibrations per second is found to produce 
resonance in an air column like that shown in Fig. 349, first when the 
water is a certain distance from the top, and again when it is 34 cm. 
lower. Find the velocity of sound. 

10. Show why an open pipe needs to be twice as long as a closed 
pipe if it is to respond to the same note. 



CHAPTER XVII 



PROPERTIES OF MUSICAL SOUNDS 

MUSICAL SCALES 
398. Physical basis of musical intervals. Let a metal or card 

board disk 10 or 12 inches in diameter be provided with four concentric 
rows of equidistant holes, the successive rows containing respectively 
24, 30, 36, and 48 holes (Fig. 357). The holes should be about J inch 
in diameter, and the rows should be about 
\ inch apart. Let this disk (a siren) be 
placed in the rotating apparatus and a 
constant speed imparted. Then let a jet 
of air be directed, as in 385, against each 
row of holes in succession. It will be found 
that the musical sequence do, mi, sol, do" 
results. If the speed of rotation is in- 
creased, each note will rise in pitch, but 
the sequence will remain unchanged. 

We learn, therefore, that the musical FIG. 357. Siren for produc- 
sequence do, mi, sol, do' consists of notes in S musical^sequence do, mi, 
whose vibration numbers have the ratios 

of 24, 30, 36, and 48, that is, 4, 5, 6, 8, and that this sequence 
is independent of the absolute vibration numbers of the tones. 

Furthermore, when two notes an octave apart are sounded 
together, they form the most harmonious combination which it 
is possible to obtain. These characteristics of notes an octave 
apart were recognized in the earliest times, long before any- 
thing whatever was known about the ratio of their vibration 
numbers. The preceding experiment showed that this ratio 
is the simplest possible, namely, 24 to 48, or 1 to 2. Again, 
the next easiest musical interval to produce, and the next 

337 




338 PROPERTIES OF MUSICAL SOUNDS 

most harmonious combination which can be found, corre- 
sponds to the two notes commonly designated as do, sol Our 
experiment showed that this interval corresponds to the next 
simplest possible vibration ratio, namely, 24 to 36, or 2 to 3. 
When sol is sounded with do', the vibration ratio is seen to be 
36 to 48, or 3 to 4. We see, therefore, that the three simplest 
possible ratios of vibration numbers, namely, 1 to 2, 2 to 3, 
and 3 to 4, are used in the production of the three no tea 
do, sol, do'. Again, our experiment shows that another har- 
monious musical interval, do, mi, corresponds to the vibration 
ratio 24 to 30, or 4 to 5. We learn, therefore, that harmonious 
musical intervals correspond to very simple vibration ratios. 

399. The major diatonic scale. When the three notes do, 
mi, sol, which, as seen above, have the vibration ratios 4, 5, 6, 
are all sounded together, they form a remarkably pleasing 
combination of tones. This combination was picked out and 
used very early in the musical development of the race. It is 
now known as the major chord. The major diatonic scale is 
built up of three major chords in the manner shown in the 
following table, where the first major chord is denoted by 1, 
the second by 2, and the third by 3. 

Syllables do re mi fa sol la, si do re 

Letters CD E F G A B C' D' 

Relative vibration numbers . . 24 27 30 32 36 40 45 48 54 

111 

22 2 
333 

The chords do-mi-sol (the tonic), sol-si-re (the dominant), 
and fa-la-do (the subdominant) occur frequently in all music. 

Standard middle C forks made for physical laboratories 
all have the vibration number 256, which makes A in the 
physical scale 426J. In the so-called international pitch A 
has 435 vibrations, and in the widely adopted American 
Federation of Musicians' pitch, 440. 






VIBRATING STRINGS 339 

400. The even-tempered scale. If G- is taken as do, and a 
scale built up as above, it will be found that six of the above 
notes in each octave can be used in this new key, but that two 
additional ones are required (see table below). Similarly, to 
build up scales, as above, in all the keys demanded by modern 
music would require about fifty notes in each octave. Hence 
a compromise is made by dividing the octave into twelve 
equal intervals represented by the eight white arid five black 
keys of a piano. How much this so-called even-tempered scale 
differs from the ideal, or diatonic, scale is shown below. 

Note C D E F G A R C' D' E' F' G' 

Diatonic .... 256 288 320 341 384 426| 480 512 576 640 682.2 768 

Diatonic key of G 384 433 480 512 576 640 720 768 

Tempered ... 256 287.4 322.7 341.7 383.8 430.7 483.5 512 574.8 645.4 683.4 767.6 

VIBRATING STRINGS* 

401 . Laws of vibrating strings. Let two piano wires be stretched 
over a box or a board with pulleys attached so as to form a sonometer 
(Fig. 358). Let the weights A and B be adjusted until the two wires 
emit exactly the same 

note. The phenomenon 
of beats will make it 
possible to do this with Afi 

great accuracy Then let ^ ^ ^ The gonometer 

the bridge D be inserted 
^exactly at the middle of one of the wires, and the two wires plucked in 
succession. The interval will be recognized at once as do, do'. Next let 
the bridge be inserted so as to make one wire two thirds as long as the 
other, and let the two be plucked again. The interval will be recognized 
as do, s#L 

Now it was shown in 398 that do 1 has twice as many 
vibrations per second as do, and sol has three halves as many. 
Hence, since the length corresponding to do' is one half as 
great as the first length, and that corresponding to sol two thirds 

*This discussion should be followed by a laboratory experiment on the 
laws of vibrating strings. See, for example, Experiment 41 of the authors 1 
Manual. 




340 PROPERTIES OF MUSICAL SOUNDS 

as great, we conclude from this experiment that, other things 
being equal, the vibration numbers of strings are inversely 
proportional to their lengths. 

Again, let the two wires be tuned to unison, and then let the weight 
A be increased until the pull which it exerts on the wire is exactly four 
times as great as that exerted by B. The note given out by the A wire 
will again be found to be an octave above that given out by the B wire. 

We learn, then, that the vibration numbers of similar strings of 
equal length are proportional to the square roots of their tensions. 

In stringed instruments, for example the piano, the differ- 
ent pitches are obtained by using strings of different length, 
tension, and mass per unit length. 

402. Nodes and loops in vibrating strings. Let a string a meter 

long be attached to one of the prongs of a large tuning fork which makes 

in the neighborhood of 

100 vibrations per second. 

Let the other end be at- 

tached as in the figure 

and the fork set into vi- ^ FlG . 359. string vibrating as a whole 

bration. If the fork is not 

electrically driven, which is much to be preferred, it may be bowed 

with a violin bow or struck with a soft mallet. By making the tension 

of the thread, for example, proportional to the numbers 9, 4, and 1 it 

will be found possible to make it vibrate either as a whole, as in Fig. 359, 

or in two or three parts 

(Fig. 360), 

This effect is due, as 
explained in 397, to FlG * 36 - String vibrating in three 

G^ segments 

the interference of the 

direct and reflected waves sent down the string from the 
vibrating fork. But we shall show in the next paragraph 
that in considering the effects of the vibrating string on 
the surrounding air we shall make no mistake if we think of 
it as clamped at each node, and as actually vibrating in two 
or three or four separate parts, as the case may be. 




FUNDAMENTALS AND OVERTONES 341 

FUNDAMENTALS AND OVERTONES 

403. Fundamentals and overtones. If the assertion just 
made be correct, then a string which has a node in the middle 
communicates to the air twice as many pulses per second as 
the same string when it vibrates as a whole. This may be 
conclusively shown as follows : 

Let the sonometer wire (Fig. 358) be plucked in the middle and the 
pitch of the corresponding tone carefully noted. Then let the finger 
be touched to the middle of the wire, and the latter plucked midway 
between this point and the end.* . The octave of the original note will 
be distinctly heard. Next let the finger be touched at a point one third 
of the wire length from one end, and the wire again plucked. The note 
will be recognized as .so/'. Since we learned in 399 that sol' has three 
halves as many vibrations as do', it must have three times as many 
vibrations as the original note. Hence a wire which is vibrating in 
three segments sends out three times as many vibrations as when it is 
vibrating as a whole. 

When a wire vibrates simply as a whole, it gives forth the 
lowest note which it is capable of producing. This note is 
called the fundamental or first partial of the wire. When the 
wire is made to vibrate in two parts, it gives forth, as has just 
been shown, a note an octave higher than the fundamental. 
This is called the first overtone or second partial. When the 
wire is made to vibrate in three parts it gives forth a note cor- 
responding to three times the vibration number of the funda- 
mental, namely, sol'. This is called the second overtone or third 
partial. When the wire vibrates in four parts, it gives forth the 
third overtone, which is two octaves above the fundamental. 
The overtones of wires are often called harmonics. They bear 
the vibration ratios 2, 3, 4, 5, 6, 7, etc. to the fundamental.! 

* It is well to remove the finger almost simultaneously with the plucking. 

t Some instruments, such as bells, can produce higher tones whose vibra- 
tion numbers are not exact multiples of the fundamental. These notes are 
still called overtones, but they are not called harmonics, the latter term being 
reserved for the multiples. Strings produce harmonics only. 




342 PROPERTIES OF MUSICAL SOUNDS 

404. Simultaneous production of fundamentals and overtones. 
Thus far we have produced overtones only by forcing the wire 
to remain at rest at properly chosen points during the bowing. 

Now let the wire be plucked at a point one fourth of its length from 
one end, without being touched in the middle. The tone most distinctly 
heard will be the fundamental ; but if the wire is now touched very 
lightly exactly in the middle, the sound, instead of ceasing altogether, 
will continue, but the note heard will be an octave higher than the 
fundamental, showing that in this case there was superposed upon 
the vibration of the wire as a whole a vibration in two segments also 
(Fig. 361). By touching the 
wire in the middle the vibra- 
tion as a whole was destroyed, 
but that in two parts re- 
mained. Let the experiment 
be repeated, with this differ- FIG. 361. A wire simultaneously emitting 
ence, that the wire is now its fundamental and first overtone 

plucked in the middle instead 

of one fourth its length from one end. If it is now touched in the 
middle, the sound will entirely cease, showing that when a wire is 
plucked in the middle there is no first overtone superposed upon the 
fundamental. Let the wire be plucked again one fourth of its length 
from one end and careful attention given to the compound note emitted. 
It will be found possible to recognize both the fundamental and the 
first overtone sounding at the same time. Similarly, by plucking at a 
point one sixth of the length of the wire from one end, and then touching 
it at a point one third of its length from the end, the second overtone 
may be made to appear distinctly, and a trained ear will detect it in the 
note given off by the wire, even before the fundamental is suppressed 
by touching at the point indicated. 

The experiments show, therefore, that in general the note 
emitted by a string plucked at random is a complex one, consist- 
ing of a fundamental and several overtones, and that just what 
overtones are present in a given case depends on where and how 
the wire is plucked. 

405. Quality. Let the sonometer wire be plucked first in the 
middle and then close to one end. The two notes emitted will have 
exactly the same pitch, and they may have exactly the same loudness, 



FUNDAMENTALS AND OVERTONES 343 

but they will be easily recognized as different in respect to somethmg 
which we call quality. The experiment of the last paragraph shows that 
the real physical difference in the tones is a difference in the sorts of 
overtones which are mixed with the fundamental in the two cases. 

Again, let a mounted C f fork be sounded simultaneously with a 
mounted C fork. The resultant tone will sound like a rich, full C, which 
will change into a hollow C when the C' is quenched with the hand. 

Everyone is familiar with the fact that when notes of the 
same pitch and londness are sounded upon a piano, a violin, 
and a cornet, the three tones can be readily distinguished. 
The last experiments suggest that the cause of this difference 
lies "in the fact that it is only the fundamental which is the 
same in the three cases, while the overtones are different. In 
other words, the characteristic of a tone which we call its qual- 
ity is determined simply by the number and prominence of the 
overtones which *are present. If the overtones present are few 
and weak, while the fundamental is strong, the tone is, as 
a rule, soft and mellow, as when a sonometer wire is plucked 
in the middle, or a closed organ pipe is blown gently, or a 
tuning fork is struck with a soft mallet. The presence of 
comparatively strong overtones up to the fifth adds fullness 
and richness to the resultant tone. This is illustrated by the 
ordinary tone from a piano, in which several if not all of the 
first five overtones have a prominent place. When overtones 
higher than the sixth are present, a sharp metallic quality 
begins to appear. This is illustrated when a tuning fork is 
struck, or a wire plucked, with a hard body. It is in order to 
avoid this quality that the hammers which strike against 
piano wires are covered with felt. 

406. Analysis of tones by the manometric flame. A very 
simple and beautiful way of showing the complex character 
of most tones is furnished by the so-called manometric flames. 
This device consists of the following parts : a chamber in the 
block B (Fig. 362), through which gas is led by way of the 



344 



PROPERTIES OF MUSICAL SOUNDS 



tubes C and D to the flame F ; a second chamber in the block 
A, separated from the first chamber by an elastic diaphragm 
made of very thin sheet rubber or paper, and communicating 
with the source of sound through the tube E and trumpet G ; 
and a rotating mirror M by which the flame is observed. 
When a note is produced before the mouthpiece G> the vibra- 
tions of the diaphragm produce variations in the pressure of 




FIG. 362. Analysis of sounds with manometric flames 

the gas coming to the flame through the chamber in B, so 
that when condensations strike the diaphragm the height 
of the flame is increased, and when rarefactions strike it the 
height of the flame is diminished. If these up-and-down 
motions of the flame are viewed in a rotating mirror, the 
longer and shorter images of the flame, which correspond 
to successive intervals of time, appear side by side, as in 
Fig. 363. If a rotating mirror is not to be had, a piece of 
ordinary mirror glass held in the hand and oscillated back 
and forth about a vertical axis will be found to give satis 
factory results. 



FUNDAMENTALS AND OVERTONES 



345 



First let the mirror be rotated when no note is sounded before the 
mouthpiece. There will be no fluctuations in the flame, and its image, 
as seen in the moving mirror, will be a straight band, as shown in 2 
(Fig. 363). Next let a mounted C fork be sounded, or some other simple 
tone produced in front of G. The image 
in the mirror will be that shown in 3. 
Then let another fork, C', be sounded 
in place of the C. The image will be 
that shown in 4. The images of the 
flame are now twice as close together 
as before, since the blows strike the 
diaphragm twice as often. Next let 
the open ends of the resonance boxes 
of the tuning forks C and C' be held 
together in front of G. The image of 
the flame will be as shown in 5. If 
the vowel o be sung in the pitch Bb 
before the mouthpiece, a figure exactly 
similar to 5 will be produced, thus 
showing that this last note is a com- 
plex, consisting of a fundamental and 
its first overtone. 



<UU.UU.ULL 



FIG. 363. Vibration forms shown 
by manometric flames 



The proof that most other tones are likewise complex lies in 
the fact that when analyzed by the manometric flame they show 
figures not like 3 and 4, which correspond to simple tones, but 
like 5) 6, and 7, which may be produced by sounding combina- 
tions of simple tones. In the figure, 6 is produced by singing 
the vowel e on C u \ 7 is obtained when o is sung on C". The 
beautiful photographs opposite page 346, taken by Prof. D. C. 
Miller, show the extraordinary complexity of spoken words. 

407. Helmholtz's experiment. If the loud pedal on a piano is 
held down and the vowel sounds do, I, a, ah, e sung loudly into the strings, 
these vowels will be caught up and returned by the instrument with 
sufficient fidelity to make the effect almost uncanny. 

It was by a method which may be considered as merely a 
refinement of this experiment that Helmholtz proved conclu- 
sively that quality is determined simply by the number and 




346 PROPERTIES OF MUSICAL SOUNDS 

prominence of the overtones which are blended with the fun- 
damental. He first constructed a large number of resonators, 
like that shown in Fig. 364, each of which would respond to 
a note of some particular pitch. By holding 
these resonators in succession to his ear while 
a musical note was sounding, he picked out 
the constituents of the note ; that is, he found 
out just what overtones were present and 

what were their relative intensities. Then he FlG - 364 - Helm - 
, . , , holtz's resonator 

put these constituents together and repro- 
duced the original tone. This was done by sounding simul- 
taneously, with appropriate loudness, two or more of a whole 
series of tuning forks which had the vibration ratios 1, 2, 3, 
4, 5, 6, 7. In this way he succeeded not only in imitating the 
qualities of different musical instruments but even in repro- 
ducing the various vowel sounds. 

408. Sympathetic vibrations. Let two mounted tuning forks of 
the same pitch be placed with the open ends of their resonators facing 
eacfy other. Let one be set into vigorous vibration with a soft mallet 
and then quickly quenched by grasping the prongs with the hand. 
The other fork will be found to be sounding loudly enough to be heard 
over a large room. Next let a penny be waxed to one prong of the sec- 
ond fork and the experiment repeated. When the sound of the first 
fork is quenched, no sound whatever will be found to be coming from 
the second fork. 

The experiment illustrates the phenomenon of sympathetic 
vibrations, and shows what conditions are essential to its appear- 
ance. If two bodies capable of emitting musical notes have 
exactly the same natural period of vibration, the pulses com- 
municated to the air when one alone is sounding beat upon 
the second at intervals which correspond exactly to its own 
natural period. Each pulse, therefore, adds its effect to that of 
the preceding pulses ; and though the effect due to a single 
pulse is very slight, a great number of such pulses produce a 




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pitch of fr 
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Illlisi 



FUNDAMENTALS AND OVEKTOKES 347 

large resultant effect. In the same way a large number of 
very feeble pulls may set a heavy pendulum into vibrations 
of considerable amplitude if the pulls come at intervals exactly 
equal to the natural period of the pendulum. On the other 
hand, if the two sounding bodies have even a slight difference 
of period, the effect of the first pulses is neutralized by the ef- 
fect of succeeding pulses as soon as the two bodies, on account of 
their difference in period, get to swinging in opposite directions. 

Let notes of different pitches be sung into a piano when the dampers 
are lifted. The wire which has the pitch of the note sounded will in 
every case respond. Sing a little off the key and the response will cease. 

409. Sympathetic vibrations produced by overtones. It is 

not essential, in order that a body may be set into sympathetic 
vibrations, that it have the same pitch as the sounding body, 
provided its pitch corresponds exactly with the pitch of one 
of the overtones of that body. 

Thus, if the damper is lifted from the C string of a piano and the 
octave below, C v is sounded loudly, C will be heard to sound after C 
has been quenched by the damper. In this case it is the first overtone 
of C l which is in exact tune with C, and which therefore sets it into 
sympathetic vibration. Again, if the damper is lifted from the G string 
while C\ is sounded, this note will be found to be set into vibration by 
the second overtone of C r A still more interesting case is obtained by 
removing the damper from E while C 1 is sounded. When C 1 is quenched, 
the note which is heard is not E, but an octave above E ; that is, ". 
This is because there is no overtone of C l which corresponds to the vi- 
bration of E] but the fourth overtone of C v which has five times the 
vibration number of C v corresponds exactly to the vibration number of 
E', the first overtone of E. Hence E is set into vibration not as a 
whole but in halves. 

410. Physical significance of harmony and of discord. Let two 
pieces of glass tubing about an inch in diameter and a foot and a half 
long be supported vertically, as shown in Fig. 365. Let two gas jets 
(made by drawing down pieces of one-fourth inch glass tubing until, with 
full gas pressure, the flame is about an inch long) be thrust inside these 
tubes to a height of about three or four inches from the bottom. Let 



348 



PEOPEETIES OF MUSICAL SOUNDS 



the gas be turned down until the tubes begin to sing. Without attempt- 
ing to discuss the part which the flame plays in the production of the 
sound, we wish simply to call attention to the fact that the two tones 
are either quite in unison or so near it that only a 
few beats are produced per second. Now let the 
length of one of the tubes be slightly increased by 
slipping the paper cylinder S up over its end. The 
number of beats will be rapidly increased until they 
will become indistinguishable as separate beats and 
will merge into a jarring, grating discord. 

The experiment teaches that discord is 
simply a phenomenon of beats. If the vibra- 
tion numbers do not differ by more than 
five or six, that is, if there are not more 
than five or six beats per second, the effect 
is not particularly unpleasant. From this 
point on, however, as the difference in the 
vibration numbers, and therefore in the num- 
ber of beats per second, increases, the un- 
pleasantness increases, and becomes worst at FIG. 365. Illustrat- 
a difference of about thirty. Thus, the notes ing ^ d ?^f ion 
B and C", which differ by about thirty-two 
beats per second, produce about the worst possible discord. 
When the vibration numbers differ by as much as seventy, 
which is about the difference between C and E, the effect is 
again pleasing, or harmonious. Moreover, in order that two 
notes may harmonize well, it is necessary not only that the 
notes themselves shall not produce an unpleasant number 
of beats, but also that such beats shall not arise from their 
overtones. Thus, C and B are very discordant, although they 
differ by a large number of vibrations per second. The discord 
in this case arises between B and C", the first overtone of C. 

Again, there are certain classes of instruments, of which bells 
are a striking example, which produce insufferable discords 
when even such notes as do, sol, do', are sounded simultaneously 



WIND INSTRUMENTS 349 

upon them. This is because these instruments, unlike strings 
and pipes, have overtones which are not harmonics, that is, 
which are not multiples of the fundamental ; and these over- 
tones produce beats either among themselves or with one of 
the fundamentals. It is for this reason that in playing chimes 
the bells are struck in succession, not simultaneously. 

QUESTIONS AND PROBLEMS 

1. In what three ways do piano makers obtain the different pitches? 

2. What did Helniholtz prove by means of his resonators? 

3. If middle C is struck on a piano while the key for G in the 
octave above is held down, G will be distinctly heard when C is silenced. 
Explain. 

4. At what point must the G^ string be pressed by the finger of the 
violinist in order to produce the note C ? 

5. If one wire has twice the length of another and is stretched 
by four times the stretching force, how will their vibration numbers 
compare ? 

6. A wire gives out the note G. What is its fourth overtone? 

7. If middle C had 300 vibrations per second, how many vibrations 
would F and A have ? 

8. What is the fourth overtone of C? the fifth overtone? 

9. There are seven octaves and two notes on an ordinary piano, the 
lowest note being A 4 and the highest one C"". If the vibration number 
of the lowest note is 27, find the vibration number of the highest. 

10. Find the wave length of the lowest note on the piano; the wave 
length of the highest note. (Take the speed of sound as 1130 ft. per sec.) 

11. A violin string is commonly bowed about one seventh of its 
length from one end. Why is this better than bowing in the middle ? 

12. Build up a diatonic scale on C = 264. 

WIND INSTRUMENTS 
411. Fundamentals of closed pipes. Let a tightly fitting rubber 

stopper be inserted in a glass tube a (Fig. 366), eight or ten inches long 
and about three fourths of an inch in diameter. Let the stopper be 
pushed along the tube until, when a vibrating C' fork is held before the 
mouth, resonance is obtained as in 391. (The length will be six or 
seven inches.) Then let the fork be removed and a stream of air blown 



350 



PEOPEETIES OF MUSICAL SOUNDS 




FIG. 366. Musical notes 
from pipes 



across the mouth of the tube through a piece of tubing b, flattened at 
one end as in the figure.* The pipe will be found to emit strongly the 
note of the fork. 

In every case it is found that a note 
which a pipe may be made to emit is 
always a note to which it is able to re- 
spond when used as a resonator. Since, 
in 392, the best resonance was found 
when the wave length given out by the 
fork was four times the length of the 
pipe, we learn that when a current of air 
is suitably directed across the mouth of a 
closed pipe, it will emit a note lohich has a 
wave length four times the length of the 
pipe. This note is called the fundamental of the pipe. It 
is the lowest note which the pipe can be made to produce. 

412. Fundamentals of open pipes. Since we found in 393 
that the lowest note to which a pipe open at the lower end 
can respond is one the wave length of which is twice the pipe 
length, we infer that an open pipe, when suitably blown, ought 
to emit a note the wave length of which is twice the pipe length. 
This means that if the same pipe is blown first when closed at 
the lower end and then when open, the first note ought to be 
an octave lower than the second. 

Let the pipe a (Fig. 366) be closed at the bottom with the hand and 
blown ; then let the hand be removed and the operation repeated. The 
second note will indeed be found to be an octave higher than the first. 

We learn, therefore, that the fundamental of an open pipe 
has a wave length equal to twice the pipe length. 

413. Overtones in pipes. It was found in 392 that there 
is a whole series of pipe lengths which respond to a given 

* If the arrangement of Fig. 366 is not at hand, simply blow with the lips 
across the edge of a piece of ordinary glass tubing within which a rubber 
stopper may be pushed back and forth. 



WIND INSTEUMENTS 351 

fork, and that these lengths bear to the wave length of the 
fork the ratios |, |, |, etc. This is equivalent to saying that 
a closed pipe of fixed length can respond to a whole series of 
notes whose vibration numbers have the ratios 1, 3, 5, 7, etc. 
Similarly, in 393, we found that in the case of an open pipe 
the series of pipe lengths which will respond to a given fork 
bear to the wave length of the fork the ratios J, J, |, |-, etc. 
This, again, is equivalent to saying that an open pipe can re- 
spond to a series of notes whose vibration numbers have the 
ratios 1, 2, 3, 4, 5, etc. Hence we infer that it ought to be 
possible to cause both open and closed pipes to emit notes of 
higher pitch than their fundamentals (that is, overtones), and 
that the first overtone of an open pipe should have twice the 
rate of vibration of the fundamental (that is, it should be 
do', the fundamental being considered as do) ; that the second 
overtone should vibrate three times as fast as the fundamental 
(that is, it should be sol'); that the third overtone should 
vibrate four times as fast (that is, it should be do") ; that the 
fourth overtone should vibrate five times as fast (that is, it 
should be mi") ; etc. In the case of the closed pipe, however, 
the first overtone should have a vibration rate three times 
that of the fundamental (that is, it should be sol') ; the 
second overtone should vibrate five times as fast (that is, it 
should be mi") ; etc. In other words, while an open pipe 
ought to give forth all the harmonics, both odd and even, a 
closed pipe ought to produce the odd harmonics but be 
entirely incapable of producing the even ones. 

Let the pipe of Fig. 366 be blown so as to produce the fundamental 
when the lower end is open. Then let the strength of the air blast be 
increased. The note will be found to spring to do'. By blowing still 
harder it will spring to sol', and a still further increase will probably 
bring out do". The odd and the even harmonics are, in fact, emitted 
by the open pipe, as our theory predicted. When the lower end is closed, 
however, the first overtone will be found to be sol', and the next one mi", 
just as our theory demands for the closed pipe. 



352 PKOPERTIES OF MUSICAL SOUNDS 

414. Mechanism of emission of notes by pipes. Blowing 
across the mouth of a pipe produces a musical note, because 
the jet of air vibrates back and forth across the lip in a 
period which is determined wholly by the natural resonance 
period of the pipe. Thus, suppose that the jet a (Fig. 367) 
first strikes just inside the edge, or Up, of the pipe. A con- 
densational pulse starts down the pipe. When it returns to 
the mouth after reflection at the closed end, it pushes the jet 
outside the lip. This starts a rarefaction down the pipe, which, 
after return from the lower end, pulls the jet in again. 
There are thus sent out into the room regu- 
larly timed puffs, the period of which is con- 
trolled by the reflected pulses coming back 
from the lower end, that is, by the natural 
resonance period of the pipe. 

By blowing more violently it is possible 
to create, by virtue of the friction of the 
walls, so great and so sudden a compression 
in the mouth of the pipe that the jet is forced FlG : 367 \ vibrat - 
out over the edge before the return of the 
first reflected pulse. In this case no note will be produced 
unless the blowing is of just the right intensity to cause the 
jet to swing out in the period corresponding to an overtone. 
In this case the reflected pulses will return from the end at 
just the right intervals to keep the jet swinging in this 
period. This shows why a current of a particular intensity 
is required to start any particular overtone. 

Another way of looking at the matter is to think of the 
pipe as being filled up with air until the pressure within it is 
great enough to force the jet outside the lip, upon which a 
period of discharge follows, to be succeeded in turn by 
another period of charge. These periods are controlled by 
the length of the pipe and the violence of the blowing, 
precisely as described above. 



WIND INSTRUMENTS 



353 











jm 
If 




( 


I U 

FIG. 368. Organ 
pipes 



With open pipes the situation is in no way different save 
that the reflection of a condensation as a rarefaction at the 
lower end makes the natural period twice as 
high, since the pipe length is now one-half 
wave length instead of one-fourth wave 
length (see 393). 

415. Vibrating air-jet instruments. The mechanism 
of the production of musical tones by the ordinary 
organ pipe, the flute, the fife, the 
piccolo, and all whistles is essen- 
tially the same as in the case of 
the pipe of Fig. 367. In all these 
instruments an air jet is made to 
play across the edge of an opening 
in an air chamber, and the reflected 
pulses returning from the other 
end of the chamber cause it to 
vibrate back and forth, first into 

the chamber and then out again. 
FIG. 369. Moutt 

net, showing the 
ton ue I which 
opens and closes 

the upper end of closed at the remote end. In the flute it is open, in 
the pipe whistles it is usually closed, and in organ pipes it 

may be either open or closed. Fig. 368 shows a cross 
section of two types of organ pipes. The jet of air from S vibrates 
across the lip L in obedience to the pressure exerted on it by waves 
reflected from O. Pipe organs are provided with a different pipe for 
each note, but the flute, piccolo, 
and fife are made to produce a 
whole series of notes, either by 
blowing overtones or by open- 
ing holes in the tube, an oper- 
ation which is equivalent to 
cutting the tube off at the hole. 
Although important orchestral 
instruments, the flute and pic- FIG. 370. The vibrating tongue of the 
colo are not rich in overtones. mouth organ, accordion, etc. 



of regularly timed puffg of air ig 
made to pass from the instrument to the ear of the 
observer precisely as in the case of the rotating disk 
air chamber may be either open or 




354 PKOPERTIES OF MUSICAL SOUNDS 

416. Vibrating reed instruments. In reed instruments the vibrating 
air jet is replaced by a vibrating reed, or tongue, which opens and closes, 
at absolutely regular intervals, an opening against which 

the performer is directing a current of air. In the clari- 
net, the oboe, the bassoon, etc. the reed is placed at the 
upper end of the tube (see /, Fig. 369), and the theory 
of its opening and closing the orifice so as to admit 
successive puffs of air to the pipe is identical with the 
theory of the fluctuation of the air jet into and out of 
the organ pipe. For in these instruments the reed has 
little rigidity and its vibrations are controlled largely 
by the reflected pulses but partly by the reed and by 
the lips of the performer. 

In other reed instruments, like the mouth organ, the 
common reed organ, or the accordion, it is the elasticity 
of the reed alone (see z, Fig. 370) which controls the 
emission of pulses. In such instruments there is no 
necessity for air chambers. The arrows of Fig. 370 in- 
dicate the direction of the air current which is inter- 
rupted as the reed vibrates between the positions z ^ ^-j T , 

an *2 reed-organ pipe 

In still other reed instruments, like the reed pipes 

used in large organs (Fig. 371), the period of the pulses is controlled 
partly by the elasticity of the reed and partly by the return of the 
reflected waves ; in other words, the natural period of the reed is more 
or less coerced by the period of the reflected pulses. Within certain 
limits, therefore, such in- 
struments may be tuned by 
changing the length of the 
vibrating reed / without 
changing the length of the 
pipe. This is done by push- 
ing the wire r up or down. 

