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
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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
< '
f ! i
- 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
i .2! r
w w ^
G S %
o>^ 2^ e
C ,-
o> a
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
Ill
*-
ai*
s
tograph by
pitch of fr
tions are t
ving photi
_ * * o
II 5 a
ag >
;
,
*
? e
C-B g
a ^ .
mi;s
fli O ir m ^ I>,T!
K89r||J
_ O m OJ EC '3
-2 J2 o '3
ij'rflH
"^ 3* C A ** ^
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
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; 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
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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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