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TWENTIETH CENTURY TEXT-BOOKS
LORD KELVIN (SIR WILLIAM THOMSON) (1824-19GT)
William Thomson ranks as one of the two or three greatest
physicists of the nineteenth century. He was born in Ireland, but
spent nearly his entire life in Glasgow, Scotland, where his father
was professor of mathematics. At the early age of seventeen he
began to write on mathematical subjects, but his attention was soon
turned to the study of physics. In 1846 he became professor of
natural philosophy at Glasgow, where he remained fifty-three years.
Thomson's early investigations led to the invention of the abso-
lute scale of temperature. Important experiments in heat were
carried out by him in collaboration with Joule from 1852-1862.
Later Thomson became almost universally known by his work
as electrician of the Atlantic cables, the first of which was laid in
1858. By the invention of the well-known mirror galvanometer
which he used in receiving messages, he increased the rate of trans-
mission from two or three to about twenty-five words per minute.
This instrument was replaced later by his " siphon recorder," which
is still in use.
Thomson was instrumental in establishing the practical system of
electrical units. He invented the absolute and quadrant electrome-
ters for measuring potentials, a sounding device for use on moving
ships, and many other practical measuring instruments. His favorite
subject, however, was the nature of the ether, which, as he said,
claimed his attention daily for over forty years. His writings are
included in his Papers on Electrostatics and Magnetism, Mathemat-
ical and Physical Papers, Popular Lectures and Addresses, and
Thomson and Tait's An Elementary Treatise on Natural Philosophy.
TWENTIETH CENTURY TEXT-BOOKS
A HIGH SCHOOL COURSE
IN PHYSICS
BY
FREDERICK R. GORTON, B.S., M.A., PH.D.
ASSOCIATE PROFESSOR OF PHYSICS, MICHIGAN
STATE NORMAL COLLEGE
or -HE
UNIVERSITY
D. APPLETON AND COMPANY
NEW YORK CHICAGO
1910
COPYRIGHT, 1910, BY
D. APPLETON AND COMPANY.
oe.
PREFACE
PHYSICS is the summary of a part of human experience. Its devel-
opment has resulted from the fact that its pursuit has successfully
met human needs. Hence it is believed that the presentation of the
subject in the secondary school should be the expansion of the every-
day life of the pupil into the broader experience and observation of
those whose lives have been devoted to the study. Human activity
and progress, therefore, should be the teacher's guiding principle,
and the bearing of each phenomenon and law on the interests of
mankind should be clearly disclosed and emphasized. The author
of this book has accordingly endeavored to give great prominence
to facts of common observation in the derivation of physical laws,
and, further, has attempted to point out plainly the service that has
been afforded mankind by a knowledge of nature's laws. No text-
book, however, can take the place of the skilled teacher in showing
clearly the relation of physical phenomena to human activities, or in
the selection of illustrative examples within the range of observation
of his pupils.
Large portions of the subject-matter of Physics deal with knowl-
edge already possessed by a pupil of high-school age, and nothing
is of more appealing interest to him than the feeling that this infor-
mation is to be made of some value. By recalling phenomena well
within the acquaintance of the pupil and supplementing them with
demonstrative experiments, the way is easily paved to the deduction
and interpretation of general principles. In the presentation of such
experiments, the author has described as simple and inexpensive
apparatus as he has found to be consistent with satisfactory results.
No effort has been spared to give the teacher and pupil every pos-
sible assistance. The sections have been plainly set off and given
suggestive headings ; references to related material have been inserted
where needed; and the numerous sets of exercises have been care-
v
209710
yi PREFACE
fully graded. In order to bring the problems near the discussions
upon which their solutions depend, they have been arranged in more
and smaller groups than is usual. The exercises throughout the
book have been selected from concrete cases, and the usual problems
in pure reductions have been omitted. Illustrative solutions of prob-
lems and suggestions have been given wherever difficulties have been
found to arise. As an aid to the pupil in reviewing and to the
teacher in conducting rapid drill exercises, a summary of the contents
of each chapter is presented at its conclusion.
The educational value of the portraits and biographical sketches
of many of the great men of science is at once apparent. Emphasis
upon the parts that these men have played in the development of
Physics has been recognized by eminent educators as an important
factor in creating an atmosphere of human interest around the sub-
ject. These names should become familiar to every student of Physics.
On account of the rapid advance at the present time in the practi-
cal uses made of physical principles, the author believes that the
sections involving new applications will be found of general interest
and utility.
The book will be found to be free from the more difficult uses
of algebraic and geometric principles. The place of first importance
has been given to the study of phenomena, and mathematical expres-
sions have been introduced as convenient means of designating exact
relations which have been previously interpreted. It is mainly in the
subject of Physics that the pupil is brought to realize the value
of his mathematical studies in the world of concrete quantities.
The author believes that the class-room work in the subject should
be accompanied by a sufficient number of individual laboratory exer-
cises to fix clearly in mind great principles and important phenomena.
Further, enough practice with simple drawing instruments should
be given to enforce the use of the simplest geometrical relations.
In addition to the many subjects whose treatment is demanded by
the achievements of recent times, the author has given careful atten-
tion to the various topics recommended by the Committee of Second-
ary School Teachers to the College Entrance Examination Board.
The author desires to acknowledge here the many helpful sugges-
tions of those who have read and criticised the proof or manuscript, and
PREFACE vii
wishes especially to mention Professor E. A. Strong of the Michigan
State Normal College ; Mr. Fred R. Nichols of the Richard T. Crane
Manual Training High School, Chicago, 111. ; Mr. Frank B. Spaulding
of the Boys' High School, Brooklyn ; Mr. Albert B. Kimball, Princi-
pal of the High School, Fairhaven, Mass. ; Professor Karl E. Guthe
of the University of Michigan; Mr. George A. Chamberlain, Prin-
cipal of East Division High School, Milwaukee; and Mr. J. M.
Jameson of the Pratt Institute, Brooklyn, N.Y.
CONTENTS
CHAPTER I
PAGE
/ INTRODUCTION 1
CHAPTER II
MOTION, VELOCITY, AND ACCELERATION
1. Uniform Motions and Velocities 13
2. Uniformly Accelerated Motion 16
3. Simultaneous Motions and Velocities . . .21
Summary ...... 26
CHAPTER III
LAWS or MOTION FORCE
1. Discussion of Newton's Laws 28
2. Concurrent Forces 35
3. Moments of Force Parallel Forces .... 39
4. Resolution of Forces 42
5. Curvilinear Motion ........ 44
Summary .......... 48
CHAPTER IV
WORK AND ENERGY
1. Definition and Units of Work 51
2. Activity, or Rate of Work 53
3. Potential and Kinetic Energy . . . . .54
4. Transitions of Energy 58
Summary .......... 61
CHAPTER V
GRAVITATION
1. Laws of Gravitation and Weight 62
2. Equilibrium and Stability 65
ix
X CONTENTS
PAGK
3. The Fall of Unsupported Bodies ... . . .69
4. The Pendulum 74
Summary . . . . . . .81
CHAPTER VI
MACHINES
1. General Law and Purpose of Machines .... 83
2. The Principle of the Pulley . . . . . .85
3. The Principle of the Lever 88
4. The Principle of the Wheel and Axle . . .93
5. The Inclined Plane, Screw, and Wedge . . . . 96
6. Efficiency of a Machine . - . . . 99
Summary 101
CHAPTER VII
MECHANICS OF LIQUIDS
1. Forces Due to the Weight of a Liquid . . . .103
2. Force Transmitted by a Liquid . . . . Ill
3. Archimedes' Principle . 119
4. Density of Solids and Liquids . . . . . . 124
5. Molecular Forces in Liquids . . . . . . 130
Summary .......... 135
CHAPTER VIII
MECHANICS OF GASES
1. Properties of Gases . . . . . . . 138
2. Pressure of the Air against Surfaces .... 139
3. Expansibility and Compressibility of Gases . . . 147
4. Atmospheric Density and Buoyancy .... 153
5. Applications of Air Pressure ...... 155
Summary . . . . . . . . . . 163
CHAPTER IX
SOUND: ITS NATURE AND PROPAGATION
1. Origin and Transmission of Sound 165
2. Nature of Sound 169
3. Intensity of Sound 173
4. Reflection of Sound 176
Summary .......... 177
CONTENTS xi
CHAPTER X
PAGE
SOUND: WAVE FREQUENCY AND WAVE FORM
1. Pitch of Tones 179
2. Resonance . . . 185
3. Wave Interference and Beats . . * . . .188
4. The Vibration of Strings 192
5. Quality of Sounds 196
6. Vibrating Air Columns 198
Summary .......... 205
CHAPTER XI
HEAT : TEMPERATURE CHANGES AND HEAT MEASUREMENT
1. Temperature and its Measurement ..... 208
2. Expansion of Bodies . .216
3. Calorirnetry, or the Measurement of Heat . . . 225
Summary .......... 229
CHAPTER, XII
HEAT : TRANSFERENCE AND TRANSFORMATION OF HEAT ENERGY
1. Change of the Molecular State of Matter . . . 231
2. The Transference of Heat 247
3. Relation between Heat and Work 256
Summary . . . . . . . . . 265
CHAPTER XIII
LIGHT : ITS CHARACTERISTICS AND MEASUREMENT
1. Nature and Propagation of Light 268
2. Rectilinear Propagation of Light 270
3. Intensity and Candle Power of Lights .... 274
Summary 277
CHAPTER XIV
LIGHT : REFLECTION AND REFRACTION
1. Reflection of Light 278
2. Reflection by Curved Mirrors 284
3. Refraction of Light 292
xii CONTENTS
PAGE
4. Lenses and Images 300
5. Optical Instruments 311
Summary 318
CHAPTER XV
LIGHT: COLOR AND SPECTRA
1. Dispersion of Light : Color 321
2. Spectra 324
3. Interference of Light . 330
Summary . . . . . . 333
CHAPTER XVI
ELECTROSTATICS
1. Electrification and Electrical Charges .... 335
2. Electric Fields and Electrostatic Induction . . . 340
3. Potential Difference and Capacity 346
4. Electrical Generators 352
Summary .......... 356
CHAPTER XVII
MAGNETISM
1. Magnets and their Mutual Action . . . I 359
2. Magnetism a Molecular Phenomenon . . . 365
3. Terrestrial Magnetism ....... 368
Summary . . . . . . . . . 372
CHAPTER XVIII
VOLTAIC ELECTRICITY
1. Production of a Current Voltaic Cells .... 374
2. Effects of Electric Currents . . . . . . 388
Summary .......... 400
CHAPTER XIX
ELECTRICAL MEASUREMENTS
1. Electrical Quantities 'and Units ..... 402
2. Electrical Energy and Power ...... 413
3. Computation and Measurement of Resistances . . 417
Summary . . . . . . . . . . 422
CONTENTS xiii
CHAPTER XX
PAGE
ELECTRO-MAGNETIC INDUCTION
1. Induced Currents of Electricity 425
2. Dynamo-Electric Machinery 432
3. Transformation of Power and Its Applications . . 442
4. The Telegraph and the Telephone 453
Summary 460
CHAPTER XXI
RADIATIONS
1. Electro-magnetic waves 462
2. Conduction of Gases ....... 466
3. Radio-activity 468
INDEX , 473
LIST OF PORTRAITS
Lord Kelvin (Sir William Thomson) . . . Frontispiece
FACING PAGE
Sir Isaac Newton 30
Galileo Galilei 70
Hermann von Helmholtz . . . . . . . . 196
Count Rumford (Sir Benjamin Thompson) .... 256
James Prescott Joule 258
Benjamin Franklin 346
Count Alessandro Volta . . . . . . . .352
Hans Christian Oersted ........ 382
Dominique Francois Jean Arago ...... 382
Andre Marie Ampere . . . 406
George Simon Ohm 406
Michael Faraday 426
Joseph Henry 426
James Clerk-Maxwell 432
Heinrich Hertz 464
Sir William Crookes 466
Wilhelm Konrad Rontgen . . . . . . .466
Antoine Henri Becquerel . . . . . . . 470
Madame Curie . ......... 470
CHAPTER I
INTRODUCTION
iX
1. Physics. In the experiences of everyday life we
witness a great variety of changes in the things around us.
Objects are moved, melted, evaporated, solidified, bent,
made^hot or cold, and undergo a change in their condi-
tion, place, or shape in a great many other ways. Physics
is the science that treats of the properties of different sub-
stances and the changes that may take place within or
between bodies, and it investigates the conditions under
which such changes occur.
yin its broadest sense Physics is the science of phenom-
ena. Every action of which we become aware through
the senses is a phenomenon. We hear the rolling thunder,
we see the shining of a live coal, we taste the dissolving
sugar, we smell the evaporating oil, and we feel moving
air. By considering his own experience the student will
be able to recall numerous examples of physical phe-
nomena and to state the sense by means of which he per-
ceives each of them.
>^ The study of physics, however, not only directs our
attention to the phenomena to which we are accustomed,
but to a multitude of m'ore unusual but not less important
ones. It also strives to put these phenomena to experi-
mental tests that will enable us to understand the laws
connecting actions with their causes.
2. Utility of the Study of Physics. Increasing acquaint-
ance with nature and naturaj_Jaw has been the means of
2 ~T"
2 A HIGH SCHOOL COURSE IN PHYSICS
elevating man from the life_of limited power and useful-
ness of the savage to his condition of present-day enlight-
enment. The early discovery of fire was a great step
toward civilization. By some crude experimental study it
was found later that fire could be produced at will, as by
the striking of flint and by rubbing two pieces of dry wood
together. Thus the observation of simple natural phe-
nomena enabled man to secure heat for cooking his food
and warming his habitation, besides aiding him in forming
implements to procure food, improve his shelter, and give
him protection from enemies.
This same observation of natural phenomena has pro-
duced every existing artificial device for our protection,
convenience, and comfort. The engineer who plans a rail-
road, with its bridges, tunnels, and grades, together with
the locomotive and its train, makes use at every step of
knowledge acquired through the study of Physics. The
surveyor ascertains how to cut through the hills and fill
the valleys by the use of instruments which involve physi-
cal principles. By the discovery and application of physi-
cal laws scientists and inventors have produced the tel-
escope, telephone, steam engine, electric car, and all the
other useful appliances which form so important a part of
our everyday life.
3. Matter. There are three general characteristics by
which matter is recognized.
(1) Matter always occupies space. On this account it
is said to possess the property of extension. Many invisi-
ble bodies of matter exist. The air in a bottle or tumbler
is such a body. We may show, however, by the following
experiment that it is as real as any other body:
1. Place a piece of cork upon the surface of water in a vessel, cover
it with an inverted tumbler, and force the tumbler deep into the
water as in Fig. 1. The air that was in the tumbler still occupies
INTRODUCTION 3
nearly all of that space, and the water is not allowed to rise and
fill it.
(2) All matter is indestructible, in the sense that it has
never been discovered that the small-
est portion can be annihilated by any
process known to man. Causing a
body, as a piece of coal, to disappear
by burning does not destroy the ma-
terial of which it is composed. A
portion is carried away in the smoke
and gases, and the remainder left be- Fia - i. inverted Tumbler
. . , & . ' Nearly Full of Air.
hind in the ash produced. In the
process of evaporation a drop of water becomes invisible ;
but the matter still exists in the atmosphere as a trans-
parent vapor.
(3) All matter has weight, i.e. is attracted by the
earth. In a more general sense it may even be said that
every body has an attraction for, or pulls upon, every
other body. The term gravitation is used to express this
characteristic of matter.
The fact that air possesses weight as well as extension
may be shown by experiment as follows :
2. Remove the brass fixture from an incandescent lamp bulb, and
carefully balance the bulb on a sensitive beam balance. Introduce a
short nail into the stem of the bulb, and tap lightly with a hammer
until the glass is broken and air admitted. If the bulb is now placed
upon the balance, a decided increase in weight will be observed.
The weight of air admitted has been added to that of the bulb, which
originally contained almost no air.
The quantity of matter in a body is called its mass. Dif- j
ferent kinds of matter, as gold, water, glass, air, mercury, <
salt, hydrogen, etc., are called substances. Substances are
recognized by their properties; as, hardness, elasticity,
tenacity, fluidity, transparency, etc.
4 A HIGH SCHOOL COURSE IN PHYSICS
4. Measurement of Quantities. A little reflection will
show the necessity of having systems of measurement for
the various quantities that we find in nature, such as
length, area, volume, weight, time, etc. The importance
of such systems has been recognized by the governments
of civilized countries, and the values of the units employed
have been fixed by law. Thus the foot, pound, second,
etc., are well-established units of quantity, and are in gen-
eral use throughout Great Britain and the United States.
The English system of measurement, however, is objec-
tionable on account of the inconvenient relations between
the units and their multiples and divisions. For example,
1 pound = 16 ounces = 7000 grains ; or 1 mile = 320 rods
= 5280 feet = 63,360 inches. It is mainly for this reason
that many countries have adopted the metric system of
measurement, in which the relations are always to be
expressed by some power of ten. This system greatly re-
duces the effort required in making correct computations. 1
Since in the United States both the English and the
metric system are employed, it will be advisable to be-
come proficient in the use of each.
5. Measures of Extension. Every body occupies space
of three dimensions : length, breadth, and thickness ; but
each of these is simply a length, the metric unit of which
is the meter. The meter is the distance between two
transverse lines ruled on a platinum-iridium bar kept in
thje Archives at Sevres, near Paris. 2 On account of the
1 Congress recognized the desirability of introducing the metric system
as early as 1866. See Congressional Globe, Appendix, Part 5, p. 422,
Chap. CCCI : An act to authorize the use of the metric system of weights
and measures. By this act the yard is defined as f ff$ of a meter.
2 The meter was originally intended to be one ten-millionth of the dis-
tance from the equator to the north pole. Accurate copies of the meter
and other metric units are kept in the U. S. Bureau of Standards at
Washington, D.C..
INTRODUCTION 5
changes in the length of the bar with variations of tem-
perature, the distance must be taken when the bar is at
the temperature of freezing water. The multiples and
divisions of the meter are designated by prefixes signify-
ing the relations which they bear to the unit. The multi- .
pies have the Greek prefixes, deka (ten), hecto (hundred),
kilo (thousand), and myria (ten thousand). The divisions
have the Latin prefixes, deci (tenth), centi (hundredth),
and milli (thousandth). The relations are shown in the
following table :
METRIC TABLE OF LENGTH
1 A myriameter equals 10,000 meters.
A kilometer (km.) equals 1,000 meters.
1 A hectometer equals 100 meters.
1 A dekameter equals 10 meters.
A decimeter 1 (dm.) equals 0.1 of a meter.
A centimeter (cm.) equals 0.01 of a meter.
A millimeter (mm.) equals 0.001 pf a meter.
The most important equivalents in the English system
are the following :
1 meter (m.) equals 39.37 inches, or 1.094 yards.
2 1 centimeter equals 0.3937 of andnch.
1 kilometer equals 0.6214 of a mile.
The metric equivalents most frequently used are :
1 yard equals 91.44 centimeters, or 0.9144 m.
2 1 inch equals 2.540 centimeters.
1 mile equals 1.609 kilometers.
The relative sizes of the inch and the centimeter are
shown in Fig. 2.
Because the meter is too large for general use in Physics,
the centimeter has been chosen as the unit. The centimeter
and the gram, which is the metric unit of mass, and the
second as a time unit, are together the fundamental units
1 Seldom used. 2 To be memorized.
A HIGH SCHOOL COURSE IN PHYSICS
Fia. 3. Relative
Sizes of the Square
Inch and Square
Centimeter.
of the so-called centimeter -gram- second (C. G. S.) system
of measurement which is in use throughout the world in
scientific work.
s 6. Surface Measure. The unit of sur-
L- ^ face, or area, in the C.
G. S. system is the square
centimeter (cm. 2 ). It is
the area of a square whose
edge is one centimeter in
length. One square
~ OT inch is thus obviously
equal to (2.540) 2 , or
6.4516 square centi-
meters. The relative
sizes of these two units are shown in Fig. 3.
7. Cubic Measure. The unit of volume
in the C. G. S. system
is the cubic centimeter
(cm. 3 ). This unit is
defined as the vol-
ume of a cube whose
^ edge is one centi-
meter in length.
One cubic inch thus
equals (2.540) 3 , or
16.387 cubic centi-
meters. The relative
o sizes of these units are shown in Fig. 4.
FIG. 2. Showing g. Measures of Capacity. The unit of
the Relative Sizes ._, ,- 7 ..
of the English capacity in the metric system is the liter
inch and the Met- (pronounced lee'ter*), which is equal in
ric Centimeter. . , . , . .* -,
size to a cubic decimeter, or one thousand
cubic centimeters. The liter is somewhat larger than the
liquid quart and smaller than- the dry quart. More pre-
CO
<N
FIG. 4. Relative Sizes
of the Cubic Inch and
Cubic Centimeter.
INTRODUCTION . 7
cisely, a liter equals 1.057 liquid quarts and 0.908 of a
dry quart. Multiples and divisions of the liter are des-
ignated by the prefixes explained in 5, but are little
used in ordinary physical measurements.
EXERCISES
1. The distance from Detroit to Chicago is 280 mi. What is the
metric equivalent of this distance ?
2. Which is the lower price for silk, $1 per yard or $1.10 per meter ?
How much is the difference ?
3. A tourist while in Paris pays the equivalent of 50 ct. per meter
for cloth worth 40 ct. per yard. How much is the loss on a purchase
of 20 m.?
4. If the cost of water is 10 ct. per thousand gallons, what is the
equivalent cost per cubic meter? (1 gal. = 231 cu. in.)
5. How much dearer in Germany is oil costing the equivalent of
5 ct. per liter than the same in the United States at 15 ct. per gallon?
Express the result in cents per gallon.
6. How much more cloth will $1 buy at 20 ct. per meter than
at 18 ct. per yard when the width is 30 in. ? Express the result in
square inches.
7. If a railroad ticket in France costs the equivalent of $19.50 per
thousand kilometers, what is the rate per mile?
8. If illuminating gas in Germany is sold at the equivalent of
3.5 ct. per cubic meter, what is the corresponding price per thousand
cubic feet ?
9. Measures of Mass. The unit of mass in the metric
system is the kilogram, and in the C. G. S. system, the
gram. The gram-mass is the one-thousandth part of the
mass of a standard platinum-iridium cylinder preserved in
the Archives of France. The entire mass of this cylinder
is one kilogram (abbreviated to kilo, pronounced kee'lo).
This standard kilogram was intended to be equal to the
mass of one thousand cubic centimeters, or one liter, of
pure water; in fact, it may be considered so without ap-
preciable error.
This relation between mass and volume in the metric
8 A HIGH SCHOOL COURSE IN PHYSICS
system is of great convenience in physics. Since one
cubic centimeter of water has a mass of one gram, if we
FIG. 5. Relation of the Unit of Mass to the Unit of Volume.
know the mass in grams of a certain volume of water, the
volume also is known, and vice versa. (See Fig. 5.)
METRIC TABLE OF MASS
1 A myriagram equals 10,000 grams (g.).
A kilogram (kg.) equals 1,000 grams.
1 A hectogram equals 100 grams.
1 A dekagram equals 10 grams.
A decigram (dg.) equals 0.1 of a gram.
A centigram (eg.) equals 0.01 of a gram.
A milligram (mg.) equals 0.001 of a gram.
The English unit of mass used in Physics is the avoir-
dupois pound containing 7000 grains and denned as being
2~23T6 f a kilogram. Its multiple is the ton, or 2000
pounds ; its divisions, the ounce and the grain.
The English and metric equivalents most frequently
used are as follows :
1 pound is equal to 453.59 grams.
1 ounce is equal to 28.35 grams.
2 1 kilogram is equal to 2.20 pounds.
1 gram is equal to 15.43 grains.
1 Seldom used. 2 To be memorized.
INTRODUCTION 9
EXERCISES
1. Express the mass of a cubic inch of water in grams.
2. What is the mass of a cubic decimeter of water in pounds ?
3. Sugar at 6 ct. per pound costs how much per kilogram ?
4. A cubic centimeter of mercury has a mass of 13.6 g. Find the
mass of a cubic inch of mercury in ounces. Ans. 7.86 oz.
5. How many pounds are there in a cubic foot of water?
6. How many grams of water will be required to fill a rectangular
vessel measuring 20 x 25 x 30 cm. ? Reduce to pounds.
7. One cubic centimeter of iron has a mass of 7.5 g. Find the
mass of an iron plate 150 cm. square and 2 mm. thick.
8. An empty flask weighs 100 g. ; when filled with water, the entire
mass is 365 g. What is the capacity of the flask ?
9. If the mass of a given volume of gold is 19 times that of an
equal volume of water, what is the mass of 25 cm. 3 of gold? What is
the volume of a gold body whose mass is 10 g. ?
10. Mass Distinguished from Weight. Mass and weight
must not be regarded as synonymous terms. If it were
not for the fact that any two masses attract each other
( 3), we should have little use for the word weight.
This attraction between common bodies is beyond our
power to detect by ordinary means, because it is so slight.
When, however, one of the attracting bodies is massive,
as the earth, and the other is some object, as a stone, the
attraction is great enough to be easily perceived as we
try to support or lift the smaller body. This downward
putt of the earth upon the stone is called the weight of the
stone. The weight, or earth-pull, of a body changes when
it is taken to a different latitude, or is elevated above, or
lowered beneath, the surface of the earth ( 68). It is
therefore obvious that the weight of a body may change
while the quantity of matter in it, i.e. its mass, remains
the same.
11. Processes of Weighing. Since equal masses are at-
tracted equally by the earth at any given place, weighing
10
A HIGH SCHOOL COURSE IN PHYSICS
FIG. 6. A Dyna-
mometer or Spring
Balance.
;^
offers one of the most convenient and accurate means for
comparing masses; thus, to make one mass equal to
another, we have only to adjust the
Co) quantity of each until they stretch the
spring of a dynamometer, Fig. 6, equally;
or, as we say, " weigh alike " when
placed on any weighing device. The
usual process of determining the mass
of a body
consists in
placing it
upon one
pan of a
beam balance, Fig. 7, and
known masses, called
"weights," upon the other pan
until the two balance. The
sum of the known masses used
gives the mass of the body. Such known masses, ranging
from one milligram up to several hundred grams, consti-
tute a so-called "set of weights."
12. Density. Everyday experience teaches us that
bodies may have the same size and yet differ greatly in
weight. A bar of iron, for example, is much heavier
than a bar of wood of the same dimensions, because its
mass is much greater. The substances are said to differ
in density. The density of a substance is measured by the
number of units of mass contained in a unit of volume.-
Thus in the C. G. S. system it is expressed as the number
of grams per cubic centimeter; in the common, or foot-
pound-second (F. P. S.), system, by the number of pounds
per cubic foot. For example, the density of lead is 11.36
grams per cubic centimeter (abbreviated 11.36 g./crn. 3 ).
FIG. 7. A Beam Balance.
INTRODUCTION
EXERCISES
1. Find the density of a liquid of which a liter has a mass of 850 g.
2. If the volume of a piece of glass whose mass is 10 g. is 3.9 cu.
cm., what is the density of the glass ?
3. The density of mercury is 13.6 g./cm. 8 Calculate the mass of
mercury that can be contained in a vessel whose capacity is 30 cm. 8
4. If mercury is 90 ct. per pound, what will half a liter cost?
5. A vessel will hold 500 g. of mercury. How many grams of water
will bb required to fill it ?
6. The diameter of a steel sphere is 4 cm. If the density of steel
is 7.8 g./cm. 3 , what is the mass of the sphere? Volume of a sphere
13. States of Matter. Matter admits of being sepa-
rated into three classes according to its ability to preserve
(1) its shape and volume, (2) its volume only, or
(3) neither its shape nor volume. A body that retains
both its shape and volume is called a solid; one that re-
tains its volume only and shapes itself to the vessel con-
taining it, a liquid; while one that occupies completely
any vessel in which it is placed, retaining neither form
nor size, is called a gas. Ice, water, and steam are exam-
ples of the same substance in the three states.
14. Time. All systems of measurement of time, used
in Physics, employ the interval called the mean solar second
as the unit. It is -gg-g^ of a mean solar day, the average
length of time intervening between two successive transits
of the sun's center across a meridian.
SUMMARY
1. Physics is the science of phenomena ( 1).
2. Matter is always recognized by its properties of ex-
pansion, indestructibility, and weight. Different kinds of
matter gold, water, air, etc., are recognized by their
properties; i.e. hardness, fluidity, etc. ( 3).
12 A HIGH SCHOOL COURSE IN PHYSICS
3. The quantity of matter in a body is called its mass.
4. There are two well-known systems of measurement
for the quantities of length, area, volume, time, etc., viz.
the English system and the metric system ( 4).
5. The units of the metric system are the centimeter,
gram, and second. This system is the more generally
used for scientific work. It is called the centimeter-
gram-second (C. G. S.) system ( 5).
6. Units of the English system are the foot, pound, and
second. This system is therefore called the foot-pound-
second (F. P. S.) system ( 12).
7. The terms mass and weight have not the same
meaning. The weight of a body refers to the downward
pull of the earth upon the body. The mass of a body
may remain constant, while the weight varies with the
latitude, the altitude above the earth's surface, and the
depth to which it may be lowered into the earth ( 10).
8. Masses are measured and compared by the process
of weighing ( 11).
9. The density of a substance is measured by the num-
ber of units of mass contained in a unit of volume ( 12).
10. Matter may be divided into three classes according
to its ability to preserve (1) its shape and volume, (2) its
volume only, or (3) neither its shape nor volume. Thus
bodies are classed as solids, liquids, and gases ( 13).
CHAPTER II
MOTION, VELOCITY, AND ACCELERATION
, l. UNIFORM MOTIONS AND VELOCITIES
15. Motion and Rest ~ Relative Terms, The position of
a body at any instant is defined by its direction and dis-
tance from some other body which is usually conceived as
being fixed, or at rest*. Motion is a continuous change in
the position of a body. It is customary to think of the
earth as the fixed body when we speak of the motion of a
train, a bird, a cloud, etc. Again, a passenger sitting in
a moving railway coach is in the condition of rest with
respect to the train, while with respect to the earth the
same person is in rapid motion. Even the earth, as we
know, is not at rest; it not only rotates on its axis, but
travels with great speed in its orbit around the sun.
Hence a body at rest with respect to the earth is not actu-
ally at rest, nor is its motion with respect to the earth
the actual motion. However, when no statement is made
to the contrary, the earth is regarded as the body to which
the motion of an object is referred*
16. Path of a Moving Body. The line described by a
small moving body is called its path. When the path
described is a straight line, the motion is rectilinear ; when
curved, the motion is curvilinear. Let us first consider
cases of rectilinear motion,
17. Uniform Rectilinear Motion, If a moving body de-
scribes equal portions of its path in equal intervals of time,
no matter how small the intervals may be, its motion is uni-
form. In other words, uniform motion is the motion of a
13
14 A HIGH SCHOOL COURSE IN PHYSICS
body when the distance passed over is proportional to the
time occupied. In the case of uniform rectilinear motion
the velocity, or rate of motion, of the moving body is con-
stant in both magnitude and direction, and is measured by
the distance which the body travels per second, per minute,
per hour, etc.; for example, 10 centimeters per second
(abbreviated 10 cm. /sec.), 25 miles per hour, etc.
18. Equation of Uniform Motion. From 17 it can easily
be seen that the entire distance passed over by a body having
uniform motion can be found by multiplying the velocity by
the time. Thus, if the velocity is 20 cm. /sec., the distance
passed over in five seconds is 5 x 20, or 100, centimeters.
This relation between the distance d, the velocity v, and
the time t is conveniently expressed by the equation
d=vt. (l)
19. Representation of a Motion. In describing com-
pletely the rectilinear motion of a body, the following
characteristics must be given: (a) the starting point,
(5) the direction, and (e) the distance traveled. It will
be observed that a straight line, since it has origin, direc-
tion, and length, is capable of representing the three char-
acteristics of rectilinear motion. Hence the line AB,
Fig. 8, drawn from the point A a distance of 4 centimeters
to the right may be used to
d , represent the three qualities
FIG. 8. Representation of a of the motion of a body 4
miles in an easterly direction
from the place represented by the point A. By letting a
centimeter represent 5 miles the same line will represent
the characteristics of the rectilinear motion of a body over
a distance of 20 miles. Thus any convenient scale may
be used, but the same scale should, of course, be used
throughout a given problem.
MOTION, VELOCITY, AND ACCELERATION 15
20. Average Velocity. Absolute uniform motion is of
very rare occurrence, except during exceedingly small in-
tervals of time^ For instance, a train on leaving a station
starts slowly and gains in speed until it acquires the veloc-
ity with which it can follow schedule time. It would be
practically impossible for the engineer so to regulate the
throttle as to maintain an absolutely constant velocity, in-
asmuch as the resistance due to the track, curves, wind,
etc., would vary from time to time. "* Finally the throttle
is closed, the brakes applied, and the ti j ain comes gradually
to rest. Although the velocity has changed greatly, the
train has passed over a certain distance in a definite time;
let us say 30 miles in 40 minutes. The train has moved
just as far as it would have traveled with a uniform
velocity found by dividing the total distance by the time
consumed, i.e. -| of a mile per minute. This is called the
average velocity of the train for the time under considera-
tion. From this explanation it is obvious that equation
(i) will hold for motions that are not uniform, provided
v is the average velocity for the time t.
21. Velocity at Any Instant. If we examine the motion
of all the objects with which we are familiar, we shall find,
as in the case of the train in 20, that the velocity in
almost every instance is either increasing or decreasing.
Hence velocity cannot be defined accurately as the distance
over which, a body moves in a unit of time. We must,
therefore, consider the velocity of a body at a given in-
stant, i.e. at some stated time. The velocity of a body at
a given instant is the distance it would move in a second if at
that instant its' motion were to become uniform.
22. Representation of a Velocity. A velocity has the
.characteristics of magnitude (i.e. speed) and direction.
Therefore, a straight line of a definite length may conven-
iently b6 used to represent the velocity of a body at a
16 A HIGH SCHOOL COURSE IN PHYSICS
given instant. Let the velocity of a body be 10 miles per
hour north. A straight line, as AB, Fig. 9, drawn from
B A to B in an upward direction and having a
length of 10 units, will completely represent
the given velocity. As in the case of mo-
tions (19), any convenient length may be
selected to represent a unit of velocity, but
the same length should be used throughout
any given discussion. Any quantity, as
velocity, having direction as well as magni-
Fia.9. Repre- tude, is called a vector quantity, and the line
sentation of
a Velocity, representing it, a vector.
EXERCISES
1. A velocity of 60 mi. per hour is how many feet per second ?
2. Express a velocity of 10 m. per minute in centimeters per
second. Draw the vector that represents the velocity when the direc-
tion is eastward.
3. A train travels 100 mi. in two and one half hours. Calculate
the average velocity in feet per second.
4. The speed of an electric car averages 2.0 ft. per second. How
tar will it travel in three hours ?
5. A train whose length is 440 yd. has a velocity of 45 mi. per
hour. How long will it take the train to pass completely over a
bridge 100 ft. long? Ans. 21.51 sec.
6. A wheel 50 cm. in diameter revolves 600 times per minute.
Express the speed of a point on its rim in centimeters per second.
Ans. 1570.8 cm. /sec.
7. Assuming that the radius of the earth is 4000 mi. and 'that it
revolves on its axis once in exactly 24 hr., ascertain the speed of a
point at the equator. Ans. 1047.2 mi./hr.
2. UNIFORMLY ACCELERATED MOTION
23. Acceleration. We have spoken of the manner in
which a train leaves a station. Starting from rest and.
gradually gaining in 'speed, it finally attains the desired
velocity. Let us suppose that after the train has been
MOTION, VELOCITY, AND ACCELERATION 17
moving one second its velocity is 20 cm. /sec.; at the end
of two seconds from the instant of starting, 40 cm. /sec.;
at the end of three seconds, 60 cm. /sec., etc. While* the
. train continues to move in this manner, the velocity is
increasing the same amount during each second, viz., 20
cm. /sec. This quantity, the rate at which the velocity
changes with the time, is called the acceleration of the train.
Since the change in velocity per second is measured in
centimeters per second, the acceleration of the train is
conveniently expressed thus: 20 cm. /sec. 2 , and read "20
centimeters per second per second." The acceleration of
a body is positive or negative according as the velocity
increases or decreases.. The acceleration of a falling body,
for example, is positive ; that of a body thrown upward,
negative.
24. Uniformly Accelerated Motion. If the rate at which
the velocity of a moving body changes with the time be con-
stant, i,e* if the acceleration remain uniform)-*- the motion
is called uniformly accelerated motion. The motion of the
train considered in 23 is of this t}^pe. There occur in
- nature many cases in which the condition that defines
uniformly accelerated motion is very nearly fulfilled ; e.g.
falling bodies, bodies thrown upward, bodies moving freely
along inclined planes, etc.
0. Velocity Acquired and Distance Traversed. The
velocity acquired in a given number of seconds by a body
having uniformly accelerated motion is found in a manner
which the following example clearly illustrates :
A body starts from rest and gains in speed 4 cm./see. in
each second of time.
At the end of one second its velocity is 4 cm. per second.
At the end of two seconds its velocity is 8 cm. per second.
At the end of three seconds its velocity is 12 cm. per second.
At the end of t seconds its velocity is 4 1 cm. per second.
18 A HIGH SCHOOL COURSE IN PHYSICS
It is plain, therefore, that the velocity v at the end of
any number of seconds t is found by multiplying the
acceleration a by the time ; or.
v = at. (2)
Again, since the initial velocity for a given interval of
time is 0, and the final velocity is v, and since the gain in
velocity is uniform, the mean velocity for the interval is
(0 + v)-*- 2. If the acceleration is 4 cm./sec. 2 as before^
the average velocity for the first second-is "t" cm. per
second ;
4- %
the average velocity for the first two seconds is ~ cm.
per second ;
the average velocity for -the -first t seconds is - - cm.
2t
per second; and if the acceleration is a cm./sec. 2 , the av-
erage velocity for t seconds is ~- cm./sec., or
Now since the distance passed over is found by mul-
tiplying the average velocity by the time ( 20), the
distance that the body moves in t seconds when the accel-
eration is 4 cm./sec. 2 is x , or J(4tf 2 ) cm.; but if the
acceleration is a, we have for the distance, ~ x , or | at 2 ,.
z
Hence d = Jat. | (3)
EXAMPLE. A car starts to move down an incline that is just sleep
enough to cause it to gain in velocity 50 cm./sec. during each second
of time. Find the velocity and the distance traversed at the end of
the fifth second, and the distance that the car moves during the fifth
second.
SOLUTION. The initial velocity is 0. The final velocity is the
product of the gain per second and the number of seconds. Hence
v = 50 x 5, or 250 cm./sec.
MOTION, VELOCITY, AND ACCELERATION
19
The total distance traversed is the product of the average velocity
multiplied by the number of seconds. The average velocity for 5
seconds is SjJT " , and the number of seconds is 5. Hence
250
d = - x 5, or 625 cm. The same result could be found by sub-
stituting the values of a and t in equation (3). The analysis of a
problem, however, is far more valuable than the mere substitution of
numbers in a formula.
The distance traversed during the fifth second is evidently the
difference between the distance traversed in 5 seconds and that in
4- 4
4 seconds. Now in 4 seconds the car moves
x 4, or 400 cm.
Hence during the fifth second the car moves 625 400, or 225 cm.
We thus observe that if any two of the four quantities
used in the discussion be given, the others can be calcu-
lated by the help of equations (2) and (3).
The relation of time and distance shown by equation (3)
may be tested experimentally as follows :
Let a grooved board AB, Fig. 10, about 15 feet long be supported
with one end elevated about 18 inches. The groove can easily be
formed by nailing a strip of wood about 2 inches wide to the side of
u -
FIG. 10. Verifying the Relation between the Distance Traversed and the Time
in Uniformly Accelerated Motion.
a wider piece, forming a cross section as shown in X. Sufficient sup-
ports should be used to keep the groove straight. Arrange a seconds
pendulum ( 84) so as to make and break an electrical contact at the
center of its path, and connect a telegraph sounder and a cell of
battery in the circuit with the pendulum. The sounder should give
20 A HIGH SCHOOL COURSE IN PHYSICS
a loud click at the end of every second. Release a marble at A pre-
cisely at the instant the sounder clicks, and place a block C at such
a point on the incline that the click of the marble against C coincides
with the click that marks the end of the third second. This point
will have to be found by trial, and should be verified by two or three
tests. The length A C gives the distance passed over by the marble
in three seconds. Let the process be repeated for two seconds and
one second. The distances found should be proportional to the
squares of the tfmes, as shown by equation (3) ; i.e. as 1 : 4 : 9.
EXERCISES
1. Solve both equations (2) and (3) for the acceleration a and the
time t.
2. Combine equations (2) and (3) so as to express the velocity in
terms of the acceleration a and the distance d. Express also the dis-
tance in terms of velocity and acceleration.
3. Letting a line 1 cm. long express the acceleration a, represent
the velocity at the end of each of the first four seconds. Represent
also the corresponding distances.
SUGGESTION. Equation (2) gives the length representing the
velocity, and equation (3), the distance.
4. A train leaving a station has a constant acceleration of
0.4 m. /sec. 2 . What will be its velocity at the end of the tenth
second? At the end of 15 seconds?
5. If the acceleration of an electric car is uniform and 2 ft./sec. 2 ,
in how many seconds will it accumulate a velocity of 25 ft. per
second ?
6. How far will the car in Exer. 5 move during the first 10 seconds?
What will be its average velocity during this interval of time ?
7. The acceleration of a car is 5 m./sec. 2 . What velocity will it
acquire in going 100 m.? x Ans. 31.62 m./sec. 2 .
8. A body has uniformly accelerated motion. What is its accel-
eration if it passes over 300 cm. in 20 seconds? Ans. 1.5 cm./sec. 2 .
9. A bicycle starts from rest at the top of a hill 150 ft. long and
has a uniform acceleration of 1 ft. per second. What will be its
velocity at the foot of the hill ? Ans. 17.32 ft./sec.
10. A car was moving at the rate of 30 mi. per hour when the
brakes were applied. What was the rate of retardation if the car
came to rest in 10 seconds, the decrease in velocity being uniform ?
Ans. 4.4 ft./sec. 2 .
MOTION, VELOCITY, AND ACCELERATION 21
11. A bicycle rider moving at the rate of 15 mi. per hour applies
the brake which brings him to rest in moving 121 ft. Assuming
that the velocity decreases uniformly, find the acceleration.
Ans. - 2 ft. /sec. 2 .
12. A fly wheel is set in motion with a uniform acceleration of
two revolutions per second per second. If the diameter of the wheel -
is 50 cm., what is the linear acceleration of a point on its rim ?
Am. 314.16 crn./sec. 2 .
13. What is the velocity of a body having uniformly accelerated
motion at the beginning of the tth second? What is the average
velocity during the t th second ? Show that the distance passed over
during the t th second is a (2 t 1).
14. Apply the formula developed in Exer. 13 to the conditions
given in Exer. 4, and calculate the distance passed over by the train
during the fifth and the tenth second. Ans. 1.8 m. and 3.8 m.
3. SIMULTANEOUS MOTIONS AND VELOCITIES
26. Composition of Motions. The actual displacement
of a body is often due to two or more causes acting to- \
gether. For example, a ball rolled along the deck of a
vessel has a displacement that is the result, of combining
the displacement of the boat with that given the ball by the
hand. Hence, to find the displacement of the ball with
respect to the earth, we must take into account all the
separate motions that enter into the case. It will be ob-
served that different cases will arise depending on the rela-
tion of the magnitudes and directions of the displacements
to be compounded.^ The individual motions effecting the
displacement are called the components, and the motion
due to the united action of the components, the resultant.
The process of finding the resultant from the components
is called the composition of motions v
27. Compounding Motions in a Straight Line. Let a
ball be rolled along the deck of a vessel toward the bow.
While the ball moves over a distance of 20 feat along thfi
the boat mxiYes forward 30 feet. Since the com-
22 A HIGH SCHOOL COURSE IN PHYSICS
ponent motions are in the same direction, it is plain that
the ball actually moves a distance of 50 feet in the direction
the vessel is going. Hence the resultant is equal to the
sum of the components. Again, imagine that the ball is
rolled toward the stern, a distance of 20 feet, while the
boat is moving forward 30 feet. In this case we can see
that the ball will be carried forward by the vessel 10 feet
farther than the distance which it rolls backward. Hence
the resultant is 10 feet, and in the direction of the motion
of the vessel, because that is the larger component. A
rule for compounding motions in the same straight line
may be stated as follows:
The resultant of two component motions in the same straight
line is equal to their sum when the directions are the same,
and to their difference when the directions are opposite. In
the latter case the resultant is in the direction of the greater
component.
28. Compounding Velocities in a Straight Line. If
the velocities of the boat and the ball considered in 27
are respectively 15 and 10 feet per second, and if the
directions are the same, it is clear that the actual velocity
of the ball will be the sum of the velocity of the boat and
the velocity given to the ball by the hand, or 25 feet per
second; and if the directions are opposite, the actual
velocity of the ball will be equal to the difference of
the velocities, or 5 feet per second. In the latter case
the resultant velocity is in the direction of the boat's
motion, since that is the greater of the two components.
29. Compounding Motions at an Angle. Let a man
starting from the point A, Fig. 11, row a boat perpen-
dicular at all times to the current of a river 40 rods
in width. If there were no current, the boat would land
MOTION, VELOCITY, AND ACCELERATION 23
at B. But, while crossing, the current carries the boat
down the stream a distance AC, which we may call 30
rods. The boat therefore lands at J9, having taken 'the
path AD. Since AD is in
this case the diagonal of a
rectangle whose sides are
40 and 30 units, represent-
ing distances measured in
rods, its length, which is
50 units, represents a dis-
tance of 50 rods, the re-
sultant motion of the boat.
If the angle between the
components is not a right
angle, a boat starting from
E takes a path Uff, the di-
agonal of an oblique paral-
lelogram EFH&.
FIG. 11. Resultant of Two Motions
at an Angle.
A thin piece of wood E, Fig.
12, is arranged to slide smoothly
along the edge of a drawing board. At m and n wire nails are driven
a short distance into the wood and a
third into the board at o. Loop one
end of a piece of thread around m,
pass it over n, and attach the other
end to a small weight at A . If the
board is now placed in a vertical po-
sition and the slide moved from E to
E', the weight undergoes a displace-
ment AB. If the loop is transferred
to nail o, on the stationary board, a
movement of the slide from E to E'
gives the weight two simultaneous
displacements represented by AB and BD, causing it to follow the
diagonal path AD. If the operations are repeated after tilting the
board in its plane, it will be seen that the weight follows the diagonal
FIG. 12. Apparatus for Show-
ing the Compounding of Two
Motions.
24 A HIGH SCHOOL COURSE IN PHYSICS
of an oblique parallelogram as the result of the two component dis-
placements.
The facts shown by this experiment may be stated as follows :
The resultant of two component uniform motions not in the
same straight line is represented by the diagonal of a paral-
lelogram whose adjacent sides represent the two component-
motions.
30. Compounding Velocities at an Angle. Velocities
may be compounded in the same manner as motions. For
example, if the velocity with which an oarsman rows his
boat is represented in magnitude and direction by the line
EF in Fig. 11, and the velocity of the stream by the line
EGr, the actual velocity of the boat is represented by the
line EH.
It should be observed that in cases where the angle between
the two components is a right angle, the resultant is the square root
of the sum of the squares of the components. In other cases the
parallelogram should be constructed accurately and the diagonal care-
fully measured.
31. Compounding Several Motions. -- When the actual
motion of a body is due to the united action of more than
two components, the final resultant is found by first deter-
mining the resultant
of any two of them;
and this resultant is
then compounded with
a third component, and
so on until each com-
ponent has been used.
Let AB, AC, and A D,
Fig. 13, be three component
motions imparted simul-
of taneously to a body at A.
Three Component Motions. The resultant of any two,
MOTION, VELOCITY, AND ACCELERATION 25
e.g. AR and AD, is found in the manner described in 29, giving the
resultant AE. AE is now treated as a component and compounded
with the third component A C. In this construction A CFE is the par-
allelogram of which AF is the diagonal. AF is the resultant of the
three given components.
32. Resolution of Motions and Velocities. The meaning
of this process, which is the reverse of composition, is most
readily understood after considering a particular case.
For example, let it be required to find the easterly velocity
of a vessel sailing with a velocity of 15 miles per hour in
a direction east by 30 south. component
Let AB, Fig. 14, represent the
given velocity of the vessel, making
the angle BA C equal to 30. If the
lines BD and BC are now drawn
parallel to A C and AD respectively, D ] '-
the line AC represents the com- '
ponent velocity of the vessel in an FIG. 14. -Resolution of a Velocity.
easterly direction. AD is the southerly component.
EXERCISES
1. A train approaches Chicago with a velocity of 30 km. per hour,
while a brakeraan runs along the tops of the cars toward the rear at
the rate of 5 km. per hour. How ra"pidly is the brakeman approach-
ing Chicago?
2. A boy is paddling a canoe along a river in the direction of the
current, which has a velocity of 4 mi. per hour ; if there were no cur-
rent, the canoe would move 3.5 mi. per hour. How fast is the canoe
moving? .
3. Suppose the boy in Exer. 2 should double his effort and paddle
upstream. How long would it take him to go 10 mi. ?
4. A ship is moving east at the rate of 15 mi. per hour. If a
person walks directly across the deck at the rate of 4 mi. per hour,
with what velocity will he actually move ?
5. A boat is rowed with a velocity of 4 mi. per hour, perpendicu-
lar to the current of a stream flowing 5 mi. per hour. Determine the
direction of the motion and the velocity of the boat.
6. A ship headed due east under a power that can move it 12 mi.
26 A HIGH SCHOOL COURSE IN PHYSICS
per hour enters an ocean current whose velocity is 4 mi. per hour south.
If a person on deck walks northeast with a velocity of 3 mi. per hour,
what is his actual velocity? Ans. 14.3 mi./hr.
7. A balloon is driven in a direction east by 30 north. How
rapidly is it drifting north if its velocity is 20 mi. per hour ?
Ans. 10 mi./hr.
8. A body moves down an inclined plane 5 m. in length. If the
angle between the incline and a horizontal plane is 60, what are the
horizontal and vertical components of its motion?
9. How rapidly is a bird approaching the equator when flying
due southeast at the rate of 20 mi. per hour ?
SUMMARY
1. Motion is a continuous change in the position of a
body. Motion and rest are relative terms. When the
motion of terrestrial bodies is under consideration, the
earth is usually regarded as being at rest ( 15).
2. The motion of a body is rectilinear or curvilinear
according as the path described by the body is a straight
or a curved line ( 16).
3. When a body moves over equal spaces in equal
periods of time, no matter how small the period may be,
the motion is said to be uniform. When the motion of a
body is uniform, the distance passed over is proportional
to the time ( 17).
4. The equation of uniform motion is d = vt ( 18).
5. The characteristics of the rectilinear motion of a
body are its starting point, the direction of the motion, and
its displacement. These three qualities may be represented
by a straight line ( 19).
6. The average velocity of a body is found by dividing
the space passed over by the time consumed ( 20).
7. The velocity of a body at any instant is measured
by the distance it would nuwe in a second if at that instant
its motion were to become uniform ( 21).
MOTION, VELOCITY, AND ACCELERATION 27
*
8. The characteristics of a velocity are its magnitude
(or speed) and direction. The qualities may be repre-
sented by the length and direction of a straight line. A
line used in this manner is called a vector ( 22).
9. The rate at which velocity changes with the time
is called acceleration ( 23).
10. A body has uniformly accelerated motion when its
velocity changes at a uniform rate. The velocity acquired
in a given time by a body starting from rest may be found
from the equation v at. The distance passed over is
given by the equation d = ^at 2 ( 24).
11. The simultaneous individual motions (or velocities)
of a body are called the components of its motion (or ve-
locity), and the motion (or velocity) due to the united
action of the components is called the resultant. The pro-
cess of finding the resultant from the components is called
the composition of motions (or velocities) ( 26 and 28).
12. The resultant of two simultaneous motions (or veloci-
ties) along the same straight line is their sum when the
directions are the same, and their difference when they
are opposite ( 27 and 28).
13. The resultant of two simultaneous motions (or veloci-
ities) not in the same straight line is represented in magni-
tude and direction by the diagonal of a parallelogram
whose adjacent sides represent the two components ( 29
and 30).
14. The resultant of more than two simultaneous motions
(or velocities) is found by compounding the resultant of
any two of them with a third component, then this new
one with the fourth, and so on until each component has
been used ( 31).
15. The process of finding the components from the
resultant is called resolution ( 32).
CHAPTER III
LAWS OF MOTION FORCE
1. DISCUSSION OF NEWTON'S LAWS
33. Momentum. It is a well-known fact that a mov-
ing body must always have been put in motion by an effort
on the part of some agent. The amount of this effort de-
pends (1) on the mass of the body moved and (2) on the
rapidity with which it is given velocity, i.e. on the acceler-
ation. 3 If we observe a locomotive as it starts a train, we
readily see that the effort required is greater as the train
is longer or more heavily loaded. Furthermore, in order
to start the train more quickly, a greater effort is requked
and a more powerful engine. Again, after the train has
acquired its running speed, an effort is required if the
motion is to be destroyed and the train brought to rest.
This, also, depends on the mass of the train and the rapid- v
ity with which its motion is reduced.
The two quantities, mass and velocity, determine what is
called the quantity of motion in a body, or its momentum.
Momentum is measured by the product of the mass and the
velocity of a body, and is expressed algebraically as mv.
For example, the momentum of a 10-gram rifle ball mov-
ing with a velocity of 25,000 cm. /sec. is 10 x 25,000, or
250,000 C. G. S. units. No name is used for the unit of
momentum.
" 34. Newton's First Law of Motion. An inanimate body
never puts itself in motion. Not only does a body with-
out motion tend to remain in that condition, but on ac-
LAWS OF MOTION FORCE 29
count of that same tendency resists the effort of any agent
that tries to start it. ~ J On the other hand, a body in mo-
tion manifests a tendency to keep moving and resists any
effort made to change its motion in any way. These
facts may be illustrated by the following experiments:
1. Stand a book upon end on a sheet of paper placed flat upon the
table. Grasp the paper and try by a quick pull to give the book a
forward motion. On account of the tendency of the book to remain
at rest, it will be found to fall backward. Repeat the experiment,
but move the paper very slowly at first ; and, while the book is in
motion, let the paper suddenly stop. On account of the fact that the
book tends to remain in motion, it will fall forward.
2. Place a card upon the tip of a finger and lay a small coin upon
the card directly above the finger tip. With the other hand give
the card a sudden snap in such a manner as to drive the card from
beneath the coin. The coin will be left upon the finger. The same
experiment may be varied by placing a card upon the top of a bottle
and a marble upon the card. The sudden removal of the card leaves
the marble resting in the mouth of the bottle.
The first to express these facts of common observation
in the language of Physics was Sir Isaac Newton 1 (1642-
1727), professor of mathematics at Cambridge, England.
The statement of his First Law of Motion is as follows:
Every body of matter continues in its state of rest or of
uniform motion in a straight line, except in so far as it is
compelled by force to change that state?
t This is known as the Law of Inertia, the tendency of
matter to act in the manner stated being often ascribed to
a property of matter called inertia. In this law Newton
has given a definition of force as that which is able to
cause or change motion. Hence the term force is the name
1 See portrait facing p. 30.
2 " Every body perseveres in its state of rest, or of uniform motion in
a right line, unless it is compelled to change that state by forces impressed
thereon." Newton's Principia, Motte's Translation.
30 A HIGH SCHOOL COURSE IN PHYSICS
given to the cause that produces acceleration, retardation, or
a change in the direction of the motion of a body.
35. Newton's Second Law of Motion. According to
Newton's First Law a moving body which could be en-
tirely freed from the action of all forces would have uni-
form motion. A stone thrown from the hand would take a
perfectly straight course, and a bullet fired upward would
never return to the earth. The curved path described by
the stone, however, indicates that a force is acting upon
the body while it is moving. This force, as we know, is
the force of gravity.
Just as the First Law defines force, so the Second Law
leads to the measurement of force. This law may be stated
as follows :
Change of motion, or momentum, is proportion&Ltp the
acting force and takes place in the direction in which the
force acts. 1
The proportion always existing between force and the
rate at which it changes the momentum of a body has led
to the adoption of a convenient C. G. S. unit of force
called the dyne (pronounced dine). The dyne is that
force which, acting uniformly for one second, imparts one
C. Gr. S. unit of momentum ; or, a dyne would give a mass
of one gram an acceleration of one centimeter per second
per second. This definition implies that the body upon
which the force acts is not at all hindered in its motion
by external resistances, as friction, etc.; i.e. the force has
simply to overcome the inertia of the body.
36. Equations of Force. The relation expressed in the
preceding section between force, momentum, and time ad-
1 " The alteration of motion is ever proportional to the motive force
impressed ; and is made in the direction of the right line in which the
force is impressed." Newton's Principia, Motte's Translation.
SIR ISAAC NEWTON (1642-1727)
The name of Newton will always be associated with the subject
of gravitation on account of the fullness with which he applies and
discusses his famous Principle of Universal Gravitation in his book
entitled Principia, published in 1687. The Principia, which ranks as
a mathematical classic, treats of the laws governing the motion of
bodies under various conditions, and especially of the motion of the
planets. This work follows close upon the achievements of Galileo
and Kepler in astronomical discovery. Kepler had found by obser-
vation that the planets move around the sun in elliptical paths, which
Newton showed would be the case if between the sun and each
planet there exists a force which decreases as the square of the
distance increases.
The Principia laid a firm and deep foundation for subsequent
discoveries in the field of astronomy; it propounded and showed the
application of a new method of mathematical investigation, the Cal-
culus, by which alone it would retain its position at the head of
mathematical treatises.
Newton must also be accredited with the announcement and elu-
cidation of the three laws of motion which bear his name and with
numerous discoveries in Light. His book entitled Optics contains
his discoveries and theories in this subject.
Newton was born in Lincolnshire, England, in 1642, graduated
from Trinity College, Cambridge, in 1665, and at once began to make
the discoveries in mathematics and physics which have immortal-
ized his name. He was professor of mathematics at Cambridge,
member of Parliament, and Master of the Mint. He was knighted
in 1705, and at his death, in 1727, was buried in Westminster Abbey.
LAWS OF MOTION FORCE 31
mits of being expressed in a concise algebraic form. Let
a mass of m grams be acted upon by a constant force f /
dynes for t seconds. If the velocity imparted to the mass
by that force is v cm./sec., the momentum produced is mv
( 33). The momentum imparted per second is found by
dividing the quantity mv by the time t. We have there-
fore, by the definition of the dyne,
f (in dynes) = ** (in ^ rams) x v
t (in seconds)
From Eq. (2) 25, we have v = at; <\ ~ "1
whence - is the acceleration a produced by the force /.
Therefore, by substituting in (l),
f (in dynes) = m (in grams) x a (in cm./sec. 2 ). (2)
In the English F.P.S. system the unit of force is the poundal. The
poundal is that force which, acting uniformly for one second, imparts one
F. P. S. unit of momentum. Hence, if the mass of the body upon which
the force acts is given in pounds, the velocity in feet per second, and
the time in seconds, substitution in equation (1) will give us the force
in poundals. A force of one poundal is equivalent to 13,825 dynes.
EXAMPLE. What constant force acting four seconds will give a
body of 15 g. a velocity of 20 cm./sec. ?
SOLUTION. The total momentum produced by the force in four
seconds is 15 x 20, or 300 C. G. S. units. The momentum imparted
to the body in one second is 300 -^ 4, or 75 units. Hence the force
is 75 dynes.
Another method is to substitute the given quantities directly in
equation (1), first being assured that all are given in C. G. S. units.
The same may be said of the F. P. S. system in obtaining the force in
poundals when the problems deal with English units.
37. Gravitational Units of Force. A gram-weight (or
a gram-force) is the downward pull exerted by the earth
upon a one-gram mass. (See 10.) If the mass is free
to fall, the acceleration due to gravity will be 980
cm./sec. 2 , or 980 C. G. S. units of momentum per second.
32 A HIGH SCHOOL COURSE IN PHYSICS
Hence, by Eq. (2), a gram-weight is equivalent to 980 dynes.
Likewise, a pound-weight (or a pound-force) is the attrac-
tion of the earth upon a one-pound mass. The accelera-
tion produced by this force when the body falls freely is
32.16 ft./sec. 2 , and the momentum is 32.16 F. P. S. units
per second. Therefore, one pound-weight is equivalent to
32.16 poundals.
Since the earth's attraction varies with the locality, as
explained in 10 and 69, the gram-weight and the pound-
weight change accordingly. Hence these units are called
gravitational units of force. On the other hand, the dyne
and the poundal, being independent of gravity, are called
absolute units.
Commonly, use is made of the pound and the gram (i.e.
pound-weight and gram-weight) as units of force. Scien-
tific work has, however, demanded a more unvarying unit
and has brought the dyne into extensive use in all cases
requiring accuracy of expression. The poundal is little
used.
38. An Application of the Second Law. Newton's
Second Law implies that any force acting upon a body
produces its own effect, whether acting alone or conjointly
with other forces. An interesting illustration of this may
be observed in the fol-
lowing experiment :
Cut notches A and B,
Fig. 15, in two of the cor-
ners of a piece of wood about
2x8 inches. By means of
a large screw attach the cen-
ter of the block loosely to the
edge of a table as shown, and
place a marble in each notch.
FIG. 15. -Illustration of Newton's Second If the end of the block P-
Law of Motion. posite A is struck with a
LAWS OF MOTION FORCE
33
mallet, ball A will be dropped vertically, while ball B is projected hor-
izontally. B is subject to two forces, an impulse which projects it in
a horizontal direction and the constant force of gravity acting along
a vertical line. The two marbles will be found to strike the floor at
the same time.
The experiment ihows that the effect of gravity in
bringing the balls to the floor is independent of the hori-
zontal component of the motion; i.e. a given force (gravity)
produces as much " change in momentum " in the vertical
direction in one ball as in the other. After ball B leaves
the block, its momentum in the horizontal direction suffers
no change.
39. Newton's Third Law of Motion. To every action
there is always an equal and opposite reaction; or, the mu-
tual actions of any two bodies are always equal in magnitude
and oppositely directed.
This law may be illustrated by experiment as follows :
Let two elastic wooden balls A and
B, Fig. 16, be suspended by threads in
such a manner that they just touch each
other when stationary. Draw A aside
and let it fall against B. A will be
brought to rest by the impact, and B will
be moved to the position B'.
In this experiment two results
are apparent : first, ball B is acted
upon by a force sufficient to carry
it to the position J9', arid, second, ball A loses an equal
amount of momentum in that it is brought to rest. In
the impact occurs a mutual effect a force exerted by
A toward the right upon J5, and an equal and oppositely
directed force from B upon A. This process goes on in
every case in which force enters. A pressure of the hand
against the table is opposed by an equal pressure of the table
against the hand. When a person leaps forward from a
4
_
FIG. 16. Action and Reac-
tion are Equal and Oppo-
34 A HIGH SCHOOL COURSE IN PHYSICS
boat, the boat is pushed in the opposite direction. When
a gun is fired, the mutual effect is to give the bullet and
the gun equal momenta; or, in other words, the mass of
the bullet multiplied by its velocity equals the mass of
the gun multiplied by its velocity. The velocity of the
gun's recoil, or "kick," is small because the mass of the
gun is many times greater than that of the bullet.
The question often arises : " Does the earth rise to meet
the falling apple ? " In the light of the Third Law of
Motion, we must admit that the action of the earth which
draws the apple down is accompanied by a reaction which
is operative for the same length of time upon the earth in
an upward direction. Hence the momentum given the
apple equals that given the earth. On account of the
enormous mass of the earth, however, the distance through
which it rises to meet the apple is infinitesimally small.
EXERCISES
1. Why does a person standing in a car tend to fall backward
when the car starts, and forward when it stops ?
2. Why does a bullet continue to move after leav-
ing a rifle?
3. A weight W, Fig. 17, is attached by a cord B
to some fixed object. A quick downward pull on a
similar cord A will break the cord below W, but a
steady pull will break cord B. Explain.
4. A blast of fine sand driven against glass soon
cuts away its smooth surface. Why ?
5. If a rifle ball is thrown against a board placed
on edge, it will knock it down ; but when fired from
a gun, it will pass through the board and leave it
standing. Why ?
6. Explain why the head of a hammer or mallet
FIG 17 can ^ e driven on by simply striking the end of the
handle.
7. Why can an athlete make a longer " running jump " than a
" standing" one?
LAWS OF MOTION FORCE 35
8. Will a stone dropped from a moving train fall in a straight
line?
9. Why do moving railway coaches " telescope " in a collision?
10. Explain how heavy fly wheels serve to steady the motion of
machinery, as in the case of the sewing machine.
11. A 4-gram rifle ball leaves a gun with a speed of 20,000 cm. per
second. Compute its momentum.
12. Which has the larger momentum, a man weighing 150 lb.,
walking 10 ft. per second, or a boy weighing 60 lb. and running 25 ft.
per second ?
13. Which has the greater momentum, a man weighing 160 lb.
in a railway coach moving 30 mi. per hour, or a 2-ton stone moving
3 ft. per second? Express the difference in F. P. S. units.
14. What force acting for 10 seconds upon a mass of 200 g. will
produce a velocity of 5 cm./sec.? Express the change of momentum
per second in C. G. S. units.
15. A body whose mass is 20 g. is given an acceleration of
45 cm./sec. 2 . What is the required force?
16. What acceleration will be given to a mass of 25 g. by a
constant force of 500 dynes ? Over what distance will the body move
in 5 seconds if the force continues to act ?
17. If the force given in Exer. 16 ceases to act at the end of the 5th
second, how far will the body move during the next 5 seconds ?
SUGGESTION. Find the velocity imparted in the first 5 seconds
and apply the First Law of Motion.
18. An inelastic ball of clay whose mass is 200 g. has a velocity
of 25 cm./sec. when it collides with a similar ball at rest whose mass
is 50 g. Find the velocity after collision.
SUGGESTION. After impact the two masses move on as one mass
with the momentum of the first before collision.
19. A projectile weighing 100 lb. is fired with a velocity of 1200 ft.
per second from a gun weighing 8 T. Find the velocity with which
the gun starts to move backward.
2. CONCURRENT FORCES
40. Representation of Forces. The three characteristics
of a force, its point of application, direction, and magni-
tude, can, as we have seen, be represented by a straight
line. One end of the line shows the point of application.
36 A HIGH SCHOOL COURSE IN PHYSICS
the length of the line shows the magnitude of the force,
and the direction in which the line is drawn shows the
direction in which the force acts. For example, (1),
Fig. 18, represents
a force of 10 dynes
acting northeast
from the point A.
The unit of force
15 Dynes , . -.
A' >B may be represented
(0 by any convenient
FIG. 18. The Representation of Forces by Means l en p-th but the
of Straight Lines.
same scale should,
of course, be used throughout a given problem.
In a similar manner, (2), Fig. 18, shows that two
concurring forces, AB and A C, representing respectively
15 dynes east and 8 dynes north, act upon the point A.
The scale adopted in this case is 2 millimeters to the
dyne.
41. Composition of Forces. When a body is acted
upon by two forces at the same time, it is easy to imagine
a single force that might be substituted for them and
would ha\&e the same effect. This single force is the
resultant of the two forces, which are the components.
The process of finding the resultant of two or more component
forces is catted the composition of forces. Forces are com-
pounded in the same manner as motions and velocities
(27-31).
42. Forces Acting in a Straight Line. When two
forces act upon a body in the same line and in the same
direction, it is clear that the resultant is the sum of the
two components. For example, if a weight is to be lifted
by two men pulling upward on a rope attached to it, and
if one man pulls with a force of 50 pounds while the other
pulls with a force of 75 pounds, the two forces result in a
LAWS OF MOTION FORCE 37
single pull of 125 pounds. Hence the resultant is 125
pounds and is directed upward.
When the two forces act in opposite directions along
the same line, the resultant is the difference of the two
components. Thus, if one man pulls upward on a weight
with a force of 75 pounds while the other pulls downward
with a force of 50 pounds, the lifting effect is the same as
a single force of 75 50, or 25 pounds. The action of the
resultant is plainly in the direction of the greater of the
two components. A special case of opposite forces is that
in which the sum of the components acting in one direction
is equal to the sum of those acting along the same straight
line in the opposite direction. In this case no motion can
result from the joint action of all the forces. In other
words, the resultant is zero. The body upon which such
forces act is said to be in equilibrium.
43. Forces Acting at an Angle. If AB and AC, (2),
Fig. 18, represent forces of unequal magnitudes, it is clear
that the resultant will divide the angle between them, but
will lie nearer the greater force. The actual magnitude
and direction of the resultant are found in the same man-
ner as in the case of the resultant of two motions ( 29).
The resultant of two concurring forces acting at an angle is
represented by the diagonal of a parallelogram constructed on
the two lines representing the component forces.
This is one of the most important laws of mechanics and
is universally known as the Principle of the Parallelogram
of Forces. The following experiment will illustrate the
truth of this principle:
Arrange two dynamometers (see Fig. 6), before the blackboard,
as shown in Fig. 19. Let the weight W be great enough to produce a
large but measurable tension in each of the oblique cords. Place a
rectangular block of wood against each of the cords and trace its
direction on the blackboard. Read the dynamometers and record the
38
A HIGH SCHOOL COURSE IN PHYSICS
magnitude of each force on the corresponding line. Adopt a conven*
ient scale and lay off each force along its line of direction, measuring
from O. Using the ob-
lique lines as sides, con-
struct the parallelogram.
Measure the diagonal OR
and write its value in
force units upon it. A
comparison will show that
the force represented by
OR is equal to W and
might, therefore, be sub-
stituted for the two
components and would
produce the same effect.
44. Equilibrant and
Resultant. -- The
force W is said to hold the component forces in equilib-
rium, arid is therefore called the equilibrant (pronounced
<? quili' brant) . From the definitions given of resultant
and equilibrant, we see that they are necessarily equal
in magnitude but opposite in direction.
FIG. 19, Principle of the Parallelogram of
Forces Illustrated.
EXERCISES
1. Represent by a diagram the resultant of two forces of 15 dynes
and 25 dynes acting (1) in the same direction and (2) in opposite
directions from the same point.
2. Find the magnitude and the direction of the resultant of two
forces, 3 Ib. acting north and 4 Ib. acting west, applied at the same
point.
3. A ball is acted upon simultaneously by two forces, one of 10 kg.
directed upward, the other of 25 kg. directed east along a horizontal
line. Find the resultant in both magnitude and direction.
4. The angle between a force of 50 dynes and one of 30 dynes is
60. Find the resultant and the equilibrant in both magnitude and
direction.
5. The angle between two equal forces of 40 Ib. each is 120. Find
the resultant.
LAWS OF MOTION FORCE 39
6. A boat is pulled by two ropes making an angle of 30. If one
force is 10 lb. and the other 20 lb., what is the resultant?
7. A weight is suspended by two cords applied at the same point
and each making an angle of 30 with a vertical line. If the tension
in each is 25 lb., what is the weight supported ?
Ans. 43.3 IK
3. MOMENTS OF FORCE PARALLEL FORCES
45. The Moment of a Force. It can often be observed
that when a mechanic wishes to loosen a nut that is diffi-
cult to start, he uses a wrench with a long handle. For
those that start easily, he uses a short-handled wrench.
The results prove that the effectiveness of a force in pro-
ducing rotation against a resistance is greater as the ap-
plied force is farther from the point about which rotation
takes place.
The effectiveness of a force in producing a rotation is called
the moment of the force. The moment of a force depends
upon two quantities: (1) the magnitude of the force and
(2) the perpendicular distance from the point about which
the rotation takes place to the line representing the direction
of the force. The moment is measured by the product of
these two factors. The following experiment will make
the matter clear:
Fasten one end of a light wooden bar to the table top by means of
a nail at 0, Fig. 20. Let a force, which
may be measured by a dynamometer (see
Fig. 6), pull upon the bar at A, and an-
other at B, as shown. Measure both forces
and the distances AO and BO. The prod-
uct of the force applied at A multiplied
by the distance A will be found equal to
the product of the other force multiplied
by the distance BO.
LJ0.
It is clear from this experiment
, FIG. 20. The Equality ol
that a force that tends to turn a body Moments illustrated.
40 A HIGH SCHOOL COURSE IN PHYSICS
to the right can be balanced by another of the same moment
that tends to produce rotation to the left.
46. Parallel Forces. Objects are frequently supported
by two or more upward forces acting at different points,
thus forming a system of parallel forces. For example,
two men may support a heavy beam or carry a loaded
bucket on a bar between them. A bridge is supported by
the upward pressures of the piers at the ends. The prin-
ciple of moments given in the preceding section is of
service in determining the resultant of such forces as
the following experiment illustrates:
Select a bar of wood 4 or 5 ft. in length, of uniform width and
uniform thickness. A pine board about 4 in. in width is convenient.
Place hooks at several points
along one edge, as shown in
Fig. 21, but place one hook
so that the bar wilMSalanee
well when hung from that
point. Call this point C.
W Suspend the bar from a dy-
namometer at C and ascer-
FIG. 21. - Law of Parallel Forces tain the we i^ht of it. This
Illustrated. . . ,. , ,,
will be the value of the re-
sultant in every case. Now release the bar at C and attach dynamom-
eters at two points, say A and B, and ascertain the forces required
to support the bar. Designating these forces by F and F', it will be
found that in every case the sum of the two components is equal to
the weight W of the bar ; or, F + F = W. Furthermore, the moment
of the force F about the point B m (i.e. F x AB) will be found equal to
the moment of the weight of the blar about the same point (i.e. W X
CB) ; or,
F x AB = W x CB. (3)
The moment of the component F 1 about the point A will be found
equal to the moment of W about the same point. Hence we may write
F x AB = W x AC. (4)
The laws of parallel forces may therefore be stated as
follows :
LAWS OF MOTION FORCE 41
1. The resultant of two parallel forces acting in the, same
direction at different points on a body is equal to their sum,
and has the same direction as the components.
2. The moment of one of the components about the point
of application of the other is equal and, opposite to the moment
of the supported weight about the same point.
EXAMPLE. Two men, A and B, carry a bucket \veighing 100 Ib.
on a bar 10 ft. long. If the bucket is 4 ft. from A, how much force
is exerted by each?
SOLUTION. The moment of the force F exerted by A about the
opposite end of the bar is 10 x F, and the moment of the weight about
the same point is 100 x (10 - 4), or 600. Hence 10 x F = 600 ; whence
F = 60 Ib. Let F' be the force exerted by B. Then considering the
moments about the other end of the bar, we have 10 x F' = 100 x 4 ;
whence F = 40 Ib. Therefore A exerts 60 Ib. and B 40 Ib.
,x
47. The Couple. When two equal parallel forces act
upon a body along different lines and in opposite direc-
tions, as shown in Fig. 22, they have no
resultant; that is, no single force will have
the same effect as the two components act-
ing jointly. A combination of this kind is
called a cougle. The tendency of a couple is
always to rotate the body on which it acts.
This tendency is measured by the moment of
the couple, which is the product of one of
the forces multiplied by the perpendicular FIG. 22. The
distance AB between the two forces. This Couple,
distance is the arm of the couple. The equilibrium of the
body acted upon can be maintained only by the applica-
tion of another couple of equal moment acting in the op-
posite direction.
A small magnet placed on a floating cork is rotated by
the couple formed by the northward-acting force at one
end and the equal southward-acting force at the other.
42 A HIGH SCHOOL COURSE IN PHYSICS
EXERCISES
NOTE. The student should first draw a'diagram representing the
conditions of the problem to be solved and then apply the general
results deduced from the experiment m 46.
1. A uniform bar of wood weighing 12 kg. is 120 cm. long; two
hooks are placed on opposite sides of the center at distances of 40 cm.
and 20 cm. respectively. What forces applied to the hooks will
support the bar? Ans. 4 kg. and 8 kg.
2. In order to support the bar in Exer. 1, what forces applied at
points respectively 15 cm. and 15 cm. from the ends of the bar will
be required ? A ns. 9 kg. and 3 kg.
3. A beam of uniform size is 60 ft. long and weighs 800 lb.; a
man at one end supports 200 lb. Find the magnitude and point of
application of the other required force.
4. Two parallel forces of 30 g. and 70 g. are applied at the ends of
a bar 1 m. long. Find what weight will be supported and its location
on the bar, neglecting the weight of the bar itself.
5. A boy and a man are carrying a weight of 150 lb. on a bar 10
ft. in length. If the forces are applied at the ends of the bar, where
must the load be placed in order that the boy may have to carry only
50 lb. ?
6. Draw a diagram showing a method for attaching three horses
to a load so that they must pull equally.
4. RESOLUTION OF FORCES
48. Resolution of Forces. In many cases it becomes
desirable to find the effect of a force in some direction
other than that in which it acts. For example, a car on a
track running east and west, Fig.
23, is acted upon by a force AB
directed northeast. The given
force has two effects : It produces
(1) a tendency to move the car
FIG. 23. Force Resolved east, and (2) a pressure against
into Two Components. the rails toward the north. It is
plain that two forces, one directed east and the other
north, might have the same effect as the single force
LAWS OF MOTION FORCE
43
directed northeast. In order to determine these two
forces, the given force is represented by the line AB, from
whose extremities, A and .#, lines are drawn completing
the rectangle, as shown in the figure. AC is called the
effective component, since it acts in the direction in which
the car can move ; and AD is designated as the non~
effective component, since it contributes nothing to the
production of motion.
A given force may be resolved into two components whose
directions are given by making the line of force the diagonal
of a parallelogram whose sides are drawn from the point of
application of the force in the directions required for the
components.
49. The Sailboat and the Aeroplane. The principle of the
resolution of forces explained above is readily applied to the opera-
tion of a sailboat. Let the boat be headed north while the wind blows
from the east. Now the pressure of the wind AC on the sail SS',
(1), Fig. 24 can be resolved into A B, perpendicular to the sail, and a
FIG. 24.
second component AD, parallel to the sail, the latter of which is non-
effective. Force AB is the effective pressure on the sail. If the
vessel were round, it would move in the direction of AB. Now let
AB be resolved as shown in (2), Fig. 24 into A E acting parallel to the
keel and AF acting perpendicular to it. The former component
44
A HIGH SCHOOL COURSE IN PHYSICS
Direction of Flight
moves the vessel forward, while the component AE is rendered non
effective by the deep keel of the boat.
In the case of the aeroplane, which is a recent invention, huge
planes or sails, AE and CD, shown in the sectional view, Fig. 25, are
attached firmly to a light frame, upon which is mounted a powerful
gasolene motor ( 271). The planes are slightly oblique, as shown.
The power furnished by the motor turns a propeller whose office it is
to drive the aeroplane rapidly forward. When the aeroplane moves
forward to the left, it is as though a strong
wind were blowing toward the right
against the planes, as shown by the dotted
lines. As in the case of the sailboat
a pressure is produced at right angles
to the planes AE and CD. Represent-
ing this force by the line EF and re-
solving it into two components, we find
the lifting force EG, and the component
EH, which tends to resist the forward mo-
tion of the aeroplane. Smaller planes whose positions can be changed
by the operator, are used in steering.
FIG. 25.
EXERCISES
1. If the force represented by the line AB, Fig. 23, is 1000 lb., and
the angle BA C, 60, find the components A C and AD.
2. Resolve a force of 2000 dynes into two components making
angles of 30 and 60 with the given force.
3. A weight of 50 kg. is suspended by two cords making angles of
30 and 60 respectively with the vertical. Find the force exerted by
each cord. Ans. 25 kg. and 43.3 kg.
4. If the mass of the car in Exer. 1 is 20,000 lb., and the resistance
offered by the rails may be neglected, what is the acceleration of the
car?
SUGGESTION. Reduce the effective component to poundals and
apply equation (2), 36. Ans. 0.161 ft. per sec. per sec.
5. CURVILINEAR MOTION
50. Uniform Circular Motion. It is a well-known fact
that a ball attached to one end of a cord and whirled
about the hand exerts a pulling force against the hand
LAWS OF MOTION FORCE 45
along the cord. This takes place because of the tendency
of the ball to move in a straight line according to New-
ton's First Law of Motion* In order, therefore, to confine
the ball to a circular path, a continual force toward the
center must be maintained. If this force is removed by
the breaking of the cord, the ball will leave its circular
path along a tangent. The force that continually deflects
a moving body from a straight line, compelling it to follow
a curve, is called centripetal force. If the motion of a
body along the circumference of a circle is uniform, the
centripetal force is constant.
The name " centrifugal " force is often applied to the reaction of
the moving body upon the fixed center. This reaction gives one the
erroneous impression that the body would fly away from the center
along a radius if the centripetal force should cease acting. If, how-
ever, we watch the course taken by water or mud as it leaves a revolv-
ing wheel, we readily observe that it moves along the tangent to the
wheel at the point where it is set free.
51. Centripetal Acceleration. Since a force-produces
a change in momentum in the direction of the force,
according to Newton's Second Law ( 35), a constant cen-
tripetal force produces a constant change in the momen-
tum of a body, which has uniform circular motion, toward
the center. Since the mass is constant, the acceleration
is constant and directed toward the center. If v is the
velocity with which a body is moving in a circular path,
and r the radius of the circle, the centripetal acceleration
a is represented as follows i 1
a = - (5)
1 Let a body m be moving around the circle whose center is o, with a
uniform velocity v. Let it move from TO to c in the very short time of t
seconds. Then the distance me will be equal to vt (Eq. 1, p. 14). If the
time is small, the arc me is practically equal to the chord me. On com-
46
A HIGH SCHOOL COURSE IN PHYSICS
Thus, if the moving body is at the point TO, Fig. 26, its tendency is
to continue in the direction mb in accordance with the First Law of
Motion. But, on account of the
cord, it is compelled to keep the
same distance from the center o and,
consequently, is deflected from b to c.
Again, at c, as at every point, the
body tends to follow the tangent ce,
but is compelled to take an inter-
mediate path along the circumfer-
ence to /. If the deflecting force
is removed at the time the body
reaches /, it continues to move in
the direction of its motion at that
FIG. 26. A Body ra Having Circu- point ; that is, along the line fg,
lar Motion Tends to Follow the which is tangent to the circle at /.
Tangent to its Path. T . . ,, , ,, , .
It is the component of the motion
ma produced by the centripetal force acting along mo whose accelera-
tion is represented in equation (5).
52. Equation of Centripetal Force. A force is equal to
the product of the mass of the body upon which it acts
and the acceleration that it produces ( 36). Hence
in circular motion the centripetal force is the product of
2
the mass m and the centripetal acceleration .
r
Therefore
the value of the centripetal force may be expressed as
follows :
pleting the small rectangle m&ca, we have, since ca is a perpendicular
dropped upon the hypotenuse "of the right triangle mch,
me* = ma x ~mh. (1)
Now the distance the mass m is drawn toward the center by the con-
stant centripetal force in the time t is be and equals ma. Since the motion
toward the center is uniformly accelerated,
!nc = ma = $ at 2 (Eq. 3, p. 18). (2)
Therefore, by substituting the values we = vt and ~m~a = | otf 2 in (1), we
have vW = \ at 2 x 2 r, where r is the radius of the circle. From this
equation v 2 = ar, whence a = .
LAWS OF MOTION FORCE 47
TH v
Centripetal |orce = . (6)
It should be observed that this equation gives the force
in absolute units only ; i.e. in dynes, when C. G. S. units
are substituted, and in poundah, when F. P. S. units are
employed.
53. Illustrations of Circular Motion. Many examples
of circular motion present themselves in everyday life.
The bicycle rider must carefully govern his speed as he
turns a corner on a slippery pavement lest the force re-
quired to change the direction of motion be too great and
the wheels slip sidewise. In the modern cream separators
the denser portions of the milk are forced to the outside
of a rapidly revolving bowl, while the lighter cream re-
mains near the center and is forced out along the axis.
Honey is extracted by rapidly whirling the uncapped comb
in a machine. Centrifugal driers are used in laundries
and factories for removing water from clothing, wool, etc.
In the " loop the loop " apparatus a car rides safely along
a track within a large vertical circle, its own tendency to
follow a tangent keeping it pressed firmly against the
rails.
The motion of the bodies of the solar system illustrates
the action of centripetal force on the grandest scale. The
earth, for example, having an initial motion, tends to move
in a straight line. However, the attraction of the sun,
like a tense cord, holds it in its orbit. If this force should
cease, the earth would at once move away into space along
a tangent to its orbit. On the other hand, if it were not
for the earth's motion along the curve, it would be drawn
with accelerated motion into the sun.
The spheroidal shape of the earth is supposed to be due
to the tendency of matter to withdraw from the axis of
48 A HIGH SCHOOL COURSE IN PHYSICS
rotation. This tendency causes bodies to weigh about ^Jg
less at the equator than at the poles.
When the centripetal force is not sufficient to keep the
parts of a revolving body in the required circular paths,
serious results often follow. This is the case of bursting
fly wheels and emery wheels in mills and factories.
EXERCISES
1. Explain why water will not fall from a pail whirled at arm's
length in a vertical circle.
2. How is the overturning of a car prevented, as it rapidly turns a
curve ?
3. Does the rotation of the earth affect the weight of bodies in this
latitude ?
4. Account for the fact that the moon moves in an orbit around
the earth.
5. What keeps the earth in rotation on its axis ?
6. Show by equation (5) that increasing the rate of rotation of the
earth seventeen fold would cause bodies at the equator to " lose " their
entire weight.
7. A body whose mass is 50 g. moves in a circle whose radius is
40 cm. with a velocity of 20 cm. /sec. What is the required centripe-
tal force? v
8. A stone leaves a sling with a velocity of 50 ft. per second. If
the mass of the stone is 2 oz. and the radius of the circle 4 ft., what
was the pull exerted on the cords of the sling ?
Ans. 78.125 poundals.
SUMMARY
1. The momentum of a body is measured by the prod-
uct of its mass and velocity. It is represented by the
expression mv ( 33).
2. The term force is the name given to the cause that
produces acceleration, retardation, or a change in the
direction of the motion of a body ( 34).
3. Force is measured by the change in momentum
produced per second. The C. G. S. unit of force is the
LAWS OF MOTION FORCE 49
dyne. The dyne is that force which, acting uniformly
for one second, imparts one C. G. S. unit of momentum
( 35).
4. The equation of force is/= , or/= ma ( 36).
t
5. The absolute units of force are the dyne and poundal ;
the gravitational units are the gram-weight and pound-weight,
etc. In everyday use the gravitational units are called
simply the "gram " and "pound " ( 37).
6. A given force produces its own effect, whether act-
ing alone or conjointly with other forces ( 38).
7. To every action there is always an equal and oppo-
site reaction; or, in other words, for every push or pull of
one body upon a second body there is always an equal pull
or push of the second body upon the first ( 39).
8. The characteristics of a force are its point of appli-
cation, direction, and magnitude. Forces are represented by
straight lines of suitable length and direction and may be
compounded in the same manner as motions and velocities
( 40).
9. The resultant of two or more forces acting in the same
direction along a straight line is equal to their sum; but
when two forces act in opposite directions in the same line,
their resultant is equal to their difference and has the di-
rection of the greater force ( 42).
10. The resultant of two forces acting at an angle is rep-
resented by, the diagonal of a parallelogram constructed on
the lines which represent the component forces. This law
is universally known as the Principle of the Parallelogram
of Forces ( 43).
11. The moment of a force about a point is the effective-
ness of the force in producing a rotation. It is measured
by the product of the magnitude of the force and the per-
5
50 ' A HIGH SCHOOL COURSE IN PHYSICS
pendicular distance from the point to the line of direction
of the force ( 45).
12. Any two parallel forces acting upward will support
a weight equal to their sum, and the moment of one
component about the point of application of the other is
equal and opposite to the moment of the supported weight
about the same point ( 46).
13. A system of two equal and opposite parallel forces
acting along different lines is called a couple. The moment
of a couple is the product of one of the forces multiplied by
the distance between the two forces. A couple can be
balanced only by another couple acting in the opposite
direction and having an equal moment ( 47).
14. A force may be resolved into two components by
making it the diagonal of a parallelogram whose sides are
drawn in the directions required for the components ( 48.)
15. When a body has curvilinear motion, a force is re-
quired to deflect the body continually from a straight line.
This is called centripetal force. The equation of centripetal
force is/ = (52).
CHAPTER IV
WORK AND ENERGY
1. DEFINITION AND UNITS OF WORK
54. Work. The use of the expression " to do work "
is restricted in the study of mechanics to cases in which
a force produces motion in the body upon which it acts.
For example, attempting to lift a stone from the ground
without succeeding in moving it is not doing work in the
scientific sense ; but lifting the stone to a higher position
implies that work is being done upon it. Similarly, bend-
ing a bow is doing work, but holding it in a bent condi-
tion is not. Lifting a weight involves the process of
doing work, but simply supporting it does not. Work
is done when the spring of a clock is wound, or a body is
moved along upon a table.
An important case in which work is done is that in
which a freely moving body is given acceleration. We
have already found ( 34) that an increase in the velocity
of a body requires the action of a force. Furthermore,
the tendency of the force is to produce motion in the
direction in which the force acts. " Hence, work is done
by exploding powder when it projects a bullet from a gun,
or by gravity when a body is allowed to fall to the earth.
55. Elements Involved in Work. In each of the ex-
amples given in the preceding section, it will be observed
that two quantities are involved in the process of doing
work. These are (1) the acting force and (2) the distance
through which the force continues to act, sometimes called
the displacement. Work is directly proportional to the force
61
52 A HIGH SCHOOL COURSE IN PHYSICS
and the distance through which the force acts, and is meas-
ured by their product. Thus
Work = force x displacement.
Or, if /represents the force, d the distance through which
the force acts.
Work = fd. (i)
56. Units of Work. Since work is measured by the
product of the force that acts upon a body and the dis-
tance the body is moved in the direction of the force, a
unit of work is done when a unit of force acts through a unit
of distance. For every unit of force ( 36 and 37) there
is a corresponding unit of work. The most important,
however, is the C. G .S. unit which is called the erg. The
erg is the work done when a force of one dyne acts through a
distance of one centimeter. The erg is also called the dyne-
centimeter.
The F. P. S. unit of work is the foot-poundal, which is the work done
when a poundal of force acts through a distance of one foot. In the
gravitational system two units are frequently used. The kilogram-
meter is the work done when a force of one kilogram ( 37) acts
through a distance of one meter. The foot-pound is the work done
when a force of one pound acts through a distance of one foot.
The following table is given to show the use of equa-
tion (l) in the computation of work in the different
systems :
ABSOLUTE SYSTEM
/-(in dynes) x d (in centimeters) = Work (in ergs) .
/ (in poundals) x d (in feet) = Work (in foot-poundals).
GRAVITATIONAL SYSTEM
/(in kilograms) x d (in meters) = Work (in kilogram-meters),
/(in pounds) x d (in feet) = Work (in foot-pounds).
WORK AND ENERGY 53
EXAMPLE. A mass of 50 g. requires a force of 10 g. to overcome
the friction and move the body at a uniform rate along a horizontal
table. Find the work done when the mass is moved horizontally
25 cm. Find also the work done when the mass is lifted 25 cm.
SOLUTION. Since the horizontal force is 10 g. or 9800 dynes
( 37). and the distance through which the force acts is 25 cm., the
work performed is 10 x 25, or 250 gram-centimeters. Measured in
ergs, the work is 9800 x 25, or 245,000 ergs.
The work performed in lifting the mass is 50 x 25, or 1250 gram-
centimeters. Measured in ergs, the work is 49,000 x 25, or 1,225,000,
ergs.
The numerical relation between the various units of
work is shown in the following table :
1 dyne-centimeter equals 1 erg.
1 kilogram-meter (kg-m.) equals 98,000,000 ergs.
1 foot-pound equals 13,550,000 ergs.
1 foot-poundal equals 421,390 ergs.
2. ACTIVITY, OR RATE OF WORK
57. Activity. The value of any agent employed in do-
ing work will depend upon the amount of work it is able
to perform in a certain time. Some agents work slowly,
others rapidly. For example, a man can lift a certain
number of bricks to the top of a building in an hour ; a
horse attached to a suitable hoisting mechanism can lift a
greater number in the same time ; and an engine can lift
the bricks as fast as several horses. Working agents are
therefore said to differ in activity, or power. Activity is
the rate of doing work, and is found by dividing the work
performed by the time consumed in the process.
58. Units of Activity. The unit of activity or power
commonly used is the horse power (abbreviated H.P.).
The horse power is the rate of doing work equal to 550 foot-
pounds per second. The activity of an agent that is able
to perform 550 foot-pounds of work per second is one horse
54 A HIGH SCHOOL COURSE IN PHYSICS
power. The unit of power in the C. G. S. system is the
watt, 1 which is equivalent to the work done at the rate of
10 7 ergs per second. One horse power equals 746 watts,
or 746 x 10 7 ergs per second.
