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GIFT OF
Agriculture education

APPLIED PHYSICS

FOR

SECONDARY SCHOOLS

V. D. HAWKINS

HEAD OF THE DEPT. OF SCIENCE

TECHNICAL HIGH SCHOOL

CLEVELAND, OHIO

LONGMANS, GREEN, AND CO.

FOURTH AVENUE & 30TH STREET, NEW YORK
LONDON, BOMBAY, AND CALCUTTA

1912

THE- PLIMPTON-PRESS

[W.D.O]
NOR WOOD- MA SS • U • S • A

PEEFACE

PHYSICS ought to be a live subject, a reasonable explana-
tion of the every-day events of life. It seems to the author
of this text-book that in recent years the attempt to include
in physics a large amount of mathematics and all applica-
tions of the principles of the science have resulted in high
school texts which are far too difficult for one year for the
average high school pupil. Applied Physics is a result of an
attempt to select the fundamental principles with barely
enough common applications to make them clear to the
pupil and to bring them home to every-day life, leaving
plenty of time for the teacher to supplement with other
applications from the pupils' lives which are of local interest
and which must differ in every locality.

The author, then, believes that the best methods of teach-
ing the subject are as follows:

1. By a brief text for all of which the pupil will.be held
responsible, and,

2. By the addition of many interesting local applications
to be supplied by both teachers and pupils.

With few exceptions illustrative experiments are not
described in the text. They should be performed. A large
amount of demonstration work is a great aid to the under-
standing of the subject. If the illustrative experiments are
performed for the class, as they should be, it is useless to
cumber the book with a detailed description of them. If
they are not performed, a description helps the student very
little and causes him to spend too much time in mastering the
details of experiments which he does not see and which,

vi PREFACE

therefore, are difficult for him to understand. The author
offers this short text with no apologies but with the con-
viction that its results will justify it.

The chapter on magnetism and electricity is a departure
from tradition. The historical method has been discarded.
Every boy has played with a toy magnet, and a start is
made from this point of interest. While he has the mag-
netic field well in mind the dynamo, which is nothing but a
loop of wire revolving in a magnetic field, is introduced.
The author finds that it is no more difficult for the pupil to
understand the three-phase alternator than to master the
influence machine. When he has mastered it, he knows
how ninety per cent of the electricity used to-day is pro-
duced, while the influence machine has a very limited appli-
cation. In this day of widespread use of electrical appliances
every high school student should become familiar with those
he meets most commonly.

The author wishes to acknowledge the valuable assistance
given by Miss Elizabeth Jackson of the English Depart-
ment and Mr. Claude Brechner of the Science Department
of Technical High School, Cleveland, Ohio. He is also
indebted to the C. H. Stoelting Co. of Chicago for permission
to reproduce the optical disks on pages 95, 96, and 97.

CONTENTS

CHAPTER I

PAGES

MACHINES 3-20

WORK — FOOT POUND — SIMPLE MACHINES — PRINCIPLE OF
MACHINES — EFFICIENCY — LEVER — WHEEL AND AXLE
- PULLEY — INCLINED PLANE — SCREW — WEDGE -
PRONY BRAKE — PULLEY CONE — WINDLASS.

CHAPTER II

DYNAMICS 21-39

FORCE — MOTION — VELOCITY — NEWTON'S LAWS OF MO-
TION — INERTIA — PARALLELOGRAM OF FORCES — AERO-
PLANE — ACCELERATED MOTION -- FORMULAS — MO-
MENTUM — UNITS OF FORCE — GRAVITY — CENTER OF
GRAVITY - - EQUILIBRIUM — CURVILINEAR MOTION —
KINETIC ENERGY — COEFFICIENT OF FRICTION — PEN-
DULUM.

CHAPTER III

MECHANICS OF FLUIDS 40-61

SOLID — LIQUID — GAS — FLUID PRESSURE — HYDRAULIC
PRESS — PRESSURE — BAROMETER — PUMPS — SIPHON —
GAS PRESSURE — DIFFUSION — OSMOSIS — BOYLE'S LAW
— PRESSURE GAUGE — AIR PUMP — SURFACE TENSION —
CAPILLARITY — BUOYANCY — ARCHIMEDES' PRINCIPLE —
SPECIFIC GRAVITY — DENSITY" — HYDROMETER.

vii

viii CONTENTS

CHAPTER IV

STRENGTH OF MATERIALS •'. . . . 62-68

ELASTICITY — STRESS — STRAIN - - TENSILE, SHEARING,
TRANSVERSE, TORSIONAL AND COMPRESSION STRENGTH.

CHAPTER V

SOUND 69-77

VIBRATION — WAVE MOTION — FREQUENCY — VELOCITY —
ECHO — WAVE LENGTH — RESONANCE — BEATS — IN-
TERFERENCE — LOUDNESS — PITCH — QUALITY — LAWS
OF VIBRATING STRINGS PHONOGRAPH.

CHAPTER VI

LIGHT 78-97

ETHER VIBRATIONS — VELOCITY — SHADOWS — REFLEC-
TION — INTENSITY — UNIT OF LIGHTING POWER — PHO-
TOMETRY — REFRACTION — CRITICAL ANGLE — INDEX
OF REFRACTION — COLOR — CONVEX LENS — EYE —
OPTICAL DISK — OPTICAL INSTRUMENTS.

CHAPTER VII

HEAT 98-107

KINETIC THEORY — TEMPERATURE — CALORIMETRY —
LATENT HEAT — SPECIFIC HEAT — COEFFICIENT OF EX-
PANSION — CHARLES' LAW.

CHAPTER VIII

HEAT ENGINES AND TRANSMISSION OF HEAT . . 108-125

BOILING POINT — SATURATED AND SUPERHEATED STEAM —
STEAM-ENGINE — BRAKE HORSE-POWER — INDICATOR
— INDICATED HORSE-POWER — TURBINE — GAS ENGINE
HOT AIR ENGINE — MECHANICAL EQUIVALENT — CON-
DUCTION — CONVECTION — RADIATION.

CONTENTS ix

CHAPTER IX

PAGES

MAGNETISM AND ELECTRICITY 126-196

MAGNETIC POLES — ATTRACTION AND REPULSION — MAG-
NETIC FIELD — THEORIES OF MAGNETISM — ELECTRICITY

- SIMPLE DYNAMO — COMMUTATOR — ARMATURE —
ELECTROMAGNETIC RELATION - - ELECTRO MAGNET -
TELEGRAPH — ELECTRIC BELL — GALVANOMETER — VOLT-
METER — AMMETER — WATT -METER — MOTOR — CHARAC-
TERISTIC CURVE OF DYNAMO — SHUNT, SERIES AND COM-
POUND DYNAMO - - ELECTROLYTIC CELL - - CHEMICAL
RELATION — VOLT — AMPERE — OHM — WATT — POLAR-
IZATION — OPEN CIRCUIT CELLS — CLOSED CIRCUIT CELLS
— GRAVITY CELL — DANIEL CELL — STORAGE BATTERY

EDISON STORAGE CELL OHM'S LAW VOLTMETER

AMMETER METHOD OF MEASURING RESISTANCE — SHUNT
CIRCUIT — CELLS IN SERIES OR SHUNT — WHEATSTONE'S
BRIDGE — RESISTANCE BOX — INDUCTION COIL — TRANS-
FORMER — ARC LIGHT — INCANDESCENT LAMP — CYCLE

- PHASE — ALTERNATOR - - THREE PHASE A. C. -
MOTORS — STARTING BOX — CONTROLLER — RECORDING
WATT-METER — A. C. MOTOR — INDUCTION MOTOR —
TELEPHONE — STATIC ELECTRICITY -- LEYDEN JAR -
ELECTROSCOPE - - ELECTRIC DISCHARGE - - X-RAY —
HERTZEN RAY — WIRELESS TELEGRAPH.