417. Vibrating lip in- 
struments. In instruments 

of the bugle and cornet -pio. 372. The cornet 

type the vibrating reed is 

replaced by the vibrating lips of the musician, the period of their vibra- 
tion being controlled, precisely as in the organ pipe or the clarinet, by 
the period of the returning pulses. In the bugle the pipe length is fixed, 




WIND INSTRUMENTS 



355 




FIG. 373 



I Cover 



and because of the narrowness of the tube all bugle calls are played with 

overtones. In the cornet (Fig. 372) and in most forms of horns, valves 
o, />, c, worked by the fingers, vary the length of the 
pipe, and hence such instruments can produce as 
many series of fundamentals and overtones as there 
are possible tube lengths. In the trombone the 
variation of pitch is 
accomplished by blow- 
ing overtones and by 

changing the length of the tube by a 

sliding U-shaped portion 

418. The phonograph. In the original 

form of the phonograph the sound waves, 

collected by the cone, are carried to a 

thin metallic disk C (Fig. 373), exactly 

like a telephone diaphragm, which takes 

up very nearly the vibration form of the 

wave which strikes it. This vibration 

form is permanently impressed on the 

w r ax-coated cylinder M by means of a 

stylus D which is attached to the back 



Glass 
Diaphragm 

C 




\Needle Point 
\D 

FIG. 374. Mechanism for form- 
ing gramophone records 



of the disk. When the stylus is run a second time over the groove which 
it first made in the wax, it receives again and imparts to the disk the 
vibration form which first fell upon it. This is the principle of the 



Vegetable- 
Tissue 
Diaphragm 




The diamond point 

FIG. 375. The Edison diamond reproducer 



356 PROPERTIES OF MUSICAL SOUNDS 

dictaphone and the ediphone, used to replace stenographers in business 
offices. The typist writes the letter by listening to the reproduction 
of the dictation. 

In the most familiar of the modern forms of the phonograph (gramo- 
phone, etc.) the needle point D, instead of digging a groove in wax, 
vibrates back and forth (see Fig. 374) over a greased zinc disk. This 
wavy trace in the disk is etched out with chromic acid. Then a copper 
mold is made by the electeotyping process, and as many as a thousand 
facsimiles of the original wavy line are impressed on hard-rubber disks 
by heat and pressure. When the needle is again run over the disk, it 
follows along the wavy groove and transmits to the diaphragm C vibra- 
tions exactly like those which originally fell upon it. Spoken words 
and vocal and orchestral music are reproduced in pitch, loudness, and 
quality with wonderful exactness. This instrument is one of the many 
inventions of Thomas Edison (see opposite p. 316). The diamond-tip 
reproducer used with the hill-and-dale Edison disks is shown in Fig. 375. 

QUESTIONS AND PROBLEMS 

1. What proves that a musical note is transmitted as a wave motion ? 

2. What evidence have you that sound waves are longitudinal 
vibrations ? 

3. Why is the pitch of a sound emitted by a phonograph raised by 
increasing the speed of rotation of the disk ? 

4. AVhat will be the relative lengths of a series of organ pipes which 
produce the eight notes of a diatonic scale ? 

5. Will the pitch of a pipe organ be the same in summer as on 
a cold day in winter? What could cause a difference? 

6. Explain how an instrument like the bugle, which has an air 
column of unchanging length, may be made to produce several notes 
of different pitch, such as C, G, C\ E', G'. (C is not often used.) 

7. Why is the quality of an open organ pipe different from that 
of a closed organ pipe ? 

8. The velocity of sound in hydrogen is about four times as great 
as it is in air. If a C pipe is blown with hydrogen, what will be the 
pitch of the note emitted ? 

9. What effect will be produced on a phonograph record made with 
the instrument of Fig. 374 if the loudness of a note is increased? if 
the pitch is lowered an octave? 



CHAPTER XVIII 



NATURE AND PROPAGATION OF LIGHT 

TRANSMISSION OF LIGHT 

419. Speed of light. Before the year 1675 light was thought 
to pass instantaneously from the source to the observer. In 
that year, however, Olaus Romer, a young Danish astron- 
omer, made the following observations. He had observed 
accurately the instant at which one of Jupiter's satellites M 
(Fig. 376) passed into 

Jupiter's shadow when 1C 

the earth was at E, 
and predicted, from the 
known mean time be- 
tween such eclipses, the 
exact instant at which 
a given eclipse should 
occur six months later 
when the earth was 
at E'. It actually took 
place 16 minutes 36 
seconds (996 seconds) later. He concluded that the 996 
seconds' delay represented the time required for light to 
travel across the earth's orbit, a distance known to be about 
180,000,000 miles. The most precise of modern determinations 
of the speed of light are made by laboratory methods. The 
generally accepted value, that of Michelson, of The University 
of Chicago, is 299,860 kilometers per second. It is sufficiently 
correct to remember it as 300,000 kilometers, or 186,000 miles. 

357 




FIG. 376. Illustrating Romer's determination 
of the velocity of light 



358 NATURE AND PROPAGATION OF LIGHT 



Though this speed would carry light around the earth 1\ times 
in a second, yet it is so small in comparison with interstellar 
distances that the light which is now reaching the earth from 
the nearest fixed star, Alpha Centauri, started 4.4 years 
ago. If an observer on the pole star had a telescope powerful 
enough to enable him to see events on the earth, he would 
not have seen the battle of Gettysburg (which occurred in 
July, 1863) until January, 1918. 

Both Foucault in France and Michelson in America have 
measured directly the velocity of light in water and have 
found it to be only three fourths as great as in air. It will 
be shown later that in all transparent liquids and solids it 
is less than it is in air. 

420. Reflection Of light.* Let a beam of sunlight be admitted to 
a darkened room through a narrow slit. The straight path of the beam 
will be rendered visible by the brightly illumined dust particles sus- 
pended in the air. Let the beam fall on the surface of a mirror. Its 
direction will be seen to be sharply 
changed, as shown in Fig. 377. Let 
the mirror be held so that it is per- 
pendicular to the beam. The beam will 
be seen to be reflected directly back 
on itself. Let the mirror be turned 
through an angle of 45. The reflected 
beam will move through 90. 




FIG. 377. Illustrating law of 
reflection of light 



The experiment shows roughly, 
therefore, that the angle IOP, be- 
tween the incident beam and the 

normal to the mirror, is equal to the angle FOR, between the re- 
flected beam and the normal to the mirror. The first angle, IOP, 
is called the angle of incidence, and the second, FOR, the angle of 
reflection. The angle of reflection is equal to the angle of incidence. 

* An exact laboratory experiment on the law of reflection should either 
precede or follow this discussion. See, for example, Experiment 42 of the 
authors' Manual. 




A. A. MICHELSON, CHICAGO 

Distinguished for extraordinarily accu- 
rate experimental researches in light. 
First American scientist to receive the 
Nobel prize 



LOUD RAYLEIGH (ENGLAND) 

Distinguished for the discovery of argon , 
for very accurate determinations in elec- 
tricity and sound and for profound theo- 
retical studies 




HENRY A. ROWLAND, JOHNS HOPKINS 

Distinguished for the invention of the 

concave grating and for epoch-making 

studies in heat and electricity 



SIB WILLIAM CROOKES, LONDON 

Distinguished for his pioneer work (1875) 
in the study and interpretation of cath- 
ode rays (pp.438 and 443) 



A GROUP OF MODERN PHYSICISTS 




X-RAY PICTURE OF THE HUMAN THORAX 

This figure is a remarkable picture of the human thorax with the apex of the 
heart showing clearly on the right of the spinal column and the base stretching 
across the column, part of it showing distinctly on the left side opposite the apex 





TRANSMISSION OF LIGHT 359 

421. Diffusion of light. In the last experiment the light was 
reflected by a very smooth plane surface. Now let the beam be allowed 
to fall upon a rough surface like that of a sheet of unglazed white paper. 
No reflected beam will be seen; but instead the whole room will be 
brightened appreciably, so that the outline of objects before invisible 
may be plainly distinguished. 

The beam has evidently been scattered in all directions by 
the innumerable little reflecting surfaces of which the surface 
of the paper is composed. The effect will be' much more 
noticeable if the 
beam is allowed 
to fall alternately 
on a piece of dead- 
black cloth and on 

FIG. 378. Regular and irregular reflection 
the white paper. 

The light is largely absorbed by the cloth, while it is scattered 
or diffusely reflected by the paper. Illumination sufficiently 
strong for sewing on white material may be altogether too 
weak for working on black goods. The difference between 
a smooth reflector and a rough one is illustrated in greatly 
magnified form in Fig. 378. The air shafts of apartment 
houses are made white to get the maximum diffusion of day- 
light into rooms that might otherwise be very dark. 

422. Visibility of nonluminous bodies. Everyone is familiar 
with the fact that certain classes of bodies, such as the sun, a 
gas flame, etc., are self-luminous (that is, visible on their own 
account), while other bodies, like books, chairs, tables, etc., can 
be seen only when they are in the presence of luminous bodies. 
The above experiment shows how such nonluminous, diffusing 
bodies become visible in the presence of luminous bodies. For, 
since a diffusing surface scatters in all directions the light 
which falls upon it, each small element of such a surface is 
sending out light in a great many directions, in much the 
same way in which each point on a luminous surface is sending 



860 NATUKE AND PROPAGATION OF LIGHT 



out light in all directions. Hence we always see the outline 
of a diffusing surface as we do that of an emitting surface, 
no matter where the eye is placed. On the other hand, when 
light comes to the eye from a polished reflecting surface, since 
the form of the beam is wholly undisturbed by the reflection, 
we see the outline not of the mirror but rather of the source 
from which the light came to the mirror, whether this source 
is itself self-luminous or not. All bodies other than self- 
luminous ones are visible only by the light which they diffuse. 
Black bodies send no light to the eye, but their outlines can 
be distinguished by the light which comes from the back- 
ground. Any object which can be seen, therefore, may be re- 
garded as itself sending rays to the eye ; that is, it may be 
treated as a luminous body. 

423. Refraction. Let a narrow beam of sunlight be allowed to fall 
on a thick glass plate with a polished front and whitened back* (Fig. 379). 
It will be seen to split into a re- 
flected and a transmitted portion. 
The transmitted portion will be 
seen to be bent toward the per- 
pendicular OP drawn into the 
glass. Upon emergence into the 
air it will be bent again, but 
this time away from the per- 
pendicular O'P' drawn into the 
air. Let the incident beam strike 




FIG. 379. Path of a ray through a 
medium bounded by parallel faces 



the surface at different angles. 

It will be seen that the greater the 

angle of incidence the greater the 

bending. At normal incidence there will be no bending at all. If the 

upper and lower faces of the glass are parallel, the bending at the two 

faces will always be the same, so that the emergent beam is parallel 

to the incident beam. 

*A11 of these experiments on reflection and refraction may be done 
effectively and conveniently by using disks of glass, like those used with the 
Hart! Optical Disk, through which the beam can be traced. 



TRANSMISSION OF LIGHT 



361 




Similar experiments made with other substances have 
brought out the general law that whenever light travels obliquely 
from one medium into another in which the speed is less it is lent 
toivard the perpendicular, and when itfia&sesfrom one medium to 
another in which the speed is greater 
it is bent away from the perpendic- 
ular, drawn into the second medium. 

424. Total reflection ; critical 
angle. Since rays emerging from 
a medium like water into one of 
less density, like air, are always 
bent /row the perpendicular (see 
II A, ImB, etc., Fig. 380), it is clear 
that if the angle of incidence on 
the under surface of the water is 
made larger and larger, a point must be reached at which the 
refracted ray is parallel to the surface (see InC, Fig. 380). It 
is interesting to inquire what will happen to a ray lo which 
strikes the surface at a still greater angle of incidence IoP f . 
It will not be unnatural to suppose that since the ray nC just 
grazed the surface, the ray lo will 
not be able to emerge at all. The 

O 

following experiment will show that 
this is indeed the case. 



FIG. 380. Rays coming from a 
source I under water to the 
boundary between air and water 
at different angles of incidence 




Let a prism with three polished edges, 
a polished front, and a whitened back be 
held in the path of a narrow beam of sun- 
light, 1 as shown in Fig. 381. If the angle 
of incidence I OP is small, the beam will 
divide at into a reflected and a trans- 
mitted portion, the former going to 5', 
the latter to S (neglect the color for the present). Let the prism be 
rotated slowly in the direction of the arrow. A point will be reached at 
which the transmitted beam disappears completely, while at the same 
time the spot at S' shows an appreciable increase in brightness. Since 



FIG. 381. Transmission and 
reflection of light at surface 
AB of a right-angled prism 



362 NATURE AND PROPAGATION OF LIGHT 

the transmitted ray OS has totally disappeared, the whole of the light 
incident at O must be in the reflected beam. The angle of incidence 
IOP at which this occurs is called the critical angle. This angle for 
crown glass is 42.5, for water 48.5, for diamond 23.7. The critical 
angle for any substance may be defined as the angle of incidence in 
that substance for which the angle of refraction into air is 90. 

We learn, then, that when a ray of light traveling in any 
medium meets another in which the speed is greater, it is totally 
reflected if the angle of incidence is greater than a certain angle 
called the critical angle. 



QUESTIONS AND PROBLEMS 

1. In Fig. 382 the portion acdb of the shadow is called the umbra, 
aec and Idf the penumbra. What kind of source has no penumbra ? 

2. The sun is much larger than the earth. Draw 
a diagram showing the shape of the earth's umbra 
and penumbra. 

3. Will it ever be possible for the moon to totally 
eclipse the sun from the 

whole of the earth's sur- 
face at once ? 

4. Sirius, the brightest 
star, is about 52,000,000,- 
000,000 miles away. If it 
were suddenly annihilated, 
how long would it shine on 
for us ? 

5. Why is a room with JT FlG - 383 ' Anti ~ 

glare " lens " for 

EIG. 382. Shadow from automobile head- 
a broad source light 





white walls much lighter 
than a similar room with 
black walls ? 

6. If the word " white : 



be painted with white paint (or whiting 
moistened with alcohol) across the face of a mirror and held in the path 
of a beam of sunlight in a darkened room, in the middle of the spot on 
the wall which receives the reflected beam the word " white " will appear 
in black letters. Explain. 

7. Compare the reflection of light from white blotting paper with, 
that from a plane mirror. Which of these objects is more easily seent 
from a distance ? Why ? 



TRANSMISSION OF LIGHT 



363 




8. Devise an arrangement of mirrors by means of which you could 
see over and beyond a high stone wall or trench embankment. This is 
a very simple form of periscope. 

9. Draw diagrams to show in what way a beam of light is bent 
(a) in passing through a prism; (b) in passing obliquely through a 
plate-glass window. 

10. Explain the effect of the anti-glare 
" lens " (Fig. 383) upon the light of the 
automobile. 

11. The moon has practically no atmos- 
phere. We know this because when a star 

appears to pass behind the moon there is FIG. 384 

no decrease or increase in its apparent 

velocity while disappearing or coming into view again. If the moon 

had an atmosphere like the earth, explain how this would affect the 

apparent velocity of the star at both these times. 

12. If a penny is placed in the bottom of a vessel in such a position 
that the edge just hides it from view (Fig. 384), it will become visible as 
soon as water is poured into the vessel. Explain. 




FIG. 385 



FIG. 386 



FIG. 387. A diagonal 
eyepiece 



13. A stick held in water appears bent, as shown in Fig. 385. Explain. 

14. A glass prism placed in the position shown in Fig. 386 is the 
most perfect reflector known. Why is it better than an 
ordinary mirror? 

15. Diagonal eyepieces containing a right-angle prism of 
crown glass (Fig. 387) are used on astronomical telescopes 
in viewing celestial objects at a high altitude. Explain. 

16. Explain why a straight wire seen obliquely through 
a piece of glass appears broken, as in Fig. 388. 

17. The earth reflects sixteen times as much light to the moon as 
the moon does to the earth. Trace from the sun to the eye of the ob- 
server the light by which he is able to see the dark part of the new 
moon. Why can we not see the dark part of a third-quarter moon? 




FIG. 388 



364 NATUKE AND PKOPAGATION OF LIGHT 

THE NATURE OF LIGHT 

425. The corpuscular theory of light. All of the properties 
of light which have so far been discussed are perhaps most 
easily accounted for on the hypothesis that light consists of 
streams of very minute particles, or corpuscles, projected with 
the enormous velocity of 300,000 kilometers per second from 
all luminous bodies. The facts of straight-line propagation 
and reflection are exactly as we should expect them to be if 
this were the nature of light. The facts of refraction can also 
be accounted for, although somewhat less simply, on this 
hypothesis. As a matter of fact, this theory of the nature of 
light, known as the corpuscular theory, was the one most 
generally accepted up to about 1800. 

426. The wave theory of light. A rival hypothesis, which 
was first completely formulated by the great Dutch physicist 
Huygens (1629-1695), regarded light, like sound, as & form 
of wave motion. This hypothesis met at the start with two 
very serious difficulties. In the first place, light, unlike 
sound, not only travels with perfect readiness through the 
best vacuum which can be obtained with an air pump, but 
it travels without any apparent difficulty through the great 
interstellar spaces which are probably infinitely better vacua 
than can be obtained by artificial means. If, therefore, light 
is a wave motion, it must be a wave motion of some medium 
which fills all space and yet does not hinder the motion of the 
stars and planets. Huygens assumed such a medium to exist, 
and called it the ether. 

The second difficulty in the way of the wave theory of 
light was that it apparently failed to account for the fact of 
straight-line propagation. Sound waves, water waves, and 
all other forms of waves with which we are most familiar 
bend readily around corners, while light apparently does not. 
It was this difficulty chiefly which led many of the most 




CHRISTIAN HUYGENS (1629-1695) 

Great Dutch physicist, mathematician, and astronomer; dis- 
covered the rings of Saturn ; made important improvements in 
the telescope ; invented the pendulum clock (1656) ; developed 
with marvelous insight the wave theory of light; discovered in 
1690 the "polarization " of light. (The fact of double refraction 
was discovered by Erasmus Bartholinus in 1669, but Huygens 
first noticed the polarization of the doubly refracted beams and 
offered an explanation of double refraction from the standpoint 
of the wave theory) 




THE GREAT TELESCOPE OF THE YERKES OBSERVATORY (UNIVERSITY 
OF CHICAGO) 

This is the largest refracting telescope in the world. The objective is an achro- 
matic lens (see 475) 40 inches in diameter, which is mounted in a tube 63 feet 
long. In order to follow the apparent motions of the heavenly bodies due to the 
rotation of the earth, the entire tube and counterpoises, weighing 21 tons, are 
driven by a giant clock. The speed of the clock is controlled by a governor, 
similar in principle to that of Fig. 184. By means of electric motors the telescope 
may be pointed in any direction. It fs then clamped to the clock, which keeps it 
pointed toward the same region of the sky as long as may be desired. The entire 
floor may be raised or lowered to accommodate the observer 



THE NATURE OF LIGHT 



365 



famous of the early philosophers, including the great Sir 
Isaac Newton, to reject the wave theory and to support the 
projected-particle theory. Within the last hundred years, 
however, this difficulty has been completely removed, and 
in addition other properties of light have been discovered 
for which the wave theory offers the only satisfactory expla- 
nation. The most important of these properties will be treated 
in the next paragraph. 

427. Interference Of light. Let two pieces of plate glass about 
half an inch wide and four or five inches long be separated at one end 
by a thin sheet of paper in the manner shown in Fig. 389, while the 
other end is clamped or held firmly together, so that a very thin wedge 
of air exists between the plates. Let a piece 
of asbestos or blotting paper be soaked in 
a solution of common salt (sodium chlo- 
ride) and placed over the tube of a Bunsen 
burner so as to touch the flame in the 
manner shown. The flame will be colored 
a bright yellow by the sodium in the salt. 
When the eye looks at the reflection of 
the flame from the glass surfaces, a series 
of fine black and yellow lines will be seen 
to cross the plate. 




Paper 



FIG. 389. Interference of 
light waves 



The wave theory offers the fol- 
lowing explanation of these effects. 
Each point of the flame sends out 
light waves which travel to the glass 
plate and are in part reflected and in 

part transmitted at all the surfaces of the glass, that is, at A'B r y 
at AB, at CD, and at C'D' (Fig. 389). We will consider, how- 
ever, only those reflections which take place at the two faces 
of the air wedge, namely, at AB and CD. Let Fig. 390 repre- 
sent a greatly magnified section of these two surfaces. Let 
the wavy line as represent a light wave reflected from the 
surface AB at the point a, and returning thence to the eye.- 



366 NATURE AND PROPAGATION OF LIGHT 



CA 



Let the dotted wavy line ir represent a light wave reflected 
from the surface CD at the point i, and returning thence to 
the eye. Similarly, let all the continuous wavy lines of the 
figure represent light waves reflected from different points on 
AB to the eye, and let all the dotted wavy lines represent 
waves reflected from corresponding points on CD to the eye. 
Now, in precisely the same way in which two trains of sound 
waves from two tun- 
ing forks were found, 
in the experiment il- 
lustrating beats (see 
396), to interfere 
with each other so as 
to produce silence 
whenever the two 
waves corresponded 
to motions of the air 
particles in opposite 
directions, so in this 
experiment the two 
sets of light waves 
from A B and CD inter- 
fere with each other 
so as to produce darkness wherever these two waves corre- 
spond to motions of the light-transmitting medium in opposite 
directions. The dark bands, then, of our experiment are sim- 
ply the places at which the two beams reflected from the two 
surfaces of the air film neutralize or destroy each other, while 
the light bands correspond to the places at which the two 
beams reenforce each other and thus produce illumination of 
double intensity. The position of the second dark band c 
must of course be determined by the fact that the distance 
from c to k and back (see Fig. 390) is a wave length more 
than from a to i and back, and so on down the wedge. This 




Interference 

Reinforcement 

Interference 

Re enforcement 

Interference 

Reenforcement 

Interference 

Reenforcement 



FIG. 390. Explanation of formation of dark and 
light bands by interference of light waves 



THE NATUKE OF LIGHT 367 

phenomenon of the interference of light is met with in many 
different forms, and in every case the wave theory furnishes 
at once a wholly satisfactory explanation of the observed 
effects, while the corpuscular theory, on the other hand, is 
unable to account for any of these interference effects with- 
out the most fantastic and violent assumptions. Hence the 
corpuscular theory is now practically abandoned, and light is 
universally regarded by physicists as a form of wave motion. 

428. The ether. We have already indicated that if the 
wave theory is to be accepted, we must conceive, with Huy- 
gens, that all space is filled with a medium, called the ether, 
in which the waves can travel. This medium cannot be like 
any of the ordinary forms of matter; for if any of these 
forms existed in interplanetary space, the planets and the 
other heavenly bodies would certainly be retarded in their 
motions. As a matter of fact, in all the hundreds of years 
during which astronomers have been making accurate obser- 
vations of the motions of heavenly bodies no such retarda- 
tion has ever been observed. The medium which transmits 
light waves must therefore have a density which is infinitely 
small even in comparison with that of our lightest gases. 

Further, in order to account for the transmission of light 
through transparent bodies, it is necessary to assume that the 
ether penetrates not only all interstellar spaces but all inter- 
molecular spaces as well. 

429. Wave length of yellow light. Although light, like sound, is a 
form of wave motion, light waves differ from sound waves in several 
important respects. In the first place, an analysis of the preceding experi- 
ment, which seems to establish so conclusively the correctness of the 
wave theory, shows that the wave length of light is extremely minute 
in comparison with that of ordinary sound waves. The wave length of 
the yellow light used in that experiment is .00006 centimeter (about 

40,000 incn > 

The number of vibrations per second made by the little particles which 
send out the light waves may be found, as in the case of sound, by 



868 NATUKE AND PKOPAGATION OF LIGHT 



dividiug the velocity by the wave length. Since the velocity of light is 
30,000,000,000 centimeters per second and the wave length is .00006 
centimeter, the number of vibrations per second of the particles which 
emit yellow light has the enormous value 500,000,000,000,000. 

430. Wave theory explanation of refraction. Let one look ver- 
tically down upon a glass or tall jar full of water and place his finger 
on the side of the. glass at the point at which the bottom appears to 
be, as seen through the water (Fig. 391). In every case it will be 
found that the point touched by the finger will be 
about one fourth of the depth of the water above 
the bottom. 



According to the wave theory this effect is 
due to the fact that the speed of light is less 
in water than in air. Thus, consider a wave 
which originates at any point P (Fig. 392) 
beneath a surface of water and spreads from 
that point with equal speed in all directions. 
At the instant at which the front of this wave 
first touches the surface at o it will, of course, 




FIG. 391. Appar- 



be of spherical form, having P as its center, ent elevation of 

Let aob be a section of this sphere. An in- th , bo " om of a 

body of water 
stant later, if the speed had not changed in 

passing into air, the wave would have still had P as its 
center, and its form would have coincided with the dotted 
line cOjd, so drawn that ac, oo^ and bd are all equal. But if 
the velocity in air is greater than in water, then at the instant 
considered the disturbance will have reached some point o 2 
instead of o^ and hence the emerging wave will actually have 
the form of the heavy line co 2 d instead of the dotted line co^d. 
Now this wave co^d is more curved than the old wave aob, 
and hence it has its center at some point P' above P. In other 
words, the wave has bulged upward in passing from water 
into air. Therefore, when a section of this wave enters the 
eye at E, the wave appears to originate not at P but at P', 
for the light actually comes to the eye from P 1 as a center 



THE NATURE OF LIGHT 



369 



rather than from P. We conclude, therefore, that if light 
travels more slowly in water than in air, all objects beneath the 
surface of water ought to appear nearer to the eye than they 
actually are. This is precisely what we found to be the case 
in our experiment. 

Furthermore, since when the eye is in any position other 
than E, for example E\ the light travels to it over the broken 
path PdE\ the construction shows that light is always bent 
away from the perpendicu- 
lar when it passes obliquely 
into a medium in which the 
speed is greater. If it had 
passed into a medium of less 
speed, the point P would 
have appeared depressed 
below its natural position, 
because the wave, on emerg- 
ing into the slower medium, 
instead of bulging upward 
would be flattened, and 
therefore would have its 
center of curvature, or 
apparent point of origin, 
below P ; hence the oblique rays would have appeared to be bent 
toward the perpendicular, as we found in 423 to be the case. 

431. The ratio of the speeds of light in air and water. The 
experiment with the tall jar of water in 430 not only indi- 
cates qualitatively that the speed of light in air is greater 
than in water, but it furnishes a simple means of determining 
the ratio of the two speeds. Thus, in Fig. 392 the line oo 2 
represents just how far the wave travels in air while it is 

traveling the distance ac (= oo^) in water. Hence 2 is the 

\ 
ratio of the speeds of light in air and in water. 




FIG. 392. Representing a wave emerging 
from water into air 



370 NATUKE AND PROPAGATION OF LIGHT 



Now the curvatures of the arcs cod and cod are measured 



by the reciprocals of their respective radii 

i 1 
Curvature of 



that is, 



Curvature of co^d 



dP 



dP' 



(1) 



Now when the arcs are small, a condition which in general 
is realized in experimental work, their curvatures are propor- 
tional to the extent to which they bulge out from the straight 
line cod^ ; that is, 



Curvature of co^d 



Curvature of co^d 
From (1) and (2) we get 
Speed in air 



_ speed in air 
speed in water 



dP 



Speed in water dP' 



(2) 



(3) 



* Construct an angle of 45 (Fig. 393, (1)). Its arc contains 45 and the 
angle formed by the tangents , t' is 45. Now with a radius three times as 
great (Fig. 393, (2)) draw an arc whose 
length is equal to that of the arc in 
Fig. 393 (1). Since the radius is three 
times as great, this arc contains 15, 
and the angle formed by the tangents 
is 15. From this we see that the arc 
whose radius is three times as great 
curves, or changes its direction, one 
third as fast ; that is, the change in 

curvature of an arc of given length varies inversely with the radius. In gen- 
eral then, the curvature of an arc is measured by the reciprocal of its radius. 

t oc (Fig. 394) is a mean proportional between the two 
segments of the diameter ; hence ao x od = oc 2 . For very 
small arcs od is practically equal to the diameter r. Hence 




FIG. 393 



ao = 



2r 



oc 2 1 

or ao = x - 
2 r 



Therefore ao is proportional to 



_. That is, the distances to which two small arcs having a 

r 

common chord bulge out from the chord are proportional to 

the respective curvatures of the arcs. 




FIG. 394 



THE NATURE OF LIGHT 371 

But in looking vertically downward, as in the experiment 

dP , oP , 

with the iar of water, -- becomes ; hence, 

dP' oP' 

Speed in air _ oP _ real depth 
Speed in water oP' apparent depth 

But in our experiment we found that the bottom was appar- 

oP 4 
ently raised one fourth of the depth ; that is, that - = - 

We conclude, therefore, that light travels three fourths as 
fast in water as in air. 

The fact that the value of this ratio, as determined by this 
indirect method, is exactly the same as that found by Foucault 
and Michelson (see opposite p. 358) by direct measurement 
(419) furnishes one of the strongest proofs of the correct- 
ness of the wave theory. 

432. Index of refraction. The ratio of the speed of light in 
air to its speed in any other medium is called the index of refrac- 
tion of that medium. It is evident that the method employed 
iii the last paragraph for determining the index of refraction 
of water can be easily applied to any transparent medium 
whether liquid or solid.* The refractive indices of some of 
the commoner substances are as follows: 

Water 1.33 Crown glass 1.53 

Alcohol 1.36 Flint glass 1.67 

Turpentine 1.47 Diamond 2.47 

433. Light waves are transverse. Thus far we have discov- 
ered but two differences between light waves and sound waves ; 
namely, the former are disturbances in the ether and are of 
vary short wave length, while the latter are disturbances in 

* To show the extreme beauty, simplicity, and accuracy of this method 
of getting index of refraction it is suggested that the teacher use the following 
method in his laboratory work. 

A very sharp pencil must be used for this exercise. Make a dot P on a 
sheet of paper. Put the glass plate (Fig. 395, (1)) on the sheet so that the 



372 NATURE AND PROPAGATION OF LIGHT 



ordinary matter and are of relatively great wave length. There 
exists, however, a further radical difference which follows from 
a capital discovery made by Huygens (see opposite p. 364) in 
the year 1690. It is this : While sound waves consist, as we 
have already seen, of longitudinal vibrations of the particles 
of the transmitting medium, that is, vibrations back and forth 
in the line of propagation of the wave, light waves are like 
the water waves of Fig. 346, p. 324, in that they consist of 
transverse vibrations, that is, vibrations of the medium at 
right angles to the direction of the line of propagation. 

In order to appreciate the difference between the behavior 
of waves of these two types under certain conditions, conceive 

edge of the label pasted around the edge of the glass coincides with the dot 
(or in case a prism (Fig. 395, (2)) is used, let the apex P coincide with the dot). 
Draw the base line ef and the other sides of the glass, holding it firmly down 
meanwhile. Be sure that 
at no time during the 
exercise does the glass 
slip the slightest from 
its first position. Lay a 
ruler upon the paper in 
a slantwise position cd 
(not touching the glass), 
and, with one eye closed, 
make its edge point ex- 
actly at the apparent 
position of P as seen 
through the glass. If you 
are now sure that your 
ruler did not push the 
glass out of position, 
draw a line cd with the 

sharp pencil. Similarly, draw another line ab about as far to the right of the 
center as cd is to the left. Remove your glass and complete the drawing 
indicated in the diagram. 

P' is the apparent position of P. As you have already learned from your 
text, the ratio of the velocities of light in air and glass is found by dividing 
dP by dP'. Measure these distances very carefully to 0.1 mm., and calculate 
the index of refraction to two decimal places. Make two or three more trials 
and compare results. 




