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>
GIFT or
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PRACTICAL PHYSICS
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THE MACMILLAN COMPANY
HIW YORK • BOSTON ■ CHICAGO • DALLAS
ATLANTA • SAN FRANCISC6 >-^\
MACMILLAN & CO., Limitbd
LONDON • BOMBAY • CALCUTTA
MBLBOUKNB
THE MACMILLAN CO. OF CANADA, Lux
TORONTO
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X
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Galileo Galilei. Born 1564, in Pisa, Italy. Died 1642. Often called
** the father of modern science " because he was one of the first who
thought it worth while to subject his ideas to the test of experiment.
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PRACTICAL PHYSICS
FUNDAMENTAL PRINCIPLES AND
APPLICATIONS TO DAILY LIFE
BY
N. HENRY BLACK, A.M.
SCIENCE MASTER, ROXBURT LATIN SCHOOL
BOSTON, MASS.
AND
HARVEY N. DAVIS, PkiSJ V
ASSISTANT PROFESSOR OF PHTfliCS^ ^ , -
HARVAKD UNIVERSltf ' " ' " '
THE MACMILLAN COMPANY
1921
ill rigfiti retervtd
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ooptbiqht, 1918,
Bt the MACMILLAN COMPANTo
• • *••' SeCji*^4id>lectrotypcd. Published June, 1913.
•: • . •
J. S. Gushing Co. — Berwick & Smith Oow
Norwood, Mass., U.S.A.
J' ■
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PREFACE
The most diflBcult problem which confronts any author of
a textbook is the selection of material. This is usually a
process of exclusion. One has always to keep in mind the
capacities and limitations, the interests and inclinations, of
the young people most directly concerned, as well as the
beauty and vast extent of the subject to be taught. This is
especially true of a first course in physics. The number of
suitable topics is far greater than can be well handled in any
one-year course, however substantial it may be. A good
book may, therefore, be judged as well by its omissions as in
any other way. In preparing this book, we have tried to
select only those topics which are of vital interest to young
people, whether or not they intend to continue the study of
physics in a college course.
In particular, we believe that the chief value of the infor-
motional side of such a course lies in its applications to the
machinery of daily life. Everybody needs to know some-
thing about the working of electrical machinery, optical
instruments, ships, automobiles, and all those labor-saving
devices, such as vacuum cleaners, fireless cookers, pressure
cookers, and electric irons, which are found in many modern
homes. We have, therefore, drawn as much of our illus-
trative material as possible from the common devices in
modern life. We see no reason why this should detract in
the least from the educational value of the study of physics,
for one can learn to think straight just as well by thinking
about an electrical generator, as by thinking about a Geissler
tube.
V
459953
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VI PREFACE
This does not mean that we have tried to make the sub-
ject interesting by selecting only the easy topics. There are
many parts of physics which' are of great practical value, but
are essentially diflScult. We have tried to present these
subjects very slowly and carefully, believing that if any
presentation is so simple and direct that the student can
understand it clearly, his very understanding begets at once
the interest which is fundamental.
Even after a careful exclusion of material, we have selected
somewhat more than it is probably advisable for any class to
undertake in a single year. This gives the teacher an oppor-
tunity to adapt his instruction to the local needs of his com-
munity and to the amount of time available. In particular,
the chapter on the strength of materials, the discussion of
momentum, the chapter on the beginnings of electricity, the
chapter on alternating currents, the chapter on electric waves
and X-rays, and even the chapter on sound, may well be
omitted altogether, or assigned for outside reading without
careful discussion, if it seems desirable. We believe that it
is most important for teachers to select carefully just what
material they can best use, and to teach that thoroughly^
rather than try to touch upon many topics superficially.
We think it of great importance that the topics in a course
in physics should be arranged in the most teachable order ;
that is, with the easiest and simplest topics first. Thus in
miechanics, the subject of acceleration and Newton's laws is
essentially hard, and so we have put it at the end of that
part of the book. On the other hand, the simple machines,
such as the lever and the wheel and axle, are essentially
easy, and so they come first.
To understand any machine clearly, the student must
have clearly in mind the fundamental principles involved.
Therefore, although we have tried to begin each new topic,
however short, with some concrete illustration familiar to
young people, we have proceeded, as rapidly as seemed wise.
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PREFACE Tli
to a deduction of the general principle. Then, to show how
to make use of this principle, we have discussed other prac-
tical applications. We have tried to emphasize still further
the value of principles, that is, generalizations, in science, by
summarizing at the end of each chapter the principles dis-
cussed in that chapter. In these summaries we have aimed
to make the phrasing brief and vivid so that it may be
easily remembered and easily used.
The problems are the result of considerable experience in
trying to find suitable numerical exercises which will empha-
size and illustrate the principles involved, with a minimum
of arithmetical drudgery. They, too, are arranged, within
^ach group, as far as possible in the order of their difficulty.
It should always be emphasized, however, that the study of
physics does not begin and end in the classroom, but is inti-
mately connected with industrial and domestic life. It is
very desirable to stimulate in students thought and imagina-
tion about what they see, and to get them into the habit of
asking intelligent questions of the mechanics, artisans, and
engineers whom they meet. We have, therefore, added at
the end of each of the earlier chapters, and in many places in
the later chapters, questions^ which require some knowledge
gained in this way from outside life. We do not expect
that every student can answer even a majority of these ques-
tions at first ; but after he has tried to answer them, he is in
a position to learn a great deal from the subsequent discussion
of them in the classroom.
Our treatment of acceleration, Newton's laws, kinetic en-
ergy and momentum, is essentially different from either the
dyne and poundal method common in physics textbooks, or
the " slug " or " wog " method of engineers, and is apparently
new. It has, however, been thoroughly tried out in the
classroom, and we find it simpler and more direct than the
usual presentation. We feel sure that it is as precise and
scientific in its logic as any other. It was first developed by
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viii PREFACE
Professor E. V. Huntington, of Harvard University, to whom
we gladly make acknowledgment of priority.
We have borrowed ideas also from the books of Mr. Frank
M. Gilley, of the Chelsea High School, and Director E.
Grimsehl, of Hamburg, Germany. We have received valu-
able assistance in the preparation of the mannscript from
Professor Frank A. Waterman, of Smith College ; Mr. Irving
O. Palmer, of the Newton Technical High School ; Professor
J. M. Jameson and Professor J. A. Randall, of Pratt Insti-
tute, and many others. To all of these gentlemen we give
our hearty thanks.
We are indebted to the Geneial Electric Company, the
Westinghouse Companies, the Columbia Graphophone Com-
pany, Stone and Webster, and others for material for certain
of the plates and illustrations.
. Finally, we wish especially to express our obligation to
Dr. William C. Collar, lately of the Roxbury Latin School,
and to Professor W. S. Franklin, of Lehigh University, but
for whose initiative, encouragement, and interest, this book
never would have been written.
We shall be grateful for corrections or suggestions from
any source.
N. H. B.
H. N. D.
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CONTENTS
CBAPTXB PAOl
I. Introduction : Weights and Measures • • . 1
11. Simple Machines 13
III. Mechanics of Liquids 47
IV. Mechanics of Gases 77
V. Non-parallel Forces 105
VI. Elasticity and Strength of Materials . . . 120
VII. Accelerated Motion 133
VIII. FoRdE AND Acceleration , . 146
IX. • Energy and Momentum 157
X. Heat — Expansion and Transmission . . . 170
XI. Water, Ice, and Steam 196
XII. Heat Engines 219
XIII. Magnetism . . 238
XIV. The Beginnings of Electricity . . ... . 24fe
XV. Battery Currents 263
XVI. Measuring Electricity 281
XVn. Induced Currents 308
XVIIL Electric Power 318
XIX. Alternating Current Machines .... 358
XX. Sound 374
XXI. Lamps and Reflectors 405
XXII. Lenses and Optical Instruments . . » . 427
XXni. Spectra and Color ....... 456
XXIV. Electric Waves: Roentgen Rays . . • . 469
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PRACTICAL PHYSICS
CHAPTER I
INTRODUCTION: WEIGHTS AND MEASURES
Why study physics — content and divisions of physics —
physics involves measurement as well as merely description
— units in English and metric systems — density.
1. Why study physics ? Every one these days has had
something to do with machines of one sort or another all his
life. In the country we mow, reap, and thresh grain with
machines ; we pump water with windmills, gas or hot-air en-
gines ; and we skim milk with a machine called a separator.
In the city we travel on electric cars; we go upstairs on
hydraulic or electric elevators ; we print our newspapers on
presses run by electric motors ; and we distribute our mail
through pneumatic tubes. In business and in commerce we
are constantly using steam, gas, and electric engines, cranes
and derricks, locomotives, ships, and automobiles, and per-
haps, in a few years, we shall all be using flying machines.
Every one has used some of these devices and almost every
one has at some time wondered and perhaps discovered how
each of them works. That is, almost every one has already
begun to study phfsies^ for it is one of the chief aims of
physics to discover all that can be known about such ma-
chines as have just been mentioned.
2. Physics a science. The sort of physics that will be
found in this book differs from the sort that every one has
been unconsciously studying all his life, chiefly in that it
seeks to answer not only the questions "why'' and "how,"
but also the questioxi "how much." It is only when we
B 1
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2 PRACTICAL PHY8IC8
begin to measttfe. things definitely that we get the kind of
information that helps us to use them to the best advantage.
Thus every one knows in a vague way that an automobile
goes up a hill because the gasolene which is burned in the
engine makes it turn the driving wheels, and these in turn
push against the road, if it is not too slippery, and thus pro-
pel the automobile. The physicist, when he had thought of
all this, would go on to ask himself such questions as " How
much gasolene does it take, how much ought it to take under
ideal conditions, and what becomes of the difference ? How
much force inust be exerted by the brakes to hold the auto-
mobile on a hill, how large a brake surface will do this, and
how strong must the brake wire be?" When he can answer
all these and many other questions, he is in a position to use
his machine more effectively, and perhaps to improve its
mechanism.
3. Divisions of physics. The object of studying physics
is, then, chiefly to learn to think accurately about very
familiar things. But these things are so various in kind
that we shall find it convenient to divide the whole- subject
into five divisions : mechanics, heat, electricity, sound, and
light. For example, suppose we wanted to make a thorough
study of the automobile. Under mechanics, we should study
about its cranks, gears, levers, valves, and brakes, including
their movements^ and the strength of the material of their
construction ; under heat, the engine, its fuel and radiator ;
under electricity, the spark plug, spark coil, magneto, and
battery ; under sound, the horns and trumpets ; and finally,
under light, the lamps and their reflectors and lenses. In a
similar way it might be shown that any piece of modern
machinery, whether it is an automobile or a locomotive, a
motor boat or an Atlantic liner, a flying machine or a sub-
marine boat, is not only an embodiment of the principles of
physics, but has in very large measure been made possible
by the science of physics.
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introduction: weights and measures 8
4. Physics contains some abstractions. While it is true
that physics has to do chiefly with familiar thing^s yet in
order to make its study effective we shall also have to consider
some things which are not so familiar, such abstractions as
density and calories and wave length and refraction and
electrical resistance, which may not be interesting at first,
and may seem to have little to do with our everyday life.
We shall also find many problems to be solved whose answers
will seem trivial and unimportant. These things should be
done patiently because they pave the way for more valuable
things later on.
5. Physics begins with measurements. At the very out-
set we may well recall an old saying of Plato's : " If arith-
metic, mensuration, and weighing be taken away from any
art, that which remains will not be much." In the labora-
tory the student will learn to measure many different kinds
of things, not mainly for the sake of the results he gets, but
rather that all through life he may know a good measure-
ment when he sees one, and may be able to discuss accurately
and with confidence the quantitative problems that are al-
ways coming up.
6. Units of meastirement. In business in the United States
the value of things that are bought and sold is measured in
dollars and cents. Fortunately this system of money is made
on the decimal plan, that is, in multiples of ten. Our sys-
tem of weights and measures, on the other hand, is not a
decimal system, and is very inconvenient. Nevertheless,
since the pound, foot, quart, gallon, and bushel are still in
general use in Great Britain and in the United States, we
must be familiar with them. During the last century most
of the other civilized nations have adopted the metric system
of weights and measures, in which the relation of the units
is expressed in multiples of ten. In scientific work the met-
ric system is almost universally used throughout the world,
because it greatly reduces the work in making computations.
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4 PRACTICAL PHT8IC8
Therefore it is advisable for us to become proficient in the
use of both the English and the metric system of weights
and measures.
7. Meter and yard. The meter is the distance between
two lines on a m^tal bar (Fig. 1) which is preserved in the
vaults of the International Bureau
of Weights and Measures near
Paris.*
Since the length of this metal
bar changes a little with the tem-
perature, the distance is measured
at the temperature of melting ice.
A very accurate copy of this bar
FiQ. 1. — The international is deposited in the United States
^^ ^' Bureau of Standards in Washing-
ton, D.C., and this copy is the legal meter of the United
States.
In the United States the yard is legally defined as |f^ of
a meter.
8. Some important units of length. In the problems of
physics we shall find that certain units of length are
very frequently used. These are given in the following
table :
ENGLISH.
Units op Length
1 foot (ft.) = 12 inches (in.).
1 yard (yd.) = 3 feet.
1 mile (mi.) = 5280 feet.
* It wag originally intended that the meter should be equal to one ten-
millionth part of the distance from the equator to either pole of the earth, but
it is impossible to reproduce an accurate copy of the meter on the basis of
this definition. Later measurements have shown that the '^ mean polar
quadrant " of the earth is about 10,002,100 meters.
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1 Square
Dentimetei
INTRODUCTION: WEIGHTS AND MEASURES 6
METBIC.
1 meter (m.) = 1000 millimeters (mm.).
1 meter = 100 centimeters (cm.).
1 kilometer (km.) = 1000 meters.
1 inch = 2.540 centimeters.
1 meter = 39.37 inches.
CEKTIMETEBS
O INCHES 12 8
Fig. 2. —Relative sizes of the inch and the centimeter.
9. Ijnits of area. The unit of area which is most exten-
sively used is the area of a square of which the side is of unit
length. Thus the area of a city house lot
is reckoned in square feet, where the unit
is a square one foot on each side. In the
laboratory, area is often measured in square
centimeters (cm^), the unit being a square
one centimeter on each side. It is evident
from figure 3 that one square inch is equal
to about 6 square centimeters. More ac-
curately, it is 2.54 X 2.54, or 6.45 square
centimeters.
The usual method of determining area is by calculation from the
measured linear dimensions. Thus the area of a rectangle or parallelo-
gram is equal m the base times the altitude (A = h x h). The area of a
triangle is equal to i the base times the altitude (A = ^h x h)» The area
of a circle is equal to 3.14 times the square of the radius (^ = ttt^).
10. Units of volume or capacity. The unit of volume that
is most extensively used is the volume of a cube of which the
edge is of unit length. Thus the volume of a freight car is
reckoned in cubic feet, the unit being a cube one foot on each
edge. In the laboratory we measure the capacity of a flask
in cubic centimeters (cm^).
1 Sqaare Inch
Fig. 3.— Relative sizes
of the square inch
and the square cen-
timeter.
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6
PRACTICAL PHYSICS
Units of Volume
ENGLISH.
1 cubic foot (cu. ft.)= 1728 cubic inches (cu. in.).
1 cubic yard (cu. yd.)= 27 cubic feet.
1 gallon (gal.) = 4 quarts (qt.) = 231 cubic inches.
METRIC.
1 liter (1.) = 1000 cubic centimeters (cm^)
1 cubic meter (m^) = 1000 liters.
1 liter ==1.06 quarts.
The usual method of determiniDg the volume of a regular
solid is by calculation from the measured linear dimensions.
Thus to get the volume of a rectangular block of stone, or a
box, we find the product, length by width by depth. In the
case of a cylindrical figure we compute the area of the circu-
lar base (^rr^), and multiply by the height.
For measuring liquids, we ordinarily use a graduated ves-
sel of metal or glass. Thus in the English system we have
gallon and quart measures, anil for small quantities, fiuid
ounces (sixteenths of a pint). In the metric system, we have
in the laboratory graduated cylinders (Fig. 4) for measur-
ing liquids in cubic centimeters.
Fig. 4. — a
graduated
cylinder.
Problems
1. Change 2.55 meters to centimeters.
2. Change 1576 cubic centimeters to liters.
3. A boy is 5 feet 6. inches tall. Express his height in centimeters.
4. Express 1 kilometer as a decimal part of a mile.
6. The Falls of Niagara on the American side are about 165 feet high
Express this in meters.
6. A standard size of automobile tire is 5 inches in diameter and
fits a 38-inch wheel. Express these dimensions in the metric system.
7. If you wanted to buy 1} yards of silk in Paris, what length should
you ask for?
8. A certain type of Bleriot monoplane has a wing surface of 15
square meters. Express this in square feet.
9. How many gallons in a cubic foot ?
10. Milk sells in Berlin for 40 pfennigs per liter. What is its cost in
cents per quart? (100 pfennigs = 1 mark = 90.238.)
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INTRODUCTION: WEIGHTS AND MEASURES 7
11. How many liters does a tank hold which is 3 meters long, 1.5
meters wide, and 1 meter deep?
12. A cylindrical berry box is measured and found to be 6.15. inches
in diameter and 2.1 inches deep. What is its capacity in dry quarts?
(In the United States it is understood that a dry quart contains 67 ^
cubic inches.)
11. Units of weight.* The kUogram is the weight of a
certain platinum-iridium cylinder that is preserved with the
standard meter near Paris, or that of a very accurate copy of
this cylinder which is deposited in the United States Bureau
of Standards in Washington. It was intended that these
cylinders should weigh the same as one liter of pure water,
but this has turned out to be not quite true.f It is, however,
nearly enough true for our present purposes. Therefore the
gram, which is the one-thousandth part of a kilogram, is the
weight of one cubic centimeter of water. It may be helpful to
remember that our 5-cent nickel piece weighs 5 grams and
our silver half-dollar weighs 12.5 grams.
In the United States the pound avoirdupois is defined
legally as 2:204622 ""* ^ ^^^1^8^*°^-
ENGLISH.
METRIC.
Units op Weight
1 pound (lb.) = 16 ounces (oz.).
1 ton (T.) = 2000 pounds.
1 gram (g.) = 1000 milligrams (mg.).
1 kilogram (kg.) = 1000 grams.
1 kilogram =2.20 pounds.
1 cubic foot of water weighs 62.4 pounds.
1 cubic centimeter of water weighs 1 gram.
* The distinction between weight and mass will be made in section 148.
t One liter of pure water at ^° C. weighs 0.999972 kilogram.
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8
PRACTICAL PHYSICS
12. Weighing machines. The spring balance (Fig. 5) is a
simple machine for getting the weight of things, or for meas-
uring forces of other kinds, such as the pull exerted
by a rope. It consists of a coiled spring, and the
force exerted is indicated by the pointer on the scale.
The spring balance is very extensively used because
of its great convenience, and its indications are close
enough for many practical purposes.
The platform balance (Fig. 6) consists of a delicately
mounted equal-arm balance-beam with pans supported
at each end. The balance is used to show the equal-
ity of the weights of two bodies ; that is, two things
are said to have the same weight if they balance each
other when supported on the ends of an equal-arm balance.
The determination
of the weight of
any given body by
the platform bal-
ance depends upon
the use of a set of
weights, which may
be combined in
such a way as to
match the weight
of a body.
Fig. 5.
Spring
balance.
Fio. 6.— Platform balance.
Problems
1. Change 755 milligrams to grams.
2. Change 1540 grams to kilograms.
3. A girl weighs 52.5 kilograms. Express her weight in pounds.
4. American railways usually allow each passenger 150 pounds bag-
gage. Express this in kilograms.
5. A metric ton is 1000 kilograms. How many pounds is this in
excess of the English ton ?
6. It is sometimes said, " A pint is a pound, the world around." How
much does a pint of water weigh? (1 quart = 2 pints.)
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INTRODUCTION: WEIGHTS AND MEASURES
9
7. A bottle is found to hold 1520 grams of water : (a) how many
cubic centimeters does it contain ? (h) how many liters ?
8. A boy 5 feet 4 inches tall, and weighing 140 pounds, can walk 3.75
miles in an hour. Express these facts in metric units.
13. Density. Every one knows that lead is "heavier "than
cork, and yet the question " which is heavier, a pound of lead
or two pounds of cork?" is foolish. The colloquial word
" heavy " has two distinct meanings. Two pounds of cork
are heavier than one pound of lead in the same sense that two
pounds of coal are heavier than one pound of coaL In this
case the word "heavy" refers to the total weight of the
material. On the other hand, lead is " heavier " than cork in
the sense that a piece of lead weighs more than an equal bulk
of cork. The word "density" is used to designate more
precisely this inherent property of the lead and the cork.
That is, lead has a greater density than cork.
The density of a substance is its weight per unit volume.
Thus the density of water is about 62.4 pounds per cubic
foot, or 8.34 pounds per gallon. The density of copper is
555 pounds per cubic foot or 0.321 pound per cubic inch.
In scientific work it is usual to specify the density of a sub-
stance in grams per cubic centimeter (g/cm^).
Table of Densities
(In grams per cubic centimeter)
Platinum
21.5
Hard woods (seasoned) 0.7-1.1
Gold
19.a
Soft woods (seasoned) 0.4-0.7
Mercury
13.6
Ice 0.911
Lead
11.4
Human body 0.9-1.1
Silver
10.5
Cork 0.25
Copper
8.93
Sulphuric acid (cone.) 1.84
Iron
7.1-7.9
Sea water 1.03
Zinc
7.1
Milk 1.03
Glass
2.4-4.5
Fresh water 1.00
Marble
2.5-2.8
Kerosene 0.8
Granite
2.5-3.0
Gasolene 0.7
Aluminum
2.65
Air about 0.0012
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10 PRACTICAL PHYSICS
14. Measurement of density. The simplest way to deter-
mine the density of a substance is to weigh the substance
and measure its volume.
Thus a piece of pine 6 feet long, 1 foot wide, and 6 mches thick has a
Yolume of 3 cubic feet. If it weighs 90 pounds, its density is 30 pounds
per cubic foot.
An empty kerosene can weighs 1.25 pounds, and when filled with kero-
sene, it weighs 36.25 pounds, so that the net weight of the kerosene in the
can is 35 pounds. If the can holds 5 gallons, the density of the kero-
sene is 7 pounds per gallon.
A block of steel is 15 centimeters long, 6 centimeters wide, and 1.5
centimeters thick and weighs 1050 grams ; then the density is J^^ or
7.8 grams per cubic centimeter.
From the preceding examples it will be seen that the
density of a body is found by dividing its weight by its
volume. In other words,
^ . weight
It is also evident that if we know the density of a substance,
we can compute the weight of any volume of the substance.
It is by this method that engineers calculate the weight of
buildings and bridges which it would be impossible to weigh.
For example, an engineer finds that a reenforced concrete
pier contains 2500 cubic feet of material, and he knows that
such material averages 150 pounds per cubic foot. Then
the weight of the pier is equal to 2500 times 150, or 375,000
pounds, or about 188 tons. In other words.
Weight = density x volume.
If it is the volume of anything that we want to know, we
have
Volume = ]?^.
density
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introduction: weights and measures
11
Problems
(Use data given in table on page 9 when necessary.)
1. A block of iron is 10 centimeters by 8 centimeters by 6 centime-
ters, and weighs 3 kilograms. What is its density expressed in grams
per cubic centimeter ?
2. A block of stone measures 4 feet by 2 feet by 15 inches, and
weighs 1625 pounds. Find its density iu pounds per cubic foot.
3. How many pounds does 1 cubic foot of aluminum weigh ?
4. The cork in a life preserver weighs 20 pounds. What is its vol-
ume in cubic feet?
5. A flask with a capacity of 120 .cubic centimeters is filled ^ith
mercury. How many kilograms of mercury does it hold ?
6. A quart bottle ie weighed empty and then full of milk. How
many pounds should it gain in weight ?
7. A cylindrical railway water tank measures on the inside 10 feet
in depth and 6 feet in diameter. How many tons of water does it hold?
8. A piece of platinum wire is 12.5 centimeters long and 0.8 milli-
meter in diameter. How much would it cost if the price of platinum is
♦1.00 per gram?
9. If a certain copper telephone wire is 0.165 inch in diameter,
what does a mile of the wire weigh ?
10. The inside diameter of a lead pipe is 1 inch, and the wall is 0.25
inch thick. How many pounds does it weigh per foot ?
15. The three fundamental units.
On account of its more convenient
size, the centimeter, instead of the
meter, is universally used in scien-
tific work as the fundamental unit
of length. For a similar reason, the
gram, instead of the kilogram, is
used as the fundamental unit of
weight. The second is taken among
all civilized nations as the standard
unit of time. It is -g^^^nj^ of the
time from noon to noon.
The process of weighing some-
thing on a balance is quite dis- Fig. 7. — stopwatch.
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12 PRACTICAL PHYSICS
tinct from the measurement of a length, and the measure-
ment of time is wholly different from the measurement either
of length or weight. Moreover, each is done with a distinct
sort of instrument. In a time measurement the instrument
is a clock or watch. For short intervals of time a special
type of watch is used, known as a stop watch (Fig. 7).
It is found that the measurement of any quantity, such as
the steam pressure in a boiler, the speed of an express train,
or the loudness of a foghorn, can, in the ultimate analysis,
be reduced to measurements of length, weight, and time.
The units of length, weight, and time are therefore the three
fundamental units of physics.
SUMMARY OF PRINCIPI<£S IN CHAPTER I
Density =^^?^8^.
volume
Questions *
1. What is the origin of the prefixes deci^ centi, and mtV/i, used in the
metric system?
2. How could you determine the volume of an irregular piece of
rock by means of a graduated cylinder partly filled with water ?
3. How would you measure the diameter of a steel ball ?
4. How does your local jeweler get " standard time " to set his clocks
and watches correctly?
5. How can the thickness of this sheet of paper be measured?
6. What is the difference between a ship's chronometer and a dollar
alarm clock ?
7. Why is it that the United States and Great Britain are the only
two civilized countries that do not use the metric system commercially ?
* In trying to find the answers to these questions, the student is expected
to consult various reference books, such as dictionaries, encyclopedias, en-
gineering handbooks, and popular science magazines. He is also expected
to keep his eyes open outside of the classroom, and to ask questions of me-
chanics and tradespeople.
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CHAPTER II
SIMPLE MACHINES
Levers of various kinds — principle of moments — force at
the fulcrum — weight of a lever — center of gravity in general
— wheel and axle — pulley systems — parallel forces.
Work — principle of work — differential pulley — inclined
plane — wedge — screw — combinations of simple machines —
power — transmission of power.
Friction — so-called " laws of friction " — coefficient of fric-
tion— advantages of friction — rolling friction — efficiency of
machines.
16. Why we use machines. A man can lift a piano up
to a window on the second floor with a rope and tackle. A
boy can roll a barrel of flour up into a wagon with a skid.
A girl can pull a nail out of a box with a claw hammer al-
though she could not move the nail at all with her fingers
alone. It is obvious that we can do many things with simple
machines that it would be quite impossible for us to do
without them because we are
not strong enough. Further-
more, some machines enable us
to do things more quickly or
more conveniently than we
could without them. Most
important of all, we often use
machines in order to make use
of forces exerted by animals,
wind, water, or steam.
.17. Equal-arm lever. —
Doubtless the simplest ma-
chine is the lever with equal
13
Fig. 8. — Equal-arm lever.
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14 PRACTICAL PHY8IC8
arms, such as a seesaw, or the walking beam on a steamboat,
or the scale beam on a platform balance. In this case we
know that equal weights or equal forces just balance when
placed at equal distances from the point of support. Thus
in figure 8, when W^ equals TTj, the distance AF must equal
the distance BF, In the technical language of physics the
point of support ( J^) of a lever is called its fulcrum.
18. Unequal-arm lever. Very often the distances of the
weights from the fulcrum are hot equal. For example, the
distances are unequal when two persons of unequal weight
are seesawing, or in the case of an ordinary pump handle.
It is evident that at equal distances, the larger weight would
have the greater tendency to tip the lever, and also that, with
equal weights, the weight at the greater distance from the
fulcrum has the greater tendency to tip the lever. There-
fore in order to have two unequal weights balance, they
must be so placed that the smaller weight is at the greater
distance from the fulcrum.
— u — I I I p.. I j
^^ 0 100 0
a
7
Fig. 9. — Two unequal forces.
If we balance an ordinary meter stick in the middle and suspend a
50-gram weight {W^) at A, which is 40 centimeters from the fulcrum
(F), and then hang a 100-gram weight {W^ on the other side at such a
point as just to balance the first weight, we shall find that the point B
where the 100-gram weight is hung is about 20 centimeters from F or
half as far from the fulcrum as the 50-gram weight.
Careful experiments show that any two unequal forces
will balance only if the force on one side multiplied hy the per-
pendicular distance, of its line of action from the fulcrum equals
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SIMPLE MACHINES 15
the force on the other side multiplied by the distance of its, line
of action from the fulcrum. For example, in figure 9,
W^xAF== W^xBF.
This relation of the forces and distances may also be ex-
pressed by a proportion
W^: W^: : BF : AF,
which may be stated in words as follows : the forces are
inversely proportional to their distances from the fulcrum.
This means that if one force is three times as great as another,
then its line of action must be one third as far away from the
fulcrum as the other to make the lever balance.
Crowbars, shears, glove stretchers, pliers, etc., are all ex-
amples of this sort of lever.-
19. One-arm lever. When the fulcrum is located at one
end of the lever, as in figure 10, the same principle is in-
volved. There are two tendencies which must balance, the
tendency of the weight to tip the lever down and the tend-
ency of . the pull applied to the lever to lift it up. The
weight multiplied by the perpendicular distance from the
fulcrum to its line of action measures its turning effect about
the fulcrum; that is, its tendency to tip the lever down.
This must be balanced by an equal turning effect in the
opposite direction, namely, the upward pull multiplied by its
distance from the fulcrum.
-1-2^
f
10 lbs.
W
Fig. 10. — One-arm levers.
Suppose we fasten a stick (Fig. 10) by a screw (F) to an upright
support, so that the stick is free to turn, and hang a weight (W)y say 10
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16 PRACTICAL PHYSICS
pounds, at a distance of 6 inches from the fulcrum (F) Then if we
pull up with a spring balance at a point (B) 12 inches from -the ful-
crum (F), we shall find that the pull measured
^ W ,^ZI>'-^u^^ ^y ^^® spring balance is about 5 pounds. (Of
^ course allowance has to be made for the weight
of the stick.)
.— u crac er. The equation representing these tend-
encies to turn the stick in opposite directions would be as
before
Wx^AF^Px BF.
It is also evident that if the 10-pound weight ( TF) were
hung 12 inches from the
fulcrum (-P), and the up-
ward pull applied 6 inches
from the fulcrum, the pull
needed would be 20 pounds.
In other words, the same
principle applies to the one-
arm lever wherever the Fig. 12. -Crowbar,
weight and the upward pull are applied.
A nut cracker (Fig. 11), a crow bar when used witn one
end on the ground (Fig. 12), and
the forearm (Fig. 13) when it sup-
ports a weight in the extended
hand are examples of levers with
the fulcrum at one end, or one-
arm levers.
-^^^ // 11 20. Lever with two weights.
(0^^J^"-vc=r- ^^^ The ordinary wheelbarrow is a
^3^ good example of a one-arm lever.
The fulcrum is located at the axle
of the wheel, the weight is the
w' load carried, and the upward pull
Fig. 13.— Forearm. is exerted on the handles- by the
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8IMPLX MACHINXS
17
Fio. 14. — Wheelbarrow with two weights.
man. In practice, however, it often happens that the load
consists of two weights, such as two bags of cement or two
boxes or kegs, as
shown in figure
14. To get the
upward pull we
have merely to
compute the turn-
ing effect of each
of the weights
( W^ and F^) about the fulcrum (^F) and make the sum of
these effects equal to the turning effect of the upward pull
(P). That is,
Fi X BF+ TTj X AF^ P x OF.
In general, then, we see that we can balance the turning
effect of two or more weights by multiplying each weight by
the perpendicular distance of its line of action from the
fulcrum, and making the sum of these products equal to the
product of the pull by the perpendicular distance of its line
of action from the fulcrum.
21. Principle of moments. It has been seen that the
turning effect of a force depends on two factors, the amount
of the force and the distance of its line of action from the
fulcrum. This product — force times perpendicular distance to
folcnun — is called the moment of the force. For a lever to be
in equilibrium, the sum of the moments of the forces tending
to turn it in one direction must equal the sum of the moments
of the forces tending to turn it in the opposite direction.
22. Force at the fulcrum. It must not be forgotten that
in examples of the lever, the fulcrum itself exerts a force,
that is, a push or a pull. When the fulcrum is between the
two weights, it evidently has to push up an amount equal to
the sum of the weights ; that is (Fig. 15, top), F^ Wi'\- W^*
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18
PRACTICAL PHT8IC8
^
F'Wi+ir^
w.
When the fulcrum is at one end of the lever, and the pull at
the other end, it is clear that the fulcrum must exert an up-
ward push, which must
be such that it and the
upward pull (P) are to-
gether equal to the
weight. That is (Fig.
15, middle), W=^F'\-P.
When the fulcrum is at
one end and the weight
at the other end, it will
be readily seen that the
fulcrum has to push down-
ward and that the upward
puU (P) must eqi;Lal the
sum of this downward
push at F and the weight
W. That is (Fig. 15,
bottom), P = W+ F. In
short, it will be seen that
in all these cases the sum
of the forces pulling up
must equal the sum of
the forces pulling down.
w
Fig. 15. — Force exerted by fulcrum of lever.
Problems
1. Identify the fulcrum, and the direction of the two forces, in the
case of a pair of shears, a glove stretcher, a pair of tongs, and a nut
cracker, regarded as examples of the lever, and think of other examples.
2. What weight placed 20 inches from the fulcrum will balance 100
pounds placed 8 inches away on the opposite side? What is the pressure
on the fulcrum ?
3. In figure 9 the movable weight on an old-fashioned steelyard
weighs 3 pounds, and is placed at such a distance as to balance a 50-pound
sack which is hung from a point 1 inch from the point of support. How
far from the point of support must the sliding weight be placed ?
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8IMPLE MACHINEB
19
4. A piece of wire, which is to be cut with shears, is placed 0.5 inch
from the rivet. If a force of 25 pounds is applied on the handles 6 inches
from the rivet, how much force is exerted on the wire ?
5. A plank 12 feet long is to be used as a seesaw by two boys who
weigh 100 pounds and 140 pounds. How far from the lighter boy must
the prop be placed ?
(Hint. — Let x = distance from small boy and 12 — a; = distance from
big boy.)
6. The handles of a wheelbarrow (Fig. 10) are 4 feet 6 inches from
the axle, and the load of 200 pounds can be considered as 18 inches from
the axle. How much effort must be exerted to raise the handles ?
23. Bent lever. Consider next a claw hammer (Fig. 16)
with a 12-inch handle. If a 60-pound pull (P) at B is
necessary to pull the nail at A^ which is
1.5 inches from -F, what is the resistance
(i2) which the nail offers ? The moment
of P is P X BF^ and the moment of R
is ^ X AF, therefore 60 x 12 = JB x 1.5,
and R = 480 pounds. In this case it will
be seen that the two arms of the lever are
inclined to each other,
but the principle of
moments applies just
as if it were a straight
lever. The bent lever
is very common as a
part oi a machine.
A great many other objects can be regarded
as bent levers. For example, suppose a door
(Fig. 17) 8 feet high and 4 feet wide, weighing
60 pounds, swings on hinges placed 1 foot from
the top and 1 foot from the bottom, (a) What
is the vertical pressure on each hiuge? If the
door is properly hung, the weight will be equally
Fig. 17.— Door as a bent divided between the two hinges, and each hinge
lever will support 30 pounds. (6) How great if
Fig.
16. — Hammer as
a bent lever.
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20
PRACTICAL PHYSICB
h\\fyi
the horizontal pull on the upper hinge? If we consider the entire
weight of the door as acting at its center, then the moment of this
weight about the lower hinge will be 2 times 60, or 120. The moment
of the pull exerted by the upper hinge, reckoned about the lower hinge,
will be 6 times the pull. Making these two moments equal, we find that
the pull is 20 pounds, (c) In a similar way, by considering the upper
hinge as a fulcrum, we may compute the pxiAh exerted by the lower
hinge, which also equals 20 pounds.
24. Center of gravity. So far in our study of levers we
have assumed that the. weight of the lever itself could be
neglected, but in practice this is not always the case. It is
our problem now to find how to make allowance for the
weight of the lever.
We have already seen that a lever carrying two weights
(Fig. 18) can be
supported at a
point in between,
which we have
called the fulcrum,
but which we may
now call the " cen-
ter of gravity"
or "center of weight." The force necessary to support this
point is the same as if the whole weight were concentrated
there. In the same way we could support a bar carrying
three or more weights on a single fulcrum, if it is placed at
the right point. That point would be the center of gravity
of the weights. In general, everything has a center of grav-
ity at which we can consider its whole weight concentrated.
To find the position of the center of gravity, we have simply
to find the point at which the object would balance on a
knife edge. This may be computed, but it is usually easier
to locate it experimentally.
25. How to find a center of gravity by experiment. If the
shape of the object is simple and its density is everywhere
the same, as in the case of a shaft or a board, we should ex-
Fio. 18. — Center of gravity of two weights.
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SIMPLE MACHINES
21
pect the center of gravity to be in the middle, and if we try
to balance the object on some sharp edge, we find that the
center of gravity is indeed located at the geometrical cent.er.
In the case of an irregularly shaped object like a baseball
bat, the simplest way is to balance the bat on a knife edge.
In the case of a chair, the center of gravity may be found by
considering that, if the chair is hung so as to swing freely,
the center of gravity will lie directly under the point of
suspension. Therefore, if a chair, or any irregular object,
is hung from two points successively, the point of intersec-
tion of the plumb lines from these points will locate the
center of gravity.
To make this clear, let us take an irregular sheet of zinc and drill
three holes near the edge, A, B, and C, in figure 19. Let the zinc be
hung from a pin put through the hole
A and let a plumb line be also hung from
the pin. Draw a line on the zinc to
show where the plumb line crosses it.
Then let the zinc be hung from another
hole and draw another line in a similar
way. The point of intersection is the
center of gravity. When the zinc is
hung from the third hole, the plumb
line will pass through the center of grav-
ity already found.
^
Fig. 19. — Finding center of
gravity.
In the case of a ring, or a cup,
or a boat, the center of gravity
will not lie in the substance itself, but in the empty space
inside ; but this will not bother us in answering questions
about how such objects act. We may, if we like, think
of such a center of gravity as rigidly attached to the object
by a very light, stiff framework.
We shall find this idea of the center of gravity especially
convenient in problems where the weight of a lever has to
be considered, for we can now assume that the whole weight
of the lever is concentrated and acting at its center of gravity.
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22 PRACTICAL PHTSICB
Suppose that an 18-ounoe hammer balances 10 inches from the handle
end. When a fish is tied to the end of the handle, the whole balances
6 inches from the end. How much does the fish weigh ? We may con-
sider the weight of the hammer, 18 oances, as concentrated at a point
10 inches from the end of the handle or 4 inches from the fulcrum. Let x
be the weight of the fish, which is applied 6 inches from the fulcrum.
Then we have
6 X = 4 X 18,
X = 12 ounces, the weight of the fish.
Problems
1. A boy has a 2-pound fish pole 10 feet long, the center of gravity
of which IB 3.5 feet from the thick end. He finds the weight of his
string of fish by hanging them from the thick end of the pole and then
balancing the pole on a fence rail. He finds that it balances at a point
15 inches from the end. How many pounds of fish has he ?
2. A pole 20 feet long weighs 120 pounds. When a 30-pound bag of
meal is hung at one end, the balancing point is 3 feet from the same
end. Where is the center of gravity of the pole?
3. A 6-foot crowbar balances at a point 2.5 feet from its sharp end.
If a weight of 30 pounds is hung 0.5 feet from this end, and 50 pounds
is hung 1 foot from the other end, it balances at its mid-point. How
heavy is the bar ?
4. A uniform beam AB, 20 feet long, weighing 600 pounds, is sup-
ported by props placed under its ends. Four feet from prop A, a weight
of 200 pounds is suspended. Find the pressure on each prop.
(Hint. — Regard as a lever, with its fulcrum at ope end.)
5. A rectangular gate 3.5 feet high and 5 feet wide has its center of
gravity at its geometrical center. It is hung on hinges placed 3 inches
from the top and bottom. The gate weighs 100 pounds, (a) What
vertical pressure should each hinge sustain? (b) What is the horizontal
pull on the upper hinge ? (c) What is the horizontal push against the
lower hinge?
26. Wheel and axle. A special form of lever consists of a
wheel or crank which is fastened rigidly to an axle or drum.
The weight to be lifted, or the resisting force of whatever
kind, is generally applied to the axle by means of a rope or
chain, and the " effort," or pull, is exerted on the rim of the
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SIMPLE MACHINES
23
or
wheel, as shown in figure 20. In calculating the effort (P)
needed to balance a given resistance ( TF) we have merely to
take moments about the center (^F) of the
wheel and axle. If we call the radius of the
wheel JS and that of the axle r, then,
Weight X axle-radius = effort x wheel-radius
or Wxr^FxBy
P r'
27. Uses of the wheel
and axle. A windlass
used in drawing water
from a well (Fig. 21) by means of a
rope and bucket is an application of
the principle of the wheel and axle.
In the windlass, a crank takes the place
of a wheel, and the length of the crank
is the radius of the wheel.
If a wheel is used in turning the rudder
of a boat, the rope attached to the rudder
is wound round the axle, and the steersman applies his effort
to the handles which project from the rim of the wheel ( Fig. 22).
In the derrick (Fig. 23), jj^
which is used in lifting
Fio. 20.— Wheel
and axle.
Fio.
21.— Windlass for a
well.
Fia. 22. — Steering wheel in a boat.
Fig. 23. — Hoistinsr derrick.
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24
PBACTICAL PHY81C8
weights, we usually have a double wheel and axle. The
effort of the workmen is applied at the cranks, which are at-
tached to one axle. This then drives, through a spur gear,
a wheel on a second axle.
28. The pulley. The fixed puUey, shown in figure 24, con-
sists of a wheel with a grooved rim, called a sheave, free to
rotate on an axle which is supported in a fixed block. A
flexible rope or cable passes over the wheel. It is evident
/MM///////////^^^^^^^^^
m
f
r
A
IP
Fig. 24. — Fixed pulley.
Fig. 25. — Movable pulley.
that if equal weights or equal forces are applied to the ends
of the rope, they just balance each other. That is, the effort
P is equal to the resistance W. So there is no advantage in
the fixed pulley, except that it is sometimes more convenient
to exert a certain pull downwards rather than upwards.
Oftentimes the block is attached to the weight to be lifted,
as shown in figure 25, and then it is called a movable pulley.
Here the effort P is not equal to the weight TFJ for it will
be seen that the load TFis supported by two ropes, and there-
fore each exerts a pull equal to one half the weight. That
^ P = iTF;or Tr/P = 2.
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SIMPLE MACHINES
25
The ratio of the weight or resistance to be overcome to the
effort pvt forth is called the mechanical advantage of a machine.
For example, the mechanical advantage of a single fixed
pulley is 1 and of a single movable pulley is 2.
29. Combinations of pulleys. In practical work it is quite
common to use a fixed block with two sheaves and a movable
block with two sheaves, as shown in figure
26. One end of the rope is attached to the
fixed block, and the efiFort is applied to the
other end of the rope. Let us compute the
relation between the weight to be lifted and
the effort applied. From figure 26 it will
be seen that the weight and the movable
block are supported by four ropes, and so
the pull on each rope, neglecting the weight
of the block, is one fourth the weight W*
It will also be seen that the pull P is equal
to that in each of the ropes, since a pulley
only changes the direction of the pull. There-
and the mechanical advantage, TF/P, is 4.
This means that, neglecting friction and the weight of the
movable block, a pull of 100 pounds applied at P would just
balance a weight of 400 pounds at W.
In general^ we can find the mechanical advantage of any
combination of pulleys by counting the number of ropes which
support the weight.
30. Parallel forces. Suppose we have a 8000-pound auto-
mobile standing on a bridge in a position one fourth of the
length of the bridge from one end (Fig. 28), and we wish to
know how much of the weight is borne by the supports at
each end of the bridge.
First let us try a very simple experiment which will make
clear the pTrinciples involved in this problem.
Fig. 26. — Double
blocks.
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PRACTICAL PHT8IC8
Nail
Id
Fig. 27.-
0
■ Parallel forces.
Hang a light "stick (Fig. 27) by two or more stirraps attached to
spring balances {A, B, C), and let several weights (Z>, E) be hung from
it at various points. If the sup-
ports do not break, the stick
will remain suspended mo-
tionless indefinitely. The
sum of the forces pulling up
is equal to the sum of the
forces pulling down. Now
suppose that there happen to
be several holes through the
stick and that a nail is care-
fully driven through one of
them into the wall behiud.
If the stick did not move
before, it certainly will not
move now. But we can now think of the stick as a lever with the nail
as a fulcrum, and it is in equilibrium about that naiL This means that
the sum of the moments of the forces tending to turn it in one direction
equals the sum of the moments of the forces tending to turn it in the
opposite direction.
Evidently this nail could have been put through a hole at any point
along the stick, and the moments calculated around that point would
balanca
This example and section 22 show that when several paral-
lel forces are in equilibrium two conditions must be fulfilled.
(1) The sum of the force% pulling in one direction rnvst eqttal
the sum of those pulling in the opposite direction,
(2) The sum of the moments tending to rotate the whole in
one direction around any point whatever must equal the sum of
the moments tending to rotate the whole in the opposite direction
around that same point.
Let us apply these
principles of parallel
forces to the problem
of the automobile
standing on the bridge.
This can be represented
by figure 28, where A
is the weight of the
t^'
t-
r
A 3000 lb8.
I
I
iJ<
■Say-
I
Fig. 28.— Bridge with automobile on it.
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SIMPLE MACHINES
27
automobile, and B and C are the upward forces exerted by the end sup-
ports. We know one force (A = 3000 pounds), and the relative dis-
tances between these forces. We are to find the magnitudes of B and C
Since B-{-C = 3000, C = 3000 - B, Suppose we take the position of the
automobile as the point about which to compute moments ; then we have
B x3x = (3000--B)x X,
B = 750 pounds, B's load,
3000 - 5 = 2260 pounds, C*a load.
We can also solve this problem by taking moments first around one
end, and then around the other. Working in this way, we do not need
the first principle at all. Do this and see if you get the same answers.
It should be noticed that all the machines so far considered,
namely, the lever (except the bent lever), the wheel and axle,
and the pulley, are simply special casiss of parallel forces, and
that we can discover anything we want to know about any
of them, by means of one or both of the general principles
mentioned just above. For the lever and the wheel and axle,
the principle of moments is enough, unless we want to know
the force at the fulcrum. For that we need the first principle.
For the pulley we need only the first principle.
Problems
1. The diameter of an axle is 1 foot, and the diameter
of the circle in which a crank on the axle moves, is 3 feet.
If 150 pounds is the weight to be raised, how much force
must be applied to the crank ?
2. The crank on a grindstone is 9 inchetj long, and the
diameter of the stone is 30 inches. If 50 poundft Ib the
force applied on the crank, what force can be exerted on
the rim of the stone ?
3. What must be the ratio of the diaitieters of a wheel
and axle, in order that 150 pounds
may suppoi*t 1 ton ? What is the
mechanical advantage ?
4. Two single fixed pulleys are
used to raise a barrel of flour, as
shown in figure 29. If a barrel of *^<»- 29. — Simple pulley system.
flour weighs 200 pounds, how much does the horse have to pull?
J^-— i:^
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28 PRACTICAL PHY8IC8
5. The gaff of a boat is to be raised by means of a movable single
block attached to it, and a fixed double block attached to the top of the
mast, one end of the rope being tied to the movable block. How
much resistance can be overcome by 100 pounds exerted on the
rope?
6. A pair of triple blocks contain three sheaves each. The rope is
attached to the upper fixed block. What force is just sufficient to bal-
ance a weight of 1 ton, neglecting friction ?
7. An automobile gets stuck in the sand. In order to pull it
out, a horse, a rope, and a couple of triple blocks are used. If the
horse exerts a steady pull of 500 pounds on the rope, and one block
is fastened to a tree and the other to the machine, how much
resistance can be overcome ? Find two solutions for this problem* the
rope being fastened in one case to the fixed block, and in the other to
the movable block.
8. Two boys, A and £, are carrying a 100-pound load slung on a
pole between them. Their hands are 10 feet apart, and the load is 3 feet
from A. How much does each carry? Neglect the weight of the
pole.
9. A nolan holds a shovelful of coal, weighing 50 pounds, with his
left hand at the end of the shovel, and his right hand 22 inches away.
Supposing the center of gravity of the shovel and coal to be 40 inches
from his left hand, how much does he push down with his left hand, and
how much does he pull up with his right hand ?
10. A man and a boy carry a load of 200 pounds on a pole 8 feet long.
Where must the load be placed if the boy is to bear only 45 pounds
of it?
31^ Work. The funqtion of .every ma,chine is to do a certain
amoi^nt of work. Now in the technical language of science,
work meem^ the overcoming of resistance. For example, we do
work fwhe^n we lift a box f rim the floor to the table, or when
we push the box along the floor against friction. But we
are not doing work in thei scientific sense of the word, no
matter how hard we push or pull, if we do not lift or move
the box. In other words, -work is measured by accomplish-
ment, not by effort or by fatigue.
If Welift iane pound one foot, we are said to do one foot
pound>^iQf work; if we lift. 5 paunds 3 feet, we do 15 foot
pounds<:0;SK!j7'Cirk ;. or if we pull hard enough gn a box to lift
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SIMPLE MACHINES 29
5 pounds and thus drag it 3 feet, we still do 15 foot pounds
of work. In other words,
Work (foot pounds) = force (pounds) x distance (feet).
It should be remembered that the distance must be meas-
ured in the same direction as that in which the force is ex-
erted. Thus, if a machinist exerts upon a file a force of 10
pounds downward and 15 pounds forward, how much work
will he do in 40 horizontal strokes, each 6 inches long?
Evidently the total distance is 20 feet and the horizontal
force is 15 pounds; therefore the work done is 300 foot
pounds. The vertical pressure does not enter into the cal-
culation of work because the motion is horizontal.
32. Principle of work. In every machine a certain resist-
ance is overcome by a certain effort exerted on another part
of the machine. The principle of work which applies to all
machines where the losses due to friction may be neglected,
may be stated as follows: 77ie work put into a machine is
eqvAd to the work got out. In short.
Input = output.
For example, in the wheel and axle (see Fig. 20, section 26) the
output is equal to the weight times the distance it is lifted, and the input
is equal to the effort times the distance through which it is exerted.
For convenience, suppose the wheel makes just one turn. Then the dis-
tance the weight is lifted is equal to the circumference of the axle, 27rr,
and the distance through which the effort is exerted, is the circumference
of the wh6el, 2 ttR. The input is P x 2 irR, and the output is PF x 2 irr.
Therefore, by the principle of work,
Px2TrR= Wx2Trr,
or Px R= Wxr^
which is exactly the equation got by considering the wheel and axle as a
modified lever.
Another example is the system of pulleys shown in figure 26 in sec-
tion 29. The outpfit is equal to the weight W times the distance it is
lifted, and the input is equal to the effort P times the distance through
which it is exerted. Suppose the distance the weight W is lifted is D,
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PRACTICAL PHT8IC8
and the distance through which the effort P is exerted is d. The outpiA
iB W X D and the input is P x d. Then, by the principle of work,
or
Wx D = Pxd,
P D
But when the weight is lifted 1 foot, it is evident that each of the sup-
porting ropes must be shortened by 1 foot, and therefore P most move 4
feet; in other words,
rf = 4i>.
Substituting this value of d in the preceding equation, we have
^=4,
P
which is the same as the result which we got by considering the pulley
as a case of parallel forces.
33. The differential pulley. In shops where heayy machin-
ery is to be lifted, constant use is made of the differential pulley,
shown in figure 30. This con-
sists of two sheaves of different
diameters in the upper block
rigidly fastened together, and
one sheave in the lower block.
An endless chain runs over
these blocks. The rims of the
sheaves have projections which
fit between the links and so
keep the chain from slipping.
Such a differential pulley
has a very large mechanical
Fig. 30. — Differential pulley. advantage.
To see just now it conies to have a large mechanical advantage, let us
set up such a pulley and study it carefully. When the chain is pulled
down as shown in the diagram, it is wound up faster on the large fixed
pulley than it is unwound on the smaller pulley. In order to compute
the mechanical advantage of the contrivance, let us suppose that P moves
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SIMPLE MACHINES 81
down far enough to turn .the fixed pulley around once. If 12 is the radius
of the large fixed pulley, then the work done by P will be P x 2 irR. If r
is the radius of the small fixed pulley, then the length of chain unwound
in one revolution will be 2 irr. The weight W will therefore be raised
J(2 irR — 2 irr) or 7r{R — r) and the work done will be TTx ir^R — r).
Therefore, if we neglect losses due to friction^ we have
whence,
TTx fl-(i2-r)=P X 2Tr/e,
W^ 2R
P R-r
Since the diflference between the radii of the two fixed
pulleys (iJ — r) is small, it is evideijt that the mechanical
advantage is large.
The differential pulley has a second practical advantage
in that there is always enough friction to keep the weight
from dropping when the force P is released.
Problems
1. A man carries in baskets a ton of coal up 20 steps, each 7 inches
high. How much work does he do on the coal ?
2. In the metric system, work is measured in kilogram meters. How
much work is done in pumping 50 liters of water 40 meters high ?
3. A man weighing 150 pounds raises himself up a mast in a sling
by means of a rope passing over a fixed pulley attached to the top of the
mast. If the mast is 100 feet high, how much work does he do ? How
hard must he pull ?
4. If in problem 1 on page 27 the weight is raised 10 feet, how
many foot pounds of work are done by the machine ?
5. If in problem 2 on page 27 the stone is turned 30 revolutions
per minute, how many foot pounds of work are put into the grindstone
per minute ?
6. In a certain differential pulley the large wheel is 6 inches and the
small wheel 5 inches in diameter. What is the mechanical advantage ?
34. Inclined plane. Barrels and casks which are too heavy
to lift from the ground into a wagon are often rolled up a
plank or skid. This is an example of what is called an
inclined plane. Every street or road which is not level is an
example of an inclined plane. Experience teaches us that
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PRACTICAL PHT8IC8
Fig. 31. — Inclined plane.
the steeper the incline, the greater the pull required to haul
the load up the grade. In order to find out just how the
effort and the weight
or load are related to
the grade, let us try a
simple experiment,
where friction can be
neglected.
Suppose we arrange a
|P very smooth plane, such as
a piece of plate glass, at an
angle, as shown in figure 31.
Let the weight or load ( W)
be a heavy metal cylinder which turns with very little friction. Attach
to the cylinder a cord and pass it over a good pulley fastened to the top of
the plane, and then hang froni the other end enough weights to pull the
load slowly up the inclined plane. You will find that the ratio P/ W is
approximately the same as the ratio H/Ly where H is the height of the
incline and L is its length.
From the general principle of work we can also arrive at
this relation of effort and resistance to the grade. Suppose
the weight W is rolled from the bottom to the top of the
incline. Then it has been lifted JTfeet, and the work done
is W (pounds) times S (feet), or WS foot pounds. But
while the weight W has been traveling up the incline whose
length is i, the force or pull P has moved down L feet, and
the work put in is equal to P (pounds) times L (feet), or
PL foot pounds. Therefore, if we neglect friction, we have
Pxi=T7xJ5r,
P^H
W L
or
35. The grade of an incline. This ratio of the height to
the length of an incline is expressed by engineers as so many
feet rise per hundred feet along the incline, and is called
the grade of the incline. For example, suppose a road rises
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SIMPLE MACHINES 38
6 feet for every 100 feet along the incline, then this road is
said to have a 5 % grade. Since a 3 ^ grade is the steepest
allowable on a really good road, it is readily seen that a
small force, such as can be exerted by a horse, can move a
much heavier load up a gradual incline than could be lifted
directly. For this reason the highways in mountain regions
are laid out as zigzags and switchbacks. If we want a
flight of steps easy to climb, we make the slope gentle.
Nevertheless it should be remembered that while the pull
is less than the weight of the load, yet the distance the load
travels is greater than when it is lifted straight up. In
other words, what we gain in the amount of effort required
we lose in the distance over which it must be exerted. The
total work to be done is independent of the grade, except for
the indirect effect of friction.
36. Wedge. If instead of pulling the load up the incline,
we push the incline under the load, the inclined plane is
called a wedge. Of course the* smaller the angle of the wedge,
the easier it is to drive it against the resistance. The fact
that friction plays a very important part in its action makes
it impossible to make a simple statement of the relation of
the effort required to force in a wedge to the resistance to
be overcome.
All cutting and piercing instruments, such as the ax, the
chisel, and the carpenter's plane, as well as nails, pins, and
needles, act like wedges. The carpenter uses wedges to
fasten the heads of hammers and axes on their handles.
The woodsman uses wedges to split logs of wood.
37. Screw. When an enormous force must be exerted,
as in lifting a building, such machines as the lever, pulley,
and inclined plane will not do, because we cannot get
enough mechanical advantage. A screw, such as the jack-
«crew (Fig. 32), is sometimes used for this purpose. In one
complete turn of the screw, the weight is lifted the distance
between two successive threads, which is called the pitch of
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PRACTICAL PHYSICS
Fig. 32.— Jackscrew.
the screw, while the effort is exerted through a distance
equal to the circumference of the circle traced by the end of
the bar or handle. In each complete turn
the output is equal to the weight times the
distance between two successive threads,
and the input is equal to the effort times
the distance through which it acts ; namely,
the circumference of a circle.
If TF equals the weight to be lifted and
p (pitch) equals the distance between
threads, the output for one turn is TF times jo.
Let P equal the effort or force applied on
the handle, and 2 tit equal the circumfer-
ence of the circle in which it acts. Then P times 2 vr is
the input. Therefore applying the principle of work to the
machine, we would have, if friction could be neglected,
Tf X jt? = jP X 2 Trr,
In other words, the mechanical advantage of the screw is equal
to the ratio of the circurnference of the circle moved over by the
end of the lever^ to the distance between the threads of the
screw.
As a matter of fact, friction consumes a
the work put in, and therefore the input is
greater than the output. But this loss is not
wholly a disadvantage,
for it keeps the screw
from turning backward
W//W//////////////?L ^^ itself.
^^^^^M^ 38. Applications of the
Fig. 33.-Wood8crew. g^g^; ^e are all fa-
miliar with carpenter's wood screws (Fig. 33) and machinist's
bolts (Fig. 84). Ordinarily, however, we do not think of the
large part of
Fig. 34. — Bolts.
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SIMPLE MACHINS8
85
[
— aj.
propeller of a boat or flying machine as a screw, but it is. The
propeller (Fig. 35), with its two, three, or four blades fas-
tened to one end of the
shaft, is driven by an en-
gine at the other end. Its
rotation is so rapid that
the water has no time to
get out o^ the way, and
the propeller screws itself
through the water like a
wood screw through wood. ^^^^ ^' - ^^^-^^ propeller.
Another example of the screw is the micrometer screw (Fig.
36), which is used to make very precise measurements. It
consists of an accurately turned thread
of small pitch, perhaps 1 millimeter.
It is evident that if such a screw is
turned -^j^j^ of a complete turn, the
spindle moves along its axis just 0.01
millimeters. This is the easiest way
of measuring so small a distance. In order to discover
readily through just what fraction of a turn the screw is
turned, the head is divided into 100 divisions.
39. Combinations of
simple machines. What
is called a single machine
in factories and shops is
usually a combination of
the simple machine ele-
ments described above.
It is, in fact, a more or
less complicated collec-
tion of levers, pulleys,
wheels, axles, and screws.
In order to show how such
a machine, may he analyzed Fig. 37.— Builder's crane.
Fig. 36. — Micrometer
screw.
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PRACTICAL PHYSICS
into its elements, let us, as it were, dissect a crane or derrick (Fig. 37)
such as is used in unloading freight cars, or in hoisting building material
into place.
The movable pulley to which W is attached gives a mechanical advan-
tage of two ; the fixed pulley at the end of the boom merely changes the
direction of the pull ; the wheel D and its axle give a mechanical advan-
tage equal to the ratio of the size of the wheel to the size of the axle.
A third mechanical advantage is gained in the wheel and axle, B and C,
an4 finally there is the mechanical advantage of the crank P and the
axle A. The total mechanical advantage of this compound machine is
the product (not the sum) of the separate advantages gained by its
separate elements. This is true of compound machines in general.
Problems
Note. FrictloD is to be neglected in these problems.
1. What force will be needed to pull a weight of 200 pounds slowly
up a slope which rises 1 foot in 25 feet ?
2. What, weight can be moved on a 10 % grade with a pull of 50
pounds ?
3. A boy, who can push with a force of 80 pounds, wants to roll a
200-pound barrel of flour into a cart 4 feet above the ground. How
long a plank will he need ?
4. What force is needed to move a 1500-pound wagon up a 3 % grade?
5. A test shows that it takes 1000 pounds more force to haul an elec-
tric car weighing 4 tons up a certain grade than to haul it along on a
level. What is the grade ?
6. What weight will be raised by a jack-
screw when a force of 40 pounds is applied at
the end of a lever arm 2 feet long, the pitch of
the screw being 0.3 inches ?
7. In a letterpress (Fig.
38) the threads are 0.25 inches .
apart and the hand wheel is
14 inches in diameter. If a
15-pound pull is applied to
the rim of the wheel, how much force is brought to
bear on the book?
8. The pitch of the screw of a bench vise (Fig. 39)
is 0.2 inches and the handle of the screw is 7 inches long.
What force could be exerted by the jaws of the vise if a force of 28
pounds were applied at the end of the handle?
FiQ. 38.— Letterpress.
Fig. 39. — Ma-
chinist's vise.
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SIMPLE MACHINES 37
9. The lever in a jackscrew extends 2 feet from the center. If a
raan is able to lift 25 tons by exerting a pressure of 100 pounds, how
many threads to the inch must there be ?
10. In the preceding problem, what is the mechanical advantage ?
11. In the crane shown in figure 37, the weight W is 6 tons, and the
radii of the three small cogwheels are supposed to be equal and each
J the radius of the crank P and of the wheels B and A which are also
equal. What is the mechanical advantage of the whole machine, and
what force, neglecting friction, must be applied at P? '
12. The pedal of a bjcycle is halfway down and is pressed down
with a force of 100 pounds. The crank arm is 6 inches long and the
sprocket wheel is 8 inches in diameter. Find the tension or pull on the
chain.
13. In the preceding problem the sprocket wheel attached to the rear
wheel is 2.5 inches in diameter and the wheel is 28 inches in diameter.
How far does the bicycle go when the pedal makes one complete revolu-
tion? How much does the tire of the rear driving wheel push backward
on the roadbed when the man presses 100 pounds on the pedal ?
40. Work and power. The words " work " and "power " are
often confused or interchanged in colloquial use. The term
" work" in physics means the overcoming of resistance. For
example, if a boy carries a pail of water weighing 50 pounds
up a flight of stairs 12 feet high, he does 600 foot pounds of
work. The amount of work done would be the same whether
he did this in one minute or one hour, but the amount of
power required to do this job in one minute would be 60
times the power required to do it in one hour. The term
"power" adds the notion of time. Power means the speed or rate
of doing work.
41. Horse power. The earliest use of steam engines was
to pump water from mines. This work had previously been
done by horses; so the power of the various engines was
estimated as equal to that of so many horses. Finally, James
Watt carried out some experiments to determine how many
foot pounds of work a horse could do in one minute. He
found that a strong dray horse working for a short time
could do work at the rate of 33,000 foot pounds per minute oi
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88 PRACTICAL PHT81V8
550 foot pounds per second. This rate is therefore called a
horse power. To get the horse power of an engine, compute
the number of foot pounds of work done per minute and then
divide by 33,000, or per second and divide by 550.
Horse ix)wer CH P ) = foot pounds per minute _ foot pounds per second,
33000 550
Suppose an engine is used to pump 10,000 gallons of water per hour
into a reservoir 50 feet above the supply. How much horse power is
required ?
One gallon of water weighs 8.34 pounds ; so 10,000 gallons of water
weigh 83,400 pounds. The work done in lifting this weight 50 feet is
83,400 X 50, or 4,170,000, foot pounds. Since this is done in one hour, the
work per minute is ^^V^^ ^^ 69,500 foot pounds. The horse power
required would be ff^ or 2.1 H. P.
42. Transmission of power. In any shop containing sev-
eral machines one easily distinguishes two kinds — the driv-
ing machines^ which may be steam, gas or hot-air engines, or
water or electric motors, and the driven machines^ sucli as
lathes, drills, planers, and saws. There must always be some
connecting link between a driving and a working ma-
chine; that is, some means
of transmission. If these ma-
chines are not far apart, the
common method is to use shaft-
ing, belts, chains, or cogwheels;
but when the prime mover and
the driven machine are widely
separated, sometimes even
miles apart, some form of elec-
trical transmission is used.
Electrical transmission will be
(b) — explained later in Chapter
Fig. 40. — Transmission of power by a XVIII.
^®^*' ' When a belt, rope, cable, or
endless chain is used, it passes over two pulleys, as shown in
figure 40. In case /i, the pulleys rotate in the same direction,
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SIMPLE MACHINES 39
while in case J, where the belt is crossed, they rotate in op-
posite directions. It is evident that the small pulley turns
just as many times as fast as the large pulley, as the circum-
ference (or diameter) of the small pulley is contained in the
circumference (or diameter) of the large pulley.
The same is true of cogwheels, and since the teeth on the
perimeters of two interlocking wheels must be the same size,
it follows that the number of cogs on each wheel is a measure
of its circumference. The speeds of two such wheels are in-
versely proportional to the number of teeth on them. Just
as in the case of two pulleys with a crossed belt, two cog-
wheels rotate in opposite directions.
Suppose a pulley A is driving a second pulley B by means
of a belt, as shown by the arrows in figure 40 ; both sides of
the belt must be under some tension in order to give the
necessary pressure on the pulleys, so that the friction may
keep the belt from slipping. It is the usual practice to drive
with the upper side of the belt slack, so that any sagging due
to the weight of the belt may increase the arc of contact.
The tension, then, on the lower side (T) must be greater
than the tension on the upper side (f). It is the difference
in tension (T— 0 of the two sides of the belt which measures
the foree involved in the transmission of power. The work
done in one minute is equal to the difference in tension times
the speed of the belt in feet per minute.
Horae Dower = ^^^''^^^^ "^ tension x speed (ft per min.)
*^ 88000
Problems
1. If it takes 22 pounds to pull a 200-pound sled along a level road
covered with snow, how much work is done in dragging the sled 50 feet?
2. In the preceding problem, if the sled is drawn at the rate of 4
miles an hour, how many horse power are required ?
3. How much work can a 5-horse-power engine do in 10 minutes ?
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40 PRACTICAL PHT8IC8
4. What is the horse power of an elevator motor, if it can raise the
car with its load, 1500 pounds in all, from the bottom to the top of a
100-foot building in 10 seconds ?
5. An aeroplane with a 50 horse-power engine makes 60 miles an
hour. What is the backward thrust of the propeller?
6. A locomotive pulling a train along a level track at the rate of
25 miles an hour expends 75 horse power. Find the total resistance
overcome.
7. A motor has a 4-inch pulley which is belted to a 16-inch pulley on
an overhead shaft. The motor is making 1800 revolutions per minute.
What is the speed of the overhead shaft ?
8. In an electric car motor a pinion or small cogwheel, attached to
the armature shaft, has 20 cogs, and the gear wheel attached to the
car axle has 36 cogs. If the car wheel is 33 inches in diameter, find
the number of revolutions the motor makes while the car goes 100
feet.
9. If the tension T in the tight side of a belt 1 inch wide can safely
be 44 pounds greater than the tension t in the slack side of the belt, how
fast must the belt run to transmit 1 horse power?
10. It takes about 4 times as great a thrust to drive an aeroplane ai
80 miles an hour, as to drive the same aeroplane at 40 miles an hour.
Compare the horse powers required at the two speeds.
43. Friction. In the study of machines thus far we have
assumed that we were dealing with ideal or perfect machines,
in which the output equals the input. But in every actual
machine the output is not quite equal to the input. This
loss or waste of work is due to friction. By friction we mean
the resistance which opposes every effort to slide or roll one body
over another. This resistance, which always opposes the mo-
tion of the machine, depends on the condition of the rubbing
surfaces. Great pains are therefore taken to diminish the
friction as much as possible by making the surfaces which
are to rub together smooth and hard, and by using various
lubricants, such as soap and paraffin on wood, and grease,
oil, and graphite on metal. For example, in a watch, the
hardened steel axles turn in jewel bearings, which are the
hardest and smoothest bearings known, and are lubricated
with a special oil made for the purpose.
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SIMPLE MACHINES 41
44. So-called laws of friction. The factors which control
friction in any actual case are so numerous and so dependent
upon the conditions, that only the most general principles may
be stated positively. (1) Experience shows that starting
friction is greater than sliding friction. For when we push
a box across the table, we find that the force necessary to
overcome the resistance of friction, which acts like a back-
ward drag, is greater at the start than when the box is once
in motion. (2) Friction does not mijch depend on velocity,
but is a little greater at slow speeds. (3) Friction depends
very much on the nature of the rubbing surfaces. (4) When
a box is loaded, it requires much more force to pull it along
than when it is empty. Careful experiments seem to show
that the force needed to slide a given box over a certain floor
is just about doubled when the pressure (weight of box and
load) is doubled, and tripled when the pressure is tripled.
That is, the force needed to overcome the friction seems to
be proportional to the pressure. Experiments show that this
force of friction may be a very small fraction of the pressure,
such as 0.06 in the case of lubricated iron on bronze, or a
large fraction of the pressure, such as 0,4 in the case of oak
on oak without lubricant,
45. Coefficient of friction. This fraction, the friction divided
by the pressure^ is called the coefficient of friction.
Coefficient of friction = force of friction
pressure or weight
In accordance with the statements in the last paragraph,
the coefficient of friction for any particular pair of surfaces
is pretty nearly constant for different loads or speeds. This
is, however, only an approximation to the truth. Thus it
has recently been found that the coefficient of friction of
brake shoes on railroad car wheels nearly doubles when the
speed drops from 60 miles an hour to 20 miles an hour.
This is why an engineer or motorman lessens the pressure of
his brakes as his train or car slows down.
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42 PRACTICAL PHT8IC8
The usefulness of even roughly accurate coefficients of
friction is that they give some idea of how much resistance
has to be overcome in any given case. Thus in the country,
farmers often haul stones and pieces of heavy machinery on
low sledges without wheels, called stone boats. To calcu-
late how much force is needed to drag such a stone boat, one
has only to look up th^ coefficient of friction between wood
and dirt (about 0.66) in an engineer's handbook, and multi-
ply it by the weight of the boat and its load. For
Force of frictioii = coefficient of frictton x pressure.
46. Advantages of friction. In general it is true that
friction reduces the amount of useful work which can be
gotten out of a machine, yet it must not be forgotten that
many machines depend upon friction for their operation.
Without friction, belts would not cling to their pulleys,
ropes could not be made, nails and screws would be useless,
and even walking would be impossible, as any one can see
who has experienced the difficulty of running on a polished
floor or on ice. It is friction which has made possible our
high-speed express trains ; first because it is the friction or
traction between the driving wheels of the locomotive and
the rails that enables them to move at all, and second, because
it is the friction between the brakes and the car wheels that
enables them to stop quickly
in case of emergency.
47. Rolling friction.
Every one knows that the
friction which opposes drag-
ging a load along can be
greatly reduced by mount-
ing the load on wheels, but it
should be noticed that even in this case there is something
equivalent to friction between the wheels and the roadbed.
When a car wheel rolls over a smooth track, as shown in
Fig. 41. — Rolling friction (exaggerated).
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SIMPLE MACHINES 48
figure 41, its own weight and that of its load flatten it a little
where it rests on the track, and also make a slight depression
in the track. So as it rolls along it is continually forced to
climb up out of the depression. Of course this depression is
not easy to detect in the case of a steel track, but in the case
of a soft dirt road it is very considerable. It is for this
reason that the wheels of wagons which carry heavy
loads are provided with wide tires so as to sink less
into the roadbed ; and for just this reason the hard sur-
faces of car wheels and tracks enable a locomotive to pull
enormous loads. This resistance to rolling is called rolling
friction.
The great advantage of ball and roller bearings is that
they substitute rolling for sliding friction between the axles
and their bearings. But even in ball bearings there is
some sliding friction where adjoining balls rub against each
other.
48. Efficiency of machines. The efficiency of a machine
is the ratio of output to input. It is usually expressed as a
per cent; that is, the output is a certain per cent of the input
delivered to the machine.
EfficiencT = ^^^P^^ = work done by machine^
input work done on machine'
or Output = efficiency x input.
For example, suppose we have an inclined plane of 5% grade (5 feet
rise in 100 feet) and a load of one ton. If, because of friction, it takes a
pull of 150 pounds to haul the load up the slope, what is the efficiency?
In lifting 2000 pounds 5 feet, we do 10,000 foot pounds of work ; this is
the output. But we must pull with a force of 150 pounds through 100
feet, or put in 15,000 foot pounds of work. Therefore the efficiency is
The efficiency of a lever where the friction is very small is nearly
100 %, but in the commercial block and tackle it is sometimes less than
50%, and in the jackscrew, the friction is so large that the efficiency is
often as low as 25 %.
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44 PRACTICAL PHYSICS
Problems
1. A tool is pressed on a grindstone with a force of 25 pounds ; the
coefficient of friction is 0.3. What is the backward pull of friction?
2. The coefficient of friction between the driving wheels of a loco-
motive and the rails is 0.25. How much must the locomotive weigh in
order to exert a pull of 10 tons ?
8. A test shows that it takes a pull of 17 pounds to pull on ice a man
weighing 150 pounds. What is the coefficient of friction ?
4. In lifting a 1250-pound block of marble to a height of 90 feet, the
hoisting engine did 125,000 foot pounds of work. What was the efficiency
of the hoist ?
5. What load can a pair of horses, working at the rate of 2 horse
power, draw along a level highway at the rate of 3 miles an hour, if the
coefficient of friction of the wagon on the road is 0.17 ?
6. With a certain block and tackle it is found that a force of 125
pounds is necessary to lift a weight of 500 pounds, and the force must
move 6 feet in order to raise the weight 1 foot. What is the efficiency
of this block and tackle ?
7. A motor whose efficiency is 90 % delivers 5 horse power. What
must be the input?
8. A hod earner, weighing 160 pounds, carries 100 pounds of brick
up a ladder to a height of 35 feet. How much work does he do in all?
How much of it is useful work ?
9. What is the efficiency of a pump which can deliver 250 cubic feet
of water per minute to a height of 20 feet, if it takes a 10 horse-power
engine to run it?
10. A steam shovel driven by a 6 horse-power engine lifts 200 tons of
gravel to a height of 15 feet in an hour. How much work is done against
friction ?
SUMMARY OF PRINCIPLES IN CHAPTER H
The principle of moments: used in solving all kinds of levers
straight and bent, the wheel and axle, etc. ; —
Effort X lever arm = resistance x lever arm.
To get force on fulcrum : or to solve a pulley system,
Sum of forces up = sum of forces down.
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SIMPLE MACHINES 46
Laws of equilibiium : applicable to any object at rest under the
action of two or more forces ; —
(1) Sum of forces in any direction
= sum of forces in opposite direction.
(2) Sum of moments clockwise around any point
= sum of moments counter-clockwise around same
point.
The principle of work; —
Work (foot pounds) = force (pounds) x distance (feet).
In any ftictumless machine,
Input = output.
If there is friction^
Input = output + work lost by friction.
Power = rate of doing work.
I horse power = 660 foot pounds per second,
= 33,000 foot pounds per minute.
Coefficient of friction = ^^^^^ ^^ ^^^^^'^^
pressure
Force of friction = cpefficient x pressure.
Effidency=?H^.
mput
Output = efficiency x input.
Questions
1. Make a list of a dozen applications of the simple machine ele-
ments described in this chapter that you have seen outside of the class-
room within a week.
2. Distinguish between the popular use of the term " work " and its
technical xiae in physics and engineering. Give an example of " work "
that is not technically " work."
3. Analyze the working of the following machines : clothes wringer,
broom, ice-cream freezer, plow, grindstone, and rotary meat chopper.
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PRACTICAL PHT8IC8
4. Distinguish between the terms ** mechanical advantage" and
" efficiency." Illustrate by an example.
5. Is there any << mechanical advantage" in an equal arm lever 1
Why is it often used in machines ?
6. Why is an unequal arm lever useful?
7. 'Show how the principle of work applies to the lever.
8. How would you calculate the moment of the
force F as applied to the grindstone in figure 42 ?
9. Why are you likely to twist off the head of a
screw by using a screwdriver in a bit brace ?
10. When a machinist speaks of " an 8-32 screw,*
what does he mean ?
11. What is meant by a perpetual -motion ma-
chine ?
12. What kind of lubricant is used on journals of
car wheels? What kind on clocks and watches?
Why the difference in kind of lubricant ?
13. What determines the " angle of repose," or
slope, of the rock waste, or talus, at the base of a cliff?
14. Why are the modern air brakes on cars more effective than the
old-fashioned hand brakes ?
Fig. 42.— Crank on
grindstone.
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CHAPTER III
MECHANICS OF LIQUIDS
Hydraulic machines — Pascal's principle of transmitted pres-
ire — applications in presses and elevators — pressure in a
jquid due to its weight — levels of liquids in connecting vessels
— upward pressure of liquids — Archimedes' principle and its
applications — specific gravity of solids and liquids — city water
works, faucets, gauges, and meters — water wheels — interaction
between solids and liquids — capillarity.
49. Hydraulic machines. As we continue our study of
machines we find some machines that involve more than the
simple elements, the lever, the pulley, and the screw. For
instance, there are a great many machines that make use of
liquids, such as the water wheel, hydraulic press, and
hydraulic elevator. These are called hydraulic machines,
and this chapter will be devoted to the
study of them. In the course of it we
shall also have to consider dams and reser-
voirs, as well as all sorts of things that
float or sink in water.
50. Pressure transmitted by a liquid.
JSuppose we fill a bottle with water and close it
"with a one-hole rubher stopper. Then let us fasten
the stopper securely, as shown in figure 43, and
force into the hole a metal rod of such a size as to
fit rather tightly. The force applied to the rod
will be transmitted to the inner surface of the
bottle, and the bottle will burst.
This experiment shows that the water Fig. 43. -Water trans-
, . , . . • a. xi 1 ^^ B ™its pressure of pis-
which 18 pressing against the bottom of ton.
47
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48
PRACTICAL PHYSICS
Fig. 44. — PascaVs principle.
the piston is also pressing against everything else that
it touches.
51. Pascal's principle. It seems reasonable to suppose
that if we had a box filled with water and fitted with
two equal pistons A and B^ as
in figure 44, the water would
press equally hard on each pis-
ton. It is also evident that* if
a third equal piston were placed
in the side of the box, as at (7,
the water would press sideways
on it with an equal force.* In
short, if a liquid is pressing
against any square inch tvith a
certain force^ it is pressing equally hard against every square
inch of everything it touches,
52. The hydraulic press. The most useful application of
this principle can be described in Pascal's (1623^1662) own
words: "If a vessel full of water, closed in all parts, has
two openings, of which the one is a hundred times the other,
placing in each a piston which fits it, the man pushing the
small piston will equal the force of a hundred men who push
that which is a hundred times as large, and surpass that of
ninety-nine. Whatever proportion these openings have, and
whatever direction the
pistons have, if the forces
that apply on the pistons sa- in,
are as the openings, they
will be in equilibrium."
100 lbs.
lib.
1 sq. in
Fia. 46. — Diagram of hydraulic press.
This refers to a mechanism
like that shown in figure 45.
Suppose there is a force of
one pound pushing down on the small piston, and that the large piston
has 100 times as great an area. Then there must be 100 pounds push-
ing down on the large piston to balance it. It will be seen, however,
* The effect of the weight of the liquid is here neglected.
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Blaise Pascal. French scientist and mathematician. Bom 1623. Died 1662.
Studied the pressures exerted by liquids and gases. Famous also for his
achievements in mathematics.
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MECHANICS OF LIQUIDS
49
that the pressure on each square inch of the large piston is one pound.
In other words the pressure has been transmitted by the liquid so as to
act with the same force on every square inch.
53. Applications of the hydraulic press. This device of
Pascal gives us an easy way of exerting enormous forces,
such as are needed in baling paper, cotton, etc., in punching
holes through steel plates, and for extracting oil out of seeds.
The commercial machine (Fig.
46) is exactly like that described
by Pascal except that there is
usually a check valve (v) between
the small piston and the big one,
and the small piston is arranged
to work like a pump, with a
valve (^d) at the bottom for admit-
ting more oil. Often the small
piston is forced down by a lever.
The method of operation is sim-
ple. On the upstroke of the
pump piston, the valve at the
bottom of the pump opens and oil flows in from the reser-
voir. On the downstroke of the pump piston, the oil is
forced over through the connecting pipe past the valve, and
pushes the large working piston up very slightly. If the
large piston is 100 times as large in cross section as the
smaU piston (i.e. diameters as 10 : 1), the large piston is
lifted only yJtj- the distance the pump piston is pushed down
each stroke. But since the force exerted by the large piston
is, neglecting friction, 100 times that applied to the small
piston, it follows that the work done on the machine is equal
to the work done by the machine. If we consider the work
done against friction, the equation becomes, —
Input = output + work done against friction.
54. Working model of a hydraulic press. Let us try to appreciate
the tremendous forces which are obtainable with the hydraulic press by
Fig. 46. — Hydraulic press.
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PRACTICAL PHT8IC8
operating a model press, such as is shown in figure 47, to break a stictt
of wood. By measuring the diameters of the pistons, and the lengths
of the lever arms, we may calculate the total mechanical advantage of
the machine.
Fig. 47. — Wprking /model of
hydraulic press.
Fig. 48. —Hydrostatic
bellows.
Another striking experiment is to let a boy bal-
ance his own weight against a column of water by
means of the hydrostatic bellows (Fig. 48). By cal-
culating the actual areas involved and the force
acting on each square inch, we may compute the
height of water that should be required and compare
this with the actual height.
55. Hydraulic elevators. Pascal's prin-
ciple is also used in hydraulic elevators,
which are commonly employed where heavy-
machinery is to be lifted. A simple form
is shown in figure 49. At the bottom of
the elevator well is a pit as deep as the building is high.
In the pit is a cylinder ((7) and in this cylinder is a plunger
<]P), to the top of which the elevator cage (^A) is firmly
fastened. Wh^n water under pressure (often simply the
pressure of the water mains) is admitted through the valve
(v^ into the cylinder, the plunger rises and forces up the
elevator. The weight of the elevator is partly counter-
Fio. 49.— Hydraulic
elevator.
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MECHANICS OF LIQUIDS 61
balanced by a weight (TT). When the operator, by pulling
the cord, turns the valve so as to connect the cylinder in
the pit with the sewer pipe, the elevator comes down.
When speed is demanded, as in high office buildings, the
motion of the hydraulic plunger is communicated to the
cage by a cable passing over a series of pulleys, so that
the cage moves four times as far and four times as fast as
the plunger.
56. Pressure and force. It is necessary to distinguish be-
tween the terms pressure and force. Force means a push or a
pull^ and is usually expressed in terms of the push or pull
necessary to hold up a given weight, such as a pound or
a kilogram. Pressure means the push or pull per unit area
of surf ace. Pressure may be expressed in various ways, for
example, as so many grams per square centimeter or so many
pounds per square inch.
The real advantage of the hydraulic press is that, although
the pressure on the large piston is exactly the same as that
on the small piston, the force exerted by the large piston is
many times greater.
Problbms
1. If the diameters of two pistons in a hydraulic press are 1 inch and
to inches, what are their areas of cross section ?
2. If the small piston in problem 1 is subjected to a pressure of
10 pounds per square inch, what pressure, neglecting friction, must be
applied to the large piston to hold it in place ?
3. If a total force of 10 pounds is applied to the small piston in prob-
lem 1, what total force must be ap{>lied to the large piston to hold it
in place?
4. The diameters of the pistons in a hydraulic press are 20 inches and
1 inch. What must be the force on the small piston if a force of 5 tons is
to be exerted by the large piston?
5. In problem 4, suppose the small piston to move 1 foot. How far
does the large piston move ?
6. If the water pressure in a city water main is 50 pounds per square
inch and the diameter of the plunger of an elevator is 10 inches, how
heavy a load can the elevator lift? If the friction loss is 25%, what
load can be lifted ?
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62 PRACTICAL PHYSICS
57. Pressure in a liquid due to its weight. Not only does
a liquid transmit pressure when it is in a closed vessel, but a
liquid in an open vessel, such as water in a tin pail, exerts a
pressure on the bottom of the vessel because the liquid is it-
self heavy. This bottom pressure, that is, the force on each
square inch, evidently depends on the depth of the liquid^ and
also an its density.
For example, suppose we have a box with a bottom 10 centimeters by
20 centimeters and 15 centimeters deep, filled with water. Then on
each square centimeter of the bottom of the box there rests a columfa of
water 15 centimeters tall, weighing 15 grams, and so the pressure on the
bottom is 15 grams per square centimeter. The total downward force of
the water against the bottom would be 200 x 15, or 3000 grams, for
Total force = area x pressure.
If the box were filled with mercury instead of water, the pressure on the
bottom would be the weight of a column of mercury 15 centimeters high
and 1 square centimeter at the base ; that is, the weight of 15 cubic
centimeters of mercury. Since 1 cubic centimeter of mercury weighs
13.6 grams, 15 cubic centimeters would weigh 15 x 13.6, or 204 grams.
The total force of the mercury pushing down on the bottom of the box
would be 200 X 204, or 40,800 grams, or 40.8 kilograms.
58. Bottom pressure and shape of vessel. So far we have
considered vessels with vertical sides such as A in figure 50.
c
Fig. 50. — Vessels with {A) vertical, (B) flaring, and (C) conical sides.
In the ordinary pail, however, the sides are not vertical, but
flare outward as shown in B in figure 50. Perhaps one
might expect that the pressure on each square centimeter of
the bottom would be greater than in case Ay because there is
so much more water in the vessel. This, however, is not
the case. Each square centimeter of the bottom has to hold
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MECHANICS OF LIQUIDS
53
up only the little column of water above it just as it did in
case A. The extra water above the slanting sides is held up
by those sides and not by the bottom. If the area of the
base and depth of liquid is the same in both A and B^ then
the total downward push of the liquid on the bottom will be
the same even though B holds more liquid than A.
In case (7, the depth of liquid and area of base are the
same as in cases A and B^ but the top is smaller than the
base. It is easy to see that the pressure on that portion of
the base ab directly under the top would be the same as in
the other vessels, but it might at first seem that the pressure
would gradually decrease as we go from a to <? and from b to
d. There is an interesting experiment devised to settle this
question.
59 Experiments with Pascal's vases. The apparatus (Fig. 51)
consists of three glass vessels of shapes to correspond roughly to A^ B,
and C in figure 50. The bottom
of each vessel is made the same
size and screws into a short cyl-
inder, across the bottom of which
is tied a disk of sheet rubber.
The pointer below is a lever with
its short arm pressing against the
center of the rubber disk, and
the long arm moves up and down
across a scale.
With this apparatus it is
possible to show that (a) the
downward pressure of a liquid
is proportional to the depths
(6) the downward pressure of a liquid is proportional to its
density^ and (<?) the dovmward pressure in a liquid is inde-
pendent of the shape of the vessel.
It seems impossible that unequal quantities of water
should exert an equal downward push against the bottom.
But if we recall that when the sides slope outward, the sides
Fig. 51. — Pascal's vases.
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PRACTICAL PHT8IC8
hold up the excess of water, we can see that when the sides
slope inward, they push down enough to make up for the
deficit in water.
60. Liquids also exert pressure sidewise. We all know
that if a hole is bored in the side of a tank or barrel of water,
the water will spurt out. This means that before the hole
was bored the liquid must have been pressing against that bit
of the side of the barrel. Liquids, then,
exert a sidewise pressure due to their
weight, as well as a downward pressure.
We can investigate how this sidewise pres-
sure varies with the depth and the direction
by means of the gauge shown in figure 52.
The apparatus consists of a rubber diaphragm,
which may be turned about a horizontal axis,
and is connected by a rubber tube to a hori-
zontal glass tube containing a globule of some
colored liquid. As we lower the pressure gauge
into the jar of water, we observe that the globule
moves to the right showing a gradual increase of
pressure with increase of depth. If we repeat
this with the diaphragm facing in another direc-
tion, we get the same result. If we hold the
frame at some fixed depth, and rotate the dia-
phragm around a horizontal axis, we find the
globule remains practically stationary, showing that the pressure is the
same in all directions.
Fig. 52. — Pressure gauge
to show pressure equal
in all directions.
The sidewise pressure of a liquid increases with the depth and
density of the liquid. At a given depth a liquid presses down-
ward and sidewise with exactly the same force.
61. Calculation of sidewise pressure. To calculate the
sidewise push of water against a dike or dam, we have to
remember that both the downward and sidewise pressure
increase gradually from zero at the surface to theii value at
the bottom. We have already seen that this bottom pressure
is equal to the weight of a column of water with a base one
unit square and with a height equal to the depth. The
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MECHANICS OF LIQUIDS
55
fio.
15 cm
20 cm,
53. — Sidewise push of water
against end of box.
average sidewise pressure is equal to the pressure halfway
down, or is one half the bottom pressure. The total side-
wise push of the water against the dam is then equal to the
area times the average pressure.
For example, suppose we have a box 10 centimeters wide, 20 centi-
meters long, and 15 centimeters deep filled with water. What is the
toted force tending to push out the end of the box ? The pressure at a
point halfway down the side would
be 7.5 grams per square centimeter.
There are in the end 10 x 15, or 150
square centimeters. Therefore the
total force against the end is 150 x
7.5, or 1125 grams.
Again, suppose the box were a
large tank full of water, and the di-
mensions, expressed in feet, were 10
by 20 by 15. What is the end thrust?
The pressure halfway down would be
the weight of a column of water with
1 square foot for its base and 7.5 feet high, i.e, 7.5 x 62.4, or 468 pounds per
square foot. Since there are 10 x 15, or 150 square feet, in the end of the
tank, the total end thrust is 150 x 468, or 70,200 pounds, or about 35 tons.
62. Levels of liquids in connecting vessels. Probably every
one has observed that water stands at the same level in the
spout of a teakettle as in the
kettle itself (Fig. 54). In other
words, liquids seek their own level,
or the same liquid in any number
of connecting vessels will have
its free surface at the same level
in each. This is to be expected
from the fact that the pressure in
a liquid depends upon the depth
below the free surface. Thus if
any point in the connecting por-
tion between the two vessels were unequally far below the
two surfaces, the pressures in either direction would not
FiQ. 54. — Water seeks its own
level in a teakettle.
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PRACTICAL PHYSICS
balance, and the liquid would flow from one vessel to the
other until the levels were equalized.
The water gauge on a steam boiler (Fig. 65) is a good
application of this principle. The
gauge consists of a thick- walled glass,
tube which connects at the top with the
steam space, and at the bottom with the
water in the boiler. The valves A and
B are closed when the glass tube is to
be replaced. The valve 0 is opened oc-
casionally to test the gauge to see that it
reads correctly and has not clogged up.