INDEX 197

APPLIED PHYSICS

INTRODUCTION

PHYSICS has more points of contact with every-day life
than any other one science. A bicycle rider runs into a
tree and is hurt, an automobile rounds a curve too fast
and skids. In either case a policeman may step to a little
box, fastened to a pole, and call an ambulance. Man
with his little strength lifts great girders weighing many
tons, or directs a huge steamship across an ocean, or makes
a waterfall furnish him with light, heat, and power. All
this is in accordance with the laws of physics. Physics
has to do with matter and energy. This is the study of
the laws of nature which control everything happening
about us. Ignorance of the law excuses no one. Nature's
laws will hold anyway and the wise man will learn to use
them to his advantage.

Matter. No one knows what matter is. There is a
theory that it may be made up of molecules and these
in turn formed from smaller particles called atoms, which
are in turn composed of smaller particles. In accordance
with this theory, the symbol for water is written H2O,
which means that a molecule of water is made of two
atoms of hydrogen and one atom of oxygen.

Energy is the ability to work. We shall meet energy
in many forms, chemical energy, electrical, mechanical,
heat, light, etc. The quantity of matter and of energy
in the universe is constant. We know that when energy
disappears in one form it appears in another form with

2 INTRODUCTION

no change in amount and that if matter disappears in one
form it appears in another and that the amount is the same.
This is the law of conservation of energy and of matter.

The relations of energy and matter are so exact that
physics must be an exact mathematical science. The
student must have a definite set of units to compare quan-
tities, and these units must be real and definite. That is,
"inch" must be not simply a word, it must be a definite
length which is suggested by the word. For that reason
instead of trying to define the units here, we shall give an
introduction to them in the first experiments in the labora-
tory. We use a convenient decimal system of money
and laugh at the clumsy English system of pounds, shillings,
pence, etc., and yet we cling to the English system of
miles, rods, feet, etc., while the continent of Europe has long
been using a decimal system. The student of science in this
country will need to be familiar with both. The units of
both systems are arbitrary, that is, when first chosen they
could as well have been different but they have now been
commonly accepted and each government has made accurate
duplicates of the units and holds them as standards. In
the C.G.S. (centimeter-gram-second) system, the centimeter
is the unit of length, the gram the unit of mass, and the second
the unit of time. Other units are built up from these.

A short time spent in the laboratory with meter stick and
yard stick, English and metric weights, will be of more
value to the pupil than many pages of explanation.

CHAPTER I
MACHINES

WE see a hod of brick carried up to the second story or
a heavy barrel rolled up a skid on to a dray, and call it
work. We may not all have in mind the same definition
of work and the same unit for measuring it. If you hold a
five-pound weight out at arm's length all day, holding it
in the same place all the time, do you do any work? Place
a post under the same weight holding it in the same place
and leave it there all day. The post will have to do the
same work that you did. Is the foundation of your school
building doing any work when it supports the weight of
the walls? What is work, then? If a weight be lifted
from the bottom of a clock to the top it can be made to
turn the wheels as it runs down. Water stored at the top
of a hill will turn the mill wheels as it runs down. We all
know from experience that in order to move any object we
must give it either a push or a pull, which we call force.
Force is a push or a pull which tends to produce motion.
Work is force acting against a resistance and moving it.

When we wish to compare distances, we have the units
of length — foot, meter, etc. Without them the architect
could not make specifications for the contractor. To com-
pare forces, we have the pound unit, which is the pull of
gravity upon a standard weight kept by the government.
The unit of work, the foot-pound, is a force of one pound
pushing or pulling through a distance of one foot. A ten-
pound weight lifted through two feet would require 2 X 10,

4 APPLIED PHYSICS

or 20 foot-pounds of work. Work requires two factors, force
and the distance through which it moves. If a man were
hired to carry two tons of coal upstairs and spent the day
leaning against the bin, that is, pushing against it, he would
accomplish no work. Is it possible to exert force without
doing work? How much work is done when a 130-pound
boy climbs from the first to the second floor, 15 feet? How
much work is done when the same boy pushes against the
side of the house for half an hour? If a pull of 300 pounds
pulls a car along a track for 10 feet, 10 X 300, or 3000
foot-pounds of work is done overcoming friction.

Often a pry or lever is used for lifting heavy weights.
In Fig. 1, if a force be applied vertically at F and move

the distance (a), while the
lever moves about the pivot
(p), the weight is lifted the
distance (6).

Every boy knows that he
can lift many times his own
FIG. 1. — Lever. weight by using such a

By a lever a man may lift many lever. He also knows that
times his own weight He makes the distance (6) which the
use of the principles of physics.

weight is lifted is small com-
pared to (a) when the weight is heavy. There is little loss
due to friction in the lever. Repeated experiment has shown
that if W = 500 pounds and is lifted 1 foot while F drops

5 feet, F must be 100 pounds. The force F is doing work
on the lever, 100 X 5, or, 500 foot-pounds. The work given
back is 500 X 1 = 500 foot-pounds. The work given out
by a machine can never be more than the work done on
the machine. In practice a part of the work done on the
machine is used by friction and is useless work, so that
the useful work from the machine is only a fraction
of the total work done on the machine. This fraction

MACHINES 5

is called the per cent efficiency. A machine which, for
every 100 foot-pounds of work received, gives back 75 has
75% efficiency. If we could build machines having no fric-
tion they would have 100% efficiency. The so-called per-
petual motion machine is impossible.

Neglecting friction, the work done by a machine is equal
to the work done on the machine. Expressed as an
equation, F X D = W X d, where F = force in pounds,
D = feet the force moves, W = resistance in pounds, d = feet
the resistance moves. That is, neglecting friction, the force
times the distance that it moves equals the resistance times
the distance that it moves. This one fundamental prin-
ciple of machines well mixed with common sense will work
all the problems in simple machines, which the student is
likely to meet.

In Fig. 1 for instance, this gives usFXa = WXboT

l/i/ sj (If*

TT= - but by similar triangles - = -• thereforeFXc=TFX<i.
r o o d

Force times the force arm = weight times the weight

^ . Weight distance the force moves

arm. The ratio — or

Force distance the weight is lifted

is called the mechanical advantage of a machine.

Any contrivance for transforming or transferring energy
is a machine. There are six simple machines. In consider-
ing machines, never forget the principle already stated that
the total amount of energy in the universe is constant. It
is not possible to get more work out of a machine than is
done upon it.