EXERCISES
1. Calculate the work done by a force of 25 dynes acting through
a distance of 120 cm.
2. Express in ergs and gram-centimeters the work done in lifting
a mass of 5 g. through a vertical height of 100 cm.
3. A horse has to exert an average force of 200 Ib. in moving a
loaded cart a distance of a mile. Find the amount of work done.
4. What amount of work is done when one cubic meter of water
is elevated to a height of 10 m.?
5. How much work is done per second by an engine that in one
hour lifts 10,000 bricks each weighing 4 Ib. to the top of a building 50
ft. in height? Find the necessary horse power.
6. A man shovels 3 T. of coal from a wagon box into a bin 6 ft.
above the coal in the wagon. How much work is involved in the
process?
7. What must be the power of an engine that hoists 50 T. of ore
per hour from a mine 300 ft. deep?
8. A pumping engine is capable of raising 300 cu. ft. of water
every minute from a mine 132 ft. in depth. If a cubic foot of water
weighs 62.5 Ib., what must be the power of the engine ?
9. How long will it take a 3-H. P. engine to elevate 5000 bu. of
wheat 50 ft.? (A bushel of wheat weighs 60 Ib.)
10. A train is moving with a velocity of 30 mi. per hour. If the
resistance to the motion is 1500 Ib., calculate the power utilized.
11. The motors of an electric car can develop 200 H. P. With
what velocity can the car run against a uniform resistance of 2200 Ib. ?
3. POTENTIAL AND KINETIC ENERGY
59. Energy. In each of the cases selected in 54 to
illustrate the process of doing work, some agent capable of
doing work was assumed to be acting. The stone, for
1 So called in honor of James Watt (1736-1819), the inventor of the
steam engine.
WORK AND ENERGY 55
example, was supposed to be lifted by this agent, which
may have been an engine, a person, a horse, or any other
working medium. In order to be able to perform work,
an agent must possess energy. The energy of a body is
its capacity for doing work, or its ability to do work.
If we examine a body upon which work has been done,
any lifted mass, for instance, we discover that the
lifting process has invested the mass with the ability to do
work upon some other body. The lifted body may be
attached by a cord to the proper mechanism and allowed
to fall back to its original position ; but during its fall it
may turn wheels, lift another body, bend a bow, wind a
spring, or do work in some other manner. Thus in doing
work the falling body gives energy or working ability to that
upon which the work is done. Similarly, a hammer by
virtue of the velocity given it by the mechanic possesses
the capacity for doing work; This is manifested by the
fact that it drives the jiail in opposition to the resistance
offered by the wood.
60. Potential Energy. The lifted weight in the illus-
tration used in the preceding, section possesses energy be-
cause of its elevated position. ~"*A bent bow has the ability
to throw an arrow because of the fact that its form has
been changed by some agent. The spring of a watch can
keep the wheels moving against resistance on account of
the fact that some one has done work upon it in winding
it up. Energy possessed by a body because of its position or
form is called potential energy. The potential energy of a
body is measured by the work that was done upon it to
bring it into the condition by virtue of which it possesses
that energy. Hence a body whose mass is 100 pounds
which has been lifted a distance of 5 feet has 500 foot-
pounds of potential energy, i.e. it is able to do 500 foot-
pounds of work because of its elevated position.
56 A HIGH SCHOOL COURSE IN PHYSICS
61. Kinetic Energy. When a lifted. weight is allowed
to fall, it does work upon the object that it strikes. At
the instant of striking it possesses energy because it is in
motion. Moreover, any moving body is able to do work
by virtue of its motion. The energy possessed by a body
because of its motion is called kinetic energy. The kinetic
energy of a body is measured by the amount of work done
upon it to put it in motion.
62. Kinetic Energy Computed. The kinetic energy of a
moving body is measured by one half its mass multiplied by
the square of its velocity. This may be shown in the fol-
lowing manner : Let a body whose mass is m grams be
acted upon by a force of / dynes which will give it an
acceleration of a cm. /sec. 2 * From (2), 36, /= ma.
Again, since the force produces uniformly accelerated
motion in the given mass, at the end of t seconds, as
shown by (3), 25, the body will have been moved
through a distance d = J at 2 . Now the velocity v
acquired by the mass in t seconds as shown by (2), 25, is
v = at cm./sec. ; whence t 2 = . Substituting this value
for t 2 in the equation for distance, we obtain d = centi-
meters.
In order to compute the work done by the force /,
we have only to multiply the force by the distance d
through which it acts ( 55). Thus
Work =fd = max- = ergs.
a A
Since the work done in producing the motion is the
measure of the kinetic energy of the mass m ( 59),
Kinetic Energy = \ mv 2 ergs. (2)
WORK AND ENERGY 57
Let the mass, velocity, and acceleration be given in the units of
the F. P. S. system. Then the product ma will give the force in
poundals ( 36), and the quantity , the distance through which
the force acts, in feet. Therefore the product of force and distance
will give the work in foot-poundals. Hence, in the F. P. S. system
Kinetic Energy = \ mv 2 foot-poundals.
It should be remembered that the formula for kinetic
energy deduced above gives the result in the absolute
system only, i.e. in ergs or foot-poundals. These can be
readily reduced to kilogram-meters and foot-pounds by
the help of the numerical relations given in 56.
EXAMPLE. Calculate the kinetic energy of a 10-gram bullet
whose velocity is 40,000 cm./sec.
SOLUTION. Using equation (2), we have for the kinetic energy
of the bullet \ x 10 x 40,000 x 40,000, or 8,000,000,000 ergs. By re-
ferring to 54, we observe that 1 kg-m. equals 98,000,000 ergs.
Therefore, the reduction from ergs to kilogram-meters gives for the
kinetic energy of the body 8163 kg-m.
EXERCISES
1. Calculate the potential energy given to a mass of 25 g. by
lifting it through a vertical height of 10 m. Express the result in
kilogram-meters.
2. A ball moving with a velocity of 3500 cm./sec. has a mass of
250 g. Find its kinetic energy in ergs. How much work must a
boy do in order to stop it ?
3. Compare the kinetic energy of the ball in Exer. 2 with that of
a mass of 25,000 g. whose velocity is 350 cm./sec.
4. What is the kinetic energy of a 5-gram bullet just as it is
leaving the muzzle of a gun with a velocity of 30,000 cm./sec.?
5. To what height would the bullet in Exer. 4 have to be taken
in order to have an equal amount of potential energy ?
SUGGESTION. First find the force required to lift the bullet in
dynes; then apply equation (1), 55.
6. Compute the kinetic energy of a 5-pound mass moving with a
velocity of 25 ft. per second. Express the result in foot-pounds.
SUGGESTION. First obtain the result in foot-poundals ; then re-
duce to foot-pounds by the help of 56.
58 A HIGH SCHOOL COURSE IN PHYSICS
7. A constant force of 200 dynes acts upon a mass of 5 g. Cal-
culate (1) the acceleration, (2) the velocity produced in 3 seconds,
and (3) the kinetic energy. What is the distance through which
the force acts during the 3 seconds ?
8. In order to move a load up a hill 250 ft. long, a horse exerts
a constant pull of 125 Ib. How much work is done ? If the load
weighs 900 Ib., to what height would an equivalent amount of work
lift it?
9. A stone whose mass is 50 kg. is placed on the top of a chimney
30 m. in height. Calculate the amount of work that must be per-
formed in kilogram-meters and foot-pounds.
10. Compute the amount of work done per minute by a pumping
engine that forces 100,000 gal. of water into a reservoir 120 ft. high
every 10 hr. Assume the density of water to be 62.5 Ib. per cubic
foot.
11. If a rifle ball whose mass is 8 g. has a velocity of 35,000
cm. /sec., how far will it penetrate a block of wood that offers a uni-
form resistance of 100,000 g.
SUGGESTION. Let x be the depth of penetration in centimeters,
and place the work done by the ball expressed in ergs equal to the
kinetic energy.
12. The elevation of a tank containing 25,000 gal. of water is
75 ft. Find the potential energy of the water.
4. TRANSITIONS OF ENERGY
63. Transference and Transformation of Energy. No
processes in nature are of more common occurrence than
transferences of energy from one body of matter to an-
other and transformations of energy from one form into
another. For example, if a body is allowed to fall freely,
the potential energy that it possesses while elevated is grad-
ually transformed into kinetic energy which resides in the
body until its motion is checked. If, however, the body
should fall upon a spring properly placed, the spring
would be compressed and thus possess potential energy at
the expense of the kinetic energy of the falling mass.
Hence energy is transferred from the falling body to the
spring. Whenever one ~body does work upon another, energy
WORK AND ENERGY
59
is transferred from the body that does the work to the one
upon which the work is done.
Let the elevated mass M, Fig. 27, be suspended by a cord wound
around an axle A to which is at-
tached a heavy wheel W. It is
plain that the downward pull of
M upon the cord will cause the
wheel to turn. Thus, as M falls
and loses potential energy, it
does work upon the wheel in pro-
ducing motion and thus impart-
ing kinetic energy.
When the cord is fully un-
wound, the action will not cease ;
but the kinetic energy of the
wheel, by winding up the cord
FIG. 27. Transformation of the Po-
tential Energy of the Raised Mass
M into Kinetic Energy in the
Wheel W.
around the axle on the opposite
side, will enable it to lift M. In
this manner the wheel performs
work upon M, losing its kinetic energy and imparting potential en-
ergy to the mass lifted. If no energy were lost in overcoming fric-
tion, the kinetic energy imparted to the wheel in the former case
would be completely restored to the mass M in the latter.
Changes in energy occur in a large number of common
processes, such as winding a clock or a watch, shooting
an arrow from a bow, running a sewing machine, turning
a grindstone, running mills by water power, etc.
64. Conservation of Energy. Although energy is pass-
ing continually through transformations and is being
transferred from one body to another around us on every
hand, no one has ever been able to prove that even the
smallest portion can be created or destroyed. The infer-
ence is, therefore, that the same quantity of energy is present
in the universe to-day as existed ages ago ; i.e. that the quan-
tity of energy present in the universe remains constant.
This is known as the Law of the Conservation of Energy.
60 A. HIGH SCHOOL COURSE IN PHYSICS
The principal aim of Physics is to trace the various trans-
formations and transferences of energy that accompany
natural phenomena. At this point in the study many of
these changes will seem obscure because all the forms in
which energy may exist have as yet not been considered.
For example, we may inquire what becomes of the kinetic
energy of a spinning top as it slowly comes to rest. As
we pursue the study further, we find that where there is
motion in opposition to friction, as in this case, heat is
produced. But heat is one of the forms that energy may
take. Hence the kinetic energy of the top will appear
somewhere in the form of heat.
65. Matter and Energy. The intimate relation be-
tween matter and energy is becoming more and more
apparent. Matter is obviously a carrier, or vehicle, of en-
ergy. We become acquainted with matter only through
natural phenomena. In each phenomenon there is in-
volved some change in energy, and it is in the transforma-
tions and transferences of energy that our senses are
affected. It is upon these processes that we base our
entire knowledge of the material world.
EXERCISES
1. In driving a well a heavy weight is elevated by a horse and
then allowed to fall upon the end of a vertical pipe, thus forcing it
into the ground. Trace the energy changes taking place in the
process.
2. Trace the transferences and transformations of energy in the
process of driving a nail; of planing a board; of shooting an
arrow ; of throwing a stone ; of winding a clock ; of running a
sewing machine; of beating an egg.
3. Account for the energy of the water above a dam in a river.
What becomes of this energy ?
4. In what form is a supply of energy taken on board an ocean
steamer ? In what form is energy supplied to a locomotive ? to an
automobile? to a horse? to a man?
WORK AND ENERGY 61
SUMMARY
1. The term work is used to express the process of pro-
ducing motion. Work involves both force and motion in
the direction of the force, and is measured by the product
of the force employed multiplied by the distance through
which it acts. The equation of work is Work =/X d
( 55).
2. The erg, or dyne- centimeter, is the C. G. S. unit of
work and of energy and is the work done by a force of one
dyne acting through a distance of one centimeter. The
foot-poundal is the English absolute unit of work and en-
ergy. The kilogram-meter and foot-pound are the gravita-
tional units in common use ( 56).
3. The activity, or power, of an agent is the rate at
which it can do work. The activity of an agent is said to
be one horse power when it can perform work at the rate
of 550 foot-pounds (or 746 x 10 r ergs) per second (57
and 58).
4. The energy of a body is its capacity for doing work,
or its ability to do work ( 59).
5. Potential energy is the energy possessed by a body
because of its position or form ( 60).
6. Kinetic energy is the energy possessed by a body by
virtue of its motion. The equation of kinetic energy is
K.E. = l mv* ( 61 and 62).
7. When one body does work upon another, energy is
transferred from the body that does the work to the one
upon which the work is done ( 63).
8. Energy cannot be created or destroyed. The quan-
tity present in the universe remains constant. This is
known as the Law of the Conservation of Energy ( 64).
CHAPTER V
GRAVITATION
1. LAWS OF GRAVITATION AND WEIGHT
66. Universal Gravitation. Ancient astronomical ob-
servations revealed the fact that the planets move through
space in curvilinear paths. Later and more refined obser-
vations led to the discovery that the sun is a center about
which they revolve in slightly elliptical orbits. Further-
more, it is universally known that several of the planets
have satellites which revolve about them, correspond-
ing to the moon which moves in an orbit encircling the
earth. Late in the seventeenth century Sir Isaac Newton
originated the theory that is now known as the Law of
Universal Gravitation, in order to account for the motion
of heavenly bodies in nearly circular orbits instead of
straight lines.
67. Newton's Law of Universal Gravitation. This law
may be stated as follows :
Every body in the universe attracts every other body with
a force which is directly proportional to the product of the
attracting masses and inversely proportional to the square of
the distance between their centers of mass ( 70).
According to this law a book and a marble, or two
bodies of any other kind of matter, attract each other.
Between ordinary masses this force remains unnoticed by
us in everyday life because it is so minute ; in fact, it
would require the most refined test to detect it. But
since the attraction is proportional to the product of the
masses, in the case of two heavy bodies the moon and
62
GRAVITATION 63
the earth, for example the force is enormous. Even
between the earth and a marble or a book the force is
quite perceptible. When the earth is one of the acting
masses, the attraction is called the force of gravity, and
when expressed in the proper units of measure, this attrac-
tion is called the weight of the marble, book, etc. Weight,
therefore, partakes of the nature of a force and is quite
distinct from mass ( 10). Hence, when we say in
ordinary language, for instance, that the intensity of a
certain force is 10 pounds, we mean that it is equal to
that force with which the earth attracts a mass of 10
pounds. Again, since weight is a force, it may be ex-
pressed in any of the units of force ( 36 and 37), i.e. in
dynes, poundals, etc.
68. Weight. Since for a given locality the mass of
the earth, as well as the distance from the center, is con-
stant, the weight of a body is strictly proportional to its mass.
Again, since the earth is not spherical but flattened
slightly at the poles, the same mass at different places
will not possess the same weight. On moving north or
south from the 'equator the radius of the earth decreases
slightly, which causes the mass to come somewhat nearer
the earth's center and thus increases the value of the
force of attraction.
69. Law of Weight. The law of universal gra vita-
ion applied to bodies outside the earth's surface is as
follows :
The weight of a body above the earth's surface is inversely
proportional to the square of its distance from the center of
the earth.
If the radius of the earth is assumed to be 4000
miles, the weight of a one-pound mass 4000 miles
above the surface, which is 8000 miles from the cen-
ter, would be only one fourth of a pound. This result
64 A HIGH SCHOOL COURSE IN PHYSICS
is obtained by applying the law of weight as follows :
x : 1 pound : : 4000 2 : 8000 2 ;
whence x = J pound.
Since the distance from the earth's center is less at
Chicago than at the equator, a mass of 1 pound weighs
about g-^g- of a pound more at the former place than at
the latter. For small differences of latitude, however,
the difference in weight is so small that it is of little
importance. In consequence of the earth's rotation the
weight of bodies at the equator is diminished ^9 ( 53)
as the result of the centrifugal reaction against the force
of gravity. In other latitudes this diminution is less.
It is of interest to consider what the effect would be upon the
weight of a given mass if it were to be taken to some point below
the surface of the earth. Let it be im-
agined that the circle in Fig. 28 repre-
sents a cross section through the center
of the earth, and that P is the location
of the body to be weighed. All that
part of the earth represented by the
shaded portion of the circle above the
plane AB will exert a resultant attrac-
tion upward, while that represented by
the unshaded part has a resultant acting
FIG. 28. A Mass at P is At- toward the center O. Since these forces
tracted Upward as well as oppose each other, the weight of the body
Downward. .,, ,. . . , ., , _,
will dimmish as it approaches the center
O. When the body reaches the center, the attractions due to the
different portions of the earth will be equal in all directions, and the
resultant of all will be zero. Therefore the body will weigh nothing
at the center of the earth.
EXERCISES
1. If the mass of the earth were doubled without any change
in its shape or size, how would a person's weight be affected?
2. Which is a definite quantity, a gram of matter or a gram of
force (i.e. a gram-weight) ?
GRAVITATION
65
3. How much will the potential energy of a mass of 2000 fb.
elevated 100 ft. at Chicago differ from that of an equal mass raised
100ft. at the equator?
4. A certain mass is weighed on a dynamometer ( 11) at New
York. Will the instrument indicate a greater or a less weight when
the same mass is weighed at the equator ?
5. If two masses are in equilibrium when placed in the pans of
a beam balance at the equator, will they still be in equilibrium when
tested in the same manner at San Francisco?
6. How far above the earth's surface would a body weigh one half
as much as at the surf ace ? Ans. 1656.8 mi.
7. What would a 100-pound body weigh at a distance of 200 ini.
above the earth's surface ?
8. An aeronaut ascends 5 mi. in a balloon. If his weight at the
surface is 150 lb., what will it be at that height ?
2. EQUILIBRIUM AND STABILITY
70. Center of Gravity. The weight of a body is the
resultant of the weights of the individual particles of
which it is composed. Since these
innumerable forces are all directed
toward the center of the earth, which
is 4000 miles away, they form a sys-
tem of essentially parallel forces
whose resultant CA, Fig. 29, is equal
to their sum ( 46). The point of
application O is called the center of
gravity of the body. Since the posi-
tion of this point depends upon the
distribution of matter in the body, it
is also called the center of mass. In many problems it is
convenient to consider the body as though all its mass
were located at this point. If a flat piece of cardboard of
any shape is balanced on the point of a pin, the center of
gravity is located at the point of contact and midway
between the two surfaces.
6
FIG. 29. Weight is the
Resultant of Innumer-
able Small Forces.
66
A HIGH SCHOOL COURSE IN PHYSICS
Let a flat piece of cardboard be pierced at any point, as A, Fig. 30,
and hung loosely on a small nail or pin. The cardboard will turn
until the center of gravity falls as low as pos-
sible. In this condition a vertical line through
A will pass through the center of gravity.
This line is easily found by hanging a plumb
line from the axis in front of the cardboard.
If a second point of support, as , be taken
and a vertical line determined as before, the
center of gravity C will lie at the point of in-
tersection of the two lines.
FIG. 30. Locating the
Center of Gravity. ^ Equilibrium Of Bodies. A body
is said to be in equilibrium when a vertical line through
the center of gravity passes through a point of support.
A common case of equi-
librium is that of a chair
or table. In such in-
stances a vertical line'
through the center of
gravity passes through
the area of the base in-
cluded within the lines
joining the feet. Four
FIG. 31. Stable, Unstable, and Neutral
Equilibrium Illustrated.
typical cases are represented
in Fig. 31. Pyramid A hangs from its apex, B stands
upon its base, and C rests with its apex at the point of
support. Obviously A and B tend to remain indefinitely
in the positions shown, but will overturn with the
slightest disturbance. If A or B should be tilted, the
center of gravity would be lifted, necessitating the
expenditure of energy upon the body. A and B are said
to be in stable equilibrium. On the other hand, a disturb-
ance of lowers the center of gravity and thus lessens
the potential energy of the body. When a body is in
this condition, it is said to be in unstable equilibrium.
A third condition is represented by a sphere of uniform
GRAVITATION 67
density resting upon a smooth horizontal plane. If the
sphere be rolled along the plane, its center of gravity will
be neither raised nor lowered. It is said to be in neutral
equilibrium. A body arranged to turn upon an axis
through its center of gravity is also in a condition of
neutral equilibrium.
72. Stability of Bodies. When a body is in stable
equilibrium, work must be performed upon it in order to
cause it to overturn. This amount of work will depend
upon the weight of the body and the distance through
which its center of gravity is lifted, and is measured by
their product ( 55). The amount of work required to
overturn a body is a measure of its stability.
EXAMPLE. Find the stability of a box 4 ft. square and 2 ft. high
and weighing 500 Ib.
SOLUTION. Referring to Fig. 32, it is plain that the center of
gravity C must be moved to the
point A while the box is being over-
turned. The height through which
C is raised is BA, equal to OC
OB. Now OC is the hypotenuse
of the right triangle OBC whose
sides are 1 ft. and 2 ft. respectively.
Hence OC equals V5", or 2.24 ft.
Therefore, AB is 1.24 ft., and the __
work done 1.24 x 500, or 620 foot- FlG . 32. Center of Gravity is Lifted
pounds. Through the Height BA.
It is clear that of two bodies having the same weight,
the more stable one is that whose center of gravity has to
be lifted through the larger vertical distance when we
overturn it. This will depend on the size and shape
of the base on which it rests and on the height of the
center of gravity above the base. Figure 33 shows a brick
in three possible positions. The center of gravity C
moves through an arc having the lower right-hand corner
68
A HIGH SCHOOL COURSE IN PHYSICS
of the brick as its center when the body is overturned
about this point. It will be seen at once that the greatest
i
~^7
\
\
/
1
i
i
i
\
\
1
1
1
a 1
\
^ \
\
^v \
I
i
i
/
> >n n
/ \
\
\
\
\
i
,'c
c / / \
\
/
i
^\
/ \
^-~>
(/) (2) (3)
FIG. 33. The Overturning of a Brick about Different Edges.
stability is possessed by the brick when lying on its largest
base ; first, because the base is largest, and second, because
the center of gravity is in the lowest possible position.
In each case c'a is the vertical distance through which the
center of gravity would have to be lifted by the overturn-
ing agent.
Note the various methods employed to give the proper
stability to objects in everyday use, as lamps, clocks, ink-
stands, chairs, pitchers, vases, etc.
EXERCISES
1. How would you place a cone on a horizontal table in positions
representing the three conditions of equilibrium ?
2. Arrange two knives in a piece of wood as shown in Fig. 34 and
support the point on the finger. Why is the
system in stable equilibrium? Where is the
center of gravity of the system ?
3. Why is it difficult to walk on stilts?
4. Explain the difficulty experienced in try-
ing to balance an upright rod upon the end of
the finger.
5. Why does not the Leaning Tower of
Pisa fall? See Fig. 36.
6. Explain the difficulty experienced in trying to balance a meter
stick on one end upon a level table.
FIG. 34. A System in
Stable Equilibrium.
GRAVITATION
69
7. The oil can B shown in Fig. 35 is loaded with lead at the bot-
tom. Explain how this can will right itself while one of the common
form A remains overturned.
8. Which of two bodies hav- A
ing equal weights possesses the
greater stability, a pyramid or a
rectangular box having the same
base and height as the pyramid? FIG. 35. Oil Cans.
SUGGESTION. The center of gravity of a pyramid is located at
one third of the distance from the base to the apex.
9. Calculate the stability in foot-pounds of a 4-pound brick placed
in three different positions on a horizontal table. Assume the dimen-
sions to be 2 x 4 x 8 in. See example in 72.
3. THE FALL OF UNSUPPORTED BODIES
73. Falling Bodies. Before the time of the Italian
mathematician and physicist, Galileo Galilei, 1 little
was known concerning the way in which
bodies fall when unsupported. It is a
well-known fact that if we drop a coin
and a piece of paper or a feather at the
same instant, the coin will reach the floor
first. Galileo rightly inferred that the
difference was due to the resistance of-
fered by the air. Nevertheless, in order
to place on an experimental basis his
conclusion that all falling bodies tend
to have the same acceleration, he dropped
bodies of different kinds from the top
of the Leaning Tower of Pisa (Fig.
36) in the presence of many learned men of the time.
These experiments demonstrated that all bodies tend to fall
from a given height in practically equal times. Furthermore,
it was readily shown that light materials, as paper, for ex-
ample, fall in less time when compressed than when spread
1 See portrait facing p. 70.
FIG. 36. Leaning
Tower of Pisa,
Italy.
70 A HIGH SCHOOL COURSE IN PHYSICS
out. Later, after the invention of the air pump, Galileo's
inference was verified by allowing a light and a heavy
body to fall in a vacuum. For this purpose
the " guinea and feather " tube (Fig. 37) is
commonly used. On inverting the tube
after the air has been exhausted, we find
that the feather falls as rapidly as the coin.
But when the air is again admitted, the
feather flutters slowly along far behind the
rapidly falling coin.
74. Uniform Acceleration of Falling Bodies.
Since the attraction existing between a
body and the earth is constant, it follows that
a body falling freely, i.e. without encoun-
tering resistance, will have uniformly accel-
erated motion ( 24 and 36). Again, since
FIG. 37. Bodies a ^ bodies fall the same distance in a given
Fall Alike in time when unimpeded, the acceleration will
be the same for all bodies. This acceleration
is called the acceleration due to gravity, and is designated
by the letter g.
75. The Acceleration Due to Gravity. The acceleration
of freely falling bodies varies according to the laws of
weight given in 69. Since the distance to the center of
the earth decreases as one travels from the equator toward
the poles, the acceleration due to gravity becomes greater.
In latitude 38 N. g is 980 cm./sec. 2 , and in latitude 50 N.
981 cm./sec. 2 . The value of g also decreases slightly with
the elevation above sea-level. (Why ?) In the latitude
of New York, 40.73 N., a freely falling body gains in ve-
locity at the rate of about 980 centimeters, or 32.16 feet,
per second during each second of its motion.
When bodies are thrown upward, the acceleration is negative ; i.e.
the velocity decreases at the rate of 980 centimeters per second
GALILEO GALILEI (1564-1642)
The first successful experimental investigations relating to falling
bodies and the pendulum must be attributed to Galileo. For nearly
twenty centuries the science of Mechanics had remained undeveloped.
Aristotle had announced that the rate at which a body falls depends
upon its weight, but Galileo was the first to disprove it by experi-
ment. This he did by dropping light and heavy bodies from the
leaning tower of Pisa, Italy, his native town. A one-pound ball and
a one-hundred-pound shot, which were allowed to fall at the same
time, were observed by a multitude of witnesses to strike the ground
together. Hence the rate of fall was shown to be independent of
mass.
At another time, while observing the swinging of a huge lamp
in the cathedral, Galileo was astonished to find that the oscillations
were made in equal periods of time no matter what the amplitude.
He proceeded to test the correctness of this principle by timing the
vibrations with his own pulse. Later in life he applied the pendu-
lum in the construction of an astronomical clock.
Galileo was the first to construct a thermometer and the first to
apply the telescope, which he greatly improved, to astronomical
observations. He discovered that the Milky Way consists of innu-
merable stars; he first observed the satellites of Jupiter, the rings of
Saturn, and the moving spots on the sun.
Galileo was made professor of mathematics in the University of
Pisa in 1589 and filled a similar position at Padua from 1592 until
1610. He died in the year 1642, the year of Newton's birth.
GRAVITATION
71
during each second of its upward motion. Hence, a body thrown
upward with a velocity of 2940 centimeters per second will continue
to rise 3 seconds, when it will stop and return to earth in the next 3
seconds. However, on account of the hindrance of the air, bodies
moving with great velocity deviate considerably from the laws govern-
ing unimpeded bodies.
76. Laws of Freely Falling Bodies. Since the motion
of an unimpeded body while falling is uniformly acceler-
ated, the equations of 25 may be applied by simply sub-
stituting for a the acceleration due to gravity g. These
equations may be written as
follows :
v = gt, (1)
and d = I gt 2 . (2)
From equations (l) and (2)
other useful formulae may be
deduced. From (l) we find that
dfor 1 sc =
AtB, V=
dfor 2 sec=4 x ^ g -" ^
At C, v^2g - -
AtD, v=3g
7 x/29
t 2 = Substituting this value
for t 2 in equation (2), we obtain
Solving equation (3) for v,
we have
v = V2~gd. (4)
77. Distances and Velocities
Represented. The distances
passed over and the velocities
acquired by a freely falling body
are represented graphically in
Fig. 38. A vertical line is
drawn on which a convenient distance AS is measured off
to represent 1 x \g (about 16 feet), the distance the
body falls during the first second. The distance AC is
FIG. 38. Motion of a Falling
Body Represented.
72
A HIGH SCHOOL COURSE IN PHYSICS
c'
'
made four times the distance AB ; AD, nine times AB ;
AE, sixteen times AB, etc., to represent the distances
fallen in one, two, three, and four seconds respectively.
The heavy arrows are drawn to represent the velocity
at the end of each second. The length of the first is
g units (representing about 32 feet per second), the
second 2#, the third 3#, etc.
78. Bodies Thrown Horizontally. It is a well-known
fact that a body projected in any direction except up or
down follows a curved path. An interesting case of this
kind is the projection of a body
horizontally from some elevated
position, as A, Fig. 39. The
motion of the body will be the
resultant of two component mo-
tions, the one vertically down-
ward due to gravity, and the
other in a horizontal direction
due to the projectile force.
Since there is no horizontal
force acting on the body after it
leaves the point A, the horizon-
tal component of the motion
will bi
F.o.39.-Mo t ionofaBodyPro-
jected Horizontally from the will move (horizontally) over
'omt A. equal distances in equal intervals
of time. Let AB' , B 1 C f , C'D', etc., represent these hori-
zontal distances for successive seconds. The distances AB,
BO, CD, etc., are drawn in the manner described in 77.
Under the combined action of its initial horizontal velocity
and the force of gravity the body will pass through the
point P 1 at the end of the first second, P 2 at the end of the
second, P 3 at the end of the third, etc. Thus the body
follows the curved path
GRAVITATION 73
The path of a stone thrown over a tree, for example, is a case in
which the initial motion of the body is not horizontal. The motion
may be divided into two parts : first, the rise of the stone to the highest
point reached ; and, second, the fall of the body back to the earth.
The latter half of the motion is precisely the case described above.
The time during which the stone is rising is practically equal to that
of its fall. The time required for the return of the stone to the earth
is the same as that of a body falling vertically. Likewise the time
occupied by the stone in rising is equal to that required by a body
thrown vertically upward to attain the same height. The shape of
the path taken by the stone depends on its initial speed and the direc-
tion in which it is thrown. The study of the motion of projected
bodies, as bullets, cannon balls, shells, etc., forms an important part of
military and naval instruction.
EXERCISES
1. A body falls freely from a certain height and reaches the
ground in 5 seconds. What velocity is acquired? From what height
must it fall?
2. How long does it take a body to fall 100 ft. ? 200 ft. ?
3. A mass of 50 g. falls for 3 seconds from a state of rest. Calcu-
late its kinetic energy. (See 62.)
4. A mass of 50 Ib. falls from an elevation of 20 ft. Calculate its
kinetic energy in foot-pounds at the time it reaches the ground. Com-
pare the kinetic energy with the potential energy of the body before
falling.
5. How far must a body fall in order to acquire a velocity of
500 ft. per second?
6. A book falls from a table 3 ft. in height. Find the velocity of
the book when it reaches the floor.
7. A stone is dropped from a train whose velocity is 30 mi. per
hour. Show by a diagram the path traced by the stone. (See 78.)
8. Find the kinetic energy of a 10-gram mass after it has fallen
from rest a distance of 1960 cm., assuming y to be 980 cm./sec. 2 .
9. The velocity of a body falling freely from rest was 200 ft. per
second. From what height did it fall?
10. Compare the velocity of a body after falling 64.32 ft. with
that of a train running 30 mi. per hour.
11. A bullet is fired vertically upward from a gun with a velocity
74 A HIGH SCHOOL COURSE IN PHYSICS
of 25,000 cm./sec. Disregarding the resistance of the air, how many
seconds will the bullet continue to rise? How high will it rise?
12. If the bullet in Exer. 11 encountered no resistance due to the
air, how many seconds would pass before it returned to earth ?
13. The weight of a pile-driver is lifted 10 ft. and allowed to fall.
With how much greater velocity will it strike if lifted 20 ft. ? With
how much greater energy ?
14. A stone thrown over a tree reaches the earth in 3 seconds.
What is the height of the tree?
15. A boy fires a rifle ball vertically upwards and hears it fall upon
the ground in 20 seconds. How high does it rise? What was its
initial velocity?
4. THE PENDULUM
79. The Simple Pendulum. A heavy particle sus-
pended from a fixed point by a weightless thread of constant
length is an ideal simple pendu-
lum. If, however, we suspend
a small metal ball A, Fig. 40,
by a thin flexible thread or wire
from a fixed point 0, it fulfills
the ideal conditions almost per-
fectly. The distance OA from
the point of suspension to the
center of the ball is the length
of the pendulum. The arc AC,
or the angle AOC, which rep re-
ef^ &\c sents the displacement of the
9 ball from the position of equi-
librium, is the amplitude of vi-
FIQ 40. The Simple Pendulum. , 7 ., . .
oration. A vibration is one to-
and-fro swing, sometimes called a complete or double vibra-
tion. A single vibration is the motion of the ball from C
to C 1 , or one half of a complete vibration. The period of
a single vibration is the time consumed by the pendulum
in moving from C to C 1 .
GRAVITATION
75
80. Pendular Motion Due to Gravity. When a pen-
dulum is in the position of rest, the weight of the ball rep-
resented by the line A W, Fig. 41, is balanced by the equal
and oppositely directed ten-
sion AT in the cord OA.
Now let the ball be drawn
aside to the position C and
released. The weight of the
ball, which always acts ver-
tically downward and is
represented by the line 6 Y P,
can be resolved into two
components. One of these
components is represented
by the line CE and serves FIG. 41. -Gravity Causes a Pendulum
solely to produce tension in to Vibrate,
the cord 00. It is plain that this component has no effect
on the motion of the ball. The other component CB acts
upon the ball along the tangent to the arc of vibration at
the point 0. The effect of this component is to give the
ball accelerated motion along the arc. After the ball passes
the point A, it is clear that the component along the tangent
tends to retard the motion and finally succeeds in stopping
the ball at the point <7', after which it returns the ball
again to A.
If the line CD is drawn perpendicular to OA, the triangles
CDO and CBP are similar. Why? We may therefore write the
proportion
CB : CP : : CD : CO (5)
This proportion may also be written as follows :
Force CB = displacement CD x weight of ball CP . (6)
length CO
Since the weight of the ball CP and the length of the pendulum
CO remain constant during a vibration, equation (6) shows that the
effective force CB is proportional to the displacement CD. Hence
76
A HIGH SCHOOL COURSE IN PHYSICS
the acceleration of the ball is not the same at all points in the arc
CA, but varies directly as the displacement.
81. Transformations of Energy in the Pendulum. A
pendulum is first set in motion by displacing the ball, or
pendulum bob. This process requires the performance of
work which elevates the ball through the height AD, Fig.
41 (measured vertically), and stores potential energy in it.
From equation (l), 55, it is clear that the amount of
potential energy given the ball is measured by the product
of its weight and the height AD. As the ball moves toward
A, velocity is acquired, and the potential energy is gradu-
ally changed into kinetic. At A the energy is all kinetic.
After passing the point A the ball rises to C', while the
kinetic energy is transformed back into potential. At O 1
the energy is all potential again. Thus recurrent trans-
formations of energy take place, which would occur with-
out loss if it were not for the resistance offered by the
air as well as by friction at the point of
suspension.
82. Laws of the Simple Pendulum.
The first three laws of the simple pendu-
lum may be deduced from the results
obtained from the following experiments :
Suspend four balls as shown in Fig. 42. Let
A, B, and C be of metal, and D of wood or wax.
Make the lengths of A, B, and C as 1:4:9; e.g.
20, 80, and 180 cm. Also let Z> be made precisely
of the same length as C. Now if C and D be set
swinging through the same amplitude, it will be
readily observed that the period of vibration of D
is the same as that of C.
Again, let C and D be set in vibration through
different amplitudes. If neither amplitude is large,
it will be seen that the period of one is still the
same as that of the other.
Finally, let A, B, and C be put in motion successively and the
A BCD
FIG. 42. Pendu-
lums of Differ-
ent Lengths and
Masses.
GRAVITATION 77
single vibrations of each counted for one minute. If the period of
vibration of each pendulum be computed from the number of vibra-
tions per minute, it will be found that the three periods are as 1 : 2 : 3,
i.e. as VI: VI: VQ.
The laws governing the vibration of simple pendulums,
therefore, may be stated thus :
(1) The period of vibration is independent of the material,
or mass, of the ball.
(2) When the amplitude of vibration is small, the period
of vibration is independent of the amplitude; i.e. the vibra-
tions are made in equal times. This is called the Law
of Isochronism (pronounced i sok'ro nism). If the ampli-
tude exceeds 5 or 6, the period of vibration will gradually
diminish as the arc becomes smaller.
(3) The period of vibration is directly proportional to
the square root of the length of the pendulum. This is
called the Law of Length. This law may be represented
thus : ^ : t 2 : : Vl 1 : VI 2 , where ^ and ^ refer to the period
and length of one pendulum, and t 2 and Z 2 , to the period
and length of the other. If, therefore, any three of the
terms are given, the fourth may be computed.
Since a pendulum is dependent upon the force of gravity,
as shown in 80, its period of vibration is found to depend
upon the value of g. Hence :
(4) The period of vibration is inversely proportional to
the square root of the acceleration due to gravity.
83. The Pendulum Equation. The relation between
the period and length of a simple pendulum and the
acceleration due to gravity is given by the equation
where t is the period of a single vibration, I the length of
the pendulum measured in centimeters (or feet), and g
78 A HIGH SCHOOL COURSE IN PHYSICS
the acceleration due to gravity measured in centimeters
per second per second (or feet per second per second).
The value of TT is 3.1416, the ratio of the circumference
of a circle to the diameter.
This equation is of great assistance (1) in calculating
the period of any simple pendulum of known length, (2)
in determining the length of a pendulum that vibrates in
any given period of time, and (3) in finding the value of
g at any place where its magnitude is unknown. (See 87. )
84. The Seconds Pendulum. A pendulum of which the
period of a single vibration is one second is a seconds
pendulum. As shown by equation (7), the length of a
simple pendulum , when the period t is
one second, will depend on the acceleration
due to gravity at the place chosen. At all
places where tfce value of g is 980 cm. /sec. 2 ,
the length I of a simple pendulum that beats
seconds is 99.3 cm. ; where g is 981 cm. /sec. 2 ,
I is 99.4 cm.
85. The Compound Pendulum. When
the conditions defining the ideal simple pen-
dulum ( 79) are not sufficiently fulfilled,
the body is called a compound or physical
pendulum. For experimental purposes a
meter bar may be siispended on a smooth
wire nail which pierces it at right angles
close to one end. The bar may be hung to
. A Com- swing freely between the prongs of a large
pound Pendu- tuning fork, as shown in Fig. 43. Let a
lum and its . _ & ' . . . . _ ' . . . ,
Equivalent simple pendulum OA be placed by the side
fum Ple Pendu " f tne suspended bar so that their points of
suspension lie in the same horizontal plane.
Set both pendulums in vibration and adjust the length of
the simple one until they vibrate in the same period of
GRAVITATION 79
time. It will be observed at once that the simple pendu-
lum must be made several inches shorter than the other.
Only those points in the compound pendulum very near
the point O swing in their natural period ; particles below
tend to swing slower, and those above, faster, than the
simple pendulum. O is called the center of oscillation of
the compound pendulum. In this case the point c is lo-
cated two thirds of the length of the bar from the point
of suspension. The simple pendulum is thus seen to be a
special case of the compound one in which the entire mass
is concentrated near the center of oscillation.
The compound pendulum in Fig. 43 may be set swinging
by being struck a sharp blow at the point 6 y , and the axis
will not be disturbed. For this reason O is called the center
of percussion. Thus, for example, when a ball is batted,
the bat should be so handled that the ball will strike its
center of percussion. This will prevent the jarring of the
hands and the breaking of the bat.
86. The Compound Pendulum Reversible. If the meter
bar shown in Fig. 43 be suspended by piercing it at the
center of oscillation and swinging it about this point,
the period of vibration will be the same as before. In
other words, the point of suspension B and the center
of oscillation C are interchangeable. This property
of a compound pendulum, which was discovered by the
famous Dutch physicist Huyghens (1629-1695), is
known as its reversibility.
87. Utility of the Pendulum. The value of the pendu-
lum in the measurement of time is due to the isochronism
of its vibrations. Although Galileo was the first to ob-
serve this property of the pendulum and the first to make
a drawing of a pendulum clock, Huyghens was the first to
use a pendulum in controlling the motion of the wheels of
a timepiece. This he accomplished in 1656.
80
A HIGH SCHOOL COURSE IN PHYSICS
The motion of a clock is maintained by lifted weights or by the
elasticity of springs. The office of the wheelwork is to move the
hands over the dial and to keep the pendulum from
being brought to rest by friction. The latter is
effected by means of the escapement shown in
Fig. 44. The wheel R is turned by mechanism
not shown in the figure. When the pendulum
swings to the right, motion is communicated to the
curved piece MN through the parts A, B, and O ;
and M is lifted. The wheel is thus released ; but,
on turning, strikes at N. While the pendulum
moves to the left, the slight pressure of the cog
against N causes A to deliver a minute force to the
pendulum. As N" rises, the wheel is again re-
leased, but is again detained a,t'M. Thus one cog
is allowed to pass for each complete vibration of the
pendulum. Every "tick" of the clock is caused
by the wheel R being stopped either at M or N.
If the wheel is allowed to turn too fast, the clock
gains time. This defect is corrected by lowering
the bob. If the clock loses time, the bob is raised.
The pendulum offers the most precise
method for measuring the acceleration of
FIQ a gravity. By carefully determining experi-
ment and Pen- mentally the period t and the length I of a
duiumofadock. p en dulum, the value of g can be easily cal-
culated by the help of equation (7), 83.
EXERCISES
1. By the help of equation (7), 83, find the period of a pendulum
80 cm. long, when g equals 980 cm. /sec. 2 .
2. Calculate the length of a simple pendulum that beats half
seconds (i.e. t equals | sec.) at a place where the acceleration is 981
cm./sec. 2 .
3. The pendulum of a clock has a period of a quarter second.
Find its length if g is 980 cm./sec. 2 .
4. How long is a simple pendulum that makes 65 single vibrations
per minute?
SUGGESTION. First compute the value of t.
GRAVITATION 81
5. What is the value of g where a simple pendulum 99.2 cm. long
makes 60 single vibrations per minute?
6. An Arctic explorer finds that the length of the seconds pendu-
lum at a certain place is 99.6 cm. What is the value of g at this place ?
7. A simple pendulum is to make 45 single vibrations per minute.
If g is 980 cm./sec. 2 , what must be its length?
8. It is found at a certain place that a simple pendulum 90 cm.
long makes 64 single vibrations per minute. Find the value of g at
this place.
9. A pendulum whose bob weighs 100 g. is drawn aside until the
distance AD, Fig. 41, is 4 cm. How much energy is stored in the
bob ? How much work was done upon it?
SUMMARY
1. Newton's Law of Universal G-ravitation states that
every body in the universe attracts every other body with
a force that is directly proportional to the product of the
attracting masses and inversely proportional to the square
of the distance between their centers of mass ( 67).
2. The attraction of the earth for other bodies is called
the force of gravity. The weight of a body is the measure
of this force ( 67).
3. The weight of a body is proportional to its mass ( 68).
4. The weight of a body above the earth's surface is in-
versely proportional to the square of its distance from the
center of the earth. On account of the spheroidal form of
the earth, a body at the equator weighs slightly less than
a body of the same mass at some other point on the earth's
surface ( 69).
5. The weight of a body is the resultant of the weights
of the individual particles that compose it. The point of
application of this resultant is the center of gravity of the
body ( 70).
6. A body is in equilibrium when a vertical line drawn
through its center of gravity passes through a point of
7
82 A HIGH SCHOOL COURSE IN PHYSICS
support, or within the area included between the extreme
points of support. The three kinds of equilibrium are
stable, unstable, and neutral ( 71).
7. The stability of a body is measured by the work that
must be performed in order to overturn it ( 72).
8. All freely falling bodies descend from" the same
height in equal times. Such bodies have uniformly ac-
celerated motion. The acceleration due to gravity is about
980 cm./sec. 2 , or 32.16 ft./sec. 2 ( 73-75).
9. The equations of freely falling bodies are (1) v = gt,
(2) d = \gt\ (3) d= ^ and (4) v = V2^d ( 76).
10. When bodies are thrown, the horizontal component
of the motion is uniform, while the vertical component is
uniformly accelerated ( 78).
11. The swinging of a pendulum is due to the force of
gravity ( 80).
12. The period of vibration o^a pendulum is independ-
ent of the mass of the bob and\the amplitude of vibra-
tion when the arc is small, and is tiirectly proportional to
the square root of the length andNinversely proportional
to the square root of the acceleration due to gravity. The
equation of the pendulum is t = TT -y^ ( 82).
13. A compound pendulum may be conceived as being
made up of simple pendulums of different lengths. The
period of vibration depends upon the position of the center
of oscillation. The center of oscillation and point of sus-
pension are interchangeable. The center of percussion
and the center of oscillation coincide ( 85 and 86).
CHAPTER VI
MACHINES
1. GENERAL LAW AND PURPOSE OF MACHINES
88. Simple Machines. The transference of energy from
a body capable of doing work to another upon which the
work is to be done is often accomplished more advanta-
geously by the use of a simple machine than in any other
way. Indeed, it is often impossible for an agent to do
the required work without the aid of a machine. For
example, a man wishes to load a barrel of lime into a
wagon, but finds that he is unable to lift it ; with the
aid of an inclined plane of suitable length, however, the
barrel is easily rolled into the wagon. In other cases use
is made of the pulley, lever, wheel and axle, screw, and wedge,
which with the inclined plane form the six simple machines.
89. The Principle of Work. The
general law of machines is illustrated by
the following experiments :
1. Let a cord be passed over a pulley, as shown
in Fig. 45. Let the pull of a dynamometer be
used to counteract the weight of the body W.
It is obvious in this case that the amount of force
F registered on the dynamometer must be equal
to the weight W. The experiment will show FIG. 45. The Effort
that this is the case. Furthermore, if force F F . Equals the
moves downward 1 foot, W will be elevated Moves Througlian
through an equal distance. Equal Distance.
If, now, we designate the distance through which the
acting force (or effort) F moves by the letter d and the
83
84
A HIGH SCHOOL COURSE IN PHYSICS
distance the weight Wis lifted by d 1 ', the work put into the
machine by the acting agent is F x d, and the work done
by the machine is W x d' . It is plain that the experiment
shows that -
2. Let the pulley be now attached to the weight W, Fig. 46, and
let one end of the cord be fastened to some stationary object at A . If
W is made 1000 grams, for example, it will be
found that the upward effort registered by the
dynamometer will be 500 grams. For any value
of W, F will be one half as great. However, when
F moves a distance of 1 meter, for example, W is
elevated only one half a meter.
In this experiment W= 2 F, and d' == \ d.
Therefore, we may write as before
Fxd = Wxd'. (l)
The relation shown by this equation is
one of the most important laws of me-
Fio. 46. TheEf- chanics and is known as the Principle of
One Half of U the Work. The principle may be stated as
Weight W, but follows:
Moves Twice as
Far - The work done by an agent upon a ma-
chine is equal to the work accomplished by the machine ; or,
the effort F multiplied by the distance through which it ads
equals the resistance W that is overcome by the machine mul-
tiplied by the distance it is moved.
This law may be applied to any machine, no matter how
simple or complicated it may be, provided the friction of
the moving parts can be disregarded.
EXAMPLE. An agent capable of doing work exerts a force of
50 Ib. upon a machine. If a weight of 250 Ib. is lifted 8ft. by the
machine, through what distance must the applied force act?
SOLUTION. The work done by the machine is 250 x 8, or 2000
foot-pounds. Hence, the force applied by the agent must act through
the distance 2000 -4- 50, or 40 ft.
MACHINES 85
It is clear from this example that the gain in force is
accomplished at the expense of distance, since the effort
must move five times as far as the resistance. Its speed
also is five times as great. On the other hand, a machine
may be made to increase the distance as well as the speed
at the expense of force. Such is the case in many practi-
cal applications of the simple machines.
90. Mechanical Advantage of a Machine. It is fre-
quently desirable to know the multiplication of force that
is brought about by the use of a machine ; or, in other
words, the ratio of the resistance W to the effort F. This
ratio is called the mechanical advantage of the machine.
From equation (l) we may write
W:F::d:d'. (2)
Hence, the mechanical advantage of a machine is the ratio
of the distance through which the effort moves to the distance
through which the resistance is moved by the machine.
For example, the mechanical advantage of the pulley as
used in the first experiment of the preceding section is 1,
in the second experiment 2, and in the example given
on page 84 it is 5.
2. THE PRINCIPLE OF THE PULLEY
91. The Pulley. The pulley consists of a grooved
wheel, called a sheave, turning easily in a block that
admits of being readily attached to objects. When the
block containing the sheave is attached to some stationary
object, the pulley is said to be fixed; when the block
moves with the resistance, the pulley is movable. A fixed
pulley is shown in (1), Fig. 47, and a single movable
pulley in (2).
Let experiments be made with pulleys arranged as shown in Figs.
47 and 48. In each case ascertain by means of a dynamometer 01
86
A HIGH SCHOOL COURSE IN PHYSICS
weights the force required
at F to balance a weight
applied at W. The effect of
friction may largely be
avoided by taking the mean
of the forces applied at F,
first when W is slowly raised
and then when it is slowly
lowered.
When a single fixed
pulley is used, W= F.
When a single movable
FIG. 47. (1) A Fixed Pulley.
(2) A Single Movable Pul-
ley. (3) A System of One
Fixed and One Movable
Pulley.
pulley is used, the re-
sistance is applied to
the movable block, as
shown in (2), Fig. 47.
A study of the figure
will show that W is
balanced by two equal
parallel forces, each of
which is equal to F.
ReiiceW^ZF. The
mechanical advantage
is therefore 2. In (3)
FIG. 48. (1) One Movable and Two Fixed also the mechanical
Pulleys. (2) Two Movable and Two Fixed advantage is 2, and the
Pulleys. (3) Two Movable and Three . ?
Fixed Pulleys. only gam secured by
MACHINES
87
the use of the fixed pulley is one of direction, i.e. the effort
may now act downward instead of upward as in (2).
In (1), Fig. 48, one end of the rope is attached to the
movable block, so that W is supported by three upward
parallel forces, each of which is equal to F. Hence
W= 3 F. A similar consideration of (2) will show that
W= 4 F, and of (3), that W= 5 F.
It is obvious from the cases already considered that
whenever a continuous cord is used in the pulley system,
the mechanical advantage is equal to the number of paral-
lel forces acting against the resistance W. If n is the
number of the parts of the rope supporting the mova-
ble block, then n is the number of these parallel and equal
forces of which Wis the sum. Therefore
W = nF. (3)
92. Principle of Work and the Pulley System. Equa-
tion (3) can be derived by applying the general law of
work stated in 89. If there are n portions of the rope
supporting the movable pulley, and W is lifted 1 foot,
for example, each portion of the cord must be shortened
that amount. Consequently the effort
F must move n feet. By the principle
of work the product of the effort and
the distance through which it acts
equals the resistance multiplied by the
distance through which it is moved ; or,
EXERCISES
1. Diagram a set of pulleys by means of
which an effort of 100 Ib. can support a load of
500 Ib.
2. What is the mechanical advantage of the
system of pulleys shown in Fig. 49 V Find the
effort required to balance a weight of 1200 Ib.
FIG. 49. A Tackle.
88
A HIGH SCHOOL COURSE IN PHYSICS
3. Each of two pulley blocks contains two sheaves. Show by a
diagram how to arrange these into a system that will enable an effort
of 75 Kg. to move a resistance of 300 Kg.
4. Show by a diagram the best arrangement of two blocks, one
containing two sheaves, the other containing one. Ascertain the
mechanical advantage.
5. In each case shown in Fig. 48 let the effort be applied to the
movable block and the resistance W to the end of the rope in place of
F. If the effort F moves 1 ft., how far will W be moved ? State the
advantage secured in each instance. NOTE. This plan is frequently
employed in the operation of passenger elevators in tall buildings.
6. In a pulley system consisting of a continuous cord attached at
one end to a movable block containing one sheave, the rope passes
through a fixed block having two sheaves. Find the effort required
to support a block of marble weighing a ton.
3. THE PRINCIPLE OF THE LEVER
93. The Lever. Of all the simple machines the lever
is the most common. It is of frequent occurrence in the
structure of the skeleton of
man and animals, as well as
in many mechanical appli-
ances. In its simplest form
the lever is a rigid bar, as
AB, Fig. 50, arranged to turn about a fixed point called
the fulcrum. The effort is applied at the point J., and the
resistance at B.
Balance a meter stick upon a long wire nail, piercing it a little above
the center, as shown in Fig.
51. By means of a small
cord or thread, suspend a
weight of 150 grains at B, 15
centimeters from the ful-
crum 0. Now place a
weight of 50 grams upon
the opposite side of the
fulcrum and move it along
the bar until it just balances
FIG. 50. The Lever.
so g
FIG. 51. The Moment of the Effect F
equals the Moment of the Resistance
W.
MACHINES 89
the weight at B. Call this point A. It will now be found that the
distance A is 45 centimeters. From this it is plain that the force F
multiplied by the arm AO is equal to the weight W multiplied by the
arm BO. The experiment may be extended by using other forces and
distances, but in every case it will be found that the product F x AO
equals the product W x BO.
The product of the applied force F multiplied by its
distance AO from the fulcrum is called the moment of
that force ( 45). Likewise, the product of the resist-
ance W multiplied by its distance BO from the fulcrum
is the moment of the resisting force. Thus the fact shown
by the experiment may be stated as follows :
The moment of the effort is equal to the moment of the
resistance.
The distances AO and BO are called the arms of the
lever. Representing these distances by I and V respec-
tively, the law of the lever is represented by the equa-
tion
F x 1= W x 1'. (4)
From this equation it is clear that the mechanical ad-
W I
vantage ( 90) is represented by the ratio - Hence, a
. I
lever will support a weight or other resistance times as
great as the effort.
94. Classes of Levers. Levers are usually divided into
three classes (Fig. 52) depending upon the relative location
of the fulcrum, the effort, and the resistance.
(1) In levers of the first class the fulcrum is between
the effort F and the resistance W\ as in the crowbar, beam
balance, scissors, steelyard, pliers, wire cutters, etc.
(2) Levers of the second class are distinguished by
the fact that the resistance W is between the fulcrum
and the effort F-, as in the nutcracker, wheelbarrow, etc.
90
A HIGH SCHOOL COURSE IN PHYSICS
(8) Levers of the third class are distinguished by the
fact that the effort F is between the fulcrum and the
resistance W\ as in the fire tongs, sheep shears, sewing-
machine treadle, etc.
F \
1st Class.
2d Class.
FIG. 52. Levers of the Three Classes.
If the forces acting on the lever are not parallel, it is
spoken of as a bent lever. A hammer used in pulling a
nail (Fig. 53) is a lever of this kind.
Bent levers are frequently found in
complicated machines ; as in farming
implements, metal- working machin-
ery, clocks, etc.
In levers of all classes the arms are
measured from the fulcrum on lines
perpendicular to the lines which rep-
resent the direction of the forces.
The law stated in the preceding sec-
tion holds for all cases.
95. Extension of the Principle of
Moments. The relation of the mo-
ments of the forces acting on the arms of a lever as ex-
pressed in 93 may be extended to cases in which any
number of forces act upon the bar, provided they pro-
duce equilibrium. The case may be illustrated by experi-
ment as follows:
mum
FIG. 53. The Hammer
used as a Bent Lever.
MACHINES 91
Let weights be placed on the balanced meter stick used in 93 pre-
cisely as shown in Fig. 54. The forces will be found to balance.
Since there is no rotation of the lever, it is obvious that
the forces tending to pro- < $ n
duce a clockwise Q rota- ~T T jfflJT T - T
tion are just balanced by /00ff zo g |I ioog $o g
those which tend to ro-
tate the bar in the coun-
ter-clockwise Q direc- FlG> 54 -
tion. On computing the moments of the forces, we find
on the right-hand side 50 x 40 and 100 x 25. On the left
we find 20 x 25 and 100 x 40. Now if the moments acting
clockwise be added, their sum will be found equal to the
sum of those acting counter-clockwise; or,
50 x 40 + 100 x 25 = 20 x 25 + 100 x 40.
This equation illustrates a general law which may be
stated thus :
An equilibrium of forces results when the sum of the mo-
ments which tend to make the lever rotate in one direction
equals the sum of the moments which tend to make it rotate
in the opposite direction.
The mechanical advantage of the lever can also be found
by applying the prin-
ciple of work set
forth in 89. Let
the lever shown in
FIG. 55. -The Work Done by the Effort F Fi g- 55 turn slightly
Equals That Done upon the Weight W. about the f ulcrum
until it has the position cd. Drawing the perpendiculars
ac and bd, we have from similar triangles
ac : bd : : Oc : Od.
But, since Oc equals OA and Od equals OB,
ac:bd : : AO :BO.
jt
O ---"""""" T
I ' f
92 A HIGH SCHOOL COURSE IN PHYSICS
Now the work done by the effort F is the product F x <?,
and the work done against the resistance W is W x bd.
Since the work done by the agent is equal to that accom-
plished by the lever,
F X ac = W X bd, or W : F : : ac : bd : : AO : BO. (5)
Therefore, the mechanical advantage of a lever is the ratio
of the arm AO to which the effort is applied to the arm
BO on which the resistance acts.
EXERCISES
1. Show by diagrams the relative position of effort, resistance, and
fulcrum in the following instruments of the lever type: oars, sugar
tongs, lemon squeezer, rudder of a boat, pitchfork, spade, can opener,
pump handle.
2. Two boys weighing respectively 60 and 45 Ib. balance on oppo-
site ends of a board. If the fulcrum is 6 ft. from the larger boy, how
far is it from the smaller one ?
3. The arms of a lever of the first class are 3 ft. and 7 ft. What
is the greatest weight that a force of 60 Ib. can support?
4. A lever of the second class is required to support a weight of 500
kg.; the effort to be applied is only 50 kg. If the bar is 20 ft.
long, where should the weight be attached ?
5. Two masses weighing respectively 10 and 15 kg. balance
when placed at opposite ends of a bar 2 m. long. Where is the
fulcrum ?
6. The short arm of a lever is 30 cm. long, the long arm 270 cm.
If the end of the long
arm moves 1 cm., how far
will the end of the short
arm move?
7. The forearm is
raised by a shortening
of the biceps muscle.
Considering the forearm
as a lever whose fulcrum
is at the elbow, to what
FIG. 56. -Wagon Scales. clasg doeg it belong?
MACHINES
93
i
What is gained, force or speed? When the arm is being extended in
striking a blow, to what lever class does it belong?
8. The scales .used in weigh-
ing heavy loads, Fig. 56, are a
series of levers arranged as shown. _______
Explain how a small weight W
can balance a load of coal weigh-
ing a ton or more.
9. Explain how a parcel is
weighed by means of the steel-
yards shown in Fig. 57. FlG - 57 ' ~ Steelyards.
4. THE PRINCIPLE OF THE WHEEL AND AXLE
96. The Wheel and Axle. A simple form of the wheel
and axle is shown in Fig. 58. The applied force, or effort,
acts tangentially to the rim of the
wheel B through a cord, thus pro-
ducing rotation. As the wheel
revolves, the cord to which is at-
tached the weight W is wound up
around the axle A, and the weight
is thus lifted.
If the force F turns the wheel
through one revolution, the dis-
tance through which it acts is
equal to the circumference of the
wheel, or 2 TT^, where R is the radius of the wheel. The
work done by the agent is therefore F x 2 irR ( 55). One
revolution of the wheel lifts the weight W a distance
equal to the circumference of the axle, i.e. to 2 Trr, where r
is the radius of the axle. The work done therefore by
the machine upon the weight is "FT X 2 TTT. Applying the
principle of work as stated in 89,
FIG. 58. The Wheel
and Axle.
whence F x R = W x r, or W : F : : R : r.
(6)
94
A HIGH SCHOOL COURSE IN PHYSICS
The mechanical advantage of a wheel and axle is there-
fore equal to the radius of the wheel divided by the radius
of the axle. Hence, a wheel and axle may be used to over-
R
come a resistance -- times as great as the effort applied to
the circumference of the wheel.
It should be observed that the circumferences of the
wheel and the axle bear the same ratio as their respective
radii, and therefore may be used to replace R and r in
equation (6).
In the compound windlass, Fig. 59, two machines of the wheel and
axle type are combined. The effort F acting along the circumference
of the circle described by
the crank produces a force
that is transmitted by
means of a small cog
wheel, or pinion, to the
rim of the second wheel
to which the axle is at-
tached. As the crank is
turned, a rope is wound
around the axle, thus lift-
ing a weight or overcom-
ing some other resistance.
The mechanical advan-
tage of a compound wind-
lass can be calculated by
resolving the machine into
simple wheels and axles.
The mechanical advan-
FIG. 59. A Compound Windlass, or Widen. tage of the compound
machine is the product of
the mechanical advantages of its constituent parts.
In many instances in which the wheel and the axle are compounded
the motion is transmitted by belts, chains, or cables, and occasionally
by the friction of the circumferences.
The wheel and axle and the pulley may be looked upon
as special cases of the lever. Fig. 60 (1) shows that the
\
\
MACHINES
95
effort F acting tangentially to the rim of the wheel really
acts upon a lever arm equal to R, the radius of the wheel.
Similarly, the resist-
ance W acts upon a
lever arm equal to the
radius of the axle.
Applying the principle
of moments,
\
F x R = W x r.
The case of a single
(3)
FIG. 60.
fixed pulley shown in
(2) may be regarded as a lever of the first class whose ful-
crum is at 0, or as a wheel and axle of which the radii are
equal. Either view leads to the relation F= W. A sin-
gle movable pulley shown in (3) is similar to a lever of
the second class, the fulcrum being at 0, and the resistance
at the center as shown. Again, applying the principle of
moments, we find that W = 2 F as in 91.
EXERCISES
1. Show that the ordinary kitchen meat chopper and coffee
grinder are examples of the wheel and axle. Give other commonplace
examples.
2. The radius of a wheel
is 3 ft., and that of its axle
12 in. What effort would be
required to overcome a re-
sistance of 600 Ib. ?
3. How much work would
be done upon the resistance
in moving it a distance of 10
ft. ? How much work would
have to be done upon the
FIG. 61. The Capstan. wheel?
4. The arm of a capstan, Fig. 61, measured from the center, is
2 m. ; the radius of the barrel is 25 cm. What effort would be re-
96 A HIGH SCHOOL COURSE IN PHYSICS
quired to produce a tension of 500 kg. in the rope attached to the
barrel?
5. What is the mechanical advantage of the machines in Exercises
2 and 4?
6. If the effort were applied to the axle, and the resistance to the
wheel, what would be gained by using a wheel and axle? Illustrate
by using the wheel and axle described in Exer. 2.
7. The pedal of a bicycle describes a circle whose radius is 7
in. If the radius of the attached sprocket wheel is 3 in., find the pull
on the chain when the foot pressure is 45 Ib.
8. If the front sprocket of a bicycle contains 21 teeth, and the rear
one 7, how far will one turn of the pedal move a 28-inch wheel along
the ground ? Find the number of turns of the pedal per mile.
9. The length of the crank
arm shown in Fig. 62 is 10 in.,
and the radius of w is 6 in.;
wheel w is belted to S, whose
radius is 3 in.; and S is at-
tached to W, whose radius is 20
in. One turn of the crank pro-
FIG. 62. ,
duces how many revolutions of
the wheel W'i A point on the rim of W moves how much faster than
the crank?
10. The large wheel of a sewing machine is 12 in. in diameter,
and the small one to which it is belted is 3 in. One up-and-down
movement of the treadle produces how many stitches?
5. THE INCLINED PLANE, SCREW, AND WEDGE
97. The Inclined Plane. Let AB, Fig. 63, represent
an inclined plane whose surface is smooth and unbending.
Let the height BO be h, and the length AB be I. If the
effort F acting parallel to AB
causes the ball whose weight is
W to move the distance AB, the
work done by the agent is F x I.
The weight W is lifted a dis- ~ -
tance equal to BO, and the WOrk F IG> 63. The Inclined Plane.
MACHINES
97
done is W X h. According to the general principle of
Fxl=Wxh.
(7)
The mechanical advantage is therefore equal to -, i.e.
F h
the ratio of the length of the plane to its height.
98. The Screw. The screw is sometimes considered
to be a modification of the inclined plane. If a right tri-
angle, Fig. 64, be cut from paper and
wound around a cylindrical rod, as
shown, the hypotenuse of the triangle
forms a spiral similar to the threads'
of a screw. The distance between two
consecutive turns of the thread measured
parallel to the axis of the rod is the FlG . 64. _ A Screw is a
pitch of the screw. Spiral Incline.
The equation giving the mechanical advantage of the
screw is readily derived by applying the principle of work
( 89) as follows :
Let the screw shown in Fig. 65 be turned once around
by applying the effort F to the end of arm J., tangent to
the circle which it de-
scribes. During one
revolution the effort
acts through the dis-
tance 27JT, where r is
the length of the arm.
The work done is F x
2 TIT. While the screw
is making one revolu-
FIG. 65. -The Screw. tion, the weight W is
obviously lifted through a distance equal to the pitch of
the screw, which may be represented by the letter s. The
work done by the screw is therefore W x s. Hence
8
98
A HIGH SCHOOL COURSE IN PHYSICS
FIG. 66. The
Jackscrew.
F x 2 IT x r = W x s. (8)
The mechanical advantage of the screw is therefore the
ratio 2 TTT/S.
The screw as a mechanical power owes its importance
to the fact that its mechanical advantage can be enor-
mously increased simply by making r large
and 8 small, as in the jackscrew, Fig. 66,
used to lift buildings from their founda-
tions. It is extremely useful in the form
of bolts, wood screws, vises, clamps, presses,
water taps, and in many other cases where
a great multiplication of force is desired.
99. The Wedge. The wedge may be con-
sidered as two inclined planes placed base to
base. It is used for splitting logs (Fig. 67), raising heavy
weights small distances, removing the covers from boxes,
etc. The importance of the
wedge is due to the fact that the
energy imparted to it is delivered
by the blows of a hammer or
heavy mallet. Although the
amount of friction to be overcome
in driving a wedge is necessarily
very large, by its use a man can
overcome enormous resistances. Since friction cannot be
disregarded, no definite relation between effort and re-
sistance can be given.
EXERCISES
1. A ball weighing 10 Ib. rests upon an inclined plane. If the
height of the plane is 6 in. and the length is 30 in., what effort acting
parallel to the plane will be required to hold the ball in equilibrium?
2. On an icy slope of 45, what force is required to haul a sled and
load weighing a ton, neglecting friction?
3. The radius of the wheel of a letter press is 12 in.; the pitch of
FIG. 67. One Use of the
Wedge.
MACHINES 99
its screw, \ in. Neglecting friction, what pressure is produced by a"n
effort of 50 lb.?
4. Neglecting friction, what constant force must a team of horses
exert in hauling a load of coal weighing 3000 lb. up an incline of 30?
5. What is gained by making an inclined plane of a given height
longer? What is lost? Illustrate by means of examples.
6. In a machine the effort of 50 lb. descends 20 ft., while a weight
is raised 10 in. What is the weight?
7. What is the mechanical advantage of a screw press of which
the pitch of the screw is 5 mm. and the diameter of the circle
described by the effort 50 cm. ?
8. A smooth railroad track rises 50 ft. to the mile. A car weigh-
ing 20 T. would require how much force to keep it from moving down
the slope?
6. EFFICIENCY OF A MACHINE
100. Friction and Efficiency. On account of the fact
that there is always a resistance due to friction wherever
one part of a machine moves over another, some work
must be done in moving the parts of the machine itself.
The useful work done by a machine is therefore less than
the work done upon it; i.e. W X d' is always less than
F X d. The ratio of the useful work done by a machine to
the work done upon it is the efficiency of the machine.
EXAMPLE. In the working of a pulley system an effort of 50 lb.
acts through a distance of 20 ft. and lifts a weight of 180 lb. 5 ft.
What is the efficiency of the system ?
SOLUTION. The work done on the machine is 50 x 20, or 1000
foot-pounds. The work done by the machine is 180 x 5, or 900 foot-
pounds. The efficiency is therefore 900 1000, or 0.9.
Efficiency is usually expressed as a percentage of the
total work applied to a machine ; thus in the example
above the efficiency is 90 %
101. Sliding and Rolling Friction. Since friction
always tends to decrease the efficiency of machinery,
advantage is taken of every method that will reduce it
to the smallest possible amount.
100 A HIGH SCHOOL COURSE IN PHYSICS
Let a block of wood or metal and a car of the same weight be
drawn up a slight incline and the force measured by a dynamometer.
It will be found that the car is more easily moved than the block.
Again, place a piece of sheet rubber on the incline under the car.
A greater force will be required to produce motion than before.
The first experiment shows clearly a great difference
between the sliding friction of the block and the rolling
friction of wheels on a hard surface. The second experi-
ment demonstrates the value of a hard, unyielding road
when heavy loads are to be drawn. If, however, the
wheels are provided with wide tires, they sink less deeply
into the roadbed and meet with less resistance. The un-
yielding surfaces of car wheels and the track enable a
locomotive to pull enormous loads on account of the small
amount of rolling friction.
It is plain that in the axle bearings of ordinary vehicles
the moving part must slide over the stationary part. The
friction thus brought about is greatly re-
duced by means of lubricating oil, but is
avoided in the construction of bicycles,
automobiles, etc., by substituting ball bear-
ings, as shown in Fig. 68. In this way the
FIG. 68. Ball a . , . J ..
Bearings of a moving part S is separated from the station-
Bicycle Axle. ar y p ar t A by balls which roll as the wheel
turns. Thus rolling friction takes the place of sliding
friction.
EXERCISES
1. In what way are we dependent upon friction in the process of
walking ? Why do we encounter difficulty in walking on smooth ice ?
2. Why is it difficult for a locomotive to start a train on wet rails ?
How' is the difficulty overcome?
3. Why do smooth nails hold two pieces of wood together? State
other ways in which we take advantage of friction.
4. Calculate the efficiency of a wheel and axle when an effort of
20 Ib. acting through 30 ft. lifts a weight of 80 Ib. 7 ft.
MACHINES 101
5. On account of the loss of energy due to friction in a pulley sys-
tem, an effort of 70 kg. acting through 30 m. moves a resistance of
340 kg. through 5.5 m. What is the efficiency of the machine?
6. What is the efficiency of a screw if an effort of 5 kg. applied at
the end of an arm 1 m. long produces a pressure of 4000 kg., the pitch
of the screw being 4 mm. ?
7. The efficiency of an inclined plane is 50 %. If the length of the
plane is 20 ft. and its height 4 ft., what effort acting parallel to the
plane will be required to move a body weighing 500 Ib. ?
SUMMARY
1. The simple machines are the pulley, lever, wheel
and axle, incline plane, screw, and wedge. Complicated
machinery is made up of simple machines ( 88).
2. The work done by an agent upon a machine is equal
to the work accomplished by it. This is known as the
Principle of Work. Hence a machine may gain force at
the expense of distance (or speed), or it may gain distance
(or speed) at the expense of force ( 89).
3. The mechanical advantage of a machine is the ratio
of the resistance overcome by it to the effort applied to it ;
i.e. TT:^(90).
4. When a continuous cord is used in a system of pul-
leys, the equation is W = nF, in which n is the number of
parts of the rope supporting the movable block ( 91).
5. When a lever is used, the moment of the effort equals
the moment of the resistance, or F x I = W x V ( 93).
6. Levers are classified according to the relative po-
sition of fulcrum, effort, and resistance. Lever arms are
always measured from the fulcrum on lines perpendicular
to the acting forces ( 94).
7. When several forces act at different points on a
lever, the sum of the moments tending to produce a clock-
wise rotation equals the sum of the moments tending to
produce rotation in the opposite direction ( 95).
102 A HIGH SCHOOL COURSE IN PHYSICS
8. The equation of the wheel and axle is F x R =
W x r ( 96).
9. The equation of the inclined plane is F x I =
IT x A (97).
10. The equation of the screw is F x 2 irr = W
x ( 98).
11. Friction tends to reduce the work accomplished by
a machine. The efficiency of a machine is the ratio of
the useful work done by a machine to the work done
upon it ( 100).
12. In general the friction of sliding parts of machinery
is greater than that of rolling parts. Friction may be re-
duced by lubricants, or by substituting rolling friction
for sliding friction, as in the case of ball and roller
bearings ( 101).
CHAPTER VII
MECHANICS OF LIQUIDS
1. FORCES DUE TO THE WEIGHT OF A LIQUID
102. Pressure of Liquids against Surfaces. When a
hollow rubber ball or a piece of light wood is forced under
water, the body resists the action of the force submerging
it and manifests a strong tendency to return to the surface.
The fact that some bodies float on water and other liquids
shows also that there exists a force acting against the
lower surfaces sufficient to counteract their weight.
Let a lamp chimney against the end of which a card has been
placed be forced partly under water, as shown in Fig. 69. The card
will be pressed firmly against the end of the
chimney by a force acting in an upward di-
rection, and a large quantity of shot or sand
may be poured into the vessel before the card
is set free. The person performing the ex-
periment will also perceive that a strong
upward force acts against the hand. By
lowering the chimney to a greater depth, the
upward force against the hand will be in-
creased and a larger quantity of shot or sand
will be required to free the card. FIG. 69. A Liquid Exerts
an Upward Pressure
103. Relation between Force and against the Vertical
Depth. The manner in which the Tube -
force exerted by a liquid against a surface varies with the
depth may be experimentally tested by means of a gauge
constructed as shown in Fig. 70.
A "thistle tube" having a stem about 80 centimeters long is
bent at an angle of 90 degrees about 35 centimeters from one end.
103
104 A HIGH SCHOOL COURSE IN PHYSICS
A piece of thin sheet rubber is tied tightly over the large end A . If a
drop of ink is placed in the tube at JB, its movements along the tube
will indicate changes in the force against the
rubber surface A. Furthermore, the dis-
tance the drop moves when A is submerged
in a liquid will be very nearly proportional
to the applied force.
Let the gauge be clamped in the position
shown in the figure, and let a graduated lin-
ear scale be attached to the horizontal tube
containing the drop of ink. Now let the po-
sition of the drop be read upon the scale and
a tall vessel of water brought up until the sur-
face A is 3 centimeters beneath the free sur-
70. The Upward ^ ace ^ tne hquid. Let the new position of
Force against A Varies the drop be read and its displacement com-
with the Depth. puted. If, now, the positions of the drop be
read after submerging the surface A successively to the depths of 6, 9,
and 12 centimeters, the movements of the drop will be found to be
proportional to the depths.
Therefore, as shown by this experiment, the upward
force exerted by a liquid of uniform density against a given
surface is directly proportional to the depth of that surface.
104. Direction of Forces at a Given Depth. Common
experience shows that liquids press against surfaces that
are vertical or oblique as well as horizontal. In every
case the force exerted is perpendicular to the surface
against which it acts. Thus water will be forced through
a hole in the side of a pail near the
bottom as well as through one in the
horizontal bottom itself. A compari-
son of the forces in all directions at
a given depth may be made by modi-
fying slightly the construction of the
gauge shown in Fig. 71 as follows :
_ Cut the glass tube about 1 centimeter
from the bulb, and insert a piece of rubber all Directions.
MECHANICS OF LIQUIDS
105
tubing about 10 centimeters long. Now, if the bulb is lowered in a
large vessel of water, the position of the drop will not change when
the rubber surface is turned in different directions, provided the depth
of its center is kept constant.
This experiment, together with the one described in
103, leads to the following conclusions :
(1) The force exerted by a liquid at a given depth is the
same in all directions, and
(2) The force exerted by a liquid in any direction is
directly proportional to the depth.
105. Pressures Due to the Weight of a Liquid. From
a study of Fig. 72 it may readily be observed that the
forces exerted by liquids against surfaces
are due to the weight of the liquid, i.e. to
gravity. If a vessel were filled with
smooth blocks of wood of .equal size and
density, block 2 would suffer a downward
force equal to the weight of block 1, and
9
1
5
10
2
6
11
3
7
12
4
8
would in turn exert an equal and opposite FIG. 72. Forces
reaction upward against it. Likewise, 3 Due to Gravity,
must support the weight of 1 and 2, 4 must support -Z, 2,
and 3, etc. In each instance the upward reaction is equal
to the downward action. Thus it is clear that at a given
surface the upward and downward forces are equal, and
also that the force against any horizontal surface is pro-
portional to the depth of that surface below the upper
surface of the blocks in the vessel*
Now liquids, unlike solids, do not tend to keep their
form, but must be supported on the sides. Hence, if we
imagine the vessel in Fig. 72 to contain a liquid, section
4, for example, will press sidewise against 8 and 12, whose
reactions back against 4 preserve equilibrium. If the
liquid were without weight, section 4, for instance, would
suffer no crushing force due to the weight of the portions
106
A HIGH SCHOOL COURSE IN PHYSICS
above it, and consequently would exert no lateral force
against the portions surrounding it.
106. Total Pressure on a Given Area. If the experiment
described in 102 be repeated, and water substituted for
the shot or sand
(Fig. 73), it will
be found that the
card is set free
from the end of
the chimney at the
instant the water
on the inside
reaches the height
of that on the out-
side.
If the chimney is
cylindrical, the
downward force
FIG. 73. Force against BC is Equal to the
Weight of Column ABCD.
within the chimney is obviously equal to the weight of the
column of water ABCD. If the area of the end of the
chimney is a square centimeters, and the depth h centi-
meters, the volume of the column of water in the chimney
is ah cubic centimeters. Since the density of water is 1
gram per cubic centimeter ( 9), the weight of the column
ABCD is ah grains. Hence the force exerted on the card
is ah grams. If another liquid is used whose density is d
grams per cubic centimeter, the weight of the column, and
hence the force, is ahd grams.
The following rule may therefore be given:
The force exerted by a liquid on any horizontal surface is
equal to the weight of a column of the liquid whose base is
the area pressed upon, and whose height is the depth of this
area below the surface of the liquid, or Force = ahd.
MECHANICS OF LIQUIDS 107
Since the force exerted by a liquid against a surface at
a given depth is the same in all directions ( 104), the
following rule for computing the force against surfaces
that are not horizontal is often employed :
The force exerted by a liquid against any immersed surface
is equal to the weight of a column of the liquid whose base is
the area pressed upon, and whose height is the distance of the
center of mass of this area below the surface of the liquid.
In the English system the area should be expressed in
square feet, the depth in feet, and the density of the liquid
in pounds per cubic foot. The density of water may be
taken as 62.5 pounds per cubic foot.
EXAMPLE. A tank 4 ft. deep and 8 ft. square is filled with water.
Find the force exerted against the bottom and one side.
SOLUTION. The area of the bottom of the tank is 8 x 8, or 64 sq.
ft. Hence the volume of the column whose weight equals the force
exerted on the bottom is 4 x 64, or 256 cu. ft. The force against the
bottom of the tank is therefore 256 x 62.5 lb., or 16,000 Ib.
The area of one side of the tank is 4 x 8, or 32 sq. ft. The depth
of the center of mass of the side is 2 ft. Hence the volume of the
column of water whose weight equals the force exerted against the
side is 2 x 32, or 64 cu. ft. The force exerted by the water upon this
side is therefore 64 x 62.5 lb., or 4000 lb.
The term pressure should be confined to the meaning of
force per unit area* The pressure at a given point is ex-
pressed in terms of the force exerted over a unit area at
that depth ; for example, 1000 grams per square centi-
meter, 15 pounds per square inch, etc.
EXERCISES
1. Find the entire force exerted against the bottom of a rectangu-
lar vessel 5x8 cm. and filled with water to a depth of 15 cm.
2. Find the pressure per square foot at the bottom of a pond 10
ft. \\\ depth.
3. A cylindrical glass jar 5 cm. in diameter is filled to a depth of
15 cm. with mercury. Find the force against the bottom and the
108 A HIGH SCHOOL COURSE IN PHYSICS
pressure per unit area. The density of mercury is 13.6 g. per cubic
centimeter.
4. A tank is 4 ft. wide, 8 ft. long, and 3 ft. deep. Compute
the force exerted against one end and the bottom when the tank is
full of water.
5. At a depth of 10 m. of sea water, what is the pressure in grams
per square centimeter? (The density of sea water is 1.026 g. per cubic
centimeter.)
6. At a depth of 25 ft. of sea water, what is the pressure per
square inch ?
SUGGESTION. Find first the force exerted on a surface 1 ft. square
at the given depth.
7. A cubic inch of mercury weighs 0.49 Ib. Compute the force
exerted against the bottom and one side of a glass tank 4 in. wide, 6
in. long, and 5 in. deep when full of mercury.
8. Find the force exerted against the bottom of a cubical vessel
whose volume is 1 liter when the vessel is filled with mercury.
9. What depth of water will produce a pressure of 1 Ib. per square
inch?
10. What is the pressure per square centimeter at the bottom of a
column of mercury 76 cm. in height? (For the density of mercury
see Exer. 3.)
11. To what height would a mercurial column be supported by a
pressure of 1000 g. per square centimeter?
12. A gauge connected with the water mains of a city showed a
pressure of 65 Ib. per square inch. What was the height of the water
in the standpipe above the level of the gauge ?
SUGGESTION. Find the depth of water required to produce a pres-
sure of 65 Ib. on a surface of 1 sq. in.
13. A diver is working at a depth of 45 ft. How much is the
pressure per square inch upon the surface of his body?
14. A rectangular block of wood is placed under water so that its
upper face, which is 8 x 10 cm., is 20 cm. below the surface. If the
thickness of the block is 4 cm., what is the force exerted by the liquid
against each of its faces?
15. How much is the force against a dam 20 ft. long and 10 ft. high
when the water rises to its top ?
16. A hole in the bottom of a ship which draws 30 ft. of water is
temporarily covered with a piece of canvas. How much is the pres-
sure against the canvas from the outside?
MECHANICS OF LIQUIDS
109
17. The water level is at the top of a dam 30 ft. high. Compute
the pressure per square foot at the bottom of the dam. How much is
the pressure halfway down ?
18. If the dam in Exer. 17 is 100 ft. long, how much is the total
force against its surface ?
107. Pressure in Vessels of Different Shapes. It may
be correctly inferred from 106 that the force exerted by
a liquid against a given area does not depend on the shape
of the vessel containing the liquid used, inasmuch as the
computation of this force involves only the area and depth
of the surface pressed upon and the density of the liquid.
This fact can be demonstrated experimentally as follows :
Let a glass funnel be selected the mouth of which is of the same area
as the end of the lamp chimney used in 106. Place a card across the
mouth of the funnel and submerge it, as shown
in Fig. 74. The card will be pressed against
the funnel with the same force as it was when
the chimney was used, i.e. with a force equal
to the weight of a column of water ABCD.
If water is now poured into the stem of the
funnel at E, the card will become free precisely
when the level of the water in the funnel has
reached the height of the water in the vessel
outside. In this condition the water in the
funnel exerts the same force downward against
the card as the water on the outside exerts
in an upward direction. Hence the downward force is equal to the
weight of the column of water ABCD. In other words, the force
downward against the card is exactly the same as it was when the cylindri-
cal chimney was used.
108. The Hydrostatic Paradox. An apparent contra-
diction arises when we
apply the laws of liquid
pressure to vessels of
the forms shown in Fig.
75. Let the vessels have
FIG. 75. The Hydrostatic Paradox. bases of equal size and
FIG. 74: Equal Down-
ward Forces in Ves-
sels of Different
Shapes.
110
A HIGH SCHOOL COURSE IN PHYSICS
be filled to the same depth with water. In each case the
force exerted by the water against the bottom is equal to
the weight of the liquid column ABOD. Because it is
apparently an impossibility for different masses of a liquid
to produce the same pressure, this conclusion is often
called the hydrostatic paradox.
An application of the laws of pressure in liquids to vessel (3), Fig.
75, will show how the total pressure on the bottom BC can be far
greater than the weight of liquid contained in the vessel. Although
the total pressure on the surface BC is equal to the weight of a column
A BCD of the liquid ( 107), there are upward forces against the
surfaces e/and gh equal to the weight of the liquid that would be re-
quired to fill the spaces Aefa and bghD. Hence the resultant of all
the forces is the difference between the downward force on BC and
the upward forces on ef and gh. This is obviously the weight of the
liquid in the vessel,
109. A Liquid in Communicating Vessels. Let tubes
of various shapes and sizes open into a hollow connecting
arm, as shown in Fig. 76. Any
liquid poured into one of the tubes
will come to rest at the same level
in all. Although different quan-
tities of the liquid are present in
the several tubes, yet for the same
depth the parts are in equilibrium.
The explanation is as follows :
Let two vessels containing water be in
communication, as shown in Fig. 77. Let A be the area of a cross-
section of the connecting tube. The force tend-
ing to move the water to the right is A hd,
where h is the depth of the center of the area
considered, and d the density of the water.
The force tending to move the liquid to the left
is Ah'd. These two forces will be in equilibrium
only when h and Ji' are equal, i.e. when the
upper surfaces in the two vessels lie in the same
horizontal plane.
FIG. 76. Liquid Level in
Communicating Vessels.
FIG. 77. A Liquid in
Equilibrium.
MECHANICS OF LIQUIDS
111
EXERCISES
1. A cone-shaped vase has a base of 100 cm. 2 and is filled with
water to a depth of 45 cm. Find the force and pressure per square
centimeter acting on the bottom.
2. The water in a reservoir supplying a city is 150 ft. above an
opening made in a pipe being laid along a street. Find the pressure
in pounds per square inch required to prevent the water from running
out. Ans. 65.1 Ib.
3. A glass tube 1 m. long is rilled with mercury (density 13.6 g.
per cubic centimeter). Find the pressure against the closed end of
the tube in grains per square centimeter when the tube is (1) vertical
and (2) inclined at an angle of 45.
Ans. 1360 g. per square centimeter.
961.7 g. per square centimeter.
4. A column of water is lifted 25 ft. in a pipe. Calculate the
pressure per square inch that it exerts against the bottom of the pipe.
2. FORCE TRANSMITTED BY A LIQUID
(1) (2)
Fia. 78. The Multiplication of Force by a Liquid.
110. Transmission of Pressure Pascal's Law. Let a
vessel of the form shown in (1), Fig. 78, be filled with
water to the point a. A pressure will be exerted on every
112
A HIGH SCHOOL COURSE IN PHYSICS
square centimeter of area depending on the depth of that
area. The force exerted upward against the shaded area
AB, assumed to be 100 square centimeters, is 100 h grams,
if h is the depth of the water in the tube. This force is
entirely independent of the area of the portion of the
vessel at a. Let this area be 1 square centimeter. Now,
if 1 cubic centimeter of water is poured into the vessel,
the depth of the liquid is increased 1 centimeter, and the
depth of the surface AB becomes h + 1 centimeters. The
force now exerted against AB is 100 (h + 1) grams,
i.e. each square centimeter of AB receives an additional
force of 1 gram. Hence, the force exerted on a unit area at
a is transmitted to every unit area within the vessel.
This fact was first published in 1663 by Pascal, a
French mathematician. The law may be expressed as
follows :
Force applied to any area of a confined liquid is trans-
mitted undiminished by the liquid to every equal area of the
interior of the containing vessel and to every part of the
liquid.
111. The Hydraulic Press. In the discussion of Pas-
cal's Law given in the preced-
ing section, it makes no dif-
ference whether the pressure
added to the small area a is
produced by a gram of water
poured into the tube or ex-
erted by a small piston fitting
the tube, as shown in (2),
Fig. 78. The shaded area AB
to which the force is trans-
mitted by the liquid may be
FIG. 79. AIL Hydraulic Press, made the area of a large piston,
MECHANICS OF LIQUIDS
113
as shown. In this case a force of 1 gram on the small
piston will be transmitted to each square centimeter
of the large one. Hence 1 gram on the small piston will
balance 100 grams placed on the large one. Furthermore,
any effort F applied to the small piston will balance a re-
sistance 100 times as great as itself. Hence a mechanical
advantage ( 90) of 100 is secured. The hydraulic press,
a machine employed in factories for exerting great force,
is one of the most important applications of Pascal's Law.
(See Fig. 79.)
The hydraulic press is analyzed in Fig. 80. When the lever L is
raised, the small piston P is lifted, and water from the cistern T
enters the cylinder B through
the valve v. As the small pis-
ton is forced down, v closes,
and the water in the cylinder
B is driven past the valve v'
into the chamber below the
large piston P'. By Pascal's
Law, the force exerted again st
the large piston P' is as many
times that applied to P as
the area of P' is times that
of P. In other words, the
mechanical advantage is
P'/P. By making P very
small and P' large, any de-
sired mechanical advantage
may be secured. Thus hand
presses are sometimes used
FIG. 80. Sectional Diagram of the
Hydraulic Press.
that are capable of exerting a force of several hundred tons.
112. Principle of Work and the Hydraulic Press. It
may be observed from (2), Fig. 78, that when the effort F
moves the small piston a distance of 1 centimeter, the
large piston, having to make room for the 1 cubic cen-
timeter forced below it, must rise -^o ^ a centimeter.
9
114 A HIGH SCHOOL COURSE IN PHYSICS
Although the larger force is 100 times as great as the
smaller, it acts through only T ^ as great a distance.
Hence the work done by the larger piston as it rises is
no greater than the work done on the smaller.
113. Artesian or Flowing Wells. The tendency of
water to flow from a point of higher level to one of lower
level has a wide application in artesian, or flowing, wells.
In many localities there are formed so-called artesian
basins of great extent in which a stratum of porous ma-
terial, as sand or other substance through which water
can pkss with comparative ease, lies between strata of
clay or rock which are impervious to water. At distant
points these layers have been crowded to the surface
by geologic processes where the porous layer has been
laid bare, thus rendering the entrance of water pos-
sible. Hence when borings are made into the earth
through the various layers and into the porous stratum,
water often rises to the surface when it is lower
than the region where the water enters the porous
layer.
Deep artesian wells exist at St. Louis, Mo. ; Columbus,
Ohio ; Pittsburg, Pa. ; and Galveston, Texas. Noted
wells are found at Passy, France (1923 feet); Berlin,
Germany (4194 feet); Leipzig, Germany (5735 feet).
114. Supplying Cities with Water. Comparatively few
cities are so favorably situated that they derive their
supply of water from mountain springs. The output of
such springs is collected in large artificial reservoirs or
lakes from which it is piped to the towns where it is dis-
tributed in the usual manner. In such cases the elevation
of the reservoir is such as to produce an adequate pressure
for all ordinary purposes. The pressure may be estimated
at 43.5 pounds per square inch for every 100 feet of
elevation.
MECHANICS OF LIQUIDS
115
In towns, however, whose location is less favored by
nature, the water from springs or wells must be elevated
by means of pumps ( 156) to suitable reservoirs or tanks
constructed upon high ground from which it is distrib-
uted through pipes to the consumers. In some large
cities no reservoir is used, the pumping engines being so
adjusted as to supply the water at a given pressure as
fast as it is consumed.
115. Water Motors. In cities where water is delivered
through pipes under sufficient pressure, its power may
be utilized in running sewing ma-
chines, polishers, lathes, etc., by
employing a rotary, water motor.
A common type is shown diagram-
matically in Fig. 81. Water is-
sues with great velocity from the
jet J against cup-shaped fans at-
tached to the axle of the motor.
These are inclosed in a metal case FIG. 81. Sectional View of a
O from which the water flows into Water Motor -
the sewer or other drain. The impact of the water against
the fans suffices to turn
the shaft to which are
connected either di-
rectly or by belts the
machines that it is de-
sired to operate.
116. Water Wheels.
An elevated body of
water, like a lifted
weight, is a source of
FIG. 82. An Overshot Water Wheel. ,. , T , .
potential energy. It is
the falling of this water to a lower level that supplies the
power for operating innumerable mills, factories, electric
116
A HIGH SCHOOL COURSE IN PHYSICS
power plants, etc., found throughout this and other coun-
tries. In order to enable water to do the required work,
the so-called overshot water wheel has long been employed.
A wheel of this kind is shown in Fig. 82. It is plain that
the impact and weight of the moving water from above
the wheel conspire to turn the wheel, to which is geared
or belted the machinery to be operated. Another old but
common form of water wheel is the undershot wheel. In
this case the wheel is turned by the impact of the current
of water against fans at the bottom.