63. Upward pressure of liquids. If
one tries to push a pail under water
bottom downward, he finds he must
overcome considerable resistance because
Fig. 66.- Water gauge on ^f ^he upward push of the water on the
pail. In order to see just how much
this upward push of the water is, let us try the following
experiment.
Let a glass cylinder, which has its bottom edge ground off smooth^
be closed with a glass plate or piece of cardboard, held in place by &
thread, as shown in figure 56. When we
push this cylinder into a jar of water, we
can let go the thread and yet the glass
bottom will not fall off. It is evident
that there is an upward pressure due to
the water, and the next question is, how
much? If we pour colored water into
the cylinder until the bottom drops
off, we shall have to fill the cylinder
until the levels inside and outside are
the same.
In general we may say that tJie
toward pressure exerted hy a liquid
at any depth is equal to the down-
FlQ.
56. — Upward pressure ol
water.
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MECHANICS OF LIQUIDS
57
ward pressure which would be exerted
the same depth.
Problbms
the same liquid at
What is the pres-
^
1. The water in a standpipe is 10 meters deep,
sure on one square centimeter of the bottom ?
2. The water in a standpipe is 40 feet deep. What is the pressure
on one square inch of the bottom ?
3. If the diameter of the tank in problem 2 is 10 feet, what is the
total force which the bottom of the tank must sustain ?
4. A diver goes down into sea water (density 1.03 grams per cubic
centimeter) to a depth of 10 meters. What is the pressure on him in
kilograms per square centimeter?
5. The hydraulic engineer speaks of pressure as "head of water/*
which means the pressure due to the weight of column of water as high
as the " head of water." Express in pounds per square inch a " head of
50 feet."
6. What is the pressure, near the keel, on a vessel drawing 6 meters?
7. Figure 57 is a cylindrical tank 10 x 12 centi-
meters ; out of the top rises a tube 20 centimeters long.
The box and tube are filled with water.
(a) Find the pressure in grams per square centimeter
at the bottom of the tank.
(b) Does the size of the tube affect the pressure on the
bottom?
(c) Find the pressure halfway up the side of the tank.
(d) Find the pressure at the top of the tank.
8. A rectangular tank is 5 feet wide, 10 feet long,
and 4 feet deep. Calculate the total force exerted on
the end when the tank is f uU of water. V-12 cm,
9. Assuming that a cubic inch of mercury weighs Fig. 57. — Box
0.49 pounds; find the pressure on the bottom of a tum- and tube full
bier in which the mercury stands 4 inches deep. ^^ water.
10. How high a column of water could be supported by a pressure of
one kilogram per square centimeter?
11. If the density of mercury is 13.6 grams per cubic centimeter, what
is the pressure exerted at the base of a column 76 centimeters high ?
12. A dam is 50 feet long and 6 feet high, and the water just reaches
the top. What is the total force against the dam?
13. A hole 6 inches square is cut in the bottom of a ship drawing lb
feet of water. What force must be exerted to hold a board tightly
against the inside of the hole?
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PBACTICAL PHYSICS
14. How much " head of water " is needed to give a
pressure of 1 pound per square inch ?
15. What must be the difference in height between a
fire hydrant and the surface of the water in a city res-
ervoir to give a pressure of 50 pounds per square inch
at the hydrant?
16. In figure 58, the U-tube is partly filled (BAC)
with mercury whose density is 13.6 grams per cubic
centimeter, and partly {CD) with a liquid of unknown
density. If the length of the column BA is 5 centi-
meters and that of the column CD is 75 centimeters,
what is the density of the liquid ?
64. Buoyant effect of liquids. When swim-
Fia. 58.— u-tube ming in deep water, we find that our bodies are
and ™nothS very nearly floated. When we pick up a stone
liquid. under water, we find it much heavier if we lift
it above the surface. Things seem to be lighter
under water ; in other words, water buoys up anything placed
in it. In order to find how much lighter anything is under
water than it is out of water let us try the following
experiment.
We have a hollow metal cylindrical cup C, and a cylindrical block
Bf which has been nicely turned to fit inside the cup C. We hang both
from a beam balance, as shown in figure 59, and counterbalance with a
weight W on the other scalepan. Then
we bring a glass of water up under
the block B, so that it is entirely
under water. The left-hand side of
the balances rises, which shows the
upward push of the water upon B,
But we can restore the equilibrium
again by pouring water into the cup
C until it is just filled. This shows
that B loses in apparent weight the
weight of its ovm bulk of water. If we
try the experiment, using kerosene
instead of water, we find that exactly
the same thing is true. Fig. 59. — Buoyant effect of liquids.
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MECHANICS OF LIQUIDS
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65. Archimedes' principle. The principle proved by this
experiment may be stated as follows : —
The loBB of wdght of a body svhmerged in a liquid is the
weight of the displaced liquid.
It is supposed that this principle about the loss of weight
of a body in a liquid was discovered by the old Greek phi-
losopher Archimedes (287-212 B.C.). Hiero, king of Syra-
cuse, suspected a goldsmith who had made a crown for him,
and ordered Archimedes to find out if any silver had been
mixed with the gold in the crown. To do this without
destroying the crown seemed a puzzle at first, but one day,
while Archimedes was in the public bath, he noticed that
his body was buoyed up by the water in which it was sub-
merged. Seeing in this effect the solution of his problem,
he leaped from the bath and rushed home shouting, " Eureka I
Eureka I" (I have found it ! I have found it I).
66. Explanation of Archimedes' principle. This principle will
be readily understood from the following example. Suppose we place a
rectangular block in ajar of water, as shown
in figure 60. Let the block be 10 x 6 x 4
centimeters and let the top be 5 centimeters
below the surface of the water, and the
bottom 15 centimeters beneath the surface.
Then the pressure on top, that is, the down-
ward push on each square centimeter, is 5
grams and the pressure on the bottom, that
is, the upward push on each square centi-
meter, is 15 grams. Since the top and
bottom each have an area of 6x4, or 24
square centimeters, the whole upward push
on the bottom is 24 x 15, or 360 grams,
while the whole downward push on the top
is only 24 x 5, or 120 grams. This leaves
a net upward force or buoyancy of 240
gi'ams. But this is exactly the weight of
the displaced water, for the volume of the displaced water is 10 x 6 x 4=
240 cubic centimeters, and we have seen in section 11 that this much
water weighs 240 grams.
Fig. 60. — Lifting effect of
water on submerged block.
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60 PRACTICAL PHT8IC8
The same sort of reasoning would hold at any depth and
for any liquid other than water and with any irregular-
shaped body. So it may be said that in any liquid of any
density a body seems lighter by the weight of the displaced
volume of that liquid.
67. Floating bodies. Let us think what will happen if
this upward force, or buoyant force, is more than the weight
of the body submerged. Evidently the body will rise and
will continue to rise as long as the upward push remains
greater than the downward pull of gravity. But as soon as
any of the body projects above the surface, less water is dis-
placed and the upward push is less. When enough of the
body projects to reduce the buoyant force to equality with
the weight, the body stops rising and floats. In this case we
see that the loss of weight is the whole weight itself.
A floating body displaces its own weight of the liquid it is
floating in.
The following experiment .will help to make this principle of Archi-
medes, as applied to floating hodies, seem more real. Suppose we balance
an overflow can on a platform scale,
as shown in figure 61. The can is
filled with water so that it just over-
flows and is balanced by the weight
on the other platform. We will place
a dish to catch the overflowing water,
and then put a block of wood gently
in the can. After the water has
^.^ ... ..^. , , stopped overflowing, it will be seen
no. 61-We^ht^f hq^id displaced ^J^j,^ scales again balance. This
means the weight of water which
flowed over was just equal to the weight of the block. This can be veri-
fied in another way by weighing the water displaced by the block.
68. Applications of Archimedes' principle. If we know
the total weight of a ship and its equipment, we can tell at
once what weight of water it will displace, and so it is possible
to compute how deep it must sink to displace its own weight
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MECHANICS OF LIQUIDS
61
of water. It is also evident that a boat must sink a little
deeper in fresh water than in salt water, and will sink deeper
when loaded than when empty. A submarine boat is so
constructed that it is only slightly lighter than water. It
can then be submerged by letting water into certain tanks
and can be made to rise by pumping the water out of the
tanks. This same idea is made use of in the floating dry-
dock shown in figure 62. When the tanks 7, 7, T are full
of water, the dock sinks
until the water level is at
LL. The ship to be re-
paired is then floated into
the dock and the water is
pumped out of the tanks
r, r, T. As the com-
partments are emptied of ^^«- 62.-Floatmg dry^ock.
water, the dock rises until the water level is at the line W, W,
lifting the ship out of water. The ship and dry-dock still
displace their own weight of water, but the displacement is
in a different place.
Problems
1. A piece of stone weighing 235 grams in air and 128 grams in water
is put into a dish just full of water. How much water runs over?
2. A rowboat weighs 200 pounds. How many cubic feet of water
does it displace ?
3. A barge is 30 feet long and 16 feet wide, and has vertical sides.
When a large elephant is driven on board, it sinks 4 inches farther in
the water. How many tons does the elephant weigh?
4. What is the volume of a 125-pound boy, if he can float entirely
submerged except his nose ?
5. A rectangular block is 22 centimeters long, 6 centimeters wide, and
4 centimeters high, and floats in water with 1 centimeter of its height
above water. How much does it weigh?
6. A cube 5 centimeters on an edge weighs 600 grams in air. How
much does it weigh in water ? ,
7. How much will a cubic foot of brass (density 8.4 grams per cubic
centimeter) weigh in gasolene (density 0.79 grams per cubic centimeter) 1
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62 PRACTICAL PHT8IC8
8 A rectangular solid 10 x 8 x 6 centimeters is submerged in water,
so that the top, whose dimensions are 10 x 8 centimeters, is horizontal
and 12 centimeters below the water surface.
(a) Find the totAl force pressing down on the top.
(b) Find the total force pushing up on the bottom.
(c) Find the lo^i of weight of the solid.
69. Specific gravity and density. Archimedes' principle
furnishes us with a convenient method of comparing the
weight of a substance with the weight of an equal bulk of
water. The ratio of these weights is called the specific
gravity of the body. In other words,
SDecific gravitv - weight of body
specific gravity - weight of equal bulk of water
For example, a piece of marble weighs 100 grams and an equal bulk
of water weighs 40 grams, then the marble is 100/40 or 2.5 times aa
heavy as the water. The specific gravity of marble, then, is 2.5i
The term specific gravity does not mean quite the same
thing as density. The specific gravity of a substance is an
abstract number ; for example, the specific gravity of mercury
is 13.6. But the density of a substance is a concrete number ;
for example, the density of mercury is 13.6 grams per cubic
centimeter, or 850 pounds per cubic foot.
In the metric system, the density of water is one gram per
cubic centimeter, and therefore
Density (g. per cm.') = (numerically) specific gravity.
In the English system, the density of water is 62.4 pounds
per cubic foot, and therefore
Density (lbs. per cu. ft.) = (numerically) 62.4 x specific gravity.
70. Methods of determining specific gravity of solids.
General Rule. First weigh the object. Next find by
some indirect method the weight of an equal bulk of water.
Finally divide the weight of the object by the weight of the
equal bulk of water.
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MECHANICS OF LIQUIDS
68
This general statement covers all the vanous processes
for finding the specific gravity either of solids or of liquids.
The different procedures vary only in the method of finding
the weight of an equal bulk of water.
1st Method. If the object is a regular geometrical solid, you
can measure its dimensions and calculate its volume, and from
that get the weight of an equal bulk of water.
Sd Method. If the object is a solid that will sink in water,
and will not dissolve, you can determine its loss of apparent
weight in water. This is the weight of an equal bulk of water.
That is.
Specific gravity =:, Z'^^^t^^ . '
^ ^ -r loss of weight in watf^r
For example, suppose a piece of copper weighs 178 grams in air and
158 grams in water. The loss, 20 grams, is the weight of an equal bulk
of water. Therefore the specific gravity of copper = 17 8/20 = 8.9.
3d Method. If the object is lighter than
water, and does not dissolve, select a suffi-
ciently large sinker and suspend it below the
object, as shown in figure 63. Then bring
a jar of water up under the whole thing
until the water level is between the sinker
and the object, and weigh. Then raise the
jar still farther until the water level is
above the object, and weigh again. This
weight will be less than the first because
in this case the water buoys up the object,
while in the first case it does not. The
difference between the two weights is equal
to the weight of the water displaced by the
object.
Fig. 63. — Specific
gravi t y with
sinker.
Specific erayity = ^ weight of body
«»iwvu«,i{rti«.y lifting effect of water on body only'
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64
PRACTICAL PHYSICa
It will be noticed that in this case the loss of weight or
lifting effect of the water on the body is larger than the
whole weight. This is why the body floats.
For example, suppose a piece of wood weighs 120 grams in air, and
that, with a saitable sinker, it weighs 270 grams when the sinker is under
water, and 90 grams when both are under water. Then the lifting effect
of the water on the wood is 270 - 90, or 180 grams. Therefore the spe-
cific gravity of the wood is 120/180 = 0.667.
71. Specific gravity of liquids.
l8t Method. Weigh a bottle empty, then full of the liquid,
and then full of water. Subtract the weight of the empty
bottle in each case, and then compare the weight of the liquid
with the weight of an equal volume of water.
Specific gravity =
weight of liquid
weight of equal volume of water
Bottles, called specific gravity flasks (Fig. 64), are made for
the purpose of determining the specific gravity of liquids
with great accuracy and facility. They are
usually made to contain a definite quantity of
pure water at a specified temperature; for
example, 250 grams.
ISd Method. Weigh a piece of glass in air,
then in the liquid, and then in water. Find
the loss of weight in the liquid and the loss of
weight in water. This loss of weight in the
liquid is the weight of the liquid displaced,
and the loss of weight in water is the weight
of an equal volume of water. Then
Specific craTitT - ^^" ^^ "^^^^^ ^ ^^^
specific gravity - ^^ ^^ ^^^^^ ^^ ^^^
For example, suppose the glass weighs 330 grams in air, 150 grams in
sulphuric acid, and 230 grams in water. The glass loses 180 grams in
acid and 100 grams in water. Since these are the weights of equal volumes
of acid and water^ the specific gravity of the acid = 180/100 = 1.8.
Fio. 64. — Specific
gravity fiask.
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MECHANICS OF LIQUIDS
65
Sd Method. * The most common way of determining the spe-
cific gravity of liquids is by the hydrometer. This is usually
made of glass, and consists of a cylindrical stem and a bulb
weighted with mercury or shot to make it float upright
(Fig. 66). The liquid is poured into a tall jar, and the hy-
drometer is gently lowered into the liquid until it floats freely.
The point where the surface of the liquid
touches the stem of the hydrometer is noted.
There is usually a paper s(jale inclosed inside
the stem, so made that the specific gravity (or
density in grams per cubic centimeter) can be
read off directly. In light liquids, like kero-
sene, gasolene, and alcohol, the hydrometer
must sink deeper to displace its weight of
liquid than in heavy liquids like brine, milk,
and acids. In fact it is usual to have two
separate instruments, one for heavy liquids,
on which the mark 1.000 for water is near
the top, and one for light liquids, on which
the mark 1.000 is near the bottom of the
stem.
72. Commercial uses of the hydrometer. Since the com-
mercial value of many liquids, such as sugar solutions, sul-
phuric acid, alcohol, and the like, depends directly on the
specific gravity, there is extensive use for hydrometers.
Perhaps the best-known form of hydrometer is the kind used
in testing milk, called a lactometer. The specific gravity of
cow's milk varies from 1.027 to 1.035. Since only the last
two figures are important, the scale of a lactometer is made
to run from 20 to 40, which means from 1.020 to 1.040.
The specific gravity of milk does not give us a conclusive
test as to its worth. Milk contains besides the water
Fig. 65.
Hydrometer.
* There is another method, using balancing columns, which will be de-
scribed in the Laboratory Manual. To understand it one must have read
Chapter IV.
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66 PRACTICAL PHT8IC8
(which is about 87%) some substances which are heaviei
than water, such as albumen, sugar, and salt, and others that
are lighter than water, such as butter fat. Besides the
specific gravity, one needs to determine the amount of fat,
and, if possible, the other solids in the milk, in order to
know its richness. Of course the very important question as
to the cleanliness of milk must be left to the bacteriologist.
Problems
1. A piece of ore weighs 42 granft in air and 25 grams in water.
Calculate its specific gravity.
2. A stone weighs 15 pounds in air and 9 pounds in water.
(a) Find its specific gravity.
(b) Find its density in the metric system.
(c) Find its density in the English system.
3. A body has a specific gravity of 8.5. What is its density in (a) the
metric system, and (b) the English system?
4. If the specific gravity of lead is 11.4, how many cubic centimeters
of lead does it take to make a kilogram weight?
5. If the specific gravity of cork is 0.25, how many cubic feet of cork
are there in 1 pound of cork?
6. A block of wood, 15 x 10 x 8 centimeters, floats with one of its
largest sides 2 centimeters out of water.
(a) Find its weight.
(b) Find its specific gravity.
7. A plank 8 centimeters thick floats with 5 centimeters under water.
Find its specific gravity.
8. A block of wood weighs 150 grams ; a sinker is suspended from it,
and when the sinker is under water and the block is in air, the combina-
tion weighs 3.50 grams. When the wood and the sinker are both under
water, they wei^h 100 grams. Find (a) the volume of the block of wood,
and (6) its specific gravity.
9. A cube of iron 10 centimeters on an edge (specific gravity 7.5)
floats in mercury (specific gravity 13.6). How many cubic centimeters
are above the mercury?
10. A can weighs 190 grams when empty, 600 grams when full of
water, and 613 grams when full of milk.
(a) What is the capacity of the can in cubic centimeters?
(6) What is the specific gravity of the milk ?
11. How much does 1 cubic centimeter of lead (specific gravity 11.4)
weigh in kerosene (specific gravity 0.79) ?
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MECHANICS OF LIQUIDS 67
12. A bottle weighs 80 grams empty,. 280 grains when filled with
water, and 250 grams when filled with a medicine. What is the specific
gravity of the medicine?
13. An empty bottle weighs 50 grams; the same bottle full of water
weighs 200 grams. Some sand is put inta the empty bottle and it then
weighs 320 grams. Finally the bottle; is filled with water, and the bottle,
sand, and water weigh 370 grams.
(a) Find the capacity of the bottle.
(6) Find the volume of the sand.
(c) Find the specific gravity of the sand.
14. K one buys 10 pounds of mercury (specific gravity 13.6), how
many cubic inches should one get?
15. If the inside of an ice chest measures 24 x 18 x 12 inches, how
many pounds of ice (specific gravity 0.92) will it hold ?
16. How many pounds of sulphuric acid (specific gravity 1.84) does
a 5-gallon carboy contain ?
73. City waterworks. Every city has to face the problem
of providing a plentiful supply of pure water for household
use, for industrial purposes, and for fire protection. Not
only must there be enough water, but it must be furnished
at sufficient pressure to force it to the tops of high buildings.
If the city is located near the mountains, as are Denver and
Los Angeles, it is an easy matter to conduct the water from
an elevated reservoir in large pipes or mains to the houses.
Since the water tends to seek its own level, it will rise in the
buildings to the height of the reservoir. But in most cities,
such as New York, Philadelphia, and Boston, the gravity
St/stem of waterworks is impossible and a pumping system
must be employed. The operation of the big steam pumps
that are used will be explained later (section 100).
74. Hydrants and faucets. The only parts of this great
system of water pipes which we ordinarily see are the hydrants
on the edge of our sidewalks, und the taps or faucets at our
sinks and bathtubs. These are merely valves for opening
and closing the pipes. The internal construction of the or-
dinary tap is shown in figure 66. Th^ handle operates a
screw which forces a disk, faced with a fiber washer, against
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PRACTICAL PHT8IC8
Fig. 66. —Cross section
of common faucet.
a circular opening or seat, and so shuts
off the water. If the handle is turned
the other way, the disk is raised, leav-
ing an opening. This sort of valve may
get out of order in two ways : the fiber
washer may wear out and the packing
about the handle rod may get loose.
Both of these can be easily replaced.
The packing consists of cotton twine
wrapped around the valve stem, and is held in place by
what is called a gland.
75. How we measure water pressure. Doubt-
less we have all found that water flows slowly
from a faucet on an upper floor. This is because
the water pressure is low there. To measure
it, we use some form of pressure gauge, and for
as small a pressure as this would be, an open
mercury manometer would be the most accurate
form of pressure gauge. It consists of a
U-shaped tube filled with mercury, as shown
in figure 67.
Suppose the water pressure is enough to balance a Fiq. 67.--Mep-
mercury column 4 feet high. How much is the pressure cury pressure
in pounds per square inch? A column of mercury 4 gauge,
feet high and 1 square inch at the base would contain
48 cubic inches, and would weigh 23.5 pounds. Therefore the pres-
sure of the water would be 23.5 pounds per square inch. With such
a gauge it is easy to show that the water pressure is less on the top floor
than in the basement.
A mercury gauge is so cumbersome and expensive that a
Bourdon spring gauge is generally used. It consists of a
brass tube of elliptical section, bent into a nearly complete
ring, and closed at one end, as shown in figure 68. The
flatter sides of the tube form the inner and outer sides of the
ring. The open end of the tube is connected with the pipe
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MECHANICS OF LIQUIDS
«ft
through which the liquid under pressure is admitted. The
closed end of the tube is free to move. As the pressure in-
creases the tube
tends to straighten
out, moving a
pointer to which
it is connected by-
levers and small
chains. These
spring gauges
have the scale so
graduated that Fio. 68.- Bourdon gauge.
they read directly in pounds per square inch.
76. Fluctuations in water pressure. Not only does one find
a decrease of water pressure in going from the basement to the
attic of a house, but if the gauge is attached at one point and
watched closely, it will be seen to fluctuate according as much
or little water is being drawn elsewhere in the building.
The following experiment shows the same thing on a smaller scale.
The tank or reservoir R in figure 69 is connected with a supply pipe AB,
The pressure along the pipe=
is indicated by the height
of the water in the tube*
C, A and E, When the
pipe is closed at JB, the level
is the same in 72, C, D, and
E ; this is called the static
condition. But when the
stopper is removed from By
and water flows out, the
' pressure is no longer the
same at all points along
the pipe, but falls off as the distance from the reservoir R increases.
This drop in pressure is due to friction against the walls of the pipe
through which the water has to run.
From this experiment we see that, when a number of
faucets are open and the water is flowing, the pressure in the
R
^-^^
-z^^r_^— ^-
Fig. 69. —Pressure falls with flow.
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neighborhood becomes small. To equalize these changes in
water pressure and also to provide some flexibility in the
system, it is quite common to have a standpipe in the water
system nearer the houses than the main reservoir. This also
serves as an auxiliary reservoir in case of emergency.
77. Water meter. It is common now to measure the
quantity of water which is used by each
house. This is done by an instrument
called a water meter. There are several
types of these meters ; one of the sim-
plest is shown in figure 70, and its action
is shown in the four diagrams in figure
71. The water enters through the left-
hand kidney-shaped opening, shown by
dotted lines, and leaves through the simi-
lar opening at the right. The moving
part, shown by the heavy line, has a hub
(the black circle) that travels around in
the little circular track provided for it, the moving part
meanwhile oscillating to and fro without turning completely
around. This makes the various annular spaces enlarge
as long as they are in connection with the inlet (watch.
Fig. 70. — Water meter.
Fia. 71. — Diagrams to show operation of water meter.
for example, the space marked a in the diagrams) and con-
tract when they are in connection with the outlet (watch,
for example, the space marked J). In this way each space
measures out its appropriate quantity of water and delivers
it to the outlet pipe. The number of revolutions of the hub
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MECHANICS OF LIQUIDS
71
Fia. 72. — Meter dials.
is registered on a series of dials (see
figure 72) which indicate the number
Df cubiu teet that have passed through
the meter. Thus the dials in figure
72 indicate 94,460 cubic feet. The
official of the water department reads
these dials periodically, and by sub-
tracting can easily compute the water
consumed during the period, and so
fix the charge in proportion.
78. Water motors. In cities where water is supplied
under considerable pressure, it may be used to run sewing
machines, small polishers, grinders, lathes^
etc., by means of a water motor. A simple
form is shown in figure 73. The stream of
water is made to pass through a small open-
ing at high velocity and to strike against
some blades or buckets on the rim of a wheel.
The wheel is inclosed in a metal case, from
which the water flows away to the drain-
pipe. The impact of the water against the
blades turns the shaft, to which the machines
to be driven are connected either directly or
by belts.
79. Water wheels. Just as a small stream of water may
be used to turn small machinery, so it is possible to make
large streams of water turn large machines, which saw wood,
grind corn, and furnish electric lights for streets and houses.
Any community possessing a waterfall or a rapid in a river
has a valuable source of power. The older types of water
wheek were the oversliot, where the weight of the water
slowly turns the wheel, and the undershot, where the wheel is
let down into a swiftly flowing current. The modern forms
of water wheels are the Pelton wheel and the turbine. The
little water motor described above is a typical form of Pelton
Fig. 73. —Water
motor.
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PRACTICAL PHYSICa
Fig. 74. —Turbine water
wheel case and runner.
wheel, the parts of a commercial wheel
being the same, but much larger (see
plate facing page 72). The efficiency
of this type of wheel is much greater
than that of the undershot wheel, and
sometimes runs as high as 83 %. By far
the most important type of water wheel
torday is the turbine. This is somewhat
like a windmill. The water is conducted
from the reservoir above the dam through
a cylindrical tube to a " penstock" which
surrounds the case of the wheel (Fig.
74). This case stands on the floor of the
penstock and is submerged in water to a
depth equal to the " head " or height of
water supply. The water is not let into
the case about the wheel at one opening,
but through mani/ inlets or passages,
which are so curved as to direct the
blades of the
Siationaru
water against the
wheel in the most favorable direc-
tion to produce rotation, as shown
in figure 75. The wheel is attached
to a shaft which transmits the power
to the machinery above. A small
shaft controls the size of the inlet
openings in the case. When the
water has done its work, it falls
from the bottom of the wheel case
into the "tail race" below the
penstock. These turbines some-
times have an efficiency of 90 %.
Pelton wheels are used in general where the fall is high
and the quantity of water small, turbines where the fall is
low and the quantity of water great.
stationary
Fio. 76. — Stationary and moving
blades of water turbine.
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Pelton water wheel, to be installed at Rjukan in Norway, where it will develop
7500 horse power. The wheels of small water motors are similar in shape.
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MECHANICS OF LIQUIDS 71
Problems
1. The water level in a tank on top of a building is 100 feet above
the ground. What is the pressure in pounds per square inch at a faucet
10 feet above the ground?
2. If 200 cubic feet of water flow each second over a dam 25 feet
high, what is the available power?
3. If the efficiency of the water wheel used at the dam described in
problem 2 is 65 %, how many horse power can it supply ?
4. How many cubic feet of water must be supplied every second to an
overshot wheel which is 20 feet in diameter and delivers 40 horse power
at an efficiency of 85 % ?
5. The Niagara turbine pits are 136 feet deep, and the average
horse power of the turbines is 5000. Their efficiency is 85%. How
many cubic feet of water does each turbine handle per minute ?
80. Molecular attractions. When a drop of water falls
through the air, it draws itself into an almost perfect sphere.
Similarly, lead shot are made by letting molten lead fall
from a sieve at the top of a tower into a pool of water at
the bottom. In general, a liquid when left to itself tends to
get into the shape which has the smallest possible surface,
as if it were composed of little particles which had great
attraction for one another. It is also observed that there is
a great attraction between many pairs of substances if they
are brought very close together, as between wood and glue,
stone and cement, paint and wood. When this attraction is
between particles of the same kind, it is called cohesion, and
when between particles of different kinds, it is called adhesion.
In soap bubbles, it is the cohesion of the little particles of
soapsuds which makes the thin film act like an elastic mem-
brane. It is this same property of liquids which makes it
possible to lay a somewhat greasy needle on the surface of
water and have it float, although steel is eight times as dense
water,
81. Capillarity. Suppose we have two U-tubes (Fig. 76) with
tiieir side tubes 30 mm. and 1 mm. in diameter. If we pour water colored
with ink into the first tube, and mercury into the second tube, we observe
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PRACTICAL PHYSICS
that in each case the surfaces in the two sides
of the U-tube are not at the same level.
The water wets the surface of the
glass and is attracted by it, i.e. the
adhesion is great. The mercury does
not wet the glass, and the cohesion of
particles of mercury for each other
makes it appear as if there were repul-
sion between glass and mercury. The
surface of the mercury is convex, and
it stands at a lower level in the nar-
row tube than in the wide one. In the case of water, each
tube is drawing the liquid up into itself against the pull of
gravity. The narrower the tube, the higher the liquid is
raised. Since these small tubes have hairlike dimensions,
they are called capillary tubes (from Latin capillus^ a hair),
and this phenomenon is called capillarity. In this way liquids
rise in wicks, in filter paper, and in the soil.
Fig
76. — Capillarity
small tubes.
SUMMARY OF PRINCIPLES IN CHAPTER HI
force
Pressure =
area
Force = pressure x area.
Por liquids under pressure (weight of liquid negligible in com-
parison) : —
Pressure eversrwhere the same.
Force varies as area.
For liquids with a free surface (weight of liquid the only thing that
counts) : —
Pressure proportional to depth, independent of direction.
Proportional to density of liquid,
Equal to weight of a column of liquid with a base one unit
square and a height equal to the depth.
Average pressure on a surface = pressure at center of surface.
Total force on a surface = average pressure x area.
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MECHANICS OF LIQUIDS 75
Archimedes' principle : —
The loss of weight of a body either partly or wholly submerged
in a liquid is equal to the weight of the displaced liquid.
If the body just floats, this loss of weight is also equal to the
. weight of the body.
Density =:«^?^i^L?Lb2dy.
volume of body
Specific gravity = weight of body
weight of equal volume of water
In the metric system, since 1 cu. cm of water weighs 1 gram.
Density (g. per cm.^) = (numerically) specific gravity.
In the English system, since 1 cu. ft. of water weighs 62.4 lbs.,
Density (lb. per ft.^) = (numerically) 62.4 x specific gravity.
To get specific gravity : —
Find weight of body.
Find weight of equal volume of water.
Divide.
To get weight of equal volume of water : —
1. Compute volume. Weight of water = volume x density of
water.
2. Loss of weight of body when wholly submerged = weight of
equal volume of water. (May have to use sinker.)
3. Weigh equal volumes of liquid and of water in a bottle.
4. Find loss of weight of a solid in the liquid and in water.
(May use either sinker or float, i.e. hydrometer.)
6. Use balancing columns (see laboratory manual).
Questions
1. What advantages has the hydraulic press in testing steam boilers ?
2. What device is used to prevent the oil or water from leaking out
ftround the pistons of a hydraulic press ?
3. How is Archimedes supposed to have done his famous experiment
with the crown?
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76 PRACTICAL PHT8IC8
4. When a ship passes from a river, where the water is fresh, into the
ocean, does it rise or sink in the water?
5. If you have a table of densities in the metric system, how could
you make a table of specific gravities ?
6. How could you determine the specific gravity of a solid soluble in
water, but insoluble in kerosene ?
7. What is the water pressure in your laboratory ?
8. Why has skimmed milk a greater density than normal milk?
9. Two faucets in a town show the same pressure on the gauge and
are the same size. If one is one mile from the reservoir, and the other
is two miles away, will each faucet deliver the same quantity of water
per minute when opened wide ?
10. Sometimes when a faucet is opened, especially on an upper floor,
the water comes with a rush at first and much more slowly after it has
been running a few seconds. Explain.
11. Why does one need to take temperature into account in using the
lactometer ?
12. What metals float in mercury ?
13. How can one pour a liquid out of a glass with the aid of a spoon
or glass rod, so that it will not run down the side of the glass ?
14. Explain the action of a towel ; of a sponge.
15. Explain the process of " fire-polishing " the broken end of a glass
tube.
16. If you know the displacement of a battleship, how could you find
its weight ?
17. Why does one use snowshoes in walking over deep snow ?
18. Why is it easier to float when swimming in the ocean than in a
river?
19. Why should life preservers be filled with cork instead of hay?
20. A schoolboy in Holland is said to have saved his country from a
flood by thrusting his arm into a hole in the dike 150 centimeters below
the surface of the sea. Could a small boy hold back the whole North
Sea?
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CHAPTER IV
MECHANICS OF GASES
Liquids and gases differ in compressibility — air compressors
— uses — Boyle's law — vacuum pumps — uses — weight of the
air — atmospheric pressure — measured by Torricelli's experi-
ment— barometer and its uses — pressure gauges — lifting effect
of air — uses in balloons and pumps for liquids — other proper-
ties of gases — absorption and diffusion — molecular theory.
Compressed Aie
82. Pneumatic machines. Just as hydraulic machines
make use of the properties of liquids, so pneumatic machines
make use of the properties of gases. Nowadays we often clean
our houses with vacuum pumps ; we stop our express trains
with air brakes ; we drive the drills and hammers in our
shops with compressed air; and we have begun to travel
through the air with dirigible balloons and flying machines.
To understand the operations of all these machines, we must
study the properties of gases.
83. Liquids and gases alike in some respects. Liquids and
gases are called fluids, because they have no definite shape,
but adapt themselves to the shape of the vessel containing
them. A liquid, however, has a definite volume under ordi-
nary conditions, filling the lower part of a containing vessel,
and being bounded by a free surface above. A gas, on the
other hand, has no fixed volume and no free surface, bnt fills
the whole of its containing vessel at once if the vessel is
closed, and escapes if the vessel is open at the top. So the
little particles of a gas have much more mobility than those
of a liquid.
77
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PRACTICAL PHYSICS
Gases' and liquids are alike in that each, when under pre»
sure, distributes that pressure undiminished in all directions
in accordance with the principle of Pascal.
The gauges which are used to measure gas pressure are
often the same gauges that would be used to measure the
pressure exerted by a liquid (see section 75).
84. Air is very compressible. In one respect gases are
very diflferent from liquids, namely, in compressibility. This
striking difference can be. shown in the fol-
lowing experiment.
When a brass tube, with a closely fitting steel rod
(Fig. 77), is filted with air, the steel plunger can be
easily pushed down by hand, and when the plunger is
released, it springs back nearly to its initial position. If
it does not come quite back to its initial position, it
means that some of the air has leaked out. The en-
trapped air acts like a spring. But when the tube is
filled with water, or any other liquid, it is quite impos-
sible to push the plunger down, to any perceptible ex-
tent, by hand, and when the end of the plunger is struck
with a hammer, the effect is as if the entire tube were a
solid steel column, because the liquid is so nearly incom-
pressible.
Fig. 77.~Ck)m-
pressibility of
fluids.
85. Air compressors. The simplest form of air com-
pressor is the ordinary bicycle pump, such as is used to in-
flate the tires on bicycles and automobiles. Figure 78 shows
a sectional view of such a
pump attached to a tire. It
consists of a cylinder O and
piston P. On the down
stroke some air is entrapped
below the piston and com-
pressed, its pressure rising
until it becomes equal to that
of the air already in the tire.
Then the valve S opens, and fig. 78.— Air compressor.
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MECHANICS OF GASES
79
during the rest of the down stroke the air is forced into the
tire. When the up stroke starts, this valve closes and
the leather washer on the piston bends down and allows air
to flow past the piston into the cylinder below. Then on
the next down stroke this air, entrapped by the spreading
of the leather flange, is compressed and forced over into the
tire. There is only one valve, and that is in the stem of
the tire.
Large air compressors driven by steam engines or electric
motors are much used in steel plants, shops, and quarries to
furnish a supply of compressed air. This is delivered as a
forced draft to blast furnaces, or stored in steel tanks and
used to drive all sorts of pneumatic machinery.
86. Uses of compressed air. There are many tools which
are driven by compressed air, such as riveting hammers for
forming the riveted heads on steel work, and the pneumatic
tools used in stone cutting, iron chipping, drilling, etc. These
are in general lighter and simpler
than other portable tools, and there
is less danger of fire. When such
tools are used in mines, the waste
air which they discharge helps to
furnish ventilation, and this is
often an important advantage.
Rock drills, and sand blasts for clean-
ing metal and stone surfaces, are
other common applications. But
perhaps the most interesting ap-
plication is the air brake.
The essential parts of the Westing-
house air brake are shown in figure 79.
P is the train pipe leading from a large
reservoir on the engine, in which the air ^«
is maintained at a pressure of about 75 fiq. 79. — Westinghouse air
pounds per square inch. As long as this brake.
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80 PRACTICAL PHYSICS
pressure is applied to the automatic valve V there is maintained a com
munication between P and an auxiliary tank R under each car, and at
the same time air is cut off from the brake cylinder C, But whenever
the pressure in P drops, either by the moving of a lever in the engine
cab or by the accidental parting of a hose coupling, the valve V shuts off
P and connects the reservoir R with the cylinder C. This pressure on
the piston in C forces the brakes against the wheels. As soon as the
pressure in the pipe is restored, the valve V reestablishes the connection
between P and /2, and at the same time the air in C escapes. The
spring S then releases the brakes by pushing up the piston.
87. How volume of air changes with pressure — Boyle's
law. In studying about compressed air we are soon con-
fronted with the question as to how much the volume of a
given quantity of air changes as the pressure changes. This
was first investigated for the case where the temperature of
the air does not change during compression, by an Irishman,
Robert Boyle (1626-1691), and a
few years later by a Frenchman,
Mariotte. The results of their ex-
periments showed that if we start
FiQ. 80. — Compression of with a given volume of air Fi
^^' subjected to a certain pressure P
(Fig. 80), and double the pressure, the volume of air will
be reduced to one half. If the pressure be made three times
as great, the volume of the air will be reduced to one third,
provided the temperature of the air is kept constant. This
principle is known as Boyle's law and applies to all gases.
It may be stated as follows : The volume of a ga% at constant
temperature varies inversely as the pressure.
This may also be expressed in symbols as
P : P' : : V : V (notice the inverse proportion),
or PV^P'V,
where P and P' are the pressures, and V and F"' the cor-
responding volumes of a given quantity of gas, kept at some
fixed temperature.
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MECHANICb OF GA8E8 81
At very low temperatures or at very high pressures, this
law of Boyle and Mariotte does not hold exactly.
It should be noticed, however, that the air in a bicycle
pump does not stay at the same temperature- when com-
pressed rapidly, but becomes considerably warmer. The
effect of this heating will be discussed in Chapter X. It
will then appear that when the air is allowed to get hot,
more work has to be done on the pump to produce the same
useful result on the tire. The same is true of large com-
pressors, and so it is customary to keep the air in them as
cool as possible during compression by circulating water
through a jacket around the cylinder, or by spraying water
into the cylinder. The ideal case is compression at constant
temperature, in accordance with Boyle's law, and large com-
pressors should come as near to this as is practicable.
Problems
NoTB. — Assume constant temperature in these problems.
1. One hundred cubic feet of air under a pressure of 15 pounds -per
square inch is compressed to 300 pounds per square inch. What does the
volume become?
2. The volume of a tank is 2 cubic feet, and it is filled with com-
pressed air until the pressure is 2000 pounds per square inch. How
many cubic feet of air under a normal pressure of 15 pounds per square
inch were forced into the tank ?
3. What is the total force applied to a brake piston 10 inches in
diameter, when the pressure is 80 pounds per square inch ?
4. One hundred cubic feet of air at a pressure of 15 pounds per square
inch are compressed to 36 cubic feet. What is the pressure then?
5. Oxygen is sold in steel tanks under a pressure of 150 pounds per
square inch. As the gas is used, the pressure drops. When it has
dropped to 50 pounds, what fractional part of the original gas remains?
Give your reasoning.
88. Vacuum pumps. We have seen how a bicycle pump
can be used to force more air into a given space, and now we
shall see how a slight changa in the valves will enable us to
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PRACTICAL PHTSICa
suck the air out of a vessel. The first of these so-called
" air pumps " was made as long ago as 1650 by a German.
Otto von Guericke, then mayor of Magdeburg, who per-
formed numerous experiments. For example, he found that
a clock in a vacuum cannot be heard to strike; a flame dies
out in it ; a bird opens its bill wide, grasps for air, and dies ;
fish perish ; and yet grapes can be preserved six months in
vacuo. Vacuum pumps used to be found only in physical
laboratories, but now they are
used so extensively in vacuum
cleaners, and in making in-
candescent lamps and X-ray
bulbs, that they sire of great
commercial importance.
A simple form of mechan-
ical vacuum pump is shown
in figure 81. It consists of a
metal cylinder Q fitted with
a piston, and having at the
lower end two short tubes, A and 5, within which are self-
acting conical valves, so arranged that the air enters at A
and leaves through B.
When the piston is raised, the air in the vessel J8, which
is to be exhausted, expands into the cylinder O through the
valve A. When the piston is pushed down, it compresses
this air, closing the valve A and opening the outlet valve B,
Thus with each double stroke a certain fraction of the air in
the vessel R is removed. It will be seen that even with a
mechanically perfect pump we never take out quite all the
air ; for by each stroke we remove only a certain fraction of
the air, and the remainder expands to fill the vessel. In
practice, no pump is perfect because of leakage. To reduce
this, it is common, in "high vacuum'* pumps, to cover the
piston and the valves with oil, and in some forms made of
glass the piston is replaced by a column of mercury.
Fig. 81. — Vacuum pump.
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MECHANICS OF GA8E8
89. Applications of the yacuum pump. Vacanm cleaning
(Fig. 82) is an application of the force of suction, created by
a vacuum, to the cleansing of buildings and their furnishings.
Some vacuum cleaners are portable
and some are stationary, some are
operated by hand and some by an
electric motor, some tend to produce
a vacuum by a punip and some by a
rotating fan, but the general prin-
ciple is the same in all.
The problem of getting the air out
of incandescent lamp bulbs is quite dif-
ferent from that of vacuum cleaning,
in that we have a very limited space
to be exhausted and this must be
very completely pumped out. Usually
less than one millionth part of the
air is left in the bulb. For this
purpose two mechanical pumps are
worked in tandem, one to take air directly from the bulb,
and the other to take it from the cylinder of the first pump.
After these have done their work, the air remaining is still
further reduced by burning phosphorus or some other com-
bustible in the bulb. X-ray tubes are made in much the
same way, except that the process must be continued longer
so as to produce a still more rarified condition of the air.
Vacuum cleaner.
Weight of the Air
90. Density of air. We are so accustomed to having air
about us that we do not ordinarily think of it as having
either volume or weight. We speak of an " empty " bottle
when we usually mean a bottle filled with air. Yet when
we try to fill a narrow-necked bottle with a liquid, we find
that we can make the liquid run in only as fast as the air
gets out. If we push a glass tumbler mouth down into a
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PBACTICAL PHT8IC8
Fio. 83. — Proof that air has weight.
pail of water, it is not filled with water, because it is filled
with air. Air occupies spacie just as does any other fluid.
Furthermore, air and other
gases have weighty although we
seldom realize this fact.
In order to make it evident that
air has weight, let us try the follow-
ing experiments. Suppose we care-
fully counterbalance on the scales
(Fig. 83) a hollow metal vessel (a tin
can with a bicycle valve soldered into
the top will serve). Then if we
pump more air into the vessel and
put it on the scales again, we find
that it has gained in weight. If we
repeat the process, we find that it weighs a little more after each
pumping.
In the same way if we take a vessel from which the air has already
been exhausted, such as an electric light bulb, carefully counterbalance
it, and then let the air in by filing off the tip, we find that the scalepan
containing the bulb and the broken pieces goes down, showing that the
air which has entered has weight.
Careful experiments show that under ordinary conditions
a liter of air weighs about 1.3 grams, or 1 cubic foot weighs
about 1.3 ounces.
Since gases have both volume and weight, we may express
their densities in the usual way, as so many grams per cubic
centimeter or so many pounds per cubic foot. For example,
the density of ordinary air is about 0.0013 grams per cubic
centimeter, or 0.08 pounds per cubic foot. Many gases have
densities even smaller than that of air. Thus the density of
hydrogen under standard conditions is only 0.000090 grams
per cubic centimeter.
Evidently if the pressure on a certain volume of air is
doubled, the volume is halved, and the air becomes twice as
dense. In other words, the density of air or of any gas
varies directly as the pressure at constant temperature.
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MMCHANICa OF GASES 85
Problems
1. If a liter of air weighs 1.3 grams, how much does the air in a room
weigh, if the room is 3 meters high, 10 meters long, and 8 meters wide?
2. If the pressure in a compressed-air tank is 150 pounds per square
inch, what does 1 cubic foot of this compressed air weigh ? (1 cubic foot
under a pressure of 15 pounds weighs 1.3 ounces.)
3. A spherical balloon 10 meters in diameter is filled with hydrogen.
Find the weight of the hydrogen.
4. A bicycle tire has about the same volume as a cylinder 85 inches
long and 1 inch in diameter. If you pump your tires up from 15 pounds
to 75 pounds per square inch, how much more will the bicycle weigh
than before?
5. A compression pump, whose capacity is 500 cubic centimeters, is
used to force air into a can whose volume is 1 liter. What is the density
of the air after 3 complete strokes?
6. A vacuum pump, whose capacity is 500 cubic centimeters, is used
to exhaust the air from a liter flask. What is the density of the air left
in the flask after 3 complete strokes?
91. Pressure of the atmosphere. Since we are living at
the bottom of an ocean of air, and this air is a fluid which
has weight, it is natural to expect that it exerts a pressure.
Ordinarily we are not aware of this pressure because it
pushes up on the bottoms of objects almost as much as it
pushes down on the tops of them. If we could get rid of
this upward pressure underneath, we would see how great
the downward pressure on top really is. This can be done
with a vacuum pump, or in part
even with the lungs.
Let us fasten a piece of sheet rub-
ber over the end of a thistle tube, as
shown in figure 84. If we suck the
air out of the bulb with the mouth,
the rubber is forced downward be- ^^ 84. -Removing the upward
cause of the atmospheric pressure. pressure of the air.
This experiment is even more strik-
ing when performed with a larger membrane and with a vacuum pump.
If we tie a piece ot rubber over the mouth of the glass vessel shown in
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86
PRACTICAL PHT8IC8
figure 85, and gradually pump out the air, the rubber will be pushed
down more and more by the pressure of the air above it, until it finally
bursts. If a piece of bladder is used instead of inibber, it will break
with a loud report x"~^x
Fig. 85. — Air pressure breaking a membrane. Fig. 86. — Fountain in vacuo.
If we pump the air out of a tall glass vessel provided with a stopcock
and jet tube, and then place the mouth of the jet tube under water
and open the stopcock, we see the water rushing up into the vacuum
like a fountain. How can we determine how much air was removed ?
One of the most interesting of Otto von Guericke's experi-
ments was that with his famous "Magdeburg hemispheres."
These were two hollow hemispheres a little over a foot in
diameter which fitted together so well that the air could be
pumped out from between them. The pressure of the sur-
rounding atmosphere then held them together firmly. In a
test before the Reichstag and the Emperor, it required six-
teeri horses, four pairs on each hemisphere, to pull them
apart.
92. "Nature abhors a vacuum." The ancients tried to
explain many phenomena by saying that " nature abhors a
vacuum," but when the great Italian philosopher, Galileo
(1564-1642), found that a suction pump would not raise
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MECHANICS OF OASES
87
water more than 33 feet, he remarked that nature's horror
of a vacuum was a curious emotion if it stopped suddenly at
33 feet. He already knew both that air has weight and that
the " resistance to a vacuum " was measured by a column of
water about 33 feet high, yet he left it to his friend and
successor, Torricelli (1608-1647), to unite these two ideas.
93. Torricelli^s experiment Torricelli devised a means of
measuring this " resistance " which nature "offers to a vacuum "
by a column of mercury in a glass tube
instead of a column of water.
We may repeat this experiment if we take a
stoat glass tube about 3 feet long, closed at one
end, and fill it completely with mercury. If we
close the opening with the finger, invert the tube,
and put its open end into a tumbler of mer-
cury, we observe that, when the finger is removed,
the mercury in the tube (Fig. 87) sinks to a level
about 30 inches above the mercury surface in
the tumbler. If we incline the tube to one side,
the metal fills the entire tube and hits the top
of the glass with a sharp click. The space above
the mercury is empty except for a minute quan-
tity of mercury vapor. It is, indeed, the most
perfect vacuum that we know how to make.
1
^
Fig. 87.— Torricelli'f
experiment.
The column of mercury in the tube
just balances the pressure of the atmos-
phere on the mercury in the larger vessel at the bottom.
In other words, liquids rise in exhausted tubes because of
the pressure exerted by the atmosphere on the surface of the
liquid outside, and not because of any mysterious sucking
power created by the vacuum.
94. How to calculate the pressure of the atmosphere. From
the law that pressure in a heavy liquid is everywhere the
same at the same depth, we know that the pressure on
the mercury in the dish (Fig. 88) is the same at a as
outside.
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88
PRACTICAL PHT8IC8
r^ffMum
Fig. 88.— Mercury
colamn sapported
by air.
Outside this pressure is exerted by the atmosphere. At a
it is exerted by the column of mercury ab. Under standard
conditions, the pressure at a, that is, the
force per square centimeter, is evidently
equal to the weight of a column of mer-
cury 76 centimeters high and 1 square cen-
timeter in cross section. This is the weight
of 76 cubic centimeters of mercury, or t6
times 13.6 grams, or 1034 grams.
In the English system it is the weight
of a column of mercury about 30 inches
high and 1 square inch in cross section ;
that is, 30 x 0.49, or 14.7 pounds. Roughly,
then, one " atmosphere " is about 1 kilogram
per square centimeter or about 15 pounds
per square inch.
95 . Pascal's experiments. Pascal reasoned
that if the mercury column was held up
simply by the pressure of the air, the column ought to be
shorter at a high altitude. So he carried a Torricelli tube
to the top of a high tower in Paris, and found a slight fall
in the height of the mercury column. Desiring more de-
cisive results, he wrote to his brother-in-law to try the
experiment on the Puy de D6me^ a high mountain in
southern France. In an ascent of 1000 meters, the mercury
sank about 8 centimeters, which greatly delighted and as-
tonished them both.
Pascal also tried Torricelli's experiment, using red wine
and a glass tube 46 feet long, and found that with a
lighter liquid a much higher column was sustained by the
pressure of the air. These experiments were carried out in
1648, five years after Torricelli's discovery.
96. The barometer. The arrangement constructed by
Torricelli may be set up permanently as a means of measur-
ing the pressure of the atmosphere. It is then called a
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MECHANICS OF GASES
89
ja.
barometer. To " read the barometer " means simply to meas-
ure accurately the height of the mercury column above the
surface of the liquid in the reservoir. In
the form of barometer shown in figure 89
this reservoir has a flexible bottom which
may be raised or lowered so as to bring the
surface of the mercury to the zero point of
the scale which is at the tip of a point pro-
jecting into the reservoir. The height of
the mercury is then read by observing the
position of the liquid in the tube.
A more convenient form to carry about
is the aneroid or metallic barometer (Fig. 90).
As the name indicates, it is "without
liquid" and consists essentially of a disk-
shaped metal box, which has a thin corru-
gated metal top. When the air has been
pumped out of the box, it is sealed up, its
top being supported by a stout spring to
prevent its collapsing. As the pressure of
the air changes, the top of the box moves
up or down, and the small motion is greatly
magnified by means of levers and a delicate
chain, and is communicated to a pointer
which moves over a scale. A hairspring
serves to take up the slack of the chain.
The scale is grad-
uated to corre-
spond to the read-
ings of a standard
mercurial barom-
eter. Aneroid
barometers are made in various
sizes. Some are even as small as
Fig. 90. — Aneroid barometer. ordinary watches.
Fio. 89. — Mercu-
rial barometer.
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PBACTICAL PBT8IC8
'l. -
Fig. 91.— Barograph, or self-recording
barometer.
97. Uses of the barometer. The barometer indicates changes
in atmospheric pressure. These changes may be due to fluc-
tuations in the atmosphere
itself or to changes in the
elevation of the observer.
If a barometer, kept
always at the same eleva-
tion, is frequently observed,
or if it makes a continuous
record, as does a barograph
(Fig. 91), it is found to
fluctuate according to the
weather. Experience shows
that a *' falling barometer," that is, a sudden decrease of
atmospheric pressure,
precedes a storm ; and a
" rising barometer," that
is, an increasing atmos-
pheric pressure, indi-
cates the approach of
fair weather; while a
steady " high barom-
eter" means settled fair
weather.
The Weather Bureau
has barometric readings
taken simultaneously at
many different places,
and the results are tele-
graphed to central sta-
tions, where weather
maps are prepared. On
these maps it is observed
Fig. 92. — Portion of a weather map.
that there are certain broad areas where the pressure is low,
and other sections where the pressure is high. The areas of
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MECHANICS OF GA8E8 91
low barometric pressure are usually storm centers, which
move in a general easterly direction. If we know where
these low pressure areas are located and their probable
movement, we may predict the weather. Figure 92 shows
a portion of a government weather map. The curved lines,
showing the places where the barometric pressure is equal,
are called isobars. The direction of the wind at places of
observation is indicated by an arrow, and it will be noticed
that these arrows usually point from a "high" to a "low."
A careful study of these phenomena (which is called mete-
orology) shows that these " lows " are really great eddies of
air slowly moving in a counterclockwise direction about
the center of the low.
Another important use of the barometer is to measure the
difference in altitude of two places. If a surveyor or explorer
carries a barometer up a mountain, he notices that it indi-
cates a decrease in atmospheric pressure as he ascends. For
places not far above sea level this decrease is about 1 milli-
meter for every 11 meters of elevation or 0.1 of an inch for
every 90 feet of ascent. Aneroid barometers graduated in
feet or meters are always carried by balloonists and aviators
to tell how high they are.
98. Pressure gauges. Besides barometers, which are really
pressure gauges designed for pressures of one atmosphere or
less, we need gauges for higher pressures such as those in
a steam boiler, or a compressed-air tank, and gauges for very
low pressures^ such as those in the condenser of a steam
engine or a vacuum pump.
To measure slight differences in pressure, the open manometer,
described in section 76, is used, usually with some liquid
lighter than mercury as the indicating fluid.
If we bend a piece of glass tubing as shown in figure 93, and partly
fill the tube with colored water, we have a suitable gauge to measure the
pressure of ordinary illuminating gas, which wiU usually cause a differ*
ence in levels, ^, ^, of about 2 inches.
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PRACTICAL PHY8IC8
For high pressures this form of gauge, even when filled
with mercury, becomes too cumbersome, so a closed manometer,
like that shown in figure 94, is used. The
mercury stands at the same level in both
arms, when the pressure is one atmosphere.
If the pressure is greater than this, the
mercury is forced into the closed arm, com-
pressing the confined air according to
Boyle's law. The scale may be made to
read in atmospheres.
For practical work, the Bourdon spring
gauge, described in section 75, is used. Such
gauges are usually graduated so as to read
zero when the pressure is really one atmos-
phere ; that is, they indicate the difference
between the given pressure and atmos-
pheric pressure. Therefore when an engi-
neer speaks of a pressure of 100 pounds
"by the gauge," he means 100 pounds per
square inch ahove one atmosphere ; when he means the total
pressure above a vacuum, he usually
says "100 pounds absolute."
When pressures less than one atmos-
phere are to be measured, such as the
vacuum in the condenser of a steam en-
gine (section 219), a barometer of the
ordinary form would be inconvenient
because the whole reservoir or cup at
the bottom would have to be exposed
to the pressure to be measured. The
gauge is, therefore, arranged so as to
admit the low pressure to be measured
to the top of the barometer tube. The
height of the mercury then indicates the difference between
the small pressure and that of the atmosphere. The better
Fia. 93. — Open ma-
nometer.
C - -1
-
jl
■
4
)
Fio. 94. — Closed manom-
eter.
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MECHANICS OF GASES 98
the vacuum, the higher such a gauge reads. Thus engi-
neers usually speak of a 26 or a 28 inch vacuum, meaning
a pressure less than the standard 30 inch atmosphere, by 26
or 28 inches of mercury. The best vacuums now obtained
in steam turbine condensers are from 29 to 29.5 inches.
Since these mercury gauges would be inconvenient in engine
houses. Bourdon gauges are used. They are graduated to
read in inches like the mercury gauges which they replace.
Problems
To how
Kerosene
1. A diver works 51 feet below the surface of the water,
many atmospheres of pressure is he subjected ?
2. When the barometer reads 74.5 centimeters, how many inches
does it read ?
3. When a mercury barometer reads 76 centimeters, what would a
glycerine barometer read ? (The density of
■ glycerine is 1.26 grams per cubic centimeter.)
4. When the barometer reads 75 centi-
meters, what is the atmospheric pressure
in grams per square centimeter?
5. During a storm the barometer
"dropped" 1.5 inches. How far would a
water barometer have fallen ?
6. If a certain pressure is 75 pounds per
square inch, how many kilograms per square
centimeter is it ?
7. During a mountain climb the barom-
eter falls 1.75 inches. What is the net
height climbed (in feet) ?
8. Two glass tubes are arranged vertir
cally (Fig. 95) so that their lower ends dip
into water and kerosene, respectively, while
their upper ends are joined to a mouthpiece.
When some of the air in the tubes is sucked
out, the water rises 26 centimeters and the
kerosene 38 centimeters. Find the specific
gravity of the kerosene. (This is a common
way of getting specific gravity.)
9. How much force is exerted against an 8-inch piston of an air
brake when the pressure is 90 pounds *' by the gauge ** ?
Water
Fig. 96. — Specific gravity by
balanced columns.
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94
PRACTICAL PHT8IC8
10. The original Magdeburg hemispheres are preserved in a mu
seura at Munich. They are about 1.2 feet in diameter inside. When
the air was exhausted, it is said to have required 8 horses on each half
to separate them. Assuming that the pressure of the atmosphere was
15 pounds per square inch, find the force exerted by each set of horses.
(Reckon pressure on circle 1.2 feet in diameter. Why?)
99. The lifting effect of air. We have seen that when one
climbs a mountain, the pressure of the air decreases. A sen-
sitive barometer will indicate this decrease of pressure even
when it is lifted from the floor to a table. Therefore the up-
ward pressure of the air on the bottom of any object is
slightly more than the downward pressure of the air on the
top. In other words, just as in the case of liquids, there is a
lifting effect on everything surrounded by air, and this lifting
effect, is equal to the weight of
the air which is displaced.
To make this principle of the buoy-
ancy of the air seem more real, let us
balance a hollow brass globe against a
solid piece of brass under the receiver of
a vacuum pump (Fig. 96). When the
air is pumped out, the globe seems to be
heavier than the solid brass weight, be-
cause the support of the air around it
has been withdrawn. If the air is re-
admitted rapidly, the rise of the globe
Fig. 96. - Lifting effect of air. will be very apparent.
Most things are so heavy in comparison with the amount
of air they displace that this loss in weight, due to the
buoyancy of the air, is not taken into account. For example,
a barrel of flour would weigh about 8 ounces more in vacuo
than in air. But if the volume of air displaced is very large
and the weight small, as in the case of a balloon, the object
is lifted just as a piece of wood is lifted when immersed in
water. A balloon is usually made of cloth which is treated
with a special varnish to make it as nearly gas-tight as possible,
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MECHANICS OF GASES
96
Fio. 97. — A dirigible balloon.
and is surrounded by a network of ropes and cords to hold
up the car and its load. The bag is filled with hydrogen,
which, volume for volume, is only one fourteenth as heavy
as air. Sometimes, for short trips, illuminating gas, or even
hot air is used. Of course a large part of the lifting force is
used in raising the car, the rigging of the balloon, and the
silk of which the bag is made. The rest is available for
lifting passengers and ballast. To compute the lifting force
of a balloon we have only
to get the diflference between
the weight of the air dis-
placed and the weight of the
hydrogen, gas, or hot air.
The dirigible balloon
(Fig. 97) is provided with
propellers driven by gas engines, and rudders to steer with.
But the bag has to be made so large to support the weight
of all this machinery, that the balloon is much at the mercy
of the wind.
100. Pumps for liquids. The ancients
used pumps to lift water from wells, even
though they did not know why a pump
works ; they thought it was because *' na-
ture abhors a vacuum." We know now
that the underlying principle is the same
as in a mercurial barometer: it is the
pressure of the atmosphere on the surface
of the water in the well that pushes the
water up into the pump.
For example, let us consider the ordi-
nary suction pump shown in figure 98.
_^ This consists of a cylinder (7, which is
iHr^ -" connected with the well or cistern by a
^ ^„ . ^, pipe T. At the bottom of the cylinder is
Fig. 98.— A suction ^ ^. i « . * .
pump. a clapper valve JS, opening up. A piston
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96 PRACTICAL PHYSICS
P can be worked up and down in the cylinder by means
of a 4iandle. This piston also contains a valve opening
up. On the wp Btroke of the piston P, the valve V remains
closed because of its weight and the pressure of the air upon
it. Between the piston and the bottom of the cylinder there
would be a partial vacuum if the valve S remained closed.
But the pressure of the air on the water in the well forces
some water up through the pipe T^ past the valve S into the
cylinder (7. On the down stroke of the piston the valve 8
closes, the valve V opens, and the water gets above the
piston. On the next up stroke it is lifted out through the
spout. The valve 8 must never
be more than 34 feet above the
water in the well, and in practice
this distance is seldom more than
30 feet. Why?
Another kind of pump, shown
in figure 99, is called a force pump.
The suction pipe T with its valve
8 are exactly like the correspond-
ing parts of the house pump just
described, but the piston has no
opening through it, and the outlet
pipe and a second valve are at the
bottom of the cylinder. Rais-
ing the piston fills the cylinder
with water ; pushing it down
again forces the water out through
the second pipe. If enough force
is exerted on the piston, the water
can be pushed up to a considerable height. The pump can
therefore be located near the bottom of a well or mine
shaft.
Since the water is forced up only on the down stroke, it
comes in jerks. To reduce the jar and shock, an air chamber
— A force pump.
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MECHANICS OF GASES
97
A is connected with the delivery pipe, so that the air may act
as a cushion or spring. Power pumps, such as are used on
fire engines, or in city waterworks,
are "double acting" (Fig. 100),
which gives a still steadier stream.
When a large volume of water is
to be lifted a short distance, a cen-
trifugal pomp (Fig. 101) is used.
This is something like a water wheel
worked backwards. As the wheel in- ^^ ^_^
side (Fig. 102) is turned, the water, ^^^^T^-^T^^^
which enters near the hub, gets
caught between the blades and
hurled outward into the delivery
space around the wheel, even against
some pressure there. Similar ma-
chines, called " blowers," are used to
force a current of air through a build-
Fig. 100. — A doable-acting
force pamp.
Fig. 101. -Centrifugal pump, because of the
extremely steady rate at which they
furnish the air needed for combustion.
Another form of pump is the " air-lift "
pump (Fig. 103). Its action depends
upon the formation of a column of
mixed water and air which, because of
ing for ventilation, or to make " forced
draft," for furnaces. Often several
of these pumps are used in series to
give higher pressures. Large tur-
bine pumps of this sort, driven by
steam turbines, have recently begun
to revolutionize
blast furnace
practice in the
United States,
Fig. 102. — Section of c6n«
trifugal piunp.
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98
PRACTICAL PHYSICS
rm
its lesser specific gravity, is raised by a shorter column ot
water. Such a pump will lift water mixed with air as much
campresBcd as 40 fcct above the level of the water. It con-
sists of two tubes, the smaller of which is
centered within the larger. The smaller pipe
conveys compressed air down into the water bo
be lifted. The mixture of water and air rises
through the outer tube.. This sort of pump
is cheap to make, is simple in its operation, and
has no wearing parts ; but its efficiency is low.
It would be especially useful in an artesian or
oil well if the water or oil naturally stands too
far below the surface to be reached by a suction
pump and if the well is so small that a force
pump cannot be put down into it.
101. Siphon. The siphon is a bent tube with
unequal arms. It is used to empty bottles and
tanks which cannot be overturned, or to draw
off the liquid from a vessel
without disturbing the sedi-
ment at the bottom. If the
tube is filled and placed in the
position shown in figure 104,
the liquid will flow out of the
Fig. 103.— Air- vessel A and be discharged at
lift pump. ^ j^^^j. J^^^l J) rpj^^ j^j.^^
which makes it flow is the weight of the
column of water (7Z), which is between the
water level AA' and the water level Diy.
If the water level Diy is raised to AA'^ this
moving force becomes nothing and the water
ceases to flow ; if the level Diy is lifted
above AA'^ the liquid flows back into the
vessel A. A siphon works, then, as long as the free surface
of the liquid in one vessel is lower than the free surface of
Fia. 104.— A
siphon.
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MECHANICS OF GA8E8 99
the liquid in the other vessel. A water siphon will not
work if the top of the bend B is more than 34 feet above
the level A4'. Why?
Siphons are often used on a large scale in engineering.
For instance, in power plants the water used to condense the
steam is often taken from the ocean, raised 10 or 15 feet to
the condenser, and carried back to the ocean, through a pipe
that is everywhere air-tight and acts like a siphon. The only
work that the pumps have to do is to keep the water moving
against the friction in the pipe. A large inverted siphon is
used at Storm King on the Hudson River, to carry the water
supply of New York City under the river, some 700 feet below
its surface. The lifting of the water on one side is done by
the water descending from a slightly greater height on the other.
Siphons on a smaller scale are used in every aqueduct to
carry water over hills or across valleys. In such cases air
bubbles carried along in the water tend to collect at the top
of every hill, and so small air pumps have to be installed to
keep the pipes full of water.
Problems
1. How many feet could water be lifted with a perfect suction pump
(a) at sea level, and Qi) in Denver, Col. (altitude about 5000 ft.) ?
2. How many feet could crude oil (density 0.89 grams per cubic centi-
meter) be lifted out of an oil well by a perfect suction pump at sea level ?
3. How much work is needed to lift 100 gallons of water 25 feet
with a perfect pump?
4. How much power is needed to raise 100 gallons of water per
minute 25 feet with a perfect pump?
5. A force pump is to deliver water at a point 20 feet above the level
of its barrel. How great is the water pressure in the barrel when the
piston is descending ?
6. The piston of a fire-engine force pump is 4 inches in diameter, and
the total force exerted on it by the engine is 600 pounds. If the pump
acts perfectly, at how great a height will it deliver water ?
7. A siphon is to be used to transfer mercury from one bottle tG
another. How far above the level of the mercury in the higher bottle
can the top of the siphon tube be?
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100 PRACTICAL PHYSICS
Other Less Important Properties op Gases
102. Absorption of gases in liquids. If we slowly heat a beakex
containing cold water, small bubbles of air will be seen to collect in
great numbers upon the walls (Fig. 105) and to rise through the liquid
to the surface. It might seem at first that these are
bubbles of steam, but they must be bubbles of air, first
because they are formed at a temperature below the
boiling point of water, and second because they do not
condense as they come to the cooler layers of water
above.
a This simple experiment shows that ordinary
water contains dissolved air, and that the
amount of air which water can hold decreases
Pig. 105.— Bub- ^® ^^® temperature rises. It is the oxygen of
bies of air in the air that is dissolved in water which sup-
^**®^* ports the life of fish. The amount of gas ab-
sorbed by a liquid depends on the pressure of the gas above
the liquid. Thus soda water is ordinary water which has
been made to absorb large quantities of carbon dioxide
gas by pressure. When the pressure is relieved, the gas
escapes in bubbles, causing effervescence. Careful experi-
ments show that the amount of gas absorbed is proportional
to the pressure. The amount of gas which will be absorbed
by water varies greatly with the nature of the gas. For
example, at 0° C. and at a gas pressure of 76 centimeters of
mercury, 1 cubic centimeter of water will absorb 0.049 cubic
centimeters of oxygen, 1.71 cubic centimeters of carbon di-
oxide, and 1300 cubic centimeters of ammonia gas. The
ordinary commercial aqua ammonia is simply ammonia gas
dissolved in water.
103. Absorption of gases in solids. Certain porous solids,
such as charcoal, meerschaum, silk, etc., have a great capacity
for absorbing gases. For example, charcoal will absorb 90
times its volume of ammonia gas and 35 volumes of carbon
dioxide. It is this property of charcoal which makes it use-
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MECHANICS OF GASES
101
ful as a deodorizer. This absorption seems to be due to the
condensation of a layer of gas on the surface of the body or
of the pores within the body. Platinum in a spongy state
absorbs hydrogen gas so powerfully that. if a small piece is
placed in an escaping jet of hydrogen, the heat developed
by the condensation is enough to ignite the jet. This has
been made use of in self-lighting Welsbach mantles.
A familiar example of the absorption of gases by liquids
and solids is the contamination of milk and butter by onions,
fish, or other kinds of food, if they are kept in the same com-
partment of a refrigerator. Onions, for instance, give off a
small quantity of gas which we can easily detect by our
sense of smell, or by the watering of our eyes. This gas,
when absorbed by milk or butter, affects its taste.
104. Diffusion of gases. One of the difficulties in the suc-
cessful construction of balloons is due to the difhision of the
gas through the bag. The diffusion of
hydrogen through a porous cup is
shown in the following experiment.
If we set up a porous cup with a stopper
and glass tube, as shown in figure 106, and
allow hydrogen (or illuminating gas) to fill the
jar which surrounds the porous cup, we observe
bubbles rising from the end of the glass tube,
which dips under water. This means that the
gas is going through the porous walls of the
cup and forcing the air out at the bottom.
If we now shut off the gas and remove the jar,
we presently see the water slowly rising in the
tube, which shows that the gas inside the cup
is going out.
Fig. 106. — Diffusion of
hydrogen throagh
porous cup.
The fact that a little ammonia (or
any other gas with a powerful odor)
introduced into a room is soon perceptible in every part of
the room shows that the gas particles travel quickly across
the room. Moreover, this mixing of gases goes on whatever
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• •• * • 2 \ •* • • •• •
, •• •»• • ••• • •••••'••••
the relative densities of the gases, so that a heavy gas like
carbon dioxide and a light gas like hydrogen will not re-
main in layers like mercury and water, but will quickly
diffuse and become a homogeneous mixture. Experiments
show that the smaller the density of the gas, the greater
the velocity of its diffusion.
105. Molecular theory of gases. To explain the pressure
of gases and their diffusion, it is now generally supposed that
all substances are made of very minute particles called
molecules. These molecules are so minute that we cannot see
them even with the most powerful microscopes. In one cubic
centimeter of a gas there are probably not less than 10^
(that is, 1 followed by nineteen ciphers) molecules. The
spaces between these molecules are supposed to be much
larger than the molecules themselves. This explains why
gases are so easily compressed and diffuse so quickly.
Then, too, these little particles are supposed to be flying
about in all directions with great velocity. They are sup-
posed to travel in straight lines except when they hit each
other and bounce off. Gas molecules seem to have no inher-
ent tendency to stay in one place, as do the molecules of solids.
This explains why gases fill the whole interior of a contain-
ing vessel. This also explains gas pressures, for the blows
which the innumerable molecules of a gas strike against the
surrounding walls constitute a continuous force tending to
push out these walls. When a gas is compressed to half its
volume, the pressure is doubled, because doubling the density
doubles the number of blows struck per second against the
walls. It has even been possible to calculate the molecular
velocity necessary to produce this outward pressure. It ap-
pears that the molecules of gases under ordinary conditions
are traveling at speeds between 1 and 7 miles per second.
The speed of a cannon ball is seldom greater than one half a
mile per second.
This, in brief, is the so-called kinetic theory of gases.
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MECHANICS OF GA8E8 108
SXTMMARY OF PRINCIPLES IN CHAPTER IV
Pascal's Law of Transmission of Pressure: For gases under
pressure, the pressure is everywhere the same ; the force varies
as the area.
Boyle's Law : Volume of gas at constant temperature varies inversely
as pressure.
Density of a gas varies directly as pressure.
Lifting effect of air is equal to weight of air displaced.
Atmospheric pressure equal to about
30 inches of mercury,
34 feet of water,
16 pounds per square inch,
1 kilogram per square centimeter.
Questions
1. Why can Torricelli's experiment be performed as well indoors as
outdoors ?
2. How and why can a glass of water be inverted with the aid of a
card without spilling the water ?
3. Why does a rubber tube often collapse when connected with a
vacuum pump? Why does not a rubber tube always collapse when con-
nected with a vacuum pump ?
4. Why must a mercurial barometer be hung in a vertical position ?
5. What would be the result of putting a mercurial barometer under
a tall bell glass on an air pump ?
6. Would a siphon work in a vacuum ?
7. What would be the effect of lengthening the long arm of a si-
phon ?
8. A boat lying on a beach is full of water. How could you empty
it with the help of a suitable length of rubber hose ? Could you use the
same method to get the bilge water out of a boat floating in the water ?
9. Why are not barometers filled with water ?
10. What advantage has a pneumatic automobile tire over a solid
tire of the same size ?
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104
PRACTICAL PHYSICS
Fig. 107. — Inkwell.
11. How can a balloon be made to sink or rise ?
12. Why does a man under water in a diving siiit have to be sup-
plied with compressed air ?
13. Explain why the liquid does not run out of
a medicine dropper.
14. Explain the action of a so-called "pneu-
matic " inkstand (Fig. 107), or of a drinking foun-
tain (Fig. 108), or of a poultry fountain (Fig. 109).
15. A man finds that cider does not flow out of
a barrel until he removes the bung. Explain.
16. A vessel 1 meter deep is filled with mercury.
Can it be entirely emptied by means of a siphon?
17. Why does a chemist usually reduce the vol-
umes of gases to standard pressure, that is, 76
centimeters ?
18. What advantages has compressed air over
electricity for the transmission of power?
19. If the area of a man's body is 20 square
feet, what is the total force exerted on him by the
atmosphere? Why is he not crushed by this
force ?
20. What facts indicate that the atmosphere be-
comes rarer and rarer as one rises above sea level ?
21. In building tunnels workmen usually have
to work in chambers filled with compressed air.
Why is this necessary ?
22. Get the dimensions and weights of some
of the large balloons used in international races, and compute their
lifting power. Estimate the amount of ballast
that can be carried in addition to the weight
of the balloon, car, and passengers.
23. How does a gas meter work?
24. Would it make any difference in the
gas bill if the meter were in the attic instead
of in the cellar? In apartment houses with
separate meters for each apartment, do the
people on the top floor get more or less gas
for their money ?
Fig.
108. — Drinkiug
fountain.
Fig. 109. — i'ouitry foun-
tain.
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CHAPTER V
NON-PARALLEL FORCES
Representation of forces by arrows — the parallelogram of
forces — composition and resolution of forces — application to
roof truss, friction, sailboat, and aeroplane.
106. Three forces acting at a point. In machines and other
contrivances it often happens that forces which are not par-
allel balance each other and are thus in equilibrium. For
example, suppose a street
lamp is suspended over a ^
street by a wire stretched
between two posts, as
shown in figure 110. .
We have here three non-
parallel forces in equilib-
rium — first, the verti-
cal pull OTT due to the
weight of the lamp; sec-
ond, the pull exerted by one of the ropes ; and third, the
pull exerted by the other rope. We are to find what relation
must exist between the magnitude and direction of any three
such forces, if they are to produce equilibrium.
107. Representation of forces by arrows. It will help us to
form a mental picture of these three forces if we represent
them by three arrows. The direction of each force will be
indicated by the direction of the arrow, the point of applica-
tion by the tail of the arrow, and the magnitude of the force
by the length of the arrow, drawn to some convenient scale.
106
Fig. 110. — Three non-parallel forces.
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106
PRACTICAL PHYSICS
Thus in figure 111 we have an arrow 5 units long, and if we
assume that each unit represents 10 pounds, the arrow AB
. . . . , V shows a force of 50 pounds applied at A^
^^'""*""'^^"^^^ acting due east. Figure 112 represents
Fig. 111.- a force of 50 ^.^^ forces, oue OA of 30 pounds, acting
pounds acting east. ,.ix^ ii , •^S
due east applied at 0, and the other OB
of 40 pounds, acting due north, applied at the same point 0.
If these two forces act simultaneously upon the body at 0,
the result will be the same as if a single force were applied,
acting somewhere between OA and 05,
but nearer the greater force OB. This
single force^ which produces the same result
as two forces^ OB and OA^ is called their
resultant,
108. Principle of parallelogram of forces.
If a parallelogram is constructed on OA and
OB^ the diagonal 0(7 represents the resultant,
as can be proved by the following experi- ^ig^ ^'^"f^^ef at
ment. right angles.
Suppose we hang two spring
balances A and B from two nails
in the molding at the top of the
blackboard, as shown in figure
113, and tie some known weight
W near the middle of a string
joining the hooks of the two
balances. If we draw lines on
the blackboard behind each of
the three strings, we shall have
represented the direction of each
of the three forces. Then, if we
note the tension in each string
as shown by the amount of the
weight W and the readings of
the spring balances A and B, we
may remove the apparatus and
complete the diagram. Choos-
ing some convenient scale, we
Fio. 113.
- Experiment to illustrate paral-
lelogram law.
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NON-PARALLEL FORCES 107
measure off on OA a distance corresponding to the tension in OA, and
place an arrowhead at X, and in the same way we locate Y on OB, Then
we construct a parallelogram on OX and OF by drawing J^R parallel to
OF and YR parallel to OX, It will be evident that the diagonal OR is
the resultant of OX and OY, for if we measure OR and determine its
magnitude from our scale of force, we find that this resultant OR is
almost exactly equal and opposite to the third force OW. That is, either
OR, or OX and OF, balances OW.
The force necessary to balance or hold in equilibrium two
forces is called the equilibrant. Thus in the case just de-
scribed, the force OTTis the equilibrant of the two forces OX
and OY.
The resultant of two forces acting at any angle may he rep-
resented by the diagonal of a parallelogram constructed on two
arrows representing the two forces.
When three forces are in equilibrium^ the resultant of any
two of the forces is equal and opposite to the thirds which can
be regarded as their equilibrant.
109. Resultant depends on the angle between components.
To determine the resultant of two or more forces, we must
know not only the magnitude of the " components," but also
the angle between them. This will be made clear by study-
ing the same two forces at different angles, as in figure 114.
It will be seen that the resultant OR gradually increases as
0
Fig. 114. — Two forces at varying angles.
the angle between the components OA and OB decreases.
For example, if the angle is 180° (case (a)), the forces OA
and OB are opposite and the resultant is the difference be-
tween the forces, 4 — 3, or 1, and acts in the direction of the
greater force, i.e. toward the right. As the angle gradually
decreases the resultant OR increases, until, when the angle is
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108
PRACTICAL PHT8IC8
0° (case (e)), the forces OA and OB are acting in the same
straight line and in the same direction, and the resultant is
the sum of the two forces, 4 + 3, or 7. When the forces are
at right angles (case (0)» ^^^ resultant can be computed from
the geometrical proposition about the sides of a right triangle,
namely, the sqtmre on the hypothenuBe is eqtMl to the sum of the
%quare% on the two sides.
Thus, OB^ = in?+OS^,
0^=32 + 42=26,
OB = 6.
For oblique angles, such as (J) and (d) in figure 114, the
resultant can be determined by plotting the forces to scale,
or by trigonometry.
The process of finding the resultant of two or more com-
ponent forces is called the composition of forces.
110. Composition of forces. — Illustrative Examples. Suppose
we have a crane arm ABy attached to the wall as shown in figure 115 (a).
4^ The weight Wis 2000 pounds and
the tension in the cable ^ C is 1500
pounds. What is the force exerted
by i45? In the solution of such
problems it will be found helpful
to draw a force diagram (Fig. 115
(6)), where A W represents the
pull of the weight W,AC the pull
of the cable, and A E the thrust
of the crane arm. As these three
forces are in equilibrium, we can
apply the principle of the parallel-
ogram of forces. We want to
find AR, the resultant of ^ C and
A W. Since ^ C and ^ TT form a
Fig. 115. — Three forces acting on crane, right angle, we know that
AR^ = AC^ + AW^ = 15002 ^ 2000^,
or AE = 2500 pounds.
Therefore the push exerted by AB is 2500 pounds.
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NON-PARALLEL FORCES
109
Again, suppose we have a lOO-pound child in a swing (Fig. 116).
A man pushes the child to one side with a
force of 20 pounds. What is the magnitude
and direction of the pull exerted by the
rope? In the force diagram (Fig. 116),
CW repfiiesents the weight of the child
(100 pounds), CP represents the ^ush
(20 pounds) of the man against the child,
and CR represents the pull of the rope
which we wish to determine. The re-
sultant CR' of CP and CW is equal to
VC/>2+ CW^ or V(20)2 + (100)2, or about
102 pounds. Therefore the tension in the
rope is also 102 pounds. Its direction can
be found from the diagram.
Problems
Fig. 116. — Three forces acting
on child in swing.
1. Find, by plotting to scale, the result-
ant of a force of 8 pounds toward the east, ai\.d one of 4 pounds toward
the north.
2. Compute the resultant in problem 1.
3. A force of 100 pounds acts north and an equal force acts west.
What is the direction and magnitude of the equilibrant ?
4. Find the resultant of a force of 10 pounds east and one of 14 pounds
southwest.
5. Two forces, 5 pounds and 12 pounds, act at the same point. Find
their equilibrant, (a) if they act in the same direction, (b) if they act in
opposite directions, and (c) if they act at right angles.
111. Resolution of forces. The principle of the composi-
tion of forces can be worked backward. If one force is
given, we can find two others in given directions which will
balance it. For example, take the case of the lamp sus-
pended above the middle of the street. If we know the
weight of the lamp and the angle of sag of the ropes, as
shown in figure 117, we can calculate the tension in the
ropes.
Suppose that the weight of the lamp is 50 pounds, and that the rope
ALB sags so as to make both the angle ALR and the angle BLR equal
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PRACTICAL PHT8IC8
to 75**. In the diagram (Fig. 117) draw the arrow L W down from L t«
represent 50 pounds on some convenient scale. As the two ropes have
to hold up the lamp, the results
ant of the forces representing
the tension in the ropes must
be equal and opposite to the
force representing the weight.
So we draw LR equal and op-
posite to LW, Then we con-
struct a parallelogram on LR
as a diagonal with its sides
parallel to LA and LB, Ry
being drawn parallel to LA,
and Rx parallel to LB, Ly represents the tension in the rope LB and
is equal to about 96.6 pounds, and Lx represents the tension in LA and
is also equal to about 96.6 pounds.
Another good example of the resolution of one force into
two forces which just balance it, is the case of a street lamp
hung out on a bracket from a pole, as shown in figure 118 (a).
Pig. 117. — Three forces acting on street lamp.
^^^P
in 50 lb.
Fig. 118. — Three forces acting on lamp hung on bracket.
Suppose the lamp i, weighing 50 pounds, is hung out from a pole PC
by means of a stiff rod AB, 10 feet long, and a tie rope or wire BCy
which is fastened to the pole at C, 3 feet above A . What is the force
fixerted by the rope BC?
In the diagram (Fig. 118 (ft)), the weight of the lamp is represented by
OW, the push of the rod AB by OP, and the tension of the tie rope BC
by OT, Since we know the force OW (50 pounds), we draw this line to
some convenient scale. The resultant oi OP and OT must be equal and
opposite to OW. Therefore we make OR equal and opposite to OW.
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NON-PARALLEL FORCES 111
Then, completing a parallelogram on 0/2 as a diagonal, we have OP
representing the pash of the rod against the lamp, and OT the tension
in the tie rope BC. If we draw these lines carefully to scale, we find
that the tension is 174 pounds.
In general, a single force may he resolved into two compo-
nents acting in given directions^ hy constructing a parallelogram
whose diagonal represents the given force^ and whose sides have
the given directions of the components.
112. Component of a force in a given direction. If a force
is given, we can find two other forces, one of which repre-
sents the whole effect in a given direction of the given force.
Thus in figure 119 we have a canal boat AB which is be-
ing towed by the rope BO. We may resolve the force along
the rope BO into two components, one of which, BS^ is
Fig. 119. — Usef al component of force on canal boat.
effective in pulling the boat along the canal, and the other,
BB^ at right angles, is useless or worse than useless, since it
tends to pull the boat toward the bank. BU^ the useful
component of jB(7, can be computed by drawing the force
BO to scale and then constructing a rectangle on BO as a
diagonal, such as BUOB.
113. Applications of the principle of parallelogram of forces.
This principle is one of the foundation stones in the study of
mechanics. When stated with the aid of a geometrical
diagram, it seems simple, but when met in a crane, derrick,
bridge, or roof truss, it is puzzling. This is because, in
solving practical problems, we seldom find bodies which are
small enough to be regarded as points at which forces act.
Nevertheless we can do problems by this method, even when
the bodies are quite large. For if any body is held still by
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112
PRACTICAL PHT8IC8
three forces, their lines of action, if prolonged, must go
through a single point, as shown in figure 120 (a). If this
were not true of
three forces act-
ing on a body
-^B i^\ \ (Fig. 120 (6)),
•^B it would spin
(5) around. So we
can think of the
forces as acting
Condition of spin and rest.
at a single point, even though the body in which the point
lies is quite large.
114. Roof truss. When a wooden house is built, the roof
is usually supported by pairs of timbers set like an inverted
V, as in figure 121. Each
pair of timbers has to
carry the weight of a sec-
tion of the roof, and, in
winter, of the snow and
ice that accumulate on it.
This weight is really dis-
tributed along the tim-
bers, but it can be thought
of as concentrated, half
at the peak and half at the eaves, where it rests directly on
the walls. The part of the load that is at the peak tends to
" spread " the inverted V, and our problem is to find what has
to be done to prevent this.
We may test this experimentally with a small model of a pair of roof
trusses (Fig. 122). These have hinges at the top instead of a stiff joint,
and frictionless wheels underneath, so that they will not stand up at all
under the load TT unless a tie is put across the bottom of the A to pre-
vent the spreading. If a spring balance is put into the tie, the pull
which the tie has to exert on the truss members can be measured. If
the load at the peak is 50 pounds, and if the truss members make a right
angle, the " tension " in the tie will be about 25 pounds.
Fig. 121.— Roof trussea.
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NON-PARALLEL FORCES
11»
In discussing this experiment, we have to apply the parallelogram of
forces at two points separately. In the first place, let us consider the pin
of the hinge at the top. This is acted on by three forces, the pull of the
weight W, and the push exerted by each rod (Fig. 122). Since these
balance, we can find each push by constructing a parallelogram whose
diagonal is equal and opposite to W. If the rods are at right angles, this
parallelogram is a square, and each push is 50/ V2, or 35.3 pounds.
Fig. 122. — Experimental roof truss, and force diagram.
Turning next to the pin at the foot of one rod, we see that it is also
acted on by three forces, the push of the rod, 35.3 pounds, the pull of the
tie wire, and the push upward exerted by the table. Since these balance,
we can get the last two by constructing a parallelogram on the known
force as a diagonal (draw this yourself). This parallelogram is composed
of two 45^ triangles, and so both the pull of the tie wire and the push of
the table are 35.3/ V2, or 25 pounds.
In building a roof, the pull exerted by the tie wire in our
experiment has to be provided for in some way. Usually
the ends of the roof timbers are nailed to the frame of the
building, which is stiff enough to exert a part or all of the
required force. Often a board is nailed across the inverted
V, either at the bottom, or a little higher up, to help exert it.
In large roof trusses, as in churches, an iron rod is strung
across and tightened with a screw coupling.
115. Bridge. Large bridges are built of wood or steel
*' members " joined to form a number of adjacent triangles.
If the members are strong enough not to stretch or shrink
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114
PRACTICAL PHYSICS
under the loads imposed on them, each triangle, having three
sides of unchanging length, keeps its shape, and so the whole
truss is rigid.
In very large bridges the members are joined together at
the corners of the triangles by boring holes in them and
thrusting a steel pin through all the holes at a joint.
Bridges made in this way are called pinned bridges. The
plate opposite page 114 shows two such bridges. In designing
a pinned bridge, an engineer computes the "stresses in the
members," that is, the forces which they have to exert to
hold the bridge stiff under load, by applying the parallelo-
gram of forces to the pin at each joint separately. The
members which have to push against the pins at their ends
are called compression members, because they tend to shorten
under load, while those that have to pull on the pins at their
ends are tension members, and tend to lengthen under load.
In large bridges it is easy to see which are compression
members and which
tension, for the com-
pression members are
made broad and stiff
with " latticing " up
their sides, while the
tension members are
steel straps or rods
with enlarged ends to
give room for the
holes. Thus the heavy
lines in figure 123 indi-
cate compression mem-
bers, while the light lines correspond to tension members.
In smaller bridges the members are not joined by pins,
but are riveted to "gusset plates" at- each joint. Such
bridges are designed as if they were pinned, the stiff joints
giving an additional factor of safety.
Fig. 123. — Diagrams of the bridges in the plate
opposite page 114.
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Framed bridges with pinned joints. The upper one is a " through-bridge *
with 9 " panels," the lower a ** deck-bridge ** with only 5 " panels.'
Notice, however, that the essential features of the two trusses are alike.
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NON-PARALLEL FORCES 115
The smallest steel bridges are supported by plate girders,
one on each side, which are simply stiff steel beams, and will
be discussed in the next chapter.
Roofs of large span are often supported by framed trusses,
made of members forming triangles, like bridge trusses.
116. How a boat sails into the wind. Let AB (Fig. 124)
represent a boat, aSaS" its sail, and TT the direction of the
wind. It is sometimes hard to see
how such a wind pushes the boat
ahead instead of forcing it back-
ward. The wind blowing it ^j , ,^
against a slanting sail SS' is de- ^ ^' A 1 'I^^^^l
fleeted and causes a pressure per-* ^ -^ ^
pendicular to the surface. This
pressure can be represented by the
arrow cP in the diagram. The
force cP can be resolved into two
components, one useful, ck^ which Fio. 124. — Action of wind on a
is parallel to the keel of the boat,
and the other useless, cw^ which tends to move the boat to
leeward. This sideways movement is largely prevented by
a deep keel or a centerboard. So the net effect of the wind
is to drive the boat forward.
117. What supports an aeroplane ? An aeroplane of the
monoplane type has one huge plane or sail, and a biplane two
such planes, one above the other. These planes are tilted so
that the front edge is a little higher than the rear edge.
There is also a light but powerful gasolene engine which, by
turning one or two large propellers, forces the aeroplane
forward. How such a machine, which is heavier than air,
is kept up, will be seen from figure 125. Let AB represent
a tilted plane moving from right to left. The conditions
are evidently the same as if the plane stood still and a strong
wind was blowing, as shown by the arrows. The air strik-
ing against the under side of the plane AB is deflected and
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116
PRACTICAL PHT8IC8
causes a pressure OP at right angles to the surface. It is the
upward component of this force which keeps the aeroplane
from falling. The weight
of the machine, including
the engine and load, is
represented by 0 W.
The driving force of the
propeller OT must be
equal to the resultant of
the two forces OP and
OW to keep the machine
from slowing up.
118. Friction on an in-
clined plane. When an
•< Direction of /light
Fio. 126. — Forces acting on aeroplane.
Fio. 126. — Friction on inclined plane.
object is placed on an inclined plane, friction tends to keep
the object from sliding down the plane (Fig. 126). If the
angle of inclination
is small enough,
this friction will
prevent the object
from sliding down
the plane.