In the operation of a machine, there are always two quan-
tities of work to be considered, the work done upon the
machine and the work done by it. The work done by the
machine equals the work done upon it. Some of the work
done by the machine may be used up in overcoming fric-
tion. In this case the effective work done by the machine

6 APPLIED PHYSICS

is less than the work done upon it. The ratio of the use-
ful work to the total work, expressed in per cent, is the effi-
ciency of the machine. The efficiency of a simple lever may
be almost 100%. The efficiency of a motor may amount to
85%. The efficiency of a locomotive may be about 10%.

The machine elements are lever, wheel and axle, pulley,
inclined plane, screw, and wedge. Other machines are
formed by combining these.

A lever is a bar capable of being turned about a pivot,
as in Figs. 2, 3, and 4 where F is the force, (p) the pivot or
fulcrum, W the weight, (a) the force arm and (b) the weight
arm.

FIG. 2.

FIG. 4.
Three classes of levers, one law W X b = F X a.

The force times the force arm equals the weight times
the weight arm; the mechanical advantage of the lever
also equals the inverse ratio of its arms.

In the lever the force tends to turn the lever one way
while the weight tends to revolve it the other way. This
tendency to cause rotation is called a moment.

The product of the force and the force arm is its moment
and the product of the weight and the weight arm is its
moment. In the lever the two moments are equal and
opposite.

MACHINES

FIG. 5.
Wheel and axle, a

The wheel and axle, Fig. 5, is a modified lever. It con-
sists of a wheel and axle rigidly fastened
together to turn about a common axis.
It is evident that the radius of the axle (r) ,
is the weight arm, and the radius of the
wheel, R, is the force arm. The wheel may
be replaced by a crank, as in the windlass.

In a train of gear wheels the resist-
ance of one becomes the force of the next,
and by continued application of the laws
of the lever the following law may be
obtained: The weight times the continued
product of the radii of the axles equals the
force times the continued product of the radii lever with another
of the wheels. name'

Pulleys. Pulleys for the transmission of power by means
of belts are readily considered by means of the principles of
the wheel and axle. Power is the time rate of doing work.
To lift a ton of coal from the basement to the first floor
requires the same number of foot-pounds of work (weight
times distance lifted) whether it takes a week or a minute.
The power required is very different; 33,000 foot-pounds of
work per minute or 550 foot-pounds per second is one horse-
power.

To lift 231,000 pounds 5 feet in 7 minutes would require
5 X 231,000 or 1,155,000 foot-pounds of work in 7 minutes
or 165,000 foot-pounds in one minute; 165,000 -f- 33,000 =
5 horse-power.

The pulley which imparts motion to the belt is called
the driver; that which receives the motion is called the
driven. If a 12-inch and a 6-inch pulley are belted together,
the 6-inch pulley will make two revolutions while the 12-
inch is making one. The number of revolutions is inversely
proportional to the diameters. Rubber, cotton, and leather

APPLIED PHYSICS

belts are used. The force tending to turn the pulley
(effective pull) is the difference between the tension on the
slack side and that on the driving side. To determine what
width of the belt to use, it is necessary to know the arc
of contact on the small pulley, the velocity of the belt,
the power to be transmitted, and a constant depending upon
the friction and the arc of contact.

FIG. 6. — A Lever.

The law of levers is easily tested and demonstrated by simple appa-
ratus. Weight X weight arm = Force X force arm.

Parallel forces are also illustrated. The sum of the weights and
the weight of the meter stick equals the scale reading. A team of
horses pulling on an evener and many other applications should be
suggested and explained by this picture.

In getting the length of a belt for pulleys not yet in place,
the millwright uses the approximate rule 3J times half the
sum of the diameters of the two pulleys plus twice the
distance between the centers of the pulleys. This will
furnish an estimate for an open belt. After the pulleys

MACHINES 9

are in place a tape is used to measure the length required
for the actual cut.

To get the width of a s'ngle belt let

k = the allowable effective pull per inch given above.

H = the horse-power to be transmitted.

v = the velocity of belt in feet per minute.

w = width in inches.

33,000 H
vk

Do not learn this formula but study it until the reason
for each part is understood, and then analyze each problem,
working without the formula.

33,000 H gives the number of foot-pounds of work per
minute. Work is the product of force times distance and
the velocity in feet per minute of the belt multiplied by
the allowable effective pull per inch of width gives the
number of foot-pounds one inch width will do per minute.
This divided into the number to be done per minute gives
the width of the belt required.

What width of belt will be required to transmit 10 horse-
power, the speed of the 'belt being 1,500 feet per minute
and the arc of contact being 135 degrees on the small pulley,
if the allowable pull per inch width is 31.3 pounds?

10 X 33,000
W= 1,500 X 3L3=

It is evident that if the speed is increased greater power
may be transmitted at the same tension.

Problems

1. A belt running 1000 feet per minute has an effective pull of
33 pounds. What horse-power is it transmitting?

2. What effective pull must a belt have to transmit 5 horse-power
when running 800 feet per minute? when running 1600 feet per minute?

10 APPLIED PHYSICS

3. The driver running 500 R.P.M. (revolutions per minute) is
12 inches in diameter, the belt is six inches wide with an effective pull
of 30 pounds per inch. What horse-power is it transmitting? The
pupil should always look for the easiest method of working applied
problems. Note here that the surface speed must be in feet per
minute. Use the diameter as 1 foot. Use -2/ for Pi. Indicate the
work before multiplying any of it, as follows:

1 X 22 X 500 X 6 X 30 =
7 X 33000

4. A driving pulley 20 inches in diameter makes 180 R.P.M. What
is the diameter of the follower making 450 R.P.M.?

5. A main line shaft running 200 R.P.M. has a 32-inch driver
belted to an 8-inch follower on the first counter; a 20-inch driver on the
first counter to a 6-inch driver on the second counter; and a 12-inch
driver on the second counter to a 2|-inch pulley on a spindle. Find
the R.P.M. of the spindle.

6. What width of belt will be required to transmit 12 H.P., the
speed of the belt being 1200 feet per minute and the allowable effective
pull 40 pounds per inch width?

7. If both driver and follower in problem 6 are 18 inches in
diameter find R.P.M. What is the effective pull? If 12-inch pulleys
are substituted on both driver and follower, and the R.P.M. and H.P.
remain the same, how are width of belt, effective pull, and speed of
belt affected? < \

Work is always the product of two factors, force times distance, and
power is rate of doing work. Whenever a problem involves quantity
of work, look for the two factors.

8. In Fig. 5 r is 4 inches and R is 12 inches and there is no friction,
What force will be required to balance 600 Ib. at Wf If \ of the
work done on the machine is lost in friction, how much weight will
this same force lift? In the second case what is the efficiency?

In Fig. 7 suppose the shafts a and b are parallel, the
pulley at a being cone-shaped as shown. The circumfer-
ence on the right-hand side being larger than that on the
left the belt is drawn ahead more rapidly than the other
side of the belt and the belt is thrown to the right and shows
a tendency to climb to the large side of the cone. Suppose

MACHINES

the pulley is made of two cones with the large diameters
placed together. The belt will be held in place as each side
will tend to climb toward the center. This is done by
crowning the pulley as in c.