The most efficient form of water wheel, however, is the
turbine, which is utilized in all modern plants employing
water power. Water
is conducted from the
+*~~ i '""* ^ '"
c r ^tt "^ - x '"'^' reservoir above a dam
through a closed cylin-
drical tube, or flume,
F, Fig. 83, to a penstock
(shown by the dotted
lines) which surrounds
the stationary iron case
T containing the rotat-
ing wheel, or turbine.
This case rests upon the
floor of the penstock
and is submerged in water to a depth equal to the " head,"
or height, of the water supply. The turbine is attached
to the shaft 8 and is set in rotation when the water is ad-
mitted. The small shaft P serves to control the size of the
openings in the case through which the water gains entrance
to the turbine. Figure 84 is a sectional view through the
turbine R and the case 8. Water enters as shown by the
arrows and strikes the blades of the turbine at the most
effective angle for producing rotation. When the water
FIG. 83. A Water Turbine.
MECHANICS OF LIQUIDS
117
FIG. 84. Section of a Water
Turbine.
has expended its energy, it falls from the bottom of the
case into the tailrace below the penstock. The efficiency
( 100) of turbines is frequently
as high as 85 or 90 per cent.
117. Hydraulic Elevators.
Another use made of the energy
of water under pressure is in the
operation of elevators, or lifts.
One form is shown in Fig. 85.
When water is admitted to the
cylinder O through the control-
ling valve F", the piston is forced
to the right, thus producing a
pull upon the cable (shown by the dotted lines) and caus-
ing the car A to ascend. Check-
ing the flow of water by means of
the rope r stops the car, while
turning valve V to the position
shown in the figure allows the
water to flow from the cylinder
and causes the car to descend by
its own weight. A study of the
figure will show that the car moves
four times as fast and four times
as far as the piston.
In another form the piston is a
long vertical cylinder extending
from the bot-
of the
1 '..> s . . > > '.
ii ii ii
Mf
deep hollow
FIG. 85. An Hydraulic Elevator. C vlinder set
in the ground. The admission of water under pressure
acting against the lower end of the long piston lifts the
118
A HIGH SCHOOL COURSE IN PHYSICS
car. The method of controlling such elevators is the same
as that shown in Fig. 85.
118. The Hydraulic Ram. The hydraulic ram is a
useful device for automatically elevating water in small
quantities when an
abundant supply of
spring water is available
which has a fall of only
a few feet. Water flows
from the source through
FIG. 86. The Hydraulic Ram. the pipe P, Fig. 86, and
out through the opening at v. As the water increases in
speed, the valve at v is lifted, which causes a sudden inter-
ruption of the flow in P. Since the momentum of the
water cannot be destroyed instantaneously, a portion of the
water is driven forcibly past valve v f into the air chamber
0. A slight rebound of the water in the large pipe re-
lieves for a moment the pressure against valve v, which
falls by its own weight, thus opening again the orifice at
that point. A repetition of the process causes more water
to enter O until finally the pressure is sufficient to lift a
portion of the water to a height of many feet. The com-
pressed air in Q acts as an elastic cushion and serves also
to keep a steady flow of water in the small pipe. The
quantity of water delivered by an hydraulic ram is de-
pendent on the height of the source, the elevation to
which it is to be lifted, the friction of the pipes, the
length of pipe P, and the size of the ram itself.
EXERCISES
1. The area of the small piston of an hydraulic press is 2 cm. 8
and that of the large one 80 cm. 2 How much force will 50 Kg.
applied to the former produce upon the latter ?
2. The small piston of an hydraulic press is operated by a lever of
the second class 4 ft. in length, and the piston rod is attached 12 in.
MECHANICS OF LIQUIDS 119
from the fulcrum. If the diameters of the pistons are 1 in. and 8 in.
respectively, how great an effort will produce a force of 2 T. ?
3. If the effort applied to the small piston in Exer. 2 moves through
1 ft., how much will the large piston be raised ?
4. A piston moves in a cylinder that is in communication with a
water system whose pressure is 65 Ib. per square inch. If a force of
1 T. is to be developed by the piston, what is the least diameter that
it can have? Ans. 6.26 in.
5. Pressure against a piston 20 cm. in diameter is produced by a
column of water 30 m. high. Calculate the force against the piston
and the work performed when the piston moves 4 m.
6. Give suitable dimensions to the pistons and lever of an hydraulic
press in order that an effort of 1 Ib. may produce a force of 3000 Ib.
. ARCHIMEDES* PRINCIPLE
119. Buoyancy of Liquids. It is a matter of common
observation that bodies apparently become lighter when
placed under water. If the hand, for example, be sub-
merged in a vessel of water, it becomes evident at once
that it is supported almost without muscular effort. Let
a one- or two-pound stone be weighed in air and then
weighed again while immersed in water. A decrease of
several ounces will be observed. When blocks of wood or
many other bodies are placed in water, the buoyancy of
the water is sufficient to cause them to float.
120. The Principle of Archimedes. 1 On account of the
importance of the laws relating to the apparent decrease
1 ARCHIMEDES (287-212 B.C.). The name of Archimedes will be re-
membered by students of Physics in connection with the buoyant action
of liquids on immersed solids. The story is related that Hiero, King of
Syracuse, had ordered a crown of pure gold which, when delivered, al-
though it was of the proper weight, was suspected to contain a quantity of
silver. Archimedes was asked to investigate. A method of procedure
occurred to him while in the public bath as he noticed that his body ex-
perienced a greater buoyancy the more completely it was submerged.
Recognizing in this effect the key to the solution of the problem, he
leaped from the bath and hurried homeward, exclaiming "Eureka!
120 A HIGH SCHOOL COURSE IN PHYSICS
in weight that bodies undergo when submerged in a liquid
three experiments will be described:
1. Measure the dimensions of a metal cylinder or rectangular
metal block, and compute its volume in cubic centimeters. From the
volume compute the weight of an
equal volume of water. Suspend
the metal body from one arm of a
balance, and ascertain its weight in
air. Weigh the body also when sub-
merged in water, and compute the
loss of weight. Compare the loss
of weight with the weight of an
equal volume of water found at first.
2. From one arm of a balance,
Fig. 87, suspend a metal cylinder A
and the bucket B whose capacity is
precisely equal to the volume of
FIG. 87. -Verifying Archimedes' the cylinder. Counterbalance these
Principle. , , '-'*,
by means of sand or weights placed
in the opposite scale pan. Submerge A in water, and equilibrium will
be destroyed. Fill the bucket with water, and equilibrium will be
restored to the system.
3. Place a small glass beaker (or tumbler) on one pan of a balance,
and suspend a stone from beneath the same pan. Counterpoise by
Eureka!" which means "I have found it!" Experiments showed
that equal masses of gold and silver weigh unequal amounts when sub-
merged in water. Therefore, when the crown was weighed against an
equal mass of pure gold, both being submerged, the fraud was at once
detected.
Archimedes is regarded as the founder of the science of Mechanics.
From his time nearly 2000 years elapsed before any great advance was
made. His investigation of levers is noteworthy. He is said to have made
this remark, "Give me a fulcrum on which to rest my lever and I will
move the earth." Among his countrymen, he was probably best known
on account of the numerous instruments of war which he invented.
As a mathematician, Archimedes was first to determine the value of IT,
and the nrst to compute the area of a circle. He is supposed to have been
killed by a Roman soldier while engaged in the investigation of a problem
in geometry.
MECHANICS OF LIQUIDS 121
using sand, shot, or weights. Next fill a vessel provided with a spout
with water, and allow all the excess to flow out at the spout. Place an
empty tumbler under the spout, and lower the counterpoised stone
into the water. Completely submerge the stone, and catch all the
displaced water, the volume of which will be equal to that of the
stone. Pour the displaced water into the beaker on the scale pan, and
equilibrium will be restored.
From the results obtained by making any one of the
experiments just described Archimedes' Principle may
be deduced:
A body immersed in a liquid is buoyed up by a force equal
to the weight of the liquid that it displaces.
121. Explanation of Archimedes' Principle. The rea-
sons for Archimedes' law become clear when the laws of
liquid pressure stated in 104 are applied
to a submerged body. Let a rectangular
block abed be immersed in a liquid, as
shown in Fig. 88. The force against the
upper surface of the block is the weight
of the column of the liquid efad and acts
downward. The force exerted by the
liquid against the lower surface of the
block cb is the weight of a column of the FlG - 88. The Up-
T i /.T i mi ward Force Ex-
liquid efbc and acts upward. The re- C eeds the Down-
sultant of these two forces is obviously ward Force -
in an upward direction and equal to the weight of a volume
abed of the liquid. The lateral forces exerted by the liquid
against any two opposite faces of the block are equal and
opposite, and therefore produce no tendency to move the
block. Hence the immersed body is buoyed up by a force
equal to the weight of a volume of the liquid equal to its
own volume, i.e. to its displacement. It should tfe ob-
served that the depth to which the body is submerged does
not affect the final result.
122 A HIGH SCHOOL COURSE IN PHYSICS
If the weight of the body submerged in the liquid just
equals the weight of the displaced liquid, the body will be
in equilibrium and remain where it is placed provided the
density of the medium be uniform. If the body weighs
more than the amount of liquid displaced, it will sink; if
less, it will rise to the surface and float.
122. Floating Bodies. 1. Obtain a square stick of pine about
30 centimeters long and 1 centimeter square. Measure its dimensions
carefully, and beginning at one end,
lay off cubic centimeters after taking
due account of the cross-sectional
area. Drill a deep hole in the end of
the bar and embed a nail heavy enough
to cause the bar to float in an upright
position, as shown in (1) Fig. 89.
Melt paraffin into the pores of the
wood over a flame in order to make it
water-proof. Float the bar in water,
and read off the number of cubic cen-
FIG. 89. Flotation Illustrated.
timeters of the portion beneath the
liquid surface, i.e. the displacement. Compare the weight of the water
displaced with the weight of the bar itself.
2. Counterpoise a glass beaker (or tumbler) on a balance. Prepare
a vessel, as shown in (2) Fig. 89, to catch displaced water. Carefully
float a piece of well-paraffined wood weighing about 100 grams, and
catch the displaced water. Wipe the block of wood dry, and place it
on one scale pan of the balance, and pour the displaced water into the
beaker placed on the other. The two should balance.
If a block of wood is entirely immersed in water, the dis-
placed water weighs more than the wood, and therefore the
buoyant force is greater than the weight of the block.
Hence the block will be forced toward the surface. As a
portion of the block rises above the surface of the water,
the displacement decreases until the weight of the block
and that of the displaced water are equal. This fact will
be found to be verified by either of the experiments just
described. The law may be expressed as follows:
MECHANICS OF LIQUIDS
123
A floating body sinks to such a depth in the liquid that the
weight of the liquid displaced equals the weight of the body.
123. Measuring Volumes by Archimedes' Principle.
Archimedes' principle affords an easy and accurate
method for ascertaining the volumes
of solid objects of irregular shapes.
A body immersed in water evidently
displaces a volume of water equal to
its own volume, and, according to
Archimedes' principle, loses in weight
an amount equal to the weight of the
displaced volume of water. (See Fig.
90. ) Since 1 cubic centimeter of water
weighs 1 gram, the body immersed
contains as many cubic centimeters as
the number expressing its loss of
weight in grams. For example, a
piece of metal that weighs 45.75
grams in air and 40.23 grams when
immersed in water displaces the difference, or 5.52 grams
of water. The volume of water displaced is therefore 5.52
cubic centimeters. Hence the volume of the immersed
body is 5.52 cubic centimeters. When the loss of weight
is measured in pounds, the volume expressed in cubic feet
is found by dividing
that loss by 62.5.
Why?
124. The Floating Dry
Dock. Among the useful
modern inventions depend-
ing upon the law of flotation
FIG. 90. Weighing a
Body in Water to Find
its Volume.
FIG. 91. The Floating Dry Dock.
(J 122) is the floating dry dock, which is shown diagrammatically
in Fig. 91. When the several water-tight compartments P, P, P are
allowed to fill with water, the dock sinks until the water level is at
124 A HIGH SCHOOL COURSE IN PHYSICS
AB. A vessel to be repaired is then floated into the dock, and the
water pumped out of the various compartments. As the chambers
are emptied the dock rises sufficiently to bring the water level to
the line CD. The boat is thus lifted clear of the water.
EXERCISES
1. A stone weighing 400 g. under water weighs 480 g. in air. What
mass and volume of water does it displace? What is the volume of
the stone?
2. What is the volume of a metal cylinder that weighs 30 g. in air
and 19 g. when immersed in water?
3. A solid weighs 20 Ib. in air and 12 Ib. when suspended under
water. What is the weight of an equal volume of water? What is
the volume of the body in cubic inches?
4. A body weighing 50 g. in air weighs 35 g. when immersed in
water and 38 g. when immersed in oil. Find the mass and volume
of the oil displaced.
5. A block of iron weighing 12 g. and a piece of wood weighing
4 g. are fastened together and weighed in water ; their weight when
immersed is 7.5 g. If the iron alone weighs 10.2 g. when immersed
in water, what is the volume of the wood?
SUGGESTION. From the combined volumes subtract that of the
iron.
6. A block of wood is floated in a vessel full of oil. If 200 g. is
the weight of the oil displaced, what is the weight of the wood?
7. A boat that weighs 450 Ib. displaces how many cubic feet of
water?
8. A ferry-boat weighing 700 tons takes on board a train weigh-
ing 550 tons. Express the total displacement in cubic feet.
9. Why does throwing the hands out of water cause the head of a
swimmer to be submerged ?
10. An egg will sink in water and float in brine. A solution of
salt may be made of such a strength that an egg will remain at any
depth. Explain.
11. What is the volume of a man weighing 150 Ib. if he floats with
2^ of his body above water ?
4. DENSITY OF SOLIDS AND LIQUIDS
125. Density of a Solid. (#) When the solid is more
dense than water. The density of a body is defined as its
MECHANICS OF LIQUIDS
125
mass per unit volume and is found by dividing the number
of units of mass by the number of units of volume ( 12).
In the C. G. S. system density is expressed in grams per
cubic centimeter. For example, the density of mercury is
13.59 grams per cubic centimeter.
In ascertaining the density of a solid that sinks in water
and does not dissolve, the mass is first found by weighing
the body in air, and the volume is then measured by the
method described in the preceding section. By definition,
mass (in grams) , >.
volume (in cm.' 6 )
But, if the number of units of volume is found, as in
practice, by ascertaining the apparent loss of weight sus-
tained when the solid is submerged in water, we have for
the numerical value of the density in the metric system,
mass (in grams) .
Density (in grams per cm. s )
Density =
(2)
weight lost in water (in grams)
(b) When the solid is less dense than water. When a
solid is not dense enough to sink in water, it may be
attached to a sinker that ._
is sufficiently heavy to
submerge it. Let a
sinker S and a light
solid A whose mass is
M grams be suspended
from the arm of a bal-
ance, as shown in Fig.
92, so that the sinker
alone is submerged.
Let the weight of the FIG. 92. Ascertaining the Volume of a
i j- 41 -, Solid Less Dense than Water.
two bodies thus arranged
be W 1 grams. Now let both solids be immersed, and the
combined weight be W 2 grams. The difference W l TF 2
126 A HIGH SCHOOL COURSE IN PHYSICS
is evidently caused by the buoyant force of the water on
the light solid A, and, according to Archimedes' principle,
is equal to the weight of the water displaced by this
body. This difference is numerically equal to the volume
of the body expressed in cubic centimeters. Hence an
equation expressing the numerical value of the density of
the solid may be written as follows :
Density = * ( gram*) (3)
w i ~ W 2 ( m grams)
126. Specific Gravity. Occasional use is made of the
term specific gravity (abbreviated sp. gr.) to express the
heaviness or lightness of a body as compared with the
weight of some standard substance. The specific gravity
of any solid or liquid is the ratio of the weight of the body to
the weight of an equal volume of pure water at 4 0. In the
case of gases the standard with which they are compared
is either air or hydrogen.
Since one cubic centimeter of pure water at 4 C. weighs
one gram, it follows that the density of a body in grams
per cubic centimeter is numerically equal to its specific
gravity. For example, the density of lead is 11.36 grams
per cubic centimeter; hence lead is 11.36 times as heavy
as an equal volume of water. Therefore, the specific
gravity of lead is 11.36.
Again, since the specific gravity of lead is 11.36, one
cubic foot of lead will weigh 62.5 pounds x 11.36, or 710
pounds. Hence in the English system of measurement
the density of lead is 710 pounds per cubic foot.
It is to be carefully observed that specific gravity and
density are not the same thing ; they are numerically equal
only when density is given in C. G. S. units. In the
English system, density is entirely different from specific
gravity, as the example plainly shows.
MECHANICS OF LIQUIDS 127
The equation of specific gravity is
weight of a hody x^^
Specific gravity = - , J . (4)
weight of an equal vol. of water
127. Density of Liquids. There are several methods
for finding the density of a liquid. Let a solid that is
denser than water be weighed in air, then in water, and
finally in a liquid whose density is to be found. The loss of
weight in water then represents numerically the volume
of the submerged solid. The loss of weight in the liquid of
unknown density represents the mass of an equal volume
of that liquid. Therefore the density of the liquid is found
by dividing the latter loss by the former. For example, a
solid weighs 80 grams in air, 55 grams in water, and 60
grams in another liquid. The mass of water displaced is
25 grams and that of the other liquid 20 grams. Hence
the volume of the liquid of unknown density displaced by
the solid is 25 cubic centimeters, and its density 20 -+ 25,
or 0.8 gram per cubic centimeter.
128. Hydrometers. The law of floating bodies ( 122)
affords a convenient method for finding the density of a
liquid. Let the bar of wood used in Experiment 1, 122,
be placed in a jar of water and the volume of the sub-
merged portion ascertained. Next place the bar in a
liquid whose density is to be found, and again find the
volume of the part beneath the liquid. If the displacement
of water is v 1 cubic centimeters, the weight of the displaced
water is v^ grams. If d is the density of the other liquid
and v z its displacement, the weight of the liquid displaced
is v 2 d grams. According to the law of floating bodies the
weight of the liquid displaced in each instance is equal to
the weight of the floating bar. Hence the two displace-
ments are of equal weight. We may therefore write
v 2 d = v x ; whence d = - (5)
128
A HIGH SCHOOL COURSE IN PHYSICS
FIG. 93.
Hydrometer
of Constant
Weight.
A floating body that is made in a convenient form for
measuring the densities of liquids is called an hydrometer.
If the weight of the hydrometer remains con-
stant as in the case of the wooden bar used
in the experiment just described, the instru-
ment is called an hydrometer of constant
weight. In some instances the densities are
indicated upon the bar and may be read off
at once by observing the point to which the
instrument sinks. Many forms of hydrom-
eters are in daily use, the size, shape, and
graduations being adapted to the particular
commercial purpose that they serve. A com-
mon form is shown in Fig. 93. A cylindri-
cal glass tube terminates below in a small
bulb filled with mercury, which causes the
instrument to float in an upright position. The upper por-
tion of the tube is made small, and the graduations are
upon a paper scale sealed within.
Nicholson's Hydrometer. The Nicholson hydrometer shown in
Fig. 94 represents the type known as hydrome-
ters of constant volume, i.e. of constant displace-
ment. This instrument is used in finding the
density of a solid body. Let w l grams be the
weights required in the upper pan A , to sink the
hydrometer to a certain mark placed on the slen-
der stem a. After placing the solid of unknown
density in the upper pan, the weight required to
sink the instrument to the same mark is w 2 grams.
Then w l w 2 is the mass of the solid. Let w s be
the weights required in the upper pan after the
solid has been transferred to the lower pan R.
Then w 3 w 2 is the mass of the water displaced
and numerically equal to the volume of the solid.
Therefore, the numerical value of the density
of the solid expressed in metric units is :
Constant Volume
Hydrometer.
MECHANICS OF LIQUIDS 129
Density = - (6)
Wo Wo
EXERCISES
1. A piece of lead weighs 56.75 g. in air and 51.73 g. when sus-
pended in water. Find the volume and density of the lead.
2. A cylinder of aluminium weighs 28.35 g. in air and 17.85 g.
when immersed in water. Calculate the volume and density of the
metal. Compute the sp. gr. of aluminium.
3. A piece of glass weighing 45 g. in air weighs 22.5 g. in water
and 23.75 g. in oil. Calculate the densities of the glass and the oil.
4. What would be the weight of the glass in Exer. 3 when im-
mersed in a liquid whose density is 0.922 g. per cubic centimeter?
5. The density of marble is 2.7 g. per cubic centimeter. What is
the weight of a rectangular block 1 m. long, 40 cm. wide, and 15 cm.
thick ? Compute the sp. gr. of marble. What is its mass per cu. ft. ?
6. Silver is 10.4 times as heavy as an equal volume of water.
What will 20 g. of silver weigh when immersed in water?
7. Ice is 0.9 as heavy as an equal volume of water. If a piece of
ice weighing 500 g. floats on water, what is the volume of the sub-
merged portion ? What is the volume of the ice?
SUGGESTION. Apply the law of floating bodies and ascertain the
weight of water displaced.
8. A bar of wood weighing 100 g. floats on water with 0.82 f its
volume submerged; when placed in oil, 0.80 of its volume is submerged.
Calculate the sp. gr. and density of the oil.
9. A piece of paraffin weighs 69 g. in air and when attached to a
sinker and suspended in water, 85.8 g. If the weight of the sinker in
water is 95.7 g., what is the volume and density of the paraffin?
10. The weight required to sink a Nicholson hydrometer to the
mark on the stem is 45 g. ; when a piece of marble is placed in the
upper pan, the weight required is 15.3 g. and with the marble in
the submerged pan 26.3 g. Find the density of the marble.
11. Find the density of paraffin from the following data :
Weight required to sink Nicholson's hydrometer to mark 56.4 g.
Weight to sink hydrometer with paraffin in upper pan 45.6 g.
Weight required with paraffin in submerged pan 57.6 g.
12. The density of mercury is 13.59 g. per cubic centimeter. If a
cubic foot of water weighs 62.5 lb., what is the weight of a cubic inch
of mercury?
10
130 A HIGH SCHOOL COURSE IN PHYSICS
5. MOLECULAR FORCES IN LIQUIDS
129. Cohesion and Adhesion. Many of the phenomena
of nature lead to the conclusion that bodies are made up
of extremely minute particles to which is given the name
molecules. The molecules of bodies possess more or less
freedom of motion among themselves depending on the
nature of the body ; this freedom is greatest in gases and
least in solids. It is due to the very perfect freedom of
motion among the molecules of a liquid (i.e. to the prop-
erty of fluidity) that they are able to transmit pressures
in all directions, thus giving rise to the principle stated in
(1) 104 and to Pascal's Law discussed in 110.
When near together molecules attract one another, thus
producing the resistance found when we attempt to break
a wire, to remove paint from glass, to tear paper, etc.
The name cohesion is given to this attraction when it is
between molecules of the same kind, and the term adhesion
applies to the attraction when the molecules are of differ-
ent kinds.
Cohesion serves to bind individual molecules into bodies,
or masses, and adhesion to hold together bodies of differ-
ent kinds. Two clean surfaces of lead will cohere when
pressed firmly together, and the dentist hammers gold leaf
into a solid lump to form the filling for a tooth. The
blacksmith brings together white-hot pieces of iron and
by blows brings their molecules into such close proximity
that cohesion takes place. Clean graphite powder is
pressed into a solid mass to form the lead of a pencil ; the
force of cohesion holds the particles together. The attrac-
tion between wood and glue, stone and cement, paint and
iron, etc., affords cases illustrating the force of adhesion.
130. Surface Films of Liquids. Although steel is
nearly eight times as dense as water, a small sewing
MECHANICS OF LIQUIDS 131
needle may be caused to " float " on water by placing it
carefully upon the surface. If the surface of the liquid
is closely examined, it will be observed that the needle
rests in a slight depression, as shown |g^ _^
in Fig. 95. In fact, the appearance
is as if a thin membrane were stretched ~
FIG. 95. An Ordinary
across the surface of the water. steel Needle "Floating"
The three following experiments on Water>
show an important property of the surface films of
liquids :
1. Let a soap bubble be blown on the bowl of a clay pipe or the
mouth of a small glass funnel. If the stem is left open a moment, it
may be observed that the bubble diminishes in size. A candle flame
held near the opening, in the stem will be deflected by the current of
air that is forced out by the contracting bubble.
2. Let a loop of thread be tied to one side of a wire frame 4 or 5
centimeters in diameter so that it will hang near the center, as shown
in (1), Fig. 96. If now the frame
is dipped into a soap solution, a
liquid film will form across it with
the loop closed, as shown. If, how-
ever, the film within the loop of
thread be broken by means of a hot
wire, the loop instantly opens out
into a circle, as shown in (2).
3. Let a mixture be made of alco-
*2\ hoi and water of such strength that
FIG. 96. An Effect of Surf ace Ten- a drop of olive oil will remain in it
sion in a Liquid Film. at any depth. The oil may be in-
troduced beneath the surface by means of a small glass tube. It
will be found that the globule of oil at once assumes a spherical
form. In order to avoid an apparent flattening of the drop of oil, a
body with flat sides should be used.
These experiments show that the surface film of a liquid
tends to contract and become as small as possible. In
Experiment 1 the contraction produces a pressure that
drives the air from the tube. In Experiment 2 the film
132 A HIGH SCHOOL COURSE IN PHYSICS
assumes the least possible area. This is the case when
the area within the loop is as large as it can become, i.e.
when it is circular. In Experiment 3 the film of oil com-
pletely incloses the globule and causes the oil to assume
the geometrical form requiring the least superficial area
for a given volume. The spherical form fulfills this con-
dition. For a similar B reason a soap bubble takes the
shape of a sphere.
131. Surface Tension. It will be seen from a study of
Fig. 97 that the conditions under which the^surface mole-
cules of a liquid exist is very
different' from that of the mole-
cules lower down. Molecule
A at the center of the small
circle is attracted equally in all
FIG. 97. Molecular Forces near directions by the neighboring
the Surface of a Liquid. molecules. This is the force of
cohesion and acts across a very small distance represented
here by the radius of the circle. Very near the surface the
forces acting downward on molecule B are greater than
those that act upward, while for molecule O there is no
upward attraction whatever. Hence the surface layers
of molecules are greatly condensed by this excess of force
acting always toward the body of the liquid. In this man-
ner is formed a tough, tense surface film whose constitution
is different from that in the interior mass. The measure
of the tendency of the surface layers of a liquid to contract
is called surface tension.
132. Capillary Phenomena. The effects of surface
films were first investigated in small glass tubes of hair-
like dimensions. Hence the name " capillarity " arises
from the Latin word capillus, meaning "hair." Figure
98 represents a series of glass tubes varying from 0.2 mil-
limeter to 2 millimeters in diameter. If the tubes are
MECHANICS OF LIQUIDS
133
moistened and then set upright in a shallow vessel of
water, the liquid will rise in the tubes, highest in the
smallest tube and least in the largest. It
may also be observed that the surface of the
liquid turns upward wherever it comes in
contact with the glass. Hence the surface
within the tube is concave, and a so-called
meniscus is formed.
If, now, glass tubes of small bore are
placed, in mercury (Fig. 99), the -liquid,
which in this case does FlG ;. 98 -- Eleva :
tion of a Liquid
not Wet the glass, will in Capillary
be depressed within
the tubes. The depression is great-
est in the smallest tube and least in
the largest. The edges of the film
in contact with the glass may be
seen to turn downward so that the
FIG. 99. Depression of surfaces within the tubes are convex,
Mercury in Capillary
Tubes. and the meniscus thus formed is 111-
^/_ verted.
The following laws of capillary action may be stated :
(1) Liquids are elevated in tubes which they wet, but are
depressed in tubes which they do not wet.
(2) The elevation or depression is inversely proportional
to the diameter of the
tubes. ^ K D
133. Capillary Ac-
tion Explained. If
a plate of glass, shown
in cross section in
(1), Fig. 100, be
placed upright in a
(1) (Z)
FIG. 100. Water Lifted by the Contraction of
the Surface Film.
134 A HIGH SCHOOL COURSE IN PHYSICS
shallow vessel of water after having been moistened,
there will be formed a continuous film ABO lying partly
upon the glass and partly upon the water. On account
of the tendency of this film to contract, as shown in 131,
the corner at B will be rounded and a small portion of the
water lifted against the glass.
Again, if a moistened tube of glass, (2), Fig. 100, be
dipped into water, a film A B CD is formed adhering to the
glass and extending across the water in the tube. Ow-
ing to the tendency of this film to contract, a force is pro-
duced that is sufficient to lift the column of water BEFC
in opposition to the force of gravity. When the tube is
dipped into mercury, the liquid forms no film adhering to
the glass above the surface level. On the other hand, the
surface film of mercury (see Fig. 99) continues down-
ward along the glass walls of the tube and then upward
into the tube at the lower end. The force which is
developed by the contraction of this film tends to pull
the liquid down within the tube. The depression thus
produced is such that the downward force of the con-
tracting film is balanced by the upward pressure of the
liquid within the tube.
134. Capillary Action in Soils. The principles of
capillary action find an important application in the
distribution of moisture in the soil. In compact soil
water is brought to the surface in much the same manner
as it rises in a piece of loaf sugar which is allowed to
come in contact with it. As rapidly as evaporation goes
on at the surface, the loss is supplied by capillarity from
below. In dry weather it is desirable to prevent this
surface loss, which is done by " mulching " and loosen-
ing the soil by cultivation. In this latter process the
grains of soil are broken apart and the interstices thus
made too large for effective capillary action to take place.
MECHANICS OF LIQUIDS 135
The moisture then rises to a level a few inches beneath
the surface, where it is made use of by growing plants.
EXERCISES
1. Why is a drop of dew spherical? Examine a small globule of
mercury placed on glass. Ho'w do you account for its form ?
2. By heating a piece of glass until it softens the sharp corners
become rounded and smooth. Explain.
3. Tn the manufacture of shot molten lead is poured through
a small orifice at the top of a tower. In falling the stream breaks
up into drops which solidify before reaching the earth. What gives
the spherical form to these masses of lead ?
4. Why does oil flow upward in the wick of a lamp? Will
mercury do the same?
5. Grease may be removed from a piece of cloth by covering it
with blotting paper and passing a hot flatiron over it. Explain.
6. Place two toothpicks upon water about a centimeter apart.
Touch the liquid surface between them with a glass rod moistened
with alcohol. From the manner in which the pieces of wood move
about, observe which liquid film has the greater tension.
7. Explain how an insect can run on the surface of water without
sinking.
8. Explain the action of a towel ; of blotting paper ; of sponges.
9. Why can we not write with ink upon unglazed paper?
10. Why are the footprints made in newly cultivated soil moist
while the loose earth is dry?
11. Explain why it is necessary to pack the earth around plants
and small trees when they are first set out. Later on we loosen the
soil about them. Why?
SUMMARY
1. The force exerted by a liquid of uniform density
against a given surface is directly proportional to the
depth of the surface ( 103).
2. At a given depth the force exerted by a liquid is the
same in all directions and acts always in a direction per-
pendicular to the surface against which it presses ( 104).
3. The force exerted by a liquid on any horizontal sur-
face is equal to the product of the area and, depth of the
136 A HIGH SCHOOL COURSE IN PHYSICS
surface and the density of the liquid. The equation is *
total pressure = ahd ( 106).
4. When the surface pressed against is not horizontal,
the product of the area and the density must be multiplied
by the depth of the center of mass of the given sur-
face ( 106).
5. The force exerted by a liquid against the bottom of
a vessel of given depth is independent of the form of the
vessel ( 107).
6. A liquid at rest in communicating vessels remains
at the same level in all its parts ( 109).
7. A force applied to any area of a confined liquid is
transmitted undiminished by the liquid to every equal
area of the interior of the containing vessel and to every
part of the vessel. This is known as Pascal's Law ( 110).
8. The mechanical advantage of the hydraulic press is
the ratio of the area of the large piston to that of the small
one ( 111).
9. A body immersed in a liquid is buoyed up by a
force equal to the weight of the liquid that it displaces.
This is known as Archimedes' Principle ( 120).
10. A floating body displaces a mass of the liquid in
which it floats, whose weight equals its own ( 122).
11. The volume of a body insoluble in water may be
found, according to Archimedes' Principle, by ascertaining
the weight of water that it will displace ( 123).
12. Density = maSS ( 125).
volume
13. Bodies are assumed to be composed of extremely
small particles called molecules. When near together,
molecules attract each other. Cohesion is the attraction
between molecules of the same kind ; adhesion is the at-
traction between molecules of different kinds ( 129).
MECHANICS OF LIQUIDS 137
14. The surface of a liquid tends to contract and be-
come as small as possible; hence the spherical form as-
sumed by soap bubbles, dew drops, globules of mercury,
etc (130).
15. Liquids are elevated in tubes which they wet, but
are depressed in those which they do not wet. The ele-
vation or the depression is inversely proportional to the
diameter of the tube ( 132).
16. Moisture rises readily in compact soils, but ceases
to rise in those of loose texture. Hence the loss of soil
water by evaporation is effectually prevented by "mulch-
ing " or by cultivation ( 134).
CHAPTER VIII
MECHANICS OF GASES
1. PROPERTIES OF GASES
135. Characteristics of Gases. Gases, like liquids,
possess the property of fluidity, i.e. they may be deformed
by any force however small. But a gas differs from a
liquid in that it has no definite size of its own ; it not
only fits itself to the shape of the vessel containing it,
but always entirely fills it. On account of their common
property of fluidity, liquids and gases are classed together
as fluids. As a consequence of this property, the laws of
pressure relative to liquids stated in 1, 104 and in 110
are equally applicable to gases. Other laws, however,
arise in the case of a gas on account of the tendency to
adapt its size to the capacity of the containing vessel.
136. Laws Common to Liquids and Gases. (1) The
force exerted against any surface is perpendicular to
that surface. (2) The force at any point is the same in
all directions ( 104). (3) An immersed body is buoyed
up by a force equal to the weight of the liquid or the gas
that it displaces ( 120).
137. Weight and Density of Air. We are taught by
everyday experience that a gaseous medium which we
call air surrounds us on every hand. The bubbles that
may be produced by blowing through a tube inserted into
water, the process of breathing, the resistance that the air
offers to a rapidly moving bicycle or train, the various
effects of the wind, and many other phenomena demon-
strate to us the presence of this medium.
138
MECHANICS OF GASES 139
It was shown by experiment in 3 that air has weight.
The same apparatus may be used in finding the density of
air in the following manner:
Let the bulb be weighed carefully before and after admitting the
air. The increase in weight will give the mass of the air contained in
the bulb. The capacity of the bulb is next ascertained by filling it
with water and weighing it. Dividing the mass of the air by the
capacity of the bulb gives the density of the air.
The density of air at the temperature of freezing water
and under the average sea-level pressure is 0.001293 gram
per cubic centimeter. Hence a liter (1000 cm. 3 ) of air
weighs nearly 1..3 grams. A cubic foot of air weighs about
an ounce and a quarter ; hence 12 cubic feet weigh nearly
a pound. The amount of air in an ordinary schoolroom
weighs more than half a ton. Thus we live submerged
in an ocean of air which extends many miles above us and
exerts a pressure of nearly 15 pounds per square inch.
2. PRESSURE OF THE AIR AGAINST SURFACES
138. Atmospheric Pressure. Since air has weight and
fluidity, the atmosphere must exert a force against all
surfaces with which it comes in contact. The existence of
such a force may be shown by the following experiments :
1. Fill a tumbler with water and invert it in a vessel of water.
Lift the inverted tumbler until its opening is horizontal and just
submerged, as in Fig. 101. The water re-
mains in the tumbler because it is sup-
ported by the force exerted by the atmos-
phere downward against the free surface
of water in the vessel.
2. While the inverted tumbler is in the
condition shown in Fig. 101, place a piece
of cardboard across its mouth, pressing it
close against the rim. Carefully lift the
tumbler from the water, and the cardboard
will not fall off. The force exerted by Water.
140
A HIGH SCHOOL COURSE IN PHYSICS
the air against the cardboard in an upward direction is sufficient to
support the weight of the water in the tumbler, as in Fig. 102.
3. Tie a piece of sheet rubber over a
glass vessel, as shown in Fig. 103. Place
the vessel on an air pump and exhaust
the air from the
space beneath
the rubber. The
membrane, no
longer supported
by the air from
below, is more
and more de-
pressed until it
FIG. 102. Action of Atmos-
pheric Pressure Upward.
FIG. 103. Atmospheric
Pressure upon a Rubber
Membrane.
finally bursts under the pressure of the air
above.
4. If a glass tube 3 or 4 feet long (or
even longer) can be secured, place it nearly
vertical with one end in a tumbler of water. Try to elevate the
water to the top of the tube by "sucking" on the upper end of
it. Now insert the lower end of the tube in mercury and try to
elevate it in the same manner. It is so much denser than water,
that it can be lifted only a few inches.
139. Limitations of Atmospheric Pressure. The atten-
tion, of Galileo was called to the fact that in wells of
unusual depth suction pumps ( 155) were unable to lift
water more than about 32 feet above the level of the water
in the wells. At that time it was supposed that " nature
abhorred a vacuum " and that she hastened to fill all such
spaces with whatever material happened to be most avail-
able. Thus Galileo was led to believe that nature's abhor-
rence for a vacuum had its limitations, and he probably
suspected that the rise of water in pumps was due to* air
pressure on the surface of the water. It remained for his
pupil, Torricelli, however, to devise a suitable method for
measuring the actual pressure of the atmosphere. He suc-
ceeded in doing this in the year 1643.
MECHANICS OF GASES
141
FIG. 104.
140. Torricelli's Experiment. This important histori-
cal experiment is performed by making use of a strong
glass tube about 80 centimeters long which is closed at one
end. The tube is first filled with
mercury in order to expel the air,
after which it is closed by the
finger and inverted in a vessel of
mercury, Fig. 104, care being
taken to prevent the entrance of
air. The mercury falls at once
and leaves a vacuum of several
centimeters at the top of' the
tube. The force due to the at-
mosphere which is exerted down-
ward against the free surface of
mercury in the vessel is trans-
mitted to the interior of the tube
in which it is able to support
a column of the liquid usually about 75 centimeters in
height.
141. Pascal's Experiment. Pascal reasoned that if the
column of mercury in a Torricellian tube were indeed
supported by the atmosphere, the column should become
shorter at a high altitude. The column was accordingly
measured at the top of a high tower in Paris and a small
decrease detected. Five years after Torricelli's discovery,
the tube was carried to the top of the Puy de Dome, a
high mountain in Auvergne, France, where a test showed
a decided decrease of about 8 centimeters in the height of
the mercurial column.
142. Variations in Atmospheric Pressure. The atmos-
pheric pressure at a given place is far from being constant.
The variations at any given place amount to about 3 cen-
timeters. At sea-level the average height of the mercurial
Torricelli's Experi-
ment.
142 A HIGH SCHOOL COURSE IN PHYSICS
column is about 76 centimeters ; hence this height is taken
as the standard of pressure and is called mean sea-level
pressure. Any pressure equivalent to a column of mer-
cury 76 centimeters high is said to be " one atmosphere.."
143. The Barometer. The mercurial barometer (pro-
nounced ba rom'e ter) is merely a mounted Torricellian
tube for showing the pressure of the atmos-
phere. In order that it may give correct
indications, the mercury must be pure, and
clean, and the space above the liquid in the
tube as free as possible from the presence of
air and other gases; i.e. the vac-
uum must be as nearly perfect
as possible. Atmospheric pres-
sure is usually measured in inches
or centimeters of mercury. The
space above the mercury in the
tube is known as the Torricellian
vacuum.
As the height of the mercurial
column changes with the pressure
of the air, the surface of the
liquid rises and falls in the res-
ervoir, or cistern, below. For an
accurate reading of the barometer
the mercury column must be meas-
ured from the surface of the liquid
in the reservoir.. In the barome-
ter shown in Fig. 105 the reser-
voir has a flexible bottom. By
FIG. 105. - A standard Mer- turn i nff the screw S the surface
curial Barometer.
of the mercury in the cistern is
brought to the zero point of the scale, whose position is
marked by an ivory index B. The height of the mercury
MECHANICS OF GASES
143
is then read by observing the position of the
upper surface of the liquid in the tube at A.
Some mercurial barometers have the form
shown in Fig. 106. The height of the mer-
cury is found by reading the positions of the
two liquid surfaces A. and .Z?, in which case
the difference between the two readings gives
the length of the mercury column supported
by the atmosphere.
144. The Aneroid Barometer. A barometer of
the form shown in Fig. 107 is in common use. As the
name indicates, the aneroid barometer is "without
liquid," and depends for its operation on a circular
chamber C
made of thin
metal with
corrugated
sides. The
air in the
chamber is
partly re-
moved, after
which the chamber is hermetically sealed. An increase
of atmospheric pressure forces the side of the box
inward, but a decrease allows it to spring out.
This motion,
Chough very
s^ght, is
transmitted
FIG. 107. The Aneroid Barometer.
Fxo.106.-A
Mercurial
Barometer,
through the
multiplying systems of levers
L and A and the small chain
B to the axle S which car-
ries the index, or movable
pointer, /. The scale is
graduated to correspond to
the readings of a standard FIG ; io8._The Barograph, or Self-registering
mercurial barometer. These Barometer.
144
A HIGH SCHOOL COURSE IN PHYSICS
instruments are made of convenient size to be used by surveyors and
explorers in ascertaining altitudes. It should be said that the words
" Rain," " Fair," etc., printed on the dial of an aneroid barometer are
merely indications of the general trend of weather changes.
The principle of the aneroid is employed in the " barograph," or
self-recording .barometer, shown in Fig. 108. This instrument is
provided with an index which carries a pen that makes a continuous
record of the atmospheric pressure on a revolving cylinder covered with
suitable paper. A portion of such a record is shown in Fig. 109.
THURSDAY /
FRIDAY
SATURDAY
4 6 8 16 jf'2 4 6 I
JNDAY /
p^'2 ji 6 8 1,6yT"
J 8 10^JJ_8rbSrt.2_4 6
M 8
1 t OYu2 468 1,0
FIG. 109. Portion of a Record Made by a Barograph.
145. Utility of the Barometer. The barometer is an
important laboratory instrument, inasmuch as the atmos-
pheric pressure must be known in carrying out many
experiments in both Physics and Chemistry. In this
respect it ranks in usefulness with the thermometer,
balance, etc.
From the readings of barometers taken simultaneously
at many places of observation and telegraphed to central
stations, the direction of atmospheric movements can be
predicted. Thus the barometer becomes an aid in fore-
casting the weather. Furthermore, a "low" barometer,
i.e. decreased pressure, usually accompanies or precedes
MECHANICS OF GASES
145
.29.7
stormy weather, while a rising barometer generally de-
notes the approach of fair weather. If a weather map
be consulted, certain regions will be found marked
"High" and others marked "Low." The places at which
the pressures are equal are joined by curves called
isobars, upon each of which is indicated the barometric
reading, Fig. 110.
The direction of the
wind at each place of
observation is indi-
cated by an arrow.
The general direc-
tion of the wind is al-
ways from places of
"high" toward those
of " low " pressure.
Another important
use of the barometer
is made in measuring
the difference in alti-
tude of two places.
This measurement de-
pends upon the fact
that the atmospheric
pressure decreases with the elevation above sea-level.
For places not far above the level of the sea the decrease
is about 1 millimeter for every 10.8 meters of elevation,
or 0.1 inch for every 90 feet of ascent. The decrease in
pressure as one climbs a mountain is easily accounted for
when it is recalled that it is the air above the level ol
a given place that produces the pressure. Descending
a mountain or into a mine simply submerges one more
deeply in the atmospheric ocean and thus puts above his
level more air to be supported.
11
FIG. 110. A Portion of a Weather Map.
146 A HIGH SCHOOL COURSE IN PHYSICS
146. Atmospheric Pressure Computed. In order to
compute the pressure of the atmosphere in grams per
square centimeter, we have only to find the pressure per
unit area due to mercury when its depth is equal to the
height of the barometric column. Consider a tube whose
cross-sectional area is 1 square centimeter and in which
the height of mercury is 76 centimeters. The pressure at
the bottom of such a tube is the product of the area, height,
and density of the mercury, as shown in 106. We have,
therefore, 1 x 76 x 13.6, or 1033.6 grams. Hence, if the
barometer reading is 76 centimeters, the atmospheric pres-
sure is 1033.6 grams per" square centimeter.
EXERCISES
1. The column of mercury in a barometer stands at a height of
74.5 cm. What is the height in inches?
2. How high a column of water could be supported by atmos-
pheric pressure when the barometer reads 75 cm.?
3. When the barometer reads 74 cm., what is the atmospheric
pressure expressed in grams per square centimeter? in dynes per
square ceptimeter?
4. If the pressure of the air is 15 Ib. per square inch, calculate
the total force exerted upon a person the area of whose body surface
is 16 sq. ft.
5. A soap bubble has a diameter of 4 in. Calculate the force
exerted by the air against its entire surface when the barometer reads
29 in. A cubic inch of mercury weighs 0.49 Ib.
6. What result would be obtained by performing
Torricelli's experiment with a tube twice as long as the
one described in 140 ?
7. How would the height of mercury be changed
if a tube of larger cross-sectional area were used ?
8. Show why a change in the area of the mercurial
surface in the cistern of a barometer has no effect on the
height of the column.
9. What result would Torricelli have obtained in his
experiment if he had used a tube only 70 cm. long?
FIG. 111. 10- Try to suck the water from a bottle (see Fig. Ill)
MECHANICS OF GASES
147
FIG. 112. Pneu-
matic Inkstand.
out of which a glass tube passes through a tightly fitting rubber
stopper. Explain the results observed.
11. Inkstands are sometimes made in the form
shown in Fig. 112. Explain why the ink in the
reservoir can remain at a greater height than that
outside.
12. Why is it necessary to make a small vent
hole in the upper part of a cask when it is
desired to draw off the liquid in a steady
stream from a faucet placed near the bottom ?
13. Explain why water will not run in
a steady stream from an inverted bottle.
14. The Magdeburg hemispheres shown
in Fig. 113 are closely fitting hollow vessels
about 4 in. in diameter. By placing the
hemispheres together and exhausting the
air the pull of two strong boys is scarcely
sufficient to separate them. Explain.
15. Assuming the atmospheric pressure
to be 15 Ib. per square inch, calculate the
force required to separate the hemispheres
shown in Fig. 113 when the air within them
FIG. 113. Magdeburg
Hemispheres.
is completely exhausted.
3. EXPANSIBILITY AND COMPRESSIBILITY OF GASES
147. Compressibility of Air and Other Gases. Gases,
unlike liquids, are easily reduced in volume by increasing
the pressure under which they exist. This is evident
from the fact that the quantity of air in the pneumatic tire
of a bicycle, for example, may be increased to double or
triple the original mass. Again, the air in a pneumatic
cushion is compressed into a smaller space when one sits
upon it, but it springs back to its original volume when
the pressure is relieved. Thus air and other gases mani-
fest the property of expansibility as well as compressibility.
The popgun and air rifle make use of these properties of
air : first the air is compressed in the cylinder of the gun,
148
A HIGH SCHOOL COURSE IN PHYSICS
FIG. 114. -II-
then as the pellet moves, the force of expansion drives the
missile with great acceleration from the barrel.
1. Place a partially inflated balloon under the receiver of an air
pump. As soon as the pump is set in action, the swelling of the
balloon will indicate the expansive tendency of the air
within it.
2. Arrange a bottle as shown in Fig. 114. Blow
forcibly into the tube, thus causing some bubbles of
air to pass into the bottle above the liquid. Quickly
remove the lips from the tube,
and water will be driven out by
the expanding air within the
bottle.
3. Place two bottles under the
receiver of an air pump as shown
in A and B, Fig. 115. A is tightly
lustrating corked and about two thirds full
Expansi- o f W ater. B is uncorked and con-
bilitv of a
Gag J tains air only. When the pump
is put into operation, the air pres-
sure on the surface of the water in B is reduced,
and the consequent expansion of the air in A above the liquid forces
the water through the tube into B. If air be now admitted into the
receiver, the water will be driven back into A . Why ?
The expansibility of gases is explained by assuming that
their molecules ( 129) are in rapid motion. As a con-
sequence of this motion, innumerable molecules strike
against every part of the walls of the containing vessel.
Although the mass of a molecule is extremely small, its
speed is so enormous (equaling or exceeding that of a
cannon ball) that it strikes the side of the vessel with an
appreciable force. Thus a continuous storm of such blows
results in the production of a steady outward pressure
against the walls of the vessel inclosing the gas.
148. Pressure and Elastic Force in Equilibrium. The
experiments just described teach us why hollow bodies,
MECHANICS OF GASES
149
such as balloons, cardboard boxes, etc., are not crushed by
atmospheric pressure. The crushing force exerted against
the external surface of a balloon only 10 centimeters in
diameter is more than 300 kilograms. This force, how-
ever, is counteracted by the expansive force of the gas
within it. If the external force is decreased, the gas ex-
pands until the forces are again in equilibrium. On the
other hand, if the external force is increased, the gas is
compressed until the inward and outward forces balance
each other. Thus the human body is able to withstand
the enormous force exerted by the atmosphere upon it.
All the cavities that might otherwise collapse are pre-
vented from doing so by the expansive force of the gases
which they contain.
149. Law of Expansion and Compression. The rela-
tion which exists between the pressure to which a gas is
subjected and its volume was
discovered by Robert- Boyle
(1627-1691) of England, in
1662, and by Mariotte, of
France, fourteen years later.
In France this relation is usu-
ally called " Mariotte's Law,"
but we speak of it as Boyle's
Law. An experiment to illus-
trate Boyle's method of dis-
covery may be performed as
follows :
Take a bent glass tubo (1), Fig.
116, of which the shorter arm is
hermetically sealed. The long arm,
left open at the top, should be about
90 centimeters long. The length FlG
of the short arm should be at least
116. Illustrating Boyle's
Law.
150 A HIGH SCHOOL COURSE IN PHYSICS
10 centimeters. Pour a small quantity of mercury into the tube so
that the liquid stands at the same level in both sides. We thus
have a quantity of air confined in the space A C under one atmosphere
of pressure owing to the transmission of pressure by the mercury.
Measure the length of the space AC, and then pour mercury into
the tube (see (2), Fig. 116), until the surface of the liquid in
the long arm is as far above that in the short arm as the height of
mercury in the barometer. If the new volume of air in the short
arm be measured, it will be found to be just one half the original
volume. The new pressure is due both to the atmospheric pressure
on the mercury at B and the column of mercury in the tube. It is,
therefore, two atmospheres.
This experiment teaches us that by increasing the pres-
sure upon a confined gas from one atmosphere to two
atmospheres, the volume is caused to be only one half as
great. This is only a special instance, however, of a more
general law. If p is the pressure of a gas whose volume
is v, then
under a pressure 2 p the volume of the gas will be | v ;
under a pressure & p the volume of the gas will be J v ;
under a pressure ^p the volume of the gas will be 2 v ;
under a pressure ^p the volume of the gas will be 3 v, etc.
Now, since
pv = 2p x I ,v = 3p x \v = \p x 2 v = p x 3 v,
we are able to state the relation as follows :
The product of the pressure and volume of a given mass of
gas at a constant temperature is constant.
Where P is the pressure of the gas when its volume is
FJ and p the pressure when the volume is v, the law may
be expressed algelxtfifelly in the forms :
PV = pv, or P : p : : v : V. (l)
EXAMPLE. The observed volume of a gas is 30 cm. 3 when the
barometer reads 74.5 cm. What volume will it occupy under a baro-
metric pressure of 76 cm.?
MECHANICS OF GASES
151
SOLUTION. According to Boyle's Law the product of the pres-
sure and volume under the first condition will be equal to their prod-
uct under the second condition. Hence, if x represents the volume
required, we have
74.5 x 30 = 76 x x.
Solving this equation for x, we obtain
x = 29.4 cm. 3 .
EXERCISES
1. If the volume of a certain gas is 200 cm. 3 when its pressure is
1000 g. per square centimeter, what volume will it occupy when its
pressure has been increased to 1200 g. per square centimeter?
2. The volume of an air bubble at a depth of 1 m. of mercury is
1 cm. 3 What will be its volume when it reaches the surface if the
barometer reading is 75 cm. ?
SUGGESTION. The first pressure is equal to the sum of the atmos-
pheric pressure and that due to the mercury in which it is immersed,
or 175 cm.,
3. A gas is often confined in a tube, as shown
in A y Fig. 117, whose open end is beneath the sur-
face of some liquid. How much is the pressure of
the gas confined in such a tube in a vessel of mer-
cury when the surface in the tube is 25 cm. below
the level of the liquid outside, the barometer read-
ing 75 crn.?
4. If the volume of the gas under the conditions
given in Exer. 3 is 15 cm., what will be its volume
if the tube is elevated until the surfaces are at the
same level ?
5. In B, Fig. 117, the surface of the mercury in
the tube is 25 cm. above that of the mercury on
the outside. If the atmospheric pressure is 75 cm.,
what is the pressure of the confined gas ?
6. Under the conditions given in Exer. 5 the volume of the gas
confined in the tube is 50 cm. 3 . What volume will the gas occupy
when the surfaces are brought to the same level?
7. The volume of an air bubble 136 cm. under vater is 0.5 cm. 3 .
Barometer reading = 75.4 cm. Calculate (1) the pressure to which
the bubble is subjected, and (2) the volume it will have as it emerges
from the water.
FIG. 117.
152 A HIGH SCHOOL COURSE IN PHYSICS
SUGGESTION. Reduce the depth of water to its equivalent in
terms of mercjiry, and compute the first pressure as in Exer. 2.
8. To what depth would the inverted tumbler shown in Fig. 1
have to be taken in order to become half filled with water if the
barometer reading is 75 cm. ?
9. A gas tank whose capacity is 3.5 cu. ft. is filled with illumi-
nating gas until the pressure is 225 Ib. per square inch. How many
cubic feet of gas at atmospheric pressure will be required in the filling
of the tank? (Assume one atmosphere to be 15 Ib. per square inch.)
10. Why is it safer to test an engine boiler by pumping in water
rather than air? l ^%^
150. Changes in Density. Since a change in the volume
of a given mass of gas occurs whenever the pressure is
changed, it follows that there will also be a change in
its density. Forcing the gas into one half its original
volumeApBubles the amount in each cubic centimeter ;
makhiJMthe volume one third multiplies the mass in each
cubic centimeter by three ; and so on. Therefore, doub-
ling the pressure of a gas, thus reducing the volume one
half, doubles the density ; tripling the pressure multiplies
the density by three ; and so on. Hence, we may state
these relations as follows :
The density of a gas at constant temperature is directly
proportional to the pressure.
Expressed algebraically,
D : d : : P : p, (2)
where D is the density of the gas when the pressure is P,
and d the density when the pressure is p.
EXERCISES
1. Hydrogen, Vhose density is 0.09 g. per liter under one atmos-
phere of pressure, is condensed in a steel cylinder until the pressure
is 15 atmospheres. Calculate the density of the gas in the cylinder.
MECHANICS OF GASES 153
2. Illuminating gas is condensed in a reservoir until its density
has increased from 0.75 g. per liter to 4.5 g. per liter. Calculate the
pressure in the reservoir. Express the result in atmospheres.
3. If 4 liters of air at ordinary atmospheric pressure are admitted
into a vacuum of 10 liters capacity, what will be the pressure and
density of the air? (Under one atmosphere the density of air is
1.29 g. per liter.)
4. What is the weight of the quantity of illuminating gas con-
densed in a cylindrical tank of 3 cu. ft. capacity until the pressure is
225 Ib. per square inch ? (The density of the gas under one atmos-
phere of pressure is 0.75 g. per liter.)
5. If the gas shown in the tubes in Fig. 117, A and B, is air, what
is the density of it under the conditions given in Exercises 3 and 5
on page 151 ?
4. ATMOSPHERIC DENSITY AND BUOYANCY
151. Atmospheric Density Changes with Altitude. The
air, unlike the water of the ocean, which is practically
incompressible, diminishes in density as one^ ascends a
mountain or rises in a balloon. As the pressure becomes
less, the density of the air decreases proportionally. Thus
at the summit of Mont Blanc in Switzerland, an altitude
of three miles, the barometer indicates only one half as
much atmospheric pressure as at the sea-level. Hence the
density of the air at "this altitude is only one half as
great.
Aeronauts 'have succeeded in ascending to an altitude
of about 7 miles, where the pressure is only 18 centimeters,
or about a quarter of sea-level pressure. Greater altitudes
have been explored by the aid of balloons equipped with
self-registering instruments until a height of about 14
miles has been attained. Figure 118 shows the changes in
the pressure and density of the atmosphere at various alti-
tudes. The numbers at the left indicate altitudes in miles
above sea-level, those at the extreme right the densities of
the air compared with the density at sea-level, while the
154
A HIGH SCHOOL COURSE IN PHYSICS
next column gives the barometric readings in inches. From
the figure it may be seen that at an elevation of 15 miles,
for example, the density of the air is only one thirtieth of
FIG. 118. Showing the Decrease of Atmospheric Pressure with Altitude.
its sea-level density, while the barometer would read about
one inch of mercury.
152. Buoyancy of Air. On account of the fact that
the pressure of the air decreases as the altitude increases,
its pressure downward upon the top surface of a box, for
example, is less than its upward pressure against the bot-
tom. It follows, therefore, as for bodies immersed in
water ( 121), that an object is buoyed up by a force equal
to the weight of the air that it displaces. In general,
bodies are so heavy in comparison with the amount of air
displaced that the consequent loss of weight is not taken
into account. A man of average size, for instance, is
buoyed up by a force equal to about 4 ounces. If, how
MECHANICS OF GASES 155 ; .
ever, the air displaced by a body should weigh more than
the body itself, it would be lifted by the air just as a piece
of wood is lifted when immersed in water. This is the
case of a balloon, in wln'ch the weight of the material com-
posing the bag, together with the gas used to fill it, ropes,
basket, ballast, etc., is less than that of the air which it
displaces. In order that this may be so, it is necessary
to inflate the balloon with a gas lighter than air, which
weighs 1.29 kilograms per cubic meter. Hydrogen gas is
sometimes used whose density is 0.09 kilogram per cubic
meter, but more frequently the material is common illumi-
nating 'gas weighing about 0.75 kilogram per cubic meter.
The balloon United States which won the first international
race at Paris in 1906 was filled with over 2000 cubic meters
of illuminating gas, thus creating a lifting force of more
than a ton.
EXERCISES
1. A balloon whose capacity is 1000 m. 3 is filled with hydrogen.
If the weight of the bag, basket, and ropes is 235 kg., what additional
weight can the balloon lift ?
SUGGESTION. Find the difference between the weight of the air
displaced by the balloon and the entire weight of the balloon and its
equipment.
2. What will be the lifting capacity of the balloon in Exer. 1 when
filled with illuminating gas?
3. When will a balloon cease to rise ? When will it begin to fall ?
4. A kilogram weight of brass (density 8.3 g. per crn. 3 ) will weigh
how much in a vacuum ?
SUGGESTION. Add to the weight of the body the weight of the air
that it displaces.
5. APPLICATIONS OF AIR PRESSURE
153. The Air Pump. The air pump is used to remove
the air or other gases from a closed vessel called a receiver.
It was invented about 1650 by Otto von Guericke (1602-
156
A HIGH SCHOOL COURSE IN PHYSICS
1686), burgomaster of Magdeburg, Germany. A simple
form of the air pump is shown in Fig. 119. O is a cylin-
der within which slides the tightly fitting piston P. R is
the receiver from which the air is to be exhausted. The
receiver is connected with the cylinder by the tube T.
8 and t are valves opening upward. The operation of
the pump is as follows :
When the piston is pushed down, the valve s permits
the air in the cylinder to escape, but closes to prevent its
return when the piston
is lifted. Raising the
piston tends to produce
a vacuum in the cylin-
der ; but the air in the
receiver and connecting
tube expands, lifts the
valve , and fills the
cylinder. Thus each
down-and-up stroke of
the piston results in the
removal of a portion of
the air in the receiver. After several strokes of the
piston, the air in the receiver becomes rarefied to such an
extent that its expansive force is no longer sufficient to
lift valve , and no further exhaustion can be produced.
Some air pumps are so constructed that the valves are
opened and closed automatically ~at the proper moment so
that a greater degree of rarefaction can be reached.
154. The Condensing Pump. The condensing pump is
used to compress illuminating gases in cylinders for use in
lighting vehicles, stereopticons, etc., and further for inflat-
ing pneumatic tires, operating drills in mines, air-brakes
on railway cars, and for many other purposes. The most
common condensing pump is that used for inflating bicycle
FIG. 119. Air Pump.
MECHANICS OF GASES
157
tires. Figure 120 shows the construction of such a pump.
When the piston P is forced down, the air in the cylindei
of the pump is driven into
an air-tight rubber bag
within the tire T. The
small valve 8 opens to ad-
mit the air into the tire,
but closes to prevent its
return. On lifting the
piston a partial vacuum is
produced in the cylinder,
and the air from outside FIG. 120. - Inllatlng a Tire r by Means
of a Condensing Pump P.
finds its way into the cyl-
inder past the soft cup-shaped piece of leather attached to
the piston. During the downward stroke of the piston,
however, this leather is pressed firmly against the sides
of the cylinder and thus prevents
the" escape of the air. Repeated
strokes of the piston add to the
mass of air already in the tire, and
the process of pumping may be con-
tinued until the tire is sufficiently
inflated.
155. The Common Lift Pump.
The simplest pump for raising water
from wells is the common lift pump.
This consists of a barrel, or cylinder,
(7, Fig. 121, connected with a well
or other source of water by a pipe
B. The entrance of this pipe into
the cylinder is covered by a valve
, opening upward. In the cylinder
is a closely fitting piston P which
FIG. 121. Common Lift , . ,
Pump. can be raised or lowered by means
158
A HIGH SCHOOL COURSE IN PHYSICS
of a rod which is usually connected with a lever for con-
venience in operating. The piston contains a valve t, also
opening upward. The action of the pump is as follows :
When the piston is raised, the pressure of the air in the
tube and lower part of the cylinder is diminished. The
atmospheric pressure on the surface of the water in the
well then forces water into the pipe. As the piston is
lowered, valve s closes, and t allows the air in the cylinder
to escape, but closes again when the piston begins to ascend.
The second stroke again reduces the pressure below the
piston, and water is forced still higher in the pipe. At
last the water reaches the piston, passes through during
the downward stroke, and is lifted toward the spout of the
pump when the piston moves upward.
It will be seen that the action of the common lift pump
is dependent on the pressure of the atmosphere to elevate
the water to a point just high enough to come within reach
of the piston ; the piston must not be farther above the water
in the well than the height of
the water column that the air
can support. When water
is to be lifted from a well
more than 33 or 34 feet in
depth, the cylinder is placed
low enough to enable the
piston to move within that
distance of the surface of
the water.
156. The Force Pump.
The force pump is used to
deliver water under consid-
erable pressure either for
spraying purposes or in or-
FIG. 122. A Force Pump. der to elevate it to a reser-
MECHANICS OF GASES 159
voir placed some distance above the level of the pump. It
is made in many different forms. Usually the force pump
has no opening or valve in the piston. The water escapes
from the cylinder through a side opening A^ Fig. 122, past
the valve , thence upward to the spout or reservoir. In
other respects the description of the action of the lift pump
applies equally well to the force pump. In order to obtain
a steady stream of water, a force pump is often provided
with an air chamber D. The entrance of the water through
t serves to compress the air in the chamber, which by its
expansive force maintains the current in pipe E while the
piston is moving upward.
157. The Siphon. The siphon is a bent tube with un-
equal arms. It is used for removing liquids from tanks or
reservoirs that have no outlet, or for P . a6
drawing off the liquid from a vessel
without disturbing a sediment lying
upon the bottom.
Let a glass tube bent in the form shown in
Fig. 123 be filled with water, and the ends
closed while the tube is inverted and placed
in the position shown. On opening the ends
water will flow through the tube from the
vessel in which the liquid has the higher
level.
The action of the siphon is explained
as follows : the upward pressure at a
due to the atmosphere is only partly
counterbalanced by the pressure of the FlG ' 123 -~ The Si P hon -
liquid column ah. If the atmospheric pressure is p, the
resultant force acting toward the right is p db. Again,
the upward pressure of the atmosphere at d is opposed
by the pressure due to the liquid column cd. Hence
the resultant pressure acting toward the left is p cd.
160 A HIGH SCHOOL COURSE IN PHYSICS
Since the pressure due to the liquid in the long arm
exceeds that of the liquid in the short arm, the excess
of force in the tube tends to move the water toward
the lower vessel. The resultant of all the forces is
equal to the difference of pressure due to the liquids in
the two arms, i.e. to a column of liquid equal to cd ab.
The liquid will therefore continue to flow until this dif-
ference is ; or, in other words, until the liquid reaches
the same level on the two sides. A second condition
necessary to the action of a siphon is that for water the
height of the lend f must not be greater than 33 or 34 feet
above a, since its elevation to the point / is due to the
atmospheric pressure.
158. Work done by Compressed Gases. Since a gas
exerts a force against the sides of the vessel containing it,
it is obvious that work will be done by the gas if the side
of the vessel is made movable and the gas allowed to ex-
pand ( 55). Imagine air to be
compressed in the cylinder O shown
in Fig. 124, in which P represents
FIG. 124. An Expanding a movable piston. If the external
resistance offered to the piston is
not as great as the force exerted
by the air inside, work will be done by the expanding
gas, and the piston will move. If the pressure remains
constant during the process, the, work done will be
measured by the product of the force exerted by the air
against the piston and the displacement produced.
EXAMPLE. A tube leads from a cylinder to a reservoir where air is
stored under a pressure of 5000 g. per cm. 2 ; the area of the piston is 50
cm. 2 . Find the work done by the gas when the piston moves 20 cm.
SOLUTION. The total force exerted by the gas against the piston
is 50 x 5000, or 250,000 g. Hence the work done is 250,000 x 20, or
5,000,000 gram-centimeters.
MECHANICS OF GASES
161
Since energy can be transferred from place to place in
a compressed gas, air under great pressure is often con-
ducted through pipes over long distances from a condens-
ing apparatus ( 154) to a point where the energy is to be
utilized. In this way a locomotive engineer is able to con-
trol a train by means of compressed air conducted from
the engine, where it is compressed, to suitable apparatus
in connection with the brakes under each car ( 159).
In mining operations and stone quarrying, pneumatic ma-
chines utilize compressed air for drilling the holes in rocks
where explosives used in blasting are to be placed. Many
other applications of the power of compressed gases have
found a place in modern engineering.
159. The Air Brake. Compressed air is widely used by the
railroads of many countries in the operation of the Westing-house air
brake, Fig. 125, which works as follows : The locomotive is provided
with a condensing pump
which keeps the air in a
large reservoir at a pres-
sure of about 80 pounds
per square inch. From
this reservoir the com-
pressed air is conducted
through the train pipe P
to an auxiliary reservoir To the
R placed under each car. Brake
As long as the pressure is
maintained in P, air is FlG 125 _ The Westinghouse Air Brake .
allowed to enter R and at
the same time is prevented from entering the cylinder C by a compli-
cated automatic valve F, and the brakes are held "off" by the spring
S. If, however, the engineer by moving a lever in the cab, allows the
pressure in the pipe P to fall, the passage between R and P is at
once closed by the v^lve F, and the compressed air in R is admitted
into C. The pressure of the air forces the piston to the left and
sets the brakes against the wheels. By admitting air from the reser-
voir on the engine into the pipe P, the valve V again establishes a
12
162
A HIGH SCHOOL COURSE IN PHYSICS
communication between P and R and allows the air in C to escape.
The spring S forces the piston back and releases the brakes. The
great advantage of this brake is
that in case of any accidental
breaking of the train pipe P,
the brakes are automatically set.
They are often arranged to be
operated from any coach in case
of emergency.
160. Subaqueous Opera-
tions. Important use is made
of compressed air in various en-
gineering operations performed
under water, as laying the foun-
dations of bridges, excavating for
tunnels, recovering the cargoes
from sunken vessels, etc. Figure
126 shows the most important
apparatus for subaqueous work,
the diving bell, and the sub-
marine diver. A condensing
pump on board the vessel forces air through a tube into the bell,
thus supplying the workman with oxygen and preventing the rise
of water in the working chamber.
Air is supplied to the workman
in diving armor in the same
manner. The foul air escapes
from the diving suit through a
valve above the chest. In many
cases the air is supplied from a
reservoir carried on the back of
the diver.
Deep excavations are fre-
quently made and foundations
built up from bed rock by the
aid of the pneumatic caisson
(pronounced kas'son). See Fig.
127. The working chamber C BedKock
is gradually lowered through soft FlG 127 _ Excavating below the Water
soil by removing the earth from Level by the Aid of Compressed Air.
FIG. 12G. Apparatus Used for Work
under Water.
MECHANICS OF GASES 163
within after loading the roof of the chamber with heavy masonry
above. When the caisson sinks below water level, air under suitable
pressure is forced into C to prevent the influx of water. The ex-
cavated earth is removed, and the foundation material introduced
through the air lock A. The bucket is lowered into A, after which
the opening around the wire cable is closed air-tight. Air is then
allowed to flow into A until the pressure there is equal to that in (7.
The semicircular doors separating A and C are now thrown open, and
the bucket lowered into the caisson. As the caisson is forced more
and more below water level, the pressure of the air is correspondingly
increased in order to prevent the water and rnud from crowding in.
EXERCISES
1. If the pressure against the 8-inch piston of an air brake is 75 Ib.
per square inch, how much force drives the piston forward?
2. When a train is broken in two, the cars are brought quickly to
rest. Explain.
3. What are the advantages gained by the use of air brakes?
4. A diver sinks 68 ft. below the surface of water. Under how
many atmospheres is he working? Explain why his body is not
crushed by this force.
5. A caisson is sunk until the bottom is 51 ft. below water level.
Under what pressure must the laborers work?
6. Explain how a bucket of earth is removed from a caisson through
the air lock.
4 SUMMARY
1. The laws of pressure relative to liquids are equally
applicable to gases, except that the pressure is not propor-
tional to the depth ( 135 and 136).
2. The density of the air under standard conditions of
pressure and temperature (i.e. 76 cm. and C.) is 1.293
g. per liter or about 1.25 oz. per cubic foot ( 137).
3. The pressure of the atmosphere is measured by the
barometer. At sea level the average height of the mer-
curial column supported by the air is 76 cm. or very nearly
30 in. Expressed in units of force, the average sea-level
pressure is 1033.6 g. per square centimeter or 14.7 Ib. per
164 A HIGH SCHOOL COURSE IN PHYSICS
square inch. The atmospheric pressure decreases with
the altitude, but not proportionally ( 139 to 146).
4. Gases adapt themselves to the form and capacity of
the vessels containing them. The expansive force of a gas
confined in a receptacle tends to prevent the collapse of the
vessel under atmospheric pressure ( 147).
5. The product of the pressure and volume of a given
mass of a gas at a constant temperature is constant. This
is known as Boyle's Law, or Mariotte's Law ( 149).
6. The density of a gas at a constant temperature is
directly proportional to the pressure to which it is subjected
(150).
7. A body in air is buoyed up by a force equal to the
weight of the air that it displaces ( 152).
8. The air pump is used in the rarefaction of gases.
The condensing pump is used in compressing air and
other gases ( 153 and 154).
9. The action of " suction " pumps is dependent upon
the pressure of the atmosphere on the water in the well or
cistern ( 155 and 156).
10. The siphon is a bent tube .having unequal arms
used for conveying a liquid over the side of a reservoir to
a lower level than that in the reservoir. Its action is
dependent on atmospheric pressure ( 157).
11. Compressed air possesses energy. This energy is
used in many important mechanical devices, as the air
brake, rock drills, etc. ( 158).
CHAPTER IX
SOUND : ITS NATURE AND PROPAGATION
1. ORIGIN AND TRANSMISSION OF SOUND
161. Cause of Sound. Whenever the sensation of sound
is traced to its external cause, we find that its source is
always something which is in a state
of vibration. Sometimes the vibra-
tion of the body emitting the sound
is sufficiently great to be visible, i.e.
to give a certain blurred indistinct-
ness to the outline of the body. This
is easily perceived when a stretched
wire is plucked or a tuning fork is
sounded.
FIG. 128. Demonstrating
the Motion in a Sound-
ing Tuning Fork.
Let a small pith ball suspended on a thread
be allowed to touch a tuning fork that is
emitting a sound. (See Fig. 128.) It will be thrown violently away.
Touch one of the prongs lightly to the water in a tumbler. A ripple
is produced, or perhaps a
spray is thrown from the
prong. Again, attach a
fine wire or bristle to the
prong of a tuning fork with
a small quantity of sealing
wax. Sound the fork, and
FIG. 129. The Motion in the Prong of a Fork
is Vibratory.
draw the bristle across a
piece of smoked glass. A
wavy line, Fig. 129, results,
showing the existence of a back-and-forth motion in the fork.
162. The Nature of a Vibration. The vibration of a
pendulum has been studied in 80. * While sounding
165
166 A HIGH SCHOOL COURSE IN PHYSICS
bodies vibrate in a manner similar to that of the pendu-
lum, they vibrate from a different cause. When a pendu-
lum is drawn aside and then set free, a component of the
force of gravity moves the pendulum bob back toward its
original position at the center of its arc. When, how-
ever, we pluck the string of a guitar, for example, or set
the prongs of a tuning fork in vibration, the motion is due
to the elasticity of the material of which the body is com-
posed. The string, on being drawn aside, is stretched
slightly. Now, on being released, its tendency to resume
its original length causes it to straighten. When we set
a tuning fork in vibration, the prongs are bent. Since
they are made of elastic steel, they immediately tend to
resume their original shape. Hence the prongs move
back to their initial positions. Again, the string of the
guitar, like the pendulum, is in the state of motion when
it reaches its original position. Hence it must continue
to move until some resistance checks it. Therefore it
swings beyond this position to a point where its velocity
is zero, whence it returns in the
same manner as before. The phe-
nomenon is repeated by the string
until, like the pendulum again, its
energy is expended in overcoming
the resistance of the air and the
friction of its own molecules.
Clamp a thin strip of wood, as a yard-
stick, by one end, Fig. 130, and set it in
vibration. As it is being drawn aside, its
tendency to move back toward its original
FIG. 130. -Thin Strip of P osition is vei T apparent. Let the stick
Wood in Vibration. move very slowly back to the original posi-
tion, and it will stop there ; but if it is set
entirely free, it will continue to move until it is some distance beyond
the center. Why ? Attach a weight of 100 or 200 grains near the
SOUND: ITS NATURE AND PROPAGATION 167
free end of the stick, and it will be found to vibrate much more slowly
than before. The force due to the elasticity of the wood cannot bring
the increased mass so quickly to the center nor stop it so quickly
when the center is, passed on account of the increased inertia. Make
a comparison between the vibrating yardstick and the sounding tuning
fork. The yardstick does not vibrate with sufficient rapidity to pro-
duce sound.
163. Transmission of Sounds to the Ear. Sounds reach
the ear through the air as the transmitting medium.
Many other substances may, however, be the means of
propagation, as the following experiments will show :
1. Let the ear be held against one end of a long bar of wood, and
let the shank of a small vibrating tuning fork be brought against the
other end. A loud sound will be heard. The scratch of a pin at one
end can easily be heard at the other.
2. Place the shank of a tuning fork in a hole bored in a large cork.
Set a tumbler full of water upon a resonance box, -and bring the cork
in contact with the surface of the water. If the fork is in vibration,
the water will transmit the motion to the box, as shown by the in-
creased intensity of the tone. Again, as most boys have found experi-
mentally, if the ear be held beneath the surface when two stones are
struck together under water, a loud sound results even at some dis-
tance from the stones.
164. Medium Necessary for Propagation of Sound. That
a sounding body cannot be heard without the presence of
some transmitting medium may be shown
by the aid of the air pump.
Let an electric bell be placed upon a thick pad of
felt or cotton, suspended by flexible wire springs
under the receiver of an air pump, as shown in Fig.
131. Make the connection with a battery, so that
the bell can be rung from the outside. Set the bell
ringing, and begin to exhaust the air from the re-
ceiver. The sounds coming from the bell become FlGt 131 -~~ Bel1
, IT T ,.i Ti Ringing in a
less and less distinct until the greatest possible ex- Partial Vac-
haustion has been produced. If now the air is slowly uuin.
168 A HIGH SCHOOL COURSE IN PHYSICS
admitted into the receiver, the loudness of the sound increases until
its full intensity is reached.
Although the sound of the bell used in this experiment
will never become entirely inaudible, mainly on account
of the transmission of sound by the vibration of the sup-
porting wires, we are given reason to believe that with com-
plete exhaustion and the removal of all other transmitting
media, no sound would be heard.
165. Velocity of Sound Transmission. Every one is
familiar with the fact that it requires time for sound to
travel over a given distance. If we watch a locomotive
from a distant point as the engineer blows the whistle, we
first observe the jet of steam as it issues from the whistle,
and a few seconds later we hear the sound. The interval
of time that often elapses between a lightning flash and
the peal of thunder is further evidence that the velocity
of sound is not exceedingly great.
Many investigators during the nineteenth century gave
their attention to the accurate determination of the ve-
locity of sound. For the most part their experiments
consisted in measuring the interval of time between the
flash of a gun and its report -heard at some distant sta-
tion of observation. The result obtained by Regnault, a
French physicist, gives sound a velocity, in air, of 1085 feet
per second at the temperature of freezing water. This ve-
locity is equivalent to 331 meters per second. At higher
temperatures the velocity is somewhat greater, the in-
crease being 2 feet, or 0.6 meter, per second for each de-
gree centigrade.
166. Velocity of Sound in Various Mediums. The
velocity of sound in solids has been the subject of many
investigations. The accepted value found for iron is
about 5100 meters per second at 20 C, The velocity of
sound in wood depends greatly upon the kind of wood.
SOUND: ITS NATURE AND PROPAGATION 169
The average value, however, is approximately 4000 meters
per second.
The most exact measurement of the velocity of sound in
water was mads in 1827 by Colladon and Sturm in Lake
Geneva, Switzerland. Two observers stationed them-
selves in boats at opposite sides of the lake. At one of
the stations a bell was sounded beneath the water and a
gun fired on deck at precisely the same instant. The
sound was received by means of a large ear trumpet held
under water at the other station. The time intervening
between the stroke of the bell and the report transmitted
by the water could thus be ascertained and the velocity
computed. The results of many observations gave an
average of 1400 meters per second as the velocity of sound
through water.
EXERCISES
1. The flash of a gun is seen 3.5 seconds before the report is heard.
If the temperature is 20 C.,-what is the distance between the observer
and the gun ?
2. A locomotive whistle was sounded 3 mi. from an observer. If
the temperature of the air was 10 D C., how long was the sound in
traversing the distance ?
3. The distance between two stations is 12 mi. If the interval of
time between the flash and the report of a gun was found by experi-
ment to be 56 seconds, what was the speed of the sound ?
4. A bullet was fired at a target 500 in. away, and in 3 seconds
was heard by the gunner to strike. The temperature of the air being
20 C., what was the velocity of the bullet?
5. When one end of an iron pipe is struck a blow with a hammer,
an observer at the other end hears two sounds, one transmitted by the
iron, the other by the air. If the pipe is 1500 in. long, and the tem-
perature 25 C., what is the interval of time between the two sounds ?
2. NATURE OF SOUND
167. Sound a Wave Motion. We have seen in 164
that a medium is essential for the transmission of sound
170 A HIGH SCHOOL COURSE IN PHYSICS
but thus far no explanation has been given of the manner
in which this transmission takes place. Sounds continue
to come from an electric bell even though we cover it
tightly with a glass jar, but it is very plain that nothing,
i.e. no material thing, can pass through the glass. The
whole process will become clear, however, if we consider
that a sound is transmitted through the air and glass in the
form of waves. Hence, the further study of Sound will be
a study of waves and wave motion.
168. Two Kinds of Waves. We are all familiar with
the waves that move over a surface of water. We have
only to observe a small boat as it rises upon the crests and
sinks down into the troughs to realize that it is not carried
along by the wave. Again, a wave is often seen to pass
over a field of grain. While the wave moves rapidly
across the field, each spear of grain simply bends with the
pressure of the wind and then rises again. The following
experiment may be used to show this manner of wave
propagation :
Let one end of a soft cotton clothesline about 25 feet long be
attached to a hook in the wall, while the other end is held in the
hand. Give the end of the rope a quick up-and-down motion, and a
wave will be seen to run along the rope from one end to the other.
In the experiment just described it is clear that the for-
ward motion of the waves produced in the rope is at right
angles to the direction of the motion of the particles compos-
ing the rope, as shown in
Fig. 132, On this ac-
count such waves are
called transverse waves.
FIG. 132. Transverse Waves in a Rope. A second kind of wave
motion takes place in bodies that are elastic and com-
pressible, as in gases, wire springs, etc. We are able to
make a study of waves of this kind by letting a coil of
SOUND: ITS NATURE AND PROPAGATION 171
wire, Fig. 133, represent the medium through which such
waves are transmitted :
Let us imagine a blow is given the spring at A that
quickly compresses a few turns of the spiral near the end.
On account of the elasticity
and inertia of these parts of A .|
the spring, they will move
F , 6 ,. . / FIG. 133. Waves Transmitted by a
forward slightly and com- Spring. The Individual Turns
press those just ahead. Move back and forth while the
* . J Waves Progress along the Spring.
These in turn will compress
the coils still farther along, and thus a pulse, or wave,
is carried along the spring from A to R.
Again let the end of the spring at A be given a very
sudden pull. The turns near the end will be drawn apart
for an instant, but the adjacent turns will be drawn toward
A, one after another, until the end B receives the impulse.
A blow against A is transmitted by the spring to the point
B, and a sudden pull at A is likewise transmitted as a
pull against the fastening at B. Waves of this kind, in
which the motion of the parts of the medium are parallel
to the direction of propagation, are called longitudinal
waves.
169. Transmission of a Sound Wave. The manner in
which a sound is transmitted by the air becomes clear
when we compare the process with that which occurs
when a wave is transmitted by a spiral spring.
Imagine a light spring, (1), Fig. 134, to be attached
at one end to one of the prongs of a vibrating tuning
fork F and at the opposite end to a diaphragm G-; Each
vibration of the fork will alternately compress and separate
the spirals of the spring near the end. These pulses will
be transmitted by the spring in the manner described in
168, and will cause the diaphragm at Gr to execute as
many vibrations per second as the tuning fork, and the
172
A HIGH SCHOOL COURSE IN PHYSICS
diaphragm will give out a sound corresponding to that
emitted by the fork.
Let the air take the place of the spring and the ear E
replace the diaphragm. When the prong of the vibrating
fork, (2), Fig. 134, moves to the right, a compression
(>) of the air is produced in front of it. This compression,
or condensation, moves to the right with the velocity of
sound, or at about the rate of about 1120 feet per second.
When the prong of the vibrating fork moves to the left,
the air just at the right is rarefied, and the adjacent por-
tions of the air move in to fill this rarefaction (>), which
F ' G\
-mmmmmmwmmmmmmmmmmmmmmmm
(2)
(3)
FIG. 134. Illustrating the Corresponding Parts of Transverse
and Longitudinal Waves.
travels to the right immediately following the condensa-
tion. Condensation and rarefaction thus follow one
another as long as the fork continues to vibrate, and the
drum of the ear at E receives as many pulses per second
as the tuning fork emits. It is therefore caused to vibrate
as many times per second as the fork. Between c and r is
w, which marks the region where there is neither conden-
sation nor rarefaction.
The curve in (3), Fig. 134, is drawn to show the parts of
a transverse wave which is sometimes used to represent
diagrammatically waves of other kinds. The crest AB
corresponds to the condensation, or compression, of the
longitudinal waves shown in (1) and (2). The trough
SOUND: ITS NATURE AND PROPAGATION 173,
BC corresponds to the rarefaction. The distance db rep-
resents the distance that each particle in the wave moves
from its original position and is called the amplitude of the
wave. A wave includes a complete crest and trough, or a
condensation and a rarefaction. The distance between the
corresponding points on any two adjacent waves, as AC,
BD, etc., is the wave length.
170. Velocity, Wave Length, and Vibration Frequency.
Imagine a tuning fork whose rate of vibration, or vibration
frequency, is 256 per second. When the fork is set in vi-
bration, it sends out 256 complete longitudinal waves dur-
ing each second. At the completion of the 256th vibra-
tion, the first wave has progressed a distance numerically
equal to the velocity of sound, or about 1120 feet. This
space, therefore, contains 256 waves, and the length of each
wave can be found by dividing 1120 feet by 256. Hence
the length of each wave is about 4.4 feet. Letting n be
the frequency, v the velocity of sound, and I the wave
length, we have
V
1 = -, or nl = v. (i\
n
3. INTENSITY OF SOUND
171. Sound Waves Spread in all Directions. If a bell
be struck, the sound is heard as readily in one direction
as another if no ob-
struction intervenes
and other conditions
are equally favorable.
Obviously a wave
emitted by the bell FIG. 135. SoundWaves Spread in all Directions
spreads out in all
directions from it. Figure 135 illustrates this fact. Each
condensation has the form of a hollow spherical shell that
174 A HIGH SCHOOL COURSE IN PHYSICS
continually enlarges as the wave advances. This is
followed by a rarefaction of a similar form. It is plain
that the energy imparted by the bell to a single wave is
carried from the source by particles of air composing a
hollow spherical shell. At a given distance from the bell
this shell will have a certain area which at twice the dis-
tance will be four times as great, since the area of a
sphere is directly as the square of its radius. Thus at
twice the distance from the bell the energy will 'be -im-
parted to four times as many particles, hence the energy
of each will be one fourth as great. At three times
the original distance, the energy will be imparted to nine
times as many particles, and the energy of each will be
one ninth as much. Hence, the intensity of sound is in-
versely proportional to the square of the distance measured
from the source of the sound.
172. Intensity and Amplitude. The energy imparted
to each wave by a sounding body will depend upon the
intensity of the vibration of that body, i.e. upon the am-
plitude of vibration. An increase in the amplitude of
vibration of the sounding body produces a corresponding
increase in the amplitude of each wave emitted. Thus
each wave is caused to carry away from the sounding
body an increased quantity of energy. When the waves
fall upon the tympanum of the ear, a corresponding in-
crease in its amplitude of vibration is produced.
Let one of the prongs of a tuning fork be struck lightly against a
soft pad or cork. A tone is emitted that is scarcely audible. Now
let the fork be struck more forcibly. On account of the greater am-
plitude of vibration the intensity of the tone will be much greater
than before.
Like the pendulum ( 79 and 80), a sounding body
completes its vibrations in equal times, the period of vi-
bration being practically independent of the amplitude
SOUND: ITS NATURE AND PROPAGATION 175.
(i.e. isochronous). Therefore when the fork is struck
forcibly against the pad, it still performs the same number
of vibrations per second as before.
173. Intensity and Density of the Medium. The ex-
periment with the bell and air pump ( 164) shows that
the intensity of a sound depends upon the density of the
medium in which the sound is produced. As the air in the
receiver becomes rarer, the intensity of the sound grows less.
Support two similar bell jars with the mouths opening downward.
Keep one filled with illuminating gas and the other with air. Set an
electric bell ringing, and place it first in the jar containing gas, then
in the one filled with air. It will be readily observed that the sounds
emitted in the rarer medium, the illuminating gas, are less intense
than those produced in the jar filled with air.
At the top of a high mountain a gun makes only a
small report when fired. At high elevations explorers
and aeronauts converse with difficulty. The denser the
gas, the greater the energy imparted to each wave by the
vibrating body. For this reason a sounding body will
cease to vibrate sooner in the denser of two media.
174. Intensity and Area. When the area of a sound-
ing body is small, as that of a small tuning fork, for
example, the condensations and rarefactions produced are
not well marked. It is obvious that of two vibrating
tuning forks of the same frequency, the smaller will have
the effect of cutting through the air without producing
more than a slight compression, while the one of larger
area will compress a greater volume of air, and thus give
out more of its energy to each wave emitted.
Set a tuning fork in vibration, and hold the shank against the
panel of the door or table. A loud sound will be heard coming from
the large area that is set in vibration by the fork.
In the construction of many musical instruments use is
made of this relation between the intensity of sound and
176 A HIGH SCHOOL COURSE IN PHYSICS
the area of the sounding body. Thus a piano utilizes two
or three wires to produce a given tone when the area of
a single wire is not sufficiently great. Again, a sounding
board of large area is often placed beneath the strings of
instruments to form a large surface of vibration when the
strings are excited.
4. REFLECTION OF SOUND
175. Reflection of Sound Waves. It is a fact frequently
illustrated in nature that sound waves may be reflected.
As long as waves proceeding from a source of sound pass
through a homogeneous medium, no reflection takes
place ; but when the density of the medium is disturbed,
the waves suffer partial or total reflection.
Let a watch be placed a few
inches in front of a concave re-
flector, as shown in Fig. 136. By
moving the ear from point to point
a place may be found, sometimes
several feet from the reflector,
where the sound of the watch may
FIG. 136. - Sound Reflected by a Con- be distinctly hea rd.
cave Surface. . . ,
The experiment may be varied
by setting a similar reflector at a distance of several feet from the
first and facing it, as shown in Fig. 137. If the watch is placed
slightly nearer the reflector than in the preceding experiment, a point
may be found a few inches in front
of the second at which the sound
is focused. This point, or focus,
may be found by using an ear
trumpet mipde by attaching a piece
of rubber tubing to a glass funnel.
When the open funnel is placed at Fl - 137. Sound Undergoes Two Re-
the focus of sound, a distinct tick- flections from Concave Surfaces "
ing* of the watch will be heard by holding the end of the rubber
tubing in the ear.
SOUND: ITS NATURE AND PROPAGATION 177
176. Echoes. The familiar phenomenon of echoes is
due to the reflection of sound. When one speaks in a
room of moderate size, the waves reflected from the walls
reach the ear so quickly that they combine with the direct
waves and produce an increase of the intensity of the sound.
But when the walls are one hundred feet or more from
the speaker, he hears a distinct echo of each syllable he
utters. Sometimes a reflecting surface is so distant that
several seconds may intervene before an echo returns.
Between two reflecting surfaces the echoes sent back and
forth are often remarkable. It is related that at a point
in Oxford County, England, an echo repeats a sound from
fifteen to twenty times. Extraordinary echoes are also
found to occur between the walls of deep canons.
In so-called " whispering galleries " we have illustrated
the formation of a sound focus due to curved surfaces. In
the crypt of the Pantheon in Paris there is a place where
the slight clapping of hands at one point gives rise to
sounds of great intensity at another. In the Mormon
Tabernacle at Salt Lake City, Utah, a whisper near one
end can be distinctly heard at the other, so perfect is the
reflection from the ellipsoidal surfaces of the walls.
EXERCISES
1. A hunter fires a gun and hears the echo in 5 seconds. How far
away is the reflecting surface, the temperature being 20 C.?
2. How far is a person from the wall of a building, if, on speaking
a syllable, he hears the echo in 4 seconds, the temperature being
15 C.?
3. A gun is fired, and the echo is returned to the gunner from a
cliff 250 ft. away in 4.5 seconds. Calculate the velocity pf ^ound.
SUMMARY y
1. Sounds are produced by bodies in a state of rapid
vibration ( 161).
13
178 A HIGH SCHOOL COURSE IN PHYSICS
2. Sounding bodies vibrate as a consequence 'of the elas-
ticity and inertia of the material composing them ( 162).
3. Sounds are transmitted from their sources by solids,
liquids, and gases. The air is the propagating medium in
most cases ( 163 and 164).
4. The velocity of sound waves in air at the freezing
temperature is 1085 ft. (331 in.) per second. The velocity
is increased 2 ft. (0.6 m.) per second for each degree
centigrade. In wood and iron the velocity of sound is
respectively 3 and 4 (approximately) times the velocity
in air ( 165 and 166).
5. Sound is a wave motion. Wave motion may be
either transverse or longitudinal ( 167 and 168).
6. The energy of a sounding body is transmitted by
longitudinal waves. The parts of such waves are called
condensations and rarefactions. The corresponding parts
of transverse waves are crests and troughs ( 169).
7. The relation between velocity, wave length, and
number of vibrations per second is given by the equation
v = ln (170).
8. The intensity of a sound depends on the amplitude
and area of the sounding body, the density of the medium
where the sound is produced, and is inversely proportional
to the square of the distance from its source ( 171 to 174).
9. Echoes are sounds reflected from walls, woods, hills,
cliffs, etc. ( 175 and 176).
CHAPTER X
SOUND : WAVE FREQUENCY AND WAVE FORM
1. PITCH OF TONES
177. Musical Sounds and Noises. In order that a
sound may be pleasing to the ear, it is essential that the
vibrations be made in precisely equal intervals of time ;
in other words, the vibrations must be isochronous. Any
device that produces isochronous pulses emits a musical
sound. If the pulses are not isochronous, the result is a
noise.