For example,
suppose an electric
car is on a grade
with the brakes set, so that the car stands still. How steep can
the grade be before the car slides down ? In the diagram,
figure 126, let OTT represent the weight of the car, OP the
pressure of the inclined plane against the car, and OF the
friction which retards its motion. When these three forces
are in equilibrium, the resultant of OP and OW, that is, OR,
must be opposed by an equal force OF. I^ovv OJ^can never
exceed a limiting value which depends on the pressure and
on the coefficient of friction, the latter being determined by the
condition of the track. But the resultant OR increases a&
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NON-PABALLEL FORCES 117
the incline becomes steeper. So, as the steepness increases,
we soon reach a condition in which OM is greater than OF
possibly can be, and the car slides down. If we know the
coefficient of friction between the wheels and the rails, we
can compute the grade at which the car will begin to slide.
Let figure 126 represent this grade. We have already
(section 45) defined the coefficient of friction as the ratio
between friction and pressure, and so, in this case, we have
Coefficient of friction = -77^:= -ttt;-
OF OP
From geometry we know that the triangles OPJR and XTZ
are similar since they are mutually equiangular. It follows
that
0^_.S"__ height of plane
OP B base of plane
Therefore
Coefficient of friction = height of plane
base of plane
This is a convenient way of measuring coefficients of
friction.
Problems
1. If the resultant of two components acting at right angles is 50
pounds, and one of the forces is 15 pounds, what is the other force ?
2. One of two components acting at right angles is three times the
other. Their resultant is 32 pounds. Find the forces.
3. A force of 8 pounds is to be resolved into two forces, one of which
is 12 pounds, and makes an angle of 90^ with the given force. Find the
other force.
4. A boy weighing 50 kilograms sits in a hammock whose ropes make
angles of 30° and 60°, respectively, with the vertical. What is the ten-
sion in each rope ?
5. Each rope in problem 4 is fastened to a hook in the ceiling. Find
the vertical pull on each hook.
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118
PRACTICAL PHYSIC 8
6. Figure 127 shows a simple crane. Find the tension in the tie rop€
BC and the push of the brace AC, when the weight W is one ton, and
the angle 5^ C is 45^
7. In figure 119 the canal boat is 10 feet from the shore, and a pull
of 200 pounds is exerted on the 60-foot towline. AVhat is the efifective
component? ^-
000 lbs.
Fig. 127. ~ Diagram of simple
crane.
Fio. 128. — Girder supported
from a wall.
8. One end of a horizontal steel girder 10 feet long rests on a ledge
in the wall, and the other end is supported by a steel cable arranged as
shown in figure 128. Assuming that the girder weighs 40 pounds per
foot, find the tension in the cable.
SUMMARY OF PRINCIPLES IN CHAPTER V
Forces can be represented by arrows.
The parallelogram of forces: —
The resultant of two forces is the diagonal of their parallelogram.
The equilibrant of two forces is equal and opposite to their
resultant
If three forces act on a body (not a point), their lines of action
must pass through a single point, and the parallelogram prin-
ciple can be used.
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non'-paballel f0bce8 119
Questions
1. Show by a diagram the useful component of the pull exerted on
a sled by a rope.
2. Why is a long towline more effective in hauling a canal boat
than a short line?
3. Why does one lower the handle in pushing a lawn mower through
tall grass?
4. A boat is rowed across a river. What two forces are acting on
the boat?
5. A child sitting in a swing ia drawn gradually aside by a force
which continually acts in a horizontal direction. Does the tension in
the swing rope grow smaller or larger?
6. Why will a long rope hanging between two points at the same
level break before it can be pulled tight enough to be straight ?
7. Find in some building a roof truss with a steel tie rod to keep it
from spreading.
8. How are the walls of Gothic cathedrals strengthened so that they
can exert the side thrust necessary to hold up the roof?
9. Examine the steel bridges in your neighborhood to see if they are
" girder bridges " or " framed bridges," and, if any of them are framed,
see whether they are pinned or riveted, and which members are com-
pression members, and which tension. Make a sketch like those in
figure 123 of one of these bridges, showing the compression members by
heavy lines.
10. Explain by diagram how an ice boat may go faster than the wind.
11. Could an ordinary balloon "tack" against the wind like a sail-
boat, if it was provided with a sail, a large keel, and a rudder, like a
sailboat? Why?
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CHAPTER VI
ELASTICITY AND STRENGTH OF MATERIALS
The different kinds of stress — stress and strain — Hooke's
law — elastic limit — breaking strength -^ factor of safety.
Unit stress and unit strain in tension — tensile strength —
.stiffness and strength of beams — cross sections of beams.
119. Importance of studying materials. A structural
engineer who is to build a bridge, a building, or a ma-
chine must know not only the forces that will be exerted
on each of its parts, but also the strength of the wood, brick,
stone, or steel of which they are to be made. This knowledge
can be gained only by testing each kind of material with
the greatest care. For this reason, every engineering hand-
book tabulates the results of a great number of tests of this
kind. Every large manufacturer of steel girders or rails
maintains a testing laboratory so that he can sell his prod-
ucts under a strength guarantee. Even textile manufac-
turers test the breaking strength of the yarn that goes into
their cloth. Indeed, the study of the properties of struc-
tural materials is regarded as of such importance to the
public that the government itself maintains a bureau for the
purpose. In this chapter we shall learn how to make such
tests on a small scale, and how the results are used.
120. The different kinds of stresses. In designing a
beam or column, or some part of a machine, an engineer must
first know how the force it is to resist will be applied.
For instance, the cable that supports an elevator, or the
rope of a swing, or a belt that is transmitting power from
one pulley to another, has to resist a pull applied at each
120
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ELASTICITY AND STRENGTH OF MATERIALS 121
^nd, which tends to stretch it, and may, perhaps, break
it by pulling one part of it away from the next. In such
a case we say that the "member " — that is, the cable, or rope,
or belt — is in tension, meaning "in a state of tension."
The pier of a bridge, or the foundation of a house, or a
post supporting a piazza roof, has to do something quite
different from this. It has to resist a push at each end,
which tends to shorten it, and may cause it to give way by
crushing it. In such a case we say that the member — that
is, the pier, or foundation, or post — is in compression, meaning
*4n a state of compression."
A floor beam in a house or a girder in a plate-girder
bridge (section 115) has to resist bending^, and if it gives
way at all, it does so by breaking in two like a stick broken
across one's knee.
The duty of the shaft that drives the propeller of a steam-
ship, or of the shafts that run overhead in many, factories
and transmit power to the various machines, is to resist
twisting^.
And, finally, the duty of a rivet in a steel structure is
different from any of these (see Fig. 129). It has to keep
one of the plates from sliding over
the other. When such a rivet gives
way, it is often because the halves
of it have been pushed sidewise
so hard that one has slid away
from the other, leaving a flat, clean
break parallel to the surface sepa-
rating the plates. It is a strain of Fig. 129. — Action of plates on
this sort that we are really putting "^®*-
on a piece of cloth or paper when we cut it with a pair of
shears. So we say that the rivet is in shear, meaning that
it is in the same state as if it were being cut in two by a
pair of huge shears.
There are, then, these five kinds of stresses: tension,
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122
PRACTICAL PHT8IC8
compression, bending, twisting, and shear. In each case
that material should be used which will best resist the
parficular kind of stress that is to be applied to it. Thus
bricks set in mortar do very well under compression, but
are of little use in resisting any of the other kinds of stress.
Steel will resist any of them well. Cast iron will resist
compression about four times as well as it will tension, and
so on.
121. Stress and strain. Whenever any one ot these
kinds of stress is applied to a body, the body yields a little.
No bridge girder is stiff enough not to bend a little under
every wagon or train that goes over the bridge. If it is
a good girder, the amount of bending is imperceptible to
ordinary observation ; but there is always some bending.
Similarly, every shaft on a steamship twists a little
when the propeller is in motion. Measuring this
very small twist is often the only way in which the
horse power delivered by the engine to the propeller
can be measured. The same can be said of the
other types of stress ; each of them always causes
some yielding or deformation of the body under
stress.
The word "strain" is used to describe the
deformation produced. The word stress always
refers to the forces which are acting, while the
word strain refers to
the effect which they
produce.
122. Relation of
strain to stress. Let
s-
Fio.l30.-Stretchmgawirewith ^S try SOmC expcri-
different loads. ments to see if there
is any relation between
the amount of stress applied to a body and the amount
of strain it produces.
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ELASTICITY AND STRENGTH OF MATERIALS 128
I. Tension, Let us fasten one end of a piece of steel or spring-brass
wire in a clamp near the ceiling, and attach a pan for weights to the
lower end of the wire (Fig. 130). Since the stretch will be small, it is
necessary to use a lever or some other device to magnify it. Having
placed just enough weight in the pan to straighten the wire, we add
weights one at a time and read the corresponding positions of the pointer.
Each time we must remove the added weights to see if the pointer comes
back to its original position. When it fails to do this, we will stop
the experiment and disregard, for the moment, the last reading of the
pointer. If we then compute from each deflection of the pointer the
actual stretch or elongation of the wire, and divide esbch stretch by
the force causing it, we will find that
all the quotients are approximately
the same. That is, the stretch is
proportional to the load.
II. Compression, The same is
true for compression. Thus experi-
ments have shown that under ordi-
nary conditions the compression of
a spring is proportional to the force
applied.
m. Bending. We can perform a
similar experiment for bending by
supporting a metal rod or tube on
knife edges, and hanging different
weights from the center. A lever,
like that used in the tension experi-
ment above, enables us to measure
the small deflections of the center of
the rod. As before, we find that the deflections are proportional to the
loads causing them.
IV". Twisting, The apparatus shown in figure 131 enables us to per-
form similar experiments on twisting. As before, we find that the twist
is proportional to the stress causing it, namely, the " torque " or moment
of the twisting forc^
In all these cases, the strain is proportional to the stress.
This is called Hooke's law, after the medieval scientist who
discovered it. Hooke's law applies to all kinds of strains,
if the stresses are not too great.
Fig. 131. — Twisting metal rods.
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124 practical physics
Problems
1. If a weight of 1 pound, when hung on a certain spring, lengthens it
2 inches, what weight would lengthen it J an inch ? How much would |
of a pound lengthen it?.
2. If 2^ force of 5 pounds is required to move the middle point of a
beam ^ of an inch, what force would move it i an inch ?
3. A 2 pound force is applied to the rim of a wheel 9 inches in diam-
eter in the torsion apparatus described in section 122, and the end of
the rod twists through 3°. What force would have to be applied to the
rim of a wheel 12 inches in diameter to make the end of the same rod
twist through 5*"?
123. Elastic limit and breaking strength. In the tension
experiment in the last section we found that when a suffi-
ciently great load was hung from the wire, the latter did not
shrink back to its original length when the load was removed.
It had acquired a permanent " set." The same thing is true
of other kinds of stress, and might have been noticed in the
other experiments. The smallest stress of any particular
kind that will cause a permanent set in a bocly is called the
elastic limit of the body for that particular kind of stress.
As long as the load is below the elastic limit, Hooke's law
holds, but stresses greater than the elastic limit cause deflec-
tions greater than Hooke's law predicts.
If we still further increase the load in the tension ex-
periment, we finally reach a load so great that the wire
stretches very rapidly and almost immediately breaks.
This is also true of other kinds of tests, such as tests for
bending. The smallest stress of any particular kind that
will cause a body to give way is called the ultimate or
breaking strength of the body for that particular kind of stress.
Usually the elastic limit of anything is much smaller than
its breaking strength. But certain materials, such as glass,
follow Hooke's law right up to their breaking points, and
never show a permanent set. In such cases, the elastic limit
and the breaking strength are equal.
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ELASTICITY AND STRENGTH OF MATERIALS 126
124. Factor of safety. An engineer, when designing a
bridge or a machine, must be absolutely sure that no part of
it will ever be subjected to a stress greater than its elastic
limit, for if this were to happen, the part would be perma-
nently deformed, and this would weaken the rest of the
structure, or at least throw it out of alignment. He there-
fore plans to make each member big enough to carry several
times as much load as will probably ever be imposed on it.
This is partly to provide for any unforeseen temporary over-
loading of the structure, and partly because there may be,
even in materials of the best quality, imperceptible flaws
that would make the completed member less strong than it
seems to be. The number of times that the load planned
for is greater than the load expected is called the factor of
safety.
The factor that should be used varies with the material;
thus it is commonly 10 for brick and stone and only 4 for
steel. It also varies with the nature of the load; thus it is
commonly larger when the load is to be intermittent, as in
machines or railroad bridges, than when it is to be steady,
as in buildings. Often the factor for buildings is taken
larger than would otherwise be necessary, so that there may
be no danger of deflections in the walls and ceilings great
enough to crack the plaster.
125. Unit stress and unit strain in tension. When we
discussed Hooke's law in section 122, we were comparing
with each other the deformations produced in the same wire
or rod by forces of different magnitudes. That is, if we
knew by experiment how much one force would stretch a
given wire, we could compute how much a different force
would stretch the same wire. Let us now see if we can com-
pute from the result of an experiment on one wire how much
anotJ^r wire of the same material but of a different shape
would be stretched by any force that might be applied to it.
This is important for the engineer because it enables him to
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126 PBACTICAL PHT8IC8
test a small piece of a particular kind of steel, and compute
from this how a large tension bar in a bridge will act. For
this purpose it will be convenient to define more precisely
than in section 121 the meaning of " stress " and " strain " in
the case of a wire or rod under tension.
If one wire is twice as long as another, a given pull will
stretch the long wire twice as much as the short one ; for
each half of the long wire is just like the whole of the short
one, and has to pull just as hard on its supports ; each half,
then, stretches as much as the whole of the short wire. In
general, the total stretch of a wire under a given load is pro-
portional to its length. The stretch per unit of length is called
the unit stretch or unit strain.
Unit stretch =^^^^^.
length
For example, a piece of steel piano wire, originally 90 inches long, is
stretched 0.033 inches by a certain load. Then the unit stretch or unit
strain is 0.033/90 or 0.00037 inches per inch of length.
Similarly if twof wires are of the same length, but one has
twice as great an area of cross section as the other, the thick
wire is equivalent to two of the thin wires side by side, and
it would take twice as much force to stretch the thick wire a
given amount as to stretch the thin wire the same amount.
In general, the pull required to produce a given stretch will
be proportional to the area of cross section. The pull per
unit area of cross section is called the unit pull or unit stress.
Unit pull = totaljuU
area of cross section
For example, a piece of steel piano wire 0.0348 inches in diameter is
subjected to a pull of 10 pounds. What is the unit pull or unit stress in
the wire ? The area of the cross section of the wire is m^ or 3.14 x 0.0174*
or 0.000950 square inches. Therefore the unit stress is 10/0.000950 or
10,500 pounds per square inch.
If we were to test with the apparatus described in section
122 a number of wires of the same material but of different
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ELASTICITY AND STRENGTH OF MATERIALS 127
sizes and lengths, we would find that in all cases the unit
stretch is proportional to the unitpviL This law enables us to
compute how much a force will stretch a wire, if we know
how much another force will stretch another wire of the same
material.
For example, if a 10-kilogram weight produces in a piece of piano
wire, 0.5 millimeters in diameter and 1 meter long, a stretch of 0.02 mil-
limeters, what will be the stretch produced in a piece of piano wire 0.4
millimeters in diameter and 2 meters long, by a 15-kilogram weight ?
For the first wire : —
The cross section is irr^ = -^ square millimeters.
The unit pull is 10 -s- :^ = kilograms per square millimeter.
16 IT
The unit stretch is 0.02 millimeters per meter.
For the second wire : —
The cross section is ttt^ = ^ square millimeters.
The unit pull is 15 -*- ^ = kilograms per square millimeter.
25 TT
Call the unit stretch x millimeters per meter.
Then, since the unit pulls and unit stretches are in proportion,
375
X _ ?r
002 "" 160'
^ x = 0.02 X ?^ = 0.047 millimeters per meter.
160 ^
Since the second wire is 2 meters long, the total stretch in it is
2 X 0.047 = 0.094 millimeters.
126. Tensile strength. The length of a wire or rod has
nothing to do with its strength under tension, unless the rod
is so long that its own weight has to be taken into account.
The strength of a wire or rod is proportional to the area of
its cross section. The strength of a wire or rod of unit cross
section (1 square inch or 1 square centimeter) is called the
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128 PRACTICAL PHYSICS
tensile strength of the material. Tables giving the breaking
strengths of various materials can be found in any engineer's
handbook.
For example, in a testing laboratory it was found that a wrought-iron
bar 0.75 inches in diameter broke under a pull of 28,700 pounds. The
tensile strength of the material was, then,
28700
^^ .^ = 65,000 pounds per square inch.
3.14 X (0.375)3 > ^ ^ ^
Problems
1. If a pull of 22 pounds will break iron wire of size 24, what pull
will break iron wire of size 30 ? (See table on page 304 for diameters.)
2. From the data given in problem 1, compute the tensile strength of
the iron.
3. An iron bar is to be subjected to a total pull of 35,000 pounds and
is to be designed so that the unit pull shall not exceed 2500 pounds per
square inch. What should be the area of its cross section, and if round,
what should be its diameter?
4. A force of 2 kilograms stretches a certain wire 3 millimeters. How
much will a force of 5 kilograms stretch the, same wire?
5. How much would 5 kilograms stretch a piece of the same kind of
wire as in problem 4, with the same diameter but twice as long?
6. How much would 5 kilograms stretch a piece of the same kind of
wire as in problem 4, of the same length but with twice the diameter ?
7. How much would 5 kilograms stretch a piece of the same kind of
wire as in problem 4, but with half the diameter and three times the length ?
127. Stiffness and strength of beams. The design of floor
beams for buildings or girders for bridges is another matter
in which it is important for engineers to be able to predict
from experiments on small test pieces how a full-sized mem-
ber will act. They have, therefore, tried many experiments
on beams of different sizes and shapes with large test ma-
chines similar in principle to the bending apparatus described
in section 122. These experiments have shown that what
may be called the stiffness factor of a beam of rectangular
cross section is
Stiffness factor = breadth x (depth) »,
(length)*
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1 ELA8TICITT AND STRENGTH OF MATERIALS 129
To compare the deflections that would be produced by a
given force in two beams, we have only to compute their
stiffness factors, and the one with the larger stiffness factor
will bend less under the given load.
For example, which of the following beams is stiff er : —
Beam A : length 10 feet, breadth 4: inches, depth 6 inches ;
Beam ^: length 20 feet, breadth 6 inches, depth 8 inches?
. Stiffness factor of ^ ^ ^ x 6^ ^ l(fi ^ 9 . cancellation).
Stiffness factor of 5 6 x 8» ^ 20* 4 ^ ^ ^
Therefore, beam A is more than twice as stiff as beam B; that is, if
equal weights were hung from the centers of the two beams, the center,
of A would drop less than half as far as would the center of B,
Experiments have shown, however, that the stiffer of two
beams is not necessarily the stronger. In fact, the strength
factor of a beam of rectangular cross section is quite different
from its stiffness factor. It is
strength factor = l»readttx(4epth)' .
For example, compare the strengths of the two beams described above.
Strength factor of A _ 4 x 6^ -i- 10 _ 3
Strength factor of B 6 x S^ -j- 20 4 '
Therefore, although beam A is more than twice as stiff as beam -B, it
could support only three quarters as much load without breaking.
128. Cross sections of beams. Wooden beams ordinarily
have a rectangular cross section, and are designed on the
basis of the laws in the last section ; but steel beams, if so
designed, would be too heavy. It is possible, however, to
distribute a much smaller amount of material in such a way
as to be just as effective. Thus we all know that a bicycle
frame made of thin tubing is much stiffer than a frame of
equal weight made of solid rods. So it pays to consider
what the different parts of the cross section of a beam have
to do to resist bending.
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130
PBACTICAL PHT8IC8
To test this experimentally we have only to bend a type*
writer eraser with our fingers. The result will be as shown
in figure 132. We find that the top layer of a beam is short-
Fig. 132. — Diagram of loaded beam.
ened, and has to resist compression^ while the bottom layer is
lengthened, and has to resist tension. Somewhere between
the top and the bottom is a layer mn^ which remains of the
same length, and does nothing ; this is
called the neutral layer. Evidently there
should be as much material as possible
in the top and bottom layers, and as
little as possible in and near the neu-
tral layer. This is the case in the
sections shown in figure 133. It will
be noticed that the material is collected
in large flanges at the top and bottom, which are joined by
one or more thin webs.
Fia. 133. — Sections
steel girders.
Problems
1. A plank sags 0.1 inches with a load of 100 pounds. How far would
it sag under a load of 1 ton ?
2. How much would a plank similar to that in problem 1, but twice
as wide, sag under a load of 1 ton ?
3. How much would a plank similar to that in problem 1, but twice
as thick (or deep), sag under a load of 1 ton?
4. A beam 4 inches wide and 2 inches thick, when standing on edge,
bends 0.1 inches per thousand pounds. How much per thousand would it
bend when laid flat side down ?
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ELASTICITY AND STRENGTH OF MATERIALS 131
5. A modem floor beam, 2x9 inches in cross section, contains only
half as much ^material as an old-fashioned one Q x Q, Compare the
modem beam, set on edge, with the old-fashioned one, as to both stiff-
ness and strength.
SUMMARY OF PRINCIPLES IN CHAPTER VJ
Stress refers to force acting.
Strain refers to deformation produced.
Hooke's law : Strain is proportional to stress.
True for all kinds of stress.
TT •-!. *- X t. total stretch
Unit stretch = — ; — -- — .
length
TT 'J, 11 total pull
Unit pull = ^ — .
area of cross section
In tension, unit stretch is proportional to unit puU, for pieces of
any size or length, if of same material.
In bending beams of rectangular cross section,
stiffness factor = ^£?5^^<i^|P*^'.
(length)*
Strength factor = breadfli x (depth)'
length
Questions
1. Why was the standard meter bar (Fig. 1, section 7) made witn a
nearly H-shaped cross section ? Why was the scale engraved on the hori-
zontal web rather than on top of one of the sides ?
2. Name . five practical applications of the elasticity of steel in
springs.
3. Arrange an apparatus to determine whether or not Hookers law
applies to a rubber band.
4. Name the kind of stresses which are acting on the following:
wires of a piano, crank shaft in engine, smokestack, table leg, belt,
pump piston, and threads holding buttons on a coat.
5. In- the loading! of long columns, what other effects besides simple
compression have to be considered ?
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132 PRACTICAL PHT8IC8
6. Where is the elastic medium in the human body which prevents
injury to the brain when we jump?
7. In the frame of a bicycle, why does a pound of steel give greater
stiffness in the form of tubing than in rods ?
.8. Which flange of a cast-iron girder should have a greater cross
section ? Notice the statement in section 120.
9. Try to find out what is meant by the "fatigue" of metals (see
encyclopedia).
10. What advantages has reenforced concrete over ordinary concrete
for building purposes ?
11. How are the walls of high office buildings supported, and why ?
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CHAPTER VII
ACCELERATED MOTION
Speed and acceleration — laws of motion at constant accel-
eration — falling is motion at constant acceleration — value of
acceleration of gravity.
129. Average speed. If a man walks 12 miles in 3 hours,
we say that he averages 4 miles an hour. To be sure, at any
particular point on his journey he may have been going
faster or slower, but his average speed or velocity is 4 miles
an hour. If we know that the average speed of a steamer is
22 miles an hour, we can find a day's run by multiplying
the average speed by the number of hours in a day; thus
22 X 24 s 528 miles. In general,
Distance = average speed x time.
Speed is expressed in various ways; for example, we say
that an automobile travels at the rate of 25 miles an hour, a
steamer does 18 knots or 18 nautical miles an hour, a sprinter
runs 100 yards in 10 seconds, and a rifle ball goes 2000 feet
per second. For purposes of comparison it is convenient to
have some uniform way of expressing speed, and so engineers
and other scientific men have come to use feet per second
(ft. /sec.) or centimeters (or meters) per second (cm. /sec. or
m./sec). The following table gives some average speeds: —
Table of Speeds
Soldiers marching
4.3 ft/sec. = 1.4 m./sec.
Horse galloping
16 ft./8ec. = 5.2 m./sec.
Ocean steamer
40 ft./8ec. = 12.2 m./sec.
Express train
82 ft./sec. = 26.9 m./8ec.
Wind in hurricane
165 ft/sec. = 54.2m./8ec.
Sound
1120 ft/sec. = 386 m./sec.
Rifle ball
1500 to 2000 ft./8ec. = 493 to 657 m./sec.
183
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134 PRACTICAL PHYSICS
QUESTIONS AITD rROBLEKS
1. Sixty miles an hour equals how many feet per second ? Tou would
do well to remember this number.
2. With the help of a time-table, compute the average speed of an
express train, and of a local.
3. If the distance across the Atlantic Ocean is about 3000 miles, how
many days will it take a steamer to cross, at the speed given in the table
above ?
4. An officer on horseback starts on the gallop to overtake his regiment
a mile away, which is marching ahead. If they travel at the speeds given
in the table, how long will it take him ?
5. How long will it take an express train to cover 50 miles, going at the
rate given in the table ?
6. A rifle is flred at a target half a mile away. How long after it is
fired does the sound it makes against the target reach the man with the
xifle?
7. There is a common rule that if any one in a train counts for 19
seconds the number of clicks as the car passes over the ends of the rails,
the number he gets will be the speed of the train in miles per hour. What
must be the length of the rails to make this rule work ?
130. Variable speed. When a train is starting out from
a station, it is gaining speed, and when it is approaching a
station where it must stop, it is losing speed. So we see
that on account of stops and differences in grade, the speed
of a train is not uniform or constant, but is changing or
variable. When a loaded sled starts at the top of a long hill,
it gains in speed as it descends the hill ; but when it reaches
the bottom, it is retarded and loses speed until it stops. Its
speed or velocity, starting at zero, has increased to a maxi-
mum and then has decreased to zero again. Similarly, the
speed of a projectile from a big gun or of the piston of an en-
gine is not uniform but variable. *
If we wished to determine the speed of an automobile at
any instant or point, we would measure off some convenient
distance near the point and then get the time which elapsed
while the automobile traveled the fixed distance. For ex-
ample, if the measured distance, sometimes called a " trap,'*
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ACCELERATED MOTION 136
was a quarter of a mile and the time was 20 seconds, the
speed was three quarters of a mile per minute or 46 miles
per hour. But if the driver of the automobile was aware
of the trap and was driving at a dangerously high speed at
the beginning of the trap, he would slow down so that his
average speed over the measured distance would be within the
limit. To catch such a driver, that is, to get his speed more
accurately at any pointy we take as short a distance as is
consistent with an accurate measurement of the time.
131. Acceleration. It is unpleasant to be on a street car
when it starts or stops too suddenly. This suggests the
problem of measuring a rate of change of speed, which is called
acceleration. It has been found that a city street car standing
at rest can safely gain speed, so that at the end of 10 seconds
it is going 15 miles per hour. Assuming that this gain in
speed is made at a constant rate (only constant accelerations
will be discussed in this book), the speed of the car increased
1.5 miles-per-hour every second. In other words, the accel-
eration was 1.6 miles-per-hour per second. Or, since 15
miles an hour is 22 feet per second, we can say that the gain
in speed each second is 2.2 feet per second.
In general.
Acceleration = gain in speed per unit time,
and acceleration is always to be expressed as so many speed
units per time unit. Since there are many different speed
units, such as miles-per-hour, kilometers-per-hour, feet-per-
second, and centimeters-per-second, there are many ways of
expressing the same acceleration. Thus the acceleration of
the electric car jusl mentioned is
Velocity Unit Timb Unit
1.5 miles-per-hour per second,
or 2.4 kilometers-per-hour per second,
or 2.2 feet-per-second per second,
or 67.0 centimeters-per-second per second.
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136 PRACTICAL PHT8IC8
All these statements mean exactly the same thing. En-
gineers use the first two expressions for acceleration, while
other ^scientific men more commonly use the last two. It
is convenient to abbreviate " f eet-per-second per second"
as ft./sec.^ and " centimeters-per-second per second" as
cm./sec.^ but each of these abbreviated expressions means
simply so many velocity units gained per second.
The accelerating rates of oars vary according to service
and equipment, but the following rates are common in prac-
tical operation : —
Steam locomotive, freight service, 0.1-0.2 mile&-per-hr. per sec.
Steam locomotive, passenger service, 0.2-0.5 miles-per-hr. per sec.
Electric locomotive, passenger service, 0.3-0.6 miles-per-hr. per sec.
Electric car, interurban service, 0.8-1.3 miles-per-hr. per sec.
Electric car, city service, 1.5 miles-per-hr. per sec.
Electric car, rapid transit service, 1.5-2.0 miles-per-hr. per sec.
132. PositiYe and negative acceleration. When the speed
is increasing, the acceleration is said to be positive, and when
the speed is decreasing, the acceleration is negative. Thus
when a baseball is dropped from a tower, it goes faster and
faster; it has positive acceleration. When, however, it is
thrown upward, it goes more and more slowly ; it has nega-
tive acceleration or retardation.
133. Relation of speed to time at constant acceleration.
If we know the acceleration of any body, we can easily com-
pute its speed at any time after it started.
For example, if the rate of acceleration of a train is 0.2 miles-per-hour
per second, how fast is it moving one minute after it starts ? One minute
equals 60 seconds. If the train gains 0.2 miles-per-hour every second,
then its speed, 60 seconds after starting, would be 60 times 0.2, or 12
miles per hour.
Law I. If the acceleration is constant^ the speed acquired
is directly proportional to the time.
Final velocity = acceleration x time.
V = at (I)
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ACCELERATED MOTION 137
Problems
(Assume constant acceleration.)
1. Express 32 f eet-per-second per second in miles-per-hour per second.
2. A body has a speed of 16 feet per second at a certain instant, and
3 seconds later it has a speed of 112 feet per second. What is its
acceleration ?
3. A train starting from rest has, after 33 seconds, a speed of 15
miles an hour. What is the average acceleration,
(a) In miles-per-hour per second?
(b) In f eet-per-second per second?
4. If a locomotive can give a train an acceleration of 5 feet-per-second
per second, how long will it take, after slowing down for a crossing, to
increase the speed of the train from 22 feet per second to 82 feet per
second ?
5. What is the acceleration of a train if the initial speed is 45 feet
per second, and after 5 seconds the speed is 15 feet per second ?
6. The negative acceleration (retardation) in stopping electric trains
is seldom greater than 4 feet-per-second per second. How long does it
take to stop a train from 60 miles an hour?
7. Which of the following accelerations is the largest : —
(a) One foot-per-second per five seconds,
(b) One f oot-per-five-seconds per second,-
(c) One fifth of a foot-per-second per second?
134. Relation of distance to time at constant acceleration.
Suppose a sled gains speed at a constant rate as it goes down
a hill. If its acceleration is 3 feet-per-second per second,
how far will it go in the first five seconds after starting
from rest ? We have already seen that its velocity at the
end of five seconds will be 5 x 3, or 15 feet per second. Now
it started from rest, that is, its initial velocity was zero, and
gradually its speed increased until its final velocity^ at the
end of 5 seconds, is 15 feet per second. Therefore its
average velocity is one half the sum of its initial and final
velocities, or 7.5 feet per second.
Ayerage velocity = toitial velodty + flnal velocity^
2
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138 PRACTICAL PHYSICS
We have already learned (section 129) that the distance
traversed is the product of the average velocity and the time.
So in this case the sled has gone 7.5 x 5, or 37.6 feet.
In general, for a body starting from rest^ the average veloc-
ity is one half the final velocity;
Average velocity = ^*
But we already know that the final velocity is t^ = o^ ; then,
Average velocity = —-•
Therefore the distance is
Law II. ^ the acceleration is constant^ the distance trav-
ersed from rest varies as the square of the tim^.
In using this law, acceleration should be expressed in
ft./sec.^ or m./sec.2 or cm./sec.V and t in seconds.
135. Relation of speed to distance at constant acceleration.
Suppose we wished to know how far the rapid transit electric
car mentioned in the table in section 131 would have to run
to develop a speed of 30 miles an hour, starting from rest.
Since the question is concerned only with speed, distance, and
acceleration, it is convenient to have an equation involving
only v^ «, and t
From equation (I), we have
a
and from equation (II),
1 ,2 1 v^ . v^
s=:--at^ = --a x-z = rr—
2 2 a2 2a
Then, if^=2as- (HI)
Law III. Jf the acceleration is constant^ the speed varies as
the square root of the distance traversed.
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ACCELERATED MOTION 139
Equation (III) enables us to answer the question about the
electric car.
t; = 30 miles per hour = 44 feet per second.
a=(say) 2.0 miles-per-hour per second = 2.93 feet-per-
second per second.
« = — = ^^ = 330 feet.
2 a 2x2.93
Notice that 30 miles per hour and 2.0 miles-per-hour per
second could not be substituted directly, because two differ-
ent kinds of time units, namely hours and seconds, are in-
volved. This is an example of the general rule that all the
quantities substituted in any equation must first be expressed
in consistent units.
It will save time to memorize equations (I), (II), and (III).
Notice that there is an equation for each pair of quantities v
and f, 8 and ^, and v and 8. Alway8 U8e the one equation that
give8 what i8 wanted difectly from the data,
136. Negative acceleration. Suppose that an engineer,
running at 50 miles an hour, sees a child on the track 200
yardsahead. If his emergency air brakes can give him a re-
tardation of 4 feet-per-second per second, can he stop in time ?
Here we have a problem in retardation or negative accelera-
tion. Let us think of the problem the other way around.
Evidently if the engineer could stop within a given distance
at a given retardation, he could get up speed within the same
distance with an equally great acceleration. So we may ask
instead, whether the engineer could get up to a speed of 50
miles an hour within 200 yards, if accelerating at 4 feet-per-
second per second. The answers to the two questions are
the same.
Since the quantities involved are a velocity v, and a dis-
tance «, we will use equation (III).
t; = 50 miles an hour = 73.3 ft. /sec.
a = 4 ft./sec.^.
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140 PRACTICAL PHT8IC8
Then « = ^ = Q^^ = 672 feet = 224 yards.
2a 2x4 ^
So the engineer could not stop in time.
Problems
(Assume constant acceleration.)
1. If a locomotive can give its train an acceleration of 5 feet-per-sec-
ond per second, in what distance can it develop a speed of 60 feet per
second, starting from rest ?
2. A boy runs toward an icy place in the sidewalk at a speed of 20 feet
per second and slides on it 16 feet. What is the (negative) acceleration?
3. How far will a marble travel down an inclined plane in 3 seconds,
if the acceleration is 50 centimeters-per-second per second?
4. A motor cycle starting from rest acquires a velocity of 40 miles an
hour in 2 minutes. What is the acceleration in miles-per-hour per
second?
5. How many yards does the motor cycle have to run in problem 4?
6. Two suburban stations are 2700 feet apart on a straight track.
The greatest practicable acceleration or retardation is 3 feet-per-second
per second. K there is no limit to the speed en route, what is the short-
est possible running time between the stations, with stops at both ?
137. Falling is motion at constant acceleration. It is pos-
sible to determine in the laboratory the time it takes a body-
to fall various distances. The results of an actual series of
such experiments are as follows : —
Distances Timbs Ratio of Times
36 cm. 0.272 sec. 3
64 0.363 4
100 0.452 5
144 0.542 6
It will be seen that these distances vary almost exactly as
the squares of the times, which we have seen to be the case
when the acceleration is constant (see law II). Therefore
falling is a case of motion at constant acceleration.
A freely falling body acquires velocity so rapidly that it
is difficult to make observations upon it directly* Long ago
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ACCELERATED MOTION 141
Galileo hit upon the plan of studying the laws of falling
bodies by letting a ball roll down an incline. In this way
he "diluted" the force of gravity and increased the time of
fall so that it could be measured more accurately.
138. Galileo's experiment on the inclined plane. Galileo
cut a trough one inch wide in a board 12 yards long, and
rolled a brass ball down the trough. After about one hun-
dred trials made for different inclinations and distances, he
concluded that the distance of descent for a given inclination
varied very nearly as the square of the time. It is remark-
able that he was so successful in this experiment when we
consider how he measured the time. He attached a very
small spout to the bottom of a water pail and caught in a cup
the water that escaped during the time the ball rolled down
a given distance. Then the water was weighed and the
times of descent were taken as proportional to the ascertained
weight.
These experiments of Galileo are especially interesting
because they led him to change his theories about the dis-
tance and time of falling bodies. He seems to have been
one of the first of the ancient philosophers who thought it
worth while to subject his theories to the test of experiment.
139. All freely falling bodies have the same acceleration.
Before the time of Galileo (1564-1642) people believed that
heavy objects fell faster than light objects; in other words,
that the speed of a falling body depended upon its weight.
But he claimed that all bodies, if unimpeded by the air, fell
the same distance in the same time, and that the only thing
that caused some objects, like pieces of paper or feathers, to
fall more slowly than pieces of metal or coins, was the re-
sistance of the air. To convince his doubting friends and
associates he caused balls of different sizes and materials to
be dropped at the same instant from the top of the leaning
tower of Pisa. They saw the balls start together, and fall
together, and heard them strike the ground together. Some
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142
PRACTICAL PHT8IC8
were convinced, others returned to then
rooms to consult the books of the old Greek
philosopher, Aristotle, distrusting the evi-
dence of their senses.
Later when the vacuum pump was in-
vented, the truth of Galileo's view was
confirmed by dropping a feather and a coin
in a vacuum tube.
If we place a piece of metal and some light object,
like a bit of paper or pith, or a feather, in a long
tube (Fig. 134), and pump out the air, we find that,
when we suddenly invert the tube, the two objects
fall side by side from the top to the bottom. If we
open the stopcock, letting the air in again, and
repeat the experiment, we find that the metal falls
to the bottom first.
140. Value of acceleration of gravity. It
Fig. 134. — Feather is possible to determine the value of the
and com fall to- acceleration of gravity from the experi-
gethermayacuum. i t t P ■%
mental data obtained m measuring the time
of a free fall (section 137), and it is also possible to compute
the value of this constant from the data got in the experiment
of rolling a ball down an incline. Neither of these methods,
however, yields as precise results as are obtained in experi-
ments with pendulums.
We are all familiar with the pendulum as a means used to
regulate the motion of clocks. It was long ago discovered
by Galileo that the successive small vibrations of a pendulum
are made in e(q[ual times, and that the time of vibration does
not depend on the weight or nature of the bob, or the length
of the swing, but does vary directly as the square root of the
length of the pendulum, and inversely as the acceleration of
gravity. This is expressed in the following formula: —
^9
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ACCELERATED MOTION
148
where t is the time in seconds of a complete vibration, I is
the length of the pendulum in centimeters, g is the accelera-
tion of gravity in centimeters-per-second per second, and
TT is 3.14.
We can measure t and I directly and ir is known, so we
may compute g from the formula ; thus,
4^
9 ^2
The value of the acceleration of gravity is about 980 centi-
meters-per-second per second^ or about 32.2 feet-per-second per
second. It varies a little from place to place.
Problems about falling bodies are ju^t like other problems
with constant acceleration. In the equations we usually rep-
resent the acceleration of gravity by g.
Thus, for bodies falling freely from rest,
V =gt,
It will be useful to remember that the speed with which a
body must be projected upward to rise to a given height is
the same as the velocity which it will acquire in falling from
the same height. (Compare this statement with section 136.)
Problems
(Neglect air resistance.)
1. Make a table like the following, running up to < = 5 seconds, and
fill it in.
NUMBKB OF
Skoonds, t
Total Distanob
Fallen, « (ft.)
Speed at End
OF Each Second,
V (ft./seo.)
Total Distance
Fallen,
8 (metebs)
Speed at End
OF Eaou Second,
« (m./sec.)
1
2
16.1
?
32.2
?
4.9
?
9.8
?
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144 PRACTICAL PHT8IC8
2. A stone is dropped from the top of a cliff and strikes at the base
in 5 seconds, (a) What velocity did it acquire ? (b) How high is the
cliff?
3. If a falling body has acquired a velocity of 150 feet per second,
how long has it been falling ? How far?
4. How many centimeters does a stone fall in 0.5 seconds ?
5. How many centimeters does a stone fall during the fifth second?
6. A rifle is fired straight up (for speed, see table in section 129).
How long before the bullet comes down again ? How high will it go ?
(Assume that air resistance is negligible, which is far from true.)
7. A baseball is thrown up in the air and reaches the ground after
4 seconds. How high did it rise ?
8. The weight of a pile driver drops 5 feet at first and later 15 feet.
How much faster is it moving when it strikes in the latter case than in
the first case ?
9. A body is thrown vertically upward with a velocity of 50 meters
per second. With what velocity will it pass a point 100 meters from the
ground ? (Hint. — How high does the body rise ?)
10. How long would it take a bomb to fall 1000 feet from an aero-
plane ? During the fall the bomb would continue to move sidewise with
the same velocity as the aeroplane, and so would always be directly under
it. If the speed of the aeroplane is 60 miles an hour, how far will the
bomb move sidewise while it is falling ?
Speed
SUMMARY OF PRINCIPLES IN CHAPTER VH
distance
time
Acceleration = i*?iHa5£d.
time
Laws of motion at constant acceleration:-*
I. v= at,
n. 5=2L^
2 '
m. tr^ = 2ii&
Value of acceleration of gravity : —
gssZ2.2 ft/sec' = 980 cm./secA
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ACCELEBATED MOTION 145
QUBSTIOHS
1. If you take two sheets of paper of the same size^ and roll one of
them into a ball^ and let both the ball and the sheet of paper fall at the
same instant from the same height, what is the result ? Why ?
2. How must the pendulum bob be moved on a clock which is nm-
ning too fast ?
8. What takes the place of a pendulum in a watch ?
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CHAPTER Vin
FORCE AND ACCELERATION
Inertia — the fundamental proportion — action and reaction — mas&
141. Newton's laws of motion. We are studying motion,
and so far we have considered how bodies move ; that is, we
have been describinff different motions, such as motion at
constant speed and motion at constant acceleration. Now
We shall begin to study why bodies move ; we shall try to
explain different motions by studying the forces that cause
them. Practically all that we know about this part of physics
dates back to Sir Isaac Newton (1642-1727), who wrote a
treatise on the principles (^Principia) of natural philosophy
or physics. His whole book, and indeed all mechanics since
his day, is based on three very simple laws, called Newton's
laws. The first of them is the law of inertia, the second the law
of acceleration, and the third the law of interaction. These will
now be discussed in turn.
142. First law — Inertia. It is a familiar fact that nothing
in nature will either start or stop moving of itself. Some
force from outside is always required. For example, a horse
when starting a wagon, even on an excellent road, has to
pull very hard at first ; once the wagon is going, the horse
can keep it moving with very little effort ; but if he tries to
stop it to avoid running over some one, he has to push back
hard. So also when a moving ship collides with another ship
or a dock, it requires an enormous retarding force to stop
her. In 1908 the Florida rammed the Republic^ and her bow
was crumpled back 80 feet before the force stopped her.
146
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Sir Isaac Newton. Born in England, in 1642. Died in 1727, and is buried
in Westminster Abbey. Founded the science of mechanics, and made
many important discoveries in light. Famous also for his achievements in
mathematics and astronomy.
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FORCE AND ACCELERATION
147
This inability of matter to change its state of motion (or of
rest), except it be influenced from outside, is called inertia.
We may illustrate this
property of inertia by bal-
ancing a card on a finger
with a coin on top. Then
we may snap the card oat,
leaving the coin on the
finger. The coin moves
only a little because there
is only a small force due
to friction to get it started.
This may also be done
with the apparatus shown
in figure 135.
Another interesting experiment is to try
to pick up a flatiron by means of a linen
thread tied to it (Fig. 136 ). If we pull slowly,
we may be able to do this, but if we pull with
a jerk, the string always breaks, because so
much extra force is required to set the flat-
iron in motion quickly.
Fio. 135.— Inertia
keeps the baU
from movlDg.
Fig.
136. — Inertia holds the
weight still.
This familiar fact that bodies act as
if disinclined to change their state, whether of rest or motion,
was expressed by Newton in the following way: —
Law I. Uvert/ body persists in a state of rest^ or of uniform
motion in a straight line^ unless compelled by external forces to
change that state.
Question
If you roll a ball along the ground, it does not keep going indefinitely.
An automobile can start by itself.
Do these facts conjbrovert Newton's First Law?
143. Applications of inertia. A nail can easily be driven
into a heavy piece of wood, even when the wood does not lie
on a firm foundation, because the quick blow of a hammer
does not set the heavy piece of wood in motion to any great
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148
PRACTICAL PHTBICa
f
^
Fig. 137. — Inertia of sledge hammer.
extent. It is very difficult, however, to drive a nail through
a light stick unless the stick is placed upon a solid foundation,
or unless the stick is steadied by the inertia of a heavy sledge
hammer, as shown in figure 137.
When the head of a hammer comes off, the best way to
drive it on again is to
hit the other end of the
handle, rather than the
head, against some solid
foundation or with an-
other hammer. (Why ?)
144. Inertia in curved
motion. This tendency of
a body to continue to
move in a straight line is very evident when it is desirable to
make the body move in a circle. In this common case, a
force is required to pull the body in toward the center of the
circle, so that it may not fly off on a tangent. Such a force is
called a centripetal force, mean-
ing a force directed toward
the center.
When an athlete swings a
16-pound hammer around his
head before throwing it, he
has to pull it inward because
of its inertia. When he stops
pulling inward, it flies off on
a tangent. So all he has to
do to throw it is to let go.
Emery wheels revolve very
rapidly. Sometimes one
bursts because the cohesion between its parts is not enough to
supply the centripetal force necessary to keep these various
parts moving in their respective circles.
The mud on a bicycle wheel stays on the wheel only if the
Mud flies off on a tangent.
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FORCE AND ACCELERATION
14&
adhesion between it and the tire is great enough to pull it
around with the tire ; otherwise it flies off on a tangent.
In a cream separator the denser part of the milk gets out-
side and crowds the lighter cream inward. This is because
the greater inertia of the milk (that is, its greater tendency
to move along a tangent) prevails over that of the cream.
When a train goes around a curve, the flanges of the wheels
are pressed inward by the outer rail ; if the rail is not strong
enough to exert the necessary force inward, the train is
wrecked on the outside of the
roadbed. This is made clear
in figure 139. The weight of ^
the train is balanced by the
upward push A of the tracks,
the centripetal force B is ex-
erted inward by the rails
against the flanges, ajid there-
fore the resultant R is in-
clined. Consequently the ^^' l^e.-Banking rails on a curve.
track should be tilted toward the center, that is, " banked,"
so as to be at right angles to R. -This equalizes the pressure
on both sides and relieves the pressure on the outside flanges,
thus making them less likely to break.
145. Second law — Acceleration. We have been discussing
what happens to a body when forces do not act on it. Let
us now consider what happens when forces do act on it.
Whenever an " unbalanced " force is acting on a body, the
body has an acceleration in the direction in which the force
acts, and the acceleration is proportional to the force. By
an unbalanced force we mean more push or pull in one direction
than in the other. For example, a locomotive is pulling a
train at a constant speed of 50 miles an hour. The engine
is certainly exerting a force on the train, but there are other
forces, due to friction and air resistance, acting in the
opposite direction, and these just balance the pull of the
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160 PBACTICAL PHT8IC8
engine. The net force forward is zero ; if it was not zer(\
the train would not only be going forward but accelerating
forward ; it would be gaining speed.
It is important to keep in mind that it is net force and acceleration
which always go together, and not net force and motion. The above
example shows that we can have motion without net force if the speed
is not changing.
Law II. The acceleration of a given body is proportional to
the force causing it
That is, if any given body is acted on at one time by a
force F^^ and at another time by another force ^2* then
li = \
where a^ and a^ are the accelerations produced by F^ and F^*
In other words, if we pull a body with a certain force, and
at another time pull it twice as hard, it will have twice as
much acceleration the second time as the first.
One way to cause a force to act on a body is to let the
body fall. In this case the force acting is known, namely,
the weight TTof the body.. The acceleration is also known,
namely, g^ which is 32.2 feet-per-second per second, or 980
centimeters-per-second per second. So the weight of the
body and its acceleration when falling can always be used
as two of the numbers in a proportion.
That is, -^ = -.
W g
This enables us to compute the force needed to give a
certain body any desired acceleration.
For example, a freight train weighs 1000 tons. How great a force
is necessary to give it an acceleration of half a f oot-per-second per second!
F ^0.5
1000 32.2'
J'=^TA^-^ = 15.6 tons.
32.2
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FORCE AND ACCELERATION 161
146* Units. In the equation F/W=a/g^ it makes no
difference in what unit F and W are expressed, provided
only that both are expressed in the same unit. Both can be
expressed in pounds, or in ounces, or in tons, or in kilograms,
or in grams, or in a less familiar unit called a " dyne." The
dyne is a /ery small unit of force much used in scientific
work, especially electrical measurements. It can be defined as
1/980 of a gram weight.* It is about the weight of a milli-
gram. If a force is given in terms of any one of these units,
it can be expressed in terms of any other of them with the
help of the following table: —
1 gram = 980 dynes. 1 dyne = 0.00102 grams.
1 pound = 454 grams. 1 gram = 0.00220 pounds.
1 pound = 445,000 dynes. 1 dyne = 0.00000225 pounds.
Similarly a and g may be in any units, provided only that
both are in the same unit. If both are to be in f eet-per-second
per second, the numerical value of g is 32.2 ; if both are to
be in centimeters-per-second per second, the numerical value
of g is 980.
Problems
1. Express 110 grams in pounds.
2. Express 110 grams in dynes.
3. Express 8,000,000 dynes in pounds.
4. What acceleration will a force of 5 pounds produce in a body
weighing l6.1 pounds?
5. What acceleration will a force of 1 gram produce in a body weigh-
ing 327 grams?
6. What acceleration will a force of 1 pound produce in a body
weighing 1 pound ?
7. What acceleration will a force of 1 dyne produce in a body weigh-
ing 1 gram ? (Note. — The answer to this problem is often regarded as
the definition of a dyne.)
8. State accurately in words the definition of a dyne that is referred
to in the last problem.
* See also problems 7 and 8 below.
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162 PRACTICAL PHYSICS
9. A body weighing 10 pounds is observed to have an acceleration of
2 feet-per-second per second. What force is acting ?
10. A force of 1 kilogram is observed to produce an acceleration of
9.8 centimeters-per-second per second in a certain body. How much
does the body weigh?
11. A force of 1000 dynes is observed to produce an acceleration of
9.8 centimeters-per-second per second in a certain body. How many
grams does the body weigh?
12. An automobile weighing 2 tons is started from rest with an
acceleration of 4 feet-per-second per second. How hard is the road push-
ing the bottoms of the rear tires forward ?
13. An elevator weighing 980 kilograms is pulled upward by a forcQ
great enough to hold up the weight and give 200 kilograms of net force
besides. What is the acceleration of the elevator?
14. What pressure will a 150-pound man exert on the floor of an
elevator which is going up with an acceleration of 4 feet-per-second per
second ?
15. A train starting from rest with a constant acceleration takes 44
seconds to get up to a speed of 30 miles an hour. If the train consists
of 4 all-steel cars, each weighing with its load 62.5 tons, what pull is exerted
by the engine? (Hint. — Compute acceleration and then find force.)
147. Third law — Interaction. Newton's third law is based
on two familiar facts. One way of stating the first of these
facts is that there can never be a force acting in nature unless
two bodies are involved, one exerting it and one on which it
is exerted. Thus, when a railroad train is pulled, there is an
engine that does the pulling ; and on the other hand, the
engine cannot exert a pull or a push without something
to be pulled or pushed. An electric car or an automobile
seems, perhaps, to push itself along, but really the track or the
road under the wheels is exerting a force on the wheels
and pushing the car along. We have all seen what happens
when the car track is so icy or the road so muddy that it
cannot push on the wheels. The motor is going just as hard
as ever, but the car does not move.
In order to make this idea seem more real to us, let us try the experi-
ment on a small scale, as shown in figure 140. If we wind up the little toy
engine, and place it on the circular track, which is so mounted as to turn
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FORCE AND ACCELERATION 158
easily, we fiDoL that the track turns around and the rails under the
wheels go backwards. If we hold the track fast, the engine goes ahead
twice as fast as at first, and if we hold the engine fast, the track turns
around backwards twice as fast as at first.
Another case is that of any heavy object : there is a force
called its weight (force of gravity) pulling it down ; but we
know that it is the earth that exerts this force.
Fig. 140. — Track pushes the engine forward.
This, then, is the fir^t fact : whenever there is a f or.eo in
nature there must be two bodies, one to exert it and one to
receive it.
But we can go farther than this. We can say thai when-
ever there is a force in nature, there must be not only two
bodies involved, but another force. That is, forces never
exist singly, but always in pairs. If the first force wa«
exerted by a locomotive on a train, the second will be exerted
by the train on the locomotive. The train will pull back on
the locomotive just as hard as the locomotive pulls forward
on the train. If a road is pushing forward on the wheels of
the automobile, the wheels must be pushing back on the road.
If, instead of the road, we substitute great rollers, we may measure this
backward push. This is the method sometimes used in testing labora^
tories in making power tests of automobiles and locomotives.
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164 PRACTICAL PHT8IC8
Finally, when any heavy object is pulled downward by the
earth, the heavy object must be pulling the earth up with an
equal force. This does not seem very likely at first, but
this is simply because the force is so small and the earth so
large that the force has an imperceptible effect on the earth.
If the heavy body which we are thinking of is the moon,
the whole thing becomes reasonable at once, for the earth and
the moon are actually rotating about a point 0 (Fig. 141),
which is not ex-
actly at the center
of the earth. So
the moon must
continually pull
the earth to make
Mooir its center of grav-
ity move in its
circle.
^^*™ This fact that
Fig. 141. — Botatiim of the moon about the earth. ^^««^« «i « «
forces always
occur in pairs, one of the pair being equal and opposite to the
other, was expressed by Newton in the following form : —
Law III. With every action (or force^ there is an eqiud
and opposite reaction,
148. Mass vs. weight. ^^Mass" and ^^ weight" are con-
stantly confused in ordinary conversation. While we have
preferred not to use the term "mass" in studying Newton's
second law, yet it is well to know its precise meaning that
we may read intelligently the books which make use of it.
Mass means quantity of matter. It is the answer to the
question, " How much matter is there in a given body ? "
Weiffht means the pull of gravity on the body. The
weight of a body is a, force acting on the body, not a descrip-
tion of what it contains.
The unit of mass is the quantity of matter contained in a
certain piece of platinum (the standard kilogram. Fig. 142).
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FOBCE AND ACCELEBATION
166
The unit of weight is the pull of the earth on that same
piece of platinum, when it is near sea level and at latitude 46^.
Since a kilogram mass weighs a kilogram under these
standard conditions, the mass aad the ^^ standard weight " of
a body are numerically equal.
But if we carry a kilogram
mass to the top of a high
mountain, and weigh it on a
very sensitive spring balance,
it will weigh less than a kilo-
gram, because it is farther
from the center of the earth,
and so the earth pulls less
hard on it. The reading of
the spring balance might be
called its "local weight."
Since all bodies on the
mountain top would weigh
less in the same proportion,
we can get the standard weight of anything without de-
scending the mountain by weighing it on an egtMl-arm bal-
ance against a set of "standard weights." This is what we
always do in the laboratory and in the outside world when
we want to know weights accurately. So when we speak of
the weight of a body we almost always mean its " standard
weight."
W
Since F=s — a, and since the standard weight W and the
Sf
mass M are numerically equal, we shall get the same value
for F if we write (when using grams, centimeters, and
seconds)
980'
Fio. 142.— Standard kilogram.
or
980 F^ Ma.
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156 PRACTICAL PHT8IC8
Here F is in gramn; if we choose, however, to express the
force as F' dynes, instead of as J' grams, then F and F' will
be different numbers, and
F = 980 F,
so F (dynes) — Jtf"(grams) X a (cm./sec.^).
This is a common way of expressing Newton's second law.
SUMMARY OF PRINCIPLES IN CHAPTER VHI
Newton's laws and the fundamental proportion : —
L Every body continues in a state of rest or of uniform
motion in a straight line, unless compelled by external
forces to change that state.
IL The acceleration of a given body is proportional to the
force causing it
W g
IIL With every action (or force) there is an equal and opposite
reaction.
Distinction between mass and weight
QUESTIONS
1. How is the water quickly removed from wet clothes in a steam
laundry?
2. Why does a train continue to move after the steam is shut ofE?
3. Why do automobiles " skid" in rounding corners rapidly?
4. What does an aviator have to do to round a comer safely, and
why?
5. Why can small emery wheels be safely driven at a greater speed,
that is, at more revolutions per minute, than larger ones ?
6. Why does a wheel, or any revolving part of a machine, sometimes
shake or hammer in its bearings?
7. Explain how a locomotive engineer can tell, when he starts up
his train, if one of the cars has been uncoupled from the train.
8. Explain why lawn sprinklers rotate. Would such a sprinkler ro*
tate in a vacuum ?
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CHAPTER IX
ENERGY AND MOMENTUM
Kinetic energy — the law of energy — potential energy — the
conservation of energy — momentum and its law.
149. Elinetlc energy. We have already seen (section 31)
that in physics work involves not only force but also dis-
placement. Whenever a force moves anything in its own
direction, the force does work on the thing, and when-
ever anything moves against a force, the thing does work
against the force.
The energy of anything may be defined as its capacity for
doing work. Thus a heavy flywheel will keep machinery
running for some time after the power has been shut ofif.
Therefore, a heavy flywheel in motion can do work; it has
energy. The energy of any body which is due to its motion
is called kinetic energy.
Let us consider more carefully the case of a heavy flywheel
on an engine. At first the engine has to push and pull on the
crank shaft to get the flywheel started and to bring it up to
speed; the engine has to do work on the flywheel. When
once the flywheel is up to speed, however, the engine does
not have to push or pull any longer to keep the flywheel
going (except for friction, which we will neglect for the
moment). From this time on all the work that the engine
does goes into the driven machinery attached to the shaft.
Suppose now that the pressure of the steain on the engine
suddenly drops, or that an extra load is thrown on the shaft.
The shaft does not stop turning suddenly, or drop instantly
to a lower speed. It slows down gradually, pulling back on
167
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168 PRACTICAL PHT8IC8
the flywheel as it does so, and taking work out of the fly-
wheel, that is, making the flywheel do work instead of
absorbing it. This continues until the engine picks up the
load again, or until the flywheel stops.
In other words, the flywheel, as long as it is moving, can
do work on the shaft if necessary, and the faster it is moving,
the more work it can do before it comes to rest. In physics
we describe this very familiar fact by saying that the fly-
wheel has energy, and since its energy depends upon its being
in motion, we call it kinetic energy, or energy of motion.
Every body in motion has kinetic energy; that is, it will do
a certain amount of work against a resisting force before it
will stop. Furthermore the kinetic energy of a body will
be greater the heavier it is and the faster it is moving.
150. How to measure kinetic energy. It will be easier to
do this for a body moving straight ahead rather than in a
circle. We will consider first how much work it takes to
get a heavy body up to a given speed, and then how much
work it will do before it stops. By definition this latter is
its kinetic energy.
The force necessary to get a body started with a given
acceleration a is, by the fundamental proportion (section
145),
9
If the distance which the body moves before it gets up to a
given speed is called «, the work done is the product of the
force by the distance, namely,
Fb=^^ as.
9
But it will be seen that the product as can be expressed in
terms of the speed acquired, v, by means of the third law of
accelerated motion (section 135). Thus,
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BNEROT AND MOMENTUM 159
or a» = ^
So the work ^one is
2
^9
Thus we see that the work required to bring a heavy
body from rest up to a given speed does not depend on the
acceleration, or on the distance covered while coming up to
speed, but only on the weight of the body and the speed
itself.
Now, how much work will the body do against a retarding
force before it comes to rest ? We have already seen that
the easiest way to think of a retardation problem is as an
acceleration problem reversed. That is, a body will stop
under a given retarding force in the same distance that it
would need to get up speed under an equal accelerating force,
and it will do the same work against the retarding force
that an equal accelerating force would have to do on it to
get it started. So the formula above gives not only the
work necessary to start it, but also the work it will do when
it stops.
Therefore,
Kinetic energy = ■?^.
151. The energy equation. The equation just found,
namely,
is called the energy equation. It applies, as we have just
seen, either to accelerating or to retarding bodies, if they
start from or come to rest. It can be stated in words as
follows : —
If the body is gaining speed.
Gain of kinetic energy = accelerating force x distance
= work done by force on body.
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160 PRACTICAL PHY8IC8
If the body is losinff speed,
Loss of kinetic energy = retarding force x distance
= work done by body against force.
152. Units. In using this equation we must be consistent
in our units. Thus jFand Tfare both forces and both must
be expressed in the same unit in any one application of the
equation. In one problem we may choose tons and in an-
other dynes, but in any single problem all forces must be in
tons if we have chosen tons, and in dynes if we have chosen
dynes.
In the same way, «, v, and ff must all involve the same unit
of length. In one problem we may choose centimeters and in
another feet, but once we have started the problem we must
stick to our choice.
In expressing the velocity, v, and the acceleration, ff, it is
customary always to use the second as the unit of time.
Therefore ff will always be either 32.2 ft./sec.^ or 980 cm./sec.^
according as we have chosen feet or centimeters as the unit
of length.
The left-hand side of the equation, jF«, is force times dis-
tance, or work, and so the right-hand member, which is equal
to it, will come out expressed in work units. There are several
work units in common use, such as the
foot pound (ft. lb.),
foot ton (ft. T.),
gram centimeter (g. cm.),
kilogram meter (kg. m.), and
dyne centimeter ("erg").
Since each of these work units is a force unit times a dis-
tance unit, we can always tell what unit the kinetic energy
will come out in, if we notice what force unit and what dis-
tance unit we started with.
For example, if W is in pounds, v in feet per second, and 17 in feet-per^
second per second (g = S2.2 ft/sec^), the kinetic energy {Wv^/2 g) will
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ENERGY AND MOMENTUM 161
be in foot pounds. But if W^ is expressed in dynes, i; in centimeters pel
second, and g in centimeters-per-second per second {g = 980 cra./sec.^),
the kinetic energy ( Wir^/2 g) will be in dyne centimeters. There is a
shorter name for a " dyne centimeter " ; it is usually called an erg. Since
the erg is a very small unit of work, the Joule = 10^ ergs is often used.
153. Applications of the energy equation. The energy equa-
tion will help lis to solve many useful problems about moving
things which involve the question " how far," or the idea of
distance in general.
For example, consider again the problem of the engineer and the
child (section 136). Suppose that the train is going 50 miles an hour,
but that we do not know its rate of retardation. If the retarding force
is equal to one eighth of the weight of the train, how far will the train
run before coming to a standstill?
We can compute the rate of retardation from the fundamental pro-
portion, and then proceed as before, but it will be easier to use the
energy equation as follows : —
The speed 50 miles an hour = 73.3 f t./sec.
So the kinetic energy is
2 X 32.2
The retarding force is W/S lbs.
Therefore, ^^s^K^^S^,
8 2 X 32.2
and since the Ws cancel out, this can be solved for s, giving
8 = 667 feet = 222 yards.
So in this case also, the engineer could not stop in time.
Again, suppose a car weighing 10 tons is going 36 miles an hour.
What force is required to stop it within a space of 100 feet?
The velocity must be expressed in feet per second since we ordinarily
do not use g in miles/hour^.
r = 36 miles/hour = 52.8 ft./sec.
But TT and F can be left in tons.
The kinetic energy is ^^^^ ^H'l^^ = 433 ft. T.
2 X 32.2
So F X 100 = 433, or F= 4.33 tons.
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162 PRACTICAL PHT8IC8
Finally, suppose that the flywheel mentioned in section 149 has a 10
ton rim, and that we can neglect the effect of the. thin spokes. Suppose
also that it is 16 feet in diameter and making 15 revolutions per minute
(r. p. m.). How much kinetic energy has it?
Each part of the rim is making 15 turns per minute and therefore
moving with a velocity ofl5x2irr = 15x2x 3.14 x 8 = 754 ft./min.,
which is equal to 12.5 ft./sec. Therefore, the kinetic energy of the
whole rim is
''^^if/= 24.3 foot tons.
2 X 32.2
This is the same as 48,600 foot pounds. It is the amount of work
which the flywheel could do before stopping.
Problems
(State the unit in which each answer is expressed.)
1. What is the kinetic energy of a baseball weighing one third of a
pound if its velocity is 64.4 feet per second?
2. What is the kinetic energy of an 80-ton locomotive going 60 miles
an hour ?
3. What is the kinetic energy of a 9.8-kilogram weight which has
been falling long enough to have a velocity of 12 meters per second ?
4. What is the kinetic energy of a 16.1-gram bullet whose velocity is
600 meters per second?
5. Find the kinetic energy in ergs of a stone weighing 80 grams when
it is thrown with a velocity of 800 centimeters per second.
6. The 14-inch guns on some of the United States warships fire a
projectile weighing 1400 pounds and are said to give it a " muzzle energy "
of 65,600 foot tons. What is the velocity of the projectile as it leaves
the gun ?
7. What resistance is necessary to stop a body whose kinetic energy
is 90,000 ergs, in a distance of 3 meters ?
8. A boy weighing 100 pounds starts to slide on ice at a speed of 20
feet per second. What is his initial kinetic energy ? If the retarding
force due to friction is 40 pounds, how far will he go before stopping?
9. How great a force in excess of that required to overcome friction
is necessary to bring a 3220-pound automobile up to a speed of 30 miles
an hour in a distance of 242 feet?
154. Potential energy. Some things have a capacity for
doing work even when they are not in motion. Thus when
a clock spring is wound up, it can drive the clock as it un-
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ENEBOT AND MOMENTUM
168
coils, because of the elastic strain in it, due to its change of
shape. If the clock has a weight instead of a spring, the
weight can drive the clock because of its elevated position.
Such energy, due to strain or to position, is called potential
energy.
Just as the kinetic energy of a moving weight can be
measured either by the work required to get it up to speed
or by the work it will do while stopping, so the potential
energy of a raised weight or of a coiled spring can be meas-
ured either by the work required to raise or coil it, or by
the work it will do when it falls or unwinds.
In a later chapter we shall see that when a lump of coal
burns, it gives out energy in another form called heat, some
of which can be used to drive a steam engine. Thus the
unburned coal has in it capacity to do work, that is, energy,
and since this energy is
not due to any motion of
the lump of coal, it must
also be potential. This
kind of potential energy
is usually called chemical
energy.
155. Transformation of
energy. In nature the
various forms of energy,
kinetic or potential, are
continually changing into
one another.
For example, when a pen-
dulum bob (Fig. 143) is at
the highest part of its swing
A, it has potential energy
because of its height. As it
swings down this potential energy disappears, but the bob gains speed
and kinetic energy. As the bob swings up again on the other side, C,
its velocity and kinetio energy decrease, but its potential energy increases.
Fio. 143. —Transformation of energy in
pendulum.
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i64 PRACTICAL PHYSICS
Similarly when coal is burned, its chemical energy changes into heat
Some of this heat may be changed into potential energy in the form of
steam under pressure. A steam engine could then change some of this
into kinetic energy in a flywhee], or into some other form of mechanical
energy in a driven machine, or into electrical energy in a dynamo.
Some of this latter might be changed into light in a lamp, while the rest
would turn back to heat.
In all these cases we may think of energy as flowing about
from one place to another, passing through the various ma- .
chines and having its outward appearance changed by them,
almost like water flowing from a reservoir through a dye-
house, where it is used for many purposes, only finally to be
dumped into a stream or sewer, changed in appearance, but
unmistakably the same kind of thing that went in.
156. The conservation of energy. After its use in the dye-
house some of the water might never get through to the
stream, having been used up in some chemical process, so
that it is no longer water. But in the case of energy this
cannot happen. Energy is never made from anything that
is not energy, or turned into anything that is not energy.
The total quantity of energy in the universe is always the
same and is changed only in form and distribution. In any
given machine there may be leaks of energy because of fric-
tion, radiation, etc., just as there may be leaks in the pipes
in the dyehouse, but the energy that leaks away is not
destroyed, but is given as heat to the surroundings of the
machine, where it is of no more use than water spilled on
the floor.
Thus in the pendulum (Fig. 143) the sum of the kinetic and potential
energies is the same wherever it is in its swing, unless there is friction.
If there is friction, some energy disappears as heat and less is left in the
pendulum, but the total quantity, counting in the heat, is unchanged.
This fact, that energy can never he manufactured or de*
Btroyed^ hut only transformed^ and directed in its flow^ was first
stated (although not very clearly) by a German, Robert
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ENERGY AND MOMENTUM 165
Mayer, in 1842. It is called the law of the conservation of energy.
It has become the most important generalization in all physics^
and its value will be more and more evident as we study the
subject.
157. << Perpetual motion" machines. One of the most interesting
applications of this principle is that it assures us that *< perpetual motion "
machines are impossible. Such a machine would be one that runs of it-
self, without being driven by an engine, and without burning any fuel,
and does something useful without cost. Such a machine, if it could be
built, would be of extraordinary value to its inventor and to the world,
and for hundreds of years people have been trying to invent one. But
the principle of the coneervation of energy shows that no such machine
can possibly be made, because it would be manufacturing energy out of
nothing.
158. Momentum and energy. In the colloquial use of
these words there is a great deal of confusion. When a per-
son is thinking of something which a body does because it
is moving, he is likely to talk about either its " momentum "
or its " energy," whichever word first occurs to him. It is
therefore worth while to take a little trouble to understand
clearly the difference between momentum and energy.
We have seen that when a force acts on a moving body
through a long distance^ it accomplishes more than when the
distance is short. The work done is greater. It is also evi-
dent that when a force acts on a moving body for a long
time^ it accomplishes more than when the time is short. In
the technical language of physics we say that the impulse of
the force is greater. Impulse may he defined as the force
multiplied by the length of time it acts. Thus,
Work = force x distance.
Impulse = force x time.
We shall find that momentum has the same relation to
impulse that kinetic energy has to work. The idea of mo-
mentum will help us to solve problems involving "how
long?" just as the idea of kinetic energy helps us to solve
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166
PRACTICAL PHT8IC8
problems involving " how far ? " To show this we will print
again the proof of the energy equation side by side with the
corresponding proof of a momentum equation.
Proof of Enbbqt Equation
F = Ea.
9
Fs^^as.
9
J? ^r.
r = — a.
9
Ft^Eat
9
But
w^ = 2 (w or ^ = as.
But
V = at.
So
So
ff
P&ooF OF Momentum Equation
The expression is called the momentum of a moving body.
If
Both kinetic energy and momentum are proportional to
the weight of the moving body; thus a railroad train has
l3oth more momentum and more energy than a motor cycle
running at the same speed.
In the second place both the momentum and the energy of
:a moving body increase when its speed increases, but not ac-
cording to the same law. The energy is proportional to the
square of the speed. That is, doubling the speed of a train
makes its kinetic energy /owr times as large. But the momen-
tum is proportional only to th^ first power of the speed. That
is, doubling the speed of a train merely doubles its momentum.
Finally, we must not forget that there is a two (2) in the
denominator of the expression for energy, but not in the
expression for momentum.
159. The momentum equation. The equation
Ft=.^
9
is called the momentum equation. It holds either for accel-
erating or retarding bodies, and can be expressed in words
as follows : —
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ENERGY AND MOMENTUM . 16T
If the body is gaining speed,
Gain of momentam = accelerating^ force x time
= impulse received from force.
If the body is lonng speed,
Loss of momentmn = retarding force x time
= impulse lost to force.
160. Units of momentum. In using the momentum equa-
tion, as in using the energy equation, we must be consistent
in our units. That is, J^and TTmust be in the same unit of
force, and v and g must involve the same unit of length.
Furthermore, v^ g^ and t must all be expressed in terms of
seconds, because it is not worth while to remember any other
way of expressing g than 82.2 ft./sec.^ or 980 cm./sec.^.
The momentum equation shows that a momentum Wv/g is
equal to a force times a time^ and so the unit of momentum
will be a force unit times a time unit. Thus, momentum
may be expressed as
pound seconds, or
ton seconds, or
gram seconds, or
kilogram seconds, or
dyne seconds,
according to ^^ force and ^tm^ units used in the equation.
The dyne second as a unit of momentum corresponds to the dyne centi-
meter or erg B^ B, unit of energy, but curiously no one has ever thought
it worth while to give it a name of its own corresponding to " erg."
161. Applications of the momentum equation. The momen-
tum equation will help us to solve many problems about
moving things which involve the question "how long?" or
the idea of time in general.
For example, a certain engine can exert a " drawbar " pull on its
train equal to ^ of the weight of the train. How long will it take to
bring the train up to a speed of 50 miles an hour, starting from rest?
w = 50 miles/hour = 73.3 ft./see.
40^"" 32.2 '
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168 PBACTICAL PHYSICS
and since the }V*s cancel out,
t = 91 seconds.
Again, an electric car weighing 12 tons, running 15 miles an hour,
can stop in 7 seconds. What is the retarding force?
r = 15 miles hour = 22 ft. /sec.
12 y 2^
F X 7 = tzJUlZ ton seconds.
32.2
F=1.17 tons.
Again, a steamboat weighing 20,000 tons is being pulled by a tug-
boat, which exerts a force great enough to overcome the friction of the
water and to give a net force of 2 tons besides. What speed will the boat
acquire in 4 minutes, starting from rest?
2x4x60 = ?25^^,
32.2
17 = 0.773 ft. /sec.
Another application, which is important in studying steam turbines,
windmills, and aeroplanes, is the case of a steady stream of fluid strik-
ing against a solid surface. For this purpose we may write the equation
F=2:x!i,
t g
and W/t is then the weight of fluid striking the surface per second.
One of the useful applications of the momentum equation
is m studying a blow, such as a bat gives a ball, or a collision,
as between two billiard balls. We naturally speak of the
forces acting in such cases as " impulses," and this explains
why the product F x t^ which was first used in Bolving such
problems, is called "impulse."
Problems
(State the unit in which each answer is expressed.)
1. What is the momentum of a 180-pound football player running
at a speed of 20 feet per second ?
2. What is the momentum of a 66,000-ton ship when it is going 24
miles an hour (about 21 knots)?
3. How fast must a 1000-kilogram automobile be going to have 3000
kilogram seconds of momentum ?
4. A car weighing 12 tons, moving 5 feet per second, is stopped by a
bumper in 0.2 seconds. What is the average force of the blow ?
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ENERGY AND MOMENTUM 169
5. An 8000-toii ship moving 4 miles an hour is stopped in 2 min-
utes. Find the average force.
6. A 5-pound hammer moving 40 feet per second strikes a nail.
If the average resistance of the wood to the nail is 1240 pounds, what
fraction of a second was required to bring the hammer to rest ?
7. A fire engine throws a 2-inch stream of water horizontally against
a brick wall with a velocity of 150 feet per second. What is the force
exerted on the wall ?
8. A gun delivers 100 bullets per minute, each weighing one ounce,
with a horizontal velocity of 1500 feet per second. What is the average,
force exerted by the gun?
SUMMARY OF PRINCIPLES IN CHAPTER IX
The law of energy ("How far?").
Work = force x distance.
Kinetic energy = — .
2g
Work done on body =: gain of kinetic energy.
Work done by body = loss of kinetic energy.
The conservation of energy : Energy can never be manufactured
or destroyed, but only transformed or directed in its flow.
The law of momentum ("How long?").
Impulse = force x time.
Momentum = — •
0
Impulse given to body = gain of momentum.
Impulse given by body = loss of momentum.
QUESTIONS
1. The pendulum of a clock would die down because of the friction
of the air around it if energy were not continually supplied to it. How
is this done ?
2. Look up "perpetual motion" machines in an encyclopedia and
try to see for yourself why some of them cannot work.
3. A certain rifle was once described in the headline of a maga-
zine advertisement as striking " a blow of 2038 pounds." Farther down
in the advertisement it appeared that the bullet weighed ^ of a pound,
and that its velocity was 2142 feet per second. What did the headline
mean?
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CHAPTER X
HEAT — EXPANSION AND TRANSMISSION
Thermometer scales ~ linear and volumetric expansion of
t3olids — expansion of liquids — maximum density of water —
expansion of gases — pressure Coefficient of gases — the gas
thermometer and the absolute scale — gas formula — hot-air
engine — convection cun-ents — heat transfer by convection —
heating and ventilation systems — conduction — radiation —
molecular theory.
Expansion by Heat
162. Sources of heat. Our most important source of heat
is the sun. The sun's rays give more heat, the more nearly-
vertical they are. This explains why we receive more heat
at noon than in the morning or evening, and more heat in
summer than in winter.
The interior of the earth also is hot. In mine shafts sunk
into the earth the temperature rises about one degree for
^very hundred feet of depth. Hot springs and volcanoes
also lead us to think that the inside of the earth is hot.
To warm our houses and run our engines, we do not as
y3t depend directly on the sun or on the heat in the earth,
but on the heat produced in burning wood, coal, oil, or gas.
The heat thus obtained comes indirectly from the sun, having
been stored as chemical energy in plants in past ages.
V/e have already learned in our study of machines and in
our everyday experience that friction produces heat. For
example, in scratching a match, in using drills, saws, and
files, indeed, whenever mechanical energy is apparently lost,
we find that heat appears.
170
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BEAT— EXPANSION AND TBAN8MI88I0N 171
John Tyndall (1820-1893) in his lectures on "Heat con-
sidered as a mode of motion " used to perform a striking ex*
periment to show that friction
produces heat.
Let us try the same experiment by
putting a little water in a metal tube
(Fig. 144). K we close the tube
with a stopper and rotate it either by
hand or with a motor, we shall find
that the friction between the rotating
tube and the wooden clamp will gener-
ate in a few minutes enough heat to
boil the water and blow the stopper
out.
163. The thermometer. A .. ,^^ „ „, ^ ^ ,^ .,
_ __ -_ . Fio. 144. — Boiling water by friction.
deep cellar seems cold m sum-
mer and warm in winter, even though it remains at nearly
the same temperature. A room often seems hot after we
have been out in the cold, although it seems chilly after
we have been in it awhile. Our sensations about the
temperature of things are therefore very imreliable and
depend on our own condition at the moment. So it is
necessary to have some kind of instrument to indicate accu-
rately how hot or cold things are, that is, a thermometer. The
usual form of thermometer is based on the fact that most
liquids, such as mercury and alcohol, expand when being
heated and contract again on cooling.
164. Making a mercury thermometer. A spherical or
cylindrical bulb is blown on one end of a piece of glass tub-
ing with a very fine uniform bore, and the bulb and part of
the stem are filled with mercury. When the mercury is
warmed, it expands and rises in the stem until it overflows.
Then the top of the tube is closed by melting the glass.
When the mercury cools again, it leaves a vacuum in the top
of the tube. If the bulb is now placed in the steam from
boiling water, the mercury rises to a definite point on the
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172
PRACTICAL PBTBIC8
Ik
10^'
-J7.S
A
■213'^
stem, which is marked with a scratch. This point is called
the boiling point. If the thermometer is then put in melting
ice, the mercury goes back down the stem and stops at a
definite point. This point is called the freezing point.
In thermometers that are used for scientific work the
distance on the stem between these two fixed points is di-
vided into 100 equal spaces, called degrees.
In this thermometer, which is called a Centi-
grade thermometer, the freezing point is marked
zero and the boiling point is marked one hun-
dred. When these divisions extend below the
zero point, they are called degrees below zero
or minus degrees.
165. Centigrade and Fahrenheit scales. In
England and in North America a scale de-
vised by Fahrenheit is in common use. On
this scale the freezing point is marked 32 de-
grees (32"^) and the boiling point 212°, so
that the space between the freezing and boil-
ing points is divided into 180 divisions (Fig.
145). Since 100 divisions on the Centigrade
scale are equivalent to 180 divisions on the
Fahrenheit scale, one division Centigrade is
il equivalent to ^ divisions Fahrenheit. To
I change a temperature expressed on the Cen-
_ !») tigrade scale to the Fahrenheit scale, we have
only to multiply by f and add 32°. For ex-
ample : —
32"
Fig. 145.— Centi-
grade and Fah-
renheit scales.
30° C = (I X 30) ^- 32 = 86° F.
To change a temperature expressed on the Fahrenheit scale
to the Centigrade scale, we must first subtract 32° and then
multiply by |. For example : - —
98.6° F = (98.6 - 32)f = 37° C.
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HEAT— EXPANSION AND TRANSMISSION
173
Inasmuch as mercury freezes at — 39° C; the thermometers
used for very low temperatures contain alcohol, which is
usually colored red or blue.
166. Special thermometers. In Weather Bureau stations
the lowest temperature during the night and the highest
temperature during
the day are auto-
matically recorded
by special thermom-
eters called mini-
mum and maximum ^°* ^^' — Minimum and maximum thermometers.
thermometers. These are usually mounted as shown in figure
146. The upper one is the minimum and the lower the maxi-
mum thermometer. In the maximum thermometer, the bore
is constricted just above the bulb, so that the mercury passes
through with some difficulty when the tempera-
ture rises and does not run back again when the
temperature falls. The minimum thermometer
is filled with alcohol, and contains within its
tube a small black index rod, which is shaped
like a double-headed pin. As the temperature
falls, the index is drawn down toward the bulb
by the surface of the alcohol, and when the tem-
perature rises, the index is left behind.
Another kind of thermometer, which is used
by doctors and nurses to detect fever, is the clin-
ical thermometer (Fig. 147). This is a maxi-
mum thermometer on the Fahrenheit scale, and
the range is from 92° F to 110° F, each degree
being divided into fifths. The normal tempera-
ture of the human body is 98.6° F or 37° C.
Fig. 147.
Clinical ther-
mometer.
Questions and Problems
1. Change to Centigrade : 70° F, 150° F, 0° F, - 1C° F.
2. Change to Fahrenheit: 15° C, 500° C, -26* C,
- 190° C.
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174
PRACTICAL PHT8IC8
3. What would a rise in temperature of 80^ on the Centigrade scal«
be in Fahrenheit divisions?
4. The temperature of the air on a certain day was 90° F at noon and
46° F late the next night. What was the " drop " in Centigrade degrees ?
5. At what temperature do a Centigrade and a Fahrenheit ther*
mometer read the same ?
6. How do primitive people start a fire ?
7. Why do sparks fly from car wheels when the brakes are quickly
applied ?
8. Why must a tool be kept wet with cold water when being sharp-
ened on a grindstone ?
9. After violent physical exercise one feels very hot. is the body
temperature higher than normal ?
10. If one wants the division marks far apart on the stem of a ther-
mometer, what must be the relative size of bulb and stem ?
167. Expansion by heat — Solids. When a railroad track
is built, a gap is usually left between the ends of the rails, to
allow for the expansion of the steel in summer. Iron rims
are placed on wheels while hot, because they are then bigger
and can be easily slipped on. When they cool, they O
Fig. 148. — Force exerted by expansion and contraction of metal bar.
contract and hold fast to the wheel. An ordinary wall
clock loses time in summer because its pendulum expands a
little, and so swings more slowly. Almost all solids expand
more or less when heated, but this expansion is so very
small that one must take special pains to see it.
When solids expand and contract, they may exert enor-
mous forces. We can show in a striking way the power
exerted by the expanding and contracting of a metal bar in
the following experiment.
First, let us show that a metal bar does expand when heated. In the
apparatus shown in figure 148, there is a metal bar which is heated by a
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HEAT— EXPANSION AND TBAN8MI88I0N 175
series of little flames below. The expansion, although very slight, is
shown by the bent lever at the end, so that as the bar gets hot, the
pointer rises. Second, let us show the great force exerted by this process.
If we put a steel rod in the slot at right angles to the bar near the lever,
when we heat the metal bar, the steel rod suddenly breaks and the pointer
is thrown violently up. If we put another steel rod through a hole in
the bar, and allow the bar to contract, the steel rod suddenly snaps and
the pointer is thrown violently down.
Careful experiments show that diflferent metals expand at
different rates. Platinum, for example, expands less and
zinc more than other common metals. If we made a platinum
meter rod correct at O^C, it would be 0.9 millimeters too
long at 100° C. Similarly a steel meter rod would be 1.3
millimeters too long, and a zinc meter rod would be 2.9
millimeters too long. If two diflferent metal strips, such
as iron and brass, are riveted together ^ ^ ^ ^ ^
(Fig. 149), forming a compound bar, the "* • ^ ^ *
bar when heated will bend or curl, because ^^4- 8 --S^^
of the unequal expansion of the metals, ^iq. 149. — Effect of
Which metal will be on the inner side heating a compound
of the arc? Such compound bars are ^"*
often used to regulate the temperature of chicken incubators.
168. Measurement of expansion. In considering how much
a given object — such as a steel rail — will expand, it is
necessary to know three things about it, namely, its length,
and the rise in temperature and the rate of expansion of the
particular substance used. For example, if we know that a
steel rail is 33 feet long and each foot of it expands 0.000013
feet per degree Centigrade, we can compute how much it
will expand from winter to summer, a range of perhaps
60^ C. The expansion is equal to the expansion per degree
for one foot, multiplied by the length in feet and by the
rise in temperature. That is.
Expansion = 0.000013 x 33 x 50
= 0.0214 feet = 0.257 inches.
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176 PRACTICAL PHYSICS
We can express this in the form of an equation, thus,
where e = expansion,
k = expansion per degree, per unit length,
I = length,
t' = temperature when hot,
t = temperature when cold.
The factor k is called the coefficient of linear expansion. It is
a very small fraction, and it varies with diflferent substances.
It should be remembered that no matter in what unit I is
expressed, e will come out in the same unit. Usually h is
given per degree Centigrade, but the coefficient for the
Fahrenheit scale can be computed by multiplying by ^.
Why?
The coefficients per degree Centigrade of some common
substances are given in the following table: —
Zinc
0.000029
Steel 0.000013
Lead
0.000029
Cast iron 0.000011
Aluminum
0.000023
Platinum 0.000009
Tin
0.000022
Glass 0.000009
Silver
0.000019
"Invar "(nickel
Brass
0.000018
steel) 0.0000009
Copper
0.000017
169. Some Illustrations. In the construction of a steel
bridge allowance has to be made for the expansion of the
steel. For example, in the great bridge over the Firth of
Forth in Scotland, which is over a mile and a half long,
the total expansion amounts to 6 feet. In steam plants,
long pipes are provided with sliding or " expansion " joints,
unless the bends in the pipe are such as to yield enough for
the expansion.
When a lamp chimney is hot, the glass expands. . If a
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HEAT— EXPANSION AND TBAN8MI88I0N
17?
drop of water strikes it, the glass in the immediate vicinity
cools rapidly and pulls away from the rest, cracking the
chimney.
Quartz is made into crucibles and other ob-
jects that are as clear as glass, but have so small
a coefficient of expansion (0.0000005) that a
red-hot crucible may be suddenly thrust into
water without cracking.
The pendulum rod of a clock is often made
of dry wood, which expands very little. It is,
however, affected by moisture ; so for the most
accurate clocks some kind of a compensated me-
tallic pendulum is used. One form of compen-
sated pendulum is that commonly seen in the
so-called French clocks. It consists of a glass
tube or tubes filled with mercury (Fig. 150),
suspended by a steel rod. When properly ad-
justed, the raising of the center of gravity of the
mercury, due to its expansion, is equal to the
lowering of the whole reservoir of mercury due
to the expansion of the steel rod, so that the ef- yiq, leo.— Com-
f ective length of the pendulum remains constant, pensated mer-
In a watch, the balance wheel if uncompen- ^^^ ^^ ^"
sated will run slower in hot weather because
the hairspring has less elasticity at a higher temperature, and
also because the expansion of the radius of the
wheel carries the rim farther from the center,
and so slows down its rotation. The rim is
therefore made of two strips of metal, brass
on the outer edge and steel on the inner,
fastened with screws as shown in figure 161.
When the temperature rises, the free ends
of the rim curl inward, thus bringing part
of the rim nearer the axis. This compensates for the expan-
sion of the crossbar and the weakening of the hairspring.
Fio. 161. — Balance
wheel of a watch.
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178 practical pht8ic8
Problems
1. A brass meter bar is correct at 15® C. What will be the error a1
20^ C?
2. A steel rail 30 feet long is found to expand 0.235 inches when
heated from — 17° F to 100° F. What is the coefficient of linear expan-
sion on the Fahrenheit scale, and also on the Centigrade scale?
3. The steel cables of a suspension bridge are 2000 feet long. How
much do they change in length between the temperatures —20° F and
97° F?
4. A steel shaft is heated to 65^ C while being shaped in a lathe, and
its diameter at that temperature is made just 5 centimeters. What will
its diameter be at room temperature (15° C) ?
5. A steel wire, 150 centimeters long at 15° C, becomes 151.3 centi-
meters long when an electric current is sent through it. How hot does
it get?
170. Cubical expansion of solids. A metal bar when heated
expands, not only in length, but also in breadth and thick-
ness ; in short, its volume increases. This expansion in vol-
ume is called cabical expansion. Suppose we have a cube 1
centimeter on an edge at 0^ C and raise its temperature to
P C; each edge of the cube will become (l+Ar) centi-
meters, k being the coefficient of linear expansion. The
original volume, 1 cubic centimeter, will become (1 + h)^
cubic centimeters. Now (1 + ky equals l + Sk + SI[^'\'Jfl;
but since A is a very small fraction, the value of 8 A^ and k^
will be so small that they may be neglected without appre-
ciable error. The volume of the cube isj then, 1 + 8 k ;
hence the volume expansion per cubic centimeter per degree
18 Sk cubic centimeters and the coefficient of cubical expansion
is three times the coefficient of linear expansion.
For example, the coefficient of linear expansion of glass is 0.000009,
and the coefficient of cubical expansion is 3 times 0.000009 or 0.000027.
A flask which held just a liter at 0° C would hold 1002.7 cubic centi-
meters at 100° C.
171. Expansion of liquids. Let us flU a small round-bottomed
flask with water colored with ink and insert a stopper with a glass tube
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HEAT— EXPANSION AND TBAN8MIS8I0N
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Fig. 162.
Expansion
of a liquid.
and paper scale (Fig. 152). Then let us put the flask into a jar of ice
water and mark on the scale the position of the liquid in. the tube. If
we then put the flask into a basin of boiling water, we shall
note at first a sudden drop of the liquid in the tube (why ?)
and then a rapid rise. Evidently the liquid expands more
than the glass.
In general it is found that liquids expand much
more than solids. For example, when a liter of
water is heated from 0° to 100° C, it increases in
volume about 40 cubic centimeters, whereas a
block of steel of the same volume would expand
only 3.9 cubic centimeters. Alcohol, oils, and
especially kerosene expand even more than water.
Liquids, like solids, expand with almost irresist-
ible force when heated, and exert enormous pres-
sures if expansion is prevented by their surround-
ings.
In the case of liquids and gases, cubical expansion rather
than linear is what is always measured. Since, however, the
vessel which contains the liquid expands as well as the liquid,
we observe only the appar-
ent expansion. In a mer-
cury thermometer the ap-
parent expansion is only
about 1^ of the real expan-
sion of the mercury. The
coefficient of cubical expan-
sion of alcohol is 0.00104,
of mercury 0.000181, and
of water from 0.000053 to
0.00059 according to the
temperature.
water. We have just seen
3 I.OOIOQ
6- 10" 15° 20°
TEMPERATURES,
Fio. 153. — Maximuin density of water.
172. Abnormal behavior of
that solids, liquids, and gases expand as a rule when heated ;
water does the same except near its freezing point.
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180
PRACTICAL PHT8IC8
If we fill a tall glass jar nearly full of cracked ice (Fig. 153) and let
it stand for a while, the temperature of the water near the top comes to
O*' C and remains so, while the temperature at the bottom will be about 4**
C. Since the heaviest liquid stays at the bottom, this means that water
at 4° C is denser than water at 0®.
Very precise measurements show that water is most dense
at 4° C. When water at 4° 0 is either warmed or cooled, it
expands and becomes lighter^ as shown hy the curve in figure 153.