Problems

1. In pulling a railroad spike a crowbar is used in which the long
arm is 4 feet and the claw is 3 inches long. If it requires a force of
50 pounds to pull the spike, what is the resistance of the spike?

2. In the forge room the machine for cutting bar iron has a lever
6 feet long, with the knife connected 4 inches from the pivot end;
the knife is 2 feet long with a

bar of iron placed under it 2
inches from the pivot end.
When a boy pulls 100 pounds on
the end of the lever, what is the
pressure on the bar of iron?
What is the strain on each
pivot?

3. A belt with a speed of
1000 feet per minute has an
effective pull of 33 pounds. How
much work is it doing per min-
ute? What horse-power is it
transmitting?

4. Twelve boys weighing 110
Ib. each are lifted from the base-
ment to the third floor, 40 feet.
How much work is done, neg-
lecting friction? What horse-
power would be required if this

FIG. 7.

A belt will run better on a crowned
pulley than on a flat one.

takes one minute? Two minutes?

5. If 5000 pounds of water per day are pumped from the basement
to the fountain on the third floor, 45 feet, how much useful work is
done? If the friction of the pump uses one fifth the energy supplied,
how much work must be done on the pump? If the motor running
the pump has 60% efficiency, how many foot-pounds of electrical
energy will be required by the motor? What horse-power motor must
be used?

APPLIED PHYSICS

Pulleys are also used for raising or hoisting loads in which
case the frame supporting the axle of the
pulley is a block.

A fixed pulley is one whose
block is not movable. A mov-
able pulley is one whose block
is movable.

If a boy weighing 100 pounds
be in a swing each rope sup-
ports 50 pounds. If a weight
of 20 pounds be supported by
one movable pulley as in Fig. 8,
each rope is under a tension of
10 pounds. By extending this
principle we may state the law
that in any combination of pul-
leys where one continuous rope is used the
mechanical advantage is equal to the num-
ber of times the rope passes from one block
to another. In actual practice it is found
that the efficiency runs from 60% to 90%,
depending upon the condition and num-
ber of the sheaves.

A combination of pulleys frequently
used has three sheaves (wheels) in each
block. There are six ropes running be-
tween the blocks. If we neglect friction,
when a force of 100 pounds is exerted

100 Lbs,
FIG. 8.

Each rope
must sup-
port part
of the
load.

FIG. 9.

Block and tackle,
jfor lifting heavy ob-

on the free end of the rope, each rope is Jec,ff •

Man applies the
put under a strain of 100 pounds and a laws of physics, and

weight of 600 pounds will be supported, machines save much
T of his heavy drudg-

ln order to remove one foot of rope from ery and do many

each of the six supporting the weight the thmss beyond the
, strength of the

force must move through six feet. See Fig. 9. strongest animal.

MACHINES 13

An inclined plane is one making an angle with the hori-
zontal as in Fig. 10. Where the force acts parallel to the
plane, as in Fig. 10, the
effort must move through a
distance equal to the length
while the load is lifted
through the height (h). The
mechanical advantage is
l/h. If a plank 16 feet

long be used in lifting a weight of 600 pounds up to a
platform 4 feet high, and the force be applied parallel
to the plank, what effort will be required to move it?
16 -f- 4 = 4, the mechanical advantage. 600 -f- 4 = 150
pounds required, neglecting friction.

When the force is applied parallel to the base the me-
chanical advantage is the base (6), divided by the height (h).

A special application of the inclined plane is the wedge.
It may be used for moving heavy weights or in the form
of key used in fastening crank to crank shaft.

If a right triangle be wound around a cylinder with one
leg forming the circumference, the hypotenuse takes the
form of a helix. A helical projection winding around the
circumference of a cylinder forms a screw. The projection
is the thread, the distance between the threads is the lead,
the number of threads to the inch is the pitch. In the case
of the jack screw for lifting heavy weights, the effort is
applied to the end of the lever. When the screw makes a
complete revolution the weight is lifted through a distance
equal to the lead, while the effort moves through the cir-
cumference of a circle with a lever as a radius. It is found
in practice that the friction is so great that the screw will
lift only about one-fifth of the theoretical weight, that is,
its efficiency is only about 20%. With a screw having four
threads to the inch a man exerts a force of 40 pounds at

14 APPLIED PHYSICS

the end of a four-foot lever. What theoretical load can he
lift? If the efficiency is 20%, what load can he actually lift?

Problems

1. Two beams are fastened together with a bolt which has an
8-pitch thread. A monkey-wrench one foot long is used to tighten the
nut. If a force of 50 pounds be exerted and one half be lost in fric-
tion, how tight are the timbers squeezed? (Use Pi as 87 and get only
approximate result mentally.)

2. A skid 16 feet long is used in pushing an 800-pound barrel on to
a dray 4 feet high. "What push must be exerted against the barrel?
How much work is done? (Find the work in two ways.)

3. In pushing an 800-pound barrel on to a platform, the skid forms
an angle of 30° with the horizontal plane. What force is required?

4. A weight of 141 pounds rests on a plane which is at 45° to the
horizontal. What force is required to hold it in place?

The micrometer, Fig. 11, much used in machine shops, is
an application of the principle of the screw. The screw (a)

is 40 pitch. The thim-
ble (b) is fast to the
screw. The beveled
edge of b is divided
into 25 equal parts.
Fastened firmly to the
FIG. 11. — Micrometer Caliper. frame is a sleeve (c)

Accurate measurements and fine ad- uPon which is a scale
justments in modern shop practice are corresponding to the
made by means of the micrometer screw. , -, £ ,-, , ,

lead of the screw, that

is, each division is ?V or .025 of an inch.

When screw (a) is against anvil (d) the zero lines coincide.
Then each complete turn of the screw (a) represents a longi-
tudinal movement of .025 inch. One division on b means
^V of a turn and therefore a separation of the jaws A-
of 41,) or .001 inch. Fig. 12 shows a sleeve reading of .325
inch and thimble reading of .017 or a total of .342 inch.

MACHINES

Problems

1. State the general rule of machines, expressing the relation be-
tween force and weight and the distances through which they move.

.342"

FIG. 12

2. If the force arm of a lever is 20 inches and the weight arm is
inches, what force will be required to lift a weight of 100 pounds?

-8

d E

-6-

J L

• 8 •

-T

^ <

-2

f —

PH*

v_<

FIG. 13. — Pulley Cone, Problem 9.

By running the belt on different combinations, several speeds
may be obtained for the machine.

3. What must be the speed of the driver, 12 inches in diameter, in
order that the driven, with a diameter of 5 inches, may make 1 000 R . P . M . ?

APPLIED PHYSICS

4. A single belt running at 1650 feet per minute is used to transmit
40 horse-power. If the allowable pull per inch width is 35 lb.,
what width of belt will be required?

5. In a set of pulleys there are three wheels in the movable block
and six ropes passing from one block to another neglecting friction,
what force will be necessary to lift 1200 pounds? If the efficiency of
this combination is only 80%, what load will the same force lift? What
is the mec'hanical advantage of this combination?