Rotate on a whirling table a metal or cardboard disk provided with
two or more circular rows of holes, Fig. 138. Let the holes in one row
be equidistant, while those in the other rows
are placed at irregular intervals. Blow a
stream of air through a rubber tube against
the row of equidistant holes, and a pleasant
musical sound will result. Now direct the
stream against another row of holes, and
it will be observed that the sound produced
is of an unpleasant character.
178. Pitch. Probably the most
striking difference in musical sounds
is in respect to that which we call
. FIG. 138. Musical Sounds
pitch, a term applied to the degree of Produced by isochro-
highness or lowness of a sound. We nous Pulses in the Air -
are accustomed to sounds varying in pitch from the low,
rumbling thunder to the shrill, piercing creak of small
animals and insects. How this wide difference in sounds is
brought about may be shown by the following experiment:
179
180 A HIGH SCHOOL COURSE IN PHYSICS
Rotate a metal or cardboard disk in which there are several circu-
lar rows of holes perforated at regular intervals, but having a different
number in each row. See Fig. 139. Keeping the
speed of rotation constant, blow a stream of air
forcibly against one row and then another. A dis-
tinct difference in pitch will be observed. Again,
keeping the stream of air directed against one of
the rows, change the speed of rotation from very
FIG 139 The s ^ ow to verv * as *' ^ e pitch will rise from a low
Siren Disk. tone to one that is very shrill.
These facts teach that the pitch of a tone depends upon
the number of wave pulses per second sent from a sounding
body to the ear. The stream of air blown against the disk
is alternately transmitted and interrupted by the motion
of the holes. The succession of pulses thus produced
constitutes the musical tone that is heard. The vibration
frequency of the tone emitted may be found by multiply-
ing the number of revolutions of the disk per second by
the number of holes in the circle. An instrument of the
kind used in the experiment is called a siren.
179. Musical Scales Produced by a Siren. The most
common series of tones of different pitches is the musical
scale. It is possible with the help of a siren designed in
a manner similar to the one shown in Fig. 139 to deter-
mine the relation of the several tones that comprise the
ordinary musical scale. The construction and use of the
siren is as follows :
On a circular disk of cardboard or metal, about 10 inches in diame-
ter, draw eight concentric circles about inch apart. Upon the circles
thus drawn, beginning with the smallest, drill the following numbers
of equidistant holes : 24, 27, 30, 32, 36, 40, 45, and 48. Mount the
disk upon a whirling table and rotate with a uniform speed. Be-
ginning with the smallest circle, blow a stream of air against each
row of holes in succession. The tones produced will be recognized
at once as those belonging to the major scale. Increase the speed of
rotation, and again direct the current of air against the several rows
SOUND: WAVE FREQUENCY AND WAVE FORM 181
in succession. Although the pitches are higher than before, yet the
scale is produced as perfectly as at first.
The experiment teaches that the major scale is a series
of tones whose vibration frequencies have the same rela-
tion as the numbers 24, 27, 80, 32, 36, 40, 45, and 48.
To these tones we give the names do, re, mi, fa, sol, la,
ti, do. These tones form the foundation upon which has
been built up our musical system.
180. The Major Diatonic Scale. Any series of tones
whose vibration frequencies bear the relations given in the
preceding section constitute a major diatonic scale. The
first tone of such a series is the key tone. The various
scales in use are named according to their key tones ; for
example, the scale of C, the scale of Gr, e<x). Physicists as-
sign to the tone called middle C, 256 vibrations per second. 1
Hence the second tone of the major scale of C must be
produced by 256 x f J, or 288 vibrations per second. This
tone is called D. The next tone, or E, must have
256 X |J, or 320 vibrations per second, etc. The follow-
ing table, Fig. 140, shows the manner in which these tones are
expressed on the musical staff, their relative and absolute
vibration numbers, and the vibration ratios.
Scale
otC
rJ '
Staff if?T\
^
-&
^
ouiu IvL/
o
Letters
T
I
1
I
1
!
i
i'
Absolute Vib. No.
256
288
320 3kl.3
38k
k26.6
k80
51^
Tone Number
1
2
3
k
R
g.
7
8
For all
Syllables
do
re
mi
fa
ftol
la
U
do
Scales
Relative Vib. No.
2k
27
30
3fi
ko
kZ
k8
Vibration Ratios
1
1
2
Fia. 140. The Major Scale.
The nature of the seven definite intervals leading from
C to 0', or one octave, may be seen from the table. Start-
1 The international standard of pitch in this country and Europe is
based upon A = 435 vibrations per second.
182 A HIGH SCHOOL COURSE IN PHYSICS
ing with C 256 vibrations, the vibration numbers of the
successive tones of the scale, as shown by the experiment
in the preceding section, bear the ratios |, f, |, |, J,
lf~, and 2 to the vibration number of O, the key tone.
These ratios are the same for all major scales, no matter
what the key tone may be.
181. Intervals. A musical interval refers to the relation
between the pitches of two tones. The experiment with the
siren in 179 shows that the value of an interval depends
upon the ratio, not the difference, between the vibration
numbers of the tones; for example, when this ratio is
If, or 2:1, the interval is an octave, as the interval be-
tween O' and C. Other important intervals are the sixth,
i.e. the interval between the first tone arid the sixth of a
major scale, given by the ratio f |, or 5:3; the fifth, |J,
or 3:2; the fourth, f |, or 4:3; the major third, f|-, or
5:4; and the minor third, f $, or 6 : 5. In order to determine
the interval between two tones, the ratio of their vibration
frequencies is first computed and then compared with the
ratios given for the several cases. Hence two tones of 500
and 300 vibrations per second respectively are a sixth apart,
because the ratio of their vibration numbers is 5:3. If
these two tones were sounded together or in succession,
the interval would be recognized at once by a musician.
182. The Major Chord. A careful inspection of the
vibration numbers of the tones of the major scale will
show the presence of three groups consisting of three tones
each, whose frequencies bear the ratios 4:5:6. Such a
group of tones is a major chord. Beginning with C= 256
vibrations per second, we have for the first chord O, E,
and Gr (do-mi-sol) whose vibration frequencies are 256,
320, and 384. This chord is called the tonic triad of the
scale of O. The second of these chords, called the sub-
dominant triad, is formed in the same manner and includes
SOUND: WAVE FREQUENCY AND WAVE FORM 183
F, A, and 0' (fa-la-do). The third is formed likewise
by making use of the tones (r, JP, and D r (sol-ti-re) and
is called the dominant triad. Since these triads include
all the tones of the major scale, it may be said that this
scale is founded upon these three major chords. The fol-
lowing table shows these relations:
Tonic Triad 4 : 5 : 6 : : 256 : 320 : 384, C, , and G.
Subdominant Triad 4 : 5 : 6 : : 341 : 427 : 512, F, A, and C>.
Dominant Triad 4 : 5 : 6 : : 384 : 480 : 576, G, B, and D'.
183. Sharps and Flats. The introduction of the black
keys on the organ or piano keyboard is (1) for the pur-
pose of accommodating the instrument to the range of the
voice in the case of songs and (2) to give variety to selec-
tions designed for instrumental performance. That it. is
necessary to insert additional tones becomes apparent at
once when we consider the tones that are required to form
a major scale beginning upon B v just below middle (?, hav-
ing 240 vibrations per second. The keys that are used in
the scale of O are all white keys, Fig. 141, and have the
frequencies indicated. ^.
In the major scale of Eg
B the . vibration fre-
quencies must be suc-
cessively 240, 270,
300, 320, 360, 400, 450,
and 480. It will be
observed that the only s s s
white keys that satisfy FIG. 141. Illustrating the Scale of C on Staff
this Scale are fl= 320 and Keyboard.
and B = 480 vibrations per second. Since the number 270
lies about midway between the frequencies of and .Z), the
black key (7* (read "(7 sharp'") is introduced. Others must
be placed between D and E, F and 6r, G- and J., and A and
B. These are called respectively D*, JF*, 6r*, and A*.
184 A HIGH SCHOOL COURSE IN PHYSICS
These four tones are also called JS^ 6r^, A , and B ,
and are read E flat," " G flat," etc.
184. Tempered Scales. In the preceding section is
shown the necessity for introducing additional tones in
order that a piano, for example, may be used to produce
the major scale of B. These new vibration numbers, how-
ever, will not satisfy scales which begin on other key
tones, for every change to another key tone increases the
demand for small changes in the vibration numbers of the
tones. The difficulty is surmounted by sacrificing the
perfect, simple ratios found in 180 to 183 and substi-
tuting others that are sufficiently near to satisfy a musical
ear. See the table given below. This method of tuning
an instrument is called tempering, and the scales derived
by the process are called tempered scales. The desired
result, which is to permit the execution of musical compo-
sitions written in any key, is secured by making the inter-
val between any two adjacent tones the same throughout the
length of the keyboard. By this process the octave is di-
vided into twelve precisely equal intervals called half
steps. The imperfection introduced by equal tempera-
ment tuning is illustrated by the following table :
CDEFGABC
Perfect scale of C 256.0 288.0 320.0 341.3 384.0 426.6 480.0 512.0
Tempered scale 256.0 287.3 322.5 341.7 383.6 430.5 483.3 512.0
EXERCISES
1. Taking G as the key tone of a major scale, compute the vibra-
tion frequency of each of the tones contained in an octave.
2. The vibration frequency of a tone is 264. Calculate the fre-
quencies of its third, fourth, and octave.
3. Calculate the vibration frequency of the tone one octave below
middle C.
4. What is the wave length of a tone whose vibration frequency is
256 when the temperature is 15 C. ? (See 165 and 170.)
SOUND: WAVE FREQUENCY AND WAVE FORM 185
5. If middle C were given the frequency 260, what would be the
frequencies of D, A , and B ?
6. A tone two octaves above middle C has how many vibrations
per second ?
7. If the keyboard of a piano extends three and a half octaves in
each direction from middle C, calculate the vibration number of the
lowest and the highest C on the instrument.
8. Ascertain the interval between the pitches of two tuning forks
making 256 and 192 vibrations per second.
9. The tones of three bells form a major chord. One makes 200
vibrations per second, and its pitch lies between the pitches of the
others. Calculate the frequency of the bells.
10. A tone is produced by a siren revolving 300 times per minute.
What is the name of the tone produced, if the number of holes in the
row is 24 ?
2. RESONANCE
185. Sympathetic Vibrations. Vibrations that are pro-
duced in one body by another near by which has the same
vibration period are called sympathetic vibrations. The
following experiments will serve to illustrate the case :
1. Tune two wires of a sonometer, Fig. 150, so that they emit tones
of the same pitch when plucked. Place a A-shaped paper rider astride
one of the wires and then pluck the other. The rider will be thrown
off, and if the wire that was plucked be stopped, a tone will be heard
coming from the other. Throw the wires slightly out of unison and
repeat the experiment. Only very slight vibrations will be imparted
to the second wire.
2. Let two mounted tuning forks having the same pitch be placed
near together, as shown in Fig.
142. Set one of the forks in vi-
bration by bowing it, or by strik-
ing it with a rubber stopper
attached to a wooden or glass
handle. On checking its vibra-
tions a sound will be heard com- FlG . 142. Sympathetic Vibrations
ing from the second fork. between Forks in Unison.
Students will find it interesting to experiment in a simi-
lar manner with a piano. For example, let the key C be
depressed so carefully that no tone is produced. The
186
A HIGH SCHOOL COURSE IN PHYSICS
damper is thus lifted from the wires of a certain vibration
frequency. Now if the tone O be sounded by a voice, the
corresponding tone will be heard coming from the instru-
ment.
These experiments show the facility with which a body
is put in vibration by another having the same frequency.
The principle may be stated as follows:
Sound waves sent out from one vibrating body impart vi-
brations to others, provided the vibration frequencies are the
same.
186. Sympathetic Vibrations Explained. The phenom-
enon of sympathetic vibrations is readily accounted for
when we consider that the body first set in vibration sends
out periodic impulses through the air or the wood connect-
ing the two bodies. The first impulse received by the
second body gives it a very small amplitude of vibration.
It returns at precisely the instant to receive the second
impulse, and the amplitude of the second vibration is caused
to be greater than that of the first.
The third impulse, in like manner,
adds energy to that already trans-
mitted to the body. Thus, after
the arrival of several impulses the
amplitude of vibration of the sec-
ond body is great enough for the
production of an audible tone.
187. Resonance. A vibrating
able Length.
FIG. 143. Recn-
forcement of a
Sound by an Air
Column of Suit- timing fork when held in the hand
produces a sound that is scarcely
audible. Its tone may be aug-
mented, however, by placing it
above a properly adjusted ir column that is caused to vi-
brate sympathetically with it.
SOUND: WAVE FREQUENCY AND WAVE FORM 187
Let a vibrating timing fork be held over a tall cylindrical jar, as
shown in Fig. 143. By pouring water into the jar while the fork is in
this position, a condition will be reached such that an intense sound
may be heard proceeding from the jar. Pouring in more water de-
stroys the effect.
Let the experiment be repeated with a fork of a different pitch.
If the pitch is higher, the air column will need to be shortened by
pouring in more water ; if lower, the column must be longer.
188. Resonance Explained. Let a and 5, Fig. 144, rep-
resent the two extreme positions of the prong of a vibrat-
ing tuning fork. Just as the prong begins a ^
a downward swing from a it starts a conden- '"'"lirrs*'
satioii downward in the tube. When the
prong begins its upward swing from 5, it
starts a condensation in the air above it.
Now, in order to have a reenforcement of
the tone emitted, the condensation started
downward in the tube must be reflected by
the water and return in time to unite with FIG 144 _ The
the condensation produced above the prong Cause of Reso-
as it moves upward. Hence the condensa-
tion must travel down the tube and back while the prong
of the fork moves from a to 6, i.e. during one half a vibra-
tion of the fork. In a similar manner the rarefaction
started in the tube as the prong leaves 5 must return from
the bottom of the tube in time to unite with the rarefaction
produced above the prong.
189. Resonance Tubes and Wave Length. "In the ex-
planation of the phenomenon of resonance given in the
preceding section, it is clear that the waves in the air of
the resonance tube travel twice the length of the air space
within the tube while the fork is making one half a vibra-
tion. The wave therefore goes four times the length
of the air column during a complete vibration of the fork.
But a wave progressesj^jlyvave length during a complete
'Bjjjk
188 A HIGH SCHOOL COURSE IN PHYSICS
vibration of a sounding body. Hence the length of the
vibrating air column is one fourth of the length of the air
wave produced by the fork.
Experiments performed with tubes of different sizes
have shown thlH diameter of the tube influences the
length of tube ^^^Hld for the best effect. It has been
found that the length of the air column must be increased
by two fifths of its diameter in order to equal a quarter of
a wave length.
Tuning forks are often mounted on properly adjusted
boxes whose air spaces act as resonators when the forks
are sounded, as shown in Fig. 142.
3. WAVE INTERFERENCE AND BEATS
190. Destruction of One Wave by Another. Let us
imagine two trains of sound waves, (1) and (2), Fig. 145.
Let the waves in the
two trains be of- the
same length, i.e. pro-
duced by sounding
145. -Two Longitudinal Waves in the b()dies Q f th game
Condition Necessary for Interference.
pitch. If the con-
densations in one train at a given instant are at <?, c and
those in the other train at c(, c', it is obvious that the two
trains cannot move through the same air simultaneously.
For, if the compressions are equal, the condensations of
the first train will unite with the rarefactions r', r' of the
second, and the result will be no change in the density of
the air. In other words, one train of waves will destroy
the other. Thus two sounds may combine and produce
silence. A study of the analogous case of transverse
waves will help to make the matter clearer.
Let (1) and (2), Fig. 146, represent two trains of trans-
verse waves. Let their lengths and amplitudes be equal.
SOUND: WAVE FREQUENCY AND WAVE FORM 189
FIG. 146. The perference of Trans-
verse Waves.
If, now, the crests <?, c, e of one train unite with the
troughs , , t of the other, then one train will obviously
destroy the other, since
t
the crests of the first
train will just fill the
troughs of the second
and vice versa. Thus
two trains of water waves,
for example, may combine and produce a level sur-
face.
The destruction of one wave train ~by another similar train
is called interference.
191. An Example of Interference. Let /,/, Fig. 147,
represent the ends of the two prongs of a tuning fork. At
the moment the prongs vibrate
toward each other a condensa-
tion is produced in the region
a and rarefactions at b, b.
When the prongs move out-
ward, a rarefaction is produced
at a and condensations in the re-
gions b, b. Now since a conden-
sation starts from the region a
at the instant a rarefaction starts
from 5, and vice versa, there will
be places in the air around the tuning fork where the parts
of the waves coming from a will unite with the unlike
parts of those from 6, and continuous interference will
result. The regions of interference near the prongs of
a fork are shown by the dotted lines in the figure. These
places may be found by rotating a tuning fork held near
the ear. Positions in which the sound becomes almost
inaudible can thus be easily located.
Fia. 147. Regions of Silence
near a Tuning Fork.
190 A HIGH SCHOOL COURSE IN PHYSICS
Hold a vibrating tuning fork above a resonance tube tuned to re-
enforce the tone emitted. Rotate the fork slowly, and a position will
be found, Fig. 148, in which the sound be-
comes practically inaudible; for, in this
position, the mouth of the jar receives the
unlike parts of waves sent out from the
opposite sides of the nearer prong of the
fork.
192. Alternate Interference and
FIG 148 An in- Reenforccment. When it is under-
terference Phe- stood how two trains of sound waves
may combine and produce an inten-
sified sound ( 188) or interfere and
produce silence ( 190) the inter-
esting phenomenon of beats is read-
ily explained. Beats are always produced when two tones
that differ slightly in pitch are sounded at the same time.
The effect is obtained as follows :
Tune two resonance jars to reenforce two tuning forks of the same
pitch. Load the prongs of one of the forks with pieces of tin bent in
such a form as to cling firmly to the fork while it is in vibration.
This will make the pitch of this fork slightly lower than that of the
other. Now sound the two forks simultaneously and hold them over
the resonance tubes. Fluctuations in the intensity of the sound (i.e.
beats") will be distinguishable at a distance of several meters. Load
the prongs of the fork more heavily, and more rapid beats will be
observed.
Since the forks used in the experiment differ in pitch,
the waves sent out will differ in length, the longer
waves being produced by the fork with the weighted
prongs. Since the pitches differ but a small amount, the
wave lengths will be almost equal. Inasmuch as the
vibrations of the weighted fork are continually falling
behind those of the other, at certain periods the two forks
will be producing condensations and rarefactions simul-
SOUND: WAVE FREQUENCY AND WAVE FORM 191
taneously ; hence reinforcement results. A little later
the weighted fork will have fallen one half a vibration
behind the other, and while one fork is producing a con-
densation, the other will be sending out a rarefaction.
Hence, at this instant, there is interference between the
two trains of waves.
Figure 149 shows portions of the two trains of waves
sent out from the forks. It will be observed that at r, r
*A\S~^7 ^ ^~ ~^ V/ \J
FIG. 149. The Production of Beats Illustrated.
the two trains unite to produce the greatest reinforcement
of the sound, while at i unlike portions of the waves unite
and thus destroy the sound. The resultant wave is repre-
sented by the line AB.
193. Law of Beats. Let one tuning fork make 100
vibrations per second, and another, 101. At a given
instant imagine each fork to be sending out a condensa-
tion. Hence, at this instant, reenforcernent takes place.
Just one half of a second later, one fork has made 50 com-
plete vibrations, and the other 50J. Therefore, at this
instant one fork is producing a rarefaction, and the other
a condensation, and thus the resulting sound is weakened.
Hence, the intensity of the sound will increase and de-
crease once per second. This effect constitutes one beat.
When the difference in vibration frequency is two, the
phenomenon occurs twice per second. In every case the
number of beats produced per second is equal to the differ-
ence between the vibration frequencies of the two sounding
bodies.
192 A HIGH SCHOOL COURSE IN PHYSICS
4. THE VIBRATION OF STRINGS
194. The Pitch of Strings. Many musical instruments
employ vibrating strings or wires on account of the fact
that such bodies emit tones of a rich quality. The wide
range of pitch necessary is obtained by varying the length,
tension, and mass of the strings used. Thus the lengths
of the wires of a piano, for example, vary from those that
are about 2 inches long to others whose lengths are 4. or
5 feet. The short wires are of a small diameter, while the
long ones are large and massive. The violin makes use
of four strings of different masses, and the performer ob-
tains the necessary pitches by fingering the strings so as
to allow the proper length to be put in vibration.
195. Law of Length. The laws governing the vibration
of strings may be shown by means of an instrument called
FIG. 150. A Sonometer.
the sonometer (pronounced so nom'e ter), Fig. 150. The
relation between the pitch of a string and its length may
be shown by the following experiment :
Adjust the tensions of the two similar wires of a sonometer until
they emit tones of the same pitch. Set up a bridge A and place a
second bridge under the middle of one of the wires and pluck first
one wire and then the other. It will be observed that the tones pro-
duced are an octave apart; i.e. one half the original length of the
wire produces a pitch of twice ( 180) as many vibrations per second.
Another test may be made by placing a bridge at C just two thirds
of the distance AB from A. By plucking both wires as before the
interval do-sol is easily recognized.
SOUND: WAVE FREQUENCY AND WAVE FORM 193
This experiment may be extended to the production of
any interval that can be recognized. In any case it will
be found that the ratio of the length of the vibrating
portion AC to the original length AB is the inverse of
the vibration ratio given in 180. Thus one half the
length produces a pitch of twice as many vibrations per
second, and two thirds of the original length emits a tone
of three halves of the vibration frequency. Hence, the
vibration frequencies of strings or wires are inversely pro-
portional to their lengths.
196. Law of Tensions. Let the two weights used to produce
the tensions in the wires of a sonometer be moved as far out as possible
on the lever arms. Set the bridges so that the wires emit tones of the
same pitch. Now move one weight back, thus shortening the lever
arm ( 93) until it produces only one fourth as much tension on this
wire a before. The pitch will now be found to be an octave lower
when the two wires are plucked.
This experiment may be applied to other intervals ; for
example, four ninths of the original tension will cause the
vibration frequencies to have the ratio of 2 : 3. Hence,
the vibration frequencies of strings or wires are directly
proportional to the square roots of their tensions.
197. Law of Masses. Let a sonometer be equipped with two
wires of the same material, lengths, and tensions, but of different sizes.
If possible, make the diameter of one twice that of the other. Since
the masses are as the squares of the diameters, the mass of a given
length of the larger will be four times that of the smaller. If now
the wires are plucked, the pitch of the smaller will be an octave
above that of the other.
The vibration frequencies of strings or wires are inversely
proportional to the square roots of their masses per unit length.
198. Vibration of a String in Parts. The vibration of
a stretched string or wire is more complicated than at first
appears. When a string is bowed or plucked, the tone
14
194
A HIGH SCHOOL COURSE IN PHYSICS
emitted is a compound tone produced by the string
vibrating as a whole simultaneously with its vibration in
parts. The readiness with which a string vibrates in parts
may be shown by the following method :
Attach one end of a white silk cord about 1 m. in length to one of
the prongs of a large tuning fork attached firmly to the table and
whose frequency is not more than 100. Let the other end pass over
FIG. 151. A Cord Vibrating as a Single Segment.
a smooth hook or pulley and support a weight, as in Fig. 151. Set
the fork in vibration and adjust the tension and length of tfce cord
until it vibrates as a single segment, as shown. Now reduce the weight
FIG. 152. The Vibration of a Cord in Two Parts.
used until the cord vibrates in two parts, Fig. 152, when the fork is
set in motion. Under suitable tensions the cord will vibrate in any
desired number of equal parts up to six or seven.
The tone emitted when a string vibrates as a whole is called
its fundamental. The fundamental is the lowest tone that
a string can produce. By the pitch of a string is meant
the pitch of its fundamental. The vibrating portions of
the string are called loops, or segments, and a point where
the amplitude of vibration is zero is called a node. Loops
are often called ventral segments and antinodes.
199. Overtones of Strings. The character of the tone
produced by a vibrating string is complicated by the divi-
sion of the string into equal parts, as shown in the preced-
ing section. Each vibrating segment of a string produces
SOUND: WAVE FREQUENCY AND WAVE FORM 195
a tone that is higher in pitch than the fundamental. The
tones emitted by the vibrating portions of any sounding body
are called overtones, or partial tones.
The presence of overtones emitted when a wire is
plucked may be detected by the sympathetic vibrations
set up in a neighboring wire.
Let the two wires of a sonometer be tuned in unison. Place a
bridge under the center of one wire and set A-shaped paper riders
near the middle of each half of this wire. If the longer wire is now
plucked near one end, the shorter wires will be thrown into vibration,
as the riders will show. Replace the riders, and pluck the longer
wire at the center. Only feeble vibrations are now set up in the
shorter wires. Again, place the bridge under one wire just one third
of the original length from one end, and place a rider astride the
shorter portion. Now if we pluck the longer wire near one end as
before, the rider will be thrown off as in the former case. Replace the
rider and pluck the longer wire one third of its length from one end.
The rider will remain stationary.
In this experiment we have used the shorter wire to
show when certain overtones are present in the tone emitted
by the longer wire. The results indicate that when a
wire is plucked near one end, the tone produced contains
an overtone an octave higher than the fundamental. The
wire not only vibrates
as a whole, but divides
into two parts, each F IG. 153.- A Wire Emitting itsFunda-
part having a frequency mental and First Overtone.
double that of the fundamental. This condition is illus-
trated in Fig. 153. When the wire is plucked near the
center, this overtone is not present, since a node would be
required at this point.
200. A Series of Overtones. The second part of the
experiment in the preceding section shows that the wire
divides into three equal parts, each of which vibrates with
three times the frequency of the fundamental. In a simi-
196 A HIGH SCHOOL COURSE IN PHYSICS
lar manner it is possible to detect the presence of still
higher overtones, all of which are produced simultaneously
OF
5th overtone, . X 256 vibs.
d 11 ov"; J S H 3ft near one end. The following table
2d overtone, 3 x 256 vibs. , , . . , ,,
overtone, 2 x 256 vibs. shows the positions and frequencies
. 256 vib.. of the overtones produced when a
middle O string is plucked near
FIG. 154. Table Showing
the Overtones Produced one end.
on a Middle c string. When the vibration frequency of
an overtone is 2, 3, 4, 5, etc., times that of the fundamen-
tal, it is called an harmonic. The relative intensity of the
various overtones produced by a wire depends chiefly up-
on the manner in which it is set in motion, the point where
it is struck or plucked, and the rigidity, density, and elas-
ticity of the wire.
5. QUALITY OF SOUNDS
201. Overtones and Tone Quality. It is a familiar fact
that two tones of the same pitch and intensity do not neces-
sarily sound alike. The tones produced by a violin, for
example, are readily distinguished from those of the piano
or flute. The tones of one violin may differ from those of
another. This difference is one of quality. The cause of
this difference between tones was long a matter of study
and investigation. It was finally explained fully by the
German physicist Helmholtz 1 (1821-1894). He tells us
that the quality of a sound depends upon the overtones
produced "by the sounding body and their relative intensities.
Let a wire be plucked at one end and the tone compared with that
emitted when the wire is plucked in the middle. Again, let the wire
be struck with a soft rubber hammer and then with something hard.
The tones produced will be of the same pitch but of different quality.
This last experiment may also be made with either a bell or a tuning
fork.
1 See portrait facing page 196.
HERMANN VON HELMHOLTZ (1821-1894)
A new era in the history of Sound was created in 1862 by the
publication of Helmholtz's Lehre von den Tonempfindungen, a
work which has been translated into English under the title Sensa-
tions of Tones. The author recognizes musical tones as periodic
motions of the air and distinguishes the three characteristics of
tones as intensity, pitch, and quality. He finds that tone quality
is due to the number and relative intensity of the upper partials, or
overtones. Helmholtz devised hollow spherical resonators of a vari-
ety of sizes by the aid of which he was able to analyze the human
voice and other musical tones. By means of a large series of
tuning forks of different pitches which were operated electrically,
he produced tones of such a composition as to imitate the vowel
sounds of the human voice, the tones of organ pipes, etc.
Helmholtz received a medical education at Berlin, and from
1855 to 1871 was professor of physiology at Bonn and Heidelberg.
He was led to the study of physics in his endeavor to understand
the principles involved in the eye and ear. Later he became an
accomplished mathematician. In 1871 Helmholtz was appointed
professor of phyics at Berlin, and in 1888 became the first director
of the well-known Reichsanstalt (Imperial Physico-Technical Insti-
tute) in Charlottenburg. His death occurred in 1894.
The first contribution of Helmholtz to the science of physics is
his famous treatise on the Conservation of Energy published in
1847, a publication which was of great influence in establishing
this doctrine. He is known throughout the medical world as the
inventor of the ophthalmoscope, an instrument used in examining
the interior of the eye.
SOUND: WAVE FREQUENCY AND WAVE FORM 197
These experiments teach that the quality of the sound
produced by a body depends upon the manner in which the
body is set in motion. As shown in 199, the sound given
out by a wire is rich in overtones when plucked near one
end; but when plucked at the center, all the overtones
that require a node at that point are absent. When a
tuning fork is struck with a hard substance, high ringing
overtones are plainly heard, while the fundamental is ex-
tremely weak. A very different quality is produced, how-
ever, by bowing the fork or striking it against a soft pad.
202. Stringed Instruments. Among the most common musi-
cal instruments which depend on the vibration of strings and wires are
the piano, violin, guitar, mandolin, and banjo. The piano consists of
a series of tightly stretched wires, which in the lower octaves are very
massive and vary in length from three to five feet. The shortest wires
of the instrument are often not more than two inches in length. When
a key is struck, the motion is transmitted through a system of levers to
a padded hammer which strikes the wires tuned to give the correspond-
ing pitch. The tone emitted is greatly intensified by the vibrations
produced in the sounding-board. When the key is released, a padded
damper falls against the vibrating wires, thus checking the motion.
A pressure of the foot upon the right-hand pedal of the instrument
raises all the dampers and thus leaves the vibration of every wire
unchecked. Changes of temperature and humidity of the atmosphere
gradually put the wires out of tune. The necessary tuning is accom-
plished by a suitable adjustment of the tension of each wire.
Instruments of the violin type which are played with a bow, as well
as the guitar, mandolin, and banjo, derive their musical tones from
properly tuned wires or strings whose lengths may be changed at will
by the performer. The violinist by long practice learns the exact
position at which to press the strings against the finger board to pro-
duce the desired tones. By this method any pitch from that of the
lowest string to the one derived from the shortest possible portion of
the string of highest fundamental can be produced. The difficulty is
reduced in the case of the guitar, mandolin, and banjo by the slightly
raised frets, or bridges, placed across the finger board to indicate the
position of the finger. These instruments owe their wide difference
in tone quality (1) to the nature of the string, (2) to the manner in
198 A HIGH SCHOOL COURSE IN PHYSICS
which the strings are put in vibration, and (3) to the size, shape, and
material of their sounding-boards.
EXERCISES
1. How are the different pitches produced which are necessary in
rendering a selection on a guitar, harp, mandolin, or cello?
2. The bridges under a stretched wire are 4 ft. apart. Where must
a third bridge be placed to raise the pitch a major third? a minor
third?
SUGGESTION. See 181 for the vibration ratios for these intervals.
3. A wire 180 cm. long produces middle C. Show by a diagram
where a bridge would have to be placed to cause the string to emit
each tone of the major scale of C.
4. What is the vibration frequency of the tone three octaves above
middle C? What length of the wire in Exer. 3 would be required
to produce this tone?
5. The tension of a string is 9 kg. What tension must it have in
order to produce a tone an octave higher? an octave lower? a fifth
higher?
6. Write the vibration frequencies of the tones one, two, and three
octaves both above and below middle C.
7. Write the vibration frequencies of the first four overtones of a
G string. Name these tones.
8. The density of steel is 7.8, and that of brass 8.7. What is the
vibration frequency of a steel wire, if that of a brass wire of equal
length, diameter, and tension is 280 ?
SUGGESTION. Let x be the vibration frequency of the steel wire
and then write the proportion based on the law of masses, 197.
9. The vibration frequency of two equal wires 155 cm. long is 300.
How many beats per second will be heard when one of the wires has
been shortened 5 cm.?
10. Two middle C forks were placed near together and the prongs
of one of them weighted with bits of sealing wax ; when both forks
were sounded, 4 beats per second were heard. Find the frequency of
the weighted fork.
6. VIBRATING AIR COLUMNS
203. Organ Pipes. The pipe organ, flute, clarinet,
cornet, etc., employ resonant air columns for the produc-
tion of musical tones. The pitch of the tones emitted by
SOUND: WAVE FREQUENCY AND WAVE FORM 199
such columns depends mainly upon the length of the
column. The relation between the length of a column
and its pitch is shown by the following experiments:
1. Measure the length of various organ pipes that are available for
experimental purposes. Compute the ratio of the length of each pipe
to the length of pipe giving the key tone of a major scale. This ratio
will be found to be the inverse of the vibration ratio for the corre-
sponding tone of the scale as given in 180.
2. Prepare a set of glass or metal tubes about 1 centimeter in diam-
eter of the lengths 10, 15, 20, and 30 centimeters. Leaving the tubes
open at both ends, blow across one end of the tube 10 centimeters
long in such a manner as to produce an audible tone. Even if the
sound is not loud, its pitch can usually be recognized and sung by
members of the class. Again, blow across the end of the 20-centi-
meter tube, and compare its pitch with that of the first tube. The
interval between the two tones will be practically an octave, the
shorter tube having the higher pitch. Verify this relation by using
the tubes whose lengths are 15 and 30 centimeters. In a similar
manner ascertain the interval between the pitches of the tones emitted
by the tubes whose lengths are 20 and 30 centimeters. This interval
will be about a fifth.
Organ pipes are either open or stopped. A stopped pipe
is formed by closing one end of a tube. The experiment
teaches that when the length ratio of two open pipes is 1:2,
the vibration ratio is 2 : 1 ; and when the former ratio is 2 : 3,
the latter is 3:2. Hence, the vibration frequencies of open
pipes are inversely proportional to their lengths.
204. Open and Stopped Pipes. Close an end of one of the tubes
used in Experiment 2 of the preceding section, and cause it to emit its
tone as before. Produce also the tone of the pipe when both ends are
open, and compare the pitches. The pitch of the closed tube is an oc-
tave lower than that of the open one. This result may be verified by
using any of the tubes. If an organ pipe is available, blow it first
while open and then while closed tightly at one end. The best re-
sults are obtained by blowing it moderately.
The pitch of a closed pipe is an octave lower than that of
an open one of the same length.
200
A HIGH SCHOOL COURSE IN PHYSICS
205. Mechanism of an Organ Pipe. Sectional views of
open organ pipes made of metal and wood are shown in
Fig. 155. Air is blown
from a wind chest into
the small chamber c and
flows in a thin stream
through the narrow ori-
fice i against the lip a.
At a the air is set in vi-
bration, and this in turn
puts the air contained in
the tube in vibration.
Since the pitch of the
pipe is determined by its
length, it can reenforce
only those vibrations at
the lip a, whose vibration
frequency corresponds to
its own.
The tube
may be re-
garded as a
resonator
for reenf orc-
A vibrating
FIG. 155. Open Organ Pipes. (1) A
Metal Pipe. (2) A Wooden Pipe.
ing a tone of a particular pitch,
tuning fork whose pitch is the same as that
of the tube would also set the air column in
vibration when held near the open end.
206. Nodes in Vibrating Air Columns. -
When an open pipe is yielding its fundamen-
tal, or lowest tone, a node n, (1), Fig. 156, is
formed at the center. The arrows indicate
that the vibratory motion of the air on opposite sides of
a nodal point is always in opposite directions. At the
FIG. 150.
Nodes in
Open and
Stopped
Pipes.
SOUND: WAVE FREQUENCY AND WAVE FORM 201
open ends of the tube aa the air is free to vibrate
and the density of the air remains practically un-
changed; hence these points are often called antinodes or
loops. Since the distance from a node to an antinode is al-
ways equal to a quarter of a wave length ( 189), the length
of the entire wave is four times na, or twice the length
of the tube.
The case of stopped pipes is different. A node is al-
ways formed at the closed end of the tube n, (2), Fig. 156,
and an antinode near a. The wave length is four times
the distance an, or four times the length of the tube. It
thus becomes clear why the fundamental of a closed pipe
is an octave below that of the open one.
207. Overtones Produced by Organ Pipes. By blowing
an organ pipe forcibly, tones of a higher pitch than the
fundamental will be produced.
a n a n a
This is also true of the tubes (i) i ? 2 a | 4
used in Experiment 2, 203. a n a n a n a
Just as in the case of vibrating (2) ' ! 2 L_I_J 5 ! 6
Strings (198), the vibrating FIG. 157. Overtones of Open
body, which is the air column in
this instance, divides into parts according to existing
conditions. It is by the vibration of these parts that the
higher tones, or overtones, are produced. Figure 157
shows the position of the nodes and antinodes when the
pipe is sounding its first and second overtones. In (1) it is
shown that the tube contains four quarter waves ; hence
the wave length is equal to the length of the tube. Simi-
larly for the second overtone (2), the division of the vi-
brating air column forms six quarter waves. Now since
the vibration frequency increases as the wave length de-
creases, the first overtone has twice the frequency of the
fundamental ; the second, three times the frequency ; and
so on. Thus the overtones of an open pipe are the same
202
A HIGH SCHOOL COURSE IN PHYSICS
as those of vibrating strings ( 200), and are therefore
harmonics.
The division of the air column in stopped pipes is other-
wise. As we have already seen, a node is always formed
at the closed end and an antinode at the open end. Hence,
in the production of the fundamental tone, only one quarter
wave is contained in the pipe. But when the first over-
tone is emitted, a node must again be formed at the closed
end w, and an antinode at the open end. Evidently, if
only one other node is to exist it must be at n' (1), Fig.
158, one third of the length of
the pipe from the open end.
The pipe then contains three
quarter waves. Similarly,
when yielding its second and
third overtones, the column
must divide into five and seven quarter waves respectively
in order to retain a node at the closed end and an antinode
at the open end. This is shown for the second overtone
in (2). Hence in a stopped organ pipe only those over-
tones can be produced whose frequencies are odd multiples
of the vibration frequency of the fundamental.
208. Wind Instruments. Under this title are classed all in-
struments whose tones are emitted by air columns. The most impor-
(0
(2)
3 : 4
FIG. 158. Overtones of Closed
Pipes.
(2)
FIG. 159. (1) The Flute. (2) The Clarinet.
tant instrument of this kind is tine pipe organ. The wide range of pitch
is derived from organ pipes (see Fig. 155) of different lengths. A
great variety in the quality of tones is secured by the use of pipes of
SOUND: WAVE FREQUENCY AND WAVE FORM 203
FIG. 160. Mouthpiece of the
Clarinet.
different kinds, as open and closed wooden pipes, metal pipes, reed
pipes, etc.
The flute, (1), Fig. 159, corresponds to an open organ pipe whose
length can be changed by the aid of
openings along the side controlled by
the fingers. The air in the instru-
ment is set in vibration by blowing a
current from the lips forcibly across
the opening at a.
The clarinet, (2), Fig. 159, is pro-
vided with a mouthpiece, Fig. 160, which contains a reed or tongue of
light, flexible wood, which alternately opens and closes the aperture.
The action of the instrument resembles that of the so-called " squawker,"
made of the stem of the dandelion or by cutting a tongue on the side
of a quill. The current of air blown by the lungs causes the reed
to close the opening momentarily. There is thus started through
the tube a wave, the returning reflected pulse from which forces the
reed outward. A series of rapid puffs is in this manner maintained
at the end of the tube. The performer secures the various pitches
by openings in the side of the instrument, as in the case of the flute.
The cornet. Fig. 161_ is provided with a mouthpiece of the form
shown in Fig. 162, within
the large opening of
which the lips are caused
to vibrate. The neces-
FIG. 161. The Cornet.
FIG. 162. Mouthpiece
of the Cornet.
sary range of pitch is obtained by blowing overtones and controlling
the length of the tube by the valves. (See Fig. 154.) The trombone,
Fig. 163, is an instrument of the cornet type, in which the pitches are
c
JUL
FIG. 163. The Slide Trombone.
204 A HIGH SCHOOL COURSE IN PHYSICS
produced by sliding the portion ab to the proper positions for chang-
ing the length of the vibrating air column.
209. Vibrating Reeds and Diaphragms. Reed organs, ac-
cordions, and mouth organs are provided with reeds similar to that
shown in Fig. 164. A current of air blown in the direction of the
arrow suffices to set the tongue a
in vibration. Different pitches
are obtained by making the reed
of suitable length and rigidity.
A vibrating disk, or dia-
phragm, is employed in the tele-
Fia.l64.-A n OrgaoRe e d. phone an(J phonograph . The
description of the electric telephone will be deferred until a study
has been made of its underlying principles. The mechanical telephone
may be made by simply connecting two metal diaphragms with a
strong cord or wire. The vibrations set up at one end by speaking
against the diaphragm are transmitted by longitudinal waves in the
wire which set up corresponding vibrations at the second instrument.
Such telephones are used for short distances only.
The phonograph affords an interesting application of the recording
and reproduction of sounds by the aid of a small diaphragm. In the
process of making a " record " a smooth, or blank, cylinder of soft ma-
terial, as wax, is placed on the rotating shaft of the instrument, and
against its surface is carefully adjusted a sharp cutting point attached
to the back of the diaphragm. The tones of a voice or instrument
produce sound waves which are collected by the horn and transmitted
to the diaphragm. When the diaphragm vibrates, its up-and-down
motion causes the point to engrave in the surface of the rotating cyl-
inder a spiral groove of ever- varying depth corresponding to the com-
plex form of the sound waves which fall upon it. In the reproduction
of sound the record is mounted on the revolving shaft, and a delicate
stylus which is attached to the back of the diaphragm is adjusted
in the spiral groove on the surface of the cylinder. When the cylinder
rotates, the stylus rises and falls with the little irregularities of the
groove and thus sets the diaphragm in vibration. Since the manner
in which the diaphragm vibrates is governed wholly by the nature of
the engraved record, the sounds which it emits resemble very closely
those by which the record was produced. In many instruments of
this type, the records are engraved on disks instead of cylinders.
SOUND: WAVE FREQUENCY AND WAVE FORM 205
EXERCISES
1. What is the wave length of the tone produced by an open pipe
2 ft. long? by a closed pipe of the same length?
2. Compute the length of a middle C open pipe, the temperature
being 20 C.
SUGGESTION. See 170 for the relation of wave length and pitch.
3. A whistle may be regarded as a stopped pipe. If the cavity of
a whistle is 1 in. long, find the vibration frequency of its tone when
the temperature of the air with which it is blown is 25 C.
4. By blowing across the end of a tube 6 in. long, closed at one
end, the first overtone is emitted. Find its frequency, the tempera-
ture being 18 C.
5. Find the vibration frequencies of the first four overtones of a
middle C pipe, (1) when the pipe is open at both ends and (2) when it
is stopped at one end.
6. When a small stream of water is allowed to run into a bottle, a
sound is heard. Does the pitch of the tone rise or fall ? Explain.
7. If the ear is held near the mouth of a tall jar or the open end of
a tube, a tone will be heard. Perform the experiment, and then ex-
plain how the so-called "sound of the sea" is heard coming from
large sea-shells.
SUMMARY
1. A musical sound is distinguished from a noise by the
isochronism of the vibrations. Pitch is governed by the
number of vibrations per second ( 177 and 178).
2. A major diatonic scale is a series of eight tones whose
vibration numbers are to each other in the relation of the
numbers 24, 27, 30, 32, 36, 40, 45, and 48, or which bear
the following ratios to the first, or key tone: 1, --, j, , f,
f, Jys and 2 ( 179 and 180).
3. An interval is the relation between the pitches of
two tones. It depends entirely upon the ratio of their
vibration numbers. The common intervals are the octave,
sixth, fifth, fourth, major third, and minor third. The
intervals are expressed by definite, simple ratios ( 181).
206 A HIGH SCHOOL COURSE IN PHYSICS
4. A major chord consists of three tones whose vibration
numbers are as 4 : 5 : 6 ( 182).
5. Sharps and flats are used for the purpose of supply-
ing the necessary tones for 'scales other than the scale of 0.
Scales are tempered in order that an instrument with fixed
tones may produce all scales equally well ( 183 and 184).
6. Resonance depends upon the fact that a vibrating
body will impart vibrations to another near by, whose
natural vibration frequency is the same as its own ( 185
to 189).
7. Two trains of waves will weaken or destroy each
other if the condensations in one train coincide with the
rarefactions of the other. The cancellation of sound is
complete when the amplitudes and wave lengths are
equal ( 190 and 191).
8. The coincidence of two trains of waves which differ
slightly in length results in the alternate reenforcement
and weakening of the resultant tone. The fluctuations of
intensity produced in this manner are called beats. The
number of beats per second is equal to the difference of
the vibration numbers of the two tones ( 192 and 193).
9. The vibration frequency of a stretched string or
wire depends on its length, mass, and tension. The
frequency is inversely proportional to the length and the
square root of the mass per unit length and directly pro-
portional to the square root of the tension ( 194 to 197).
10. A string as a rule vibrates as a whole and at the
same time in parts. The tone produced by the vibration
as a whole is its fundamental, and the tones emitted by
the vibrating parts are its overtones ( 198 and 199).
11. Since a string divides into equal parts, i.e. into
halves, thirds, quarters, etc., the vibration numbers of
the overtones are 2, 3, 4, 5, etc., times the frequency of the
SOUND: WAVE FREQUENCY AND WAVE FORM 207
fundamental. Such overtones are called harmonics
( 200).
12. The quality of a sound is dependent on the over-
tones present and their relative intensities ( 201).
13. The pitch of an organ pipe depends upon its length.
The vibration numbers of the fundamentals emitted by
pipes are inversely proportional to their lengths. The
fundamental of a stopped pipe is an octave lower than
that of an open pipe of equal length (203 to 205).
14. The wave length of the fundamental of an open
pipe is twice, and of a stopped pipe four times, the length
of its air column ( 206).
15. The overtones of open pipes are all the harmonics,
as is the case for strings ; but the overtones of stopped pipes
are only those that have respectively. 3, 5, 7, etc., times
the vibration frequency of the fundamental ( 207).
CHAPTER XI
HEAT: TEMPERATURE CHANGES AND HEAT
MEASUREMENT
1. TEMPERATURE AND ITS MEASUREMENT
210. Temperature. Among the most common experi-
ences of everyday life are the sensations of warmth and
coldness as we come near or in contact with objects around
us. These sensations enable us to distinguish between
different bodies with respect to that condition called
temperature. If several vessels of water or pieces of iron,
for example, are placed before us, we are able by the sense
of feeling to arrange them in the order of their various
temperatures. On this account, we find in common lan-
guage many terms made use of to express what may be
called the degree of hotness of bodies ; as hot, warm,
tepid, lukewarm, cool, and cold. We say that one body
is warmer than another; or, to use another expression, has
a higher temperature than the other.
Although our temperature sense is of great value to us
at all times, it does not afford an infallible guide in every
instance, as the following experiments will show :
1. Place the hand against the wooden portion of the class-room
seat, and then transfer it to the iron part. State which feels the
warmer.
2. Let three vessels of water be prepared : the first very warm,
the second very cold, and the third lukewarm. Place the right hand
in the cold water and the left hand in the warm water, and hold them
there about a minute. Now transfer the left hand to the third vessel.
The water will feel cold. Now remove the right hand from the cold
water, and place it in the third vessel. The same water feels warm.
208
UNIVERSITY
OF
'"TIRE CHANGES AND MEASUREMENT 209
In the first experiment the temperatures of the iron
and wood are practically the same ; but the hand which
is warmer than either the wood or iron falls most rapidly
in temperature when in contact with the iron than when
touching the wood. Furthermore, it is a well-known fact
that a room may be considered warm by a person who has
been running, and cold by another who has been sitting
quietly in the house.
211. Relation between Temperature and Heat. When a
body which has a certain temperature becomes hotter, we
ascribe the cause of this change to the acquisition of heat.
We say that hea.t has been added to it. When such a
body becomes colder, we say that heat has been taken
from it. The rise in the temperature of a body may
be produced in many different ways, e.g. an iron is heated
in a fire, a piece of steel by its friction with a moving
grindstone, an electric lamp by a current of electricity, or
the earth by the rays of the sun.
It is necessary for us to distinguish carefully between
the temperature of a body and its heat. The fact is well
known that a cup of water taken from a boiling kettle is
just as hot as the water remaining in the kettle ; or
a pail of water dipped from a pool has at that instant
precisely the same temperature as the pool. But it is
also very evident that of two hot-water bottles filled
from the same kettle, the one containing the greater
quantity of water will give out more heat and for a
longer time than the smaller bottle. Hence, while the
temperatures of two bodies may be equal, the amounts
of heat contained within them may be very different.
Thus a thermometer placed in a vessel of water, for
example, indicates the temperature of the water, but in
no way does it show the amount of heat which the water
contains.
15
210 A HIGH SCHOOL COURSE IN PHYSICS
212. Nature of Heat. In order to investigate the
nature of that which brings about the changes in the tem-
peratures of bodies, let the following experiments be per-
formed :
1. Rub the face of a coin or button against a hard-wood
board for a minute or two. The metal will become very
hot.
2. Bend a piece of iron wire back and forth, and then
feel of the place where the bending occurred. The wire
becomes too hot to hold in the fingers.
3. Give the end of a nail or a piece of lead a dozen
rapid blows witn a hammer. A decided rise in temperature
will be detected.
4. Place some tinder in the end of the piston of a "fire
syringe," Fig. 165, and then force the piston into the cylin-
der. When the piston is withdrawn, the tinder will be
FIG. 165. found to be burning.
These cases are alike in that the heat required to bring
about the rise in temperature is produced in every instance
at the expense of work on the part of the person perform-
ing the experiment. Thus energy is given up by the per-
son, and heat appears. Again, a moving train apparently
loses its kinetic energy when the brakes are applied; but
an examination of the brakes and wheels reveals the fact
that the energy has been converted into heat, as is shown
by a large increase in temperature.
On the other hand, heat is constantly used in steam
engines for hauling trains, running machinery, and for
performing work in many other ways.
The conclusion to which experimental results lead is
that heat is a form of energy. The steam engine is simply
a device for converting heat energy into a form of energy
which can be utilized, i.e. into the energy of mechanical
motion. When, however, this motion is checked, the
mechanical energy is changed back into heat energy.
TEMPERATURE CHANGES AND MEASUREMENT 211
213. Molecular Theory Applied to Heat. The explana-
tion of such phenomena as we have before us is greatly
aided by the so-called molecular theory of matter which was
briefly stated in 129. It is assumed that all matter is
composed of small particles called molecules. The molecules
of a body are separated by small spaces within which they
move rapidly about, probably with frequent collisions. In
solids each molecule is restricted in its motion to a certain
space which it does not leave. When this restriction is
removed, the body assumes the liquid state and the only
constraint is the mutual attraction between the molecules
(cohesion). In gases even this last limitation is practi-
cally removed, and hence the space occupied by a given
mass of gas is governed only by the size of the vessel
containing it.
With the help of the molecular theory it is now pos-
sible to give a more definite idea of the nature of heat.
If m represents the mass of a molecule and v the average
velocity of the molecules of a body, it is plain that each
molecule possesses kinetic energy of the amount ^mv 2
(Eq. 2, 62), and the entire body will have within it as
many times this amount as there are molecules. This
energy is called heat. Hence, we may define heat as the
kinetic energy of molecular motion.
214. Some Effects of Temperature Changes. When by
increasing or decreasing the amount of heat in a body its
temperature is raised or lowered, one or more resulting
changes may take place : (1) the body may expand or
contract ; (2) the body may undergo a change in its prop-
erties, as in hardness, elasticity, ductility, etc.; (3) the
body may change its pressure against other bodies, e.g.
a gas may increase or decrease its pressure against the
walls of the containing vessel.
The application of heat to a body, however, does not
212 A HIGH SCHOOL COURSE IN PHYSICS
always change its temperature. The body may be changed
from a solid to a liquid, or from a liquid to a gas while
its temperature remains constant, e.g. melting ice, boiling
water, etc. These different classes of phe-
nomena are commonly known as heat-effects.
215. Measurement of Temperatures.
The instrument most widely used for the
determination of temperatures is the mer-
curial thermometer. It is constructed upon
the principle that mercury expands when
warmed. This thermometer consists of a
capillary tube at the lower end of which is
a bulb containing mercury, Fig. 166. The
mercury completely fills the bulb and ex-
tends some distance into the tube. Since
the expansion of mercury is greater than
that of glass, the thread of mercury in the
tube rises when the temperature of the
mercury in the instrument is increased, and
falls when it is decreased. Before the tube
of a thermometer is sealed, the mercury in
the bulb is heated until it entirely fills the
instrument, in which condition the glass
at A is sealed off in a hot flame. When
the mercury cools and contracts, it leaves
a good vacuum above it in the tube.
FIG. 166. Tube 216. The Fixed Points of a Thermometer.
a^ier curial In order to make it possible to compare
Thermometer. \\^Q temperature measurements of one ther-
mometer with those of another, two fixed points that are
easily obtained are located on the tube of the instrument.
The first of these is the freezing point of pure water. This
point is found by packing the thermometer in ice or
snow, as shown in Fig. 167. When the mercury has
TEMPERATURE CHANGES AND MEASUREMENT 213
ceased to fall, the position of the end of
the column is marked upon the tube.
The second fixed temperature point is
the loiling point of pure water. The ther-
mometer is suspended over boiling water
in a tall vessel so that the thread of mer-
cury in the tube is completely enveloped
by the steam, as in Fig. 168. The mer-
cury rises for a time, but
finally comes to a posi-
tion at which it remains
stationary. Since, how-
ever, this temperature
changes with the pres-
sure of the atmosphere,
it should be taken under
normal atmospheric
pressure (i.e. 760 milli-
meters of mercury). Otherwise a cor-
rection must necessarily be made.
The points thus obtained on a ther-
mometer scale are often marked with
FIG. i68.-Determin- the words "freezing" and "boiling,"
ing the Boiling ,, , .
Point on a Tner- these being the names given to the
mometer Tube. nxe( j points of temperature.
217. Graduation of Thermometer Scales. The space
between the freezing and boiling points is now divided
into temperature units called degrees. According to
the centigrade 1 scale the freezing point is marked 0,
and the boiling point 100. The interval between the
two points is then divided into 100 equal parts. Similar
divisions are produced on the tube above the boiling
point and below the freezing point. Centigrade ther<
1 From centum and gradus, meaning a hundred degrees.
FIG. 167. Locat-
ing the Freez-
ing Point on a
Thermometer
Tube.
214
A HIGH SCHOOL COURSE IN PHYSICS
mometers are almost exclusively used for scientific pur-
poses.
The Fahrenheit thermometer scale was introduced by a
German physicist of that name about 1714. On this scale
the freezing point is marked 32 , 1 and the
boiling point 212. The interval between
these two points is therefore divided into 180
equal parts, and similar divisions are laid
off both above the boiling point and below
the freezing point. The Fahrenheit ther-
mometer is the household instrument in use
among most English-speaking people, and
is that employed by the United States
Weather Bureau and by physicians.
On all thermometers, temperatures below
the zero point are read as negative quan-
tities. In every case the initial letter of
the name is affixed to indicate the scale
used. For example, 25 C., 100 F.
218. Thermometer Scales Compared. It
is obvious that any thermometer can be pro-
vided with both the centigrade and the
Fahrenheit scales, as shown in Fig. 169. It
FIG. 169. Centi-
grade and will readily be observed that 100 centigrade
Fahrenheit d e nr rees measure the same interval as 180
Thermometer
Scales. .Fahrenheit degrees. Hence,
32 C
or
100 centigrade degrees 180 Fahrenheit degrees,
1 centigrade degree = | Fahrenheit degree.
But in order to change a temperature reading from one
system into the other, it is necessary to take account of
the fact that F. is 32 Fahrenheit degrees below C.
1 Fahrenheit placed at the temperature which he produced by a mixture
of ice, water, and salainnioniac.
TEMPERATURE CHANGES AND MEASUREMENT 215
For example, 68 F. is 68 - 32, or 36 Fahrenheit degrees
above the freezing point. But 36 Fahrenheit degrees are
equivalent to $ x 36, or 20 centigrade degrees. Now a
temperature that is 20 centigrade degrees above the freez-
ing point is 20 C. Therefore the temperature 68 F. is
equivalent to 20 C.
Letting F represent a Fahrenheit reading and C the
corresponding reading on the centigrade scale, we have :
F - 32 = f C. (l)
219. Range of a Mercurial Thermometer. The use of a
mercurial thermometer in the measurement of high and
low temperatures is limited by the boiling and freezing
points of mercury. The former is about 350 C., and the
latter 38.8 C. The boiling of the mercury can be pre-
vented by increasing the pressure upon it by the presence
of nitrogen gas above it in the tube. Such thermometers
may register temperatures up to about 500 C. For temper-
atures below 39 C. liquids having low freezing points
must be used. Such a liquid is alcohol, which freezes at
111 C. Many alcohol thermometers are in common use.
220. Galileo's Air Thermometer. The ^
first instrument designed for the meas-
urement of temperatures was Galileo's air
thermometer, Fig. 170. The use of this in-
strument dates from 1593. The device con-
sists of a vertical glass tube of small bore,
on the upper end of which is a large bulb
containing air. This air is warmed slightly,
and the end of the tube is placed in some
liquid, such as colored water. When the
air cools, the liquid rises in the tube, being
forced up by the atmospheric pressure. Ob- FlG - 170 - Gali -
i v -j i -fi j c n leo'sAirTher-
viously the liquid column will rise and fall mometer.
216 A HIGH SCHOOL COURSE IN PHYSICS
according as the temperature of the air in the bulb is re-
duced or increased. On account of its sensitiveness to
small changes of temperature, this thermometer is fre-
quently used for experimental purposes.
EXERCISES
1. Would the range of a mercurial thermometer of given length
be increased or decreased by reducing the size of the bulb ? by mak-
ing the bore of the tube smaller? Would the distance representing
a degree be increased or decreased?
2. If the bulb of a mercurial thermometer should permanently
contract after its graduation, how would the fixed points be affected ?
3. In a certain experiment only the bulb of a thermometer is ex-
posed to the temperature that it is desired to measure. If this tem-
perature is above that of the room, will the reading of the instrument
be too large or too small ?
4. How would you proceed to test experimentally the points on a
mercurial thermometer ?
5. The boiling point of water falls 0.1 of a centigrade degree for
a decrease of 0.27 cm. in the atmospheric pressure. What is the
boiling point when the barometer reads 73.3 cm. ? A ns. 99 C.
6. Reduce the following centigrade readings to the corresponding
values on the Fahrenheit scale : 20, 35, 50, -20, -40.
7. How many centigrade degrees lie between the Fahrenheit and
centigrade zero marks?
8. The following temperature measurements were taken with a
Fahrenheit thermometer: 77, 41, 14, -4, -40. What would a
centigrade thermometer have indicated in each case ?
9. The difference in temperature of two vessels of water is 25
centigrade degrees. Express the difference in Fahrenheit units.
10. One room is 18. Fahrenheit degrees warmer than another.
What is the difference between their temperatures on the centigrade
scale ?
11. The boiling point of water at a certain place was found to be
98.8 C. What was the atmospheric pressure at the time ? See Exer. 5.
Ans. 72.76 cm.
2. EXPANSION OF BODIES
221. Linear Expansion. We have already observed
the use made of the expansion of mercury when heated.
TEMPERATURE CHANGES AND MEASUREMENT 217
It is generally true of all bodies that an increase in size
accompanies a rise in temperature. Thus a metal rod, for
example, undergoes an increase in length, which, although
usually small, must be taken into account in planning
bridges, laying railroad tracks, etc.
1. Figure 171 illustrates the well-
known ring and ball. When both
are of the same temperature, the ball
passes readily through the ring. When,
however, the ball is heated, it becomes
too large to fit the ring. If cooled, it
will be found to resume its original size.
2. Let a metal bar, preferably of brass, rest at one end upon
a block of wood, as A, Fig. 172, and at the other end upon a
round glass or metal rod B about 2 millimeters in diameter placed
FIG. 171. Ring and Ball.
FIG. 172. Expansion of a Metal Rod.
upon a smooth block of wood. Attach a very light index of glass or
paper about 20 centimeters long to the small rod in such a manner
that it can move over a scale C, as shown. Now heat the bar by mov-
ing a flame along it. The movement of the index will indicate an
elongation of the bar. When the bar cools, the index returns to the
original position.
222. Coefficients of Linear Expansion. Not all solids
expand equally. For example, a bar of copper a meter
long expands more than a bar of iron of equal length
for the same increase in temperature. The ratio of the
increase in length of a metal bar for an increase of one degree
218
A HIGH SCHOOL COURSE IN PHYSICS
in temperature to its length at C. is called the coefficient
of linear expansion of the metal.
Thus a rod of metal one meter long that expands
1 millimeter when the temperature rises from C. to
100 C. has a coefficient of linear expansion equal to 1 -r-
(1000 x 100), or 0.00001. The coefficient of linear ex-
pansion of a substance is expressed by the equation
where ? a and Z 2 are the lengths before and after heating,
and j and t 2 are the initial and final temperatures.
COEFFICIENTS OF LINEAR EXPANSION
Aluminium . . 0.000023
Brass 0.000018
Copper .... 0.000017
Glass 0.000009
Invar . , 0.00000087
Iron 0.000012
Lead 0.000027
Platinum .... 0.000009
Steel . , 0.000011
223. Applications of Unequal Expansion. By referring to
the table of the coefficients of expansion of metals given in 222, it
will be seen that the common metals, brass
and iron, expand unequally. Hence if two
flat bars of these metals are riveted together,
as shown in (a), Fig. 173, an increase in tern-
the iron and cause the bar to bend, as in
The bending of a compound bar of two metals
is employed in the dial thermometer in common
use. The bar in this case is made circular in
form and -has one end fixed, as at A, Fig. 174.
The other end is attached by means of a cord
or chain at B to a small axle (7, which carries
the pointer D. A rise in temperature causes
the free end of the bar B to move inward and FlG 174 _r)j a i Ther
the pointer to register a higher temperature on mometer.
TEMPERATURE CHANGES AND MEASUREMENT 219
the graduated scale. For a fall in temperature the reverse movement
takes place.
The same principle is ingeniously applied to the balance wheel
of a watch, in o^der to make the period
of vibration independent of temperature
changes. An increase in temperature weak-
ens the hairspring which controls the vibra-
tion of the wheel and lengthens its spokes,
the effect in each instance being to make
the watch lose time. In order to correct this
tendency, the balance wheel is constructed
as shown in Fig. 175. The outer rim of each
of the compound bars A and B is made of FIG. 175. Balance Wheel
brass, and the inner part of iron. An in- of a Watch -
crease in temperature causes the portions A and B to bend toward
the center just enough to keep the period of vibration constant.
EXERCISES
1. Ascertain how steel tires are tightened or "set "by a black-
smith, and explain the various steps of the process.
2. In what manner do engineers take account of the expansion
and contraction of the rails when laying a railroad track ?
3. Consult the table of linear coefficients of expansion, and ascer-
tain why platinum wires can be sealed in glass without danger of
breakage when the glass cools. Examine an incandescent lamp bulb,
and see that this is the case.
4. Why is one end of a long steel bridge often supported on rollers ?
5. Invar is an alloy of nickel and steel. Consult the table of linear
coefficients of expansion, and show why it is a valuable metal from
which to make tapes for measuring, standards of length, and pendulum
rods.
6. Glass stoppers can often be loosened by carefully heating the
neck of the bottle. Explain.
7. How much does the length of a 90-foot steel rail vary if the
extremes of temperature are - 24 C. and 35 C. ?
8. At the temperature of C. an iron pipe is 100 ft. long. What
will be its length when steam at 100 C. is passing through it?
9. A metal rod is 60 cm. long and expands 1.02 mm. when the
temperature is raised from C. to 100 C. Compute the coefficient
of linear expansion of the metal.
220 A HIGH SCHOOL COURSE IN PHYSICS
224. Cubical Expansion. In general, substances when
heated expand in all directions, i.e. a rise in temperature
is accompanied by an increase in volume. This may be
shown to hold true for water by the following experi-
ment:
Fill a flask with water, and insert a rubber stopper through which
passes a small glass tube about 40 centimeters long. Some of the
liquid will rise in the tube. Mark the position of the top of the
liquid column, and set the flask in a vessel of warm water. The liquid
at first falls slightly in the tube as the flask expands and then rises
slowly because of the increase in volume of the water.
225. Coefficients of Cubical Expansion. The cubical
expansion of a substance is related to volumes in the same
manner as linear expansion is related to lengths. Thus
the coefficient of cubical expansion of a substance is the ratio
of the increase in volume for a change of one degree in tem-
perature, to the volume at O.
The cubical expansion of a substance may be expressed
by the equation
k = Il^O, (3)
V Q I
where v l and V Q are the volumes at the temperatures t C.
and C. respectively. This equation is easily reduced
to the form
Vl =v (l+kt). (4)
The coefficient of cubical expansion of any substance is
three times the coefficient of the linear expansion of that
substance. Hence the cubical expansions for the sub-
stances given in the table in 222 are easily computed.
226. Abnormal Expansion of Water. If a quantity of
water at freezing temperature is warmed, its volume
decreases until it reaches a temperature of 4 C. Upon
being heated above this point it expands as do other
TEMPERATURE CHANGES AND MEASUREMENT 221
liquids. This exception to the general rule is of vast
importance in nature. As the atmosphere grows colder,
the water at the surface of lakes and ponds falls in tem-
perature, and its density at first increases. The surface
layers of water then sink and are replaced by the warmer
water from below. This continues until the temperature
of 4 C. is reached, when further cooling makes the sur-
face water less dense than that underneath. Hence the
water that has cooled below 4 C. does not sink, but
remains at the top and is frozen. Thus, since practically
the entire quantity of water in a lake must be reduced to
4 C. before the surface is frozen, ice is much slower in
forming on deep bodies of water than on shallow ones.
Furthermore, on account of the fact that the colder ice
and water at the top do not transmit the heat rapidly
away from the warmer layers of the liquid below, the
unfrozen water remains at a temperature of about 4 C.
Hence, animal life flourishes at the bottom of a lake in
winter, even when a little lower temperature would prove
fatal.
227. Cubical Expansion of Gases. When the temper-
ature of a gas is raised, its volume is increased, unless
the expansion is prevented by an increase of the pres-
sure upon the gas. Under a constant pressure the ex-
pansion of gases is much greater than that of liquids or
solids. When the temperature of a gas is increased, the
change is simply an increase in the average speed of its
molecules. As a consequence, there results an increase in
the force delivered by each molecule in its collision with
the sides of the containing vessel. There will also be an
increase in the number of blows delivered per second.
Now the pressure of the gas outward is nothing more
than the result of this continuous bombardment of mole-
cules ; and thus an increase in the average molecular
222 A HIGH SCHOOL COURSE IN PHYSICS
speed produces a corresponding increase in the pressure
of the gas. By permitting the gas to expand, the pres-
sure may be kept constant. Under a constant pressure,
all gases have the same coefficient of cubical expansion (Law
of Charles 1 ). This number has been found experimen-
tally to be 2^, or 0.00366, of the volume of the gas at
C. Thus a gas whose volume at C. is 100 cubic cen-
timeters, when heated to 25 C. increases in volume -ff^
of 100 cubic centimeters. Its volume becomes, therefore,
100 + ffig x 100, or 109.1 cubic centimeters.
228. The Absolute Scale of Temperatures. If a body of
air, for example, at C. is kept at a constant pressure
and heated, its volume will increase -%fa of its original
volume for every degree that its temperature is raised.
Thus, at 273 C. its volume will be doubled. On the other
hand, if the original body of air is cooled below 0, its
volume will be diminished ^3- of its volume at for every
degree that its temperature is lowered. If, now, the volume
were to continue to diminish at this rate until the tem-
perature should reach 273 C., mathematically it would
become nothing. Practically, however, the air and other
gases become liquids before reaching this temperature, and
thus lose the properties of gases. A temperature 273 cen-
tigrade degrees below the freezing point of water is called
absolute zero, and temperatures measured from this point
as the of the scale are called absolute temperatures. It is
clear that temperatures on the centigrade scale can be re-
duced to the absolute by simply adding 273. Thus 20 C.
= 293 Ab., and - 40 C. = 233 Ab.
Although no one has ever succeeded in cooling a body
to absolute zero, temperatures approaching within a very
few degrees of this point have been attained by the evapo-
ration of liquefied gases. The following table will serve
1 Also called Gay-Lussac's Law.
TEMPERATURE CHANGES AND MEASUREMENT 223
to show some facts regarding the history of low tempera-
ture production :
DATE
TEMPERATURE
EXPERIMENTER
1714
_ 170 c
Fahrenheit
1778
_ 40 C
Van Marum
1823
102 C
Faraday
1877
_ 103 C
Cailletet
1877
_183C
Pictet
1898
1908
-262C
269 C
Dewar
Onnes
229. Laws of Gaseous Bodies. Since the volume of a
gas is doubled when its temperature is raised from 273
Ab. (0C.) to 2 x 273, or 546 Ab. (273 C.), and the
increase in volume is uniform ( 227), it is clear that the
following law may be stated :
The volume of a given mass of gas under constant pressure
is proportional to its absolute temperature.
Again, if the body of gas is confined in a vessel of suffi-
cient rigidity to keep the volume constant at all tempera-
tures, the pressure of the gas against the walls of the
vessel will increase as the temperature rises. Further-
more, the pressure will increase gr^- of the pressure at
C. for every degree that the temperature is raised, and
will decrease g-fj of the pressure at 0C. for every
degree that the temperature is lowered. In other words,
when the volume of a gas remains constant, the change in
pressure takes place according to a law similar to that
governing the change in volume. Hence
The pressure of a given mass of gas whose volume remains
constant is proportional to the absolute temperature.
224 A HIGH SCHOOL COURSE IN PHYSICS
EXAMPLE. At 25 C. the volume of a certain mass of gas is 400
cm. 8 . Compute its volume when the temperature is lowered to C.
and the pressure kept constant. If the original pressure is 740 mm.,
compute the pressure after the decrease in temperature, assuming
that the volume remains constant.
SOLUTION. Letting x be the volume of the gas at C., we have,
by applying the law of volumes stated above,
400 : x : : 25 + 273 : 273 ;
whence, x = 366.4 cm. 8 .
In the second place, by applying the law of pressures, if x is the
pressure at C.,
740 : x : : 25 + 273 : 273 ;
whence, x = 677.9 mm.
230. Laws of Charles and Boyle Combined. Boyle's
Law ( 149) states that the product of the pressure and
volume of a given mass of gas remains constant when
the temperature remains the same. In practice, volume,
pressure, and temperature may all vary. In such cases
the following law will hold :
The product of the pressure and volume of a given mass of
gas is proportional to the absolute temperature.
EXAMPLE. The volume of a gas collected in a vessel under a
pressure of 740 mm. and at a temperature of 20 C. is 500 cm. 8 . Com-
pute the volume that the gas would have at C. and under a pressure
of 760 mm.
SOLUTION. Let x be the required volume. By combining the
laws of Boyle and Charles we have
740 x 500 : 760 x x :: 20 + 273 : 273 ;
whence, x = 453.6 cm. 8 .
EXERCISES
1. What fractional part of its volume at C. does a cubic meter
of gas expand when warmed from that temperature to 50 C., the
pressure remaining constant? What is the final volume of the gas?
TEMPERATURE CHANGES AND MEASUREMENT 225
2. The volume of a certain gas at 20 C. is 300 cm. 8 . What is its
volume when the temperature is reduced to C., the pressure being
constant ?
3. The pressure exerted by a gas confined in a reservoir is 500 g.
per square centimeter when the temperature is 10 C. What is its
pressure when the temperature is raised to 40 C. ?
4. The volume of a gas collected in a chemical experiment is
30 cm. 8 , its temperature 25, and its pressure 750 mm. Find the vol-
ume of the same gas at C. and under a pressure of 760 mm.
5. If the mass of a cubic centimeter of air at C. and under a
pressure of 760 mm. is 0.001293, what will be its density in a room
where the temperature is 22 C. and the barometer reads 745 mm. ?
6. The quantity of air in a room 8 x 12 x 15 ft. will contract to
what volume when its temperature falls from 20 C. to C. ?
7. To what temperature would the air confined in a flask at atmos-
pheric pressure and a temperature of 10 C. have to be heated in order
to exert a pressure of 3.5 atmospheres?
8. Upon heating 300 cm. 8 of a gas from C. to 30 C., the volume
was found to be 333 cm. 8 . Ascertain the coefficient of expansion of
the gas.
9. The capacity of a steel gas cylinder is 3 cu. ft. Illuminating
gas is compressed in the cylinder until the pressure is 15 atmospheres
at a temperature of 10 C. What volume will this quantity of gas
assume when allowed to escape into a space where the pressure is
1 atmosphere and the temperature 25 C. ?
3. CALORIMETRY, OR THE MEASUREMENT OF HEAT
231. The Unit of Heat. The unit employed in the
measurement of heat is called the calorie. The calorie is
the quantity of heat required to raise the temperature of a
gram of water one centigrade degree. When the tempera-
ture of a gram of water is raised from C. to 100 C.,
100 calories of heat are required. Again, to change the
temperature of 1 kilogram of water from 20 C. to 45 C.
requires that 1000 x (45 - 20), or 25,000 calories of heat
be taken on by the water. Thus, if a mass of water be
changed in temperature a given amount, the quantity of
heat involved is measured ~by the product of the mass of water
1ft
226 A HIGH SCHOOL COURSE IN PHYSICS
and its change of temperature. Hence, to change the
temperature of a mass of m grams of water t centigrade
degrees, we may write for the required quantity of heat,
H (in calories) =
m (in grams) x t (in centigrade degrees). (5)
232. Specific Heat. If a given quantity of heat be ap-
plied to equal masses of different kinds, of matter, as lead,
mercury, water, iron, and copper, the temperatures will not
all be changed equally. The amount of heat that will
warm a gram of water one degree (i.e. one calorie) will
raise the temperature of an equal mass of lead or of
mercury about 30 degrees and that of the iron or the
copper about 10 degrees.
Place 100 grams each of lead shot, iron cuttings, and bits of alumin-
ium wire in three large test-tubes. Set the tubes upright in a vessel
of boiling water, and allow them to remain there several minutes
while the .water continues to boil. Also place 100 grams of water at
the temperature of the room in each of three beakers. Now pour the
lead shot whose temperature is 100 C. into the water in one of the
beakers, stir the mixture thoroughly, and ascertain the rise in temper-
ature of the water. Do the same with the other metals. Although
the metals fall in temperature almost equal amounts, they deliver to
the water very unequal quantities of heat. The aluminium will warm
the water through about twice as many degrees as the iron and about
six times as many as the lead.
Experiments like those just described lead to the con-
clusion that each gram of lead gives out, upon cooling one
degree, about one sixth as much heat as one gram of
aluminium. Also that a gram of iron delivers only one
half as much heat as an equal mass of aluminium when
cooled an equal amount. For this reason substances are
said to differ in thermal capacity, or specific heat.
The specific heat of a substance is the ratio of the quantity
of heat required to raise the temperature of a certain mass
TEMPERATURE CHANGES AND MEASUREMENT 227
of it one degree to the quantity of heat required to raise the
temperature of an equal mass of water one degree.
The specific heat of a substance is numerically equal to
the number of calories received by one gram of the sub-
stance when its temperature rises 1 C. Thus the heat
required to raise the temperature of 1 g. of iron 1 C. is
0.113 calories; of 1 g. of lead, 0.032 calories, etc.
233. Specific Heat Determined. When a hot substance,
as heated mercury, for example, is placed in cold water,
the two bodies assume the same temperature. The heat
given up by the substance which cools is utilized in raising
the temperature of the water. In other words, the quantity
of heat gained by the cold body equals that lost by the warm
body.
Place 300 grams of lead shot in a large test-tube, and suspend the
tube in boiling water for at least ten minutes. While the lead is
heating, the tube should be kept closed with a cork. Place 100 grams
of water in a beaker, and cool it a few degrees below the temperature
of the room. Now pour the shot quickly into the water and stir care-
fully until the temperature of the mixture becomes stationary. Note
and record the rise in temperature of the water. In order to complete
the solution of the problem, we must form an equation that expresses
the equality between the heat lost by the lead and that gained by the
water. The following illustration will make the process clear:
In an experiment the initial temperature of the water was 17 C.,
the temperature of the mixture 24.2 C., and the boiling point 100 C.
Let x be the specific heat of lead.
The fall in temperature of the lead = 100 - 24.2.
The heat lost by the lead = (100 - 24.2) 300 a; calories.
The rise in temperature of the water = 24.2 - 17.
The heat gained by the water = (24.2 - 17) 100 calories.
Hence, (100 - 24.2) 300 x = (24.2 - 17) 100 ;
whence, x - 0.0316.
This process for determining the specific heat of a sub-
stance is known as the "method of mixtures." It can be
228 A HIGH SCHOOL COURSE IN PHYSICS
applied successfully to a large number of substances that
do not dissolve when placed in water. The specific heats
of some common substances are given in the following
table:
SPECIFIC HEATS
Aluminium .... 0.212 Mercury 0.033
Copper 0.093 Platinum 0.032
Ice 0.502 Silver . 0.050
Iron 0.113 Tin 0.055
Lead 0.032 Zinc 0.093
EXERCISES
1. A mass of 75 g. of water is cooled from 95 C. to 32 C. How
much heat is given up ?
2. A 100-gram mass of copper rises in temperature from 15 C. to
100 C. How much heat does it absorb?
3. If 500 calories are applied to 500 g. of mercury at 10 C., to
what point will the temperature of the mercury rise?
SUGGESTION. Let x be the final temperature of the mercury.
4. A mass of iron weighing 400 g. and having a temperature of
98 C. is placed in 100 g. of water at 14 C. ; the temperature of the
combined masses is 40 C. Compute the specific heat of the metal.
SUGGESTION. See example given in 233.
5. Find the resulting temperature when 400 g. of water at 90 C.
are mixed with 150 g. of water at 10 C.
SUGGESTION. If a: is the resulting temperature, the former mass
falls in temperature 90 x degrees, while the latter rises x 10
degrees. Express the equality between the heat lost by the former
and that gained by the latter.
6. A vessel contains 250 g. of lead shot and 150 g. of water. Find
the amount of heat required to raise the temperature of the mixture
from 15 C. to 80 C. An*. 10,270 calories.
7. The temperature of a block of ice weighing 100 kg. rises from
15 C. to the melting point. What quantity of heat is absorbed ?
8. If 100 g. of aluminium at 97 C. were dropped into 50 g. of
water at 10 C., what would be the temperature of the mixture?
TEMPERATURE CHANGES AND MEASUREMENT 229
SUMMARY
1. Temperature is the degree of hotness of a body and
is the condition which determines in what direction a
transfer of heat will take place ( 210 and 211).
2. Heat is a form of energy into which all other forms
are convertible. It is the kinetic energy of the moving
molecules of a body ( 212 and 213).
3. Changes in the temperature of bodies produce
(1) expansion and contraction, (2) change in their prop-
erties, and (3) changes in pressure. The application of
heat may change the state of matter without producing a
change in temperature ( 214).
4. The mercury thermometer makes use of the expan-
sion of mercury in the measurement of temperatures.
Each instrument is graduated according to the position of
two fixed points, the boiling point and the freezing point
of pure water ( 215,and 216).
5. On the centigrade scale the freezing point is marked
0, and the boiling point (under a pressure of 760 mm.)
is marked 100. On the Fahrenheit scale the correspond-
ing points are marked 32 and 212. The relation be-
tween temperatures expressed on the two scales is
F- 32 = f O ( 217 and 218).
6. The coefficient of linear expansion of a body is the
ratio of its increase in length for an increase of 1 C. to
its length at C. ( 221 to 223).
7. The coefficient of cubical expansion of a substance is
the ratio of its increase in volume for a change of 1 C.
to its volume at C. ( 225).
8. The volume of a given mass of water when heated
from C. contracts until the temperature reaches 4 C.
Further heating causes it to expand. Hence the greatest
density of water is at 4 C. ( 226).
230 A HIGH SCHOOL COURSE IN PHYSICS
9. The coefficient of cubical expansion of all gases is
practically the same and is expressed by the fraction ^j-g
(227). "
10. Absolute temperatures are measured from absolute
zero, which is the same as 273 C. Hence temperatures
measured on the centigrade scale are reduced to the abso-
lute by adding 273 ( 228).
11. The volume of a given mass of gas under constant
pressure is proportional to its absolute temperature
( 229).
12. The pressure of a gas under constant volume is
proportional to its absolute temperature ( 229).
13. The product of the pressure and volume of a given
mass of gas is proportional to its absolute temperature
( 230).
14. Heat is expressed in terms of a unit called the
calorie. The calorie is the quantity of heat required to
raise the temperature of 1 g. of water 1 C. ( 231).
15. Like masses of different substances require different
quantities of heat to produce equal changes of temper-
ature, i.e. they differ in specific heat. The specific heat of
a substance is the ratio of the quantity of heat required
to raise the temperature of a certain mass of it 1 C. to
the quantity required to raise the temperature of an
equal mass of water the same amount ( 232).
16. The quantity of heat required to raise the tem-
perature of any mass of a substance a given amount is the
product of the mass, the rise in temperature, and the
specific heat of the substance ( 233).
17. Specific heat is determined by the "method of
mixtures" (233).
CHAPTER XII
HEAT: TRANSFERENCE AND TRANSFORMATION OF
HEAT ENERGY
1. CHANGE OF THE MOLECULAR STATE OF MATTER
234. Fusion. If the motion of the molecules of a body
is principally of a vibratory nature, we find difficulty in
changing the form of the body and, therefore, call it a
solid. When, however, by the application of heat, the
molecular motion is so increased that the particles break
away from the constraining forces and thus overcome
their "fixedness of position," the mass assumes the prop-
erty of fluidity and becomes a liquid. Hence the state in
which a substance exists depends largely upon its tem-
perature. Thus mercury, which is a liquid under ordinary
conditions, changes into a gas at 350 C. and remains a
solid at all temperatures below 39 C. The temper-
ature at which a solid changes into a liquid is called its
melting or fusing point, and the process is called fusion.
The reverse change, i.e. from a liquid to a solid, is called
solidification. In the case of water, the process is called
freezing.
Collect a quantity of snow in a vessel, preferably when the out-door
temperature is several degrees below the freezing point. In summer
broken ice must be used v Place a thermometer in the snow so that it
can be read easily and set the vessel outside the window. When ready
to proceed with the experiment, bring the snow into the warm room,
and read the thermometer at brief intervals. The temperature of the
snow will be found to rise gradually to C., where the mercury re-
mains while the snow is melting. The vessel of snow may be gently
heated, and, if the mixture is kept thoroughly stirred, the temperature
231
232 A HIGH SCHOOL COURSE IN PHYSICS
will remain C. Continued heating after the snow has melted will
raise the temperature of the resulting liquid.
The melting point of a crystalline substance, as snow, is
well marked, but amorphous bodies, as glass, tar, pitch,
etc., pass through a semiliquid state several degrees below
the temperature of liquefaction. It is due. to this property
that glass can be formed into vessels of any desired shape,
and that wrought iron can be fashioned according to the
demands of the blacksmith.
235. Laws of Fusion. The laws governing the fusion
of crystalline substances and the reverse change of solidifi-
cation are as follows :
(1) A crystalline substance under a constant pressure has
a definite fusing point which is also the temperature at which
solidification takes place.
(2) When a crystalline substance begins to melt, its tem-
perature remains constant until all of it is liquefied.
(3) A substance that contracts while melting has its fusing
point slightly lowered by increased pressure, but a substance
that expands while melting has its fusing point slightly raised
by an increase of pressure.
(4) In the presence of a dissolved substance, the solid
forms by crystallization at. a temperature below the freezing
point of the pure solvent.
MELTING POINTS
Mercury ... - 39. C: Tin 232 C.
Ice 0. C. Lead 325 C.
Benzine .... 7. C. Silver 954 C.
Acetic acid . . . 16. C. Copper 1100 C.
Paraffin .... 55. C. Cast iron .... 1200 C.
236. Effect of Pressure on the Fusing Point of Ice. It
is well known that water expands when it freezes. This
HEAT: TRANSFERENCE AND TRANSFORMATION 233
is shown by the floating of ice and the bursting of frozen
water pipes. Ice therefore contracts when it melts.
Hence, according to the third law of fusion stated in
235, an increase of pressure lowers the melting or fusing
point. The lowering is very slight, amounting to about
0.0075 C. for an increase of one atmosphere.
1. Let two pieces of ice be pressed firmly
together. When the pressure is removed, the
pieces will be found to. be frozen together.
2. Connect two heavy weights by means of
a strong wire, and hang them over a block of
ice, as shown in Fig. 176. In a short time the
wire will cut into the block and, at last, en-
tirely through, leaving the ice still in one piece. FlG - 176 - ~ Wire Cutting
through a Block of
In each of these cases the melting ice.
point at the places where the pressure is applied is slightly
lowered ; hence some of the ice melts, forming a film of
water a little below C. When the pressure is removed
the film, which is at a temperature below the freezing point,
solidifies, cementing the two pieces of ice together. In Ex-
periment 2 the melting under pressure takes place below
the wire ; then, as the liquid flows up above the wire, the
pressure is removed, and it freezes. This process is
known as regelation (pronounced re ge Id'tiori).
237. Heat of Fusion. In general, the fusion of any
solid requires the application of heat. If the substance
is of a crystalline structure, as ice, the heat energy im-
parted to it does not sensibly raise its temperature during
the melting process. In all such cases the energy sup-
plied to the solid is used in producing the change of state.
Non-crystalline solids, such as Waxes, iron, glass, etc.,
become plastic when heated, and have no definite melting
point.
1. Note the temperature of snow or finely chipped ice placed in a
metal vessel. Place a flame under the vessel, and allow some of the
234 A HIGH SCHOOL COURSE IN PHYSICS
ice to melt. Remove the flame, stir the contents of the vessel well,
and again take the temperature. Apply more heat, and note the
temperature after stirring. In every case the temperature will be
found to be the same.
2. Place equal quantities of ice and ice water in two similar vessels,
and set both in a large vessel of hot water placed over a flame. In one
vessel heat is changing ice into water; in the other the temperature
of the water is being raised. If the contents of the vessels are con-
tinually stirred, it will be found that when the ice is melted, the tem-
perature of the water will have risen to about 80 C.
Heat energy is applied about equally to the ice and ice
water in Experiment 2. That applied to the cold water
increases the average kinetic energy of the molecules,
( 213), and thus the temperature is raised. The heat
applied to the ice, however, does not produce any increase
in the kinetic energy, but suffers a transformation into
potential energy by producing molecular separation in op-
position to the mutual attraction (cohesion) between the
particles that compose the body. In other words, the heat
energy expended in melting the ice has ceased to be heat and
simply represents the work necessary to change the ice
from the solid to the liquid state. The number of calories
per gram required to liquefy a substance without producing
any change in its temperature is called the heat of fusion 1
of that substance.
238. Heat of Fusion of Ice Measured. The quantity of
heat required to melt a gram of ice can be measured by
the method of mixtures as shown in the following experi-
ment:
Let 300 grams of water at about 35 C. be placed in a beaker and
its temperature accurately noted. Prepare also a quantity of ice in
lumps about as large as walnuts. Dry the pieces of ice with a towel,
and drop them in small quantities into the warm water. Stir
thoroughly to melt the ice. When enough ice has been added and
1 Sometimes called " latent " heat of fusion.
HEAT: TRANSFERENCE AND TRANSFORMATION 235
melted to make the temperature of the water about 5C., weigh the
contents of the beaker and compute the mass of ice melted. An equa-
tion is now formed between the heat lost by the water and that gained
by the ice. An illustration will make the process clear.
In an experiment the temperature of the warm water was 36.5 C.
After adding 110 grams of ice the resulting temperature of the water
was 5.5 C.
Let x be the heat of fusion of ice.
The heat lost by the warm water = 300 (36.5 - 5.5) calories.
The heat required to warm 110
grams of water formed by the
melted ice from C. to 5.5 C. = 110 x 5.5 calories.
The heat required to melt the ice = 110 x calories.
Hence, 110 x + 110 x 5.5 = 300 (36.5 - 5.5) ;
whence, x = 79.9 calories.
Careful investigation lias shown that the heat of fusion
of ice is 80 calories.
239. Heat Given out by Freezing Water. According
to the doctrine of the Conservation of Energy ( 64),
heat energy equivalent to that which is required to
change a solid into a liquid must be given out -when the ,
reverse change (i.e. solidification) takes place.
Make a freezing mixture of snow and salt stirred well together.
Into this mixture, which will be several degrees below C., set a
test-tube containing water and a thermometer. If the water in the
tube is not disturbed, it may reach a temperature below C. without
freezing. If, however, the thermometer be moved gently against the
wall of the test-tube, the water quickly begins to freeze and the tem-
perature rises at once to C.
In the freezing mixture of snow and salt used in the
experiment, both solids pass into the liquid state. Just as
in the case of fusion ( 238) heat is absorbed by both the
salt and snow during the change,. The heat energy
(kinetic energy) acquired by the solids in liquefying is
converted into potential energy in giving their molecules
the molecular freedom which exists in a liquid. In fact
236
A HIGH SCHOOL COURSE IN PHYSICS
the solids cannot liquefy unless they can acquire heat
somewhere. In this case the heat is taken from the water
in the test-tube, and thus its temperature is lowered and
a portion solidified. On the other hand the rise in tem-
perature indicated by the thermometer which was placed
in the test-tube shows that heat is given out when the
water changes to ice.
When a gram of water freezes, 80 calories are given out to
its surroundings. The enormous amount of heat evolved
by the freezing of water in large lakes is of great eco-
nomic importance, since it prevents large and sudden falls
of temperature in the vicinity.
EXERCISES
1. How does the presence of tubs of water in a cellar tend to pre-
vent the freezing of vegetables?
2. What has the large heat of fusion of ice to do with the rapid-
ity with which snow and ice disappear on a warm day?
3. In freezing cream a metal vessel B (Fig. 177) containing it is sur-
rounded by a rapidly liquefying mixture of
ice and salt, A. Give a complete explanation
of the process.
4. Can a piece of ice be warmed above
C. ? Can it be cooled below C. ?
5. Find the amount of heat required to
melt 50 g. of ice at C. and to raise the tem-
perature of the resulting water to 15 C.
6. A kilogram of ice at C. is placed in
an equal mass of water at 100 C. Find the
FIG. 177. Liquid B Fro-
zen by the Melting of resulting temperature.
Ice in A.
Ans. 10 C.
7. A piece of ice weighing 100 g. and
having a temperature of 15 C. is brought into a room where the
temperature is 30 C. What thermal processes take place ? What
quantity of heat is involved in each process ?
8. What mass of ice at C. will be required to reduce the tem-
perature of a kilogram of water from 100 C. to 20 C. ?
SUGGESTION. Let x be the required mass, and form an equation
similar to that used in 238.
HEAT: TRANSFERENCE AND TRANSFORMATION 237
240. Evaporation and Ebullition. We have seen in
235 that the change from the solid to the liquid state
takes place at a definite temperature in crystalline sub-
stances. The change, however, from the liquid to the
gaseous state occurs at all temperatures by the slow pro-
cess of evaporation. The gas that rises from a liquid sub-
stance is called the vapor of that substance. Even ice and
ice water evaporate. But by sufficient heating a liquid
reaches a certain temperature at which the familiar pro-
cess of boiling, or ebullition, begins. This temperature,
which is called the boiling point, varies greatly with dif-
ferent substances and with the atmospheric pressure.
241. Evaporation Explained. The process of evapora-
tion is made clear by the help of the molecular theory
( 213). At the exposed surface of a liquid the velocity
of many of the molecules is sufficient to enable them to
break through the surface beyond the range of attraction
of the molecules of the liquid. If the temperature be
raised, the average velocity of the molecules in the liquid
is increased, and a more rapid surface loss will result.
The removal of a large number of the most rapidly mov-
ing molecules in this manner decreases the average kinetic
energy of those that are left behind. Consequently, the
temperature of the remaining liquid is lowered by the pro-
cess. Evaporation always takes place at the expense of the
heat energy contained in the liquid.
242. Laws of Evaporation. (1) The rate of evaporation
becomes greater as the exposed or free surface of the liquid
is increased.
A pint of water, for example, will evaporate faster when
placed in a broad, shallow pan than when left standing in
a pitcher. When spread over the floor, it disappears in a
short time. Hence a wet cloth will dry faster when spread
out than when left folded.
238 A HIGH SCHOOL COURSE IN PHYSICS
(2 ) The rate of evaporation becomes greater as the tempera-
ture of the liquid and vapor is increased.
As the temperature rises, the increased molecular motion
enables molecules to break away from the surface at a
greater rate.
(3) The rate of evaporation is increased by the removal of
the vapor from the space above the liquid.