This fact has many important conse-
quences. For example, if it were not for this,
the water in lakes would freeze in winter, not
merely at the surface, but solidly from top
to bottom, thus destroying all aquatic life.
173. Expansion of gases. We may easily
show the great expansion of a gas when heated,
with the apparatus shown in figure 164. Even
the heat of the hand on the flask causes bub-
bles of air to be expelled from the tube and to
rise through the water. If the heat of a flame
is applied to the flask, the bubbles rise rap-
idly. If after a time the flame is removed and the flask allowed to
cool, water rises into the flask to take the place of
the escaped air. From the volume of water thus
drawn up into the flask, it is evident that a considera-
ble fraction of the air was expelled during the expan-
sion.
Fig. 164. — Expan
sion of gas.
lOO^C
The expansion of gases, such as air, illumi-
nating gas, or acetylene, is remarkable for two
reasons: first, because it is so large — being
about nine times as much as for water, and
second, because it is nearly the same for all
\o\
The coeflBcient of expansion of a gas can be meas-
ured as follows. Suppose we have a tube of uniform
bore (Fig. 155), which is closed at one end and has
a little pellet of mercury to separate the inclosed gas
I
Fio. 166. — Expan-
sion of a gas un-
der constant pres-
sure.
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HEAT — EXPANSION AND TBAN8MI88I0N
181
from the atmosphere. (Dry air is a good gas to experiment with.) It
we put the tube in a freezing mixture at 0*^ C, the gas in the tube will
contract, and we can measure the length, which we will suppose is
273 millimeters. If we put the tube in steam at 100° C, the gas will
expand, and we can measure the length again. We shall find that it is
about 373 millimeters. From this it is evident that the gas has ex-
panded 1 millimeter for each degree rise in temperature (the expansion of
the glass can be neglected). That is, it has expanded 7^ or 0.00366
of its volume at 0° C for each degree rise in temperature.
study
found
Gay-Lussac (1778-1850) was one of the first to
the expansion of gases under constant pressure. He
that different ga%e8 have nearly the
same coefficients of expansion^ namely
^\^ or 0,00366.
174. Pressure coefficient of gases.
Since the volume of a gas increases
as the temperature rises, it is reason-
able to expect that if a certain quan-
tity of gas were heated and yet con-
fined in the same space, the pressure
would increase. The following ex-
periment shows that this is true.
Let us start with a gas like dry air, con-
fined in a bulb C, which is connected with
an open manometer AB^diA shown in figure
156. At first we will surround the bulb by
melting ice, so that the gas is at 0° C, and
have the mercury at the same level in each
arm of the manometer, so that the gas is
at atmospheric pressure. Then we will
surround the bulb with boiling water at
100° C, and keep the gas from expanding Fig. 166. — Pressure of gas,
by pouring mercury into the manometer ^«**^ ** ^^^^ ^^'"°^®' *°-
creases
arm By thus increasing the pressure. This
increase of pressure is measured by the difference in levels B' and A,
From this we may calculate the increase per degree rise in temperature,
and finally what fraction it is of the pressure at 0° C. The result is
called the pressure coefSLdent of the gas.
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182 PRACTICAL PHT8IC8
Very careful experiments of this sort were first carried
out by a Frenchman, Regnault (1810-1878), who found that
the pressure of a gas kept at constant volume increases for each
degree very nearly ^^ or 0.00366 of the pressure at O^y no
matter what the gas is. It will be noticed that this is the
same fraction which we found for the increase of volume.
To sum up —
I. Different gases have nearly the same coefficients of ex-
pansion;
II. Different gases have nearly the same presstire coeffi-
cients;
III. Hie pressure coefficient of any gas is numerically about
the same as its coefficient of expansion; each is about ^^ or
0.00366,
175. Gas thermometers. It is evident that by measuring
the increase of volume of a gas under constant pressure or
the increase of pressure of a gas kept at constant volume,
we have a means of measuring temperature changes. Such
a thermometer^ filled with hydrogen^ is used as the world's
standard thermometer at the International Bureau of Weights
and Measures near Paris. Since the hydrogen thermometer
has been chosen as the standard, it is important to know
just how closely a good mercury thermometer agrees with it.
Of course they agree exactly at the two fixed points 0° and
100° C, and a careful comparison shows that between 0° and
100° the diflference is not over 0.12° at any point.
176. Absolute temperature scale. In the experiment de-
scribed in section 173, we started with an air column 273
millimeters in length at 0° C; if we had cooled the gas from
0° to — 1° C, the length AB would have been shortened a
millimeter, and if we had cooled it to —10° C, the length of
the air column would have become 263 millimeters. If, then,
the air column continued to contract at the same rate if cooled
indefinitely, the volume of the air at — 273° C would be zero.
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HEAT — EXPANSION AND TRANSMISSION
188
Cent, Absolute
Scale Scale
100^
-1-573 water boils
•273 ice melts
As a matter of fact, we can never get a gas to so low a tem-
perature as — 273°C, for every known gas, before that
temperature is reached, becomes a liquid. This temperature
— 273*^ C is, however, one of unusual interest in the study of
gases. It is called the absolute zero, and temperatures meas-
ured from this point as zero are called absolute temperatures.
Absolute temperatures may be designated by the letter A.
Thus, 0^ C is 273° A, 50° C is 323°
A, and 100° C is 373° A. To
change any temperature from the
Centigrade to the absolute scale, o-
we have merely to add 273 de-
grees (Fig. 157).
From the above discussion of
absolute temperature it will be ^273
seen that the volume of any g^as
is doubled when its temperature
is raised from 273° A (0° C) to 2 x 273°, or 546° A (273° C).
In general^ the volume of a gas 1% very nearly proportional to its
absolute temperature when the pressure is kept constant.
Now since, by section 174, the coefficient of expansion of
a gas at constant pressure is the same as the pressure coeffi-
cient at constant volume, when the volume is kept constant^ the
pressure of a gas is proportional to the absolute temperature,
177. Gas formula. The relation between the volume and
the temperature of a gas can be very concisely expressed
algebraically, thus,
^=^. (I)
7 absolute zero
Fio. 167. — Absolute and Centi-
grade scales.
where V and V^ represent the volumes of a certain gas at
the same pressure, but at diflferent absolute temperatures T
to T' . lit is the temperature on the Centigrade scale when
the volume is T, then r= 273 -}- « ; similarly F = 273 + ^'.
The relation between the volume and pressure of a gas at
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184 PRACTICAL PHT8IC8
constant temperature may be concisely expressed by Boyle's
law (see section 87),
PV=P'V\ (II)
where V is the volume of a given quantity of gas under a
pressure P, and V is the volume of the same gas under a
pressure P', the temperature in the two cases being the same.
The relation of the volume to both pressure and tempera-
ture can be expressed by the equation,
iZ=P^, (III)
for it is readily seen that this equation reduces to equation
(II), if T^Tj and that if P=^P'^ the equation becomes
V/T^ V /T^^ which is another form of equation (I). Equa-
tion (III) is called the gas formula.
A problem will make clear the use of the gas formula. Suppose we
wish to find the volume of a certain quantity of gas under standard con-
ditions, that is, at 0® C, and 760 millimeters pressure, when ^ is known
to occupy 120 cubic centimeters at 15" C and under a pres ure of 740
millimeters. Substituting in equation (III), we have
120 X 740 V X 760
273 + 15 273 + 0 '
whence
F' = 111 cubic centimeters.
Problems
1. At what temperature on the Centigrade scale will a liter of air at
O*' expand to occupy 2 liters, the pressure being held constant ?
2. A certain quantity of gas occupies 350 cubic centimeters at 27^ C.
What will be its volume at 0° C, the pressure being held constant ?
3. A steel tank full of air at 15° C under atmospheric pressure was
sealed and thrust into a furnace, where it was heated to 1000° C. How
many atmospheres of pressure did the air then exert? Neglect the
thermal expansion of the steel.
4. A liter of air at 0° C and atmospheric pressure weighs 1.293 grama
What is the density of air at 100° C and atmospheric pressure?
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BEAT— EXPANSION AND TRANSMISSION
18fi
5. A student in a chemical laboratory generates 50 liters of hydrogen
at 10° C, and at a pressure of 700 millimeters. Find the volume of the
gas under standard conditions ; that is, at O'' C and at 760 millimeters.
6. At the beginning of the so-called <* compression stroke" in an
automobile engine, its cylinder contains 42 cubic inches of gas and air at
atmospheric pressure, and at a temperature of 40® C. At the end of the
compression the volume is 6 cubic inches and the pressure is 15 atmos-
pheres. What is the temperature ?
178. Low temperatures. The investigations of Lord Kel-
vin (1824-1907) and of other scientific men all point to the
conclusion that the temperature — 273^ C is really an absolute
zero in the same sense that it is the lowest possible temperature
in the universe. Although no one has as yet succeeded in
cooling a body to absolute zero, temperatures within a very
few degrees of this point have been attained by the evapora-
tion of liquefied gases. With liquid air, temperatures as low
as — 200^ C may be obtained, and with liquid hydrogen
— 268° C. In 1908 Professor Onnes, at the University of
Leyden in Holland, found that the boiling
point of liquid helium is —268.6° C, or only
about 4.5° above the absolute zero, and he
has since cooled liquid helium to within 2°
of the absolute zero. At these low temper-
atures rubber and steel become as brittle as
glass, and metals become much better con-
ductors of electricity than at ordinary tem-
peratures.
179. Hot-air engine. An interesting ap-
plication of the expansion of gases is the
hot-air engine. Its operation can be best
understood by studying figure 158. A
loosely fitting plunger A moves up and
down and thus shifts the air back and
forth in the cylinder (7, which is heated at
the bottom and kept cool at the top. The working cylinder
C has a nicely fitting piston B.
Fig. 168. — Diagram
of hot-air engine.
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186
PRACTICAL PHTBICa
When the plunger A moves down, the hot air below is
transferred to the top, where it is cooled. This makes it con-
tract. The piston B is then forced down
by the external pressure of the atmosphere.
As soon as the piston B is near the bottom
of its stroke, the plunger A is raised, caus-
ing the air to flow back under A, where it
is heated by the fire. This makes it ex-
pand and forces the piston JS up again, and
so the cycle is repeated.
These engines are commonly used for
pumping water on a small scale at isolated
places, for they do not require expert at-
tendants, and they use any kind of fuel.
In general they cannot compete with gas
engines on account of their bulk and the
rapid wearing out of the heating surfaces.
180. Convection currents. All systems
of heating and ventilation depend upon
what are called convection currents,
which in turn depend upon the expan-
sion of liquids and gases. To make these
clear, let us try two simple experiments.
We cut off the bottom of a bottle and
bend a glass tube (Fig. 159) so that the
ends can be slipped through a stopper
which fits the neck of the bottle. If we
invert the bottle and fill it with water
containing a little sawdust, we can see a
circulation of the water when a flame is
waved back and forth from AU)B. We
note that the direction is from A io B.
Why?
A box (Fig. 160) has a glass front, and
two holes in tho top, which are covered
with glass chimneys. If we put a candle yiq, 160. — Convection current
under one chimney, convection currents of air.
Fig. 159. — Convection
current of water.
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HEAT — KXPANSION AND TBANSllISaiON
187
of air go down the cool chimney and up the warm one. A. bit of lighted
touch paper held near the top of the cool chimney makes the convection
currents more evident.
The draft in a lamp, stove, fireplace, or power-house
chimney is a convection current.
The explanation of the movement of convection currents
is that any gas or liquid expands when heated, so that a
given quantity of fluid increases in volume and consequently
decreases in density. In a convection current, the lighter
fluid is pushed up by the heavier surrounding fluid, just as
a block of wood under water is pushed up by the surround-
ing water. , r;^^^^^.9iif
Transmission of Heat
181. Heat transfer by convection.
Since the up-going part of a convec-
tion current is warmer than the re-
turning part, there is a transfer of
heat from the flame or other source
of heat at the bottom, to the cooler
parts of the circuit at the top. This
process of transporting heat by carry-
ing hot bodies or hot portions of a fluid
from one place to another is called con-
vection. It is the basis of almost all
systems for heating buildings.
182. Hot-water heating. The ar-
rangement for heating water in the
kitchen range for general use in laundry
and bathroom is shown in figure 161
ters the tank through a pipe which reaches nearly to the bottom.
From the bottom of the tank the water is led to a heating
coil along the side of the fire box in the range. When the
water becomes hot, it is pushed up and goes back into the
Fig. 161.— Hot- water heater.
The cold water en-
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PRACTICAL PHT8IC8
tank at a point nearer the top. Thus a circulation is set up
which continues until practically all the water in the tank
has passed through the stove and the whole* tankful is hot.
The hot-water system of heating houses depends on this same
principle of convection. Water is heated nearly to the boil-
ing point in a furnace in the basement. The hot water is
led from the top of the furnace through pipes to iron radia-
tors in the various rooms of the building. On account of
the large exposed surface in each radiator, heat is rapidly
given out by the hot water to the surrounding air. The
cooled water is then carried
from the radiators through
return pipes to .'the base of
the furnace. To prevent ra-
diation from the pipes, a thick
non-conducting coating of as-
bestos is often provided.
183. Hot-air system of heat-
ing and ventilating. The hot-
air furnace in the basement
(Fig. 162) is simply a big
stove, surrounded by a shell
or jacket of galvanized sheet
iron. The air between the
stove and outer shell is heated, and is then pushed up into
the flues by the heavier cold air which comes in from out of
doors through the cold-air inlet flue. The smoke, of course,
goes up the chimney. The warm air which enters the rooms
finds an outlet around the doors and windows.
In the hot-water system of heating there is no provision
whatever for changing the air in the room ; that is, for venti-
lation. In the hot-air system, a small quantity of fresh air
is continually flowing into the rooms. This is enough for a
private house. But in schools, churches, and other public
buildings, large quantities of clean, fresh, warm air have to
Fig. 162. — The hot-air furnace.
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HEAT — EXPANSION AND TRANSMISSION
189
be continually supplied by other means. For the propel
ventilation of a room it is estimated that each person in it
requires about 50 cubic feet of fresh air every minute. In
large modern school buildings the air is drawn in from out
of doors by powerful fans, filtered through cloth, warmed by
passing around steam pipes, and then distributed in ducts
throughout the building. The vitiated air in each room is
forced out through ducts near the floor. This indirect system
of heating, while expensive, furnishes excellent ventilation.
184. Conduction in solids. Besides transporting heat from
one place to another by carrying hot bodies about, or making
hot fluids flow through pipes, we can transmit heat from one
place to another, without moving any material thing, by
either of two methods called conduction and radiation.
Every one knows that the handle of a silver spoon gets
hot when its bowl is in a cup of hot tea or coffee. If one
end of an iron poker is put in the fire, the other end gets un-
comfortably hot and must be provided with a wooden handle.
Yet if a wooden rod is plunged into a fire, it is hard to feel
any warmth at the other end. So we conclude that silver
and iron conduct heat better than wood. In general, metals
are good conductors of heat.
There are some substances, such as stone, glass, wood,
wool, fur, and ashes, whicH are poor conductors of heat and
are therefore called heat insulators. The metals, such as silver,
copper, brass, iron, lead, etc., are good conductors as compared
with the non-metals. Careful study shows that even the
metals vary in their power to conduct heat, that is, in con-
ductivity, p. [s^
This can be shown .r^; I ^ ir" . ■ ^ .
by the following ex- jm^
periment.
Let us fasten with ^^ir^^A
sealing wax a number /r^Z>
of steel balls at regular Fig. 163.
-Relative conductivity of copper and iron.
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190
PRACTICAL PHYSICS
Fig. 164. — Water a non-conductor.
intervals on the under side of two rods, one of copper and the other of iron.
If we heat one end of each rod in a flame (Fig. 1Q3), the balls on the
copper rod soon begin to drop off, beginning near tlie flame. Later the
balls on the iron rod begin to drop off. Often half the balls will have
dropped from the copper rod before the first one drops from the iron rod.
185. Conduction in liquids and gases. Liquids and gases
are much poorer conductors
than metals. This can be
shown by the following ex-
periments.
Let us take a test tube full of
water and place in it a few pieces
of ice which are held in the bottom
by a wire, as shown in figure 164.
Then we may boil the water at the
top of the tube for some time with-
out melting the ice in the bottom.
Another more striking experiment to show the poor conductivity of
water is shown in -figure 165. The bulb of the air thermometer is placed
only half an inch below the surface of the water in the funnel. When
a spoonful of ether is poured on the surface of the water and lighted, the
liquid in the tube of the air thermometer will re-
main practically stationary, in spite of the fact that
the air thermometer is very sensitive to changes in
temperature.
Experiments to measure conductivity
show that iron conducts 100 times as well
as water, and that water conducts 25 times
as well as air. In general, it may be said
that liquids and gases are very poor con-
ductors of heat.
It is an interesting fact that substances
which are good conductors of heat are
good conductors of electricity as well.
186. Applications. These differences in fig. 165.— Burning
conductivity explain why teapots have ^^^^^ ^^ *^ ^*'®'
, . t . t ^ -,, , . does not affect the
wooden or insulated handles ; why steam ah: thermometer.
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HJBAT — JBXPAN8I01T AND TBAN8MI8SI01T
191
i 1
Section of
pipes are covered with wool, magnesia, or asbestos ; why
double windows are used in cold climates ; why a vacuum
bottle (Fig. 166) keeps things hot or
cold; and why we wear woolen clothing
in winter. Woolen clothing of loose
texture, furs and feathers, or eiderdown
quilts are effective as heat insulators be-
cause so much air is inclosed in their
pores.
Differences in conductivity also account
for many of our curious sensations of heat
and cold. Thus in a cool room some things
feel much colder than others. Metallic
objects, which are good conductors, take Fia. im
heat rapidly from the hand, and so give lZ:Vis'l'V.^
the sensation of cold. While other ob- poor conductor of
jects, such as wood and paper, do not ^®^*'
carry off the heat of the hand and so do not feel cold. Sim-
ilarly a piece of metal lying in the hot sun feels much
warmer than a piece of wood beside it.
187. Radiation. If an iron ball is heated and hung up in
the room, the heat can be felt when the hand is held undef
the ball. This cannot be due to convection, because the hot-
air currents would rise from the ball. It cannot be due to
conduction because gases are very poor conductors. Simi-
larly a lighted electric light bulb feels hot if the hand is
held near it, but when the light is turned off, the sensation
stops very quickly. The glass of the bulb is a very poor
conductor and there is practically no air left inside the bulb,
so that the sensation of heat can be due neither to convection
nor to conduction. Furthermore, an enormous quantity of
heat comes to us from the sun. Yet men who make ascents
in balloons and aeroplanes find that the air becomes less and
less dense, so that it seems reasonable to suppose that the
earth's atmosphere forms a coating only a few miles thick
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192 PRACTICAL PHYSICS
and that the space beyond is absolutely empty. So the sun's
heat cannot come by convection or conduction.
Scientists, to explain these phenomena, have imagined a
weightless, elastic fluid called the ether which fills all space
and transmits heat and light by a process called radiation.
When a body not in contact with conducting bodies cools,
it is said to radiate heat, or to cool by radiation. If one
places a screen, such as a book, between a lighted lamp and
his face, he no longer feels the heat. So we think that heat
rays, like light rays, travel in straight lines. Experiments
also show that heat rays, like light rays, can be reflected by a
mirror, or brought to a focus by a burning glass.
Some substances, such as glass and air, let the sun's heat
rays pass through almost unimpeded and are warmed but
little by this radiant heat ; that is, they are " transparent-to-
heat." Other substances, such as water, do not let heat pass
through and are warmed by any radiant heat rays that
strike them ; they are "opaque-to-heat."
A mirror, or any highly polished surface, is a good heat
reflector, and yet itself remains cold. Fresh snow melts
slowly in the sun's rays, but snow covered with soot or
black dirt melts rapidly. In general, reflecting or white
objects . do not easily absorb radiant heat, while rough or black
objects absorb heat readily.
It has also been found that reflecting and bright-colored
objects, when hot, cool by radiation more slowly than rough
and dark objects. For example, a brightly polished silver
cup radiates heat twenty times more slowly than a sooty
black cup. In general, good absorbers are good radiators, and
poor absorbers are poor radiators.
188. Theory as to what heat is. There are many reasons
for thinking that heat is a rapid vibratory motion of the
molecules of substances or of the ether which fills the spaces
between the molecules. We imagine that the molecules in
a hot flatiron are vibrating more rapidly than when it was
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HEAT— EXPANSION AND TRANSMISSION 193
cold, and that this molecular vibration extends to the sur-
rounding ether and so is sent out in straight lines in all di-
rections as radiant heat.
At a temperature of about 550° C iron becomes " red hot,"
and at 1300° C it gets « white hot." We imagine that the
iron, before it begins to glow, is sending out dark heat rays,
but that, when red hot or white hot, it is sending out
visible heat rays, that is, light rays. We think that these
heat rays and light rays differ only in the rapidity of the
vibratory motion, and in their effect on man's organs of
sense. If the vibrations are under 400 trillion per second, we
recognize them as heat; but if the vibrations are between 400
and 800 trillion per second, the nerves of the eye recognize
them as light. Heat and light are both forms of radiant
energy. This radiant energy travels at the enormous speed
of 187,000 miles per second, which means that radiant
energy could circle the earth seven times in one second.
On this theory, the expansion of bodies when heated is
due to the more violent vibration of their molecules, which
require more room to move about in. At a certain tem-
perature this motion becomes so violent that the molecules
break away from their former position and the body changes
its state ; that is, it melts or boils.
SUMMARY OF PRINCIPLES IN CHAPTER X
100 Centigrade degrees = 180 Fahrenheit degrees.
Temp. Fahr. = (| Temp. Cent.) -f 32.
Temp. Cent. = | (Temp. Fahr. — 32).
Coefficient of linear expansion = expansion per degree for unit length
total expansion
total length x rise in temperature *
Total expansion = coefficient x length x rise in temperature,
o ♦
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194 PRACTICAL PHYSICS
Coeffident of volume expansion
= expansion per degree for unit volumei
total eicpansion
total volume x rise in temperature
Total expansion = coefficient x volume x rise in temperature.
For solidSy volume coefficient = 3 x linear coefficient
Pressure coefficient of gases = total pressure rise
pressure x nse m temperature
Total pressure rise = coefficient x pressure x rise in temperature.
Value—.
273
Volume coefficient of all gases nearly the same.
Pressure coefficient of all gases nearly the same.
Volume and pressure coefficients nearly equaL
Gas law: ?^=?^.
T T
QUESTIONS
1 Is friction ever a sooroe of useful heat ?
2. Are the sun's rays ever used practically as a direct source of heat
for engines?
3. Why does spring water seem warm in winter and cool in summer ?
4. Why does the water seem much colder before a bath than after-
wards?
5. Why can a platinum wire be sealed or melted into glass while a
copper wire cannot ?
6. Why do glass bottles crack when placed on a hot stove ?
7. Why do apples and pieces of green wood swell when heated ?
8. Why is there a cold indraft of air at the bottom of an open
window?
9. Is there any other reason than oonyenience for putting furnaces
in cellars rather than in attics ?
10. How is the water which is standing in the hot-water pipes in a
house kept hot ?
11. Does a hot body cool more rapidly if placed on metal than if
placed on wood? Why?
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BEAT — EXPANSION AND TRANSMISSION 195
12. Why does a glowing coal die out quickly on a metal shovel, and
yet glow for a long time in ashes?
13. How does a fireless cooker work ?
14. Look up Davy's lamp for miners in an encyclopedia. What is its
advantage ? Why is it that a flame will not strike through the fine-net
wire gauze ?
15. Why are the walls of ice houses often packed with sawdust?
16. Why should an air space be left in building the walls of brick and
cement houses ?
17. Does woolen clothing supply any heat to maintain the body's
temperature ?
18. Why do people prefer to wear white clothes in summer and in
hot countries ?
19. Why should the surface of a teakdttle be brightly polished and
the bottom blackened ?
20. Is it advisable to put any sort of aluminum or gold paint on a
radiator that is to heat a room ?
21. Describe carefully the " dampers " of some stove or furnace you
have seen, and explain how they accomplish the desired result&
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CHAPTER XI
WATER, ICE, AND STEAM
MeasuremeDt of heat — B. t.u. and calorie — specific heat —
freezing point — change of volume in freezing — latent heat,
ice to water — boiling point under yarious pressures — dis-
tillation— latent heat, water to steam — humidity — fog, rain,
and snow — artificial ice.
189. How we measure heat. If a man buys a ton of coal,
what does he get for his money? One answer would be,
about 2000 pounds of material, of which, perhaps, 40 pounds
is water, 320 pounds is ash, and the rest mostly carbon and
hydrogen. What the man is really interested in, however,
is not the sort of material, but the amount of beat he has
bought. Since heat is not a substance, but a form of energy,
we cannot measure it directly in pounds or quarts, but must
measure it by the effect it can produce. For example, if one
pound of hard coal could be completely burned, and if all
the heat generated in this process could be used to heat
wat^r, it would be found that about 7 tons of water could be
raised 1° F in temperature. Engineers reckon the heat value
of fuel in units such that each represents the heat required to
raise one pound of water one degree Fahrenheit. This heat
unit is called the ** British thermal unit," and is written B. t. u.
For example, the heat value of a pound of coal varies from
11,000 to 16,000 B. t. u. ; a pound of petroleum gives about
25,000 B. t. u., a pound of gasolene about 19,000 B. t. u., and
a pound of dry wood about 5000 B. t. u.
The heat unit employed in Europe, and in all physical and
chemical laboratories, is a metric unit called the calorie. The
calorie is the heat required to raise the temperature of a gram
of water one degree Centigrade,
196
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WATER, ICE, AND STEAM 197
190. Heat absorbed by different substances. It is well
known that a kettle of water on a stove gets warm much less
quickly than a flatiron of the same weight. For example,
the heat required to warm a kilogram of water 1 degree will
warm the same weight of copper 10 degrees, of silver or tin
20 degrees, and of lead or mercury 30 degrees. In fact
experiments show that water requires more heat per unit
weight per degree rise of temperature than any other common
substance.
Since one calorie is required to raise the temperature of
one gram of water one degree, only one tenth of a calorie would
be needed to raise the temperature of one gram of copper a
degree, one twentieth of a calorie to raise a gram of silver
one degree, and one thirtieth of a calorie to raise a gram of
lead one degree. The number of calories required to raise the
temperature of a gram of a substance one degree Centigrade
is called its specific heat. Thus the specific heat of water is
1, of copper about 0.1, etc.
The following experiment of Tyndall's illustrates how
much substances differ in their specific heats.
We may heat a number of balls of the same
weight but of different metals, such as iron, zinc,
copper, lead, and tin, to about 150'^ C in oil.
Then if we place them all at the same time on a
thin cake of paraffin wax which is held on a ring,
as shown in figure 167, they will melt the wax
and sink into it, but at different rates. The
iron works its way most vigorously into the
wax, and even through the cake. The zinc and
copper balls come next, while the lead ball
makes but little headway. The metal with
the largest specific heat, iron, gives out the
largest amount of heat in cooling and so melts Fig. 167. — Metals differ
the most paraffin. in specific heat.
191 How specific heat is determined. When a hot sub-
stance, such as hot mercury, is poured into cold water, the
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198 PRACTICAL PHT8IC8
water and mercury soon come to the same temperature. The
heat given up by the cooling mercury is used in warming
the water. If no heat is lost in the process, the heat units
given out by the hot body are equal to the heat units gained by
the eold body.
This method of mixtures is accurate only when no heat is
lost during the transfer. This is rather difficult to manage in
practice. Nevertheless, this method is the one generally used
in laboratories to determine the specific heat of substances.
For example, suppose that 300 grams of mercury are heated to 100° C
and then quickly poured into 100 grams of water at 10° C, and that, after
stirring, the temperature of the water and mercury is 18.2° C.
K we let X be the specific heat of the mercury, the mercury gives out
300(100 — 18.2)a; calories. Since the specific heat of water is 1, the
water absorbs 100(18.2 —10)1 calories. Therefore we may make the
equation
300(100 - 18.2)x = 100(18.2 - 10)1,
whence ar = 0 . 033 calories .
By very careful experiments of this sort the specific heats
of some of the common substances have been found to be as
follows : —
Table of Specific Heats
0.19
0.12
0.094
0.093
0.033
It is remarkable that of all ordinary substances water has
the (greatest specific heat. Thus it takes about four times as
much heat to raise a pound of water one degree as to raise a
pound of solid earth one degree, and so the ocean acts as a
great moderator of temperatures. In summer the water
absorbs a vast amount of heat which it slowly gives up in
winter to the land and air. This explains why the tempera-
ture on some ocean islands does not vary more than 10° F
during the whole year.
Water
1.00
Sand
Pine wood
0.65
Iron
Alcohol
0.60
Copper
Ice
0.50
Zinc
Aluminum
0.22
Mercury
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WATEB, ICE, AND STEAM 199
Problems
1. How many calories of heat are needed to raise the temperature
of 10 grams of water 5° C ?
2. How many calories are required to heat 15 grams of iron 20° C ?
3. Compute the calories given out by a kilogram of copper in cool-
ing from 110*^0 to 15*^0.
4. How many B. t. u. are necessary to heat a 2-pound flatiron from
70°.Fto350°F?
5. If the heat value of coal is 14,000 B. t. u. per pound, how many
tons of water can be heated from 32° to 212° F by the combustion of one
ton of coal in a boiler whose efficiency is 75 % ?
6. If 400 grams of water at 100° C are mixed with 100 grams of
water at 20° C, what will be the temperature of the mixture ?
7. If 500 grams of copper at 100° C, when plunged into 300 grams of
water at 10° C, raise the temperature to 22° C, what is the specific heat
of copper?
8. A piece of iron weighing 150 grams is warmed 1° C. How many
grams of water could be warmed 1° by the same amount of heat ? (The
answer is called the water equivalent of the piece of iron.)
9. A 50-pound iron ball is to be cooled from 1000° F to 80° F, by
putting it in a tank of water at 32° F. How many pounds of water must
there be in the tank?
10. A platinum ball weighing 100 grams is heated in a furnace for
some time, and then dropped into 400 grams of water at 0° C, which is
raised to 10° C. How hot was the furnace? (Sp. heat = 0.04.)
192. Melting and freezing. If one brings in from out of
doors on a cold winter day a pailful of snow or ice and sets
it on a stove, he finds that its temperature is at first below
0° C and slowly rises to that point. It then remains
stationary, or nearly so, until all the snow is melted. Then
the temperature of the water gradually rises. This stationary
temperature, where the ice (snow) changed to water, is
called the melting point of ice, and is 0° C or 32° F.
We may also determine the freezing point of water by
making a freezing mixture of cracked ice and salt and placing
in it a test tube containing some pure water. The tempera-
'ture of the water will be observed to fall slowly until the
water begins to freeze. Then the temperature remains con-
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200
PRACTICAL PHYSICS
Platinum
above 1700'' C
Steel
1300 to 1400° C
Glass
1000 to 1400<» C
Copper
1083° C
Gold
1062° C
Silver
960° C
Lead
327° C
stant until all the water is frozen. This stationary tempera-
ture at which water changes into ice is called the freezing
point of water, and is 0° C or 32° F.
Substances which are crystalline, such as ice and many
metals, change into liquids at a definite temperature, and
the melting point of such a substance is the same as its freez-
ing point.
Table of Meltikg or Freezing Points
Tin 232° C
Sulphur 115° C
Naphthalene (moth balls) 80° C
Paraffin about 54° C
Ice 0° C
Mercury - 39° C
Alcohol about - 112° C
Non-crystalline substances, such as iron, glass, and paraffin,
pass through a soft, pasty stage as the melting point is ap-
proached. In the case of some substances, such as the fats,
the melting point is not the same as the freezing point.
Thus butter will melt between 28° and 33° C and yet solidi-
fies between 20° and 23° C.
There are several alloys of metals which melt at a much lower
temperature than any of the metals of which they are made.
" Wood's metal " (2 tin + 4 lead + 7 bismuth + 1 cadmium
by weight) melts at 70° C, although the lowest melting point
of any of its constituents is that of tin (232° C). Wood's
metal will melt even in hot water. Such alloys are used to
seal tin cans and automatic fire sprinklers. Other similar
alloys are used for fusible plugs for boilers.
193. Expansion in freezing. When a liquid freezes, we
would naturally expect it to contract, because it would seem
that the molecules would be more closely knit together in the
solid than in the liquid state. This is generally true. But
when we recall that ice floats and pitchers of water are often
cracked by freezing, we see that water expands on freezing.
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WATER, ICE, AND STEAM
201
In fact a cubic foot of water becomes 1.09 cubic feet of ice.
Cast iron is another substance that expands a little iu
solidifying, and it is therefore adapted to making castings,
for in this way every detail of the mold is sharply re-
produced. In making good type we must have a metal
which expands a little on solidifying, and so an alloy of lead,
antimony, and copper, which has this property, is used.
That the expansive force of water in freezing is enormous
can be seen from the following experiment.
Let us fill a cast-iron bomb with water, close the hole with a screw
plug (Fig. 168), and put the bomb in a pail of ice
and salt. When the water in the bomb freezes, the
pressure inside increases more and more, and the
bomb eventually explodes.
This shows why water pipes burst on
nights cold enough to freeze the water in
them. A similar process is active every
winter in breaking the rocks of mountains
to pieces. Water percolates into the crev-
ices, freezes, and expands.
194. Effect of pressure on melting ice. If we suspend a weight
of 40 or 50 pounds by a wire loop over a block of ice (Fig. 169), the wire
will cut slowly through the ice. The pressure causes the ice to melt
under the wire; but the water flowing around the wire freezes again
above it, and leaves the block as solid as be-
fore.
This experiment shows that pressure
causes ice to melt by lowering the freez-
ing point. This might be expected, for
pressure on any body tends to prevent
its expansion, and since water does ex-
pand on freezing, pressure will tend to
prevent freezing; that is, it lowers the
^ „, ^ , freezing: point. It requires, however, a
Fio. 169. -Wire cutting i: i 4. x ^1 orn j\
through a block of ice. pressure of almost a ton (1850 pounds)
Fig. 168. — Expan-
sive force exerted
by freezing water.
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202 PRACTICAL PHYSICS
per square inch to lower the freezing point one degree Cen-
tigrade.
In skating, the pressure of the edge of the skate blade
melts the ice and so forms a film of water which is very slip-
pery. This also explains how snowballs can be made by
pressing the snow between the hands. The pressure at the
points of contact between the flakes of snow melts them and
then the film of water that is formed freezes again when the
pressure is released. The flow of glaciers of solid ice around
corners is explained in the same way.
195. Latent heat : ice to water. If a dish of ice and water
at 0° C is kept in a room where everything else is at 0% the
ice will not melt and the water will not freeze. But if the
dish is surrounded by a freezing mixture, such as salt and ice,
the water will freeze, or if the dish is brought into a warm
room, the ice will melt. In either case, however, the temper-
ature of the mixture will remain steady at 0° until either all
the ice is melted or all the water is frozen.
It seems evident, then, that when ice melts, heat energy,
called latent heat, is absorbed, which does not show itself in a
rise of temperature.
196. How much heat to melt 1 gram of ice ? In solving
this problem we may apply the method of mixtures which
was used in determining the specific heat of a metal.
If we put 200 grains of ice at 0° C into 300 grams of water at 70"* C
and stir them thoroughly, the temperature of the water, after the ice is
all melted, will be lO*" C.
Let a: = no. of calories required to melt 1 g. of ice.
Then 200 x = no. of calories required to melt 200 g. of ice.
Also 200 X 10 = no. of calories required to raise melted ice from 0^
to 10°,
and 300 (70 — 10) = no. of calories given out by the water in cooling.
Then 200 a; -f 200 x 10 = 300 (70 - 10),
whence ar = 80 calories.
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WATER, ICE, AND STEAM
203
The best experiments that have been made show that the
latent heat of melting ice is just about 80 calories, which
means that 80 calories are absorbed in changing 1 gram of
ice at 0° C into water at 0° C.
197. Heat given out when water freezes. We have just
seen that heat energy is required to pull apart the molecules
of the solid ice and change it into the liquid state, where we
believe the molecules are held together less intimately.
Now we want to show that in the reverse
process, that is, in freezing, this energy ap-
pears again as heat. We may show that
freezing is a heat-evolving process in the
following experiment.
If we repeat the experiment described in section
192, except that we keep the water, thermometer, and
test tube (Fig. 170) very quiet, we shall be surprised
to find that the water will cool several degrees below 0°
C before the freezing begins. When once started by
stirring or dropping in a crystal of ice, the crystals of
ice form rapidly, but the temperature jumps to 0° C
and remains stationary until all the water is frozen,
even though the freezing mixture in the jar outside ^iq 170 — Freezing
the test tube is as cool as - 10° C. water eVolves heat.
People sometimes make use of the heat given out by water
when it freezes, by putting pails or tubs of water in a green-
house or a cellar to prevent the freezing of the plants or
vegetables. As the water begins to freeze first, the heat
evolved in the process prevents the temperature from falling
much below O"* C. When a large lake freezes, the heat
evolved helps to keep the temperature in its vicinity from
falling as low as it does farther away.
Problems
1. How many calories of heat are required to melt 20 trrams of ice at
O^C?
2. How much heat is evolved in cooling and freezing 12 grams of
water originally at 10° C?
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204
PRACTICAL PHYSICS
3. How many B. t. u. are required to melt one pound of ice at 0® C 1
4. How much water at 100^ C will be needed to melt 300 grams of
snow at 0° C, and raise its temperature to 20° C ?
5. If a 500-gram iron weight is heated to 250° C and placed on a
block of ice, how many grams of the ice will be melted ?
198. Process of boiling water. Let us fill a round-bottomed flask
(Fig. 171) half full of water and put through the stopper a thermometer,
an open manometer, and an outlet tube for
the steam. At first, as the water is heated,
the air, which is dissolved in the water, rises
to the surface in little bubbles. Then bubbles
of steam form at the bottom, but these col-
lapse when they strike the upper, cooler layers
of water, and disappear, causing the rattling
noise known as "singing" or "simmering."
When the bubbles of steam begin to reach
the surface, the water is said to "boil." It
will be noticed that the steam in the flask is as
clear as air, but as it leaves the outlet tube it
condenses and forms a white cloud or mist.
As soon as boiling begins, the thermometer,
which has been rising rapidly, reaches 100° C
and remains stationary.
If we partly close the outlet valve, the
manometer will show an increase of pressure,
while the thermometer will show a rise in the
temperature of the boiling water.
Finally if we remove the burner, and let the water cool a bit, we may
connect the outlet tube with an aspirator, which will reduce the pressure
and make the water boil again.
The process of boiling consists in the formation in a
liquid of bubbles of vapor, which rise to the surface and es-
cape. The temperature at which this takes place is the
boiling point of the liquid.
There is a second and more exact definition of the boiling
point. It is evident that a bubble of water vapor can exist
within the liquid only when the pressure exerted outward
by the vapor within the bubble is at least equal to the atmos-
pheric pressure pushing down on the surface of the liquid.
Fig. 171. — Boiling water.
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WATER, ICE, AND STEAM 201
For if the pressure within the bubble were less than the outside
pressure, the bubble would immediately collapse. Now the
pressure that would exist inside a bubble, if it could form at
all, would be diflferent at different temperatures. It is called
the vapor pressure, or vapor tension, of the liquid, and we shall
soon see how to determine its values at diflferent temperatures.
The boiling point of a liquid may therefore be defined as the
temperature at which its vapor pressure is one atmosphere.
199. Effect of changing pressure. We have just seen in
the experiment about boiling that if the pressure on the
surface of the liquid is increased, the temperature has to be
raised before the liquid wrill boil. If the pressure is de-
creased, the liquid will boil at a lower temperature. We
can understand this if we recall that ordinarily the atmos-
phere is exerting a pressure of about 15 pounds per square inch
on the surface of the liquid. If we reduce this pressure, it
is easier for the bubbles of vapor to form ; if the pressure is
increased, it is more diflBcult for the bubbles to form. In
any case, they will form only when the temperature is higfh
enough so that, when they have formed, the pressure in
them is equal to the pressure on the surface of the liquid.
So by observing the temperatures at which a liquid boils
under diflferent pressures, we can determine how the vapor
pressure of the liquid changes with temperature. Experi-
ments have shown that, near 100® C, the vapor pressure of
water increases by about 27 millimeters of mercury for each
Centigrade degree rise of temperature.
Benjamin Franklin devised the following interesting ex-
periment to show water boiling under reduced pressure.
I^t a flask half full of water, which is boiling vigorously, be removed
from the flame and instantly corked air-tight with a rubber stopper. We
may then invert the flask, as shown in figure 172, and cool the top by
pouring on cold water. The water in the flask immediately begins to
boil again. This is because the steam in the top of the flask is
condensed and so the pressure on the surface of the liquid is much
reduced.
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206
PRACTICAL PHT8IC8
water under re-
duced pressure.
Sometimes it is very desirable to boil liquids at as low
a temperature as possible. For example, the water is
boiled away from sirup and from milk in
what ar.e called yacuum pans, which are merely
closed kettles with part of the air pumped
out. The water boils away at about 70° 0
and leaves the granulated sugar or milk
condensed, but not cooked.
On the tops of high mountains the temper-
ature of boiling water is so low that eggs
cannot be cooked. In Cripple Creek, Col.,
about 10,000 feet above sea level, it takes
about twice as long to cook potatoes as in
Boston. In some high altitudes closed ves-
FiG. 172.— Boiling sels provided with safety valves, called
"digesters" or "pressure cookers" (Fig. 173),
have to be used in cooking. Digesters
are also used for extracting gelatine from bones. The
effect of the increased pressure in a digester or pressure
cooker is the same as in a boiler. The water in a boiler
whose gauge reads 100 pounds is boil-
ing, not at 100° C, but at 170° C or
338° F.
Since we have defined the 100° point
on the Centigrade scale as the tempera-
ture of boiling water, and since the tem-
perature at which water boils is so much
affected by changes in pressure, it is
necessary to fix on some standard pressure
at which thermometers are to be " cali-
brated" or marked. By common agree-
ment, this standard pressure is the pressure exerted by a
column of mercury 760 millimeters high, the temperature of
the mercury being 0° C. The temperature at which water
boils under this pressure is, by definition, 100° C.
Fio. 173. — Pressure
cooker.
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WATER, ICE, AND STEAM
207
200. Summary. What has been said about the process of
boiling can be summarized as follows : —
(1) A liquid will boil only when its temperature is such that
its vapor pressure is equal to the pressure on its surfaee.
(2) What is called " the boiling point ^^ of a liquid is the
temperature at which it will boil under atmospheric pressure ;
that is, the temperature at which its vapor pressure is one
atmosphere, or 760 millimeters of mercury.
(3) Every liquid has its own boiling point. The boiling
point of water is by definition 100° C.
(4) The rule about boiling under other pressures than one
atmosphere is^ the higher the pressure, the higher the tempera-
ture required to make the liquid boil.
Table of Boiling Points
(At a pressure of 760 millimeters )
Zinc
918° C
Alcohol
78° C
Sulphur
445° C
Ether
35° C
Mercury
357° C
Ammonia
- 34° C
Saturated salt solution
108° C
Oxygen
- 183° C
Water
100° C
Hydrogen
- 253° C
201. Distillation. In many localities the only way to be
sure of getting pure water is by what is called distillation.
Let us set up a boiler B and
a condenser C as shown in
figure 174, and color the water
in the boiler with blue vitriol
(copper sulphate). Wheu the
solution is boiled, the vapor
or steam given off is con-
densed, by the continual cir-
culation of cold water through
the jacket, as a colorless, taste-
less liquid, pure or distilled
water. The non -volatile impurities, including the vitriol, are left behind
in the boiler.
Fig. 174.--Purification of water by distillation.
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PRACTICAL PHYSICS
The process of distillation consists
of boiling a liquid and condensing
its vapor. In commercial work this
is usually done in a "worm con-
denser." This consists of a pipe
coiled into a spiral and surrounded
by circulating cold water (Fig
175). In this way a large condens-
ing surface is obtained in a small
space.
When a mixture of two liquids is
distilled, the liquid with the lower
boiling point vaporizes and is con-
densed first. It can thus be sepa-
rated from the one with the higher
boiling point. Thus alcohol is
Fia. 176.— wprm condenser, distilled from fermented liquors
by this process of fractional distillation. It is in this way
that gasolene and kerosene are got from crude petroleum.
Problems and Questions
1. How is the temperature of boiling water affected by taking the
water to the bottom of a deep mine ?
2. If water boils at 99° C, what is the atmospheric pressure ?
3. If water boils at 208° F, what does the barometer read ?
4. An elevation of 900 feet makes a difference of about 1 inch in the
barometer. At what temperature would water boil 1500 feet above the
sea?
5. What effect does salt or sugar have on the boiling point of water ?
Try it.
6. In distilling a mixture of alcohol and water, which liquid begins
to distill over first ?
7. How could you obtain fresh water from sea water?
8. Mark Twain in his " Tramp Abroad " tells of stopping on his way
jup a mountain to <<boil his thermometer/' What did he do, and
why?
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WATEBy ICE, AND STEAM 20S
202. Latent heat: water to steam. When a kettle of
water is put on a stove, it gets hotter and hotter until it
boils. Then no matter how much heat we apply to the
kettle, if there is a free outlet for the steam to escape,
the temperature remains constant at 100° C or 212° F.
The heat energy which seems to disappear in boiling the
water is called the latent heat of steam or the latent heat of
vaporization. When steam flows from a steam pipe into a
radiator in a room, some of it condenses and gives back the
heat which apparently disappeared when the water changed
into steam. This latent (or hidden) heat is now understood
to represent the energy needed to pull the molecules of
water away from each other and set them free as steam.
203. How much heat is needed to make a gram of steam?
When we want to determine the amount of heat needed
to change a gram of water at 100° C into steam at 100° C,
we usually apply the method of mixtures. In practice we
generally try to determine the heat evolved in condensing a
gram of steam by running dry steam into a given quantity
of water at a known temperature for some time. We meas-
ure the rise in temperature and the increase in weight, which
is the weight of the condensed steam. Then we make an
equation in which the number of calories received by the
water in being warmed is put equal to the calories given out
by the steam in condensing to water at 100° C and by this hot
water in cooling from 100° C to the temperature of the mixture.
Suppose we take 400 grains of water at 5*^ C and run in 20 grams of
steam at lOO'' C, which raises the temperature of the water to 35** C.
What is the number of calories of heat given out by 1 gram of steam in
condensing to water at 100° C ?
Let X = latent heat of steam.
Since 400(35 — 5) = heat absorbed by cold water,
and 20 a? = heat given out by condensing of steam,
and 20(100-35) = heat given out by water in cooling from 100*to35°C,
then 400(35 - 5) = 20 x + 20(100-35),
and X = 535 calories.
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210 PRACTICAL PHYSICS
Recent experiments have shown that the latent heat ol
steam is about 540 calories. In other words^ it takes more
than five times as much heat to change any quantity of water
into steam as to raise the same quantity of water from the freez-
ing to the boiling point. In English units it requires 540 x 1. 8
or 972 B. t. u. to change a pound of water at 212® F into
steam at 212® F.
Problems
1. Find the number of calories required to change 15 grams of water
at 100'" C into steam.'
2. Compute the heat evolved by condensing 10 grams of steam at
100° C and cooling it down to 50° C.
3. How much heat will be required to convert 1 kilogram of ice at
0° C into steam at 100° C?
4. How much steam at 100° C must be run into 500 grams of water at
10° to raise it to 40°?
5. In the illustrative example in section 203, the latent heat came out
535, which is a little too low. This shows that the temperature of the
mixture (35° C) was not acccurately observed. What should it have
been?
6. How many pounds of coal will be needed in a boiler whose efficiency
is 65%, to convert 100 pounds of water at 50° F into steam at 212° F?
Assume that the heat value of the coal is 14,500 B.t. u. per pound.
204. Evaporation. Everybody is familiar with the fact
that water left in an open dish gradually disappears or
evaporates. Bvaporation is different from boiling, in that evap-
oration takes place at any temperature but only at the surface
of a liquid, while boiling goes on inside the liquid but only
at a fixed or definite temperature. Evaporation goes on
more rapidly the warmer and drier the surrounding air is.
For example, wet clothes dry more quickly on a hot day than
on a cold, foggy day.
205. Cooling by evaporation. If one pours a few drops of
alcohol or ether on his hand, the liquid quickly evaporates,
causing a marked sensation of cold. Whenever a liquid
evaporates, it must get heat from somewhere, and so the
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WATER, ICE, AND STEAM 211
temperature of the liquid itself and of anything near it drops.
That is to say, heat is absorbed in the process of evaporation.
It is always more comfortable on a hot day to ride in a car
than to sit still, because the rapid circulation of the air makes
the moisture of the skin evaporate more rapidly. This is
why one can tell the direction of the wind by lifting a
moistened finger ; the wind blows from the side which feels
cool.
206. Moisture in the air. In the summer time a pitcher of
ice water is usually covered with little drops of water or
*' sweat.*' It might at first be thought that these were due
to the water oozing through the pores in the side of the
pitcher ; but the microscope does not show any pores in glazed
porcelain or glass, so we must conclude that the drops come
from the surrounding air. The air is cooled by coming in
contact with the cold pitcher and deposits some of its mois-
ture. If we put a little water in a bottle and cork it tightly,
tiie water does not evaporate because the air above the water
quickly becomes "saturated" with moisture. Thus we see
that air can take up only a definite quantity of moisture,
depending on the temperature. This can be better under-
stood from the following experiment.
Let us place a little water in a thin -walled flask and cork it. If we
place the cask in a warm place until it becomes warm, and then cool it,
its walls become dim, due to the drops of water. The warm saturated
air becomes " supersaturated ** on cooling.
Careful experiments show that a cubic meter of saturated
air contains at different temperatures the following amounts
of water vapor : —
2 grams at - 10° C.
5 grams at
0°C.
9 grams at
10° C.
17 grams at
20° C.
30 grams at
30° C.
597 grams at
100° C.
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PRACTICAL PHYSICS
From this table it will be seen that air, which is saturated
at one t'^mperature, can, at a higher temperature, take up still
more water vapor before becoming saturated ,• but if cooled, it
must deposit some of the water vapor which it already has.
207. Relative humidity. Usually the air does not contain
all the moisture which it can hold ; that is, it is not saturated.
If, however, the temperature suddenly drops, the same ac-
tual amount of moisture will saturate the air.
For example, if the water in a polished nickel-plated cup is cooled
with ice below the temperature of the room, a mist will appear on the
outside of the beaker. The temperature of the water when this occurs is
the " dew point."
The dew point is the temperature at which the
water vapor in the air begins to condense. If
the air is cooled below the dew point, some of
its vapor condenses, and dew collects on objects.
Thus we see that the words " dry " or "moist,'*
as applied to the atmosphere, have a purely rel-
ative significance. They involve a comparison
between the amount of water vapor actually
present, and that which the air could hold if
saturated at the same temperature. The ratio
of these two quantities is called the relative
humidity. For example, we may read in the
newspaper that the relative humidity is 75%.
This means that the amount of water vapor
actually present in the air is 75 % of what the
air might have contained at the given tempera-
ture if it had been saturated.
Dry Wet
Fig. 176.— Wet
and dry bulb
thermometers.
Wet and dry bulb thermometers. Let two
thermometers be arranged as shown in figure 176. The bulb
of the thermometer at the left is dry, while the other ther-
mometer has its bulb wrapped with cotton cloth which is
kept moist by a cup of water. If we keep the air around
the thermometers circulating by an electric fan, after a
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WATER, ICE, AND STEAM 213
little while the wet-bulb thermometer will indicate a lower temperature
than the dry-bulb thermometer. This is because of the cooling caused
by the evaporation from the cotton cloth. The drier the surrounding air,
the more rapid will be the evaporation, and so the greater will be the
difference between the wet and dry bulb thermometers. With the aid
of tables furnished by the Weather Bureau, we may determine from
these thermometer readings the so-called << relative humidity " of the air.
209. Practical importance of determining humidity. It is well
known that a hot day in Boston is much more uncomfortable
than an equally hot day in Denver. This is because a city
near the ocean, like Boston, has a higher relative humidity
than a city which is inland and a mile above sea level, like
Denver. When the relative humidity is high, we feel
" sticky " because the perspiration of the skin does not evap-
orate readily. On the other hand, too little humidity is in-
jurious. Special precautions are taken to keep the air in
schools, hospitals, and private houses from getting too dry in
winter, and the air in greenhouses must be kept quite damp for
the growth of plants. In cotton mills it has been found that
the air must be rather moist to make the spinning of yarn suc-
cessful.
Since the occurrence of frost in the late spring or early
fall is injurious to many crops, it is often highly important
that farmers should know in the afternoon whether freezing
weather during the night is to be expected. The tempera-
ture of the dew point gives a ready means of predicting how
low the temperature at night will drop ; for when the dew
point is reached, further cooling is retarded. So if the dew
point is above 40° F, it is seldom that the temperature will
fall to freezing in the night.
210. Dew, fog, rain, and snow. On clear, still nights the
ground radiates the heat that it has received during the
daytime. The grass and leaves, which can radiate heat freely,
cool rapidly and soon bring the air near them below its dew
point. Then moisture condenses as dew or at lower tern-
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214
PRACTICAL PHYSICS
peratures as frozen dew or frost. This phenomenon is exactl^r
like the formation of drops of water on a pitcher of ice
water, or on one's spectacles when he comes from the cold out-
doors into a warm room. Clouds covering the sky hinder
the formation of dew because they restrict radiation. If the
condensation of the moisture of the air is not brought about
by contact with cold solid objects at the surface of the earth,
but by great masses of cold air high above the earth, clouds
are formed and rain may result. Fog is merely clouds very
near the earth.
Clouds at very high altitudes may be composed of bits of
ice, but, in general, clouds are made up of minute drops of
water. Like particles of fine dust, very small drops of water
tend to fall, but can do so only very slowly. Sometimes they
fall into warm and not yet saturated layers of air, and then
they change back again into vapor. Sometimes they are
carried up by ascending
currents of air faster than
they can fall through
them, and so seem to
float. For example, the
cloud of steam above a
locomotive stack is com-
posed of minute drops ot
water and yet rises with
the warm air. Clouds
are not durable. They
simply mark the place in
the atmosphere T/here the
process of condensation
of water vapor i-: going
on. In rain clouds the
little particles of water
come together and form
Via. in.— Snow crystals. drops which easily over-
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WATER, ICE, AND STEAM 215
come the resistance of the air and fall to the ground. If the
temperature of the cloud is below 32° P, the particles of
water unite to form little delicately fashioned hexagonal
snow crystals (Fig. 177).
Snow and rain together make what the " weather man "
calls "precipitation." Thus in New York there are about
150 days of rain or snow each year, and the total precipitation
in a year, if it did not dry up, would cover the earth to a
depth of about 3 feet.
Questions and Problems
1. A room is 3 meters high, 10 meters long, and 6 meters wide. How
many grams of water will be required to saturate the air at 20° C ?
2. An experiment showed that on a certain day, when the tempera-
ture was 30° C, the air contained 12 grams of water per cubic meter.
What was the relative humidity?
3. How do undue dryness and undue dampness affect wooden furni-
ture?
4. What change in the thermometer usually goes with a rising ba-
rometer?
5. What happens when a moist wind from the ocean strikes a
mountain range ?
6. In some hot countries the people cool their drinking water by
setting it in jars of porous earthenware, in a shady place, where there is
a current of aii\ Explain.
7. Milk used to be set away in shallow pans for the cream to rise.
Now they use cylindrical tanks of small area and quite deep. Which is
the better, and why?
8. Why do clothes dry best on a windy day ?
9. Why does sprinkli|;ig the street on a hot day cool the air?
211. Freezing by boiling. The fact that a large quantity
of heat is needed to vaporize a substance is often made use
of in getting low temperatures.
If a cylinder of liquefied carbon dioxide is tilted, as shown in figure
178, and the valve is opened, the liquid released from pressure vaporizes
so rapidly as to cool everything, including the rest of the liquid, and so
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216
PRACTICAL PHYSICS
some of it is frozen. After the valve has been open a short time, the
bag is filled with a white solid, frozen carbon dioxide. This solid evap-
orates very readily, and gives a temperature as low as —80*^0. K the
solid is put in a beaker and mixed with ether,
the mixture will freeze a test tube of mercury. The
ether serves to carry the heat quickly from the test
tube to the solid.
212. Artificial ice. In the manufacture
of artificial ice and in refrigerating plants
(Fig. 179), gaseous ammonia is compressed
by a pump and then cooled until it
liquefies. During this process of com-
pression and of condensation, heat is
evolved, which is removed by passing
the ammonia through a pipe covered with running water.
The liquefied ammonia is then piped to the ice tank or cold-
storage room, and allowed to expand through a valve with a
small opening. This
Fig. 178. — Liquid
carbon dioxide be-
ing frozen.
^
i(m
^
M
m
m:
checks the flow, and
so enables the pump to
maintain enough pres-
sure to keep the am-
monia in liquid form
on its way to the valve ;
while beyond the valve
the pressure is very
small, so that the am-
monia expands and
evaporates rapidly.
While doing so, it
absorbs heat from the refrigerating room. It is then ready
to be compressed again.
In the manufacture of ice, the expansion pipes pass through
a brine tank in which are smaller tanks of pure water.
When the water in these tanks is frozen, the tanks are pulled
up and the ice removed and stored. The ammonia is used
EzpanBion
III™ Valvfi
^To neircr
Fig. 179. — Diagram of cold-storage plant.
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WATER, ICE, AND STEAM 217
over and over again, but power must be constantly supplied
to keep the compressor working.
SUMMARY OF PRINCIPLES IN CHAPTER XI
Heat units : —
1 B. t u. = heat to raise 1 lb. of water I'' F.
1 calorie = heat to raise 1 gram of water I'' C.
Specific heat = calories to raise 1 gram of substance V C.
Specific heat of water = 1.
Method of mixtures : —
Heat given up by hot bodies = heat absorbed by cold bodies.
Pressure : —
Lowers freezing point of water 0.0072° C per atmosphere.
Raises boiling point of water O.OST'' C per millimeter of mercury.
Latent heat of melting = heat absorbed during melting,
= heat yielded during freezing.
Value for. water, 80 calories.
Latent heat of vaporization = heat absorbed during evaporation,
= heat yielded during condensation.
V&lue for water, 540 calories. ^
Relative hiunidity
actual moisture in air
moisture sufficient to saturate air at same temp.
Questions
1. If you know the dew point to be 10° C, how could you find the rel-
ative humidity at 20° C ?
2. Human hair when treated with ether is very sensitive to mois-
ture'. When it is moist it contracts, and when it dries it elongates.
Explain how a moisture gauge or " hygrometer " could be made with a
hair.
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218 PRACTICAL PHT8IC8
3. Why do they not cast gold money instead of stamping it with a
die?
4. Why is a bum from live steam so severe?
5. Why does one sometimes " catch cold " by sitting in a draft of
cool air after taking violent exercise ?
6. How low may the temperature fall during a rain?
7. Why can mercury mixed with zinc and tin be purified by distills
tion?
8. Why is it difficult to make snowballs out of dry snow?
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CHAPTER XII
HEAT ENGINES
The invention of the steam engine — boilers — slide-valve
and Corliss engines — expansion — compounding — condensers
— efficiency — steam turbines — 2-cycle and 4-cycle gas engines
— balance sheets of engines — mechanical equivalent of heat.
213. The invention of the steam engine. In our age no
other machine is of such importance as the steam engine. It
furnishes the driving power for running a countless number
of machines in our shops and factories, as well as for trans-
portation on land and sea.
Up to about two hundred
years ago steam had been used
only in various devices, called
steam fountains, for raising
water. In 1705 the first suc-
cessful attempt to combine the
ideas of these devices into an
economical and convenient ma-
chine was made by Thomas New-
comen (1663-1729), a blacksmith
of Dartmouth, England. This
machine was called an " atmos-
pheric steam engine" (Fig. 180).
It consisted of a boiler A^ in
which the steam was generated,
and a cylinder -B, in which a
piston moved. When the valve V was opened, the steam
pushed up the piston P. At the top of the stroke, the valve
219
iJ^Q. 180. — Newcomen's steam
engine.
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220
PRACTICAL PHYSICS
V was closed, the valve F^ was opened, and a jet of cold
water from the tank Q was injected into the cylinder, thus
condensing the steam and reducing the pressure under the
piston. The atmospheric pressure above then pushed the
piston down again.
This machine was used to pump water from mines. It
consumed a great deal of fuel, because the cold water cooled
the cylinder walls so much that
when the steam was turned in,
much steam condensed before
the piston was raised.
The next great step in the
development of the steam en-
gine came through a Scotch in-
strument maker, James Watt
(1736-1819). He arranged a
separate vessel for condensing
the steam, as shown in figure
181. This condenser, (7, was
connected with the cylinder
through a valve F'. When the
piston had reached the top of the
Fig. 181. -Watt added a separate cylinder, the valve Twas closed
condenser. t -r-ri t rr»i i
and V was opened, ihen the
steam rushed from the cylinder into the condenser, which
was kept cold and under less than atmospheric pressure.
At first these valves V and V had to be operated by hand,
but later, it is said, a boy named Potter, whose job it was
to turn these valves, connected the valve handles by cords
to the beam ED in such a way that the machine became
automatic.
In all these crude machines the steam simply furnished
the vacuum, and atmospheric pressure did the work. Later,
Watt made a machine with a closed cylinder and a piston
that was pushed down as well as up by steam. By the use
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BEAT ENGINES
221
of a connecting rod and crank shaft, he contrived to change
the back-and-forth motion of the piston to a rotary motion,
and so made the steam engine available for many new uses.
Within a few years the development of the steam engine
revolutionized most lines of industry.
214. A modem steam plant. In a modern steam plant the
steam is made in a boiler, is used in a steam engine, and is
got rid of in an exhaust or condenser. We will discuss
these in turn.
215. Steam boilers. A fire-tube boiler consists of a steel cyl-
inder which sometimes stands on end, as in the small " donkey
engines " used with derricks, but generally is set on its side,
Fig. 182. — Section of a locomotive boiler.
L^l ""VU
as in locomotives (Fig. 182). Running through this cyl-
inder are tubes, three or four inches in diameter, through which
the fire and smoke pass. The water and steam fill the rest
of the cylinder outside the tubes. These tubes give the boiler
a much greater heating surface, so that it makes more steam
per hour. Such boilers are called fire-tube boilers. In an-
other type, called a water-tube boiler (Fig. 183), the water is
inside the tubes and the fire is outside. Such a boiler consists
of a large number of tubes, inclined at an angle and fastened
at each end into vertical "headers": these headers communi-
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222
PRACTICAL PHT8IC8
Fig. 183. — Section of water-tube boiler.
cate with a drum above, which is half full of water, the re
mainder of the drum forming a space for steam. The watei
descends by the
back headers,
rises through
the inclined
tubes, and passes
up the front
headers, thus
maintaining a
very good circu-
lation. The fire
is placed under
the front end of
the tubes ; the
gases are de-
flected by brick
walls, so that
they pass completely over and under the whole length of the
tubes. In some water-tube boilers the fire grate is sloping
and arranged like a flight of steps. The coal is automati-
cally fed through a chute from the coal loft above to the
grate. The principal advantages of this type of boiler are
its great freedom from risk of explosion and its ability to
make steam quickly. A modified form of this boiler is
generally used in marine work.
Not only is it desirable to get the greatest quantity of
steam with the least expenditure of fuel, but it is also essen-
tial to keep the steam pressure constant and to prevent an
explosion which may have frightful consequences. There-
fore every boiler is equipped with a steam gauge, which is
merely a Bourdon pressure gauge (section 75), and a water
gauge (section 62), which enable the engineer in charge to
watch the pressure and water level in the boiler. If the
water level is too low, there is danger of burning the tubes
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HEAT ENGINES 223
and plates and perhaps of wrecking the boiler ; if it is too
high, water is liable to be carried along with the steam and
so damage the engine. Besides
these devices, every boiler must
have a safety valve, which auto-
matically lets the steam blow
off when the pressure exceeds a
certain limit. A simple form „ ,„^ ^ , ,
- -, , . 1 . /5 Fio. 184. — Safety valve.
ot safety valve is shown m fig-
ure 184. In some forms a spring is set so as to release the
steam if the steam pressure becomes too great inside the
boiler.
In order to make steam rapidly, the fire must burn fiercely,
which requires a good draft. To get this, tall chimneys are
sometimes used, and at other times a forced draft is made by
a big fan. On battleships a forced draft is often obtained
by making the whole fireroom, within which the stokers
work, air-tight, and keeping it full of air under pressure,
supplied by blowers or pumps as fast as it can escape through
the fires.
One pound of coal, whose heat value is 14,000 B. t. u., could
change 14.4 pounds of water at 212° F into steam at 212° F
if no heat were wasted. In actual practice, one pound of
coal evaporates between 8 and 10 pounds of water " from and
at 212° F," which means an efficiency of from 55 to 70 %.
One great source of loss of heat is the flue gases. Smoke
pouring from the chimney means that just so much unconsumed
fuel is going to waste, and, what is worse, is adding to the
dirty atmosphere of the neighborhood. To-day steam engi-
neers are able to design boilers which, when properly stoked,
produce no smoke.
216. Steam engine. The type of engine most commonly
used for small plants and for locomotives is the slide-valve
engine (Fig. 185). Steam comes from the boiler into a box
or steam chest, and then into the working end of the cylinder
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224
PBACTICAL PHT8IC8
through a passage shown by the arrows at the right of the
picture. At the same time the spent steam in the other end
of the cylinder is escap-
ing through the hollow
interior of the valve, to.
the exhaust passage. It
then escapes to the air,
or to the condenser,
through a pipe at the
back, which does not
show in the figure. At
the end of the stroke
the valve is pulled far
enough to the right to
admit live steam to the
left-hand end of the
Fia. 185. — Slide-valve steam engine.
cylinder, while the spent steam in the right-hand end es-
capes into the exhaust.
In large steam engines Corliss valves are more often used.
A Corliss valve (Fig. 186) opens and closes by turning a little
in its seat. In a Corliss engine there are four such valves —
two at each end of the cylinder. Two of them, A and -B,
are for admitting the
steam, and two, O
and D, for letting the
steam out. When
valve B is open to
admit steam, valve D
is also open to let
steam out of the other
end of the cylinder,
while A and C are
Fig. 186.— Corliss steam engine.
closed ; on the reverse stroke, A and O are open, while B
and D are closed. These valves are automatically opened
and closed at the proper time by the engine itself. The fact
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MEAT ENGINES 225
that the time at which each valve opens can be accurately
adjusted independently of the other valves makes Corliss
engines more eiScient than slide-valve engines, and has led
to their extensive use in large installations.
217. Expanding steam. If live steam from the boiler is
allowed to push the piston through its entire stroke, and is
then thrown away, that is, al-
lowed to pass into the atmos-
phere or into a condenser, it is
evident that much energy is
wasted. To get more work out
of the steam, the valve is closed
after the piston has made about ^^'"**^*
J or J of its stroke, and the Fig. 187.- Pressure in cylinder of
steam is allowed to expand
through the rest of the stroke. The pressure continues to
drop after the " cut-off," as shown in figure 187, where the
pressure P is represented vertically and the stroke horizon-
tally. Such pressure diagrams can be made automatically by
the engine itself while in actual operation, and enable those
in charge to adjust the valves properly.
218. Compound engine. Another device for jgetting more
work out of the steam is to use the steam at high pressure
in one cylinder, then allow it to pass into a second, larger
cylinder, where it expands some more, and sometimes into a
third and a fourth cylinder. These are called compound, triple
and quadruple expansion engines. When the expansion and
consequent cooling of the steam take place in steps, there is
no large drop in temperature in any one cylinder. So the
walls of a cylinder never get much cooler than the incoming
steam, and there is little condensation in the cylinders. In
a simple engine, the initial steam pressure varies from 80 to
100 pounds, while in compound engines the initial pressure
is usually higher, from 100 to 175 pounds. A simple engine
requires from 17 to 35 pounds of steam an hour for each
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226 PRACTICAL PHT8IC8
horse power developed, while a compound engine may need
as little as 11.2 pounds of steam per horse-power hour.
Triple-expansion engines are usually used in marine work.
219. Condenser. When its exhaust pipe opens directly
into the atmosphere, an engine is called a non-condensing
engine. The power depends on the excess of the steam
pressure in the boiler above that of the atmosphere outside.
Ordinary locomotives and most small engines are of this
type. In fact the locomotive depends on the escaping steam
to furnish a draft for the boiler.
Greater economy is obtained by sending the exhaust steam
to a vacuum chamber, or condenser. In one type the steam
coming from the engine is condensed by a jet of cold water,
and in another type it is condensed in tubes surrounded by
cold water. A small pump is used to pump out the condensed
steam as well as any air which may have leaked in. Such
engines are known as condensing engines. Marine engines are
always condensing engines.
220. Efficiency of a steam plant. We have already seeft
that the modern steam boiler has an efficiency of about 70%,
but there are still larger losses in the engine itself. The
escaping steam from an engine always carries away a large
amount of unutilized heat energy. It can indeed be proved
that the greatest efficiency possible for a steam engine is
represented by the fraction
where T^ is temperature (Absolute) of the steam supplied
and j?2 is temperature (Absolute) of the steam rejected.
For example, an engine running at 163 pounds boiler pressure takes in
steam at about 185° C, and 7\ is 458°. If the temperature of the exhaust
steam is 100° C, T^ is 373°. Such an engine cannot possibly have an
efficiency greater than
i§8-=^ = 18.50/.
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HEAT ENGINE8 227
For this reason steam engineers try to use high-pressure
steam, because of its high temperature, so as to make ( Ij — T^)
as large as possible. The temperature T^ is sometimes still
further increased by passing the steam through pipes (Fig.
183) in the furnace to " superheat " it.
It must be remembered that this 18.5 % is the efficiency
of the engine alone, so that the efficiency of the engine and
boiler would be 18.5 % of 70 %, or only about 13 %. This
means that about 87 % of the energy of the coal would not
be converted into mechanical energy. By using very high
temperatures, the latest style of .quadruple expansion and
condensing engine has been made to utilize about 20% of
the energy originally in the coal. The ordinary locomotive,
however, does not utilize more than 8 %.
Problems
1. The area of the piston of a steam engine is 120 square inches and
its stroke is 2 feet. If the ^^ mean effective pressure " of the steam is 50
pounds per square inch, what is the total force exerted on the piston ?
2. In problem 1, how many foot pounds of work are done in one
revolution of the shaft (two strokes) ?
3. If the engine in problem 1 is making 150 revolutions per minute,
what is its '^ indicated horse power " ; that is, what is the rate in H. P. at
which the steam does work on the piston ?
4. A locomotive with cylinders 18 inches in diameter and a stroke of
2 feet is provided with driving wheels 6 feet in diameter. If the mean
effective pressure of the steam in the cylinder is 60 pounds per square-
inch, and the engine is making 50 miles an hour, what is the indicated
horse power ?
5. How much mean effective steam pressure will be needed to get
10 horse power from a " donkey engine ** running at 200 revolutions per
minute ? (Assume area of piston to be 50 square inches, and stroke 1 foot.)
221. Steam turbine. Thus far we have been describing
reciprocating engines, in which the back-and-forth motion of
the piston rod is turned into rotary motion by means of a
crank and connecting rod^ Since the piston must come to a
standstill at the end of each stroke this means in high-
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228
PRACTICAL PHT8IC8
'speed engines very frequent starting and stopping, which
causes so much shaking as to require big and expensive
foundations. On steamships the continual jarring causes a
disagreeable vibration. A new and distinctly different
type of engine called a steam turbine has been developed
in recent years in which there is no reciprocating motion.
222. Curtis turbine. Steam turbines can be divided into
two main classes, of which the Parsons and the Curtis tur-
bines are typical representatives.
The Curtis turbine is, in principle,
like the Pelton water wheel (sec-
tions 78 and 79). Steam is de-
livered to the machine through
nozzles in which it expands and
gains a high velocity. It then
strikes against blades fastened to
the edge of a revolving disk and .
gives up its kinetic energy to
them. In some forms of turbine
(Fig, 188) there is only one set
of nozzles, and the steam expands
in one step from the boiler pressure to the condenser vacuum.
Under such conditions the speed of the steam as it strikes
the blades is so great, often
more than 4000 feet per second
or 2700 miles per hour, that
it is difficult to handle it effi-
ciently. Curtis turbines are
therefore built in from three
to six sections, each section be-
ing a complete turbine with its
nozzles and wheel, and the steam
is run through the sections in
succession, as in a compound „ ,^ ^, .
... . ^. Fig. 189. — Moving and stationary
or multiple-expansion engine. blades in a Curtis turbine.
Fig. 188. — Steam turbine with one
set of nozzles.
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A Curtis turbine (at the right) with the upper half of its casing removed.
There are three wheels and two rows of blades on each wheel. It is used to
drive the generator at the left.
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f'T^^^"
^
fe
> P
A Westinghouse turbine with the upper half of its casing lifted. There are a
great many rows of moving blades. The balancing dummies are at the
near end. The generator is at the other end, and is cooled by air drawn
in through the duct.
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In order to reduce still further the speed at which the
blade wheels have to run, they are so designed that each jet
has two or three chances at a given blade wheel before losing
all its velocity. As it escapes at reduced speed from each
set of moving blades, it is caught by guides attached to the
surrounding casing and turned around so as to strike another
set of moving blades on the same wheel, as shown in figures
189 and 190.
223. Parsons turbine. The Parsons turbine is somewhat
like a succession of windmills set in line behind each other.
The steam flows along the turbine from one end to the other
in the annular space between the cylindrical drum or rotor
and a slightly larger cylindrical casing, and acts on the wind-
mill-like blades fastened to the drum. In passing through
these rows of moving vanes, the steam would quickly get to
spinning with the rotor and would then fail to act effectively
on the later vanes, if it were not for the rows of stationary
guide blades attached to the casing. These project between
the rows of moving blades, catch the steam as it comes
through, and direct it against the next row of moving blades
at the proper angle. Thus the steam goes zigzagging down
the annular space, striking first a row of fixed blades, then a
row of moving blades, then
another row of fixed blades, i^-^^/ .-/l'C-''1J[TT
and so on. As the steam nMlZ-ifsTrsiiiffl^ Wl^ t
flows along, its pressure
decreases and it expands ;
so the space between the fc^^^hi^d^s
rotor or drum and the ^ ,_, a * , i, TT
, . Fig. 191. — Section of a Parsons turbine.
outer case has to increase
gradually as the low-pressure end is approached, to give the
steam the extra space it requires. This is done by making
the blades short at the inlet end and long at the outlet end,
and by occasionally increasing the diameter of both rotor
and casing, as shown in figure 191.
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230 PRACTICAL PHT8IC8
224. Advantages of turbines. Turbine engines always
run at high speed, so a large amount of power can be de-
livered by a small machine. This makes them especially
valuable in city power stations where land is expensive.
Furthermore, their lightness and steadiness make smaller and
cheaper foundations sufficient. They have been installed also
on large, high-speed passenger vessels and on torpedo boats
and destroyers. To be operated most efficiently they should
work through a wide range of temperature, corresponding to
a boiler pressure of from 200 to 250 pounds, and a very per-
fect condenser vacuum (often better than 29 inches). A
large supply of cool condensing water is therefore desirable,
and turbines are especially adapted for power stations on
rivers, lakes, or the ocean. Under such conditions, when
working at their maximum capacity, they are slightly more
efficient than even the best reciprocating engines.
225. Gas engine. The essential difference between a
steam engine and a gas engine is that in the steam engine
the fuel is burned under a boiler and the working substance,
steam, is conducted to the engine in pipes, while in the gas
engine the fuel is burned in the cylinder of the engine and
the hot products of combustion are themselves the working
substance. In other words, the gas engine is an internal com-
bustion engine. The fuel, gasolene, is a liquid which is con-
verted into a gas in what is called a carbureter. The liquid
fuel is sprayed into the carbureter, vaporizes, and is mixed
with the proper amount of air. This mixture of gas
and air is compressed in the cylinder of the engine and then
exploded by an electric spark, which causes the exceedingly
rapid burning of the gas. This results in an enormous in-
crease in pressure, which pushes out the piston. Then the
exploded gases are forced out of the cylinder and a new
charge of gas and air are taken in.
Inasmuch as the cylinder has to be a furnace as well as a
cylinder, it would get dangerously hot if it were not cooled
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BEAT ENGINES
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from the outside. It may be water-cooled by surrounding it
with a jacket or outer ease, in which water is circulated ; or it
may be air-cooled by giving it a corrugated outer surface
which radiates heat rapidly, and forcing a stream of air
against this surface.
226. Two-cycle engine. In the two-cycle gas engine, we
have one explosion for every two strokes or for each revolution of
the crank shaft. A simple form, such as is used on motor,
boats, is shown in figure
192. The explosive mix-
ture is taken into an air-
tight crank case and
slightly compressed on
the outward or down
stroke of the piston. As
the piston nears the bot-
tom of its stroke, it un-
covers first the outlet port,
J?, letting part of the
spent gases in the cylin-
der blow off, and then
the inlet port B. The slightly compressed charge in the crank
case then rushes into the cylinder, sweeping out the rest of
the exploded gases before it. On the upstroke of the piston
the ports are covered and the fresh charge is considerably
compressed. As the piston passes its upper dead center
(or soon afterward) the charge is exploded, and expands at
a much higher average pressure than during the compres-
sion, giving back the work of compression and considerably
more besides. Such an engine is called single acting, meaning
that work is done only on one side of the piston.
If the spark does not come at the upper dead center, but
part way down the expansion stroke, the power yielded is much
less. This is done to make a boat run slowly. Adjusting
the electrical connections so as to bring the time of explosion
Fig. 192. — Two-cycle engine.
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232
PRACTICAL PHYSICS
nearer the upper dead center is called " advancing the spark.**
Running on a ^^ retarded spark " wastes gasolene, because the
amount used per stroke is the same as at full power.
The only true valve in this engine is a light clap valve,
where the fresh gases enter the crank case.
The disadvantage of this style of engine is that some of the
fresh gas is lost with the spent gases through the exhaust, so
that it uses more gasolene than some other styles. But, on the
other hand, it is very simple and gives a push every revolution.
227. Four-cycle engine. In the four-cycle engine, we get
•a push or thrust only once in every two revolutions or every
four strokes of the piston. Four-cycle engines, like two-cycle
engines, are usually single acting.
The four-cycle type is the one most commonly used for
;automobiles and for stationary work. The four strokes of
the piston, corresponding to
JijlL JiLJiL ill i[ JjUkL ^^^ revolutions of the shaft, are
^ \ I I I N V| shown in figure 193. It will be
noticed that whereas the two-
cycle type has no valves in the
cylinder, the four-cycle has two
valves, one for the intake of gas
and air and another for the ex-
haust of the spent gases. These
valves are operated mechani-
cally by cams on a small half-time shaft, which is driven
through gears at half the speed of the main shaft. In figure
193, (1), the intake valve is open, and the piston is going down,
thus drawing in the explosive mixture. In (2) the return
or back stroke of the piston compresses the mixture. In (3)
the mixture has been ignited by an electric spark or flame,
and power is obtained from the thrust of the expanding gas
on the outward stroke. This is the working stroke. In (4)
the exhaust valve is open and the spent gases are being
pushed out of the cylinder by the returning piston. Then
Fig. 193. — Four cycles of a gas
engine.
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HEAT ENGINES 238
the whole cycle is repeated again. Since power is obtained
only on every alternate outward stroke, a heavy flywheel is
used to keep the engine going during the other three strokes,
or, as in automobiles, four such engines may act on the same
shaft, so arranged that the explosions in the several cylinders
take place successively, one for every half revolution of the
shaft.
228. Disadvantages of the gasengine. Although the internal
combustion engine has been immensely improved in the last
decade, it is still a very sensitive machine. The spark must
come at just the right time, and must come every time. The
method for producing the spark will be described in Chapter
XVII. The steam engine is more easily varied in speed than
the gas engine. To be sure, it is possible to vary the speed of a
gas engine somewhat by advancing or retarding the spark, and
by controlling the supply of gas ; nevertheless, automobiles
have to use gears to get a suiBcient variety of speeds at full
power. Then, too, a steam locomotive will run either way
by simply shifting the slide valve, while the gasolene auto-
mobile has to use a reversing gear. Finally a gas engine is
not always free from noise and smell.
229. Advantages of the gas engine. On account of light-
ness and compactness, and the small space occupied by the
fuel, there has been a phenomenal development in the manu-
facture of gasolene engines for small pumping stations, shops,
and factories, as well as for automobiles, launches, and aero-
planes. The gas engine does not require any stoking of a
boiler or constant care to keep up the right pressure of
steam. In fact, once started it requires very little attention.
It can be started at a moment's notice, while if a steam
engine and its boiler have been " shut down," it takes a good
while to get up steam. Furthermore, no fuel is wasted
when a gas engine is shut down at. night or between periods
of use. In efficiency the modern gas engine ranks much
higher than the steam engine.
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PBACTICAL PHT8IC8
230. Balance sheet of heat engines. When an engine i»
tested, a heat balance sheet is usually made up. This is
somewhat like a cash account, in that it accounts for all the
energy delivered to the engine by the fuel. These heat bal-
ance sheets vary somewhat for different engines eve» of
good design, but the following are fairly typical for large
and efficient engines of the two types : —
Steam Enoinb
Useful work
Friction
Exhaust
Up the chimney
15%
5%
45%
35%
100%
Gas Engine
Useful work
Friction, etc.
Exhaust
Jacket
25%
10%
30%
100%
231. Mechanical equivalent of heat. We have been con-
sidering the efficiency of engines without stopping to de-
scribe how it is measured. Evidently we must have some
way of comparing the output, which would naturally be
measured in foot pounds or kilogram meters, with the input,
which would naturally be measured in B. t. u. or calories.
This involves finding a definite relation between a foot
pound and a B. t. u., or between a kilogram meter and a
calorie. This problem wa&
not solved until about the
middle of the last century,
when an Englishman, Joule
(1818-1889), did his famous
experiment of churning
water.
He arranged a paddle
wheel in a box of water
(Fig. 194). The paddles
were turned by weights
which descended and thus unwound cords on the spindle
of the wheel. The water was kept from following the rotat-
FiG. 194. — Joule's machine to find me-
chanical equivalent of heat.
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HEAT ENGINES 235
ing paddles by fixed paddles which projected from the sides
of the box.
In this experiment the mechanical work put in could be
measured by multiplying the weights by the distance through
which they fell ; and the heat produced could be measured
by multiplying the weight of the water by the rise in tem-
perature. Great care was taken to prevent any loss of heat.
The result of this and many other experiments of a similar
nature led Joule to announce this principle: 77ie number of
units of work put in is always proportional to the number of
units of heat produced.
As a result of Joule's experiments and also of the more
accurate experiments of Rowland (1848-1901) and of many
others, we believe that 778 foot pounds of work are equivalent
to the heat required to raise one pound of water one degree
Fahrenheit^ or that the energy required to heat one kilogram of
water one degree Centigrade is equal to the work done in rais-
ing one kilogram to a height of 427 meters.
1 B. t. u. = 778 foot pounds of work.
1 kilogram calorie = 427 kilogram meters of work.
To compute the efficiency of an engine we have, therefore,
to divide the work done by the heat put in, expressing both
in the same units by means of the above relationships.
This work of Joule's was a clinching argument in favor of
the principle of the conservation of energy, for it meant that
heat and work are but different forms of energy.
Problems
1. If a horse power is equal to 33,000 foot pounds of work per minute,
how many foot pounds are there in a horse power hour ; that is, in the
total amount of work produced by a 1 H. P. engine working for 1 hour ?
2. A pound of average coal yields 14,500 B. t. u. when burned. To
how many foot pounds is this heat equivalent •?
3. From the results of problems 1 and 2, calculate the horse power
hours per pound of coal.
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236 PRACTICAL PHYSICS
4. A test of a certain steam engine showed that 1 pound of coal
generated 1 horse power hour; from the three preceding problems com-
pute the efficiency.
5. Calculate the efficiency of a gasolene engine from the following
data : 16 cubic feet of gas were used per horse power hour ; 1 cubic
foot of gas yields 700 B. t. u.
SUMMARY OF PRINCIPLES IN CHAPTER XII
The mechanical equivalent of heat is the value in foot pounds
of one B. t. u. or in kilogram meters of one calorie.
1 B. t u. = 778 ft lb.
1 kg. cal. = 427 kg. meters.
Efficieiicy = 2H^*.
input
Both must be expressed in same unit by means of above
relations.
The conservation of energy in engines requires that all
energy supplied as heat of combustion' of the fuel be accounted
for as useful output or specified waste (''making up the heat
balance sheet of the engine ").
Questions
1. Why does the steam jacket increase tUe efficiency of a steam
engine ?
2. Does the water jacket increase the efficiency of a gasolene engine ?
3. What did Count Rumford learn about heat while boring cannon
for the Bavarian government ?
4. How are the cylinders of engines lubricated?
5. How does a ship equipped with steam turbines reverse its pro-
pellers?
6. Describe the reversing mechanism of a locomotive.
7. Is an ordinary gas engine self-starting? How are automobile
engines made self-starting?
8. When you see steam coming from the exhaust pipe of a steam
engine in puffs, do you know whether it is a condensing or non-condens-
ing engine ?
9. Why are condensers not used on locomotives?
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HEAT ENGINES 237
10. What advantages has oil as a fuel for locomotives and steam-
ships ?
11. Why are marine engines always condensing engines?
12. How would you compute the efficiency of a gun regarded as a
heat engine ?
13. What makes the water circulate in a water-tube boiler?
14. Why does a high-speed turbine give more power than a low-
speed reciprocating engine of about the same size ?
15. What is the use of the radiator on an automobile ?
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CHAPTER XIII
MAGNETISM
The lodestone — magnetic poles — attraction and repulsion
— the compass and magnetism -of the earth — magnetic field —
induced magnetism — permeability — theory of magnetism.
232. The lodestone. For many centuries it has been
known that a certain kind of rock, called the lodestone, has
the power of attracting iron filings and small fragments of
the same rock. Its abundance near Magnesia in Asia Minor
led the Greeks to call it " magnetite " or
' magnetic " iron ore.
t^i
Let us take a piece of magnetite (Fe804) and show
that it picks up pieces of iron (Fig. 195), but does not
pick up copper or zinc. We may magnetize a knitting
needle by stroking it with a piece of magnetite.
This kind of iron ore occurs in many places
in this country as well as in Norway and
Fig. 196. — Lode- Sweden. When a steel bar is rubbed with
stone attracts such a natural magnet, the steel itself becomes .
^^^^' magnetic and is then called an artificial mag-
net. In a later chapter we shall learn how to make magnets
by using an electric current.
233. Magnetic poles. It was a good many years before
any one in Europe noticed that the magnetic property of a
lodestone was concentrated more or less definitely in two or
more spots, and that if a somewhat elongated lodestone with
only two of these spots, and those near its ends, is hung by
a thread, it will set itself with one spot toward the north
and the other toward the south. We now use magnetized
238
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MAGNETISM 239
needles instead of lodestones, and call such an arrangement
a comiMss, and we all know how valuable it is to mariners
and explorers. Probably the Chinese had compasses many
years before Europeans reinvented them.
The two spots which point one to the north and one to
the south are called the poles of the magnet ; one is called
the north-seeking pole (^N) and the other the south-seeking
pole (aS').
234. Magnetic repulsion. It was many centuries after
people had known that magnets would at-
tract things before they learned that mag-
nets sometimes repel things.
If we bring the north-seeking or iV-pole of a
magnet near the iNT-pole of a suspended magnet, the
poles repel each other (Fig. 196). If we bring the
two 5-poles together, they also repel each other. Fick. 196. — Magnetic
But if we bring an iV^-pole toward the 5-pole of the repulsion,
moving magnet, or an 5-pole to the iV-pole, they attract each other.
That is,
Like poles repel each other^
Unlike poles attract each other.
Experiment shows that these attractive or repulsive forces
vary inversely as the square of the distance between the
poles.
235. Declination and dip. Soon after the compass was
invented, it was noticed that it did not point true north
and south. For a long time it was supposed that this de-
viation or declination was everywhere the same, until Colum-
bus, on his way to America in 1492, discovered near the Azores
a place of no declination. Evidently an exact knowledge of
the declination at different places is of the greatest impor-
tance to mariners and surveyors, and so careful maps are
published by the different governments giving lines of equal
declination. Figure 197 shows such a map. From this map
it will be observed that in the extreme eastern section of the
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240
PBACTICAL PHY8IC8
United States the declination is as much as 20® W. This
decreases to zero at a place near Cincinnati, O., and becomes
an easterly declination amounting to 20® E. in the northwest.
Fio. 197. —Map showing declination of the compass in the United States.
It was nearly a hundred years after Columbus' time before
it was discovered that if a compass needle is
perfectly balanced so that it can swing up and
down as well as sidewise, its north-seeking pole
9 will dip down at a considerable angle (Fig.
y^ 198) . This angle increases as one goes farther
Y north, and decreases as one goes south. Along
a line near the equator there is no dip. In
the southern hemisphere the north-seeking
pole of a needle points up in the air, and re-
cently Shackleton's South Polar Expedition
Fio. 198. — Com- found a point on the great Antarctic conti-
pass needle to ^^^^ where a needle would hang vertically
show magnetic .,, .^ .i i . i j^
dip. With its north-seeking pole on top.
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MAGNETISM
241
236. The earth a magnet. An Englishman, Gilbert, in
the sixteenth century was the first to explain these curious
magnetic phenomena. He had ground a little lodestone into
the shape of a globe, and noticed that when tiny compass
needles were brought near it, they acted just
like compasses on the surface of the earth.
So he called his lodestone globe the "ter-
rella " or " little earth " (Fig. 199), and came
to believe that it gave a true representation
of the earth itself.
The earth is, then, simply a huge magnet,
much thicker in proportion to its length than fig. 199.— Gilbert's
the magnets with which we are familiar in labo- terreiia or uttie
ratories, but otherwise exactly like them. ®*'^^'
It has a north-seeking and a south-seeking pole like any other
magnet, but from the laws of attraction and repulsion we see
that, curiously enough, its south-seeking pole must be at
Peary's end, and its north-seeking pole at Amundsen's end.
These magnetic poles are not exiactly at the geographical
poles. One of them is in North America near Hudson's Bay
and the other is nearly opposite.
Since the lines of equal declination and of equal dip are
not true circles, the magnetization of the earth must be
somewhat irregular. Furthermore, the positions of its mag-
netic poles are known to be changing slowly from year to
year. Why these things are so, and, for that matter, why
the earth is magnetized at all, is not yet known.
Questions
1. Does a magnet ever have more than two poles ?
2. In what direction did Peary's compass point when he reached the
North pole ?
3. How far is the magnetic pole from the geographical North pole ?
4. How can you tell whether or not a steel rod is a permanent
magnet ?
5. Why are knives, files, and scissors sometimes found to be magnetized!
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242 PRACTICAL PHYSICS
6. Will a magnet attract a tin can ? Explain.
7. Would a magnet floating on a cork in a dish of water float toward
the north, as well as turn north and south ?
8. What advantage is there in making a magnet in the shape of a
horseshoe ?
237. The field around a magnet. Michael Faraday (1791-
1867) was the first to see that a true understanding of the
action of magnets could be had only by studying the empty
space around them, as well as the magnets themselves.