FIG. 395. Index of refraction 




THE NATURE OF LIGHT 373 

of transverse waves in a rope being made to pass through two 
gratings in succession, as in Fig. 396. So long as the slits in 
both gratings are parallel to the plane of vibration of the 
hand, as in Fig. 396, (1), the waves can pass through them 
with perfect ease ; but 
if the slits in the first 
grating P are parallel to 
the direction of vibra- 
tion, while those of the 
second grating Q are 
turned at right angles 

to this direction, as in 

_,. nf .~ x ~ x ., . . FIG. 396. Transverse waves passing 

Kg. 896, (2), it is evi- through site 

dent that the waves 

will pass readily through P, but will be stopped completely 

by Q, as shown in the figure. In other words, these gratings 

P and Q will let through only such vibrations as are parallel 

to the direction of their slits. 

If, on the other hand, a longitudinal instead of a transverse 
W ave such, for example, as a sound wave had approached 
such a grating, it would have been as much transmitted in 
one position of the grating as in another, since a to-and-fro 
motion of the particles can evidently pass through the slits 
with exactly the same ease, no matter how they are turned. 

Now two crystals of tourmaline are found to behave with 
respect to light waves just as the two gratings behave with 
respect to the waves on the rope. 

Let one such crystal a (Fig. 397) be 
held in front of a small hole in a screen 
through which a beam of sunlight is FlG> 39L Tourmaline tongs 
passing to a neighboring wall ; or, if the 

sun is not shining, simply let the crystal be held between the eye and a 
source of light. The light will be readily transmitted, although some- 
what diminished in intensity. Then let a second crystal b be held in 
line with the first. The light will still be transmitted, provided the axes of 




374 NATURE AND PROPAGATION OF LIGHT 



the crystals are parallel, as shown in Fig. 308. When, however, one of the 
crystals is rotated in its ring through 90 (Fig. 399), the light is cut off. 
This shows that a 
crystal of tourma- 
line is capable of 
transmitting only 




FIG. 398. Light pass- 
ing through tourmaline 



FIG. 399. Light cut off 

by crossed tourmaline 

crystals 



light which is vibra- 
ting in one particu- 
lar plane. 

From this ex- 
periment, there- 
fore, we are forced to conclude that light waves are transverse 
rather than longitudinal vibrations. The experiment illustrates 
what is technically known as the polarization of light, and 
the beam which, after passage through , is unable to pass 
through b if the axes of a and b are crossed, is known as a 
polarized beam. It is, then, the phenomenon of the polariza- 
tion of light upon which we base the conclusion that light 
waves are transverse. 

434. Intensity of illumination. Let four candles be set as 
close together as possible in such a position B as to cast upon a white 
screen C, placed in a well-darkened room, a shadow of an opaque object O 
(Fig. 400). Let one single candle be placed in a position A such that 
it will cast another shadow of upon the screen. Since light from A 
falls on the shadow cast by B, and light from B falls on the shadow 
cast by A, it is clear that the two 
shadows will appear equally dark 
only when light of equal intensity 
falls on each ; that is, when A and 
B produce equal illumination upon 
the screen. Let the positions of A 
and B be shifted until this condition 
is fulfilled. Then let the distances 

from B to C and from A to C be measured. If all five candles are burning 
with flames of the same size, the first distance will be found to be just 
twice as great as the second. Hence the illumination produced upon 
the screen by each one of the candles at B is but one fourth as great as 
that produced on the screen by one candle at A, one half as far away. 




FIG. 400. Rumford's photometer 



THE NATURE OF LIGHT 375 

The above is the direct experimental proof that the intensity of 
illumination varies inversely as the square of the distance from 
the source. 

The theoretical proof of the law is furnished at once by 
Fig. 401, for since all the light which falls from the candle L 
on A is spread over four times as large an area when it reaches 
B, twice as far away, and over nine times as large an area 




FIG. 401. Proof of law of inverse squares 



when it reaches (7, three times as far away, obviously the in- 
tensities at B and at C can be but one fourth and one ninth as 
great as at A. 

The above method of comparing experimentally the inten- 
sities of two lights was first used by Count Rumford. The 
arrangement is therefore called the Rumford photometer (light 
measurer). 

435. Candle power. The last experiment furnishes a method 
of comparing the light-emitting powers of various sources of 
light. For example, suppose that the four candles at B are 
replaced by a gas flame, and that for the condition of equal 
illumination upon the screen the two distances BC and AC are 
the same as above, namely, 2 to 1. We should then know that 
the gas flame, which is able to produce the same illumination 
at a distance of two feet as a candle at a distance of one foot, 
has a light-emitting power equal to four candles. In general, 
then, the candle powers of any tivo sources which produce equal 
illumination on a given screen are directly proportional to the 
squares of the distances of the sources from the screen. 

It is customary to express the intensities of all sources of 
light in terms of candle power, one candle power being denned 
as the amount of light emitted by a sperm candle J- inch in 



376 NATURE AND PROPAGATION OF LIGHT 

diameter and burning 120 grains (7.776 grams) per hour. The 
candle power of an ordinary gas flame burning 5 cubic feet 
per hour is from 16 to 25, depending on the quality of the gas. 
A standard candle at a distance of 1 foot gives an intensity 
of illumination called & foot-candle. A 100-candle-power lamp, 
for example, at a distance of 1 foot gives an intensity of illu- 
mination of 100 foot-candles ; at 2 feet, of 25 foot-candles ; at 
5 feet, of 4 foot-candles ; and at 10 feet, of 1 foot-candle. 

436. Bunsen's photometer. Let a drop of oil or melted paraffin be 
placed in the middle of a sheet of unglazed white paper to render it 
translucent. Let the paper be held near a window and the side away 
from the window observed. The oiled spot will appear lighter than the 
remainder of the paper. Then let the paper be held so that the side 
nearest the window may be seen. The oiled spot will appear darker 
than the rest of the paper. We learn, therefore, that when the paper is 
viewed from the side of greater illumination, the oiled spot appears dark ; 
but when it is viewed from the side of lesser illumination, the spot appears light. 
If, then, the two sides of the paper are equally illuminated, the spot 
ought to be of the same brightness when viewed from either side. Let 
the room be darkened and the oiled paper placed between two gas flames, 
two electric lights, or any two equal sources of light. It will be observed 
that when the paper is held closer to one than the other, the spot will 
appear dark when viewed from the 
side next the closer light; but if it 
is then moved until it is nearer the 
other source, the spot will change 
from dark to light when viewed always 
from the same side. It is always pos- ^IG. 402. Bunsen's photometer 
sible to find some position for the oiled 

paper at which the spot either disappears altogether or at least appears 
the same when viewed from either side. This is the position at which 
the illuminations from the two sources are equal. Hence, to find the 
candle power of any unknown source it is only necessary to set up a 
candle on one side and the unknown source on the other, as in Fig. 402, 
and to move the spot A to the position of equal illumination. The can- 
dle power of the unknown source at C will then be the square of the 
distance from C to A, divided by the square of the distance from B to A. 

This arrangement is known as the Bunsen photometer. 




THE NATURE OF LIGHT 377 



QUESTIONS AND PROBLEMS 

1. Distinguish between candle power, intensity of light, and inten- 
sity of illumination. 

2. How many candles will be required to produce the same intensity 
of illumination at 2 m. that is produced by 1 candle at 30 cm. ? 

3. A 500-candle-power lamp is placed 50 m. from a darkly shaded 
place along the street. At what distance would a 100-candle-power 
lamp have to be to produce the same intensity of illumination ? 

4. If a 2-candle-power light at a distance of 1 ft. gives enough 
illumination for reading, how far away must a 3 2-candle-power lamp 
be placed to make the same illumination? How strong a lamp should 
be used at a distance of 8 ft. from the book ? 

5. A Bunsen photometer placed between an arc light and an incan- 
descent light of 32 candle power is equally illuminated on both sides 
when it is 10 ft. from the incandescent light and 36 ft. from the arc 
light. What is the candle power of the arc ? 

6. A 5-candle-power and a 30-candle-power source of light are 2 m. 
apart. Where must the oiled disk of a Bunsen photometer be placed in 
order to be equally illuminated on the two sides by them ? 

7. If the sun were at the distance of the moon from the earth, in- 
stead of at its present distance, how much stronger would sunlight be 
than at present? The moon is 240,000 mi. and the sun 93,000,000 mi. 
from the earth. 

8. If a gas flame is 300 cm. from the screen of a Rumford photom- 
eter, and a standard candle 50 cm. away gives a shadow of equal inten- 
sity, what is the candle power of the gas flame ? 

9. Will a beam of light going from water into flint glass be bent 
toward or away from the perpendicular drawn into the glass ? 

10. When light passes obliquely from air into carbon bisulphide it is 
bent more than when it passes from air into water at the same angle. 
Is the speed of light in carbon bisulphide greater or less than in water? 

11. If light travels with a velocity of 186,000 miles per sec. in air, 
what is its velocity in water, in crown glass, and in diamond? (See table 
of indices of refraction, p. 371.) 







CHAPTER XIX 

IMAGE FORMATION 
IMAGES FORMED BY LENSES 

437. Focal length of a convex lens. Let a convex lens be tfeld 
in the path of a beam of sunlight which enters a darkened room, where 
it is made plainly visible by means of chalk dust or smoke. The beam 
will be found to converge to a focus F, as shown in Fig. 403. 

The explanation is as follows: The waves from the sun 
or any distant object are without any appreciable curvature 
when they strike the lens; 
that is, they are so-called 
plane waves (see Fig. 403). 
Since the speed of light is less 

in glass than in air, the cen- Fic " 403 ' prhlci P al focusFand focal 

length CF of a convex lens 
tral portion of these waves 

is retarded more than the outer portions in passing through 
the lens. Hence, on emerging from the lens the waves are con- 
cave instead of plane, and close in to a center or focus at F. 

A second way of looking at the phenomenon is to think 
of the " rays " which strike the lens as being bent by it, in 
accordance with the laws given in 423, so that they all 
pass through the point F. 

The line through the point C (the optical center) of the 
lens, perpendicular to its faces, is called the principal axis. 

The point F at which rays parallel to the principal axis 
(incident plane waves) are brought to a focus is called the 
principal focus. 

The distance CF from the center of the lens to the prin- 
cipal focus is called the focal length (/) of the lens. 

378 



IMAGES FORMED BY LENSES 



379 




FIG. 404. Focal plane of a convex lens 



The plane F'FF" (Fig. 404) m which plane waves (parallel 
rays) coming to the lens from slightly different directions, as 
from the top and bottom of 
a distant house, all have 

their foci F', F", etc. is //UmUWmffiqttttffl -F 

called the focal plane of 
the lens. 

Since the curvature of 
any arc is defined as the reciprocal of its radius (see footnote, 
p. 370), the curvature which a lens impresses on an incident 

plane wave is equal to - Moreover, no matter what the 

J 
curvature of an incident wave may be, the lens will ahvays 

change the curvature by the same amount, - 

c/ 

Let the focal length of a convex lens be accurately determined by 
measuring the distance from the middle of the lens to the image of a 
distant house. 

438. Conjugate foci. If a point source of light is placed at 
F (Fig. 403), it is obvious that the light which goes through 
the lens must exactly retrace its former path ; that is, its 




FIG. 405. Conjugate foci 

waves will be rendered plane or its rays parallel by the lens. 
But if the point source is at a distance D greater than / 
(Fig. 405), then the waves upon striking the lens have a 

curvature (sin<3e the curvature of an arc is defined as 
the reciprocal of its radius), which is less than their former 
curvature, -. Since the lens was able to subtract all the 



380 IMAGE FORMATION 

curvature from waves coming from F and render them plane, 
by subtracting the same curvature from the flatter waves 
from P it must render them concave ; that is, the rays after 
passing through the lens are converging and intersect at P'. 
If the source is placed at P', obviously the rays will meet at 
P. Points such as P and P', so related that one is the image 
of the other, are called conjugate foci. 

439. Formula for conjugate foci ; secondary foci. Since in 
Fig. 405 the curvature of the wave when it emerges from 
the lens is opposite in direction to its curvature when it 

reaches the lens, the sum of these curvatures, -- 1 -- , repre- 
sents the power of the lens to change the curvature of the 
incident wave, which by 437 is Hence 

' 



that is, the sum of the reciprocals of the distances of the conju- 
gate foci from the lens is equal to the reciprocal of the focal 
length. If D = D f , then the equation shows that both D and 
D { are equal to 2/. 

The two conjugate foci S and S 1 which are at equal dis- 
tances from the lens are called the secondary foci, and their 
distance from the lens is twice the focal distance. 




FIG. 406. Formation of a real image by a lens 

440. Images of Objects. Let a candle or electric-light bulb be 
placed between the principal focus F and the secondary focus S at PQ 
(Fig. 406), and let a screen be placed at P'Q'. An enlarged inverted 
image will be seen upon the screen. 



IMAGES FORMED BY LENSES 381 

This image is formed as follows: All the light which 
strikes the lens from the point P is brought together at a 
point P'. The location of this image P' must be on a straight 
line drawn from P through C ; for any ray passing through C 
will remain parallel to its original direction, since the portions of 
the lens through which it enters and leaves may be regarded as 
small parallel planes (see 423). The image P'Q' is therefore 
always formed between the lines drawn from P and Q through C. 
If the focal length / and the distance of the object D are 
known, the distance of the image D. may be obtained easily 
from formula (1). 

The position of the image may also be found graphically as 
follows : Of the cone of rays passing from P to the lens, that 




FIG. 407. Ray method of constructing an image 

ray which is parallel to the principal axis must, by 43 7, 
pass through the principal focus F . The intersection of this 
line with the straight line through C locates the image P r 
(see Fig. 407). Q', the image of Q, is located similarly. 

441. Size of image. Since the image and object are always 
between the intersecting straight lines PP f and QQ', the 
similar triangles PCQ and P'CQ' show that 



, . Length of object _ distance of object from lens 
Length of image distance of image from lens 

It may be seen from Fig. 407, as well as from formulas (1) 
and (2), that 

1. When the object is at S the image is at ', and image 
and object are of the same size. 



382 



IMAGE FORMATION 




FIG. 408. Virtual image formed 
by a convex lens 




2. As the object moves out from S to a great distance the 
image moves from S f up to F' 9 becoming smaller and smaller. 

3. As the object moves from S 
up to F the image moves out to a 
very great distance to the right, 
becoming larger and larger. 

4. When the object is at F the 
emerging waves are plane (the 
emerging rays are parallel), and 
no real image is formed. 

442. Virtual image. We have seen that when the object is 
at F the waves after passing through the lens are plane. If, 
then, the object is nearer to 

the lens than F, the emerg- 
ing waves, although reduced 
in curvature, will still be con- 
vex, and, if received by an - , 

eye at E, will appear to come 

/ . *, r ,. . FIG. 409. Ray method of locating 

from a point P* (Fig. 408). a virtual image in a convex lens 

Since, however, there is actu- 
ally no source of light at P', this sort of image is called a 
virtual image. Such an image cannot be projected upon a 
screen as a real image can, but must be observed by an eye. 

The graphical location of a virtual image 
may be accomplished precisely as in the case 
of a real image ( 440). It will be seen that 
in this case (Figs. 408 and 409) the image 
is enlarged and erect. 

443. Image in concave lens. When a plane 
wave strikes a concave lens, it must emerge 

as a divergent wave, since the middle of the wave is retarded 
by the glass less than the edges (Fig. 410). The point F 
from which plane waves appear to come after passing through 
such a lens is the principal focus of the lens. For the same 




FIG. 410. Virtual 
focus of a con- 
cave lens 



IMAGES IN MIRRORS 



383 



reason .as in the case of the convex lens the centers of the 
transmitted waves from P and Q (Fig. 411), that is, the images 
P 1 and Q', must lie upon the lines PC and QC; and since the 





FIG. 411. Image in a concave lens 



FIG. 412. Ray method of locating 
an image in a concave lens 



curvature is increased by the lens, they must lie closer to the 
lens than P and Q. Fig. 411 shows the way in which such a 
lens forms an image. This image is always virtual, erect, and 
diminished. .The graphical method of locating the image is 
shown in Fig. 412. 

IMAGES IN MIRRORS 

444. Image of a point in a plane or a curved mirror. We 

are all familiar with the fact that to an eye at E (Fig. 413), 
looking into a plane mirror mn, a pen- 
cil point at P appears to be at some 
point P' behind the mirror. We are 
able in the laboratory to find experi- 
mentally the exact location of this 
image P' with respect to P and the 
mirror, but we may also obtain this 
location from theory as follows : Con- 
sider a light wave which originates in 
the point P (Fig. 413) and spreads in 
all directions. Let aob be a section of 
the wave at the instant at which it 
reaches the reflecting surface mn. An 
instant later, if there were no reflecting surface, the wave 
would have reached the position of the dotted line cofl. 




FIG. 413. Wave reflected 
from a plane surface 



384 



IMAGE FORMATION 



Since, however, reflection took place at win, and since the 
reflected wave is propagated backward with exactly the same 
velocity with which the original wave would have been prop- 
agated forward, at the proper instant the reflected wave must 
have reached the position of the line co 2 d, so drawn that oo^ 
is equal to oo z . Now the wave co^d has its center at some 
point P', and it will be seen that P' must lie just as far below 
mn as P lies above it, for cofl and co^d are arcs of equal circles 

JXlM 





FIG. 414. Wave reflected from a 
convex surface 



FIG. 415. Wave reflected 
from a concave surface 



having the common chord cd. For the same reason, also, P' 
must lie on the perpendicular drawn from P through mn. 
When, then, a section of this reflected wave co 2 d enters the 
eye at E, the wave appears to have originated at P' and not 
at P, for the light actually comes to the eye from P' as a 
center rather than from P. Hence P 1 is the image of P. 
We learn, therefore, that the image of a point in a plane mir- 
ror lies on the perpendicular drawn from the point to the mirror 
and is as far back of the mirror as the point is in front of it. 
Precisely the same construction applied to curved mirrors 
shows at once (Fig. 414 and Fig. 415) that the image of a 
point in any mirror, plane or curved, must lie on the perpen- 
dicular drawn from the point to the mirror ; but if the mirror 



IMAGES IN MIRRORS 



385 




is convex, the image is nearer to it than is the point, while if it is 
concave, the image, if formed behind the mirror at all (that is, 
if it is virtual), is farther from the mirror than is the point. 

445. Construction of image of object in a plane mirror. 
The image of an object in a plane mirror (Fig. 416") may 
be located by applying the law 

proved above for each of its 
points, that is, by drawing from 
each point a perpendicular to the 
reflecting surface and extending it 
an equal distance on the other side. 
To find the path of the rays 
which come to an eye placed at FIG. 416. Construction of image of 

,, ,, , , . object in a plane mirror 

E from any point of the object, 

such as A, we have only to draw a line from the image A' of 
this point to the eye and connect the point of intersection 
of this line with the mirror, namely C, with the original 
point A. ACE is then the path of the ray. 

Let a candle (Fig. 417) be placed exactly as far in front of a pane of 
window glass as a bottle full of water is behind it, both objects being 
on the same perpendicular drawn through 
the glass. The candle will appear to be 
burning inside the water. This explains a 
large class of familiar optical illusions, such 
as the w figure suspended in mid-air," the 
"bust of a person without a trunk," the 
** stage ghost," etc. In the last case the illu- 
sion is produced by causing the audience to 
look at the actors obliquely through a sheet 
of very clear plate glass, the edges of which 
are concealed by draperies. Images of strongly illuminated figures 
at one side then appear to the audience to be in the midst of the actors. 

446. Focal length of a curved mirror half its radius of curva- 
ture. The effect of a convex mirror on plane waves incident 
upon it is shown in Fig. 418. The wave which would at a 





FIG. 417. Position of image 
in a plane mirror 



386 



IMAGE FORMATION 



given instant have been at co^d is at co z d, where oo l = oo 2 . 
The center F from which the waves appear to come to the 
eye E is the focus 
of the mirror. 

Now so long 
as the arc cod is 
small its curva- 
ture may, without 
appreciable error, 
be measured by 
o^p (see footnote, 
p. 370); that is, 
by the departure 
of the curved 
line cod from the 
straight line co^d. 




FIG. 418. Reflection of a plane wave from a 
convex mirror 

Since o o was made equal to oo , we 



have 0^ = 2 o^o ; that is, the curvature of the reflected 
wave is equal to twice the curvature of the mirror, or 

In other words, the focal length of 



1 1 ' , R 

- = 2x-; hence /=- 



a mirror is equal to one half its radius. 

447. Image of an object in a convex mirror. We are all 
familiar with the fact that a convex mirror always forms 
behind the mirror a virtual, 
erect, and diminished image. 
The reason for this is shown 
clearly in Fig. 419. The 
image of the point P lies, as 
in plane mirrors (see 444), 
always on the perpendicular 
to the mirror, but now neces- 
sarily nearer to the mirror than the focus F, since, as the point 
P is moved from a position very close to the mirror, where 






SECTION OF A ft MOVIE" FILM SHOWING SECRETARY or WAR BAKER 

TURNING HIS HEAD TO SPEAK TO GENERAL PERSHING 

The moving-picture camera makes a series of snapshots upon a film, usually at 
the rate of 10 per second. The film is drawn past the lens with a jerky movement, 
being held at rest during the instant of exposure and moved forward while the 
shutter is closed. The pictures are |-inch high and 1 inch wide. Since 1 foot of 
film per second is drawn past the lens, a reel of film 1000 feet long (the usual length) 
contains 16,000 pictures. From the reel of negatives a reel of positives is printed 
for use in the projection apparatus. The optical illusion of " moving " pictures is 
made possible by a peculiarity of the eye called persistence of vision. To illustrate 
this let a firebrand be rapidly whirled in a circle. The spot of light appears 
drawn into a luminous arc. This phenomenon is due to the fact that we continue 
to see an object for a small fraction of a second after the image of it disappears 
from the retina. The period of time varies somewhat with different individuals. 
The so-called "moving" pictures do not move at all. In normal projection 
16 brilliant stationary pictures per second appear in succession upon the screen, 
and during the interval between the pictures the screen is perfectly dark. It is 
during this period of darkness that the film is jerked forward to get the next 
picture into position for projection. The eye, however, detects no period of ,dark- 
ness, for on account of persistence of vision it continues to see the stationary 
picture not only during this period of darkness but dimly for an instant even 
after the next picture appears upon the screen. This causes the successive station- 
ary pictures, which differ but slightly, to blend smoothly into each other and thus 
give the effect of actual motion 






r 





5 6 

PHOTOGRAPHS OF SOUND WAVES HAVING THEIR ORIGIN IN AN ELECTRIC 
SPARK BEHIND THE MIDDLE OF THE BLACK DISK 

1. A spherical sound wave. 2. The same wave .00007 second later. 3. A wave re- 
flected from a plane surface, curvature unchanged. 4. A wave reflected from a 
convex surface, curvature increased. 5. The source at the focus of a SO 2 lens. The 
photograph shows first, the original wave on the right ; second, the reflected wave, 
with its increased curvature ; and third, the transmitted plane wave. 6. Source at 
focus of a concave mirror ; the reflected wave is plane. (Taken by Professor A. L. 
Foley and Wilmer H. Souder, of the University of Indiana) 



IMAGES IN MIRKORS 



387 



its image is just behind it, out to an infinite distance, its image 
moves back only to the focal plane through F. Hence the 
image must lie somewhere between F and the mirror. The 
image P'Q' of an object PQ is always diminished, because it 
lies between the converging lines PC and QC. It can be 
located by the ray method (Fig. 419) exactly as in the case 
of concave lenses. In fact, a convex mirror and a concave lens 
have exactly the same opti- 
cal properties. This is be- 
cause each always increases 
the curvature of the incident 

waves by an amount - 

448. Images in concave 
mirrors. Let the images ob- 
tainable with a concave mirror 
be studied precisely as were 
those obtainable from a convex lens. It will be found that exactly the 
same series of images is obtained : when the object is between the 
mirror and the principal focus, the image is virtual, enlarged, and 
erect; when it is at the focus the reflected waves are plane, that is, 
the rays from each point are a parallel bundle ; when it is between the 




FIG. 420. Real image of candle formed 
by a concave mirror 




FIG. 421. Method of formation of a real image by a concave mirror 

principal focus and the center of curvature, the image is inverted, en- 
larged, and real (Figs. 420 and 421) ; when it is at a distance R (= oC) 
from the mirror, the image is also at a distance R and of the same size 
as the object, though inverted ; when the object is moved from R out to 



388 



IMAGE FORMATION 




a great distance, the image moves from C up to F, and is always real, 
inverted, and diminished. The most convenient way of finding the 
focal length is to find where 
the image of a distant object is 
formed. 

We learn, then, that a con- 
cave mirror has exactly the 
optical properties of a con- 
vex lens. This is because, 

like the convex lens, it always FlG ' 422 ' Ra 7 method of locating rea ' 

J image in a concave mirror 

diminishes the curvature of 

the waves. The same formulas hold throughout, and the 

same constructions are applicable (see Fig. 422). 

449. Summary for lenses and spherical mirrors.* 
1. Real images, inverted ; virtual images, erect. 
The length of all images is given by 

L n D n 



where L and L t - denote the length of object and image respec- 
tively, and D and D f their distances from the lens or mirror. 

2. Convex lenses and concave mirrors have the same optical proper- 

ties (always diminish the curvature of the waves). 

a. If object is more distant than principal focus, image is real and 

(1) enlarged when object is between principal focus and twice 
focal length ; 

(2) diminished when object is beyond two focal lengths. 

b. If object is less distant than principal focus, image is virtual and 
always enlarged. 

3. Concave lenses and convex mirrors have the same optical prop- 

erties (always increase the curvature of the waves). 
Image always virtual and diminished for any position of object. 



4. 



- 

DO A / 



( 439) 



* Laboratory experiments on the formation of images by concave mirrors 
and by lenses should follow this discussion. See, for example, Experiments 
45 and 46 of the authors' Manual. 



IMAGES IN MIKKORS 389 

This formula may be used in all cases if the following points are 
borne in mind : 

a. D is always to be taken as positive. 

b. D { is to be taken as positive for real images and negative for 
virtual images. 

c. f is to be taken as positive for converging systems (convex lenses 
and concave mirrors) and negative for diverging systems (con- 
cave lenses and convex mirrors). 

QUESTIONS AND PROBLEMS 

1. Show from a construction of the image that a man cannot see 
his entire length in a vertical mirror unless the mirror is half as tall as 
he is. Decide from a study of the figure whether or not the distance of 
the man from the mirror affects the case. 

2. A man is standing squarely in front of a plane mirror which is 
very much taller than he is. The mirror is tipped toward him until 
it makes an angle of 45 with the horizontal. He still sees his full 
length. What position does his image occupy ? 

3. How tall is a tree 200 ft. away if the image of it formed by a 
lens of focal length 4 in. is 1 in. long? (Consider the image to be formed 
in the focal plane.) 

4. How long an image of the same tree will be formed in the focal 
plane of a lens having a focal length of 9 in.? 

5. What is the difference between a real and a virtual image? 

6. When does a convex lens form a real, and when a virtual, image ? 
When an enlarged, and when a diminished, image? When an erect, 
and when an inverted, one ? 

7. When a camera is adjusted to photograph a distant object, what 
change in the length of the bellows must be made to photograph a near 
object? Explain clearly why this adjustment is necessary. 

8. Rays diverge from a point 20 cm. in front of a converging lens 
whose focal length is 4 cm. At what point do the rays come to a focus? 

9. An object 2 cm. long was placed 10 cm. from a converging lens 
and the image was formed 40 cm. from the lens on the other side. Find 
the focal length of the lens and the length of the image. 

10. An object is 15 cm. in front of a convex lens of 12 cm. focal 
length. What will be the nature of the image, its size, and its distance 
from the lens ? 

11. Why does the nose appear relatively large in comparison with 
the ears when the face is viewed in a convex mirror? 

12. Can a convex mirror ever form an inverted image? Why? 



390 



IMAGE FORMATION 




FIG. 423. Image formed 
small opening 



by a 



OPTICAL INSTRUMENTS 

450. The photographic camera. A fairly distinct, though dim, 
image of a candle flame can be obtained with nothing more 
elaborate than a pinhole in a piece of cardboard (Fig. 423). 
If the receiving screen is replaced 
by a photographic plate, the ar- 
rangement becomes a pinhole 
camera, with which good pictures 
may be taken if the exposure is 
sufficiently long. If we try to 
increase the brightness of the 
image by enlarging the hole, the 
image becomes blurred, because the narrow pencils a^' ^ <*$ $ 
etc. become cones whose bases a' ^ a' z , overlap and thus destroy 
the distinctness of the outline. 

It is possible, without sacrific- 
ing distinctness of outline, to 
gain the increased brightness due 
to the larger hole by placing 
a lens in the hole (Fig. 424). 
If the receiving screen is now a 
sensitive plate, the arrangement 
becomes a photographic camera (Fig. 425). But while with 
the pinhole camera the screen may be at any distance from 
the hole, with a lens the plate and the 
object must be at conjugate foci of 
the lens. 

Let a lens of, say, 4 feet focal length 
be placed in front of a hole in the shutter 
of a darkened room, and a semitransparent 
screen (for example, architect's tracing 
paper) placed at the focal plane. A per- 
fect reproduction of the opposite landscape 
will appear 




FIG. 424. Principle of the photo- 
graphic camera 




FIG. 425. The photographic 
camera 



OPTICAL INSTRUMENTS 



391 



451. The projecting lantern. The projecting lantern is essen- 
tially a camera in which the position of object and image have 
been interchanged ; for in the use of the camera the object is 
at a considerable distance, and a small inverted image is formed 
on a plate placed somewhat farther from the lens than the 
focal distance. In the use of the projecting lantern the object 
P (Fig. 426) is placed a trifle farther from the lens L 1 than 
its focal length, and an enlarged inverted image is formed on 




Fiu. 426. The projecting lantern (stereopticon) 

a distant screen S. In both instruments the optical part is 
simply a convex lens, or a combination of lenses which is 
equivalent to a convex lens. 

The object P, whose image is formed on the screen, is usu- 
ally a transparent slide which is illuminated by a powerful 
light A. The image is as many times larger than the object 
as the distance from L' to S is greater than the distance from 
L' to P. The light A is usually either an incandescent lamp 
or an electric arc. The moving-picture projector employs a 
long film of small " positives " which moves swiftly between 
the condensing lens L and the projecting lens L 1 (see opposite 
p. 386). 

The above are the only essential parts of a projecting lantern. In 
order, however, that the slide may be illuminated as brilliantly as pos- 
sible, a so-called condensing lens L is always used. This concentrates 
light upon the transparency and directs it toward the screen. 



392 



IMAGE FORMATION 



In order to illustrate the principle of the instrument, let a beam of 
sunlight be reflected into the room and fall upon a lantern slide. When 
a lens is placed a trifle more than its focal distance in front of the slide, 
a brilliant picture will be formed on the opposite wall. 

452. The eye. The eye is essentially a camera in which the 
cornea C (Fig. 427), the aqueous humor I, and the crystalline 
lens o act as one single 
lens which forms an 
inverted image P'Q' on 
the retina, an expan- 
sion of the optic nerve 
covering the inside of 
the back of the eyeball. 