When the space above the liquid contains a quantity of
the vapor, a great number of the vapor molecules moving
about in all directions by chance strike the surface and
reenter the liquid. The greater the number of molecules
present in the vapor, the larger will be the number which
return to the liquid. The return of the molecules which
have once detached themselves from the liquid can be pre-
vented by removing the vapor as fast as it is formed.
This accounts for the fact that roads dry quickly on windy
days, and ink is frequently evaporated by blowing upon
the paper.
243. Vapor Pressure. When a liquid is placed in a
vacuum, it rapidly evaporates until a condition is reached
when the quantity of vapor present becomes constant,
i.e. when the number of molecules leaving the liquid per
second is just equaled by the number which reenter it in
the same length of time. The vapor is then said to be
saturated. A vapor, like any other gas, exerts a pressure
against the walls of the containing vessel. The amount
of pressure exerted depends upon the temperature ; if
the temperature rises, more of the liquid evaporates and
the pressure increases; if the temperature falls, some of the
vapor condenses and the pressure decreases. The pressure
exerted by a saturated vapor above its liquid is catted the
maximum vapor pressure at the existing temperature. For
example, if a vessel of water be placed in a vacuum, it
HEAT: TRANSFERENCE AND TRANSFORMATION 239
vaporizes at 0C. until the vapor pressure is 4.6 millime-
ters of mercury; at 10 G., 9.16 millimeters; at 20 C.,
17.39 millimeters, etc.
It is a peculiar fact that the maximum pressure exerted
by a particular vapor in a closed space is independent of
the pressure of other vapors that may be present. In other
words, the quantity of vapor required to produce saturation
in a given space is the same whether that space is a vacuum
at the beginning or is occupied by other vapors.
244. Unsaturated Vapors. When the vapor present in
a given space is not enough to produce the condition of
saturation, i.e. to produce the maximum vapor pressure at
that temperature, the vapor is called unsaturated vapor.
This will always be the case in a closed space in which an
insufficient quantity of liquid is placed. On the other
hand, when a vapor is kept in contact with its liquid, it is
always saturated. For example, the vapor above a liquid
in a tightly corked bottle is saturated, and evaporation
cannot occur; but when the bottle is open, the vapor
is always slightly unsaturated, and therefore a continual
change of the liquid into a vapor takes place.
245. Atmospheric Humidity. Since evaporation of water
is always taking place at the surface of lakes, rivers, and
other bodies of water, and also from the soil and vegetation,
there is always more or less water vapor present in the
atmosphere. That this is the case may be shown by the
following experiment:
Fill a polished vessel or a glass beaker with ice water, and allow it
to stand exposed to the air. In a short time drops of moisture will be
seen forming on the exterior surface of the vessel.
Ordinarily the air does not contain saturated water
vapor. But since the quantity of vapor necessary to pro-
duce the condition of saturation in a given space is less at
low temperatures, the air in contact with the cold vessel
240 A HIGH SCHOOL COURSE IN PHYSICS
soon reaches a temperature at which the water vapor
already present becomes saturated. When the tempera-
ture is reduced below the point at which the water vapor
is saturated, the vapor is condensed, and moisture is de-
posited upon the cold surface of the vessel. The tempera-
ture at which moisture begins to form from the atmospheric
water vapor is called the dew-point.
We think of the air as being dry or moist (i.e. arid or
humid) according as we feel that it contains little or much
water vapor. These conditions of the air, however, involve
(1) the amount of vapor actually present and (2) the quantity
necessary to produce saturation under the given conditions.
It is upon the relation of these two elements that the sen-
sations of dry ness and moisture depend. The condition of
the air, in regard to the water vapor which it contains^ is
expressed by the ratio of the mass of water vapor in a given
volume of air to the mass of vapor required to produce the
condition of saturation at the same temperature* This ratio
is called the relative humidity of the air. For example, if
the quantity of water vapor actually present in a given
space is 15 grams, and the amount required to produce
saturation at that temperature is 20 grams, the relative
humidity is f , or 75 % -
If air containing water vapor is caused to undergo a
decrease of temperature, the relative humidity increases
since the cool air is nearer to its point of saturation. If
the cooling is carried far enough, moisture which we call
dew is deposited on solid objects. The experiment of the
beaker of ice water described above is an illustration of
this effect. If the temperature at which the moisture is
deposited is below C., it is frozen as fast as it is formed
and is called frost. Similarly, when any region of the air
cools below the dew-point, particles of water produced by
slow condensation collect about dust particles and produce
HEAT: TRANSFERENCE AND TRANSFORMATION 241
fogs and mists. When a condensation takes place at high
altitudes, clouds are formed. The slowly falling cloud
particles may unite to produce a drop of rain. In cool
seasons condensation may take place at temperatures
below the freezing point. In this case the result is snow,
sleet, or hail.
246. Ebullition. It has already ( 243) been stated
that the saturation pressure (maximum vapor pressure) of
water increases with the temperature. While at 10 C. it
is only 9.16 millimeters of mercury, at 90 C. it is 525 milli-
meters, and at 100 C., 760 millimeters. It is clear, there-
fore, that at some definite temperature (viz. 100 C. for
water) the maximum vapor pressure must be equal to a
pressure of one atmosphere, or 760 millimeters. At this
temperature the average speed of the molecules of the
liquid becomes so great as to render the cohesive force be-
tween them unable longer to retain them. Hence small
groups of molecules nearest the heated areas assume
greatly enlarged volumes (bubbles) within which practi-
cally no cohesion exists, because of the vastly increased
distance between the particles. Thus at this temperature
ebullition, or boiling, takes place. This phenomenon is
marked by the formation of bubbles of saturated vapor
that rise to the surface and burst. The temperature at
which this condition of the liquid is reached is the boil-
ing point of the liquid.
247. Laws of Ebullition. 1. Fit a 2-hole rubber stopper in a
test-tube. Thrust a thermometer through one of the holes and an open
glass tube through the other. Place a small quantity of sulphuric
ether in the test-tube, and hold it in a vessel of water at a temperature
of about 70 C. Soon the ether will begin to boil, and the thermome-
ter will indicate a steady temperature of about 35 C. (CAUTION.
On account of the high inflammability of ether vapor, the tube con-
taining it should not be brought near a flame.) Place a finger over
the end of the open glass tube, and thus carefully allow the pressure
17
242 A HIGH SCHOOL COURSE IN PHYSICS
of the ether vapor to increase. The boiling point will he observed to
rise several degrees.
2. Let a round-bottomed flask be half filled with water, and the
water boiled for two or three minutes to
enable the steam to expel the air. Close
the flask with a rubber stopper, and in-
vert it on a stand, as shown in Fig. 178.
Although the temperature of the water
will fall rapidly, the water can be made
to boil vigorously by pouring cold water
upon the flask.
3. Set a beaker of water at 90 C. or
less under the receiver of an air pump
and begin to exhaust the air. The
FIG. 178. Water Boiling water will boil vigorously as long as the
under Reduced Pressure. pres sure is kept sufficiently reduced.
The experiments just described illustrate the following
general laws of ebullition :
(1) Every liquid has its own boiling point, which is in-
variable under the same conditions.
(2) The boiling point of a liquid rises or falls as the
pressure upon the liquid increases or decreases.
The cold water poured upon the flask containing steam
causes a portion of the vapor to condense. This reduces
the pressure within the flask, thus lowering the boiling
point to the temperature of the water. If the air has been
very thoroughly expelled from the flask, the water may be
kept boiling until it is scarcely lukewarm.
Because of the decrease of atmospheric pressure with
an increase of altitude, the boiling point of water at
Altman, Colo., probably the highest town in the United
States, is about 88. 5 C. Cooking processes at such
heights are frequently accompanied by many difficul-
ties. In a steam boiler, however, where the pressure is
125 pounds per square inch, the boiling point of water
reaches 170 C.
HEAT: TRANSFERENCE AND TRANSFORMATION 243
Solid substances dissolved in a liquid raise its boiling
point. A saturated solution of common salt boils at about
109 C. But the vapor rising from boiling brine is pure
water vapor and condenses at 100 C. under an atmospheric
pressure of 760 millimeters.
TABLE OF BOILING POINTS
Pressure 760 millimeters
Ether. 35 C.
Chloroform .... 61 C.
Alcohol . 78.2 C.
Benzine 80 C.
Turpentine 160 C.
Mercury ' 350 C.
248. Distillation. When a liquid is vaporized in one vessel and
the vapor afterwards condensed in anoth'er, the process is known as
distillation. By this pro-
cess pure water can be ob-
tained from water contain-
ing dissolved substances.
and other foreign matter.
The liquid to be distilled is
placed in a vessel A, Fig.
179, and boiled. The va-
por is conducted through
the tube B, which is sur-
rounded by a larger tube
C containing a stream of
cold water. The vapor is
condensed on the cold walls of the small tube, and the resulting liquid
runs out at the lower end into the vessel D.
If two liquids are mixed together and heated in vessel A, the
one having the lower boiling point will be vaporized first. Its vapor
can be condensed and- collected in a separate vessel D. Alcohol is
thus separated from fermented liquors, and gasoline and kerosene
from crude petroleum.
249. Heat of Vaporization. Fill a glass flask about half full
of water, and place it over a flame to boil. Suspend one thermometer
in the liquid and another a little above it. While the water is boiling,
read both thermometers. They will continue to read practically alike.
FIG. 179. Illustrating the Process of
Distillation.
244
A HIGH SCHOOL COURSE IN PHYSICS
Continue to apply heat until it is evident that the temperature of the
water and steam is not raised above the boiling point.
The experiment shows clearly that the heat applied to
the flask is not utilized in raising the temperature of the
water or of the steam. As in the process of melting a solid
( 238), heat is here transformed from kinetic into poten-
tial energy while changing the molecular condition of the
water. For every gram of water vaporized a definite
quantity of heat disappears. The amount of heat required
to change a gram of any liquid at its boiling point into vapor
at the same temperature is called the heat of vaporization 1 of
that liquid. It represents the work that has to be done in
producing a separation of the molecules of the liquid
against their mutual attractions.
When condensation, the reverse of vaporization, takes
place, an amount of energy equal to the heat of vaporiza-
tion is given up by the condensing vapor. Thus the
quantity of heat required to vaporize a certain mass of
water at 100 C. is all delivered up
by the steam when it returns to the
liquid state.
250. Heat of Vaporization of Water
Measured. The heat of vaporiza-
tion of water can be readily meas-
ured by allowing a known mass of
steam to condense in, and deliver
its heat to, a known mass of water.
Allow steam from a flask of boiling
water, Fig. ISO, to p'ass through a tube into
a beaker containing, say, 400 grams of cold
water. A trap T should be introduced in
Water. cold water. During the experiment note
1 Sometimes called "latent" heat of vaporization.
HEAT: TRANSFERENCE AND TRANSFORMATION 245
the initial and final temperatures of the water. From 5 C. to 35 C.
is a good range over which to work. The mass of steam condensed
is found by ascertaining the gain in the mass of water in the beaker
during the process.
For example, let the initial temperature of the water in an experi-
ment be 5.6 C., the final temperature 35 C., and let the mass of
water at the beginning be 400 grams, and at the close 419.5 grams.
Let x be the heat of vaporization of water.
The heat gained by the cold water = 400 (35 - 5.6) calories.
The heat lost by the 19.5 grams of
water which was formed by the
condensed steam on cooling from
100 C. to 35 C. = 19.5 (100 - 35) calories.
The heat delivered by the steam at
100 C. in changing to water at
100 C. = 19.5 x calories.
Hence, 19.5 x + 19.5 (100 - 35) = 400 (35 - 5.6) ;
whence, x 538 calories.
The heat of vaporization of water accepted by physicists
is 536 calories."
251. Artificial Ice. Certain substances that are gases under
ordinary conditions of temperature and pressure become liquids when the
pressure is sufficiently increased. This is the case of ammonia gas, the
gas that is given off from common aqua ammonia. The pressure re-
quired to liquefy this gas under ordinary temperatures is about 10
atmospheres, or 150 pounds per square inch. On the other hand,
liquefied ammonia returns to the gaseous state when the pressure is
reduced, and for each gram that vaporizes a quantity of heat equal to its
heat of vaporization ( 249) is abstracted from its surroundings. Upon
these principles is based the operations of the artificial-ice machines
in common use.
An artificial-ice machine consists of three .essential parts : (1) the
compressor, (2) the condenser, and (3) the evaporator. See Fig. 181.
The compressor is a pump which is run by an engine or motor whose
function is to force ammonia gas under a pressure of about 10 atmos-
pheres into the coils of the condenser C. Here the gas liquefies and
gives up heat to the surrounding water which carries it away. From
the condenser coils the liquefied ammonia passes through the regulat-
ing valve V into the coils of the evaporator E, where the pressure is
246
A HIGH SCHOOL COURSE IN PHYSICS
kept below two atmospheres by the continual removal of ammonia gas
by the compressor. The rapid vaporization of the liquid ammonia
under the reduced pressure in these coils causes it to take heat from
the surrounding brine. By this abstraction of heat the temperature
of the brine is reduced to a point several degrees below the freezing
point of water.
FIG. 181. Artificial Cooling and Ice-making Apparatus.
In the production of ice the evaporator E is so constructed that
metal vats of pure water of the desired size can be- lowered into the
cold brine and left until frozen. These vats are then withdrawn from
the brine, and the ice removed to some place of storage.
The artificial cooling of storage rooms is brought about by cooling
brine, as in the manufacture of ice. From the evaporator the cold
brine is forced through coils of pipe placed about the walls of the
rooms to be cooled. Inasmuch as there is no chance for the ammonia
to escape, it can be used repeatedly with very little loss. The pres-
sures are controlled by the regulating valve and may be read at any
time from the gauges placed as shown in the figure.
EXERCISES
1. Explain the formation of moisture on the interior surface of
windows.
2. The temperature of blades of grass and leaves of trees falls
rapidly on cloudless evenings. What has this to do with the forma-
tion of dew ?
3. Does heating the air in a room remove the water vapor ? Why
is the air in an artificially heated room usually " dry " ?
SUGGESTION. It is shown in 245 that the dryness of the air does
HEAT: TRANSFERENCE AND TRANSFORMATION 247
not depend wholly upon the water vapor present in a given space.
The student should try to write out in full the entire explanation.
4. Heat a beaker of water over a flame, and observe that small
bubbles rise to the surface long before the boiling point is reached.
Compare this with the phenomenon of boiling.
5. When steam is allowed to flow through a tube into cold water,
a loud sound is produced. Explain.
6. What becomes of the cloud that one sees near the spout of a
teakettle ? Is it steam ?
7. Will clothes dry more quickly on a still or a windy day?
Why?
8. How much heat is required to raise the temperature of 30 g.
of water from C. to 100 C. and convert it into steam?
9. If 50 g. of steam at 100 C. change into water at 40 C., how
much heat is given out ?
10. If the heat delivered by 10 g. of steam in condensing at
100 C. and cooling down to C. were all applied to ice at C., how
many grams of ice would be melted? Am. 79.5 g.
11. A vessel containing 600 g. of water at 20 C. is heated until
it is one half vaporized. How many calories have been received ?
12. The boiling point "of water falls 1 centigrade degree for a de-
crease in pressure of 2.7 cm. Find the boiling point when the
barometer reads 74.5 cm.
13. The boiling point of water falls 1 centigrade degree for an
elevation of 295 m. above sea level. Find the temperature of boiling
water at Denver, Colo., altitude 1600 m. above sea level.
14. If water boils at 85.5 C. at the top of Mont Blanc, what is the
altitude?
15. If 20 g. of steam at 100 C. are passed into 500 g. of water at
5 C., what will be the resulting temperature? Ans. 29.2 C.
16. How much heat will be required to convert 150 g. of ice at
C. into steam at 100 C. ?
2. THE TRANSFERENCE OF HEAT
252. Three Modes of Heat Transmission. Heat is trans-
ferred from one point to another in three different ways ;
viz. by conduction, convection, and radiation. By conduc-
tion, heat passes through the metal walls of a stove or along
a metal rod from heated regions toward cold ones. By
248 A HIGH SCHOOL COURSE IN PHYSICS
convection, the currents of air set up by a hot stove trans-
fer heat to the distant parts of the room. By radiation,
energy from the sun reaches the earth ; and, by this pro-
cess, the hands held before the fire in an open grate or
near a hot stove become warm.
253. Conduction. The conduction of heat is simply the
transference of molecular motion from those portions of a
body where such motion is greatest to those where the mo-
tion is less, i.e. from the warmest parts of a body to colder
parts, without producing any sensible motion in the inter-
vening parts. The facility with which the conduction of
heat takes place varies widely with the nature of sub-
stances.
Join together three similar bars of copper, brass, and iron as shown
in Fig. 182, and heat the junction in a flame for several minutes. By
sliding the tip of a sulphur match from the
cold end of each bar toward the flame, ascer-
tain at what point it ignites. In this manner
it may be shown that the copper has conducted
heat the farthest from the source and is, conse-
quently, the best conductor. The iron will
prove to be the poorest conductor of the three
metals.
Make tests by using a piece of glass tubing,
FIG. 182. Testing the the stem of a clay pipe, a piece of crayon, etc.
Conductivity of These substances will be found to conduct very
Metals " poorly.
254. Liquids and Gases Poor Conductors of Heat. The
conductivity of a liquid can be tested as follows :
Through a cork fitted in the neck of a glass funnel pass the tube
of a simple air thermometer (Fig. 170), as shown in Fig. 183. Fill the
funnel with water until the bulb is covered by about half an inch of
the liquid. Pour about a spoonful of ether upon the water and ignite
it. Although the flame is at all times separated from the bulb of the
thermometer by only a thin layer of water, the liquid in the tube will
remain stationary.
HEAT: TRANSFERENCE AND TRANSFORMATION 249
The experiment shows clearly that water is a very poor
conductor of heat. Its conductivity is less than
of copper. In general, all liquids,
except mercury and other metals
in a molten state, are to be classed
as poor conductors.
Gases have a lower conductivity
than liquids. For this reason many
substances, as wool, which inclose
a large amount of air are poor con-
ductors and are therefore used ex-
tensively in the manufacture of
winter garments. Such articles of
clothing owe their warmth to the
fact that they prevent the loss of
the natural heat FIG. 183. Testing the Con-
oft he body. ductivity of Water.
Winter wheat and fruit trees are pro-
tected in a similar manner by a de.ep
covering of snow. A flannel " holder "
prevents the transference of heat from
the flatiron to the hand, and a piece of
ice wrapped in a woolen blanket is
shielded from the heat of the atmos-
phere. ^
255. Convection. Heat is trans-
ferred in liquids and gases by the pro-
cess of convection^ i.e. by a general mass
movement of the heated portions away
from the source of heat.
FIG. 184. The Con-
vection of Heat by
Water.
1. Pass the ends of a glass tube, bent as
shown in Fig. 184, through a rubber stopper
fitted to the neck of a bottle from which the
bottom has been removed. Fill the apparatus
250 A HIGH SCHOOL COURSE IN PHYSICS
with water, and place a small quantity of oak sawdust in the liquid to
serve as an index of the motion. If a flame is moved back and forth
between the points A and B, it
will be seen that a current is set
up in the direction from A to-
ward B. In a short time the en-
tire mass of water in the reservoir
C will become hot.
2. Make two openings in the
side of a crayon box, as shewn
in Fig. 185. Set a short candle
over one hole, leaving an opening
into the box. Set a lamp chim-
FIG. 185. Convection Currents in Air.
ney over each hole and attach it
to the box by means of melted candle wax. Light the candle and then
hold some burning paper above chimney A . It will be observed that the
flame and smoke of the burning paper will be drawn downward, thus
showing the direction of the draft of air. At the same time heat is
transferred upward from chimney B by the convection currents of the
hot gases.
256. Convection Explained. Convection is brought
about by the expansion of fluids (i.e. liquids and gases)
when heated. When a portion of the fluid is warmed, its
volume increases, thus decreasing the density of the fluid.
This portion of the body of the fluid is then forced upward
in a manner similar to that in which a submerged piece of
cork is forced up by water. (See 121.) As the heated
portions of the fluid rise, they carry their heat with them,
and colder portions flow in to replace them. Convection
currents are applied to the heating of buildings with hot
air and hot water arid to mine ventilation. The trade-
winds and the Gulf Stream are convection currents of
enormous proportions.
257. A Hot-air Heating System. Figure 186 shows the
method employed in heating a house by means of hot air.
A furnace is placed in the cellar and supplied with fresh
air through the duct A leading to the heating chamber c, c.
HEAT: TRANSFERENCE AND TRANSFORMATION 251
Here the air is heated and thence conducted through large
pipes to the various rooms of the building. A large part
of the air thus led
into the rooms finds
an outlet around the
windows and doors.
Sometimes provision
is made for its escape
into a cold-air flue
leading through the
roof. A cold-air duct
B is often introduced
for the purpose of re-
conducting the par-
tially cooled air to
the furnace, where it
is again heated and
sent into the rooms.
For good ventilation,
however, an abundant supply of fresh out-door air should
be admitted to the system at A. The circulation of air
is indicated by the arrows. The fire in the fire-box is
controlled by dampers. These are often regulated by
chains extending to a room above, and shown here by the
dotted lines.
258. A Hot- water Heating System. A hot- water system
of heating depends upon convection currents produced as
shown in Experiment 1, 255. Water is raised nearly to
the boiling point in a heater H, Fig. 187, placed in the
basement. From the heater it is conducted through pipes
to iron radiators R placed in the various rooms of the
building, while the cooler water from the radiators is led
in return pipes back to the heater. Thus a continuous
current of water is maintained until the pipes are closed by
FIG. 186. Hot-air Heating System.
252
A HIGH SCHOOL COURSE IN PHYSICS
valves placed near the radiators. On account of the large
exposed surface in each radiator, the heat emitted by the
hot water is transferred to
the surrounding air. In or-
der to prevent the radiation
of heat from the conducting
pipes, a thick covering of as-
bestos, a very poor conductor
of heat, is frequently pro-
vided. This plan of heating
affords no means of ventila-
tion.
259. Radiation. - - When
we stand before a hot stove
or a grate full of glowing
coals, we readily perceive that
the surface of the body near-
est the fire is rapidly heated.
FIG. 187. Heating a House by However, the intervening air
Means of Hot Water. . -. , ,
is not warmed as it would
be if the heat passed to us by conduction or convection.
Again, a room is frequently heated by the sun's rays, while
the glass through which the rays pass remains cold.
Plainly, the medium which transmits the heat energy in
these instances is not the air nor the glass. In order that
the phenomena just described and others of a similar na-
ture may admit of explanation, it is assumed by physicists
that all space is filled with an exceedingly light medium
called the ether. 1 The properties of the ether are such that
transverse wave motions are transmitted by it in a manner
somewhat similar to that in which the waves produced by
a falling pebble are carried along upon the surface of
1 The term must not be confused with " ether," which is a well-known
liquid and is used in several experiments.
HEAT: TRANSFERENCE AND TRANSFORMATION 263
water. Energy thus transmitted is called radiant energy,
and the process is called radiation. If this energy affects
the sense of sight, it is called light. When it falls upon
the hands, it produces warmth. Radiant energy becomes
real heat only as it falls upon matter which is capable of ab-
sorbing it and converting it into the energy of molecular
motion.
260. Absorption of Radiant Energy. The ability of a
body to radiate energy depends both upon its temperature
and the nature of its surface. Smooth and highly polished
bodies radiate poorly, while rough, black bodies radiate
well. On the other hand, bodies differ in their power to
absorb radiant energy. Those that radiate well also ab-
sorb well.
Nail two pieces of tin A and jB, Fig. 188, to a block of wood as
shown. Coat the interior surface of B with lampblack and attach a
match to the exterior surface of each with
melted paraffin. Now place a hot iron ball
midway between the plates. In a moment
the wax on B will soften, and the match will
fall. A
C:
The experiment clearly shows that
the blackened surface B absorJbs the
energy radiated by the ball faster than
xi * i_^ A rr r 1-1 i FlG - 188. The Black
the bright one A. If pieces of black surface B Absorbs
and white cloth are placed upon snow, Heat Better than the
Polished Surface A.
the rapid absorption of the radiant-
energy of sunlight will cause the black body to melt
its way into the snow. Since the white cloth reflects
and transmits the greater portion of the energy, little re-
mains to be converted into heat. This fact accounts for
the general use of light-colored clothing in summer and,
in part, for the stifling heat developed in attics under dark-
colored roofing.
254 A HIGH SCHOOL COURSE IN PHYSICS
261. The Radiometer. This interesting instrument,
Fig. 189, was invented by Sir William Crookes, 1 of Eng-
land, in 1873. It is used to detect radiant
energy. The instrument consists of a
glass bulb from which the air has been
almost exhausted and within which four
diamond-shaped mica vanes are delicately
pivoted on light cross arms. One face
of each vane is coated with lampblack.
When radiant energy falls upon these
vanes, a rotation is produced.
Since the blackened faces of the vanes
FIG. i89~^oke's absorb radiant energy, they are raised to
Radiometer. a higher temperature than the bright
faces. Thus the few remaining molecules of gas in the
bulb have their speed greatly quickened as they
come in contact with the black surfaces, and hence rebound
from these faces with a strong reaction. It is this reaction
that causes the vanes to move. The speed of rotation
depends upon the intensity of the radiation falling upon
the instrument.
262. Selective Absorption Of Bodies. Place a radiometer
near a lighted lamp and between them set a glass beaker. After the
rate of rotation of the vanes has become uniform, fill the beaker with
water. The rate of rotation will be greatly diminished. Repeat the
experiment, but fill the beaker with carbon disulphide. It will be
found to have little effect on the motion of the vanes. Substitute a
solution of iodine in carbon disulphide. Although nearly opaque to
light, the solution will be found to transmit the radiations perfectly.
Water, which is transparent to the short, or visible,
ether waves emitted by the lamp, transmits very poorly
the longer waves of a slower rate of vibration. Likewise,
glass transmits well the visible radiation (i.e. light) from
the sun, but retards effectively the longer waves emitted
1 See portrait facing page 466.
HEAT: TRANSFERENCE AND TRANSFORMATION 2,55
by the objects in a room. Substances like glass and water
which absorb long waves are called athermanous substances.
While the glass in a window admits light energy into a
room, the energy of the longer waves sent out from the
heated objects within is retained. The glass of a green-
house or hot-bed transmits well the energy of short waves
to the soil within, but the longer waves emitted by the
heated soil cannot escape. Hence the temperature rapidly
rises.
On the other hand, the carbon disulphide and the iodine
solution transmit well the waves of the ether that are far
too long to affect the sense of sight. Such substances are
called diathermanous substances.
263. The Sun as a Source of Heat. The process of
radiation plays an important part in everyday life. The
sun is continually sending out great quantities of radiant
energy in all directions in space. A small fraction of
this energy falls upon the earth's atmosphere, passes read-
ily through it without producing any appreciable change,
and reaches the earth's surface. Here a large part of the
energy of the ether waves is transformed into heat, i.e. is
absorbed. The earth also radiates heat; but being of a
low temperature, the waves emitted by it are longer.
Since the presence of water vapor in the atmosphere
renders it athermanous, the radiation of energy away
from the earth is greatly hindered.
It is the radiant energy from the sun converted into
heat that evaporates water, resulting in the production
of vapor and rain. Rains produce the flow of rivers and
thus give rise to the energy derived from waterfalls. The
wood we use and the food we consume owe their value to
the energy which they have stored up within them. This
they derive from the sunlight and warmth in which they
grow. Coal received its energy from the plants that
256 A HIGH SCHOOL COURSE IN PHYSICS
flourished under the solar radiation of past ages. It is
this energy that we utilize in warming our houses, cook-
ing our food, and that we convert into mechanical energy
through the help of the steam engine for running factories
and aiding transportation over both land and water.
EXERCISES
1. In the construction of brick and cement houses the walls are
often made hollow. Why?
2. Why does a piece of iron feel colder than a piece of wood when
both have, the same temperature?
3. What is the normal temperature of the blood on the centigrade
scale? of a living room?
4. Does woolen clothing supply the heat that maintains the tem-
perature of the body ?
5. Explain under what conditions a workman might be led to wear
woolen garments to keep himself cool.
6. Why are coverings of sheets of paper often sufficient to prevent
plants from freezing on frosty nights?
7. Why does dew seldom form on cloudy nights? Why are frosts
almost entirely prevented by the presence of clouds?
8. In a fireless cooker a kettle containing vegetables that have been
boiled a short time is surrounded by wool, felt, etc., and left a few
hours to complete the process of cooking. Explain.
9. The poor conductivity of glass causes a tumbler to crack when
hot water is poured into it. Explain. Why does not a thin glass
beaker crack from the same cause ?
3. RELATION BETWEEN HEAT AND WORK
264. Heat and Mechanical Energy. The experiments
made in section 212 show clearly that an intimate relation
exists between heat and work. The production of heat at
the expense of mechanical energy is one of the most com-
mon phenomena of nature. In fact, the energy expended
in nearly all mechanical processes passes finally to the form
of heat. An inquiry into the reverse transformation of
COUNT RUMFORD (SIR BENJAMIN THOMPSON)
(1753-1814)
The name of Rumforrl is prominent among the early physicists
who engaged in confuting the theory that heat was a substance.
His attainments as a soldier and public benefactor, however, are of
no less interest.
Thompson was born on a farm near Woburn, Massachusetts, and
as a young man was employed in teaching school. Having been
made a major in the local militia by the governor of New Hamp-
shire, he became the object of mistrust by the friends of American
liberty. On this account, in 1776 he removed to London. Here his
advance was rapid; within four years he became undersecretary of
state. In 1779 he was elected a member of the Royal Society. In
1783 he planned to aid the Austrians against the Turks, but while
on his way he met Prince Maximilian (afterwards elector of Bava-
ria), who induced him to enter the Bavarian military service. For
eleven years he remained at Munich as minister of war, minister
of police, and grand chamberlain to the elector. He reorganized
the Bavarian army, suppressed begging, provided employment for
the poor, and established schools for the industrial classes.
In 1791 Thompson was made a count of the Holy Roman Empire
and took the name of Rumford. In 1799 he was instrumental in
founding the Royal Institution of London and selected Sir Humphry
Davy as the first lecturer. In remembrance of the help that he
received in his early days from attending some lectures by Professor
Winthrop at Harvard, Thompson later gave an endowment which
founded the professorship that bears his name. His last years were
passed near Paris, where he died in 1814. His tomb is at Auteuil.
PIEAT: TRANSFERENCE AND TRANSFORMATION 257
FIG. 190. Water raised
by Heat Energy.
energy, i.e. from heat into mechanical energy, is an inter-
esting consideration.
Let a tube, bent as shown in Fig. 190, project through a rubber
stopper into a flask A half filled with water. The tube should extend
nearly to the bottom of the vessel. Heat the
water over a burner, and the water will be
elevated into a tumbler at B.
In this experiment work is per-
formed .upon the water, and heat is
converted into potential energy, which
is stored in the elevated water.
265. Early Historical Experiments.
In the early development of the
subject scientists looked upon heat as
a kind of material substance called
calbric. An important step toward ascertaining the true
nature of heat is found, in the experiments of Count Rum-
ford. 1 He showed that one horse used as a source of power
could develop sufficient heat by friction to raise 26.5 pounds
of water from the freezing to the boiling point in 2| hours.
About this time Sir Humphry Davy (1778-1829) showed
that two pieces of ice kept below the freezing point could be
melted by rubbing them together. The first, however, to
establish the relation between heat and work by expressing
one in terms of the other was James Prescott Joule 2
of Manchester, England.
266. Joule's Experiment. The method employed by
Joule to ascertain the exact relation between the calorie
and the unit of mechanical energy consisted in measuring
the heat produced by a definite quantity of work. The
heat under consideration was produced by the rotation of
paddles in a vessel of water C, Fig. 191. The work
done upon the water produced heat enough to raise its
1 See portrait facing page 256.
18
2 See portrait facing page 258.
258
A HIGH SCHOOL COURSE IN PHYSICS
\M
FIG. 191. Illustrating Joule's Method for
Determining the Mechanical Equivalent
of Heat.
temperature an appreciable amount. The rise in tempera-
ture being measured, the quantity of heat developed could
be computed as the
product of the mass of
water and its change
in temperature ( 231).
The paddles were
turned by two weights
IF, IF, attached to cords
so arranged as to ro-
tate the main shaft.
The work performed
by the paddles could be computed as the product of the
weights and the distance through which they descended
( 55). Thus the work corresponding to a calorie of heat
could readily be determined.
267. The Mechanical Equivalent of Heat. Joule's ex-
periments upon the relation of heat and work extended
over more than one half his life. They have been care-
fully repeated (1879) by Professor Rowland of Johns
Hopkins University, with apparatus of more refinement
and precision. As a result of these experiments the follow-
ing value of the calorie is generally accepted by physicists:
1 calorie = 427 gram-meters, or 41,900,000 ergs.
This result is known as the mechanical equivalent of
heat, or simply Joule's equivalent.
268. Conversion of Energy. The experiments per-
formed by Rumford, Joule, Rowland, and others, relative
to the conversion of mechanical energy into heat, serve to
verify the principle of the Conservation of Energy first
stated in 64. Ignorance of this great law of nature has
led men at all times, and even in this enlightened period,
to undertake to construct ^devices whereby useful work
JAMES PRESCOTT JOULE (1818-1889)
The attention of Joule was turned at an early age in the direc-
tion of physics and chemistry by the influence of his teacher, John
Dalton, the chemist. Under his tuition, Joule was initiated into
mathematics and trained in the art of experimentation. His renown
rests upon the thoroughness with which he established the doctrine
of the Conservation of Energy (64) upon an experimental basis.
His epoch-making experiments were made to determine the mechan-
ical equivalent of heat, which is recognized as one of the most im-
portant physical constants. Measurable quantities of energy were
expended in revolving paddles in water, mercury, and oil, and cast
iron disks were rotated against each other and the resulting quantity
of heat ascertained. The results of these experiments left no doubt
that the amount of heat produced by a definite quantity of mechan-
ical work is fixed and invariable. For this great scientific achieve-
ment Joule received the Royal Medal of the Royal Society of
England in 1852, and eight years later, when men of science more
fully understood the value of the discovery, he was presented with the
Copley Medal.
Joule was the son of a wealthy brewer of Manchester, England,
at which place he carried on his experiments. Important laws
relating to the heating of electrical conductors and valuable con-
tributions to the subject of electro-magnetism must also be accred-
ited to him. The joule, which is used as a unit of energy, has been
so named in his honor.
HEAT: TRANSFERENCE AND TRANSFORMATION 250
can be obtained without the expenditure of an equivalent
amount of energy of some form. Such devices, if possible,
would supply enough energy to keep their parts in motion
when once started, and are therefore called perpetual-motion
machines. Any attempt, however, to secure useful energy
from the wind, sunlight, ocean waves, tides, etc., is praise-
worthy, and should be encouraged. To some extent, such
efforts have not been fruitless. But since in the best ma-
chines that can be made some friction will exist, there will
be a continual conversion of a part of the energy supplied
to the machine into heat. If, therefore, energy is supplied
only in starting the machine, no matter how it is con-
structed, it is sure to come to rest. Consequently, a ma-
chine at best can only transfer or transform the energy
with which it is supplied.
The transformation of mechanical energy into heat is
easily accomplished. .For example, a bullet is warmed by
its impact with a target, mercury can be warmed by being
shaken vigorously in a bottle, a mass of shot will rise in
temperature if allowed to fall several feet, a button grows
hot when rubbed upon a piece of flannel, etc. The reverse
transformation, i.e. from heat into mechanical energy, is
not, however, so readily effected. The process, neverthe-
less, is accomplished in steam and gas engines by making
use of certain properties of gases.
269. Gases Heated by Compression and Cooled by Expan-
sion. We have seen in 212 that the energy used in com-
pressing a gas is converted into heat. On the other hand,
when a gas is allowed to expand against pressure and perform
work, heat is given up and the temperature of the gas falls.
In other words, molecular energy is expended by the gas
when it does work. In order to utilize this process in
converting heat into useful work, the gas is allowed to ex-
pand in a cylinder and thus move a piston P, Fig. 192.
260
A HIGH SCHOOL COURSE IN PHYSICS
It is clear that, in the case illustrated, the gas performs
work in raising the weight W to a higher position. A
modification of this process is employed in all
\w\ steam and gas engines.
270. The Reciprocating Steam Engine. The
essential parts of an ordinary steam engine are
the cylinder, the piston, and the slide-valve
mechanism, represented diagram matically in
Fig. 193. The gas employed is steam gener-
ated by the combustion of fuel. A to-and-fro
motion is given to the piston P by the force
FIG. 192. By exer ted by the steam which is applied to its
Piston Pa two faces alternately. The operation is as fol-
Gas Doe S1
Work on
the Weight
W.
Steam under a pressure of several atmospheres (i.e.
100 to 250 pounds per square inch) enters the steam
chest S from the boiler. From S the steam finds an entrance into the
cylinder through the port N and drives the piston to the left, forcing
any gas that may be contained in the space C"
through the port M and out of the engine through
FIG. 193. Section of the Steam
Engine.
the exhaust pipe E. The motion of the piston is communicated to the
main shaft A through the connecting rod R and the crank D. As the
piston approaches the left end of the cylinder, the sliding valve V is
moved to the right by the eccentric F and the eccentric rod R', thus
HEAT: TRANSFERENCE AND TRANSFORMATION 261
admitting " live " steam through M into the cylinder chamber C", and
opening the port N to allow the expanded steam to escape. The
piston is now driven back to the right, and the sliding valve V is forced
back to its former position just before the piston reaches the end of
its stroke as at first. The operations just described are then repeated.
The shaft of the engine is provided with a heavy fly wheel E in order
to maintain uniformity of speed.
In the so-called non-condensing or high-pressure engines the exhaust
steam escapes through the exhaust pipe E into the open air. The pis-
ton of such an engine therefore moves continually in opposition to the
pressure of the atmosphere. This disadvantage is partially removed
in condensing engines. In engines of this type the exhaust pipe E
conducts the exhaust steam to a condensing chamber in which a
spray of cold water hastens its condensation. By the aid of a pump
operated by the engine, the water together with the condensed steam
is removed from the condensing chamber, leaving a back-pressure of
only a few ounces per square inch instead of one atmosphere. Thus
by decreasing the back-pressure against the piston, a larger quantity of
useful work can be obtained from the steam, and the efficiency of the
engine correspondingly increased. Condensers are not used on loco-
motives (1) because of the large supply of cold water necessary and
(2) because of their inconvenient size.
271. The Gas Engine. With the development of the automo-
bile has come that of the gas engine as a source of power. To this
class of machines belong all engines utilizing an explosive mixture of
gases as the working agent, such as air and illuminating gas, or air
and gasoline vapor. The operation of the so-called " four-cycle " gas
engine in common use is shown in Fig. 194.
C is a cylinder within which moves the piston P. The piston is
connected with the crank B by means of the rod A. Upon the crank
shaft D is mounted a heavy fly wheel W, which is set in motion by
the hand on starting the engine. When the piston moves downward
to the position shown in (1). an explosive mixture of gas and air is
drawn into the cylinder through the inlet valve I. As the motion
continues, the piston moves upward and compresses the mixture in
the top of the cylinder, as shown in (2). At about the instant the
piston reaches the highest point, as in (5), an electric spark at the
spark-plug S ignites the gas; an explosion ensues, with the produc-
tion of much heat, and the expanding gases exert an enormous pres-
sure on the top of the piston. This forces the piston violently down-
262
A HIGH SCHOOL COURSE IN PHYSICS
ward, giving motion, and hence kinetic energy, to the heavy fly wheel
W. On the next upward stroke the products of the combustion of the
gas are driven out of the cylinder through the exhaust valve, as shown
in (4). This valve is opened automatically at the proper instant.
The piston having traversed the length of the cylinder four times, the
FIG. 194.
(2) ('3)
Operation of a Four-cycle Gas Engine.
initial conditions are restored, and the operations are repeated. It is
obvious that the fly wheel must be made heavy, since the energy given
it during the third stroke of the piston has to keep the engine and ma-
chinery in motion with almost constant speed during the three fol-
lowing strokes of the cycle.
When gasoline is used as fuel, the inlet pipe 7 leads from the " car-
buretor," into which the liquid enters as a spray, vaporizes, and is
mixed with the proper amount of air. In order to prevent undue
heating of the cylinder and piston, a current of water is kept in circu
lation through cavities cast in the walls of the cylinder. Some manu-
facturers supply so-called " air-cooled " engines, the cylinders of which
are cooled by the circulation of air about their exterior surface. In
this instance the cylinder is cast with numerous projections for the
purpose of increasing as much as possible the amount of radiating
surface.
HEAT: TRANSFERENCE AND TRANSFORMATION 263
On account of the lightness and compactness of the engine, and the
small space occupied by the fuel, gasoline engines are extensively used
to propel automobiles, in which motors of from one to six cylinders
may be seen. Such engines are also widely used in launches, dirigible
balloons, aeroplanes, pumping stations, machine shops, factories, etc.,
on account of the small attention required in their operation.
272. The Steam Turbine. In the common reciprocating form
of the steam engine a large amount of energy is lost in stopping and
starting the piston and connecting rods at the end of each stroke. It
(2)
FIG. 195. Principle of the Steam Turbine.
is only within the last few years that inventors Have succeeded in
'designing efficient engines of the purely rotary type. The operation
of a steam turbine is as follows :
Steam under high pressure is conducted through a series of stationary
jets A, (/), Fig. 195, arranged in a circle, which directs it obliquely
against a series of blades B which are attached to a rotating drum,
called the rotor. The rotor is fastened to the main shaft of the engine.
By the impact of the steam these movable blades are impelled in an
upward direction and thus produce rotation. (2), Fig. 195, shows the
arrangement of several series of movable and stationary blades used
in the more powerful turbines. Each movable blade is a curved pro-
jection attached to the exterior surface of the rotor ; each stationary
blade is fastened to the interior surface of the metal case surrounding
the rotor. The concave surfaces of the two sets of blades are turned
264 A HIGH SCHOOL COURSE IN PHYSICS
opposite to each other as shown. The number of series used will vary
largely in turbines of different power. After the steam has passed
through the first series of movable blades B, a series of blades C,
which are stationary, serves to direct it at the proper angle against
the next series of movable blades D, and so on through the entire
turbine.
The steam turbines will find extensive use in ocean-going steamships
on account of the fact that they are free from the objectionable vibra-
tion that always accompanies engines of the reciprocating form. At
the present time they are replacing the ordinary steam engine in the
generation of electrical power, and in a few years, no doubt, will be
found wherever energy is to be derived from steam.
EXERCISES
1. Explain how the energy contained in coal can be utilized in
performii^g work.
2. What energy other than that of coal is often employed in run-
ning factories, etc. ?
3. The heat developed by the combustion of a gram of coal of a
certain grade is 5000 calories. How many kilogram-meters of work
could be done if all the energy could be used for this purpose ?
4. If all the potential energy stored in a 500-kilogram mass of
rock at an elevation of 200 m. were converted into heat, how many
calories would be produced ?
5. The energy of a falling body is transformed into heat when it
strikes. Compute the number of calories of heat produced when a
10-gram mass of iron falls 25 m.
SUGGESTION. Compute in gram-meters the energy of the given
mass at an elevation of 25 m., then reduce to calories.
6. A steam engine raises 8000 four-pound bricks to the top of a
building 75 ft. high. How many calories of heat are thus expended ?
If the efficiency of the engine is 10 % ( 100), how many calories must
be developed by the combustion of the coal that is used?
7. How high could 100 g. of ice be elevated by the amount of heat
required to melt the same amount, if all the heat could be utilized for
that purpose?
8. Show that the energy required to vaporize 1 g. of water at
100 C. is equivalent to the work done by a force of 10 kg. in moving
a body a distance of 22.89 m. in the direction of the force.
9. Show that it requires more energy to raise the temperature of
HEAT: TRANSFERENCE AND TRANSFORMATION 265
100 g. of iron from C. to 100 C. than to elevate a weight of 400 kg.
through a height of 1 m.
10. The average pressure of the steam in the cylinder of an engine
is 125 Ib. to the square inch and the area of the piston is 50 sq. in.
Compute the work done by the steam during each 20-inch stroke of the
piston.
11. If the mechanical equivalent of the calorie denned in 231 is 3.1
foot-pounds, compute the heat units lost by the steam in Exer. 10 at
each stroke of the piston.
12. At what rate does a 2-horse-power engine consume coal when
working at its full capacity, if its efficiency is 10 % and the coal pro-
duces 5500 calories per grain ?
SUMMARY
1. The state of a body depends largely on its temper-
ature. The temperature at which a solid changes to a
liquid is its melting or fusing point. Definite laws gov-
ern the fusion of all crystalline bodies ( 234 to 236).
2. The process of liquefaction is accompanied by an
absorption of heat. Molecular kinetic energy (heat) is
converted into molecular potential energy in the process.
The heat of fusion of a substance is the number of calories
per gram required to liquefy it without changing its tem-
perature. The heat of fusion of ice is 80 calories. Non-
crystalline substances when heated pass through a plastic
state and have no definite melting point ( 237 and 238).
3. When a liquid solidifies, an amount of heat equal
to the heat of fusion is given up for each gram ( 239).
4. ^Evaporation may take place at any temperature.
It is a process by which many of the more rapidly moving
molecules of a body become detached and pass into the
surrounding space. The gas composed of these detached
molecules is called a vapor ( 240 and 241) .
5. The rate of evaporation of a liquid varies with the
amount of exposed surface and its temperature, and is de-
266 A HIGH SCHOOL COURSE IN PHYSICS
creased by the presence of the vapor of the liquid in the
space around it ( 242).
6. When the number of molecules leaving a liquid per
second equals the number reentering it, the vapor is satu-
rated. Its pressure at this time is called the maximum va-
por pressure at that temperature ( 243).
7. The quantity of a given vapor required to produce
saturation in a given space is the same whether the space
is occupied by other vapors or not. This quantity de-
pends, however, on the temperature ( 243 and 244).
8. On account of the abundance of water, the atmos-
phere always contains more or less water vapor. The
temperature to which air would have to be reduced to
cause moisture to form is called its dew-point ( 245).
9. The relative humidity of the air is the ratio of the
amount of water vapor present in a given volume to the
amount required to produce saturation at that tempera-
ture ( 245).
10. Every liquid has its own boiling point, which is in-
variable under the same conditions. This point rises or
falls according as the pressure upon the liquid is increased
or decreased ( 246 and 247).
11. The heat of vaporization of a liquid is the number
of calories required to convert 1 g. of it at its boiling point
into vapor at the same temperature. The heat of vapori-
zation of water is 536 calories. This amount of heat is
given up by the vapor when it condenses ( 249 and 250).
12. Heat is transferred by conduction, convection, and
radiation. Substances are classed as good and poor con-
ductors of heat. In general, liquids (except liquid metals)
and gases are poor conductors ( 252 to 254).
13. Liquids* and gases transfer heat by a general mass
HEAT : TRANSFERENCE AND TRANSFORMATION 267
movement of the heated portions away from the source of
heat, i.e. by convection. Convection is the result of the
expansion which accompanies a rise in temperature.
Heating systems depend on the convection of heat by air,
steam, or hot water ( 255 to 258).
14. Radiation is the process in which energy is trans-
ferred by ether waves. The energy of these waves is trans-
formed into heat when absorbed by bodies. The best
radiators and absorbers are rough, black bodies. The sun
is our great source of energy. This energy we receive
through the process of radiation ( 259 to 263).
15. Heat may be made to perform work. One calorie
is equivalent to 427 gram-meters, or 41,990,000 ergs. This
result is known as Joule's equivalent, or the mechanical
equivalent of heat ( 264 to 267).
16. Heat energy is transformed into mechanical energy
in steam and gas engines. A gas does work in expanding
against a movable piston. As a result of the work done,
the temperature of the working gas is lowered ( 268
to 272).
CHAPTER XIII
LIGHT: ITS CHARACTERISTICS AND MEASUREMENT
1. NATURE AND PROPAGATION OF LIGHT
273. Meaning of the Term "Light." -Just as sound is
defined as undulations in the air, or some other medium,
that produce the sensation which we call " sound," so light,
in the same sense, consists of undulations or waves in the
ether that produce the sensation which we often call by
the name "light." (See 259.) Not all ether waves can
be regarded as light waves, since not all affect the organ
of sight; but all ether waves, from the longest to the
shortest, transfer energy, and therefore may properly be
classed as carriers of radiant energy.
274. The Ether and Ether Waves. The theory that
light is wave motion in the ether was advocated by the
Dutch physicist Huyghens (1629-1695) in 1678. The
theory, however, was not well established until the begin-
ning of the nineteenth century, when the experiments by
Thomas Young of England and Fresnel of France placed
it on a firm basis. Ether fills all interstellar space as well
as the spaces between the molecules in bodies of matter.
The ether is also of extreme rareness, or tenuity, since
planets passing through it suffer no appreciable retarda-
tion in their orbits.
Ether waves possess several well-known characteristics.
They are transverse waves and are propagated with a defi-
nite speed, and this speed becomes less when they pass
through matter such as glass, air, water, etc. Ether
waves may be reflected, transmitted, bent from their
LIGHT: CHARACTERISTICS AND MEASUREMENT 269
courses, or their energy may be transformed into other
forms than radiant energy.
Ether waves that produce an effect upon the sense of
vision vary in length between about 0.00004 and 0.00008
centimeter. Hence our sense of sight, with its narrow lim-
itations, does not enable us to perceive directly ether waves
which are shorter than the former of these two numbers or
longer than the latter.
275. Speed of Light. An achievement of great scien-
tific importance was the discovery that light travels with a
definite speed. Previous to the year 1676 it was supposed
that light moved infinitely fast, because no one had found
a way to measure so great a velocity. In that year the
Danish astronomer Roemer (16441710), as the result of
several months' work with the instruments at the Observa-
tory of Paris, correctly inferred that the time required for
light to traverse the- diameter of the earth's orbit (about
186,000,000 miles) was almost 1000 seconds. Roemer was
led to this conclusion
after making a series
of observations upon
the eclipses of one of
the satellites of -the
planet Jupiter. At
each revolution of the ^ ^ ^
satellite s, Fig. 196,
in its orbit around
Jupiter J", it passes FIG. 196. Roemer's Method for Determining
behind that planet the Speed of Light,
into its shadow and becomes invisible from the earth at
E. By measuring the interval between two successive
eclipses of the satellite it was apparently possible to pre-
dict the precise time of each eclipse for many months in
advance. But when the earth was at E* ', on the opposite
Sk
270 A HIGH SCHOOL COURSE IN PHYSICS
side of the sun, the time of each eclipse of the satellite was
found to be about 1000 seconds later than predicted. In
order to account for this difference, Roemer advanced
the idea that this interval was precisely the time that
light requires to pass over the diameter of the earth's
orbit. On this assumption the speed of light is 186,000,000
-j- 1000, or 186,000 miles per second.
Recent measurements of the speed of light by different
methods continue to show that it is about 186,000 miles, or
300,000 kilometers, per second.
EXERCISES
1. The circumference of the earth is about 25,000 mi. How many
times could this distance be traversed by light in a second?
2. The distance of the north star from the eartli is so great that it
requires about 43 yr. for its light to reach the earth. Express the
distance in miles.
3. How many minutes are required for light to reach the earth
from the sun ?
4. Since the sun moves (apparently) through 360 in 24 hr., over
what arc will it move while a light wave is on its way from the sun to
the earth ?
2. RECTILINEAR PROPAGATION OF LIGHT
276. Light Travels in Straight Lines. Set up a small screen
about midway between a candle flame and the wall so that it casts a
well-defined shadow. Mark the edge of the shadow, and extinguish
the candle. Stretch a cord between the candle wick and the line mark-
ing the edge of the shadow, and it will be found to graze the edge of
the screen. Since the cord is straight, the course taken by the light
from the candle to the wall is a straight line.
Further evidence regarding the fact that light follows
straight lines may be obtained by observing the path taken
by a beam of light as it enters a partially darkened room
where the air contains dust. We unconsciously utilize
this important fact in many ways. In order that we may
see an object, light must come from that object to the eye ;
LIGHT: CHARACTERISTICS AND MEASUREMENT 271
and we always assume that the object sending the light to us
is located in the straight line which marks the direction of
the light as it enters the eye. The marksman trains his gun
along the line of direction of the light which comes from
the object he wishes to hit, and the carpenter selects a
straight piece of lumber by " sighting " along its edge.
We shall see later, however, that light deviates from a
straight line under certain conditions, but that the devia-
tion is ordinarily inappreciable.
277. Shadows. A. shadow is a space from which the light
from a luminous body is wholly or partially excluded by an
opaque body. The nature of a shadow depends both upon
the form of the opaque body and upon the form of the
source of light.
1. Hold an opaque body, as a book, between a very small source
of light, as an electric arc light, and a white wall or screen. A very
sharply outlined shadow will be produced upon the screen for all posi-
tions of the opaque body.
2. Place two electric arc lights about 15 centimeters apart in a
line parallel to a screen or wall, and produce a shadow, as in Experi-
ment 1. Two portions of the shadow are now easily distinguished,
viz. a dark central part and a partially illuminated area just outside.
The experiment may be performed with a single gas flame or by using
two oil lamps placed a few centimeters apart.
When the source of light L, Fig. 197, is small, and an
opaque body AB intercepts the light, a region of darkness
FIG. 197. Illustrating the Shadow Cast by a Sphere.
ABCD is produced behind it -as shown by the shading.
This space is the shadow of AB. It is obvious that the
272 A HIGH SCHOOL COURSE IN PHYSICS
form of the shadow may be found by drawing straight lines
from L just touching the edge of the object AB. If AB
is a sphere, it is clear that the form of the shadow will be
that of a truncated cone whose top rests against the
sphere.
When two sources of light L and L', Fig. 198, are
used, no light from the source L enters the region CABD 1 ,
FIG. 198. Showing the Production of Umbra and Penumbra.
and none from L' enters the space C'ABD. Now the
space CABD lies within both of these spaces and hence
receives no light from either source. The remaining shaded
portions receive light from one or the other of the sources.
Furthermore, if other luminous points exist between L and
L 1 ', the space CABD will receive no light from any of them.
The portion of a shadow that is wholly dark is called the
umbra, and the portions that are only partially illuminated
are called the penumbra.
278. Eclipses Produced by Shadows. In the preceding
section it was seen that the section of a shadow that falls
upon a wall or the ground will have a distinct outline
only when the source of light is small. If, therefore, the
source of light is the sun, we find no sharply defined
shadows, i.e. every shadow is surrounded by an indistinct
region which is partially illuminated.
Let the sun, Fig. 199, be the source of light, and the
earth the opaque body. By drawing lines tangent to
both sun and earth, as shown, we find that the earth casts
LIGHT: CHARACTERISTICS AND MEASUREMENT 273
a shadow of which the umbra is cone-shaped and has its
apex at A. Surrounding this is the penumbra whicli
varies from total dark-
ness near the umbra to
practically full illumi-
nation near its outer
limits. If the moon
M in its monthly, re VO- FIG. 199. Showing the Moon Eclipsed by
lution about the earth, Entering the Earth ' s Umbra "
in the orbit shown by the dotted line, passes completely into
the earth's umbra, it receives no light from the sun and is
thus eclipsed. Since we see the moon only by the light
which it reflects from the sun to the eye, this phenomenon
constitutes a total eclipse of the moon. But if only a por-
tion of the moon enters the earth's umbra, it suffers only
a partial eclipse.
279. Pin-hole Images. Images are readily produced by means
of small apertures. If a hole 2 or 3 millimeters in diameter is made
in the window shade of a darkened room, images of trees, clouds, and
other outdoor objects will be produced on a screen held a short dis-
tance from the opening. Each dimension of an image is proportional
to the distance from the aperture to the screen, but the larger the im-
age, the less distinct it is in
every detail, since the light
is distributed over a larger
area.
The reason for the for-
mation of images in this
manner is made clear in
Fig. 200. CD is a candle,
A an opaque piece of wood
or cardboard having a small
aperture at jET, and B is a
white screen. Light from
the tip of the candle C,
FIG. 200. An Image Produced by a Small for example, falls at all
Aperture. points on A, but only that
19
274 A HIGH SCHOOL COURSE IN PHYSICS
falling at H is transmitted. This portion follows the straight line
"CH to F. Likewise, only light from D can fall at E on the screen.
Thus the portions of light from the several points of the object CD
build up the inverted image EF.
Numerous images of the sun may often be observed upon" the side-
walk when the light passes through the small openings between the
leaves of a tree. These images assume interesting, crescent-shaped
figures during a partial eclipse of the sun.
EXERCISES
1. Hold a book in direct sunlight, and from the section of the
shadow that is outlined upon the floor, infer whether we should treat
the sun as a point source of light. Describe the shadow.
2. Hold a ball in direct sunlight about 5 ft. from the floor or wall,
and ascertain whether or not it casts a distinct shadow. Do the same
beneath an uncovered electric arc light. Draw figures to illustrate the
difference in the two shadows.
3. Describe the shadow cast by the moon, 'in what direction does
its umbra point ? Does its umbra ever reach the earth ?
4. When the moon enters the earth's umbra, is its darkening
gradual or sudden? Explain.
5. If the earth should pass into the moon's umbra, what phenom-
enon would be observed by a person standing in the shadow ? Would
any of the sun be visible? Would any of the sun be visible to a per-
son standing in the moon's penumbra?
SUGGESTION. Draw a figure representing sun, moon, and earth
in such a position that the umbra of the moon just touches the earth.
6. If the sun's rays make an angle of 45 with the horizontal plane,
how long is the shadow cast on level ground by a vertical pole 50 ft.
high?
7. A vertical rod 10 ft. in height casts a shadow 12 ft. long on a
level sidewalk. How tall is a tree whose shadow at the same time is
72 ft. in length ?
8. How could one find the height of a building by employing the
method suggested by Exer. 7 ?
3. INTENSITY AND CANDLE POWER OF LIGHTS
280. Intensity of Illumination. If one realizes that the
waves of light that are sent out from any given source
LIGHT: CHARACTERISTICS AND MEASUREMENT 2Y5
spread out in all directions, it is readily inferred that the
intensity of illumination will decrease as one recedes from
the luminous body. We are also led to the same conclu-
sion by the fact that we decrease the distance from a lamp
to a printed page when we wish to increase the amount of
illumination. The exact law is readily shown by experi-
ment.
Cut in a large cardboard screen A, Fig. 201, an aperture just 2
inches square. Place the screen 1 meter from a point source of
FIG. 201. The Intensity of Light Varies Inversely as the Square
of the Distance.
light, preferably an electric arc. Now place a second screen B, upon
which is drawn a square precisely four times as large as the aperture
in A, i.e. 4 inches square, 2 meters from the light. The light, which
at a distance of 1 meter falls upon an area A, at a distance of 2
meters is found to cover precisely 4 equal areas. Hence each area at
B receives only one fourth as much light as a similar area at A.
When the second screen is carried to C, a distance of 3 meters from
Lj the light which passes through A illuminates 9 equal areas at C.
Hence each area at C receives only one ninth as much light as an
equal area at A.
It is now plain that when the distance from a source of
light is doubled, the intensity of illumination is divided
by 4 ; and when the distance is made three times as great,
the intensity of illumination is J. Hence the experiment
leads us to the conclusion that the intensity of illumina-
tion is inversely proportional to the square of the distance
from the source of light.
281. Candle Power of Lights. The law of intensity
shown in the preceding section is used to compare the
276 A HIGH SCHOOL COURSE IN PHYSICS
illuminating powers of two sources of light. If the
intensity of one of the lights is known, that of the other
can be found.
Place a lighted candle A, Fig. 202, 1 meter from a paper screen S
and four similar candles at a point B, the same distance on the oppo-
site side of S. It is now clear that the side of the screen facing the
4 candles receives 4 times as much illumination as the other. But
the two illuminations may be equalized by moving the 4 candles to a
greater distance. If, now, a drop of oil or candle wax is placed on the
paper screen, it becomes possible to ascertain when the illuminations
are equal, since the spot will look alike on the two sides when viewed
at the same angle. To pro-
duce equal illumination on
S A the two sides of S (i.e. to di-
vide the illumination pro-
duced by the stronger light by
4), it' will be found necessary
to move the 4 candles to a dis-
FIG. 202. Showing a Method of Meas-
uring the Candle Power of Lights.
screen. Hence the light-pro-
ducing powers of the two lights are directly proportional to the squares
of their respective distances from the screen. \
It is clear that this method may be employed in the
comparison of the light-emitting powers of two sources.
The process is to set the lights so that they illuminate
the two sides of a screen equally; then the ratio of the
squares of their respective distances from the screen ex-
presses the ratio of the intensities of the two lights. A screen
upon which is an oiled spot is used in the Bunsen photo-
meter for the measurement of the power of lights.
The unit used in the measurement of the power of
lights is called a candle power and is approximately the
power of a sperm candle of the size known as "sixes"
(meaning six to the pound), burning 120 grains per hour.
The candle power of a Welsbach gas lamp consuming
about 3 cubic feet of gas per hour is from 50 to 100, and
LIGHT: CHARACTERISTICS AND MEASUREMENT 277
that of ordinary open gas flames is from 15 to 25, while the
consumption of gas is from 5 cubic feet per hour upward.
The incandescent electric lamps containing a carbon fila-
ment in most common use are of 16 candle power, but
those of greater power can be procured.
EXERCISES
1. A 2-candle-power light is placed 1.5 m. from a screen. Where
muvSt an 8-candle-power light be placed to produce the same illumina-
tion on the screen ?
2. In measuring the candle power of an electric light it was found
that a 4-candle-power light placed 2 in. from a disk produced the same
illumination as the electric light at 10 m. Compute the power of the
electric light.
3. If a book receives ample illumination when placed 10 ft. from
a 50-candle-power lamp, how far must it be placed from a light of
5-candle-power to be equally well illuminated ?
SUMMARY '
1. Light, physically speaking, consists of ether waves
which produce the sensation called light, i.e. which excite
the optic nerve ( 273 and 274).
2. The speed of light is about 186,000 miles (300,000
km.) per second ( 275).
3. Light is propagated in straight lines in a uniform
medium. This fact gives rise to shadows, eclipses, pin-
hole images, etc. ( 276 to 279).
4. When a luminous body is of appreciable size, the shad-
ows of opaque bodies consist of two parts, the umbra, or re-
gion of no illumination, and the penumbra, or partial shadow.
5. The intensity of illumination is inversely proportional
to the square of the distance from a source of light ( 280).
6. The illuminating power of a source of light is meas-
ured in terms of the candle power. This unit is about
equal to the power of the ordinary household candle ( 281).
CHAPTER XIV
LIGHT: REFLECTION AND REFRACTION
1. REFLECTION OF LIGHT
282. Reflection and Transmission. It is a familiar fact
that a piece of glass both reflects and transmits light ; for
we frequently see the bright sunlight reflected by the
glass of a window when we are outside, although, as we
know, a large portion of the light is transmitted to the
interior of the house.
By means of a mounted mirror M, Fig. 203, reflect a bright beam of
sunlight upon a pane of glass AB, held obliquely. If a sheet of paper
be placed behind the glass
at (7, the transmitted light
will fall upon it ; if, again,
i* ke pl ace d i the position
A it will be brightly il-
luminated by reflected
The ordinary mirror
FIG. 203. Reflection and Transmission of makes US6 of the re-
Light by a Pane of Glass. flection of light from
the surface of the opaque film of mercury that covers its
back. Polished metals are often excellent reflectors.
283. The Law of Reflection. Every one is accustomed
to the manner in which light is reflected by a mirror on
account of the many purposes which it serves in everyday
life ; but the following experiments may be performed in
order to establish the law which ordinary observation does
not reveal :
278
LIGHT: REFLECTION AND REFRACTION 279
1. By means of a mirror held in the hand, reflect a beam of sun-
light in various directions, and observe the position of the mirror in
each case. Attach a cardboard index so
that it shall be perpendicular to the mir-
ror, and observe how it points in relation
to the beam of light before and after its
reflection. It will be found that the in-
dex always points in a direction midway
g between the
direct and re-
flected beams
of light, as
shown in Fig.
204.
Mirror
FIG. 204. Illustrating the
Reflection of Light by a
Mirror.
2. Attach a block of wood to a plane
mirror, and set it upon a line ruled across
a large sheet of paper. Place a small
FIG. 205. The Angle of Re- candle about a foot from the mirror at C,
flection r Equals the Angle Fig. 205. Now place the eye near the plane
of Incidence i. of the paper? and get two pins in line with
the image of the candle wick seen in the mirror. Draw a line, as BO,
through these pins to the mirror. Draw also a line, as CO, from the
center of the candle to the point where the first line intersects the
mirror. Draw the line OS perpendicular to the mirror at this point.
Angles COS and BOS will be found to be equal.
Now part of the light from the candle O follows line CO
to the mirror and line OB after being reflected. Angle
COS is called the angle of incidence, and angle BOS the
angle of reflection. In every case it will be found that
these two angles are equal. Hence, the angle of reflection
equals the angle of incidence. It is to be observed that these
two angles are in the same plane, which in Experiment 2 is
represented by the plane of the paper.
284. Diffused or Scattered Light. Objects are visible
to us either by the light which they emit, as in the case of
the sun, a candle, or a live coal, or by the light which,
after falling upon them from some luminous body, they
scatter, or diffuse. Most objects, unlike a smooth piece of
280
A HIGH SCHOOL COURSE IN PHYSICS
glass, reflect light in many directions. Thus the sunlight
which falls upon the snow is diffused ; but when it falls
upon smooth ice, it is reflected as from a mirror. This is
because the tiny reflecting surfaces of snow lie in all con-
() (2)
FIG. 206. Diffusion Compared with Reflection from a Smooth Surface.
ceivable positions, as shown in (1), Fig. 206, while those
of ice all lie in one smooth plane, as in (2).
By the help of the light which objects send to our eyes,
we judge of their distance, form, size, color, and brilliancy.
Leaves, grass, flowers, etc., diffuse in every direction the
sunlight that falls upon them. The moon also is visible
because of the sunlight diffused from its illuminated sur-
face ; and we are often able to
trace the dim outline of the
new moon, although it is in
shadow, because of the sunlight
which the earth diffuses back
upon the moon's dark area.
285. Image of a Point in a
Plane Mirror. It was found in
283 that light is reflected by
a plane mirror so that the angle
FIG. 207. Production of an im- of reflection is equal to the
age by a Plane Mirror. angle Q f incidence. HeriCC the
light which starts from the point A, Fig. 207, and
LIGHT: REFLECTION AND REFRACTION 281
takes the direction AB is reflected by the mirror MN
in the direction BC, so that angle OBD equals angle ABD.
All other rays that may be drawn from A to the mirror
are reflected in the same manner ; and when the eye is
placed at E or E', the reflected rays appear to come from
a point A' behind the mirror.
286. Waves and "Rays." -It is easy to conceive of a
train of waves moving outward from the point A> Fig.
208, and striking against a plane mirror MN. The waves
are sent back from the mirror as though they emanated
from the point A' behind the mirror. Hence, to an eye
placed at E the effect is just the same as though A were
the light-emitting point. It is obviously more convenient
to locate the image of a point
by the help of "rays," as in
Fig. 207, rather than by the use
of waves, as in Fig. 208. How-
ever, it should always be remem-
bered that a so-called " ray " of
light is simply a symbol used to
represent the direction taken by
a portion of a wave. Thus that
part of a Wave of light which
starts from A toward B in Fig.
207 follows
FIQ
Light from A Seem to Come to
the Eye from A ''
L
the course ABO.
287. Image of an Object in a
Plane Mirror. -- By applying
the law of reflection it is easy to
locate the image produced by a
plane mirror. Let AB, Fig.
FIG. 209. Manner of Locating 209, be an object and MN the
an image illustrated. mirror. Let A be an incident
ray from A drawn perpendicular to the mirror. The re-
flected ray will take the direction OA. (Why ?) Let AD
282
A HIGH SCHOOL COURSE IN PHYSICS
be another incident ray from A, whose direction DE,
after being reflected, is found by making angle EDF equal
angle ADF. The image of A lies at the intersection A 1 of
the reflected rays CA and DE produced backward behind
the mirror. It is plain from the equality of the triangles
ACD and A! CD that AC equals A'C; i.e. the image of a
point is as far behind a plane mirror as the point itself is
in front. We may now employ this fact in locating the
image of the point B at B 1 .
288. Seeing the Image. Imagine an eye to be placed
at E, Fig. 209. Light enters the eye from the mirror
MNas though it came from A 1 ', although it actually comes
from A. Similarly, the eye receives light by other rays
as if its origin were at J?', whereas it is really at B.
TfrefeT'is nothing behind the mirror that concerns our
vision, and the light is not propagated by the medium
except in front of the mirror. The image is called a vir-
tual image to distinguish it from the real images formed by
small apertures ( 279) and in other cases, to be studied
later.
FIG. 210. A Result of Double
Reflection.
FIG. 211. Diagram. Illustrating
Double Reflection.
289. Double Reflection. If two plane mirrors are placed
at right angles to each other, as shown in Figs. 210 and
LIGHT: REFLECTION AND REFRACTION 283
211, it is clear that a large portion of the light emanating
from a point A will be reflected twice, once at the surface
of each mirror. Thus the ray AB is reflected from B to
by the vertical mirror OM, and from toward D by the
horizontal mirror ON. Likewise, the ray AE takes the
course AEFGr, being reflected at E and F. Now FG and
CD, and all other rays that have undergone double re-
flection, diverge as though they emanated from the point
A", which is at one corner of the rectangle A'AA^A! 11 .
It is therefore evident that three images may be seen by
placing the eye in such a position as to receive light that
has suffered two reflections as well as that which has been
reflected but once.
EXERCISES
1. A pole is inclined at an angle of 45 to the surface of water in a
quiet pond. Construct the image of the pole seen in the water.
2. Look at your image in a mirror, and lift your right hand.
Which hand of the image appears to be lifted ? Is the image direct
or reversed ?
3. Set a candle or a tumbler on a horizontal mirror, and observe
the position of the image.
4. What would be the result of covering the mirror OM in Fig.
211 ? How could the formation of image A '" be prevented without
interfering with image A ' or A " ?
SUGGESTION. Place an opaque screen so that no light can be re-
flected twice. Show how this can be done. s
5. A man approaches a plane mirror with a velocity of 3 m. per
second. How rapidly is he approaching his image ?
6. Try to read a printed page by looking at its image in a mirror.
Write your name backward on a sheet of paper, and then look at the
image of the writing in a mirror. What eifect is produced by the
mirror in each case ?
7. Find by construction the shortest vertical mirror in which a
man 6 ft. tall can see his entire image when standing erect.
SUGGESTION. Diagram the case, and then draw lines from the
man's eye to the highest and lowest points of the image. Consider
the length of the mirror employed between these two limits.
284 A HIGH SCHOOL COURSE IN PHYSICS
8. Two lines AB and BC make an angle of 60 with each other.
Show how to place a mirror so that A B may represent an incident
ray of which BC is the reflected ray.
2. REFLECTION BY CURVED MIRRORS
290. Spherical Mirrors. A spherical mirror is a
polished or silvered portion of the surface of a sphere.
If the side of the surface toward the
center of the sphere is used to re-
flect light, see Fig. 212, the mir-
\ ror is concave; if th outer surface
is used, the mirror is convex. The
center of the sjphere O is the center
of curvature, and the radius GO of
FIG. 21U. Section of a
Spherical Mirror. the sphere is the radius of curvature.
The line of symmetry XO is called flie principal axis.
Let direct sunlight fall upon a concave <mirror parallel to the prin-
cipal axis, and hold a small card in front of, the mirror to receive the
reflected light. Move the card back and forth until the illuminated
spot is as small as possible. Measure the distance from this spot to
the mirror. If a piece of tissue paper be held at the spot where the
reflected light is concentrated, it will probably take fire. If the air in
front of the mirror be filled with crayon dust, the convergence of the
reflected light is easily made visible.
Figure 213 shows the effect produced when parallel rays
of sifhlight fall upon a concave mirror. At every point
011 the mirror light is re-
flected according to the law
of reflection ( 283) ; but
on account of the curvature
of the mirror, each reflected
ray from the beam of par-
allel rays is sent through
the point F, which is therefore called the principal focus.
When the energy thus concentrated at the principal focus
LIGHT: REFLECTION AND REFRACTION 285
falls upon paper, enough of the energy is transformed into
heat to ignite it. The principal focus is located midway
between the center of curvature and the mirror; i.e. OF
eo^als one half OC. The distance OF is called -the focal
length of the mirror or the principal focal distance.
291. Convex Mirrors. Try to concentrate direct sunlight by
employing a convex mirror in the same manner as the concave mirror.
While sunlight is falling upon the mirror, look toward its convex
surface through a piece of black glass. An exceedingly bright point
will be seen located apparently behind the mirror.
Figure 214 illustrates the manner in which a convex
mirror reflects the parallel rays of sunlight. The light at
every point follows the law of reflection ; but on account
of the form of the surface, it
diverges as though it came I
from the point .F behind the ii
mirror. Of course" no heat
will be produced at the point ^^
F, inasmuch as the light does FIG. 214.^ Parallel Rays are Made
net actually pass through it.
Since F is only an apparent meeting point or focus of the
reflected rays, it is called a virtual or unreal focus. The
principal focus of a con-
cave mirror, ho\i*ever,
is a real focus. See
*. ^l*-^ 288.
To locate the principal
focus of a convex mirror,
let a beam of sunlight pass
FIG. 215. Determining the Focal Length through a round hole in a
piece of cardboard, as shown
in Fig. 215. Around this aperture draw a circle whose radius is just
twice that of the aperture. Let the beam fall upon a convex mirror,
and then move the mirror back and forth until the reflected light
just covers the larger circle. Triangles abc and coF are practically
286
A HIGH SCHOOL COURSE IN PHYSICS
FIG. 216. Image Formed by
a Convex Mirror.
equal. (Why ?) Hence the distance from the cardboard to the mir-
ror oe is equal to oF, the focal length of the mirror.
292. Images Formed by a Convex Mirror. The student
is probably familiar with the small image that is seen as
one looks at the polished sur-
face of a glass or metal ball
or the convex side of the
bowl of a spoon. The experi-
ment may be made with a
lighted candle, as shown in
Fig. 216. The image will ap-
pear to be behind the mirror
and is always smaller than the
object, which in this case is
the candle. Compare with Fig. 208.
293. Constructing the Image. To show diagrammati-
cally how an image is produced by a convex mirror, let
the arc MN, Fig. 217,
whose center of curva-
ture is at (7, represent
a convex mirror. Let
the arrow AB be the
object, and draw the
ray AG- parallel to
the principal axis OX.
The reflected ray GD
will apparently come
from F ( 291), which is midway between and O. Let
a second ray AH be drawn from A along a radius of the
mirror. Since this ray falls perpendicularly upon the
mirror, it will be reflected back along the same line HA.
Now let the reflected rays GrD and HA be produced until
they intersect at some point, as a behind the mirror. This
locates the image of the point A. The image of the point
FIG. 217. Locating the Image of AB by
Construction.
LIGHT: REFLECTION AND REFRACTION 287
B may be located in the same manner at b. A line drawn
from a to b represents, therefore, the image of the object
AB. Is the light from A actually focused at a ? Is the
image therefore real or virtual? Is it erect or inverted?
Is it larger or smaller than the object? Could any rays
other than those selected be employed ? How would you
find the direction of any other reflected ray ? (See 283.)
294. Images Formed by a Concave Mirror. The nature
of the images produced when light from some object, as a
candle, falls upon a concave mirror is readily shown by a
series of experiments. Excellent results can be obtained
by using a mirror whose radius of curvature is 20 inches
or more.
1. Let a lighted candle be placed before a concave mirror at a
distance somewhat greater than the radius of curvature. Place a small
FIG. 218. Production of a Real Image by a Concave Mirror.
cardboard screen between the candle and the mirror, and move it
back and forth until a good image of the candle appears upon it. The
image will be found between the principal focus and center of curva-
ture.
This image differs greatly from that produced by a con-
vex mirror in that it can be caught upon a screen. We
are not obliged to look into the mirror to see the image,
because the light that emanates from a point in the candle
is actually reflected to a corresponding point on the screen.
Such an image is a real image. The experiment plainly
288 A HIGH SCHOOL COURSE IN PHYSICS
shows that ivhen the object is beyond the center of curvature,
the image is between the center and the principal focus, is
real, inverted, and smaller than the object.
2. Let the candle be placed at any point between the center of curva-
ture and the principal focus and the image caught upon a screen. In
this case the screen has to be placed beyond the center. (See Fig. 218.)
Here we shall readily find that when the object is placed
between the center and the principal focus, the image is
beyond the center, is real, inverted, and larger than the object.
3. Let the candle be placed between the principal focus and the
mirror. In this case, in order to locate the image, direct the eye
toward the mirror in such a manner as to receive some of the
reflected light.. An erect image will be seen.
When the object is between the principal focus and the
mirror, the image is behind the mirror, is virtual, erect, and
larger than the object.
4. Project upon a screen the images of some distant object, clouds,
trees, buildings, etc. In all cases it will be found that the images are
small and lie practically midway between the mirror and its center of
curvature. Parallel rays of sunlight are also focused at this point.
The experiment shows that the image of an object at a
great distance lies near the principal focus, is real, inverted,
and smaller than the object itself.
295. Construction of Images Formed by Concave Mirrors.
We have seen in 293 how an image can be located
by geometrical construction. The same method may be
applied to the cases arising from the use of a concave
mirror.
Case I. When the object is beyond the center of curva-
ture.
Let MN, Fig. 219, be a concave mirror whose center is C. Let the
object be AB. Locate first the principal focus F ( 290). Now let a
ray AG be drawn from the point A of the object parallel to the
principal axis. This ray will be reflected through the point F.
LIGHT: REFLECTION AND REFRACTION 289
(Why?) Let a second ray A D be drawn through the center of curva-
ture C. Since this ray is perpendicular to the surface of the mirror at
M
FIG. 219. A Real Image of AB is Located at ab.
Z), the reflected ray takes the direction DC. The two reflected rays
GF and DC obviously meet at the point a. Could other incident rays
be drawn from A ? How could their direction be found after reflection ?
Where would they meet the reflected rays already drawn/? Hence the
image of A is at the point a. In a similar manner the image of the
point B is located at b. Thus ab is the image of the object AB.
When two points -are so related that the image of one
falls at the other, as A. and a, or B and >, they are called
conjugate foci (pronounced /o' si).
Case II. When the object is between the center and the
principal focus. I
The conjugate foci of the points A and B are located by a method
similar to that used in the preceding case. (See Fig. 220.) The two
AT
b
FIG. 220. A Real Image of AB is Located at ab.
cases should be compared, and the constructions actually made. A
real, inverted, and magnified image is found at ab.
20
290
A HIGH SCHOOL COURSE IN PHYSICS
Case HI. When the object is between the principal focus
and the mirror.
As we undertake here to carry out the method of construction used
in the preceding cases, we find that the reflected rays emanating from
FIG. 221. - A Virtual Image of AB is Formed at ab.
the point A diverge after leaving the mirror. (See Fig. 221.) This
fact shows at once that A can have no real focus. The image will be
seen only by looking into the mirror. In such cases the reflected rays
DC and GF are to be produced until they meet at some point as a
behind the mirror. Similarly the image of B is found at 6. Thus
a magnified, erect, and virtual image is found at ab.
Case IV. When the object is at the center of curvature or
at the principal focus.
When light from a point at the center of curvature falls upon a
concave mirror, it strikes at an angle of 90 with the reflecting sur-
face and is, consequently, reflected back along the same path. Hence
all such rays will be focused at the center of curvature. But, when
light from a point placed at the principal focus is reflected, it follows
lines parallel to the principal axis ; e.g. FGA and FHB, Fig. 219.
Since such rays never meet, no image of the point F could be
produced.
296. A Real Image Viewed Without a Screen. We have
already seen ( 294) that a real image of a bright object can
be projected by a concave mirror upon a suitable screen.
Now if the eye be placed about 10 inches beyond the image
and turned toward the mirror, the screen may be removed,
LIGHT: REFLECTION AND REFRACTION 291
and the image will be visible. Imagine an eye at JK,
Fig. 222. Light waves emanating from A, a point in the
object, advance toward the mirror with convex wave fronts,
as those of water waves
s
which are started by a
falling pebble. These
are here represented by
arcs, having their com-
inon center at A. But
on account of the curva-
ture of the mirror MN,
'the waves are reflected
with concave fronts
having as their common
center the point #, which is called the conjugate focus of A.
As the waves are not obstructed by a screen, they leave a
with convex fronts and enter the eye at E.
FIG. 222. The Eye Can Observe a Real
Image without a Screen.
EXERCISES
1. An object is placed 6 in. in front of a convex mirror whose
radius of curvature is 12 in. Find by construction the position of
the image.
SUGGESTION. Make a drawing, using for blackboard work the di-
mensions and distances given, but divide each by 4 for pencil drawings.
2. An object is placed 44 cm. from a concave mirror whose radius
of curvature is 50 cm. Find by construction the location of the image.
3. Place a small object slightly above the center of curvature of a
concave mirror whose principal axis is horizontal, and find its image
by construction. Does this exercise suggest a method for finding the
radius of curvature by experiment ?
4. An object 8 in. in height is placed 30 in. in front of a concave
mirror whose radius of curvature is 15 in. Find the distance from
the mirror to the image.
5. Make an accurate construction of the case described in Exer. 4,
and carefully measure the size of the image. Measure also the dis-
tances of the object and the image from the center of curvature. Do
292 A HIGH SCHOOL COURSE IN PHYSICS
you find any relation between the distances and the sizes of image and
object? If so, express it in a single sentence. Can you prove the
same relation by similar triangles?
3. REFRACTION OF LIGHT
297. Refraction of Light. Numerous examples of the
refraction or bending of the course taken by light come
before our attention daily, although we seldom give the
phenomenon much thought. A simple case is the apparent
bending of a spoon standing in a tumbler of water, or an
oar at the point where it enters the water. Again, if a
coin be placed in a tumbler of water and viewed obliquely,
two coins become visible, a small one seen through the
horizontal surface of the water and a magnified one seen
through the side of tlie vessel. If, now, a pencil be placed
obliquely in the water contained in the tumbler, a bent
section may be seen below the upper surface of the liquid,
while a magnified portion is visible through the side of the
vessel. In every case the illusion is due to the bending of
light rays as they pass from one medium into another. No
principles of optics are of more value to us than those relat-
ing to the phenomenon of refraction, for upon this effect
,//, are based not only our
most important optical
instruments, including
the microscope, tele-
scope, and camera, but
also the structure of
the eye.
298. Refraction II-
FIG. 223. - Refraction of Light as it lustr ated. 1. By means
Enters Water.
of the mirror M, Fig. 223,
about one half an inch in width, let a beam of sunlight be re-
flected obliquely upon the surface of water in a tank. By scat-
tering crayon dust in the air above the water, the course of the
LIGHT: REFLECTION AND REFRACTION 293
beam before and after entering the water becomes visible. Another
excellent way to make the path of the light easy to trace is to hold
apiece of white cardboard or tin partly under water so that it receives
the beam of light both above and below the liquid surface. The result,
will show that at the surface of the liquid O the beam of light turns
toward the perpendicular, or normal, NN' which is drawn at 0. If
the obliquity of the incident light is increased, the bending of the
beam is made more pronounced.
This experiment shows that when light passes obliquely
from air into water, it undergoes a refraction or bending
toward the perpendicular to the surface at the point where the
beam enters the water.
2. Place a plane mirror in the bottom of the tank used in the pre-
ceding experiment so as to reflect a beam of light from water into the
air, as shown in Fig. 224. The course
of the beam MOP may be traced before
and after entering the air by employing
the means used in the preceding experi-
ment. In fact, the path of the light
MOP is precisely the reverse of that
which the beam would take if it were
passing into water along the line PO.
,., , T . FIG. 224. Refraction of
It will readily be observed in Light as it Emerges from
this experiment that when light Water.
passes obliquely from water into air it undergoes refrac-
Uon away from the perpendicular to the surface at the point
where the beam emerges from the water.
The angle MON, Fig. 223, is called the angle of inci-
dence, and angle PON' , the angle of refraction. The per-
pendicular ON is usually called the normal at the point 0.
299. Cause of Refraction. It has been found by direct
experimentation that light waves travel with less speed in
water than in air ; in fact, the speed of light in water is
almost exactly three fourths of that in air. When a beam
of light AB, (1) Fig. 225, strikes at right angles to the
surface of water (71), all parts of a given wave front strike
294 A HIGH SCHOOL COURSE IN PHYSICS
the medium at the same time. Within the water the
waves travel with less speed and are shorter. Likewise, if
all parts of the wave front emerge at the same time, they
resume their original speed without being refracted. But
when the waves fall obliquely upon the surface, the case is
quite different. See
(2), Fig. 225. The
parts of a given wave
front abed do not enter
the medium at the
same instant; but a
enters first and con-
(2) tinues with reduced
FIG. 225. Illustrating the Cause s P eed ' while the other
of Refraction. parts bed are still in air.
Similarly, b enters the medium before c and d, then c be-
fore d, and finally d. Thus the portion a travels the dis-
tance act,', while d is traveling the larger distance dd' .
The result is that the wave is " faced " in a different di-
rection, namely aF, having suffered a bending toward the
normal to the surface, NN 1 . From this explanation of re-
fraction it is clear that the ratio of the distance dd r to the
distance aa' is the same as the ratio of the speeds of liylit in
the two media.
300. Index of Refraction. It is obvious from Fig. 223
that the amount which the course of light is changed when
it enters a medium where its speed is less than it is in air
depends upon the relation that the distance aa' bears to
the distance dd':, or, in other words, upon the relation
between the speeds of light in the two media. Although
it is not easy to measure the speed of light in a medium,
it is comparatively a simple matter to measure the amount
of refraction and from this to compute the relative speed
of light. The number which expresses the ratio of the speed
LIGHT: REFLECTION AND REFRACTION 295
of light in air to its speed in another medium is called the
index of refraction of that medium. Hence
speed in air
Index of refraction^ =
= dd| (l)
'
speed in other medium aa'
301. Index of Refraction Measured. By referring to
Fig. 225 in which xx' is the normal at the point d 1 ', we
observe that angle dad' = angle dd'x, which is the angle
of incidence. (Why?) Angle ad' a' = angle x'd't, the
angle of refraction. (Why ?) Now the ratio - is de-
ad
fined in mathematics as the sine of angle dad', and is writ-
ten sin dad 1 . Similarly, the ratio is the sine of angle
ad
ad'a' , and is written sin ad f a f . Hence
sindd'x sin dad r ad' dd'
aa
f ref ractlon '
ad'
Therefore the index of refraction of D
a substance is equal to the quotient ob-
tained by dividing the sine of the angle
of incidence by the sine of the angle of
refraction.
302. Index of Refraction by Experi-
ment. Let a glass cube A BCD, Fig. 226, be
placed against a pin P set upright in a hori-
zontal board or table. Place the eye at some
point as E, and set two other pins F and G in
Jine with P as seen through the glass. Draw FlG . 22 6.- Measuring the
line AB and remove the cube. Next draw index of Refraction of
lines GFo and oP. The line PoG is the Glass.
1 The term " absolute " index is used to refer to the ratio of the speed
of light in a vacuum to its speed in a medium. The index of refraction
defined above is often called the " relative " index.
296 A HIGH SCHOOL COURSE IN PHYSICS
course taken by the light that enters the eye from the pin P. Draw
the normal bd at the point o, and then draw the lines ab and cd per-
pendicular to the normal after making oa = oc. Now ab H- ao is the
sine of angle aob, and cd * co is the sine of angle cod. Hence, by
equation (2), and substituting ao for its equal, co, we have
ab
. , //... ao ab m
index of refraction : =
J J cd cd
Therefore we can readily find the value of the index of refraction by
dividing the length ab by the length cd.
RELATIVE SPEED OF LIGHT OR ABSOLUTE INDEXES OF REFRACTION
FOR SOME COMMON TRANSPARENT SUBSTANCES
Air 1.00029 Flint glass . . . . 1.54 to 1.71
Water 1.333 Carbon disulphide . . . 1.64
Crown glass .... 1.51 Diamond 2.47
303. Total Reflection. Since the rays of light which
pass from water or glass into air are bent away from the
normal, as POA and PO'B, Fig.
227, it is readily observed that
Air OsC/jo^tf"^ s wnen t ne angle of incidence below
water /// \^^\ the surface is great enough, the
refracted ray will follow close to
the surface, as ray PO"S. Hence
the ray P 0" is the last one that
FIG. 227. The Total Reflec- can emerge from the surface. If
the angle of incidence 'is still in-
creased, the light is reflected wholly beneath the surface,
as PO'"C. This phenomenon is called total reflection.
1. Examine the glass cube used in 302 by looking through the
face A By Fig. 226, toward face BC, which has the appearance of a
mirror. Place the finger upon face BC. It cannot be seen through
AB. Transfer the finger to face CD. It can now be seen in face BC
by reflected light.
LIGHT: REFLECTION AND REFRACTION 297
2. Look obliquely upward against the surface of water in a tum-
bler. It will be seen to have the appearance of a plane mirror. If
the point of a pencil is held in the water, only that part of it is visible
that projects below the surface, and this portion can also be seen by
reflected light.
3. Reflect a narrow beam of sunlight obliquely upward through
the side of a glass tank containing water. (See Fig. 228.) By vary-
ing the angle of incidence below the
surface until it is greater than 48.5,
the totally reflected beam can be traced
back into the water. Both the incident
and reflected beams may be made vis-
ible in the manner described in
298.
4. Hold a test-tube obliquely about
5 centimeters under water, and look vertically downward upon it.
The portion of the tube below the liquid surface has the appearance
of a mirror.
FIG. 228. An Illustration of
Total Reflection.
These experiments serve to illustrate the fact that when
the angle of incidence with which light undertakes to
emerge from glass or water exceeds a certain value, the
light is totally reflected at the point of incidence back into the
medium. The angle of incidence at which the effect changes
from refraction to total reflection is called the critical angle.
The phenomenon of total re-
flection occurs only when light
is proceeding in one medium
toward another in which the
speed is greater. (See Fig.
229.) The critical angle for
water is 48. 5; for crown glass,
41; for diamond, 24.
FIG. 229. illustrating the 304. Critical Angle Con-
Critical Angle. structed. If the index of re-
fraction of a medium is known, the critical angle can be
found readily from the following construction :
298
A HIGH SCHOOL COURSE IN PHYSICS
Let the line AB, Fig. 230, be the boundary between air and water,
and let the index of refraction be $ . With 0, the point of incidence,
as the center draw two concentric cir-
cles whose radii have the ratio of 4:3.
Since the ray that emerges for the crit-
ical angle follows the surface, erect the
normal at the point (7, where the sur-
face intersects the inner circle. This
cuts the larger circle at E. The line
EO produced below the surface gives
the angle DOF as the critical angle.
The proof is as follows : When light
of Con- passes from water into air, the index of
refraction is ; and for the critical angle
of incidence below the surface, the angle of refraction is 90. It is
sin DOF 3
4
FIG. 230. Method
structing the Critical Angle.
to be shown that
sin 90
= -.. Now, angles DOF and OEC are
equal.
and sin 90= 1.
(Why ?) Further, sin OEC = = - by construction ( 301),
OE 4
Therefore
sin DOF sin OEC
sin 90
sin 90
305. Total Reflecting Prism. The most important use that is
made of the phenomenon of total reflection is accomplished by em-
ploying a right-angled prism of glass whose cross
section is an isosceles triangle, as shown in Fig.
231. If incident light enters the prism perpendic-
ular to either of the faces forming the right
angle, it will not suffer refraction and will strike
the oblique face at an angle of incidence of 45.
Since the critical angle for glass is less than 45,
the light will be totally reflected in the direction
perpendicular to the third face, from which it
will emerge without undergoing refraction. Such
prisms are used when it is desired to turn the
course of light through an angle of 90 without excessive loss.
306. Path of Light through Plates and Prisms. The
effect of a parallel-sided plate of glass upon a ray of light
is readily determined by the following experiment :
FIG. 231. Turning
the Course of
Light through 90
hy Total Reflec-
tion.
LIGHT: REFLECTION AND REFRACTION 299
Look obliquely through a glass cube or a parallel-sided tank of
water and set four pins, two on each side of the cube or tank, so that
they will form apparently a straight line. Remove the refracting ob-
ject, and draw the lines connecting the two pins of each pair. If these
two lines are produced, it will be found that they are parallel.
Hence, when light passes obliquely through a medium
with parallel faces, it does not suffer a permanent change
in direction. In other words, the
refraction toward the normal at the
first surface DO, Fig. 232, is can-
celed by the refraction from the nor-
mal at the second surface AB. As
the experiment shows, the ray suf-
fers a lateral displacement only.