One way to do this is to lay a stiff piece of paper over a magnet and
sprinkle iron filings on it (Fig. 200). When the paper is tapped lightly
so as to shake the filings about a little, they arrange themselves in
regular lines leading from one pole to the other. This is because each
Fio. 200. — Magnetic lines of force around a bar magnet.
filing gets slightly magnetized by the influence of the original magnet,
and sets itself in the direction in which a tiny compass needle would
lie if it were at the same place. This can be verified by actually using
a small compass instead of the filings. The lines can be mapped in this
way, but it is not as quickly done.
In this way, Faraday drew what he called lines of force
around a magnet. A line of force may be defined as a line
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MAGNETISM 243
which indicates at its every point the direction in which a
north- seeking pole is urged by the attractions and repul-
sions of all the poles in the neighborhood. When lines
of force are thought of in this way, they should have little
arrowheads on them, pointing in the direction of their
journey from a north-seeking pole to a south-seeking pole.
We shall find this conception of lines of magnetic force or
magnetic flux a convenient way of remembering how a magnet
will affect other magnets in its vicinity.
238. Lines of force like elastic fibers. Faraday himself
thought of these lines of force as having a much more real
meaning than this. He thought of them as actually existing
throughout the space around every magnet, even when there
are no filings to show them. He believed that they repre-
sent a real state of strain in the ether (see section 187), in
which all material bodies are immersed. Even now we
know very little about what the ether really is. We know
simply that it is not a kind of matter, but something much
more subtle and fundamental.
At any rate, these lines of force of Faraday's aet as
if they were stretched fibers in the ether which are con-
tinually trying to contract and are thus pulling on the
poles at their ends. They also aet as if they were trying
to swell up sidewise as / \ ^
they contract^ and thus
seem to crowd each other "--, \ / ^.'- ^-., \ / /
apart. It is not easy to --.^^^"-.^ \ //V- "^-^\\ / y'
see why lines of force — -— —
have these properties, '---.^^-^.^l
but once the properties 'Z-
are assumed (as rules of ,y / \ '^^^^ — ^'^i \ ^^-l
the game), it is easy to ''' / \ "" — ''^ / \ "^''
reason out from them / \ / \
what will happen in mQ,ny „ ' ^. \, { ^ , ^ ,.^
■^■'^ *^ Fig. 201. — Lines of force between two unlike
practical cases. poles.
^■iiiiiiiyiiiiiiiiiiiiii
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244
PRACTICAL PHYSICS
"' v\'ijp!iiii|iiii«ii^
--*- —
Fig. 202.— Lines of force between two like poles.
For example, if two magnets are placed with their unlike poles to-
gether and their lines of force traced with iron filings, the result will be as
shown in figure 201. If we
\ I / N I , assume that the lines of force
'x^ ; / \^ J / tend to contract, it is easy to
^^ \ / ^^'"■'-^^ \ / / see that two unlike poles
\ \ / /\^^ -. '\\ / y must a«rac/ each other. Like.
poles, however, would show
a field of force as shown in
figure 202, and if we assume
that lines of force squeeze
against each other side wise,
and tend to separate, evi-
dently two like poles must
repel each other. This is not
an explanation of why these
things happen ; it is, however,
an easy way of seeing what will happen, and it will be useful later on.
239. Induced magnetism. If we plunge one end of a piece of
unn)agneti2ied soft iron into some iron filings, it does not attract them,
but if we bring near it a permanent magnet, as
shown in figure 203, the soft iron becomes a
magnet and attracts the filings. When the per-
manent magnet is removed, the soft iron loses its
magnetism, and drops the filings.
A piece of iron which is magnetized by
being near a magnet is said to be magnet-
ized by induction. If the pole of the mag-
net, which was brought near the iron, was
A north-seeking pole, the induced magnet
can be shown by a compass to have a
iV-pole away from the magnet and a /S'-pole
near the magnet.
Experiments show that very soft iron
quickly becomes magnetized by induction
and quickly loses its magnetism when re-
moved from the field. Hardened steel, however, is magnet-
ized with difficulty, but retains its magnetism well. For
Fig. 203. — A magnet
by induction.
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MAGNETISM 245
this reason the magnets used in telephones and magnetos are
made of hardened steel.
240. Permeability. Although a magnet will act through
a vacuum or through glass or wood, yet the magnetic flux
seems to prefer soft iron to any other medium.
We can show this by the following experiment. We will take a
horseshoe magnet and lay across its poles a sheet of stiff paper, and then
bring up a mass of iron filings under the paper. The iron filings will
cling under the poles as shown in figure 204. If we slip a plate of glass
between the paper and the poles at ^^, most of
the filings still stick, but when we substitute an
iron plate for the glass, most of the filings drop
off immediately. This shows that an iron plate
screens the region beyond from the magnetic
action.
AZZZZZZZZZZZZZZZZA
Lord Kelvin has called the ease with g^:5 ' ^^ ?fe
which lines of force may be established Fio. 204. — iron is more
in any medium as compared with a pernieabie than glass,
vacuum, the permeability of the medium. Thus iron has a
permeability several hundred times greater than air. When
a watch is brought near a powerful magnet, its balance
wheel is often magnetized. This disturbs its working. To
protect it from such magnetic disturbances a good watch is
often inclosed in a soft iron case.
241. Theory of magnetism. Our present theory of magnet-
ism was suggested by the following experiment.
Let us harden a knitting needle or a piece of watch spring by first
heating it red hot, and then plunging it into cold water. Then let us
magnetize it and mark the i\r-pole. If we now break it near the middle
S N
t ■■■■■■■...■■.■■■..■n.....p...M,,,,niii.iinmiiii««iiiiiiniiiiimiii»imt
s ^^ N s jr s_^ S N
Fio. 205. — A broken magnet shows poles at the break.
where it does not show any magnetism, we shall find, by bringing the
broken ends near a compass needle, that we have an iV-pole and an
S-pole as indicated in figure 205. If we repeat the process, we shall
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246 PRACTICAL PHT8IC8
find that each time the magnet is broken, new poles are formed at
the break.
A magnet can be broken into a great number of little
magnets. A glass tube full of iron filings can be magnetized,
but when shaken, it loses its magnetism. Any magnet
loses a part or all of its power if it is heated red hot, jarred,
hammered, or twisted.
All these facts point to a molecular theory of magnetism,
which was suggested by a Frenchman, Ampere, and elaborated
by a German, Weber, and an Englishman, Ewing. Every
molecule of a bar of iron is supposed to be itself a tiny
permanent magnet — why, no one yet knows. Ordinarily,
these molecular magnets-
are turned helter-skelter
throughout the bar (Fig.
206), and have no cumu-
FiG.206.-Unmagnetizedbar. lative effect that can be
noticed outside the bar. When the bar is magnetized, how-
ever, they get lined up more or less parallel (Fig. 207),
like soldiers, all facing the same way. Near the middle of
the bar the front ends of one row are neutralized by the
back ends of the row in front; but at the ends of the bar a
lot of unneutralized poles
caoiaiaiCBaiDiciDiaiaiaiCBiaaiDicB
caiaiCBDiCBDmoicacaaiaioiaicaoiai
noicaciaiDicaDicacBaiDiCBiaaiCBca
EBOicBiaaiaiDiciaiaitaaiaiaioiaiGB
Fig. 207. — Magnetized bar.
are exposed, north-seeking
at one end and south-seek-
ing at the other. These
free poles make up the ac-
tive spots which we have called the poles of the magnet.
On this theory it is easy to see that when a magnet is
broken in two without disturbing the alignment of the
molecular magnets, the new poles which appear at the break
are simply collections of molecular poles that have been
there all the time, but are now for the first time in an
independent, recognizable position.
It will also be evident that, if this theory is true, there
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MAGNETISM 247
is a perfectly definite limit to the amount of magnetism a
given piece of iron can have. For when all the molecular
magnets are lined up in perfect order, there is nothing more
that can be done, no matter how strong the magnetizing
force may be. Such a magnet is said to be saturated.
SUMMARY OF PRINCIFL£S IN CHAPTBR Xm
Like poles repel each other.
Unlike poles attract each other.
The earth is a magnet with its << south-seeking " pole at Peary's
end.
Lines of force tend to contract and swell sidewise ; that is, there
is tension along them, and compression at right angles to them.
Questions
1. If two bar magnets are to be kept side by side in a box, how
should they be arranged ? Why ?
2. If a magnetic needle is attracted by a certain body, does that
prove that the body is a permanent magnet ?
3. What is meant by the " aging " of magnets ?
4. How must a ship's compass box be supported so as to remain
steady during the rolling of the ship ?
5. A long soft iron bar is standing upright. Why does its lower end
repel the north pole of a compass needle ?
6. Does hammering the bar while it is in the position described in
problem 5 increase or decrease the effect ? Why ?
7. Why are the hulls of most iron ships permanently magnetized?
What determines the direction in which they are magnetized ?
8. How can the compass on an iron ship be " compensated " for the
induced magnetism in the ship?
9. The Carnegie Institute has a special ship built almost without
iron. What kind of a survey of the world do you suppose it is made
for ? What is the advantage of such a ship for this purpose ?
10. How does a jeweler demagnetize a watch ?
11. What effect does the angle of dip have on the horizontal intensity
of the earth's magnetism at any point ?
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CHAPTER XIV
THE BEGINNINGS OP ELECTRICITY
Frictional electricity — conductors and insulators — positive
and negative charges — electroscope — frictional electric machine
— the lightning rod — induction — Leyden jar — electrophorus
— theories as to nature of electricity.
242. Electricity by friction. As far back as 600 B.C.,
Thales of Miletus, one of the " seven wise men," knew that
the yellow resinous substance called amber, of which pipe-
stems and jewelry are now often made, would, when rubbed,
attract bits of paper or other light objects. We now know
that many other substances, such as rubber, glass, and sul-
phur, have the same property. Any one can observe this on
a cold, dry morning after combing his hair vigorously with a
hard rubber comb. The comb will then support long chains
of bits of paper. Another way to show this is to scuff one's
feet on a carpet, or to rub a cat's back. In either case, if
the knuckle is brought near a gas fixture, tiny sparks
will pass. Since amber, in common with gold and certain
bright alloys, was called " electron," by the Greeks, these
phenomena were many years later named by Gilbert
" electric" that is, " amberous," phenomena.
243. Electric vs. magnetic attraction. These electric at-
tractions are in many ways so much like magnetic attractions
that it was not until the sixteenth century that it was clearly
seen that two very different kinds of phenomena are involved.
Magnetization can be produced only in three metals, iron,
nickel, and cobalt, and in one or two uncommon alloys, while
electrification can be produced by rubbing almost any sub-
248
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THE BEGINNINGS OF ELECTRICITY
249
stance, especially non-metals. A magnetized body always
has at least two poles where its magnetism is more or less
concentrated, and these poles are unlike^ for if one of them
attracts the north-seeking end of a compass, the other will
always repel it. A metallic body electrified by friction will
ordinarily not have its properties concentrated in spots, and
all parts of it will act very much alike in their attracting
power. Nevertheless, we shall presently see that there are
two kinds of electricity, just as there are two kinds of
magnetic poles.
244. Conductors and Insulators. Some substances will con-
duct electricity, while others will not. Thus a metal sphere
can be charged with electricity by touching it with some
electrified substance, such as a stick of sealing wax which
has been rubbed with a cat's skin, if the sphere is suspended
by a dry silk thread, but not if suspended by a wire. In the
latter case just as much electricity get^ into the sphere as in
the former, but it all runs out again through the wire. So
we distinguish between conductors, the best of which are the
metals, and non-conductors or insulators, such as dry silk, glass,
hard rubber, sulphur, porcelain, paraffin, and resin. It is to
prevent the leakage of the electricity in the conductor that
electric light, telephone, and telegraph wires are supported
on glass or porcelain knobs called " insulators."
There is no sharp line between conductors and insulators ;
most substances conduct a little, and even the good con-
ductors vary greatly in conductivity.
In the following table a few common substances are ar
ranged according to their insulating powers.
iNSlfLATOBS
Amber
Sulphur
Glass
Hard rubber
Dry air
Poor Condugtobs
Dry wood
Paper
Alcohol
Kerosene
Pure water
Good Conductors
Metals
Gas carbon
Graphite
Water solutions of
salts and acids
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260 PRACTICAL PBT8IC8
It will be noticed that the substances which can be easily
electrified by friction are all insulators. One reason for
this is that when electricity is generated at any point on
a body by rubbing, it stays there and makes its presence
known, if the body is an insulator ; but if it were a conduc-
tor, the electricity would leak away at once.
It will also be noticed that those substances which are
good conductors of electricity are also good conductors of
heat. This curious fact, long not understood, seems to be
due to the fact that both heat and electricity are carried
through metals by a swarm of tiny particles, called elec-
trons, which drift about between the much larger molecules
of metal like wind through a forest.
245. Positive and negative electricity. K we hang up in a
stirrup, suspended by a silk thread, a glass rod which has been rubbed
with silk, and then bring near one end of it
another glass rod which has also been rubbed,
they repel each other (Fig. 208). In a simi-
lar way two hard rubber rods or sticks of seal-
ing wax repel each other. But when we
bring a rubbed stick of sealing wax near a
rubbed glass rod in the stirrup, they attract
each other.
Fio. 208. — Two electrified From such experiments as these
rods repel each other. , I j« x* • i_ i_
we have come to distinguish be-
tween two states of electrification. We call one kind
"vitreous'* (glass) electricity or positive electricity, and
the other "resinous" electricity or negative electricity.
Bodies charged with the same kind of electricity repel each
other, and bodies charged with different kinds of electricity
attract each other. That is.
Like charges repel and unlike charf es attract
246. How to detect electricity. To test the electrical con-
dition of a body we use an electroscope. A simple form of
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THE BEGINNINGS OF ELECTRICITY
251
electroscope consists of a pith ball hung by a silk thread
from a glass support (Fig. 209).
If an uncharged body is brought near the pith
ball, nothing happens. If a positively charged body
is brought near the pith ball, the latter is attracted,
becomes itself positively charged, and is then repelled.
Then if a negatively charged body is brought near,
the positively charged pith ball is attracted, but when
it touches, it becomes negatively charged and flies
back. If we now bring a negatively charged body
near, the negatively charged pith ball is repelled.
If, then, we know what the nature of the charge on
the pith ball is, and find that a body repels it, we
know the body must be charged the same way. If
there is attraction, we cannot be sure whether the
body is uncharged or oppositely charged.
Fio. 209.-Pith.ball
electroscope.
A more reliable form of electroscope is the so-called " gold-
leaf " electroscope, although nowadays they are quite commonly
made of two aluminum leaves hung
from a brass rod. These are usually
mounted in some sort of a glass case,
as shown in figure 210.
When one brings near the top of the brass
rod a charged glass rod, the aluminum leaves
separate and hang like an inverted V. If the
rod is removed, the leaves come together again.
v^ 11 If, however, one actually touches the charged
! ^^^T^^ ^ i rod to the electroscope, the leaves separate and
--^--— 1 stay apart.
^ L.-------y :»:^^ J*--pH The electroscope is then said to be charged.
Jl ■ " ■ JU If ^e bring near a positively charged electro-
scope a positively charged body, the leaves
will fly farther apart ; but if the body brought
near has a negative charge, the leaves will
fall toward each other. In either case they will return to their origi-
nal charged position when the outside charged body is taken away.
So with an electroscope one can tell the electrical condition of a
body.
Fig. 210.~Thealainiiium-
leaf electroscope.
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252
PRACTICAL PHYSICS
With such an electroscope it is possible to learn much
about electrified bodies. For example, when an insulated
conductor is rubbed, it becomes charged with electricity;
so we conclude that all bodies become electrified by friction.
If we stand on an insulated stool, while we rub a glass rod,
our body becomes negatively charged ; and by rubbing seal-
ing wax with cat's fur, we become positively charged. In
general, whenever two different substances are rubbed on one
another^ one becomes positively charged with electricity^ while
at the same time the other is negatively charged.
247. Prictional electric machine. All the early forms of
electrical machines were frictional, and such machines are
still used for demonstration purposes. A circular glass
plate is mounted firmly on an axle, so that it can be turned
between two silk-covered cushions, which are pressed against
the glass by springs. The charge on the glass is drawn off
by a metal comb which is supported on a glass rod. When
the plate is rotated, it becomes positively charged and this
charges the metal comb positively;
at the same time the rubbers be-
come negatively charged and
should be connected with the
ground by a wire or chain, that
is, grounded, so that the negative
charges can escape.
248. Distribution of electricity
on a conductor. Let us place a metal
can, such as is used for heat measure-
ments, on a glass plate as shown in fig-
ure 211, and connect it with an electrical
machine by a wire. After we have
charged the can as much as possible, we
may test it at various points by means
of a little metal disk or ball mounted
on an insulating handle and known as a proof plane. If we touch it to
the outside surface of the charged can and bring it near the knob of
Fio. 211. — Charging a metal can.
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THE BEGINNINGS OF ELECTRICITY 258
a charged electroscope, and then repeat the test, touching it to the inside
surface, we find that there is a strong charge on the outside but none on
the inside.
Such experiments show that the charge is entirely on the
outer surface of a conductor and that its greatest density is at
the corners and projecting points. In fact the density of the
charge at sharp points is so great that the charge will escape
into the air easily at such points.
If we attach a tassel of tissue paper to the insulated conductor of the
electric machine and charge it, the little paper streamers repel each other
and stand out in all directions, but if a needle point is
held near them, they fall together at once.
We may fasten to a friction machine an " electric
whirl," balanced on a pin point. When the machine
is started, the whirl turns as shown in figure 212.
If a bent point is attached to the machine, and a
candle flame is held near the point, the so-called << elec-
tric wind " may blow the candle flame aside. It is not,
however, the electricity itself that blows the candle, but
the surrounding air which is in some way set in motion
by the discharge.
Such experiments show that a conductor can
be charged or discharged more easily at a sharp ^\j^ ^^,i ®°"
point than at a rounded surface.
249. Lightning and lightning rods. For a long time people
supposed that thunder and lightning were caused by the com-
bustion of some kind of gas in the clouds. But when elec-
tricity began to be studied, it occurred to some philosophers
that lightning might be an electrical phenomenon. Thus we
find Benjamin Franklin in his notebook, under the date of
November 7, 1749, making a list of the respects in which
lightning resembled electric sparks^ such as "giving light,
color of the light, crooked direction, swift motion, being con-
ducted by metals, crack or noise in exploding, rending bodies
it passes through, destroying animals, heating metals and
kindling inflammable substances, and its sulphurous smell "
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264 PRACTICAL PHT8IC8
(now known to be due to ozone). He then wondered ii
•lightning, like electricity, could be drawn ofip by points.
"Since they agree in all the particulars wherein we can
already compare them, is it not probable that they agree like-
wise in this? Let the experiment be made."
But this was not easyi Franklin thought he would require
a tower or steeple high enough to reach into the clouds
themselves, and his friends set about raising the money to
build one by. giving popular lectures on electricity all over
the country. In the meantime two Frenchmen were bold
enough to try the experiment with insulated pointed rods
less than a hundred feet high, and were successful in drawing
off sparks from the lower ends of the rods during thunder
showers. But Franklin was not satisfied, because the rods
did not reach into the thunder clouds, and might have been
electrified some other way. Suddenly in 1752 a new idea
flashed into his mind, and he set about making his famous
kite. The result is known to every one. Almost the most
wonderful part of it was that Franklin was not killed at once.
Within a year one Richman was killed while making a similar
experiment in St. Petersburg.
So Franklin invented the lightning rod to conduct elec-
tricity safely from the clouds to the earth. Nowadays in
cities where the houses are built in blocks with frameworks,
tops, and cornices of metal, the lightning rod is not much
used. But tall chimneys, church steeples, and isolated houses
are often provided with lightning rods.
It should be remembered that unless a lightning rod is
put up with considerable care, it is a menace rather than a
protection. In particular, its lower end must be well
" grounded," as by soldering to large copper plates buried in
damp soil, and no part of the rod should turn a sharp corner.
If these precautions are not observed, a lightning. rod will
often discharge into the house itself, rather than into the
ground, the electricity which it has attracted.
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the beginnings of electricity 25ft
Questions
1. Compare the behavior of a magnetic pole with the behavior of an
electrically charged body.
2. Does a freely swinging charged body take a definite direction ?
3. What becomes of the mechanical energy exerted in rubbing a glass
rod to electrify it?
4. What kind of electricity is generated by rubbing a fountain pen
on woolen cloth?
5. Why do experiments with frictional electricity work better on a
cold, dry winter day ?
6. Does one remove magnetism from a magnet by touching it with iron?
7. Faraday built a large box and lined it with tin foil. He then took
his most sensitive electroscope into the box and found that even when
the outside of the tin foil was so charged that it sent forth long sparks,
he could not observe any electrical effects inside. Explain.
8. What evidence have you that the human body is a good conductor ?
250. Charging by induction. If one brings a positively
electrified ball near an insulated conductor, such as a metal
cylinder on a glass support, and then removes it again, the
cylinder is not electrified. But if, while the electrified
body is near, one touches the cylinder with his finger or a
grounded wire for an instant, the cylinder is found to be
negatively charged after the charged body has been removed.
If one repeats this experiment using a negatively charged
ball, the metal cylinder becomes positively charged. Since
the electricity is not diminished in the ball, we must look
to the cylinder, for the electricity. Charges produced in
a conductor by virtue of its proximity to a charged body
are called induced charges.
This process of charging by induction may be explained
as follows. When the posi-
tively charged ball is brought
near the cylinder, the positive
and negative electricity in the ^'^- 2i3. - Charging by induction.
cylinder are distributed as shown in figure 213.
When one touches the cylinder, the positive electricity,
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256
PRACTICAL PHT8IC8
Fig. 214. — Bound charge.
which is repelled, finds its way to the ground through the
body, but the negative electricity remains bound (Fig. 214).
It does not flow oflf
when the conductor is
touched, but is held
by the presence of the
charged body.
This helps us to
understand the gold-leaf electroscope. When a charged
body is brought near the knob of the electroscope, the
leaves separate because they are
charged by induction with the
same kind of electricity as the
charged body (Fig. 215). If
the electroscope is charged by
contact positively and a posi- ^
tively charged body is brought /\
near, it repels more of the posi- „ « . ^.. ,
' , \ ., . , , ,^ Fig. 215. — Charging an electro-
tive electricity into the leaves scope by induction,
and so they diverge more widely.
On the other hand if a negatively charged body is brought
near, it draws some of the positive electricity up into the
knob, and the leaves come together more or less according
to the amount of the charge.
251. Condenser. In many practical applications of elec-
tricity,, it is necessary
to increase the capac-
ity of a conductor for
holding electricity.
This is done in what
is called a condenser.
A
t^-.^.^^:^^
t
To earth
W^^^^^¥^¥^
Fig. 216. — Action of a condenser.
Let us arrange a metal
plate on an insulating base
and connect the plate by
a wire to an electroscope, as shown in figure 216. If we charge the
plate Ay we see the leaves of the electroscope diverge. We will now
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THE BEQINNINOS OF ELECTRICITY 257
bring up a second metal plate B similar to plate A , but connected with
the ground. As we bring the plate B near plate A, the electroscope
leaves begin to fall together, but if we remove plate B again, the leaves
separate as before.
Let us now bring the plate B back to a position near plate A^ and
charge plate A until it shows the same deflection as before. It will be
evident that the capacity of plate A for holding electricity is much in-
creased by being close to a similar grounded plate B.
We may also show the influence of the insulating material between
the conducting plates, by introducing a pane of glass. The leaves *of
the electroscope fall nearer together, but rise again when the glass is
removed. This shows that the capacity of the condenser is increased by
the glass plate.
A combination of conducting plates separated by an insu-
lator is called a condenser. The capacity of a condenser for
holding electricity is proportional to the size of the plates
and increases as the distance between them decreases. It
also depends on the nature of the insulator, or dielectric, as it
is called. Mica and paraffin paper are much used in com-
mercial work.
252. Leyden jar. At the University of Leyden in Hol-
land, as early as 1745, they used a condenser in the form of a
wide jar or bottle (Fig. 217), coated inside
and out with tin foil. Inside the jar, and
connected at the bottom to the inside coating,
is a rod with a knob on top. If one allows a
charge of positive electricity to jump to the
knob the positive electricity on the inner lin-
ing attracts through the glass the negative elec-
tricity of the outer coating, while at the same
time the compensating positive electricity origi-
nally in the outer coating is repelled and escapes
through its support or the hand which holds
^^ de^iar^^" it. It is possible to make a great number
of sparks jump to the knob before it ceases
to receive them. Then the jar is charged. If one connects
the outer coating and the knob by a metal wire, the elec
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258
PRACTICAL PHT8IC8
A ^ B
Fio. 218. — Hydraalic analogy of a
condenser.
trical strain or pressure is released with a bright crackling
spark. If the jar is discharged through a piece of paper, the
spark makes a hole in the paper. If one makes the connec-
tion through his own body, he feels a lively sensation, known
as a shock.
253. Hydraulic analogy of a condenser. We may illustrate
a condenser by two standpipes filled to different levels with
water, as shown in figure 218.
The coatings of the condenser
correspond to the standpipes.
The pipe J., with the water
standing at a higher level, rep-
resents the positively charged
plate or coating, while the
other pipe B is the negatively
charged plate. The connect-
ing pipe at the bottom of the
tanks corresponds to the wire
connecting the coatings. When the connection is made,
the water rushes through the pipe and equalizes its levels
very qtiickly.' This ifepresents the discharge of the con-
denser.
When the valve V in the pipe is first opened, the water
rushes through so fast that it usually overdoes things, and
rises to a higher level in B than in A. Then it flows back
again and so on, oscillating back and forth until the
motion dies out because of friction in the pipe. In much
the same way, when a condenser is short-circuited, the dis-
charge of electricity goes too far and charges up th^ condenser
the other way. Then it discharges back again, and so the
electric charges oscillate very quickly back and forth until
the motion of the electricity dies out because of something
akin to friction, called the electrical resistance of the wire.
The technical way of describing this is to say that the dis«
charge of a condenser is oscillatory.
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THE BEGINNINGS OF ELEGTBICITT
259
254. Indttction machines for producing electricity. The
simplest machine for producing electricity by induction is
the electrophorus. It
consists of a hard
rubber disk and an-
other somewhat smaller
metal disk, which is
provided with an in-
sulating handle (Fig.
219).
If we rub the hard rubber
plate of an electrophorus
with cat's fur, we find it
Fig. 219. — Electrophorus.
is charged negatively. Then we place the metal disk on the plate and
touch the finger to the metal disk so as to " ground " it. When we lift
up the disk and bring it near the knuckle, or the knob of a Leyden* jar,
a spark jumps across the gap. We may charge a Leyden jar with an
electrophorus by repeating this process again and again.
When the rubber plate is electrified, it becomes negatively
charged. When the metal disk is placed upon it, a positive
charge is attracted to the lower surface of the disk next to
the plate, while the negative electricity is repelled. When
we touch the metal disk, this negative electricity escapes
through the hand to the ground. In this process the disk
becomes charged positively throughout. After the rubber
plate is once charged, any
number of charges can be
obtained from the electro-
phorus, without producing
any appreciable change in
the charge on the plate.
This is because the energy
comes from the agent who
lifts the disk.
255. Toepler-Holtz ma-
FiG. 220.— Toepler-Holtz machine. ChlnC. Among the ma-
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260 PBAGTICAL PHT8IC8
chines which make use of this principle of induction to pro-
duce electricity is the so-called Toepler-Holtz machine, shown
in figure 220. The details of construction are so many, and
the explanation of its operation is so complex, that it is left
to the special books on electricity.' If one of these machines
is in working order, many entertaining experiments can be
done with it.
256. Theories as to the nature of electricity. To explain
these electrical phenomena, du Fay, a Frenchman, assumed
that there were in all bodies two fluids, namely vitreoua
electricity and resinous electricity. When these are present
in equal quantities, they neutralize each other. If a glass
rod is rubbed by silk, the silk, which has a greater " affinity "
for the resinous fluid than the glass, absorbs some of it from
the glass, and at the same time the glass, having a greater
affinity for the vitreous fluid than the silk, absorbs some
from the silk. So each body gets an excess of its preferred
fluid and becomes charged.
Later Franklin suggested that there was only one kind
of fluid, namely, vitreous electricity, of which a certain
amount " belonged " in every body. If it had an excess,
it was what had been called vitreously charged. If it had
less than enough, it was resinously charged. This led . to
the terms " positive " and " negative " charge, which are
still in use.
Lately, we have come back to something nearer du Fay's
idea. We do not think of electricity as a kind of matter, as
the word "fluid" indicates, but we believe that there are
two kinds, a negative or resinous kind occurring in very
small lumps which we now call corpuscles or electrons, and
a positive kind of a different nature, not yet understood.
Even in the modern electron theory, however, there are some
who prefer to believe with Franklin that there is only one
kind of electricity, namely electrons, which may be present
either in excess or in defect. If this turns out to be true,
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THE BEGINNINGS OF ELECTRICITT 261
Franklin's only mistake was that he hit on the wrong kind
of electricity as positive.
It makes very little difference whether we talk and think
in terms of the one-fluid or the two-fluid theory, inasmuch
as everything we know can be expressed either way, and we
do not yet know which is right.
257. Conclusion. Practically all that people knew about
electricity up to the beginning of the nineteenth century has
been briefly outlined in this chapter in very much the order
in which it was discovered. Few discoveries were made, and
they dealt only with electricity at rest (electrostatics). Almost
the only useful electrical invention was the lightning rod,
and its usefulness has been much overestimated. The most
useful instrument which had been devised was the condenser.
Nevertheless, the people of the eighteenth century were fas-
cinated by electricity. It was the most exciting topic with
which scientific men dealt; it was lectured about and
shown off to large audiences, and was as much talked
about by everybody as radium or wireless telegraphy have
been recently. But it was merely a plaything in labora-
tories.
In the last half of the nineteenth century, as we shall see
in the following chapters, electricity suddenly leaped into a
commanding position in the arts and engineering. Probably
no more spectacular service has ever been rendered to the
welfare of mankind by what practical men like to call " pure
science." The story of this development is a most convinc-
ing answer to those who, even now, distrust "pure science"
as " impractical " and " useless."
SUMMARY OF PRINCIPLES IN CHAPTER XIV
All bodies can be electrified by friction^ becoming charged
either positively (vitreously) or negatively (resinously).
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PRACTICAL PHT8IC8
Like charges repel each other.
Unlike charges attract each other.
All conductors can be electrified by mhtctkm^ showing both
a positive and a negative charge in different places. Of these one
is bound by the inducing charge, but the other is free.
Questions
1. Why cannot a Leydenjar be appreciably charged if the jar stands
on a glass plate ?
2. If a charged Leyden jar is placed on a glass plate, why does one not
get a shock if he touches the knob ?
3. How would you arrange four Leyden jars to get increased capacity ?
4. How would you arrange four Leyden jars to get as long a spark as
possible ?
5. If an insulated metal globe is negatively charged, how can any
number of other insulated globes be positively charged ?
6. If an insulated metal globe is negatively charged, how can any
number of other insulated metal globes be negatively charged ?
7. In the experiment shown in figure 214, why must the finger be
removed before the removal of the charged body ?
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CHAPTER XV
BATTERY CURRENTS
The voltaic cell — action in a cell — hydraulic analogy— de-
fects of simple cell — commercial cells.
Magnetic field around a current, and around a coil — electro-
magnet — electric bell — telegraph.
Batteries
258. Beginnings of the electric battery. For nearly two
thousand years friction and induction were the only meth-
ods known for producing electricity. But, in 1786, an
unexpected observation of an Italian anatomist, Galvani, in
Bologna, started a series of most important discoveries and
inventions. He observed that the legs of frogs which he had
been dissecting twitched every time there was a discharge
from his electric machine. Later he found that if strips of
two different metals, such as copper and zinc, were fastened
together like an inverted V, and their free ends applied to frogs'
legs, there were the same nervous twitchings as
followed the discharge of electricity. There-
fore he concluded that he had found a new way
of producing electricity. He thought the elec-
tricity was formed at the contact of the dissimi-
lar metals. *
While investigating this question, Volta
invented a chemical method of producing elec-
tricity continuously, called an electric battery.
259. Voltaic battery. A glass tumbler, with
a strip of zinc and a strip of copper dipping into dilute sul-
phuric acid (Fig. 221), is one form of voltaic cell, and when
several cells are combined, they constitute a battery.
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PRACTICAL PHT8IC8
Cu
[JJzn
Fig. 222. — To show
charges on plates
of Yoltaic cell.
To show that the copper and zinc strips are each charged with electric-
ity, we will connect six such cells in series as shown in figure 222. To
detect the feeble charge we will put a 3-inch disk
on the top of the brass rod of the aluminum-
leaf electroscope. Then we will take another
similar disk which is provided with an insulating
handle and has a thin coating of shellac on the
bottom, and place this disk on top of the other.
This forms a condensing electroscope. If we touch
the wires leading from the zinc and copper strips of
the battery to the lower and upper disks of the con-
denser, as shown in figure 222, and then remove the
wires and lift off the upper disk, we find that the
leaves of the electroscope diverge. If we bring a
charged stick of sealing wax near the electroscope,
the leaves spread still farther apart, which shows
that the electroscope and the zinc are negatively charged.
If we repeat the experiment with the wires reversed, we can show that
the copper is positively charged.
The copper (or the carbon which often replaces it) is called
the positive electrode or -f pole, while the zinc is called the
negative electrode or — pole. The solution in the cell is
called the electrolyte. When the poles of a cell are joined
by a conductor, we have an electric path or drciiit con-
sisting of the electrodes, the electrolyte, and the metallic
conductor joining the poles. If a bell or lamp is to be oper-
ated by an electric battery, it is so connected that the elec-
tricity passes through it as a part of the circuit. When
this circuit is broken at any point by a switch, key, or push
button, so that no electricity jumps the gap, the circuit is
said to be open. When Ihe switch or key is closed so as to
make a continuous path, the circuit is said to be closed or made.
260. Action of an electric cell. We have already seen that
when a Leyden jar is discharged, or any two charged bodies are
connected by a wire, there is what we call a flow of electricity ;
that is, an electric current. By convention we say that the
electricity in the connecting wire flows from the positive to the
negative conductor. In a single electric cell we shall speak,
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BATTERY CURRENTS 265
therefore, of the electricity as flowing through the outside
circuit from the copper or carbon electrode (4-pole) to the
zmc electrode (— pole). Inside the cell the electricity must
evidently flow " uphill " through the solution or electrolyte
back to the copper electrode. We shall see presently why
it is able to flow uphill inside the cell.
To understand a little better just what is happening inside the cell,
let us dip a strip of ordinary zinc into very dilute sulphuric acid. We
shall see bubbles rising from the zinc and coming to the surface of the
acid. These bubbles are a gas called hydrogen. If we leave the zinc in the
acid, it gradually dissolves, leaving behind only a few insoluble impurities.
If we repeat the experiment, using a copper strip, we shall find no
action ; but if we put both the zinc and the copper strips into the acid
and connect them with copper wires to some instrument that indicates a
current of electricity (a galvanometer), we see that a current is produced,
and that bubbles are coming from both the copper and the zinc strips.
Next we will remove the zinc strip and rub a little mercury on it.
The mercury clings to the zinc and can be spread over its surface. Such a
union of a metal with mercury is called amalgamation. If this amalga-
mated zinc is used in the cell, no bubbles are formed on it. When the
circuit is closed, bubbles rise from the copper plate, and when the circuit
is broken or open, these bubbles stop. A galvanometer in the circuit
shows a current as before, but now the amalgamated zinc is consumed
only when the circuit is closed. The copper is not consumed by the acid
at all.
In general it can be said that the electric current depends
on the difference in the chemical action of the acid on the
two metals used as electrodes. The metal which is dissolved
or acted upon by the acid is the negative electrode; the
metal which is apparently unchanged and from which the
hydrogen bubbles rise while the circuit is closed is the posi-
tive electrode.
261. The chemistry of the cell. In chemistry we learn
that sulphuric acid is made up of two parts hydrogen, one
part sulphur, and four parts oxygen, as expressed by the
symbol HgSO^. When sulphuric acid is dissolved in water,
some of it breaks up into two parts, Hj and SO^. These
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PRACTICAL PHT8IC8
two parts, called ions, carry opposite kinds of electricity.
The Hj is positively charged and the SO^ is negatively
charged.
When zinc (Zn) is placed in the acid, a little of it dis-
solves, becoming zinc ions (Zn), which unite with the SO^
ions to form zinc sulphate (ZnSO^). The displaced hydro-
gen (Hj) goes to the copper plate, gives up its charge to the
plate, and then rises as bubbles of gas. It is important to
remember that the pontively charged part of the electroljrte
(Hg) goe% tvith the current through the cell. The electric
current will flow through the wire from the copper to the
zinc as long as the chemical action is maintained. Thus we
see that it is the energy of the chemical action which forces
the electricity to run uphill inside the cell. In this way
chemical energy is transformed into electrical energy.
In a good commercial cell the chemical action takes place
only when the cell is delivering electrical energy. The rate
at which this energy is delivered by the cell determines the
rate at which the zinc is used up ; just as the rate at which
steam energy is delivered by a boiler determines the rate of
coal consumption. Zinc i«, then^ the
fuel of the electric cell.
262. Electric currents and water
currents. Although it must not be
supposed that electricity is a material
flowing through the circuit as water
flows through a pipe, yet it will
greatly help us to form a mental pic-
ture of the situation if we compare
electric currents with water currents.
In figure 223 we have two tall open
vessels containing water. These are
connected by a pipe which contains a pump driven by the
weight Tf. The water will evidently be pumped from A to £,
Fig. 223.— Water at different
levels.
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BATTERY CURRENTS
267
Pig. 224.— Water in circn-
lation.
until the back pressure on the pump due to the higher level
of the water in B is enough to balance the weight W. This
difference in level does not depend on
the size of the vessels.
Suppose now that the vessels are
connected by a second pipe, as shown
in figure 224. Then the difference
in levels will cause the water to flow
from B to A. The water level in B
drops a little and that in A rises, so
that the difference in levels between
A and B becomes less. When the
back pressure against the wheel of
the pump is thus reduced, the weight
drops and drives the water around the circuit. This will
continue as long as the weight can move downward.
The difference in level in A and B^ in figure 223, repre-
sents the difference in the electrical condition of the two
electrodes, copper and zinc. This is called the difference of
potential between the positive and negative poles of the cell.
The pump represents the chemical action of the acid on the
zinc, which produces this difference of potential. Figure 223
is, then, analogous to the cell with its circuit open.
The cell with its circuit closed is represented by figure 224.
The tube connecting A and B represents the outside circuit
between the copper and the zinc. The circulation of the
water represents the flow of electricity. The rate at which
the water circulates depends on the difference in level which
the pump can maintain ; that is, on the power of the pump.
Similarly the rate of flow of electricity depends on the
electromotiye force which the chemical action of the acid and
zinc can maintain. Furthermore, the rate of flow of the
water depends on the friction in the connecting pipes, and
similarly, the rate of flow of the electricity depends on the
electrical friction or resistance of the circuit. Finally, just
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268
PRACTICAL PHY8IC8
as the energy needed to circulate the water comes from the
action of gravity on the weight, so the energy needed to drive
the electric current is supplied by the chemical changes which
take place at the electrodes.
263. Two defects in a simple cell. Volta's simple cell,
which has been described, was soon found to have two
defects, local action and polarization. When ordinary zinc
is used, bubbles of hydrogen are formed at the surface of the
zinc strip even before it is connected with
the copper. This means a wearing away
of the zinc to no purpose, and is called
local action. It is due to impurities, such
as iron or carbon, embedded in the zinc.
These impurities form with the zinc a
minute voltaic cell, as shown in figure 225.
The local current flows from the iron or
carbon directly to the zinc and then back
through the acid to the iron again. In
this process, the zinc is e^ten away near
the impurity, and hydrogen is set free. To
avoid this useless wasting away of the zinc,
it is necessary to use strictly pure zinc or else to amalgamate
the zinc electrode with mercury to cover up the impurities.
The second defect is the fact that, when the poles of a
simple cell are connected by a wire, the current does not
remain constant, but rapidly gets weaker. This polarization,
as it is called, is caused by the hydrogen bubbles which col-
lect on the copper strip and thus form a gaseous coating.
This layer of hydrogen is a poor conductor of electricity and
therefore weakens the current. Furthermore the hydrogen
layer has a slight battery action of its own, tending to send
a current in a direction opposite to that desired, and this
also weakens the current delivered by the cell.
Let us set up a zinc-sulphuric-acid-copper cell, connect it to a high
resistance galvanometer, and observe the deflection. If we then short
C\
"1 —
Zn
—
Carbon
so)ii
[
Pig. 226. — Local ac
tion in a cell.
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B ATTEST CURRENTS
269
circuit the poles of the cell by a short wire, which polarizes the cell
quickly, we shall observe, on removing the wire, that the deflection is
less than before. We may restore the cell by lifting the copper plate
out of the acid for a moment or by brushing off the hydrogen bubbles.
We may also show polarization in a carbon-zinc cell in a similar way,
but we can easily restore the cell by pouring into the acid a solution id
potassium dichromate, a substance rich in oxygen. This increases the
current because the hydrogen is taken up chemically by the oxydizing
agent. If we now " short-circuit " the cell, that is, connect the terminals
with a low-resistance conductor, the cell recovers quickly when the short
circuit is removed. Such a substance as the potassium dichromate is
called a depolarizer.
264. Commercial cells. There is a two-fluid cell, called
the Daniell cell, which is free from polarization. In this cell
the copper plate (Cu) stands in a solution of copper sulphate
or blue vitriol (CuSO^) and the zinc (Zn) in a solution of
zinc sulphate (ZnSO^). Both the copper sulphate and the
zinc sulphate break up into ions. When the circuit is
closed, both copper and zinc ions carry the current toward
the copper electrode. The zinc ions, however, do not reach
the copper plate, because zinc in copper sulphate replaces
copper, forming zinc sulphate. The result
is that the zinc goes into a solution form-
ing zinc sulphate, and metallic copper is
deposited on the copper electrode.
One form of this cell, much used in teleg-
raphy, is called a gravity cell (Fig. 226)
because the two liquids are separated by
gravity. The dilute solution of zinc sul-
phate is lighter and therefore floats on
the saturated solution of copper sulphate.
The copper plate in the bottom of the jar
is surrounded by crystals of copper sul-
phate to keep the solution saturated. In
the dilute zinc-sulphate solution above is a heavy piece of
zinc in the shape of a " crowfoot."
Fig. 226. — Gravity
cell.
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PRACTICAL PHT8IC8
\Zn
If the gravity cell is allowed to stand with its circuit open,
the liquids mix slowly, and copper is deposited on the zinc in
long festoons which cause local action, and sometimes grow
long enough ibo short-circuit the cell. To prevent this, the
external circuit must be kept closed. The cell is therefore
well adapted for telegraphy, where a wnall^ constant current
is needed, but is not good for ringing doorbells or other
intermittent work. In another form of Daniell cell, the
solutions are sep-
arated by a cup
of porous earthen-
ware.
For open-circuit
work, such as ring-
ing doorbells, the
sal-ammoniac cell
(Fig. 227) is used.
The electrodes are
zinc and carbon,
and the electrolyte
is a solution of sal-
ammoniac (ammonium chloride, NH^Cl). To reduce the
polarization as much as possible, the carbon electrode is made
with a large surface, and the cell often contains, as a depolar-
izer, a mixture of carbon and manganese dioxide. Since this
depolarizer is slow in its action, the cell is adapted only to
open-circuit work. It gives oflF no fumes, has very little
local action, and so, when once set up, requires very little
attention. Occasionally the water which has evaporated
must be replaced and the zinc renewed.
The type of cell now most used for small intermittent
work is the dry cell. This diflfers from the sal-ammoniac
cell just described only in that the electrolyte is in the form
of a paste instead of being a liquid. The negative electrode
is the zinc can which contains the carbon and paste
Fio. 227. — Sal-ammoniac celL
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BATTERY CURRENTS
271
(Fig. 228). The zinc is protected on the inside by several
layers of blotting paper, and the space around the carbon is
filled with a mixture of carbon, man-
ganese dioxide, and sawdust, saturated
with a solution of sal-ammoniac. The
top is sealed with wax, and the whole
cell is slipped into a pasteboard box.
The dry cell is much used for ringing
doorbells, running clocks, and operating
the spark coils used to ignite gas engines
on boats and automobiles. It requires
no attendance, but must not be left on
dosed circuit. Sometimes the life of
an exhausted dry cell can be extended slightly by punching
a hole in the top and pouring in water, but usually exhausted
cells are thrown away.
Fig. 228. — Dry cell.
Questions
1. What are the points which a good cell should possess ?
2. Why would you not use a gfravity cell for ringing a doorbell ?
3. What is the " fuel " in the dry cell ?
4. Why are the small motors for fans, sewing machines, etc., never
run by batteries if any other source of power is available ?
5. If a person touches the poles of a cell, why does he not get a
^* shock"?
6. K you touch the two wires from a dry cell to the tip of your tongue,
4o you taste anything, and if so, why?
Magnetic Effect of Electric Cueebnt
265. Oersted's discovery. In 1819 a Danish physicist,
Oersted, made a discovery which aroused the greatest int^r*
«st because it was the first evidence of a connection betwei^in
magnetism and electricity. He found that if a wire connect-
ing the poles of a voltaic cell was held over a compass needle^
the north pole of the needle was deflected toward the west
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272
PRACTICAL PHT8IC8
when the current flowed from south to north, as shown in
figure 229, while a wire placed under the compass needle
caused the north end of the needle to be
deflected toward the east.
266. Magnetic field around a current.
Inasmuch as the compass needle indi-
cates the .direction of magnetic lines of
force, it is evident from Oersted's ex-
periment that a current must set up a
magnetic field at right angles to the
To make this clear, the
Fia. 229. — Deflection of student may perform the following ex-
magnetic needle by periment.
electric current. ^
We will send a strong current down a vertical
wire which passes through a horizontal piece of cardboard. To indicate
the magnetic lines of force, we will sprinkle iron filings on the cardboard
and tap it gently
while the current is
on. The filings ar-
Wire above wire under onnAuofnv
needle needle COnUUCtor.
range themselves in
concentric rings
about the wire. By
placing a small com-
pass at various posi-
tions on the board,
we see that the di-
rection of these lines
of force is as shown
in figure 230.
Fio. 230. ~ Magnetic lines of force around a current.
A convenient rule for remembering the direction of the
magnetic flux around a straight wire carrying a current is the
so-called thumb rule.
If one gra%fp% the wire with the
right hand (Fig. 281) %o that the
thumb points in the direction of
the current^ the fingers mil point
^
M.
=§=
Fig. i23r. — Thumb rule for mag-
netic field around a wire.
in the direction of the magnetic field*
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BATTERY CUREENT8
273
If we know the direction of the magnetic field near a con
ductor, we can, by applying this rule, find the direction of the
current.
Figure 232 shows the field around the wire with the current
going in and figure 233, with the current coming out.
FiQ. 232. — Current going in, clock-
wise field.
Fio. 233. —Current coming out, anti-
clockwise field.
267. Magnetic field around a coil. If a wire carrying a cur-
rent is bent into a loop, all the lines of force enter the loop
at one face and come out at the other face. If several loops
are put together to form a coil, practically all the lines will
thread the whole coil and return to the other end outside the
coil.
(1) We may thread a loose coil
of copper wire through a board
or sheet of celluloid in such a
way that when iron filings are
evenly scattered over the smooth
surface of the board, while a
strong current is sent through
the wire, they will indicate the
lines of magnetic force (Fig.
234). By tapping the board
gently and using a small com-
pass, we can see the general di-
rection of t}v% lines of magnetic
flux. It will be noticed that
there are a few circular lines around each wire, and that these lines go
out between the loops. They are callecl the ** leakage flux " of the coil.
FiQ. 234. — Magnetic flux around a coiL
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274 PRACTICAL PHYSICS
(2) If we send a current through a close-wound coil of insulated coppei
wire, and bring it near a compass needle, we find that it behaves like a
bar magnet. If tlie current is reversed, the poles of the coil are reversed.
(3) If we put a soft iron core inside the coil when the current is on,
the iron exerts a very strong pull on bits of iron ; but when the current
is off, the iron loses this magnetism almost at once.
(4) If we use a large horseshoe electromagnet, or a model of a mag-
netic hoist, and considerable current, we may show that a tremendous
force can be exerted by an electromagnet.
An iron core in a coil of wire is so much more permeable
than air that the same current in the same coil produces
several thousand times as many lines of forces in the iron
core as it would in air alone.
268. Electromagnet. An iron core, surrounded by a coil
of wire, is called an electromagnet. It owes its great utility
not so much to the fact of its great strength, as to the fact
that, if it is made of soft iron, its magnetmn can be controlled
at will. Such an electromagnet is a magnet only when cur-
rent flows through its coil. When the current is stopped,
the iron core returns almost to its natural state. This loss
of magnetism is, however, not absolutely complete ; a very
little residual magnetism remains for a longer or shorter time.
An electromagnet is a part of nearly every electrical
machine, including the electric bell, telegraph, telephone,
dynamo, and motor..
To determine its polarity, we shall find it convenient to ex-
press the thumb rule as used for a straight wire, in another
way, as follows : —
Thumb rule for a coil.
Grasp the coil with the right hand
80 that the fingers point in the di-
rection of the cvrrent in the coil^
Fig. 235.— Rule for polarity of and the thumb wiU point to the
coil carrying current. ^^^^j ^^^^ ^f ^j^ ^^^ (pjg^ 235).
The strength of an electromagnet depends on the strength
of the current and on the number of loops or turns of wire.
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Michael Faradat. Born in London, in 1791, the son of a blacksmith.
Died in 1867. A chemist who made many wonderful discoveries in elec-
tricity and magnetism.
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Joseph Henry. Bom in Albany, N. Y., in 1799. Died in 1878. Was for
six years a schoolmaster at Albany Academy, for fourteen years a
professor at Princeton, and for the rest of his life the head of the
Smithsonian Institution in Washington. Made the first careful study of
the electromagnet, and shares with Faraday the honor of discovering
the laws of electromagnetic induction.
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BATTERY CURRENTS
275
It is the practice, in order to
make use of both poles of an elec-
tromagnet, to bend the iron core
and the coil into the shape of a
horseshoe, as shown in figure 286.
Practical electromagnets were
made in 1881 by Joseph Henry,
a famous American schoolmaster
and scientist, then teaching in the
academy at Albany, N.Y., and
by Faraday in England. Henry's
magnet was capable of supporting
fifty times its own weight, which
was considered very remarkable
at the time.
Magnetic hoists are now built
p
Fio. 236.— Electromagnet.
SO powerful that when the face of the
iron cores is brought in contact with
iron or steel castings and the current
is turned on, the magnets will lift
from 100 to 200 pounds of iron per
square inch of pole face, and yet re-
lease the load of iron the moment the
current is cut off.
Applications of the Electro-
magnet
Fig. 237. — Electric-beil
circuit.
Electric bell. An electric-bell
circuit usually includes a battery of
two or more cells, a push button, and
connecting wires, besides the bell itself
(Fig. 237). When the circuit is closed
by pushing the button P, the current
flows through the electric magnet (w)
and attracts the armature (A), As
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276 PRACTICAL PHT8IC8
the armature swings to the left, it pulls the spring (/S) away
from the screw contact (-B) and breaks the circuit. This
stops the current, and the electromagnet
releases the armature. It then springs,
back again and closes the circuit at
the screw, and the whole process is re-
peated. The swinging of the armature,
which carries a hammer, causes a series
of rapid strokes against the bell as long as
, the button is pushed. It does not mat-
ter in which direction the current flows.
The construction of the push button P is
Fig. 238.-Pu8h button, ^j^^^ ^^^^ ^^^^^.j^ ^^ g^^^,^ ggS.
270. What to do when the bell won't ring. First make sure
that the connecting wires at the bell, push button, and battery are firmly
screwed into the binding posts.
Next inspect the battery. The liquid should fill the jar within an inch
of the top. The zinc should be clean and free from crystals and should
dip into the solution, but should not touch the carbon.
If the battery consists of dry cells, you will do well to get a pocket
ammeter and try each cell. A new cell will indicate about 20 amperes.
If a cell has dropped much below 5 amperes, it is dead.
Next test the push button by removing the cover and holding a
a piece of metal across the terminal wires. If the bell rings, it shows
that, the trouble is a poor connection in the button. Brighten up the
contact points with sandpaper.
Finally look over the bell itself carefully, especially the point where the
make and break occurs. Sometimes the screw with the platinum point
gets loose or gets worn off and needs readjustment.
271. Telegraph. The word " telegraph " means an instru-
ment which "writes at a distance," for the early forms in-
vented by Samuel F. B. Morse, in 1844, were designed to
make dots and dashes on a moving strip of paper. Nowa-
days the receiving instrument, called the sounder, makes a
series of clicks separated by short or lon^ intervals of time
to represent the dots and dashes.
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BATTERY CURRENTS
271
The telegraph consists essentially of a battery, a key, and a
sounder, as shown in figure 239. Gravity cells are used in
rKey Sounder Sounder Key^
^Key Sounder
mtitch ^-*-^
-T- Station A ^ain Li\
Battery
Bunoi
LEG^i LEG
Fig. 240.— Tel^raph key.
Earth Earth-
Fig. 239. — Simple telegraph circuit.
practical work, but for experimental purposes any kind of
battery will serve.
The key (Fig. 240) is a device, something like a push
button, for making and tmiKmur vofw<i
, , . ,, . .^ rr»T_ ADJUSTING SCREWS -
breaking the circuit. ihe CONTACT^
sounder (Fig. 241) consists
of an electromagnet with a
soft iron armature which is
fastened to a brass bar. This
bar is pivoted so as to move
up and down. When a cur-
rent flows through the elec-
tromagnet, the armature is pulled down ; when the circuit
is broken, a spring pulls the
bar up again. Two set screws
above and below the bar limit
its motion and make the clicks.
As the clicks made by the bar
hitting these two set screws
are different, the ear recog-
nizes the time between these
Fig. 241. Telegraph sounder. tWO clicks aS a dot or a dash
according as the key is depressed a short or a long time.
When the telegraph came into commercial use, it was
found that the resistance of the connecting wires, called the
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278
PRACTICAL PHYSICS
line, was so great that the current was too feeble to operate
the sounder, even when many cells were connected in series.
A relay (Fig. 242) is there-
fore employed to open and
close the circuit of a local
battery which operates the
sounder. This relay contains
an electromagnet whose coil
has many turns of very small
no. m -Telegraph relay. ^^^^^^ ^^^ j^ ^^^^^ ^^ ^y^^
magnet is a light iron lever which is held away from the
electromagnet by a very delicate spring. The connections
are shown in figure 243. When the
key in the main circuit is closed, the
weak current excites the relay magnet
enough to pull the armature against a
set screw, thus closing the local circuit
which sends a strong current through
the sounder.
In ordinary telegraphy it is custom-
ary to use a single wire of galvanized
iron or hard-drawn copper, and to use
the earth as a return circuit. At each
station along the line there is a local
circuit consisting of battery and
sounder, which is closed by a relay. The relay is in anothei
circuit containing a key and the main-line battery or gen-
erator. Each key is provided with a switch so that the main
circuit is kept closed everywhere except at the station where
the operator is sending a message.
272. Other forms of telegraphs. Through the inventions
of Edison and others we are now able to send two messages
simultaneously in each direction. In other words, we can
send four messages over a single wire all at the same time.
This is called quadruplex telegraphy.
Earth "
Fig. 243. — Diagram of re
lay telegraph circuit.
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BATTERY CURRENTS 279
Submarine telegraphy began as early as 1837, but it was not
till 1866 that a really successful Atlantic cable was laid.
Such a cable contains a central conducting core of copper
wires twisted together. This is surrounded by a thick in-
sulating coating of rubber and outside of this is a protective
covering of hemp and steel wires. The copper core and the
steel sheath act like the coatings of an immense Leyden jar.
The effect of this is to make the sending of messages very
slow. The impulses received at the other end are also very
weak. It was only when an exceedingly delicate receiving
instrument had been devised by Lord Kelvin, that the first
Atlantic cable could be used at all.
SUMMARY OF PRINCIPLES IN CHAPTER XV
Current flows downhill^ from + to — » in outside circuit.
Current is pumped uphill^ from — to +, inside of celL
Energy is supplied by chemical action of acid on zinc.
Zinc is fuel of cell
Current carried through cell by charged ions (pieces of molecules).
Lines of magnetic force around a straight current are concentric
circles.
Thumb rule for straight wire: Use right hand. Thumb points
with current. Fingers curl with field.
Lines of force around a coil mostly go through inside and come
back outside.
Thumb rule for coil: Use right hand. Thumb points with field
toward A'-pole. Fingers curl with current.
Questions
1. An electromagnet is found to be too weak for the purpose intended.
How may its strength be increased ?
2. In looking at the N end of an electromagnet, in which direction
does the current go around the core, clockwise or anticlockwise ?
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280 PBACTICAL PHYSICS
3. If you find that •the iV-pole of a compass held under a north and
south trolley wire points toward the east, what is the direction of the
current in the wire?
4. In a certain factory, steel was once used by mistake instead of soft
iron to make the cores of the electromagnets for some bells. What
would be the matter with the bells?
5. What would be the effect of winding an electromagnet with bare
copper wire instead of insulated?
6. What sort of material is used to insulate copper wire which is to
be used (a) to wind electromagnets, (b) to wire electric doorbell circuits,
and (c) for electric lights ?
7. What is the difference between a relay and a sounder that makes
it possible for a weak current to work one and not the other?
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CHAPTER XVI
MEASURING ELECTRICITY
(ralyanoiiieters — the ampere — ammeters — the ohm — in-
ternal and external resistance — the volt — voltmeters.
Ohm's law for whole circuit and for part of circuit — resist-
ances in series and in parallel — cells in series and in parallel.
Specific resistance and the circular rail — effect of tempera-
ture on resistance — resistance boxes — measurement of resist-
ance by voltmeter-ammeter method, and by Wheatstone bridge.
273. Necessity for a unit of current strength. In the con-
struction, study, and use of electrical machinery, we are con-
stantly dealing with electric currents. We say a current is
strong or weak, just as we speak in a rough way of things'
being fast or slow, hot or cold. When, however, we go a
step farther and ask how %trong this current is or how weak
that current is, we are forced to have some unit of current
strength, and some means of measuring currents in terms
of it.
274. Galvanometers. — We can get an idea of the relative
strength of two currents by means of a galvanometer. There
are two kinds of galvanometers in common use, the older of
which is the moving-magnet galvanometer (Fig. 244). This
consists of a compass needle pivoted or hung at the center
of a large wooden frame on which are wound one or more
turns of wire. This coil is set facing east and west so that
the compass needle lies parallel to its plane. When a cur-
rent is sent through the wire, an east and west magnetic field
is set up at the center of the coil and the compass is deflected
more or less according as the current is stronger or weaker.
281
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282
PRACTICAL PHYSICS
In the type of galvanometer just described, the coil is
large and is fastened firmly to the base, while the magnet is
Fig. 244. — Moving-magDet galvanometer and diagram of essential parts.
small and movable. In the moving-coil type (Fig. 245), the
magnet is large and is fastened firmly to the base, while the
coil is small and movable. The
magnet, iViS, is usually made in the
shape of a horseshoe so that it may
be as strong as possible. The coil is
wound on a very light rectangular
frame and hangs between the jaws
of the magnet. Usually there is
a cylinder, JJ of soft iron in the
space inside the moving frame to
still further increase the field.
The bottom of the coil is con-
nected with a binding post, 5, by
a spiral of very fine wire which
carries the current into the coil
without disturbing its freedom to
rotate ; the current leaves the coil
through the fine suspension wire, AC. The top of this wire
is twisted until the coil hangs in the plane of the poles N
Fig. 245. — Moving-coil galva-
nometer and diagram of essen-
tial parts.
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MEASURING ELECTRICITY 283
and /? when no current is passing through it. If there is a
current, the coil acts like a tiny magnet with poles pointing
to the front and rear, and tries to turn itself so that these
poles may get as near possible to the iVand /S' poles of the
magnet. The amount by which it is able to twist the sus-
pension wire measures the current.
The moving-coil type is much more convenient for ordi-
nary work, but the moving-magnet type can be made much
more sensitive, and is used when very small currents have to
be detected or measured.
275. The ampere. Having learned how to compare cur-
rents by means of a galvanometer, let us consider what the
unit is, in terms of which currents can be measured. When
we open the faucet at a sink, a current of water flows through
the pipe. The rate of this flow can be easily measured in
cubic feet (or gallons) of water per minute (or per second).
Thus we speak of water as flowing at the rate of 1 gallon per
second or 5 gallons per second. In much the same way we
speak of electricity as flowing along a wire at the rate of 1
coulomb per second or 5 coulombs per second. The coulomb
is the unit quantity of electricity, just as the gallon is the
unit quantity of water. We have to consider the rate of
flow of electricity so often that we have a special name for
the unit rate of flow, l coulomb per second. We call it an
ampere. Thus 5 amperes means 6 coulombs per second.
It is possible to define the ampere in terms of the magnetic
effect of an electric current, but, as a matter of fact, electrical
engineers have agreed to define the ampere in terms of its
chemical effect. If two silver (Ag) plates are placed in a
jar of silver nitrate solution (AgNOg), and if the + and —
terminals of a battery are connected, one to one plate and one
to the other, it will be found that the plate where the current
goes in (the anode) loses in weight because silver is dissolved,
and the plate where the current comes out (the cathode) gains
in weight because silver is deposited. By international agree-
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284
PRACTICAL PHYSICS
fnent the quantity of electricity which deposits 0.001118 gram%
of silver is one coulomb, and the current which deposits silver
at the rate of 0.001118 grams per second
is one ampere. The apparatus used in
the accurate measurement of current
by this method is shown in figure 246.
The anode is the silver disk at the left,
and the cathode is the silver (or plati-
num) cup at the bottom. The porous
cup at the right is put between the
anode and the cathode in the solution
like the cup in a Daniell cell.
276. Illustrations of the ampere. When
Fig. 246. -— Silver coulomb- * °®^ ^^ ^®^ ^ short-circuited with a short stout
meter. wire, about 20 amperes flow through the wire.
An ordinary 16 candle power carbon filament
electric lamp takes a little less than half an ampere, while the arc lamps
used for street lighting require from 6 to 10 amperes. A telegraph sounder
operates on 0.25 amperes, and a telephone receiver on less than 0.1 am-
peres, while the motor on a street car
often takes as much as 40 pr 50 amperes.
277. The ammeter. The legal
method, described above, of defin-
ing an ampere is not, of course, a
convenient method of measuring
current strength. The coulomb-
meter is used only for standardiz-
ing the ammeters which are used
in everyday life to indicate cur-
rent strength.
The commercial ammeter (ampere-
meter) is a shunted^ moving coil gal-
vanometer. The instrument (Fig.
247) contains a coil of fine insulated copper wire, wound on
a light frame, and mounted in jeweled bearings between the
Fia. 247.— Ammeter.
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MEASURING ELECTRICITY 285
poles of a strong permanent horseshoe magnet. A fixed soft
iron cylinder midway between the poles of the magnet concen-
trates the field. The moving coil rotates in the gap between
the core and the pole pieces. The coil is held in equilibrium
by two spiral springs, which serve also to carry the current
into and out from the coil. Only a small fraction, perhaps .
0.001 of the current to be measured, goes through the mov-
able coil, the major part being carried past the coil by a
metal strip called a shunt. Since the current through the
coil is a constant fraction of the whole current, the pointer
which is attached to the moving coil can be made to indicate
directly on a graduated scale the number of amperes in the
total current.
It will be seen that the resistance of an ammeter, which is
practically the resistance of the shunt, is very small, and that
the whole current passes through the instrument.
278. Electrical resistance. Although we divide substances
into two classes, conductors and non-conductors or insu-
lators, yet even the best conductors of electricity are not
perfect. This means that all conductors offer some resistance
to the flow of electricity and transform a part of the energy
which they carry into heat. We are already familiar with
the fact that a stream of water flowing through a pipe is
held back or retarded by the friction of the pipe. The
amount of this friction depends on the smoothness of the
inner surface, the length and the size of the pipe. So with
electricity, the resistance of a conductor depends : —
(1) On the material used ; iron, for example, has nearly T
times as much resistance as copper ;
(2) On the length ; a wire 10 feet long has twice as much
resistance as a wire 5 feet long ;
(3) On the size of the wire ; a wire 0.04 inches in diameter
has one fourth the resistance of a wire 0.02 inches in diameter ;
(4) On the temperature ; heating a copper wire from 0° to
100° C increases its resistance about 40 %.
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286 PRACTICAL PHYSICS
279. Legal ohm, the unit of resistance. The legal unit of
resistance, called the ohm, is the resistance at 0° C of a column
of mercury 106.3 centimeters long, with a cross section of
about 1 square millimeter (more exactly, of uniform cross
section and weighing 14.4521 grams). This legal definition
of the ohm fixes the material, length, cross section, and tem-
perature of the conductor whose resistance is taken as the
standard. Since a column of mercury is not convenient to
handle, we ordinarily use "standard coils" made of some
high-resistance alloy, such as German silver or manganin.
280. Illustrations of the ohm. About 157 feet of # 18 copper wire
(the size ordinarily used to connect electric bells), or 26 feet of iron wire
or 6 feet of manganin wire of the same size, has a resistance of 1 ohm.
The resistance of a small electric bell is about 3 ohms, of a telegraph
sounder 4 ohms, of a relay 200 ohms, of a telephone receiver 60 ohms,
and of 16 candle power incandescent lamp 220 ohms when hot.
281. Internal and external resistance. It must not be for-
gotten that there is resistance to the flow of electricity in
every part of an electric circuit. In the case of the electric-
bell circuit, there is the bell itself, the push button, the con-
necting wires, and the battery. The resistance of the
generator, whether it be a battery or a dynamo, is called
the internal resistance, and that of the rest of the circuit is the
external resistance. It is the gradual increase in the internal
resistance of a long-used dry cell which cuts down the cur-
rent it can deliver and so destroys its usefulness.
282. Electromotive force. In hydraulics we know that to
get water to flow along a pipe it is essential to have some
driving or motive force, such as that furnished by a pump.
In much the same way, to get electricity to flow along a wire
we must have an electromotive force, such as that furnished by
a battery or dynamo. The unit of electromotive force is the
volt. A volt may he defined as the electromotive force needed to
drive a current of one ampere through a resistance of one ohm.
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MEASURING ELECTBICITT 287
niustrations of volts. A common dry cell gives about 1.4
volts, and a storage cell about 2 volts. A gravity cell gives about 1.08
volts, and the so-called Weston Standard cell, used in very exact voltage
measurements, gives 1.0183 volts at 20° C. The current for lighting a
building is usually delivered at 110 or 220 volts, and street cars op-
erate on about 550 volts.
284. Distinction between volts and amperes. The intensity
of an electric current is measured in amperes, the electromotive
force driving the current is measured in volts. In a given cir-
cuit the greater the electromotive force is, the greater is the
current. We know that we must have a certain " head " of
water in order to get a given number of gallons of water to
flow through a given pipe each second ; so we must have a
certain electromotive force to make a given current of elec-
tricity flow through a given wire. With both water and
electricity we must have a motive force in order to have a
current, but we may have the motive force and yet have no
current. If the valve is closed in the water pipe or the
switch is open in the electric circuit, we might have motive
force (volts) but no current (amperes).
Comparison op Hydraulic
AND Electrical Units
Units Watbe
Elbcteicitt
Quantity Gallon
Coulomb
Current Gallon per sec.
Ampere = 1 coulomb per sec*
Motive force " Feet of head "
Volt
Resistance
Ohm
285. The voltmeter. The commercial voltmeter is simply a
hiffh-reBistanee galvanometer. When electromotive force is
applied to a galvanometer, the current it allows to pass is
proportional to the voltage, and so the scale can be gradu-
ated to read the' voltage directly. The instrument (Fig.
248) is usually a moving coil galvanometer, like an ammeter.
Indeed the same instrument is often used for both purposes.
A voltmeter does not have a shunt between its terminals.
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288
PBACTICAL PHT8IC8
^^ — \ %
f)
h
T^'
FiQ. 248.— Voltmeter.
like an ammeter, but does have a
large resistance coil inserted in se-
ries, so that only a very small cur-
rent passes through the instrument,
but all of it goes through the mov-
ing coil. In fact such a voltmeter
gives correct values only when the
current used is so small as not to
affect appreciably the voltage to be
measured.
This will be understood by considering
the water analogy shown in figure 249. It
is evident that the current in the connecting pipe AB is & good measure
of the difference in level between L and Z', only when the current in ^i^
is so small as not to change appreciably the
levels whose difference is to be measured.
To make voltmeters usable over dif-
ferent ranges we have merely. to con-
nect coils of different resistance in
series with the same galvanometer.
Since the voltmeter is an instrument
for measuring the electromotive force
between the two ends of a circuit or of
part of a circuit, it must have its ter-
minals connected to the two points; ^Q- 249. — Water analogue
that is, it must be put across the circuit, o a vo me
not in it. The proper connections for both ammeter and
voltmeter are shown in figure 250.
286. Electromotive force of a cell.
If the electromotive force of a simple cell is
observed with a voltmeter, it will be found
that the voltage of the cell is not changed
by moving the plates near together or far
apart, or by lifting them almost out of the
liquid so as to change greatly their effective
size. These changes affect the current sent by the cell through an ex-
ternal circuit by changing the interned resistance of the cell, not its voltage.
y ) no Volts
vjjfe
<?
.5 Amps.
Fio. 260. — How to connect a
Yoltmeter and ammeter.
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MEASURING ELECTRICITY 289
If a stick of carbon is used instead of a copper plate, the voltage of
the cell will be found to be greater; if, however, hydrochloric acid is
used instead of sulphuric, the voltage is less.
All this shows that the voltage of a cell depends, not on
its size, but on the materials of which it is made. A very
large storage cell with plates several square feet in area, such
as is used in power stations, gives exactly the same 2 volts
that a tiny cell in a test tube would if made of the same
materials. The large cell can drive more current through a
given circuit than a small one because its internal resistance
is so small. Of course, with constant use, the small cell
would be exhausted much more quickly.
287. Ohm's law. Let a DanieU cell be connected in series with a
considerable resistance, perhaps 100 ohms, and a galvanometer, and the
current noted. If two cells are used in series, the current will be about
twice as great. If, without changing the number of cells, we double the
external resistance, the current will be about half as great. If we halve
the external resistance, the current will be doubled.
In general, we find that the current increases as the
electromotive force increases, and that the current decreases
as the resistance in the circuit increases. A German physi-
cist. Ohm (1789-1854), was the first to state this relation
between current, electromotive force, and resistance. The
law is: The intensity of the electric current along a conductor
equals the electromotive force divided by the resistance.
Current = electromotiye force ^
resistance
In electrical units: —
Amperes = ^^.
ohms
In symbols: —
/=^
where J= Intensity of current in amperes,
JS = Electromotive force in volts,
a = Resistance in ohms.
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290 PRACTICAL PHTSICa
If we know the current and resistance and want the
electromotive force, we have
E^IR.
If we know the electromotive force and current and want
to calculate the resistance, we have
I
288. Examples using Ohm's law.
1. What is the intensity of the current sent through a resistance of
5 ohms by an electromotive force of 110 volts ?
/ = :| = 115 = 22 amperes.
R 5
2. What electromotive force is needed to send a current of 0.03
amperes through a resistance of 1000 ohms?
E = IR = 0.03 X 1000 = 30 volts.
3. Through what resistance will 110 volts send a current of 10
amperes ?
iJ = :^ = M2 = llohm8.
/ 10
Problems
1. Find the intensity of the current which an electromotive force ot
10 volts sends through a resistance (a) of 3 ohms, (b) of 40 ohms.
2. How much electromotive force is needed to send 2 amperes through
(a) 2 ohms, (b) 50 ohms?
3. What is the resistance of a circuit when the electromotive force is
110 volts and the current intensity is 2 amperes ?
4. An electric heater of 10 ohms resistance can safely carry 12
amperes. How high can the voltage run ?
5. An electromagnet draws 4 amperes from a 110- volt line. How
much would it draw from a 220-volt line ?
6. A certain dry cell has an electromotive force of 1.5 volts and will
give about 27 amperes when short-circuited. What is its internal
resistance? What is the internal resistance of the same cell when, after
much use, it will give only 9 amperes ?
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MEASURING ELECTRICITY 291
289. Application of Ohm's law to partial circuits. Not only
does Ohm's law apply to an entire circuit, the current in the
entire circuit being equal to the total electromotive force
divided by the resistance of the entire circuit, but it also
applies to any part of a circuit.
That is, the current in a certain ^— "
part of a circuit equals the volt-
age across that same part divided
by the resistance of the part.
For example, suppose the electromo-
tive force of a battery is 3 volts, the re-
sistance of the bell (Fig. 251) is 3 ohms. Battery
the resistance of the wires and button is pia. 251. — Bell circuit.
1.5 ohms, and the internal resistance of
the battery is 0.5 ohms. To find the intensity of the current, we have
J= ^ = - — -4 — -- = 0.6 amperes.
R 3 + 1.5 + 0.5 ^
The current has the same intensity throughout the circuit. To find the
voltage across the bell, we have
E = IR = 0,QxS = 1.8 volts.
To find the voltage drop within the battery, we have
E = IR = 0.6.x 0.0 = 0.3 volts.
Since the total electromotive force of the battery is 3 volts, and it
takes 0.3 volts to send the current through the battery itself, the terminal
voltage of the battery is 3 — 0.3, or 2.7 volts. Of this 1.8 volts is needed
to send the current through the bell and the remainder, 0.9 volts, is used
to send the current through the connecting wires and push button.
If a voltmeter were connected across the battery, it would read 2.7
volts, or the terminal voltage. The total electromotive force (e. m. f.) is
computed by multiplying the current in the circuit, 0.6 amperes, by the
total resistance, 3 + 1.5 + 0.5 = 5 ohms.
E = IR = 0,Q X 5 = 3.0 volts total e. m. f .
3.0 ~ 0.3 = 2.7 volts terminal voltage.
290. Terminal voltage of a cell depends on its current.
Connect a voltmeter to the terminals of a dry cell, and note the e. m. f .
Then connect a coil of very high resistance (1000 ohms) across the ter*
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292 PRACTICAL PHYSICS
minals. The terminal voltage, as indicated by the voltmeter, is very
nearly the same 'as before. But if we connect a short, thick wire
across the terminals, so as to draw a large current, we see by the volt-
meter that the terminal voltage drops instantly.
Thus we see that the voltage drop in a cell depends di-
rectly upon the current used, and that the terminal voltage
decreases when the current increases.
291. Series arrangement. Let us consider still further
the electric current in apparatus arranged in series.
A Be
A/WWW^ /yyVW AAA-
6 ohms, 3 ohms. 1.5 ohms,
2 3
. IH'
0.5 0.5 0.5
Battery
Fio. 262. — Three cells and three resistances in series.
In figure 252 we have three cells and three resistances connected in
series. By this we mean that the carbon of cell 3 is joined to the zinc
of cell 2, and the carbon of cell 2 is joined to the zinc of cell 1. The
circuit then runs from the carbon of cell 1 through the resistances A^ B,
and C in succession, back to the zinc of cell 3.
The laws governing series circuits are as follows: —
2%6 current in every part of a series circuit is the same.
The resistance of several resistances in series is the sum of the
separate resistances.
The voltage across several resistances in series is equal to the
sum of the voltages across the separate resistances.
Moreover, since the voltage is equal to the resistance times
the current ( JP = JB), and since the current (/) in every
part of a series circuit is the same, it follows that the voltage
across any part of a series circuit is proportional to the resist-
ance of that part.
For example, in figure 252, if the e. m. f. of each cell is 2 volts, the
e. m. f . of the three cells in series is 3 times 2, or 6 volts.
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MEASURING ELECTRICITY 293
K the resistance of ^ is 6 ohms, of B, 3 ohms, of C, 1.5 ohms, and of
each cell, 0.5 ohms, the total resistance is 6 + 3 + 1.5 + (3 x 0.5) = 12
ohms.
The current is ^j, or 0.5 amperes.
The voltage across -4 is 6 times 0.5, or 3 volts, across J5, 3 times 0.5,
or 1.5 volts, and across C, 1.5 times 0.5, or 0.75 volts.
The voltage " drop ** in each cell is 0.5 times 0.5, or 0.25 volts, so that
the terminal voltage of each cell is 2 — 0.25, or 1.75 volts.
292. Parallel arrangement When the several resistances
are so arranged that the current divides between them, as
shown in figure 253, part ^ ^^^
going through A^ part
through B^ and the rest
through (7, they are said — >.
to be in parallel or multiple
or shunt.
The voltage across each
separate resistance of the
three parallel resistances ^^- 2«3.-Three resistances in parallel.
is the %ame.^ For example, if the voltage across A is 12 volts,
then the voltage across B is 12 volts, and also across (7, for
each resistance lies between the same two points, X and T.
The currents, however, in each of the resistances in parallel
are not the aame^ unless the resistances are all equal. If, for
example, the resistances of -4., -B, and 0 are each 6 ohms, the
current in each is 2 amperes. But if the resistances are
unequal, the greatest current will flow through the smallest
resistance. Of course the total current passing through a
parallel arrangement of resistances is equal to the sum of the
currents in the separate conductors. Thus if the current in
-4l is 1 ampere, in B^ 2 amperes, and in (7, 3 amperes, the total
current through the combination, and through the rest of
circuit, is i + 2 + 3, or 6 amperes.
293. Calculation of resistances in parallel. If we know the
voltage and total current through a set of resistances in
parallel we have merely to apply Ohm's law to compute the
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294 PRACTICAL PHT8IC8
total resistance of the combinatiou. Thus, if the voltage
across A^ By and 0 in figure 253 is 12 volts, and the total
current is 6 amperes, the total resistance is 2 ohms.
In case we know only the separate resistances and want to
compute their combined resistance in parallel, we may well
make use of the idea of conductance. By conductance we
mean the ease with which a current flows along a wire, while
resistance represents the difficulty.
Conductance is the reciprocal of resistance ; that is,
Conductance = — r— .
resistance
The unit of conductance is the mho, which is the unit of
resistance (ohm) spelled backwards.
1 mho = -
1 ohm
Thus a wire has a conductance of 1 mho when its resistance is 1 ohm,
and a conductance of 2 mhos when the resistance is 0.5 ohms.
It can be easily shown that the conductance of a parallel
arrangement is equal to the sum of the conductances of the
separate parts.
Thus suppose three resistances, A, B, and C, are arranged in parallel
and are 12, 6, and 4 ohms respectively. Find their combined resistance.
Let R = resistance of ^, jB, and C in parallel.
Then _ = _ + - + -.
Whence R = 2 ohms.
294. Cells arranged in parallel. Not only may the separate
external resistances be arranged in parallel, but the cells or
generators themselves may be so arranged. For example, in
figure 254 we have a battery of three cells arranged in
parallel.
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MEASURING ELECTRICITY 295
The laws governing such a ease are as follows : —
The voltage of the battery %% the voltage of one cell.
The internal resistance of the battery is the resistance of one
cell divided by the number ofcells^ since three celU^ r
for example^ have three times the conductance of rAAAAAAn
one cell.
The current will be the sum of the currents
through each cell.
For example, suppose that in figure 254 the ^
HP
voltage of each cell is 2 volts, the resistance of | . ^
each cell is 0.6 ohms, and the external resist- I ^
ance iJ is 0.3 ohms, and we desire to find the Fig. 254.— Three
current through each cell. ^^^ ^ p*"^^^'
The total current /is found by Ohm's law; thus
T ^ 2 2 .
Then the current in each cell will be J of 4 amperes or
1.3 amperes.
S295. Best arrangement of cells of a battery. By means of a
lecture table voltmeter we may show that the e. m. f. of 6 cells in series is
6 times that of one cell, and that the e. m.f. of 6 cells in parallel is the
same as that of one cell.
By using an ammeter and a small external resistance, we can show
that 6 cells arranged in parallel give more current than 6 cells in series ;
but with considerable external resistance, the series arrangement fur-
nishes the greater current.
In general, to make the intensity of the current as large
as possible, when the external resistance is large, arrange the
cells in series, but when the external resistance is small, arrange
the cells in parallel.
We can easily see the reason for this if we recall from the
foregoing discussion that in a series battery the voltage and
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296 PRACTICAL PHT8W8
the internal resistance of each cell are both multiplied by the
number of cells. In the parallel arrangement of cells the
voltage is not increased, and the internal resistance of each
cell is divided by the number of cells. From Ohm's law
we have
^ B+r'
where R is the external resistance and r the internal. If iJ
is much larger than r, it does not make much difiference just
how large r is, and we should make JS as large as possible by
arranging the cells in series. But if iJ is small, r becomes
the important part of the denominator, and it pays to make
r as small as possible by arranging the cells in parallel.
In practical work the external resistance is usually large
compared with the internal resistance, so the cells of a
battery are generally arranged in series*
Problems
1. Three rerastances, ^ = 80 ohms, ^ = 60 ohms, and C = 40 ohms,
are pat in parallel and the voltage across the combination is 120 volts.
Find the current in each, the total current, and the resistance of the
combination.
2. If a battery is used to light 20 lamps arranged in parallel, and
each lamp requires 0.5 amperes, how many amperes must the battery
supply?
3. What e. m. f. will be needed to force 2 amperes through a series
circuit, containing a battery of resistance J ohm, a line of resistance 1
ohm, and a lamp of resistance 100 ohms?
4. Three lamps of 150 ohms each are joined in series. If ea)ch lamp
requires 0.5 amperes, what is the total current required ? What is the
total voltage required ?
5. If the three lamps of problem 4 were arranged in parallel, what
would be the total current and total voltage needed ?
6. Six cells, each having an e. m. f. of 2 volts and an internal resist-
ance of 0.3 ohms, form a series battery to send a current through a
resistance of 50 ohms. How strong is the current?
7. If the cells of problem 6 are arranged in parallel, what is the cur
rent strength ?
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MEASURING ELECTRICITY 297
8. Calculate the current strength sent by the six cells of problem ^
arranged in series, through an external resistance of 0.1 ohms. Also the
current when the cells are in parallel.
9. If a current of 0.25 amperes is needed in a telegraph circuit, how
many gravity cells in series will be required, if each has an e. m. f . of
1.08 volts and a resistance of 2 ohms, and if the line resistance is 500
ohms?
10. Six cells are arranged 3 in series and 2 in multiple (Fig. 255) to
send a current through an external resistance of 4 ohms. If each cell
has an e. m. f. of 1.5 volts and a resistance of 0.5 _
ohms, how intense will the current be ?
11. A galvanometer, whose resistance is 299 ohms, -r y
has a short stout wire of 1 ohm resistance connected J I
across the terminals. What fraction of the total cur-
rent goes through the galvanometer
JL 1
12. A storage battery is sending current through "^ 7* -
two wires in parallel, each having a resistance of 10
ohms. K the current through the battery is 6 am- ^'f* 255- -Six cells,
1- 1. • xi_ li. J • u • o three m series, and
peres, what is the voltage drop m each wire ? ^^^ ^ multiple.
13. A wire of 4 ohms is connected in series with
2 wires joined in parallel and having resistances of 8 and 12 ohms. Find
the total resistance.
14. A dry cell when tested with a voltmeter showed 1.5 volts, and
when tested with an ammeter whose resistance was negligible, gave 7.5
amperes. Find the internal resistance of the cell.
15. If the voltage drop in a trolley line carrying 150 amperes is 12.5
volts, what is the resistance of the line?
296. Computation of resistance. For the measurement of
voltage and of intensity of current we have direct reading
voltmeters and ammeters, but as yet we have no simple
instrument for measuring resistance directly in ohms. In
many cases, however, we can compute the resistance of a
wire, if we know its material, length, size, and temperature.
Since wires are usually round, it is inconvenient to com-
pute their area of cross section in square inches. Conse-
quently electrical engineers call a wire, which is one
thousandth of an inch in diameter, 1 mil in diameter and
its area of cross section 1 circular mil. Inasmuch as the
areas of circles vary as the squares of their diameters, the
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298 PRACTICAL PHTSICS
area of a wire expressed in circular mils is equal to the square
of its diameter expressed in mils.
For example, suppose a wire is 0.015 inches in diameter. What is its
cross section in circular mils?
0.015 inches = 15 mils ; area = (15)^ = 225 circular mils.
The resistance of a wire is usually computed by comparing
it with the resistance of a wire of the same material and of
a standard size and length. The standard usually chosen
is 1 foot long and 1 circular mil in area of cross section.
Such a piece of wire is called a mil foot of wire.
The resistance of a mil foot of wire is sometimes called
the specific resistance of the substance of which the wire is
made. For example, the specific resistance of copper is about
10.4 ohms, of aluminum 17.4 ohms, and of iron 64 ohms.
Since the resistance of a conductor varies directly as its
length and inversely as its area of cross section, we can
readily compute the resistance of a wire when its length and
diameter are given.
Suppose we wish to find the resistance of 500 feet of #18 copper wire.
Since the specific resistance of copper is 10.4, we know that the resist-
ance of 1 mil foot of copper wire is 10.4 ohms. So that of 500 feet of
copper wire 1 mil in diameter is 500 x 10.4, or 5200 ohms. But from the
wire tables given on page 304, we find that # 18 wire is 40.3 mils in diam-
eter. Therefore its cross section is (40.3)^, or 1624 circular mils. There-
fore the resistance will be x«'^t of the resistance of a wire 1 mil in
diameter, or
tA, X 5200 = 3.2 ohms.
As this computation has to be made very often in practical work, it is
convenient to put it in the form of an equation.
^ = 1'
where R — resistance in ohms,
k = specific resistance (ohms per mil foot),
I = length in feet,
d = diameter in mils.
Thus ^ = ^^;i^ofo^= 3.2 ohms.
(40.3)2
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MEASURING ELECTBICITT
299
297. Effect of temperature on resistance. If we coil about 10
feet of #30 iron wire around a piece of asbestos and send a current
through it,^we can observe with a lecture-table ammeter that, as we heat
the wire in a Bunsen flame, the intensity of the current is greatly reduced.
If we connect an incandescent lamp in series with a coil of iron wire,
as shown in figure 256, we can observe by the dimming of the lamp that
the current becomes less when the iron wire is heated.
Experiments show that the resistance of 1 mil foot of copper
wire at 20° C or 68° F is 10.4 ohms, while at 0° C it is 9.6
ohms. The resistance of a one-ohm coil of copper, correct at
0° C, increases as the temperature
rises, approximately 0.0042 ohms
for each degree. For example, a
coil which measures 10 ohms at 0°
C will at 50° C have a resistance
of 10 + (0.0042 X 50 X 10) = 12.1
ohms. By carefully measuring
the resistance of a wire when cold
and then when hot, we have an
electrical method of measuring Fig. 256.— iron wire when hot has
temperature. "^""^ v^i^t^r.^^ than when cold.
Most pure metals have nearly the same rate of increase of
resistance with rise of temperature. Most alloys of metals
not only have a much higher resistance than the pure metals
of which they are made, but are much less afifected by tem-
perature changes. For example, "manganin" is an alloy
of copper, nickel, and iron manganese, which has a specific
resistance of from 250 to 450 ohms according to the propor-
tion of the metals used, but its resistance shows scarcely any
change with temperature.
There are a few substances, such as carbon, glass, and
porcelain, which decrease in resistance when heated. For
example, the resistance of a carbon filament lamp when it is
hot is about half of the resistance of the same filament when
it is cold.
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800 PBACTICAL PHT8IC8
Problems
Find the resistance of each of the wires described in problems 1 to 6 : -^
1. One mile, # 10 copper wire, diameter 0.102 inches.
2. Fifty feet, # 16 copper wire, diameter 0.051 inches.
3. Twenty feet, # 30 copper wire, diameter 0.010 inches.
4. Two miles, # 14 iron wire, diameter 0.064 inches.
5. Two hundred feet, 4 10 iron wire, diameter 0.102 inches.
6. Five thousand feet, # 6 aluminum wire, diameter 0.162 inches.
7. Find the number of feet of # 20 iron wire needed to make a resist-
ance of 5 ohms.
8. Find the diameter of a copper conductor which has a rerastance
of 2 ohms per 1000 feet.
9. What size of copper wire must be used for a trolley wire 4 miles
long, if the line resistance must not exceed 2 ohms?
10. What is the " line drop," that is, voltage drop, in a 4-mile copper
wire carrying 100 amperes, if the wire is 0.325 inches in diameter? (Volt-
age drop E = IR.)
298. Rheostats and resistance boxes. To control an elec-
tric current, we must regulate either the voltage or the
resistance. As electricity is usually supplied to us at fixed
voltages, such as 110, 220, or 500 volts, we have to control
the intensity of the current by a variable resistance, called a
rheostat. For example, in starting a motor, for reasons which
will be discussed in Chapter XVIII, the current must not be
thrown on at full intensity at first, and so a rheostat (Fig.
257) is inserted. By moving a lever arm the resistance is
gradually cut out as the motor comes up to speed. Rheostats
are usually made of some high-resistance alloy such as German
silver, or of carbon (lamps), or sometimes of water with a
little salt dissolved in it.
It is not enough to know the resistance of a rheostat. We
must know also its carrying capacity, for the electrical energy
consumed in the rheostat is converted into heat and must be
radiated off as fast as it is produced. Otherwise the temper-
ature will rise to a dangerous point, so that the wire melts or
sets on fire things which are near it.
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MEASURING ELECTRICITY
801
A resistance box is also made of resistance coils, but since
they are used for electrical measurements which involve only
Fio. 257. — Starting rheostat.
small currents, they have very small carrying capacity. The
coils have definite resistances, such as 1, 2, 8, 6, 10, 20 ohms,
and are made of a wire which is only slightly affected by
temperature changes. The resistance box corresponds for
electrical measurements to a set of weights used in weighing.
For convenience, the coils are usually mounted in a box, as
shown in figure 258, which has an insulating hard rubber
Fio. 258. —Resistance box.
top. On this are fastened a series of brass blocks which can
be connected by brass plugs which fit between them. Inside
the box are the various coils wound on spools. The ends of
a coil are connected to adjoining blocks, so that each gap is
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802 PRACTICAL PHT8IC8
bridged inside by a coil. At each end of the series of blocks
is a terminal binding post. When all the plugs are firmly in
place, the only resistance is* that of the series of blocks and
of the plugs themselves, which is
Voltmeter usually negligible; but when a cer-
tain plug is removed, the resistance
Ammeter of that coil is introduced.
299. Measurement of resistance
by voltmeter-ammeter method. As
has been said, there is no simple
instrument for measuring a resist-
, — L>VWWVA_
Resistance
\MA
Battery ancc directly, as the voltmeter
Fig. 259.— Resistance measured measures voltage, or an ammeter
by a voltmeter and an am- current. But there are t WO way sof
meter. . i. •
measuring a resistance indirectly.
If extreme accuracy is not required, the method shown in
figure 269 is commonly used. The unknown resistance is
placed in series with an ammeter, arid the voltage across the
resistance is obtained by a voltmeter. Then, by Ohm's law,
It is essential that the resistance of the voltmeter be so high
that practically no current goes through it. This method
also requires that both ammeter and voltmeter be accurately
calibrated ; that is, compared with standard instruments and
the errors noted.