In the case of the camera the images of objects at different 
distances are obtained by placing the plate nearer to or farther 
from the lens. In the eye, however, the distance from the 
retina to the lens remains constant, and the adjustment for 
different distances is effected by changing the focal length 
of the lens system in such a way as always to keep the image 
upon the retina. Thus, when the normal eye is perfectly 




Q 



FIG. 427. The human eve 





FIG. 428. The pupil dilates when the light is dim and contracts when 
it is intense 

relaxed, the lens has just the proper curvature to focus plane 
waves upon the retina, that is, to make distant objects dis- 
tinctly visible. But by directing attention upon near objects 
we cause the muscles which hold the lens in place to contract 



OPTICAL INSTRUMENTS 



393 



in such a way as to make the lens more convex, and thus bring 
into distinct focus objects which may be as close as eight or ten 
inches. This power of adjustment or accommodation, however, 
varies greatly in different individuals. 

The iris, or colored part of the eye, is a diaphragm which 
varies the amount of light which is admitted to the retina 
(Figs. 428, (1) and (2)). 

453. Nearsightedness and 
farsightedness. In a normal 
eye, provided the lens is re- 
laxed and resting, parallel rays 
come to a focus OR the retina 
(Fig. 429, (1)) ; in a near- 
sighted eye they focus in front 
of the retina (Fig. 429, (2)) ; 
and in a far sighted eye they 
reach the retina before coming 
to a focus (Fig. 429, (3)). 

Those who are nearsighted 
can see distinctly only those 
objects which are near. The 
usual reason for nearsighted- 
ness is that the retina is too 
far from the lens. The diverging lens corrects this defect 
of vision because it makes the rays from a distant object 
enter the eye as if they had come from an object near by ; 
that is, it partially counteracts the converging effect of the 
eye (Fig. 429 (2)). 

Those who are farsighted cannot when the lens is relaxed 
see distinctly even a very distant object. The usual reason 
for farsightedness is that the eyeball is too short from lens to 
retina. The rays from near objects are converged, or focused, 
towards f behind the retina in spite of all effort at accom- 
modation. A converging lens gives distinct vision because 




FIG. 429. Defects of vision 



394 



IMAGE FORMATION 




it supplements the converging effect of the eye (Fig. 429, 
(3)). In old age the lens loses its power of accommodation, 
that is, the ability to become more convex when looking at a 
near object; hence, in old age a normal eye requires the 
same sort of lens as is used in true farsightedness. 

454. The apparent size of a body. The apparent size of a 
body depends simply upon the size of the image formed upon 
the retina by the lens of the eye, and hence upon the size 
of the visual angle pCq (Fig. 430). The size of this angle 
evidently increases as the object is brought nearer to the 
eye (seeP(7$). Thus, the image formed on the retina when 
a man is 100 feet from the eye is 

in reality only one tenth as large 

as the image formed of the same 

man when he is but 10 feet away. 

We do not actually interpret the 

larger image as representing a 

larger man simply because we have 

been taught by lifelong experience to take account of the 

known distance of an object in forming our estimate of its 

actual size. To an infant who has not yet formed ideas of 

distance the man 10 feet away doubtless appears ten times 

as large as the man 100 feet away. 

455. Distance of most distinct vision. When we wish to 
examine an object minutely, we bring it as close to the eye as 
possible in order to increase the size of the image on the retina. 
But there is a limit to the size of the image which can be pro- 
duced in this way ; for when the object is brought nearer to 
the normal eye than about 10 inches, the curvature of the 
incident wave becomes so great that the eye lens is no longer 
able, without too much strain, to thicken sufficiently to bring 
the image into sharp focus upon the retina. Hence a person 
with normal eyes holds an object which he wishes to see as 
distinctly as possible at a distance of about 10 inches. 



FIG. 430. The visual angle 



OPTICAL INSTRUMENTS 



395 



Although this so-called distance of most distinct vision varies 
somewhat with different people, for the sake of having a 
standard of comparison in the determination of the magnify- 
ing powers of optical instruments some exact distance had 
to be chosen. The distance so chosen is 10 inches, or 25 
centimeters. 

456. Magnifying power of a convex lens. If a convex lens 
is placed immediately before the eye, the object may be brought 
much closer than 25 centimeters without loss of distinctness, 
for the curvature of the 
wave is partly or even 
wholly overcome by the 
lens before the light en- 
ters the eye. 

If we wish to use a lens 
as a magnifying glass to 
the best advantage, we 
place the eye as close to 
it as we can, so as to 
gather as large a cone of 
rays as possible, and then 
place the object at a distance from the lens equal to its focal 
length, so that the waves after passing through it are plane. 
They are then focused by the eye with the least possible 
effort. The visual angle in such a case is PcQ (Fig. 431, (1)) ; 
for, since the emergent waves are plane, the rays which pass 
through the center of the eye from P and Q are parallel to the 
lines through PC and Qc. But if the lens were not present, and 
if the object were 25 centimeters from the eye, the visual angle 
would be the small angle pcq (Fig. 431, (2)). The magnify- 
ing power of a simple lens is due, therefore, to the fact that 
by its use an object can be viewed distinctly when held closer 
to the eye than is otherwise possible. This condition gives a 
visual angle that increases the size of the image on the retina. 




FIG. 431. Magnifying power of a lens 



396 IMAGE FORMATION 

Tl}e less the focal length of the lens, the nearer to it may the 
object be placed, and therefore the greater the visual angle, 
or magnifying power. 

The ratio of the two angles PcQ and pcq is approximately 
25/f, where / is the focal length of the lens expressed in 
centimeters. Now the magnifying power of a lens or microscope 
is defined as the ratio of the angle actually subtended by the image 
when viewed through the instrument, to the angle subtended by the 
object when viewed with the unaided eye at a distance of 25 centi- 
meters. Therefore the magnifying power of a simple lens is 
25/f. Thus, if a lens has a focal length of 2.5 centimeters, it 
produces a magnification of 10 diameters when the object is 
placed at its principal focus. If the lens has a focal length 
of 1 centimeter, its magnifying power is 25, etc. 

457. Magnifying power of an astronomical telescope. In the astronom- 
ical telescope the objective, or forward lens, forms at its principal foe UK an 
image P'Q' of an object PQ which is usually very distant. This image 




Q 

FIG. 432. The magnifying power of a telescope objective is F/25 

may be viewed by the unaided eye at a distance of 25 cm. (Fig. 432). 
The focal length of the objective is usually very much longer than 25 cm. 
(about 2000 cm. in the case of the great Yerkes telescope shown opposite 
p. 365), so that the visual angle P'EQ' is increased by means of the 
objective alone, the increase being F/'25*, that is, in direct proportion 
to its focal length. 

In practice, however, the image is not viewed with the unaided eye, 
but with a simple magnifying glass called an eyepiece (Fig. 433), placed 
so that the image is at its focus. Since we have seen in 456 that the 
simple magnifying glass increases the visual angle 25// times, / being 
the focal length of the eyepiece, it is clear that the total magnification 

*The angle PoQ = angle P'oQf. Consider the short line Q'P' as an arc, 
and the angles Q'EP' and Q'oP' are inversely proportional to their radii, 
F and 25. 



OPTICAL INSTRUMENTS 



397 



produced by both lenses, used as above, is F/25 x 25/f=F/f, The. 
magnifying power of an astronomical telescope is therefore the focal length of 
the objective divided by the focal length of the eyepiece. It will be seen, 
therefore, that to 
get a high mag- 
nifying power 
it is necessary Objective ^-\^ Eye- 

to use an objec- Top - MIMllliniinnn, ^P l f ce l 

tive of as great To Q 
focal length as 
possible and an 
eyepiece of as 
short focal length 
as possible. The 
focal length of 




FIG. 433. The magnifying power of a telescope is F/f 



eyepiece 



the great lens at the Yerkes Observatory is about C2 feet, and its diam- 
eter 40 inches. The great diameter enables it to collect a very large 
amount of light, which makes celestial objects more plainly visible. 

Eyepieces often have focal lengths as small as -| inch. Thus, the 
Yerkes telescope, when used with a ^-inch eyepiece, has a magnifying 
power of 2976. 

458. The magnifying power of the com- 
pound microscope. The compound micro- 
scope is like the telescope in that the 
front lens, or objective, forms a real image 
of the object at the focus of the eyepiece. 
The size of the image P'Q' (Fig. 434) 
formed by the objective is" as many times 
the size of the object PQ as v f the dis- 
tance from the objective to the image, 
is times u, the distance from the objec- 
tive to the object (see 441). Since the 
eyepiece magnifies this image 25// times, 
the total magnifying power of a com- 



, . . . t-25 
pound microscope is 




Ordinarily v 



FIG. 434. The compound 
microscope 



is practically the length L of the micro- 
scope tube, and u is the focal length F of the objective. Wherever 
this is the case, then, the magnifying power of the compound micro- 

. 25 L 
scope is- 



398 IMAGE FORMATION 

The relation shows that in order to get a high magnifying power with 
a compound microscope the focal length of both eyepiece and objective 
should be as short as possible, while the tube length should be as long 
as possible. Thus, if a microscope has both an eyepiece and an objective 
of 6 millimeters focal length and a tube 15 centimeters long, its magni- 
fying power will be = 1042. Magnifications as high as 2500 or 

.5 x .0 

3000 are sometimes used, but it is impossible to go much farther, for the 
reason that the image becomes too faint to be seen when it is spread 
over so large an area. 

459. The opera glass. On account of the large number of lenses 
which must be used in the terrestrial telescope, it is too bulky and awk- 
ward for many purposes, and hence it is often replaced by the opera 
glass (Fig. 435). This instrument consists of an objective like that of 




FIG. 435. The opera glass 

the telescope, and an eyepiece which is a concave lens of the same focal 
length as the eye of the observer. The effect of the eyepiece is there- 
fore to just neutralize the lens of the eye. Hence the objective, in effect, 
forms its image directly upon the retina. It will be seen that the size 
of the image formed upon the retina by the objective of the opera glass 
is as much greater than the size of the image formed by the naked eye 
as the focal length CR of the objective is greater than the focal length 
cR of the eye. Since the focal length of the eye is the same as that of 
the eyepiece, the magnifying power of the opera glass, like that of the astro- 
nomical telescope, is the ratio of the focal lengths of the objective and eyepiece. 
Objects seen with an opera glass appear erect, since the image formed 
on the retina is inverted, as is the case with images formed by the lens 
of the eye unaided. 

460. The stereoscope. Binocular vision. When an object is seen with 
both eyes, the images formed on the two retinas differ slightly, because 
of the fact that the two eyes, on account of their lateral separation, are 
viewing the object from slightly different angles. It is this difference 



OPTICAL INSTRUMENTS 



399 



in the two images which gives to an object or landscape viewed with 
two eyes an appearance of depth, or solidity, which is wholly wanting 
when one eye is closed. The stereoscope is an in- 
strument which reproduces in photographs this 
effect of binocular vision. Two photographs of the 
same object are taken from slightly different points 
of view. These photographs are mounted at A and 
B (Fig. 436), where they are simultaneously viewed 
by the two eyes through the two prismatic lenses m 
and n. These two lenses superpose the two images 
at C because of their action as prisms, and at the 
same time magnify them because of their action as 
simple magnifying lenses. The result is that the 
observer is conscious of viewing but one photograph ; 
but this differs from ordinary photographs in that, FIG. 436. Principle 
instead of being flat, it has all of the characteristics of the stereoscope 
of an object actually seen with both eyes. 

The opera glass has the advantage over the terrestrial telescope of 
affording the benefit of binocular vision ; for while telescopes are usually 
constructed with one tube, opera glasses always have two, one for each eye. 

461. The Zeiss binocular. The greatest disadvantage of the opera 
glass is that the field of view is very small. The terrestrial telescope 
has a larger field but is of inconvenient length. An instrument called 
the Zeiss binocular (Fig. 437) 
has recently come into use, 
which combines the compact- 
ness of the opera glass with the 
wide field of view of the ter- 
restrial telescope. The compact- 
ness is gained by causing the 
light to pass back and forth 
through total reflecting prisms, 
as in the figure. These reflec- 
tions also perform the function 
of reinverting the image, so 
that the real image which is 
formed at the focus of the eye- 
piece is erect. It will be seen, therefore, that the instrument is essen- 
tially an astronomical telescope in which the image is reinverted by 
reflection, and in which the tube is shortened by letting the light pass 
back and forth between the prisms. 




FIG. 437. The Zeiss binocular 



400 



IMAGE FORMATION 



A further advantage which is gained by the Zeiss binocular is due to 
the fact that the two objectives are separated by a distance which is 
greater than the distance between the eyes, so that the stereoscopic 
effect is more prominent than with the unaided eye or with the ordinary 
opera glass.* 

462. The periscope. A periscope is a sort of double-jointed telescope 
which makes use of total reflection twice, at the top and at the bottom. 
The system of lenses gives a magnification of about 1^ diameters, as 




FIG. 438. A parabolic reflector 

this has been found best to make ships appear at their true distances 
from the submarine. There is no stereoscopic effect, since the periscope 
is not double like a binocular. 

463. Parabolic reflectors. For the projection of a more nearly cylin- 
drical beam than is possible with spherical mirrors, it is customary to 
use parabolic reflectors, as in automobile headlights (Fig. 438, (1) and 
(2)). The light is placed a little closer to the reflector than the princi- 
pal focus, so that the reflected light may spread somewhat. The same 
principle is employed in searchlights, except that the source of light 
(usually a powerful arc) is kept more nearly at the principal focus of 
the reflector. The Sperry 60-inch searchlight, the most powerful in the 
world, has a beam candle power of approximately two thirds that of the 
sun, and its light is plainly visible at a distance of one hundred miles. 

* Laboratory experiments on the magnifying powers of lenses and on the 
construction of microscopes and telescopes should follow this chapter. See 
for example, Experiments 47, 48, and 49 of the authors' Manual. 



OPTICAL INSTRUMENTS 401 

QUESTIONS AND PROBLEMS 

1. Why is it necessary for the pupils of your eyes to be larger in a 
dim cellar than in the sunshine? Why does the photographer use a 
large stop on dull days in photographing moving objects ? 

2. If a photographer wishes to obtain the full figure on a plate of 
cabinet size, does he place the subject nearer to or farther from the 
camera than if he wishes to take the head only? Why? 

3. A child 3 ft. in height stood 15 ft. from a camera whose lens had 
a focal length of 18 in. What was the distance from the lens to the 
photographic plate and the length of the child's photograph? 

4. If 20 sec. is the proper length of exposure when you are printing 
photographs by a gas light 8 in. from the printing frame, what length 
of exposure would be required in printing from the same negative at 
a distance of 16 in. from the same light? 

5. If a 20-second exposure is correct at a distance of 6 in. from an 
8-candle-power electric light, w T hat is the required time of exposure 
at a distance of 12 in. from a 32-candle-power electric light? 

6. The image, on the retina, of a book held a foot from the eye is 
larger than that of a house on the opposite side of the street. Why do 
we not judge that the book is actually larger than the house? 

7. W^hat sort of lenses are necessary to correct shortsightedness? 
longsightedness? Explain with the aid of a diagram. 

8. What is the magnifying power of a J-in. lens used as a simple 
magnifier? 

9. If the length of a microscope tube is increased after an object 
has been brought into focus, must the object be moved nearer to or 
farther from the lens in order that the image may again be in focus ? 

10. Explain as well as you can how a telescope forms the image 
that you see when you look into it. 

11. Is the image on the retina erect or inverted? 



CHAPTER XX 



COLOR PHENOMENA 
COLOR AND WAVE LENGTH 
464. Wave lengths of different colors. Let a soap film be formed 

across the top of an ordinary drinking glass, care being taken that both 

the solution and the glass are as clean as possible. Let a beam of sun- 

light or the light from a projecting lantern pass through a piece of red 

glass at A, fall upon the soap film F, and be reflected from it to a white 

screen S (see Fig. 439). Let 

a convex lens L of from 6 

to 12 inches focal length be 

placed in the path of the re- 

flected beam in such a posi- 

tion as to produce an image 

of the film upon the screen 

S, that is, in such a position 

that film and screen are at 

conjugate foci of the lens. 

The system of red and black 

bands upon the screen is 

formed precisely as in 427, 

by the interference of the 

two beams of light coming 

from the front and back sur- 




FIG. 439. Projection of soap-film fringes 



faces of the wedge-shaped 
film. Now let the red glass 
be held in one half of the beam and a piece of green glass in the other 
half, the two pieces being placed edge to edge, as shown at A. Two 
sets of fringes will be seen side by side on the screen. The fringes will 
be red and black on one side of the image, and green and black on the 
other ; but it will be noticed at once that the dark bands on the green 
side are closer together than the dark bands on the other side ; in 

402 



COLOR AND WAVE LENGTH 



403 



fact, seven fringes on the side of the film which is covered by the 
green glass will be seen to cover about the same distance as six fringes 
on the red side.* 

Since it was shown in Fig. 390 that the distance between 
two dark bands corresponds to an increase of one-half wave 
length in the thickness of the film, we conclude, from the fact 
that the dark bands on the red side are farther apart than those 
on the green side, that red light must have a longer wave length 
than green light. The wave length of the central portion of 
each colored region of the spectrum is roughly as follows : 

Red. . . ... .000068cm. Green . . . .000052cm. 

Yellow . . . . . .000058cm. Blue 000046cm. 

Violet 000042cm. 

Let the red and green glasses be removed from the path of the beam. 
The red and green fringes will be seen to be replaced by a series of 
bands brilliantly colored in different hues. These are due to the fact 
that the lights of different wave length 
form interference bands at different 
places on the screen. Notice that the 
upper edges of the bands (lower edges 
in the inverted image) are reddish, 
while the lower edges are bluish. We 
shall find the explanation of this fact 
in 473. 

465. Composite nature of white 
light. Let a beam of sunlight pass 
through a narrow slit and fall on a 
prism, as in Fig. 440. The beam which 
enters the prism as white light is 

dispersed into red, yellow, green, blue, and violet lights, although each 
color merges, by insensible gradations, into the next. This band of 
color is called a spectrum. 

We conclude from this experiment that white light is a mix- 
ture of all the colors of the spectrum, from red to violet inclusive. 




FIG. 440. White light decom- 
posed by a prism 



* The experiment may be performed at home by simply looking through 
red and green glasses at a soap film so placed as to reflect white light to the eye. 



404 COLOR PHENOMENA 

466. Color of bodies in white light. Let a piece of red glass be 
held in the path of the colored beam of light in the experiment of the 
preceding section. All the spectrum except the red will disappear, thus 
showing that all the wave lengths except red have been absorbed by the 
glass. Let a green glass be inserted in the same way. The green portion 
of the spectrum will remain strong, while the other portions will be 
greatly enfeebled. Hence green glass must have a much less absorbing 
effect upon wave lengths which correspond to green than upon those 
which correspond to red and blue. Let the green and red glasses be held 
one behind the other in the path of the beam. The spectrum will almost 
completely vanish, for the red glass has absorbed all except the red rays, 
and the green glass has absorbed these. 

We conclude, therefore, that the color wHich a body has in 
ordinary daylight is determined by the wave lengths which 
the body has not the power of absorbing. Thus, if a body 
appears white in daylight, it is because it diffuses or reflects 
all wave lengths equally to the eye, and does not absorb one 
set more than another. For this reason the light which comes 
from it to the eye is of the same composition as daylight or 
sunlight. If, however, a body appears red in daylight, it is 
because it absorbs the red rays of the white light which falls 
upon it less than it absorbs the others, so that the light which 
is diffusely reflected contains a larger proportion of red wave 
lengths than is contained in ordinary light. Similarly, a body 
appears yellow, green, or blue when, it absorbs less of one of 
these colors than of the rest of the colors contained in white 
light, and therefore sends a preponderance of some particular 
wave length to the eye. 

467. Color of bodies placed in colored lights. Let a body which 

appears w T hite in sunlight be placed in the red end of the spectrum. It 
will appear to be red. In the blue end of the spectrum it will appear to 
be blue, etc. This confirms the conclusion of the last paragraph, that 
a white body has the power of diffusely reflecting all the colors of the 
spectrum equally. 

Next let a skein of red yarn be held in the blue end of the spec- 
trum. It will appear nearly black. In the red end of the spectrum 



COLOR AND WAVE LENGTH 



405 



it will appear strongly red. Similarly, a skein of blue yarn will appear 
nearly black in all the colors of the spectrum except blue, where it 
will have its proper color. 

These effects are evidently due to the fact that the red yarn, 
for example, has the power of diffusely reflecting red wave 
lengths copiously, but of absorbing, to a large extent, the others. 
Hence, when held in the blue end of the spectrum, it sends 
but little color to the eye, since no red light is falling upon it. 

Soak a handful of asbestos or cotton batting in a saturated salt solu- 
tion ; squeeze out most of the brine ; pour over the material a quantity 
of strong alcohol. When ignited, this will produce a large flame of al- 
most pure-yellow light. In a darkened room allow the yellow light to 
fall strongly upon a spectrum chart of six colors. The only color on the 
chart that appears natural is the yellow. 

468. Compound colors. It must not be inferred from the 
preceding paragraphs that every color except white has one 
definite wave length, for the same effect 
may be produced on the eye by a mix- 
ture of several different wave lengths 
as is produced by a single wave length. 
This statement may be proved by the 
use of an apparatus known as Newton's 
color disk (Fig. 441). The arrangement 
makes it possible to rotate differently 
colored sectors so rapidly before the eye 
that the effect is precisely the same as 
though the colors came to the eye simul- 
taneously. If one half of the disk is 
red and the other half green, the rotat- 
ing disk will appear yellow, the color 
being very similar to the yellow of the 
spectrum. If green and violet are mixed 
in the same way, the result will be light blue. Although the 
colors produced in this way are not distinguishable by the eye 




FIG. 441. Newton's 
color disk 



406 COLOK PHENOMENA 

from spectral colors, it is obvious that their physical constitu- 
tion is wholly different ; for while a spectral color consists of 
waves of a single wave length, the colors produced by mix- 
ture are compounds of several wave lengths. For this reason 
the spectral colors are called pure and the others compound. 
In order to tell whether the color of an object is pure or com- 
pound, it is only necessary to observe it through a prism. If 
it is compound, the colors will be separated, giving an image 
of the object for each color. If it is pure, the object will appear 
through the prism exactly as it does without the prism. 

By compounding colors in the way described above we 
can produce many which are not found in the spectrum. 
Thus, mixtures of red and blue give purple or crimson ; 
mixtures of black with red, orange, or yellow give rise to 
the various shades of brown. Lavender may be formed by 
adding three parts of white to one of blue ; lilac, by adding 
to fifteen parts of white four parts of red and one of blue ; 
olive, by adding one part of black to two parts of green and 
one of red. 

469. Complementary colors. Since white light is a combi- 
nation of all the colors from red to violet inclusive, it might 
be expected that if one 

or several of these colors L 

were subtracted from a frrTrrrrl 0fi(^ . 

white light, the residue 
would be colored light. 

To test this experimentally 
let a beam of sunlight be 
passed through a slit s, a 
prism P, and a lens L, to a r IG< 442. Recombination of spectral colors 
screen S, arranged as in into white light 

Fig. 442. A spectrum will be 

formed at R V, the position conjugate to the slit s, and a pure white 
spot will appear on the screen when it is at the position which is conju- 
gate to the prism face ab. Let a card be slipped into the path of the 




COLOR AND WAVE LENGTH 407 

beam at E, so as to cut off the red portion of the light. The spot on S 
will appear a brilliant shade of greenish blue. This is the compound 
color left after red is taken from the white light. This shade of blue 
is therefore called the complementary color of the red which has been 
subtracted. Two complementary colors are therefore denned as any two 
colors which produce white when added to each other. 

Let the card be slipped in from the side of the blue rays at V. The 
spot will first take on a yellowish tint when the violet alone is cut out; 
and as the card is slipped farther in, the image will become a deep shade 
of red when violet, blue, and part of the green are cut out. 

Next let a lead pencil be held vertically between R and V so as to 
cut off the middle part of the spectrum ; that is, the yellow and green 
rays. The remaining red, blue, and violet will unite to form a brilliant 
purple. In each case the color on the screen is the complement of that 
which is cut out. 

470. Retinal fatigue. Let the gaze be fixed intently for not less 
than twenty or thirty seconds on a point at the center of a block of any 
brilliant color for example, red. Then look off at a dot on a white 
wall or a piece of white paper, and hold the gaze fixed there for a few 
seconds. The brilliantly colored block will appear on the white wall, 
but its color will be the complement of that first looked at. 

The explanation of this phenomenon, due to so-called " ret- 
inal fatigue," is found in the fact that although the white sur- 
face is sending waves of all colors to the eye, the nerves which 
responded to the color first looked at have become fatigued, 
and hence fail to respond to this color when it comes from the 
white surface. Therefore the sensation produced is that due 
to white light minus this color ; that is, to the complement of 
the original color. A study of the spectral colors by this 
method shows that the following colors are complementary. 

Red Orange Yellow Violet Green 

Bluish green Greenish blue Blue Greenish yellow Crimson 

471. Color of pigments. When yellow light is added to the 
proper shade of blue, white light is produced, since these 
colors are complementary. But if a yellow pigment is added 
to a blue one, the color of the mixture will be green. This is 



408 COLOR PHENOMENA 

because the yellow pigment removes the blue and violet by 
absorption, and the blue pigment removes the red and yellow, 
so that only green is left. 

When pigments are mixed, therefore, each one subtracts cer- 
tain colors from white light, and the color of the mixture is that 
color which escapes absorption by the different ingredients. 
Adding pigments and adding colors, as in 468, are therefore 
wholly dissimilar processes and produce widely different results. 

472. Three-color printing. It is found that all colors can be 
produced by suitably mixing with the color disk (Fig. 441) 
three spectral colors, namely red, green, and blue-violet. 
These are therefore called the three primary colors. The so- 
called primary pigments are simply the complements of these 
three primary colors. They are, in order, peacock blue, crim- 
son, and light yellow. The three primary colors when mixed 
yield white. The three primary pigments when mixed yield 
black, because together they subtract all the ingredients from 
white light. The process of three-color printing consists in 
mixing on a white background, that is, on white paper, the 
three primary pigments in the following way: Three differ- 
ent photographs of a given-colored object are taken, each 
through a filter of gelatin stained the color of one of the 
primary colors. From these photographs halftone " blocks " 
are made in the usual way. The colored picture is then made 
by carefully superposing prints from these blocks, using with 
each an ink whose color is the complement of that of the 
" filter " through which the original negative was taken. The 
plate on the opposite page illustrates fully the process. It will 
be interesting to examine differently colored portions with a 
lens of moderate magnifying power. 

473. Colors of thin films. The study of complementary colors 
has furnished us with the key to the explanation of the fact, 
observed in 464, that the upper edge of each colored band 
produced by the water wedge is reddish, while the lower edge 










THREE-COLOR PRINTING 

1, yellow impression (negative made through a blue-violet filter) ; 2, crimson im- 
pression (negative made through a green filter) ; 3, crimson on yellow ; 4, blue 
impression (negative made through a red filter) ; 5, yellow, crimson, and blue 
combined (the final product). The circles at the right show the colors of ink used 
in making each impression. Notice the different colors in 5, which are made by 
combining yellow, crimson, and blue 



COLOE AND WAVE LENGTH 



409 



is bluish. The red on the upper edge is due to the fact that 
there the shorter blue waves are destroyed by interference and 
a complementary red color is left; while on the lower edge 
of each fringe, where the film is thicker, the longer red waves 
interfere, leaving a complementary blue. In fact, each wave 
length of the incident light produces a set of fringes, and it is 
the superposition of these different sets which gives the result- 
ant colored fringes. Where the film is too thick the overlapping 
is so complete that the eye is unable to detect any trace of 
color in the reflected light. 

In films which are of uniform thickness, instead of wedge- 
shaped, the color is also uniform, so long as the observer does 
not change the angle at which the film is viewed. With any 
change in this angle the thickness of film through which the 
light must pass in coming to the observer changes also, and 
hence the color changes. This explains the beautiful play of 
iridescent colors seen in soap bubbles, thin oil films, mother 
of pearl, etc. 

474. Chromatic aberration. It has heretofore been assumed 
that all the waves which fall on a lens from a given source 
are brought to one and the 
same focus. But since blue 
rays are bent more than red 
ones in passing through a 
prism, it is clear that in 
passing through a lens the 

blue light must be brought to a focus at some point v (Fig. 443) 
nearer to the lens than r, where the red light is focused, and 
that the foci for intermediate colors must fall in intermediate 
positions. It is for this reason that an image formed by a 
simple lens is always fringed with color. 

Let a card be held at the focus of a lens placed in a beam of sunlight 
(Fig. 443). If the card is slightly nearer the lens than the focus, the 
spot of light will be surrounded by a red fringe, for the red rays, being 





FIG. 443. Chromatic aberration in a lens 



410 COLOB, PHENOMENA 

least refracted, are on the outside. If the card is moved out beyond the 
focus, the red fringe will be found to be replaced by a blue one ; for 
after crossing at the focus it will be the more refrangible rays which 
will then be found outside. 

This dispersion of light produced by a lens is called chromatic 
aberration. 

475. Achromatic lenses. The color effect caused by the 
chromatic aberration of a simple lens greatly impairs its use- 
fulness. Fortunately, however, it has been found possible to 
eliminate this effect almost completely by 
combining into one lens a convex lens of 
crown glass and a concave lens of flint 
glass (Fig. 444). The first lens then pro- 
duces both bending and dispersion, while 

FIG. 444. An achro- 

the second almost completely overcomes maticlens 

the dispersion without entirely overcoming 
the bending. Such lenses are called achromatic lenses. The first 
one was made by John Dollond in London in 1758. They are 
used in the construction of all good telescopes and microscopes. 

QUESTIONS AND PROBLEMS 

1. What determines the color of an opaque body? a transparent 
body? What is the appearance of a bunch of green grass when seen 
by pure red light? Explain. 

2. What is w white " ? What is " black " ? Explain why a block of ice 
is transparent while snow is opaque and white. 

3. Why do white bodies look blue when seen through a blue glass ? 

4. What color would a yellow object appear to have if looked at 
through a blue glass? (Assume that the yellow is a pure color.) 

5. A gas flame is distinctly yellow as compared with sunlight. What 
wave lengths, then, must be comparatively weak in the spectrum of a 
gas flame ? 

6. Why does dark blue appear black by candle light? 

7. Certain blues and greens cannot be distinguished from each other 
by candle light. Explain. 

8. Does blue light travel more slowly or faster in glass than red light ? 
How do you know? 



SPECTRA 



411 




SPECTRA 

476. The rainbow. There is formed in nature a very beau- 
tiful spectrum with which everyone is familiar the rainbow. 

Let a spherical bulb F (Fig. 445) 1J or 2 inches in diameter be filled 
with water and held in the path of a beam of sunlight which enters the 
room through a hole in a piece of cardboard AB. A miniature rainbow 
will be formed on the 
screen around the open- 
ing, the violet edge of the 
bow being toward the cen- 
ter of the circle and the 
red outside. A beam of 
light which enters the 
flask at C is there both 
refracted and dispersed ; 
at D it is totally reflected ; 
and at E it is again re- 
fracted and dispersed on 
passing out into the air. 
Since in both of the re- 
fractions the violet is bent more than the red, it is obvious that it must 
return nearer to the direction of the incident beam than the red rays. 
If the flask were a perfect sphere, the angle included between the inci- 
dent ray OC and the emergent red ray ER would be 42 ; and the angle 
between the incident ray and the emergent violet ray E V would be 40. 