The course taken by a ray of light FlG D m ~ u ^ Suffers no
*. Permanent Change in Di-
whlCll tails obliquely Upon One of rection in Passing through
the faces of a glass prism may be Parallel Surfaces -
traced in a manner similar to that just described:
Set four pins, two upon each of the opposite sides of a glass prism,
Fig. 233, whose angle at A is about 60, so that all four pins lie
apparently in a straight
line. Draw a line around
the prism and remove it.
Join the two pins in each
pair by a straight line, and
produce these lines until
they meet the sides of the
prism AB and AC &t
and 0'. Then 00' is the
FIG. 233. - ^fraction of Light by Means P ath of the H S ht throu S h
of a Prism. the prisrn.
Since the ray which enters the prism is bent toward the
normal at and away from the normal at ? where it
emerges, it is clear that the effect of the prism is to turn
the ray always away from the refracting angle A of the
prism.
300 A HIGH SCHOOL COURSE IN PHYSICS
EXERCISES
1. What is the speed of light in water, the index of refraction be-
ing |? The speed of light in air is 186,000 mi. per sec.
2. Compute the speed of light ill crown glass, assuming that the
index of refraction is *.
3. Compare the speed of light in water with that in crown glass.
What simple fraction will represent the relative speed? Show how to
get this same fraction from the indexes of refraction given in Exer-
cises 1 and 2.
4. The answer obtained in Exer. 3 is called the relative index of
refraction for light on passing from water into crown glass. In a
similar manner find the relative index of refraction for light which
passes from flint glass into carbon disulphide, using the indexes given
in the table.
5. For a given angle of incidence will light be refracted more in
passing from air into crown glass or from water into crown glass?
From water into crown glass or from carbon disulphide into flint
6. Construct the critical angle for air and water. On which side
of the boundary surface does the critical angle lie ? Does the critical
angle lie within the medium where the speed of light is the greater
or the less ?
7. Upon which side of the boundary surface separating water and
crown glass does the critical angle lie?
8. The angle of incidence at which a ray of light enters a medium
from air is 45, and the angle of refraction 38. Find by construction
the index of refraction of the medium.
SUGGESTION. By the help of a protractor construct accurately
a figure. Measure the lines db and cd, as in 302, and compute the
index of refraction.
9. Draw the figures, and ascertain the indexes of refraction for the
following angles : angle of incidence 30, angle of refraction 22; angle
of incidence 50, angle of refraction 31 ; angle of incidence 60, angle
of refraction 40.
4. LENSES AND IMAGES
307. Lenses. The student will call to mind many in-
struments with which he is acquainted that make use of
of lenses, the camera, microscope, spyglass, spectacles,
LIGHT: REFLECTION AND REFRACTION 301
opera glass, etc. The value of these instruments can
hardly be too highly estimated. The study of lenses
and their application is therefore of great interest and
utility.
A lens is usually made of glass and has either two
curved boundary surfaces or one curved and one plane
surface. The curved surfaces are usually (not necessarily)
spherical, and the lens thus formed is
called a spherical lens. The center of
the sphere (7, Fig. 234, of which the
lens surface is a part, is called the
center of curvature, and the radius of
the sphere, the radius of curvature.
Lenses are of two general classes,
convex lenses, which are thicker at
the middle than at the edge, and con-
caw lenses, which are 'thickest at the edge. Figure 235
shows the three lenses belonging to each of the two gen-
eral classes.
FIG. 234. A Spherical
Lens.
!5
FIG. 235. Forms of Lenses.
(1. Double Convex
2. Piano-Convex Concave, or Diverg-
3. Concavo-Convex, ing Lenses
or a Meniscus
(4. Doul
5. Plan
6. Com
Double Concave
o-Concave
Convexo-Concave
308. Effect of a Convex Lens on Light. The most im-
portant feature of any lens is not its form, but the manner
302
A HIGH SCHOOL COURSE IN PHYSICS
in which it acts upon light. The effect of a lens that
is most familiar to all is that employed in the so-called
"burning glass," which was in general use for producing
fire before the introduction of cheap matches. The
following experiment shows this effect :
Allow a beam of sunlight to fall upon a large convex lens in a
darkened room. If the air
be made dusty, the light
will be seen to form a cone-
shaped figure as A A, Fig.
236. If a piece of tissue
paper be placed at the ver-
tex of the cone, it is readily
ignited. Beyond this point
FIG. 236. - Effect of a Convex Lens on the H g ht diver S es Precisely
Parallel Rays. as from the principal focus
of a concave mirror ( 290).
If a convex lens of another form be substituted for the first, the action
is practically the same.
The vertex of the cone formed by the sunlight trans-
mitted by a convex lens is called the principal focus of the
lens. The distance from the principal focus to the center
of the lens is the focal length, or principal focal distance,
of the lens. Since all convex lenses cause rays of sun-
light to converge to a point, they are often called converging
lenses. (See Fig. 235.)
Figure 237 shows the
change in form that
waves of light undergo
while passing through
a double convex lens.
The plane waves of
sunlight, whose direc-
tion of motion is represented by arrows drawn in the figure,
are retarded by the lens in proportion to the thickness of
FIG. 237. Plane Waves are Converged to
the Principal Focus F.
LIGHT: REFLECTION AND REFRACTION
303
the glass through which they pass. As a result of this re-
tardation, the emerging light has concave wave fronts
whose centers are at F, the principal focus. On leaving F,
however, the waves have convex fronts ; or, in other words,
the light diverges from the point F.
Ordinary glass lenses, whose index of refraction is very
nearly |, have a focal length equal to the radius of curva-
ture, if they are double-convex and the two surfaces have
the same curvature. If one surface is a plane, the focal
length is double the radius of curvature.
309. Concave Lenses. The effect of a concave lens on
sunlight is very different from that of a convex lens, as
the following experiment will show :
Let a beam of sunlight fall upon a concave lens mounted in a wide
board. By making the air dusty, or holding a piece of cardboard
obliquely in the transmitted light, it will be readily observed that
the light diverges as it leaves the lens.
The part of a plane wave that passes through the center
of a concave lens, Fig. 238, is retarded least on account of
the fact that the lens is
thin at that point, while
that passing through
near the edge suffers
the greatest retarda-
tion. The result is that
the front of the emerg-
ing waves is convex, as
though the light had
emanated from the point F, which in this case is a virtual
focus and located very near the center of curvature. Since
the general effect of all concave lenses is to cause rays of
sunlight to diverge, they are classed together as diverging
lenses. (See Fig. 235.)
FIG. 238. Parallel Rays of Light are
Scattered by Concave Lenses.
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A HIGH SCHOOL COURSE IN PHYSICS
310. Conjugate Foci. Place a candle flame close to a small
hole P in a piece of tin S, Fig. 239. Now set a convex lens about
twice its focal length away from the hole P, and place a screen S'
on the opposite side of the lens upon which will be produced a sharp
FIG. 239. The Conjugate Focus of P is at P'.
image of P at P'. Cover up one half the surface of the lens, and the
image will remain at P'. Cover the lens almost entirely, and the image
will be weakened but not destroyed.
It is to be observed that all the light emanating from
the point P and passing through the lens is collected at
P' . Likewise, any other point beyond the principal focus
F has a corresponding point on the opposite side of the
lens where its image would appear. Two points so related
that the image of one of them, as P, falls at the other, as P' ,
are called conjugate foci. See also 295.
311. Virtual FOCUS. Let the candle and screen S that were
used in the experiment of the preceding section be placed between a
convex lens and its principal
focus, and the result shown
in Fig. 240 will be secured.
The rays diverging from the
point P will not be brought
to a focus by the lens, but
the divergence will be greatly
reduced. Of 'course no im-
age of P can be produced
upon a screen; but upon looking through the lens the eye E locates
(apparently) the image of P at the point P'. If the screen be removed
a virtual image of the caudle ma^ be seen.
FIG. 240. The Conjugate Focus of P is
Virtual and at Point P'.
LIGHT: REFLECTION AND REFRACTION
305
In the location of an image the eye is always governed
by the divergence of rays which enter it ( 276). The
divergence is in this case as if the rays had come from P'
FIG. 241. A Concave Lens always Forms a Virtual Focus.
instead of P. Since the point P' is only the apparent
meeting place of the rays that enter the eye, this point is
called the virtual focus of P. If the experiment be
repeated with a diverging (concave) lens, as shown in
Fig. 241^ the conjugate focus of P is virtual no matter
what the position of P may be, because the effect of such
a lens is always to scatter the transmitted light.
312. Images Formed by Convex Lenses. Every one
who has viewed the pictures projected by a stereopticon
or a moving-picture machine has seen the real images that
convex lenses are able to produce. In the process of
forming images the convex lens presents precisely as
FIG. 242. Focusing a Real Image on a Screen by Means
of a Convex Lens.
21
306 A HIGH SCHOOL COURSE IN PHYSICS
many cases as the concave mirror ( 295). These cases
are easily illustrated by experiments.
1. Let a lighted candle C, Fig. 242, be placed at a little more than
twice the focal length from a convex lens L. By moving the screen 5
back and forth an image will be found distinctly focused upon it.
The distance from the lens to the image should be measured and
compared with the focal distance.
When the object is situated at more than twice the focal
length from a convex lens, the image is at less than twice and
more than once the focal length from the lens on the opposite
side, is real, inverted, and smaller than the object.
2. Let the candle be placed at less than twice but more than once
the focal length from the convex lens. The image may be found by
moving the screen away from the lens. The distance to the image
should be measured and its position and size noted.
When the object is situated at more than once and less
than twice the focal length from a convex lens, the image is
at more than twice the focal length on the other side, is real,
inverted, and larger than the object.
3. Let the candle be placed at less than the focal length from the
convex lens. Of course no image can be produced upon the screen
since the conjugate foci of all points in the object are virtual. (See
311.) But by allowing some of the transmitted light to enter the
eye (i.e. by looking through the lens), an apparent magnified image
may be seen behind the lens.
When the object is situated at a point between a convex
lens and its principal focus, the image is apparently behind
the lens, is virtual, erect, and larger than the object.
4. Focus upon a screen the images of objects which are situated
at a great distance, clouds, trees, buildings, etc. If, now, the dis-
tance from the lens to the images be measured, it will be found prac-
tically equal to the focal length of the lens. Repeat the experiment
with different lenses. Let the size and position of these images be
noted.
LIGHT: REFLECTION AND REFRACTION 307
When an object is at a great distance from a convex lens,
its image is at the focal distance from the lens, is real,
inverted, and smaller than the object.
It will be observed that this follows from the fact that
the rays which come from a given point on the object to
the lens are practically parallel to each other like rays of
sunlight. This case affords a good method for determin-
ing the focal length of a lens.
Since rays of light which diverge from the principal focus
of a convex lens become parallel to the principal axis after
passing through, it follows that there can be no image of a
small object placed at the principal focus.
313. Images Formed by Concave Lenses. It is obvious
from 311 that a concave lens cannot produce a real
image, since it always tends to scatter the light. This
fact, however, is of value in the construction of certain
optical instruments, as will appear later.
Hold a concave lens between the eye and a candle flame. No mat-
ter how far the flame is from the lens, the only image produced is a
small erect one behind the lens.
Hence the image produced "by a, concave lens is always ap-
parently on the same side of the lens as the object, is virtual,
erect, and smaller than the object.
314. Construction of Images Formed by Lenses. The
construction of the images produced by lenses will serve
to bring out clearly the nature of the image in each of the
cases illustrated by experiment in 312.
The different cases of lenses now to be studied will be
found to correspond closely to those of curved mirrors
which were treated in section 295. In each case the com-
plete construction should be accurately made on a scale
somewhat larger than that used in the illustrations as
here given.
308
A HIGH SCHOOL COURSE IN PHYSICS
Case I. When the object is placed at more than twice the
focal distance from a convex lens.
Let ED, Fig. 243, be a convex lens whose centers of curvature are
at C and C'. Let AB represent an object so placed that the distance
FIG. 243. Method of Locating the Image Produced by a Convex Lens.
OI is more than twice the focal length OC. Now if rays A E and BD
be drawn parallel to the principal axis ///, the refracted rays will
pass through the principal focus jP, which is at C' ( 308). Again,
the*-ays that pass through the optical center of the lens O enter the
lens and emerge from it at points where the surfaces are parallel and there-
fore suffer no permanent change in direction. (See 306.) Let the
line AO be produced through the lens until it meets the line EFak a.
Thus a is the conjugate focus of A. Similarly b is found to be the
conjugate focus of B. Therefore ab is the image of the 'object AB.
Case II. When the object is at more than once and less
than twice the focal distance from a convex lens.
In this case the method of construction is precisely the same as in
the preceding one; but on account of the fact that the object has
been brought nearer the lens, the divergence of the rays before refrac-
FIG. 244. Illustrating the Production of a Real and Magnified Image.
tion (which is represented by angle OAE) is greater than before, and
hence they are brought to a focus a at a greater distance from the lens.
LIGHT: REFLECTION AND REFRACTION 309
Figure 244 shows clearly the construction. Does the description given
in 312 apply to the image that is found by construction ?
It is to be observed that Case I changes to Case II when
the object is placed at twice the focal length from the lens.
In this instance the image and obje'ct are of equal size and
are equidistant from the lens.
Case III. When the object is at less than the focal dis-
tance from a convex lens.
Two rays are drawn from each of the points A and B, Fig. 245,
precisely as in the two preceding cases. But since the angle of
divergence EA is so large, the lens is not able to cause the rays to
converge to a real focus ; i.e. the refracted rays EF and A never meet
after leaving the lens. If, however, the refracted rays enter an eye, an
apparent image of A will be seen at a, which is the intersection of the
FIG. 245. The Production of a Virtual Image by a Convex Lens.
refracted rays when produced behind the lens. Since the effect is an
illusion, the image is a virtual one. Does the description given in
312 apply to this image?
Case IV. When an object is viewed through a concave lens.
r~i
FIG. 246. Constructing the Image Produced by a Concave Lens.
310 A HIGH SCHOOL COURSE IN PHYSICS
Rays A and BO, Fig. 246, are drawn as in the preceding cases.
But the parallel rays AE and BD are turned away from the principal
axis CC' as if their origin were at the center of curvature C 1 ( 309).
Thus the angle of divergence EA is increased by the lens to the
value EaO. Consequently, when the refracted light is received by an
eye, the image which is virtual and erect appears to be behind the
lens, but nearer and always smaller than the object.
315. The Lens Equation. The experiments of the preceding
sections have shown that the position of an image formed by a lens is
determined by the focal length of the lens and the distance from the
lens to the object. If p represents the distance from the lens to the
object, q the distance from the lens to the image, and f the focal
length, then the following relation between these distances will be
found to exist :
H+ J - ( 3 >
f p q
Referring to Fig. 243, we observe that the triangles -407 and aOH
are similar. Hence = ~ - If the lens be thin and a line be
an Un
drawn from E to D, it may be assumed to pass through the point 0.
EO OF
Then the triangles EFO and aHF are similar. Therefore, 77 = 7
an tir
Since A I = EO, the first member of these two proportions are equal.
Hence, by substituting p for 01, q for OH, and f for OF, we obtain
Clearing of fractions, transposing, and dividing by pqf gives
UI+i.
/ P q
Equation (3) is useful in determining the focal length of a lens.
For example, let the image of an object which is 60 cm. from a lens
be focused 40 cm. from the lens. By substituting these values for p
and q, we find the value of f, the focal length, to be 24 cm.
316. Relative Size of Object and Image. By referring
to Fig. 243 and the above discussion the following propor-
tion is found to be true:
AI OI
LIGHT: REFLECTION AND REFRACTION 311
But aHis the image of AL Therefore, the ratio of the
size of the object to the size of the image is equal to the ratio
of their respective distances from the lens. This relation
may be easily verified by experiment.
EXERCISES
1. What kind of mirrors and lenses always produce virtual
images ?
2. Under what conditions do convex lenses produce real images?
When is the image produced by a convex lens virtual ?
3. If one half of a convex lens be covered with an opaque card,
what will be the effect upon the real images produced by it ? Test
your answer by experiment.
4. How can you test a spectacle lens to ascertain whether it is
convex or concave ?
5. By the help of equation (3) compute the focal length of a
lens when the image of a candle flame 120 cm. away is focused at a
distance of 60 cm.
6. The focal length of a lens is 50 cm. If an object is situated
at a distance of 75 cm. from the lens, how far from the lens will its
image be focused ?
7. An object is placed 30 cm. from a lens whose focal length is
45 cm. Locate the image by employing equation (3).
SUGGESTION. When the minus sign precedes the result obtained
by using the equation, the inference is that the image is virtual.
8. What is the height of a tree 350 ft. away when its image on a
screen 10 in. from a convex lens is 2 in. in height? Ans. 70 ft.
5. OPTICAL INSTRUMENTS
317. The Simple Magnifier or Reading Glass. It is a
common occurrence to see a botanist examining the details
of a flower or a jeweler adjusting the minute parts of a watch
by the help of a convex lens. Large convex lenses are
frequently used as an aid in reading, and are therefore
often called reading glasses. In these cases the object to
be examined is placed a little nearer the lens than the
principal focus, while the image is viewed by placing the
312 A HIGH SCHOOL COURSE IN PHYSICS,
eye on the opposite side of the lens, as shown in Fig. 240.
The instrument owes its importance to the fact that a
magnified image is visible behind the lens, as shown in
Fig. 245.
318. The Photographic Camera. Two important prin-
ciples are employed in the photographic camera : (1) a
convex lens produces a real image of objects placed beyond
its principal focus, and (2) light has the property of pro-
ducing chemical changes in certain compounds of silver.
The camera is a light-proof
box, or chamber, Fig. 247,
provided at the front with
a convex lens L and at the
back with a ground-glass
screen which can be replaced
by a "sensitized" plate or
film for receiving the image.
The image is first focused on
the screen by varying its dis-
tance from the lens, after
which the sensitive plate is introduced in a light-proof
holder. The shutter of the lens is now closed, and the
cover of the plate-holder removed. When all is in readi-
ness, the lens is uncovered for a sufficient time to enable
the transmitted light to produce the desired effect upon the
plate. The plate is now covered and taken to a dark room,
where a "developing" process brings out a visible and per-
manent image. The plate thus treated is called a " neg-
ative " because of the reversal of light and shade in the
picture upon it, and may be used in the reproduction of
any number of positive photographs on prepared paper.
319. The Eye. Although the eye is a very complicated
structure, its action depends on one of the simplest cases
of refraction that we have studied. The eye is essentially
LIGHT: REFLECTION AND REFRACTION 313
a small camera at the front of which the cornea <7, Fig. 248,
the aqueous humor A, and the crystalline lens take the
place of the convex lens of that
instrument. When the eye is
directed toward an object, a
small, real, and inverted image
is produced on the retina,
which is an expansion of the
optic nerve N and covers the
inner surface of the eyeball at
the back. This does not mean, FlG - 248 - -Sectional View
of the Eye.
however, that we see things
upside down. The relative position which we ascribe to
objects is the result of experience aided by the sense of
touch, etc., and the fact that images are inverted on the
retina has little effect on the ideas which the impression
gives us. It will be observed that the impressions remain
the same even when the eye is tilted or inverted.
The eye adjusts itself to objects near and far by chang-
ing the focal length of the crystalline lens. When a
normal eye is completely relaxed, the lens has the proper
curvature for focusing light from distant objects (i.e. par-
allel rays) upon the retina. When, however, we wish to
view an object near at hand, as in reading, small muscles
within the eye cause the curvature of the crystalline lens
to increase until the image is again focused upon the sen-
sitive retina.
320. Spectacles and Eyeglasses. Although a normal
eye with complete relaxation focuses parallel rays upon
the retina, as in Fig. 249, it should also be able to focus
with ease light that comes from an object at a distance of
10 inches or more. The eye is defective when it cannot
accomplish the performance of these functions without
unnatural effort.
314
A HIGH SCHOOL COURSE IN PHYSICS
If the retina is too far from the crystalline lens, parallel
rays will not be brought to a focus upon it, but in front
of it. This defect is called myopia, or near-sightedness.
(.Z) Fig. 250 illustrates this con-
dition. It is at once obvious that the
crystalline lens produces too great a
FIG. 249. A Normal Eye convergence of the light. This can
be corrected by using a concave lens
of suitable curvature, as shown in
(.2) Fig. 250. Hence concave spec-
tacles are used to assist myopic eyes.
Again, the eyeball may be too short
. (2) from front to back, in which case the
focus of parallel rays will be behind
when Relaxed.
(2)
FiG.250.-TheMy7picEye the retina > aS sh wn in
and its Correction. It is clear in this instance that the
crystalline lens does not converge the
rays sufficiently for distinct vision.
This defect is called hypermetropia, or
far-sightedness. In order to correct
the fault, a
convex lens
of suitable
FIG. 251. The Hyperme-
tropic Eye and Its Cor- Curvature
rection. is needed,
which assists the crystalline lens
to produce an adequate conver-
gence of the light, as shown in (2).
The most prevalent defect in
^ r, T . ,, , FIG. 252. An Astigmatic Eye
the eyes of young people IS that Sees these Lines with Unequal
known as astigmatism. Astigma- Distinctness.
tism is due to the fact that the crystalline lens is not sym-
metrical about its axis. In other words, a vertical section
through the lens differs in form from a horizontal section.
LIGHT: REFLECTION AND REFRACTION 315
Such an eye sees the lines of Fig. 252 with unequal distinct-
ness. This defect is corrected by the use of a lens whose
vertical and horizontal sections possess suitable curvatures
to make up for the deficiencies in the crystalline lens.
321. The Compound Microscope. The compound micro-
scope consists of a convex lens (9, Fig. 253, of short (say -^ in.)
focal length, which is called
the objective, and a larger con-
vex lens E, called the eye-
piece. When the object to
be viewed, AB, is placed a
little beyond the principal
focus of 0, a ieal, inverted,
and magnified image is pro-
duced at ab ( 312). When
this real image is viewed
through the eye-pie^e, a
magnified virtual image is'
seen at a'b' .
322. The Astronomical
Telescope. The principal
part of a modern astronomi-
cal telescope is the large
convex lens 0, Fig. 254,
called the object glass. This is designed to collect a large
amount of light in order that the real inverted image ab
that is formed may be sufficiently brilliant. This image
FIG. 254. The Astronomical Telescope.
316
A HIGH SCHOOL COURSE IN PHYSICS
falls close to the eye-piece E whose function is precisely
the same as in the compound microscope which is described
in the preceding section. The inversion of the image is of
little consequence in astronomical telescopes, but for view-
ing terrestrial objects this feature would be a defect.
323. The Opera Glass, or Galileo's Telescope. The
honor of having invented the original form of the tele-
FIG. 255. Illustrating the Principle of tke Opera Glass.
scope belongs to Galileo, 1 who constructed the. first instru-
ment about 1610. Two Galilean telescopes arranged side
by side form an opera glass or a field glass. An object
glass <?, Fig. 255, converges the light to form a real image
at ab. Before the rays reach the focus, however, they are
intercepted by a concave lens which gives them a slight
divergence as they enter the eye. As a consequence, an
erect and magnified virtual image is seen at a'b' .
324. The Projecting Lantern. The projecting lantern,
Fig. 256, consists of a powerful source of light A whose
FIG. 256. Illustrating the Principle of the Projecting Lantern.
1 See portrait facing page 70.
LIGHT: REFLECTION AND REFRACTION 317
rays are concentrated upon a transparent picture B by the
convex condensing lenses L. At the front of the instru-
ment is placed the projecting lens P which forms a real,
inverted, and enlarged image 'of B upon the screen S.
The source of light is usually an electric arc lamp or
a calcium light. The latter is produced by directing an
exceedingly hot flame, produced by burning a mixture of
hydrogen and oxygen, against a piece of lime. When
raised to a high temperature, the lime becomes intensely
luminous.
325. Binocular Vision. The Stereoscope. On account of
the fact that the two eyes are separated by a distance of 6 or 7 centi-
meters, the images produced upon the two retinas are not precisely alike.
This has the effect of giving to an object the appearance oi solidity or
depth. Advantage has been taken of this fact in the stereoscope, an
instrument which is so constructed as to present to each eye a similar
image to that which it would receive if the object itself were present.
A double photograph is first made by means of a camera having two
objectives separated by a distance about equal to that between the
two eyes. The two pictures thus taken differ just as much as would
the corresponding images upon the .
retinas of the eyes. These pictures P
are now mounted on the stereoscope /?.
at A and B, Fig. 257, so as to be
viewed by the two eyes through the f
half -lenses m and n. These lenses FIG. 257. Illustrating the Principle
are so adjusted that the images pro- of the Stereoscope,
duced upon the retinas are related in position precisely as in ordinary
vision. On this account a perfectly natural blending of the two im-
pressions is brought about as though the object itself were in the di-
rection of C. The observer is therefore conscious of the presence of
only one photograph, which gives the effect of extension in a degree
that is remarkably true to nature.
326. The Kinetoscope The kinetoscope, kinematograph, or
moving-picture machine, is a common object in most cities and
villages. A life-like motion is given to pictures projected on a
screen by means of a series of transparent photographs taken as
follows :
318 A HIGH SCHOOL COURSE IN PHYSICS
A camera is provided with a shutter that opens and closes auto-
matically about 12 times a second. The instrument also contains a
long, narrow, sensitive film ivhich moves along about 2 centimeters while
the shutter is closed, and remains stationary while the shutter is open.
With this a series of pictures is taken, each of which differs slightly
from the preceding, provided any moving object is in the field of the camera.
These pictures are thrown upon a screen with a projection lantern
in precisely the same order and with the*same rapidity as they were
taken. On account of the fact that the sensation produced by one
picture remains until the next picture appears, the observer is uncon-
scious of any interruption in the illumination of the screen upon
which the pictures are produced.
EXERCISES
1. While changing the attention from a distant object to a near
one, does the crystalline lens flatten or thicken?
2. A photographer finds that the desired image of a building more
than covers the area of the plate to be used. How can the size of the
image be reduced to fit the plate?
3. When the spectacle lens used to correct a myopic eye is placed
in front of a normal eye, is the image of a distant object behind or in
front of the retina?
4. How can you test your eyes for astigmatism?
5. The crystalline lens becomes less elastic with age. Account for
the spectacles with double lenses which are frequently worn.
6. The picture projected on a screen by a projecting lantern is
found to be too large. Which way must the instrument be moved in
order to reduce its size?
7. Why is it necessary to " focus " a microscope or a telescope upon
the object to be viewed ?
SUMMARY
1. Light is reflected from polished surfaces in such a
manner that the angle of reflection equals the angle of
incidence ( 282 and 283).
2. Light is diffused from unpolished surfaces. Tt is
the power of diffusing light that renders objects visible
from different points of observation when light falls upon
them ( 284).
LIGHT: REFLECTION AND REFRACTION 319
3. The image produced by a plane mirror is as far be-
hind the mirror as the object is in front of it ( 285 to 289).
4. The tendency of a concave mirror is to collect rays of
light. Thus parallel rays are reflected through a common
point called the principal focus ( 29(0.
5. The tendency of convex mirrors is to scatter light.
Hence the principal focus is unreal, or virtual ( 291).
6. The images formed by a convex mirror are always
virtual, erect, smaller than the object, and behind the
mirror ( 292).
7. The images formed by a concave mirror depend on
the position of the object relative to the center of curva-
ture ( 294).
8. Light is refracted or bent toward the perpendicu-
lar to the surface where it enters a medium as glass or
water from the air, -and away from the perpendicular
when it emerges from the medium into the air. Refrac-
tion is due to the fact that the speed of light is less in
water, glass, etc., than in air or a vacuum ( 297 to 299).
9. The index of refraction of a medium expresses the
ratio of the speed of light in air to its speed in that
medium ( 300 to 302).
10. Total reflection always takes place when light
travels in one medium toward another in which its speed
is greater, provided the angle of incidence upon the
boundary surface is greater than the critical angle ( 303
to 305).
11. Lenses are classed as convex or concave according to
form, and as converging or diverging according to their
effect on light ( 307).
12. Convex, or converging, lenses tend to collect light.
Rays which are parallel before reflection are caused to
320 A HIGH SCHOOL COURSE IN PHYSICS
pass through a common point, called the principal focus
( 308).
13. Concave, or diverging, lenses tend to scatter light,
and therefore the principal focus is unreal or virtual ( 309).
14. The images formed by convex lenses depend upon
the relative position of the object and the principal focus
( 312).
15. The images formed by a concave lens are always
virtual, erect, smaller than the object, and on the same side
of the lens as the object ( 313).
16. Conjugate focal distances p and q are related mathe-
matically to the focal distance / as shown by the following
equation :
17. The sizes of image and object are in proportion to
their respective distances from the lens ( 316).
18. The convex lens is employed in the reading glass,
camera, spectacles, and the eye. Two or more convex
lenses are used in the compound microscope, telescope,
projecting lantern, etc. Concave lenses are used in some
spectacles, and in the eye-piece of the opera glass ( 317
to 326).
CHAPTER XV
LIGHT: COLOR AND SPECTRA ^/
1. DISPERSION OF LIGHT: COLOR
327. Decomposition of White Light. Let sunlight pass
through a narrow slit into a well-darkened room and fall obliquely on
a glass prism, as shown
in Fig. 258. As previ- \Suniight,
ously shown ( 306), the
beam will be refracted;
but when the refracted
light is allowed to fall on
a white screen, a beautiful
band of different colors -
will be seen. Among
these will be recognized
red, orange, yellow, green,
FIG. 258. The Separation of White Light into
its Components.
blue, indigo, and violet, although there is no sharp line of demarca-
tion between them.
From this experiment we can only infer that white light
is a mixture of the several colors seen on the screen. In
fact, if a similar prism is available, the colors may be
turned together again to form
white light by placing the two
prisms as shown in Fig. 259.
The band of color produced
by the separation of light of
any kind is called a spectrum,
and the process of separation
in which the light of different colors is refracted in vary-
ing degree is called dispersion.
22 321
FIG. 259. Colors of the Spectrum
Added to Produce White.
322 A HIGH SCHOOL COURSE IN PHYSICS
328. Cause of Dispersion. Direct measurements of the
waves of light of different colors show that they are of very
different lengths, those of red light being longest and of
violet shortest. It is therefore clear that waves of differ-
ent lengths are refracted unequally by the prism, the red
or longest waves being bent least, and the violet or shortest
waves most. The following table shows the approximate
wave lengths of the various colors:
WAVE LENGTHS OF LIGHT
Red . . . 0.000068 cm. Green . . . 0.000052 cm.
Orange . . 0.000065 cm. Blue . . . 0.000046 cm.
Yellow . . 0.000058 cm. Violet . . . 0.000040 cm.
329. Achromatic Lenses. When white light passes through a
simple lens, it is dispersed as well as refracted, i.e. the violet light is
brought to a focus somewhat nearer the lens than the red, since it suffers
the greater refraction ( 328). On this account the images formed by
simple lenses are always fringed with color, which is a serious fault in
optical instruments. It is, however, possible to
remedy this defect by combining two lenses,
one being a double convex lens of crown glass, the
other a plano-concave lens (plane on one side,
FIG. 260. Achro- ' concave on the other) of flint glass, as shown in
matic Lens. Fig. 260. In this lens system the dispersion pro-
duced in one part is just neutralized by the other,
while the refraction is reduced only about one half. Such a system
of lenses is called an achromatic lens, since all color is eliminated.
330. Color of Objects. Let the spectrum of sunlight be pro-
jected on a white screen. Hold small pieces of paper or cloth of differ-
ent colors in the various parts of the spectrum, and observe the effect.
A red object will be a brilliant red when held in the red of the spectrum,
and black in other parts. Blue and violet objects show a coloration
only when placed near the violet end of the spectrum. A black object
will appear black everywhere, and a white one reflects that color of
the spectrum in which it is placed.
The experiment shows that the color of an object
depends (1) on the light which falls upon it and (2) on
LIGHT: COLOR AND SPECTRA 323
the light it reflects to the eye. A red object is red be-
cause it reflects mainly red light, all other incident light
being absorbed by the material, i.e. transformed into heat
( 259). If, therefore, no red light falls upon it, it can
reflect no light and is black. A black object appears black
because it absorbs practically all colors alike ; and a white
body is white because it reflects all colors to the same
extent.
331. Color of Transparent Bodies. Project the spectrum of
sunlight, and hold pieces of glass of different colors in the beam at
any point. It will be observed that a red glass, for example, transmits
mainly red light and absorbs the rest, that green glass transmits
mainly green light, etc. Placing two pieces at once in the path of the
light results in the transmission of that light only which neither can
absorb.
It is therefore clear that the color of a transparent body
depends on the color of the light which it transmits. The
color that we see in any body is the combination of all the
light that is not absorbed by that body. A colorless body is
one that transmits all colors equally.
332. Complementary Colors. Project the spectrum of sunlight
or the light from an electric arc,
and reunite the colors by means of
a similar prism, as shown in Fig.
261. The result is, of course,
white. Now place a card C be-
tween the prisms, and let it in-
,-,,.' . _, FIG. 261. Production of Comple-
tercept the red light only. The mentary Colors.
spot of light on the screen S turns
to bluish green. If the card is now caused to cut out the violet and
blue, a greenish yellow results.
Two colors, as red and bluish green, into which white
light can be resolved are called complementary colors. The
union of complementary colors results in the production of
white. When any color, or combination' of colors, is
324 A HIGH SCHOOL COURSE IN PHYSICS
removed from the spectrum of white light, the color pro-
duced by combining the remaining colors is the comple-
mentary of the part removed. The two complementary
colors most easily obtainable are yellow and blue. If one
half of a circular disk be colored blue and the other half
yellow, the color effects may be combined by rotating the
disk on a whirling machine. If the whirling disk be
strongly illuminated, it appears white.
TABLE OF COMPLEMENTARY COLORS
Red and bluish green. Green and purple.
Orange and greenish blue. Violet and greenish yellow.
Yellow and blue.
333. Color of Pigments. The color of pigments used
in paints and coloring materials is due to their power of
absorbing incident light, similar to that shown in 330 in
the case of colored cloth and paper. The mixing of pig-
ments is a very different thing from mixing lights or
colors. A striking example is furnished by pigments that
reflect the complementary colors blue and yellow.
Pulverize pieces of yellow and blue crayon, but keep the
powders separate. If now about equal portions of the two
powders be thoroughly mixed together, a bright green
appears.
The cause of the phenomenon is the imperfect absorption
of the pigments. The yellow powder subtracts from white
light all except yellow and green, and the blue powder sub-
tracts all except blue and green. Hence the only color not
absorbed by one powder or the other is green.
2. SPECTRA
334. The Solar Spectrum. The spectrum of sunlight,
or the solar spectrum, frequently presents itself in nature
in the rainbow. In the production of the rainbow the sun-
LIGHT: COLOR AND SPECTRA
325
light is dispersed by spherical raindrops. Light from the
sun .strikes a drop at A, Fig. 262, and is refracted to B.
At B a portion of the
light is reflected to (7,
where it emerges and
enters the eye E. At
the points A and dis-
persion accompanies re-
fraction, and the red
light takes the direction
rrr, while the violet fol-
lows the path vvv. A
study of Fig. 263 will
show that the eye re-
ceives the red from a greater angle of elevation than the
violet ; hence red lies at the outside of the rainbow.
FIG. 262. Dispersion of Sunlight by
a Raindrop.
FIG. 263. Showing the Spectrum Colors in their Relative Positions in the
Rainbow.
The secondary rainbow often accompanies the primary
one. In this case, as Fig. 264 shows, light suffers two
326
A HIGH SCHOOL COURSE IN PHYSICS
reflections within the drop and emerges with the violet at
the greater angle of elevation ; hence here in the secondary
bow the red band is the inner circle of color.
FIG. 264. Showing the Formation of a Secondary Bow.
335. Absorption of Light by the Medium. Let a narrow,
horizontal beam of sunlight come into a darkened room through a
vertical slit S, Fig. 265, and pass through a convex lens L to the
carbon disulphide prism P. (The dispersion produced by a glass
Sunlight
FIG. 265. Method of Projecting the Solar Spectrum
prism is too small to give satisfactory results.) Reflect some of the
light from the back of the prism to the screen AB where the spec-
trum is to be formed, and adjust the lens until it focuses a sharp
LIGHT: COLOR AND SPECTRA 327
image of the slit on the screen. A good spectrum can now be produced
by setting the prism in the position shown in the figure.
While the spectrum is on the screen, place before the slit at C a
flat tank or bottle containing a dilute solution of chlorophyl, made by
soaking a quantity of grass in warm alcohol. It will be observed
that a broad dark band is formed in the red portion of the spectrum
and a less marked band appears in the green.
It appears from this experiment that a certain portion
of the solar spectrum may be removed by the absorption
of certain wave lengths in the medium through which the
light passes. The resulting spectrum is called an absorp-
tion spectrum to distinguish it from the continuous spec-
trum that is obtained when none of the light is absorbed.
Continuous spectra are, in general, given off by all lu-
minous solids and liquids. It will appear presently that
the solar spectrum is an absorption spectrum.
336. The Solar Spectrum in Detail. The most interest-
ing and remarkable features of the solar spectrum are not
revealed in the rainbow, nor in the spectrum ordinarily
projected by a prism, on account of the overlapping color
bands. In order to produce a pure spectrum in which the
colors are more distinctly separated than before, it is nec-
essary to work with a narrow slit which is very sharply
focused by a lens on a white screen.
Let the solar spectrum be projected as before, but make the slit
about one half a millimeter in width and use a long focus (about
50 centimeters) lens. Place the screen about 1 meter from the lens and
prism. By making all the adjustments with care, it will easily be
seen that the spectrum is crossed vertically by many dark lines. By
moving the screen back and forth the best position for showing the
lines can readily be found.
These dark lines across the solar spectrum are known as
Fraunhofer lines in honor of the German astronomer
who first mapped them out about 1814. When the spec-
trum is magnified sufficiently, hundreds of these lines
328 A HIGH SCHOOL COURSE IN PHYSICS
become visible. The presence of the Fraunhofer lines
shows that certain wave lengths are either absent
entirely from sunlight or that they are go weak as to
appear dark by contrast. The solar spectrum is thus
observed to be an absorption spectrum.
337. Fraunhofer Lines Produced by Absorption. The
explanation of the dark lines of the solar spectrum is due
to Stokes and Kirchhoff, the former an English, the latter
a German, physicist. The theory is based on the follow-
ing experiment:
Project a well-defined solar spectrum as in the preceding experi-
ment. Now sprinkle common salt (sodium chloride) on the wick
of an alcohol lamp, place the lamp just below the slit at C, Fig. 265,
and ignite the alcohol. A bright yellow light will be emitted by
the volatilized salt, but on the screen will appear a darkening of a
Fraunhofer line in the yellow part of the spectrum.
It thus appears that when light passes through the so-
called sodium flame, the absorption of a certain wave
length takes place. In the same manner the light from
the white-hot central mass of the sun, which alone would
give a spectrum without dark lines, passes through sur-
rounding vapors, each of which, like the sodium vapor,
has the power of removing light of certain wave lengths.
The wave lengths absorbed by a heated gas or vapor are pre-
cisely those which the
vapor itself is capable of
emitting.
338. Bright-line Spec-
tra. Prepare an alcohol
lamp for producing yellow
light as in the preceding
FIG. 266. Apparatus Arranged for Bright- experiment. Place the lens
line Spectra. L> Fig> 2 66, so that the slit
A is at its principal focus, and set the prism as shown in the figure.
Focus a small telescope T on a distant object, and then place it for
LIGHT: COLOR AND SPECTRA 329
receiving light from the prism. Place the lamp at F, and ignite
the alcohol. If all is properly adjusted, a bright double yellow line
will be visible in the telescope. This is the spectrum of incandes-
cent sodium vapor. Repeat the experiment by using strontium
chloride in another lamp. Red and blue lines should appear. By
using calcium chloride, red and green lines become visible. The
yellow sodium spectrum will always appear, since sodium exists as an
impurity in the lamp wick and in practically all salts.
These experiments show that incandescent vapors emit
light in which only certain wave lengths are present. The
spectra of such bodies are therefore bright-line spectra.
Since these spectra are characteristic of the chemical ele-
ments, many substances can be identified by the wave
lengths of the light which their incandescent vapors emit.
The spectra of the chemical elements are as well known as
their densities, specific heats, and other physical and chemi-
cal properties. Several new elements have been discovered
by the observation of bright spectral lines which could not
have been produced by any known substances. An incan-
descent vapor also affords a convenient means of obtaining
light of one wave length or color, i.e. monochromatic light.
339. Solar Elements. Since the spectra of many incan-
descent vapors have been examined and compared with
the Fraunhofer lines of the solar spectrum, most of these
lines have been accounted for just as the existence of
incandescent sodium vapor surrounding the sun accounts
for the dark sodium line. (See 337.) If the corre-
spondence between lines of the solar spectrum, shown in
the middle in Fig. 267, and the spectrum of iron vapor, be
noted, there can be no doubt as to the existence of iron
FIG. 267. Showing the Coincidence of the Bright Lines of the Spectrum of
k Iron with Some of the Dark Lines of the Solar Spectrum.
330 A HIGH SCHOOL COURSE IN PHYSICS
in the sun. Other solar elements are calcium, hydrogen,
sodium, nickel, magnesium, cobalt, silicon, aluminium,
titanium, chromium, manganese, carbon, barium, silver,
zinc, and many others. It is an interesting fact that the
element helium was first discovered in the sun by Sir
Norman Lockyer, of England, by means of its dark lines
in the solar spectrum. Later, in 1895, Sir William
Ramsay discovered an element that gave the same spec-
trum, and which was therefore given the same name.
Helium is at present a comparatively well-known gas that
can be produced in all chemical laboratories.
The instrument by which the spectra of celestial and
terrestrial objects are produced is called the spectroscope.
By combining the spectroscope with the telescope, astrono-
mers have succeeded in ascertaining to some extent the
composition of many stars and in collecting other informa-
tion of great scientific value.
EXERCISES
1. What kind of a spectrum should moonlight give ?
2. What kind of a spectrum would you expect to obtain by dis-
persing the light from a live coal by means of a prism?
3. The luminosity of an oil or gas flame is due to heated particles
of carbon. What should be the nature of the spectrum of a kerosene
lamp flame ?
4. What is the position of the sun relative to falling rain and an
observer when a rainbow is seen?
5. Why do colored fabrics often appear different when viewed by
artificial light?
6. If the waves producing the sensation of red were all absorbed
from sunlight, what color would remain? What color would objects
that were formerly red appear to have ?
3. INTERFERENCE OF LIGHT
340. Color Bands by Interference. We have seen how
composite light can be separated into its component colors
LIGHT: COLOR AND SPECTRA
331
by means of a prism, but there
still remain a great many cases
of color formation which are not
at all due to dispersion or ab-
sorption.
Let two strips of plate glass, A and
B, Fig. 268, about 1 inch wide and 5
inches long, be separated at one end by
a piece of tissue paper C (exaggerated
in cut) and the other ends clamped
tightly together. (The plate glass
covers accompanying sets of small
weights may be used.) Produce a yel-
low sodium flame by bringing in con-
tact with a Bunsen or alcohol flame a
FIG. 268. Alternate Dark and
Bright Bands Produced by In-
terference of Light Waves.
piece of asbestos D, wet with a solution of common salt. Now hold
the glass strips behind the flame, and observe the images produced.
A series of dark and yellow bands will be seen extending transversely
across the glass.
The explanation of
this interesting phe-
nomenon depends on
the wave theory of
light. The flame, as
we know, sends out
only yellow light
(338). This is in
part transmitted and
in part reflected at
each glass surface
(282). Let AB and
AC, Fig. 269, repre-
sent the interior sur-
faces of the plates much
enlarged, and let the
wave line ab represent
Interference.
Re-enforcement,
interference.
Re-enforcement
FIG. 269. Diagram Showing Points of In-
terference and Reinforcement.
332 A HIGH SCHOOL COURSE IN PHYSICS
the light reflected at the point a on the surface AC.
Also let the dotted line a'b represent the waves reflected
at a' on the surface AB. These two trains of waves ob-
viously interfere and destroy each other just as do two
trains of sound waves when they coincide in this manner
( 190). Therefore, since at this place on the glass
plates the light waves cancel each other, we see a dark
band. But at the point c the case is different. Since
the thickness of the air film is here a quarter of a wave
length greater than at a, the train of waves reflected
from c' coincides with that reflected at c in such a manner
as to produce reenforcement. Hence at this point we see
the bright yellow band. Similarly the wave trains re-
flected at e and e' interfere and cancel, while at g and g 1
we again find reenforcement. Thus the dark and bright
bands appear alternately in the plates.
341. Color Bands in Soap Films. The following ex-
periment can easily be performed by letting a soap film take
the place of the wedge-shaped air film of the preceding
experiment.
Let a film of soapy water be produced on a wire loop as described
in 130. Hold the film behind a yellow sodium flame, and observe
the image in the film by reflected light. Many narrow bands of
yellow will appear which continue to grow broader and farther apart
until the film breaks.
When the wire loop is held in a vertical position, the
liquid runs slowly down from the top, forming a wedge-
shaped film that is thinnest at the upper edge. One por-
tion of the yellow incident light is reflected from the
front surface, and another portion from the back, after
traversing the thickness of the film. Hence the portion
reflected from the back passes through the film twice.
Now if the two reflected trains interfere, a dark band is
LIGHT: COLOR AND SPECTRA 333
produced ; but if they reenforce, a bright band of yellow
appears, precisely as described in the preceding section.
342. White Light Decomposed by Interference. The
result of the experiment described in 341 leads to the
explanation of the beautiful coloration produced when
the sunlight falls on soap bubbles, oil films on water, etc.
Let sunlight fall upon the plates of glass arranged as in 340.
Variegated bands occurring alternately will appear instead of the
yellow bands obtained when sodium light is used.
On account of the fact that sunlight, or white light, is
a composite of different wave lengths, the interference
of the reflected waves of red, for example, takes place at
a different point from that of the yellow. When the
waves of red are canceled by interference, the comple-
mentary color, or bluish green, is left. At the point where
waves of yellow interfere, its complement, or blue, appears.
Thus bands consisting of the complements of all the
spectral colors are produced.
SUMMARY
V. White light is decomposed into the spectral colors by
passing through a triangular prism of glass, water, ice, etc.
The cause of dispersion lies in the fact that different wave
lengths are retarded different amounts, and hence are
refracted in differing degree by the prism. Long waves
(red) suffer the greatest refraction, while the shorter
waves (violet) suffer least ( 327 to 329).
2. The color of an object depends both on the light
which falls upon it and that which it reflects to the eye.
Various wave lengths are absorbed by all except white
bodies ( 330).
3. The color of a transparent body depends on the color
of the light which it transmits ( 331).
334 A HIGH SCHOOL COURSE IN PHYSICS
4. Complementary colors are those which when added
in proper proportions produce white ( 332).
5. The color of pigments used in the manufacture of
paints, etc., is due to the absorbing power of the material
( 333).
6. The solar spectrum is the spectrum of sunlight. The
rainbow is an example. The pure spectrum is crossed by
numerous dark lines produced by the absorption of certain
wave lengths by heated gases in the solar atmosphere.
These lines reveal the chemical elements in the sun's com-
position ( 334 to 339).
7. Interference of light is brought about by the coinci-
dence of waves in such a manner as to weaken or cancel
each other. The alternate interference and reinforcement
of light waves in thin wedge-shaped films gives rise to the
colors seen in oil films, soap bubbles, etc. ( 340 to 342).
CHAPTER XVI
ELECTROSTATICS
1. ELECTRIFICATION AND ELECTRICAL CHARGES
343. An Electric Charge Produced. It is a matter of
common observation that a hard rubber comb acquires the
power of attracting bits of tissue paper and other very
light bodies simply by being drawn through dry hair. The
comb may also be put into this condition by being rubbed
with silk or flannel. Knowledge of this phenomenon
dates from the Greeks of 600 B.C., when it was known
that amber would attract light objects after having been
rubbed with silk. No advance was made in the science
of electricity until the time of Sir William Gilbert of
England, about 1600 A.D. At this time Gilbert found
that a great many substances, as glass, ebonite, sealing
wax, etc., could be given this power of attraction by
rubbing with fur, wool, or silk.
Test rods of glass, ebonite, sealing wax, etc., for the power of
attracting small pieces of dry pith before and after being rubbed
with silk, fur, and flannel.
See Fig. 270.
When a body pos-
sesses the property of
attracting light objects,
as hair, pith balls, and
bits of paper, it is said
to be electrified. The Fia 27(X ~ Action of an Electrified Glass Rod -
change is brought about by a charge of electricity. The
process by which a body is electrified is called electrifica-
335
336 A HIGH SCHOOL COURSE IN PHYSICS
tion. These terms are all derived from the Greek word
electron, meaning amber.
344. Electrical Charges of Two Kinds. Procure two large
sticks of sealing wax and
a glass rod. Electrify a
stick of sealing wax by rub-
bing it with a flannel or
fur and suspend it in a wire
stirrup as shown in Fig.
^ 271. Rub the other stick
Jto. 271. - Repulsion between Two Simi- of sealin S wax and brin S it;
larly Charged Bodies. near the suspended one. A
decided repulsion will be
observed. Now rub the glass rod with silk and bring it near the sus-
pended wax. Attraction takes place.
The experiment shows that the electrified glass and
sealing wax cannot be in precisely the same condition,
since they act differently toward the suspended body.
This difference in the behavior of electrified bodies is
said to be due to the kind of charge developed when they
are rubbed. Thus glass is said to be charged positively
when rubbed with silk ; and sealing wax, negatively when
rubbed with flannel or fur. Some specimens of glass are
electrified negatively when rubbed with cat's fur or flannel.
345. A Law of Electric Action. The preceding experi-
ment shows tluit two sticks of sealing wax repel each
other after being charged negatively. In the same man-
ner two positively charged glass rods will show a repulsion.
But any negative charge will attract a positive charge,
just as the glass attracts the suspended sealing wax when
both are electrified. Hence, we may infer that electrical
charges of a similar kind repel each other, and those that are
dissimilar attract.
346. The Electroscope. In order to detect the presence
of a charge upon a body, an instrument called the electro-
ELECTROSTATICS 337
scope is employed. The gold-leaf electroscope is shown in
Fig. 272. This instrument consists of a metal rod which
penetrates the rubber stopper of a flask. At the top the
rod terminates in a plate or ball, and at
the lower end it is provided with two
strips of gold foil. Under ordinary con-
ditions the leaves hang parallel ; but when
an electrical charge is brought near, they
diverge and thus show the presence of
electrification.
347. Determining the Kind of Charge. FIG. ^72. The
The electroscope is frequently used to Gold-leaf Eiec-
i. ^ i j F troscope.
ascertain the kind of charge on an elec-
trified body. The following experiment will show how
this can be done.
Make a proof plane by sealing a small coin or tin disk to the end
of a small glass rod to be' used as a handle. Touch the disk of the
proof plane to a positively charged glass rod, and then to the plate
of the electroscope. The divergence of the leaves will show that the
instrument is charged. Now, if the charged glass rod is carefully
brought near the electroscope, the divergence will increase ; but if
the negatively charged sealing wax is brought near, the divergence
at once decreases. While the electroscope is thus charged, bring up
an electrified rod of ebonite or a charged rubber comb, and note
whether the divergence increases or decreases. In this case the charge
on the ebonite will be found to act like that on the sealing wax and
hence produce a decreased divergence of the leaves.
In a word, the nature of an unknown charge is deter-
mined by observing whether its effect on a charged electro-
scope is like that of a positively charged glass rod or the
negatively charged sealing wax.
348. Positive and Negative
Charges Developed Simultane-
OUsly.-Let a flannel cap about 6
Time. inches long be made that will fit closely
23
338 A HIGH SCHOOL COURSE IN PHYSICS
over the end of an ebonite rod as in Fig. 273. A represents a silk
thread by which the cap may be handled. Now turn the rod in the
cap to electrify it and, without removing the cap, hold the rod near
the plate of the electroscope. Little or no charge will be detected.
Remove the cap by means of the thread A and present it to the elec-
troscope. When tested as in 347, the cap will be found to be charged
positively. If the rod be now tested, a negative charge will be found.
On account of the fact that the rod and cap together
produce no effect on the electroscope, we may infer that
their charges exactly cancel. The conclusion is, there-
fore, that when a certain quantity of one kind of electrifica-
tion is produced by rubbing a rod, an equal amount of the
opposite kind appears on the object with which it is rubbed.
349. Charging by Contact. By
means of a silk thread or silk fiber suspend
a small ball of dry elder pith as shown in
Fig. 274. Hold near the ball a positively
charged glass rod. The ball is at first at-
tracted to the rod and then violently repelled.
The repulsion shows that the ball by contact
with the rod has been charged with a kind of
electrification similar to that in the rod. In
FIG. 274. Experiment this case the charge is positive. Likewise the
with a Suspended ball will be charged negatively by contact
with a negatively charged body.
The experiment shows clearly that when an insulated
body comes in contact with a charged body, it becomes
charged with electricity of the same kind as that on the
charged body. In this way the proof plane used in 347
carried from the glass rod to the electroscope an electrical
charge of the same kind as that on the glass.
350. Conductors and Insulators. Select a number of pieces
of wood, metal, glass, ebonite, cardboard, leather, etc. Let one end of
a metal rod be supported on the electroscope and the other end on an
ebonite rod A, Fig. 275. Bring a charged body R against the end of
the rod opposite the electroscope. A sudden divergence of the leaves
ELECTROSTATICS 339
shows the transfer of a charge from R to the instrument. Experi-
ment with a rod of wood in the same manner. The divergence, if any
is produced, takes place more slowly than before if the wood is dry.
Glass and ebonite should be found
not to transfer any appreciable
charge unless their surfaces are
moist.
Some substances have the
power to transfer charges of FIG. 275. Testing the Conductivity
electricity, while others do of Rods,
not. Metals are shown to be good conductors ; dry wood
is a poor conductor, while glass and ebonite are practically
non-conductors. Non-conductors are called insulators.
Among the best insulators may be mentioned dry air,
glass, mica, shellac, silk, rubber, porcelain, paraffin, and oils.
Substances of all degrees of conductivity exist, varying
from the best conductors down to the best insulators.
EXERCISES
1. Place a piece of paper against the wall and stroke it with cat's
fur.^Lt will be found to adhere to the wall for several minutes.
Explain.
2. Why is it more difficult to brush lint from clothing in cold dry
weather than at other times ?
3. Draw a rubber comb through dry hair and test the charge de-
veloped on the comb. Now present a positively charged rod to the
charged hair and observe whether it is repelled or attracted. Com-
pare this experiment with that of 348.
4. After walking on a silk or woolen rug or over a glass floor, one
often finds that sparks will jump between the finger and a gas fixture
near which it is held. The gas may even be lighted in this manner.
Explain.
5. Support a dry pane of glass about 1 in. above a quantity of
small pieces of dry pith. Rub the glass with silk and explain the
agitation of the pith observed.
6. Balance a meter stick on the smooth bottom of a flask and see
if it is affected by a charged glass rod. Are only very light bodies
attracted?
340
A HIGH SCHOOL COURSE IN PHYSICS
2. ELECTRIC FIELDS AND ELECTROSTATIC INDUCTION
351. Lines of Force. We have already observed that
an electrified body has an effect upon another body even
when placed at a distance of several inches. Light objects
will rise from the table toward a charged glass rod, and
the leaves of an electroscope will often show a divergence
at a distance of four or five
feet from the charge. The
space in which an electric
charge affects surrounding
objects is called the electric
field due to that charge.
If lines are drawn in an
electric field to represent
at every point the direction
in which a charge, as A,
P.O. 276. -Lines of Force Emanating Fi g' 276 ' tends tO . mOV6
from a Charge. a very small, positively
charged body B, they are called lines of force. Thus every
electric field is assumed to be filled with lines of force.
Lines of force extend from positive charges to nega-
tive charges, as shown in Fig. 277. In other words, a
positive charge always exists at
one end of a line of force and
a negative one at the other.
Therefore, since each line of /
force must have two extremi-
ties, for every positive charge FIG. 277. The Electric Field be-
,, , , , tween Two Unlike Charges.
there must be somewhere a cor-
responding negative charge. This fact gives rise to 'the
phenomena shown in the following sections.
352. Electrification by Induction. Let a charged glass rod
be brought near a gold-leaf electroscope. The leaves begin to diverge
ELECTROSTATICS
341
when the rod is at a distance and spread more and more as the rod
approaches. On removing the rod the leaves fall together again.
The temporary effect produced in the electroscope, due
to the presence of a neighboring charge, is the result of
electrostatic induction. The leaves of the instrument are
obviously affected only while they are in the electrical
field around the charged rod, since they collapse as soon
as the rod is removed. In this case there is no change in
the amount of electrification on the glass rod, and the
effect can easily be shown to take place through an inter-
vening plate of glass or other insulating material. Hence,
in the process of electrostatic induction a transfer of elec-
tricity from one body to the other does not take place.
353. Electrical Separation by Induction. The condition
of an electroscope which is placed near a charged body, as
in the preceding section, is readily understood after the
following experiment f
Place two metal vessels A and B, Fig. 278, in contact on an elevated
block of paraffin, or some other good insulating material. Each ves-
sel should be provided with
a small pith ball attached
to the top by means of a
piece of cotton thread. Now
bring a positively charged
glass rod R near one of the
vessels, as B, and, by means
of the silk thread C, sepa-
rate the vessels before re-
moving the rod. When the
rod is taken away, the pith
balls will show that each
FIG. 278. Separation of Positive and
Negative Charges.
vessel has acquired a charge, but the charge on the rod R has not been
diminished. With the help of the proof plane and electroscope test
each charge ; that of B will be negative, that of A positive.
From this experiment it is clear that whenever an electri-
fied body is brought near an unelectrified insulated conductor,
342 A HIGH SCHOOL COURSE IN PHYSICS
the opposite kind of electrification is induced on the nearer
side and the same kind on the remote side.
354. Charging by Induction. An insulated metallic
body may be charged by making use of the separation of
positive and negative electricity, as shown in the preceding
section.
Hold the positively charged glass rod about 6 in. from the plate of
the gold-leaf electroscope. The leaves
diverge because the positive charge
--H -4- ,u " "% ^C- on the r d induces a negative charge
in the plate and a positive charge in
the leaves, as shown in Fig. 279.
While the rod is in this position,
touch the electroscope with the finger.
f / \ + The leaves collapse. Now remove the
FIG. 279. Charged RodjVcting finger and then the rod. The leaves
diverge again, thus showing that a
charge is left on the instrument. If
this charge be tested by bringing a negative charge near the elec-
troscope, an increased divergence will show that it is negative.
355. Explanation of the Process. The electrical con-
ditions that exist during the process of charging a conduc-
tor by induction are represented in Fig. 280. The presence
(I) (2) (3)
FIG. 280.- Illustrating the Process of Charging by Induction.
of the positively charged rod R produces a separation of
positive and negative electricity in the conductor A ( 353),
just as if an uncharged body possessed equal amounts of
these two kinds, as shown in (1). Lines of force extend
from the positive on the rod to the induced negative on
ELECTROSTATICS
343
the conductor, while other lines extend away from the
positive at the remote end to the walls of the room,
near-by objects, etc. When the conductor is touched with
the finger, as in (2), the repelled or "free" charge, which
in this case is positive, is permitted to escape through the
body to the earth. The negative or " bound " charge re-
mains on the conductor on account of the influence of the
charged rod R. On removing first the finger and then
the rod, the negative charge
distributes itself over the con-
ductor, as shown in (3). If R
is a negatively charged body,
the signs of all the charges will
simply be reversed.
356. Distribution of Electric-
ity on a Conductor. Insulate a
metal vessel A, Fig. 281, by placing
it on a dry tumbler B, or a plate of
paraffin or beeswax. Charge the ves-
sel as highly as possible and then
try to take charges from its interior
surface to the electroscope by means
of a proof plane c. It will be found
that no charge can be obtained in
this way. Now try to take a charge
Fia. 281. No Charge can be
Taken from the Interior Sur-
face of a Charged Body.
from the exterior surface of the vessel. The electroscope will show
that this attempt is successful.
This experiment shows very conclusively that an elec-
trical charge distributes itself over the exterior surface of
an insulated conductor. This is just the result that is to
be expected if we consider that the various parts of any
charge are mutually repellent. On this account they will
separate to the greatest extent possible, which is the case
when the charge is distributed over the exterior surface of
the body charged.
344 A HIGH SCHOOL COURSE IN PHYSICS
357. Distribution of a Charge not Uniform. Charge a large
insulated egg-shaped conductor, Fig. 282. By means of a proof plane
transfer a charge from the large end of the body to
the electroscope and observe the divergence of the
leaves. Now discharge the electroscope and test the
small end of the conductor in a similar manner. A
greater divergence of the leaves will be obtained.
It thus appears that an electrical charge
" IG tricai~Den- distributes itself over a conducting surface
sity is Great- in accordance with the shape of the body.
Printed End The quantity per square centimeter is
of this Con- greatest at the small end. In other words,
the electrical density is greatest where the
conductor is the most sharply pointed. In fact, if a sharp
point be attached to the charged conductor, the density at
the point may be so great that the charge will be sponta-
neously discharged into the surrounding air.
358. Effect of Points. By the help of sealing wax or shellac
attach the center of a sharp needle to a glass handle. Bring a charged
glass rod over the electroscope, and, while the rod remains in this
position, bring the eye end of the needle against the plate of the
electroscope and the point toward the charged rod. Now remove
both needle and rod, and the electroscope will be positively charged.
Again, hold a charged glass rod near an insulated conductor, as a
metal vessel, and then place the eye end of the needle against the
opposite side of the conductor. Remove the needle and then the rod
and test the conductor for a charge. A negative charge will be found.
The results of these experiments depend upon the electri-
cal discharge from pointed conductors. On account of
the great electrical density at a point, an intense field of
force exists in the immediate neighborhood. Air particles
are forcibly drawn against the point and charged by con-
tact with the same kind of electricity, after which they are
violently repelled. Thus a so-called electrical wind is set
up which conveys away the charge at a rapid rate.
ELECTROSTATICS 3^5
359. Lightning Rods. Positive evidence regarding the
identity of lightning and electrical discharges was secured
by the classical experiments of Benjamin Franklin 1 in 1752,
when he succeeded in drawing an electrical charge from a
thunder cloud along the string of a kite. Through his
suggestion lightning rods were first used as a protection for
buildings against damage by lightning. The principle has
been demonstrated in the preceding section. A strongly
charged cloud passes over a building, and between the cloud
and the building there is set up an intense field of force
( 851). If this field becomes of sufficient intensity, the
air, being no longer able to insulate, breaks down as an
insulator. The sudden discharge tears the roof of the
building, and the intense heat often produces a conflagra-
tion. The presence of a pointed conductor, however, lead-
ing from above the roof to the earth, permits a gentle and
harmless discharge of jelectricity to take place between the
cloud and the earth. The effectiveness of lightning rods
is often impaired by the use of dull points and poor ground
connections.
The thunder that accompanies a lightning flash is caused
by the impact of the air as it is forced in to fill the partial
vacuum which is developed along the line of electrical dis-
charge. At a distance from the discharge, the direct
report is followed by echoes from the clouds and woods,
causing the rumblings so common in most localities.
EXERCISES
1. In testing a charge, why is it necessary to work with a charged
electroscope ?
2. AVhen a gold-leaf electroscope is charged with negative elec-
tricity, for example, why will the approach of a positively charged
body produce first a decrease and then an increase of the divergence
of the leaves?
1 See portrait facing page 346.
346
A HIGH SCHOOL COURSE IN PHYSICS
3. If several insulated metal vessels are placed in a row, but not in
contact with each other, what will be the electrical condition of each
when a positively charged rod is held near one end of the row? Illus-
trate by means of a diagram showing four such vessels.
4. If the vessel at the end of the row near the charged rod is
touched with the finger and then both finger and rod are removed,
what will be the electrical condition of each vessel ? Illustrate this
case by a diagram.
5. Represent by diagrams the fields of force existing under the
conditions described in Exer. 3.
6. Represent the fields of force as they exist under the conditions
given in Exer. 4 and compare each field with the corresponding one
of the preceding exercise.
3. POTENTIAL DIFFERENCE AND CAPACITY
360. Electrical Flow. It has already been observed in
349 that a charge of electricity can be transferred by a
conductor from an electrified body to the electroscope.
The effects that accompany such a transmission of elec-
tricity, as will be seen later, enable it to be employed as
one of the most important agents under the control of man.
The following experiment will bring out more clearly the
conditions under which a
transfer of electricity takes
place.
Provide two similar metal ves-
sels A and B, Fig. 283, with pith
balls and insulate them on blocks
of paraffin. Let each vessel be
positively charged, but A more
highly than B, as measured by the
repulsion of the pith balls. Now
connect the vessels by means of a wire attached to a sealing wax
handle C. The pith ball on A will fall slightly while that on B will
rise. Thus some of the charge on A moves along the wire to B.
FIG. 283. Conductor A has a Higher
Potential than B.
Although both insulated vessels were originally charged
with the same kind of electricity, in the language of
BENJAMIN FRANKLIN (1706-1790)
The achievements of Franklin in the field of electricity are no
less brilliant than his successes as a statesman and diplomat. His
attention was first turned to the study of electrical phenomena by
witnessing some experiments which at that time (1746) were re-
garded as no less than marvelous. His experiment to prove the
electrical nature of lightning has become classic. In order to ascer-
tain whether electricity could be obtained from clouds during a storm,
Franklin constructed a kite which was provided with a pointed metal
rod for " drawing off " the electrical charge, if there should prove
to be any. At the approach of a storm, Franklin and his son raised
the kite, which was held by a hempen cord. The lower end of the
cord was tied to a metal key through which was passed a ribbon
of silk to protect the body from severe and dangerous shocks. As
soon as the cord became moistened by the rain, electric sparks were
readily drawn from the key. In regard to this experiment, Franklin
writes: "At the key the Leyden jar may be charged; and, from the
electric fire thus obtained, spirits may be kindled and all other
electrical experiments performed which are usually done by the
help of a rubbed glass globe or tube, and thereby the sameness of
the electrical matter with that of lightning completely demonstrated."
" Antiquity would have erected altars to this great and powerful
genius who, to promote the welfare of mankind, comprehending both
the heavens and the earth in the range of his thought, could at once
snatch the bolt from the cloud and the scepter from tyrants."
MIRABEAU
ELECTROSTATICS
347
Physics, A was charged to a higher potential than B. Thus
a charge moves from a point of higher to one of lower poten-
tial, just as heat flows along a heat conductor from a point
of higher to one of lower temperature.
361. Potential Difference. It has just been observed
that an electrical charge will flow along a conductor as
long as there exists a potential difference. It is precisely
this difference of poten-
tial that determines
whether electricity will
flow and the direction
it will take. Figure
284 will show to some
extent the differences
that may exist between
electrical charges. AB
represents the levei
ground, and a, b, <?, and
d four tanks containing water. Tank a is analogous to
an insulated body charged positively to a high potential,
as vessel a', while tank b represents one of a lower poten-
tial than a f , as b' . It is assumed that all positive charges
are of a higher potential than the earth and will discharge
to the earth unless insulated from it. On the other hand,
negative charges, as c f and d f , are assumed to have lower
potentials than the earth. The potential of the earth is
thus on the dividing line between positive and negative
charges; hence, the potential of the earth is regarded as
zero.
Connecting any two of the tanks shown in the figure
would evidently result in a transfer of water from left to
right ; thus joining any two of the charged vessels by
means of a conductor would bring about a transfer of
electricity in the same direction.
FIG. 284. Analogy between Electrical
Potential and Water Level.
318 A HIGH SCHOOL COURSE IN PHYSICS
362. Mixing Positive and Negative Charges. Let the two
insulated metal vessels used in 360 be charged with equal amounts
of positive and negative electricity as shown by the divergence of the
pith balls. Now connect them by means of a wire provided with an
insulating handle as before. Both balls fall against the sides of the
vessels, showing that the two charges have neutralized each other.
Repeat the operations just described after charging A positively until
its pith ball diverges considerably more than that of B, which is
charged negatively. After the connection has been made between
the vessels, a positive charge will be found on each vessel.
Not only does electricity tend to flow from a positively
to a negatively charged body, but a mixture of unlike
charges tends to produce a cancellation of both. If, how-
ever, one of the charges exceeds the other in amount, the
excess remains distributed over both surfaces. In the
final condition both bodies are of the same potential.
363. The Electrostatic Unit of Quantity. Unit charges
of electricity are such equal quantities as exert upon each
other a force of one dyne ( 35) when separated by one
centimeter of air. The force, as we have seen, is repellent
when the charges are of the same kind and attractive
when they are different. If two equal quantities of posi-
tive and negative electricity are mixed, they cancel each
other; but if both of the two mixed charges are of the
same kind, the resulting charge is their sum.
EXAMPLE. If 10 units of positive electricity are mixed with 12
units of negative, what will be the result?
SOLUTION. The 10 positive units will cancel 10 negative units,
leaving 2 units of negative electricity, which will be distributed
over the surface of the conductors.
364. Electrostatic Capacity. By means of a proof plane
transfer a charge from an electrified glass rod to the electroscope and
note the approximate divergence of the leaves. Now place one of the
metal vessels used in 353 upon the plate of the electroscope and again
transfer a charge with the proof plane as before. In this case the
divergence will be found to be much smaller than before. Continue
to transfer charges until the divergence is the same as at first.
ELECTROSTATICS
349
By placing the metal vessel upon the electroscope, the
surface over which a charge will distribute itself is
materially increased. Hence a given quantity of elec-
tricity will produce a smaller electric density, and the
mutual repulsion of the gold leaves will be lessened. On
this account, a larger quantity will be required to produce
the same divergence of leaves ; or, in other words, to produce
the same potential as at first. The change produced in the
condition of the conductor is expressed by saying that the
electrostatic capacity is increased by the increased area
presented by the metal vessel.
365. Condensers. In many of the practical applica-
tions of electricity, it is necessary to make use of some
device that has many times the capacity of anything we
have used in the preceding experiments. The manner in
which the desired result is accomplished is made clear by
the following experiments :
1. Place a flat metal plate (7, Fig. 285, having well-rounded cor-
ners, upon the plate of the gold-leaf electroscope and charge the in-
strument with the glass rod and proof plane. Now bring a similar
metal plate B, which is provided with a handle
of sealing wax A, near C, but not touching
it. The divergence of the gold leaves will
decrease, showing that the potential of the
leaves has been lowered. Withdraw B and
the potential of the leaves will rise to its
original value. Repeat these operations while
the fingers are allowed to remain in contact
with B, thus connecting it with the earth.
The divergence of the leaves becomes very
small when B and C are near together, but
returns to its former value when the plates
are again separated.
2. Mount a plate B in a clamp so that it
is about | cm. from C and insulated. Count
the number of charges that must be carried
FIG. 285. Showing the
Effect of a Neigh-
boring Conductor on
Capacity.
to C by a proof plane to produce a given divergence, i.e. to produce a
350 A HIGH SCHOOL COURSE IN PHYSICS
given potential. Now discharge C and connect B with the earth by
means of a wire, and see how many charges must be transferred
to C to produce approximately the same divergence as before. A
large number will be required.
These experiments show (1) that the potential that a
given charge produces when placed on an insulated con-
ductor depends upon the proximity of other conductors
and whether they are " earthed " or not, and (2) that the
capacity of a conductor is enormously increased by the
presence of an earthed conductor placed very near, but
insulated from it. A combination of plates separated by an
insulator constitutes an electrostatic condenser. The capac-
ity of a condenser is proportional to the size of the plates
and becomes greater as the distance between them is
reduced.
366. Influence of the Insulating Material Arrange the
electroscope and plates as in Experiment 2 of the preceding section.
Connect B with the earth and charge C until a moderate divergence
of the leaves is produced. Now introduce between B and C a pane of
glass and note the effect upon the divergence. The potential of C
will fall when the glass is introduced, and will rise again when it is
removed. Let the experiment be made by using beeswax or paraffin
instead of glass. The effect is more marked than before.
Since the introduction of another insulator, or dielectric,
to replace the air between the plates of a condenser, re-
duces the potential, it is obvious that it will require a
greater charge to bring the potential back to its original
value. Hence the capacity of the condenser is increased.
One of the best insulators used in condensers is mica, not
only because it can easily be obtained in thin sheets, but
because of its advantageous influence as a dielectric upon
the electrical capacity of the condenser.
367. Forms of Condensers. One of the earliest forms
of condensers is known as the Ley den jar, from Ley den
ELECTROSTATICS
351
FIG. 286. The Ley-
den Jar.
in Holland, the place of its origin. It was first used in
1745. This condenser consists of a glass jar, Fig. 286,
which is coated with tin foil to about
two thirds of its height on its interior
and exterior surfaces. Through a cover
of insulating material passes a metal rod
terminating at the top in a ball and at
the lower end in a chain which makes
contact with the inner coating of the jar.
Another form of condenser that is
widely used is represented diagrammat-
ically in Fig. 287. This condenser con-
sists of a large number of sheets of tin
foil of which alternate sheets are con-
nected at A and the intervening sheets at B. In the
best condensers of this type the insulating material sepa-
rating the sheets of foil is mica; but in cheaper forms,
paraffined paper is used. The capacity
of such condensers is large on account
of the large area of tin foil and the
extremely small distance between the
conducting surfaces of the foil ( 365).
368. Charging and Discharging a Ley-
den Jar. In order to charge a Ley-
den jar, the outer coating is connected with the earth by
a metallic conductor, or the jar is simply held in the hand.
A very imperfect earth connection is produced by setting
the jar upon a table oi/dry wood. If now the knob of the
jar be connected with some source of electricity, a charge
is communicated to the inner surface. If this is positive,
an equal amount of negative will be induced on the inner
surface of the outer coating, and a similar quantity of
positive repelled to the earth. In this manner a strain
is set up in the glass which in some instances is suffi-
cient to break the jar.
FIG. 287. Diagram of
a Mica, or Paper,
Condenser.
352 A HIGH SCHOOL COURSE IN PHYSICS
To discharge a Leyden jar, it is necessary to make an
electrical connection between the two tin-foil coatings.
If the charge is not large, this can be done safely by
simultaneously touching the knob and the outer coating
with the hands. The best method, however, is to bend a
metal conductor in such a form that one end can be kept
in contact with the outer coating while the other is brought
near the knob. At the instant of discharge a bright spark
will be seen to jump between the knob and the end of the
conductor.
EXERCISES
1. Three Leyden jars are charged with 4, 7, and + 10 units
respectively. How many units will remain in the jars after the knobs
have been connected?
2. A Leyden jar that is placed on a plate of glass has a small
capacity. Why ?
3. If a Leyden jar be highly charged and then placed on a plate
of glass or paraffin, the knob can be safely touched with the hand.
In this condition only a small portion of the entire charge will be
taken from the jar. Explain.
4. Having a metal globe positively electrified, how could you
electrify any number of other globes with negative electricity ?
5. With a positively charged globe, how could you positively
charge one of the other globes without reducing the charge on the
first?
4. ELECTRICAL GENERATORS
369. The Electrophorus. In order to produce larger
electrical charges than those used in any of the preceding
experiments, the principle of induction
( 352) is advantageously employed.
The simplest form of generator for this
purpose is the electrophorus (pronounced
e lek trof'o rus), an apparatus invented
FIG. 288. The by Volta, 1 an Italian physicist, in 1777.
Electrophorus. XM S instrument consists of a plate of
1 See portrait facing page 352.
COUNT ALESSANDRO VOLTA (1745-1827)
The age of practical electricity began with the invention of the
voltaic cell by Volta, an Italian, professor of physics at the Uni-
versity of Pavia. Before his invention it was not known that a
continuous current of electricity could be produced. In 1793, Volta
announced to the Royal Society of London a discovery made by
Galvani (1737-1798), professor of anatomy at Bologna. Galvani
had observed that by joining together two different metals and
touching one to the muscle of a frog's leg and the other to the
nerve, violent contractions were produced even after the animal's
death. Most extravagant hopes were founded on this discovery, and
many believed that a cure had been found for all diseases. In
reality, the discovery paved the way to other and greater ones which
have become a vital part of the history of the nineteenth century.
The use of the two metals in Galvani's experiment suggested to
Volta the basic principle of the modern cell consisting of two plates
of different metals immersed in a liquid. This, as we know, becomes
a continuous source of electricity. The invention was received with
great enthusiasm. In a short time batteries made by joining several
of the so-called " voltaic piles " were used in experimental work in
many of the laboratories of Europe. With the advent of this means
of generating electric currents began the series of discoveries that
have led up to the phenomenal use of electricity at the present day.
To Volta is ascribed the invention of the electrophorus, electro-
scope, and the condenser. The practical unit of potential difference
is called the volt in his honor.
ELECTROSTATICS 353
ebonite or a shallow metal dish B, Fig. 288, about 25 cm. in
diameter, into which has been poured melted resin or
shellac, and a flat circular metal disk J., somewhat smaller
than the plate and having well-rounded edges. The metal
disk is provided with an insulating handle of ebonite.
Let the plate of an electrophorus be stroked with cat's fur and its
electrification tested. Place the metal disk upon the plate and test
the kind of electricity that can be taken from its upper surface.
Touch the disk with the finger in order to "ground" or "earth" it,
lift it by the insulating handle, and test its charge. Repeat the ex-
periment, without " grounding " the disk. Explain the result.
The action of the electrophorus is as follows : When
the non-conducting plate B is stroked with fur, it is given
a negative charge. If, now, the metal n
disk A be placed upon the plate, the
negative on the plate induces a posi-
tive charge on the lower surface of the \^ ~^|
disk and repels a negative charge to n
the upper side, as shown in Fig. 289.
When the disk is touched with the (+ + + + +^ A
finger, the negative charge escapes,
leaving the positive charge, which is
-,.,., , ^ v i i -,. FlG - 289. Represent-
aistributecl over the disk when it is i ng the Theory of
lifted. Compare 355. Any number the Electrophorus.
of charges may be obtained from the electrophorus with-
out producing any appreciable change in the charge on
the plate.
370. Source of the Energy Derived from the Electrophorus.
Although any number of charges can be produced by
the electrophorus, we know that the energy obtained in
this manner cannot be brought into existence without the
expenditure of a like quantity on the part of some work-
ing agent ( 64). The source of the energy is obvious
from the following :
24
354
A HIGH SCHOOL COURSE IN PHYSICS
After the metal disk of an electrophorus has been placed on the
electrified plate and touched on its upper surface to draw away
the negative charge ( 369), connect a gold-leaf electroscope with the
disk by means of a slender wire. No divergence in the leaves is pro-
duced, although we know that the disk has a positive charge induced
by the negative charge on the plate. Slowly lift the disk by the
insulating handle and the leaves will diverge widely.
When the disk with its induced positive charge rests
upon the charged plate, it is at zero potential because it
has been in connection with the earth. The disk, like a
weight lying on the ground, manifests no energy until its
positive charge is separated from the negative charge on
the plate in opposition to their attractive force. The
agent, therefore, that lifts the disk from the plate furnishes
the energy which appears in the disk as electrical energy.
When the disk is discharged, the electrical energy is
transformed into heat which appears in the spark that is
produced. The heat of the spark can be utilized to light
illuminating gas or explode powder.
371. The Toeppler-Holtz Influence Machine. The dis-
covery of X-rays and their necessity for generators capa-
FIG. 290. The Toeppler-Holtz Electrical Machine.
ELECTROSTATICS 355
ble of producing a continuous supply of electricity has
brought such generators into extensive use. The simplest
form of induction, or influence, machines is the Toeppler-
Holtz, shown in Fig. 290. This machine makes use of a
glass plate about 50 cm. in diameter, which is provided
with six or eight metallic disks, as shown. This plate
revolves in front of a second stationary plate of glass P,
which is furnished with two strips of tin foil 6, 6', covered
with paper sectors called arma-
tures, or inductors. In front
of the revolving plate is the
stationary neutralizing bar J5,
provided with points and tinsel
brushes at the ends. (7, C' are
two conductors having at their
other extremes points that come
close to the revolving plate. _
The action of the machine is FlG< 391. -Diagram Showing
best Understood from a Study of Action of the Toeppler-Holtz
the diagram shown in Fig. 291.
Imagine a small positive charge placed on the sector b.
This charge acts inductively through the glass on the rod
BB', attracting a negative charge to B and repelling a
positive one to B 1 '. These induced charges rapidly escape
from the points ( 358) and electrify the glass plate as well
as each metallic disk as it passes. As the plate rotates in
the direction shown by the arrow, the disks at the top
carry negative charges to the right, while those at the bot-
tom carry positive charges to the left. These disks touch
the small brushes c and c', through which negative charges
are given to sector b f and positive to b. The charges on the
sectors are thus continually increased, an effect which con-
tinually increases the first inductive action through the
glass on BB' . Again, when the negatively charged glass
356 A HIGH SCHOOL COURSE IN PHYSICS
plate reaches Q\ positive electricity is drawn from the
points and negative left on the ball 0'. Similarly, on
the opposite side of the machine, the positively electrified
plate neutralizes the negative charge that it induces at
the points (7, and thus leaves a positive charge on ball 0.
The unlike charges on and 0' continue to increase until
the difference of potential is sufficient to force a dis-
charge to take place through the air between them. If
the distance is not too great, a stream of sparks will appear
to pass without interruption. The energy transformed in
each spark is greatly increased by the presence of the two
Leyden jars shown in Fig. 290.
EXERCISES
1. Why is the metal disk of the electrophorus not charged nega-
tively by contact with the negatively charged plate?
SUGGESTION. Consider the nature of the plate and the fact that it
touches the disk in only a very few places.
2. Explain why an influence machine turns with greater difficulty
when it is developing a high potential between the balls and O'.
SUGGESTION. Consider the nature of the electrical forces existing
between the stationary and moving charges.
3. Small Leyden jars (see Fig. 290) used in connection with the
balls of the influence machine cause the production of much brighter
sparks than would be produced without them. Explain.
4. With the Leyden jars removed, would the frequency with which
sparks pass between and 0' be increased or decreased ?
SUMMARY
1. Many substances, as glass, ebonite, sealing wax, etc.,
when rubbed with silk, flannel, fur, etc., possess the prop-
erty of attracting light objects, and are therefore said to
be electrified ( 343).
2. Electrical charges are of two kinds, called positive
and negative charges ( 344).
ELECTROSTATICS 35?
3. Similar charges repel each other and dissimilar
charges attract ( 345).
4. The electroscope is used to determine the presence
of a charge and its kind ( 346).
5. Equal amounts of positive and negative electricity
are always developed simultaneously ( 848).
6. Charges of electricity are transferred by conductors,
as metals, carbon, etc. A substance that will not act as
a conductor is called an insulator; such are dry air, glass,
mica, rubber, shellac, etc. ( 349 and 350).
7. Au electric field is the space around a charged body
within which neighboring bodies are affected by the
charge ( 351).
8. The electrical effect of an electrified body upon a
neighboring conductor insulated from it is the result of
electrostatic induction ( 352).
9. The effect of induction by a given charge is to cause
a dissimilar kind of electricity to appear on the nearer
side of an insulated conductor and the similar kind on the
remote side ( 353 to 3.55).
10. Charges of electricity distribute themselves over
the exterior surfaces of conductors. The relative quan-
tities per square centimeter depend on the curvature of
the surface, being greatest at places of the greatest curva-
ture, as at points ( 356 and 357).
11. Charges are rapidly conveyed away from sharp
points by air particles, which become charged by contact
and are then repelled ( 358).
12. Charges flow along conductors from places of higher
to places of lower potential. The potential of the earth is
regarded as zero ( 360 and 361).
13. The union of positive and negative charges of the
same size produces a cancellation of both ( 362).
358 A HIGH SCHOOL COURSE IN PHYSICS
14. Unit charges are such equal quantities of electricity
as exert upon each other a force of one dyne when the
distance between them in air is one centimeter ( 363).
15. Electrostatic capacity is measured by the number of
units of electricity required to produce a given potential.
The capacities of two insulated conductors are proportional
to the number of units required to bring them to the same
potential ( 364).
16. The capacity of a condenser is made very large by
bringing the conductor to be charged near another which
is connected with the earth, but thoroughly insulated from
the former. The most common form of condenser is the
Leyden jar ( 365 to 368).
17. The process of induction is employed in the genera-
tion of large electrostatic charges. See the electrophorus
( 369) and the Toeppler-Holtz machine ( 371).
CHAPTER XVII
MAGNETISM
1. MAGNETS AND THEIR MUTUAL ACTION
372. Production of a Magnet. Magnets present at least
two properties that are familiar to every one: (1) the ends
of a magnet will pick up small pieces of iron, as iron filings,
etc., and (2) a magnet will take a north-and-south posi-
tion when properly suspended. The following experiment
will serve to show that an intimate relation exists between
electricity and magnetism :
Break off several pieces of watch spring, and balance each of them
on the head of a pin, as shewn in Fig. 292. Observe that they will
remain indefinitely in any position and will not ^f^""^ ==
pick up iron filings. Now wrap the pieces of *r^
spring in a small sheet of paper and place them f^rfe^
within a helix, or spiral, made by winding ten
or twelve turns of insulated copper wire upon FIG. 292. Piece of
a lead pencil. Discharge a Leyden jar through Watch Spring Bal-
the helix of wire and then remove the pieces of
spring. They will be found able to pick up iron filings and small sew-
ing needles ; and, when balanced on the head of a pin, each piece will
become stationary only when in a north-and-south position.
The experiment shows (1) that a moving charge of
electricity which flows in a helix around a piece of steel
magnetizes it, and (2) that a magnetized bar of steel re-
tains at least a portion of the magnetism produced by the
electric flow.
373. Natural Magnets or Lodestones. In ancient times
iron was mined on some of the islands of the Mediterranean
and along the coasts of the ^Egean sea. It was early
359
360 A HIGH SCHOOL COURSE IN PHYSICS
observed that an occasional piece of the ore, magnetite
(chemical symbol, Fe 3 O 4 ), possessed the power of attracting
small pieces of iron and also
imparted this property by
contact to pieces of iron and
steel. According to some
writers, the word " magnet "
is derived from Magnesia in
Asia Minor, a province in
which magnetic iron ore is es-
pecially abundant. Speci-
mens of ore that possess the
properties of magnets are
called lodestones, or natural
magnets. See Fig. 293.
374. Poles of a Magnet.
If a magnet be placed on a
FIG. 293. A Natural Magnet.
sheet of paper and covered
with iron filings, it will be found on lifting the magnet
that the filings cling to the ends in great tufts but leave
it bare in the middle, as
shown in Fig. 294. The
centers of attraction near
the ends are called the
poles of the magnet. The FIG. 294. Showing the Polarity
pole that points toward of a Magnet.
the north when the bar is suspended is the north-seeking,
or N-pole, and the other the south-seeking, or S-pole.
375. Law Of Magnetic Poles. Balance upon a pinhead each of
the magnetized pieces of steel used in 372 and mark the N-poles
with small labels. Now bring the N-pole of one piece near the N-pole
of a suspended one and observe the effect. Present the N-pole of the
former to the S-pole of the latter. In every case that can be tested it
will be found that an N-pole repels another N-pole and attracts an
S-pole. Likewise S-poles repel each other and attract N-poles.
MAGNETISM
361
FIG. 295. A Horseshoe
Magnet.
The general law of pole action is made clear by this
experiment, viz. like poles repel each other and unlike poles
attract.
The force of attraction or repulsion between two poles is
inversely proportional to the square of the distance between
them, i.e. doubling the distance between two poles divides
the force by four, tripling the distance divides the force
by nine, etc. Compare with gravitation, 67.
376. Artificial Magnets. The fact that artificial mag-
nets may be made of any desired form is of great practical
value. The commonest forms are
the straight bar magnet and the
horseshoe magnet shown in Fig. 295.
These can be produced in any size
from the small toy magnet up to
large ones capable of lifting an iron weight of several
pounds.
Draw the N-pole of a magnet along a steel nail, from the head
toward the point. Present the head of the nail to the N-pole of a
suspended magnet. The observed repulsion shows the head to be
an N-pole. Also test the polarity of the point of the nail. Repeat
the processes, using the S-pole of the
first magnet, and ascertain the poles
produced in the nail.
In every case it will be found
that when a bar is magnetized by
contact with one of the poles of
a magnet, a pole of the opposite
name is formed at the point last touched by the magnet,
as -illustrated in Fig. 296.
377. Magnetic Substances. Practically only iron and
steel are affected by a magnet, although the substances
nickel and cobalt are slightly attracted. Bismuth, anti-
mony, and some other substances are appreciably repelled
FIG. 296. Magnetizing a
Bar of Steel.
362 A HIGH SCHOOL COURSE IN PHYSICS
when placed near a strong magnetic pole. Bodies belong-
ing to the former class are called paramagnetic or simply
magnetic, substances ; and those of the latter, diamagnetic
substances.
378. Magnetic Induction Let a strong magnet support
an iron nail by its head. Test the polarity of the point of the nail.
Let the point of the first nail support 'a second
one by its head and test the polarity of this
one also. If the nails are not too large, a
chain of them may be formed as in Fig. 297.
Now carefully remove the magnet from the
first nail, and all will fall apart. Repeat the
experiment after placing a piece of paper be-
tween the magnet and the first nail. Ascer-
tain whether absolute contact between the
FIG. 297. Each magnet and the nail is necessary in order to
Nail Becomes enable the first nail to support the second.
a Magnet. The action of the maglie t O n the nail is
simply weakened by the intervention of the
paper.
A piece of iron or steel becomes a magnet by induction
when brought in contact with, or close to, a magnetic pole.
The effect takes place through all substances except large
masses of iron or steel. When the polarity of the nails
is tested, it is found that the N-pole of the magnet, for
example, produces an S-pole on the near end of the nails
and an N-pole at the remote end. When the magnet is
removed, it will be found that a portion of the induced
magnetism is retained by the nails.
379. Retentivity of Magnetism. It has. been evident
in many of the preceding experiments ( 372, 376, 378)
that a magnetized piece of steel loses only a part of its
magnetism when it is removed from the magnetizing in-
fluence. It is almost impossible to find a piece of iron
that will not retain a little magnetism after being brought
in contact with a magnet, although the amount retained is
MAGNETISM 363
often very slight. The property of retaining magnetism is
called retentivity. Hardened steel possesses the property
of retentivity in a high degree, but in soft iron the reten-
tivity is very small.
380. Magnetic Fields. A magnetic field is a region in
which magnetic substances experience magnetic forces. A
magnetic field may be represented in the same manner as
an electric field ( 351). Each magnetic line of force
shows at every point in it the direction of the force at that
point. Magnetic fields are easily mapped by the help
of iron filings, as in the following experiment :
Let a bar magnet be covered with a sheet of paper and fine iron
filings strewn over its surface. If the paper is slightly jarred by tap-
ping the table on which the magnet rests, the filings will arrange
themselves in chains stretching from pole to pole. These chains
show the direction of the magnetic forces at the points through which
they pass.
The direction of the lines of force in the field around a
short bar magnet is shown in Fig. 298. Each particle
becomes a magnet by induction ( 378) and turns until it
lies lengthwise in a line of force. The poles of one parti-
cle attract the opposite poles of the neighboring particles,
and thus the filings unite and form chains which extend
from pole to pole.
The direction of a line
of force is assumed to
be from an N-pole to
an S-pole through the
air. The strong parts
of the field are the re-
gions near the poles,
as shown by the
heavy, distinct lines ' FIQ ^ _ The ^^ Fwd ai . ound .
of filings. Bar Magnet.
364
A HIGH SCHOOL COURSE IN PHYSICS
FIG. 299. Showing the Magnetic Field
between Unlike Poles.
Figure 299 was
made by placing two
bar magnets side by
side with their unlike
poles pointing in the
same direction. It
is at once evident that
an intense field of
force is produced be-
tween unlike poles
when placed near
each other. This fact
is utilized in some of
the practical applica-
tions of magnetism.
Figure 300 shows
the result obtained by
placing two short bar
magnets parallel, but
with their like poles
turned in the same
direction. A comparison of this with the figure just pre-
ceding shows at once the presence of a weak field of force
between similar poles. In fact, the re-
pellent action between the lines of force
is obvious. No lines of force from one
pole enter another pole of the same
name. Since the poles are alike, it is
plain that this field represents the case
of repulsion, while Fig. 299 shows the
condition for attraction.
381., Magnetic Permeability. Mag-
netic lines of force find an easier path
through iron or steel than through air.
FIG. 200. Showing the Magnetic Field
between Like Poles.
FIG. 301. A Magnetic
Field Distorted by a
Piece of Iron A.
MAGNETISM 365
When a piece of iron, A, Fig. 301, is placed in a magnetic
field, lines of force bend from their original course in
order to pass through the iron. Thus lines of force are
sent through the metal. The relative ease with which mag-
netic lines of force pass through a substance is called its mag-
netic permeability. The permeability of air is regarded as
unity.
EXERCISES
1. What would be a suitable substance for permanent artificial
magnets ?
2. It is desirable in a certain instrument to use a substance that is
easily magnetized, but which will lose its magnetism when the mag-
netizing influence is removed. What would be the proper substance ?
3. Each of two nails hangs from the N-pole of a permanent mag-
net. Will the ends of the nails remote from the magnet attract or
repel each other ?