FIG. 14. — The Principles of Simple Machines.
Simple apparatus for demonstrating the principles of simple machines.

6. If a railroad track has a rise of 6 inches in 200 feet of its length,
what force pulling on the draw bar will be necessary to hold a car
without friction, weighing 10 tons and loaded with 40 tons? If the
same car is being pulled up this incline 20 feet per second, what horse-
power is used? If 200 pounds pull is necessary to overcome the fric-
tion of the car, what horse-power is used in overcoming friction at the
above rate?

7. Measure the chain of gears on a planer in the machine shop
and compute the mechanical advantage.

MACHINES

8. There are several screw presses in the building. Neglecting
friction, find the pressure exerted by ten pounds pull on the wheel of
one of them.

9. If in the turning shop the shaft has a speed of 500 R.P.M.
and a pulley cone is used having diameters 6, 8, 10, and 12
inches while a lathe has a pul-
ley cone with diameters of 8,
6, 4, and 2 inches, what speed
will the lathe have on each
combination? See Fig. 13.

10. In the first combina-
tion of the above problem,
what effective pull must the
belt have to transmit 3 horse-
power?

The Prony brake is
commonly used to meas-
ure the delivered or brake
horse-power of an engine
or the brake horse-power
at the shafting in any
part of a shop. As shown
in the Fig. 16, two pieces
of timber are fitted to a
pulley and placed as
shown. A long lever arm
L is bolted to the pieces,
and with the pulley
standing still a weight (x)
is placed to balance the arm L. The pulley is revolved left-
handedly at speed and a weight (w] gradually added until the
friction on p is all it will carry and stay up to speed. Horse-
power is speed in feet per minute multiplied by force divided
by 33,000. Surface speed = 2^Nr} and force = WR/r.

FIG. 15. — The Principles of Simple
Machines.

Simple apparatus for demonstrating
the principles of simple machines.

Therefore, the foot-pounds per minute =
3

and

18 APPLIED PHYSICS

2v&NW

the r divides out, hence the horse-power = ~oo~7jrjrT

N = Revolutions per minute.

W = weight.

R = arm in feet.

QlP

J||j 'llll

FIG. 16. — The Prony Brake.

A brake with an arm 5 feet long was placed on a gas
engine. The pulley made 300 revolutions per minute and
the brake balanced with a twelve-pound weight. What
horse-power was developed?

2 X 3.1416 X 5 X 300 X 12

-33^00- -°r3'4

Problems

1. Work is the product of two factors, force and distance. Where
do these two appear in the formula for the Prony brake?

2. Where do the two factors of work appear when power is being
transmitted from a shaft to a machine by means of pulleys and belt.?

3. Why has every perpetual motion machine so far invented failed
to work?

4. How might a micrometer be constructed to read to 1/500 of
an inch?

5. If a train is pulled at a uniform speed along a level track, is
any work done against gravity ? Is any work done ? If so what
becomes of the energy thus used ?

MACHINES

lliw

FxR=Wx

M-' Weston
R-r Different]
-W^~ .Pulley

FIGS. 17, 18, 19.

Start with general principle of machines. (Neglecting friction, the
force times the distance it moves equals the resistance times the distance it
moves} prove the formulae, opposite Figs. 17, 18, and 19.

Problems

1. In testing a small motor with the Prony brake, the brake arm is 30
inches long, weight 3 pounds, motor running 900 R.P.M. Find brake
horse-power.

2. An engine making 200 R.P.M. will support 500 pounds at the
end of a six-foot lever. What is the horse-power?

3. A gasoline engine making 1100 R.P.M. balances a 25-pound
weight at the end of a 4-foot lever. What is the horse-power ?

4. If in Fig. 5, R is a crank 15 inches long (r) is 2 inches and
the rope (w) is fastened to F of Fig. 9, what load (w) will a force of
100 pounds lift if the combined machine works at 60% efficiency?
How far will the crank move to lift the weight 5 feet?

APPLIED PHYSICS

6. If the front sprocket of a bicycle contains 27 teeth and the
rear one 9, how far will the wheel move along the ground while
the pedal makes one turn ? How many turns of the pedal per mile ?

7. If the crank (problem 6) is 7 inches long how far does the

wheel move along the ground while
the pedal moves one foot ?

8. When the crank is in the hori-
zontal position what is the mechani-
cal advantage ? If the efficiency is
80 % how much is the forward push
when a force of 50 pounds is exerted
on the pedal ?

9. What is the "gear" of the
above bicycle ? Why will a low gear
climb hills better than a high gear?
Why will a high gear run faster than a
low gear on a smooth level pavement ?

10. Suppose R be 4| inches and r
be 4 inches and a force of 100 pounds
be exerted at F, Fig. 19, what load
can be lifted? Consider the efficiency
to be 75%.

11. Refer to Fig. 13, page 15. With
the driver running at 500 R.P.M.
compare the speed of the driven and
the mechanical advantage of each
combination.

12. A shaft and a counter-shaft
each have a pulley one foot in di-
ameter. The shaft runs 1000 R.P.M.
and 4 horse-power is being trans-
mitted, find speed of belt, effective
pull, and R.P.M. of counter-shaft if

FIG. 20. — Weston Differential there is no sliP- Find the same if
Pulley. pulleys 2 feet in diameter are substi-

The wheels of the pulley are tuted on both line shaft and counter-
fastened rigidly together. One shaft,
wheel is a little larger than
the other and revolving the
wheels once lifts the weight
half the difference between the
circumferences.

CHAPTER II
DYNAMICS

DYNAMICS treats of force producing motion. Watch a
locomotive starting a heavy freight train. How slowly the
train starts. It gradually moves faster and faster until
it is at full speed. When the breaks are set the friction
with the rails pulls back on the train and soon stops it. If
a train runs at high speed around a curve it presses against
the outer rail. We might say the outer rail pushes against
the train pushing it out of a straight line. If you tie a
string to a lead ball and swing it in a circle you must pull
on the string to keep the ball in the curved path. Such a
push or pull is called force. That which changes or tends
to change motion in direction or quantity is force.

If you push against the side of a building, the building
will not move, yet if you exert the same push on a light
wagon it will move. In each case you used force, but in one
case motion is produced and not in the other, because the
resistance is too great. We found that work expressed
in foot-pounds required two factors, force times distance.
We must agree, then, that force may be exerted without
doing any work, as when you push against the side of a
house.

Motion is change of position with reference to some other
body. On a fast train one day a mother said to her little
girl, " Now, Susan, do sit still." The train was running 60
miles an hour which is 88 feet per second. What do you
think about sitting still? The rate of motion, the speed,

22 APPLIED PHYSICS

the number of units of space passed over in one unit of time,
is velocity. Velocity may be either constant or variable.
When the velocity is variable the change in speed per unit
time is called acceleration and may be either an increase
or decrease in speed.

Forces can be compared only by their tendency to pro-
duce or change motion. Sir Isaac Newton stated the
.relation between force and motion in three laws:

1. All bodies continue in a state of rest, or of uniform
motion in a straight line, unless acted upon by some external
force that compels a change.