The actual rainbow seen in the heavens is due to the 
refraction and reflection of light in the drops of water in 
the air, which act exactly as did the flask in the preceding 
experiment. If the observer is standing at E with his back 
to the sun, the light which comes from the drops so as to 
make an angle of 42 (Fig. 446) with the line drawn from 
the observer to the sun must be red light ; while the light 
which comes from drops which are at an angle of 40 from 
the eye must be violet light. In direct sunshine the pris- 
matic color seen in a dewdrop changes to another color when 
the head is shifted side wise. It is clear that those drops 



FIG. 445. Artificial rainbow 



412 



COLOR PHENOMENA 



Sal 




whose direction from the eye makes any particular angle 
with the line drawn from the eye to the sun must lie on a 
circle whose center is 
on that line. Hence 
we see a circular arc 
of light which is 
violet on the inner 
edge and red on the 
outer edge. A sec- 
ond bow having the 

n . -i FIG. 446. Primary and secondary rainbows 

red on the inside 

and the violet on the outside is often seen outside of the one 
just described, and concentric with it. This bow arises from 
rays which have suffered two internal reflections and two 
refractions, in the manner shown in Fig. 446. 

477 . Continuous Spectra. Let a Bunsen burner arranged to produce 
a white flame be placed behind a slit ,s (Fig. 447). Let the slit be viewed 
through a prism P. The spectrum will be a continuous band of color. 
If now the air is admitted 

f. 



at the base of the burner, 
and if a clean platinum wire 
is held in the flame directly 
in front of the slit, the white- 
hot platinum will also give a 
continuous spectrum.* 

All incandescent solids 
and liquids are found to 
give spectra of this type 
which contain all the 
wave lengths from the extreme red to the extreme violet. 

O 

The continuous spectrum of a luminous gas flame is due to 

*By far the most satisfactory way of performing these experiments with 
spectra is to provide the class with cheap plate-glass prisms, like those used 
in Experiment 50 of the authors' Manual, rather than to attempt to project 
line spectra. 




FIG. 447. Arrangement for viewing spectra 



SPECTRA 413 

the incandescence of solid particles of carbon suspended in the 
flame. The presence of these solid particles is proved by the 
fact that soot is deposited on bodies held in a white flame. 

478. Bright-line Spectra. Let a bit of asbestos or a platinum wire 
be dipped into a solution of common salt (sodium chloride) and held in 
the flame, care being taken that the wire itself is held so low that the 
spectrum due to it cannot be seen. The continuous spectrum of the 
preceding paragraph will be replaced by a clearly defined yellow image 
of the slit which occupies the position of the yellow portion of the 
spectrum. This shows that the light from the sodium flame is not a 
compound of a number of wave lengths, but is rather of just the wave 
length which corresponds to this particular shade of yellow. The light 
is now coming from the incandescent sodium vapor and not from an 
incandescent solid, as in the preceding experiments. 

Let another platinum wire be dipped in a solution of lithium chloride 
and held in the flame. Two distinct images of the slit, &' and s" (Fig. 447), 
will be seen, one in red and one in yellow. Let calcium chloride be intro- 
duced into the flame. One distinct image of the slit will be seen in the 
green and another in the red. Strontium chloride will give a blue and a 
red image, etc. (The yellow sodium image will probably be present in 
each case, because sodium is present as an impurity in nearly all salts.) 

These narrow images of the slit in the different colors are 
called the characteristic spectral lines of the substances. The 
experiments show that incandescent vapors and gases give rise 
to bright-line spectra, and not continuous spectra like those pro- 
duced by incandescent solids and liquids (see on opposite page). 
The method of analyzing compound substances through a study 
of the lines in the spectra of their vapors is called spectrum 
analysis. It was first used by Bunsen in 1859. 

479. The solar spectrum. Let a beam of sunlight pass first 
through a narrow slit S (Fig. 448), not more than i millimeter in width, 
then through a prism P, and finally let it fall on a screen S', as shown in 
Fig. 448. Let the position of the prism be changed until a beam of 
white light is reflected from one of its faces to that portion of the screen 
which was previously occupied by the central portion of the spectrum, 




414 COLOR PHENOMENA 

Then let a fens L be placed between the prism and the slit, and moved 
back and forth until a perfectly sharp white image of the slit is formed 
on the screen. This adjustment is made in order to get the slit S and 
the screen S' in the positions of conjugate foci of the lens. Now let the 
prism be turned to its original 
position. The spectrum on the 
screen will then consist of a 
series of colored images of the 
slit arranged side by side. This 
is called a pure spectrum, to dis- 
tinguish it from the spectrum 
shown in Fig. 440, in which no 
lens was used to bring the rays 
of each particular color to a FlG 448> Arrangement for obtaining a 
particular point, and in which pure spectrum 

there was therefore much over- 
lapping of the different colors. If the slit and screen are exactly at con- 
jugate foci of the lens, and if the slit is sufficiently narrow, the spectrum 
will be seen to be crossed vertically by certain dark lines. 

These lines were first observed by the Englishman Wol- 
laston in 1802, and were first studied carefully by the German 
Fraunhofer in 1814, who counted and mapped out as many 
as seven hundred of them. They are called, after him, the 
Fraunhofer lines. Their existence in the solar spectrum shows 
that certain wave lengths are absent from sunlight, or, if not 
entirely absent, are at least much weaker than their neighbors. 
When the experiment is performed as described above, it 
will usually not be possible to count more than five or six 
distinct lines. 

480. Explanation of the Fraunhofer lines. Let the solar spec- 
trum be projected as in 479. Let a few small bits of metallic sodium be 
laid upon a loose wad of asbestos which has been saturated with alcohol. 
Let the asbestos so prepared be held to the left of the slit, or between 
the slit and the lens, and there ignited. A black band will at once ap- 
pear in the yellow portion of the spectrum, in the place where the color 
is exactly that of the sodium flame itself ; or, if the focus was sufficiently 
sharp so that a dark line could be seen in the yellow before the sodium 



SPECTRA 



416 



was introduced, this line will grow very much blacker when the sodium 
is burned. Evidently, then, this dark line in the yellow 
part of the solar spectrum is in some way due to sodium 
vapor through which the sunlight has somewhere passed. 

The experiment at once suggests the ex- 
planation of the Fraurihofer lines. The white 
light which is emitted by the hot nucleus of 
the sun, and which contained all wave lengths, 
has had certain wave lengths weakened by 
absorption as it passed through the vapors and 
gases surrounding the sun and the earth. For 
it is found that every gas or vapor ivill absorb 
exactly those wave lengths which it is itself ca- 
pable of emitting when incandescent. This is for 
precisely the same reason that a tuning fork 
will respond to, that is, absob, only vibrations 
which have the same period as those which 
it is itself able to emit. Since, then, the dark 
line in the yellow portion of the sun's spectrum 
is in exactly the same place as the bright yellow 
line produced by incandescent sodium vapor, 
or the dark line which is produced whenever 
white light shines through sodium vapor, we 
infer that sodium vapor must be contained in 
the sun's atmosphere. By comparing in this 
way the positions of the lines in the spectra of 
different elements with the positions of various 
dark lines in the sun's spectrum, many of the 
elements which exist on the earth have been 
proved to exist also in the sun. For example, 
Kirchhoff showed that the four hundred sixty 
bright lines of iron which were known to him 
were all exactly matched by dark lines in the 
solar spectrum. Fig. 449 shows a copy of a and iron spectra 



416 COLOR PHENOMENA 

photograph of a portion of the solar spectrum in the middle,, 
and the corresponding bright-line spectrum of iron each side 
of it. It will be seen that the coincidence of bright and dark 
lines is perfect. 

481. Doppler's principle applied to light waves. We have seen 
(see The Doppler effect, 387, p. 326) that the effect .of the motion of 
a sounding body toward an observer is to shorten slightly the wave length 
of the note emitted, and the effect of motion away from an observer is to 
increase the wave length. Similarly, when a star is moving toward the 
earth, each particular wave length emitted will be slightly less than 
the wave length of the corresponding light from a source on the earth's 
surface. Hence in this star's spectrum all the lines will be displaced 
slightly toward the violet end of the spectrum. If a star is moving 
away from the earth, all its lines will be displaced toward the red end. 
From the direction and amount of displacement, therefore, we can cal- 
culate the velocity with which a star is moving toward or receding from 
the solar system. Observations of this sort have shown that some stars 
are moving through space toward the solar system with a velocity of 
150 miles per second, while others are moving away with almost equal 
velocities. The whole solar system appears to be sweeping through 
space with a velocity of about 12 miles per second ; but even at this rate 
it would be at least 70,000 years before the earth would come into 
the neighborhood of the nearest star, even if it were moving directly 
toward it. 

QUESTIONS AND PROBLEMS 

.1. From the table on page 403 calculate how many waves of red and 
of violet light there are to an inch. 

2. In what part of the sky will a rainbow appear if it is formed in 
the early morning ? 

3. Why do we believe that there is sodium in the sun? 

4. What sort of spectrum should moonlight give? (The moon has 
no atmosphere.) 

5. If you were given a mixture of a number of salts, how would you 
proceed, with a Bunsen burner, a prism, and a slit, to determine whether 
or not there was any calcium in the mixture ? 

6. Draw a diagram of a slit, a prism, and a lens, so placed as to- 
form a pure spectrum. 

7. How can you show that the wave lengths of red and green lights 
are different, and how can you determine which one is the longer ? 



CHAPTER XXI 



INVISIBLE RADIATIONS 
RADIATION FKOM A HOT BODY 

482. Invisible portions of the spectrum. When a spectrum 
is photographed, the effect on the photographic plate is found 
to extend far beyond the limits of the shortest visible violet 
rays. These so-called ultra-violet rays have been photographed 
and measured at the Ryerson Physical Laboratory, University 
of Chicago, down to a wave length of .00000273 
centimeter, which is only one fifteenth the wave 
length of the shortest violet waves. 

The longest rays visible in the extreme red 
have a wave length of about .00008 centimeter, 
but delicate thermoscopes reveal a so-called 
infra-red portion of the spectrum, the investiga- 
tion of which was carried, .in 1912, by Rubens 
and von Baeyer of Berlin, to wave lengths as 
long as .03 centimeter, 400 times as long as the 
longest visible rays. 

The presence of these long heat rays may be detected 
by means of the radiometer (Fig. 450), an instrument 
perfected by E. F. Nichols at Dartmouth. In its common form it consists 
of a partially exhausted bulb, within which is a little aluminium wheel 
carrying four vanes blackened on one face and polished on the other. 
When the instrument is held in sunlight or before a lamp, the vanes 
rotate in such a way that the blackened faces always move away from 
the source of radiation, because they absorb ether waves better than do 
the polished faces, and thus become hotter. The heated air in contact 
with these faces then exerts a greater pressure against them than does 
the air in contact with the polished faces. 

417 




FIG. 450. The 
Crookes radi- 
ometer 



418 



INVISIBLE RADIATIONS 



FIG. 451. A simple 
thermoscope 



A still simpler way of studying these long heat waves was devised 
in 1912 by TrowJbridge of Princeton. A rubber band AC (Fig. 451) a 
millimeter wide is stretched to double its length over a glass plate FGHI, 
and the thinnest possible glass staff ED, carrying a 
light mirror E about 2 millimeters square, is placed 
under the rubber band at its middle point B. When 
the spectrum is thrown upon the portion A B of the 
band, the change in its length produced by the 
heating causes ED to roll, and a spot of light 
reflected from E to the wall to shift its position 
by an amount proportional to the heating. 

Let either the radiometer or the thermoscope 
described above be placed just beyond the red end of 
the spectrum. It will indicate the presence here of 
heat rays of even greater energy than those in the 
visible spectrum. Again, let a red-hot iron ball and one of the detectors 
be placed at conjugate foci of a large mirror (Fig. 452). The invisible 
heat rays will be found to be reflected and focused just as are light 
rays. Next let a .flat bottle filled with water be inserted between the 
detector and any source of heat. It will be found that water, although 
transparent to light rays, absorbs nearly all of the infra-red rays. But 
if the water is replaced by carbon bisulphide, the infra-red rays will 
be freely transmitted, 
even though the liquid 
is rendered opaque to 
light waves by dissolv- 
ing iodine in it. 

483. Radiation and 
temperature. All bod- 
dies, even such as are 
at ordinary tempera- 
tures, are continually 
radiating energy in the form of ether waves. This is proved 
by the fact that even if a body is placed in the best vacuum 
obtainable, it continually falls in temperature when surrounded 
by a colder body, for example, liquid air. The ether waves 
emitted at ordinary temperatures are doubtless very long as 
compared with light waves. As the temperature is raised, 




FIG. 452. Reflection of infra-red rays 



RADIATION FROM A HOT BODY 419 

more and more of these long waves are emitted, but shorter 
and shorter waves are continually added. At about 525 C. 
the first visible waves, that is, those of a dull red color, 
begin to appear. From this temperature on, owing to the 
addition of shorter and shorter waves, the color changes 
continuously, first to orange, then to yellow, and, finally, 
between 800 C. and 1200 C., to white. In other words, all 
bodies get "red-hot" at about 525 C. and "white-hot" at 
from 800 C. to 1200 C. 

Some idea of how rapidly the total radiation of ether waves 
increases with increase of temperature may be obtained from 
the fact that a hot platinum wire gives out thirty-six times 
as much light at 1400 C. as it does at 1000 C., although 
at the latter temperature it is already white-hot The radi- 
ations from a hot body are sometimes classified as heat 
rays, light rays, and chemical, or actinic, rays. The classifi- 
cation is, however, misleading, since all ether waves are heat 
waves in the sense that, when absorbed by matter, they pro- 
duce heating effects, that is, molecular motions. Radiant 
heat is, then, the radiated energy of ether waves of any and all 
wave lengths. 

484. Radiation and absorption. Although all substances 
begin to emit waves of a given wave length at approximately 
the same temperature, the total rate of emission of energy at 
a given temperature varies greatly with the nature of the 
radiating surface. In general, experiment shows that surfaces 
which are good absorbers of ether radiations are also good radiators. 
From this it follows that surfaces which are good reflectors, like 
the polished metals, must be poor radiators. 

Thus, let two sheets of tin, 5 or 10 centimeters square, one brightly 
polished and the other covered on one side with lampblack, be placed 
in vertical planes about 10 centimeters apart, the lampblacked side of 
one facing the polished side of the other. Let a small ball be stuck 
with a bit of wax to the outer face of each. Then let a hot metal 




420 INVISIBLE KADIATIONS 

plate or ball (Fig. 453) be held midway between the two. The wax on 
the tin with the blackened face will melt and its ball will fall first, 
showing that the lampblack ab- 
sorbs the heat rays faster than 
does the polished tin. Now 
let two blackened glass bulbs 
be connected, as in Fig. 454, 
through a U-tube containing 
colored water, and let a well- 
polished tin can, one side of 

which has been blackened, be FlG>453< Goodre _ FlG . 4 54. Goodab- 
filled with boiling water and flectorg ^ pQor ^^ ^ ^ 
placed between them. The mo- absorbers radiators 

tion of the water in the U-tube 

will show that the blackened side of the can is radiating heat much more 
rapidly than the other, although the two are at the same temperature. 



QUESTIONS AND PROBLEMS 

1. The atmosphere is transparent to most of the sun's rays. Why 
are the upper regions of the atmosphere so much colder than the lower 
regions ? 

2. When one is sitting in front of an open-grate fire, does he receive 
most heat by conduction, by convection, or by radiation ? 

3. Sunlight in coming to the eye travels a much longer air path 
at sunrise and sunset than it does at noon. Since the sun appears 
red or yellow at these times, what rays are absorbed most by the 
atmosphere ? 

4. Glass transmits all the visible waves, but does not transmit the 
long infra-red rays. From this fact explain the principle of the hotbed. 

5. Which will be cooler on a hot day, a white hat or a black one? 

6. Will tea cool more quickly in a polished or in a tarnished metal 
vessel ? 

7. Which emits the more red rays, a white-hot iron or the same iron 
when it is red-hot ? 

8. Liquid-air flasks and thermos bottles are double-walled glass 
vessels with a vacuum between the walls. Liquid air will keep many 
times longer if the glass walls are silvered than if they are not. Why ? 
Why is the space between the walls evacuated ? 



ELECTRICAL RADIATIONS 



421 



ELECTRICAL RADIATIONS 

485. Proof that the discharge of a Leyden jar is oscillatory. 

We found in 408, p. 346, that the sound waves sent out 
by a sounding tuning fork will set into vibration an adjacent 
fork, provided the latter has the same natural period as the 
former. Following is the complete electrical analogy of this 
experiment. 

Let the inner and outer coats of a Leyden jar A (see Fig. 455) be 
connected by a loop of wire cdef, the sliding crosspiece de being arranged 
so that the length of the loop may be altered at will. Also let a strip 
of tin foil be brought over the edge of this jar from the inner coat to 
within about 1 millimeter 
of the outer coat at C. Let 
the two coats of an exactly 
similar jar B be connected 
with the knobs n and n by 
a second similar wire loop 
of fixed length. Let the 
two jars be placed side by 
side with their loops par- FlG 455 Sympathetic electrical vibrations 
allel, and let the jar B be 

successively charged and discharged by connecting its coats with a 
static machine or an induction coil. At each discharge of jar B through 
the knobs n and n a spark will appear in the other jar at C, provided 
the crosspiece de is so placed that the areas of the two loops are equal. 
When de is slid along so as to make one loop considerably larger or 
smaller than the other, the spark at C will disappear. 

The experiment therefore demonstrates that two electrical 
circuits, like two tuning forks, can be tuned so as to respond to 
each other sympathetically, and that just as the tuning forks 
will cease to respond as soon as the period of one is slightly 
altered, so this electric resonance disappears when the exact 
symmetry of the two circuits is destroyed. Since, obviously, 
this phenomenon of resonance can occur only between systems 
which have natural periods of vibration, the experiment proves 
that the discharge of a Leyden jar is a vibratory, that is, an 





422 INVISIBLE RADIATIONS 

oscillatory, phenomenon. As a matter of fact, when such a 
spark is viewed in a rapidly revolving mirror, it is actually found 
to consist of from ten to thirty flashes following each other at 
equal intervals. Fig. 456 is a photograph of such a spark. 

In spite of these oscillations the whole discharge may be 
made to take place in the incredibly short time of I , OO Q, OOO 
of a second. This fact, coupled 
with the extreme brightness of 
the spark, has made possible the 
surprising results of so-called 

instantaneous electric-spark pho- 

-, r~, , , ., FIG. 456. Oscillations of the 

tography. The plate opposite electric spark 

page 425 shows the passage of 

a bullet through a soap bubble. The film was rotated continu- 
ously instead of intermittently, as in ordinary moving-picture 
photography. The illuminating flashes, 5000 per second, were 
so nearly instantaneous that the outlines are not blurred. 

486. Electric waves. The experiment of 485 demonstrates 
not only that the discharge of a Leyden jar is oscillatory but 
also that these electrical oscillations set up in the surrounding 
medium disturbances, or waves of some sort, which travel to a t 
neighboring circuit and act upon it precisely as the air waves 
acted on the second tuning fork in the sound experiment. 
Whether these are waves in the air, like sound waves, or dis- 
turbances in the ether, like light waves, can be determined by 
measuring their velocity of propagation. The first determina- 
tion of this velocity was made by Heinrich Hertz (see oppo- 
site p. 102) in 1888. He found it to be precisely the same as 
that of light, that is, 300,000 kilometers per second. This 
result shows, therefore, that electrical oscillations set up ivaves in 
the ether. These waves are now known as Hertzian waves. 

The length of the waves emitted by the oscillatory spark 
of instantaneous photography is evidently very great, namely, 
about VoVoV.AV = 30 meters > since the velocity of light is 



ELECTRICAL RADIATIONS 423 

300,000,000 meters per second, and since there are 10,000,000 
oscillations per second ; for we have seen in 382, p. 323, 
that wave length is equal to velocity divided by the number 
of oscillations per second. By diminishing the size of the jar 
and the length of the circuit the length of the waves may be 
greatly reduced. By causing the electrical discharges to take 
place between two balls only a fraction of a millimeter in 
diameter, instead of between the coats of a condenser, elec- 
trical waves have been obtained as short as .3 centimeter, 
only ten times as long as the longest measured heat waves. 

487. Detection of electric waves. In the experiment of 485 
we detected the presence of the electric waves by means of a 
small spark gap C in a circuit almost identical with that in 
which the oscillations were set up. The visible spark may be 
employed for the detection of waves many feet away from 
the source, but for detecting the feeble waves which come in 
from a source hundreds or thousands of miles away we must 
depend upon sounds produced in an extremely sensitive tele- 
phone receiver, as explained in the next section. 

488. Wireless telegraphy. Commercial wireless telegraphy 
was realized in 1896 by Marconi (see opposite p. 316), eight 
years after the discovery of Hertzian waves. The essential 
elements of a tuned wave-train, or " spark," system of wireless 
telegraphy are as follows: 

The key K at the transmitting station (Fig. 457, (1) ) is depressed 
to allow a current from the alternator A to pass through the primary 
coil P of a transformer T" 13 the frequency of the alternations in practice 
being usually about 500 cycles per second. The high-voltage current- 
induced in the secondary S charges the condenser C l until its potential 
rises high enough to cause a spark discharge to take place across the 
gap s. This discharge of C^ is oscillatory ( 485), and the oscillations 
thus produced in the condenser circuit containing C v s, and L 1 may, in 
a low-power sfiort-wave transmitting set, have a frequency as high as 
1,000,000 per second. An oscillation frequency much lower than this 
is generally used and is subject to the control of the operator through 



424 



INVISIBLE RADIATIONS 



the sliding contact c, precisely as in the case illustrated in Fig. 455. 
The oscillations in the condenser circuit induce oscillations in the aerial- 
wire system, which is tuned to resonance with it through the sliding 
contact 6-'. 



(1) 




(2) 




FIG. 457. Transmitting and receiving stations for wireless telegraphy 



As long as the key K is kept closed (assuming a 500-cycle alternator 
to be used), 1000 sparks per second occur at s, and therefore a regular 
series of 1000 wave trains (Fig. 458) pass off from the aerial every 
second and move away with the velocity of light. If the oscillations 
which produce a wave train have a frequency 
of, say, 500,000 per second, each wave in the 

It , 300,000,000 
wave train has a length of 



Direction of 
Propagation 




500,000 

600 meters ; and if these wave trains are 
produced at the rate of 1000 per second, 
they follow each other, at regular distances 
of 300,000 meters, that is, nearly 200 miles. 
The waves sent out by the aerial system 
of the transmitting station induce like os- 
dilations in the distant aerial system of the 
receiving station (Fig. 457, (2) ), which is 

tuned to resonance with it. In case the receiving aerial must be tuned 
to respond to very long waves, the switch is closed to cut out the 
condenser C 2 , and the inductance, or loading coil, B^ is used ; whereas, 
to tune to very short waves, the switch is opened and the variable 



FIG. 458. One wave train 
from oscillatory discharge 





itih WIKELESS TELEPHONE UTILIZED IN AVIATION 

One of the most notable developments of the war was the directing of a squadron 
of airplanes in intricate maneuvers by wireless telephone either from the ground 
or by the commander in the leading plane. The upper panel shows the pilot and 
the observer conversing with special apparatus designed to eliminate plane noises, 
and the lower panel shows President Wilson talking by wireless to airplanes 



CINEMATOGRAPH FILM OF A BULLET FIRED THROUGH A SOAP BUBBLE 

The flight of the missile may be followed easily. It will be seen that the bubble 

breaks, not when the bullet enters, but when it emerges. (From " Moving Pictures," 

by F. A. Talbot. Courtesy of J. B. Lippincott Company) 




ELECTRICAL RADIATIONS 425 

condenser C' is brought into use, the loading coil not being utilized. 1 
The oscillations in the aerial circuit of the receiving station induce 
exactly similar ones in the detector circuit, which is tuned to resonance 
with the receiving aerial by means of L 2 , B 2 , and C 3 . The so-called 
detector of these oscillations may be simply a crystal of galena D in 
series with the telephone receivers R. This crystal, like the tungar 
rectifier of 374, has the property of transmitting a current in one 
direction only. 2 Were it not for this property the telephone could not 
be used as a detector, because its diaphragm cannot vibrate with a fre- 
quency of the order of a million; and even if it could, it would produce 
sound waves far above the limit of 
hearing. Because of this rectifying 
property of the crystal the receiver 
diaphragm is drawn in only once 
while the oscillations produced by a 
given wave train last, this effect being- 
due to the rectified pulsating current 
which passes in one direction through 
the receivers and then ceases until the 
oscillations due to the next spark ar- FlG 459 United gtates navy 
rive. Since 1000 of the intermittent standard radio receivers 

wave trains strike upon the aerial each 

second, the operator at the receiving station hears a continuous musical 
note of this pitch as long as the key K is depressed. The working of the key, 
however, as in ordinary telegraphy, breaks the regular series of wave 
trains into groups of wave trains, so that the short and long notes heard in 
the receivers (Fig. 459) correspond to the dots and dashes of telegraphy. 
The receiving circuit, when tuned as shown in Fig. 457, (2), is highly 
selective ; that is, it will not pick up waves of other periods. The loading 
coils B l and 5 2 , as well as the two variable condensers C 2 and C 3 , are 
usually omitted from small amateur receiving sets ; but when this is 
done, the receiving set is less selective and less sensitive. The resist- 
ance of the receivers is so high, usually from 1000 to 4*000 ohms, that 

1 In the diagram an arrow drawn diagonally across a condenser indicates 
that, for the sake of tuning, the condenser is made adjustable. Similarly, an 
arrow across two circuits coupled inductively, like the primary and secondary 
of the "oscillation transformer " J" , indicates that the amount of interaction 
of the two circuits can be varied, as, for example, by sliding one coil a longer 
or shorter distance inside the other. 

2 Crystal detectors have been largely superseded by the "audion " for both 
wireless telegraphy and wireless telephony. 



426 INVISIBLE RADIATIONS 

they do not interfere with the oscillations of the condenser system 
across which they are placed. The receiving station shown in Pig. 457, (2), 
may also be used for receiving tvireless- telephone messages. The simplified 
circuit of an audion receiving station is shown opposite page 441. 

Although the spark, or wave-train, system of wireless teleg- 
raphy is still widely used, the " continuous wave " system is 
rapidly displacing it. Just as sound waves differing slightly 
in frequency combine to produce the phenomenon of beats 
( 890), so electrical oscillations differing in frequency give, 
when combined, a "beat effect." For instance, if electrical 
oscillations of, say, 30,000 per second and 31,000 per second 
combine, beats will occur at the rate of 1000 per second, 
which is a frequency within the limit of hearing. The elec- 
trical oscillations mentioned above have a frequency beyond 
the limit of hearing and hence are said to have radio fre- 
quency ; but the beats being within the range of hearing 
have an audio frequency. Now let us assume that there is 
at the transmitting station an alternating-current generator 
which throws into the aerial powerful undamped oscillations 
of 30,000 per second; and suppose further that at the receiv- 
ing station there is an oscillation generator which maintains 
relatively weak oscillations of 31,000 per second in the local 
receiving aerial. These weak oscillations produced in the 
receiving aerial by the local generator make no sound in the 
receiver, being above the limit of hearing ; but whenever, and 
as long as, the operator at the transmitting station depresses 
his key, waves come in at the rate of 30,000 per second, 
strike against the receiving aerial and develop therein weak 
oscillations which combine with those already present to make 
1000 beats per second. These beat effects are rectified by a 
crystal or by a vacuum tube and passed through the receiver. 
The listener, therefore, hears long and short musical sounds 
just as he does when receiving by the spark system. The 
beat method of receiving is called the heterodyne system. 



ELECTKICAL RADIATIONS 427 

489. Modulated continuous waves.* The vibrations consti- 
tuting articulate speech are exceedingly complex, as may be 
seen from an inspection of the full-page halftone opposite 
page 346. Because of this complexity it is impossible to trans- 
mit speech by means of discontinuous waves (Fig. 460) such 
as are employed in the system of spark telegraphy described 
in the preceding section. The parts of the voice lost because 

Direction of propagation > 

-4 4 4 -4 4 -4 -* -4- 

FIG. 460. A series of wave trains 

of the gaps between the wave trains would render the language 
unintelligible. Theoretically the voice could be transmitted 
by continuous electromagnetic waves having the frequencies 
of voice vibrations, but such a method is entirely impracti- 
cable on account of the enormous length of aerial needed 
to produce such long waves and the tremendous amount of 
power which would be required. Therefore, the only satis- 
factory method thus far developed is to transmit speech 



FIG. 461. Continuous, or carrier, waves of radio frequency 

on continuous, or " carrier," waves (Fig. 461) having a 
frequency (radio frequency) above the limit of hearing. 

At the sending station the continuous waves (Fig. 461) 
are " modulated " by the voice at the transmitter ; that is, 
the sound waves of the voice act upon the apparatus in such 
a way as to alter the otherwise uniform amplitude of the series 
of continuous waves (Fig. 462). These "modulated" con- 
tinuous waves on reaching the aerial of the receiving station 
produce corresponding oscillatory currents in the wires of the 

* The pupil should master 374, 375, 376, 485, 486, 487, and 488 before 
reading the six sections following. 



428 



INVISIBLE RADIATIONS 



aerial. By means of a crystal or a vacuum tube, the oscilla- 
tory currents are rectified into a series of unidirectional elec- 
trical currents, or pulses, somewhat after the mann-er indicated 




FIG. 462. Modulated radio-frequency waves 

in Fig. 463. These variable pulses of radio frequency, on 
reaching the telephone receivers of the listener, produce dia- 
phragm vibrations of low frequencies (audio frequencies), which 



(Innnnnfl 



Innnflnnr 



FIG. 463. Rectified oscillations 



rarely go outside the limits of 100 and 3000 vibrations per 
second. They are represented by the irregular line in Fig. 464. 
The vibrations of the diaphragms of the receivers, therefore, 



FIG. 464. Audio-frequency variations 

correspond to the vibrations of the voice of the speaker at 
the distant transmitting station. 

490. Method of producing continuous waves. One of the 
most important of the different means of producing high- 
power continuous waves is by use of the Alexanderson high- 
frequency alternator (see on opposite page). This is an 
alternating-current dynamo made in various powers up to 
200 kilowatts (= 268 horse power), the rotor in some of the 
machines having the very high speed of 20,000 revolutions 
per minute. For transoceanic telegraphy these machines cause 
currents of from 600 to 1200 amperes to oscillate in the sending 
aerial. This powerful sustained oscillation of electrons in an 
aerial produces continuous electromagnetic waves (Fig. 461). 




1 >> 



3 -2 2 



11s 



3 w S 


ill 
111 



I III 

w ^s.t? > 

>-^ +^ 'Z* & 

" M S I 

pT ^ ,2 



^5 O 
g 



2 73 



; H* 

2; o 02 

H 

3 



O) O t-i 



<M fl 

002 
33 - 3 



11 

*w 2 



-S < 



S g 




< * 



ELECTRICAL RADIATIONS 



429 



491. The vacuum tube. There are several devices by which 
the voice waves may modulate, or vary the amplitude of, the 
carrier waves, the most important being the highly exhausted 
" vacuum tube " (see Fig. 465, the halftone opposite p. 441, 
and the drawing and legend opposite p. 33). 