300. Measurement of resistance by Wheatstone bridge. A
more accurate method of measuring resistance is the Wheat-
stone bridge, which is a machine for balancing resistances. It
consists essentially of a loop of four resistances, R^ JST, m,
and w, arranged as in figure 260. When the key (^) is
closed, the current from the cell flows into the loop at A^
and there divides so that part (J^) goes through AO and
part (J^) through AD. A sensitive galvanometer is con-
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MEASURING ELECTRICITY
80&
nected between (7 and D.
Then the resistances M^
m, and n are so adjusted
that no current flows
through the galvanom-
eter, which means that
all of I^ has to go on
through CB and all of i^
through DB^ and also that
O and D are "equipo-
tential " points. When
this adjustment has been
made, the voltage drop
across -4(7 is I^B^ and
the voltage drop across
AD is l^m. But since
C and D are at the same
potential, these voltage drops are equal, and
I^R^L^m. (1)
For similar reasons
I,X=L,n. (2)
Dividing equation (1) by equation (2), we have
X n
From this fundamental equation of the Wheatstone bridge,
if we know i2, w, and w, we can compute X.
In one form of this apparatus the resistance ADB consists
of a wire of uniform cross section one meter long. Since
the resistances m and n are then directly proportional to the
distances AD and i>JB, the equation becomes
Fig. 260. ~ Wheatstone bridge to balance re-
sistances.
X
. Distance AD
Distance DB^
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804
PRACTICAL PHT8IC8
Wire Tables
American or Brown and Sharp (B. and S.) Gkiuge
Cabbyivg Ca-
Gauoz
DiAMSTBR IN
ArKA. IK GlKOXTLAR
DlAMBTBR IN
PACmr, RuBBZR
Mils
Mils
MiLLIMBTSBS
Insulation,
Ampbrbs
0000
460.
211,600.
11.68
210.
000
410.
167,800.
10.40
177.
00
365.
138,100.
9.27
150.
0
325.
105,500.
8.25
127.
1
289.
83,690.
7.35
107.
2
258.
66,370.
6.54
90.
8
229.
52,630.
5.83
76.
4
204.
41,740.
5.19
65.
6
181.9
33,100.
4.62
54.
6
162.0
26,250.
4.12
46.
7
144.3
20,820.
3.67
8
128.5
16,510.
3.26
33.
9
114.4
13,090.
2.91
10
101.9
10,380.
2.59
24.
11
90.7
8,234.
2.31
12
80.8
6,630.
2.05
17.
13
72.0
5,178.
1.83
14
64.1
4,107.
1.63
12.
15
57.1
3,267.
1.46
16
50.8-
2,583.
1.29
6.
17
45.8
2,048.
1.15
18
40.3
1,624.
1.02
3.
19
36.4
1,288.
.90
20
32.0
1,022.
.81
21
28.5
810.
.72
22
25.3
643.
.64
23
22.6
509.
.57
24
20.1
404.
.51
26
17.90
320.
.46
26
16.94
264.
.41
27
* 14.20
202.
.36
28
12.64
159.8
.32
29
11.26
126.7
.29
30
10.02
100.5
.26
31
8.93
79.7
.23
32
7.96
63.2
.20
33
7.08
50.1
.18
34
6.30
39.7
.16
36
5.61
31.6
.14
36
6.00
25.0
.13
37
4.45
19.83
.11
88
3.96
15.72
.10
39
8.53
12.47
.09
40
3.14
9.89
.08
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MEASURING ELECTRICITY 806
where JB is a known resistance, such as a resistance box,
and the distances AD and BB are read off on a meter stick.
It may help one to remember this equation to observe that
Left resistance _ Left distance
Right resistance Right distance
For example, sappose R ia 5 ohms aud ^D is 45.5 centimeters; then
DB is 54.5 centimeters, and
5 ^45.5
X 54.5'
X = 6.05 ohms.
Problems
1. Compute the resistance of a lamp through which a voltage of 113
volts sends a current of 0.4 amperes.
2. Find the resistance of a street-car heater which takes 5 amperes
of current from a 550 volt line.
3. A wire 50 feet long has a drop of 2 volts across it. Find the drop
across 20 feet.
4. In a slide-wire Wheatstone bridge, the known resistance is 12
ohms, and the balance is obtained when AD (Fig. 260) is 42.5 centi-
meters. Compute the value of the unknown resistance.
5. In testing a Wheatstone bridge, 4 ohm and 6 ohm coils are in-
serted in the loops AC and GB. Find the position which D should
have on the meter wire ADB,
SUMMARY OF PRINCIPLES IN CHAPTER XVI
Unit of current is ampere. Corresponds to gallons per second.
Unit of resistance is ohm. Corresponds to friction in pipe.
Unit of e. m. f. is volt Corresponds to '* head."
Ammeter — low resistance — put in series — carries whole cur-
rent
Voltmeter — high resistance — put across circuit — diverts small
current.
£. M. F. of cell = total pump action in cell.
Terminal voltage = potential difference between terminals.
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806 PRACTICAL PHYSICS
Tenninal voltage less than e. m. f. by amount needed to keep
current moving through internal resistance of cell.
Ohms law: —
Current = ^'^'^'
resistance
Applies to whole circuit, or to any part of circuit
If applied to whole circuit, must take account of internal resist'
once of cell, as well as of external resistance.
For resistances in series : —
Current ever3rwhere the same.
Resistance of combination is sum of resistances of parts.
Voltage across combination is sum of voltages across parts.
For resistances in parallel : —
Total current through combination is sum of currents through
parts.
Conductance of combination is sum of conductances of parts.
Voltage across conductors same for all.
For cells in series : —
£. m. f. is sum of e. m. f.'s of parts.
Resistance is sum of resistances of parts.
Current same in all cells as in ezttrnal circuit
For cells in parallel : —
£. m. f. is same as e. m. f. of one cell.
Resistance of n cells in parallel is ~ th the resistance of any
one alone. ^
Current in each cell is - th the current in external circuit
Resistance of wire = specific resistance (mil foot) x length (feet)^
square of diameter (mils)
In slide-wire Wheatstone bridge: —
Left resistance left distance
Right resistance right distance
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MEASURING ELECTRICITY 807
Questions
1. Why are telegraph lines usually made of iron wire, while trolley
wires are made of copper ?
2. Why should the circuit of a dry cell be kept open when the ceU
is not in use ?
3. Why should a gravity cell be left on closed circuit when not
in use?
4. What would happen if an ammeter were connected across the
line? (Don't try it 1)
5. What would happen if a voltmeter were put in series in a line ?
6. Why is the moving-magnet type of galvanometer inconvenient?
7. What is the use of the shunt in an ammeter ?
. 8. A copper wire and an iron wire of the same length are found to
have the same resistance. Which is the larger?
9. Why do we get a more intense current by moving the plates of a
■cell close together?
10. What is the effect on the current strength of allowing the liquid to
-evaporate to half its volume in a sal-ammoniac cell, and why ?
11. What instruments would we need in addition to a coulombmeter
to measure the intensity of a current?
12. Why should keys be inserted in both the battery line and the
galvanometer line of a Wheatstone bridge ?
13. Why are electric bells usually arranged in parallel instead of in
series ?
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CHAPTER XVn
INDUCED CURRENTS
Induction by permanent magnets — direction of induced cur-
rent— induction by electromagnets — induction coil — jump
spark ignition — self-induction — make and break ignition —
telephone.
301. Faraday's discovery. If we had to depend on bat-
teries for all our electric currents, we should not be lighting
our streets and houses with electric lamps or riding on electri«»
cars. The cost of zinc as a fuel in the voltaic cell makes the
battery too expensive as a source of large quantities of
electricity.
It is, however, possible to turn mechanical energy directly
into electrical energy by means of a machine called a dy-
namo, in which currents are induced by moving magnets. It
was the discovery of the dynamo
that made possible the modern
age of electricity.
302. Currents induced by mag-
nets. If we connect the ends of a coil
of many turns of fine insulated wire to
a lecture-table galvanometer, and then
move the coil quickly down over one
pole of a strong horseshoe magnet, as
shown in figure 261, we observe a de-
flection. When we raise the coil again,
we observe a deflection in the opposite direction. If we lower the coil
again and hold it down, we find that the galvanometer pointer conies
back to zero. If we repeat the experiment, moving the coil down slowly
and up slowly, we find that the deflection is less than before.
808
Fia. 261. — A coil moving in a mag-
netic field generates a current.
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INDUCED CURRENTS 80»
Such experiments show that it is possible to produce
momentary electric currents without a battery. An electric
current produced by moving a coil in a magnetic field is called
an induced current. It is evident from the experiment that
the current is induced only when the wire is moving and that
the direction of the current is reversed when the motion
changes direction. Since an electric current is always made
to flow by an electromotive force, the motion of a coil in a
magnetic field must generate an induced electromotive force.
Experiments have shown that this induced electromotive
force varies directly as the speed of the moving coil.
303. Direction of induced currents. If we take the same apparatus
(Fig. 261) and move the coil down over the iV-pole of the magnet and
then down over the 5-pole, we find that the deflections are in opposite
directions in the two cases. To determine in which direction the induced
current is flowing in the coil, one may make a little voltaic cell by putting
in his mouth a copper wire and a zinc wire connected to the galvanometer.
Since we know that the copper is the positive electrode, we can compare
the direction of the galvanometer deflection caused by the cell current
with that caused by the induced current, and so determine the direction
of the latter. In this way we find that when the coil is moving down
over the iV-pole of the magnet, the induced current is in such a direction
that the lower face of the coil is an iV-pole. In a similar way we find
that when the coil is brought down over the 5-pole of the magnet, the
induced current is in such a direction that the lower face of the coil is an
<S-pole. In both cases the lower face of the coil is a pole of such a sort
as to be repelled by the pole toward which it is moving.
The direction of induced currents may be stated as
follows: An induced current has such a direction that its
magnetic action tends to resist the motion by which it is pro-
duced.
304. Currents induced b j currents. Since an electromagnet
can be made more powerful than a steel magnet, we would
expect greater induced currents when we move an electro-
magnet near a coil.
We will connect the secondary coil S in figure 262 to a galvanometei
and the primary coil P to a battery. When we move the current-carry*
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810
PRACTICAL PHT8IC8
ing primary coU P either into or out of the other coil S, a current is ir*.
duced, just as when we move a magnet in and out of a coil. The induced
current is, however, much greater. We
find also that a stronger current in the
coil P increases the strength of the
magnetic field, and so of the induced
current.
We may also increase the induced
currents by inserting an iron core in-
side the primary coiL This greatly
strengthens the magnetic field and so
increases the number of lines of force
about the coil.
K we put the primary coU with its
iron core inside the secondary coil, we
can generate an induced current by
opening and closing a switch in the primary circuit. * When the switch is
opened and closed, the deflections are in opposite directions.
Ill general we see that an induced current is set up in a
coil whenever there is a change in the number of lines of mag-
netic force passing through the coil.
Fig. 2t>2. — A movlDg electromagnet
generates a current.
Questions
1. Show how a current can be produced in a coil of wire by the motion
of a magnet.
2. Why is it necessary in the experiment just described to use a coil
of many turns ?
3. Show how a coil of wire should be rotated in the earth's magnetic
field to get the maximum induced current.
4. Show how a coil of wire can be rotated in the earth's magnetic
field so as to get no induced current.
305. Induction coil. In the induction coil (Fig. 263) the
core c is made of soft iron wires; the primary coil P consists
of a few turns of large copper wire, and the secondary coil «,
which is carefully insulated from i he primary, contains many
turns of very small silk-covered copper wire. To make and
break the primary current very rapidly, an interrupter H is
commonly made to operate on the end of the coil. This
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INDUCED CURBENTS
811
automatic make and break works exactly like the electric
bell described in section 269. When the primary circuit in
such a coil is broken, the current tends to keep on as if it
had inertia, and may jump the switch gap at A even after it
has opened slightly. This slows up the " break " and weakens
Fig. 263. — Induction coil.
the induced e.ra.f. So a condenser J is connected across
the gap. It is usually made of sheets of tin foil, insulated
by paraffin paper, arranged as shown in figure 263. This
furnishes a storage place into which the current can surge
wlien broken, and diminishes the sparking at the interrupter.
Even with a* condenser there is some sparking, and so the
contact points have to be tipped with silver or platinum and
frequently cleaned.
Coils aye generally rated according to the distance between
the terminals of the secondary across which a spark will
jump. When the coil is in operation, sparks jump across
this gap in rapid succession, provided the terminals are close
enough together. This type of coil is sometimes called the
Ruhmkorff coil and is the one in general use for lump-spark
ignition on gas engines.
306. Uses of induction coils. Jump-spark ignition is the
most important practical application of the induction
coil. Small induction coils are also used under the name of
medical or household coils. These are usually so made that the
strength of the induced current in the secondary can be
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312
PRACTICAL PHT8ICS
varied either by moving the primary coil in and out of the
secondary, or by moving in and out a brass tube which fits
around the core. In recent years very large and powerful
induction coils have been built for exciting X-ray tubes and for
setting up electric waves for wireless telegraphy. These uses
will be described in Chapter XXIV.
307. Self-induction. It is a familiar fact in mechanics that
bodies act as if disinclined to change their state, whether of
rest or motion, and we call this tendency inertia. We have
found a similar electrical phenomenon, when the primary of
an induction coil is broken. Let us examine it more closely.
If an elecfric circuit contains a coil of wire with many
turns and with a soft iron core, it opposes the building up of
a current at the start, and when the
circuit is broken, the current, once
started, tries to keep on flowing, as
shown by the spark at the gap. This
electromagnetic inertia of a circuit is
called its self-induction.
Fig.
^^^\*\*h^
264. — Self-induction of
an electromagnet.
To show self-induction, we ttiay put a small
lamp across the terminals of a large electro-
magnet. If we throw on some supply of
direct current, as from a storage battery, as
shown in figure 264, the lamp lights up at
first, but quickly dies down when the current
becomes steady. When the switch is opened,
the lamp again lights up.
In this experiment, when the circuit is closed, the self-
induction of the coil opposes the flow of current through the
electromagnet, and so the current has to go through the lamp.
When the circuit is opened, self-induction causes the current
to continue to flow, and the lamp is its only available path.
Self-induction, then^ occurs only when the current is changing.
308. Applications of self-induction. The principle of self-
induction is made use of in make-and-break ij^tion. A singU
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INDUCED CUBRENTa
81&
Fig.
265.~-Make-aiid-break spar^
coil.
coil is used, consisting of many turns of wire wound on a
soft iron core. When such a coil is employed to furnish a
spark in the cylinder of a gas
engine, the circuit is as shown
in figure 265. The terminals
are two points inside the cylin-
der of the engine, one stationary
(J.) and the other moving (B).
When A and B separate, the
self-induction of the coil causes
enough induced e.m.f. to make
a spark jump across the gap
between them.
This is the kind of coil which is used to light gas burner*
in houses by means of a battery current. If the circuit of a
large electromagnet, such as the field of a dynamo, is broken,
while one is touching the conductors on either side of the
gap, the current due to self-induction sometimes gives a
severe shock.
309. Telephone receiver. In 1876
Alexander Graham Bell astonished
the world by showing that the
sound of the human voice could be
transmitted by electricity. The
essential part of his apparatus was
what we still use and know as the
Bell receiver. The hard rubber case
contains a steel (J -shaped magnet,
which has around each pole a coil
of many turns of very fine wire
(Fig. 266). A disk of thin sheet
iron is so supported that its center
does not quite touch the ends of
the magnet. A hard rubber cap or earpiece with a hole in
the center holds the disk in place.
Fig. 266. — Bell telephone re-
ceiver.
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PRACTICAL PHYSICS
To show the operation of the telephone receiver, we will connect a
receiver, in series with a lamp, to the A.C. mains or to a magneto,
which furnishes an alternating current. We immediately hear a loud
hum. If we hold the receiver upright and stand a pencil on the dia-
phragm, it dances up and down. The alternating current, sent through
the coil, alternately opposes and strengthens the magnet, which attracts
the disk alternately more and then less, thus causing it to vibrate. This
sets the air to vibrating and produces sound.
310. The microphone. To understand how the right sort
of currents can be produced to make a telephone receiver
speak words instead of
merely humming, we will
set up an old fashioned
instrument called a mi-
crophone.
„ „ ^ A simple microphone can be
Fig. a>7.-Carbon microphone. ^^^ ^^^ ^j ^^^^^ j^^^ p^^^y^
or three pieces of electric light carbon, or out of a single carbon resting
across two old safety razor blades (Fig. 267). If such a microphone is
connected in series with a battery and telephone receiver, and a watch is
laid on its baseboard, the ticks can be heard in the telephone even if it
is some distance away. The little jars which the watch gives the base-
board shake the carbons so that the resistance at their points of contact
varies and thus changes the current. The changing current then pulls
the telephone diaphragm back and forth, and sets the surrounding air in
motion.
311. The telephone transmitter. The modern " solid back '*
telephone transmitter is simply a carefully designed microphone.
It contains a little box O (Fig. 268)
which is filled with granules of hard car-
bon. The front and the back of the box
are polished plates of carbon, and the
sides of the box are insulators. The
front carbon is attached to the center
of the diaphragm D, and moves in and
out a little when the diaphragm vi- ^ .^o r. u *
_ _- _ 1 . p 1 Fig. 268.— Carbon trans-
brates. The other plate is fastened mitter.
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INDUCED CURRENTS
815
rigidly to the solid back of the case. A current from a battery
flows through the diaphragm to the front plate, then back
through the granules to the other plate, and then out along
the telephone line to a receiver. When the diaphragm moves
back a little, it compresses the granules, their resistance de-
creases, and the current gets stronger and pulls the diaphragm
of the receiver back also. When the transmitter diaphragm
moves out, the current decreases and the receiver diaphragm
moves out also. So all the motions of the transmitter
diaphragm are reproduced by the receiver diaphragm. If
one speaks into the transmitter, causing its diaphragm to
move in a corresponding way, the receiver diaphragm moves
in the same way and produces the same kind of waves in the
surrounding air.
312. Central us. local batteries. The system we have just
described is the one in use in all large cities. The battery
is a large storage battery (or a dynamo) at the central sta-
tion and is used on all the lines that happen to be busy at
any instant.
In many country exchanges and on isolated lines anotner
system, called the local
battery system, is used «^ ^Smm^ . ■. *^. ■■ > ^Jne
because it is cheaper to
install and maintain.
Even in cities some-
thing equivalent to this
system is used in "long-
distance " work.
In this system (Fig. 269) each subscriber's telephone set
contains a few dry cells which are connected in series with
his transmitter, as already described. But the varying cur-
rent produced, instead of being sent directly out on to the
line, goes to the primary of a little induction coil and back
to the battery. The secondary of the induction coil mean-
while sends out into the line an induced current that varies
'Transmitter— „„-—,
Receiver
Fig. 269. — Local battery telephone system.
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816 PRACTICAL PHYSICS
exactly like the primary current, but is at much higher volt-
age. This, as we shall see in Chapter XVIII, makeb the
** line losses " much smaller, and so more energy gets through
to the receiver than if the original current had been trans-
mitted directly.'
This system is really better, electrically, than the central
battery system
(Fig. 270). It is
not used in large
_ cities, chiefly be-
** cause of the trouble
Fig. 270.— Telephone with central battery. . , i . ,
involved m keep-
ing so many local batteries in proper working condition.
313. Return wire necessary. Telephone circuits used to
be made like telegraph circuits, with only one wire, the
return being through the earth. But in cities this is imprac-
tical because of the noise and confusion caused by stray cur-
rents in the earth due to trolley cars ' and other electrical
disturbances. So in cities two wires are used, and they are
put close together so that no currents can be induced in them
by stray magnetic fields from other circuits (which would
cause " cross-talk "), or from lighting and power circuits.
SUMMARY OF PRINCIPLES IN CHAPTER XVH
Induced current exists only when the number of lines of force
through the circuit is changing.
Induced current has such a direction as to oppose the motion that
causes it.
Self-induction appears only when the current is changing.
The effect of self-induction is always to oppose the change of the
current.
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INDUCED CURRENTS 317
Questions
1. Why is it that the self-induction of a circuit is not apparent as
long as the current is steady ?
2. Why is the lamp described in the experiment in section 307 not
bright all the time that the switch is closed ?
3. Why is it dangerous to touch the terminals of the secondary of a
large Ruhmkorff coil ?
4. What is likely to happen to an induction coil if you short-circuit
the secondary while the coil is running?
5. Why is the induced e. m. f. in the secondary of an induction coil
so much greater at the break of the primary than at the make?
6. What furnishes the energy of an induced current?
7. Upon what three factors does the e. m. f. of an induced current
depend?
8. In a central battery telephone system, what arrangements are
made to keep the battery from sending cufrent all the time through tele-
phone lines not in use ?
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CHAPTER XVin
ELECTRIC POWER
The generator — wire cutting lines of force — dynamo rule
for direction of current — law of induced e. m. f. — revolving
loop commutator — Gramme ring — drum armature — field ex-
citation.
Electric power — how measured — the joule and watt — com-
mercial units.
Electric heating — common applications — fuses — computa-
tion.
.Electric lighting — the arc — modern forms — incandescent
lamps — metal filaments — efficiency.
The motor — side push on wire carrying current — motor rule
for direction of motion — forms of motor — back e. m. f. — start-
ing box — applications — efficiency.
Chemical effects — electrolysis — bleaching — electroplating
— electrotyping — refining metals — electrochemical equiva-
lents — storage battery.
The Genebator
314. The importance of the generator. The most useful
application of induced currents did not come until nearly
forty years after Henry and Faraday made their wonderful
discovery. Then the generator was developed, by means of
which the enormous energy of steam engines and water
wheels can be transformed into electricity. The electricity
generated in this way can be transmitted many miles, and
used in motors to turn all sorts of machinery, in lamps of
various kinds to light our streets and homes, in heaters to
warm cars and sometimes houses, to toast bread and heat
flatirons, and in furnaces to melt steel in iron mills. Thus
318
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ELECTRIC POlfER
319
B and A with a galvanometer,
stationary no current flows,
the generator has revolutionized modern industry by furnish-
ing cheap electricity.
315. Wire cutting lines of magnetic force. A simple way
to get at the fundamental idea of the generator is to fhink, as
Faraday did, of the induced
e. m. f . produced in a single
wire when it is moved through
a magnetic field. Suppose
the straight wire AB is pushed
down across the magnetic
field shown in figure 271.
An induced e. m. f . is set up
in AB^ which makes B of
higher potential than A, as Fig. 271. -induced e. m f. ia a wire
° , ^- _ ' . catting lines of force.
can be shown by connecting
As long as the wire remains
Even if the wire does move,
if it moves in a direction parallel to the lines of force, no
current flows. In short, a wire, to have an e. m. f. induced
in it, must move so as to cut lines of force.
316. Direction of induced e. m. f. We have just seen that
when the wire AB in figure 271 is moved down, the induced
current in it is from Ato B. If the wire were moved up, the
induced current would be from B to
A. Furthermore, if the field is re-
versed without changing the direction
of motion of the wire, the current re-
verses. It will be seen, then, that
the direction of the induced e. m. f.
depends upon two factors, (a) the di-
rection of the motion of the wire and
Fio. 272.-Right-hand rale (J) the direction of the flux or mag-
for induced e. m. f. 1- i- £ £ mi. i x- jj
netic lines of force. Ihe relation of
these three directions may be kept in mind by Fleming's
rule of three fingers, as shown in figure 272.
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PBACTICAL PHYSICS
Fleming's Rule. Extend the thumbs forefinger^ and center
finger of the right hand so as to form right angles with each
other. If the thumb points in the direction of the motkm of the
tffire, and the fartfinger in the direction of the magnetic ftux, the
center finger will point in the direction of the induced current.
To remember this rule, notice the corresponding initial
letters in the words "fore" and "flux," " center" and "cur-
rent."
317. Amount of induced e. m. f. If we have a large electromagnet
with flat-faced pole pieces (Fig. 273), we can demonstrate the various
laws about induced currents
in a conductor. If we move
a wire down through the gap
between the pole pieces, a mil-
livoltmeter will show the in-
duced current. If we hold the
wire at rest in the gap, we ob-
serve no current. If we move
the wire horizontally parallel
to the lines of magnetic flux,
we get no current. If we move
the wire up through the gap,
we observe a current in the opposite direction, as predicted by Fleming's
rule. If we increase the magnetic field by increasing the current through
the electromagnet, we increase the induced current. If we move the wire
more quickly through the gap, we increase the induced current. Finally,
if we bend the wire into a loop of several turns, and move the loop down
over one pole so that all the wires on one side of the loop pass through
the gap, we find that the current is increased.
In this experiment we see that the induced e. m. f. is in-
creased by moving the wire faster across the magnetic field,
by making the magnetic field stronger, and by using more
turns of wire. In short, the amount of induced e, mf de-
pends on three factors : (1) the speed; (2) the magnetic field ;
and (3) the number of turns.
Experiments show that
Induced e. m. f . varies as speed x flux x turns.
Fio. 273. — Electromagnet for demonstrating
indaced e. m.f.
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ELECTRIC POWER
321
318. Commercial generators. A machine for converting
mechanical energy into electrical energy is called a dynamo
or generator. Its essential parts are two, (1) the magnetic field,
which is produced by permanent magnets, as in the magneto,
or by electromagnets, as in larger generators, and (2) a
moving coil of copper wire, called the armature, wound on a
revolving iron ring or drum. The armature wires corre-
spond to the moving wires in the experiments above.
319. Current in a revolving loop of wire. If we rotate a rectan-
gular coil between the poles of a large horseshoe magnet, or better, of an
electromagnet, we can detect an electric current in the revolving coil by
connecting it with flexible leads to a galvanometer. As we turn the
coil, the current is reversed every half revolution.
It will help us to understand just what is happening in the
revolving coil if we
first consider what
would happen in a
single loop of wire
which is rotated in
a magnetic field, as
shown in figure 274.
If we start with the
plane of the loop ver-
tical and turn the
handle in a clockwise direction, the wire BC moves dovm
during the first half turn, and so, by Fleming's rule, we
should expect the induced e. m. f. to tend to send the
current from C to B. At the same time the wire AD is
moving up^ and the current will tend to flow from A to D.
The result is that during the first half turn the current
goes around the loop in the direction AD OB. During
the second half turn the current is reversed and goes around
in the direction ABCD.
To show that this really does happen in the loop, we can
cut the wire and connect the ends to slip rings x and «/, as
Fig. 274.
- Single loop of wire turning in a mag-
netic field.
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PRACTICAL PHYSICS
shown in figure 275. The brushes 5' and -B", which rest
on the rings, are connected to a galvanometer. In this
way it can be shown that there
is generated in the coil an
alternating current which reverses
its direction twice in every rev-
olution. Moreover, it is pos-
sible to show that the induced
Fig. 275.— Single loop connected to e.m.f. starting at ZCrO gOes up
to a maximum and then back
to zero in the first half turn; then it reverses and goes to a
maximum in the opposite direction and finally back to zero.
The induced e. m. f. reaches its maximum when the coil is
horizontal, because in this position the wires AD and BO
are cutting lines of
force most rapidly.
This is illustrated
by the curve
shown in figure §'"^"
276. ^~^
Machines which
are built to deliver
alternating cur-
rents are called alternators or A. C. generators.
320. Commutator. To get a direct current, that is, one which
flows always in the same direction, we have to use a
commutator. To under-
stand how this works, let
us study a very simple
case. If the ends of the
loop in section 319 are
connected to a split ring,
as shown in figure 277,
g^ .g_- we may set the brushes
FiG.277.-Split.ringcommutotor. ^+ and B- on opposite
POSfTION Of LOOP <N D^GintES
Fig. 276. — Curve to show relation of Induced e.m. f .
to position of loop.
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ELECTRIC POWEn
323
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LOOP
IN DEGBEER
Fio. 278. ~ Pulsatiug e. m. f. delivered by loop Utted
with commutator.
sides of the ring, so that each brush will connect first with one
end of the loop and then with the other. By properly adjust-
ing the brushes, so that they shift sections on the commutator
just when the current reverses in the loop, that is, when the
loop is in a vertical position, we may get the current to
flow only out at one brush B+^ and only in at the
other brush -B— . The direction of the current in the ex-
t-ernal circuit is always the same, even though the current
in the loop itself
reverses twice in
every revolution.
The current de-
livered by such a
machine can be
represented by the
curve in figure
278. Although it
is always in the same direction, it is pulsating.
A machine with a commutator for delivering direct current
is called a direct-current d3riiamo or D.C. generator.
321. Generators of steady currents. The e.m.f. produced
by rotating a single loop in a magnetic field can be raised
by using many turns of wire* and by rotating the coil very
fast. Nevertheless the current will be pulsating, and this
is unsatisfactory for many purposes. To get a machine
to deliver a Bteady current, a Frenchman, named Gramme,
invented in 1870 the so-called Gramme ring form of arma-
ture.
The Gramme ring armature is now very seldom used, but
it is worth studying carefully because the fundamental prin-
ciples of its action can be understood from very simple dia-
grams, whereas most armatures of the common or drum type,
although based on exactly the same principles, cannot be
represented by simple diagrams.
A rotating soft-iron ring or hollow cylinder is mounted be-
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PRACTICAL PHYSICS
Fig. 279. — Magnetic field in a Gramme ring.
tween the poles of an electromagnet, as in figure 279. The
ring serves to carry the flux across from one pole to the
other. There are
scarcely any lines of
force in the space in-
side the ring. A con-
tinuous coil of insu-
lated copper wire is
wound on the ring,
threading through the
hole every turn. When
the ring rotates, as in figure 280, the wires on the outside are
cutting lines of force, but those inside are not. Furthermore,
according to the right-
hand rule, the outside
wires on the right-hand
side are moving in such
a direction that the in-
duced current tends to
flow towards us. The
wires lying on the other
side of the ring are mov-
ing so as to induce a cur- Fig. 280.— Gramme ring rotating in a mag-
rent away from us. If netic field,
there were no outside connections, these two opposing e. m. f.'s
r < 1 would just balance, and
V.7
j^CAV
fa)
V^
Fig. 281.
no current would flow.
This would be like ar-
ranging a lot of cells in
series with an equal
number turned so that
they are opposed to the
first group [Fig. 281
(a)] ; obviously no cur-
Batteries (a) without, and (6) with •„, .„^„i j n^„.
an external circuit.
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ELECTRIC POWEM
326
But if we imagine the copper wires on the outer surface
of the ring to be scraped bare, and if two metal or carbon
blocks or brushes at the top and bottom rub on the wires as
they pass, a current could be led out of the armature at one
brush, and, after passing through an external resistance, such
as a lamp, could be led back to the armature again at the
other bf ush. In this case the armature circuit is double^ con-
sisting of its two halves in parallel. It is like adding an
external circuit to the arrangement of cells described above.
This battery analogue for a Gramme ring armature is shown
in figure 281 (6).
In the Gramme ring
arrangement there are
at every instant the same
number of active con-
ductors in each half of
the armature circuit, and
so the current delivered
by the armature is not
only direct but also
Bteady.
In practice, however, it would be difficult to make a good
contact directly with the wires of the armature, because the
wires must be carefully insulated from each other and from
the iron core, and so the various turns
of wire, or groups of turns, have branch
wires which lead off to the commutator
segments, as in figure 282.
The commutator consists of copper
bars or segments which are arranged
around the shaft and insulated from
each other by thin plates of mica (Fig.
283). To get a satisfactorily steady
^ „„„ ^ , , current there should be many segments
Fig. 283. — Commutator . ^ ^ _ , i i
and brush. lu a commutator, SO that the brushes
Fig. 282. — King armature with commutator.
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PRACTICAL PHYSICS
Fig. 284. — Slotted armature core, drum type.
may always be connected to the armature circuit in the most
favorable way.
322. Drum armature. Since very little flux passes across
the air space in the center of a Gramme-ring armature, the
wires on the in-
ner surface of
the ring do not
cut lines of mag-
netic force and
are useless, ex-
cept to connect
the adjoining
wires on the outer surface. Furthermore, it is very incon-
venient to wind the wire on an armature of the ring form.
For these reasons, most armatures are now of the drum type.
In this form, the core is made with slots along the circum-
ference for the wires to lie in (Fig. 284). Since the active
wires in one slot are connected across the end to active wires
in another slot, there are no idle wires inside the core.
323. Multipolar generators. The machines which have
been described are called bipolar machines. For commercial
purposes, especially in large ma-
chines, it is common practice to use
four, six, eight, or even more poles.
Such machines are called multipolar.
By increasing the number of poles
we can get the commercial voltages
(110, 220, or 500 volts), at much
slower speeds than would be neces-
sary in a bipolar machine. We
have already seen that the voltage
depends on the rate at which the
wires of the armature cut the lines Fig. m- Four-pole generator.
of magnetic force. But in a four-pole machine (Fig. 285)
each wire on the armature cuts a complete set of lines of
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ELECTRIC POWER
327
force four times in each revolution instead of twice as in
a two-pole machine. For this reason the speed of a four-
pole machine is one half the speed required in a two-pole
machine for the same voltage. Furthermore, the multipolivr
machine is more economical to build because it requires
less iron to carry the magnetic flux. It will be observed
from the diagram (Fig. 285) that every other brush is
positive and is connected to the positive terminal of the
machine.
Questions
1. If a person stands facing in the direction of the magnetic flux, and
thrusts downward a wire which he holds in his two hands, in which
direction is the induced e. m. f . ?
2. What are the three factors which determine the voltage of a
dynamo V How does each affect the voltage ?
3. How many revolutions per minute (r. p. m.) would a single-coil
bipolar dynamo have to make in order that the current might have 120
alternations per second?
4. How many revolutions per minute would an eight-pole generator
have to make to have the current alternate 120 times a
second?
5. Why are carbon blocks generally used instead of
copper brushes?
324. Excitation of the field of generators.
In the magneto (Fig. 286) the magnetic field
is supplied by permanent steel magnets. In
most other generators, the magnetic field is
furnished by powerful electromagnets. Some-
times the current needed to excite these mag-
nets is supplied by some outside source, such
as a storage battery, but generally the machine
itself furnishes the exciting current. There
are three types of generators differing in the method of excit-
ing the field coils ; (1) Beries-wound^ in which the whole cur-
rent generated passes through the field coils on its way to
Fig. 286.— Mag-
neto has perma-
nent steel mag-
nets.
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PBACTICAL PHT8IC8
Fig. 287.— Series-wound
generator supplying
arc lamps.
the external circuit ; (2) shunt-wound^ in
which the field is excited by diverting a
small part of the main current, the field
coils and the external circuit being in
parallel or in shunt ; and (3) compound-
wound^ which has both a series coil and a
shunt coil.
In the series generator (Fig. 287), the
field coils are wound with a few turns of
large wire. When the current in the ex-
ternal circuit increases, the field is more
highly magnetized, and so a higher volt-
MUnC/ratit
"mi
age is available to supply the current,
This machine is used to furnish current
for arc lamps, which operate on a constant
current.
When the field is shunt-wound (Fig.
288), the coils have many turns of small
wire, for in this case it is desirable to di-
vert as little current as possible from the
main circuit, and so the resistance of the
field coils should be high. Such machines
are run at constant speed. When more
load is thrown pn the machine, that is,
when more lamps are turned on, so that
more current is needed, the terminal volt-
age drops a little* This decreases the
current in the field coils and still further
reduces the terminal voltage. A shunt ma-
chine, therefore, cannot be used when very
constant voltage is desired.
This drop in the terminal voltage of shunt
generators under heavy loads can be over-
a> oo,. r. 3 come by the use of the compound-wound ffen-
Fio. 289.— Compound- . i^, ^^^. i_. i . ^i ^
wound generator. crator (Fig. 289), wmch IS the one most
Fig. 288.— Shunt-wound
generator suppljring
incandescent lamps.
Mjunaratii
TS5
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XLECTBIC POWEB 829
commonly used. Here the yoltage is kept constant by adding
a series coil of a few tarns, which tends to raise the voltage
when the current increases, just as in a series generator. If
the coils are carefully adjusted, the voltage remains practi-
cally constant at all loads.
325. Source of energy In the dynamo. It is important to
remember that the electric generator or dynamo can not of
itself make electricity^ but can only transform mechanical en-
ergy into electrical energy. For example, if we want to light
a house with electricity, it is not enough for us to buy a
dynamo, we must get also a steam engine, or a gas engine or
a water wheel to drive the dynamo. We have already seen
that the induced current is always in such a direction as to
oppose the motion of the wire. Consequently, the greater
the current in the dynamo, the greater the power needed to
turn it. Large generators, such as are used in power sta-
tions to furnish electricity for street railways, sometimes re-
quire steam engines of 16,000 to 20,000 H. P. capacity.
Elegtbig Power
326. How electric power is measured. To measure water
power, we must know the quantity of water flowing per
minute and the ** head " of the water. Thus
Water power = quantity of water per minute x head.
Tj T, lb. per min. x ft.
^•^ 88000
To measure electric power, we must multiply the quantity
of electricity flowing per second — that is, the intensity of
the electric current — by the voltage. Thus
Electric power = intensity of current x voltage.
The watt is the unit of electric power and may be defined as
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330 PRACTICAL PHT8IC8
the power required to keep a current of one ampere flowing
under a drop or " head " of. one volt.
Watts = amperes x Tolts.
Since the watt is a very small unit of power, we commonly
use the Idlowatt (K. W.) which is 1000 watts.
^ ^ _ amperes x volts
1000
Inasmuch as mechanical power is reckoned in horse power
(H. P.), it will be convenient to know the relation of the
unit of mechanical power to the unit of electrical power.
Experiment shows that
1 horse power = 746 watts.
1 miowatt (K.W.) = 1.34 horse power (H. P.).
Since we have to compute electrical power very often, we
may find a formula convenient.
P=/E,
where P = power in watts,
J=3 current in amperes,
U= e. m. f. in volts.
For example, if a lamp draws 0.5 amperes from a 110 volt circuit, it
is using power at the rate of 0.5 times 110 or 55 watt^
Again, suppose a street-car heater has a resistance of 110 ohms. At
what rate is it consuming electricity on a 550 volt line ? The current is
m or 5 amperes, and the power is 5 times 550 or 2750 watts or 2.75 K. W.
327. Commercial units of electrical work. Power means
the rate of doing work. The total work done is equal to the
product of the rate of doing work by the time. Thus if a steam
engine is working at the rate of 15 horse power for 8 hours,
it does 8 times 15 or 120 horse-power hours of work. In a
similar way, if an electric generator is delivering electricity
at the rate of 15 kilowatts for 8 hours, it does 8 times 15 or
120 kilowatt hours of work.
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ELECTRIC POWER 331
For example, we buy electricity by the kilowatt hour. In Boston the
price is about 10 cents per kilowatt hour. K a store uses 100 lamps for
3 hours, each consuming electricity at the rate of 50 watts, it will cost
100x3x50x0.10 ^--^
iooo = ^^-^'
328. Small units of electrical work. In the laboratory we
often find it convenient to use a smaller unit of work, the
watt second or joule.
Work (joules) = current (amperes) x e. m. f. (volts) x time (seconds).
Or W^IEt,
since 1 Kilowatt-hour = 3,600,000 watt seconds or joules^
1 Horse-power hour = 1,980,000 foot pounds.
Therefore 1 joule = 0.74 foot-pounds.
Problems
1. How much electrical power (watts) is required to light a room
with 5 lamps, if each lamp draws 0.4 amperes from a 110-volt line?
2. A street railway generator is delivering current to a trolley line
at the rate of 1500 amperes and at 550 volts. At what rate (kilowatts)
is it furnishing power?
3. How many horse power will be required to drive the generator in
problem 2, if its efficiency is 90 % ?
4. A 10 kilowatt generator is working at full load. If the voltmeter
reads 115 volts, how much does the ammeter read ?
5. How many lamps, each of 120 ohms and requiring 1.1 amperes,
can be lighted by a 25 K. W. generator?
6. How much power is required by a laundry using 5 electric flat-
irons of 50 ohms each on a 110-volt line ?
7. How much will it cost at 10 cents per kilowatt hour, to run a 220-
volt motor for 10 hours, if the motor draws 25 amperes ?
8. Would it be cheaper to buy the power needed in problem 7 at 8
cents per horse-power hour ?
9. How much energy is consumed in a line whose resistance is 0.5
ohms, and which carries a current of 150 amperes for 10 hours ?
10. How many joules of energy are consumed when a 40- watt lamp
burns 10 minutes ?
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PRACTICAL PHT8IC8
Fig. 290. — Flatiron
heated by electricity,
and the resistance wire
in it shown separately.
Electric Heating
329. Heating by electricity. We are familiar with the
fact that electric cars are heated by electricity, and that an
electric light bulb gets hot, and we may
have used or seen electric flatirons (Fig.
290), electric ovens, or electric furnaces ;
but perhaps we do not realize that every
electric current, however small, gener-
ates heat. This is because heat is gen-
erated so slowly in an electric bell, tele-
graph, or telephone, that it is radiated
off without raising the temperature of
the wires appreciably. It is this heat-
ing effect which limits the output of a
generator, for if too heavy a current is
drawn from the machine, the armature and field coils get so
hot that the insulation is set on fire.
330. Fuses and circuit breakers. To protect electrical
machines from too much
heat caused by excessive cur-
rent, some sort of "electrical
safety valve " has to be in-
serted in the circuit. Fuses
are used for the small cur-
rents in house lights and
small motors, and circuit
breakers for larger currents
in power stations. The es-
sential part of a fuse is a
strip of an alloy [Fig. 291
(a)], which melts at such a
low temperature that the
melted metal can do no ^ ^^ „ , s , ^
1. rr«i_ • i! j.i_ i! Fig. 291.— Fuses: (a) wire fuse; (6) cai^
narm. ine size oi tne luse tridge fuse; (c) plug fuse.
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ELECTRIC POWEB
Pig. 292.— Circuit breaker.
is such that if by accideDt too heavy a current is sent through
the wires, the fuse melts and break^ the circuit. At the mo-
ment the fuse melts there is an arc across the gap which
might set things on fire. So the fuse
is commonly inclosed in an asbestos
tube, as in the "cartridge fuse"
[Fig. 291 (6)], or in a porcelain cup,
which screws into a socket like a
lamp, as in the "plug fuse" [Fig.
291 (<?)]. When the fuse wire melts
because of excessive current, the fuse
is said to " blow out."
A circuit breaker (Fig. 292) is
simply a large switch which is
automatically opened by an electromagnet when the cur-
rent is excessive.
331. How much heat is generated by an electric current?
The energy delivered to an electric heating coil, such as a
flatiron, or soldering iron, is, as we
have seen in section 326, JEI joules
per second, or JEIt joules in t seconds.
But since Ohm's law tells us that JE =
ZB, if there is no cell, generator,
or motor in the part of the circuit
considered, we have the alternative
statement, which is often more
convenient in discussing electric
heaters : —
Jfiaje
Energy turned into heat = I^Rt (joules).
To measure the heat generated by
lire 292. This type is used can let it raise the temperature of
for very large curreDts, and ^ known weight of water. Careful
needs only one **turn*' of • i. i. i_ i
wire on the electromagnet, experiments snow that a current of
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334 PRACTICAL PHT8IC8
one ampere flowing through a wire of one ohm resistance for
one second will generate ejaough heat to raise the tempera-
ture of one gram of water 0.24° C. That is,
H = 0.2^ PRt,
where JE[= heat in calories, .
I = current in amperes,
li = resistance in ohms,
t = time in seconds.
Problems
1. How many calories of heat are generated per hour in a 30 ohm
electric flatiron using 4 amperes ?
2. What is the cost of each calorie in problem 1, if the electricity
costs 10 cents per kilowatt hour ?
3. How much energy is turned into heat each hour by a current of
35 amperes in a wire of resistance 2 ohms ? What size rubber-covered
copper wire should be used to carry this current safely ? (See table at
end of Chapter XVI.)
4. If 88 % of the energy received by an electric lamp is converted into
heat, how many calories are developed in one hour by a 35 candle power
lamp drawing 0.9 amperes at 115 volts?
5. A 10 ohm coil of wire is used to heat 1000 grams of water from
15*^ C to 75° C in 10 minutes. How much current must be used?
6. How long will it take 5 amperes at 55 volts to raise the tempera-
ture of a kilogram of water from 20° to 100° C ?
Electric Lighting
332. The electric arc. About a hundred years ago Sir
Humphrey Davy (1778-1829), by using a battery of 2000
cells, made an electric arc between rods of charcoal. This
was merely a brilliant lecture experiment, and it was not
until sixty years later, when practical dynamos had been
built, that arc lights became commercially possible. It was
soon found that the coke which is formed in the ovens of gas
furnaces makes a more durable material for the carbon than
wood charcoal.
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ELECTRIC POWEB
336
To show the form of the electric arc we may connect a current of
50 or more volts to two carbons, in series with a suitable rheostat. The
light is so intense that the eyes must be shielded
by blue glass from the direct glare. The arc can
be projected on a screen with a convex lens. If
D. C. current is used, the crater formed on the
positive carbon and the cone on the negative car-
bon can be seen as shown in Fig. 294. The great
heat evolved is shown by the fact that iron wire
can be melted in the arc.
Fig. 294.— Positive and
negative carbons of
the arc.
Out%
F'urnaces built on the principle of the
electric arc are used to prepare artificial
graphite, carborundum, calcium carbide,
and various kinds of steel.
333. Modern arc lamps. Even coke
carbon burns away, and so automatic
lamps have been invented which feed
their carbons gradually toward each
other. Some of the early forms of these
lamps made use of clockwork to feed the carbons, but now
it is common to use a clutch which is worked by an electi*o-
magnet. One form of this mechanism consists of a "bal-
lasting" resistance B (Fig.
296), which opposes any in-
crease or decrease of current
between the carbon tips, and
of a *• regulating" coil aS, to
control the distance between
the carbon tips. When there
is no current, the plunger P
drops and releases the friction
clutch on the upper carbon (7.
When the current is on, the
plunger P is pulled up and
V on. A 1 J ji * lifts the clutch and upper
Fig. 295. — Arc lamp, and diagram of j •
automatic feed. carbon the proper distance.
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PRACTICAL PHYSICS
Recently an inclosed arc lamp (Fig. 296) has come into
general use. When the arc is surrounded by a glass globe
which is nearly air-tiglit, the available supply
of oxygen is quickly used up and the same
pair of carbons lasts 100 hours instead of
only 7 or 8 hours.
If the carbon rods are made with a core of
calcium fluoride, the vapor given off is very
luminous and gives a light of a golden
Fig. 296 — Inclosed orange color. These so-called flaming arcs
arc lamp. ^^^ extensively used on streets for advertis-
ing purposes. In this type the carbons are
long and slender, and both carbons feed
down, as shown in figure 297.
Another form of flaming arc is the mag-
netite arc. In this lamp the lower electrode
is made of magnetite or some similar sub-
stance, powdered and compressed in a sheet-
iron tube, while the upper electrode is of
solid copper which wastes away very little.
In the mercury arc or Cooper-Hewitt
lamp, use is made of the luminescence of mercury vapor.
The mercury is held in
the lower end of a glass
vacuum tube 2 to 4 feet
long (Fig. 298). Some
special device has to be
used to start the current
through the mercury
vapor; but once started,
the current flows easily
through the hot vapor,
which glows with a light
Fio. 298. -Mercury arc lamp, started by CO^^POSed of green, blue,
tilting. and yellow, but no red.
Fig. 297.— Impreg-
nated carbons of
flaming arc.
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ELECTRIC POWER 337
This gives a peculiar color to objects thus illuminated. (See
Chapter XXIII.)
334. Carbon filament lamps. In incandescent lamps, there
is a wire or filament which is heated white hot by the electric
current. The light emitted is the same as it would be if the
same wire could be heated to the same temperature in any
other way, as by an oxyhydrogen flame. In the early ex-
periments platinum was tried for the filament,
but even though its melting point is as high
as 1600^ C, it could not stand the temperatures
required. Carbon is one of the few known
substances with a higher melting point, and in
1880 Edison and others succeeded in making a
lamp with a carbon filament. Since the fila- fiq. 299.— Car-
ment would burn up at once if there were any ton filament
air present to support the combustion, it has to *™^*
be inclosed in a glass bulb (Fig. 299) in which there is a
very high vacuum.
The electricity is led into and out of the filament through
two short platinum wires, melted into the glass bulb at one
end. These platinum wires are connected by copper wires
to the brass collar and metal tip at the end of the bulb.
Such lamps are usually made for 110 or 220 volts. If a
lamp made for 110 volts is used on a 105 volt line, it will
probably last twice as long, but will only give 80% as much
light. If it is used on a 113 volt line, even though it gives
about 18% more light, it will last only half as long. • So it
is very desirable to use lamps on the voltage for which they
are intended. This means we must have good regvlation on
the electric lighting service; that is, constant voltage at all
loads.
335. Commercial rating of electric lights. To measure the
output of light from a lamp, we need some standard lamp for
comparison. As will be explained in Chapter XXI, this
standard is the so-called international candle. The ordinary
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838 PRACTICAL PHYSIC 8
incandescent light is equivalent to about 16 such standard
candles, and it said to be 16 candle power (16 c.p.). Since
lamps do not show the same brightness on all sides, it is
customary to take the average candle power in all directions
in a horizontal plane. Thus incandescent lamps are often
rated according to their mean horizontal candle power.
The injnit of electrical energy is measured in watts. The
commercial rating, which is also called the " efficiency^''' * of elec-
tric lamps is the number of watts per candle power. For
example, an ordinary 50 watt lamp gives 16 candle power ;
so its commercial rating is \^ or 3.1 watts per candle power.
By a special firing process, carbon filaments can be
" metallized " The efficiency of such filaments is about
2.5 watts per candle power.
336. Metal filament lamps. Still more efficient incan-
descent lamps are made with metallic filaments. The metals
most used are tantalum and tung^ten^ both
of which have melting points much higher
than that of platinum. Since their specific
resistance is much lower than that of carbon,
a metal filament must be very much longer
and thinner (about 0.02 millimeters in di-
ameter) than a carbon filament to have the
FiQ 300 —Metal ^^^^^sary resistance. So long a wire can be
filament lamp, put in a bulb of the ordinary size only by
winding it zigzag on star-shaped reels, as
shown in figure 300.
One difficulty with these metal filaments is their brittle-
ness and liability to breakage. Furthermore, they soften
somewhat when hot, and if a metal-filament lamp is used in
a horizontal position, the filament may sag and short-circuit.
Nevertheless, the extremely high efficiency of these lamps,
their long life (except for breakage), and their wonderful
*Thi8 is really a measure of inefficiency ; the larger the number the worse
the lamp.
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ELECTRIC POWER
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white light, which is the same color as daylight, have made
them very popular.
Comparative "Efficiency" of Electric Lamps
Name of Lamp
Watts per
Candle
Power
Name of Lamp
Watts per
Candle
Power
Carbon filament . .
Metallized carbon . .
Tantalum
Tungsten
3 to 4
2.5
2.0
1.0 to 15
Arc lamp
Mercury arc
Flaming arc
0.5 to 0.8
0.6
0.4
Questions and Problems
1. Why must a rheostat be used in series with the arc lamp in a pro-
jection lantern ?
2. Why are the flaming arc lamps, which are used for street lighting,
placed high above the street ?
3. When an incandescent light bulb gets very hot and blackens on
the inside, what does it indicate ?
4. What must be the voltage of an arc-lighting dynamo which is to
furnish 8 amperes to 25 street lamps arranged in series, if each lamp re-
quires a terminal voltage of 50 volts?
5. What would be the kilowatt output of the generator in problem 4 ?
6. How may a street car, which is operated on a 550 volt line, be
lighted by 110 volt lamps? Draw a diagram of the connections.
7. In considering the proper kind of electric lamp for illumination,
what other factors must be considered besides watts per candle power?
8. How many 0.5 ampere lamps, connected in parallel, can be pro-
tected by a 20-ampere fuse ?
9. How many candle power should a 50 watt tungsten lamp give, if
its efficiency is 1.2 watts per candle power?
10. It was found on testing a 32 candle power lamp that it consumed
100 watts of electric power, of which 88 watts were turned into heat.
What was its efficiency for heating? What was its light efficiency in
the true sense? What was its commercial rating?
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840
PRACTICAL PHYSICS
Electric Motor
337. The djrnamo as a motor. We have already seen that
a dynamo, when driven by a steam engine, gas engine, or
water wheel, may generate electricity. Now we shall see
how this electric current can be supplied to a second machine,
exactly like a dynamo, but called a motor, which may be used
to drive an electric car, a printing press, a sewing machine,
or any other machine requiring mechanical energy. In short,
the dynamo is a reversible machine, and sometimes in shops,
and often on self -starting automobiles, the same machine is
driven as a generator part of the time, and used as a motor
to drive another machine the rest of the time.
Structurally, the motor, like the dynamo, consists of an
electromagnet, an armature, and a commutator with its
brushes. To understand how these act in the motor, how-
ever, we must get a clear idea of the behavior of a wire
carrying an electric current in a magnetic field.
338. Side push of a magnetic field on a wire carrying a cur-
rent. We will stretch a flexible conductor loosely between two binding
FiQ. 301. — Side push on wire carrying a current.
posts A and B^ so that a section of the conductor lies between the poles
of an electromagnet, as shown in figure 301. Let the exciting current
be so connected to the electromagnet that the poles are iVand S as shown.
Then, if a strong current from a storage battery is sent through the con-
ductor from ^ to -B by closing the key K, it will be seen that the wire
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ELECTRIC POWER
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Fio. 302. — Magnetic
field about a wire
with current going
in.
between the magnet's poles is instantly thrown upward, 11 the current
is sentirom ^ to ^, the motion of the conductor is reversed, and it is
thrown downward.
It will help us to understand this
side push exerted on a current-carrying
wire in a magnetic field, if we recall
that every current generates a magnetic
field of its own, the lines of which are
concentric circles. Figure 302 shows a
wire carrying a current in, that is, at
right angles to the paper and away from us. The lines
of force are going around the wire in clockwise direc-
tion.
The magnetic field between the
poles of a strong magnet is practi-
cally uniform and is represented
by parallel lines of force shown in
figure 303.
If we put the wire, with its cir-
cular field, in the uniform field be-
tween the JV and S poles of the
magnet, the lines of force are very much more crowded
above the wire (Fig. 304) than below. But we have seen in
section 238 that we can think of magnetic lines of force as act-
ing like rubber bands which would,
in this case, push the wire down.
If the current in the wire is re-
versed, the crowding of the lines
of force comes below the wire, and
it is pushed up.
339. Motor rule of three fingers.
The rule for remembering which
way this side push on a wire in a magnetic field will move
the wire is precisely the same as that for the generator
except that the left hand instead of the right is used.
Fig. 303.— Unitorm magnetic
field.
Fig. 304.— Lines of force aboat
a wire carrying current in a
magnetic field.
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842 PRACTICAL PHYSICS
340. The action of a motor. In motors, as in dynamos,
the drum type of armature is almost exclusively used. It
will be remembered (see section 322) that in this type the
active wires lie in slots along the outside of the drum, as in
figure 306, and the wiring con-
nections across the ends of the
armature are such that when
the current is coming out on one
side, — say the right, — it will be
going in on the other side — the
left. Just how these wiring con-
Fio. 305. -Drum-wound motor, nections are made is not important
for the present purpose, and in-
deed there are many different ways in which they can be ar-
ranged. In any case, from what has just been said, it will be
clear that the wires (©) on the right side of the armature
will be pushed upward, and those (®) on the left side of the
armature will be pushed downward by the magnetic field.
In other words, there will be a torque tending to rotate the
armature counter-clockwise. The amount of this torque de-
pends on the number and length of the active wires on the
armature, on the current in the armature, and on the strength
of the magnetic field.
Another way of looking at this action is to notice that
the effect of these armature currents is such as to make the
armature core a magnet, with its north pole at the bottom
and its south pole at the top. The attractions and repulsions
between these poles and those of the field magnet cause the
armature to rotate as indicated by the arrows.
The function of the commutator and brushes is, as in the
generator, to reverse the current in certain coils as the
armature rotates, so as to keep the current circulating, as
shown in figure 306.
341. Forms of motors. D.C. generators and motors are
often of identical construction. Thus we have series motors.
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ELECTRIC POWER 343
such as are used on street cars aud automobiles, and shunt
motors, such as are used to drive machinery in shops. So
also we have bipolar and multipolar motors. When it is de-
sirable that a motor shall run at a slow speed, it is built with
a large number of poles.
342. Back e. m. f . in a motor. Suppose we connect an incandescent
lamp in series with a small motor. If we hold the armature stationary,
and throw on the current from a battery, the lamp will glow with full
biilliancy, but when the armature is running, the lamp grows dim.
This shows that a motor uses less current when running
than when the armature is held fast. The electromotive force
of the battery and the resistance of the circuit are not
changed by running the motor. Therefore, the current
must be diminished by the development of a back electromotive
force, which acts against the driving e. m. f .
Since a motor has a series of armature wires cutting mag-
netic lines of force, it is bound to generate an e.m. f. in these
wires. That is, every motor is at the same time a dynamo.
The direction of this induced e. m.f. will always be opposite
to that driving the current through the motor. .
Just as in the generator, when the armature revolves
faster, the back e. m. f . is greater, and the diflference between
the impressed e. m. f . and the back e. m. f . is therefore smaller.
This difference is what drives the current through the re-
sistance of the armature. So a motor will draw more current
when running slowly than when running fast, and much
more when starting than when up to speed.
For example, suppose the impressed or line voltage on a motor is 110
volts, and the back e.m. f. is 105 volts. Then the net voltage which will
force current through the armature is 110—105, or 5 volts. If the armfr-
ture resistance is 0.50 ohms, the armature current is 5.0/0.5, or 10 am-
peres. But if the whole voltage (110 volts) were thrown on the arma-
ture while at rest, the current would be 110/0.5 or 220 amperes.
343. Starting a motor. When a motor starts from rest,
there is, of course, no back e. m. f . at first, and if the motor
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344
PRACTICAL PHYSICS,
is thrown directly on the line, there will be such an exces-
sive current as to " burn out " the armature. To prevent
this first rush of current, a starting resistance is put into the
circuit at first, and cut out step by step as the machine speeds
up. The device for doing
this is shown in figure 306.
See also figure 257.
344. Applications of the
motor. The transmission of
power through shops and
factories by means of shaft-
ing, cables, and belts is
dangerous, noisy, and un-
economical. In a modern
system, electric power is
generated in a central power
house, is transmitted to va-
rious parts of the plant,
and is used in electric
motors to drive either indi-
vidual machines or groups
of machines. When electrical transmission is used, the
danger and inconvenience of belts and shafting are avoided,
the machines can be set in any position, and their speed can
be easily controlled by field rheostats. In shops and factories
thus equipped, shunt motors are commonly used, for constant
speed motors are required, and the speed of a shunt motor
under no load, or a light load, is nearly the same as at full
load.
Series motors are used on cranes, automobiles, and electric
cars, because this type o£ motor has a large starting torque.
The torque in a series motor is proportional to the square
of the current, while in a shunt motor it is directly propor-
tional to the current. The fact that the torque in a series
motor is largest when the speed is slowest (because there is
Motor
Fig. 306.— Motor with starting resistance.
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ELECTRIC POWER
845
little back e. m. f .) makes it just the kind of motor for crane
or vehicle work. When the load on a series motor drops ta
zero, the motor may " race " ; that is, go faister and faster
until the armature flies to
pieces. For this reason, series
motors are connected, either
directly (on same shaft) or by
cogwheels, to the machines to
be driven, . so that they can
never escape their load.
Figure 307 shows a street-
car motor with its case lifted
to show the inside arrangement.
The field consists of four short
poles projecting from the case,
which serves both to protect the
motor, and as a path for the
magnetic flux. The armature
revolves so rapidly that its
speed has to be reduced by a pair of cogwheels, the larger of
which is on the axle of the driving wheels, and is not shown
in the picture. These make the speed of the axle about one
fourth that of the motor.
Street cars are usually operated on a direct-current system.
A large multipolar compound-wound generator (Fig. 308)
at the power station maintains about 660 volts between
the trolley or third rail and the track. A " feeder " or cable
of low resistance
is run parallel to
the trolley wire
and connected
Fig. 308. — General scheme of a trolley line. ^q ^j^ 2X inter-
vals, to avoid a large voltage drop in the line when a
number of cars are taking current at a distance from the
power plant. The current passes down the trolley pole
FiQ. 307. - Street-car motor with top
of case lifted up.
I
T.
vtw, ■^\J^
(^Q
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84t>
PBACTICAL PHYSICS
into the controller (Fig. 309). This is an ingenious ap
raugement of switches by which the motorman can start
jTroiiev Trolley his Car with both motors
in series and with the
starting resistance all in;
then by moving a lever
he gradually cuts out the
starting resistance and
finally throws both the
motors in parallel, as
shown in figure 310.
Thus, when starting,
each motor receives less
than - half the line volt-
age, and when running
at full power, gets full
voltage. The current
leaves the motors by the
wheels, and goes back to
the power station through the rails.
345. Efficiency of the electric motor. One reason for the
extensive use of electric motors is their great efl&ciency,
sometimes as high as 80 % or 90 % . The efficiency of a motor,
just as of any machine, means the ratio of out-put to in-put.
We can easily measure the number of amperes and the num-
ber of volts supplied to the motor and thus compute the
watts pat in.
To get the output of mechanical work, engineers usually
make a "brake-test." One simple form of brake consists
of a belt or cord attached to two spring balances and
passing under a pulley on the motor shaft, as shown in
figure 311.
If the pulley rotates as indicated, it is evident that one
spring balance will have to exert more force than the other
because of the friction of the pulley on the cord. The amount
Armature
Rail Rail
Series Barallel
Fio. 310. — Series-parallel control of electric
cars.
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Fig. 309 (above at left) . — Street car controller.
Fig. 324 (below at right). — Transmisaion line.
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Direct Current Motor with field coils shown above.
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ELECTRIC POWER
847
of friction is equal to the difference between the readings of
the two balances^ and it is exerted each minute through a dis^
tance equal to the
circumference of
the pulley times
the revolutions per
minute. The work
done in one minute
is equal to the
friction times the
distance per min-
ute.
Finally, if we
express the out-
put and input in
some common unit
of power and di- ^^* ^^l* ~ Measuring output of a motor by means of
. J -I . V a brake.
Vide, we have the
efficiency. It will be helpful to know that
1 watt = 44.3 foot pounds per min. = 6.12 kilogram meters per min.
Questions and Problems
1. Figure 312 represents a bipolar motor with the armature revolving
counter-clockwise. Copy it and indicate by
dots and crosses* in circles, the direction of
the various currents.
2. What is the armature resistance . of a
motor in which the armature current is 4 am-
peres, the impressed e. m. f. is 115 volts, and
the back e.m.f. is 112 volts?
3. Find the back e. m. f. in a motor in
which the armature resistance is 0.3 ohms,
the current is 15 amperes, and the impressed
voltage is 110 volts.
Fig. 312 — Bipolar motor.
* A cross in a circle represents the feathers of an arrow sticking into the
paper, and means current going in. A dot in a circle means a current com-
ing out.
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348
PBACTICAL PHYSICS
4. How much current will be drawn by a motor whose efficiency i&
90%, when it is developing 5 H. P. and is connected to the 110 volt
service?
5. When a certain motor was tested by the brake test, it took 67
amperes at 113 volts and developed 8.5 H. P. Calculate its efficiency.
Chemical Effects of Electric Currents
346. Conduction by solutions. When an electric current
flows along a copper wire, the wire becomes warm and is
surrounded by a magnetic field. When an
electric current flows through a solution of
salt and water, the solution is warmed
and is surrounded by the magnetic field,
and it is at the same time decomposed or
broken up. For example, under certain
conditions an electric current will decom-
pose brine into a metal, sodium, and a gas,
chlorine, which are the two elements com-
posing salt. Not all liquids conduct elec-
tricity ; thus alcohol and kerosene are non-
conductors. But all liquids which do
conduct electricity are more or less decom-
posed in the process.
347. Electrolysis of water. Water (made slightly
acid with sulphuric acid) can be decomposed by an
electric current in the apparatus shown in figure 313.
The platinum electrodes are connected with a battery
or generator, giving at least 5 or 6 volts. The elec-
trode in tube Ay which is connected to the positive
( + ) pole, is called the anode, and the other electrode
in B is the cathode. The current passes through the
solution from the anode A to the cathode B. Small bubbles of gas are seen
to rise from both electrodes, and the gas collects in tube B twice as fast
as in tube A, When tube B is full, we open the switch, and test the
collected gases. To test the gas in tube B, we open the stopcock at the
top and apply carefully a lighted match. This gas burns with a pale
Fig. 313.— Water is
broken up into
oxygen and hy-
drogen.
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ELECTRIC POWER
849
blue flame which shows it to be hydrogen. If we open the stopcock in
tube A and bring a glowing pine stick near, it bursts into a flame, which
shows the gas to be oxygen.
Thus we see that water is decomposed by electricity into
its constituent elements, hydrogen and oxygen. This pro-
cess of decomposing a compound by means of an electric
current is called electrolysis.
348. Theory of electrolysis. The theory of this process
may be stated as follows: The small quantity of sulphuric
acid (HjSO^), when put into the water, breaks up into
hydrogen ions (2 H+) and sulphate ions (SO^" "), which have
positive and negative charges of electricity respectively.
When the current is sent through the solution, the positive
hydrogen ions (2 H+) wander toward the cathode and the
negative sulphate ions (SO^""") toward the anode. At the
cathode, the hydrogen ions give up their positive charges and
rise to the surface as bubbles of hydrogen. At the anode,
the sulphate ions give up their negative charges of electricity
and react with the water (HgO) to form sulphuric acid
(H2SO4) and to set free oxygen (Og). In this way the sul-
phuric acid, which is added to conduct the electricity, is not
used up, while the water (2 HgO) is broken into hydrogen
(2 H2) and oxygen (Og).
349. Electroplating. We may
illustrate the process of electroplat-
ing by the following experiment.
We will put two platinum electrodes in
a U-tube filled with copper sulphate solu-
tion (CUSO4), as shown in figure 314. After
the electric current has passed through the
solution for a few minutes, we find the
cathode is coated with metallic copper,
while the anode is unchanged. If we re-
verse the direction of the current, we find
that copper is deposited on the clean platinum plate which is now the
cathode, and the copper coating on the anode gradually disappears.
Fig. 314. — Electrolysis of.
copper sulphate.
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860 . PRACTICAL PHYSICS
In this way one metal can be coated with another. F'ot
example, articles of brass and iron, which corrode in the air,
can be coated with nickel, which does not corrode. Similarly,
much cheap jewelry is gold or silver plated. Many knives,
forks, and spoons are silver plated, the best being what is
called "triple" or "quadruple plate."
In practice the process is done in vats, as in figure 315.
The objects to be plated are hung from one copper " bus " bar,
and the metal to be deposited, in this
case pure silver, is hung from the other
bar. The vat contains a solution of the
metal to be deposited. For silver plat-
ing a solution of silver and potassium
cyanide is used. The bar carrying the
Fia. 315. — Diagram of nietal to be deposited is connected with
electroplating vat. ^^^ ^ terminal of a low- voltage gener-
ator and the other bar to the — terminal. The silver plates at
the anode dissolve as fast as the silver is deposited on the cath-
ode, the strength of the solution remaining unchanged. When
the coating has reached the proper thickness, a final process of
buifing and polishing gives the surface the desired appearance.
350. Electrotyplng. One might at first suppose tha*^^ this
book was printed from the actual type which was set up, but
that is not the case. Most books which are made in large
numbers are printed from electrotype "plates." A wax im-
pression of the page as set up in type is made in such a way
that every letter leaves its imprint on the wax mold. Since
the wax is itself a non-conductor, it has to be coated with
graphite. This mold is then placed in a solution of copper
sulphate and attached to the negative bus bar, so that it
becomes the cathode, while a copper plate acts as the anode.
After the current has deposited copper on the wax mold to
the thickness of a visiting card, this shell of copper is sepa-
rated from the mold and "backed up" with type metal to
give it the necessary strength for printing.
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ELECTRIC POWER 861
351. Refining of metals. Copper as it comes from the
smelting works is not pure enoiigh for some purposes, such
as making wires and cables for carrying electricity. So the
copper for electrical machinery is refined by electricity.
The crude copper is the anode, a thin sheet of pure copper
is the eathode, and the solution is copper sulpha^^e. The
copper deposited by the electric current is remarkably pure.
The anode of crude copper gradually dissolves, and the
impurities drop to the bottom of the vat as mud. In this
mud there is generally enough gold and silver to pay the
expense of the process. Copper purified in this way is known
commercially as electrolytic copper.
352. Electrochemical equivalents of metals. Experiments
show that a given current always deposits the same amount
of a given metal from a solution in a given time. In fact,
this is so accurately true that it is the basis of the most
accurate method known for calibrating standard ammeters
(see section 275). The amount of metal deposited by a
current depends (1) on the strength of the current, (2) on
the time it flows, and (3) on the nature of the metal. The
definite quantity of a substance deposited per hour by elec-
trolysis when one ampere is flowing through a solution is
called the electrochemical equivalent of the substance.
Elbctrochbmical Equivalents
Blbmsnt Symbol Qrams per Ampbbb Houb
Aluminum
Al
0.337
Copper
Cu
1.186
Gold
Au
3.677
Hydrogen
H
0.0376
Nickel
Ni
1.094
Oxygen
O
0.298
Silver
Ag
4.025
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852 PRACTICAL PHTSIC8
QUSSTIONS AND PROBLEMS
1. To determine which is the + and which the — pole of a generator,
two copper wires are sometimes connected to the terminals and the bared
ends dipped in a glass of water. One will soon turn dark. How does
this experiment show which is the positive terminal?
2. How many grams of silver are deposited in 8 hours from a silver
nitrate solution by a current of 5 amperes ?
3. How many liters of hydrogen will be generated by a current of 10
amperes in 4 hours? (A liter of hydrogen weighs 0.09 grams under
standard conditions.)
4. How many amperes will be needed to deposit 1.5 pounds of copper
per day of 24 hours ?
5. How long will it take a current of 200 amperes to refine a ton of
copper?
6. In calibrating an ammeter the current was allowed to run 2 hours
and 15 minutes, and deposited 39.5 grams of silver. What would be the
reading of the ammeter, if correct?
7. Two electroplating vats are arranged in series, one for gold and
the other for silver. How much gold is deposited while 1 gram of silver
is being deposited ?
8. An electroplater buys his electricity by the kilowatt hour. The
metal deposited in electroplating is proportional to the number of am-
pere hours. Why does he use as low a voltage as possible?
9. What is meant by triple and quadruple plate?
353. Storage battery. Some people think a storage bat-
tery is a sort of condenser where electricity is stored, but it
is not that. In the storage battery, as in any other battery,
the electrical energy comes from the chemical energy in the
cells. The charging process consists in forming certain chemi-
cal substances by passing electricity through a solution, just
as hydrogen and oxygen are formed in the electrolysis of
water. In the discharging process, electricity is produced by
the chemical action of the substances which have been
formed in the charging process.
354. Lead storage ceU. We may make a small lead storage cell by
putting two sheets of ordinary lead in a glass battery jar with a very
dilute solution of sulphuric acid. To charge it or "form" the plates
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ELECTRIC POWER
353
quickly we connect this cell and an ammeter in
series with a battery of three or more cells, or
better, a generator of about 6 volts (Fig. 316).
While the current is passing, bubbles of gas rise
from each plate. If, after a few minutes, we
disconnect the generator and touch the wires of
a voltmeter to the lead terminals, it shows an
e. m. f . of about 2 volts. K we then connect an
electric bell in series with the ammeter and the
lead cell, the bell rings, which shows that a cur-
rent is produced, and the ammeter shows that
the current on dis-
Ammei&r
-.-<s>— -,
HHH'
A ^
MS)— '
Voltmeter
Fia. 316. — Forming a
lead storage cell.
Fio. 317.* — Commercial lead
storage cell.
charge is opposite to
that used in charg-
ing the cell. When the plates are lifted out
of the solution after charging, plate 5, the
anode, is hrown^ due to a coating of lead per-
oxide (PbOa), and plate A^ the cathode, is
the usual gray of pure lead (Pb).
In the commercial lead storage
(Fig. 317) cell, the negative plates
are pure spongy lead (Pb), the posi-
tive are lead peroxide (PbOg), and
the electrolyte is dilute sulphuric
acid. In the charging process, the pos-
itive plate, which is dark brown, is coated with lead peroxide,
and the negative, which is gray, is
made into spongy lead. In the dis-
charging process, both plates gradu-
ally return to a condition where
each is covered with lead sulphate
(PbSO^). This is shown in figure 318.
The chemistry of these changes can
be briefly described by the equation
Charge •< —
PbOjj + Pb 4- 2 H3SO4 = 2 PbSO, -h 2 HgO
— >- Discharge
FiQ. 318.
Discharging a lead
ceU.
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354 PRACTICAL PHYSICS
It will be noticed that during the charging process the
acid becomes more concentrated. So the condition of a
storage cell can be determined, at least roughly, by the spe-
cific gravity of the acid. The plates in the commercial lead
battery are either roughened and then changed into the
proper active materials, lead peroxide and lead, by a chemi-
cal process, or are punched full of holes which are filled with
the active material.
355. Advantages and disadvantages of the storage cell.
The lead cell is heavy and expensive, and requires careful
handling to get an efl&ciency even as high as 76%. Its
principal use is not as yet for automobiles, but in three other
fields. First, it is often used to carry the " peak " of the
load of a power station. In certain hours of the, day the
demand for current is too great for the generators to carry,
so a large storage battery, which has been charging while the
load was light, is used to help out the generators. Second,
many companies, which have to furnish electricity without
interruption or pay a heavy fine, use a storage battery as a
reserve supply of electrical energy. In case of accident, .the
storage battery can be drawn upon at a moment's notice.
Third, in some small plants the load on the generators is very
light for a considerable time each day or night. In such
cases a storage battery is sometimes used to take care of this
long-continued light load, and the engine and generators are
shut down.
356. Edison storage battery. Edison Jias invented a stor-
age cell in which the ntJgative plate is pure iron in a steel
frame, the positive plate is nickel oxide, and the solution is
eaustic potash. Since this cell is intended for traction work,
great pains have been taken to make it light, strong, and com-
pact. Instead of being placed in a glass or hard-rubber
tank, it has a thin nickel-plated sheet-steel case. In a lead
cell the normal voltage on discharge is 2 volts ; in the
Edison cell it is 1.2 volts. For the same capacity of output,
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ELECTBIC POWER 365
the Edison cell is about half as heavy as the lead cell. As
the internal resistance of the Edison is a little more than
that of the lead cell, its efficiency is a little lower. Whether
or not the Edison cell is going to be better than the lead cell
depends on its "life" under commercial conditions, and this
is not yet settled.
Questions and Problems
1. In a trolley system the generator maintains 565 volts on the line.
How many lead storage cells, each of 2.1 volts, will be needed to help the
generator carry the peak of the load ?
2. Storage cells are sold according to their "capacity** in ampere
hours. What " capacity ** will be required to deliver 10 amperes contin-
uously for 8 hours?
3. Most manufacturers of lead cells allow about 55 ampere hours for
each square foot of positive plate area. How large a plate area will be
required in problem 2 ?
4. If the e. m. f . of a lead cell is 2.3 volts on open circuit, while the
terminal voltage when the cell is delivering 10 amperes is only 2 volts,
what is the internal resistance of the cell ?
5. A battery of 24 lead storage cells in series, each having an e. m. f.
of 2.1 volts, a normal charging rate of 15 amperes, and an internal
resistance of 0.005 ohms, is to be charged by a dynamo, what must be the
terminal voltage of the dynamo V
SUMMARY OF PRINCIPLES IN CHAPTER XVIH
When a wire cuts lines of force, an induced e. m. f. is set up
in the wire.
To get direction of current, use right hand.
Thumb = Motion,
Forefinger = Flux,
Center finger = Direction of Current.
Magnitude of e. m. f. varies as speed x flux x turns.
Slip rings give alternating current.
Commutator gives direct current
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356 PRACTICAL PHT8IC8
D3aiamo does not make energy; it transforms mechanical into
electrical energy.
Motor transforms electrical energy into mechanical energy.
Power delivered to circuit = intensity of current X voltage.
Watts = amperes X volts.
1 H. P. = 746 watts.
Power turned into heat = current squared X resistance.
Watts = (amperes)^ X ohms.
Heat in calories = 0.24 I%t
A wire carrying a current, when set at right angles to a mag-
netic field, is pushed sideways by the field.
To get direction of motion, use left hand. As before,
Thumb == Motion,
Forefinger = Flux,
Center finger = Current.
Every motor, when running, is acting at the same time as a
dynamo. The e.m.f. of this dsmamo action opposes the current
driving the motor, and is the back e. m.f.
Net e. m. f ., which drives current through armature, equals im-
pressed e. m. f. minus back e. m. f .
Ohm's law applies to a motor armature only if net e. m. f . is
used.
Weight of a substance deposited by a current
= electrochemical equivalent X current X time
Questions
1. Why cannot a lead storage cell be charged from a dry cell ?'
2. Why do the lights on an electric car often grow dim when the car
is crowded and going up grade ?
3. Would it be possible to drive the propellers of an ocean liner by
electric motors ? Why is it not commonly done ? Why are some people
seriously considering doing it in the near future?
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ELECTRIC POWER 367
4. Which will yield the more heat for warming an electric car, a 60
ohm resistance connected across a 50 volt line, or a 100 ohm resistance
connected across a 100 volt line ?
5. Compare the cost per honr of running a 55 ohm electric heater on
a 55 volt circuit and on a 110 volt circuit, if power costs 10 cents per
kilowatt hour.
6. The " carrying capacity " of a wire is limited by the rate at which
it can radiate the heat generated in it. Which will require wires of
larger cariying capacity, a 1100 volt power transmission line, carrying
1000 amperes, or a 11,000 volt line, carrying 100 amperes?
7. Which of the lines in the last problem will deliver more power at
the other end ?
8. Why are electric cars not more generally operated on gtorage cells
instead of by an overhead or a third -rail system of transmission ?
9. Why are electric light bills made out in kilowatt hours instead of
kilowatts ?
10. Why does it take twice as much power to keep a generator going
when there are 200 incandescent lamps lighted in parallel as when there
are only 100 lamps in use ?
11. What methods are used to make the track of a street-car system
a better conductor ?
12. If you were to charge a storage battery so incased that you could
see only the two terminals which were marked + and — , how would
you connect it to a generator?
13. How does the back e. m. f . of a motor vary with its speed ?
14. A belt-driven shunt dynamo is used to charge a storage battery.
The belt breaks, but the dynamo keeps on running. Explain.
15. Does it make any difference which end of the field coils of a
shunt-wound dynamo is connected with the positive brush? If you
have an experimental dynamo, try it.
16. The speied of a shunt-wound motor can be controlled by putting
an auxiliary resistance, called a field rheostat, in series with its field coils,
so as to decrease the current through them. Will this increase or de-
crease its speed ? Why ? If you have an experimental motor, try it.
17. What is the advantage of electrotype plates over the original
type in printing a book?
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CHAPTER XIX
ALTERNATING CURRENT MACHINES
Why alternating currents are used — the transformer — long-
distance transmission — eddy currents — alternators — polyphase
circuits — A. C. motors — rotating field — squirrel-cage rotor —
A. C. power — wattmeters.
357. Why alternating currents are used. For heating and
lighting an alternating current is just as satisfactory as a
direct current. For plating and refining an alternating car-
rent cannot be used because a unidirectional current is neces-
sary to make a metal deposit. If motors are to be run by an
alternating current, a special type of motor is generally used,
which is quite different from the ordinary direct-current
motor. The real advantage in the use of alternating currents
is economy of transmission. This is
made possible by a simple and
efficient machine known as a
transformer.
358. Induced currents in a
transformer. As long ago as
1831 Faraday wound two coils
of wire on a soft iron ringf, as
Fia. 319. —Paraday*8 ring trans- , » n oir\ t^ri^ m
former. shown in figure ol9. When coil
A was connected with a battery
and coil B with a galvanometer, he found that the needle of
the galvanometer was disturbed every time the circuit was
made and every time it was broken.
The modern transformer consists of two coils side by side on
a common iron core not unlike Faraday's ring. When an
868
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ALTERNATING CURRENT MACHINES
359
alternating current is set up in one coil, called the primary,
it magnetizes the iron core, causing surges of magnetic flux,
first in one direction and then in the opposite direction.
Since this magnetic flux passes through the second coil, called
the secondary, as well as the first, it induces an alternating
current in the secondary. Since the same number of lines
of force pass through both coils, the volts per turn are the
same. Therefore the total voltage in the primary/ coil is to the
total voltage in the secondary/ coil as the number of turns in
the primary is to the number of turns in the secondary.
The line voltage in the street is often 2200 volts, which is too high to
be safely used in private houses. It is therefore necessary to transform
or " step down " to 110 volts. A primary coil of
fine wire is connected to the 2200 volt circuit, and
a secondary coil of coarse wire is connected with
the lamp circuit of the house. The primary coil
must have 20 times as
many turns as the sec-
ondary. The secondary
coil must be made of
larger wire than the
primary coil, because the
secondary current is
about twenty times the
current taken by the
primary. Thus the trans-
former delivers the same
amount of energy which
it receives, except for a
small amount (from 2 % to 5 %), which is lost
as heat in the transformer. The efficiency of
a transformer is therefore very high, from
95% to 98%.
Fio. 320. — Core type
of transformer.
Fio. 321. —Shell type of
transformer.
359. Commercial forms of trans-
former. Transformers are built in two
general types : (a) the core t3rpe (Fig.
320), in which the coils are wound around two sides of a
rectangular iron core, and (6) the shell tjrpe (Fig. 321), in
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860
PRACTICAL PHYSICS
Fig. 322. — Transformer case
mounted on pole.
which the iron core is built around the coils. The iron core
of both types is made of sheets of mild steel. To keep the
coils insulated, the transformer is
put in an iron case and surrounded
with oil. These iron cases (Fig.
322) are commonly attached to poles
near houses wherever the alternat-
ing current is used for lighting
purposes.
360. Uses of transformers. In
electric light stations it is common
practice to use alternators to gener-
ate electricity at 2200 volts. The
current is transmitted at this high
voltage to the various districts,
where it is transformed or " stepped
down" to 110 volts for use in light-
ing houses. Another important use
of the transformer is to furnish large currents at very low
voltage for electric furnaces and electric welding.
To illustrate this, we may wind a turn or two of very large copper
wire around the core of a small step-down transformer (Fig. 323), and
connect its primary to a 110 volt A.C.
circuit (if one is available). The
ends of the large wire should be at-
tached to a couple of iron nails. If,
when the current is on, the tips of
the nails are brought together, they
get red hot and can be welded.
The adjoining rails of a car
track are often welded together
in this way. A heavy current
is required for a short time,
and is obtained by using a step-
down transformer, in which the secondary consists of only
one or two turns, made of very large copper bars. The ends
Fig. 323. — Step-down transformer,
used for welding.
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ALTERNATING CURRENT MACHINES 361
of this secondary are clamped to the rails to be welded, one
on each side of the junction.
361. Long-distance transmission of power. By the use of
alternating currents of high voltage, even up to 100,000
volts, power is now transmitted very long distances. For
example, electric power is generated in hydroelectric power
plants in the Sierra Nevada Mountains of California, and
transmitted 200 miles to San Francisco. To understand
why the economical transmission of electricity demands
such high voltage, we have only to recall that the power
transmitted is the product of the voltage and the current
strength. Evidently, then, if we can make the voltage high,
the current can be low. But a smaller current means
smaller losses in transmission, for they are due to the heat*
ing effect of the electric current, and we have already seen
that this varies as the iquare of the current.
It is an impressive sight to see three or six copper cables,
each about | of an inch in diameter, suspended about 75 feet
above the ground on steel towers (Fig. 324, opposite page
347), and to know that those wires are carrying 30,000 H. P.
of electrical energy. Hydroelectric power plants are being
developed all over the country. For example, at Niagara
power plants are generating electricity, raising the voltage
to 60,000 and transmitting some of the enormous energy
available at the Falls to distant cities like Buffalo, Rochester,
and Syracuse. Just outside the city limits there are sub-
stations where the voltage is reduced to about 2000, and
then it is distributed to factories and for general use in
lighting and traction. Before the current actually enters
the buildings, the voltage is again stepped down to 220 or
110 volts.
362. Eddy currents. We have seen that the cores of
transformers are made of soft sheet-iron, or "mild steel,"
stamped out in the desired shape and then assembled. In
the construction of induction coils the cores are made of
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PRACTICAL PHT8IC8
Fig. 325. — Laminated core of
a dynamo armature.
soft iron wires which are put together in a bundle. If we
examine the armature of a dynamo, we find that the iron
drum is made of laminie (sheets) of mild steel which are
stamped out in the shape of disks with
notches around the edge (Fig. 326),
and then assembled on a framework
called the " spider," and mounted on
the shaft. In all these cases the
sheets or wires are insulated from
each other by a coating of shellac,
which eliminates what are sometimes
called Foucault or eddy currents.
We have already seen, in studying the generator, that
when any conductor cuts lines of force, an induced electro-
motive force tends to send a current along the conductor.
In the generator copper wires are provided to carry this
current; but these wires are wound on an iron core, and if
this core is itself an electrical conductor, an induced e. m. f.
will be set up in it as it revolves in the magnetic field.
This induced e. m. f . would send electric currents through
certain portions of the core. These so-
called eddy currents would soon heat
the core, and would also retard the mo-
tion of the armature and waste power.
To reduce these currents to as small a
value as possible, the core is laminated
in such a way that the insulation is
transverse to the direction in which the
eddy currents tend to flow.
363. Use of eddy currents in damping.
To show that eddy currents tend to retard the
motion of a conductor in a magnetic field, we may
set up between the poles of a strong electro-
magnet a pendulum made of thick sheet copper (Fig. 326) . If the mag-
net is not excited, the pendulum swings back and forth as any pendulum
Fio. 326. — Damping by
eddy currents.
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ALTERNATING CUBRENT MACHINES 86S
does, but when we throw on the current in the magnet, the copper pendu-
lum cannot swing through the magnetic field, and is instantly checked.
The eddy currents set up in the copper tend to retard the motion of the
pendulum, much as if it were swinging in thick sirup.
This effect is very useful in stopping the vibrations of the
moving coil of a d' Arson val galvanometer (section 274).
The wire is usually wound on a light copper or aluminum
frame, and the eddy currents in this metal frame check its
swinging. Such a galvanometer is called "dead-beat." We
shall see, in section 372, that this same principle is used to
check the rotation of a wattmeter.
Questions and Problems
1. What limits the voltage which it is practicable to use on high-
tension transmission lines?
2. Why are the cables for long-distance transmission sometimes made
of aluminum instead of copper?
3. If a step-down transformer is to be used to change the voltage
from 1100 to 220, what must be the ratio of turns of wire on the primary
and secondary coils?
4. A transformer has 1000 turns on the primary and 50 turns on the
secondary and the primary current is 20 amperes. About how much is
the secondary current ?
6. What generates the heat required to weld the nails in the experi-
ment shown in figure 323 ? Why does not the copper wire S melt as
well as the the tips of the nails?
364. Alternators. When a coil of wire is rotated in a
magnetic field, we have seen (section 319) that the current
changes its direction every half turn. That is, there are two
alternations for each revolution in a bipolar machine. In a
D. C. generator this alternating current is rectified by the use
of a commutator. In tlie alternating current (A. C.) gener-
ator, called an alternator, the current induced in the armature
is led out through slip rings, or collecting rings, as shown
in figure 275. So almost any direct-current generator can be
made into an alternator by substituting slip rings for the.
commutator.
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PRACTICAL PHY8IC8
The field magnet of an alternator is usually an electro-
magnet which is excited by direct current from a small
auxiliary generator called the exciter.
Since it is only the relative motion of the armature wind-
ings and field magnet which is essential in any generator^
large alternators are usually
built with a stationary arma-
ture and a revolving field. The
revolving projecting poles
(iV, S, N, S, in figure 327)
sweep past the armature
wires which are placed in
slots around the inner pe-
riphery of the stationary
structure A* The direct
current for exciting the
field coils is led in through
Fig. 327.— Revolving field and stationary , , i- i t_ ,
, armature. brushes which rub on two
insulated metal rings. The
alternating current is led directly from the windings of the
stationary armature through cables to the switchboard.
Figures 328, 329, and 330 (opposite pages 364 and 366) show
the revolving field and stationary armature of commercial
machines of this type, and an assembled machine.
365. Cycles and
phase of alternating
currents. When a
conductor is moved
past a magnetic N-
pole, the induced
e. m. f . is in one di-
rection, and when it
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Fio. 331. — Alternating e. m. f . one complete cycle.
moves past an /S-pole, the induced e. m. f . is in the opposite
direction. This can be best represented by the curved line-
shown in figure 331. One complete wave is produced when^
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Fig. 329 (above) . — Stationary armature of alternator.
Fig. 330 (below). — Alternator, belt driven. The long shaft allows the arma-
ture to be slid to one side so that the rotor can be examined and repaired.
The small " exciter '* is on the end of the shaft at the right.
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ALTERNATING CURRENT MACHINES
865
a wire moves through a complete revolution in a bipolar
machine, or from a north pole past a south pole to the next
north pole in a multipolar machine, and is called a cycle.
In practice it is common to use for lighting an alternating
current whose frequency is 60 cycles per second, while for
power purposes 25
15
are
cycle
com-
or even
currents
mon.
A complete wave
or cycle is called
360 electrical degrees
by analogy with the
complete revolution
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Fio. 332. ~ Two alternating currents which differ in
phase.
of a bipolar generator. Any point or position in the cycle is
spoken of as a certain phase. When, for example, the cycle
is half completed, the phase is said to be 180 degrees, and
when the cycle is one fourth completed, the phase is 90 de-
grees. Two alternating currents of electricity, flowing in
branch circuits, may be
at different phases, as
represented in figure
332, where one curve
represents the current in
one branch and the other
curve the current in the
other branch. In the
case shown, one current
is said to lag behind the
other by 90 degrees.
366. Single and poly-
phase circuits. If we
connect all the stationary armature coils of a generator in
series, and revolve the field as shown in figure 333, a single*
phase alternating current is produced whose /regw^wey we can
Mr
Fio. 333. — Diagram to represent armature and
field coils on alternator.
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866
PRACTICAL PHY8IC8
determine by multiplying the number of revolutions per second
of the rotor by the number of pain of poles. To make use of
this current for any purpose, such as electric lighting, we
have simply to cut this armature circuit at any convenient
tranttform
2300 volts
2300 volts
2300 volts
1$ 110 V
g^ 110 V
110 V
Fio. 331. — Alternating system three phases and six wires.
point and connect the ends directly to the mains. It will be
noticed that there are as many coils on the armature as there
are poles in the field magnet in the single-phase machine.
It has been found more economical of space to have more
than one coil for each pole of the field, and so we have
two-phase and three-phase machines, in which there are two or
three sets of coils on the armature. In the three-phase
machine, which is the type
/T\ /T\ /C\ /T\ /^ X~ most used to-day, the three
sets of armature coils may
each be used separately to
furnish electricity for three
separate lighting circuits, B/S
shown in figure 334.
The currents in the three
circuits differ in phase by
will be seen that the currents
Fig 336. — Curves for three-phase current
system.
120 degrees (Fig. 335). It
are such that at any instant their sum is zero
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ALTERNATING CURRENT MACHINES
367
To save wire, electrical engineers 'have devised ways of
connecting the three sets of coils so as to have only three-
line wires, instead of six, as shown in figure 336.