2. Every change of motion is proportional to the acting
force, and takes place in the direction in which the force
acts.

3. To every force there is always an equal reaction in
the opposite direction.

The first law, often called the law of inertia, states that
a body once put in motion by any force will keep on forever
in a straight line unless some force acts upon it. Inertia
is not a force, and should not be considered as such. A car
moving with a high velocity may strike a blow upon a
stationary body and expend considerable energy in doing
damage. The force which it exerts is not force of inertia
but is due to inertia. The amount of work it is able
to do while coming to rest is the same as the amount
of work done upon it in starting it from rest to the given
velocity. Inertia has enabled it to store the energy in
itself.

The second law has many important applications. If
a ball be thrown due north and the wind is blowing from the
east, the ball will be blown out of a straight line and toward
the west. The distance it is moved toward the west will
depend upon the velocity of the wind and will be the same
per second regardless of its velocity toward the north.

DYNAMICS

< 100 — J< 100 — >

< 100 >

< — 100 — >

—

"~— -.^

16.1

~~"^N^ 6

^x H

\ ,

(

\
I

)

FIG. 21.

Two marbles, shot out from a table top, one to fall straight
down and the other shot out in a horizontal direction, will
strike the floor at the same time. See Fig. 21.

We see that gravity acted on each ball in exactly the same
way, and produced the same downward motion regardless
of other motion. This is
all as it should be, as
stated in the second law
of motion. A more com-
plete explanation of the
term " change of motion"
will be found on page 27.

A boy weighing 120
pounds can usually lift
more than his own weight.
Now, suppose he stands

in the rings in the gymnasium and taking a rope in each
hand lifts 150 pounds. He weighs only 120 pounds. Will
he lift himself any farther than the ceiling of the gymna-
sium? Explain this by the third law of motion.

When two or more forces act upon a body at the same
time at a common point, their combined effect, called

the resultant, may be found by
the parallelogram of the forces.
A force may be represented
by a straight line, the direc-
tion being the direction of the
force and the length being the
force drawn to scale. If two
forces (a) and (6) act on a body
at A as in Fig. 22, draw the line in the direction of the
forces and lay them off to some convenient scale. Com-
plete the parallelogram as in 22, and the diagonal represents
the resultant force both in direction and size. A third

FIG. 22. — Parallelogram of
Forces.

a and 6 combine to produce
the resultant r.

APPLIED PHYSICS

force acting at A, equal and opposite to r, will balance the
forces a and 6 and prevent motion.

For an application of the parallelogram of forces refer

FIG. 23. — Proving the Parallelogram of Forces.

The resultant of A and B is equal to and opposite C. A tug of war
with the opposing teams evenly matched.

to Fig. 24. The end pole of a telephone line of 6 wires
must be held in by a guy wire. Each line is under tension

DYNAMICS 25

of about 200 pounds. The guy is fastened at 45°, how much
will it have to pull? The guy is made by twisting together
wires. If each wire will hold 500 pounds before breaking,
and two extra are to be put in for safety, how many wires
must be used in the guy?

The parallelogram of forces may be used in explaining

1600

FIG. 24.

The "Line Boss" often estimates the number of wires needed in
a guy by drawing a parallelogram in the dust of the road.

the flight of a kite or of the heavier-than-air flying machine,
the aeroplane. The kite is pulled forward by a string or the
aeroplane is forced forward in the direction d, Fig. 25, by the
action of the propeller. This motion causes the air resistance

APPLIED PHYSICS

to develop a pressure against the plane in the direction c

-y perpendicular to the plane.
This may be resolved into
two forces, one, a, resisting
the motion of the plane,
and one, b, opposed to the
weight of the machine.
If the speed be great and
the planes are large the
portion b will be equal to

or greater than the weight and the plane will rise. Means of

stability and steering must be provided by auxiliary planes

and rudders.

Problems

1. Neglecting weight of 6,
Fig. 27, what is the tension
on c ? Compare with Fig. 22.

2. If in the Fig. 27 the
weight of b be 50 pounds,
how much does it add to the
tension of c?

3. If in Fig. 24 the guy
wire makes an angle of 60°
with the horizontal, how
many strands must be placed
in the guy?

When a locomotive
starts a heavy train from
rest, it does not reach full
speed at once but in-
creases its rate of motion
slowly. If you kick a

FlG

football and some boy has made a mistake on the first of
April and filled the ball with lead instead of air, you will

DYNAMICS

find that a heavy body does not start from rest easily.

This helplessness of matter is Inertia. Inertia causes a

body in motion to keep on

in a straight line unless

acted on by some force; it

keeps a body at rest from

starting unless some force

starts it. Inertia is a prop- a

erty of all matter and is

proportional to the amount

of matter present. In the

case of the train starting,

it takes time and force to

The Force Polygon.
FIG. 27.

500 Lbs.

overcome the inertia of the

train, and when the train

is running 60 miles per hour it takes time and force to

stop it.

Suppose a locomotive be coupled to a heavy train which
is carried on such perfect bearings that it has no friction.
If the engine pulls for one second it will start the train a
little. If the coupling breaks at the end of the second, the
train will run during the next second with a constant speed.
Suppose the train starts from rest and at the end of one
second has a speed of one foot per second, that is, if left
to itself, would run one foot the next second. At the end of
two seconds it has a speed of two feet per second, at the end
of three seconds it has a velocity of three feet per second, and
so on until it is running at full speed. The increase in speed
per unit time is acceleration, and in this case is the same each
second and is therefore uniform acceleration. The speed in-
creases one foot per second every second. That is, if we have
a body free to move without friction and couple a force which
exerts the same pull all the time in one direction, the body
will begin to move slowly at first and at the end of one

28 APPLIED PHYSICS

second will have a certain speed. At the end of two seconds
it will have twice as great a speed and at the end of three
seconds three times as much speed and so on. Such a force
is a constant force, and such increase of speed is constant
or uniform acceleration, and the motion is uniformly accel-
erated motion. The velocity equals the acceleration times
the time if the body starts from rest. V = at is the same
thing in a formula which must be learned.

A train starting from Chicago runs for a while at 50
miles per hour; after stopping at a small station it runs
at a slower speed for a time. At the end of five hours it
is found that including all stops and changes of speed it
has averaged 30 miles per hour. How far has it traveled?
You answer at once 150 miles or the average speed times
the time equals the distance traveled. If a body starts
from rest and moves with a uniform acceleration so that
its increase in speed is 4 feet per second each second, at
the end of three seconds it will have a velocity of 4 X 3 or
12 feet per second. Experiments have shown that its
average speed is the average of the speed at the beginning
and at the end of the time when it has uniform accelera-
tion. In this case the average of 0 and 12 is (0 + 12) -f-
2 = 6. The distance traveled is 6 X 3 = 18 feet. Sup-
pose the body has an acceleration of a feet per second
each second, then at the end of t seconds its speed will be
v = at feet per second. Its average speed is (at + 0) -r-
2 or |a£. The distance traveled is the time (t) multiplied
by the average velocity, (?at), that is (\at) X t = JaZ2.
The formula is written S = %at2. S is the distance traveled,
a the acceleration per second, and t the time in seconds.