In attempting to reach an understanding of an " audion " 
amplifier or other form of vacuum tube, it is well to remember 



(in center) 
Grid (surrounding filament) 

late (surrounding grid 
' front half cut away) 





Terminals ^Filament 

Filament 



FIG. 465. A popular form of vacuum tube used in radio receiving 

that a current of electricity is a stream of negative elec- 
trons which, when passing through a vacuum, move with 
enormous velocity (thousands of miles per second ( 498)), 
but when passing along a wire (ordinary conduction) move 
quite slowly (a few centimeters per second). Now we found 
in studying the tungar rectifier ( 374) that these negative 
electrons escape freely from an incandescent filament under 
certain conditions. When the battery B (Fig. 466) has its 
+ terminal connected to the plate P of the vacuum tube and 



430 



INVISIBLE RADIATIONS 




FIG. 466. A two-electrode 
vacuum valve 



its terminal to the filament F, no current can flow across 
the vacuum so long as the filament is cold. When, however, the 
filament is maintained at incandescence by a battery J, the 
negative electrons escape from it and are drawn in a steady 
stream across the vacuum by the 
attraction of the + plate P. This 
flow of electrons from filament to 
plate constitutes what is considered 
by convention to be a current of 
electricity flowing the opposite way, 
namely, from plate to filament. We 
now see how battery J, by keeping 
the filament in a state of incandes- 
cence, merely establishes and main- 
tains one of the conditions under which battery B may discharge 
a steady current through the vacuum. No electronic flow 
from the cold plate to the filament is ever possible, because 
cold bodies do not, except in rare instances (see pp. 441 ff.) 
eject electrons from themselves. The vacuum tube can 
therefore be utilized as a 
vacuum valve, or rectifier, for 
evidently, if a source of alter- 
nating current be substituted 
for the direct current source 
(battery B), the vacuum. valve 
would transmit current in one 
direction only, half of each 
cycle being held in check. 

If a screen of fine wire G, 
known as a 1{ grid," be introduced between the filament and 
the plate of Fig. 466 (see Fig. 467) and the grid be main- 
tained at a sufficiently high potential by a battery (7, the 
electrons are repelled back into the incandescent filament 
and cannot escape from it, and thus the electronic flow is 




FIG. 467. A three-electrode vacuum 
tube 



ELECTRICAL RADIATIONS 



431 



completely checked; that is, no current flows across the vacuum. 
If now the potential of the grid be varied, say, from zero 
to the amount required to stop the electronic flow, the current 
from battery B through the vacuum is thereby varied from 
the possible maximum in Fig. 466 to zero. Variation of the 
grid potential, therefore, affords us a means of controlling 
and of varying the flow 
of current through a 
vacuum tube. Indeed, 
it is found that slight 
changes in the grid volt- 
age produce surpris- 
ingly great changes in 
the current through the 
tube ; that is, the tube 
is an amplifier. 

492. Transfer of energy 
through a condenser. In 
Fig.468,(l),theE.M.F. 



generator 




\Cm 



Condenser 



(1) 



The lamp docs not burn 



A. C. generator 



(2) 




"Too 



Condenser 



The lamp burns 



FIG. 468. Energy transferred through a 
condenser 



of the direct-current dy- 
namo causes a rush of 
electrons out of one side 
of the condenser while 
electrons to an equal 
extent rush into the other side. The sides of the condenser 
are thus charged -f- and and they remain so as long as the 
dynamo runs. It is evident that under these conditions there 
is no flow of current and that consequently the lamp does 
not burn. If, however, an alternating-current dynamo is used 
(Fig. 468, (2)), the alternating E.M.F. causes an alternat- 
ing rush of electrons which charges the condenser first one 
way and then the opposite way. It is clear, then, that with 
an alternating-current dynamo, lamp, and condenser thus 
arranged we may have an alternating current through the 



432 



INVISIBLE RADIATIONS 



lamp which will cause it to light up. Condensers of variable 
capacity are widely used in the circuits of wireless apparatus 
as aids in tuning, and they permit passage of electrical energy 
in the manner explained above. 

493. The receiving station. Fig. 469 represents a "regenera- 
tive " receiving circuit capable of receiving long or short 
waves. When the modulated waves (Fig. 462) reach the 
tuned aerial of the receiving station, they develop therein 
feeble electrical oscillations which induce oscillations in L Z 
of the tuned grid circuit. This varies the potential of the 




FIG. 469. A regenerative receiving circuit 

grid 6r 2 , thus causing corresponding changes in the strength 
of the electronic current flowing from the incandescent fila- 
ment F Z to the plate P 2 and thence back through the plate 
coil PC. The plate circuit is so tuned with respect to the 
grid circuit that these current variations in the plate coil 
react inductively on the coil L 2 connected with the grid cir- 
cuit to strengthen the original grid-circuit current. This 
intensifies the variations in potential at the grid, which in 
turn intensifies the variations in strength of the electronic 
current from filament to plate, and this still further intensi- 
fies the variations in potential at the grid, and so on, up to 



ELECTRICAL RADIATIONS 



433 



the limit of the electron supply in the tube. This is the 
Armstrong regenerative principle by which very feeble oscilla- 
tions produced by the incoming waves may be amplified and 
then used to intensify the original oscillations. The energy 
for regeneration comes from the battery B Z . When the tube is 
in use the grid tends to accumulate a negative charge which, 
as we have seen ( 491), would tend to block completely 
the action of the tube. Therefore, a high-resistance grid leak 
r is shunted around the condenser (7 4 to permit the return 



Variometer 




FIG. 470. A two-variometer tuned-plate-circuit for receiving short waves 

of such a detrimental accumulation of electrons to the fila- 
ment F^ by way of r and L 2 . The telephone receivers used 
in wireless work contain thousands of turns of very fine wire 
wound upon iron and because of the consequent " choke- 
coil " effect, or impedance, of these coils for high-frequency 
changes in current strength, the mcfo'o-frequency variations 
(Fig. 463) of the plate current pass largely by way of the 
variable condenser (7 9 , while the slower aw^'o-frequency varia- 
tions (Fig. 464) of the plate current pass readily through 
the receivers to actuate the diaphragm. 

Fig. 470 shows a two-variometer circuit for the reception 
of short waves. A variometer is a variable inductance used 



434 INVISIBLE BADIATIONS 

for tuning and it consists of two coils in series, one of which 
revolves within the other. If current is passed through the 
variometer when the inner coil is turned so that its magnetic 
field combines with that of the other coil to make the greatest 
resultant magnetic field, the inductance of the variometer is 
found to have its greatest value and the adjustment is then 
for the longer waves, or slower oscillations. If the inner coil 
is now turned through 180, the resultant magnetic field is 
at minimum strength ; and, because of the small inductance, 
the variometer is adjusted to the shorter waves. Intermediate 
positions of the inner coil are used for wave lengths lying 
between these limits. Complete tuning is accomplished by 
use of the two variometers, the two variable condensers and 
the sliding contact on the aerial coil. 

494. The transmitting station. The vacuum tube may be 
used not only as a rectifier, a detector, a modulator, and an 
amplifier, but under certain conditions as a generator of oscil- 
lations varying over an extremely wide range of frequency 
from less than 1 oscillation per second to 300,000,000 or 
more per second. Nearly all present-day " broadcasting " is 
done by use of vacuum-tube generators. For high-power 
long-distance transmission banks of vacuum-tube amplifiers 
may be used to throw into an aerial an aggregate power of 
many hundreds of kilowatts. Indeed, at the present time 
rapid progress is being made in the experimental construc- 
tion of power tubes each one of which is capable of giving an 
amazing output. The life of a vacuum tube is generally from 
1000 to 5000 hours, whereas a high-frequency alternator, such 
as the Alexanderson, will last for many years. 

It is entirely beyond the scope of this book to explain the 
actual details of a wireless-telephone transmitting station. 
However, the method used at present in high-power long- 
distance .transmission is indicated in Fig. 471 and may be 
outlined as follows: Air vibrations produced by the voice 



ELECTRICAL RADIATIONS 



435 



make variations in the current of the primary circuit of the 
telephone transmitter ( 376). This induces corresponding 
E. M.F.'s in the secondary circuit, which impresses audio- 
frequency variations of potential upon the grid of a vacuum- 
tube modulator. The resulting changes of audio frequency 
in the current of the plate circuit of the modulator corre- 
spondingly affect the output of the high-frequency oscil- 
lation generator. This modulated radio-frequency output is 



Three-electrode vacuum-tube 
high-frequency oscillation generator 



\/4.eri 




Telephone 
Transmitter 






Bank of 
power -tube amplifiers 



erial 



Oscillation 
Transformer 



Ground 



Vacuum-tube modulator 



FIG. 471. High-power long-distance wireless-telephone transmitting station 

amplified by a bank of three-electrode power tubes and is 
then delivered to the aerial through an oscillation trans- 
former. In broadcasting stations (see opposite p. 429) a 
weaker and somewhat simpler arrangement of tubes is used. 

NOTE. The following reference books will prove helpful to teachers and 
to those pupils who desire a more complete understanding of "wireless " : 
(1) BUCHER, Practical Wireless Telegraphy, Wireless Press, 326 Broad- 
way, New York City ; (2) GOLDSMITH, Radio Telephony, Wireless Press, 
326 Broadway, New York City ; (3) HAUSMANN and others, Radio Phone 
Receiving, Van Nostrand Co., 8 Warren St., New York City ; (4) MORE- 
CROFT, Principles of Radio Communication, John Wiley and Sons, 432 
Fourth Ave., New York City; (5) SCOTT-TAGGART, Thermionic Tubes in 
Radio Telegraphy and Telephony, Wireless Press, 326 Broadway, New 
York City ; (6) Elementary Principles of Radio Telegraphy and Teleph- 
ony (Radio Communication Pamphlet 1), 79 pages, illustrated, 10 cents. 
Superintendent of Documents, Government Printing Office, Washington, 
D.C., 1922. 



436 INVISIBLE RADIATIONS 

Although transoceanic telephonic communication has been suc- 
cessfully and repeatedly accomplished (see opposite p. 441), 
no regular service for such communication has yet been 
established. 

495. The electromagnetic theory of light. The study of 
electromagnetic radiations, like those discussed in the pre- 
ceding paragraphs, has shown not only that they have the 
speed of light but that they are reflected, refracted, and 
polarized, in fact, that they possess all the properties of light 
waves, the only apparent difference being in their greater 
wave length. Hence modern physics regards light as an electro- 
magnetic phenomenon ; that is, light waves are thought to be 
generated by the oscillations of the electrically charged parts 
of the atoms. It was as long ago as 1864 that Clerk-Maxwell, 
(see opposite p. 102), of Cambridge, England,, one of the 
world's most brilliant physicists and mathematicians, showed 
that it ought to be possible to create ether waves by means 
of electrical disturbances. But the experimental confirmation 
of his theory did not come until the time of Hertz's experi- 
ments (1888). Maxwell and Hertz together, therefore, share 
the honor of establishing the modern electromagnetic theory 
of light. 

CATHODE AND RONTGEN RAYS 

496. The electric spark in partial vacua. Let a and b (Fig. 472) 

foe the terminals of an induction coil or static machine ; e and/", electrodes 
sealed into a glass tube 60 or 80 
centimeters long ; g, a rubber 
tube leading to an air pump by 
which the tube may be ex- 
hausted. Let the coil be started 
before the exhaustion is begun. 
A spark will pass between a and FlG 4?2 Di scharge in partial vacua 
6, since ab is a very much shorter 

path than ef. Then let the tube be rapidly exhausted. When the pres- 
sure has been reduced to a few centimeters of mercury, the discharge 




CATHODE AKD KONTGEN RAYS 437 

will be seen to choose the long path ef in preference to the short path ab, 
thus showing that an electrical discharge takes place more readily through a 
partial vacuum than through air at ordinary pressures. 

When the spark first begins to pass between e and /it will 
have the appearance of a long ribbon of crimson light. As 
the pumping is continued this ribbon will spread out until 
the crimson glow fills the whole tube. Ordinary so-called 
Geissler tubes are tubes precisely like the above except that 
they are usually twisted into fantastic shapes and are some- 
times surrounded with jackets containing colored liquids, 
which produce pretty color effects. 

497. Cathode rays. When a tube like the above is exhausted 
to a very high degree, say, to a pressure of about .001 milli- 
meter of mercury, the character of the discharge changes 
completely. The glow almost entirely disappears from the 
residual gas in the tube, and certain invisible radiations called 
cathode rays are found to be emitted by the cathode (the 
terminal of the tube which is connected to 
the negative terminal of the coil or static 
machine). These rays manifest themselves, 
first, by the brilliant fluorescent effects which 
they produce in the glass walls of the tube, 
or in other substances within the tube upon 
which they fall; second, by powerful heat- 
ing effects ; and third, by the sharp shadows 
which they cast. 

Thus, if the negative electrode is concave, as in 
Fig. 473, and a piece of platinum foil is placed at 
the center of the sphere of which the cathode is a 
portion, the rays will come to a focus upon a small 
part of the foil and will heat it white-hot, thus showing that the rays, 
whatever they are, travel out in straight lines at right angles to the 
surface of the cathode. Tnis may also be shown nicely by an ordi- 
nary bulb of the shape shown in Fig. 475. If the electrode A is made 
the cathode and B the anode, a sharp shadow of the piece of platinum 




438 



INVISIBLE RADIATIONS 



in the middle of the tube will be cast on the wall opposite to A, thus 
showing that the cathode rays, unlike the ordinary electric spark, do 
not pass between the terminals of the tube, but pass out in a straight 
line from the cathode surface. 

498. Nature of the cathode rays. The nature of the cathode 
rays was a subject of much dispute between the years 1875, 
when they first began to be carefully studied, and 1898. Some 
thought them to be streams of . negatively , 
charged particles shot off with great speed 
from the surface of the cathode, while others 
thought they were waves in the ether, 
some sort of invisible light. The following 
experiment furnishes very convincing evidence 
that the first view is correct. 



NP (Fig. 474) is an exhausted tube within which 
has been placed a screen sf coated with some sub- 
stance like zinc sulphide, which fluoresces brilliantly 
when the cathode rays fall upon it; mn is a mica 
strip containing a slit s. This mica strip absorbs all 
the cathode rays which strike it; but those which 
pass through the slit s travel the full length of the 
tube, and although they are themselves invisible, y IG 474 Deflec- 
their path is completely traced out by the fluores- t i on o f ca thode 
cence which they excite upon sf as they graze along rays by a magnet 
it. If a magnet M is held in the position shown, the 
cathode rays will be seen to be deflected, and in exactly the direction 
to be expected if they consisted of negatively charged particles. For we 
learned in 298, p. 244, that a moving charge constitutes an electric 
current, and in 350, p. 293, that an electric current tends to move in 
an electric field in the direction given by the motor rule. On the other 
hand, a magnetic field is not known to exert any influence whatever on 
the direction of a beam of light or on any other form of ether waves. 

When, in 1895, J. J. Thomson (see opposite p. 440), of 
Cambridge, England, proved that the cathode rays were also 
deflected by electric charges, as was to be expected if they 
consist of negatively charged particles, and when Perrin in 



CATHODE AND KONTGEN BAYS 439 

Paris had proved that they actually impart negative charges 
to bodies on which they fall, all opposition to the projected- 
particle theory was abandoned. The mass and speed of these 
particles are computed from their deflectibility in magnetic 
and electric fields. 

Cathode rays are then to-day universally recognized as streams 
of electrons shot off from the surface of the cathode with speeds 
which may reach the stupendous value of 100,000 miles per second. 

499. X rays. It was in 1895 that Rontgen (see opposite 
p. 446) first discovered that wherever the cathode rays im- 
pinge upon the walls of a tube, or upon any obstacles placed 
inside the tube, they give rise to another type of invisible 
radiation which is now ...,<*H..I,, ( ,,... 

known under the name 
of X rays or Rontgen 
rays. In the ordinary 
X-ray tube (Fig. 475) 
a thick piece of plati- 
num P is placed in the 

FIG. 475. An X-ray bulb 
center to serve as a tar- 
get for the cathode rays, which, being emitted at right angles 
to the concave surface of the cathode (7, come to a focus at 
a point on the surface of this plate. This is the point at which 
the X rays are generated and from which they radiate in all 
directions. The target P is sometimes made of a heavy piece 
of tungsten. 

In order to convince one's self of the truth of this statement it is only 
necessary to observe an X-ray tube in action. It will be seen to be 
divided into two hemispheres by the plane which contains the p 1 itinum 
plate (see Fig. 475). The hemisphere which is facing the source of the 
X rays will be aglow with a greenish fluorescent light, while the other 
hemisphere, being screened from the rays, is darker. By moving a 
fluoroscope (a zinc-sulphide screen) about the tube it will be made evident 
that the rays which render the bones visible come from P. 




440 INVISIBLE RADIATIONS 

500. Nature of X rays. While X rays are like cathode rays 
in producing fluorescence, and also in that neither of them can 
be refracted or polarized, as light is, they nevertheless differ 
from cathode rays in several important respects. First, X rays 
penetrate many substances which are quite impervious to cath- 
ode rays; for example, they pass through the walls of the 
glass tube, while cathode rays ordinarily do not. Again, X 
rays are not deflected either by a magnet or by an electro- 
static charge, nor do they carry electrical charges of any sort. 
Hence it is certain that they do not consist, like cathode rays, 
of streams of electrically charged particles. 

It has recently been shown that X rays are extremely short 
waves similar to but very much shorter than light waves, and 
of a variety of lengths. They are so short that the smoothest 
mirror we can manufacture is so rough in comparison that it 
diffuses them. By taking advantage of the regular arrange- 
ment of the molecules in the faces of crystals (mica, for 
example) a kind of reflection known as interference reflection 
is obtained when the X rays strike at certain favorable angles 
(see opposite p. 447 for X-ray spectra). Many of the X rays 
from an ordinary X-ray tube are so short that it would require 
250,000,000 of them to make an inch. This represents a rate 
of vibration of 3,000,000,000,000,000,000 per second. 

501. X rays render gases conducting. One of the notable 
properties which X rays possess in common with cathode rays 
is the property of causing any electrified body on which they 
fall to slowly lose its charge. 

To demonstrate the existence of this property let any X-ray bulb be 
set in operation within 5 or 10 feet of a charged gold-leaf electroscope. 
The leaves at once begin to fall together. 

The reason for this is that the X rays shake loose electrons 
from the atoms of the gas and thus fill it with positively and 
negatively charged particles, each negative particle being at the 
instant of separation an electron, and each positive particle an 








SIR JOSEPH THOMSON (1856- ) 

Most conspicuous figure in the development of the "physics of the electron"; 
born in Manchester, England; educated at Cambridge University; Cavendish 
professor of experimental physics in Cambridge since 1884 ; author of a number of 
books, the most important of which is the " Conduction of Electricity through 
Gases," 1903; author or inspirer of much of the recent work, both experimental 
and theoretical, which has thrown light upon the connection between electricity 
and matter ; worthy representative of twentieth-century physics 




The extraordinary developments in electronics, in 
which Sir Joseph Thomson has played so important 
a part, have had commercial consequences, of which 
the following are perhaps the most significant : In 
July, 1914, through the development of the DeForest 
audion into a distortionless telephone relay and 
amplifier, and the insertion of these amplifiers into 
suitably chosen places in the telephone line between 
San Francisco and New York, the research physicists 
of the Western Electric Company were able to give 
numerous demonstrations in which audiences in 
New York and Boston were able to hear with per- 
fect distinctness the splashing of the waves in the 
San Francisco harbor. By the summer of 1915 the 
same group of men had succeeded in throwing tele- 
phonic speech up into the antennae of the wireless 
station at Arlington with such intensity that it 
traveled without wires a third of the way around 
the world and was heard so distinctly at receiving 
stations in both Honolulu and Paris that even the 
voices of the speakers in Washington could be recog- 
nized. The illustration at the left is a cut (1 size) 
of one of the tubes with which this extraordinary 
scientific feat was performed. The simplified circuit 
of a thermionic amplifier is shown in the diagram 
above. The enfeebled incoming speech frequencies 
vary the potential of the grid G, and these varia- 
tions produce like variations in the electronic cur- 
rents flowing from the hot filament F to the 
plate P and thence into the circuit in which the 
amplified current is needed. By the use of these 
devices the enormous energy amplifications of 
10,000,000,000,000-fold have been obtained 



AMPLIFIER, AND DIAGRAM OF RECEIVING AND AMPLIFYING SET 



RADIOACTIVITY 441 

atom from which an electron has been detached. Any charged 
body in the gas therefore draws toward itself charges of sign 
opposite to its own, and thus becomes discharged. 

502. X-ray pictures. The most striking property of X rays 
is their ability to pass through many substances which are 
wholly opaque to light, for example, cardboard, wood, 
leather, and flesh. Thus, if the hand is held close to a photo- 
graphic plate and then exposed to X rays, a shadow picture 
of the denser portions of the hand, that is, the bones, is formed 
upon the plate. Opposite page 359 is shown an X-ray picture 
of the thorax of a living human being. 

RADIOACTIVITY 

503. Discovery of radioactivity. In 1896 Henri Becquerel 
(see opposite p. 446), in Paris, performed the following ex- 
periment. He wrapped a photographic plate in a piece of per- 
fectly opaque black paper, laid a coin on top of the paper, 
and suspended above the coin a small quantity of the mineral 
uranium. He then set the whole away in a dark room and 
let it stand for several days. When he developed the photo- 
graphic plate he found upon it a shadow picture of the coin 
similar to an X-ray picture. He concluded, therefore, that 
uranium possesses the property of spontaneously emitting rays of 
some sort which have the power of penetrating opaque objects 
and of affecting photographic plates, just as X rays do. He 
also found that these rays, which he called uranium rays, 
are like X rays in that they discharge electrically charged 
bodies on which they fall. He found also that the rays are 
emitted by all uranium compounds. 

504. Radium. It was but a few months after Becquerel's 
discovery that Madame Curie (see opposite p. 446), in Paris, 
began an investigation of all the known elements, to find 
whether any of the rest of them possessed the remarkable 



442 INVISIBLE RADIATIONS 

property which had been found to be possessed by uranium. 
She found that one of the remaining known elements, namely, 
thorium, the chief constituent of Welsbach mantles, is capable, 
together with its compounds, of producing the same effect. 
After this discovery the rays from all this class of substances 
began to be called Becquerel rays, and all substances which 
emitted such rays were called radioactive substances. 

But in connection with this investigation Madame Curie 
noticed that pitchblende, the crude ore from which uranium- 
is extracted, and which consists largely of uranium oxide, 
would discharge her electroscope about four times as fast as 
pure uranium. She inferred, therefore, that the radioactivity 
of pitchblende could not be due solely to the uranium con- 
tained in it, and that pitchblende must therefore contain some 
hitherto unknown element which has the property of emitting 
Becquerel rays more powerfully than uranium or thorium. 
After a long and difficult search she succeeded in separating 
from several tons of pitchblende a few hundredths of a gram 
of a new element which was capable of discharging an electro- 
scope more than a million times as rapidly as either uranium 
or thorium. She named this new element radium. 

505. Nature of Becquerel rays. That these rays which are 
spontaneously emitted by radioactive substances are not X 
rays, in spite of their srnilarity in affecting a photographic 
plate, in causing fluorescence, and in discharging electrified 
bodies, is proved by the fact that they are found to be deflected 
by both magnetic and electric fields, and by the further fact 
that they impart electric charges to bodies upon which they fall. 
These properties constitute strong evidence that radioactive 
substances project from themselves electrically charged particles. 

But an experiment performed in 1899 by Rutherford (see 
opposite p. 446), then of McGill University, Montreal, showed 
that Becquerel rays are complex, consisting of three differ- 
ent types of radiation, which he named the alpha, beta, and 



RADIOACTIVITY 443 

gamma rays. The beta rays are found to be identical in 
all respects with cathode rays ; that is, they are streams of 
electrons projected with velocities varying from 60,000 to 
180,000 miles per second. The alpha rays are distinguished 
from these by their very much smaller penetrating power, by 
their very much greater power of rendering gases conductors, 
by their very much smaller deflectibility in magnetic and 
electric fields, and by the fact that the direction of the deflec- 
tion is opposite to that of the beta rays. From this last fact, 
discovered by Rutherford in 1903, the conclusion is drawn 
that the alpha rays consist of positively charged particles; 
and from the amount of their deflectibility their mass has 
been calculated to be about four times that of the hydrogen 
atom, that is, about 7400 times the mass of the electron, 
and their velocity to be about 20,000 miles per second. 
Rutherford and Boltwood have collected the alpha particles 
in sufficient amount to identify them definitely as positively 
charged atoms of helium. 

The difference in the sizes of the alpha and beta particles 
explains why the latter are so much more penetrating than the 
former, and why the former are so much more efficient than the 
latter in knocking electrons out of the molecules of a gas and 
rendering it conducting. A sheet of aluminium foil .005 centi- 
meter thick cuts off completely the alpha rays but offers practi- 
cally no obstruction to the passage of the beta and gamma rays. 

The gamma rays are very much more penetrating than even 
the beta rays, and are not at all deflected by magnetic or electric 
fields. They are regular waves in the ether, like X rays, only 
shorter ; and they are commonly supposed to be produced by 
the impact of the beta particles on surrounding matter. 

506. Crookes's spinthariscope. In 1903 Sir William Crookes (see oppo- 
site p. 358) devised a little instrument, called the spinthariscope, which 
furnishes very direct and striking evidence that particles are being 
continuously shot off from radium with enormous velocities. In the 



444 INVISIBLE KADIATIONS 

spinthariscope a tiny speck of radium R (Fig. 476) is placed about a 

millimeter above a zinc-sulphide screen S, and the latter is then 

viewed through a lens L, which gives from ten to r?-**^^ 

twenty diameters magnification. The continuous 

soft glow of the screen, which is all one sees with 

the naked eye, is resolved by the lens into hundreds 

of tiny flashes of light. The appearance is as 

though the screen were being fiercely bombarded 

by an incessant rain of projectiles, each impact 

being marked by a flash of light, just as sparks fly 



from a flint when struck with steel. The experi- p IG- 473. Crookes's 
ment is a very beautiful one, and it furnishes very spinthariscope 
direct and convincing evidence that radium is 

continually projecting particles from itself at stupendous speeds. The 
flashes are due to the impacts of the alpha, not the beta, particles 
against the zinc-sulphide screen. 

A mixture composed of a radium compound and zinc sulphide glows 
constantly and is used for the dials of airplane instruments, compasses, 
and watches, as well as on gun sights, making them visible for night use. 

507. The disintegration of radioactive substances. Whatever 
be the cause of this ceaseless emission of particles exhibited 
by radioactive substances, it is certainly not due to any ordi- 
nary chemical reactions; for Madame Curie showed, when she 
discovered the activity of thorium, that the activity of all the 
radioactive substances is simply proportional to the amount 
of the active element present, and has nothing whatever to do 
with the nature of the chemical compound in which the ele- 
ment is found. Furthermore, radioactivity has been found to 
be independent of all physical as well as chemical conditions. 
The lowest cold or greatest heat does not appear to affect it 
in the least. Radioactivity, therefore, is as unalterable a 
property of the atoms of radioactive substances as is weight 
itself. It is now known that the atoms of radioactive sub- 
stances are slowly disintegrating into simpler atoms. Uranium 
and thorium have the heaviest atoms of all the elements. For 
some unknown reason they seem not infrequently to become 



EADIOACTIVITY 445 

unstable and project off a part of their mass. This projected 
mass is the alpha particle. What is left of the. atom after 
the explosion is a new substance with chemical properties 
different from those of the original atom. This new atom is, 
in general, also unstable and breaks down into something 
else. This process is repeated over and over again until 
some stable form of atom is reached. Somewhere in the 
course of this atomic catastrophe some electrons leave the 
mass; these are beta rays. 

According to this point of view, which is now generally 
accepted, radium is simply one of the stages in the disintegra- 
tion of the uranium atom. The atomic weight of uranium is 
238.2; that of radium, about 226; that of helium, 4.00. 
Radium would then beuranium after the latter has lost 3 helium 
atoms. The further disintegration of radium through four 
additional transformations has been traced. It has been con- 
jectured that the fifth and final product is lead. If we subtract 
8 x 4.00 from 238.2, we obtain 206.2, which is very close to 
the accepted value for lead, namely, 207.2. In a similar way 
six successive stages in the disintegration of the thorium atom 
(atomic weight, 232.4) have been found, but the final product 
is unknown. 

508. Energy stored up in the atoms of the elements. In 
1903 the two Frenchmen, Curie and Labord, made an epoch- 
making discovery. It was that radium is continually evolv- 
ing heat at the rate of about one hundred calories per gram 
per hour. More recent measurements have given one hundred 
eighteen calories. This result was to have been anticipated 
from the fact that the particles which are continually flying 
off from the disintegrating radium atoms subject the whole 
mass to an incessant internal bombardment which would be 
expected to raise its temperature. This measurement of the 
exact amount of heat evolved per hour enables us to estimate 
how much heat energy is evolved in the disintegration of one 



446 INVISIBLE RADIATIONS 

gram of radium. It is about two thousand million calories, 
fully three hundred thousand times as much as is evolved 
in the combustion of one gram of coal. Furthermore, it is 
not impossible that similar enormous quantities of energy are 
locked up in the atoms of all substances, existing there per- 
haps in the form of the kinetic energy of rotation of the 
electrons. The most vitally interesting question which the 
physics of the future has to face is, Is it possible for man to 
gain control of any such store of subatomic energy and to use 
it for his own ends ? Such a result does not now seem likely 
or even possible ; and yet the transformations which the study 
of physics has wrought in the world within a hundred years 
were once just as incredible as this. In view of what physics 
has done, is doing, and can yet do for the progress of the 
world, can anyone be insensible either to its value or to its 
fascination ? 

QUESTIONS AND PROBLEMS 

1. Why is it necessary to use a rectifying crystal or an audion in 
series with a telephone receiver to detect electric waves? 

2. Explain why an electroscope is discharged when a bit of radium 
is brought near it. 

3. The wave length of the shortest X rays is about .00000001 cm. 
How many times greater is the wave length of green light? 




WILLIAM CONRAD RONTGEN, 

MUNICH 
Discoverer of X rays 



ANTOINE HENRI BECQUEREL, 
PARIS 

Discoverer of radioactivity 




MADAME CURIE, UNIVERSITY 

OF PARIS 
Discoverer of radium 



E. RUTHERFORD, CAMBRIDGE 
UNIVERSITY (ENGLAND) 

Discoverer of radioactive trans- 
formations 



A GROUP OF MODERN PHYSICISTS 





> tfs t: s 

^ r2 g '3 * oa g 

III ! i 



PH 2 



5 6 






e J * r. pi - T * 

" 



r- _~ 

o -2 -5 



5 g IS 

.2 be o a 4J a 

~ 1 1 



APPENDIX 



SUPPLEMENTARY QUESTIONS AND PROBLEMS 

CHAPTER I. 1. A new lead pencil is 7 in. long. How many centi- 
meters long is it? 

2. From the bed rock upon which the Woolworth Building in New 
York rests to the top of the tower is 278.3 m. How many feet is it? 

3. The wing spread of the NC-4 is 126 ft. How many meters is it? 

4. How many kilograms are there in the 16-pound shot? 

5. Name three uses made of lead because of its great density, and 
two uses of cork due to its small density. 

6. A flask held 2520 g. of glycerin when filled. What was the capac- 
ity of the flask in liters? (See table of densities, p. 9.) 

CHAPTER II. 1. A standpipe 100ft. high is filled with water. Find 
the pressure at the bottom in pounds per square foot and in pounds per 
square inch. ca 

2. Deep-sea fish have been caught in nets at a depth 
of a mile. How many pounds pressure are there to the 
square inch at this depth? (Specific gravity of sea 
water = 1.026.) 