367. Use of alternators. The revolving-armature type of
alternator is generally used only in small electric lighting
stations. Large alternators of the re-
volving-field type are usually mounted
on the same shaft (direct-connected)
with the driving engine or water
wheel. Alternators of very large ca-
pacity are now extensively used with
steam turbines. They can be com-
paratively small in size because they
are driven at such high speed. These
alternators have a revolving field of
only a few poles (sometimes only two)
and a wide air gap between the ar-
mature core and the field poles. Figure
337 shows a 7600 kilowatt alternator
mounted on the crank shaft of a 10,000
horse-power steam turbine, having a
speed of 1800 revolutions per minute.
In high-tension transmission, the three-wire three-phase sys-
tem is commonly used.
Fio. 336. —Y and A con-
nections on three-phase cir-
cuit.
QUESTIONS
1. How can the engineer at the power house control the frequency of
an alternating current?
2. How many revolutions per minute will an 8-pole machine have to
make to give a 60-cycle current ?
3. What objection is there to using a 15-cycle current for lighting
purposes ?
4. Draw a diagram to show two alternating currents which differ in
phase by 45 degrees.
5. How much do the two currents generated by a two-phase alternator
differ in phase?
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PRACTICAL PHT8IC8
368. Alternating cuitent motors. An A. C. generator can
be run as a motor, provided it is first brought up to the exact
speed of the alternator which is supplying current to it and
put in step with the alternations of the current supplied.
Such a machine is called a synchronous motor. Since it is not
self -starting, it is not convenient for general use, but is used
in substations to drive D. C. generators.
An ordinary series motor, by certain modifications in its
design, can be made to operate on either D. C. or A. C.
systems. These so-called A. C. commutator motors or sin|;le-
phase series motors are coming into use for electric cars and
locomotives when an alternating current is used. They
are also to be found, in very
small sizes, on egg-shaking
machines in drug stores,,
and on vacuum cleaners.
They are labeled ." A.C. or
D.C." on the name plates.
The A. C. motor most
frequently used is the in--
duction motor. The distinc-
tive features of this motor
are that the stationary
winding, or " stator," sets
Line U
Fio. 338. — Iron ring excited by two currents
90 degrees apart.
up a rotating magnetic field, and that the rotating part of the
motor, or "rotor," is built on the plan of a squirrel cage.
These will be discussed in turn.
369. Rotating magnetic field. To produce a rotating field,
we will suppose that we have two alternating currents of
the same frequency, but differing in phase by 90 degrees, and
that we connect them to two sets of coils wound on a ring,
as shown in figure 338.
When the'current in line I is at a maximum, it will be seen
from the curves (Fig. 339) that the current in line II is-
zero. The top of the ring is therefore a north pole, N-^^ and
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ALTERNATING CURRENT MACHINES
869
the bottom is a south pole, S. One eighth of a cycle (45
degrees) later, current 1 has decreased in strength and cur-
rent 2 has increased in strength. The result of both currents
is to form a north pole in th6 position JV^, 45 degrees farther
along. One eighth of a cycle (45 degrees) later, current I
has dropped to zero and current II is at a maximum. This
brings the north
pole of the ring
to the right side
(JVg). Evidently
the north pole is
traveling around
the ring, and will
make a complete
circuit for each complete cycle of the current. This produces
a rotating field, and would cause a magnet, such as NS^ to ro-
tate with the field. We should then have a little two-phase
A. C. motor.
Figure 340 shows a working model to demonstrate the rotating field
produced by a two-phase current system.
370. The rotor of an induction motor. The rotating mag-
net can, of course, be replaced by an electromagnet, which
Fio. 339. — Curves of two alternating currents, which
differ in phase by 90 degrees.
Fio. 340. — Working model of two-phase rotating field.
is excited by some outside source of direct current. The
rotor of a commercial A.C. motor is, however, much simpler,
It consists of an iron core, much like the core of a drum
2b
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370 PRACTICAL PHT8IC8
armature, with large copper bars placed in slots around the
circumference and connected at both ends to heavy copper
rings. This is called a squirrel-cage rotor (Fig. 342).
When it is placed in a rotating magnetic field, the con-
ductors on the two sides and the rings across the ends act
like a closed loop of wire, and a large current is induced,
even though the rotor has no electrical connection with any
outside circuit. This large induced current makes a magnet
of the iron core, and the field, acting on this magnet, drags
it around.
The rotor can never spin quite as fast as the magnetic field.
If it did, there would be no cutting of lines of force, no cur-
rents would be induced, and there would be no power avail-
able to drive the rotor against its load.
As in the case of the Gramme ring dynamo, the ring wind-
ing is not used in practical motors. The common construc-
tion is to slip coils into slots in the inner periphery of a
laminated iron " stator," as shown in figure 341. A squirrel-
cage rotor (Fig. 342) is simple and strong, and needs only to
be kept cool. This is done by air circulated through the
core by fan blades. The assembled machine (Fig. 343) is
simple, strong, compact, and almost " fool-proof." For these
reasons, the induction motor is finding a wide field of useful-
ness in shops and factories, and even on electric locomotives.
371. A. C. power. We have seen that we can determine
the power of a direct-current circuit by multiplying the volts
and amperes together. With a non-inductive circuit, such
as a lamp, we can do the same with alternating currents.
In the case of machines which have self-induction, that is,
coils of wire with iron cores, the number of volt amperes is
greater than the true number of watts. Although we cannot
attempt to show in this book just how the watts may be
computed from the volts and amperes of an alternating cur-
rent, yet we can see why it is not a simple case of multipli-
cation.
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FiQ. 337. — 7500 k.w. alternator driven by steam turbine.
Fig. 341. — Stator of an induction motor.
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FiQ. 342. — Squirrel-cage rotor of induction motor.
Fig. 343. — Induction motor.
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ALTERNATING CURRENT MACHINES 371
In the first place, we will represent the varying electro-
motive force by the " pressure " curve in figure 344, and the
varying current by the current curve in the same figure. It
will be noticed that the current curve lags^ that is, it starts
after the e. m. f . curve. This is due to the self-induction of
the circuit which impedes the flow of the alternating current.
To get the power of such a current, we should have to mul-
tiply the simultaneous values of current and pressure for a
great number of points, and then get
a general average of these products.
Now what an A.C. ammeter (which
we will not attempt to describe) re-
cords, is the " effective value " of the
alternating current ; that is, the value
in amperes of the direct current which
would produce the same heating Fig. 344.— Voltage and cur-
effect. It can be shown that this rent curves.
" effective value " of an alternating current is about 0.7 of its
maximum value. The effective value of an electromotive
force is said to be one volt, when it will develop an alternat-
ing current of one ampere in a non-inductive resistance of
one ohm. It is also about 0.7 of the maximum value of the
e. m. f. Evidently it will not do to multiply these effective
values of current and voltage together, because, in the averag-
ing process described above, large values of the current are
likely to be paired with small values of the e. m. f., and vice
versa.
It can be shown that the A. C. watts are equal to the volt-
amperes times a factor, which is called the power factor. This
factor varies according to the circuit. It is always less than
1 for an inductive circuit.
372. Wattmeters. Every user of electricity should be in-
terested in the recording wattmeter, which records on dials, like
those of a gas meter, the number of kilowatt hours of elec-
tricity consumed. It is on the readings of this instrument
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872
PRACTICAL PHYSICS
that the monthly bills are based. Figure 845 shows the
Thomson form of wattmeter. It is really a little shunt
motor, the armature of which turns at a speed proportional
to the rate at which electrical energy is passing through it.
This armature is geared to the recording dials. The field of
the instrument is made by stationary field coils which are
connected in series with the line. The field strength is
YiQ. 345. — Thomson's watt-hour meter^
therefore proportional to the current flowing in the main
line. The armature is connected across the line, and takes a
current proportional to the voltage across the line. There-
fore, the torque which turns the armature is proportional to
the product of the current and the voltage ; that is, to the
watts in the line.
The inertia of such a machine would make it run too fast,
or fail to stop when the current stopped, if it were not for the
electric damping caused by the rotation of an aluminum disk
between the poles of permanent magnets. The eddy cur-
rents generated in the disk tend to retard its motion.
This type of wattmeter is used for both A. C. and D. C.
work. When used with alternating currents it automatically
averages the products mentioned at the top of page 871.
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ALTERNATING CURRENT MACHINES 873
SUMMARY OF PRINCIPLES IN CHAPTER XIZ
In a transf onner : —
Voltage on primary __ tixms of primary
Voltage on secondary "^ turns of secondary
In an alternator : —
Frequency = revolutions per second x number of pairs of poles.
C. power = amperes x volts x power factor.
Power factor usually less than one.
Questions
1. The iron case of a transformer is of ten corrugated. Why?
2. Why must the dielectric strength of the oil used in transformers be
carefully tested ?
3. In long-distance transmission of power by high-tension lines, the
wires are often supported on steel towers 50 feet or more above the
ground, and the company gets a right of way to a strip of land 100 feet
wide over which to run its wires. Why these precautions ?
4. What is gained by making the armature of big alternators station-
ary, and rotating the field?
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CHAPTER XX
SOUND
What makes sound — what carries sound — velocity of sound
— water waves — velocity, wave length, and frequency — longi-
tudinal waves — sound waves — loudness and distance — direct-
ing sound — reflecting sound — musical tones — intensity, pitch,
and quality — resonators — overtones — beats — the musical scale
— stringed instruments — wind instruments -— membranes —
the phonograph.
373. What makes sound ? When a bell rings, we see the
hammer or clapper hit the bell, and hear the sound which it
makes. If we hold a pencil against the edge of the bell just
after it has been struck, we find that the metal is moving to
and fro very rapidly. When a guitar string is plucked, it
gives forth a note which we can hear, and
at the same time we can see that the string
looks broader than when at rest. We con-
clude that the string is vibrating or oscil-
lating back and forth. When we strike a
tuning fork and hold it near the ear, we
hear a note, and if we touch the fork to
the lips, we feel its vibratory motion.
To make visible the vibration of a tuning fork
let us touch it to a light glass bubble suspended on
a thread (Fig. 346). The bubble is set violently
in motion.
Another way to show the vibratory motion of a
fork is to attach a point of stiff paper to one prong.
Let us set such a fork in vibration and draw it over
a piece of smoked glass (Fig. 347). The curve which is traced is easily
made visible by putting white paper behind the glass.
374
FiQ. 346. — Vibration
of tuning fork made
visible.
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BOUND
375
FiQ. 347. — Curve traced by a vibrating
fork.
Whenever we look for the source of a sound, we find that
something has been set in motion. It may be that something
has fallen, a bell has been
struck, a whistle has been
blown, or some one has
shouted; always some-
thing has been set vibrat-
ing which has caused the
sensation of sound.
374. What carries sound? Ordinarily the air, which is
everywhere about us, brings sound to our ears. To make
this evident let us try the following experiment.
Let us suspend an electric bell under the receiver of a good vacuum
348. If we set the bell to ringing and then
pump out the air, we find that the sounds be-
come fainter and fainter. When we let the
air in again, the bell sounds as loud as at first.
It seems probable that the bell would become
quite inaudible if we could get a perfect vacu-
um, and if no sound were conducted out by the
suspension wires.
pump, as shown in figure
We know that both heat and light
can traverse a vacuum, as in the case
of the electric incandescent light bulb,
but we see from the last experiment
that sound does not traverse a vacuum.
It can be shown that other gases be-
sides air carry sound, and that liquids
and solids are even better carriers of
sound than gases. For example, if one holds his ear under
water while some one hits two stones together at some dis-
tance away, the sound is heard very distinctly. It is also a
familiar fact that one can hear a train a long distance away
by putting one's ear close to the steel rail. Loud sounds, like
those of cannon, or of volcanic eruptions, can be heard at a
Fig. 348. — Sound is not car-
ried through a vacnom.
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876 PBACTICAL PHYSICS
distance of several hundred miles by putting one's ear to
the ground.
To show that liquids ttansmit sound, let us put the stem of a tuning
fork into a hole bored in a large cork. If we set the fork in vibration,
it is hardly audible ; but if we hold it with the cork resting on the sur-
face of a glass of water, we hear it distinctly. The sounds seem to be
coming from the table on which the tumbler of water stands. This ex-
periment shows that the vibration of the tuning fork is transmitted
through the cork and the water to the air in the room.
To show that solids transmit sound, we may hold one end of a long
wooden stick against a door, and rest a vibrating tuning fork on the
other end ; the sound of the fork seems to be coming from the door.
The wooden stick here serves as the sound carrier and transmits the
vibration of the fork to the door.
So we conclude that solids, liquids, and gases may serve
as carriers of sound.
375. How fast does sound travel ? In an ordinary room one
is not aware that it takes any appreciable time for sound to
travel fr6m its source to one's ears; but in a large hall, or out
doors, one often hears an echo, which shows that sound does
take time to travel to a reflecting surface and back. During
a thunder shower we hear the roll of the thunder after we
see the flash. The farther away the lightning discharge is, the
longer the interval between seeing the flash and hearing the
rumble. Every one has doubtless seen the steam from a dis-
tant whistle, and then later heard the whistle. So there is
no doubt that sound travels much more slowly than light.
One way to measure how fast sound travels is to discharge
a cannon on a distant hill and measure the time betwefen see-
ing the flash of the cannon and hearing its report. In one
such experiment, which was performed by two Dutch scien-
tists in 1823, the cannons were set up on two hills about eleven
miles apart, and observations were made first from one hill
and then from the other, to eliminate the error due to wind.
They concluded that sound travels 1093 feet (or 333 meters)
per second, which was remarkably near the truth, considering
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SOUND 871
the instruments they had. Since then, several men have
made determinations of the velocity of sound in air, which
show that at 0° C and 76 centimeters pressure the velocity
of sound i% 1087 feet ( or 331 meters^ per second. The speed
of sound in water is about 4.6 times the speed in air, and in
steel it is more than 15 times as great as in air. It has also
been found that the speed of sound in air increases about 2
feet (or 0.6 meters) per second for each degree centigrade
rise in temperature. For practical purposes it is enough to
remember that sound travels about 1100 feet per second.
Problems
(Assume that the time taken by light to travel ordinary distances is negligibly
small)
1. The sound of a steam whistle is heard 2.6 seconds after the steam
is seen. About how far away is the whistle?
2. A man can see the hammer strike a bell once every 2 seconds. If
the man is a mile away, what is the interval between the sounds of each
stroke?
3. On a hot summer day, when the temperature is 30*^ C, the flash of
a gun is seen 2 miles away. How long after the flash will the report
of the gun be heard ?
4. A stone is dropped from the top of the Woolworth Building in
New York, which is 750 feet high. How long before a man on top
would hear the sound of the stone as it struck the pavement? (The
time includes the time for the stone to fall and for the sound to return.)
5. If an experiment shows that sound travels in water 4814 feet per
second at 14° C, how many times as fast does sound travel in water as in
air at this temperature ?
376. Sensation of sound. We have been considering the
transmission of " sound " through gases, liquids, and solids,
although we know that it is merely a sort of motion which
is transmitted. Ordinarily we find it hard to think of
sound without thinking of an ear to hear it. Thus we find
people asking whether a waterfall in a very remote part of
the earth, never visited by any man or animal, makes any
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878 PBACTICAL PHYSICS
sound. Evidently there are two things which are called
" sound " the vibrations, and the sensation they produce when
they strike against the tympanum or eardrum. The study
of what happens in the ear and brain is properly left to
physiology and psychology. In physics we shall study only
the vibrations in the air or other transmitting medium, and
shall refer to them when we say "sound." In this sense the
waterfall makes just as much sound whether there is an ear
to hear it or not.
377. Sound a wave motion. Evidently nothing material
(that is, weighable) travels from the source of a sound to the
ear; otherwise, how did the sound of the electric bell under
the bell jar get through the glass ? This and other facts point
unmistakably to the conclusion that what is transmitted is
merely a vibration or mode of motion, called a wave.
378. Water waves. Since sound waves are usually invisi-
ble, we will start with a study of water waves. When a stone
is dropped into a smooth pond, a disturbance is produced
which extends over the surface of the water in circles centered
at the place where the stone struck. The water is pushed
down and aside by the stone, forming a circular ridge which
expands into a larger circle, and is followed by a second cir-
cular ridge which expands, and so on. The result is that the
surface is soon covered with a series of circular swells which
are separated by circular troughs, all moving away from the
center of the disturbance.
To study these water waves more carefully, let us pour water into a
long tank with glass sides (Fig. 349) to a depth of 2 inches, set a paddle
upright about 6 inches from one end of the tank, and start a wave by
drawing the paddle to the end of the tank. It will be obsei-ved that the
wave travels to the other end of the tank. There it is turned back or
reflected, returning to the first end, undergoing another reflection, and so
on. By measuring the length of the tank and observing the time of six
round trips of a wave (observe the rise and fall of the water at one side)
we can calculate the speed of the wave.
If we pour more water into the tank until the depth is 3 inches, and
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SOUND
379
Again time six round trips and calculate the speed of the wave motion,
we shall find that waves travel faster in deep water.
To study stationary water waves we place a little block on the water
at one end of the tank. By raising and lowering the block periodically,
FiQ. 349. — Tank for water waves.
we may set up stationary water waves, in which the water simply " see-
saws " up and down with no apparent backward and forward motion.
The surface of a water wave may be represented by the
curved line shown in figure 350. The stationary points,
j4, J8, (7, 2), etc., are called the nodes ; the intervening spaces
are called the loops, or intemodes. The water between nodes
oscillated up and down; when it is up, it forms a crest, and
when it is down, it is a trough. A crest and trough together
form a wave, as from A to (7, or J8 to 2>.
The length of a wave (Z) is measured
horizontally from any point on one
wave to the corresponding point in the
next wave. Corresponding points are
called points in the same phase. The
amplitude (rf) of the wave vibration is half the vertical dis-
tance from trough to crest.
379. Relation between velocity, wave length, and frequency.
In the case of the waves started by throwing a stone into a
quiet pool, we know that while the circular waves grow
larger and larger, any particular crest seems to move out
radially until it reaches the bank* or dies away. The dis-
tance which a crest travels in one second is called its velocity.
The number of crests passing a fixed point in one second is
called the frequency. The time it takes one wave to pass a
FiQ. 350. — Surface of a
water wave.
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880 PRACTICAL PHYSICS
given point, that is, the time between crests, is called the
period of the wave motion.
If n is the number of waves passing a given point in one
second, that is, the freqvsnci/^ and if p is the time required for
one wave to pass a given point, that is, the period^ then.
Again, if I is the length of one wave in feet, and n is the
number of waves passing any point in one second, the dis-
tance traveled by a wave in one second, that is, its velocity v
in feet per second, is equal to n times I ; that is,
v = nl
It should be remembered that it is only the wave form that
travels over the surface of the water, not the water particles
themselves. Thus if we float a cork or a toy boat on a pool
over whose surface waves are passing, the cork or boat
merely bobs up and down as a wave passes, but is not carried
along with it.
380. Transverse and longitudinal waves. An easy way of illus-
trating wave motion is to fasten one end of a piece of rubber tubing about
20 feet long to a hook
^tp^'^r^ v;^^^^^ ^Pl in the wall. If we
'Hy — '«^ ^s^^ ^^ take the free end in
Fig. 351. —Waves in a rubber tube. the hand, we can, by
a quick shake, send
a wave along the tube (Fig. 351) . If a single depression is sent along
the tube to the fixed end, it is reflected and returns as an elevation ; in
like manner a single elevation sent along the tube comes back as a de-
pression.
In the case of water waves and of the waves in a tube or
cord, the particles of water or tubing oscillate up and down,
while the disturbance moves horizontally. Such waves are
called transverse waves.
A second kind of wave motion takes place in substances
such as gases and wire springs, which are elastic and corn-
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SOUND
381
pressible. This kind of wave can be studied by letting a
coil of wire represent the substance through which such waves
are transmitted.
Figure 352 represents a spring whose turns are large and are supported
by threads. K we strike the spring at one end, we compress a few turns
near that end. These move slightly and compress those just ahead, and
Fio. 362. — Spring wave model.
these in turn squeeze together the turns still farther along. Thus a
pulse or wave goes along the spring.
Next let one end of the spring be given a quick pull, so that the turns
near by are drawn apart for an instant. Then the adjacent turns will be
pulled over, one after another, until this disturbance reaches the other
end. Thus it is seen that any push or pull given to the spring at one
end is transmitted as a push or pull to the other end.
Waves of this sort, in which the particles of the transmit-
ting material move back and forth in the direction of the
advance of the wave, are called compression or longitudinal
waves.
381. Longitudinal vibration in solids. Not only springs,
but gases and even solids like steel, transmit vibrations longi-
tudinally.
If we clamp a steel rod in the middle and rub it lengthwise with a
cloth dusted with rosin, a clear, ringing sound may be produced. That
the rod has been set in vibration longitudinally can be shown by a little
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PRACTICAL PHYSICS
jA o
FiQ. 353. — Ball driven from end of rod.
ivory ball hung by a cord so as to rest against the end of the rod. When the
rod is vibrating, the ball will swing violently out, as shown in figure 353-
Another mechanical illustration of the method by which a
push or pull may travel a long distance, although the individ-
ual particles move
only very minute
distances, is shown
in the following ex-
periment : —
The apparatus shown
in figure 354 consists of
several glass-hard steel
balls hung up in a line
so that they just touch
each other. If we pull
aside the first ball and
let it fly back and strike the line of balls, the ball it strikes does not
seem to move, nor the next one. In fact none seem to be affected by the
blow except the ball on the opposite
end, which flies out about as far as
the first ball fell.
Since steel is very elastic,
the impact of the first ball is
handed along from ball to
ball until it reaches the end
one. It is as though a push
were given to the first of a
column of boys standing in
line. It is transmitted along
the line, and the last boy is
pushed over.
382. Sound waves. We
think of the air in sound
waves as vibrating to and fro in the direction of propagation
like the turns of the spring; that is, sound waves are longt-
tudinal or co7npre3sion waves^ made up of alternate condensations
FlQ.
364. — Illustrating how sound travels
from particle to particle.
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SOUND
383
and rarefactions. Just as a stone thrown into a pool makes
waves which spread out in ever widening concentric circles,
so we think of a bell as sending out spherical waves. These are
made up of alternate spherical shells of compressed and rare-
fied air, traveling out in every direction through space.
To form a picture of a sound wave traveling through a
speaking tube, let us imagine that the spiral spring of the
model (Fig. 352) is replaced by a column of air, which has a
Fig. 365. — Diagram to show soand waves by a curve.
tuning fork at one end, giving little pulses to the air column,
while an eardrum at the other end receives these pulses
(Fig. 365).
The successive condensations and rarefactions of the air
are indicated by c and r in A. The disturbance travels from
the fork to the air, but the intervening air at any point
merely oscillates a very little to and fro. The curve in
figure 355 is a graphical representation of these sound
waves, in which the crests, 1-2, 3-4, etc., represent conden-
sations or compressions, and the troughs, 2-3, etc., represent
rarefactions. The amplitude of the wave corresponds to the
distance each particle of air moves to and fro from its origi-
nal position. A sound wave includes a complete crest and
trough, that is, a condensation and rarefaction, and the dis-
tance between two corresponding points in any two adjacent
waves is called the wave length.
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884 PRACTICAL PHY8IC8
Since the same relation between velocity, wave length, and
frequency holds for sound waves as for water waves, we can
easily compute the length of a sound wave.
Suppose a tuning fork is giving 256 vibrations each second, and that
the velocity of sound is 1120 feet per second. Then the length of each
wave is 1120 feet divided by 256, or about 4.4 feet.
Or substituting in the wave equation,
17= nly
1120 = 256 /,
/ = 4.4 feet.
To picture a sound wave spreading through the open air,
we may imagine a great number of spiral springs radiating
out from a common center at the source of the sound, all re-
ceiving an impulse at the same time.
Problems
1. An A tuning fork on the " international scale " makes 435 vibra-
tions per second. What is the length of the sound wave given out?
2. A vibrating string gives out sound waves 2 feet long. What is the
frequency of the waves?
3. The period of a sound wave is found to be 0.0025 seconds. What
is the length of the wave ?
4. A bell whose frequency is 150 vibrations per second is sounded
under water, in which sound travels at the rate of 4800 feet per second.
Find the wave length produced by the bell.
5. If the highest tone which the ear can recognize makes 30,000 vi-
brations per second, what is the shortest wave which the ear appreciates?
383. Intensity or loudness of sound. It must always be re-
membered that when a bell is struck, the sound is heard in all
directions, which means that sound waves spread out in all
directions as shown in figure 356. As the distance from the
source increases, the spherical waves spread out over more
surface, and so the intensity of the sound decreases. For
example, a bell 10 feet away will sound one fourth as loud
as the same bell 6 feet away, and if 15 feet away, it sounds
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SOUND
385
one ninth as loud as when 5 feet away. This is because the
energy of the wave must be imparted to nine times as many
particles at a distance of 15 feet as at a distance of 5 feet.
In general^ the intensity of sound varies inversely as the square
of the distance.
If one ascends to a high altitude, as on a mountain top or
in a balloon or aeroplane, the air becomes less dense and so
not so good a carrier of sound.
This makes it difficult to transmit
sounds. In general^ the intensity
of sound depends on the density of
the medium through which the sound
is transmitted,
384. Speaking tubes and mega-
phones. The speaking tubes used to
connect rooms in buildings and
ships serve to prevent the spread-
ing out of sound waves in all di-
rections, and so the sound is heard
with almost its original intensity
at the distant point. Sharp bends
in such tubes should be avoided, as they cause reflected waves,
which run back.
In the megaphone the sound waves which come from the
mouth are not permitted by the walls of the instrument to
spread out in all directions. In this way the energy of the
voice is sent largely in one direction.
385. Reflection of sound. Just as any elastic body like a
rubber ball bounds back when thrown against a brick wall,
or a water wave is turned back by a stone enbankment, so a
sound wave is turned back or reflected when it strikes against
another body, such as a building, clifif, or wooded hillside, or
even a cloud. The returning wave is called an echo. If the
reflecting wall is near, as in a closed room, one may hear an
echo almost at the same instant as the sound. This confuses
2c
Fig. 356. — Sound waves spread
out in all directions from this
source.
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PRACTICAL PHT8IC8
a hearer, and is an acoustical defect in the room. It can often
be remedied by putting an absorbing material on the reflect-
ing wall. When the reflecting surface is 25 or more yards dis-
tant, the echo is distinct from the original sound, and excites
interest and curiosity. The
greater the distance, the longer
is the time before the reflected
wave strikes the ear, and there-
fore the more distinct the echo
becomes. When we have par-
allel walls, as in a narrow canon,
or objects at different distances,
the echo is multiple or repeated,
which means that the same
sound is heard several times.
For example, the roll of thunder
results in part from the reflection of the sound from a suc-
cession of mountains or clouds.
Fig. 367. — Sound of a watch reflected
by mirrors.
The following experiment shows that sound waves, like light waves,
are reflected by curved surfaces. If two large parabolic mirrors face
each other, as in figure 357, a watch at the principal focus of one mirror
can be distinctly heard
across the room by hold-
ing an ear trumpet at
the focus of the other ^
B
I^G. 368. — Curves to represent (A) noise and {B)
music.
In buildings with
arched ceilings it is
sometimes possible
to hear a whisper at a very distant place in the room because
the sound is reflected from the ceiling and, concentrated at
the ear of the listener.
386. Musical sounds and noises. We all recognize some
sounds, such as the slamming of a door or the rumbling of a
wagon over cobblestones, as noises; while we recognize the
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SOUND 387
sounds from a piano wire or an organ pipe as musical sounds
or tones. The difference between these kinds of sounds can
be best expressed by the curves in figure 368, where A is
the curve of a noise, and B the curve of a musical note.
It will be seen from these curves that a noise makes a very
irregular and haphazard curve, while a musical note makes
a uniform and regular curve. The latter produces an agree-
able sensation on the ear, while the former makes a disa-
greeable sensation. The great German scientist, Helmholtz,
expressed this distinction by saying, "The sensation of a
musical tone is due to a rapid periodic motion of a sounding
body; the sensation of a noise to a non-periodic motion.''
387. Three characteristics of a musical note. A musical
sound or tone has intensity or loudness, pitch, and quality or
timbre, and each of these characteristics depends upon some
physical property of the sound wave. The intensity of a
sound depends on the amplitude of the vibration; the pitch
depends on the frequency of the waves; and the quality de-
pends on the vibration form.
388. Intensity. We have already seen that the intensity
of sound in general diminishes as the distance of the ear
from the source of the sound increases and also as the density
of the air. diminishes. The intensity of a musical sound for
a given ear and at a given distance depends on the amplitude
of vibration of the waves sent out. For example, a piano
string or a tuning fork gives a louder sound when struck
hard than when struck gently.
389. Pitch. When we speak of a musical note as high or
loWr we refer to its pitch. When we strike the keys of a
piano in succession, beginning at one end of the keyboard, we
recognize the difference in the tones produced as a difference
in pitch. By holding a card against the teeth of a rapidly
revolving wheel (Fig. 359) we can show that the pitch of the
note produced depends on the number of vibrations per second;
that is, upon the frequency of the vibrations.
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PRACTICAL PHYSICS
We can show this very clearly by means of a siren. This is a metal
disk (Fig. 360) with holes equally spaced around the edge, which can
be rotated by some sort of whirling apparatus.
If a current of air is directed through a tube
against the holes, the regular succession of
puffs produces a musical tone. As we in-
crease, the velocity of the wheel, the tone be-
comes higher ; that is, its pitch is raised.
One way to measure the frequency
of vibration of a musical tone is by
Fig. 359.— The pitch varies means of such a rotating disk. Sup-
with the speed. ^^^^ ^-^^ ^^^ j^^^ g^ j^^^^^^ ^^^ -^ ^^_
tached to a motor making 1800 revolutions per minute.
Since the disk makes 30 revolutions per second, there are
30 X 80= 2400 puffs per second. The fre-
quency of the tone emitted would be 2400
vibrations per second. This would be a
rather shrill note. A standard A tuning
fork makes only 435 vibrations per second.
390. Limits of audiblUty. The lowest
tone which the human ear can recognize as
a musical tone has a frequency of about
16 vibrations per second. If the sound
has a frequency above a certain number,
the ear does not recognize it at all. This
upper limit of audibility varies with differ-
ent people from 20,000 to 40,000 vibrations
per second. A young person can usually
recognize sounds of a higher pitch than an
older person. In fact this is one of the
evidences of the impairment of hearing with advancing age.
391. Quality or timbre. The third characteristic of a
musical note is its qiiality. It is quality which enables us
to distinguish between notes of the same pitch and inten-
sity as produced by different instruments or sung by differ-
ent voices. Even the same kind of instrument may produce
Fig. 360. — Pitch de-
pends upon the rate
of vibration.
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Hermann VON Helmhoi/tz. Bom near Berlin, in 1821. Died in 1894. Trained
as a physician and physiologist, he made important discoveries in mechanics,
sound, and light, as well as in mathematics and in philosophy.
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SOUND
389
notes of different quality. For example, it is the quality of
the tones produced by two violins which makes the great
difference in their value. We recognize the voice of a friend
over the telephone by its quality.
Helmholtz (1821-1894) first discovered the cause of these
subtle differences in musical tones, which are called quality.
In this investigation he made use of resonators which vibrated
in sympathy with the tones to be studied.
392. Sympathetic vibrations. Every one has learned by
experience how easy it is to set a swing vibrating by a suc-
FiG. 361. — Sympathetic yibration of forks of the same pitch.
cession of gentle pushes applied at just the right time, so
that each push helps rather than hinders the swinging.
Mere random pushes, on the other hand, accomplish very
little. In much the same way sound waves or other slight
impulses may set up strong vibrations in a body if they are
timed to correspond exactly to its natural frequency of
vibration. This is called sympathetic vibration.
It can be strikingly shown by holding down the loud pedal of a piano,
so that the dampers are lifted from the strings, and singing a clear, strong
tone into the instrument. After the voice is silent, the sound is returned
by the strings with enough fidelity to make the effect almost startling.
Another way to illustrate sympathetic vibrations is to put two tuning
forks of the same pitch several feet apart (Fig. 361). If we strike one
fork vigorously with a soft mallet, and then quickly stop it with the hand,
the other will be heard even in a large room. It has been set in motion
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890
PBACTICAL PHT8IC8
by the sound waves from the first fork. If we change the pitch oi
one fork by sticking a bit of beeswax on one prong, the fork^ will be
thrown slightly out of unison and will no longer respond to eacli other.
From this experiment it is evident that two tuning forks
must vibrate at exactly the same rate to vibrate in sympathy.
Certain articles of furniture and of glassware have definite
rates of vibration of their own, and are
set vibrating sympathetically when their
particular note is sounded. It is the
cumulative effect of feeble impulses re-
peated many times at regular intervals
which sets up this sympathetic vibration.
393. Resonators. That property of a
sounding body which enables it to take
up the vibrations of another body by
sympathy, and to vibrate in unison with
it, is called resonance. In the last experi-
ment each tuning fork stood on a wood
box open at one end and so constructed
that the air column within the box has
the same rate of vibration as the fork
itself. ' Such an air column is called a resonator. It was the
resonator rather than the fork itself that
picked up the vibrations.
To show resonance, we may raise and lower the
tube A (Fig. 362) in the jar of water B, and at
the same time hold a vibrating tuning fork over
the tube. We shall find a position where the
sound of the fork is reenforced by the sound
of the air column and seems loudest.
Fig. 3ti2, — Re enforce-
ment of a sound by an
air column.
This reenforcement or intensification
of sound by a resonator is due to the uni-
son of direct and reflected waves. For
example, it can be shown that the
length of air column used in the ex-
m
=2^
.:!:.
Fig. 363. —The oaose
of resonance
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SOUND 391
periment is one quarter of a wave length. This will be
readily understood from the diagram (Fig. 363), where
ac is one prong of a fork vibrating over an air column in
resonance. When the prong moves dozm past its central
position, it causes a condensation in the column of air, which
goes to the bottom and gets back just as the fork is moving
up past its central position. This reenforces the vibration
of the fork. Since the sound traveled twice the length of
the air column in the time of half a vibration of the fork, it
traveled the length of the air column in the time of a quarter
vibration. So the vibrating air column is a quarter of a
wave length. Further experiments would show that a
resonance column 'may be 3, 5, 7, or any odd number of
quarter wave lengths.
394. Fundamentals and overtones. When a piano wire vi-
brates as a whole, it gives out what is called its fundamental
note. This fundamental is the lowest note which it can give
out. Its pitch depends on the _,,^^-::rr:==«^-<^--.
length, tension, size, and ma- ^-^s^— —rr^sa^llii*.;}
terial of the wire. When a Fig. 364. — a wire emitting its f unda-
wire is vibrating as a whole, mental and first overtone.
it may at the same time be vibrating in segments; that is, as
if it were divided in the middle. Such a secondary vibration
gives an oyertone which has twice the frequency of the funda-
mental and is said to be an octave higher. Figure 364 shows
an instantaneous picture of a vibrating string giving both its
fundamental and its first overtone. In a similar way, a string
may vibrate as a whole and, at the same time, as if divided
into thirds, in which case it gives its fundamental and its
second overtone. Higher overtones or "harmonics" are
also possible.
395. Helmholtz' experiment. Helmholtz proved that the
quality of a tone is determined simply by the number and
prominence of the overtones which are blended with the
fundamental. To prove this, he constructed a large number
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892
PRACTICAL PHYSICS
of spherical resonators (Fig. 366), each having a large open-
ing, and also a small one adapted to the ear. A resonator
of this form is especially useful because it responds easily to
vibrations of one pitch only^ and so can
be used to analyze sounds. By holding
each of these resonators in succession to
his ear, he was able to pick out the con-
stituents of any musical note which was
being sounded, and to judge of their
relative intensities. Then he reversed
the process and combined these constit-
uent overtones, reproducing the original
tone. He succeeded in imitating in this way the qualities
of different musical instruments and even of various vowel
sounds.
396. Koenlg's manometric flames. Another method of
showing that the quality of any note depends on the /orm of
Fig. 365. — Helmholtz'
resonator.
Fig. 366. — Analysis of sounds with manometric flames.
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the wave was devised by a Frenchman, Koenig. This method,
called manometric flames, has the advantage of making the
phenomenon visible.
The apparatus is shown in figure 366. The essential part
is a small box divided into two chambers by an elastic
diaphragm, made of very thin sheet rubber or goldbeater's
skin. The cavity on one side is connected with a funnel,
while the cavity on the other
side has two openings, one for
illuminating gas to enter, and
the other connected with a fine
jet where the gas burns in a
small flame. The vibrations of
the air on one side of the dia-
phragm change the pressure of
the gas on the 'other side, and
cause the flame to dance up and
down. When such a flame is
viewed in a rotating mirror, its
image is a straight band of light
[Fig. 367 (top)] if the flame is still, and a serrated band
[Fig. 367 (lower three curves)] when sound vibrations are
striking against the diaphragm.
Let US' set up the apparatus as showu in figure 366, and first rotate
the mirror when no note is sounded before the funnel. There will be
no fluctuations in the flame as the mirror is turned. Next let a mounted
tuning fork be sounded in front of the mouthpiece. Then let each of
the vowels be spoken into the funnel with the same pitch and loudness.
The ribbon of flame seen in the mirror is different in each case.
Manometric flames can be used to study sound vibrations
of such high frequency that they are quite inaudible.
Problems
1. If two men are 1000 feet and 2500 feet from a foghorn, how many
times as loud does the horn sbund to one man as to the other?
nuuimuiuiumi
miiimmmmim
Fio. 367. — Forms shown by mano-
metric flames.
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894 PRACTICAL PHYSICS
2. Six seconds elapse between the firing of a gun and its echo from a
cliff. If the temperature is 15° C, how far away is the cliff?
3. A tuning fork is reenforced when held over an air column 6.5
inches long. What is the wave length ?
4. A tuning fork, whose normal frequency is 435, is mounted on a
wooden box, which acts as a resonator. If we neglect the correction
for the end, how long must the box be ?
5. A whistle has a resonating column of air 1.5 inches long. Find
the vibration frequency of its tone.
397. Interference of sounds. We have seen in studying
resonators that two sound waves may unite so as to reenf orce
each other. It is also possible to make two sound waves
unite so as to interfere with or destroy each other. That is,
under certain conditions the union of two sounds can produce
silence. This is the cause of the phenomenon called beats.
If we place two mounted tuning forks of the same pitch side by side,
and strike the forks in succession with a soft mallet, we hear a smooth,
even tone. But if we change the pitch of one fork by attaching a slider
to one prong, and repeat the experiment, we hear a throbbing or pulsat-
ing sound. The throbs are called beats. They are due to the alternate
interference and reenforcement of the sound.
If two adjoining notes of a piano or organ are struck at the same
time, beats are heard, especially if the notes are in the lower part of the
scale.
Beats are made use of when it is desired to tune two
strings or forks to the same pitch. The forks are adjusted
until no beats are heard.
398. Explanation of beats. To show how two sound
waves can combine to produce no sound, let A in figure 368
represent a sound wave,
>ri:~:rvr------:^^^^^^^^^V:- -s^^^rf^::^^ *^^ -^ another wave of ex-
t t actly the same period, but
c c' opposite in phase; that is,
Bs;~-_~;,^rc-_:::i^,_^ ^.^^^ ^ j^^^^ wave length
« o.,o m_ M • ^ V * behind the first. If the
Fig. 368. — Two waves of same period but .
opposite phase. two impulses, which would
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SOUND
395
generate two such waves, were applied to the air, it would
not sufifer any disturbance at all. This is interference of
sound waves.
If two waves of the same period, A and 5, in figure 369,
are in phase or in step,
they reenforce each
other, and produce a
sound of double ampli-
tude, as shown by the
dotted curve O. This
« - . £ J Fia. 369. — Two waves in step resalt in
18 reinforcement of sound reenforcement.
waves.
Finally, if two waves of slightly different period (-4 and -8,
in figure 370) are superposed, there will be reenforcement
at some points and interference at other points, as shown in
the third curve O.
Evidently, if the waves make respectively 255 and 256 vibrations per
second, there will be one reenforcement and one interference (that is, one
Fig. 370. — Curves to show how beats are prodaced.
beat) each second. In general, the number of beats per second is equal to
the difference between the frequencies of the waves.
399. Discord and beats. Experiments show that discord
is simply a matter of beats. If there are six beats or less
per second, the result is unpleasant, but if there are about
thirty, there is the worst possible discord. When the vi-
bration numbers differ by as much as seventy, as do the notes
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396 PRACTICAL PHT8IC8
C and E, the effect is harmonious. If two musical tones
with strong overtones are to be harmonious, it is essential
that there shall not be an unpleasant number of beats between
any of their overtones. This is the reason why the bells of
chimes are struck in succession, not simultaneously.
400. The musical scale. So far we have been studying
^he behavior of a single train of waves in the air, and the
propagation of a single musical tone ; now we will consider
some of the fundamental relations between musical tones.
That is, we shall seek a scientific basis of music.
When we wish to compare two musical tones, we first con-
sider their pitch; that is, their frequencies. Notes of the
same frequency are said to be in unison. When two notes
have frequencies as 1 to 2, the relation or interval is called
an octave. For example, a note whose frequency is 512 is
one octave higher than another whose frequency is 266 ; and
one whose frequency is 128 is an octave below the note whose
frequency is 266.
It has been found that the ear recognizes as harmonious
only those pairs of notes whose frequencies are proportional
to any two of the simple numbers, 1, 2, 3, 4, 6, and 6. It is
still more remarkable that the ear of man has for centuries
recognized that three notes are harmonious when their fre-
quencies are as 4 : 6 : 6. This combination is called the major
triad. Any combination or rapid succession of tones not char-
acterized by simple frequency ratios produces a discord.
The major scale is a sequence of tones so related that the
1st, 3d, and 6th form a major triad ; also the 4th, 6th, and
8th ; and also the 6th, 7th, and 9th (or octave of the 2d). This
is shown in the following table, where the tones of the scale
are represented by the letters used in musical notation.
The arrangement of the notes of an octave on the key-
board of a piano is shown in figure 371. The white keys
correspond to the notes of an octave, the black keys to in-
termediate notes, used in forming other scales.
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SOUND 897
Table op Relations between Notes of an Octave
c
(do)
D
(re)
E
(mi)
F
(fa)
G
(sol)
A
(la)
B
(8l)
c
(do)
d
(re)
4
5
6
4
5
6
4
ft
5
6
1
1
1
1
1
f
¥
2
1
Any frequency or vibration number may be given to the
first note C of the octave and the series built up as indicated.
In fact several
such pitches have piano
been in common Keyboard
use as the starting
point. The so-
called international Treble \^—
pitch, which is <^'^ \^^ ^^:r- 9 fi ?=
now almost ex-
clusively used,
takes 4S5 vibra- ^'®* ^^' — ^^^^ ^^ *° octave on piano keyboard.
tions for middle A (second space on the treble cleff), and
this makes middle C (the lower C on the treble clefif) 258.6.
In physical laboratories C forks usually have a frequency of
256, to make the arithmetic easier.
Absolute pitch -^
on international
scale
CO
00
00
Musical Instruments
401. Piano. We are all familiar with the piano, or at
least we have seen its keyboard, which usually has 88 keys.
When we open the case, we find 88 wires of various lengths
and sizes. Each key operates a little hammer which strikes
a wire and thus produces a note of definite pitch. We may
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PB ACTIO AL PHT8IC8
also notice that the notes of lower pitch are produced bj
long, large wires and the notes of higher pitch by short, thin
wires. Perhaps we have watched a piano tuner loosen or
tighten a wire by turning with a wrench a pin at one end.
If we stretch a piece of steel wire along the table and set
it vibrating, we find its tone is very weak compared to the
tone of a piano. This is because the piano has a sounding
board directly beneath the wires. The vibrations of the
wires are transmitted through the frame to this large thin
board, causing it to vibrate also. The board then sets a
Fia. 372. — A sonometer.
larger quantity of air in vibration than the string could af-
fect alone, and produces a louder tone.
402. Laws of vibrating strings. We may show by means of a so-
nometer (Fig. 372), which is simply a metal wire stretched across a long
wooden box, that the pitch or frequency of a wire is raised by tightening
ithe wire. If we introduce a movable bridge or fret, the pitch is raised.
The shorter we make the wire or string, the higher is the pitch. Finally
we may show that a larger wire of the same length and under the same
tension gives a lower note.
Careful experiments of this sort have proved the following
laws : —
(1) 77ie vibration frequency varies inversely as the length of
the vibrating string. For example, a wire under constant
tension can have its pitch raised an octave by putting the
movable bridge in the middle.
(2) The vibration frequency varies directly as the square
root of the tension. For example, if a pull of 4 pounds on a
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string gives 100 vibrations per second, a pull of 16 pounds
is required to raise the pitch an octave, or produce 200
vibrations per second.
(3) The vibration frequency or pitch varies inversely as the
square root of the weight per unit length of the string. For
example, the wires on the piano which give the low notes
are wound with wire, to get the necessary weight.
403. Other stringed instruments. The violin, mandolin, and
guitar have sets of strings tuned to give certain notes, and
wooden bodies to reenforce the tones of the strings. These
instruments differ from the piano in that they have but few
strings, and in that their strings are set in vibration by bow-
ing or picking instead of by striking them
with a hammer. Each string is made to give
a large number of notes by pressing on it at
various places and so changing its length.
The particular place and manner in which the
string is plucked or bowed determines the
overtones and thus the quality of the tone.
In this way the violin may be made to give
tones with a wide range not only of pitch
but also of quality.
404. Wind instruments. The simplest
wind instrument is the organ pipe. Sometimes
the tube is open at the upper end and is called
an open pipe [Fig. 878 (-1)]; at other times
the pipe is closed at the upper end and is
called a closed pipe [Fig. 373 (^)].
If we blow an open pipe, the current of air strikes against a sharp
edge and is set in vibration. The tube acts as a resonator. The lowest
note which such a pipe gives out is the one whose wave length is twice
the length of the pipe. This note is called its fundamental. If we close
the end of the tube with the hand, thus making a closed pipe, we shall
find that the lowest note is an octave lower, or one whose wave length
is four times the length of the pipe. This is called the fundamental
note of the closed pipe.
Fig. 373. — Organ
pipes: {A) open,
and {B) closed.
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400 PRACTICAL PBT8IC8
In general, then, the length of an open pipe is one half the
wave length of its fundamental^ and the length of a closed pipe
is one quarter of a wave length of its fundamental.
It will be noticed that the resonance tube in the experi-
ment in section 898 is a closed pipe upside down, the tuning-
fork end corresponding to the lip end of an organ pipe.
When air is blown more violently into an organ pipe,
overtones may be produced.
The flute, clarinet, comet, and trombone are also wind instru-
ments. In the first two, the column of air is broken up by
means of holes. The opening of a hole in the tube is equiva-
lent to cutting the tube off at the hole. In the trombone
the length of the air column can be varied by sliding a por-
tion of the tube in and out. It is also possible to vary the
notes by blowing harder and so getting overtones.
In wind instruments of the bugle or comet type, the vibra-
tion of the air is caused by the vibrating lips of the musician.
405. Vibrating membranes. One example of this sort of
musical instrument is the drum. Another is the most won-
derful musical instrument of all, the human voice. It is pro-
duced by the vibration of a pair of membranes on each side
of the throat, called the vocal cords, and also by the vibration
of the tongue and lips. By changing the muscular tension
on the vocal cords one changes the pitch of his voice, and by
changing the shape of the mouth, one changes the overtones,
and so the quality of tone.
Problems
1. An open pipe is 4 feet long. What wave length does it give ?
2. What is the length of an open pipe which gives a tone an octave
above that in problem 1 ?
3. A siren has 50 holes. How many revolutions per minute will it
have to make to produce a tone whose frequency is 435 ?
4. A fork making 256 vibrations per second is reeuforced by a tube
of hydrogen 4 feet long. What is the velocity of sound in hydrogen ?
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5. Find the number of vibrations of a note three octaves below a
note whose frequency is 264.
6. What is the fourth overtone of a string whose fundamental tone
has a frequency of 256 ?
7. The keyboard of a piano has 7 octaves and 2 notes. If the lowest
note is A^ (27), what is the frequency of the highest note c"" ?
8. How long would an open organ pipe need to be to give the note
middle A (international pitch) ?
9. How many centimeters long would the closed pipe of a whistle
need to be to give middle C (international pitch) ?
406. The phonograph. The phonograph (Fig. 374), which
was invented by Thomas Edison, is a remarkable machine
Fia. 374. — Cylinder form of phonograph and diaphragm with recording and
reproducing points.
for reproducing sound, especially music and speech. When
tbe instrument is recording sound, the waves set a diaphragm
vibrating, and this makes a fine metal or sapphire point,
which can move up and down, cut a spiral groove of varying
depth in a wax cylinder. The bottom of this groove is a
wavy line representing the condensations and rarefactions of
the sound waves.
To reproduce the sound a small round-ended needle is at-
tached to the diaphragm and follows the groove in the wax
as the cylinder turns. The varying depth of the groove
moves the needle up and down and thus makes the diaphragm
2d
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402 PRACTICAL PHYSICS
vibrate in such a way as to reproduce the original sounda
In the machine shown in figure 374, the sharp and the round-
ended points are both mounted near the center of the same
diaphragm, as shown at the right. The diaphragm can be
moved forward and back a little so that only one of these
points touches the cylinder at any time.
In another style of phonograph (Fig. 375) the wax is
made in the form of a disk instead of a cylinder, and the
Fio. 375. — Disk form of phonograph and diaphragm.
needle point vibrates from side to side instead of up and
down.
A phonograph does not reproduce the consonant sounds
very distinctly, words being chiefly recognized by the vowel
sounds which come out strong and clear. This is because
the vowel sounds are more or less clearly defined musical
tones, and produce regular vibrations, but the consonant
sounds are noises produced by the mouth at the beginning
and end of vowel sounds.
SUMMARY OF PRINCIPLES IN CHAPTER XX
Sound, in physics, is a vibratory motion transmitted through ail
or other gases, liquids, or solids.
Velocity of sound is about 1100 feet per second.
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(Accurately it is 1087 ft/sec. at 0° C, and it increases about 2
ft/sec. for each degree C rise.)
Wave length = distance from crest to crest (or from condensation
to coQdensation).
Frequency = number of waves passing given point in one second.
Velocity = frequency x wave length.
Intensity or loudness depends on amplitude.
Pitch (of musical tone) depends on frequency.
Quality (of musical tone) depends on wave farm; i.e. on number
and prominence of overtones.
Pitch of a string (l) Rises when length is decreasedy
(2) Rises when tension is increasedj
(3) Is higher for small, light strings.
Length of open pipe = ^ wave length of fundamental.
Length of closed pipe = ^ wave length of fundamental.
Questions
1. How can the pitch of the sound. from a phonograph be raised ?
2. What causes a difference in the pitch of an organ pipe between a
hot day in summer and a cold day in winter ?
3. How can a bugler produce notes of varying pitch on an instru-
ment of unchanging length ?
4. Why is it better to bow a violin string near one end rather than
in the middle ?
5. Is any difference in the quality of a violin tone noticeable when
the bow is moved nearer the finger board ? Why ?
Q. How does the piano tuner go to work to tune a piano?
7. A distant band sounds much the same, except for loudness, as a
band near by. What does this indicate about the velocity of sounds of
different wave lengths ?
8. When an electric light bulb breaks, there is a loud crash. Ex-
plain.
9. A man has two open organ pipes just alike. He saws off a
little from the end of one. Explain what is heard when they are both
sounded together.
10. How do the valves on a comet operate to produce the different
notes ?
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404 PRACTICAL PHYSICS
11. There is an old saying that " if you can count three between a
flash of lightning and its thunder clap, the storm is not dangerously
near/' According to this how far away must the thunder cloud be for
safety ?
12. Explain just why the resonance experiment described in section
■393 will not work if the length of the air column is half a wave length.
13. Explain how sound is produced by some form of automobile horn
or signal in common use.
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CHAPTER XXI
LIGHT: LAMPS AND REFLECTORS
Illumination — law of inverse squares — standard lamps
and " candle power " — Bunsen photometer — " foot candles "
— laws of regular reflection — plane mirrors — concave mirrors
— convex mirrors — graphical construction of image — size of
image — the mirror formula.
407. Problem of illumination. We have to do so much of
our work and play by lamplight, that we ought to know
something about illumination. Of course the first essential
is to have enough light to see things distinctly: Further-
more, experience shows that we may have enough light and
yet not be able to distinguish the position and shape of
objects well, because the lamps are not properly distributed
to cast such shadows as we are accustomed to. Then there is
the very difficult problem of getting lamplight which wiU
give colored objects the same appearance which they have in
daylight. Finally, we have to protect our eyes from the
glare of the modern powerful electric and gas lamps, which
are likely to give us too much light in spots. Besides these
purely physical aspects of the problem of illumination, we
have the economic question of its cost.
408. Some optical terms. We all know that we cannot
see things in a perfectly dark room and that the something
which enables us to see things is light. There are some
objects, such as the sun, the stars, and lamps, which we can
see because they are luminous, but almost everything that we
406
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PRACTICAL PHYSICS
see is visible because of the light which falls upon it and
then comes from it to the eye. Such objects are illaminated'
For example, we can see the pages of this book, if they are
sufficiently illuminated, and if no obstacle is put between
them and the eye. We know that light passes through
some substances, like water, glass, and air, which are called
transparent, and that practically no light gets through other
substances, such as wood and iron, which are called opaque.
Between transparent and opaque substances there is, how-
ever, no sharp line ; for example, we ordinarily think of
water as transparent, and yet in the depths of the ocean
utter darkness prevails. On the other hand, some opaque
substances transmit light if cut in thin enough sections ; for
example, thin gold foil appears green when looked through.
In general, light is in part turned back or reflected by sub-
stances, in part transmitted, and in part absorbed. An object
which absorbs all the light falling upon it is called black.
409. Light advances in straight lines. Everybody knows
by experiemje that it is impossible to see around a corner.
This is because light
under ordinart/ cir-
eumstanees advances
-^ in straight lines.
Ji we set up a screen S
and a candle C, as shown
in figure 376, with an
opaque screen O pierced by
a pinhole in between, we
see an inverted image of
the flame. This shows
that the light goes through the hole in straight lines. Simple " pinhole "
cameras are sometimes made on this principle.
Fio. 376. *— Light travels in straight lines.
The precise measurement of angles by surveyors depends
upon the fact that light comes from the distant object to the
observer's instrument in straight lines.
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LIGHT: LAMPS AND SEFLSCT0B8
407
Fig. 377. — Shadow cast by the earth.
Another consequence of this fact is the formation of a
shadow when an opaque object obstructs the passage of light.
The edge of the shadow is, however, a sharply defined tran-
sition between light and dark, only when the source of light
is very small. For ex-
ample, the shadows cast
by an arc lamp are more
sharply defined than those
cast by a gas flame or a
Welsbach mantle. This
is also shown in the case of the shadow cast by the earth, as
shown in figure 377. The region A is in the full shadow and
is called the umbra, while in the region BB^ on either side, the
light grades off from full shadow to full illumination. This
region is called the penambra. When the moon happens to
get wholly inside the umbra, we have what is called a total
eclipse of the moon. When the moon is partly in the
penumbra, the eclipse is partial.
410. Intensity of illumination : law of inverse squares. It
scarcely needs to be stated that a book is more brilliantly
illuminated when it is held near a lamp than when it is held
far from the same lamp. In other words, the intensity of
illumination, that is, the amount of light falling on a unit
area, decreases when the distance increases.
Fio. 378. — Intensity decreases as the square of the distance.
Let a sheet of metal which has in it a small pinhole P (Fig. 378) be
set up in front of a flame, so that the source of light may be considered
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40S PRACTICAL PBYaica
-a point. Then, one foot away, let us put a piece of cardboard A which
has a hole ifi it one inch square. At a distance of two feet from the pin-
""hole, we will put a screen B. It is evident that the ]ight which passes
through the inch hole in ^ is spread at B over a 2-inch square ; that is,
•over 4 square inches. If we move the screen B so that it is 3 feet from i^,
the light which passes through the inch hole at ^ is spread over a 3-incIi
^uare ; that is, over 9 square inches. The areas of these squares increase
^as the square of the distance. But the amount of light falling on each
%otal area is the same. Therefore the amount on each square inch de-
Creases as the square of the distance.
Intensity of illumination (like the intensity of %ound and for
the %ame rea%on) varies inversely as the square of the distance.
This law assumes that the source of light is a point, and
that the surface is placed at right angles to the rays of light.
In all practical cases, however,
the source of light is a surface
or region, every point of which
is giving light, and in such cases
this law is only approximately
true. When the receiving sur-
face is inclined (Fig. 879), it
Pig. 379. — Surface not at right does not receive as much light
angles to the light. ^^^ square inch as when held at
right angles, and allowance has to be made for this fact.
411. Illuminating power of a lamp. In computing the
amount of light received on a given area we have to con-
sider not only the distance from the source, but also the
illuminating power of the lamp itself. A room, for example, is
much more brilliantly illuminated by a modern electric or
gas lamp than by a kerosene lamp. Since there are now-
many different forms of lamps on the market, and every
householder has to buy some kind of lamp, it is highly im-
portant that we have some way of measuring the illuminat-
ing power of a lamp. To do this we must have a standard
lamp and some instrument for the comparison of lamps, that
is, a photometer.
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LIGHT: LAMPS AND BEFLECTOBS 409^
412. The standard lamp. Although many standard lamps
have been proposed, none are altogether satisfactory. The
oldest standard lamp, which is still used in calculation, but
seldom in actual practice, is the English standard candle,,
which is a sperm candle made according to certain specifica-
tions. The illuminating power of a horizontal beam from
this candle is called a candle power.
The present value of the candle power as used in the
United States is that established by a set of standard incan-
descent lamps maintained at the Bureau of Standards in
Washington, D.C. This unit of intensity is called the
international candle, and has been accepted by England and
France. In Germany the legal unit of intensity is the
Hefner, which is equal to 0.9 international candles.
In testing gas, sperm candles are still used in routine
work, although the intensity of so-called standard candles
may vary by as much as 5 per cent. For more accurate
work, the pentane lamp is coming into use. The Harcourt
form of this lamp burns a mixture of air and pentane vapor
and has an intensity of 10 candles.
The ordinary open gas flame consumes from 5 cubic feet
of gas per hour upward and gives from 15 to 25 candle
power. In Massachusetts the legal standard for gas is that
it shall give 15 candle power in a burner consuming 5 cubic
feet an hour. The gas tested by the state in 1911 averaged
18.42 o.'p. Welsbach lamps consume only about 3 cubic feet
of gas per hour and give from 50 to 100 candle power.
413. Bunsen photometer. This is an instrument for com-
paring the illuminating power of a beam from a given lamp
with the illuminating power of a horizontal beam from a
standard lamp. This " grease-spot " photometer was in-
vented by the great German chemist, Robert Bunsen. It
consists essentially of a white paper screen with a translucent
spot in the center, which transmits light freely. The screen
is placed between the lamps to be compared, so that one side is
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410 PRACTICAL PHYSICS
lighted by one lamp and one by the other. If the screen
is lighted more on one side, that side appears bright with a
dark spot in the center, while the other side is darker with a
bright spot in the center. If the two sides are equally illu-
minated, the spot disappears, or at least looks equally bright
on each side. The arrangement of the Bunsen photometer
i
I
($ A j, B ^
Fig. 380. — Bunsen photometer.
is shown in figure 880. The grease-spot screen is inclosed in
a box, shown in figure 881, which is open at the ends A and
A....^li
^jM^>y^g I ^ toward the lamps to be compared.
r.\
;!}^^ A The eye is held in front at E. Two
mirrors, m^ and Wj, are placed on either
side of the screen, as indicated in the
figure, so that the two sides of the
screen can be seen at the same time.
Fio. 381.— Bunsen light box 414. Usc of Bunscn photometcr.
with screen. rpj^^ photometer must be us'ed in a
dark room or else in light-tight box. The lamp X to
be tested is placed at one end of the photometer bar and
the standard lamp S at the opposite end. The screen is
then moved back and forth until a position is found where it
is equally illuminated on both sides, and the distances A and
B are measured.
It is evident that if the distances A and B are equal, the
candle powers of the two lamps are the same. If the dis-
tances are not equal, the lamp which is farther from the screen
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LIGHT: LAMP 8 AND BEFLECT0R8
411
haB the greater candle power. Furthermore, since the intensity
of illumination decreases as the square of the distance, tTie
candle powers of the two lamps are directly proportional to the
squares of their distances from the screen.
For example, let 16 = candle power of lamp S,
and X = candle power of lamp X
Let 80 cm. = distance of screen from lamp S,
and 100 cm. = distance of screen from lamp X
Then X^jlOOy,
16 (80)2'
so ^ = 25 candle power.
415. Distribution of light. No lamp gives light uniformly
in all directions. Thus in the ordinary kerosene lamp the
burner and oil reservoir cut
off the light which would be
radiated downward from the
flame, and if the flame is
broad and thin, it will give
more light broadside on than
edgewise. Similarly an in-
candescent lamp gives differ-
ent intensities in different di-
rections because of the shape
of the filament.
Since an incandescent lamp
can be easily turned in any po-
sition (Fig. 882), it is not dif-
ficult, with the Bunsen pho-
tometer, to measure its candle power in various positions. If
the candle power is measured for several points in a horizontal
plane, and the results of the tests averaged up, the result is
called its mean horizontal candle power. Such tests show that
the candle power in various directions in a horizontal plane
does not vary very much. In a factory the lamp under
test is rotated around a vertical axis at a speed of about 300
Fig. 382. — Apparatus for turning lamp
to be tested.
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PRACTICAL PHYSICS
11^ a ^
Fig. 383. — Curve to show
vertical distribution.
revolutions per minute, and the photometer reads directly the
mean horizontal candle power of the lamp. A " 16 candle
power lamp" means a lamp of which
the mean horizontal intensity is 16
candles.
If the lamp to be tested is tilted at
various angles in a vertical plane, the
results show that the lamp has very
low candle power directly under the
tip. The results of such tests may be
best shown graphically by a diagram
(Fig. 383). In this figure the inten-
sity of the light in various directions in a vertical plane is
indicated by the curve, which varies in its distance from the
center of the concentric circles according to the intensity of
the light. For example, the candle power directly under the
tip of the bulb (0°) is a little
under 8, while horizontally
(90°) it is 16 candles.
When it is desirable to
throw as much light as pos-
sible directly downward, some
kind of a reflector or shade is
used. Figure 384 shows the
vertical distribution of light
when the bulb is fitted with a
special shade. From this
curve it will be seen that the
horizontal intensity is cut
down to 6 candles, while the
downward intensity runs over
50 candles. Such shades, made in a great variety of forms
to give different desirable distributions, make it possible to
work out scientifically the problem of lighting a given room
or work shop efficiently.
Fig. 384. — Vertical distribution, when
fitted with shade.
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light: lamps and rbflectobs 413
416. Measurement of intensity of illumination. We have
just seen that the unit of intensity for a source of light is
the international caudle. The illumination which such a
standard candle throws upon a surface placed one foot away
and at right angles to the rays of light is called a foot candle.
It is the unit of intensity of illumination. For example, a 1&
candle-power lamp would illuminate a surface placed 1
foot from it with an intensity of 16 foot candles. Again if
the lamp were a 32 candle power lamp and the object were
4 feet away, the intensity of illumination would be 32;
divided by (4)^ or 2 foot candles.
In these examples we have assumed that there is only one
source of illumination and that the surface is perpendicular
to the rays of light. In practice this is almost never the
case, so that the problem of computing or measuring the in-
tensity of illumination on any given surface is very difficult.^
One reason for this difficulty is that we have as yet no satis-
factory simple instrument for measuring intensity of illu-
mination directly.
The amount of illumination needed to furnish " good light
to see by" varies greatly with conditions. For example,
drafting rooms, theater stages, and stores require about 4 foot
candles ; while churches, residences, and public corridors may
need but 1 foot candle. Excessive light is as undesirable as
not enough. Exposed light sources of great brilliancy (more
than 5 candle power per square inch) constitute a common
source of eye trouble. To avoid this, electric bulbs should
be frosted and distributed in small units, or covered with
shades which diffuse the light, or else concealed entirely from
view, in which case the illumination is obtained by light re-
flected from the ceiling and walls. This indirect system of
illumination gives by far the best light, especially for large
rooms in public buildings, but costs more than other systems,
and is to be regarded as a luxury.
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414 PRACTICAL PHT8IC8
Problems
1. If the page of your book is sufficiently illuminated at a distance of
3 feet from an 8 candle power lamp, how many candle power will be
needed when you move 2 feet farther away ?
2. If a photographic print can be made in 30 seconds when held 3
feet from a light, how long an exposure will be needed when the print is 6
feet away ?
3. A 4 candle power lamp is 120 centimeters from a screen. How far
away must a 16 candle power lamp be to illuminate the screen equally ?
4. In measuring the candle power of a lamp, a Hefner standard lamp
(0.90 candle power) is 50 centimeters from the grease spot of a Bunsen
photometer, and the lamp to be tested balances it when 150 centimeters:
from the grease spot. How many candle power has the lamp?
5. Two lamps are 16 and 32 candle power respectively, and are 200
■centimeters apart. Where between the lamps may a grease-spot pho-
tometer screen be placed for its two sides to be equally illuminated ?
6. What is the illumination in foot candles on a surface 5 feet from an
■80 candle power lamp ?
7. The necessary illumination for reading is about 2 foot candles. How
far away may a 16 candle power lamp be placed?
8. If the lamp with the special shade described in section 415 were
hung above a reading table, how high should it be hung? (See curve of
distribution, Fig. 384.)
9. Compare the cost of illumination with gas and electricity. A gas
jet burning 5 cubic feet of gas per hour gives a flame of 18 candle
power. The gas costs 85 cents per 1000 cubic feet. A 16 candle power
lamp consumes 40 watts. Electricity is 10 cents per kilowatt hour.
417. Reflectors, regular and irregular. We have already-
said that we are able to see most objects about us by the light
which they reflect to our eyes. The surface
of visible objects is rough, and so the light
striking the irregular surface is reflected in
an irregular fashion, as shown in figure 385.
Fig. 385.— Diffused This kind of reflection or turning back of
rSuitr^'sV^^^^ the light we call diffused reflection. Thus the
light striking a piece of paper or unvar-
nished wood is scattered. If, however, light strikes a flat
metallic surface so carefully polished that it is very smooth.
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LIOHT: LAMPS AND BEFLECTOBS
415
n
E,
V
/^
f
m
A
/^
m
p
Mirror
n
the light comes to the eye as though coming directly from a
distant object, instead of from the reflecting surface. This is
called regular reflection, and is illustrated in figure 386, where
mm is the reflecting surface or mirror. The line OP in-
dicates the direction of the light falling on the mirror and
PJE indicates the direction of the reflected light.
418. Law of reflection. When light comes through a small
opening, the stream of light is called a beam. A narrow beam
may be called a ray.* When a beam of light comes from a
very distant source, such as the sun, the
rays of which it is composed are parallel,
and so it is called a parallel beam.
In figure 386, let OP be the direction of a
parallel beam striking the mirror mm obliquely,
and PE that of the reflected beam. K a line
nn, called the normal, is drawn perpendicular to
the reflecting surface at the point P, the angle
between the normal and the direction OP of the
incident beam is called the angle of incidence,
and the angle between the normal and the
direction of the reflected beam is called the angle of reflection.
Careful experiments have shown that, whatever the size
of these angles,
I. The incident ray^ the normal^ and the reflected ray lie
in one plane.
II. The angle of incidence is equal
to the angle of reflection.
419. Images in a plane mirror. We
all know that if one stands in front of
a plane mirror, he sees his own image
and that of the objects about him, as if
they were behind the mirror. In figure
387 we see that light coming from any
Fig. 386. — Regular re-
flection from smooth
surface.
Image
Fio. 387. — linage m a plane
mirror.
* A more accurate definition of a •
next chapter.
' ray '^ will be given in section 487 of the
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416
PBACTICAL PHT8IC8
point A of an object is reflected by the mirror to the eye as if
coming from a point A^ back of the mirror. Similarly, light
coming from a group of points (an object AB^ seems to come
from a similar group of points (the image A'B) back of the
mirror. The group of points from which the light appears
to come is called the image of the object. A line AA' drawn
from any point in the object to its corresponding point in the
image is perpendicular to, and is bisected by, the mirror mm.
In general, the im^e of an object in a plane mirror is the
same size as the object^ and as far behind the mirror as the
object is in front.
Indeed, such an image is so much like a real object that
conjurors often make use of the illusions due to the invisibility
of a well-polished mirror. It should, however, be remem-
bered that the image is reversed from right to left, as is seen
when a printed page is held in front of a mirror, so that in
conjuror's tricks no letters or clock faces are allowed to be
seen in mirrors.
420. Uses of plane mirrors. Good mirrors for household
use are made of plate glass backed by a thin coating of silver
or mercury. Only a very small
fraction of the light is reflected
from the front surface of the
glass; the rest is reflected from
the metal back.
Large plate-glass mirrors are
sometimes placed in the walls of
public places to give the impres-
sion of spaciousness. In scien-
tific instruments a very small
mirror is often attached to a ro-
tating part, such as the coil of a
galvanometer. Such a mirror will turn a reflected beam of
light through twice the angle through which the mirror itself
is turned. A rotating mirror, Jf, is an essential part of the
Fio,
. — Sextant used to meas-
ure angles.
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417
Fig. 389.— Center of a corred
mirror.
sextant which the mariner uses to get the altitude of the sun.
By means of a heliostat, which is simply a plane mirror
turned by clockwork so as to keep up with the sun, the
sun's rays may be reflected into a room, through an opening
in the wall, for projection purposes.
421. Curved mirrors. A curved mirror is usually spheri-
cal ; that is, it is a portion of the surface of a sphere. If it
is a portion of the outer surface, it is ^, ^,^
called a convex mirror ; if it is a por-
tion of the inner surface, it is called a
concave mirror. The center of the
sphere, of which the curved mirror
is a portion, is called the center of cur-
vature ((7 in Fig. 389). The line CM
connecting the middle of the mirror
M with the center of curvature O is
called the principal axis. Any other straight line through the
center of curvature, such as OS, is called a secondary axis. It
will be noted that any axis is perpendicular to the reflecting
surface.
422. Principal focus. When a beam of light parallel to
the principal axis strikes a concave mirror, the rays are so
,n. reflected as to pass through,
> ^^v^ > ^\ or very close to, a single
'^'^^ point CFin Fig. 390).
This point is called the
principal focus of the mirror.
It may be defined as that
point where all rays parallel
to and near the principal axis
meet after reflection.
The principal focus is located halfway between the mirror
and its center of curvature.
Suppose the ray QP in figure 391, parallel to the axis AB, strikes the
mirror at the point P and is reflected back in the direction PF, so as to
2e
Fig. 390.-
- Concave mirror converges par-
allel rays.
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PRACTICAL PHT8IC8
make the angle of incidence t equal to the angle of reflection r. Since
QP and AB are parallel lines, the angle t is equal to the angle a. There-
fore the angle a must be equal to the
angle r, and CF = PF. But when P is
near 0, PF is nearly equal to F6>, which
means that F is about midway between
C and 0, It can be proved that the
principal focus which is very close to F
is exactly halfway between C and O.
FiG.^ 391. —Location of principal
focus.
\
*
~J\
*
1 /\
/ /\
I J
/y\
i J
'"^^''''i
3 rJr-
"^ — "x
Jm-
- — 1
c'
^// h
f \
Fio. 392. — Aberration in
spherical concave mirror.
The distance from the princi-
pal focus to the mirror is called
the focal length of the mirror and
is one half the radius of curvature.
All the rays parallel to the principal axis of a concave
spherical mirror do not meet exactly at
the same point after reflection. This
failure of the rays to converge accu-
. rately at a point is called spherical aber-
ration. This imperfection is slight
when only a small portion of a sphere
is used as a mirror. Spherical aber-
ration in a large mirror is shown in
figure 392, where it will be observed
that only the central rays are reflected through the focus F^
while the rays which strike the mirror near the edge are bent
decidedly to the right of F.
It is sometimes necessary, as in the
case of a searchlight, to take the diver-
gent rays of an arc lamp and reflect
them all in one direction. This can be
done roughly with a concave spherical
mirror, by putting the arc at the prin-
cipal focus ; for then the rays travel the
same paths as above, but in the opposite
Fig 393 —Parabolic direction. To avoid spherical aberiti-
mhror. tion, howcvcr, a parabolic mirror (Fig. 393)
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LIGHT: LAMPS AND BEFLECT0B8
419
is generally used. These mirrors are also used in the head-
lights of locomotives and automobiles.
423. Applications of concave mirrors. The ophthalmoscope is
a concave mirror with a little hole in its center. With this
instrument a physician is able to reflect light from a lamp
into a patient's eye, and at the same time to look through
the hole into the eye thus illuminated.
Fio. 394. —Reflecting telescope.
A certain type of telescope, called a reflecting telescope, con-
sists of a long tube with a concave mirror mn at one end,
which forms an image of a distant object. The only pur-
pose of the tube is to support near its open end an eyepiece
or magnifying glass, JE^ through which the image can be
advantageously examined.
In a compound microscope the light from a window or lamp
is concentrated upon the small object to be examined by
means of a concave mirror.
We have already stated that
co.ncave mirrors are extensively
used in searchlights and headlights.
424. Convex mirror. When
a beam of light parallel to the
principal axis strikes a convex
mirror, the rays are reflected
as if they came from a point
behind the mirror. This is
shown in figure 395, where C is the center of curvature
and F is the point from which the reflected rays diverge.
The point F is called a virtual focus because the rays do not
FlQ
Convex mirror and virtual
focus.
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PRACTICAL PHYSICS
actually pass through it, but simply look as if they had come
from it. In the case of the concave mirror the rays do ac-
tually pass through the point -F, as shown by the fact that a
large concave mirror of short focal length causes so great a
concentration of the sun's radiant energy that paper and
wood may be ignited if placed at F. Such a focus is a real
focus.
425. Construction of images. It is possible to learn a great
deal about the position and size of images formed by mirrors,
by carefully constructing dia-
grams to show the paths of the
rays of light.
Suppose mn in figure 396 is a convex
mirror, and AB an object. Let us
draw AC, Si ray normal to the mirror.
This ray will be reflected directly back
on itself. Again let us draw AL par-
allel to the principal axis. This ray
will be reflected as if it came from i^.
The image point of A will be where these two reflected rays cross ; that
is, at A'. Another ray from A that might be used in this construction is
the ray through F. It would be reflected parallel to the axis and would
also pass through A'.
This construction shows that the image in a convex mirror
always seems to be behind the mirror and smaller than the
object. It is erect and is nearer the mirror than the object is.
It 18 always a virtual image.
Thus one sees a virtual image
of his face in a polished ball.
It is always right side up and
of small size.
Suppose MON (Fig. 397) is a
concave mirror, of which C is the
center of curvature. Let -45 be an
object which is placed beyond the
center of curvature. To determine the position of the image, let us trace
two rays from A, The point A\ where they intersect after reflection, is
Fig. 396.— Image in a convex mirror.
Fig. 397.-
Construction of image in con-
cave mirror.
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421
4he image oi A, If -4iV is one such ray passing through C, it will hit the
mirror perpendicularly and be reflected back along the line NC. If the
other ray from A is AM, parallel to the axis, it will be reflected so as to
pass through the focus F, Since B is on the axis, its image B' will also
be on the axis ; so that the image of the arrow AB will be the arrow A^B\
Another ray from A that might be used in this construction is the ray
through F, It would be reflected parallel to the axis and would also
pass through A\
It will be seen that when the object is beyond the center of
curvature, the image is inverted and in front of the mirror.
Since the rays of light
from A really do pass
through -4.', the image is
real.
426. Size of a real
image. Let us draw the
rays AO and OA (Fig.
398). From the law of
reflection, the angle of in-
FiG. 398. — To get the size of a real image.
cidence i is equal to the angle of reflection r. Therefore,
the right triangles -A 0J5 and A!OB^ are similar, and their cor-
responding sides are in proportion. That is,
AB BO
AB' "B^a
The size of the image is to the size of the object as the distance
of the image from the mirror is to the distance of the object
from the mirror,
427. Conjugate foci. We have seen that when A is the
object point, the image point is at A'. But figure 397 shows
that if A' is the object point, the image point is at .4. ; for
the rays will travel the same paths in the other direction.
For example, if a candle were put at AB^ an inverted smaller
image would be formed on a screen placed at A^B^ ; also if
the candle were put at AB\ the image would be inverted,
larger, and located at AB.
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422 PRACTICAL PHYSICS
Two points, so situated that light from one is concentrated
at the other, are called conjugate fod. For example, B and W
are two such points and therefore are conjugate foci.
428. Virtual image in a concave mirror. We have just
seen that when the object is beyond the center of curvature,
the image is between the principal focus F and the center of
curvature O. Also when the object is between F and (7, the
^^ image is beyond C. In
m ^^,^/<s5' both these cases, the image
A^^^i^^'^ i is real; that is, the image
^^^^'^•^j/l I i% always real when the oh-
— •^^—- — j^^ — V^ ^^ ject is outside the principal
j focus F.
I When, however, the ob-
n ject is placed inside the prin-
Fig. 399.— Construction of virtual image ^ipal focUB, that is, between
in concave mirror. _, -, -.jr i * n
F and ilf, as shown m figure
899, the image is behind the mirror, erect, enlarged, and virtual.
To show this we may, as before, trace two rays from the point A, one
parallel to the axis, which is reflected through F, and the other perpen-
dicular to the mirror, which is reflected back on itself through C, They
will diverge after reflection and must be produced backward to find the
point of intersection A'» The image ^' is a
virtual image, because the light from A does
not actually pass through A\
429. Size of a virtual image. Since
every ray from A (Fig. 400) is re-
flected so as to seem to come from
J.', the ray from A to 3£, the middle
of the mirror, will be reflected in the
direction A'MC. Since the angles of ^^^- ^oo.-Toget thesizeoi
" a virtual image,
incidence and reflection are equal.
Angle -4MB = angle BMO.
But A! MS and BMQ are vertical angles and equal. So
Angle ^J£B=angle A! MS.
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LIGHT: LAMPS AND BEFLECT0B8 428
Therefore the right triangles AMB and AIMS are similar,
^^"^ AB^ ^ NM
AB BM'
So in this case, as before, the size of the image is to the size of
the object, as the distance of the image from the mirror is to the
distance of the object from the
mirror.
430. The mirror formula.
Let 0 be an object on the
axis, OM any ray from 0
meeting the mirror at M,
Draw the radius CM and ^ _ ,
J. i .1 n J. 3 Fio. 401. — Real image in concave mirror,
construct the reflected ray
MI, making angle Oil/(7= angle OMI. Then /is the image of
0. Since CM\^ the bisector of the angle OMI, it follows that
OM^qq ...
IM ic' ^ ^
Let IN=^Diy and ON—Dq, When the aperture, that is, the
angle MON, is small, we have the approximate relations
OM=ON=Do, and IM=IN=Di.
Now, since FN^^f
00= ON- CN=Do- 2/,
IC = CN-IN=2f-Di.
Substitutincr these values in the proportion (1), we have
A 2/- A'
and so DJ-\- Z>o/=2>oA.
Dividing by DqX Ax/, we have
where
Do Di /
Dq = distance of object from mirror,
A = distance of image from mirror,
/= focal length of mirror.
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424 PRACTICAL PHTSICa
Stated in words
1 . 1 _
Object distance Image distance Focal length
This equation gives a relation between the distance of the
object, the distance of the image, and the focal length. If
any two of these three quantities are known, the third can
be calculated.
It can be proved that this equation holds as it stands for
all cases of images either real or virtual, formed in a concave
mirror. If the value of 2>i comes out negative, for certain
values of Bq and /, as it will when Bq is less than /, the
meaning is that the image is behind the mirror; that is, the
image is virtual. It can be shown that it holds also for con-
vex mirrors, if the focal length / of a convex mirror is
regarded as negative.
In the next chapter we shall see that the same formula
holds for lenses.
Problbms
1. If a ray of light strikes a plane mirror so that the angle between
the ray and the mirror is 25°, what is the angle between the incident and
reflected rays ?
2. If the mirror in problem 1 is turned 1°, so that the angle between
the incident ray and the mirror becomes 26°, through how many degrees
has the reflected ray been turned ?
3. An object is placed 15 inches from a concave mirror whose radius
of curvature is 12 inches. How far from the mirror is the image ? Is it
real or virtual, erect or inverted ?
4. If the object in problem 3 is 4.5 inches long, how long is the
image?
5. An object is placed 12 inches from a concave mirror whose focal
length is 8 inches. How far from the mirror is the image ? Is it real or
virtual, erect or inverted ?
6. If the object in problem 5 is 2 inches long, how long is the image?
7. An arrow 1 inch long is placed 4 inches from a concave mirror
whose radius of curvature is 12 inches. Find the position, length, and
nature of the image.
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light: lamps and reflectors 425
8. If the image of a candle flame, placed 10 inches from a concave
mirror, is formed distinctly on a screen 30 inched from the mirror, what
is the radius of curvature ?
9. How far from a concave mirror, whose focal length is 2 feet, must
a man stand to see an erect. image of his face twice its natural size?
10. Where must an object be placed, to form, in a concave mirror
whose focal length is 10 inches, a real image one half as long as the
object ?
SUMMARY OF PRINCIPLES IN CHAPTER XXI
Intensity of illtunination varies inversely as the square of the
distance.
Candle powers of lamps giving equal illumination are directly
proportional to the squares of their distances from screen.
(That is, lamp farther away is more powerful.)
Unit intensity of illumination, or foot candle, is illumination due
to a one candle power lamp one foot away.
(Desirable intensity from 1 to 4 foot candles.)
In regular reflection: —
I. Incident, normal, and reflected rays all in one plane.
II. Angle of reflection = angle of incidence.
Plane mirror: Image always behind mirror, erect, virtual, same
size as object, and at same distance from mirror as object.
Principal focus of curved mirror (either concave or convex),
Defined as convergence point for rays parallel to axis of mirror.
Located halfway between mirror and center of curvature.
Concave mirror : —
If object is outside focus, image is also outside focus, and center
of curvature is between object and image. Image is inverted
and real.
If object is inside focus, image is behind mirror, erect and
virtual.
Convex mirror : Image always behind mirror, erect and virtual.
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426 PRACTICAL PHYSICS
Mirror formula (holds for both concave and convex mirrors): —
L__+ 1 L__.
Object distance Image distance Focal length
For concave mirror, focal length is positive.
For convex mirror, focal length is negative.
For real image in front of mirror, image distance comes out
positive.
For virtual image behind mirror, image distance comes out
negative.
Size nde (holds for both concave and convex mirrors) : —
Length of image __ image distance (from mirror)
Length of object object distance (from mirror)
Questions
1. What is the difference between 16 candle power and 16 foot
candles?
2. Explain how a Welsbach gas lamp consuming only 3 cubic feet
of gas per hour gives over 50 candle power, while the ordinary gas jet
uses 5 or more cubic feet per hour and gives only about 18 candle power,
3. If light from a very distant object, such as the sun, falls on a
concave mirror, where is the image formed?
4. How does the curve of a parabola differ from the arc of a circle?
6. How does the action of a parabolic mirror differ from that of a
concave spherical min*or.
6. What is the danger in too great intensity of illumination?
7. Explain how the image of a man standing in front of a plane
mirror, which is tilted so as to make an angle of 45° with the floor,
appears horizontal.
8. A person looking into a mirror sees a very small image of his face
upside down. What kind of mirror is it ?
9. Show by a diagram how a tailor arranges two mirrors so that
a customer can see the back of his coat.
10. A room 20 feet square has plane mirrors on opposite walls. A
man in the room holds a candle close to his head. Where should he
stand so as to be as near as possible to the twice reflected image of the
candle in the mirrors?
11. Why is an image in a plane mirror reversed from right to left>
but not up and down ?
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CHAPTER XXII
LENSES AND OPTICAL INSTRUMENTS
Refraction — law of refraction — velocity of light — wave
fronts — explanation of refraction — index of refraction as
ratio of speeds — total reflection — prism — lens — lens for-
mula — size rule — defects of lenses.
Camera — projecting lantern — moving pictures — eye — de-
fects of eye — magnifying glass — microscope — telescope —
erecting telescope — opera glass — prism binocular.
431. Optical instruments. The human eye is the most
common and at the same time one of the most remarkable
optical instruments known. Human eyes are often imper-
fect in various ways, and have to be " corrected," or rather
aided in their work; for defective eyes themselves are seldom
changed by spectacles or eyeglasses. These, too, we shall
study in this chapter. Even a healthy eye has its limitations,
and many optical instruments have been devised to help it to
see things too far away or too small for ordinary vision.
And finally, there are many devices, such as cameras, stereop-
ticons, and moving-picture machines, that enable us to see
things far away from, or long after, their actual occurrence.
All these devices for enabling us to see better, farther, or at
a different time are called optical instruments.
In all of them we find lenses, and in some of them also
prisms. To understand how optical instruments work, we
must first study the passage of light through lenses and
prisms; that is, the refraction of light.
432. Refraction in water. When a stick stands obliquely
in water, it appears to be broken at the surface of the water
in such a way that the part under water seems to be bent
427
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PRACTICAL PHYSICS
FiQ. 402. — Stick partly in water appears
broken.
upward (Fig. 402). The bottom of a tank of water always
appears to be nearer the surface than it really is. A fisb
appears to be higher in the
water than it actually is,
so that if one wishes to
spear it, he must aim under
its image. All these phe-
nomena are due to the re-
fraction of the light as it
passes from water into air.
We have said that light
advances in straight lines^
but this is only true in a
single substance. In general^ when light goes from one substance
into another of different density^ it is bent or
refracted at the dividing surface.
433. Law of refraction. To measure
how much a beam of light is bent in pass-
ing from water into air, we may perform
the following experiment.
We will set a board
vertically in a jar of
water . and fasten a
wire of solder with
pins along the board
(Fig. 403). If we fill
the jar with water,
and then look down along the wire, we see
that the part under water appears to be
bent upward. If we bend the part that is
out of water, until the whole wire seems to
be straight, we have a model to show the
path of the light in air and water. We may
now remove the board from the water and draw the water line and the
perpendicular COD (Fig. 404).
From this experiment we see that a beam of light in pass-
ing from water into air is bent away from the perpendicular.
Fig. 403. —Light is bent
when leaving water
obliquely.
Fig. 404.— Diagram of ex-
periment of figare 403.
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LEN8E8 AND OPTICAL INSTRUMENTS 425j
It might also be shown that a beam of light in passing
from air into water, in the direction BO^ is bent in the direc-
tion OA (Fig. 404). That is, a beam of light in passing
from air into water is bent toward the perpendicular. In
this case the line BO represents the incident ray and the line
OA the refracted ray. The angle (^OOB^ between the incident
ray and the normal is called the angle of incidence, and the
angle (-4 Oi>) between the refracted ray and the normal is
called the angle of refraction. When light passes from air into
water, the angle of incidence is greater than the angle of
refraction.
To show the relation between the angles of incidence and
refraction, we will lay off equal distances on the incident and
refracted rays (-40 = J50), and draw perpendiculars to the
normal {AI> and J5(7). We shall find that, whatever the
angle of incidence, the line BC is always a definite number
of times greater than AD. For example, in this case BO
might be 4 inches, while AD might be 3 inches, and then
the ratio BO/ AD is |- or 1.33. This ratio is called the index
of refraction. Experiments show that this ratio is always the
same for the same two substances, no matter what the angle
of incidence may be.
This ratio may also be expressed in terms of the ** sines " of the angles
of incidence and refraction. Sine is the name used in trigonometry for
the ratio of the opposite side to the hypotenuse ; thus the sine of the
angle of incidence (t) is BC/BO and the sine of the angle of refraction
(r) is AD/AO. Since AO = BO hy construction,
^^±2^ = m^^^ = inde^oi refraction.
sine of Zr AD/AO AD
434. Refraction of light by glass. We may also show that
a beam of light is refracted in passing from air into glass.
Let a block of glass of semicircular shape be attached to an optical
disk, as shown in figure 405. It will be seen that part of the ray is re-
flected by the glass as if it were a mirror, and part is refracted as it
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PRACTICAL PHT8IC8
Fig. 405.— Ray is partly reflected,
partly refracted.
passes into the glass. It will also be seen that the angle of incidence is
equal to the angle of reflection, but is greater than the angle of re-
fraction. We may measure the perpendicular distances from the ends
of the incident and refracted rays to the
normal 00, and compute the index of
refraction for glass and air.
Ordinary crown glass bends a
ray of light less — that is, has a
smaller index of refraction — than
glass made with lead, known as
flint glass. The lead glass, which
is denser, has an index of refrac-
tion with respect to air of about
1.7, while that of crown glass
and air is about 1.5.
In general, light is bent in passing obliquely from one
substance into another, as from water to glass, diamond to
air, or even from vacuum to air or from a layer of air of one
density to one of another. Thus light is refracted in pass-
ing through the rising column
of warm air over a stove, and
things seem to shimmer or dance
about. The general rule is that
the lesser angle is in the denser
medium.
435. Some effects of refraction.
An interesting case of refraction
of light occurs in the atmos-
phere surrounding the earth.
The air extends only a few miles above the surface of the
earth, thinning out as it goes, and beyond is empty space.
So when a ray of sunlight (Fig. 406) comes through th3 air
obliquely, it is bent gradually toward the normal in passing
from one layer to another; the result is that the eye at 0
sees the sun in the direction of the dotted line in the figure,
,*^
Fig. 406. — Refraction by the earth *8
atmosphere.
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LENSES AND OPTICAL INSTRUMENTS 431
instead of in its real position. For this reason the heavenly
bodies rise somewhat earlier and set somewhat later than they
would if this were not the case. This makes the day some 7
or 8 minutes longer.
436. Speed of light through space. The reason for the
refraction of light was not understood until the velocity of light
in different substances had been determined. Indeed, up to
1675 it was believed that light traveled instantaneously ;
that is, that light consumed no time in its passage between
two points. About that time Roemer, a young Danish
Fio. 407. — Ulastrating Boomer's way of measuring speed of light.
astronomer at the Paris Observatory, was observing the
moons of Jupiter. With great precision he observed just
when one of the satellites JIf (Fig. 407) passed into the shadow
cast by Jupiter, J. The beginnings of these successive
eclipses of Jupiter's satellite may be thought of as signals
flashed at equal intervals. When the earth is traveling
away from Jupiter, the interval between signals is greater
than the true interval because the light from each succeed-
ing signal has a greater distance to travel to reach the earth.
But when we are traveling toward Jupiter, the interval
between signals is less than the true interval, because the
light from each succeeding signal has a shorter distance
to travel to reach the earth. Thus while the earth is travel-
ing from A to J5, the observed times of the eclipses are delayed
more and more, and when the earth has reached -B, the total
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delay has amounted to 16 minutes and 36 seconds (abom
1000 seconds). This means that it takes about 1000 seconds
for the light to travel across the earth's orbit, a distance
of 186,000,000 miles. Therefore the velocity of light is
186,000 miles per second (300,000 kilometers per second). In
recent years the velocity of light has been directly measured
on the earth's surface by several methods, and while the
measurements have been made with great precision, the
results agree very closely with those obtained so long ago by
Roemer.
This velocity is so enormous that it is not strange that the
earlier experimenters could not determine it. In fact, it
takes only 0.001 of a second for
light to travel as far as one can see
on the earth. Light travels a very
little more slowly in air than in a
vacuum. In denser substances,
such as water and glass, light
travels much more slowly.