Sometimes we wish to find the distance traveled in any
one second, as the fifth second. Suppose a body starting
from rest receives a uniform acceleration of 6 feet per second
each second, how far will it travel in the fifth second? Its

DYNAMICS

velocity at the end of 5 seconds is 5 X 6 = 30 feet per second.
At the beginning of the fifth second it is 4 X 6 = 24 feet per
second. The average velocity is J (30 + 24) or 27. The
distance traveled for the fifth second is the average velocity,

FIG. 28. — Stick, String, and Spring Balance.

Only a stick, string, and spring balance required to illustrate several
important applications of physics in trusses, hoisting cranes, etc.
Every student of physics should experiment with several combina-
tions, and apply his results to many local illustrations. See Figs.
22 and 23.

30 APPLIED PHYSICS

27, multiplied by the time, or 27 X 1 = 27 feet. For the
general formula find out how far a body receiving uniform
acceleration travels the second (t) which may be the fifth
or any other second. At the end of the second (t) the
velocity is at. At the beginning of the second it is (at — a).
The average speed is (at + at — a) -r- 2 or fa (2t — 1).
The distance traveled is the time, 1 second, multiplied by
the average velocity fa (2t — 1), or d = la (2t — 1) where
d is the distance traveled in any one second.

The three formulas for uniformly accelerated motion
then are v = at; S = \a&; d = fa (2t - 1).

The best example of a constant force producing uniform
acceleration in a body free from friction is gravity acting
upon a freely falling body. Experiment has shown that
the acceleration due to gravity differs a little in different
parts of the earth but is about 32.2 feet, or 980 cms. per
second each second. In working with falling bodies the form-
ulas explained above are used; g is susbtituted for a and the
formulas then become S = \g$; v = gt; d = %g(2t — 1).

Problems

1. If a train pulling out of a station has an acceleration of \ foot
per second, what velocity would it have at the end of 20 seconds? 1
minute? 2 minutes, 56 seconds? How many miles per hour is the
last velocity? How far will the train travel the first second, first
20 seconds, first minute?

2. A train running 60 miles per hour has its brake set and slows
down at the rate of two feet per second. How long will it take to
stop it? How far will it go before stopping?

3. A stone falls from the top of a cliff in three seconds. How high
is the cliff? With what velocity does the stone strike?

4. A man in a balloon drops a piece of iron and finds it takes 10
seconds to fall. How high is he?

5. If the building is 64 feet high, how long would it take a ball to
fall to the ground if it should blow off the top?

6. How far will a freely falling body fall in 10 seconds?

DYNAMICS 31

The quantity of motion which a body possesses is often
expressed as momentum, the product of mass times velocity.
The momentum of a locomotive weighing 50 tons moving
with a velocity of 20 feet per second is 100,000 X 20 =
2,000,000. The unit of momentum has never been named.
In comparing momenta the same units of mass and velocity
must be used.

We have found that motion can be changed in quantity
or direction only by the action of force, and the second law
of motion means that the change in momentum is propor-
tional to the force. The change of momentum may be made
the means of measuring the force applied. The unit of force
depending upon this principle is called a dynamic unit. The
force which will produce unit change of momentum in unit
time is called the dyne in the metric system. That is, the
force which acting for one second on a mass of one gram
will give it a velocity of one centimeter per second is one
dyne. The gravitational units of force, the gram weight
and pound weight, that is, the pull of gravity for a mass
of one gram or one pound have already become familiar
and will be used except when it is necessary to have a unit
which is absolute and independent of all variation. If a
mass of one gram is let fall freely at this latitude it will
receive an acceleration of 980 centimeters per second in
each second. Since a dyne is a force which will accelerate
a gram one centimeter per second every second, it follows that
a gram is equal to 980 dynes at this latitude. Momentum
equals mass times velocity. Change of momentum or force
equals mass times rate of change of velocity or / = ma where
force is expressed in dynamic units. To change this to
gravitational units, divide by g and we have / = ma/g.

For gravitational units the author prefers to use / = -

y
where w = weight in grams, a = acceleration in centi-

32 APPLIED PHYSICS

meters per second per second, and g = 980; or w = weight in
pounds, a = acceleration in feet per second per second, and
g = 32.2 in which case / = force in pounds. Substituting

v/'t for a, we have / = - - or w = weight in pounds, v —

velocity in feet per second, t = time in seconds the force
acts.

Problems

1. What force (neglecting friction) will be required to start a rail-
way coach weighing 20 tons and give it an increase in speed of £ foot
per second every second, on a level track. If friction adds 10 pounds
per ton weight what total force must be exerted?

2. What force must be exerted on a 100-pound weight to give it an
acceleration of 32.2 feet per second per second?

3. If a boy weighing 100 pounds stands on the platform of a set
of scales placed in a passenger elevator what will his apparent weight
be while the elevator is getting up speed at the rate of 1^ feet per second
each second, going up? going down? running at full speed without
acceleration?

4. A 200-pound man stands in a street car while the motorman
sets the brakes slowing down with a negative acceleration of 2 feet
per second per second. What is the force required to keep him from
being thrown forward? What force to brace him when the car starts
up with an acceleration of 1 foot per second per second?

Gravity is the pull drawing the earth and any other body
toward each other. Gravitation is a similar attraction
existing between all bodies at a distance. Sir Isaac Newton
watched an apple fall and asked himself why. If a one
pound ball and a ten pound ball were tied together by a
stretched rubber band and then left free to move, they
would both move toward each other but not with equal
acceleration. The momentum of each would be the same
but the larger one receives only one-tenth as great a velocity
as the smaller one. The same condition exists when an
apple falls to the earth, the earth also falls toward the
apple, and the momentum of each is the same. If your

DYNAMICS 33

mass was the same as that of the earth and you should
fall down, the earth would fall half-way to meet you.

What the force of gravitation is no one knows, and no
one knows how it acts between bodies. If a horse is to
pull a load it is necessary to hitch him to it, but gravita-
tion acts through a great distance and always keeps hold,
yet the best scientists cannot tell us how. Newton was
able to state some of the laws by which it acts: " The
attraction between two bodies varies directly as the product
of their masses, and inversely as the square of the dis-
tance between their centers of mass." The laws of weight
are derived from this: — 1. The weight of a body varies
directly as its mass at any given place. 2. The weight
of a body above the surface of the earth varies inversely
as the square of the distance between its center of gravity
and the center of the earth. 3. Below the surface the
weight varies directly as the distance from the center of
the earth.

The center of gravity of a body is the same as the center
of mass. It is the point at which the whole weight of
the body may be considered as centered. If a brick be
resting on a plain surface any attempt to overturn it raises
the center of gravity and it falls back to place again.
This is called stable equilibrium. A pyramid balanced
on its apex is in such a position that any movement will
lower its center of gravity and it will tend to fall farther.
Such a body is in unstable equilibrium. The unsupported
bicycle standing still is in unstable equilibrium. If a ball
lying on a plain surface be rolled along, its center of gravity
is neither raised nor lowered. This is neutral equilibrium.