4. Four nails are placed lengthwise in a row without touching each
other. Draw a figure showing the magnetic fields produced when the
S-pole of a magnet is placed near one end of the row.
5. The N-pole of a magnet is held near a point on the circumfer-
ence of an iron ring. Show by a diagram the position of the induced
magnetic poles.
2. MAGNETISM A MOLECULAR PHENOMENON
382. Demagnetization by Heating. Magnetize a piece of
watch spring and note the" quantity of iron filings that it will support.
Heat the spring red-hot and test its magnetism again. It will be found
to have lost its power of picking up filings as well as repelling either
pole of a suspended magnet.
We have already learned in 213 that heating a body
simply increases its molecular motion. This experiment
shows, therefore, that when the molecular motion reaches
a certain degree, practically all magnetism is destroyed.
383. Demagnetization by Molecular Rearrangement
Bend a piece of iron wire in the form shown in Fig. 302. Magnetize
it by stroking it several times with a strong magnet. Test its power
366 A HIGH SCHOOL COURSE IN PHYSICS
to pick up filings and to repel the pole of a suspended magnet. Now
grasp the ends with pliers and give the wire a vigorous twist. If the
wire is now tested as before, it will be found
" to have lost its magnetism.
FIG. 302. Wire may
be Demagnetized by It is obviOUS that the effect of twist-
ing is to give all parts of the wire a new
molecular arrangement. Accompanying this disarrange-
ment is the disappearance of the magnetism, as shown by
the experiment.
384. Magnetism Not Simply at the Poles. - Magnetize a
piece of watch spring about 5 in. long and test the location of its poles
by presenting it to a suspended magnet. Break it at the center and
test the pieces. It will be found that each piece is a perfect magnet,
for two new poles will have developed at the point which was at first
neutral. Break one of the pieces at its center and again each piece
will be a perfect magnet.
Let the original magnet be represented by (1), Fig. 303.
The polarity manifests itself only at the ends. When the
magnet is broken, as
at P, the condition JS^jjij? :g| ( / )
shown in (2) is the
result. Again, on
breaking the two - * "
_ . P(3)
parts, the result FIG. 303. -Effect of Breaking a Magnet.
shown in (3) is ob-
tained. It may be imagined that this process be carried on
even to the separation of ultimate particles, i.e. the mole-
cules. There can be no doubt that each molecule would
prove to be a magnet having two poles.
385. Theory of Magnetization. The results obtained
in the experiments of the preceding sections lead to the
theory of magnetization which assumes that every molecule
of iron or steel is a magnet even when the bar of which it is a
part is not magnetized. Magnetization consists in causing
MAGNETISM
367'
FIG. 304. Illustrating the Condition in an Un-
magnetized Bar of Iron or Steel.
FIG. 305.
Illustrating the Condition in a
Magnetized Bar.
the molecules to arrange themselves in a certain order.
In an unmagnetized bar of iron the condition is repre-
sented as in Fig. 304. Here each of the little rectangles
represents a pivoted magnet, the N-pole being shaded. It
will be seen that the small magnets arrange themselves in
small groups so that
unlike poles neu-
tralize each other
throughout the bar.
The bar, therefore,
manifests no polar-
ity.
When a magnet-
izing influence is
brought to bear
upon the bar of iron,
the molecules swing
round until a condi-
tion approximating
that shown in Fig.
305 results. Since
., -IT. , . FIG. 306. Illustrating the Condition in a
the general direction Saturated Magnet,
of the N-poles is to-
ward the left and the S-poles toward the right, the ends of
the bar will show polarity. At a short distance from the
ends and throughout the middle of the bar the proximity
of unlike poles brings about a neutralization of polarity in
these places. A jar serves to break up this artificial ar-
rangement, which thereby destroys the magnetism, and the
condition shown in Fig. 304 is resumed.
386. A Saturated Magnet. If the theory of magnetiza-
tion just described is correct, it will be found impossible
to magnetize a piece of iron beyond the limit reached
when all the molecules have been turned as represented
una ma ma mna ma ma na ma ran ma
ma HDD na ID ID oa ma
368 A HIGH SCHOOL COURSE IN PHYSICS
in Fig. 306. This has been found experimentally to be
the case. In this condition a magnet is said to be satu-
rated. Hence, a saturated magnet is one upon which an
increase of the magnetizing influence has no effect.
EXERCISES
1. How would you determine the poles of a magnet? Give two
methods.
2. Why is a permanent magnet injured when dropped?
3. If iron be heated and then cooled in a magnetic field, it will be
found to be magnetized. Explain.
4. Explain how jarring a bar of steel will aid in magnetizing it,
but jarring a magnetized piece of steel will weaken its magnetism.
3. TERRESTRIAL MAGNETISM
387. The Compass. One of the earliest properties dis-
covered regarding a magnet is its tendency to take a defi-
nite position when placed on a pivot or suspended. A
magnet that is so pivoted as to turn freely in a horizontal
plane is called a compass. The invention of the compass
is attributed to the Chinese.
The first satisfactory explanation of the action of the
compass was given by Gilbert 1 about 1600 A.D. The
1 WILLIAM GILBERT (1540-1603). The renown of Gilbert rests largely
upon the fact that he was one of the first to recognize the value of experi-
mentation and also upon his great work entitled De Magnete, which was
published in London in 1600. His most celebrated experiments were
made with magnets and magnetic bodies, and his results and conclusions
are contained in the book just named. Gilbert made the discovery that
the earth is a great magnet and demonstrated this by constructing a
small sphere of lodestone. With this "terrella," or "little earth," he
was not only able to show why magnets point to the north, but he also
explained the declination and inclination of magnetic needles.
Gilbert also made important discoveries in the subject of Electricity.
He was probably the first to clearly recognize a distinct difference between
magnetized and electrified bodies. He showed that many substances be-
sides amber could be electrified by rubbing ; e.g. glass, resins, sealing wax,
MAGNETISM 369
assumption is made that the earth is a great magnet, but
the reason for its being one still remains a mystery.
However, we are sure that the earth is surrounded by a
magnetic field, and, in proof of this fact, the following
experiment can easily be made.
Hold a bar of iron or a slender gas pipe about 2 feet long in a north-
arid-south plane, tilting the north end down 60 or more. Now give
the bar several vigorous taps with a stone and then test the ends for
polarity by presenting them to the poles of a suspended magnet. The
end of the bar toward the north will be an N-pole, and the other an
S-pole. Reverse the bar and repeat the processes. The polarity of
the bar will be found reversed.
This experiment makes use of the earth's magnetic field
in the magnetization of the iron bar. The jarring is ef-
fective only in lending assistance to the rearrangement of
the molecules under the inductive influence of the earth's
field ( 380, 385). The compass needle simply behaves
as any small magnet would in a magnetic field, pointing
in a general north-and-south direction because of the
influence of the earth's lines of force.
388. Declination of the Needle. Suspend a magnetized knit-
ting needle on a fiber taken from the cocoon of a silkworm, or on an
untwisted filament of silk floss. Stretch a cord below the needle pre-
cisely in a north-and-south line (given by the shadow of a plumb line
or a vertical window frame at noon, sun time). The experiment
should not be made within several feet of an iron pipe or beam, nor
within a foot of steel nails. It will be observed that the needle does
not take a position parallel to the north-and-south line except in
certain localities.
etc. These he named " electrics,' 1 from the Greek word electron, meaning
amber. He was also the first to use the word " electricity."
Gilbert was educated in medicine at Cambridge, England, and was
appointed court physician by Queen Elizabeth. At the death of the queen
in 1603, he was reappointed by her successor, James I, but his death
occurred in November of that year.
25
370
A HIGH SCHOOL COURSE IN PHYSICS
The earth's magnetic lines do not coincide with the geo-
graphical meridians ; consequently the magnetic needle,
directed by the earth's field, will not point geographically
north. This fact was known as early as the eleventh
century ; but it was first discovered by Columbus, on his
memorable voyage of 1492, that the direction indicated
by the compass changes as one passes from place to place
over the earth's surface. The angle between the direction
of the needle and the geographical meridian is the declina-
tion of the needle.
Lines that are so drawn upon a map as to pass through
places at which the declination is the same are called
FIG. 307. Map Showing Magnetic Declinations. Lines of no Declination
are Marked "0." The Numbers Show the Declination in Degrees and the
Letters Show Whether it is East or West.
isogonic lines. Figure 307 shows approximately the mag-
netic declination at all places on the surface of the earth.
The heavy line, called the agonic line, shows the regions
where the needle points due north. At all points in the
United States and Canada lying east of the agonic line,
MAGNETISM 371
the declination is towards the west ; for all points west
of this line, the declination is east. At the present time
(1910) the agonic line passes a little west of Lansing, Mich.,
and slightly east of Cincinnati, Ohio, and Charleston, S.C.
It is moving very slowly westward.
389. Inclination of the Magnetic Needle. Thrust an unmag-
netized knitting needle through a cork, and close to and at right angles
with it pass a straight, slender sewing needle. Cut away a portion
of the cork until the system will balance in
any position on the edges of two tumblers
when the longer needle is placed east-and-
west. Magnetize the knitting needle by strok-
ing one end with the N-pole of a magnet and
the opposite end with the S-pole. Now place
the system in a north-and-south position on
the tumblers. The N-pole of the needle will
appear heavier than the S-pole and will dip
until the angle between the needle and the
horizontal plane is about 70. (See Fig. 308.) FlG 3Q8 _ The N _ pole
The balanced, or dipping, needle
simply places itself parallel with the
lines of force of the earth. In the Northern States these
lines are inclined about 70 from the horizontal. The
angle between the earth's magnetic lines of force and a hori-
zontal plane is called the inclination, or dip, of the needle.
The angle of inclination increases as one approaches the
magnetic poles of the earth, where it is 90. Near the
geographical equator the inclination is about 0, and in
the southern hemisphere the needle inclines with its S-pole
below the horizontal plane passing through its axis.
EXERCISES
1. Account for the fact that the iron beams of a building, gas and
water pipes, and other bars of iron are usually magnetized.
2. How would a compass behave while being carried entirely
around the earth's magnetic pole along the Arctic Circle ?
372 A HIGH SCHOOL COURSE IN PHYSICS
3. How would a dipping needle be of assistance in locating the
magnetic poles of the earth ?
4. Account for the fact that a surveyor's compass needle is often
provided with a small adjustable weight for balancing.
5. Place a ruler upon the table, giving it approximately the declina-
tion of the needle at New York ; at Los Angeles ; at Iceland.
6. Ascertain by experiment whether a floating magnet tends to
drift toward the north. Account for the result.
SUGGESTION. Consider whether the attraction of one of the
earth's poles for a pole of a magnet is greater than its repulsion for
the opposite pole of the same magnet.
7. The upper end of a pipe driven into the ground was found to be
an S-pole. Explain. Suggest an experiment by which your explana-
tion can be tested.
SUMMARY
1. A bar of steel may be made a magnet by discharging
a Ley den jar through a helix of wire wound around it
( 372).
2. Magnets also appear in nature in an ore of iron
called magnetite. Specimens of this ore that are magnets
are called natural magnets ( 373).
3. On account of the tendency of a magnet to place
itself in a north-and-south position, one end is called the
north-seeking, or N-pole ; the other, the south-seeking, or
S-pole ( 374).
4. Poles of the same name repel each other, and
those of unlike name attract ( 375).
5. Artificial magnets may be made by stroking bars
of steel with a magnetized body ( 376).
6. Substances ^that are attracted by a magnet are called
paramagnetic (or simply magnetic) substances ; those that
are repelled, diamagnetic. Iron is the most magnetic of
all substances ( 377).
7. A piece of iron or steel becomes a magnet by indue-
MAGNETISM 373
tion when brought near the pole of a magnet. An N-pole
always induces an S-pole on the nearer end of a neighbor-
ing bar of iron or steel, and an S-pole induces an N-pole
( 378).
8. The region around a magnet in which magnetic
substances experience magnetic forces is called a magnetic
field ( 380).
9. Magnetic lines of force pass more readily through
iron than air. Different grades of iron and steel differ
also in the ease with which lines of force pass through
them. They are therefore said to differ in permeability
( 381).
10. The magnetism which would ordinarily be retained
by iron or steel may be reduced or entirely destroyed by
heating, jarring, twisting, etc. Hence magnetism is con-
sidered to be a molecular phenomenon. The molecules of
iron and steel are supposed to be small magnets having two
poles. Magnetization consists in giving the molecules a
new arrangement in which the N-poles point in general in
one direction and the S-poles in the other ( 382 to 386).
11. A magnet so 'pivoted as to turn freely in a horizontal
plane is called a compass. It takes a general north-and-
south position on account of the earth's magnetism ( 387).
12. The angle that measures the deviation of the compass
from the geographical meridian is called the declination of
the needle. This angle varies greatly with different lo-
calities. The agonic line is the line passing through points
where the declination is zero. It is now moving slowly
westward ( 388).
13. The angle between the earth's magnetic lines and a
horizontal plane is called the inclination, or dip, of the
needle. The dip varies from zero at the magnetic equator
to 90 at the earth's magnetic poles ( 389).
CHAPTER XVIII
VOLTAIC ELECTRICITY
1. PRODUCTION OF A CURRENT VOLTAIC CELLS
390. Maintaining a Continuous Discharge of Electricity.
It was shown in 372 that the moving charge of elec-
tricity obtained when a Leyden jar is discharged through
a helix of wire is able to magnetize pieces of steel. But
electricity would be of very little service if we were obliged
to depend upon the momentary flow occasioned by such a
discharge. The great practical value of electricity as a
working agent lies in the fact that it is possible by differ-
ent means, now to be studied, to maintain a continuous flow
of electricity, or in other words, a steady current. The
following experiments afford an opportunity to compare
these two kinds of discharge, viz. the momentary and
the continuous.
1. Place one end of a coil of insulated wire within which are several
pieces of soft annealed iron wire near one of the poles of a light
pivoted magnetic needle as
shown in Fig. 309. Discharge
a highly charged Leyden jar
through the wire of the coil
and observe the effect upon
the needle. The pole will be
either attracted or % repelled.
Except for the effect of the
magnetism remaining in the
iron, the action is only tempo-
rary. Recharge the jar and
FIG. 309. Magnetizing Iron by a Mo-
mentary Discharge of Electricity.
374
discharge it through the coil
VOLTAIC ELECTRICITY 375
in the opposite direction. If the first discharge produced repulsion,
this one will set up an attraction.
2. Attach one end of the coil shown in Fig. 310 to a strip of copper
about 10 cm. long and the other to a strip of zinc. Now dip both
plates in a very dilute solu-
tion (about 1 : 40, by volume)
of sulphuric acid, keeping
the plates from touching
each other. One of the mag- N
netic poles of the pivoted
needle will swing round
toward the coil and will not
resume its original position
so long as the plates remain
in the liquid. Reverse the FIG. 310. -Magnetizing Iron by a Continuous
,. , , Current,
connections at the ends of
the coil, and the opposite end of the needle will be attracted.
These experiments show a marked similarity between
the effect produced by the discharge of a Leyden jar and
that produced by the plates of zinc and copper suspended
in a solution of sulphuric acid. The iron is magnetized
in both instances, and the magnetism is even reversed by
reversing the connections. But since the effect in Ex-
periment 2 lasts as long as both plates remain in the
liquid, it is clear that a continuous discharge can be main-
tained by the means employed. A. continuous discharge,
or movement, of electricity is called an electric current.
391. The Voltaic Cell. The combination of zinc, cop-
per, and dilute sulphuric acid used in Experiment 2 of the
preceding section constitutes a voltaic cell. This method
of producing a current was first used by Volta 1 in
the year 1800 ; hence the name. There are many kinds
of voltaic cells, differing from one another in respect to
the materials used in their construction. Some of the
most important ones are treated later on.
1 See portrait facing page 352.
376 A HIGH SCHOOL COURSE IN PHYSICS
392. Electrical Charges produced by Voltaic Cells.
Provide two perfectly flat metal disks about 3 in. in diameter. Attach
one disk to the top of a sensitive gold-leaf electroscope and give it a thin
coating of shellac. To the second disk attach an insulated handle
and place it upon the first. The two plates thus form a condenser of
large capacity. Why? See 365. Form a series 1 of voltaic cells
(discarded dry cells will usually do) and touch the wire leading from
the zinc plate to the upper disk A,
Fig. 311, and the wire leading from
the carbon (or copper) to disk B.
Remove the wires and lift the
upper disk. The leaves of the
electroscope will diverge. On bring-
ing an electrified stick of sealing
wax near the instrument, the diver-
gence will be decreased, thus show-
ing that the carbon (or copper)
FIG. 311. -Charging an Electroscope late conve yed to the lower disk a
from Voltaic Cells.
positive charge. By repeating the
experiment with the wires reversed, it will be found that a negative
charge can be taken from the zinc of the cell.
It becomes clear from this experiment that the terminals
of a voltaic cell and the wires leading from them are electri-
cally charged^ a positive charge being borne by the carbon
(or copper) and a negative charge by the zinc. Hence the
copper of a cell is called the positive pole, and the zinc, the
negative pole. The voltaic cell, therefore, affords a case of
two oppositely electrified bodies, which on being joined by
a conductor set up an electrical discharge. Furthermore,
this discharge, or ^current, is continuous; for, as fast as
the charges become neutralized, they are renewed by the
chemical changes taking place within the cell.
393. Electromotive Force. As shown in the preceding
section, a voltaic cell develops a charge of positive electri-
fication on the copper plate and a charge* of negative on
1 If the disks are perfectly flat and the insulating material between
them is thin enough, the experiment can be made by using a single cell.
VOLTAIC ELECTRICITY 377
the zinc. The difference of potential that the cell maintains
between these two charges when the plates are not connected by
a conductor is the electromotive force (abbreviated E. M. F.)
of the cell. E. M. F. is sometimes called electric pressure
and is the cause of an electric flow in a circuit. It is not
a force in the sense in which that term is used in mechanics,
since its tendency is to move electricity and not matter.
The unit of E. M. F. is the volt, which is approximately
the E. M. F. afforded by a cell containing zinc, copper, and
dilute sulphuric acid.
394. An Electrical Circuit. The entire conducting path
along which a current of electricity flows is called an elec-
trical circuit. The circuit comprises not only the wire
with which the plates are connected, but also the plates
and the liquid of the cell. When an instrument, for ex-
ample, is to be introduced into the circuit, it is so connected
with the plates of the cell as to be traversed by the cur-
rent and is thus made a part of the circuit. Separating
the circuit at any point is called opening, or breaking, the
circuit ; and joining the separated ends is called closing, or
making, the circuit. When a circuit is broken, no current
can flow, and the circuit is therefore said to be interrupted.
395. Action of a Voltaic Cell. 1. Place a strip of commer-
cial zinc in very dilute sulphuric acid (about 1 : 40, by volume) and
observe the effect. Very small bubbles will be seen to rise from the
zinc and pass off at the surface of the liquid. These are bubbles of
hydrogen gas which is liberated from the acid by the chemical action.
If a small piece of zinc be left in the acid, it will soon dissolve, leaving
behind only a few small flakes of insoluble impurities. Repeat the
experiment with the strip of copper. No action will be observed.
2. Touch the zinc plate just used to a small quantity of mercury.
Some of the mercury will be found to cling to the plate. With a cloth
or sponge spread the mercury over the wet surface of the zinc. Now
on placing the zinc in the acid, no bubbles will be seen. Place the
copper plate in the acid with the zinc, but not in contact with it, and
connect the two rnetals by means of a wire. Bubbles will now be
378
A HIGH SCHOOL COURSE IN PHYSICS
observed rising from the copper plate. It is under these conditions,
as we have seen in 390, that a magnetic effect is derived from the
wire which connects the two plates. If the circuit be now broken at
any point, the bubbles cease to form. The mercury has thus pre-
vented the formation of hydrogen bubbles at the zinc plate, which,
nevertheless, continues to dissolve and decrease in size as long as the
electrical connection is maintained between it and the copper.
It is clear from Experiment 1 that the acid used acts
very unequally upon the two plates of a voltaic cell.
It is this difference in the chemical action that gives
rise to the difference of potential between the positive and
negative charges found in 392. The greater the disparity
in the chemical actions at the two plates, the greater the dif-
ference of potential maintained by the cell. Furthermore,
the experiment shows that the negatively charged plate
(i.e. the zinc) is dissolved by the acid, while the posi-
tive copper plate from which hydrogen rises during the
operation of the cell remains apparently unchanged.
Zinc
Copper
00
396. .Theory of a Voltaic Cell. The theory of the simple
voltaic cell described in 390 rests upon the hypothesis of Clausius,
(1822-1888), a German physicist. This
hypothesis, which is based upon a large
amount of experimental evidence,
states that many of the molecules in
a dilute solution of a substance " split
up " into two parts called ions. Hence,
when sulphuric acid (HgSO^ 1 is di-
luted, two kinds of ions are formed,
those of hydrogen (H) and those of
SO 4 , called the sulphions. See Fig.
312. Furthermore, the hydrogen ions
bear positive charges of electricity, while the sulphions carry negative
charges. As shown in 395, zinc has a strong tendency to dis-
solve in dilute sulphuric acid, while copper has not. In the process
1 This chemical formula expresses the fact that each molecule of
sulphuric acid is composed of two atoms of hydrogen, one of sulphur,
and four of oxygen.
FIG. 312. Diagram Showing
Ions in a Voltaic Cell.
VOLTAIC ELECTRICITY
379
the sulphions in the liquid attack the zinc plate, from which they
abstract some of the metal to form zinc sulphate (ZnSO 4 ), a white
substance that dissolves at once in the liquid. In this process the
negative charge carried by each sulphion concerned in the action is
given up to the zinc plate, which thus becomes charged with negative
electricity. Again, for each negatively charged ion that engages with
zinc, a positive hydrogen ion from the liquid gives up its charge to
the copper, thus charging it with positive electricity. After the hy-
drogen ions have discharged their electricity to the copper plate, they
become free hydrogen, which collects in small bubbles at this plate
and rises to the surface.
397. Local Action and its Prevention. The results of
Experiment 2 ( 395) show that a coating of mercury
upon the zinc plate prevents the formation of hydrogen at
its surface when it comes in contact with the acid. The
reason is because pure zinc will not dis-
solve in pure sulphuric acid ; and the
mercury dissolves from the plate only the
pure zinc which is then coated over the
surface, thus overlaying the impurities
with an amalgam of zinc. After a time
these impurities, which are mainly carbon
and iron, become exposed to the acid,
and local currents are set up between
them and the neighboring portions of the
plate, as indicated by the arrows in Fig. 313. The gen-
eration of electric currents between the zinc of a cell and its
impurities is called local action. Local action is a wasteful
process, but can obviously be prevented by employing
pure zinc or by coating an impure zinc plate with mer-
cury. This treatment is known as the amalgamation of
the zinc plate.
398. A Mechanical Analogy. The mechanical device
shown in Fig. 314 is of assistance in making clear the
action of a voltaic cell. Imagine a rotary pump P to be
FIG. 313. Wasting
of the Zinc by
Local Action.
380
A HIGH SCHOOL COURSE IN PHYSICS
FIG. 314. A Mechan-
ical Analogy of Cell
Action.
placed in a U-fcube and arranged to be turned by the
weight W. When the wheel of the pump is turned, water
is forced to a greater height in one arm
than in the other. The wheel, how-
ever, will come to rest when the back
pressure due to the difference of level
on the two sides of it just equals the
pressure exerted by the wheel. If there
is no friction, the device will maintain
the difference in level h as long as no
water escapes.
In this system the difference of level
h maintained by the pump is analogous
to the difference of potential (E. M. F.) maintained be-
tween the plates of a voltaic cell. Just as the pump
ceases to turn when a certain difference of level is reached,
so the chemical action of a perfect cell stops when the
difference of potential between the positive and negative
charges on the plates has attained a certain value, which
will depend on the nature of the ma-
terials used in its construction.
399. A Cell in Action. The case
of a voltaic cell is modified as soon
as the circuit is completed and a cur-
rent allowed to flow ; so also is that
of the pump and water. Imagine a
pipe T 7 , Fig. 315, to connect the two
arms of the U-tube. On account of
the difference of water level, the liquid
will flow through T, and the wheel will
continue to turn, since now the back
pressure will have been reduced. The
difference of level will decrease to h', whose value will
depend on the friction offered to the current flow in T.
FIG. 315. When Water
is Allowed to Flow
through T, the Wheel
at P will Continue to
Turn.
VOLTAIC ELECTRICITY 381
Similarly, when the plates of a voltaic cell are connected
by a conductor, the charge on the positive plate (copper)
moves toward the negative plate (zinc), and the potential
difference is diminished. The chemical action now goes
on vigorously in its attempt to restore the charge that
has passed through the conductor. Hence the difference
of potential between the two poles of a cell when a current
is flowing will be less than that when the circuit is open.
This value is no longer called the E. M. F. of the cell, but
is termed the fall of potential, or difference of potential
between the plates of the cell.
400. Deflection of a Magnet by a Current Hold the wire
joining the plates of a simple voltaic cell over and parallel to a pivoted
magnetic needle, Fig. 316, and
then close the circuit by placing
the plates in the liquid, or by
means of a key inserted anywhere
in the circuit. The needle will be
turned on its pivot and finally come
to rest at an angle with the con>-
ductor carrying the current. If FIG. 316.- A Magnetic Needle is De-
/, * fleeted by an Electric Current,
the current be passed in the op-
posite direction above the needle, the deflection is opposite to the
first. The wire may now be placed below the needle, and the direction
of the deflections obtained. If the conductor be placed at the side,
or near the end, Of a suspended magnet, deflections are also obtained.
This experiment confirms the result previously found
in 390, viz. that the region around a wire through which
an electric charge is moving has magnetic properties.
This experiment was first performed by Oersted, 1 a Danish
physicist, in 1819. Oersted's discovery is of great his-
torical interest, since it was the first evidence obtained in
regard to the magnetic effect of a current of electricity
and has led to results of the greatest practical importance,
1 See portrait facing page 382.
382
A HIGH SCHOOL COURSE IN PHYSICS
FIG. 317. The Thumb Shows the
Direction in Which the N-Pole
Moves.
By observing the direction in which the N-pole of the
magnetic needle is moved in relation to the direction of
the electric current, the following rule will be found to
apply : Let the fingers of the out-
stretched right hand point in the
direction of the current flow in
the wire and the palm be turned
toward the needle; the extended
thumb will then show the direction
of the deflection of the N-pole of
the needle. The rule is of convenience in determining the
direction of a current when its effect upon a magnetic
needle is known. The manner of applying this rule is
made clear by Fig. 317.
401. The Galvanometer. The effect discovered by
Oersted is of great service in the galvanometer, an instru-
ment used for detecting and measuring electric currents.
The following experiment will show how the effect of a
current on a magnetic needle can be so increased as to
make it possible to discover even very feeble currents.
Place a compass needle, below which is a graduated circle, within
a single turn of wire as in (1), Fig. 318, and read the deflection on the
scale. Now wind the same wire three or four times around the com-
pass, always keeping the wire parallel to
the original position of the needle, and
again read the deflection. The second
reading will be much greater than the
first. A current that will scarcely move
the needle when a single turn of wire is
used will be found to produce a marked
effect when tested with the coil of several
turns.
The magnetic forces due to the
electric current in all parts of the
coil tend to turn the needle in one eter.
HANS CHRISTIAN OERSTED (1777-1851)
Oersted's famous experiment of 1819 on
the deflection of a magnet by an electric
current was the beginning of the science of
electro-magnetism. This experiment dem-
onstrated the long-sought connection be-
tween electricity and magnetism and served
to point out the line of experimentation
that has brought the science up to its pres-
ent-day development.
Oersted was born in Langeland, a por-
tion of Denmark, studied at Copenhagen,
and afterwards became a professor at the
university and polytechnic schools of that
city.
DOMINIQUE FRANCOIS JEAN ARAGO (1786-1853)
The year following Oersted's discovery,
Arago, a noted Parisian astronomer and
physicist, observed that iron filings cling to
a conductor carrying an electric current.
A little later it was shown by Sir Humphry
Davy of England that the filings arrange
themselves in magnetized chains around the
conductor.
Arago was one of the first advocates of
the wave theory of light. The beautiful
tints produced when polarized light passes
through certain crystals were discovered by
him in 1811. Arago planned a method for
measuring directly the velocity of light in
air and water, but failing eyesight pre-
vented carrying out his experiments. He lived, however, to see the
work done by Fizeau and Foucault.
VOLTAIC ELECTRICITY 383
particular direction, a fact that becomes clear when the
rule given in 400 is applied. Hence by introducing
a sufficient number of turns of wire and making the
needle extremely light, a very small current will suffice
to produce a deflection.
402. Polarization of a Voltaic Cell. i. Connect a simple
zinc and copper cell with a voltmeter 1 ( 430) or a high-resistance
galvanometer and read the deflection produced. Short-circuit the cell
for a short time by means of a wire, thus allowing hydrogen to form
in large quantities at the copper plate, remove the wire, and again
read the deflection. It will be less than at first. If the liquid is
now stirred, the deflection will be increased. Keep the bubbles
brushed from the copper plate and see if the current can be kept the
same as at first.
2. Substitute a carbon plate for the copper and repeat Experi-
ment 1. (A good carbon plate may be taken from a discarded dry cell.)
A similar decrease in the current will be observed. While the cell is
connected with the instrument, pour into the sulphuric acid a small
quantity of sodium (or potassium) dichromate or chromic acid solu-
tion. The index of the galvanometer promptly indicates a strong
increase of electromotive force. The cell may now be short-circuited
as before, but the E. M. F. quickly resumes its original value after
the short circuit is removed.
These experiments show clearly that the collection of
hydrogen on the copper (or carbon) plate of a cell reduces
the E. M. F. and, consequently, the current that it sends
through the conductor. This effect arises from the fact
that a hydrogen-coated plate now takes the place of the
copper plate. The diminution of the E. M. F. of a cell
by the presence of hydrogen on the copper (or carbon) plate
1 For classroom demonstration purposes it is desirable that a volt-
meter be provided having upwards of 50 ohms resistance and reading
to about 5 volts. An ammeter having less than an ohm resistance and
reading to 3 or 4 amperes will also be found of great service. In case
such instruments are not available, a galvanometer of large resistance (50
ohms or more) may be substituted for a voltmeter, and one of small
resistance (less than 1 ohm), for an ammeter.
384
A HIGH SCHOOL COURSE IN PHYSICS
is called the polarization of the cell. If the bubbles be
removed by stirring, the current will remain near its
original value. Experiment 2 serves to demonstrate the
fact that the effect of the hydrogen can be largely overcome
by chemical means, a method of which advantage is taken
in many kinds of voltaic cells. In the prevention of
polarization by chemical action the dichromate acts as a
depolarizer for removing the hydrogen from the carbon
plate. This it does by supplying an abundance of oxygen,
with which the hydrogen unites chemically to form
water.
403. The Dichromate, or Grenet, Cell. In this cell a
zinc plate Z, Fig. 319, is usually placed between two
plates of carbon which are joined together
by metal at the top. The liquid is dilute
sulphuric acid (H 2 SO 4 ) to which is added
dichromate of sodium (or potassium) or
chromic acid as a depolarizer. See 402,
Exp. 2.
The dichromate cell is capable of giving
a strong current for a short time and for
this reason has been largely used in ex-
perimental work. It has, however, been
largely replaced by the " dry " cell ( 407)
and storage battery on account of their
greater convenience. One disadvantage of
the dichromate cell is the necessity of with-
drawing the zinc from the acid by the rod
A when the cell is not in use.
404. The Daniell Cell. The Daniell cell, Fig. 320,
consists of a glass jar containing a saturated solution of
copper sulphate (blue vitriol, CuSO 4 ) in which stands
a large sheet copper plate O. The copper plate encircles
a porous cup of unglazed earthenware which contains a
FIG. 319. The
Grenet, or
Dichromate
Cell.
VOLTAIC ELECTRICITY
FIG. 320. The
Daniell Cell.
heavy bar of zinc Z immersed in a dilute solution of zinc
sulphate (ZnSO 4 ). The porous cup does not check the
flow of electricity, but does prevent the rapid mixing of
the two solutions. Dilute sulphuric acid may be used
in place of zinc sulphate.
In this cell the zinc is continually being dissolved and
in the course of time must be renewed. On the other
hand, copper (Cu) from the solution of
copper sulphate (CuSO 4 ) is deposited slowly
upon the copper plate, which in time grows
into a massive sheet. In order to maintain
c, constant supply of copper ions in the
solution, crystals of copper sulphate are
added from time to time. Since copper,
instead of hydrogen, is deposited on the
copper plate, the nature of the plate' is
not changed, and, consequently, no polarization takes
place. On account of the complete non-polarization of the
Daniell cell, it is often used when currents of great con-
stancy are required.
405. The Gravity Cell. A dilute solution of zinc
sulphate has less density than a saturated solution of
copper sulphate; hence, the two will be
kept separate by gravity and the former
will .float upon the latter. This fact is
employed in the so-called gravity cell, Fig.
321, in which a copper plate lies upon the
bottom of a jar surrounded by crystals of
copper sulphate and a saturated solution
of the same substance. Above this solu-
tion is one of dilute zinc sulphate which surrounds a
massive zinc plate.
If a gravity cell be allowed to stand on an open circuit,
the liquids slowly mix. In order to prevent this and thus
26
FIG. 321. The
Gravity Cell.
386 A HIGH SCHOOL COURSE IN PHYSICS
keep the copper sulphate from reaching the zinc plate, the
cell must be kept in more or less active operation. While
producing a current the copper ions are continually mov-
ing away from the zinc, in which respect the action is the
same as that of the Daniell cell, of which this cell is
a modification. Gravity cells are extensively used in
telegraphy and in circuits where constant currents are
desired.
406. The Leclanche Cell. The positively charged plate
of the Leclanche (pronounced Le dan'shd 1 ) cell, Fig. 322,
is a bar of carbon C which is packed in
a porous cup together with small pieces
of carbon and manganese dioxide. The
porous cup is placed in a solution of
- ammonium chloride (salammoniac) in
which stands a bar of zinc Z to serve as
the negative plate of the cell.
When the circuit containing a Leclanche
FIG. 322. The Le- C Q\\ j s closed, hydrogen is liberated at the
clanche' Cell. J
carbon ; but, on account of the presence
of the manganese dioxide, the hydrogen is slowly oxidized,
forming water. In this manner polarization is largely
prevented. As a rule, however, the hydrogen is liberated
so rapidly that the cell slowly polarizes, but regains its
normal condition when allowed to stand for a time on
an open circuit.
The Leclanche cell has had a very extensive use on
account of the fact that it produces currents that are
suitable for ringing bells, operating signals, regulating
dampers, etc. The cell will remain in good condition for
years with very little attention. At the present time it
is being rapidly replaced by the more convenient and in-
expensive "dry" cell, which is a modified form of the
Leclanche.
VOLTAIC ELECTRICITY
387
407. The "Dry " Cell. The Leclanche cell is made in
the form of the so-called " dry " cell by embedding the car-
bon plate (7, Fig. 323, in a paste A made by mixing zinc
oxide, ammonium chloride,
plaster of Paris, zinc chlo-
ride, and water. The whole
mass is contained in a zinc
cup Z, which serves as the
negative plate of the cell.
Evaporation is prevented by
hermetically sealing the cup
with melted bitumen or
asphalt. Many different
forms of dry cells are now
on the market and are in
great demand for operating
the sparking devices of gas
and gasoline engines, ring-
ing bells, etc. A " dry " cell deteriorates rapidly on a
closed circuit, and hence should always be connected with
a spring key that automatically opens the circuit when
the cell is not in use.
EXERCISES
1. Explain how the direction of the current in a telegraph wire
could be determined by means of a small compass.
2. Is the difference of potential between the plates of a voltaic cell
large enough to cause a spark when wires from them are brought
near together ? Is it great enough to produce a shock when the plates
are simultaneously touched?
3. Would you expect to get an E. M. F. by forming a cell of two
copper plates or two zinc plates in dilute sulphuric acid ? Make the
experiment, using a sensitive galvanometer. Try the experiment with
a polarized copper plate and one that is not polarized and account for
the results.
4. Would you expect to derive a current from a zinc and copper
cell containing a solution of common salt? Perform the experiment
FIG. 323. The "Dry " Cell.
388
A HIGH SCHOOL COURSE IN PHYSICS
5. Why is the combination of zinc, copper, and dilute sulphuric
acid a suitable one for experiments like those described?
6. Study the description of the Daniell cell and state which solu-
tion grows weaker and must ultimately be renewed. What materials,
therefore, must be kept on hand for replenishing a system of Daniell
or of gravity cells ?
2. EFFECTS OF ELECTRIC CURRENTS
408. The Magnetic Effect. It has already been shown
that a current of electricity is capable of magnetizing bars
of iron and steel ( 390), and also that a magnetic needle
placed near a current is deflected from its normal position.
These are only special cases of the more general one illus-
trated by the following experiments:
1. Join several new dry cells in series and connect them through
a key to a vertical wire passing through a horizontal sheet of card-
FIG. 324. Magnetic Field
around a Conductor Carrying
a Current.
FIG. 325. Iron Filings Arranged
around a Conductor.
board as in Fig. 324. A current of at least 2 amperes is desirable.
Sprinkle iron filings on the cardboard and close the key for a short
time, meanwhile tapping lightly to jar the filings. The filings will
arrange themselves in circular lines (see Fig. 325) around the wire
as the center, thus showing the shape of the magnetic field about the
conductor. Small pivoted magnets placed near the wire will turn
VOLTAIC ELECTRICITY 389
until they are tangent to the circles with their N-poles as shown in
Fig. 324.
2. Make a helix, or spiral, of insulated copper wire by winding
about 30 turns upon a lead pencil. Connect the ends of the wire with
a cell and present one end of the helix to the N-pole of a suspended
magnet or compass needle, One end will be found to attract the
N-pole while the opposite end repels it, and the end that attracts
the N-pole will repel the S-pole. Reverse the connections of the cell
and repeat the experiment. The end of the helix which formerly
attracted a magnetic pole will
now repel it.
3. Thread a spiral of cop-
per wire through holes in a
flat piece of cardboard or wood
as shown in Fig. 326. Strew
iron filings evenly over the FIG. 326. Magnetic Field Produced by a
f , ,1 Current in a Helix, or Solenoid,
surface and send the current
(about 3 amperes are required) from several new dry cells through
the wire. If the apparatus be tapped lightly, the filings will arrange
themselves as shown in the figure.
It is clear from these experiments that a conductor
carrying an electric current is surrounded by a magnetic
field. If the conductor is a straight wire, Experiment 1
shows that the lines of force are concentric circles around
the conductor as the center. The direction of the lines is
given by the direction in which an N-pole is urged when
placed in the field. It is clear, therefore, from Fig. 324,
that the direction of the lines is that indicated by the
arrows. A convenient rule may be stated as follows :
G-rasp the conductor with the right hand with the out-
stretched thumb in the direction the current is flowing. The
fingers encircle the wire in the direction of the lines of force.
The shape of the field depends on the form of the con-
ductor ; for, when the conductor is a helix, the magnetic
field resembles that about a straight bar magnet. (See
Fig. 327.) In fact, it is shown in Experiment 2 that the
390
A HIGH SCHOOL COURSE IN PHYSICS
helix has the properties of a magnet while a current is
flowing through the wire. If the coil could be properly
suspended and a current sent through it, the axis would
assume the direction taken by a compass needle. Such a
helix is also called a solenoid.
FIG. 327. Showing the Relation between the Direction of the Current and
the Magnetic Lines.
409. Poles of a Helix. Let Experiment 2 of 408 be repeated
and the N-pole and the S-pole ascertained. Tracing the current from
the positive pole of the cell, it will be found to flow around the N-pole
in a direction contrary to the motion of the hands of a clock as one
faces the pole and in the reverse direction about the S-pole as shown
in Fig. 327.
The experimental result leads to the following conven-
ient rule : If the helix be grasped with the right hand so that
the fingers point in the direction
the current is flowing, the ex-
tended thumb will point in the
direction of the N-pole of the
helix. (See Fig. 328.)
Another convenient rule is
applied by facing the end of the
helix ; if the current is flow-
ing clockwise, the end of the helix is an S-pole, and,
conversely, if counter-clockwise, an N-pole.
FIG. 328. Rule for Determining
the Poles of a Helix Carrying
a Current.
VOLTAIC ELECTRICITY 391
410. The Electro-magnet. Probably none of the effects
that can be produced by electric currents are of greater
practical value or employed more extensively than the
magnetic effect. The scale on which this effect can be
produced is limited only by the dimensions of the appa-
ratus used and the strength of the current.
Wind a helix consisting of about 75 turns of No. 22 insulated
copper wire and provide an iron core that can be inserted into, or
removed from, the helix as de-
sired. Test the magnetic action
of the helix without the core
by presenting it to a magnetic
needle while a current is flow-
ing. Now insert the core and
note the change. Its effect is
more marked than before. Next
send the current from a new Fia ' 329. - Magnetization of Iron by
, ,. , ,. , ,. . , Means of an Electric Current,
dry cell through the helix and
dip one end of the core into a box of tacks, Fig. 329. A large
quantity of tacks will cling to the core and remain there until the
current is interrupted.
Although a coreless helix of wire has magnetic proper-
ties when a current is flowing through it, its magnetic
field is insignificant when compared to that which the
same current will produce when an iron core is present,
on account of the large permeability of iron ( 381).
The introduction of the core adds the lines of force of
the magnetized iron to those produced by the current in
the helix alone. Any mass of iron around which is a helix
for conducting an electric current is called an electro-magnet.
The small amount of magnetism retained by the core after
the circuit is broken is termed residual magnetism.
Electro-magnets are made in many forms and often of
extremely large dimensions for holding heavy masses of
iron. The horseshoe form shown in Figs. 330 and 331 is
392
A HIGH SCHOOL COURSE IN PHYSICS
most frequently used in electrical devices. The wire is
so wound as to produce an N-pole at N and an S-pole
at S. The bar of iron A which is held by the magnetism
of the poles is called the armature. When
the armature is against the poles, it will
be observed that the lines of force find a
i
FIG. 330. An Electro-magnet
Showing Poles and Armature.
FIG. 331. Showing
the Path of the
Lines of Force in
an Electro-magnet.
FIG. 332. A Large
Electro-magnet
Used for Han-
dling Masses of
Iron in Factories.
complete magnetic circuit through iron, as shown by
the dotted lines in Fig. 331. Figure 332 shows a large
form of the electro- magnet that is widely used in manu-
facturing plants for the purpose of handling heavy masses
of iron, as castings,
plates, pig iron, etc.
The lifting power is con-
trolled mainly by the
current used.
411. The Electric Bell.
An important application
of the magnetic effect of an
electric current is found in
the electric bell. The instru-
ment consists of an electro-
magnet %, Fig. 333, near the
poles of which is an armature
of iron attached to a spring.
Extending from the armature
FIG. 333. The Electric Bell. is a slender rod bearing at its
VOLTAIC ELECTRICITY
393
extremity the bell hammer H. The armature carries a spring that
touches lightly against the screw point at>C. The connections are made
as shown in the figure. When the push button P is pressed, the circuit
is completed by a metallic contact within the button, and the current
from the cell B flows through the electro-magnet coils. This causes
the magnet to attract the armature, and the hammer strikes the bell.
The movement of the armature, however, breaks the circuit at C and
thus interrupts the current. Since the cores of the magnet now lose
their magnetism, the armature is thrown back by the spring ; the
contact at C is restored, and all the operations are repeated. Hence
a steady pressure on the push button causes the hammer to execute a
number of rapid strokes against the bell. The direction of the cur-
rent is immaterial to the operation of the bell.
412. Mutual Action of Two Parallel Currents. Suspend
two light wires about 30 cm. long from two other wires a and b,
Fig. 334, which are bent as
shown. Let the lower ends of
the vertical wires just dip into
a mercury cup below. Now send
a strong current through the ap-
FIG. 334. Illustrating the Mutual
Action between Parallel Currents.
FIG. 335. Parallel Currents in the
Same Direction.
paratus (an alternating current of from 4 to 8 amperes suffices), which
will flow down one wire and up the other. The two conductors will
repel each other. Again, hang both wires on a and make the con-
nections as shown in Fig. 335. Both currents will now flow in the
same direction and an attraction will be observed.
394
A HIGH SCHOOL COURSE IN PHYSICS
The results of the experiments may be stated as follows:
Currents flowing in the same direction attract each other,
and those flowing in opposite directions repel each other. The
FIG. 336. Magnetic Fields around Parallel Conductors : (1) When Currents
are Flowing in the Opposite Directions ; (2) When Flowing in the Same
Direction.
magnetic field around the two wires in each of the two
cases is shown in Fig. 336.
413. Heating Effect of Electric Currents. It is a familiar
fact that electric currents produce heat. This is at once
evident when the hand is placed in contact with the warm
bulb of an incandescent lamp. The following experiment
shows in another way the transformation of electrical
energy into heat.
If an electric lighting current is available, construct a device for
controlling it by mounting several lamp sockets on a board and join-
ing them in parallel (444). Connect each side to a binding post,
screw a lamp into each socket, and a safe adjustable resistance is
ready for use. Put the device just described in circuit with a piece
of fine iron wire joined to one of copper wire of the same diameter.
The pieces may be each several inches in length. Screw one lamp at
a time into its socket until sufficient current flows to heat the wire.
The iron wire will at length glow with heat while the copper wire of
the same dimension is still comparatively cool. If a lighting current
cannot be used, the experiment may be made by using shorter pieces
of wire with several good dry cells joined in series. In this case no
controlling resistance is necessary.
An experiment that succeeds well with a small current is made by
connecting a cell with a fine insulated copper or iron wire that has
VOLTAIC ELECTRICITY
395
been wound in a coil about the bulb of a thermometer,
mercury indicates the heating effect of the current.
The rise of
The heating effect of a current of electricity is employed
in electric cooking devices, in various methods of heating,
and in electric lighting.
An electrically heated
flatiron is shown in Fig.
337.
414. Chemical Effects
of Electric Currents.
Seal two platinum wires to
which are attached platinum FIG. 337. An Electrically Heated Flatiron.
strips about 1 cm. wide and
3 cm. long in small bent glass tubes e and /, Fig. 338. Over each
of these place an inverted test tube filled with water to which has
been added a number of drops of sulphuric acid. Place a small
. quantity of mercury in each of the small
tubes and connect the strips of platinum
in circuit with three or four dry cells
joined in series by inserting the con-
necting wires into the mercury. Small
bubbles of gas will be seen rising from
the platinum in each tube and collect-
ing at the top. If e is joined to the
FIG. 338. Electrolysis of positive pole of the battery, the gas
al tand% y !^n C a"r ed bove that strip of platinum will collect
only one half as fast as that over the
other. When the action has progressed until one of the tubes
is filled with gas, remove it carefully and apply a lighted match.
A blue flame will be seen caused by the burning of this gas, which is
hydrogen. Now remove the other tube and insert a glowing pine
stick, which will be observed to burst into a flame because of the
oxygen contained in the tube.
The platinum strips employed in making electrical con-
tact with the liquid in the tubes are called electrodes.
While conducting the electric current from one electrode
to the other, the water is decomposed into its constituent
396 A HIGH SCHOOL COURSE IN PHYSICS
elements, hydrogen and oxygen. This decomposition is
characteristic of all liquids, except liquid metals. The
process of decomposing a compound substance by means of
an electric current is called electrolysis. The substance
decomposed is called an electrolyte. The electrode at
which the current enters the electrolyte is the anode;
the one at which it leaves, the cathode.
415- Theory of Electrolysis. In the light of the theory of
solutions stated in 396, the process of electrolysis is easily explained.
When a small quantity of sulphuric acid (H 2 SO 4 ), for example, is
introduced into water, the molecules split up into hydrogen (H) ions
and sulphions (SO 4 ), the former bearing positive charges of electric-
ity, the latter, negative charges. Now when two platinum electrodes
that are connected to the poles of a battery are placed in the liquid,
the cathode, which is charged negatively, attracts the positively
charged H ions, while the anode, which is positively charged, attracts
the negatively charged SO 4 ions. The H ions discharge their positive
electricity to the cathode and are then free to collect and rise in
bubbles to the surface. The SO 4 ions, on the other hand, discharge
their negative electricity to the anode, where they react chemically
upon the water (H 2 O), setting free the oxygen (O). Thus each
sulphion (SO 4 ) together with the hydrogen (H 2 ) taken from the
water forms new molecules of sulphuric acid (H 2 SO 4 ) . In this manner
the amount of acid present in the solution remains constant, while the
quantity of water diminishes as the process of electrolysis advances.
416. Electrolysis of Copper Sulphate. Introduce two plati-
num electrodes into a solution of copper sulphate (CuSO 4 ) and place
them in circuit with three or four dry cells. After a few seconds the
cathode, or negative electrode, will be found to be coated with me-
tallic copper, while the anode remains unchanged. If the direction of
the current be now reversed, copper will be deposited on the clean
plate (now the cathode), while the copper coating on the anode gradu-
ally disappears.
In the electrolysis of copper sulphate, the ions present are copper
(Cu) ions and sulphions (SO 4 ), the former bearing positive charges
of electricity and the latter, negative. When platinum electrodes are
introduced into the solution, the copper ions are attracted to the
cathode, where they discharge their electricity and become free. Thus
VOLTAIC ELECTRICITY
397
we find copper deposited upon this electrode. At the anode the sul-
phions react with water as in the case just described ( 415). How-
ever, if the anode is a copper plate, the sulphions (SO 4 ) abstract copper
from the plate at the instant they discharge their electricity and form
copper sulphate (CuSO 4 ), which dissolves in the liquid.
The experiment illustrates the process of electroplating,
a method by which one metal is given a coating of another.
Thus by electrolytic action corrosive iron may be plated
with non-corrosive nickel, or tarnishing brass with pure
gold.
In the experiment, copper (Cu), which is a constituent
of the copper sulphate (CuSO 4 ) in the solution, is always
deposited on the cathode, or negative electrode. If the
anode is made of platinum, oxygen will be liberated at its
surface. If, however, the anode is made of copper, the
case is modified ; for, instead of setting oxygen free,
copper is removed from the plate and carried into the
solution.
417. Electroplating. When we consider the vast num-
ber of plated articles in everyday use, we can scarcely
overestimate the great commercial value of the electrolytic
action of an electric cur-
rent. When, for ex-
ample, silver is to be
plated upon the surface
of a spoon, an anode
plate of silver is sus-
pended in a solution of
., . n T ., FIG. 339. Illustrating the Process of Elec-
silver cyanide, while tropiating.
the spoon is made the
cathode by being connected with the zinc of a battery
and completely submerged in the solution. See Fig.
339. The current is allowed to flow until the coating
is of the desired thickness. In the nickel-plating pro-
398 A HIGH SCHOOL COURSE IN PHYSICS
cess an anode of nickel is used in a solution of nickel
nitrate and ammonium nitrate. The article to be plated
is always the cathode. When the coating reaches the
proper thickness, the final process of polishing gives the
surface the desired appearance.
418. Electrotyping. As a rule, books of which a large
edition is to be printed are first electrotyped. In this
process an impression is made in wax after the type has
been set up, so that each letter leaves its imprint in the
mold. A thin layer of finely powdered plumbago, or
graphite, is brushed over the surface of the wax in order
to render it a conductor of electricity. When thus pre-
pared, the mold is placed in an electrolytic bath of copper
sulphate and joined to the negative pole of a battery or
other source of electricity. The anode is simply a copper
plate. The current is allowed to flow until the coating
of copper upon the wax is somewhat thicker than a sheet
of paper. While the copper is being deposited upon the
conducting graphite, it penetrates into even the smallest
depressions of the mold and thus reproduces in copper
the exact form of the type. The coating of copper is
then removed from the wax, trimmed, and filled in at
the back with molten type metal. The advantage gained
by electrotyping is convenience, durability, and perma-
nence, and the type from which the impression is taken
on the wax may be distributed and used again without
delay.
419. Refining Copper. Copper as it comes from ordi-
nary smelting works contains many impurities. Such
copper is refined electrolytically by casting the crude
metal in huge plates which are afterwards used as anodes
in large depositing vats. The solution used is copper
sulphate, and the cathode is a thin plate of pure copper.
When a current of electricity is sent through the solution,
VOLTAIC ELECTRICITY
399
copper is deposited on the cathode until it grows into a
heavy plate. The copper anode is carried into the solu-
tion, while its impurities collect at the bottom of the vat.
Copper thus refined is called electrolytic copper, and is
much used in the manufacture of wire and in the construc-
tion of dynamos, motors, etc.
420. The Storage Battery. The principle of the storage cell
may be illustrated by making a small cell of two plates of lead about
2x6 inches and a solution of sulphuric acid consisting of one part of
acid and about eight parts of water. Attach the plates to a piece of
wood and hang them in the solution. Connect the lead plates to two
good dry cells joined in series and allow the current to flow for a minute
or more. Disconnect the dry cells and run wires from the lead plates
to an electric bell. The bell will ring vigorously for a short time and
then gradually cease. The power of the cell can be restored by again
connecting it with the dry cells. If a galvanometer be introduced in
the circuit, it will be found that the discharging current flows in
opposition to the current used in charging. If the E. M. F. of the
charged plates is measured by a voltmeter, it will be found to be
about two volts.
The charging current decomposes the water as in 414. Hydrogen
is liberated at the cathode plate; but the oxygen produced at the
anode changes the surface of the plate from lead (Pb) into lead peroxide
(PbO%), which may be recognized by its brownish color. When the
plates are connected with the electric
bell, a current flows from the peroxide
plate through the bell to the other,
which is simply lead. The current
continues until the thin coating is
used up.
It should be observed that the
storage cell stores energy but not elec-
tricity. The work done by the charg-
ing current results in the production
of the energy of chemical separation
in the cell. When the circuit is
closed, this amount of potonuiiul energy
is transferred to the bell, where it ap-
pears as mechanical energy which is
340. A Storage Cell, or
Lead Accumulator.
400 A HIGH SCHOOL COURSE IN PHYSICS
finally dissipated as sound and heat. A complete storage cell is
shown in Fig. 340.
EXERCISES
1. What would be the effect produced upon the strength of the
poles of a bar magnet if it were placed in a helix in which the direc-
tion of the current around the N-pole of the magnet was counter-
clockwise ? In which it was clockwise ?
2. A helix is suspended so as to turn freely in a horizontal plane
and is placed above a strong bar magnet. If a current be sent through
the helix, what will be its direction around that end which stops over
the S-pole of the magnet ?
3. Place a compass box upon one of the rails of an electric railway
running north and south and see if you can detect the presence and
direction of a current.
4. Would you expect a compass needle to point north and south
in a moving trolley car ? Why ?
5. Which is most readily magnetized when placed in a helix, iron
or steel? Which will retain the greater amount of magnetism?
How could you produce a permanent, magnet by the help of a dry
cell and a helix ?
6. How could the direction of an electric current be determined by
means of an electrolytic cell through which it could be caused to flow ?
7. What change would finally occur in the copper sulphate solu-
tion in an electrolytic cell having platinum electrodes if the current
were allowed to flow?
8. Would the result in Exer. 7 be at all modified if the anode
were copper ? Explain.
9. Electric circuits in buildings are protected against too strong
currents by lead wire fuses of the proper size placed in the circuit.
If by accident the current becomes strong enough to be unsafe, the
wire melts. Explain in full. If possible, inspect the wiring of some
building and report on the form in which the fuses are made.
SUMMARY
1. An electric current is a continuous discharge, or
movement, of electricity ( 390).
2. Electric currents may be produced by chemical
action, as in voltaic cells. It may be shown that one of
the terminals of such a cell is charged with positive elec-
tricity, the other with negative ( 391 and 392).
VOLTAIC ELECTRICITY 401
3. The E. M. F. of a cell is the difference of potential
between these charges when no current is flowing ( 393).
4. Much of the potential energy of the zinc of a cell
is wasted by "local action." This may be largely pre-
vented by amalgamation ( 397).
5. A current flowing in a conductor near and parallel
to a magnetic needle tends to deflect it from its position.
This principle is used in many electrical measuring instru-
ments, as galvanometers, etc. ( 400).
6. The E. M. F. is diminished by the accumulation of
hydrogen on the copper (or carbon) plate. This effect
is known as polarization. ( 402).
7. An electric current is surrounded by a magnetic
field. When the conductor carrying the current encircles
a bar of iron or steel, the bar becomes a magnet ( 408).
8. The electro-magnet consists of a helix of insulated
wire wound upon a core of iron. The principle of the
electro-magnet is employed in the electric bell and many
other important devices ( 410 and 411).
9. Parallel currents flowing in the same direction
attract each other, and those flowing in opposite directions
repel ( 412).
10. When an electric current flows through a con-
ductor, the conductor is heated. This effect is applied in
electric lighting, in heating and cooking devices, etc.
( 413).
11. An electric current decomposes water into hydro-
gen and oxygen, hydrogen being liberated at the cathode.
When a current flows through a solution of a metallic
salt, the compound is decomposed and the metal liberated
at (or plated upon) the cathode. This effect of an electric
current is known as electrolysis and is used in electro-
plating, etc. ( 414 to 420).
27
CHAPTER XIX
ELECTRICAL MEASUREMENTS
1. ELECTRICAL QUANTITIES AND UNITS
421. Fundamental Electrical Magnitudes. In every
electric circuit there are three fundamental quantities
which admit of measurement; viz. current strength, elec-
trical resistance, and difference of potential. The first of
these, current strength, may be likened to the rate at
which water is delivered through a pipe ; electrical resist-
ance, to the friction encountered by a liquid current ;
and difference of potential, to a difference of level (or
pressure) for any two chosen points between which the
current is flowing.
422. Current Strength the Ampere. In many of the
preceding experiments it has been obvious that the mag-
nitude of many of the effects produced depended on a
quantity that has been frequently referred to as the
"strength of the current." For some effects the current
must be strong, for others, weak. The expression refers
to the rate at which positive electricity is being discharged
from the positive to the negative pole through the circuit.
The unit of current strength is the ampere, so called in
honor of Ampere, 1 a French physicist. The ampere is that
current which will deposit in an electrolytic cell 0.001118
grams of silver or 0.0003287 grams of copper per second.
Of the currents used in the experiments described in the
preceding sections, the largest were required in 413 and
1 See portrait facing page 406.
402
ELECTRICAL MEASUREMENTS
403
amounted to 6 or 7 amperes. As a rule, the current used
in most classroom demonstrations is less than 1 ampere in
value. In the comparison and measurement of electric
currents, different kinds of galvanometers are used.
423. The Tangent and Astatic Galvanometers. The tan-
gent galvanometer is a common form found in most laboratories.
It consists of a circular coil of wire wound on a frame about 30 cm.
in diameter. See
(1), Fig. 341. The
ends of the coil
lead to binding
posts on the base.
At the center of
the coil is placed
a compass needle
below which is a
graduated circle.
When in use the
coil of the instru-
ment is placed
north and south and
the current sent through the coil. The instrument derives its name
from the fact that the current is proportional to the tangent of the angle
of deflection. If the current necessary to deflect the needle 45 is
known, other currents are easily measured.
For the measurement and detection of small currents the astatic gal-
vanometer (2), Fig. 341, is sometimes used.
Two similar magnets are attached to a ver-
tical rod so that their N-poles point in op-
posite directions. This system is then
suspended so that the lower needle swings
within a coil of wire, as shown in Fig. 342.
When a current is sent through the coil, all
parts of it tend to throw the needles out of
FIG. 342. The Arrange- the north-and-south positions. This form of
ment of the Magnets in galvanometer may be made extremely sen-
an Astatic Galvanometer. sitiye to gmaU currents>
424. The d'Arsonval Galvanometer. Galvanometers of the
d'Arsonval type differ from those described in 423 in that the
FIG. 341. (7) The Tangent Galvanometer;
(2) The Astatic Galvanometer.
404
A HIGH SCHOOL COURSE IN PHYSICS
magnet is stationary and the coil of wire movable. As shown in
Fig. 343, the instrument consists of a light coil of many turns of fine
wire, one end of which is the
supension wire AC, while
the other end extends below
the coil and connects at B.
When the instrument is
joined in an electric circuit,
the current is conducted
through the wire of the coil.
When no current is flowing,
the plane of the coil is held
by the suspending wire par-
allel to a line joining the
.two poles of a permanent
magnet N and S. Since a
current through the coil de-
velops a magnetic field of its
own at right angles to that of
the magnet, the coil will turn
until the magnetic forces are
in equilibrium with the torsional resistance of the suspension wire.
The deflections are read by the movement of a beam of light reflected
from a small mirror M attached to the coil. For small angles of de-
flection the current is practically proportional to the angle J hence the
instrument may be used in current measurements. The instrument
also affords a very sensitive detector of currents and is, on this account,
indispensable in a large class of experiments.
The principle involved in this galvanometer
is employed in many electrical measuring
instruments.
425. The Ammeter. An instrument
i for measuring the strength of an electric cur-
rent is called an ammeter, or amperemeter. In
most ammeters the magnetic effect of a cur-
rent is employed. The instrument may con-
sist simply of a magnetic needle, which shows
by the amount of its deflection the number
of amperes of current. The best instruments, however, consist of a
delicately pivoted coil of wire A, Fig. 344, turning between the poles
FIG. 343. The d' Arson val Galvanometer.
FIG.
344. Section of au
Ammeter.
ELECTRICAL MEASUREMENTS
405
of a strong permanent magnet N and S and held in position by two
hair springs a and &. The principle involved in this class of instru-
ments will be recognized at once as that of the d'Arsonval galvanom-
eter. When a current is
sent through the coil, the
magnetic field developed by
the current causes the coil
to turn, and the pointer p
moves over a scale which is
graduated to read in am-
peres. When the current
is interrupted, the coil is
restored to its initial posi-
tion by the springs which
also serve to conduct the
current into and out of the FlG - 345. An Ammeter,
coil. The complete instrument is shown in Fig. 345.
426. Electrical Resistance. It was observed in 350
that substances differ in respect to the readiness with
which they transmit an electrical charge ; thus bodies are
classed as good or poor conductors. The opposition that a
conductor offers tending to retard the transmission of elec-
tricity is called electrical resistance. Hence, with a given
source of electricity, as a Daniell cell, the current strength
will diminish as the resistance of the circuit is increased,
and will rise in value as the resistance is decreased.
427. Laws of Resistance. Construct a frame about 1 meter
long and upon it stretch 4 wires terminating in binding posts. Let
No. 1 consist of 1 meter of No. 30 (diameter 0.010 inch) German silver
wire ; No. 2, of 2 meters of No. 30 German silver wire ; No. 3, of 2 meters
of No. 28 (0.013 inch) ; and No. 4, about 20 meters of No. 30 copper
wire. Connect wire No. 1 in series with one or two Daniell cells and
a low resistance galvanometer, and read the deflection of the needle.
Replace No. 1 by No. 2, and the deflection will be found to be less
than before, thus indicating a greater resistance for the greater length.
When the current is sent through No. 3, which is a larger wire, an
increased deflection shows a decreased resistance. Finally, when the
current is sent through wire No. 4, the deflection will be even largei
406 A HIGH SCHOOL COURSE ^N PHYSICS
than for No. 2, which is of the same size and only one tenth as long.
Thus copper is shown to be more than 10 times as good a conductor
as German silver. The experiment may be extended to other wires
of various substances.
Accurate measurements verify the following laws :
1. The resistance of a conductor of uniform size and com-
position is directly proportional to its length.
2. The resistance of a conductor is inversely proportional
to its cross-sectional . area ; or, if circular inform, to the
square of its diameter.
3. The resistance of a conductor depends upon the nature
of the substance of which it is composed.
For example, if the resistance of a copper wire of a
certain diameter and length is 1 unit, the resistance of a
wire of the same kind and size and twice the length is
2 units. If, now, the diameter be doubled, the resistance
is divided by 2 2 , i.e. reduced to 2 units -s- 4, or | a unit.
428. The Unit of Resistance. The unit of resistance
is called the ohm in honor of Dr. G. S. Ohm, 1 a German
physicist. The ohm is the amount of electrical resistance
offered by a column of pure mercury 106.3 cm. in height,
of uniform cross section, and having a mass of 14.4521
grams, the temperature being 0<7. The cross-sectional area
of such a column is almost exactly one square millimeter.
Since such a column of mercury would be inconvenient to
handle, coils of wire whose resistances have been carefully
measured and recorded are used in practical measure-
ments. A piece of No. 22 (0.025 inch) copper wire 60
feet in length has approximately one ohm of resistance.
One meter of No. 30 German silver wire has a resistance
of about 6.35 ohms. A convenient unit for rough work
can easily be made by winding 9 feet and 5 inches of
1 See portrait facing page 406.
ANDRE MARIE AMPERE (1775-1836)
The fame of Ampere rests mainly on
the services he rendered to science in es-
tablishing the relation between electricity
and magnetism and in developing the sci-
ence of electro-dynamics. His chief experi-
ments deal with the magnetic action be-
tween conductors in which electric currents
are flowing. Ampere was also the first to
magnetize needles by inserting them in a
helix in which a current was flowing.
Ampere was born at Lyons, France.
During the French Revolution his father
was beheaded, an event which for years
clouded the spirit of the young scientist.
In 1805 he became professor of mathe-
matics in the Polytechnic School in Paris, and later professor of
physics in the College of France. In 1823 he published his mathe-
matical classic on the theory of magnetism. The practical unit of
current strength is named in his honor.
GEORGE SIMON OHM (1787-1854)
Following closely upon the experiments
of Ampere on the magnetic action between
currents came the researches of Ohm, a
German, whose discoveries concerned the
strength of an electric current.
Ohm's first experiments dealt with the
conductivity of wires of different metals.
He observed the deflections of a magnetic
needle by currents from a given source,
but flowing through different conductors.
By changes in the E. M. F. in the circuits
used, he obtained results which led him
pj
to the well-known expression C = .
R ~r v
He then investigated cells joined in paral-
lel and series, and published his results in 1826. During the following
year he published the theoretic deduction of the law bearing his name.
This law is one of the most fruitful of the early electrical discoveries.
Ohm was born in Erlangen, where he was educated. His ambi-
tion to become a university professor was not realized until 1849,
when he was elected to a professorship at Munich. The practical
unit of resistance is called the ohm in his honor.
ELECTRICAL MEASUREMENTS 407
No. 30 copper wire on a spool and connecting its ends to
binding posts.
429. Potential Difference the Volt. It was shown
in 393 that the difference of potential between the poles
of a voltaic cell when no current is flowing is its elec-
tromotive force. This quantity is conceived to be the
cause of current flow, and is analogous to the difference
in level between two bodies of water, to" the difference in
pressure of gases compressed in two reservoirs, or to a
difference of temperature in the case of heat. The unit
of potential difference and, consequently, of E. M. F., is
the volt. The volt is that difference of potential between the
ends of a wire having a resistance of one ohm which will
produce a current of one ampere. The E. M. F. of some
of the voltaic cells in ^common use is given in the follow-
ing table :
E.-M.F. OF CELLS
Daniell, 1.1 volts. Dry cells, 1.5 volts.
Leclanche, 1.5 volts. Dichromate, 2.0 volts.
A Daniell cell would then cause a current of 1.1 am-
peres through a wire having a resistance of 1 ohm, pro-
vided there were no other resistance in the circuit. It is
evident, however, that the resistance of the cell itself
must always be considered in any given circuit.
430. The Voltmeter. In order that an instrument may
measure the E. M. F. of a cell, it is necessary that no ap-
preciable current be permitted to flow. See the definition
of E. M. F., 393. In order, therefore, that a galvanom-
eter may be adapted to this use, it must contain a large
amount of resistance. Instruments of several hundred
ohms are made whose deflections are practically propor- \
tional to the E. M. F. of cells to which they may be
attached. When such instruments are graduated to read
volts they are called voltmeters. Figure 346 shows the
408
A HIGH SCHOOL COURSE IN PHYSICS
manner of connecting a voltmeter for determining the
E. M. F. of the cell J5, and Fig. 347 shows its connection
FIG. 346. Illustrating FIG. 347. The Voltmeter Shows the
a Use of the Volt- Fall of Potential through Coil C and
meter. the Ammeter Measures the Current
Strength.
for giving the potential difference between the terminals
of a coil of wire placed in the circuit. One well-known
form of a voltmeter is
shown in Fig. 348.
431. Ohm's Law. Connect
a Daniell cell in circuit with a
galvanometer or ammeter and a
resistance box. Make the resist-
ance of the circuit a suitable
amount (say 200 ohms, including
the galvanometer resistance) and
measure the current strength.
Replace the Daniell cell by a new
dry cell and again ascertain the current. The two currents will be
found proportional to the E. M. F. of the cells as stated in the table in
429. Again introduce the Daniell cell and make the resistance of
the entire circuit double the first amount. The current strength will
be only one half as great. Make the resistance one half as great as at
first, and the current will be doubled.
The experiment illustrates the law first published by
Dr. G. S. Ohm in 1827. This law states that the strength
of an electric current is directly proportional to the E. M. F.
FIG. 348. The Voltmeter.
ELECTRICAL MEASUREMENTS 409
furnished by the voltaic cell or combination of cells, and in-
versely proportional to the total resistance of the circuit.
The ampere, volt, and ohin are so chosen that Ohm's law
may be written
The law may be applied to any portion of an electric
circuit, in which case it becomes
current (amperes) = Potential difference (volts) ^
resistance (ohms)
For example, the current produced by a Daniell cell
(1.10 volts) in a circuit in which the total resistance
(including that of the cell) is 44 ohms is 1.1-5-44, or
0.025 ampere. It is clear from equation (l) that if any
two of the quantities are given, the third can easily be
computed.
432. Internal Resistance. The current that any cell
can produce is limited by the resistance which the current
encounters in passing through the liquid of the cell. This
is called the internal resistance of the circuit. In a fresh dry
cell the resistance is a fraction of an ohm, but with age and
use it increases to several ohms. That of a Daniell cell varies
from about one to three or four ohms. The resistance of cells
may be decreased by using larger plates and also by reducing
the distance between the plates. It is furthermore depend-
ent on the conductivity of the liquid. When more than
one cell is connected in a circuit, the entire internal resist-
ance depends on the manner in which they are joined
together.
410 A HIGH SCHOOL COURSE IN PHYSICS
433. Cells Connected in Series. Join each of three Daniell
cells successively to a voltmeter, or a galvanometer of high resistance
(not less than 50 ohms), and record the deflections produced. They
should be about equal. Now connect two
of the cells in series, as shown in Fig. 349,
and lead wires to the instrument. The de-
flection will be twice as great as for one cell,
and the addition of the third cell will make
the current three times as strong. The de-
flections under these conditions are propor-
FIG. 349. Two Cells tional to the number of cells, because their
Joined in Series. electromotive forces are added together when
they are joined in this manner.
Cells are in series when the positive pole of the first is
joined to the negative pole of the second, the positive pole of
the second to the negative pole of the third* and so on. A
study of the figure will aid greatly in making the method
clear. See also Fig. 311.
Although the electromotive forces are added by con-
necting cells in series, the resistances of the separate cells
also add together and thus tend to reduce the current
strength. For example, four similar cells in series will
have four times the internal resistance of one cell.
Since the strength of the current is obtained by divid-
ing the E. M. F. by the total resistance of a circuit,
C = i 2 . q 4 .
R + r x + r 2 + r 3 + r 4 + etc. '
where E v E^ E y E^ etc. are the electromotive forces of
the individual cells, r v r 2 , r 3 , r 4 , etc. are the correspond-
ing internal resistances and R is the external resistance of
the circuit. If we have, for example, five similar cells,
the equation becomes
, and for n cells, C = nE , (4)
R + nr
ELECTRICAL MEASUREMENTS 411
where E is the E. M. F. and r the resistance of a single
cell.
434. Cells Connected in Parallel. 1. With the apparatus
used in the experiment of the preceding section, record the deflec-
tion produced by each
cell alone and then con-
nect the positive poles of
two of them to one termi-
nal of the instrument and
the two negative poles to
the other terminal. The
deflection will be the same
as that obtained when
only one cell is used. If
all the cells are joined as
shown in Fig. 350, the de- FIG. 350. Four Cells Joined in Parallel,
flection of the instrument will not be greatly increased, if at all.
2. Join the cells while connected in parallel to an ammeter or
galvanometer of very small "resistance and record the reading. Do
the same with the cells connected in series and also with only one cell.
It will be found that one cell alone will produce about as much cur-
rent as all the cells when joined in series, but a much stronger current
will be derived from them when they are in parallel.
The experiments show that the parallel arrangement of
cells has an advantage over the series connection when the
external resistance is small. In fact, when the external
resistance is very small, as it is in some cases, the series
arrangement of cells produces practically no more current
than a single cell. 1 The following example will make ihe
matter clear.
The current obtained from a single cell whose E. M. F. is 1.5 volts
when the internal resistance is 3 ohms and the external resistance
0.2 ohm is, by equation (1), C = L5 , or 0.469 ampere.
0.2 + 3
1 When cells of extremely small internal resistance are used, as new
dry cells, the series arrangement is the better under nearly all circum-
stances. A poor cell, however, having a large resistance may prove to be
more of a hindrance than a help.
412 A HIGH SCHOOL COURSE IN PHYSICS
Now if ten such cells are connected in series, the current is, by
equation (4), C = 10 x 1>5 , or 0.496 ampere, which is only slightly
0.2 + 30
larger than the current obtained from one cell.
Experiment 1 shows that the E. M. F. remains un-
changed when cells are connected in parallel ; hence,
for the ten cells just considered, the E. M. F. is just the
same as that of one cell, viz. 1.5 volts. Again, since like
plates are joined together, the entire combination of cells
is like one cell having plates of ten times the area of those
of one cell. Therefore, by 427, the internal resistance is
only one tenth as much, i.e. 3 -r- 10, or 0.3 ohm. The equa-
tion for the parallel arrangement becomes C = - 1 -,
or 3 amperes, which is about six times as much as the
series arrangement would produce. Hence for n similar
cells joined in parallel, Ohm's law is
E.M.F. of one cell E
~~ . resistance of one cell 1 D . r
-K- 1 : ~ ~ K- ~\
number of cells n
EXERCISES
The pupil should represent each of the following cases diagram-
matically.
1. In the discussion of the two methods of combining cells, for
what kind of circuits is the series arrangement of cells shown to be
suitable ?
2. How much current will a dry cell of 2 ohms resistance and
1.43 volts send through a wire of 25 ohms resistance?
3. How much current would three cells similar to the one in
Exer. 1 send through the same wire (1) when joined in series and
(2) in parallel? Ans. (1) 0.13 ampere ; (2) 0.0557 ampere.
4. What current would 8 Dauiell cells of which the E. M. F. is
1.08 volts and the resistance 3 ohms each send through an ammeter of
0.4 ohm, when joined in series? What would be the current from
one cell alone ?
ELECTRICAL MEASUREMENTS 413
5. What would be the current produced from the same 8 cells
connected in parallel and using the same ammeter ?
6. Which is the better arrangement of 4 Daniell cells (E. M. F.
= 1.1 volts and r = 2.5 ohms each) when the external resistance is
6 ohms?
7. Show that a small Daniell cell will give practically as much
current as a large one through 1000 ohms of resistance, the resistance
of the small one being 30 ohms while that of the large one is 4 ohms.
8. If a galvanometer gives the same deflection when connected
with a very small cell as it does when connected with one several
times as large but having the same E. M. F., is the resistance of the
instrument large or small ?
9. A dry cell whose E. M. F. is 1.5 volts produces a current of
0.2 ampere through an instrument whose resistance is 7 ohms. Find
the resistance in the cell.
10. Which will produce the greater effect in an external circuit of
5 ohms, a dry cell whose resistance is 3 ohms or a copper-oxide cell
(E. M. F. = 0.8 volt) having a resistance of 0.2 ohm?
11. What current will be derived from a Daniell cell whose resist-
ance is 3 ohms and a dry cell with a resistance of 2 ohms when they
are joined in series and the external resistance is 2.74 ohms?
12. What would be the value of the current in the preceding
exercise if the poles of the Daniell cell were set in opposition to those
of the dry cell? Diagram the connections.
13. A circuit contains 4 dry cells (E.M. F. of each = 1.5 volts)
joined in series. Three of the cells are known to have a resistance
of 0.5 ohm each, and the external resistance is 10 ohms. If the
current is 0.15 ampere, what is the resistance offered by the fourth
cell ? Would the current be increased or decreased by removing this
cell from the circuit?
2. ELECTRICAL ENERGY AND POWER
435. Energy of an Electric Current. We have learned
under the study of the effects of electricity ( 411, 413,
414) that the energy of a current may be expended in
three ways: (1) it may produce mechanical motion, as in
the electric bell ; (2) it may produce chemical separation ;
and (3) it may be converted into heat in a conductor.
414 A HIGH SCHOOL COURSE IN PHYSICS
Let us imagine an electric circuit as shown in Fig. 351.
Between the points A and B is a resistance of 4 ohms.
If the battery produces a current of 5 amperes, for ex-
ample, the potential dif-
4 Ohms, 5 Amperes B
^AAAAAAAA/V-+-V ference between A and B
20 Volte \
will be, by Ohm's law
(-431), 4x5, or 20
volts -
FIG. 351. -Electrical Energy is Trans- Now the Work done, Or
formed into Heat between A and B. energy expended, by the
current between A and B depends on three factors,
(1) the potential difference, (2) the current strength, and
(3) the time, and it is measured by their product.
Therefore we have the relation
energy = potential difference x current strength x time.
If the time is in seconds, the potential difference in
volts, and the current strength in amperes, this product
gives the energy in terms of a unit called the joule,
which is equal to 10,000,000 ergs. Hence
volts x amperes x seconds = joules. (6)
In the electric circuit shown in Fig. 351 the amount of
energy expended in 5 minutes (300 seconds) between the
points A and B is, then, by equation (6), 20 x 5 x 300, or
30,000 joules.
436. Power of an Electric Current. Since power refers
to the rate at which work is done or energy expended
( 57), it may be found by simply dividing the total
energy expended by the time. In an electric circuit,
therefore, the power is measured by the product of the
potential difference and the current strength ; or,
power = volts x amperes. (?)
It is plain that power is the number of joules per second
expended by the current. A power of one joule per
ELECTRICAL MEASUREMENTS 415
second is called a watt, in honor of James Watt (1736-
1819) of Scotland. One horse power is equal to 746 watts.
In the example chosen in 435, the power of the current
in the circuit between A and B is 20 x 5, or 100 watts ;
i.e. if the energy of the current which is expended be-
tween the points A and B could be converted into mechani-
cal energy, there would be developed ^J horse power.
437. Quantity of Heat Developed by a Current. When
no mechanical or chemical work is done by a current of
electricity, the energy is used simply in overcoming the
resistance of the conductor and is converted into heat.
Now one heat unit (a calorie) has been found by experi-
ment to be equivalent to 4.2 joules; or, one joule equals
- , or 0.24 calorie.
If we express the potential difference between two points
of a circuit by E and the current strength by (7, the num-
ber of joules expended in t seconds is, by equation (6),
EOt joules. But by Ohm's law ( 431), O= ^; whence
.K
E = OR. Now if we substitute this value of E, we obtain
for the energy expended C 2 Rt, which represents the amount
of electrical energy that is converted into heat in a resist-
ance of R ohms when the current is O amperes and the
time t seconds. Reducing joules to calories gives
Heat = 0.24 C 2 Rt calories. (8)
This equation represents Joule's law, which may be
stated as follows:
The heat developed in a conductor by an electric current is
proportional to the square of the current, to the resistance of
the conductor, and to the time the current is flowing.
438. Loss of Energy in Transmitting Electricity. The
conversion of electrical energy into heat in a conductor
416 A HIGH SCHOOL COURSE IN PHYSICS
through which it flows has an important commercial bear-
ing on the transmission of electric power over long lines.
For example, if the resistance of the wires leading from a
distant source of electrical power to a group of lamps is
only 2 ohms, the waste of power in transmitting a current
of 10 amperes is 10 2 x 2, or 200 watts. Now 10 amperes
at 110 volts would operate 20 lamps, each of which con-
sumes 55 watts. The total power required would be,
therefore, 20 x 55 + 200, or 1300 watts. The loss in
transmission is therefore -fy of the total power produced.
Now if the number of lamps is increased to 100, the lamp
consumption is 5500 watts, while the line loss (since the
current is now 50 amperes) is 50 2 x 2, or 5000 watts.
Hence, of the 10,500 watts which must be produced at the
power station, 5000 watts, or 47.6 per cent, are lost by
being converted into heat in the line.
The loss of energy in long lines of wire can be reduced
by constructing the line of larger wire and thus decreasing
the resistance factor, but in many cases this method is im-
practicable from a commercial standpoint. However, by
using modern devices involving principles that we shall
study later, economical transmission of power over long
distances is rendered possible.
EXERCISES
1. Compute the number of joules transmitted by a current of 10
amperes maintained for 20 minutes at a potential difference of 110
volts.
2. Compute the heat loss per hour in an electric line of 3 ohms
resistance when the current is 5 amperes. What is the result if the
current is 10 amperes ?
3. If the power required for an incandescent lamp is 60 watts, what
is the consumption of 50 lamps measured in terms of the horse power?
4. A piece of platinum wire is heated by a current of 2 amperes,
and the potential difference between its ends is 8 volts. Compute the
heat developed per minute.
ELECTRICAL MEASUREMENTS 417
3. COMPUTATION AND MEASUREMENT OF RESISTANCES
439. Resistances Computed. It is customary to com-
pute the resistance of a wire of given material, length,
and size from the known resistance of a wire of that kind
which is 1 foot in length and 0.001 inch (called 1 mil)
in diameter. The following table gives this value in
ohms for some of the common metals.
OHMS OF RESISTANCE IN WIRES 1 FOOT LONG AND 0.001 INCH IN
DIAMETER
Silver 9.5 Platinum 80
Copper 10.2 German silver .... 180
Iron 61.5 Mercury 570
According to the laws of resistance stated in 427, the
resistance of a wire can be calculated by simply multiplying
the number given in the table by the length of the wire in feet
and dividing by the square of the diameter, which must first
be reduced to thousandths of an inch. For example, the
resistance of a mile of iron wire 0.08 inch in diameter is
61.5 ohms x 5280 -5- 80 2 , or 50.7 ohms.
EXERCISES
1. What is the resistance of each of the wires given in the follow-
ing table?
KIND OF WIRE NUMBER DIAMETER LENGTH
Copper 8 0.128 inch 1 mile
Copper 22 0.025 inch 500 feet
Copper 36 0.005 inch 40 feet
Copper 40 0.003 inch 25 feet
Iron 9 0.114 inch 1 mile
Iron 14 0.064 inch 25 feet
Iron 10 0.102 inch 5000 feet
German silver 20 0.032 inch 35 feet
German silver 30 0.010 inch 10 meters
Platinum . . .... 24 0.020 inch 2 feet
"28
418 A HIGH SCHOOL COURSE IN PHYSICS
2. How long must a No. 36 copper wire be to offer a resistance of
one ohm ?
3. Find the diameter of a copper wire that has a resistance of 10
ohms per thousand feet.
4. A No. 22 wire 1000 ft. long offers a resistance of 285 ohms.
Of what material mentioned in 439 might the wire be made ?
440. Resistance Boxes. Coils of wire whose resistances
have been carefully adjusted and
marked are incased in boxes and
sold by electrical supply houses.
Such a box is shown in Fig. 352.
The ends of each coil are sol-
dered to brass blocks A, B, C,
FIG. 352. A Resistance BOX. 'etc., Fig. 353, between which
brass plugs may be inserted. The blocks are mounted on
an ebonite or hardwood plate which forms the cover of
the box. When the plugs are all in place,
no resistance is encountered by an electric
current in passing from one block to the
next ; but when a plug is withdrawn, the
current must pass through the correspond- FIG. 353. Showing
ing coil whose resistance is marked on
the top of the box. Thus, by removing
plugs, any resistance from the smallest up to the sum of
all the resistances in the box can be obtained.
441. Resistance Measured by Substitution. Place a coil
of wire whose resistance is to be determined in circuit with a Daniell
cell and a galvanometer and read the deflection produced by the current.
Remove the coil from the circuit and insert a resistance box. With-
draw plugs from the box until the deflection of the galvanometer is
the same as before. The sum of the resistances corresponding to the
plugs that have been removed gives the resistance of the coil. Why ?
442. Resistances Measured by Voltmeter and Ammeter.
The coil of wire C, Fig. 347, whose resistance is to be found, is placed
in a circuit with the cell B and an ammeter. A voltmeter of high
ELECTRICAL MEASUREMENTS 419
resistance is joined to the terminals of the coil C to indicate the
potential difference at those points. Since by Ohm's law ( 431)
the current through C equals
the potential difference in volts
divided by the resistance in
ohms (Eq. 2, 431), the value
of C can be found by dividing
the reading of the voltmeter
by that of the ammeter. It is
essential that the resistance of
the voltmeter be so large that
practically none of the current FIG. 354. Diagram of Wheatstone's
can pass through it. Bridge.
443. The Wheatstone Bridge. When the current from a cell
J3, Fig. 354, passes through the point A, it divides into two parts, the
portion C flowing through the resistance R ohms, and the portion C'
through the resistance R' ohms in the straight uniform wire. AD.
Now a sensitive galvanometer G joining points E and F will be
deflected unless E and F do not differ in potential. The point F which
has the same potential as E is found by moving the contact along
the wire AD until no deflection can be observed.
Under these conditions the difference of potential between A and
E must equal that between A and F. By Ohm's law ( 431),
fall of potential -4- resistance = current.
Hence fall of potential = current x resistance',
whence CR = C'R'. (l)
Again, the same current flows through X as through R, since the
galvanometer is not deflected ; and the same current flows through
R" as though R' for the same reason. Now, since the difference of
potential between E and D is the same as that between F and D, we
have CX = C'R". (2)
Dividing (2) by (1) we have
Now the resistances R' and R" are proportional to the lengths of
the wire AF and FD ( 427). Therefore,
X = R. (3)
420 A HIGH SCHOOL COURSH IN PHYSICS
Four resistances combined in this manner constitute Wheatstone's
Bridge. It is obvious that if the resistance R and the lengths of the
wire AF and FD are known, the value of the unknown resistance X
can be calculated. The point F must be found experimentally as
described above.
444. Conductors in Series and Parallel. Conductors
are said to be joined in series when they are connected in
>> i succession as shown in
-""W^^-*-^^ Fig. 355. In this con-
FIG. 355. -Conductors Joined in Series. dition the entire current
passes through each conductor. The combined resistance
between A and B is the sum of the resistances of the sev-
eral parts.
The case is very different when the conductors are
joined as shown in Fig. 356. Resistances combined in
this manner are said to
be connected in parallel.
The most important com-
bination of this kind is
that of two wires thus con-
nected. The current from
the cell O will obviously
divide into tWO parts at FIG. 356. -Conductors Joined
point A which reunite at in Parallel.
B. When the two resistances are equal, the two parts of
the current are, of course, equal. But if the resistances
are, for example, 3 and 7 ohms respectively, and the poten-
tial difference between A and B common to both branches
is 1 volt, the current through the upper branch is J am-
pere and that through the lower one ^ ampere. Hence,
while the resistances are as 3 is to 7, the currents are as 7
is to 3. The currents from the cell, therefore, in a two-
branched circuit are inversely proportional to the correspond-
ing resistances.
ELECTRICAL MEASUREMENTS 421
Again, the total current flowing between A and B
is ^ + ijr ampere. If, now, we let R be the combined
resistance between A and B, the total current is ampere.
R
Therefore issl+i, (4) ^
3x7 V
whence R = -, or 2.1 ohms. It is clear from the
3 + 7
example chosen, that the combined resistance offered by the
two branches of a divided electric circuit is the product of
the two resistances divided by their sum; or, expressed as
an equation, R = ?12<l2. (5)
445. Shunts. A shunt is a conductor which is con-
nected in an electric circuit parallel to another conductor.
It may be likened to a side-track, or to a by-pass that is
frequently used in the case of
the conduction of water or gas
through pipes. The term is
applied to a resistance coil $,
Fig. 357, which is joined in a
circuit parallel to a galvanom-
eter Gr or some other instru-
C\ '
ment. In this case it is used FlG 357. -illustrating the Use of
to reduce the flow of electricity a Shunt,
through the instrument; for, as shown in 444, the cur-
rent divides into parts that are inversely as the two resist-
ances. Suppose, for example, the resistance of Q- is 45
ohms and that of S is 5 ohms. Then ^ of the entire cur-
rent passes through the galvanometer .and jj- of it through
the shunt. Thus it is clear that when a shunt contains ^ as
much resistance as a galvanometer, yL- of the total current
passes through the galvanometer, and ^ through the
422 A HIGH SCHOOL COURSE IN PHYSICS
shunt. In the same manner the division of a current in
any given case may be computed.
EXERCISES
The pupil should diagram the conditions expressed in each of the
following exercises.
1. A current of 4 amperes divides and passes through two parallel
coils of wire, one of 5 ohms and the other of 8 ohms. What is the
current that goes through each branch?
Ans. 2.461 amperes and 1.539 amperes.
2. Find the combined resistance offered by the two parallel con-
ductors in Exer. 1.
3. Two instruments of 3 and 4 ohrns respectively are connected
parallel between the poles of a dry cell (E.M. F. 1.5 volts) whose re-
sistance is 1 ohm. Find (1) the external resistance of the circuit,
(2) the current strength of the cell, and (3) the current flowing
through each branch.
Ans. (1) 1.714 ohms; (2) 0.553 ampere; (3) 0.316 ampere,
0.237 ampere.
4. Two electro-magnets of 4 and 12 ohms respectively are connected
in parallel to each other and then placed in a circuit containing a
coil of 3 ohms and a battery of 10 ohms. Find (1) the total resist-
ance of the circuit, and (2) the strength of the current in each part
of the circuit, the E. M. F. being 4.8 volts.
Ans. (1) 16 ohms; (2) 0.225 ampere and 0.075 ampere.
5. A galvanometer of 30 ohms has a shunt of 30 ohms. When
connected in an electric circuit, what part of the whole current will
pass through the instrument? By what number must the cur-
rent measured by the galvanometer be multiplied to give the entire
current ?
6. If the resistance of the shunt in Exer. 5 is reduced to 20 ohms,
what part of the total current will the galvanometer carry, and what
will be the multiplier? Ans. The multiplier will be 2.5.
7. If a galvanometer has 300 ohms of resistance, what must be the
resistance of a shunt so that only one tenth of the entire current will
pass through the wire of the instrument? Ans. 33 ohms.
SUMMARY
1. The unit of current strength is the ampere. It is
the current that will deposit 0.001118 g. of silver per
ELECTRICAL MEASUREMENTS 423
second. Current strength is measured by an ammeter
( 422).
2. The electrical resistance of cylindrical wires of
uniform size and composition is directly proportional to
the length and inversely proportional to the square of the
diameter. It also varies with the nature of the substance
of which it is composed. The unit of resistance is the
ohm ( 427 and 428).
3. The unit of potential difference is the volt. It is
the potential difference required to force a current of an
ampere through a resistance of one ohm. Potential dif-
ferences are measured by the voltmeter ( 429 and 430).
4. Current, potential difference, and resistance are re-
F
lated mathematically as shown by the equation C= , or
R
amperes = volts -^ ohms. - This relation is known as Ohm's
Law ( 431).
5. The resistance of circuits includes internal and
external resistances ; the former is the resistance offered
by the cells, the latter, that of the remaining portion of
the circuit ( 432).
6. For n similar cells joined in series the current is
0= nE ( 433).
R + nr ^
7. For n similar cells joined in parallel the current is
0= ( 484).
8. The energy expended in any part of a circuit is the
product of the potential difference, current strength, and
time, or
energy = ECt joules ( 435).
424 A HIGH SCHOOL COURSE IN PHYSICS
9. The power, or rate at which the current is working,
is power = EC watts ( 436).
10. The quantity of heat developed by a current of
O amperes in a resistance R ohms in t seconds is
heat= 0.24 C*Rt calories ( 437).
11. The resistance of a cylindrical wire may be com-
puted by multiplying the resistance of one foot of it one
mil in diameter by the whole length and dividing by the
square of the diameter in mils ( 439).
12. The combined resistance of conductors joined in
series is their sum. The combined resistance of two con-
ductors joined in parallel is
CHAPTER XX
ELECTRO-MAGNETIC INDUCTION
1. INDUCED CURRENTS OF ELECTRICITY
446. Currents Induced by Magnetism. Oersted's dis-
covery of the effect of a current of electricity upon a mag-
netic needle ( 400) in 1819 led to the invention of the
electro-magnet by Sturgeon in 1825, and induced many
experimenters to seek for a method of producing an elec-
tric current by means of a magnet. Two physicists,
Joseph Henry 1 in America and Michael Faraday 1 in Eng-
land, independently discovered the process for doing this
about 1831.