437. Light waves. Just as we
think of sound as transmitted from
a source through the air by a series
of waves, so we think of light as
transmitted through space by a
series of ether waves. When the
light comes from a point source,
the "crest" or wave front of a
wave, as it spreads in all direc-
tions with equal velocity, is spherical, and the direction of
advance, being radial, is at right angles to the wave front.
Figure 408 (a) represents such a series of expanding waves,
in which the curved lines are the wave fronts and the lines
of arrows indicate the direction of advance of a small section
of the wave front. These lines of advance of light are what
were called rays in the last chapter. A bundle of light rays
^
Fig. 408. — Wave fronts.
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LEN8E8 AND OPTICAL INSTRUMENTS
433
is a beam. In a " parallel beam " [Fig. 408 (5)] the wave
fronts are plane and the rays are parallel.
By means of a lens or curved mirror a beam of light may
be made to converge toward a point, called the focus. In
this case the wave fronts are concave spherical surfaces
which contract as they approach the focus, as shown in fig-
ure 408 ((?).
438. Why light is refracted. When a beam of light passes
from air into water, there is a change in its velocity. To
see that this must cause a bending
of the beam, let the parallel lines in
figure 409 represent wave fronts
advancing in the direction of the
arrows. As soon as the edge B of
a wave front enters the water, it
begins to advance slowly, while the
part A^ which is still in the air, ad-
vances with the same speed as be-
fore. Consequently the direction
of the wave front is changed into ; / A^d
the position (7i>, and the beam is ' *"
bent into a direction nearer the per-
pendicular PM.
This is somewhat analogous to a column of soldiers march-
ing from a smooth, hard field into a rough, plowed field,
where they are slowed up. The man at B hits the rough
ground before the man at A does, and so, while A travels
the distance AO^ B has gone a shorter distance BD. The
result is that if B cannot hurry, and if A does not slow up,
the column swings around from its original direction into
one nearer the perpendicular PB.
439. Speed of light and index of refraction. From figure
409 it will be seen that the amount which the beam of light
is refracted when passing from air into water depends upon
the relation between the distances AO and BB; that is, upon
2f
Fig. 409.
Refraction of oblique
waves.
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434 PRACTICAL PHT8IC8
the relation between the speed of light in air and its speed
in water* Although it is not easy to measure the speed of
light in water, yet it has been done. The speed in water
has thus been proved to be about three fourths that in air.
This means that the speed of light in air is 1.33 times the
speed in water, which is the same number that we found for
the index of refraction of water and air. It can be shown
that in general
Index of refraction = speed in air
speed in other substance
We may prove this as follows :
Index of refraction = ^^^ (see section 433).
smr
But t is equal to the angle ABC, and sin ABC = AC/BC; also r is
equal to the angle BCD, and sin BCD = BD/BC.
Therefore,
rinl ^ AC/BC ^AC^ »P^d in air ^ .^ ^^^ ^f refraction.
Sin r BD/BC BD speed in water
440. Sometimes no change in direction. When a stick
stands vertically in water, it does not appear to be bent,
because when a beam of light leaves a substance such as
water perpendicvlar to the surface^ it suffers no refraction.
The change in velocity is, of course, just the same whether
the light leaves the substance normally to the surface or
obliquely, but bending or refraction occurs only when the
light leav3s obliquely.
441. Total reflection. We have seen in section 432 that
when a beam of light passes obliquely from water or glass
into air, the refracted ray is bent away from the perpendicu-
lar. For example, in figure 410 the light coming from a
point 0 under water, in the direction oa, is refracted in the
direction aa'\ the ray ob is refracted along IV and oc is re-
fracted along ccf. As the angle in the water increases, we
come finally to a ray od which is refracted along dd*^ and
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LENSES AND OPTICAL INSTRUMENTS
435
The angle which is
just grazes the surface of the water,
formed between the ray od and
the normal NM is called th6
critical angle. For water and
air it is about 49°. If this angle
is exceeded, as in the case of
the ray oe^ the ray cannot leave H^-
the water at all, but is totally £3£:
reflected at e, just as if it had
fallen on a polished metal sur-
face, and takes the direction ee^. ' Fig. 410. —Total reflection of light by
The critical angle is the angle water.
in the denser medium which must not he exceeded if the ray is
to get out.
To illustrate total re-
flection, we may hold a
tumbler containing
water and a spoon above
the eye, and look up at
the surface of the water.
A very bright image of
the part of the spoon in
the water will be seen
by total reflection.
If the apparatus
shown in figure 411 is available, the paths of various refracted and re-
flected rays, including some that are totally reflected,
can be studied with great ease.
In optical instruments it is frequently
necessary to have a very perfect reflector,
and for this purpose a right-angle prism with
polished sides is used. Let a ray of light
A strike the side XZ of such a prism (Fig.
412) at right angles. It suffers no refrac-
tion, but passes on through the glass to B
on the side FZ, where it makes an angle of 45° with the
Fig. 411. — Refraction and reflection of light by water.
V
A
r/^**
%
X
c
Fig. 412. — Total re-
flection of light by
right-angle prism.
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PRACTICAL PHTSICa
Fig. 413. — Path of ray
through plate glass.
normal mn. But the critical angle for crown glass is about
42^ ; therefore the ray AB does not emerge from the glass,
but is totally reflected in the direction BO. It then strikes
the face XY perpendicularly and emerges without refraction.
^ The result is that the ray is bent 90°,
as if there had been a plane mirror at
YZ.
442. Refraction by plate with paral-
lel sides. When a ray of light (-4.-B,
in figure 413) passes through a glass
plate with parallel faces, such as a
good window pane, it is refracted at B
towards the normal iV, and at 0 away
from the normal M,. The result is
that the ray CD is parallel to the ray
AB. Consequently when we look at
any object through a glass plate, we see it slightly displaced
in position, but otherwise unchanged. When the plate is
thin, this change of position is too slight to attract attention.
443. Refraction by a prism. When a
ray -XT' enters one side of a prism {ABO^
in figure 414), it is bent in the direction
YZ^ and on emerging, it is again bent in
the direction ZW. Thus the ray XO is
bent out of its original course to X'TFl
The total change of direction is measured
by the angle XOX!^ called the angle of de-
viation. Any substance which has two
plane refracting surfaces inclined to each other is a prism.
The angle A is called the refracting angle of the prism.
The path of a ray of light through a prism can be worked
out by drawing a diagram, like figure 404, at Y and again
Fia. 414. — Refraction
of light by a prism.
at-^.
It should be remembered that the
toward the thicker 'part of a prism.
learn is always herd
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LEN8E8 AND OPTICAL IN8TBUMENT8
437
Problems
(The stndent should have a small protractor.)
1. If the angle of incidence of a ray of light passing from air into
glass is 68°, and the angle of refraction is 36°, find by construction the
index of refraction.
2. If the index of refraction for air and water is 1.33, and the larger
angle is 60°, find by construction the smaller angle.
3. Taking the index of refraction as 1.33, find by construction the
critical angle for water.
4. If the critical angle for crown glass is 42°, find by construction the
index of refraction.
6. Assuming the velocity of light in air to be about 186,000 miles per
second and the index of refraction of flint glass to be 1.6, compute the
velocity of light in flint glass.
6. The angles of a prism are 20°, 70°, and 90°. A ray of light enters
normally the face bounded by the angles 90° and 70°. The glass has a
critical angle of 42°. Prove that the ray will be twice reflected before it
leaves the prism.
444. Lenses, convergent and divergent. A lens is a piece
of glass, or. other transparent substance, with polished spher*
Double Consuex PlMn
COSUiBX
Fig. 415. — Converging lenses.
ical surfaces. A straight line drawn through the centers Oj
and OIj (Fig. 415) of the two spherical surfaces is called
the principal axis of the lens.
Lenses are divided into two classes, converging or " thin-
edged'* lenses (Fig. 415), and diverging or "thick-edged"
lenses (Fig. 416). A converging lens is thinner at the edge
than in the center. A common type of this class is the
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PRACTICAL PHYSICS
double convex lens,
than at the center.
A diverging lens is thicker at the edge
The double concave lens is a common
Double Concave
Plane
Concave
Diverping
Meniscus
Fig. 416. — Diverging lenses.
Fig. 417. — Focus of convex lens.
lens of this class. It should be remembered that when a ray
of light passes through a lens^ it is always henU just as in a
prism, towards the thicker part
of the lens,
445. Action of converging
lens. Suppose a converging lens is
held so that the sunlight comes to it
along its principal axis (Fig. 417).
The rays of light will be so re-
fracted as to converge at a point F
on the axis. If a piece of paper is
held at jP, a small but very bright image of the sun is formed and the
paper is quickly charred. The thicker the lens,
the nearer the point jP is to the lens, as shown
in figure 418.
The point F^ where rays parallel to
the principal axis converge, is called
the pincipal focus of the lens. The dis-
tance from the lens to the principal focus
is called the focal length,/, of the lens.
Since an incident ray and its corre- ^^t^^-i^^^lt^^,""^
sponding refracted ray are reversible^ it
follows that a light, placed at the principal focus jP, would
send its rays through the lens in such a way as to come out
parallel.
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LENSES AND OPTICAL INSTRUMENTS 489
446. How a lens is made. The surface of a lens is shaped
by grinding together the glass. and an iron matrix with every
possible variety of sliding motion. The glass and the matrix
are thus brought automatically to an almost perfect spher-
ical shape. The polishing is done by using finer and finer
grinding materials in succession (usually powdered emery or
carborundum), ending with rouge. In the later stages the
matrix is l^ned with a layer of stiff pitch with cross grooves
cut in its surfaces to hold the rouge.
447. Conjugate foci. When the light from an object 0 on
the principal axis passes through a double convex lens, the
rays, after leaving the
glass, converge at a point ^^^
L Two such points, 0
and /, are called conjugate
foci, for if the object were
placed at 7, the image yig, 419. — image of distant object is at F.
would be at 0. If the
point 0 is not on the principal axis, the line joining 0 and 1
passes through the center of the lens, called its optical center,
and the line is called a secondary axis.
When the lens is thin, the same formula holds as was used
for mirrors (section 430).
Do D, f
where Dq = distance of object from lens.
J) J = distance of image from lens,
/= focal length of lens.
448. Discussion of the lens formula. If the object is so far
away that the rays from any point of it to different parts of
the lens are practically parallel, the image is formed at F;
for Dq is very large, and so — is nearly zero; this leads to
Bf =/, as shown in figure 419.
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PRACTICAL PHT8IC8
If the object is brought nearer the lens, the image moves
farther away from the lens. When -Do = 2/, 2)/= 2/ also,
as shown in figure 420.
- Object at J^, rays emerge
parallel.
Fig: 420. — Image at same distance as object.
If the object is brought still nearer the lens, the image
moves still farther away from the lens, until, when the
object is at the principal focus -F,
the distance of the image becomes
infinitely great, and the rays that
go out from the lens are parallel,
as shown in figure 421.
If the object is brought even
nearer the lens, the rays on the
farther side diverge as if they came from a focus I behind
the lens (Fig. 422). In this case, the formula shows that i>/is
negative. This means that
the image is behind the lens.
For divergent lenses, the
same formula can be used, if
the focal length f is regarded
as negative.
449. Images formed by
lenses. The geometrical
construction of images formed by lenses will indicate the size
and position of these images. The method of procedure is
the same as that used for spherical mirrors (section 425). If
we trace two rays from any point of the object to their
intersection, we have the position of the corresponding point
of the image. For example, in figure 428, a ray from A
parallel to the principal axis must, after refraction by the
S- -fx—T •><
negative
Fig. 422. — Object inside F, image vir-
tual.
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LEN8E8 AND OPTICAL INSTRUMENTS
441
lens, pass through the
principal focus F. An-
other ray from A^ passing
through the center of
lens, is undeviated. The
point A^ where these rays
meet is the image point
of A. Then from similar triangles it is readily seen that
Fio. 423. — Size of real image.
^--x-w^'
Lens
Length of image __ distance of image from lens
Length of object distance of object from lens'
The ratio of the length of the image to the length of the
object is called the linear magnification.
In figure 423 the object AB was beyond the principal focus of
the convex lens,
and the image
A'B' is inverted,
real, and in this
case smaller than
the object.
In figure 424
the object AB is
between the prin-
cipal focus F
and the lens. The 'image A^B' is erect, virtual, and larger,
and can only be seen by looking through the lens.
In figure 425 the lens is concave Lens
and the image is erect, virtual, and
smaller.
In all these cases it will be seen
that straight lines drawn from the
extremities of the object through
the center of the lens pass through
the extremities of the image, and ^^ 426.-Virtuai image formed
therefore the diameters or lengths by concave lens.
^^^^^^irtual Image
Fig. 424. — Size of virtual image.
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442 PRACTICAL PHT8IC8
of object and image are to each other as their respective dis-
tances from the center of the lens, as stated in the formula
above.
450. Defects of images formed by lenses. In figure 423 it
was assumed that the real image A'B' was a straight line.
But it will be seen that the point A of the object is at a
greater distance from the center of the lens 0 than the
point J5, and, therefore, according to the lens equation, B'
ought to be farther from the. center of the lens than A'. In
other words, the image is curved. This means that if a cam-
era is equipped with a simple convex lens, and the center
of the plate is sharply focused, the edges will be fuzzy, since
the image does not lie in one plane. This is especially notice-
able for a large object comparatively close to the lens.
In the construction of figure 423 it was assumed that all
the rays coming from a point in the object are accurately re-
fracted by the lens to one point. But as a matter of fact the
rays that strike the outer portions of a lens are refracted
more strongly than the rays which fall on the central portion
of the lens, and so come to a focus nearer to the lens. This
lack of exact concurrence is called spherical aberration.
The effects of spherical aberration are to make the image
indistinct and to distort its shape. If the outer rays are
cut out by means of a diaphragm or stop, the sharpness of the
image is improved, but at the same time its brightness is
diminished. In large lenses, such as those used in telescopes,
the outer portions are so ground that their refracting power
is diminished by the proper amount to insure distinct images.
This whole geometrical theory of lenses applies only to
very thin lenses, and to cases where the light may be assumed
to pass through the lens in a direction not greatly inclined to
the axis of the lens. In practice, combinations of lenses are
nearly always used instead of simple lenses, and these com-
binations are designed so that the imperfections of one lens are
compensated or balanced by the imperfections of another lens.
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LEN8E8 AND OPTICAL INSTRUMENTS
443
Problems
1. A convex lens has a focal length of 16 centimeters. Find the posi^
tion and nature of the images formed when objects are placed 10 meters,
60 centimeters, and 10 centimeters respectively from the lens.
2. If an object is placed* 32 centimeters from the lens described ii.
problem 1, how far is the image from the lens?
3. A lamp placed 60 centimeters from a lens forms a distinct image on
a screen 20 centimeters away on the other side. Find the focal length of
the lens.
Fia. 426. — A simple camera.
Optical Instruments
451. Photographic camera. The simplest form of camera
consists of a light-tight box (Fig. 426) with a converging lens
at one end, so mounted as to form
an image of an outside object upon
a sensitive plate. This plate consists
of a silver compound spread on a
glass plate or celluloid sheet (film).
The light is allowed to pass through
the lens for a time which varies
from a thousandth of a second up
to several minutes, according to the
lens, the brightness of the object to be photographed, and the
" speed" of the sensitive plate. The image
on the plate is not visible until the plate is
placed in a mixture of chemicals called a
"developer." To obviate the spherical
aberration of a single lens a diaphragm is
put in front of the lens so as to limit the
size of the pencil of light. With a small
opening, or " stop," we get great sharpness
in the picture, but must expose it for a
longer time. A " combination lens," with
^MonYenTf^r'^ra^id *^® diaphragm between the two lenses
work. (Fig. 427), is used to take clear pictures
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444
PRACTICAL PHYSICS
Fio. 428. — Projecting lantern.
of a rapidly moving object. Since the plate on which the
image is formed must be in the position which is the conjugate
focus of the position occupied by the object, the camera is
usually made with a
^11 viii|| s bellows so that it can
~^'^^****""****' ~ be " focused " on ob-
jects at varying dis-
tances.
452. Projecting lan-
tern. The projecting
lantern, or stereopticon,
is used to throw an
image of a brilliantly
illuminated object or
picture upon a screen.
It consists essentially
of a powerful source of light, such as an electric arc A (Fig. 428),
the condensing lenses (7, which converge the light through the
slide or transparent picture /S, and the front lens or objective
Z,- which forms a real image of the picture on the screen JS'.
It will be noticed that the lantern is much like the camera
except that the object and image
have been interchanged. Since the
screen is usually at a considerable
distance, the slide S is only a little
beyond the principal focus of the
objective L. It is very important
to have a powerful light source
which is small in size. For this
purpose electric arcs, calcium lights,
acetylene lights, and electric glow
lamps, in which the filament is coiled
into a small space, are sometimes
used. Figure 429 shows the arrangement of the lantern to
project opaque pictures, such as post cards.
Fio. 429. — Projection of opaque
objects.
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LENSES AND OPTICAL INSTRUMENTS 445
The moying-pictore machine, which is now so common^ is a
projecting lantern designed to show lifelike motion. A
series of photographs is taken with a camera provided with
a shutter which automatically opens and shuts about 12 times
a second. A long narrow film moves a little while the
shutter is closed, but remains stationary while it is open.
Each of such a series of pictures differs slightly from the
preceding one, if anything is moving in the field of the
camera.
Then this series of pictures is thrown on the screen at the
same rate as that at which they were taken. The sensation
produced by one picture re-
mains until the next picture
appears, so that we are not
aware of any interruption be-
tween the pictures. pupo^
453. The eye. The human
eye (Fig. 430) is essentially
a little camera, with a lens
system in front, and a sensi-
tive film, made of nerve fibers,
, , , , 1 Fig. 430. — Section of the human eye.
at the back.
It has the great advantage over any other camera in that
it can take a continual succession of pictures all on the same
film, "developing" them by some unknown chemical or
electrical process in the nerve fibers instantaneously, and
transmitting the results equally instantaneously over a
"private wire" (the optic nerve) to "headquarters" (the
brain).
The structure of the eye is shown in figure 430. There
is an outer horny membrane, the cornea, holding a watery
fluid called the aqueous humor. There are also an adjustable
diaphragm, or " stop," called the iris, and a crystalline lens.
The latter is of somewhat higher index of refraction than
either the aqueous humor in front or a similar fluid, the vitre-
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446 PRACTICAL PHYSICS
0U8 humor, behind. At the back is the nerve layer or retina,
which acts as the sensitive film.
It should be noticed that most of the converging power
of the eye comes, not in the lens, but at the front surface of
the cornea. This explains why we can never see objects
distinctly when swimming under water. The aqueous fluid
and the water outside are so much alike that there is no
longer any refraction of the light as it strikes the cornea,
and the lens by itself is not powerful enough to bring the
light to a sharp focus on the retina.
454. Focusing the eye. If an object is moved nearer a
camera, the distance between the plate and lens must be
increased, or else a lens of greater convexity, that is, of
shorter focus, must be substituted, if the picture is to be
sharp. Of these two possibilities, the eye chooses the sec-
ond. It adapts itself to varying distances, not by moving
the retina, but by changing the focal length of the lens.
When the muscles of the eye are relaxed, the lens is usually
of such a shape as to focus clearly on the retina objects
which are at a considerable distance. When one wishes to
look at near objects, a ring of muscle around the crystalline
lens causes the lens to become more convex, so as to form
a distinct image on the retina. It is often said that objects
are seen most distinctly when held about 10 inches (25
centimeters) from the eye. This simply means that 10
inches is about as near as one can usually focus an object
distinctly, and since the shortest distance gives the largest
image, this is where we automatically hold an object when
we want to see its details.
455. Imperfections of the eye. In the short-sighted eye
the image of a distant object is formed in front of the retina
(at J., in figure 431). This may be due to too great con-
vexity in the crystalline lens, or to the oval shape of the eye-
ball. A person who is short-sighted must bring objects
close to the eye to see them distinctly.
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LEN8E8 AND OPTICAL INSTRUMENTS
447
In the far-sighted eye the image of an object at an ordinary
distance would be formed behind the retina (at -B, in figure
432). This is because the crystalline lens is too flat, or the
Fig. 431. — Short-sighted eye.
Fig. 432. — Far-sighted eye.
length of the eyeball is too short. To see distinctly, such a
person must hold objects at a distance.
Spectacles with concave lenses are used to correct short-sighted
eyes, and convex lenses are used for far-sighted eyes.
Another defect of the eye is astig-
matism, which occurs when the lens of
the eye, or the cornea, does not have
truly spherical surfaces. The efifect is
that a spot of light, like a star, is seen
as a short, bright line. In a case of
astigmatism all the lines in such a
diagram as figure 433 .will not appear
equally distinct. Those in one direc-
tion will be sharply defined, while Fig. 433. — Lines to test as-
those at right angles to them will ap- tigmatism.
pear broadened and blurred. This defect is corrected by the
use of cylindrical lenses.
456 Apparent distance and size. The apparent size of an
object depends on the size of the
image formed on the retina, and
consequently on the visual angle.
From figure 434 it is evident
that this angle increases as the
object is brought nearer the eye.
For example, when we look along a railroad track, the
rails seem to come nearer together as their distance from ua
Fig. 434. — The visual angle.
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448 PRACTICAL PHT8IC8
increases. The image of a man 100 yards away is one tenth
as large as the image of the same man when he is 10 yards
oflF. We do not actually interpret the larger image and
larger visual angle as meaning a larger man, because by ex-
perience we have learned to take into account the known
distance of an object in estimating its size.
Distant objects seen in clear mountain air often seem
nearer than they really are. This is because we see the ob-
jects more clearly and distinguish the details more sharply;
and this often leads us to think that they are smaller than
they really are. The moon, on the other hand, seems bigger
when near the horizon, because we can compare it with ob-
jects whose size we know. It is only by long experience that
we learn to estimate the actual size and distance of objects.
457. The simple microscope or magnifying glass. We
have said, in section 454, that the distance of most distinct
vision is about 10 inches. If an object is placed at a greater
distance than this, the image on the retina is smaller and
the details of the object are not seen so distinctly. If the
object is placed nearer than
this, the image on the retina
is blurred. When an object
is examined by a magnifying
glass, the distance between the
lens and the object is made
less than the focal lenerth.
Fig. 435. — Magnifying glass. , j- i. j i.i. i.
and so adjusted that an
erect enlarged virtual image is formed about 10 inches away
(Fig. 435). The magnifying power of a simple microscope
is the ratio of the size of the image to the size of the object.
This is equal to the distance of the image divided by the dis-
tance of the object, that is, 10/i>o, Dq being the distance of
the object (in inches) from the lens.
Thus if a magnifying glass can be held 1 inch from an
insect, the magnification will be 10 diameters.
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LEN8E8 AND OPTICAL INSTBUMENTS
449
458. Compound microscope. Very small objects are made
visible by the compound microscope. It consists of two lenses
or lens systems which are placed at the ends of a tube. The
object AB is put just outside the principal focus of the
smaller lens L (Fig. 436), called the objective, which forms
an enlarged, real image CD. This real image is then ex-
Fia. 436. — Compound microscope.
amined through the eyepiece J?, which acts like a magnifying
glass, giving a still larger virtual image at (7'D', about 10
inches from the eye.
The image CD is magnified as many times as its distance
from the lens L is greater than the focal length of that lens.
Usually the distance of CD from L is about 150 millimeters,
and so, if the lens has a focal length of 6 millimeters, the
2g
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PRACTICAL PHYSICS
image CD is 30 times as long as the object AB, If the eye
piece still farther magnifies the image 10 times, the magni-
fying power of the combination is 10 x 30, or 300 diameters.
Microscopes which magnify as much as 2500 diameters are
sometimes used.
We are indebted to the microscope for many of our most
valuable discoveries about the structure and life of plants
and animals, about the smallest living things, and about the
causes of disease.
459. The telescope. The telescope enables us to see clearly
objects so far away that we could not otherwise see their
_, r
Fig. 437. — Astronomical telescope.
details. The simpler sort, called the astronomical telescope,
consists of two lenses or lens systems, the large objective 0
(Fig. 437) and the eyepiece JE. The inverted real image
/, formed by the lens 0, is much smaller than the object,
but it is brought so near to the observer that it can be exam-
ined through the eyepiece JE, which acts like a magnifying
glass. The two lenses are mounted in an extension tube so
that the eyepiece can be drawn farther from the objective
when objects near at hand are to be examined. Since the
magnifying glass or eyepiece does not reinvert, the observer
sees things upside down, just as he does in a microscope.
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LENSES AND OPTICAL INSTRUMENTS
451
It can be shown that the magnifying power of an astronomi-
eal telescope is equal to the number of times the focal length of
the eyepiece is contained in the focal length of the object glass,
460. The erecting telescope or spyglass. This instrument
(Fig. 438) is like the astronomical telescope except that an
additional converging lens or lens system L is introduced
between the object glass 0 and the eyepiece JE. This lens
L inverts the image Z» forming another real image at J' ;
Fia. 438. — Erecting telescope or spyglass.
then this erect image J' is magnified by the eyepiece, which
forms an enlarged, erect, virtual image J". In the ordinary
spyglass the eyepiece is a combination of two lenses, which
act like a single magnifying glass. The introduction of the
erecting lens L lengthens the telescope tube considerably.
461. Telescope used for sighting. A gun cannot be
sighted with the greatest possible accuracy if its sights are
pins or pointed projections. This is because it is impossible
to focus the eye both on the sights and on a distant object
at the same time. For example, the best that can be done
with the naked eye at a distance of 100 yards is subject to
error of one or two inches. Therefore many of the best long-
range rifles are provided with telescopic sights. Similarly,
surveyors make use of the telescope in their " transits " and
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PRACTICAL PHYSICS
"levels." In all such cases two very fine wires or spider
lines are stretched across the telescope in the plane where
the image of the distant object is formed by the object glass,
and the intersection of these
two cross hairs is made to
coincide with the image, of
any given point of the object.
When this adjustment is
made, a line drawn from the
point of intersection of the
cross hairs through the center
of the object glass passes
through the given point of
the object.
The opera glass and field glass. The opera glass (Fig.
Fig. 439. — Surveyor's level.
462.
440) is a telescope whose eyepiece is a di-
verging or concave lens. Since the eye-
piece has approximately the same focal
length as the eye of the observer, its effect
is practically to neutralize the lens of the
eye. So we may consider that the object
glass forms its image directly on the ret-
ina. The field of view of the opera glass
is small, and so the opera glass is usually
made to magnify only three or four times.
But it has the advantage of being compact
and gives an erect image. Galileo made
a telescope on this plan which magnified
about 30 diameters and enabled him to
make some exceedingly important dis-
coveries. A large-sized opera glass is
usually called a field glass.
463. The prism field glass or binocular.
An instrument, called a binocular, has come
into use in recent years which has the wide
Fig. 440.— Opera glass
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LEN8X8 AND OPTICAL INSTBUMENTa
453
FiQ. 441.— Prism binocular.
field of view of the spyglass and at the same time the com*
pactness of the opera glass. This compactness is obtained by
causing the light to pass back and forth between two reflect-
ing prisms, as shown in figure 441. This device enables the
focal length of the object glass to be three times as great as
in the ordinary field
glass for the same
length of tube, and
so the magnifying
power is correspond-
ingly increased.
Furthermore, the
reflections in the
two prisms secure
an erect image with-
out using the erect-
ing lens of the ordinary terrestrial telescope; for one double
reflection tips the image right side up, and the other shifts
right and left, thus restoring it completely to its natural
position.
Problems
1. When a camera is focused on an automobile 100 yards away, the
plate is 8 inches from the lens. How much must the distance between
the lens and the plate be changed when the automobile is only 10 yards
away? Must the distance be shortened or lengthened?
2. A 5 inch post card is to be projected on a screen 20 feet away so
as to be 5 feet long. Find the focal length of the lens required.
3. A photographer with a " 12 inch lens " wants to make a full-length
picture of a 6 foot man standing 10 feet from the lens. How near the
lens must the plate be placed ?
4. How long a plate must be used in problem 3 ?
5. How near to an object must a hand magnifier of 1.2 inches focal
length be held to magnify it 6 diameters?
6. A reading glass of 5 inches focal length is held 4 inches from a
printed page. How much does it magnify?
7. It is necessary to project a slide 3 inches wide on a wall 40 feet
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454 PRACTICAL PBT8IC8
distant, so that the picture shall be 10 feet wide. What must be the
focal length of the objective of the lantern ?
8. In a compound microscope the objective lens L (Fig. 436) has a
focal length of one inch and the object AB is 1.1 inches away. How fax
from the lens is the image CDl How many times is it magnified? If
the eyepiece magnifies this image 20 times, what is the magnifying
power of the instrument?
9. A telescope has an objective whose focal length is 30 feet, and an
eyepiece whose, focal length is 1 inch. How many diameters does it
magnify ?
10. The focal length of the great lens at the Yerkes Observatory is
about 60 feet and its diameter 40 inches. The eyepiece has a focal
length of 0.25 inches. Calculate its magnifying power.
SUMMARY OF PRINCIPLES IN CHAPTER XXII
Refraction occurs when light passes obliquely from one substance
to another.
Smaller angle is always in denser medium.
Index of refraction = -^^eofjargeran^,
sine of smaller angle
_ speed in rarer medium
speed in denser medium'
Velocity of light = 186,000 miles per second,
= 3 X ltf° centimeters per second.
Critical angle is smaller angle, when larger angle is 90^
Prism bends light toward thick edge.
Convergent (thin edged) lens bends light inward.
Divergent (thick edged) lens bends light outward.
Principal focus defined as convergence point for rays parallel to
axis.
Lens formula: Holds for both converging and diverging lenses: —
1 + 1 _ 1
Object distance image distance focal length
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LEN8E8 AND OPTICAL INSTRUMENTS
456
For convergent lens, focal length is positive.
For divergent lens, focal length is negative.
For real image, beyond lens from object, image distance
comes out positive.
For virtual image, on same side of lens as object, image
distance comes out negative.
Size rule: Holds for both converging and diverging lenses:^
Length of image _ image distance
Length of object object distance
//
/>
Questions
1. Which people would be likely to become short-sighted early,
those who live much out of doors or those who stay much indoors?
2. Compare the eye, part by part, with the camera.
3. How does a " wide-angle " lens differ from a long-
focus lens?
4. What are the defects of a pinhole camera ?
5. What is the difference between a refracting and
a reflecting telescope ?
6. Prism glass, with a section like that shown in
figure 442, is often used for the upper part of shop windows
and doors and for windows facing on narrow courts. Why ?
7. Why is it necessary to build powerful telescopes
very wide as well as very long?
8. Why must a compound microscope be so accu-
rately focused on the object?
9. Why is it best to have your light for writing or
sewing come from over your left shoulder?
10. Explain how the wheels of moving vehicles in a
moving picture sometimes seem to be rotating backwards.
11. What part do the condensing lenses play in the
action of a stereopticon?
/
Fig. 442.— Sec-
tion of plate oi
prism glaps.
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CHAPTER XXIII
SPECTRA AND COLOR
Prism spectrum — achromatic lenses — spectroscope — types
of spectra — spectrum analysis — Fraunhofer lines — wave length
of light — colors of objects — colors of thin films — infra-red
and ultra-violet — electromagnetic theory.
.464. Analysis of light by prism. If we let a beam of sunlight pass
through a narrow slit into a dark room, and put a glass prism in its path
(Fig. 443), the beam of light is
refracted. If - we put a white
screen in the path of the re-
fracted light, a band of colors is
formed. In this band are red,
yellow, green, blue, and violet,
though there are no sharp lines
of division between them.
This colored band, which
shades off gradually from
red to violet, is called a
spectrum. This shows that
the ordinary white light of the sun is complex and contains
different kinds of light. The light which is refracted least,
the eye recognizes as red, and that which is most refracted,
as violet. It will be shown later that the physical property of
light which determines this difference in refrangibility is the
wave length.
To show that the prism itself did not produce the different
colors, but simply separated various kinds of light already
present in the beam of sunlight. Sir Isaac Newton placed a
second prism in the spectrum, so that only violet light fell
on it. He found that the violet light was again refracted,
but that there was no further change in color.
456
Fio. 443. — light decomposed by prism.
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SPECTRA AND COLOR
457
Fia. 444. — Combining spectral colors into
white light.
He also found that when these dispersed or spread out,
colored lights were brought together by a converging lens
(Fig. 444), white light was
the result.
465. Achromatic lenses.
When sunlight passes
through an ordinary double
convex lens made of a single
piece of glass, the light is
refracted and converges at
a point called the focus. But the light is also dispersed,
just as in a prism, and the focus for red light (iZ, in figure
445) is at a greater distance from the lens than that for
violet light (F). Such a
single lens cannot give a
sharp image of an object
illuminated by ordinary
white light, for all the lines
of separation between light
and dark portions of the
image will be colored.
This defect, which is known as chromatic aberration, may be
remedied by combining a lens of crown glass with a lens of
flint glass, as shown in figure 446.
By carefully designing the two
component lenses which are in
contact, it is possible to make
achromatic lenses, which produce the
necessary refraction without dis-
persion. The two parts of small
achromatic lenses are cemented to-
gether with Canada balsam.
466. Spectroscope. In the spec*
trum produced by a prism the different colors overlap each
other to some extent. This can be remedied by using a
FiQ. 445. — Dispersion produced by a lens.
Converging Diverging
Fia. 446. — Achromatic lenses.
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PBACTICAL PHY8IC8
spectroscope. There are four main parts in a spectroscope
(Fig. 447) : the collimator, which has a slit at one end and a
convex lens at the other ; a prism, commonly of flint glass ; a
telescope, which has an object glass and eyepiece, and a scale
tube, which has a ruled scale at one end and a lens at the other.
In the collimator the slit is at the principal focus of the lens,
and so light diverging from the slit is made parallel by the lens
before it reaches the prism.
Here it is refracted and dis-
^-^ — -^^^^^ persed, each color going off as
a parallel beam in its own
Fig. 447. — Spectroscope.
direction. The telescope forms a sharply defined image of
the spectrum. The scale tube, which is added to locate the
parts of the spectrum, is so mounted that the light from the
illuminated scale is reflected from the second face of the
prism into the telescope along with the spectrum.
467. Kinds of spectra. The spectrum of sunlight, or solar
spectrum, is frequently seen in summer time after a shower in
the form of a rainbow. The sunlight is refracted and dis-
persed by the raindrops. When the solar spectrum is studied
carefully with a spectroscope, it is found not to be a contin-
uous band of colors, but to be crossed by many vertical dark
lines. Since these lines were first studied by a German
astronomer, Fraunhofer, they are known as Fraonhofer lines.
Not all sources of white light give these dark lines. For
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SPECTRA AND COLOR 459
example, an electric arc lamp, an incandescent lamp with a car-
bon filament, an ordinary gas flame which contains many par-
ticles of incandescent solid carbon (soot), and indeed all
incandescent solids give continuous spectra.
The spectrum of an incandescent vapor or gas is quite
different. It is what is called a bright-line spectrum, and is
characteristic of the substance used.
If we dip a platinum wire or bit of asbestos into a solution of common
salt (sodium chloride) and hold it in a blue Bunsen flame, we get a
bright yellow flame. K we examine this flame with a spectroscope, we
sifee a bright yellow line which occupies the position of the yellow part of
the spectrum. This yellow light comes from the incandescent sodium
vapor.
If we repeat the experiment with a wire dipped in a chemical, called
lithium chloride, we get a red flame, which gives in the spectroscope two
bands, one yellow and one red. Calcium chloride also gives two bands,
green and red. (The yellow band, which is likely to be seen also, is due
to sodium present as an impurity.)
468. Spectrum analysis. When the spectroscope is used
to examine the spectrum of other gaseous substances, it is
found that each element has its own characteristic spectrum.
It may be simple as in the case of sodium, or it may be com-
plex as in the case of iron vapor, which has more than four
hundred lines. Since a very small quantity of a substance
will show its characteristic spectrum lines (for example, less
than one millionth of a milligram of sodium can be detected),
we have a very delicate method of analyzing substances.
Spectrum analysis was first used by the chemist Bunsen in 1859.
469. Absorption spectra. Kirchhoff (1824-1887), while a
professor of physics at Heidelberg, worked conjointly with
Bunsen in these investigations with the spectroscope. Kirch-
hoff observed that when he held an alcohol flame colored
with common salt in front of the slit of the spectroscope and
allowed a beam of sunlight to pass through the slit, the
sodium line became especially dark and sharp, although he had
expected it to be especially bright. He concluded that the
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460
PRACTICAL PHYSICS
sunlight had been in part absorbed by the yellow sodium
flame and that the special part had been removed which the
sodium flame itself ordinarily gives out. This fact was
generalized by Kirchhoff in the following law : —
A glovring gas absorbs from the rays of a hot light-source
those rays which it itself sends forth.
The demonstration of KirchhofPs law may be conveniently performed
with the apparatus shown in figure 448. The source of light L is the
glowing positive carbon of the electric arc, whose rays are made parallel
by a lens 0. Two strips of asbestos board, soaked in salt water, are
Fig. 448. — Absorption of light by sodium vapor.
heated by a wing top Bunsen burner. The light from the electric arc
passes directly through the sodium flame into a " direct-vision " spectro-
scope which disperses the light on the screen Sc,
First we set the sodium flame burner to one side, and produce a con-
tinuous pure spectrum on the screen.
Then we bring the sodium flame into position, and we see in the yel
low portion of the spectrum a dark line.
K we cover the lens 0 with an opaque cardboard, of course the spec-
trum disappears, but in the place of the dark line we now have the bright
sodium line.
Finally, if we place a small white screen with a narrow slit where the
dark line is located just in front of the screen Sc, the dark line on the
screen Sc shows as a yellow line.
This shows that the dark absorption band is not absolutely black, but
is so much less intense than the direct radiation from the arc that it ap-
pears black by contrast.
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SPECTRA AND COLOR 461
It is evident, then, that to produce black absorption lines
the absorbing vapor must be colder than the luminous source.
470. Meaning of Fraunhofer lines. We have said in sec-
tion 467 that the solar spectrum contains a large number
of dark lines. Kirchhoff concluded that these dark lines
were caused by the presence in the glowing solar atmosphere
of those substances w;hich themselves produce bright lines in
the same positions. The core of the sun is at a very high
temperature and gives forth a continuous spectrum. But
this core is surrounded by a layer of gas which is cooler and
absorbs those light rays which it itself would send out. On
this basis he concluded that such metals as iron, magnesium,
copper, zinc, and nickel exist as vapors in the solar atmos-
phere. After much study he found that the bright-line
spectra of all the elements on the earth correspond in position
to certain Fraunhofer lines, and concluded that all the ele-
ments found on the earth exist in the atmosphere of the sun.
There were certain other Fraunhofer lines whose elements
were not known on the earth in Kirchhoff's time. One of
these new elements, helium, has since been found on the
earth, and perhaps the others also will sometime be found. ^
Kirchhoff's explanation of the Fraunhofer lines was epoch
making. Helmholtz said, "It has excited the admiration^
and stimulated the fancy of men as hardly any other dis-
covery has done, because it has permitted an insight into
worlds that seemed forever veiled to us."
471. The nature of light. We have said that light is con-
sidered to be a vibration of the ether. That is, light and
heat are both forms of radiant energy. But we must not
think that this has always been the accepted theory. To be
sure, the great Dutch physicist, Huygens (1629-1695), worked
out very completely the wave theory, but his rival, Sir Isaac
Newton, in England, maintained the older corpuscular theory,
according to which light consists of streams of very minute
particles, or corpuscles, projected with enormous velocity
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462 PRACTICAL PHYSICS
from all luminous bodies. Newton's reputation as a scientist
was so great that his unfortunate corpuscular theory con-
trolled scientific thought for more than a hundred years, and
it was not until the beginning of the nineteenth century
that the experiments of Thomas Young in England and oi
Fresnel in France placed the wave theory on a firm basis.
472. Different colors due to different wave lengths. It is
now possible to measure directly the length of the waves of
light of different colors, and to show that the waves of red
light are longest and those of violet are shortest. So in the
dispersion of sunlight by a priam^ it is the long waves (red)
which are refracted leasts and the short waves (violet) which
are refracted most. The following table gives the approxi-
mate wave lengths of some of the colors.
Wave Lengths of Light
Red, 0.000068 cm. Green, 0.000052 cm.
Orange, 0.000065 cm. Blue, 0.000046 cm.
Yellow, 0.000058 cm. Violet, 0.000040 cm.
473. Colors of objects. The color of any object depends
(1) on the light which illuminates it, and (2) on the light it
reflects or transmits to the eye.
A skein of red yarn held in the red end of the spectrum appears red.
But when held in the blue end of the spectrum, it appears nearly black.
Similarly a skein of blue yarn appears nearly black in all parts of the
spectrum except the blue, where it has its proper color.
Another striking experiment is to illuminate an assortment of bril-
liantly colored worsteds or paper flowers by the light from a sodium
flame. This light contains but one group of wave lengths. Those wor-
steds which reflect these wave lengths look bright, while those which do
not reflect them look dark. They all look either yellow or dark.
Thus it appears that when a piece of paper looks white in
daylight, it is because it reflects all wave lengths equally,
and when a piece of cloth looks red in daylight, it is because
it reflects only those long waves which produce red light.
If the white paper receives only waves of red light, it appears
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SPECTRA AND COLOR
46a
red, and if the red cloth receives only waves which have no
red in them, it appears dark. That is, the color of an opaque
object depends on the wave length of the light it reflects. The
Cooper-Hewitt mercury vapor lamp is a very efficient electric
lamp, but it cannot be used in places when colors must be
distinguished, for it does not furnish waves of red light.
If we place a piece of red glass in the path of the light which is dispersed
by a prism to form a spectruni) we see only the red portion of the spectrum.
This shows that all the wave lengths except the long red ones have been
absorbed. In a similar way a green glass lets the green light through, but
greatly reduces the other parts of the spectrum. If we insert both the
green and the red glasses, the spectrum almost completely vanishes.
Thus we see that the color of a transparent object depends on
the wave length of the light it transmits. Ordinary red glass,
such as photographers use for their red lanterns, transmits
freely only red light, and absorbs almost
completely the yellow, green, blue, and
violet light, which especially afifect the
chemical compounds used on photo-
graphic plates.
474. Mixing colors and mixing pig-
ments. There are other colors besides
white which do not have a definite wave
length. A mixture of several wave
lengths may produce the same sensation
as a single wave length.
Let us rotate a disk part red and part green
(Fig. 449) so rapidly that the effect on the eye is
the same as though the colors came to the eye
simultaneously. The revolving disk appears yel-
low, much like the yellow of the spectrum. By
mixing red and blue we get purple, which is
not found in the spectrum. By mixing black
with red or orange or yellow we get the various shades of brown.
The colors of the spectrum are called pure colors and the
others compound colors. If yellow light is mixed with just
Fig. 449. — Newton's
color disk.
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PRACTICAL PRT8IC8
the right tint of blue, white light is produced. Such colors
are called complementary colors.
Let us pulverize a piece of yellow crayon and a piece of blue crayon.
If we mix the two together about half and half, the color of the resulting
mixture is bright green.
This shows that while mixing yellow and blue light pro-
duces white, mixing yellow and blue pigments produces green.
This is because the yellow pig-
ment absorbs or subtracts from
white light all except yellow and
green^ and the blue pigment sub-
tracts all except blue and green^
therefore the only color not ab-
sorbed by one pigment or the
other is green. In other words, in
miodng pigments^ the color of the
mixture is that which escapes absorp-
tion by the different ingredients.
475. Colors of thin films. The
brilliant colors produced by the reflection of light from thin
transparent films, like the film of a soap bubble, furnishes
one of the strongest arguments
for the wave theory of light.
Let us bind two pieces of plate glass
A and B (Fig. 450) together with rub-
ber bands, in such a way that they will
be separated at one end by a piece of
tissue paper C If we hold the glass
strips behind a sodium flame, we see in
the reflected image of the yellow flame
a series of horizontal fine dark lines. -
To explain this effect we will
draw a much-enlarged section of
the glass plates with the wedcfe ^ , . „ ,
^?,,^ T/! APH Fig. 451.— Explanation of forma-
Ot air between. In figure 451 tlon of bright and dark Unes.
Fig. 400. — Interference of light
waves.
Interference
G Re-enforcement
7 Interference
Be-enforcement
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SPECTRA AND COLOR 465
let AB and BO he the glass plates, and let the yellow so-
dium light b^ coming from the right as a series of trans-
verse waves which we can represent by the wavy lines.
We know that this light is in part transmitted and in part
reflected at each glass surface. But we are interested only
in what Jiappens at the interior faces AB and BO ot the
plates. Let the full line BJS represent the light reflected at
the point J) on the surface J.-B, and let the dotted line B^U
represent the wave reflected at D' on the surface BO. If
the distance from D to D' is such as to make one reflected
wave just half a vibration behind the other in phase, they
will neutralize each other or interfere. At this point we have
a dark line. But at another point Fthe distance between
the plates may be such that the wave reflected at F' coin-
cides with or reeoforceB the wave reflected at F, At this
point we see a bright yellow line. If we select any two
consecutive dark lines, we know that the double path between
the plates at one line must be just one wave length longer
than that at the other line. This gives us a method of com-
puting the length of a wave.
For example, we may compute the wave length of sodium light, if we
know the length of the air gap, the thickness of the paper wedge, and
the distance between two dark lines. Thus suppose the length of the
air wedge is 100 millimeters, the thickness of the paper is 0.03 milli-
meters, and the distance between adjacent lines is 1 niillimeter. Since
the width of the wedge increases 0.03 millimeters in a distance of 100
millimeters, it increases 0.0003 millimeters in 1 millimeter, and the in-
crease in the double path between adjacent dark lines would be 0.0006
millimeters. This is approximately the wave length of sodium light.
476. Sunlight decomposed by Interference. We may sub-
stitute a soap film for the wedge-shaped air film used in the
preceding experiment, and illuminate it by sunlight instead
of the yellow light of the sodium flame.
Let us dip a clean wire ring into a soap solution and set it up so that
the film is vertical. The water in the film will run down to the lower
2h
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466
PBACTICAL PHT8IC8
edge, and the film becomes wedge-shaped. Let a beam of sunlight, oi
the light from a projection lantern, fall on this soap film and be reflected
to a white screen. Furthermore, let a convex lens be arranged, as in fig-
ure 452, so as to produce a sharp image of the film F on the screen S,
We shall see on the screen a series
of horizontal bands of the various
colors of the spectrum.
The white sunlight is com-
posed of different colors and
so of different wave lengths.
The interference of the red
waves takes place at one
point, and that of the yellow
at a different point. Where
there is interference of the
red waves, the complemen-
tary color, a sort of bluish-
green is left ; and where
there is interference of the
yellow waves, the color com-
plementary to yellow, namely, blue, is produced. In this way
we have a series of colored bands which are complementary
to all the colors of the spectrum.
Many beautiful color effects are caused by the interference
of light waves by very thin films. The colors of oil films on
the surface of water, of the thin films of oxide on metals
and on Venetian glass, of the feathers of the peacock and of
changeable silk are due to the interference of light waves.
477. Infra-red and. ultra-violet rays. In the last few years
we have come to know that the sun is sending out not only
the light waves which affect the optic nerve, but also other
longer ether waves which, though invisible, yet can produce
strong heating effects, and are called the infra-red rays (Fig.
453). We have also learned, by photographing the spectrum
of the sun, that it is sending out rays too short to be seen, which
affect a photographic plate, and are called ultra-violet rays. •
Fio. 452. — Interference of white light in
soap film.
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SPECTRA AND COLOR 467
478. Electromagnetic theory of light. As we have seen,
Faraday was led to believe that his *' lines of force " trans-
mitted electricity and magnetism through some medium,
probably the ether. A few years later Maxwell developed
this theory of Faraday's and put it on a mathematical basis.
The argument was finally clinched in 1887 by a young
German, Hertz. His experiments proved that electric waves
really exist, and have the same velocity as light, although
I I I 1 I I n I I I I I I I I I
400 700 1000 1600 2000
Fig. 453.— Chart of waves of varying lengths.
they are sometimes many meters long. These electromag-
netic waves are reflected and refracted like light waves.
Therefore, we feel sure that light waves are electric waves. This
conception, and that of the conservation of energy, are the
most remarkable achievements of physics in the nineteenth
century.
SUMMARY OF PRINCIPLES IN CHAPTER XXIII
Continuous spectrum formed by incandescent solids.
Bright-line spectrum formed by incandescent gases.
Dark-line spectrum formed by incandescent solid shining through
an absorbing layer of cooler gas.
Wave length of visible spectrum ranges from about 0.000068 cm.
(red) to about 0.000040 cm. (violet).
Short waves most refracted by prism.
Color of an object depends on wave lengths reaching eye.
Colors of thin films due to disappearance of certain wave lengths
by interference.
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468 PBACTICAL PHT8IC8
Questions
1. A clean platinum wire is held in a blue Bunsen flame and observed
through a spectroscope. What sort of a spectrum would you expect to
get?
2. What kind of Fraunhofer lines must one get in the light of the
moon?
3. What kind of a spectrum would you get if you looked at the
mantle of a Welsbach lamp through a spectroscope?
4. The complete spectrum of the sun's rays is said to consist of three
parts : heat spectrum, light spectrum, and chemical spectrum. Explain
the appropriateness of these terms.
6. What causes the various colored lights used in fireworks?
6. Why does a blue dress look black by the light of a kerosene lamp ?
7. Why does a reddish lampshade make a room seem more cheerful
at night?
8. How are colored moving pictures produced?
9. Why do they not use glass lenses in the ultra-violet microscope ?
10. What sort of waves are used in wireless telegraphy?
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CHAPTER XXIV
ELECTRIC WAVES: ROENTGEN RAYS
Discharge of condenser is oscillatory — electrical resonance
— electric waves — detectors — wireless telegraphy.
Discharge through gases — cathode rays — Roentgen rays —
radium.
Electrical Waves
479. Discharge of Leyden jar is oscillatory. In 1842
Joseph Henry discovered that when a Lej^den jar was dis-
charged through a coil of wire surrounding a steel needle,
the needle was magnetized. Not only that, but he was
astonished to find that sometimes one end was made the
north pole and sometimes the other, even though the jar was
always charged' the same way.
He accounted for this fact by
supposing that the discharge cur-
rent kept reversing back and
forth, that these oscillations grad-
ually died away, and that the
direction in which the needle was
magnetized depended on which fig. 454.— Oscillatory eiectric
way the last perceptible oscilla- discharge,
tion happened to go. This oscillatory current is represented
by the curve in figure 454.
A few years later Lord Kelvin, the great English physicist
and engineer, proved mathematically that the discharge must
be oscillatory. Finally, in 1859, Feddersen succeeded in
photographing an electric spark by means of a rapidly rotat-
469
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470
PRACTICAL PHT8ICS
ing mirror. Figure 465 shows such a photograph. The
oscillatory discharge is drawn out into a band by the rotating
mirror, and thus makes a zigzag trace on the camera plate.
From this experiment it is possible to calculate the time of
one oscillation. It is exceedingly short, varying from one
one-thousandth to one ten-millionth of a second.
480. Electrical resonance. Tlie frequency of the oscillatory
current produced by discharging a condenser depends upon
the capacity of the condenser, and upon the resistance and
self-induction of the circuit through which the current surges.
Now we have already seen, in studying
sound waves, that two objects having the
same frequency of vibration tend to vibrate
in sympathy, and that this property of a
vibrating body is called resonance. Mechan-
ical resonance also occurs in the case of
two pendulums.
Let us stretch a piece of rubber tubing between
two supports and suspend two weights x and y by
threads of equal length, as shown in figure 466. If
we set one pendulum y swinging, the other pen-
Fig 456. -Resonance ^^j^^ ^ ^^^ ^^ .^^ ^ ^^.^ ^^^ ^^^ ^^^^ ^^^
in two pendulums. ,. , ® « x xu xu rrx.-
dies down as energy flows across to the other. This
will happen only if the pendulums are of the same length and so of the
same frequency. That is, resonance is necessary for the transfer of energy.
In a similar way, if two Leyden jar circuits have the same
capacity and the same self-induction, they will have the same
frequency, and one circuit will influence the other.
In figure 457 let A and B be two Leyden jars of the same
size and thickness of wall. To the jar A is connected a rec-
tangular circuit of thick wire, one end of which touches the
outer coating of the jar, while the other is separated from
the knob of the jar by a small spark gap. The jar B is con-
nected to a similar circuit, except that the end CD of the
rectangle can be slid back and forth, and there is no spark
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bla. 455 (in upper comer). —Oscillations of electric spark.
Fig. 466.— X-ray picture of a broken ankle, which had been called "sprained ••
by a doctor. Taken in a physics laboratory by the brother of the patient.
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ELECTRIC WAVES: ROENTGEN RAYS
471
gap. Finally, let the inner coating of B be connected to its:
outer coating by a strip of foil cut sharply across at X.
If we place the two electrical cir-
cuits a foot apart and parallel, and
send sparks across the gap of A by
means of an induction coil, we find
that there is a position of the slider
CD such that tiny sparks appear at
the gap X in the foil strip on B,
When the slider is moved a short dis-
tance from this position either way,
the sparks at X cease.
This phenomenon is called
electrical resonance. Although ^o. 457.— Resonance between elec-
. 1 . x* i_ X trical circuits.
there is no connection between
the two circuits, yet the energy in one circuit surges over
into the other, which is in tune with it, and causes a spark
there. In seeking for an explanation of this experiment,
and many others, we must conclude that an oscillatory dis-
charge or spark sends out waves in the surrounding ether.
The ether does for the electric circuits what the rubber
tubing did for the pendulums. It serves as a medium for
the transfer of energy.
These electric waves were first detected and measured by
Hertz, in 1888, and are therefore called Hertzian waves. They
travel with the same velocity as light.
481. Electric wave detectors. Very sensitive means for de-
tecting these electric waves have been invented. One means,,
invented by Branly and used by Marconi in his first wireless
telegraphs, is called a coherer. It consists of a small glasa
tube closed at each end by metal pistons. A space of a mil-
limeter or two between the pistons is filled with rather coarse^
filings of nickel and silver. When electric waves fall on
this coherer, the mase of filings " coheres " or sticks together
and becomes a conductor. A slight tap causes the resistance
of the coherer to return to its original high value.
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PRACTICAL PHYSICS
The microphone, described in section 310, is an excellent
wave detector. Another form, called a crystal detector, con-
sists of a piece of silicon, or of any one of several crystal-
line substances, such as galena, embedded in soft metal
on one side and touched on the other by a metal point. In
the electrolytic detector a fine metal point just touches the sur-
face of a conducting solution or electrolyte. The operation
of crystal and electrolytic detectors seems to depend on some
mysterious property whereby they let electricity flow through
them in one direction much more easily than in the other.
482. Wireless telegraphy. Through the efforts of the
Italian inventor, Marconi, and many others, electric waves
are now being extensively used in wireless
telegraphy.
A simple sending station, such as Marconi
used in his earliest experiments, is shown in
figure 458. The essential part is a conductor
called the aerial or antenna, extending to a con-
siderable height above the ground. Powerful
electrical oscillations are set up in this con-
ductor, like the oscillations in the spark dis-
charge shown in figure 455. These send
waves out through the ether,
just as a stick laid on water
and shaken up and down
sends out ripples over the
surface of the water.
One way to set up oscilla-
tions in an aerial is to put a
spark gap in it, and to send
sparks across this gap by
Fig. 468.— Simple sending station.
means of an induction coil fed by batteries, as in figure 458.
Another way is to put a condenser in parallel with the gap in
the aerial, and to fill the condenser many times a second by
means of a step-up transformer fed by an alternating current.
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ELECTRIC waves: ROENTGEN RATS
473
Such a condenser will send a spark across the gap each time
it fills. Another way is to put a very high frequency alter-
nating current dynamo in the place of the spark gap in the
antenna.
The simplest kind of a receiving station is represented in
figure 459. There is an aerial like that at the sending sta-
tion, except that instead of a spark gap, it contains a detector
of some sort. In parallel with this detector is a telephone
receiver. Every time a train of waves
reaches such a receiving station, some
of the energy is absorbed by the aerial,
and electrical oscillations are set up in
it. These cannot get through the tele-
phone because of its self-induction, and
so they have to pass through the de-
tector. But since a crystal detector
lets more electricity through one way
than the other, an excess of electricity
accumulates in the antenna. This ex-
cess then discharges through the tele-
phone, and the diaphragm moves over
and back once. Since this happens
every time a train of waves comes in,
which is many times every second, as
long as th(B key of the sending station
is closed, the telephone diaphragm is Fio. 469.— a simple receiv-
kept vibrating and emits a steady ing station,
musical note. The duration of this note can be made shorter
or longer by holding the sending key down a shorter or a
longer time, and so the dots and dashes of the Morse code
can be transmitted.
The circuits used in commercial wireless telegraphy are
much more complicated than these, because it is necessary
to " tune " the sending and receiving stations accurately to
the same frequency, and to make them insensitive to waves
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474 PRACTICAL PHYSICS
of any other frequency, so that one pair of stations may not
interfere with another. For an explanation of commercial
sending and receiving stations the reader may consult any
of the numerous popular or technical books on wireless
telegraphy.
Wireless telegraphy is now used on all ocean steamships,
so that they are in constant communication with other ships
or with land stations. Timely aid has thus been called to
ships in distress. Warships are kept in touch with th6 naval
headquarters of their governments, which have powerful
sending stations. One of the largest of these uses the Eiffel
Tower in Paris as the support of its antenna, and sends oiit
time signals to ships all over the Atlantic Ocean. Messages
have been sent even as far as across the Atlantic Ocean by
the Marconi stations at Wellfleet, Cape Cod, Massachusetts,
and at Poldhu, England.
483. Wireless telephony. A wireless sending station ordi-
narily sends out wave trains at unvarying intervals, 1000
every second, because it is fed by an alternating current of
unvarying frequency, say 500 cycles per second, and emits one
wave train for every loop of the current. Since the tele-
phone diaphragm of the receiving station moves once for
each train received, its vibration is also at a uniform rate
(1000 vibrations per second in the case just mentioned) and
it emits a musical note of unvarying pitch. Recently send-
ing stations have been devised that emit wave trains at vary-
ing intervals corresponding to the varying pitches and qual-
ities of human speech. When such a succession of wave
trains falls on an ordinary wireless receiving station the dia-
phragm in its telephone vibrates like the diaphragm of an
ordinary telephone receiver, or like the diaphragm of a phon-
ograph, and emits speech. Wireless telephone messages can be
picked up by any one who has a properly tuned wireless tele-
graph set. Wireless telephony is already practicable over con-
siderable distances, but is not yet (1913) a commercial success.
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ELECTRIC WAVES: ROENTGEN RATS 476
Electrical Discharge through Gases
484. Sparking voltage. The voltage needed to make a
spark jump between two knobs depends on several factors,
such as the size of the knobs, the distance between them, and
the atmospheric pressure. It takes less voltage to cause a
spark to jump between two sharp points than between two
round balls. For example, the sparking voltage for two sharp
points 1 centimeter apart is about 7500 volts, and for two
round balls 1 centimeter in diameter and 1 centimeter apart
is about 27,000 volts. The sparking voltage between two
sharp points varies so nearly as the distance that this is a.
method used to measure very high voltage.
To show the effect of atmos-
pheric pressure we may connect
a glass tube 2 or 3 feet long with
an induction coil, as shown in
figure 460. The tube is connected
with a vacuum pump by a side
tube. When the coil is first
started, the discharge takes place
between x and y, the terminals of
the coil, which are only a few Fio. 460.— Discharge in partial vacuum,
millimeters apart, but as the air
is pumped out of the tube, the discharge goes through the long tube in-
stead of across the short gap xy. This shows that the Sparking voltage
decreases when the pressure is diminished.
485. Discharges in partial vacua. Reducing the atmos-
pheric pressure between two points makes it easier for an
electric discharge to pass, until a certain point in the exhaus-
tion is reached. Then it begins to be more difficult. At
the very highest degree of exhaustion yet attainable it is
hardly possible to make a spark pass through a vacuum tube.
The changes in the appearance of such a tube as the ex-
haustion proceeds are very interesting. At first the dis-
charge is along narrow flickering lines, but as the pressure
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476
PBACTICAL PHYSICS
is lowered, the lines of the discharge widen out and fill the
whole tube until it glows with a steady light. With still
higher exhaustion, a soft, velvety glow covers the surface of
the negative electrode or cathode, while most of the tube is
filled with the so-called positive column which is luminous
and stratified, and reaches to the anode. The so-called
Geissler tubes (Fig. 461)
are little tubes of this sort
which are usually made in
fantastic shapes and serve
JPiQ. 461. — Geissler tube, made to study
spectra of hydrogen.
as pretty toys. The color of the light from a Geissler tube
depends on the gas which is in the tube, and on the kind
of glass used.
486. Cathode rays. When the exhaustion of a tube is
carried to a very high degree, so that the pressure is equal
to about 0.0001 of a millimeter of mercury, the positive glow
is very faint and the dark space around the cathode is per-
vaded by a discharge. An invisible radiation streams out
nearly at right angles to the cathode surface, no matter where
the anode is located in the tube. This radiation from the
cathode is called cathode rays and shows itself in several
ways : first by a yellowish green fluorescence
wherever it strikes the glass of the tube ;
^econd^ by the fact that it can be brought to
a focus where it produces intense heat ; and
thirds by the sharply defined shadows which,
a metal interposed in its path produces in
the fluorescence on the end of the tube.
A Crookes' tube, arranged as in figure 462, shows
the heating effect of the cathode rays. When an in-
duction coil sends a discharge through the tube from
top to bottom, the cathode rays are focused on a piece
of platinum which becomes red hot.
Another Crookes"* tube, arranged as in figure 463, yiq. 462. — Heatiog
shows that a shadow is formed on the end of the tube effect of cathode
by an aluminum cross. rays.
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ELECTRIC WAVES: ROENTGEN BAT8
477
Fig. 463. — Shadow formed by
cathode rays.
487. Bending of cathode rays.
A Crookes' tube, mjide as in figure
464, sends a narrow band of
cathode rays through the slit 8 in
the aluminum screen mn against
a fluorescent screen / slightly in-
clined to them. When a strong
magnet M is held near the side of
this tube, it is found that the
stream of cathode rays is deflected
in the direction which would be expected if they were a stream
of negatively charged particles. From this and other experi-
ments we believe that cathode ray% are nega-
tively charged particles projected at very high
velocity from the cathode,
J. J. Thomson, the English physicist, has
estimated from various experiments on cath-
ode rays that the negatively charged particles,
which he calls electrons, have each a mass
about sixteen hundred times smaller than
that of a hydrogen atom, and move with a
velocity of from one tenth to one third that
of light. It is supposed that each particle
carries a negative charge of electricity equal
to that of the hydrogen atom in electrolysis.
Fig. 464.— Bending 488. Roentgen layB. In 1895, while ex-
of cathode rays by perimenting with a vac-
a magnet. ^ u. u t> i. j-
uum tube. Roentgen dis-
covered another kind of rays which he
called X-rays. When cathode rays strike
against a platinum target, as shown in
figure 465, Roentgen rays are sent off
from this target. They affect a photo-
graphic plate somewhat as sunlight does ;
x-ray FUld
but, like cathode rays, they will penetrate
Fia. 465.— Roentgen raj
tabe.
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478 PBACTICAL PHT8IC8
many substances opaque to ordinary light, such as wood^
pasteboard, and the human body. That they are not the
same as cathode rays is shown by the fact that they are not
deflected by a magnet.
When a photographic plate, inclosed in the usual plate-
holder with sides of hard rubber or pasteboard, is exposed,,
with a hand held over it, to Roentgen rays, a shadow pic-
ture like that seen on the fluorescent screen is formed.
We may demonstrate the action of Roentgen rays by operating an.
X-tube with an induction coil, and holding a fluorescent screen in front
of the bulb. If the room is dark and the hand is interposed between
the tube and the screen, the flesh, which is easily penetrated by the rays^
will be seen faintly outlined, while the bones will cast a strong shadow.
Figure 466 (opposite page 478) is from a photograph taken by means
of X-rays, and shows how valuable they are to doctors.
Roentgen rays are produced at, and sent forth from, any^
solid body upon which cathode rays fall. They are now
known to be ether waves^ just like light waves and wireless
telegraph waves^ but of very short wave length.
489. Radioactivity. Near the end of the nineteenth cen^
tury, scientists discovered that something which resembles-
Roentgen rays is radiated from certain rare minerals, such
as uranium, pitch-blende, and thorium. It affects a photo-
graphic plate through an envelope of black paper. It has
also the power of discharging electrified bodies, and so by
using a very sensitive electroscope it is possible to detect
and measure the intensity of this radiation. This new phe-
nomenon is called radioactivity, and a new element, which
is remarkably radioactive, has been discovered and called
radium. In this interesting and novel field of research many
scientists are now seeking to learn the answer to the great
questions "What is electricity?" and "What is inside the
atoms of substances?"
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INDEX
(Numbers refer to pages.)
Aberration, lens, 442; mirror, 418.
Absolute, pressure, 92; temperature,
182; zero, 183.
Absorption of gases, 100.
Absorption spectra, 459.
A. C, see Alternating current.
Acceleration, 135, 149; of gravity, 142.
Achromatic'lens, 457.
Adhesion, 73.
Aeroplane, 115.
Air, compressibility of, 78, 80; ex-
pansion of, 180 ; weight of, 84.
Air-brake, 79; -compressor, 78; -lift
pump, 98.
Alternating current, 322. 358 to 373;
power, 370.
Alternator, 322, 363.
Altitude by barometer, 91.
Amalgamation, 265.
Ammeter, 284.
Ampere, 283, 287.
AmpUtude, 379, 387.
Aneroid barometer, 89.
Anode, 283.
Arc, 334; automatic feed, 335; in-
closed, 336 ; flaming, 336 ; mercury,
336.
Archimedes' principle, 59.
Armature, of bell, 275; of circuit-
breaker, 333; drum, 326, 342; of
generator, 321, 362 ; Gramme ring,
323, 370; of motor, 340; station-
ary, 364.
Astigmatism, 447.
Atmosphere, moisture in, 211 ; pres-
sure of, 85, 88 ; refraction in, 430.
Attraction, electric, 248; magnetic,
238 ; molecular, 73.
AudibiUty, limits of, 388.
Back e. m. f., 343.
Balance, platform, 8 ; spring, 8.
Ball bearings. 43.
Balloon, 95.
Banking rails, 149.
Barograph, 90.
Barometer, 88.
Battery, 263; best arrangement of,
295; Edison storage, 354; lead
storage, 352.
Beam, stiffness and strength of, 128.
Beats, 394.
Bell, Alexander Graham, 313.
Bell, electric, 275.
Belting, 38.
Bending, 121, 123.
Bicycle pump, 78.
Binocular, 452.
Boiler, 221.
Boiling point, 172, 205 ; effect of pres-
sure on, 205 ; table of, 207.
Bound charge, 256.
Bourdon gauge, 68, 92.
Boyle's law, 80.
Breaking strength, 124.
Bridge, pinned, 114; riveted, 114;
girder, 115; Wheatstone, 302.
British thermal unit (B. t. u.), 196.
Bugle, 400.
Bunsen, 459 ; photometer, 409.
Buoyancy, in air, 94 ; in liquids, 58.
Calorie, 196.
Camera, 443.
Candle power, 338, 409.
Capacity, 256.
Capillarity, 74.
Carbon, filament, 337; microphone,
314, 472 ; transmitter, 314.
479
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480
INDEX
Carbureter, 230.
Cathode, 283 ; rays, 476.
Cell, chemistry of, 265 ; Daniell, 269 ;
dry, 270; gravity, 269; ions in,
266; local action in. 268; sal-
ammoniac, 270; storage, 352; vol-
taic, 263.
Center, of gravity, 20; of curvature,
417.
Centigrade scale, 172.
Central battery system, 315.
Centrifugal pump, 97.
Centripetal force, 148.
Chemical effects of currents, 348.
Circuit, electric, 264.
Circuit breaker, 333.
Clarinet, 400.
Clinical thermometer, 173.
Clouds, 214.
Coefficient, of expansion, 176, 178, 181 ;
of friction, 41, 117.
Coherer, 471.
Cohesion, 73, 148.
Cold storage, 216.
Color, 462 to 466.
Columbus, 239.
Commercial rating of electric lights,
337.
Commutator, 322, 325 ; -motor, 368.
Compass, 239.
Complementary colors, 464.
Component, 111.
Composition of forces, 108.
Compound, color, 463 ; engine, 225.
Compound-wound generator, 328.
Compressed air, 79.
Compressibility of fluids, 78.
Compression, 121, 123.
Compression members, 114.
Compressors, air, 78.
Condenser, electric, 256; steam, 220,
226.
Conductance, 294.
Conduction, of electricity, 249; of
heat, 189.
Conjugate foci, for lens, 439; for
mirror, 421.
Conservation of energy, 164.
Controller, 346.
Convection, 186.
Cooper-Hewitt lamp, 336 ; color of, 463.
Corliss valve, 224.
Comet, 400.
Coulomb, 283.
Coulombmeter, 284.
Crane, 23, 35, 108, 118.
Critical angle, 435.
Crookes' tube. 476.
Crystal detector. 472.
Current, alternating. 322 ; convection,
• 186 ; direct, 322 ; electric, 264, 283 ;
heating effect of, 333 ; induced, 309 ;
magnetic field about, 272; water,
283.
Curtis turbine, 228.
Curvature, center of, 417.
Cycles, 365
Damping, 362.
DanieU ceU, 269.
Davy, 334.
Declination, 239.
Density, 9 ; table of, 9 ; of air, 83 ; of
water,. 179.
Derrick, 23, 35.
Detectors, 471.
Dew, 213.
Dew point, 212.
Dielectric, 257.
Diffusion, of gases, 101 ; of light, 414.
Dip, 239.
Direct current (D. C.) , 322 ; generator,
323 ; motor, 342 ; power, 329 ; uses
of, 274 to 279, 332 to 355.
Discord, 395.
Dispersion, 457.
DistiUation, 207.
Double-acting pump, 97.
Drum, 400.
Drum armature, 323, 326, 342, 362.
Dry cell. 270.
Dry dock, 61.
Dynamo, 318, 321 to 329 ; alternating
current, 363 to 367 ; energy source
in, 329 ; kinds of, 326, 328 ; rule, 319.
Dyne, 151.
Earth, as magnet, 241.
Echo, 385.
Eddy currents. 361.
Edison, incandest;ent lamp, 337 ; phon-
ograph, 401 ; storage battery, 354.
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INDEX
481
Efficiency, defined, 43 ; of air-lift pump,
98 ; of boiler, 223 ; of Edison cell,
355 ; of electric lights, 338 ; of gas
engine, 233 ; of motor, 346 ; of
steam engine compared with gas
engine, 234; of steam plant, 226;
of steam turbine;- 230; of storage
cell, 354; of transformer, 359; of
water turbine, 72.
Elastic limit, 124.
Electric, arc, 334; attraction, 248;
bell, 275; circuit, 264; current, 263;
generator, 318, 321 to 329, 363 to
367; heating, 332; lighting, 334;
machines, frictional, 252 ; machines,
mduction, 259 ; motor, 340 ; power,
329; waves, 471; welding. 360;
whirl, 253 ; work, 330.
Electricity, two kinds of, 250.
Electro, -chemical equivalent, 351 ;
-magnet, 274; -magnetic theory of
light, 467; -plating, 349; -statics,
248; -typing, 350.
Electrolysia, 348.
Electrolytic, copper, 361; detector,
472.
Electromotive force, 267; back, 343;
of cell, 288 ; induced, 309, 319 ; unit
of, 286.
Electrons, 260.
Electrophorus, 259.
Electroscope, 250 ; condensing, 264.
Energy, 157 ; chemical, 163 ; conserva-
tion of, 164 ; equation, 159 ; kinetic,
157 ; potential, 162 ; transforma-
tions of, 163.
Engine, balance sheet of, 234; com-
pound, 225; condensing, 226; Cor-
liss, 224 ; 4-cycle, 232 ; hot air, 185 ;
internal combustion, 230; recipro-
cating, 227 ; slide valve, 223 ; single
acting, 231; steam, 219; 2-cycle,
231.
Equilibrant, 107.
Equilibrium, conditions of, 26.
Erg, 161.
Ether, 192, 243, 471, 478.
Evaporation, 210.
Exciter, 364.
Expansion, coefficient of, 176, 178, 181 ;
in freezing, 200; of gases, 180; of
2i
liquids; 178; of solids, 174; ol
steam, -225 ; of water, 179.
Eye, 445 ; defects of, 446.
Factor of safety, 125.
Fahrenheit icale, 172.
Falling bodies, 140; acceleration of,
142 ; laws of, 143.
Faraday, electromagnet, 275, 308, 318 ;
field around magnet, 242 ; properties
of lines of force, 243 ; transformer,
358.
Faucet, 67.
Feddersen, on spark discharge, 469.
Field, of generator, 321, 327, 364;
magnetic, 242 ; of motor, 340, 368 ;
revolving, 364; rotating, 368; side
push of, 340.
Field glass, 452.
Filament, incandescent, 337.
Fire engine pump, 97.
Firth of Forth Bridge, 176.
Flatiron, electric, 332.
Fleming's rule, 319.
Floating bodies, 60.
Fluids, 77.
Flute, 400.
Flux, magnetic, 243, 359.
Flywheel, 157.
Foci, conjugate, for lens, 439; for
- mirror, 421.
Focus, of lens, 438 ; of mirror, 417 ;
real, 420 ; virtual, 419.
Fog, 214.
Foot, 4 ; -candle, 413 ; -pound, 28.
Force, buoyant, 59; centripetal, 148;
of expansion, 175, 201 ; of friction,
42 ; lines of, 242 ; moment of, 17 ;
V8. pressure, 51 ; unbalanced, 149 ;
unit of, 7, 155; useful component
of. 111.
Force pump, 96.
Forces, composition of, 108; equili-
brant of, 107 ; molecular, 73 ; non-
parallel, 105 ; parallel, 25 ; parallelo-
gram of, 106 ; represented by arrows,
105 ; resolution of, 109 ; resultant of,
106.
Franklin, 205, 253, 260.
Fraunhofer linea, 458; meaning of,
461.
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482
INDEX
Freezing, by boiling, 215; evolves
heat, 203; -point, 172,* 199, 200
(table).
Frequency, of alternating current, 365 ;
of sound waves, 382 ; of water waves,
379.
Friction, 40; on incline, 116; produces
electricity, 248 ; produces heat, 170 ;
in water pipes, 69.
Frost, 214.
Fulcmm, 14 ; force at, 17.
Fundamental, of string, 391 ; units, 11.
Furnace, 188.
Fuses, 332.
Galileo, 86, 141.
Galvani, 263.
Gtlvanometers, 281.
Gas, engine, 230; formula, 183;
standards for, 409; thermometer,
181.
Gases, properties of, see Air.
Gauge, Bourdon, 69, 92 ; mercury, 68,
92 ; steam, 222 ; water, 56, 222.
Gay-Lussac, 181.
Geissler tube, 476.
Generator, 318, 321 to 329; A. C, 322,
363 to 367 ; compound, 328 ; multi-
polar, 326; series, 328; shunt, 328.
GUbert, 241.
Girder, 115, 130.
Grade, 32.
Gram, weight, 7 ; mass, 154.
Gramme ring, 323, 370.
Gravity, acceleration of, 142 ; cell, 269 ;
center of, 20 ; specific, 62.
Guericlre, Otto von, 82, 86.
Guitar, 399.
Half-time shaft, 232.
Heat, conduction of, 189; convection
of, 186; generated by electric cur-
rent, 333 ; latent, 202, 209 ; mechani-
cal equivalent of, 234; molecular
theory of, 192; radiation of, 191;
sources of, 170; specific, 197;
units of, 196.
Heater, for hot water, 187.
Heating, electric, 332; hot air, 188;
hot water, 187 ; indirect, 189.
Hefner, 409.
Helmholtz, 387, 389 ; resonator, 391.
Henry, Joseph, electromagnet, 275,
318 ; study of spark, 469.
Hertz, 467, 471.
Hooke's law, 123.
Horse power, 37.
Horse-power hour, 330.
Hot-air, engine, 185 ; furnace, 188.
Humidity, 212.
Huygens, 461.
Hydraulic, elevator, 50 ; machines, 47 ;
press, 48.
Hydraulic analogue, of condenser, 258 ;
of current, 266 ; of voltmeter, 288.
Hydrometer, 65.
Hydrostatic bellows, 50.
Hygrometer, 217.
Ice, artificial, 216.
Ignition, 312.
Illumination, 405.
Image, construction of, lens, 440,
mirror, 420; defects of, 442;
formed by lens, 440, by plane
mirror, 415, by pinhole, 406 ; size of,
lens, 441, mirror, 421; virtual, 420.
Impulse, 165.
Incandescent lamp, 337; vacuum in,
83.
Incidence, angle of, 415, 429.
Inclined plane, 31, 116.
Index of refraction, 429, 433, 434.
Induced, current, 309; e.m. f., 319;
magnetism, 244.
Induction, electric, 255 ; magnetic, 244.
Induction coil, 310.
Induction motor, 368.
Inertia, 146, 312; in curved motion,
148.
Infra-red, 466.
Insulators, electric, 249 ; heat, 189.
Interaction, 152.
Interference, of light, 465; of sound,
394.
Ions, 266.
Isobars, 91.
Jackscrew, 33.
Joule, 161, 331.
Joule, James Prescott, 234.
Jump-spark ignition, 311.
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INDEX
483
Kelvin. 469.
Key, telegraphic, 277.
Kilogram, mass, 154 ; weight, 7.
Kilowatt, 33^0.
Kilowatt hour, 330.
Kinetic energy, 157.
Kinetic theory, 102.
Kirchhoff, 459.
Koenig's manometric flame, 392.
Lactometer, 65.
Laminated core, 362.
Lamps, illuminating power of, 408;
kinds of, 334 to 339.
Lantern, projecting, 444.
Latent heat, ice to water, 202 ; water
to steam, 209.
Left-hand rule, 341.
Length, units of, 4.
Lens, achromatic, 457 ; camera, 443 ;
converging, 437 to 441 ; crystalline,
445; cylindrical, 447; diverging,
438, 441 ; focal length of, 438; for-
mula, 439 ; images formed by, 440 ;
magnifying power of, 448.
Levers, 13 to 21.
Leyden jar, 257 ; discharge of, 469.
Lifting effect, of air, 94; of water,
59.
Light, analysis of, 456; color of, 456
to 467; electric, 334; electromag-
netic theory of, '467; illiunination
by, 405 to 413 ; interference of, 465 ;
nature of, 461 ; reflection of, 414 to
424; refraction of, 427 to 442;
speed of, 431 ; wave length of, 462.
Lightning, 253.
Lines of force, 242.
Liquids, buoyant effect in, 58 to 61 ;
compressibility of, 78; conduction
of electricity by, 340 ; conduction of
heat by, 190; in connected vessels,
55; expansion of, 178; molecular
attractions in, 78 ; pressure in, 52 to
57; pressure transmitted by, 47 to
51 ; sound transmitted by, 375.
Liter, 6.
Local action in cell, 268.
Local battery system, 315.
Locomotive boiler, 221.
Lodestone, 238.
Longitudinal vibrations, 381.
Loudness, 384, 387.
Machines, 1, 13 ; alternating current,
358 to 370; direct current, 318 to
329, 340 to 347 ; electrostatic, 252,
259; frictional electric, 252; hy-
draulic, 47 to 51, 70 to 72 ; induction
electric, 259; pneumatic, 77 to 83,
95 to 99 ; simple, 13 to 43 ; talking,
401, 402 ; for testing materials, 128 ;
thermal, 185, 219 to 234.
Magdeburg hemispheres, 86.
Magnet, artificial, 238; broken, 245;
current induced by, 308; earth a,
241; electro-, 274 to 278, 320;
electro-, self-induction of, 312 ; field
aroimd, 242; by induction, 244;
natural, 238 ; permanent, 326.
Magnetic field, around coil, 273;
aroimd current, 272 ; around magnet,
242 ; of generator, 321 ; rotating, 368 ;
side push of, 340 ; wire cutting, 319.
Magnetic poles, 239.
Magnetism, 238 to 247 ; induced, 244 ;
molecular theory of, 246; residual,
274.
Magnetite, 238.
Magneto, 327.
Magnifying glass, 448.
Magnifying power, of binocular, 453;
of lens, 448 ; of microscope, 450 ; of
opera glass, 452 ; of telescope, 451.
Major, scale, 396 ; triad, 396.
Make-and-break ignition, 312.
Mandolin, 399.
Manometer, 68, 91.
Manometric flame, 392.
Marconi, 472.
Mariotte, 80.
Mass, 154.
MazweU, 467.
Mayer, 165.
Mechanical advantage, 25.
Mechanical equivalent of heat, 234.
Mechanics, Chapters II to IX, «ee
table of contents.
Medical coU, 311.
Megaphone, 385.
Melting point, 199, 200 (table), effect
of pressure on, 201.
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484
INDEX
Metallized filament, 338.
Meter, 4 ; water-, 70.
Mho, 294.
Micrometer screw, 35.
Microphone, 314, 472.
Microscope, 449 ; use of mirror in, 419.
Mil-foot, 298.
Milk, testing of, 65.
Mirror, concave, 417; convex, 419;
focus of, 417, 418; formula, 423;
parabolic, 418; plane, 415.
Mixtures, method of, 198.
Moisture, in atmosphere, 211.
Molecular forces, 73.
Molecular theory, of gases, 102; of
heat, 192 ; of magnetism, 245.
Moments, principle of, 17.
Momentum, 165 ; equation, 166 ; units
of, 167.
Moon, attracts earth, 154 ; eclipse of,
407.
Morse, 276.
Motion, laws of, 133 to 143.
Motor, alternating current, 368;
commutator, 368; efficiency, 346;
electric, 340; forms of, 342; in-
duction, 368 ; rule, 341 ; series, 344 ;
shunt, 344; starting a, 343; syn-
chronous, 368; water, 71.
Moving pictures, 445.
Musical, instruments, 397 to 400;
scale, 396; sounds, 386.
Neutral layer, 130.
Newcomen, 219.
Newton, corpuscular theory of light,
461 ; laws of mechanics, 146.
Nodes, 379.
Noise, 386.
Octave, 396.
Oersted, 271.
Ohm, 286.
Ohm's law, 289. '
Onnes, 185.
Opera glass, 452.
Optical instruments, 416, 419, 443 to
453,458.
Organ pipe, 399.
Oscillations of spark, 469.
Overtones, 391.
Ozone, 254.
Parallel, circuits, 293 ; forces, 25.
Parallelogram of forces, 106.
Parsons turbine, 229.
Pascal, experiments with barometer
88 ; principle, 48 ; vases, 53.
Pelton wheel, 71.
Pendulum, 142, 177 ; resonance of, 470.
Penumbra, 407.
Period, 380.
Permeability, 245.
Perpetual motion, 165.
Phase, of alternating current, 365 ; of
wave, 379.
Phonograph, 401.
Photometer, 409.
Physics, description of, 1 ; divisions
of, 2.
Piano, 397.
Pigments, 463.
Pitch, international, 397 ; of screw, 34 ;
of sound, 387.
PUto, 3.
Pneumatic machines, 77.
Polarization, in cell, 268.
Poles, of magnet, 238.
Polyphase circuit, 365.
Potential, difference of » 267.
Potential energy, 162.
Pound, mass, 154 ; weight, 7.
Power, 37; alternating current, 370;
electric, 329; electrical transmission
of 361; factor, 371; horse, 37; me-
chanical transmission of, 38.
Precipitation, 215.
Pressure, of atmosphere, 85; coeffi-
cient of, gases, 181 ; cooker, 206 ;
effect of, on boiling, 205 ; effect of,
on freezing, 201 ; vs. force, 51 ; in
heavy liquid, 52 ; vapor, 205.
Prism, 435, 436 ; colors formed by, 456
Projecting lantern, 444.
Pulley, 24, 25, 29 ; differential, 30.
Pumps, 95 to 98.
Quality, of sound, 388.
RadUtion, 191.
Radio-activity, 478.
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INDEX
486
Radittm, 478.
Rain, 214.
Rays, cathode, 476; infra-red and
ultra-violet, 466; light, 415, 432;
Roentgen, 477.
Reaiction, 154.
Receiver, telephone, 313.
Refining metals, 351.
Reflection, diffused, 414 ; law of, 415 ;
of light, 414 to 424 ; of sound, 385 ;
total, 434.
Refraction, by atmosphere, 430; ex-
planation of, 433; in glass, 429;
index of, 433 ; law of, 428 ; in plate,
436 ; in prism, 436 ; in water, 427.
Regnault, 182.
Relay, telegraphic, 278.
Resistance, 258, 267 ; bok, 301 ; compu-
tation of, 297 ; internal and external,
286; measurement of, 302; specific
(with values), 298; unit of, 286.
Resolution of forces, 109.
Resonance, acoustical, 390 ; electrical,
470 ; of pendulums, 470.
Resultant, 106.
Retina, 446.
Rheostat, 300.
Right-hand rule, 319.
Rivet. 121.
Roentgen rays, 477.
Roller bearings, 43.
Rolling friction, 42.
Roof truss, 112.
Rotating field, 368.
Rowland, 235.
Rtthmkorff coil, 311.
Safety valve, 223.
Siil boat, 115.
Sal-ammoniac cell, 270.
Scale,, musical, 396.
Screw, 33.
Self-induction, 312.
Self-Ughting mantle, 101.
Series, circuits, 292; generator, 328;
motor, 344.
Sextant, 416.
Shadow, 407.
Shear, 121.
Shunt, circuits, 293; generator, 328;
motor, 344.
Sighting, 451.
Siphon, 98.
Siren, 388.
Snow, 214.
Solids, conductivity, electrical, 298;
thermal, 189; density of, 9; ex-
pansion of, 174 ; sound transmitted
by, 375; specific gravity of, 62.
Solutions, conduction by, 348.
Sonometer, 398.
Sound, 374 to 404 ; intensity of, 384,
387; interference of, 394; nature
of, 378, 382 ; reflection of, 385 ; sen-
sation of, 378 ; velocity of, 376.
Sounder, telegraphic, 277.
Sounding board, 398.
Spark, oscillations of, 469.
Sparking voltage, 475.
Speaking tubes, 385.
Specific, gravity, 62 to 66 ; heat, 197,
198 (table).
Spectroscope, 457.
Spectrum, 456; absorption, 459;
bright line, 459; continuous, 459;
solar, 458.
Spectrum analysis, 459.
Speed, 133 (table); of electric waves,
471 ; of light, 431 ; of light in water,
434 ; of sound, 376.
Spyglass, 451.
Squirrel-cage rotor, 370.
Standard, lamp, 409 ; weight, 155.
Steam, engine, 219; latent heat oi,
209 ; turbine, 227.
Stereopticon, 444.
Stiffness of beams, 128.
Storage battery, 352.
Strain, 122.
Street-car motor, 345.
Strength, of beams, 129 ; breaking, 124.
Stress, 122.
Strings, vibrating, 391, 398.
Submarine telegraph, 278.
Suction pump, 95.
Surveyor's level, 452.
Tables, accelerations, 136; accelera-
tion units, 135 ; boiling points, 207 ;
coefficients of expansion, 176; den-
sities, 9; "efficiency" of ^ectric
lamps, 339; electrical concftictorii
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486
INDEX
and insulators, 249 ; electrical units,
287 ; electrochemical equivalents,
351 ; force units, 151 ; heat distri-
bution in engines, 234 ; of intervals
in musical scale, 397 ; length units,
4 ; melting points, 200 ; moisture in
air, 211; momentum units, 167;
specific heats, 198; specific resist-
ance, 298 (in text) ; speeds, 133 ;
volimie units, 6; wave length of
light, 462; weight units, 7; wire
(gauge, diameter, area, carrying
capacity), 304; work units, 160.
Tantalum lamp, 338.
Telegraph, 276 ; wireless, 472.
Telephone, 313 ; wireless, 474.
Telescope, astronomical, 450; erect-
ing, 451 ; reflecting, 419.
Temperature, absolute, 182; low, 185;
regulator, 175.
Tensile strength, 127.
Tension, 121, 123 ; vapor, 205.
Tension members, 114.
Terminal voltage, 291.
Thermometer, Centigrade, 172; clini-
cal, 173 ; Fahrenheit, 172 ; gas, 181 ;
maximum, 173 ; mercury, 171 ;
minimum, 173 ; wet and dry bulb,
212.
Thermos bottle, 191.
Thomson, 477.
Thumb rule, for coil, 274; for wire,
272.
Toepler-Holtz machine, 259.
Torque, 344.
TorricelU, 87.
Transformer, 358.
Transmitter, telephone, 314.
Transverse vibrations, 380.
Triad, major, 396.
Trombone, 400.
Truss, roof, 112.
Tungsten lamp, 338.
Tuning fork, 374.
Turbine, Curtis, 228; Parsons, 229;
steam, 227 ; water, 72.
Twisting, 121, 123.
Tyndall, 197.
Ultra-violet Ught, 466.
Umbra, 407.
Units, 3; of acceleration, 235; ol
area, 5; of current, 281, 283; of
density, 9 ; electrical, 287 ; of elec-
trical power, 329, 347 ; of electrical
work, 330, 331 ; of electromotive
force, 286 ; of force, 151 ; funda-
mental, 11; of heat, 196, 235; of
illumination, 413 ; of kinetic energy,
160 ; of length, 4 ; of light intensity,
409 ; of mass, 154 ;J of momentum,
167; of power, 38, 329, 347; of
pressure, 51 ; of resistance, 286, 298 ;
of speed or velocity, 133 ; of volume,
6 ; of weight, 7 ; of work, 28, 235,
330, 331.
Unit stress and strain, 125.
Vacuum, bottle, 191 ; cleaner, 83 ;
discharge in, 475 ; gauge, 92 ; pan,
206 ; pumps, 81 ; sound not carried
by, 375.
Vapor pressure, 205.
Velocity, of light, 431 ; of molecules,
102 ; of sound, 376.
Ventilation, 188.
Vibration, made visible, 375; sym-
pathetic, 389.
Violin, 399.
Virtual image, lens, 441 ; mirror, 420.
Visual angle, 447.
Voice, 400.
Volt, 286.
Volta, 263.
Voltage, sparking, 475 ; terminal, 291.
Voltmeter, 287.
Watch, balance wheel, 177 ; stop-, 12.
Water, density of, 179; gauge, 56;
meter, 70 ; motor, 71 ; turbine, 72 ;
waves, 378 ; wheds, 71 ; works, 67.
Watt, 329, 347.
Watt, James, horse power, 37; steam
engine, 220.
Wattmeter, 371.
Wave, front, 432; length of light,
462 ; model, 381 ; theory of light,
461.
Waves, electric, 469, 471; light, 432:
longitudinal, 381 ; sound, 382 ; trans-
verse, 380 ; water, 378.
Weather map, 90.
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INDEX
487
Wedge, 33.
Weight, of air, 84 ; standard and local,
155 ; units of, 7.
Welding, electric, 360.
Wheatstone bridge, 302.
W&eel and axle, 22.
Wind instruments, 399.
Wireless, telegraphy,. 472 ; telephony,
474.
Wire table, 304.
Work, definition of, 28 ; electrical, 330 ;
and energy, 157; and power, 37;
principle of, 29; units of, 28, 235,
330, 331.
X-rays, 477.
X-ray tube, vacuum in, 83.
Toung, 462.
Zero, absolute, 183.
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YB 35984
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UNIVERSITY OF CALIFORNIA UBRARY
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