3. If the pressure at a tap on the first floor reads 
80 Ib. per square inch, and at a tap two floors above, 
68 Ib., what is the difference in feet between the levels 
of the two taps? 

4. Find the total force against the gate of a lock if 
its width is 60 ft. and the depth of the water 20 ft. Will 
it have to be made stronger if it holds back a lake than 
if it holds back a small pond ? 

5. Fig. 477 represents an instrument commonly known 
as the hydrostatic bellows. If the base C is 20 in. square 
and the tube is filled with water to a depth of 5 ft. above 
the top of C, what is the value of the weight which the 
bellows can support ? 

6. A hydraulic press having a piston 1 in. in diameter exerts a force 
of 10,000 Ib. when 10 Ib. are applied to this piston. What is the diam- 
eter of the large piston ? 

447 




FIG. 477 

Hydrostatic 
bellows 



448 



APPENDIX 




B = 



7. A floating dock is shown in Fig. 478. When the chambers c are 
filled with water, the dock sinks until the water line is at A. The vessel 
is then floated into the dock. As soon as it is in place, the water is 
pumped from the chambers until the 

water line is as low as B. Work- 
men can then get at all parts of the 
bottom. If each of the chambers is 
10 ft. high and 10 ft. wide, what 
must be the length of the dock if 
it is to be available for the Beren- 
garia (Cunard Line), of 50,000 tons' 
weight? 

8. If each boat of a pontoon 

bridge is 100 ft. long and 75 ft. wide at the water line, how much will 
it sink when a locomotive weighing 100 tons passes over it? 

9. What must be the specific gravity of a liquid in which a body 
having a specific gravity of 6.8 will float with half its volume submerged V 

10. A block of wood 10 in. high sinks 6 in. in water. Find the density 
of the wood. 

11. If this block sank 7 in. in oil, what would be the density of the oil '( 

12. A graduated glass cylinder contains 190 cc. of water. An egg 
weighing 40 g. is dropped into the glass ; it sinks to the bottom and 
xaises the water to the 225-cc. mark. Find the density of the egg. 



FIG. 478. Floating dock 



CHAPTER III. 1. Explain the process of making air enter the lungs; 
of making lemonade rise in a straw. 

2. If a circular piece of wet leather having a string attached to the 
middle is pressed down on a flat, smooth stone, as in Fig. 479, the latter 
may often be lifted by pulling on the string. Is it pulled up or pushed 
up ? Explain. 

3. Make a labeled drawing of a simple Torricellian 
barometer, naming all the parts in the diagram. 

4. The body of the average man has 15 sq. ft. of sur- 
face. What is the total force of the atmosphere upon 
Mm ? Why is he unconscious of this crushing force ? 

5. If the variation of the height of a mercury 
barometer is 2 in., how far did the image rise and fall 
in Otto von Guericke's water barometer ? (See 42.) 

6. What is Boyle's law ? A mass of air 3 cc. in volume is introduced 
into the space above a barometer column which originally stands at 
760 mm. The column sinks until it is only 570 mm. high. Find the 
Tolume now occupied by the air. 




FIG. 479 



QUESTIONS AND PEOBLEMS 449 

7. There is a pressure of 80 cm. of mercury on 1000 cc. of gas. 
What pressure must be applied to reduce the volume to 600 cc. if the 
temperature is kept constant? 

8. Pressure tests for boilers or steel tanks of any kind are always 
made by filling them with water rather than with air. Why ? 

9. If the water within a diving bell is at a depth of 1033 cm. beneath 
the surface of a lake, what is the density of the air inside if at the sur- 
face the density of air is .0013 and its pressure 76 cm. ? What would 
be the reading of a barometer within the bell ? 

10. If a diver descends to a depth of 100 ft., what is the pressure to 
which he is subjected? What is the density of the air in his suit, the 
density at the surface where the pressure is 75 cm. being .0012? (Assume 
the temperature to remain unchanged.) 

11. How many of the laws of liquids and gases do you find illustrated 
in the experiment of the Cartesian diver? 

12. Pascal proved by an experiment that a siphon would not run if 
the bend in the arm were more than 34 ft. above the upper water level. 
He made it run, however, by inclining it sidewise until the bend was 
less than 34 ft. above this level. Explain. 

13. How high will a lift pump raise water if it is located upon the 
side of a mountain where the barometer reading is 71 cm.? 

14. Find the lifting power of a kite balloon whose capacity is 
37,000 cu. ft., the lifting power of the gas being 64.4 Ib. per 1000 cu. ft. 
and the weight of the balloon, cordage, car, and observer being 1300 Ib. 

CHAPTER IV. 1. W T hy does a confined body of gas exert pressure 
inversely proportional to its volume ? 

2. A lump of copper sulphate placed at the bottom of a graduate 
filled with water will dissolve and very slowly pass upward, although 
a copper-sulphate molecule is many times heavier than a water molecule. 
Explain. 

CHAPTER V. 1. An airplane which flies in still air with a velocity of 
120 mi. per hour is flying in a wind whose velocity is 60 mi. per hour 
toward the east. Find the actual velocity of the airplane and the 
direction of its motion when headed north ; east ; south ; west. 

2. Represent graphically a force of 30 Ib. acting southeast and a 
force of 40 Ib. acting southwest at the same point. What will be 
the magnitude of the resultant, and what will be its approximate 
direction? 

3. Two concurrent forces, each of 50 Ib., act at an angle of 60 with 
each other. Find the resultant graphically. 



450 APPENDIX 

4. A child weighing 100 Ib. sits in a swing. The swing is drawn 
aside and held in equilibrium by a horizontal force of 40 Ib. Find the 
tension in each of the two ropes of the swing. 

5. Four clothes posts were arranged to form a square. A clothes- 
line was drawn around the outside of the posts with a force of 
GO Ib. With what force is each post drawn toward the center of 
the square ? 

6. A man weighing 150 Ib. stood at the middle of a tight-rope 
whose two parts were each 50 ft. long. What was the tension on the 
parts of the rope, the weight of the man depressing the center of the 
rope 1 ft.? 

7. A boy pulls a loaded sled weighing 200 Ib. up a hill which rises 
1 ft. in 5 measured along the slope. Neglecting friction, how much force 
must he exert? 

8. A cask weighing 100 Ib. is held at rest upon an inclined plank 
8 ft. long and 3 ft. high. By the resolution-and-proportion method find 
the component of its weight that tends to break the plank. 

9. What force will be required to support a 50-lb. ball on an inclined 
plane of which the length is 10 times the height? 

10. A boy is able to exert a force of 75 Ib. Neglecting friction, how 
long an inclined plane must he have in order to push a truck weighing 
350 Ib. up to a doorway 3 ft. above the ground? 

11. Could a kite be flown from an automobile when there is no 
wind? Explain. 

12. Why is it unsafe to stand up in a canoe? 

13. If a lead pencil is balanced on its point on the finger, it will be 
in unstable equilibrium, but if two knives -are stuck into it, as in Fig. 480, 
it will be in stable equilibrium. Why? 

14. Why does a man lean forward when he climbs 
a hill? 

15. A boy dropped a stone from a bridge and 
noticed that it struck the water in just 3 sec. How 
fast was it going when it struck? How high was 
the bridge above the water ? 

16. If a body sliding without friction down an 
inclined plane moves 40 cm. during the first second 
of its descent, and if the plane is 500 cm. long and 
40.8 cm. high, what is the value of </? (Remember 

that the acceleration down the incline is simply the ^ 

component ( 80) of g parallel to the incline.) 

17. A ball shot straight upward near a pond was seen to strike the 
water in 10 sec. How high did it rise ? What was its initial speed? 




QUESTIONS AND PEOBLEMS 451 

18. A trolley car moving from rest with uniform acceleration acquired 
a velocity of 10 mi. per hour in 15 sec. What was the acceleration and 
the distance traversed? 

19. A bombing airplane is flying 60 mi. per hour in still air at a height 
of 1000 ft. In order to score a " bull's-eye," at what distance in advance 
of the target must the bomb be let go ? 

20. A rifle weighing 5 Ib. discharges a 1-oz. bullet with a velocity of 
1000 ft. per second. What will be the velocity of the rifle in the opposite 
direction ? 

21. A steamboat weighing 20,000 metric tons is being pulled by a 
tug which exerts a pull of 2 metric tons. (A metric ton is equal to 
1000 kg.) If the friction of the water were negligible, what velocity 
would the boat acquire in 4 min.? (Reduce mass to grams, force to 
dynes, and remember that F = mv/t.') 

22. If a train of cars weighs 200 metric tons, and the engine in pull- 
ing 5 sec. imparts to it a velocity of 2 m. per second, what is the pull of 
the engine in metric tons? 

CHAPTER VI. 1. W T hat must be the cross section of a wire of copper 
if it is to have the same tensile strength (that is, break with the same 
weight) as a wire of iron 1 sq. mm. in cross section? (See 107.) 

2. How many times greater must the diameter of one wire be than 
that of another of the same material if it is to have five times the tensile 
strength ? 

3. If the position of the pointer on a spring balance is marked 
when no load is on the spring, and again when the spring is stretched 
with a load of 10 g., and if the space between the two marks is then 
divided into ten equal parts, will each of these parts represent a gram ? 
Why? 

4. A wire which is twice as thick as another of similar material 
will support how many times as much weight? 

5. A force of 3 Ib. stretches 1 mm. a wire that is 1 m. long and .1 mm. 
in diameter. How much force will it take to stretch 5 mm. a wire of the 
same material 4 m. long and .2 mm. in diameter? 

6. Why does a small stream of water break np into drops instead 
of falling as a continuous thread? 

7. Give four common illustrations of capillary attraction. 

8. Explain the watering of flowers by setting the pot in a shallow 
basin of water. 

9. Why does a new and oily steel pen not write well? Why is it 
difficult to write on oiled paper? 

10. Would mercury ascend a lamp wick as oil and water do? 






452 



APPENDIX 



11. Why do some liquids rise while others are depressed in capillary 
tubes? 

12. If water will rise 32 cm. in a tube .1 mm. in diameter, how high 
will it rise in a tube .01 mm. in diameter? 

13. How can you tell whether bubbles which rise from the bottom of 
a vessel which is being heated are bubbles of air or bubbles of steam? 

CHAPTER VII. 1. A woman in sweeping a rug moved the nozzle of a 
vacuum sweeper a total distance of 130 ft., using an average force of 
one-half pound. How much work did she do ? 

2. Analyze several types of manual labor and see if the definition 
( W = Fs) holds for each. Is not F x s the thing paid for in every case ? 

3. Explain the use of the rider in weighing (see Fig. 22). 

4. Two boys are carrying a bag 
of walnuts at the middle of a long 
stick. Will it make any difference 
whether they walk close to the bag 
or farther away, so long as each is at 
the same distance ? 

5. If 3 horses are to pull equally 
on a load, how should the whippletree 
be designed? 

6. W T hy is it that a couple cannot be balanced by a single force? 

7. If the ball of the float valve (Fig. 481) has a diameter of 10 cm. v 
and if the distance from the center of the ball to the pivot S is 20 
times the distance from S to the pin P, with what force is the valve 
R held shut when the ball is half immersed ? Neglect weight of ball. 




FIG. 481. The automatic 
float valve 





FIG. 482. Yale lock 
(1), the right key; (2), the wrong key 

8. In the Yale lock (Fig. 482) the cylinder G rotates inside the 
fixed cylinder F and works the bolt through the arm H. The right key 
raises the pins a', b', c', d' t e f until their tops are just even with the top 
of G. What mechanical principles do you find involved in this device ? 



QUESTIONS AND PROBLEMS 



458 




FIG. 483. Differential 
windlass 



9. A lever is 3 ft. long. Where must the fulcrum be placed so that a, 
weight of 300 Ib. at one end shall be balanced by 50 Ib. at the other ? 

10. Two horses of unequal strength must 
be hitched as a team. The one is to pull 
360 Ib., while the other pulls 288 Ib. In 
a doubletree 50 in. long, where must the 
pin be placed to permit an even pull? 

11. In the differential wheel and axle 
(Fig. 483) the rope is wound in opposite 
directions on two axles of different diameter. 
For a complete revolution of the axle the 
weight is lifted by a distance equal to one 
half the difference between the circumfer- 
ences of the two axles. If the crank has a 
radius of 2 ft., the larger axle a diameter of 

6 in., and the smaller one a diameter of 4 in., find the mechanical 
advantage of the arrangement. (See differential pulley, p. 119.) 

12. With the aid of Fig. 484 describe the process of winding and 
setting a watch. The rocker R is pivoted at S ; C carries the mainspring 
and E the hands ; S. P. is a light spring which normally keeps the 
wheel .4 in mesh with C. Pressing 

down on P, however, releases A 
from C and engages B with D. 
What mechanical principles do 
you find involved ? What happens 
when M is turned backward ? 

13. A 150-lb. man runs up a flight 
of stairs 60 ft. high in 10 sec. What 
is his horse power while doing it? 
How do you account for the result ? 

14. A thousand-barrel tank at a 
mean elevation of 50 ft. is to be 
filled with water. How much work 
must be done to fill it, assuming a 
barrel of water to weigh 260 Ib. ? 
How long would it take a 2-horse- 
power electric motor to fill it? 

15. What must be the horse power of an engine which is to pump 
10,000 1. of water per second from a mine 150 m. deep? (Take 76 kilo- 
gram meters per second = 1 horse power.) 

16. A water motor discharges 100 1. of water per minute when fed 
from a reservoir in which the water surface stands 50 m. above the level 




FIG. 484. Winding and setting mech- 
anism of a stem-winding watch 



454 APPENDIX 

of the motor. If all of the potential energy of the water were transformed 
into work in the motor, what would be the horse power of the motor ? 
(The potential energy of the water is the amount of work which would 
be required to carry it back to the top of the reservoir.) 

17. A rifle weighing 8.5 Ib. discharges a bullet weighing 0.4 oz. with 
a velocity of 2600 ft. per second. What is the kinetic energy of the bullet ; 
the velocity of recoil of the rifle ; the kinetic energy of the rifle? 

CHAPTER VIII. 1. What fractional part of the air in a room passes 
out when the air in it is heated from -15C. to 20C.V (-15C. = 258 A. ; 
20C. -293 A.) 

2. If the volume of a body of gas at 20 C. and 76cm. pressure is 
500 cc., what is its volume at 50C. and 70cm. pressure? 

3. An automobile tire contained air under a pressure of 70 Ib. per 
square inch at a temperature of 20C. On being driven, the temperature 
of the air rose to 35 C. What was the increase in pressure within 
the tire? 

4. Find the density of the air in a furnace whose temperature is 
1000 C., the density at 0C. being .001293. 

5. When the barometric height is 76 cm. and the temperature 0C., 
the density of air is .001293. Find the density of air when the tem- 
perature is 38 C. and the barometric height is 73 cm. Find the density 
of air when the temperature is 40 C. and the barometric height 74 cm. 

6. If an iron steam pipe is 60 ft. long at 0C., what is its length 
when steam passes through it at 100 C. ? 

7. If iron rails are 30 ft. long, and if the variation of temperature 
throughout the year is 50 C., what space must be left between their ends ? 

8. If the total length of the iron rods b, <1, e, and i in a compensated 
pendulum (Fig. 151) is 2 m., what must be the total length of the cop- 
per rods c if the period of the pendulum is independent of temperature ? 

9. Two metal bars, one aluminium and the other steel, are both 
100 cm. long at 0C. How much will they differ in length at 30C.? 
(See table on page 140.) 

CHAPTER IX. 1. Name three uses and three disadvantages of friction. 

2. There is a Pelton wheel at the Sutro tunnel in Nevada which is 
driven by water supplied from a reservoir 2100 ft. above the level of the 
motor. The diameter of the nozzle is about J in., and that of the wheel 
but 3 ft, yet 100 H. P. is developed. If the efficiency is 80%, how many 
cubic feet of water are discharged per second ? 

3. A turbine having an efficiency of 80% was supplied with 200 cu. ft. 
of water per second at a head of 50 ft. What horse power was developed ? 



QUESTIONS AND PROBLEMS 455 

4. How many calories of heat are generated by the impact of a 200- 
kilo bowlder when it falls vertically through 100 m.? (The mechanical 
equivalent of heat = 427 g.ni.) 

5. Thousands of meteorites are falling into the sun with enormous 
velocities every minute. From a consideration of the preceding example 
account for a portion, at least, of the sun's heat. 

6. The kinetic energy of mass motion of an automobile running 
20 mi. per hour was 37,34-4 ft. Ib. In stopping this car how many B. T. U. 
were developed in the brakes ? 

7. 400 g. of aluminium at 100 C. were dropped into 500 g. of water 
at 20 C. The water equivalent of the calorimeter was 40 grams. Find 
the resultant temperature. (See table on page 160.) 

8. A copper ball weighing 3 kg. was heated to a temperature of 
100 C. When placed in water at 15 G. it raised the temperature to 
25 C. How many grams of water were there ? (See table on page 160.) 

9. 100 g. of water at 80 C. are thoroughly mixed with 500 g. of 
mercury at C. What is the 'temperature of the mixture? 

10. A piece of platinum weighing 10 g. is taken from a furnace and 
plunged instantly into 40 g. of water at 10 C. The temperature of the 
water rises to 24 C. What was the temperature of the furnace ? 

11. How many grams of ice-cold water must be poured into a tum- 
bler weighing 300 g. to cool it from 60 C. to 20 C., the specific heat 
of glass being .2 V 

12. If you put a 20-g., silver spoon at 20 C. into a 150-cc. cup of tea 
at 70 C., how much do you cool the tea ? 

13. Which would be heated more, a lead or a steel bullet, if they were 
fired against a target with equal speeds ? 

14. If the specific heat of lead is .031 and the mechanical equivalent 
of a calorie 427 g. m., through how many degrees centigrade will a 
1000-g. lead ball be raised if it falls from a height of 100 m., provided 
all of the heat developed by the impact goes into the lead ? 

15. A car weighing 60,000 kilos slides down a grade which is 2 m. 
lower at the bottom than at the top and is brought to rest at the bottom 
by the brakes. How many calories of heat are developed by the friction ? 

16. Explain why the cylinder of an automobile-tire pump becomes 
hot when the pump is being used. Why is the air cooled as it escapes 
from the valve of an automobile tire? 

CHAPTER X. 1. What is the temperature of a mixture of ice and 
water ? What determines whether it is freezing or melting ? 

2. Why does ice cream seem so much colder to the teeth than ice 
water ? 



456 APPENDIX 

= ; 

3. If water were like gold in contracting on solidification, what 
would happen to lakes and rivers during a cold winter ? 

4. Equal weights of hot water and ice are mixed, and the result is 
water at C. What was the temperature of the hot water ? 

5. Which is the more effective as a cooling agent, 100 Ib. of ice at 
C. or 100 Ib. of water at the same temperature? Why? 

6. What temperature will result from mixing 10 g. of ice at C. 
with 200 g. of water at 25 C.? 

7. From what height must a gram of ice at C. fall in order to 
melt itself by the heat generated in the impact ? 

8. If dry air were placed in a closed vessel when the barometer was 
76 cm., and if a dish of water were then introduced within the closed 
space, what pressure would finally be attained within the vessel if the 
temperature were kept at 18 C.? 

9. If there were moisture on the face, would fanning produce any 
feeling of coolness in a saturated atmosphere ? 

10. Would fanning produce any feeling of coolness if there were no 
moisture on the face ? 

11. Explain the formation of frost on the window panes in winter. 

12. In the fall we expect frost on clear nights when the dew point is 
low, but not on cloudy nights when the dew point is high. Can you see 
any reason why a large deposit of dew should prevent the temperature of 
the air from falling very low ? 

13. Why does the distillation of a mixture of alcohol and water 
always result to some extent in a mixture of alcohol and water ? 

14. How much heat is given up by 30 g. of steam at 100 C. in con- 
densing to water at the same temperature ? 

15. A vessel contains 300 g. of water at C. and 130 g. of ice. If 25 g. 
of steam are condensed in it, what will be the resulting temperature ? 

16. To convert 1 g. of water at C. into steam at 100 C. requires 
636 calories. When the boiling point of water is 100 C., how many of 
these calories are used to vaporize the water? At an elevation where 
water boils at 90 C., how many calories are required for the vaporization? 
(Specific heat of steam = 0.5.) 

17. Bearing in mind that the cooler the water the less the kinetic 
agitation of its molecules, why should you expect a larger result at 90 C. 
than 536 calories ? 

18. When the steam gauge of a locomotive records 250 Ib. per square 
inch, the steam is at a temperature of 406 F. Explain how the steam 
produces this great pressure. 

19. If the average pressure in the cylinder of a steam engine is 10 
kilos to the square centimeter, and the area of the piston is 427 sq. cm., 



QUESTIONS AXD PROBLEMS 457 

how much work is done by the piston in a stroke of length 50 cm. ? 
How many calories did the steam lose in this operation? 

20. The total efficiency of a certain 600-horse-power locomotive is 6% ; 
8000 calories of heat are produced by the burning of 1 g. of the best 
anthracite coal ; how many kilos of such coal are consumed per hour 
by this engine ? (Take 1 H. P. = 746 watts and 1 calorie per second 
= 4.2 watts.) 

CHAPTER XI. 1. Why are the pipes that carry steam from the boiler 
to the radiators often covered with cellular asbestos? Why is the cellular 
structure an advantage ? 

2. Explain the cause of the sea breeze which occurs in coast regions 
on summer afternoons. 

3. Is the draft through the fire of a kitchen range pushed through 
or drawn through? Explain. 

4. Why should steam radiators be installed on the cold side of a room, 
for example, near outside walls or windows? 

5. Describe all the processes involved in the transference of heat 
energy from the fire under the steam boiler in a cellar to the rooms con- 
taining the radiators. 

CHAPTER XII. 1. If a bar magnet is floated on a piece of cork, will 
it tend to float toward the north ? Why ? 

2. The dipping needle is suspended from one arm of a steel-free 
balance and carefully weighed. It is then magnetized. Will its apparent 
weight increase ? 

3. When a piece of soft iron is made a temporary magnet by bringing 
it near the N pole of a bar magnet, will the end of the iron nearest the 
magnet be an N or an S pole ? 

4. To which do isogonic lines as a rule correspond most nearly, the 
parallels or the meridians ? 

5. Lines connecting those places on the earth where the inclination 
of the dipping needle is the same are called isoclinic lines. Do isoclinic 
lines in general trend approximately N and S or E and W? 

6. With what force will an N magnetic pole of strength 6 attract, at 
a distance of 5 cm., an S pole of strength 1? of strength 9 ? 

CHAPTER XIII. 1. Why is repulsion between an unknown body and 
an electrified pith ball a surer sign that the unknown body is electrified 
than is attraction? 

2. If you charge an electroscope and then bring your hand toward 
the knob (not touching it), the leaves go closer together. Why? 



458 APPENDIX 

3. Two small spheres are charged with + 16 and 4 units of elec- 
tricity. With what force will they attract each other when at a distance 
of 4cm.? 

4. If the two spheres of the previous problem are made to touch and 
are then returned to their former positions, with what force will they 
act on each other ? Will this force be attraction or repulsion ? 

5. Why is the capacity of a conductor greater when another con- 
ductor connected to the earth is near it than when it stands alone? 

6. A Leyden jar is placed on a glass plate and 10 units of electricity 
placed on the inner coating. The knob is then connected to a gold-leaf 
electroscope. W'ill the leaves of the electroscope stand farther apart now 
or after the outside coating has been connected to the earth ? 

CHAPTER XIV. 1. Why would an electromagnet made by winding 
bare wire on a bare iron core be worthless as a magnet? 

2. The plane of a suspended loop of wire is east and west. A cur- 
rent is sent through it, passing from east to west on the upper side. 
What will happen to the loop if it is perfectly free to turn ? 

3. When a strong current is sent through a suspended-coil galva- 
nometer, what position will the coil assume ? 

4. If the earth's magnetism is due to a surface charge rotating with 
the earth, must this charge be positive or negative in order to produce 
the sort of magnetic poles which the earth has? (This is actually the 
present theory of the earth's magnetism.) 

5. Why must a galvanometer which is to be used for measuring 
voltages have a high resistance ? 

6. Why is the E. M. F. of a cell equal to the P. D. of its terminals when 
on open circuit? (Explain by reference to the water analogy of 318.) 

7. Can you prove from a consideration of Ohm's law that when 
wires of different resistances are inserted in series in a circuit, the P. D.'s 
between the ends of the various wires are proportional to the resistances 
of these wires ? 

8. How long a piece of No. 30 copper wire will have the same 
resistance as a meter of No. 30 German-silver wire ? (See table of 
specific resistances, p. 262.) ' 9 

9. The diameter of Xo. 20 wire is 31.96 mils (1 mil = .001 in.) and 
that of No. 30 wire 10.025 mils. Compare the resistances of equal 
lengths of No. 20 and No. 30 German-silver wires. 

10. What length of No. 30 copper wire will have the same resistance 
as 20 ft. of No. 20 copper wire ? 

11. AVhat length of No. 20 German-silver wire will have the same 
resistance as 100 ft. of No. 30 copper wire ? 



QUESTIONS AND PROBLEMS 459 

12. A galvanometer has a resistance of 588 ohms. Jf only one fiftieth 
of the current in the main circuit is to be allowed to pass through the 
moving coil, what must be the resistance of the shunt ? 

13. Ten pieces of wire, each having a resistance of 5 ohms, are con- 
nected in parallel (see Fig. 278). If the junction a is connected to one 
terminal of a Daniell cell and b to the other, what is the total current 
which will flow through the circuit when the E. M. F. of the cell is 1 volt 
and its resistance 2 ohrns? 

14. Jf a certain Daniell cell has an internal resistance of 2 ohms and 
an E. M. F. of 1.08 volts, what current will it send through an ammeter 
whose resistance is negligible? What current will it send through a 
copper wire of 2 ohms resistance? through a German-silver wire of 
100 ohms resistance? 

15. A Daniell cell indicates a certain current when connected to a 
galvanometer of negligible resistance. When a piece of No. 20 German- 
silver wire is inserted into the circuit, it is found to require a length of 
5 ft. to reduce the current to one half its former value. Find the resist- 
ance of the cell in ohms, No. 20 German-silver wire having a resistance 
of 190.2 ohms per 1000 ft. 

16. A coil of unknown resistance is inserted in series with a con- 
siderable length of No. 30 German-silver wire and joined to a Daniell 
cell. When the terminals of a high-resistance galvanometer are touched 
to the wire at points 10 ft. apart, the deflection is found to be the 
same as when they are touched across the terminals of the unknown 
resistance. What is the resistance of the unknown coil? (See 316, 
p. 263.) 

17. How do we calculate the power consumed in any part of an 
electric circuit ? What horse power is required to run an incandescent 
lamp carrying .5 ampere at 110 volts? 

18. An electric soldering iron allows 5 amperes to flow through it 
when connected to an E. M. F. of 110 volts. What will it cost, at 12 cents 
per kilowatt hour, to operate the iron 6 hr. per day for 5 da.? 

19. An electric motor developed 2 horse power when taking 16.5 
amperes at 110 volts. Find the efficiency of the motor. (One horse 
power = 7-1 G watts.) 

CHAPTER XY. 1. If the coil of a sensitive galvanometer is set to 
swinging while the circuit through the coil is open, it will continue 
to swing for a long time ; but if the coil is short-circuited, it will come 
to rest after a very few oscillations. Why? (The experiment may easily 
be tried. Remember that currents are induced in the moving coil. 
Apply Lenz's law.) 



460 APPENDIX 

2. Show that if the reverse of Leuz's law were true, a motor once 
started would run of itself and do work; that is, it would furnish a case 
of perpetual motion. 

3. If a series-wound dynamo is running at a constant speed, what 
effect will be produced on the strength of the field magnets by dimin- 
ishing the external resistance and thus increasing the current? What 
will be the effect on the E.M. F.? (Remember that the whole current 
goes around the field magnets.) (See 357.) 

4. If a shunt-wound dynamo is run at constant speed, what effect 
will be produced on the strength of the field magnets by reducing the 
external resistance ? What effect will this have on the E.M.F.? 

5. In an incandescent-lighting system the lamps are connected in 
parallel across the mains. Every lamp which is turned on, then, dimin- 
ishes the external resistance. Explain from a consideration of Problems 
3 and 4 why a compound-wound dynamo (Fig. 318) keeps the P. D. 
between the mains constant. 

6. When an electric fan is first started, the current through it is much 
greater than it is after the fan has attained its normal speed. Why ? 

7. If the pressure applied at the terminals of a motor is 500 volts, 
and the back pressure, when running at full speed, is 450 volts, what is 
the current flowing through the armature, its resistance being 10 ohms? 

8. Two successive coils on the armature of a multipolar alternator 
are cutting^lines of force which run in opposite directions. How does 
it happen that the currents generated flow through the wires in the 
same direction? (Fig. 310.) 

9. A multipolar alternator has 20 poles and rotates 200 times per 
minute. How many alternations per second will be produced in the 
circuit ? 

10. With the aid of the dynamo rule explain why, in Figs. 313 and 
315, the current in the conductors under the north poles is moving 
toward the observer and that in the conductors under the south poles 
away from the observer. 

CHAPTER XVI. 1. A bullet fired from a rifle with a speed of 1200 ft. 
per second is heard to strike the target 6 sec. aftei*wards. W r hat is the 
distance to the target, the temperature of the air being 20 C.? (Let 
x the distance to the target.) 

2. A church bell is ringing at a distance of 1 mi. from one man 
and ^ mi. from another. How much louder would it appear to the 
second man than to the first if no reflections of the sound took place ? 

3. A stone is dropped into a well 200 m. deep. At 20 C. how much 
time will elapse before the sound of the splash is heard at the top? 



QUESTIONS AND PROBLEMS 461 

4. As a circular saw cuts into a block of wood the pitch of the note 
given out falls rapidly. Why ? 

5. A clapper strikes a bell once every two seconds. How far from 
the bell must a man be in order that the clapper may appear to hit the 
bell at the exact instant at which each stroke is heard ? 

6. The note from a piano string which makes 300 vibrations per 
second passes from indoors, where the temperature is 20 C., to outdoors, 
where it is C. What is the difference in centimeters between the 
wave lengths indoors and outdoors? 

7. A man riding on an express train moving at the rate of 1 mi. 
per minute hears a bell ringing in a tower in front of him. If the bell 
makes 280 vibrations per second, how many pulses will strike his ear 
per second, the velocity of sound being 1120 ft. per second? (The 
number of extra impulses received per second by the ear is equal to the 
number of wave lengths contained in the distance traveled per second 
by the train.) What effect has this upon the pitch? Had he been going 
from the bell at this rate, how many pulses per second would have reached 
his ear ? How would this affect the pitch ? 

8. Explain the loud noise that results from singing the right pitch 
of note into the bunghole of an empty barrel. 

9. Why do the echoes which are prominent in empty halls often 
disappear when the hall is full of people ? 

CHAPTER XVII. 1. What is the wave length of middle C when the 
speed of sound is 1152 ft. per second? 

2. What is the pitch of a note whose wave length is 5.4 in., the speed 
being 1152 ft. per second? 

3. A wire gives out the note Cwhen the tension on it is 4 kg. What 
tension will be required to give out the note G ? 

4. A wire 50 cm. long gives out 400 vibrations per second. How 
many vibrations will it give when the length is reduced to 10 cm. ? What 
syllable will represent this note if do represents the first note ? 

5. Two strings, each 6 ft. long, make 256 vibrations per second. If one 
of the strings is lengthened 1 in., how many beats per second will be heard? 