Connect the ends of a coil of insulated wire C, Fig. 358, consisting
of a large number of turns, directly to the termi-
nals of a sensitive d'Arsonval galvanometer. Ar-
range a large horseshoe magnet with its poles
upward as shown. Now move the coil down quickly
into the magnetic field. The galvanometer will re-
veal the presence of a current of electricity, but the
index will go back to zero as soon as the coil stops mov-
ing. If the coil be now removed from the magnetic
field, the galvanometer will show that a current is
produced in the opposite direction. Repeat the ex-
periment, but move the coil more slowly. Turn the
coil over and repeat the experiment. Each deflec-
tion will be in a direction opposite to the corres-
ponding one produced at first. FIG. 358. Induc-
ing an Electric
The experiment shows clearly the produc- Current.
tion of an electric current without the aid of a voltaic cell.
1 See portraits facing page 426. See also Maxwell, facing page 432.
425
426 A HIGH SCHOOL COURSE IN PHYSICS
Such a current is called an induced current. The experi-
ment shows also that the induced current flows only while
the coil is moving in the magnetic field, i.e. only while the
number of lines of force through the coil is changing.
Since a current is always due to an E. M. F., it is obvious
that the movement of a coil of wire in the magnetic field
develops such an electromotive force in the wire. This
is called an induced electromotive force. Furthermore; the
slower the movements, the less rapid the change, and the
smaller the induced E. M. F. The following general laws
may be stated :
1. A change in the number of magnetic lines of force
threading through a coil (or a single loop) of wire induces
an electromotive force in that coil.
2. The induced electromotive force is proportional to the
rate at which the number of lines of force is changed.
447. Special Cases of Current Induction. According to
the laws of induction given in the preceding section, an
induced electromotive force may be brought about either
by an increase or by a decrease in the number of magnetic
lines through a coil of wire. This effect may be produced
in several different ways, as the following experiments
will show.
1. Connect the ends of a coil of wire with a sensitive galvanometer
and thrust the N-pole of a magnet into the coil. A deflection will be
produced. On pulling the same pole out of the coil, a deflection in
the opposite direction results. Turn the coil over and repeat the
operations. Every effect is just the reverse of the corresponding one
produced at first. The experiment should be repeated, using the S-
pole in the same manner.
2. Connect a coil of wire, Fig. 359, to the poles of a voltaic cell
and thrust this coil into the coil used in Experiment 1. In every
operation similar to those performed above, the effect is the same as
that produced by using a magnet. Repeat with a soft iron core within
the smaller coil.
MICHAEL FARADAY (1791-1867)
Faraday was one of the most distin-
guished chemists and physicists of the
nineteenth century. He was the son of
a blacksmith at Newington, near London,
England, and became a bookbinder in 1804.
Hearing by chance some lectures on chem-
istry by Sir Humphry Davy of the Royal
Institution, he became interested in the
subject, and in 1813 was appointed assist-
ant in Davy's laboratory. In 1825 he be-
came director of this laboratory, and in
1833 was made professor of chemistry in
the Royal Institution for life. He died at
Hampton Court in 1867.
Faraday's achievements in the domain
of chemistry are largely overshadowed by his numerous and brilliant
discoveries in electricity, of which the most far-reaching was that
of the induction of electric currents by magnets, made in 1831. This
subject has led to results of tremendous value in the commercial
applications of electricity.
His further discoveries d_cal with the capacity of condensers, the
laws of electrolysis, the rotation of the plane of polarized light by
a magnetic field, and diamagnetism.
Faraday was a prolific writer and a popular lecturer on scien-
tific subjects. He is best known by his Experimental Researches
in Chemistry and Physics.
JOSEPH HENRY (1797-1878)
After the time of Franklin, Henry was
the first in the United States to make orig-
inal researches in the subject of electricity.
After the invention of a practical electro-
magnet by Sturgeon in 1825, Henry devel-
oped a magnet, in the construction of which
he employed many turns of copper wire in-
sulated with silk. The magnet was capable
of supporting over fifty times its own weight.
It is believed on good evidence by many
physicists that the discovery of electro-
magnetic induction was made by Henry at
Albany, N T ew York, in 1830, although he did
not publish his results until 1832, a year later
than the publication of Faraday's results.
ELECTRO-MAGNETIC INDUCTION
427
3. Open the battery circuit used in Experiment 2, insert a key, and
place one coil within the other. Complete the battery circuit by press-
ing the key. A deflection
of the galvanometer will
indicate the presence of an
induced current which at
once dies away. Open the
key, and an induced cur-
rent in the opposite direc- Q
tion will be obtained.
4. If the galvanometer
is sufficiently sensitive, aim- FlG " m - Inducin S a Current ^ a Cl nt.
ply turning the coil with which it is connected in the earth's magnetic
field will suffice to produce an appreciable current.
It is to be observed that in each of the cases chosen in
the experiments, a change in the number of magnetic lines
through the coil is brought about in the process. In Ex-
periment 1, the magnet- carries its lines of force with it
when it is thrust into the coil ; in Experiment 2, the mag-
netic lines of force set up by the battery current in one
coil are carried through the second coil when the former
is thrust into the latter ; in Experiment 3, the change in
the number of lines is produced by alternately making
and breaking the circuit which contains the battery. In
every case the induced current
is set up by magnetic action, i.e.
' ni either by an increase or a decrease
in the number of magnetic lines
through the coil connected with
the galvanometer.
Induced
448. Direction of the Induced
Current. Lenz's Law. Connect
a small piece of zinc with one terminal
of a sensitive galvanometer and a piece
FIG. 360. Showing the Direc- of c PP er with the other. Hold the two
tion of the Induced Current, metals in the fingers and observe the
428 A HIGH SCHOOL COURSE IN PHYSIC'S
deflection of the galvanometer. The moisture of the hand is sufficient
to establish a current from the copper to the zinc through the instru-
ment. Now repeat the experiment of 446, and from the direction
in which the galvanometer is deflected, determine the direction of the
induced current in the wire.
While the coil is moving into the magnetic field placed
as shown in Fig. 360, the current in the wire will be
found to have the direction shown by the arrows. Thus
the induced current tends to set up a magnetic field of its
own whose lines of force are opposite in direction to those
of the magnet. This fact is easily verified by applying the
rule given in 408. See Fig.
361 Hence, increasing the mag-
netic lines through the coil produces a
current which tends to oppose that in-
crease. On the other hand, moving
the coil away from the magnet in-
duces in the coil a current in the
direction opposite to the former cur-
FIG. 361. Applying rent. Hence, a decrease in the num-
Lenz's Law. 7 /. 7 . , 7 7 , 7 . 7
per of lines through the coil sets up a
current that tends to prevent that decrease in number. In
fact, every case of current induction may be shown to obey
the following law:
The direction of an induced current is such as to produce
a magnetic field that will tend to prevent a change in the
number of magnetic lines of force through the coil.
This is known as Lenz's Law and may be viewed as an
application of the more general law of the Conservation of
Energy ( 64). From this law we know that neither elec-
trical nor any other form of energy can be derived unless
an equivalent amount of work be performed. In this
case the work is done when the coil is forced into the
ELECTRO-MAGNETIC INDUCTION
429
FIG. 362. Diagram Showing the Parts of
an Induction Coil.
magnetic field in opposition to the repulsion between the
field of the magnet and that of the induced current.
449. The Induction Coil. One of the most important
applications of the principles of electro-magnetic induction
is found in the induction
coil. The instrument
consists of a so-called
primary coil of coarse
wire J., Fig. 362, wound
on a core of soft iron, a
secondary coil of several
thousand turns of very
fine insulated wire S,
and a current interrupter
I. The terminals of the
secondary coil are at p
and q.
When the current from a battery B flows through the
primary coil, it magnetizes the iron core. The iron ham-
mer a is then drawn toward the core and away from the
screw b. This operation breaks the primary circuit at the
screw point d. The interruption of the current at d causes
the core to lose its magnetism and release the hammer a,
which is restored to its original position by the spring to
which it is attached. The contact at d is thus made again,
and all the operations are repeated. It is clear that most
of the lines of force set up by the battery current in the
primary coil pass through each turn of the secondary.
Hence, when the current is interrupted and the lines of
force decrease, an E. M.F. is induced in the secondary coil.
Even with small coils, the potential difference between p
and q is often sufficient to cause a spark to pass across a
short gap from one to the other. Again, when the primary
circuit is made at d, the resulting increase in the number
430 A HIGH SCHOOL COURSE IN PHYSICS
of lines of force induces a contrary E. M. F. in the second-
ary, but this is of a much smaller intensity than the former
induced E. M. F. Lenz's law applied to the induction
coil shows the following statements to hold true :
1. When a current is started in the primary coil, a momen-
tary current is induced in the secondary in the opposite
direction.
2. When the current in the primary coil is interrupted, a
momentary current is induced in the secondary in the same
direction as that in the primary.
The condenser is introduced as an accessory part of the
induction coil in order to increase the rate of demagnetiza-
tion of the iron core. By its aid a very quick interruption
of the current in the
primary coil is ac-
complished, and
consequently the in-
duced E. M. F. is
proportionately in-
FIG. 363. An Induction Coil. , r
creased. The use
of an extremely large number of turns of wire in the
secondary coil makes it possible to secure a sufficiently
large potential difference between p and q to produce
sparks many inches in length. The actual form of the in-
strument is shown in Fig. 363.
If metallic handles that can be grasped with the hands are joined
to the terminals of the secondary coil, it will be found that the
shock experienced when the primary circuit is made is much lighter
than at the break. When the primary circuit is made, the current
requires a large fraction of a second to attain its maximum value ;
consequently the rate of change of the lines of force is comparatively
small. At the break of the primary, however, the current falls to zero
very suddenly, thus producing a high rate of decrease in the lines of
force. For this reason ( 446) the E. M. F. is correspondingly greater
ELECTRO-MAGNETIC INDUCTION
431
at the interruption of the primary than at the making of the
circuit.
The induction coil is widely used in many operations. It is used
in gasoline engines to ignite the mixture of air and vapor (271),
for igniting explosives in blasting, and in chemical laboratories for
many experimental purposes. Small induction coils are used in medi-
cine for the remedial effect of the electric current and in the speaking
part (transmitter circuit) of the modern telephone. Coils of large
dimensions are employed in sending messages by wireless telegraphy
and in the production of X-rays.
450. An Induced E.M.F. in a Moving Conductor. By
referring to Fig. 360 it becomes clear that in order to
change the number of lines of force threading through the
coil of wire, the conductor has to cut through, or across,
some of these lines. The following experiment will show
the effect of this operation in another way.
Hang a loose copper wire across the classroom and connect its ends
with a sensitive galvanometer. m If the wire be set swinging, the galva-
nometer will be deflected first to the right and then to the left as the
conductor cuts through the earth's lines of force. Connect one of the
galvanometer wires to the center of the swinging conductor and repeat
the experiment. The induced E. M. F. will be about one half as great
as before, as shown by the reduced deflection of the galvanometer.
The experiment shows that when a conductor cuts across
magnetic lines offeree, an E.M.F. is induced within it.
If, for example, the con-
ductor ab, Fig. 364,
move from right to left,
and the galvanometer be
used to determine the
direction of the E.M. F.,
it will be found that the
E. M. F. acts through
the conductor from a
towards b: i.e. b will
., ... . FIG. 364. A Conductor ab Cutting Mag-
act temporarily like the netic Liues of Force. \
432 A HIGH SCHOOL COURSE IN PHYSICS
positive pole of a cell, and a like the negative pole. While
the wire is swinging in the opposite direction, the lines
of force are cut from the opposite side, and the induced
E. M. F. is reversed. In the second part of the experi-
ment the lines of force are cut only one half as fast, and
the reduced deflection shows that the value of the E. M. F.
varies with the rate at which the lines of force are cut by
the moving conductor.
It is clear that the direction of the induced E. M.F. (or
current) depends (1) on the direction of the lines of force
and (2) on the direction of the motion of the conductor.
The three quantities, viz. Motion, Force, and Current, have
a definite relation which has given rise to the following
rule:
Let the thumb and the first two fingers of the right hand be
bent at right angles to each other, as
in Fig. 365. If, now, the thumb
point in the direction of the Motion
of the wire, and the First finger
point in the direction of the lines of
force in the Field, then the Center
finger indicates the direction of the
FIG. 365. Finding the Di- p * r _ f
rection of an Induced Cur- ^ urreni; -
The key to the rule is found in
the corresponding initial letters in the words First and
Field, Center and Current.
2. DYNAMO-ELECTRIC MACHINERY
451. Principle of the Dynamo. The laws of induced
currents find their most important application in the
dynamo, a machine which facilitates the conversion of
mechanical energy into electrical. The familiar examples
of electric street lighting and the operation of city and
JAMES CLERK-MAXWELL (1831-1879)
Maxwell ranks as one of the greatest of mathematical physicists
on account of the important practical results to which his theories
have led. He was born in Edinburgh, Scotland, where he received
his early education. In 1856 he became professor of physics in
Marischal College at Aberdeen, in 1860 professor of physics and
astronomy in King's College of London, and in 1871 first pro-
fessor of physics in Cambridge University.
Maxwell built upon the experimental discoveries of Faraday, so
arranging and relating them as to make them yield to mathematical
treatment. He advocated the view that electric and magnetic forces
result from certain changes in the distribution of energy in the
ether. He showed that electro-magnetic action must travel through
space in the form of transverse waves and with the velocity of light.
Later on this theory was corroborated by the experiments of Hertz,
who was first to produce such waves and show that they could be
reflected, refracted, and polarized like light. By these two physicists,
the one attacking problems from the mathematical standpoint, the
other building his experiments upon the theoretical results obtained,
the intimate relation between light and electricity has been amply
confirmed.
Among other subjects investigated by Maxwell was the kinetic
theory of gases. The results were published with others in a
memorial edition of two volumes by the Cambridge Press.
Maxwell's works also include his Theory of Heat (1871), Elec-
tricity and Magnetism (1873), and a clear and concise treatise of
dynamics entitled Matter and Motion (1876).
OF THE
UNIVERSITY
OF
ELECTRO-MAGNETIC INDUCTION
433
FIG. 366. Illustrating the
Dynamo Principle.
interurban railroads have been brought about by the devel-
opment of the dynamo.
Make a rectangular coil of 200 or 300 turns of very small copper
wire of such dimensions as to rotate between the poles of a horse-
shoe magnet. Connect the ends with a
d'Arsonval galvanometer and place the coil
in the magnetic field as shown in Fig. 366.
Starting with the plane of the coil at right
angles to the lines of force, i.e. vertical, ro-
tate it through 90. A deflection will show
the presence of an induced current. Con-
tinue the rotation through the next 90. A
deflection in the same direction will be ob-
served. If, now, the rotation be continued,
a deflection in the opposite direction will
be produced until the coil has returned to
its initial position.
When the coil is revolved from
the position shown in Fig. 367, the two portions a and b
begin to cut the lines of force of the magnet and thus de-
crease the number of lines passing through
the coil. A current is therefore set up
by the induced E. M. F., which, accord-
ing to the rule given in the preceding
section, is upward in a and downward in
b. For the first 180 of rotation, the por-
tion a of the coil continues to cut the
FIG. 367. Loops of li ne s of force in the same direction ; and
Wire Perpendicu- .
lar to Lines of the same is true of portion 6; hence the
Force - induced current thus far is continuous
and in one direction. When, however, the coil begins to
revolve through the second 180, each part of it begins
to cut magnetic lines in the opposite direction; hence the
induced current will accordingly flow through the wire in
the opposite direction. It is now obvious that a continuous
rotation of the coil develops a current whose direction reverses
29
434 A HIGH SCHOOL COURSE IN PHYSICS
every time the plane of the coil is perpendicular to the lines
.of force. Such a current is called an alternating current.
452. The Alternating-current Dynamo. Alternating-
current dynamos, or alternators, are based upon the prin-
x ciples of induction as shown by
the experiment in the preceding
section. In its simplest form,
the machine consists of a coil of
several turns of wire arranged
to rotate between the poles of a
strong electro-magnet, as shown
in Fig. 368. The wire is wound
FIG. 368. Diagram of a Simple O n a core of soft iron C and
Alternating-current Dynamo. , , , , ~ . ~,
mounted on a shaft A. The re-
volving coil is called the armature, and the electro-magnet
whose poles are N and S is called the field magnet.
In order to provide for the flow of the induced current to'
and from the rotating coil, the ends of the wire of the ar-
mature are connected with the two insulated metal collect-
ing rings a and a'. Stationary " brushes," b, 5, rest against
these rings as shown and conduct the induced current to
the external circuit X. The efficiency of the machine is
greatly increased by the presence of the iron core 0, since
it multiplies and concentrates the number of magnetic
lines of force between the poles -ZV and S.
When the armature is rotated, an induced alternating
current is set up in the coil, and through the rings and
brushes is transmitted to the external circuit. The E.
M. F. will be determined by the number of lines of force
cut per second. This will of course be greatest when the
coils are moving at right angles to the magnetic lines, i.e.
when the plane of the coils is horizontal. The E. M. F.
is zero at the instant of reversal, for at that time all por-
tions of the coil are moving parallel to the lines of force.
ELECTRO-MAGNETIC INDUCTION
435
Hence, the E. M. F. rises from zero to a maximum value
and then decreases to zero again, at which time it reverses.
Such a current is shown
diagrammatically by the
curve in Fig. 369.
FIG. 369. Diagram of an Alternating
Current.
FIG. 370. Diagram of a Multipolar
Machine.
453. Multipolar Ma-
chines. Alternators are
of great commercial value in generating electricity for both
lighting and power. They have largely replaced the so-
called direct-current dy-
namos which have had a
world- wide use. But for
practical purposes it is
desirable that the rever-
sals of an alternating
current attain, or even
exceed, 120 per second.
This, of course, cannot be
accomplished with the
two-pole machine described in the preceding section. In
the multipolar machine there are several poles arranged
around the armature as shown in Fig. 370. In this ma-
chine there are as many coils of wire in the armature as
there are poles in the field magnets.
As the moving coils cut through the lines of force, an
induced E. M. F. is set up in each. The several coils are
so connected that the E. M. F. at the brushes is the sum
of that produced in the separate coils. The field magnets
are excited by means of a continuous direct current from
a small dynamo ( 454). Figure 371 shows a type of
multipolar alternator which is in common use.
454. The Direct-current Dynamo. The alternating-cur-
rent dynamo described in 452 may be employed to pro-
duce a unidirectional current by the introduction of a
436 A HIGH SCHOOL COURSE IN PHYSICS
so-called commutator. The commutator in this case con-
sists of a metal ring divided into two semicircular parts
FIG. 371. A Multipolar Alternator.
a and a! , Fig. 372, called segments. These are insulated
from each other and mounted on the shaft which car-
ries the armature. Each of the two ends of the arma-
ture coil connects with a seg-
ment of the commutator as
shown in the figure. The
brushes b and b f which conduct
the induced current to and from
the external circuit X are set on
opposite sides of the commuta-
FIG. 372. Diagram of a Direct- tor. Their position is very im-
portant. They must be so placed
that each brush changes its point of contact from one segment
to the other at the instant the current reverses in the armature
coil. Thus 5, for example, will continually be in contact
ELECTRO-MAGNETIC INDUCTION
437
(0
FIG. 373. (J) Diagram of the Armature
Current. (2) Diagram of the Current
Taken from the Brushes.
with a positively charged segment, and b r with a negatively
charged one. Hence, in this case, the current will always
flow into the external
circuit through b and
return to the armature
through b f . Such a
current is pulsating in
nature, since the
E. M. F. falls to zero
twice during each revo-
lution ( 452). A comparison of the alternating current
in the armature with the pulsating current taken off at the
brushes is made in Fig. 373.
455. Dynamos for Steady Currents. The pulsating cur-
rents produced by dynamos of one coil (Fig. 373) are un-
satisfactory for most purposes. The difficulty may be
overcome and a continuous current developed by the use
of several coils distributed uniformly over the armature.
The first armature
wound in this manner
was the so-called
Gramme ring, invented
by a Frenchman in 1870.
The core of the arma-
ture is an iron ring so
mounted on an axle as to
turn between the poles,
N and S, Fig. 374, of a strong electro-magnet. The ring
is wound with several coils of copper wire placed at equal
distances. These are represented in the figure by the sin-
gle turns numbered from 1 to 12. At each junction of
two adjacent coils a connection is made with a segment of
the commutator (7, which consists of as many insulated
bars as there are coils in the armature. The lines of force
From the Exte
Circuit
FIG. 374. Diagram of the Gramme
Ring Armature.
438
A HIGH SCHOOL COURSE IN PHYSICS
follow through the iron of the ring from N to $, as shown
by the dotted lines ; hence the outer portions of each coil
are the only ones that cut the lines when the armature re-
volves.
If, now, the armature is revolved in the direction shown
by the arrow at the top, the conductors from 1 to 5 cut
through the lines in a downward direction ; hence the
E.M. F. throughout these coils is in the direction shown
by the arrowheads on the wire ( 450). At the same
time the conductors from 7 to 11 are cutting the lines in
an upward direction, which develops an E.M.F. within
them as shown by the affixed arrows. An inspection of
the figure will show that upon both the right and the left
side of the armature the tendency is to raise the lowest
segment of the commutator to a high potential and to
reduce the topmost one to a low potential. Therefore,
by placing the brushes b and b r in contact with these
points, a direct current is led through the external cir-
cuit in the direction
shown in the figure. The
E. M. F. produced by such
an armature is practically
constant when the rate of
rotation is uniform.
456. The Drum Arma-
ture. The modern direct-
current dynamo is pro-
vided with an armature
ture of the "drum" type.
This consists of a cylindrical core, or drum, of iron
upon which are wound numerous coils of wire equally
spaced. The construction is made clear by a study of
Fig. 375. If the windings are traced, the coils will be
found to be joined in series, and at four points connec-
FIQ. 375. Diagram of the Drum Arma
ture.
ELECTRO-MAGNETIC INDUCTION
>
439
tions are made with the segments of the commutator 0.
If the armature is now rotated between the poles of a
magnet, the E. M. F. will at no time be zero at the
brushes ; for at every instant some of the conductors are
cutting magnetic lines. By setting the brushes at the
proper points, a direct and fairly steady current will be
transmitted to the external circuit.
457. Field Magnets. The magnetic poles between
which the armature of a dynamo rotates receive their ex-
citation from coils of wire carrying an electric current.
In direct-current machines this current is produced by
the dynamo itself. The initial current developed in the
armature depends upon the residual magnetism ( 379)
of the pole pieces, which serves to induce a small current.
This in turn increases the magnetism until the poles
finally reach their full strength.
In the series-wound 'dynamo, (1), Fig. 376, the entire
current is led from the brushes through the few turns of
Main Circuit
Main Circuit
(0
FIG. 376. (1) Series-wound Dynamo. (2) Shunt-wound Dynamo.
(3) Compound-wound Dynamo.
thick wire of the field magnets, which are joined in series
with the external circuit as shown.
In the shunt-wound dynamo, (2), Fig. 376, only a portion
of the entire current is led through the many turns of rather
440
A HIGH SCHOOL COURSE IN PHYSICS
fine wire in the coils of the field magnet, while the main
portion is conducted through the external circuit. The
field magnet coils thus form a shunt ( 445) to the ex-
ternal circuit.
In the compound-wound dynamo, (3), Fig. 376, the field
magnets are wound with two coils, one being joined in
series with the external circuit, and the other connected
as a shunt between the brushes. A compound-wound
machine adjusts itself to variations in the resistance of
the external circuit in such a way as to maintain a con-
stant difference of potential between the brushes.
458. The Acyclic, or Unipolar, Generator. It is of in-
terest to note that the alternations of the current induced
in the armature of a dynamo can be prevented by employ-
ing a mechanism of the proper form. Figure 377 shows a
sketch of a so-called acyclic, or unipolar, generator, which
FIG. 377. Diagram of an Acyclic Generator.
consists of two collecting rings R and R 1 joined together
by conducting bars 1, 2, 3, etc. These bars are attached
at their centers to a revolving shaft Z>, but are insulated
from it. Magnets are placed with their poles as shown
at JVand S. When the armature is revolved in the direc-
ELECTRO-MAGNETIC INDUCTION
441
tion shown by the arrows MM[, conductor 1 cuts through
the field of the magnets, and an E. M. F. is induced in it
( 450) in the direction shown by the arrow at (7. Hence
a current may be taken from the brush at B ', which
rests continually against the collecting ring, through the
external circuit X back to the brush B. Since each con-
ductor cuts the magnetic lines of force in the same direc-
tion, B' is always the positive brush and B the negative,
and hence a direct current flows through both the inter-
nal and external parts of the circuit.
In the commercial form of this type, Fig. 378, the mag-
netic field extends completely around the armature and is
FIG. 378. An Acyclic Generator.
excited by means of a current in the field coils FF which
lie in concentric circles around the cylindrical steel core
A A. The armature conductors 1, #, #, etc., are attached
to the periphery of a steel cylinder from which they are
insulated.
Unipolar generators are designed to run at a high speed,
and a desired E.M.F. is obtained by arranging several
442 A HIGH SCHOOL COURSE IN PHYSICS
independent sets of conductors and their corresponding
collecting rings in the armature of the machine and join-
ing their brushes in series. In this manner the E. M. F.s
of the separate sets are added together. The greatest
advantages of this form of generator over that of the
commutator type are the elimination of commutator diffi-
culties and lower cost of construction.
EXERCISES
1. In order to show that a current of electricity is produced when
a magnet is thrust into a coil of wire, why is it usually necessary to
employ a coil of many turns?
2. Account for the enormous difference of potential induced be-
tween the terminals of the secondary of an induction coil?
3. Connect one terminal of a spark coil (induction coil) to the
outer coating of a Leyden jar and bring the other close to the knob.
Put the coil in operation and show that the jar becomes charged.
Explain how the charge can "jump" into the jar, but cannot escape.
4. How many revolutions per minute would have to be made by
a two-pole alternator to produce 120 alternations of the current per
second ?
5. An alternator has 16 poles. How many alternations per second
will be produced when the speed is 375 revolutions per minute?
6. What will be the effect upon the E. M. F. of a shunt-wound
dynamo of introducing resistance into the field magnet circuit?
SUGGESTION. Consider the effect of the added resistance on the
current in the field coils and also on the magnetic field.
7. Does this suggest a way in which the E. M. F. of a shunt-wound
machine can be regulated ?
3. TRANSFORMATION OF POWER AND ITS APPLICATIONS
459. The Electric Motor. Electrical energy is trans-
formed into mechanical by means of electric motors. The
direct-current motor does not differ greatly in construction
from the dynamo. The principle underlying its action is
illustrated by the following experiment.
ELECTRO-MAGNETIC INDUCTION
443
Suspend a wire on the apparatus described in 412 so that its
lower end just dips into mercury. Hold a horseshoe magnet as
shown in Fig. 379 and send a /-tfftrx^
current from a new dry cell
through the wire. The wire
will be found to move at right
angles to the lines of force, as
shown by the arrow. If the cur-
rent is nowre versed, the wire will
move in the opposite direction.
The experiment shows
clearly that a conductor in
which a current is flowing
tends to move in a direction
at right angles to the lines
of force of a magnetic field FIG. 379. Movement of a Conductor in
in which it is placed. The a M*s* eiic Field -
motion may be determined by applying the rule of 450,
but by using the left hand instead of the right.
Let this principle be applied to Fig. 374. If a current-
from some source be sent through the armature from b f to b,
the current through the coils will take the direction indi-
cated by the arrows, dividing as it leaves b r . According to
the principle shown in the experiment, all the conductors
from 1 to 5 will be urged in an upward direction, and those
from 7 to 11, downward. Since the current employed by
the motor flows through the field magnet coils, a powerful
magnetic field is produced in which the armature will ro-
tate with sufficient power to turn the wheels of factories
and propel electric cars, launches, automobiles, etc.
460. The Electric Railway Car. A familiar applica-
tion of the electric motor for the generation of mechanical
power is found in the electric railway, Fig. 380. A
current from the generator at the power house is trans-
mitted through the trolley wire, or in some cases through
444 A HIGH SCHOOL COURSE IN PHYSICS
a third rail, and by means of a metallic arm A to the
motors placed under the floor of the car at M. The axles
of the car are so geared to those of the motors that the
car is propelled by the rotation of the motor armatures.
I Feed Wire \ \ <
Trolley Wire
JJUUUUL
f
Dynamo or
Track
It
FIG. 380. Diagram of an Electric Railway System.
From the motors the current returns to the power house
through the track, the rails being carefully " bonded "
together with copper conductors. In circuit with the
motors is placed the controller (7, operated by the motor-
man. By means of a series of resistance coils connected
with the controller, the current can be increased or di-
minished and the speed of the car thus regulated. An-
other device enables the motorman to reverse the motors.
A third accessory serves in applying the air brakes
( 159) to check the speed after the current has been
completely interrupted at the controller.
461. The Alternating-current Transformer. Alternat-
ing currents owe their extensive application to the fact
that the potential difference between two points can be
easily reduced from a dangerous one of many thousand
volts to one of a safe value for dwelling-house use and
for many other purposes. This is accomplished by means
of a transformer, which is simply a modified induction
coil.
The principle involved in the transformer is easily
understood from a study of Fig. 381. An iron core R
is wound with two independent coils of wire P and 8.
ELECTRO-MAGNETIC INDUCTION
445
Let an alternating current be sent through the primary
coil P, and let the secondary be connected with a group
of lamps L. The cur-
rent in P magnetizes
the iron core in one
direction, then demag-
netizes and remagnet- FIG. 381. Diagram of a Transformer.
izes it again in the
opposite direction, while the magnetic lines follow the iron
core through the secondary coil 8. As a result of these
magnetic changes in the core an alternating current is in-
duced in S and flows through the lamps.
If there are more turns of wire on the secondary coil
S than on the primary coil P, the potential difference at
the terminals of S will be
greater than at P, because
of the larger number of
loops of wire in which the
magnetic changes occur.
In this case the transformer
is called a step-up trans-
former. If, however, the
secondary contains the
fewer turns, its potential
difference is lower than that
of the primary, and the transformer is a step-down trans-
former. The ratio of the two potential differences is
equal to the ratio of the number of turns of wire in the two
coils. For example, a transformer that is to be used to
reduce a voltage of 2000 to a lower one of 100 volts would
be constructed by winding the primary coil with 20 times
as many turns as the secondary. The same transformer
would reduce a potential difference of 2200 volts to one
of 110 volts.
fHmary
'Secondary
FIG. 382. A Commercial Trans-
former.
446 A HIGH SCHOOL COURSE IN PHYSICS
462. Utility of the Transformer. The value of the
transforming process is made clear by the study of a
specific case. For example, electric power is to be trans-
ferred from a power station to a large city over several
miles of wire. It is desired that the number of amperes
( in Eq. 8, 437) be small in order to reduce to a mini-
mum the loss of energy due to the heating of the con-
ducting wires. The alternator used at the power house
develops a potential difference of 2000 volts. This cur-
rent is led through the primary coil of a " step-up "
c
FIG. 383. The Transformer System of a Long Distance Power Circuit.
transformer A, Fig. 383, where the potential difference
is raised to 11,000 volts, while the number of amperes
becomes proportionately reduced. At this voltage the
current would be about 7 amperes per 100 horse power.
Since wires of so great a potential difference are unsafe
to lead into houses, the voltage is reduced from 11,000 to
2000 volts, by a "step-down" transformer B where the
line enters the city, and again at the houses, from 2000 to
100 volts by the transformer O.
Since the power transmitted by^an electric current is the product
of the number of volts and amperes (Eq. 7, 436), a current of 10
amperes under a potential difference of 11,000 volts, for example,
delivers a power of 110,000 watts, which is about 147.5 horse power.
It is plain, therefore, that a large amount of power under a high
voltage can be transferred by a small current. The power generated
at Niagara Falls is distributed to Buffalo, Syracuse, and other places
with potential differences of from 22,000 to 60,000 volts.
Again, if the transformer C, Fig. 383, deliver a current of 5 amperes
under a potential difference of 100 volts for lighting a building, the
ELECTRO-MAGNETIC INDUCTION 447
power delivered is 5 x 100, or 500 watts. In the long distance circuit
between A and B where the voltage is 11,000, the current would be
500 -4- 11,000, or 0.045 ampere. Hence, to take 5 amperes at 100 volts
would increase the current in the long line only 0.045 ampere.
The heat losses in long distance power transmission render it
impracticable to convey large currents, as shown in 438. But the
examples above show that by raising the potential difference to sev-
eral thousand volts the current is proportionately reduced; conse-
quently a given power can be transferred with far less heat loss,
since the heat generated is proportional to the square of the current.
It is in this manner that the transformer has solved the problem of
long distance transmission of power from places where power is com-
paratively cheap to distant manufacturing centers where it would be
expensive. The distribution of power over long electric railway lines
is accomplished by means of so-called high tension, i.e. high potential,
apparatus.
The alternating current transformer affords one of the
most striking examples of the transformation and trans-
ference of energy to be found. The power in one circuit
is transferred to another entirely without any mechanical
connection between the two. It is necessary only that the
magnetic lines set up by the current in the primary coil
pass through the secondary. No mechanical motion is
concerned in the process. The power loss in a good
transformer is usually not more than 3 or 4 per cent.
463. Incandescent Lighting. It is a
familiar fact that the heating effect of an
electric current is employed in the process
of electric lighting. The simplest case
to study is the incandescent lamp. See
Fig. 384. In this lamp the current is
sent through a carbon filament (7, which
is heated to incandescence. In order to
prevent the carbon from burning, as well FIG. 384. An incan-
as to prevent loss of heat by convection, JjJJ|
it is inclosed in a highly exhausted glass and Socket.
448 A HIGH SCHOOL COURSE IN PHYSICS
bulb. Connections are made with the ends of the filament
by means of two short pieces of platinum wire sealed in
the glass. One of these leads to the contact A in the
center of the base, the other to the brass rim B which holds
the lamp in its socket S. Through these the current is
transmitted to and from the lamp.
On account of its large consumption of power (about
3.5 watts per candle power), many efforts have been made
to produce lamps of higher efficiency. At the present
time the carbon filament lamp is being rapidly replaced
by those provided with metallic filaments of the rather
uncommon metals tantalum or tungsten. These metals
admit of being drawn out into very thin wires which can
be heated white-hot without melting. These thin fila-
ments are mounted in glass bulbs in much the same man-
ner 'as the carbon filaments. Not only is the light which
metallic filament lamps emit whiter than that given off by
the carbon filaments, but the efficiency is far greater. In
the tungsten lamp the consumption is about 1.25 watts per
candle power.
Ordinarily the potential difference on a lamp circuit is
maintained at 110 or 220 volts. Lamps are adapted to the
voltage of the circuit on which they are to be used. A
16-candle-power lamp with a carbon filament requires a
current of slightly more than 0.5 ampere when the voltage
is 110 and about 0.25 ampere when the voltage is 220.
The power necessary is, by equation (?), 436, 110 x 0.5,
or 55 watts.
The Nernst lamp employs a short rod, or " glower," Fig. 385, com-
posed of oxides which are maintained at a high temperature by the
passage of a current of electricity. Although the glower is a non-
conductor at ordinary temperatures, it becomes a conductor when
heated. The glower is mounted close to a heater coil of fine platinum
wire through which a current passes when the lamp is turned on.
ELECTRO-MAGNETIC INDUCTION 449
As soon as the glower becomes sufficiently hot, the heater coils are
automatically thrown out of circuit, and the current then flows only
through the glower. Since the glower is in-
combustible, it can be used without being-
inclosed. The efficiency of the Nernst lamp
is considerably below 2 watts per candle
power.
464. Incandescent Lamp Circuits.
Incandescent lamps are connected in
parallel between the two main wires FIG. 385. Showing Parts
leading into a building. These wires of a Nernst Lamp -
are maintained by the dynamo D, Fig. 386, at a potential
difference of 110 volts, so that any lamp may be turned
1 | - - ^ on or off without interfer-
p O O O O D fy > * n g w ith the others. Each
I 1 I I I ^ 16-candle-power lamp re-
quires a current of half an
ampere and, consequently,
has a resistance when hot
FIG. 386. Showing the Connection of of 220 ohms. Lamps are
Incandescent Lamps in a Circuit. o f ten joined in groups, as
shown at A. In this case the switch placed at S controls
all the lamps of the group.
465. Cost of Electric Power. Electrical energy is sold
at a certain rate per watt-hour. A watt-hour is a volt-
ampere-hour ; in other words, an ampere of current flow-
ing under a potential difference of one volt for one hour
delivers a watt-hour of energy. Hence a 110-volt lamp
carrying 0.5 ampere requires 110 x 0.5 x 1, or 55 watt-
hours for every hour it is used. In commercial lighting
a meter which is designed to register the consumption of
energy in kilowatt- hours is placed in the circuit at the
point where the wires enter each consumer's house. Thus
readings of the meter show the amount of electrical energy
for which' the user is charged.
30
450 A HIGH SCHOOL COURSE IN PHYSICS
466. The Electric Arc. The first electric arc was ex
hibited in 1809 by the great English scientist, Sir Hum-
phry Davy. For this purpose Davy employed over 2000
voltaic cells joined to two pieces of charcoal which were
touched and then slightly separated. The same experiment
may be easily made on any commercial lighting circuit.
Wind bare copper wire, about No. 18, around pieces of electric
light carbons. Join these in series with a resistance of about 10 ohms
of iron wire to the terminals of a 110-volt lighting circuit. The re-
sistance may be made by winding 150 to 200 feet of No. 18 or 19 iron
wire on a suitable frame. Touch the tips of the carbons together and
at once separate them about a quarter of an inch. An intensely
bright light will be produced as the current continues to flow across
the gap.
By the separation of the carbon rods, a high tempera-
ture is produced by the current, which vaporizes some of
the carbon, forming a conducting
layer from one to the other. The
resistance of this mass of vapor may
not be more than 3 or 4 ohms. If
the current is a direct one, the tem-
perature of the positive carbon rises
above that of the negative, and from
it comes the greater portion of the
light. In this case the positive car-
bon is consumed about twice as fast
as the negative and becomes hollowed
out, as in Fig. 387, while the negative
remains pointed. When an arc is
produced by an alternating current,
FIG. 387. The Electric light i s given out equally from the
Arc Produced by a Di- J
rect Current. two points, and the two rods are con-
.sumed at the same rate.
467. Arc Lamps. With the development of the dy-
namo, the arc lamp as a means of illumination has come
ELECTRO-MAGNETIC INDUCTION
451
FIG. 388. The Hand-feed Electric
Lamp.
into extensive use. In the so-called hand-feed lamp,
Fig. 388, the positions of the carbons are controlled by
the screw heads S. They are
at first permitted to touch
and then are separated. As
fast as the
rods are
consumed,
they are
slowly fed
together
by the op-
erator. Such lamps are used mainly in
projection lanterns ( 324). In the arc
lamp of automatic feed, Fig. 389, the
mechanism has two duties to perform:
(1) to separate the carbons when the
current starts, and (2) to
feed the carbons together
as fast as they are con-
sumed, always keeping the
FIG. 389. -The Auto- P rO P flr 8 P aC6 be t ween
matic Arc Lamp. them.
The consumption of the carbon rods in the arc lamp
can be largely reduced by inclosing the arc in a globe
that is nearly air-tight as shown in Fig. 390. In this
form of lamp the carbon burns from 60 to 100 hours.
In the lamps just described the light is emitted by
the incandescent ends of the carbons. If the carbons, -c,
r IG. o9U. 111-
however, are cored with a mixture of carbon and closed Elec-
metallic salts, a highly luminous vapor is maintained trie Arc
by the current between the two terminals. In flaming Lamp.
arc lamps the carbons are cored with calcium salts which serve to give
the light a bright yellow color.
The open arc is operated by a current of from 5 to 10 amperes and
45 to 50 volts, and the candle power in the direction of greatest in-
452 A HIGH SCHOOL COURSE IN PHYSICS
tensity is about 1000. The inclosed arc lamp requires a voltage of
about 80 and a current of from 5 to 8 amperes.
EXERCISES
1. According to Lenz's law, in what direction in a circuit will a
current be induced by the sudden interruption of a current in a neigh-
boring conductor ?
2. If the experiment of 450 be repeated with a long loop of wire,
it will be found that no deflection of the galvanometer will be produced
by swinging both parts of the loops together across the earth's lines of
force. Explain. By swinging the two parts of the loop in opposite
directions, a large deflection is obtained. Why?
3. Would you class the induction coil as a " step-up " or a " step-
down" transformer?
4. Explain why the interrupter is an accessory part of the induc-
tion coil but not of the transformer.
5. A transformer carries a current of 10 amperes in its primary
coil, under a potential difference at its terminals of 2000 volts. If it
delivers a current of 194 amperes with a potential difference of 100
volts, how much energy is transformed per hour, how much delivered,
and how much wasted?
6. If a building contained 50 110-volt incandescent lamps, what
voltage would have to be supplied to operate them if they were all
joined in series? Show that this would be impracticable.
7. Show by a diagram the manner of connecting ten 16-candle-
power 110-volt incandescent lamps in parallel. What would have to
be the voltage and how much current would be required ?
SUGGESTION. Consider that in the case of parallel conductors the
total^urrent is the sum of that in the separate parts.
8. Why would the alternating-current transformer be entirely in-
effective in transforming a continuous current?
9. Compute the monthly cost of operating five 1 6-candle-power in-
candescent lamps when current costs 10 ct. per kilowatt-hour, allow-
ing an average use of 3 hr. per day and 3 watts per candle power.
10. Compute the monthly cost of current for an open arc lamp re-
quiring 8 amperes at 50 volts, allowing 3 hr. per day and 10 ct. per
kilowatt-hour.
11. If the potential difference between the trolley of an electric
railway and the track is 550 volts, show how it would be possible to
ELECTRO-MAGNETIC INDUCTION
453
operate 110- volt incandescent lamps by properly connecting them
together. Diagram the system.
12. Show how a workman standing on the top of an electric car
can safely handle the trolley wire with bare hands, while one standing
on the ground would be severely shocked by coining in contact with
any wire forming a connection with the trolley wire.
13. 25 street lamps each operated by a potential difference at its
terminals of 45 volts are joined in series. What potential difference
must be maintained at the terminals of the dynamo ? What would
have to be the current strength? Disregard the line loss.
14. What has been the effect of economical long distance powei
transmission upon manufacturing industries, railway development,
etc.?
4. THE TELEGRAPH AND THE TELEPHONE
468. The Morse Telegraph. The most extensive use
of the magnetic effect of electric currents is made in the
telegraph systems in common use. In 1831 Joseph Henry
produced audible signals at a distance, but the system
generally employed in this country is that designed by
Samuel F. B. Morse and first used in 1844. The instru-
ments found at each station are the key, sounder, and re-
lay.
The key, Fig. 391, is
merely a convenient
device for making and
breaking an electric cir-
cuit at A by operating
the lever L. It is also
provided with a switch
S, so that the circuit
may be left closed when
the key is not in use.
The sounder, Fig.
392, consists of an elec-
tro-magnet M which at- FIG. 392. Telegraph Sounder.
FIG. 391. Telegraph Key.
454 A HIGH SCHOOL COURSE IN PHYSICS
tracts the iron armature A whenever a current is sent
through it, thus causing the heavy brass bar B to be
drawn down against (7 with a sharp click. When the cur-
rent is interrupted, the armature is no longer attracted,
and the bar is lifted against D by an adjustable spring.
Transmitted messages are read by ear from the clicks of
this instrument.
469. Plan of a Short Telegraph Line. Short lines in
which the resistance is small require at each station only
the key and sounder, as in Fig. 393. The connection is
Sounder Sounder Key ,
Line Battery TV/H wY*
|.|i|i|i|i|i HJL ~~L^ r-*- 1 Slult h
Station A Maln Lln0 Station B
Earth ==
Earth
Fro. 393. A Short Telegraph Line.
usually made by a single wire, the circuit being completed
by joining a wire at each end to a metal pipe or to a metal
plate buried in the ground. Thus the earth forms a part
of the circuit. The battery may be placed anywhere in
the line.
When the operator at Station A wishes to send a mes-
sage to Station B, he opens the switch on his key, which
breaks the circuit. The sounder cores are thus demag-
netized, and the bars are thrown up by the springs. Now,
by means of the key, the operator A can make and break
the circuit which will cause both sounders to click off the
" dots " and " dashes " composing the message. A dot is
produced by a quick stroke of the key which closes the
circuit for only an instant ; a dash is a slower stroke
which leaves the circuit closed for a slightly longer time.
ELECTRO-MAGNETIC INDUCTION 455
The operator at B, skilled in the interpretation of the
clicks of the sounder, reads and records the message.
Since a telegraph circuit is left closed when not in use, a
" closed circuit," cell like the Daniell or gravity must be
used.
The Morse code given below is composed entirely of
dots, dashes, and spaces. A small space is left between
letters and a slightly longer one between words.
THE MORSE TELEGRAPH CODE
a - h o-- u
b i-- p v
c--- j . <1 w
d k r x
e - 1 s y
f m t z -
g U __-
470. The Relay and Its Use. In long telegraph lines
on which there are many instruments, the resistance is
usually so great that
the current in the main
line is too feeble to op-
erate the sounders with
sufficient loudness. The
difficulty is avoided by
the use Of the relay, FIG. S94.- The Telegraph Relay.
which is a more sensitive instrument than the sounder.
The relay, Fig. 394, consists of an electro-magnet M con-
taining several thousand turns of wire (about 150 ohms)
which is placed in the main line at each station together
with the key. The armature and bar H of the relay are
made very light, and all the adjustments of the instru-
ment may be made with great precision. The function
of the relay is to open and close at K a local circuit which
contains merely the sounder and two or three cells. It
456
A HIGH SCHOOL COURSE IN PHYSICS
will readily be seen that since there is little resistance to
reduce the current, very distinct clicks will be produced
on the sounder by the current from this local battery every
time the relay automatically closes and opens the local
circuit.
471. The Long Distance Telegraph System. The usual
arrangement of the parts of a telegraph system is shown
diagrammatically in Fig. 395. In sending a message irom
FIG. 395. A Long Distance Telegraph System.
Detroit to Buffalo, for example, the Detroit operator uses
precisely the method described in 469. When the circuit
is opened at Detroit, no current flows from the main line
battery, and all the relays on the line release their arma-
tures and thus open every local circuit. When the De-
troit operator presses his key, the main line battery sends
a current out over the line, and the electro-magnets of the
relays draw the armatures down and thus close the local
circuits, causing every sounder to produce a sharp click.
Thus the dots and dashes comprising a message may be
read by every operator along the line.
The relay may also be used to repeat a message to
ELECTRO-MAGNETIC INDUCTION
457
another line instead of transmitting it to a short local
circuit. A message from Chicago to New York may be
repeated to a Detroit-Buffalo line at Detroit, to a Buffalo-
Syracuse line at Buffalo, and finally to a Syracuse-New
York line at Syracuse. Since the repeating is performed
automatically at each of these stations, no time is lost in
the transfer from one line to another. The , relay when
used in this manner is called a repeater.
472. The Telephone. The simplest manner in which
speech produced at one station can be reproduced by elec-
trical means at another is by means of two telephone
Line
FIG. 396. A Simple Telephone System.
" receivers " connected by two wires, or by one wire and
the earth. See Fig. 396. The telephone receiver was
invented in 1876 almost simultaneously by Alexander
Graham Bell and Elisha
Gray, both Americans. It
consists simply of a perma-
nent bar magnet M, Fig. 397,
surrounded at the end by a
Coil of fine insulated copper FIG. 397. Section of a Telephone
wire O. An iron disk D is
mounted so as to vibrate freely close to the end of the
magnet.
458
A HIGH SCHOOL COURSE IN PHYSICS
If a person speaks into the receiver, the sound waves
set the disk in vibration. Each vibration of the disk
changes the number of magnetic lines of force through
the coils of wire and thus induces a current whose nature
depends entirely upon the loudness, pitch, and quality of
the sound. In this manner a pulsating current is sent
over the line to a similar instrument at the distant station.
When the current generated at the
first station flows in such a direction
as to strengthen the magnet at the
second one, the disk is drawn in;
when it flows in the opposite direc-
FIG. 398. A Recent Type n on the magnet is weakened and the
of Receiver. y ,
disk released. Thus the vibrations
at the first station are reproduced on the instrument at the
second. A modern receiver is shown in Fig. 398.
473. The Transmitter. The telephone receiver just
described is not sufficiently powerful when used as a trans-
mitter, or sender, of speech ; but it is a receiver, or repro-
ducer, of sound of extremely great sensibility. For this
reason the transmitters in general use
are based on an entirely different
principle from that of the receiver.
The modern form used in long-dis-
tance telephony consists of two car-
bon buttons c and c', Fig. 399,
between which are carbon granules g.
The metal disk, or diaphragm, D is
attached to the button <?. When the
disk is set in vibration by the sound waves, the variation
of pressure against the carbon granules causes large vari-
ations in the electrical resistance between the buttons.
Hence, if such an instrument be placed in a battery circuit
and so connected that the current passes through the
FIG. 399. The Trans-
mitter.
ELECTRO-MAGNETIC INDUCTION
459
granules from c to c\ the strength of the current changes
precisely in accordance with the vibrations of the diaphragm.
474. A Long Distance Telephone System. In all tele-
phones operating with a local battery, the connections are
made as shown in Fig. 400. The current from the local
Line Wire
FIG. 400. A Long Distance Telephone System.
battery B is led through the transmitter and the primary
of a small induction coil back to the battery. The main
line contains at each station the secondary of the induction
coil and the receiver. Two wires are generally used to
connect the two stations, although one may be replaced by
the earth.
When a person speaks into the transmitter, the vibration
of the diaphragm changes the pressure at the contact
points of the carbon granules which Conduct the current
flowing through the primary coil. When the diaphragm
is forced in, the resistance of the transmitter is lowered,
and a comparatively large current flows ; when it moves
outward, the current is reduced. These changes in the
primary coil induce currents in the secondary which pass out
over the line and set up vibrations in the receiver at the dis-
tant station.
For the purpose of calling attention, an electric bell is
placed at each station. When the receiver is lifted from
the hook upon which it hangs, the bells are disconnected
from the line, and the connections are made as shown in
460 A HIGH SCHOOL COURSE IN PHYSICS
Fig. 400. The downward motion of the hook restores the
bell to the line when the receiver is hung up.
In cities and villages the telephones are all connected
with a central exchange, where the operator upon request
connects the line from any instrument with the line lead-
ing to any other. Such exchanges can now be found in
even the small towns and will serve to show to the student
of electricity one of the ways in which the study of physi-
cal principles has contributed to the prosperity and con-
venience of mankind.
EXERCISES
1. Compute the resistance of an iron telegraph line 150 mi. long,
the size of the wire being 0.1 in., the line containing also 10 relays of
150 ohms each. Allow nothing for the earth connections.
2. A telegraph wire offers a resistance of 35 ohms per mile. If the
line contains five 150-ohm instruments, what current will be produced
by 30 Daniell cells of 2 ohms each in a line 80 mi. long? Do you
think this current would operate a sounder ?
3. Connect a telephone receiver with the terminals of a very sensi-
tive galvanometer and press in on the diaphragm. A deflection will
be produced. Why? Release the diaphragm. A contrary current
will be obtained. Why?
4. If the telephone receiver can be used as a transmitter and re-
quires no battery in its operation, why is it not so used?
SUMMARY
1. Currents of electricity may be produced by induction
by increasing or decreasing the number of magnetic lines
of force which thread through a coil of wire if it is in a
" closed circuit." The induced E. M. F. is proportional to
the rate of change in the number of lines ( 446 and 447).
2. The direction of an induced current is always such
as to produce a field that tends to prevent a change in the
number of lines of force through the coil ( 448).
ELECTRO-MAGNETIC INDUCTION 461
3. When an electrical conductor cuts magnetic lines of
force, an E. M. F. is induced within it ( 450).
4. Currents of electricity are produced on a large scale
by making use of the dynamo, which depends for its action
on the principles of electro-magnetic induction. Dynamos
are alternators or direct- cur rent dynamos according as they
produce alternating or direct currents ( 451 to 458).
5. Dynamos are series-wound, shunt-wound, or compound-
wound, depending on the manner in which the field cores
are excited ( 457).
6. The direct-current motor depends upon the tendency
of a conductor carrying an electric current to move in a
magnetic field. Motors are used wherever electric power
is to be converted into mechanical power for moving
machinery ( 459).
7. Alternating-current transformers are used to convert
alternating currents of low potential into alternating cur-
rents of high potential and vice versa. By their use
unsafe currents of many thousand volts can be reduced to
safe ones for domestic and commercial use ( 461 to 464).
8. Electric power is sold by the kilowatt-hour. The
number of kilowatt-hours consumed is given by the equa-
tion
kilowatt-hours = 0.001 EC x hours ( 465).
9. The telegraph and telephone employ the magnetic
effect of the electric current in transmitting messages
( 468 to 474).
CHAPTER XXI
RADIATIONS
1. ELECTRO-MAGNETIC WAVES
475. An Electrical Discharge is Oscillatory. When an
electric spark jumps across a short gap, it appears to be
only a single flash. The eye is incapable of determining
whether or not this is actually the case. The following
experiment may be used to investigate the nature of such
a discharge.
Bend 2 or 3 feet of wire into a hoop R, Fig. 401, leaving a gap of
about 1 millimeter at S. Connect the hoop in series with a Leyden
jar L and the spark gap of an induction coil
7 as shown. If the induction coil be now put
into operation, sparks will be observed to pass
across S every time they jump across the gap
at /.
The spark at S indicates that the air
gap offers a better path than the metal
loop STR. But we know that the re-
sistance of the wire STR is but a frac-
tion of an ohm, while that of the air
at S is perhaps millions of ohms. The
discharge through the loop, therefore,
must meet with some impedance other
than that which would be encountered by a direct current.
From this and other effects we are led to infer that the
discharge at I is a rapid surging of electricity back and
forth, but one which lasts only for a fraction of a second.
At the first rush of current in the ring a magnetic field is
462
Induction
Coil
FIG. 401. Illustrat-
ing an Effect of
an Electric Dis-
charge.
RADIATIONS
463
FIG. 402. Result Obtained by Photo-
graphing an Electric Spark.
suddenly'set up within the loop. This sudden magnetic
change induces, according to Lenz's law ( 448), an op-
posing E. M. F. which effec-
tually prevents the flow of a
large portion of the current
in the loop. Likewise the
sudden reversal of the dis-
charge reverses the magnetic
lines and again induces an opposing E. M. F. in the loop.
Hence the greater portion of the discharge finds a better
outlet through the gap iS.
Stronger proof of the oscillat-
ing nature of a discharge has
been obtained by photograph-
ing a spark by the help of a
revolving mirror. The result
is shown in Fig. 402. The
period of oscillation has been
shown by this method to be
'of the order of a millionth of a second. As a rule the
oscillations subside very quickly, as shown by the curve
in Fig. 403.
476. Electro-magnetic Waves in the Ether. In 1888
Hertz 1 of Germany showed that each electrical oscillation
that occurs when a spark passes across an air gap pro-
duces a disturbance in the surrounding ether which is
propagated outward in wave form in much the same
manner as water waves move outward from a falling
pebble, or sound waves from a vibrating bell. These
ether waves are called electro-magnetic waves. Inasmuch
as light itself is propagated in wave form in the ether,
it might be inferred that the speed of the two should be
the same. Such has been found to be the case.
FIG. 403. Diagram of a Spark
1 See portrait facing page 464. See also Kelvin, frontispiece.
464 A HIGH SCHOOL COURSE IN PHYSICS
477. Detection of Electro -magnetic Waves. Tne process
of transmitting messages by means of electro-magnetic
ether waves is dependent on the detection of such waves
at the receiving station. One method that can be em-
ployed for this purpose is illustrated by the following
experiment.
Bend a glass tube about 5 centimeters long and 3 or 4 millimeters
in diameter as shown in Fig. 404. Place a few coarse iron filings in
the bend and introduce a globule of clean mercury into each end of
the tube as shown at A and B. Insert small
iron wires into the mercury and connect the
device in series with a cell and an ammeter or
galvanometer. No deflection should be pro-
FIG. 404. A Coherer duced. Now cause a spark to jump a short air-
gap several feet away by using an induction
coil, an influence machine ( 371), or a Ley den jar. A deflection
will be observed at once. If the tube of filings be now tapped lightly,
the circuit is again broken, and the experiment may be repeated.
The tube of metal filings used as a detector of electro-
magnetic waves is called a coherer. Ordinarily the filings
offer a large resistance to the flow of electricity through
the many points of contact between the several pieces.
The waves emitted by the oscillatory discharge at the
spark gap cause the filings to cling together, and the
resistance of the tube immediately falls to a few ohms.
A tap or jar breaks the filings apart, and the resistance
rises again to its former value.
478. Wireless Telegraphy. The possibility of sending
out electro-magnetic waves from an induction coil and of
detecting them by a coherer has led to the transmission
of messages by the so-called wireless telegraph systems.
A plan of a simple sending and receiving equipment is
shown in Figs. 405 and 406.
Connect the coherer described in the preceding section in series
with the electro -magnet of a relay R and a cell C, Fig. 406. In the
HEINRICH HERTZ (1857-1894)
About the middle of the last century Maxwell advanced the idea
that waves of light are electro-magnetic in character. If this were
true of light, then it would also be true of radiant heat. In 1888
Hertz of Germany succeeded in demonstrating experimentally the
truth of this assumption. During the discharge of electricity between
two polished knobs, so-called electro-magnetic waves are radiated into
space. Hertz was able to detect these waves and to reflect, refract,
and polarize them and to cause interference to take place between
them. He also measured the velocity with which they are propa-
gated through space, and found it to be equal to the velocity of
light. Thus the hypothesis of Maxwell was placed upon an experi-
mental basis, and the way opened for long-distance communication
between stations without the necessity of connecting wires. The
practical value of Hertz's results can hardly be overestimated.
Among others who have contributed greatly to the knowledge of
electro-magnetic waves may be mentioned Sir Oliver Lodge of Eng-
land, Righi of Bologna, and Branly of Paris.
In 1880 Hertz was made assistant to Helmholtz at Berlin. In
1885 he became professor of physics in the Technical High School
at Karlsruhe. It was in the latter place that his epoch-making
experiments were first performed. In 1889 he was elected professor
of physics at Bonn, where he died at the age of thirty-seven years.
Electro-magnetic waves are called Hertzian waves in his honor.
RADIATIONS
465
H'l'l'-
make-and-break circuit of the relay connect an electric bell B ( 411)
and a cell C'. The bell is so placed that its hammer strikes the co-
herer D whenever it is set in vibration. One end of the coherer
should be connected to the earth and the other joined to a high aerial
wire. For short distances the aerial wire may be very short or left
off altogether. At the sending station (Fig. 405), simply connect
one side of a spark gap of an induction coil with the earth and
join the other side with an aerial conductor which is merely a
rod or wire, one end of which is lifted some distance above
the apparatus. A key K should be placed in the circuit of
the primary coil. Closing the key and thus producing sparks
at S causes the bell to ring at the receiving station until the
circuit at the sending station is broken.
When sparks pass at the so-
called oscillator S, electro-mag-
netic waves are emitted which
affect the coherer at the receiving
station, causing the filings to con-
duct as shown in 477. The cur-
Earth
FIG. 405. Apparatus for
Sending Wireless Tele-
graph Signals.
rent from the cell then flows
through the coherer and the
electro-magnet of the relay
R. The relay closes at A the
circuit through the bell which
is rung by the current from
the cell 0'. The filings con-
tinue to cohere until sparks
cease to pass at $ when the
taps of the bell hammer jar FIQ m _ A Receiving Station for
them apart. The circuit Wireless Messages.
31
Earth
466
A HIGH SCHOOL COURSE IN PHYSICS
through the relay is thus broken, which in turn opens
the bell circuit at A. Another spark at S again causes
D to conduct and the bell to ring. Many other forms
of receiving devices are in common use.
Systems of wireless telegraphy have reached such a
state of development that ocean-going vessels are, as a
rule, at all times in communication with land stations or
with one another. Passengers on sinking vessels have
thus been rescued by timely assistance obtained through
wireless messages which were received at stations many
miles away. Naval fleets equipped with a good system
may be kept continually informed by the controlling
department of the government, and the department may
be kept acquainted with every movement of the fleet.
Even transatlantic messages are now transmitted without
the use of wires or cables.
2. CONDUCTION OF GASES
479. Conduction through Vacuum Tubes. Connect the ter-
minals of an induction coil with electrodes A and B, Fig. 407, which
are sealed in the ends of a glass
tube 2 or 3 feet in length. Con-
nect the tube with an air pump
and put the coil in operation.
Sparks will jump across the gap S
because it is the better path.
Put the air pump in action and
exhaust the tube while the coil
is running. When the pressure
has been sufficiently reduced, the
discharge will begin to take place
through the long exhausted tube
rather than over the shorter path through the air at S.
When the exhaustion of the gas has been carried much
farther, there may be seen a radiation from the cathode
proceeding in straight lines and traceable by a slight
FIG. 407. Discharge through a Par-
tial Vacuum.
SIR WILLIAM CROOKES (1832- )
The discharge of electricity through
partially exhausted tubes has been a sub-
ject of much research since the middle of
the last century. In 1853 Masson of Paris
discharged electricity from a large induc-
tion coil through a Torricellian vacuum.
Later Geissler, a German, constructed ex-
cellent tubes containing small amounts of
different gases, which became famous on
account of the great beauty of color mani-
fest upon discharging electricity through
them. Crookes began his experiments in
1873 with tubes in which the exhaustion
was carried to a high degree. In these he
showed that so-called " radiant matter " is
thrown out from the electrodes in straight lines, casts shadows when
intercepted by solids, and is capable of producing mechanical effects
when brought into collision with light movable vanes. Furthermore,
he showed that the stream of particles is deflected from a straight
line by a magnet.
WILHELM KONRAD RONTGEN (1845- )
The most striking phenomena accom-
panying discharges in highly exhausted
tubes were discovered by Professor Ront-
gen at Wiirzburg, Germany, in 1895. A
Crookes tube was left in operation on a
table. Beneath it was a book containing
a key as a bookmark; below the book was
a photographic plate in a plate holder.
Later, on using the plate in a camera, and
developing it in the usual manner, a well-
defined shadow of the key became visible
upon it. Further experimentation showed
the discoverer that he had found a new
kind of radiation which he named X-rays.
The important ends attained by the use of
X-rays in the practice of medicine and surgery will always serve to
keep the name of Rontgen before the public.
OF THE
UNIVERSITY
AUFO!
RADIATIONS 467
luminescence occasioned in the gas remaining in the tube.
Where these rays fall upon the glass, it is made warm
and luminous. Ordinary glass glows with a soft greenish
yellow light ; and a solid, as marble, placed in the path
of the radiations will glow with a characteristic color.
These radiations are known as cathode rays. Such highly
exhausted and hermetically sealed tubes are known as
Crooked l tubes.
480. Cathode Rays. Cathode rays are characterized
by three main properties, viz. (1) they are deflected from
a straight line when caused to pass through an electric or
a magnetic field, (2) they convey a negative charge of
electricity to the object upon which they fall, and (3) they
raise the temperature of any solid object which obstructs
their path. The inference is, therefore, that cathode rays
are swiftly moving particles charged with negative electricity.
The velocity with which the particles move sometimes
reaches the enormous value of over 50,000 miles per
second, nearly one third of the velocity of light. A
continuous stream of such particles, all of which carry
negative charges, is equivalent to a current of electricity ;
hence their deviation in passing through a magnetic field.
481. X-Rays. The most important application of the
action of cathode rays is employed in the production of
the so-called X-rays,
which were discovered
in 1895 by Rontgen, 1 a
German physicist. A
special vacuum tube of
the form shown in Fig.
, FiG.408.-AnX-RayTube.
408 is used for this pur-
pose. This is connected with the secondary of an induc-
tion coil in such a manner that (7, a concave electrode, is
1 See portrait facing page 466.
468 A HIGH SCHOOL COURSE IN PHYSICS
the cathode, and P the anode. Since the cathode particles
are sent off at right angles to the surface which they leave,
they are focused against the solid piece of platinum P
placed near the center of the tube. Accompanying the
impact of the cathode rays against P appears a new radia-
tion of an entirely different character. It is to these that
the name of X-rays, or Rontgen rays, has been given.
482. Properties of X-Rays. The properties which give
to X-rays their great practical utility is their power (1) to
penetrate bodies of matter that are opaque, and (2) to
make a permanent impression upon photographic plates.
Substances are not all equally transparent to the rays ;
e.g. they more readily penetrate a thick book than a thin
coin ; and while flesh is quite transparent, bones are more
or less opaque. Hence, if the hand be held between an
X-ray tube and a photographic plate, the bones will shield
the plate more than the flesh and thus produce shadows.
Fig. 409 shows an X-ray picture of a broken wrist, and
the same wrist is shown in Fig. 410 after having healed.
3. RADIO-ACTIVITY
483. Radio-active Substances. Place a gas mantle that has
been pressed out flat upon a photographic plate and inclose it in a
light-proof box. After three or four weeks develop the plate in the
usual way. A distinct image of the fabric of the mantle will become
visible. Such a plate is shown in Fig. 411.
Similar experiments may be made with compounds con-
taining uranium, especially by using the mineral uraninite,
or pitchblende. These experiments show that certain sub-
stances spontaneously emit a kind of radiation capable of
affecting a photographic plate. Such substances are said
to be radio-active, or to possess the property of radio-activ-
ity. The radio-active element contained in a gas mantle
is thorium. The element radium is remarkable for its
FIG. 409. X-Ray Picture Showing
the Fractured Bones of a Wrist.
FIG. 410. X-Ray Picture of the
Wrist Shown in Fig. 409, after the
Bones had Knitted.
FIG. 411. The Radio-active Effect of a Portion of a Gas Mantle on
Photographic Plate.
RADIATIONS 469
intense radio-activity. The discovery of this element by
Monsieur and Madame Curie l of Paris, in 1898, resulted
from the fact that its presence in microscopic quantities
in tons of the mineral from which it was taken was de-
tected by its exceptionally large radio-active effects.
484. Radio-Activity. The property of radio-activity
was discovered by Henri Becquerel 2 of Paris in 1896. In
honor of the discoverer the radiations emitted by radio-
active substances are often called Itecquerel rays. Ex-
perimental researches have shown that Becquerel rays are
of a complex nature. They consist (1) of negatively
charged particles called beta rays, (2) of positively
charged particles called alpha rays, and (3) of radia-
tions resembling X-rays in nature, which are called
gamma rays.
Becquerel rays are detected not only by their power to
affect a photographic plate as shown in 483, but also by
their power to discharge electrified bodies near which they
are placed. This effect is due to the fact that the air
surrounding a radio-active body is rendered a conductor
of electricity by the radiations emitted. Furthermore,
if minute crystals of zinc sulphide be placed in the
immediate neighborhood of an extremely small quantity
of radium, they show intermittent flashes of light as they
are bombarded by the alpha particles expelled by the
radium.
485. Electrons. Beta rays, or the negatively charged
particles emitted by a radio-active substance, are called
negative electrons. Negative electrons are separated from
alpha and gamma rays on passing through a strong electric
or magnetic field on account of the difference in the kind of
charge carried by them. The path of the negative elec-
trons is curved in one direction by the field, while that of
1 See portrait facing page 470.
470 A HIGH SCHOOL COURSE IN PHYSICS
the alpha rays is bent in the opposite direction. The
gamma rays remain unchanged in direction.
Knowledge of electrons began with the discovery by Sir
J. J. Thompson of England that the cathode rays pro-
duced in a vacuum tube ( 480) consist of swiftly moving
particles charged with electricity. These particles have
since been found to be identical with the negative elec-
trons emitted by a radio-active substance. The speed
attained by the electrons in a cathode tube is about
62,000 miles per second, but the electrons emitted by
radium move with speeds that reach as high as 165,000
miles per second, which is about -f$ the velocity of
light.
The mass of an electron has been ascertained and found
to be about yyVir ^ ne mass f an atom of hydrogen. Dif-
ferences in the electrical, magnetic, and other properties
of matter are attributed to variations in the arrangements
and movements of the electrons associated with the mole-
cules. For example, in electrical conductors the electrons
are less firmly attached to the molecules than they are in
non-conductors, and are consequently moved readily by
potential differences. This motion of electrons through
a conductor constitutes an electric current.
486. Alpha Particles. The alpha rays emitted by a
radio-active substance are of atomic size and have been
found to be charged with positive electricity. Experi-
ments have also shown that they are atoms of the well-
known gas helium, and that their velocity may reach as high
as -^-Q the speed of light. The energy that is developed
by a radio-active body is due mainly to the alpha particles
which it hurls outward with this enormous rate of motion.
It is estimated that the total amount of energy that can
be given off by a gram of radium is about equal to that
developed by the combustion of a ton of coal.
ANTOINE HENRI BECQUEREL (1852-1908)
A new epoch in the theory of matter was
inaugurated by the discovery of radio-
activity in 1896 by Becquerel of Paris. It
had long been known that compounds con-
taining the element uranium would produce
an effect upon photographic plates in the
dark, This singular action had been attrib-
uted merely to their property of phosphor-
escence. Becquerel proved that all com-
pounds containing uranium act similarly on
plates, even those which are not phosphor-
escent. This phenomenon corresponds to a
continuous emission of energy, for which
the old view of matter did not account.
MADAME CURIE (1867- )
Soon after the discovery of radio-activ-
ity, investigations were made by Madame
Curie of Paris and others in order to as-
certain if radio-activity were not a general
property of matter. Various compounds
were tested; but the strange property
appeared to be confined to substances
containing uranium and another element,
thorium. However, it was observed by
Madame Curie that certain pitchblendes
(minerals containing oxide of uranium and
other well-known elements) were many
times more radio-active than uranium. It
therefore seemed probable that an unknown
element of great radio-activity was pres-
ent in the mineral. From this grew up the celebrated experiments of
Monsieur and Madame Curie which led to the discovery of the re-
markable element radium. Although the separation of radium from
minerals is attended with enormous difficulties on account of the
small quantity which they contain, enough of it has been secured for
experimental research in the laboratories of the world to lead to the
generalizations in regard to the constitution of matter contained in
the concluding sections of this book.
RADIATIONS 471
487. Disintegration of Matter. The emission of elec-
trons and of positively charged particles which are compar-
able in mass with atoms of hydrogen leads at once to the
conclusion that a radio-active substance must be continu-
ally experiencing a molecular change. Although a gram
of radium develops hourly an amount of heat equal to 100
calories, its transformation is so slow that nearly 13 centu-
ries would elapse before one half its mass would suffer a
change in its nature. Experiments have shown that it is
along with this transformation that the element helium is
produced. Thus the radio-active elements are not perma-
nent, but by the emission of electrons and alpha particles
they are being constantly transformed into elements of
smaller atomic weights. Uranium, for example, is sup-
posed to be breaking up and forming for one of its products
the element radium ; radium in turn forms so-called radium
emanation, and so on through a series. It is while these
transformations are going on that the alpha, beta, and
gamma rays are emitted.
According to the disintegration theory of matter ad-
vanced by Rutherford and Soddy, the atoms of radio-active
substances are unstable systems which break up spontane-
ously with explosive violence, expelling a small portion
of the fractured atom with great velocity. The remaining
portion of each atom forms a new system of a smaller
atomic weight and possessing properties differing from
those of the atoms of the parent substance. This new
substance may be unstable also and undergo an atomic
change similar to the preceding. The process may con-
tinue by stages until at last a stable form is finally
attained.
488. The Domain and Future of Physics. The study
of Physics is primarily an investigation of environment to
the end that the knowledge obtained shall be conducive to
472 A HIGH SCHOOL COURSE IN PHYSICS
the comfort of mankind, arid lead to an increase of man's
power in his range of action. If this were all, the pursuit
of physical science would be amply justified, for the field
is a broad one, and the results to which the study has led
are overwhelming. It has opened the entire world to
the traveler, it has brought the West within speaking
distance of the East, it has overthrown the dangers and
solitude of the sea, it has brought distant worlds within our
range of vision and exposed the sources of disease, it re-
veals the secret of aerial flight, and, now, at the present
rate of advancement man may soon acquire that knowledge
which the human mind has long sought to secure in answer
to the all-important question, " What is matter ? "
INDEX
Absolute temperature, 222.
Absolute units of energy, 52.
Absolute units of force, 30, 31.
Absorption, of heat, 253; of ra-
diant energy, 253; selective,
254; spectra, 327.
Accelerated motion, 17.
Acceleration, 16; due to gravity,
70; centripetal, 45.
Activity, 53.
Adhesion, 130.
Aeronauts, altitude reached by,
153.
Aeroplane, 43.
Air, buoyancy of, 154; compres-
sibility of, 147; density of,
138; pressure of, 139, 155;
variations in pressure of, 141.
Air brake, 161.
Alpha particles, 470.
Alternating currents, 434.
Alternator, 435.
Altitude, effect of, on barometer,
153; effect of, on boiling point,
242.
Amalgamation of zinc, 379.
Ammeter, 404.
Ampere, sketch and portrait of,
facing 406.
Amplitude, 74; effect of, on in-
tensity of sound, 174.
Aneroid barometer, 143.
Anode, 396.
Antinode, 194, 201.
Arc, lamp, 451; light, 450; elec-
tric, 450; enclosed, 451; flam-
ing, 451; open, 451.
Archimedes, 119; principle of,
119.
Armature, 392, 434; drum, 438;
Gramme ring, 437.
Artesian wells, 114.
Athermanous substances, 255.
Atmosphere, as unit of pressure,
142; density of, 138, 152, 153;
humidity of, 239; pressure of,
139.
Atoms, 471.
Attraction, electrical, 335; mag-
netic, 361; molecular, 130.
Balance, 10; spring, 10.
Balloon, 155.
Barometer, 142; aneroid, 143;
self-recording, 143; utility of,
144.
Battery, storage, 399.
Beats, 190; law of, 191.
Becquerel, sketch and portrait of,
facing 470.
Bell, diving, 162; electric, 392.
Binocular vision, 317.
Bodies, falling, 70; thrown, 72.
Boiling, 241; laws of, 242.
Boiling point, of liquids, 243 ; on
thermometers, 213.
Boyle's law, 149.
Bright-line spectra, 328.
Bunsen photometer, 276.
Buoyancy, of air, 154 ; of liquids,
119.
Caisson, pneumatic, 162.
Caloric, 257.
Calorie, denned, 225; electric
equivalent of, 415; mechanical
equivalent of, 258.
Camera, 312.
473
474
A HIGH SCHOOL COURSE IN PHYSICS
Candle power, defined, 276; of
lights, 275.
Capacity, electric, 348.
Capillarity, 132; in soil, 137; in
tubes, 133.
Capstan, 95.
Cathode, 396.
Cathode rays, 467.
Cell, chemical action in, 377 ;
Daniell, 385; dichromate, 384;
"dry," 387; gravity, 385; Le-
clanche", 386; local action in,
379; storage, 399; theory of,
378; voltaic, 375.
Cells, in parallel, 411; in series,
410.
Center of gravity, 65; of mass,
65; of oscillation, 79; of per-
cussion, 79.
Centimeter-gram-second system,
6.
Centrifugal force, 45.
Centripetal acceleration, 45.
Centripetal force, 45, 46.
Charges, electrical, 335; mixing,
348.
Charging, by contact, 338; by in-
duction, 342.
Charles, law of, 222.
Chemical effects of currents, 395.
Chord, major, 182.
Circuit, divided, 420; electric,
377.
Coefficient of expansion, of gases,
220; of liquids, 220; of solids,
217.
Coherer, 464.
Cohesion, 130.
Coil, induction, 429; magnetic
action of, 389.
Cold storage, 245.
Color, 321; and wave length,
322; by dispersion, 321; by in-
terference, 323; of films, 332;
of objects, 322; of pigments,
324; of transparent bodies,
323; complementary, 323.
Commutator, 436.
Compass, 368.
Component forces, 36.
Component motions, 21.
Composition, of forces, 36; of
motions, 21.
Concave lens, 301, 303.
Concave mirror, 284, 287.
Condenser, 349.
Conduction, of electricity, 338;
of gases, 466; of heat, 248.
Conductors, of heat, 248; charge
on outside of, 343.
Conjugate foci, of lenses, 304;
of mirrors, 289.
Conservation of energy, 59.
Convection, 249.
Convex lens, 301, 305.
Convex mirror, 284, 285.
Cooling, by expansion, 259; arti-
ficial, 245.
Couple, 41.
Critical angle, 297.
Crookes, sketch and portrait of,
facing 466.
Crookes' tubes, 467.
Curie, Mme., sketch and portrait
of, facing 470.
Currents, electric, 375; chem-
ical effect of, 395; heating
effect of, 394; induced, 425;
magnetic effect of, 388; meas-
urement of, 402; mutual effect
of, 393.
Curvature, center of, 284, 301.
Curvilinear motion, 44.
Daniell cell, 385.
Declination, 369.
Density, 10, 124; of air, 138;
of liquids, 127; of solids, 124;
atmospheric, 153; electric, 344.
Dew point, 240.
Diamagnetic substances, 362.
Diathermanous substances, 255.
Diatonic scale, 181.
Dichromate cell, 384.
INDEX
475
Dielectric, 350.
Dip, magnetic, 371.
Discharge, electric, 351; oscil-
latory, 462.
Dispersion, 321.
Distillation, 243.
Diver, 162.
Drum armature, 438.
"Dry" cell, 387.
Dynamo, 432 ; alternating-cur-
rent, 434; compound-wound,
440; rule of, 432; series-
wound, 439 ; shunt-wound,
439; unipolar, 440.
Dyne, 30.
Earth's magnetism, 368.
Ebullition, 237, 241; laws of,
241.
Echoes, 177.
Eclipses, 272.
Efficiency, 99; of lamps, 448,
449; of simple machines, 99.
Elastic force in gases, 148.
Electric bell, 392.
Electric car, 443.
Electric charge, unit of, 348 ; dis-
tribution of, 343.
Electric motor, 442.
Electrical attraction, 335.
Electrical circuits, 377.
Electrical currents, 375.
Electrical machines, 354.
Electrical repulsion, 336.
Electrical resistance, 405.
Electricity, current, 375; static,
335.
Electrolysis, 396.
Electro-magnet, 391.
Electro-magnetic induction, 425.
Electromotive force, 376; in-
duced, 426, 431.
Electrons, 469.
Electrophorus, 352.
Electroplating, 397.
Electroscope, 336.
Electrotyping, 398.
Energy, 54; of the sun, 255;
conservation of, 59; electric,
413; equation for, 56; heat,
210; kinetic, 56; potential,
55; radiant, 253; transfer-
ences and transformations of,
58.
Engine, gas, 261; steam, 260;
turbine, 263.
English equivalents of metric
units, 5, 6, 8, 53.
Equilibrant, 38.
Equilibrium, 66; neutral, 67;
stable, 66; unstable, 66.
Erg, ^
Ether, 252, 268, 463.
Evaporation, 237; laws of, s 237.
Expansion, 216; of gases, 147,
221; coefficient of, 217; un-
equal, 218.
Extension, 2, 4.
Eye, 312.
Falling bodies, 69.
Faraday, sketch and portrait of,
facing 426.
Field, electric, 340; magnetic,
363.
Field-magnet of dynamo, 439.
Floating bodies, 122.
Floating dry dock, 123
Fluids, 138.
Focal length, of lens, 302; of
mirror, 285.
Focus, conjugate, 289, 304; prin-
cipal, 284, 302; real, 285; vir-
tual, 285, 304.
Foot-pound, 52.
Foot-pound-second system, 10.
Force, 29; centrifugal, 45; cen-
tripetal, 45, 46; component of,
36; composition of, 36; field
of, 340; lines of, 340, 363;
moment of, 39; parallelogram
of, 37; representation of, 35;
resolution of, 42; units of,
30, 31.
476
A HIGH SCHOOL COURSE IN PHYSICS
Forces, parallel, 40.
Franklin, sketch and portrait of,
facing 346.
Fraunhofer lines, 327.
Freezing, 231; heat given out
during, 235.
Friction, 99; rolling, 100.
Fundamental tone, 194, 200.
Fusion, 231; of ice, 234; heat of,
233; laws of, 232.
Galileo, sketch and portrait of,
facing 70.
Galvanometer, 382; astatic, 403;
d'Arsonval, 403; tangent, 403.
Gas engine, 261.
Gases, characteristics of, 138;
compressibility of, 147.
Gilbert, 368.
Gram, of force, 32; of mass, 7.
Gramme ring, 437.
Gravitation, law of, 62.
Gravity, acceleration due to, 70;
center of, 65; force of, 63;
variation of, 70.
Gravity cell, 385.
Guericke, Otto von, 155.
Harmonic, 196.
Heat, 210; due to absorption of
radiant energy, 255; due to
electric current, 415; of fusion,
233; of sun, 255; of vaporiza-
tion, 249; conduction of, 248;
convection of, 249; measure-
ment of, 225; mechanical
equivalent of, 258; produced
by compression, 210; produced
by friction, 210; radiation of,
252; specific, 226; unit of,
225.
Heating, by hot air, 250; by hot
water, 251; electrical, 394.
Helmholtz, sketch and portrait
of, facing 196.
Henry, sketch and portrait of,
facing 426.
Hertz, sketch and portrait of,
facing 464.
Horse power, 53; electric equiva-
lent of, 415.
Humidity, 240.
Huyghens, 79, 268.
Hydraulic elevator, 117.
Hydraulic press, 112.
Hydraulic ram, 118.
Hydrometers, 127.
Hydrostatic paradox, 109.
Ice, artificial, 245.
Images, by double reflection, 282 ;
by lenses, 305, 307; by plane
mirror, 280; by spherical mir-
rors, 284; pin-hole, 273; real,
287; size of, 310; virtual, 287.
Incandescent lamp, 447.
Incandescent lighting, 447, 449.
Incidence, angle of, 279, 293.
Inclination of magnetic needle,
371.
Inclined plane, 96.
Index of refraction, 294; meas-
ured, 295.
Induced charges, 342.
Induced magnetism, 362.
Induction, charging by, 342;
electro-magnetic, 425; electro-
static, 340; magnetic, 362.
Induction coil, 429.
Inertia, 29.
Influence machine, 354.
Insulators, 338.
Intensity, of light, 275; of
sound, 173.
Interference, of light, 330; of
sound, 188.
Intervals, 182.
Ions, 378, 396.
Isobars, 145.
Isogonic lines, 370.
Jackscrew, 98.
Jar, Leyden, 351.
INDEX
477
Joule, sketch and portrait of,
facing 258.
Joule's equivalent, 258.
Joule's law, 415.
Kelvin, Lord, sketch and por-
trait of, frontispiece.
Key, tone, 181; telegraph, 453.
Kilogram, standard, 7.
Kilogram-meter, 52.
Kinetic energy, 56; equation of,
56.
Kinetoscope, 317.
Kirchoff, 328.
Lamps, arc, 450; incandescent,
447; Nernst, 448.
Lantern, projection, 316.
Laws of motion, 28.
Leclanche cell, 386.
Lenses, 300; achromatic, 322;
concave, 301, 303; converging,
302; convex, 301, 305; diverg-
ing, 303; equation of, 310.
Lenz's law, 427.
Level, liquid, 110.
Lever, 88; kinds of, 89; mechan-
ical advantage of, 89.
Ley den jar, 351.
Light, dispersion of, 321; inter-
ference of, 330; meaning of,
268; reflection of, 278; refrac-
tion of, 292; speed of, 269.
Lightning, 345.
Lightning rods, 345.
Lines, of force, 340; isogonic,
370.
Liquefaction, see Fusion.
Liquid, in communicating ves-
sels, 110; density of, 127; pres-
sures in, 103; pressures trans-
mitted by, 111; surface ten-
sion of, 132; thermal conduc-
tivity of, 248.
Liter, 6.
Local action, 379.
Lodestone, 359.
Longitudinal loops, 194.
Longitudinal waves, 171.
Loudness of sound, 173.
Machines, efficiency of, 99; elec-
trical, 354; general law of, 84;
simple, 83.
Magdeburg hemispheres, 147.
Magnet, artificial, 361 ; electro-,
391; horseshoe, 361; natural,
359; poles of, 360.
Magnetic attraction, 361.
Magnetic field, 363.
Magnetic induction, 362.
Magnetic lines of force, 363.
Magnetic needle, 368.
Magnetic repulsion, 361.
Magnetic substances, 361.
Magnetism, induced, 362; terres-
trial, 368; theory of, 366.
Magnifier, simple, 311.
Major chord, 182.
Major scale, 181.
Mass, 3; center of, 65; measure-
ment of, 9; unit of, 7.
Matter, 2; indestructibility ol,
3; states of, 11.
Maxwell, sketch and portrait of,
facing 432.
Mechanical advantage, 85.
Mechanical equivalent of heat,
258.
Melting point, 231; laws of, 232.
Meter, standard, 4.
Metric system, 4.
Microphone, see Transmitter.
Microscope, 315.
Mirrors, 278; concave, 284; con-
vex, 285; images by, 281, 286,
287; principal focus of, 284.
Mixtures, method of, 227.
Molecular energy, 211.
Molecular forces, 130.
Molecular theory of heat, 211.
Molecules, 130.
Moment of force, 89.
Momentum, 28.
478
A HIGH SCHOOL COURSE IN PHYSICS
Mont Blanc, 153.
Morse, 453.
Motion, 13; accelerated, 17; cir-
cular, 44 ; compounded, 24, 29 ;
first law of, 28; perpetual,
259; rectilinear, 13; second law
of, 30; third law of, 33; uni-
form, 13.
Motor, electric, 442; water, 115.
Musical instruments, 197, 202.
Musical scale, 180.
Needle, dipping, 371; magnetic,
368.
Newton, sketch and portrait of,
facing 30.
Newton's law of gravitation, 62.
Newton's lawa of motion, 28,
30, 33.
Nodes, in pipes, 201; in strings,
194.
Noise, 179.
Non-conductors, 339.
Octave, 182.
Oersted, sketch and portrait of,
facing 382.
Ohm, sketch and portrait of,
facing 406; unit, 406.
Ohm's law, 408.
Opaque bodies, 271.
Opera glass, 316.
Optical center, 308.
Optical instruments, 311.
Organ pipes, open, 199; overtones
in, 201; stopped, 199.
Oscillation, center of, 79.
Oscillatory discharge, 462.
Overtones, 194, 201.
Parallel connection of cells, 411.
Parallel forces, 40.
Parallelogram of forces, 37.
Partial tones, 194.
Pascal, 112, 141.
Pascal's law, 111.
Pendulum, compound, 78; sim-
ple, 74.
Percussion, center of, 79.
Period of vibration, 74.
Permeability, 3G4.
Phenomenon, 1.
Phonograph, 204.
Photoweter, Bunsen's, 276.
Physics, definition of, 1.
Pigments, color of, 324; mixing,
324.
Pisa, tower of, 68, 69.
Pitch, 179; of pipes, 109; of
strings, 192; wave length and,
173.
Points, effect of, 344.
Polarization of cells, 383.
Poles, magnetic, 360.
Potential, difference of, 347; fall
of, 381; zero, 347.
Potential energy, 55.
Power, 53; candle, 276; electri-
cal, 414.
Pressure, in liquids, 1Q3-; of com-
pressed air, 160; of gases, 148;
of saturated vapor, 238; at-
mospheric, 139.
Primary coil, 429.
Principle of Archimedes, 119.
Prism, dispersion by, 321; re-
fraction by, 298.
Pulley, 85.
Pump, air, 155; common lift,
156; condensing, 156; force,
158.
Quality of sounds, 196.
Radiant energy, 253; absorption
of, 253.
Radiation, 252; electrical, 463.
Radio-activity, 468.
Radiometer, 255.
Radium, 468.
Rainbow, 325.
Ray, of light, 281; alpha, 469;
beta, 469; cathode, 467; gam-
ma, 469.
Receiver,' telephone, 457, 458.
INDEX
479
Reeds, 204.
Reflection, of light, 278; of
sound, 176; angle of, 279;
double, 282 ; law of, 278 ; total,
296.
Refraction, 292; explained, 293;
index of, 294; laws^pf, 293.
Regelation, 233.
Relay, 455.
Resistance, of batteries, 409; of
wires, 417; electrical, 409;
laws of, 405; measurement of,
418; unit of, 406.
Resistance coils, 418.
Resolution of forces, 42.
Resonance, 185; explained, 187.
Resultant, 21, 38.
Retentivity, 362.
Reversibility of pendulum, 79.
Roemer, 269.
Rontgen, sketch and portrait of,
facing 466.
Rontgen rays, 467.
Rowland, 258.
Rumford, sketch and portrait of,
facing 256.
Rutherford, 471.
Sailboat, 43.
Saturation, of vapors, 238.
Saturation pressure, 238; mag-
netic, 267.
Scale, diatonic, 181 ; musical, 180.
Screw, 97; mechanical advantage
of, 98.
Secondary coil, 429.
Seconds pendulum, 78.
Series connections, 410, 420.
Shadows, 271.
Sharps and flats, 183.
Shunts, 421.
Siphon, 159.
. Siren, 180.
Soap films, 130; color in, 332.
Soddy, 471.
Solar spectrum, 324 ; elements of,
329.
Solenoid, 390.
Solids, density of, 124; sound in,
168.
Sonometer 192.
Sound, 166; air as a medium of,
167 r> cause of, 165; intensity
of, 173$ interference of, 188;
musicafc 179; quality of, 196;
reflecti&i of, 176; speed of,
168; wi-ve motion of, 169.
Sounder, ilelegraph, 453.
Sounding boards, 176.
Spark, electric, 352, 356, 430,
463.
Specific gravity, 126.
Specific heat, 226; measurement
of, 227.
Spectacles, 313.
Spectra, 324; bright-line, 328;
conti|ajDUS, 327 ; elements iden-
tifiecnSy, 329.
Speed, of light, 269; of sound,
168.
Stability, 67.
Stable equilibrium, 66.
Steam engine, 260.
Steam turbine, 263.
Steelyard, 93.
Stereoscope, 317.
Storage cell, 399.
Strength, current, 402.
Strings, laws of, 192, 193.
Substance, 3.
Suction pump, 157.
Sun, as source of energy, 255.
Surface tension, 132.
Suspension, point of, 79.
Sympathetic vibrations, 185.
Telegraph, 453; wireless, 464.
Telephone, electric, 457; mechan-
ical, 201.
Telescope, 315; Galileo's, 316.
Temperament, 184.
Temperature, 208 ; absolute, 222 ;
low, 223 ; measurement of, 212 ;
scales of, 213.
480
A HIGH SCHOOL COURSE IN PHYSICS
Tempered scales, 184.
Tempering, 184.
Thermal capacity, 226.
Thermometer, centigrade, 213;
comparison of, 214; dial, 218;
Fahrenheit, 214; fixed points
of, 212; Galileo's air, 215;
* graduation of, 213; range of,
215.
Thunder, 345.
Time, unit of, 11.
Toeppler-Holtz electrical ma-
chine, 354.
Torricelli's experiment, 141.
Transformation of energy, 58.
Transformer, 445.
Transmission, of electricity, 415;
of heat, 247; of light, 268; of
sound, 167.
Transmitter, 458.
Transparent bodies, color of, 323.
Transverse waves, 170.
Tuning fork, 185.
Turbine, water, 116; steam, 263.
Units, of area, 6; of candle pow-
er, 276 ; of capacity, 6 ; of cur-
rent, 402; of electricity, 348;
of force, 30; of heat, 225; of
length, 4; of mass, 7; of po-
tential, 407; of power, 53; of
resistance, 406; of time, 11;
of volume, 6; of work, 52.
Vacuum, Torricellian, 142.
Vapor, 237; saturated, 238.
Vapor pressure, 238.
Vaporization, 243; heat of, 249.
Vector, 16.
Velocity, 14; at any instant, 15;
of falling bodies, 71; of light,
269; of sound, 168; average,
15; composition of, 22, 24;
representation of, 15.
Ventilation, 451. .
Vibrating body, 165.
Vibration, of pipes, 200; of
strings, 192; sympathetic, 185.
Vibration numbers, 181, 184.
Volt, 407.
Volta, 375; sketch and portrait
of, facing 352.
Voltaic cell, 375.
Voltmeter, 407.
Water, abnormal expansion of,
220; city supply of, 114; den-
sity of, 10J.; greatest density
of, 221.
Water wheels, 115.
Water turbine, 116.
Watt, 54, 415.
Watt-hour, 449.
Wave length, 173; of light, 322;
equation of, 173.
Waves, electrical, 463; kinds of,
170; longitudinal and trans-
verse, 170; sound, 171; trans-
mission of, 171.
Wedge, 98.
Weighing devices, 10.
Weight, 263; and mass, 9; law
of, 63.
Wheatstone's bridge, 419.
Wheel and axle, 93; mechanical
advantage of, 94.
White light, 321.
Windlass, 94.
Wireless telegraphy, 464.
Work, 51; principle of, 83; rate
of, 53; units of, 52.
X-rays, 467; properties of, 468.
Yard, metric equivalent of, 5.
Zero potential, 347.
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