6. If a vibrating string is found to produce the note C when stretched 
by a force of 10 lb., what must be the force exerted to cause it to pro- 
duce (a) the note ? (b) the note ? 

7. When water is poured into a deep bottle, why does the pitch of 
the sound rise as the bottle fills ? 

8. Show what relation exists between the wave lengths of a note and 
the lengths of the shortest closed and open pipes which will respond to 
this note. 



462 



APPENDIX 



9. What must be the length of a closed organ pipe which produces 
the note E ? (Take the speed of sound as 340 m. per second.) 

10. What is the first overtone which can be produced in an open G 
organ pipe ? 

11. What is the first overtone which can be produced by a closed 
C organ pipe ? 

CHAPTER XVIII. 1. If the opaque body in Fig. 382 is moved nearer 
to the screen cf, how does the penumbra change ? 

2. The diameter of the moon is 2000 mi., that of the sun 860,000 mi., 
and the sun is 93,000,000 mi. away. W^hat is the length of the moon's 
umbra? 

3. If the distance from the center of the earth to the center of the 
moon were exactly equal to the length of the moon's umbra, over how 
wide a strip on the earth's surface would the sun be totally eclipsed at 
any one time ? 

4. Look at the reflected image of an electric-light filament in a 
piece of red glass. Why are there two images, one red and one white ? 

5. Show by a diagram and explanation what is meant by critical angle. 

6. The vertical diameter of the sun appears noticeably less than its 
horizontal diameter just before rising and just before setting because of 
refraction due to the earth's atmosphere. Explain. 

7. In what direction must a fish look in order 
to see the setting sun ? (See Fig. 485.) 




FIG. 485. To an eye under water all exter- 
nal objects appear to lie within a cone whose 
angle is 97 




FIG. 486. Prism 
glass 



8. Fig. 486 represents a section of a plate of prism glass. Explain why 
glass of this sort is so much more efficient than ordinary window glass in 
illuminating the rears of dark stores on the ground floor in narrow streets. 

9. In which medium, water or air, does light travel the faster? 
Give reasons for your answer. 

10. Does a man above the surface of water appear to a fish below it 
farther from or nearer to the surface than he actually is ? Make an 
explanatory wave diagram. 



QUESTIONS AND PKOBLEMS 



463 



11. How far from a screen must a 4-candle-power light be placed to 
give the same illumination as a 16-candle-power electric light 3 m. away? 

12. If two plane surfaces placed 1 m. and 2 m. respectively from a 
given light receive perpendicularly the same quantity of light, how must 
their areas compare? State the law involved. 

13. If two foot-candles are desired for reading, at what distance from 
the book must a 32-candle-power lamp be placed ? 




CHAPTER XIX. 1. An object 5 cm. long is 50 cm. from a concave 
mirror of focal length 30 cm. Where is the image, and what is its size ? 

2. Describe the image formed by a concave lens. Why can it never 
be larger than the object? 

3. What is the focal length of a lens if the image of an object 10 ft. 
away is 3 ft. from the lens ? 

4. If the object in Prob- 
lem 3 is 6 in. long, how 
long will the image be ? 

5. A beam of sunlight 
falls on a convex mirror 
through a circular hole in 

a sheet of cardboard, as in Fm 487> Determination of focal length of a 
Fig. 487. Prove that when convex mirror 

the diameter of the re- 
flected beam rq is twice the diameter of the hole np, the distance mo from 
the mirror to the screen is equal to the focal length oF of the mirror. 

6. If a rose R is pinned up- 
side down in a brightly illumi- 
nated box, a real image may be 
formed in a glass of water W by 
a concave mirror C (Fig. 488). 
Where must the eye be placed 
to see the image ? 

7. How far is the rose from FlG 48g> Image of object at center 
the mirror in the arrangement of curvature 

of Fig. 488 ? 

8. A candle placed 20 cm. in front of a concave mirror has its image 
formed 50 cm. in front of the mirror. Find the radius of the mirror. 

9. The parabolic mirror used as an objective in one of the telescopes 
at the Mount Wilson observatory is 100 in. in diameter and has a focal 
length of about 50 ft. What magnification is obtained when it is used 
with a 2-inch eyepiece; with a 1-inch eyepiece? What is gained by the 
use of a mirror of such enormous diameter ? 




464 APPENDIX 

10. A compound microscope has a tube length of 8 in., an objective 
of focal length ^ in., and an eyepiece of focal length 1 in. What is its 
magnifying power ? 

11. If the focal length of the eye is 1 in., what is the magnifying 
power of an opera glass whose objective has a focal length of 4 in.? 

12. Explain as well as you can how a telescope forms the image 
which you see when you look into it. 

13. The magnifying power of a microscope is 1000, the tube length 
is 8 in., and the focal length of the eyepiece is ^ in. What is the focal 
length of the objective ? 

CHAPTER XX. 1. If a soap film is illuminated with red, green, and 
yellow strips of light, side by side, how will the distance between the 
yellow fringes compare with that between the red fringes? with that 
between the green fringes? (See table on page 403.) 

2. What will be the apparent color of a red body when it is in a room 
to which only green light is admitted ? 

3. Will a reddish spot on an oil film be thinner or thicker than an 
adjacent bluish portion? 

4. Explain the ghastly appearance of the face of one who stands 
under the light of a Cooper-Hewitt mercury-vapor arc lamp. 

5. Draw a figure to show how a spectrum is formed by a prism, 
and indicate the relative positions of the red, the yellow, the green, and 
the blue in this spectrum. 

6. Why is a rainbow never seen during the middle part of the day? 

7. If you look at a broad sheet of white paper through a prism, it 
will appear red at one edge and blue at the other, but white in the 
middle. Explain why the middle appears uncolored. 

8. Can you see any reason why the vibrating molecules of an incan- 
descent gas might be expected to give out a few definite wave lengths, 
while the particles of an incandescent solid give out all possible wave 
lengths ? 

9. Can you see any reason why it is necessary to have the slit narrow 
and the slit and screen at conjugate foci of the lens in order to show the 
Fraunhof er lines in the experiment of 480 ? 

CHAPTER XXI. 1. How are ultra-violet waves detected? What 
apparatus is used to reveal infra-red waves? 

2. Explain how the heat of the sun warms the earth. 

3. What is electric resonance? How may it be demonstrated? 

4. Describe the construction of an X-ray tube. Describe as well as 
you can the action within it when in use. 



INDEX 



Aberration, chromatic, 409 

Absolute temperature, 134 

Absolute units, 6 

Absorption of gases, 102 ff. ; of light 
waves, 414 ; and radiation, 419 

Acceleration, defined, 75 ; of gravity, 
77 

Achromatic lens, 410 

Adhesion, 92 ; effects of, 98 

Aeronauts, height of ascent of, 37 

Air, weight of, 26 ; pressure of, 27 ; 
compressibility of, 34 ; expansi- 
bility of, 34 

Air pump, 33, 41 

Airplane, frontispiece ; principle of 
gliding of, 78-80; principle of 
flight of, 80 ; Vickers-Vimy, 153 ; 
Liberty motor in, 191 ; Wright, 317 

Airship, 44 

Alternator, 298 

Amalgamation of zinc plate, 272 

Ammeter, 257 

Ampere, portrait of, 256 

Ampere, definition of, 251, 257 

Ampere turns, 255 

Amplifier, 431 

Amundsen, 222 

Anode, 248 

Arc light, 286; automatic feed for, 
287 

Archimedes, principle of, 21 ; por- 
trait of, 22 

Armature, ring type, 255, 299 ; drum 
type, 297, 300, 301, 310 

Atmosphere, pressure of, 29 ; extent 
and character of, 36 ; humidity of, 
175 

Atoms, energy in, 445 

Audion, 429 

Automobile, 195, 198 ; clutch and 
transmission, 196; differential, 197 ; 
carburetor, 198, 199 ; ignition sys- 
tem, 198, 199; anti-glare "lens," 
362 



Back E. M. F. in motors, 303 

Baeyer, von, 417 

Balance, 7 

Balance wheel, 141 

Ball bearings, 145, 146 

Balloon, kite, 44, 45 ; dirigible, 44 ; 
helium, 45 

Barometer, mercury, 30 ; von Guer- 
icke's, 31; the aneroid, 31; the self- 
registering, 32, 38 

Batteries, primary, 272 ff. ; storage, 
281, 283 

Battleship, 152 

Bearings, ball, 145, 146 ; roller, 146 

Beats, 332, 348 

Becquerel, 441 ; portrait of, 446 

Bell, Alexander Graham, 316 ; por- 
trait of, 316 

Bell, electric, 259 

Bicycle pedal, 146 

Binocular vision, 398 

Boiler, steam, 191 

Boiling points, definition of, 183 ; 
effect of pressure on, 183 

Boyle's law, stated, 36; explained, 51 

British thermal unit, 152 

Brittleness, 92 

Brooklyn Bridge, 143 

Brownian movements, 52 

Bunsen, 376 

Caisson, 46 

Calories, 152 ; developed by electric 

currents, 289 
Camera, pinhole, 390 ; photographic, 

390 
Candle power, of incandescent lamps, 

285 ; of arc lamps, 286 ; defined, 

375 

Canner, steam-pressure, 184 
Capacity, electric, 240 
Capillarity, 96 ff. 
Capstan, 117 
Carburetor, 198, 199 



466 



466 



INDEX 



Cartesian diver, 43 

Cathode, defined, 248 

Cathode rays, 436 

Cells, galvanic, 245 ; primary, 272 ff.; 
local action in, 272 ; theory of, 
273 ; Daniell, 275 ; Weston, 277 ; 
Leclanche", 277 ; dry, 278 ; com- 
binations of, 279, 280 j storage, 281, 
283 

Center of gravity, 68 

Centrifugal force, 84 

Charcoal, absorption by, 102 

Charles, law of, 136 

Chemical effects of currents, 248 

Cigar lighter, platinum-alcohol, 103 

Ciwrnont, 135 

Clouds, formation of, 174 

Clutch, automobile, 196 

Coefficient of expansion of gases, 136; 
of liquids, 138 ; of solids, 140 

Coefficient of friction, 145 

Cohesion, 92; properties of solids 
depending on, 92 ; in liquids, 93 ; 
in liquid films, 93 

Coils, magnetic properties of, 252 ff. ; 
currents induced in rotating, 294 

Cold storage, 202 

Color, and wave length, 402; of 
bodies, 404 ; compound, 405 ; com- 
plementary, 406 ; of pigments, 40 7; 
of thin films, 408 

Commutator, 298 

Compass, 222. See also Gyrocompass 

Component, 61 ; magnitude of, 62 

Concurrent forces, 60 

Condensation of water vapor, 173 

Condensers, 240 

Conduction, of heat, 203 ; of electric- 
ity, 227 

Conjugate foci, 379 

Conservation of energy, 155 

Convection, 206 ff . 

Cooling, of a lake, 139; by expansion, 
155 ; and evaporation, 176 ; arti- 
ficial, by solution, 187 

Cooper-Hewitt lamp, 288 

Coulomb, 251 

Couple, 112 

Crane, 121 

Cream separator, 85 

Crilley, 46 

Critical angle, 361, 362 

Crookes, 358, 443 ; portrait of, 358 



Curie, 441, 442, 444 ; portrait of, 446 
Currents, wind and ocean, 207 ; elec- 
tric, defined, 245 ; effects of elec- 
tric, 248 ff . ; magnetic fields about, 
252 ; measurement of electric, 
256 ff. ; induced electric, 290 ff. 
Curvature, of a liquid surface, 97 ; 
of waves, 369 ; defined, 370 ; of a 
mirror, 386 ; center of, 463 

Daniell cell, 275 

Davy safety lamp, 205 

Declination, 222 

Densities, table of, 8, 9 

Density, defined, 8; formula for, 9; 
of air, 26 ; maximum, of water, 
138 ; of saturated vapor, 171 ; of 
electric charge, 234 

Descartes, 43 

Dew, formation of, 174 

Dew point, 175 

Dewar flask, 209 

Differential, automobile, 197 

Diffusion, of gases, 50, 52 ; of liquids, 
54 ; of solids, 55 ; of light, 359 

Digester, 184 

Dipping needle, 223 

Discord, 347 

Dispersion, 403 

Dissociation, 249, 273 

Distillation, 185 

Diving bell, 45 

Diving suit, 46 

Doppler effect, in sound, 326 ; in 
light, 416 

Dry cell, 278 

Ductility, 92 

Dynamo, principle of, 290 ; rule for, 
293; alternating-current, 296; four- 
pole direct-current, 300 ; series- 
wound, shunt-wound, and com- 
pound-wound, 301 ; defined, 302 

Dyne, 86 

Eccentric, 191 

Echo, 327 

Edison, 356 ; portrait of, 316 

Efficiency, defined, 147 ; of simple 
machines, 147 ; of water motors, 
148, 149 ; of steam engines; 193 j 
of electric lights, 285 ff. ; of trans- 
formers, 312 

Elasticity, 90 ; limits of, 91 



INDEX 



467 



Electric charge, unit of, 227 ; distri- 
bution of, 233 ; density of, 234 

Electric iron, 269 

Electric motor, principle of, 292 ; 
construction of, 301 ; defined, 302 

Electricity, static, 225 ff. ; electron 
theory of, 229, 438 ff. ; current of, 
244 ff. 

Electrolysis of water, 248 

Electromagnet, 247, 255 

Electromotive force, defined, 263 ; 
of galvanic cells, 266 ; induced, 
291 ; strength of induced, 294 ; 
curve of alternating, 297; curve of 
commutated, 299; back, in motors, 
303 ; in secondary circuit, 307 ; at 
make and break, 308 

Electron theory, 229, 438 ff . 

Electrophorus, 242 

Electroplating, 249 

Electroscope, 227, 232 

Electrostatic voltmeter, 239 

Electrotyping, 250 

Energy, denned, 122 ; potential and 
kinetic, 123 ; transformations of, 

124, 157, 162, 163 ; formulas for, 

125, 126; conservation of, 155; 
from sun, 157 ; expenditure of 
electric, 284 ; stored in atoms, 445 

Engine, steam, 189 ; steam, defined, 
191 ; compound steam, 193, 298 ; 
gas, 191, 194 

English equivalent of metric units, 5 

Equilibrant, 60 

Equilibrium, stable, 69 ; neutral, 71 ; 
unstable, 71 

Erg, 106 

Ether, 367 

Evaporation, 53 ; effect of tempera- 
ture on, 168 ; of solids, 168 ; effect 
of air on, 171, 172 ; cooling effect 
of, 176 ; freezing by, 178 ; effect of 
air currents on, 178 ; effect of sur- 
face on, 179 ; and boiling, 184 

Expansion, of gases, 136 ; of liquids, 
138 ; of solids, 139 ; unequal, of 
metals, 142 ; cooling by, 155 ; on 
solidifying, 165 

Eye, 392 ; pupil of, 392 ; nearsighted, 
393 ; f arsighted, 393 

Fahrenheit, 131 
Falling bodies, 72-78 



Faraday, 251, 290 ; portrait of, 290 

Fields, magnetic, 219 

Films, contractility of, 95 ; color of, 
408 

Fire syringe, 155 

Tireless cooker, 206 

Float valve, 452 , 

Floating dry dock, 448 

Floating needle, 100 

Flotation, law of, 22 

Focal length, of convex lens, 378; 
of convex mirror, 385, 463 

Fog, formation of, 174 

Foley, 387 

Foot-candle, 376 

Force, beneath liquid, 11 ; definition 
of, 57 ; method of measuring, 57 ; 
composition of, 59; resultant of, 
59 ; component of, 61, 62 ; centrifu- 
gal, 84 ; lines of, 218 ; fields of, 219 

Formula for lenses and mirrors, 388 

Foucault, 358 

Foucault currents, 309 

Franklin, 236 ; portrait of , 230 ; kite 
experiment of, 231 

Fraunhofer lines, 414 

Freezing mixtures, 188 

Freezing points, table of, 164 ; of 
solutions, 187 

Friction, 144 ff. 

Frost, formation of, 174 

Fundamentals, denned, 341 ; in pipes, 
349, 350 

Fuse, electric, 269 

Fusion, heat of, 161, 162 

Galileo, 72, 73, 128, 132; portrait 

of, 72 

Galvani, 245 
Galvanic cell, 245 
Galvanometer, 256, 257 
Gas engine, 191, 194 
Gas heating coil, 213 
Gas mask, 103 
Gas meter, 46 ; dials of, 48 
Gay-Lussac, law of, 136 
Geissler tubes, 437 
Gilbert, 225 ; portrait of, 222 
Gliding, principle of, 78-80 
Governor, 192 
Gram, of mass, 4 ; of force, 57 ; of 

force, variation of, 58 
Gramophone, 355 



468 



INDEX 



Gravitation, law of, 66 

Gravity, variation of, 58, 67 ; center 

of, 68 
Guericke, Otto von, 31, 41 ; portrait 

of, 32 

Gun, 354-mm., in action, 73 
Gyrocom^ss, 83, 223 

Hail, formation of, 174 

Hardness, 92 

Harmony, 347 

Hay scales, 120 

Headlight, automobile, 400 

Heat, mechanical equivalent of, 
151 ff. ; unit of, 152 ; produced by 
friction, 153 ; produced by colli- 
sion, 154 ; produced by compres- 
sion, 154 ; specific, 158 ; of fusion, 
161 ; of vaporization, 181 ; trans- 
ference of, 203 

Heating, by hot air, 211 ; by hot 
water, 212 ; by steam, 213 

Heating effects of electric currents, 
284, 289 

Helium, 45, 445 

Helmholtz, 345 

Henry, Joseph, portrait of, 246 

Henry's law, 104 

Hertz, 422, 436 ; portrait of, 102 

Heusler alloys, 216 

Hiero, 21 

Him, 154 

Hooke's law, 91 

Horse power, 122 

Humidity, 175 

Huygens, 364, 372 ; portrait of, 364 

Hydraulic elevator, 18 

Hydraulic press, 17 

Hydraulic ram, 88, 89 

Hydrogen thermometer, 132 

Hydrometer, 23 

Hydrostatic bellows, 447 

Hydrostatic paradox, 14 

Hygrometry, 173 

Ice, manufactured, 201 

Ignition, automobile system of, 198, 
199 

Images, by convex lenses, 378 ff. ; 
size of, 381 ; virtual, 382 ; by con- 
cave lenses, 382 ; in plane mirrors, 
383 ; in convex mirrors, 384, 386 ; 
in concave mirrors, 384, 387 



Imp, bottle, 43 

Incandescent lighting, 285 

Incidence, angle of, 358 

Inclination, 223 

Inclined plane, 63, 117 

Index of refraction, 371 

Induction, magnetic, 216; electro- 
static, 228 ; charging by, 230 ; of 
current, 290 

Induction coil, 308 

Induction motor, 291 

Inertia, 83 

Insect on water, 100 

Insulators, 227 

Intensity, of sound, 326 ; of illumi- 
nation, 374 

Interference, of sound, 333 ; of light, 
365 

Ions, 235, 249, 273 

Iron, electric, 269 

Isoclinic lines, 457 

Isogonic lines, 223 

Jackscrew, 118 

Joule, 106, 122, 151 ff.; portrait of, 122 

Kelvin, portrait of, 134 
Kilogram, the standard, 4 
Kilowatt, 122 
Kilowatt hour, 285 
Kinetic energy, 123, 126 
Kirchhoff, 415 

Laminated cores, 310 

Lamps, incandescent, 285 ; arc, 286 ; 
Cooper-Hewitt, 288 

Lantern, projecting, 391 

Leclanch<* cell, 277 

Lenses, 378 ff . ; optical center of, 378 ; 
principal axis of, 378 ; principal 
focus of, 378 ; formula for, 380 ; 
magnifying power of, 395 ; achro- 
matic, 410 

Lenz's law, 291 

Level of water, 13 

Lever, 110 ff. ; compound, 120 

Leviathan, 135 

Leyden jar, 241 

Liberty motor, 191 

Light, speed of, 357 ; reflection of, 
358 ; diffusion of, 359 ; refraction 
of, 360; nature of, 364; corpuscular 
theory of, 364; wave theory of, 



INDEX 



469 



364; interference of, 365; wave 
length of, 367, 403 ; intensity of, 
374; electromagnetic theory of, 436 

Lightning, 236 

Lightning rods, 236 

Lines, of force, 218 ; isogonic, 223 

Liquids, densities of, 9 ; pressure in, 
13 ; transmission of pressure by, 
15; incompressibility of, 33; ex- 
pansion of, 138 

Liter, 3 

Local action, 272 

Locomotive, 192; Mallet, 123; Kocket, 
123 

Loudness of sound, 326 

Machines, general law of, 116, 124, 

156 ; efficiencies of, 147 
Magdeburg hemispheres, 33 
Magnet, natural, 214 ; laws of the, 

215; poles of the, 215; lifting, 247 
Magnetism, 214 ff. ; nature of, 220 ; 

theory of, 221 ; terrestrial, 222 ; 

residual, 301 
Magnifying power, of lens, 395 ; of 

telescope, 396 ; of microscope, 397 ; 

of opera glass, 398 
Malleability, 92 
Manometric flames, 343 
Marconi, 423 ; portrait of, 316 
Mass, unit of, 4; measurement of, 6 
Matter, three states of, 55 
Maxwell, 436 ; portrait of, 102 
Mechanical advantage, 109 
Mechanical equivalent of heat, 153 ff. 
Melting points, table of, 164 ; effect 

of pressure on, 166 
Meter, standard, 3 
Michelson, 357 ; portrait of, 358 
Microphone, 315 
Microscope, 397 
Mirrors, 383 ff.; convex, 384, 386; 

concave, 384, 387 ; formula for, 388 
Mixtures, method of, 159 
Molecular constitution of matter, 49 
Molecular forces, in solids, 90 ; in 

liquids, 93 
Molecular motions, in" gases, 49, 50 ; 

in liquids, 53 ; in solids, 55 
Molecular nature of magnetism, 220 
Molecular velocities, 52, 129 
Moments of force, 111 
Momentum defined, 84 



Morse, 260 ; portrait of, 260 

Motion, uniformly accelerated, 75 
laws of, 76 ; perpetual, 156 

Motor, Liberty, 191 ; electric-induc- 
tion, 291 ; street-car, 302. See also 
Electric motor 

Motor rule, 293 

Moving pictures, 386 

Newton, law of gravitation, 66 ; laws 
of motion, 83-87 ; portrait of, 84 ; 
principle of work, 116; corpuscular 
theory, 364 

Niagara, 157 

Nichols, E. F., 417 

Nodes, in pipes, 334 ; in strings, 340 

Noise and music, 325 

Nonconductors, of heat, 205 ; of elec- 
tricity, 227 

North magnetic pole, 222 

Ocean currents, 207 

Oersted, 246 ; portrait of, 246 

Ohm, 263 ; portrait of, 268 

Ohm's law, 267 

Onnes, Kamerlingh, 135, 178 

Opera glass, 398 

Optical instruments, 890 ff . 

Organ pipes, 353, 354 

Oscillatory discharge, 422 

Overtones, 341 ; in pipes, 350 

Parabolic reflector, 400 

Parachute, 44 

Parallel connections, 270, 280 

Parallelogram law, 61 

Pascal, 15, 16, 30 

Pendulum, force moving, 64 ; laws 
of, 81 ; compensated, 141 

Periscope, 400 

Permeability, 217 

Perpetual motion, 156 

Perrier, 30 

Phonograph, 355 

Photometers, 374, 376 

Pisa, tower of, 72 

Pitch, cause of, 325 

Pneumatic inkstand, 33 

Points, discharging effect of, 234 

Polarization, of galvanic cells, 274 ; 
of light, 374 

Potential, defined, 237 ; measure- 
ment of, 239, 265 j unit of, 277 



470 



INDEX 



Power, definition of, 121 ; horse, 122 ; 
electric, 284 

Pressure, in liquids, 13 ; defined, 13 ; 
transmission of, by liquids, 15 ; in 
air, 27 ; amount of atmospheric, 
29 ; coefficient of expansion, 133, 
136; effect of, on freezing, 166; of 
saturated vapor, 1 70 ; in primary 
and secondary, 311 

Projectile, path of, 78 

Pulley, 108 ff.; differential, 119 

Pump, air, 33, 41 ; compression, 41 ; 
lift, 42 ; force, 43 

Quality of musical notes, 342 
Quebec Bridge, 70 

E-34, dirigible airship, 44 

Radiation, thermal, 208; invisible, 
417 ff.; and temperature, 418 ; and 
absorption, 419 ; electrical, 421 

Radioactivity, 441 ff. 

Radiometer, 417 

Radium, discovery of, 441 

Rain r formation of, 174 

Rainbow, 411 

Ratchet wheel, 146 

Rayleigh, portrait of, 358 

Rays, infra-red, 417 ; ultra-violet, 
417 ; cathode, 437 ; Rontgen, 439 ; 
Becquerel, 442 ; a:, /3, and 7, 
442 ff. 

Rectifier, tungar, 314 ; crystal, 425 

Reflection, of sound, 327 ; of light, 
358; angle of, 358; total, 361, 
462 

Refraction, of light, 360 ; explana- 
tion of, 368 ; index of, 371 

Refrigerator, 163 

Regelation, 167 

Relay, 260 

Resistance, electric, defined, 262 ; 
specific, 262; laws of, 262; unit of, 
263 ; internal, 268 ; measurement 
of, 269 

Resistances, table of, 262 

Resonance, acoustical, 328 ff.; elec- 
trical, 421 

Resonators, 331 

Resultant, 59 

Retentivity, 217 

Retinal fatigue, 407 

Right-hand rule, 252, 254 



Rise of liquids, in exhausted tubes, 

27 ; in capillary tubes, 97 
Roller bearings, 146 
Romer, 357 

Rontgen, 439 ; portrait of, 446 
Ross, 222 

Rotor, generator, 257 
Rowland, 155 ; portrait of, 358 
Rubens, 408 
Rumford, 151, 374 
Rutherford, 442 ; portrait of, 446 

Saturation of vapors, 169 ; magnetic, 
222 

Scales, musical, 337 ; diatonic, 338 ; 
even-tempered, 339 

Screw, 118 

Sea breeze, 207 

Searchlight, 400 

Secondary cells, 281 ff. 

Self-induction, 307 

Separator, cream, 85 

Series connections, 270, 279 

Shadows, 362 

Shunts, 258, 270 

Singing flame, 348 

Siphon, explanation of, 40; inter- 
mittent, 40 

Siren, 337 

Sleet, formation of, 174 

Snow, formation of, 174 

Soap films, 95, 402 

Solar spectrum, 414, 415 

Sonometers, 339 

Sound, sources of, 319; nature of, 
319 ; speed of, 320 ; musical, 325 ; 
intensity of, 326 ; reflection of, 
327 

Sound foci, 328 

Sound waves, interference of, 333 ; 
photographs of, 346, 387 

Sounder, 260 

Sounding boards, 331 

Spark, oscillatory nature of the, 422 ; 
in vacuum, 436 

Spark length and potential, 240 

Spark photography, 422 

Speaking tubes, 326 

Specific gravity, 9 ; methods of find- 
ing, 22 ff. 

Specific heat, defined, 158; meas- 
ured, 159 

Specific heats, table of, 160 



INDEX 



4T1 



Spectra, 411 ff. ; continuous, 412 ; 

bright-line, 413 ; pure, 414 ; solar, 

414; X-ray, 447 
Spectrum, 403 ; invisible portions of, 

417 

Spectrum analysis, 413 
Speed, of sound, 320 ; of light, 357 ; 

of light in water, 369 ; of electric 

waves, 423 ff. 
Spinthariscope, 443 
Starting box, 304 
Steam engine, 189 ff. 
Steam turbine, 199 
Steelyards, 115 
Stereoscope, 398 
Storage cells, 281, 283 
Strings, laws of, 339 
Sublimation, 168 
Submarine, 23, 44 

Sun, energy derived from, 157 ; spec- 
trum of, 414 
Surface tension, 95 
Sympathetic electrical vibrations, 421 
Sympathetic vibrations of sound, 

346 ff. 

Tank, British, 190 

Telegraph, 259 ff. ; wireless, 423 ff. 

Telephone, 316 ff. ; wireless, 427 ff. 

Telescope, astronomical, 396; Yerkes, 
365, 396, 397 

Temperature, measurement of, 128 ; 
absolute, 134 ; low, 134 

Tenacity, 90 

Thermometer, Galileo's, 128 ; mer- 
cury, 129 ; Fahrenheit, 131 ; gas, 
132-134; alcohol, 132, 134; the 
dial, 143 

Thermos bottle, 209 

Thermoscope, 418 

Thermostat, 142 

Thomson, 438 ; portrait of, 440 

Three-color printing, 408 

Torricelli, experiment of, 28 

Tower, high-tension, 241 

Transformer, 312-314 

Transmission, of pressure, 15 ; elec- 
trical, 312 ; of sound, 321 

Transmission, automobile, 196 

Transmitter, telephone, 316, 317 

Trowbridge, 418 

Tungar rectifier, 314 

Turbine, water, 149 ; steam, 199 



Units, of length, 2 ; of area, 2 ; of 
volume, 2 ; of mass, 4 ; of time, 5 ; 
three fundamental, 5 ; C. G. S., 6 ; 
of force, 57, 86 ; of work, 106 ; of 
power, 122, 284 ; of heat, 152 ; of 
magnetic pole, 215 ; of magnetic 
field, 219 ; of current, 251, 257 ; 
of resistance, 267 ; of potential, 
277 ; of light, 375, 376 

Vacuum, sound in, 320; spark in, 
436 

Vaporization, heat of, 181, 182 

Velocity, of falling body, 75; of 
sound, 320 ; of light, 357 

Ventilation, 210, 211 

Vibration, forced, 331 ; of strings, 
339 ; sympathetic, 346 ff. 

Vibration numbers, 337 

Vision, distance of most distinct, 
394 ; binocular, 398 

Visual angle, 394 

Volt, 239, 277, 294 

Volta, 245 ; portrait of, 240 

Voltmeter, electrostatic, 239; com- 
mercial, 265, 266 

Watch, balance wheel of, 141 ; wind- 
ing mechanism of, 453 

Water, density of, 4 ; city supply of, 
19 ; maximum density of, 138 ; ex- 
pansion of, on freezing, 166 

Water wheels, 148-150 

Watt, 122, 284 

Watt, James, 122, 189 ; portrait of, 
122 

Watt-hour meter, 304 

Wave length, defined, 322 ; formula 
for, 323 ; of yellow light, 367 ; of 
other lights, 403 

Wave theory of light, 364 

Wave train, 322, 424, 425 

Waves, condensational, 323 ; water, 
324 ; longitudinal and transverse, 
325 ; light, are transverse, 371 ; 
electric, 422 ; modulated, 427 

Weighing by method of substitu- 
tion, 6 

Welsbach mantle, 442 

Weston cell, 277 

Wet- and dry-bulb hygrometer, 178 

Wheel, and axle, 116; gear, 119; 
worm, 119 ; water, 148-160 



472 INDEX 

White light, nature of, 403 X-ray picture of human thorax, 359 

Wind instruments, 349 X-ray spectra, 440, 447 

Windlass, 120, 453 X-rays, 439 ff. 

Winds, 207 

Wireless telegraphy, 423 ff. Yale lock, 452 

Wireless telephony, 427 ff . Yard, 2 

Work, defined, 105 ; units of, 106 ; Yerkes telescope, 365, 396, 397 

principle of, 116, 125, 156 

Wright, Orville, 317 ; portrait of, 316 Zeiss binocular, 399 



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