If a body be fastened to a string and whirled so as to

give it a circular motion, there will be a pull on the string

which will be greater or less as the velocity is increased

or diminished. If a body be revolved in a horizontal

34 APPLIED PHYSICS

plane so that the gravity will always be the same, we may
consider that, according to the first law of motion, the
body tends to move in a straight line and would so move
unless some force causes a change in direction. If the
string be cut, the force which pulled the body out of a
straight line would be removed and it would move on in
a straight line tangent to the circle. To compute the

centrifugal force of a body use the formula / = — ; / =

force, w = weight, v = velocity per second, g = accelera-
tion due to gravity, r = radius of circle. If this formula
be used for bodies revolving in a circle, it may be simpli-
fied to the following: / = 0.00034 wrn2 where / = force in
pounds, w = weight in pounds, r = radius of circle in feet,
and n = number of revolutions per minute. In comput-
ing the centrifugal force of a locomotive rounding a curve
the first form is usually used. For computing the force
tending to tear apart fly-wheels and pulleys, the latter form
is used.

Problems

1. What centrifugal force must be exerted when a locomotive
weighing 100 tons runs at 40 miles per hour around a curve of 1000 feet
radius?

2. In the above problem plot the centrifugal force as a horizontal
line and the weight as a vertical line and find how much the track
must be banked in order to make the resultant perpendicular to the
track. What effect on this parallelogram would result if the weight
of the locomotive were one half as great?

Energy has been defined as the ability to do work. We
may measure energy in the same engineering units used
for work, that is, foot-pounds. A foot-pound of energy is
the ability to do one foot-pound of work.

If a pound weight be lifted four feet, four foot-pounds
of work are done on it and it has four foot-pounds of possible

DYNAMICS 35

energy called potential energy. When it is dropped this
potential energy is transformed to energy of motion. Just
as it strikes it has the four foot-pounds of energy stored
up as energy of motion. This is called Kinetic Energy.

Kinetic energy is the energy of any body due to its
motion. Such is the energy of the sledge, the trip
hammer, etc. The work done in lifting a body is the
weight times the distance E = WS. E = foot-pounds of
work, W = weight, S = distance weight is lifted. If a
body falls this potential energy is all transformed to kinetic
energy and the energy in foot-pounds is WS.

But S = \gt~ (Falling bodies) (1)

Substitute in (1) S = %g~ = V2/2g but E = W S and

t = V/g; squaring both sides of the equation I2 — V2 g2.

and

WV2

substituting the value of S we have: E = WS = — ~ —

foot-pounds.

E = energy in foot-pounds, W = weight in pounds,
V = velocity in feet per second,
g = acceleration of gravity

It makes no difference whether the velocity was acquired
as a falling body or by the application of any force, the
result is the same. We may use this formula then to find
the foot-pounds of energy possessed by a base ball, cannon
ball, trip hammer, locomotive, or any other moving body.

Problems

1. The Lake Shore Railroad uses a pile driver with a 1000-pound
hammer lifting it 30 feet and letting it fall. How many foot-pounds
of energy has it when it strikes? What kind of energy? Note two
ways of working this problem, select the short method, and tell how to
work it the other method.

36 APPLIED PHYSICS

2. If the pile is driven 3 feet at a blow, what is the force of the blow?
If driven 2 feet? 1 foot? 6 inches? 3 inches? 2 inches? (The force
of the blow multiplied by the distance the resistance is moved gives
the foot-pounds of work done and this must equal the energy expended.
If a hammer strikes a piece of iron will the force of the blow be the
same with the iron on an anvil as it would be with the iron on a feather
pillow?)

3. What is the energy of a 200-pound trip hammer moving 20 feet
per second?

4. What is the energy of a 50-ton locomotive moving 20 feet per
second? Moving 40 feet per second? What is the ratio of the last
two results? Why is this?

5. Why does an automobile running into a stone wall have nine
times as much energy to use in smashing itself if it is running at sixty
miles per hour as when running 20 miles per hour?

If a heavy block, placed on a smooth table, be pulled
along on the surface by a spring balance, it will be found
that some force must be exerted to keep it moving. This
is used in overcoming friction. If the block weighs ten
pounds and has a flat face with 100 square inches area
and an edge with only 10 square inches surface, the force
to overcome friction is found to be the same whether the
block is on the edge or on the face. This is approximately
summed up by the statement that the friction depends
upon the pressure and is independent of the size of the
surface. It will vary with the nature of the substance and
the nature of the surface. The friction is less when the
body is in motion than when it is at rest. If the pressure
between the two bodies is 10 pounds and one pound pull is
required to keep one of them sliding on the other at a uni-
form speed, the coefficient of friction is one tenth. The
force required to keep a body moving at a uniform velocity
divided by the pressure is the coefficient of friction. The
coefficient of friction of bronze on bronze, or bronze on cast
iron when dry is about 0.2. The coefficient of friction for
the same surface well lubricated is from 0.05 to 0.07.

DYNAMICS 37

Problems

1. What is inertia?

2. What are Newton's laws of motion?

3. If two forces act on a body at a certain point at one time, what
is the resultant and how may it be found?

4. Describe, illustrate, and give a unit of each of the following:
work, power, energy, momentum, force.

5. If a force of 500 pounds is pulling directly east on a body and a
second force of 900 pounds is pulling south on the same body, what is
the resultant force?

6. If a belt running over a pulley has a tension downward of 750
pounds, and the other side of the belt, running from the pulleys at an
angle of 45 degrees to the vertical, has a tension of 250 .pounds, find
the direction and magnitude of the resultant pull on the hanger. If
this belt is transmitting 20 horse-power, what speed must it have?

7. If a boat be rowed across a river at right angles to the current
at 4 miles per hour, and the current carry it down at the rate of 2
miles per hour, find the actual velocity and direction.

8. What horse-power is required to raise a weight of 99,000 pounds
a height of 40 feet in one half hour?

9. A cross head weighing 500 pounds, having bronze shoes, slides
on a well-lubricated cast-iron surface. What is the total friction?

10. A locomotive weighing 40 tons has to exert a force of ten pounds
per ton in overcoming friction when it is in motion. What total force
must the locomotive exert to increase its speed 2 feet per second in
one second? What will be the momentum of this locomotive when
it is running 60 miles per hour? What will be the centrigufal force
if it runs at the above speed around a curve with a radius of 2000 feet?

11. If the rim of a fly-wheel weighs 500 pounds, and has a diameter
to the center of the rim of 8 feet, how large is the force tending to tear
it apart when revolving 20 times per minute?

12. If a body will fall from the top of a building in 2 seconds, how
high is the building in feet and in meters?

13. At one of the amusement parks, on a certain railroad, there
is a stretch of track 60 feet long with a drop of 20 feet. If the car
runs without friction down this incline, starting from rest, what velocity
will it have? how many miles per hour is this? If it drops vertically
20 feet, what velocity will it attain?

APPLIED PHYSICS

If a heavy weight be suspended by a light cord as
shown in Fig. 29 and pulled to one side of its lower

point as in that figure,
the forces of gravity
and the string will re-
sult in the force caus-
ing the weight to move
as shown; a is a line
to represent the force
of gravity, B the pull
of the string, and r the
resultant which is un-
balanced and therefore
produces motion. This
was known before the
time of Galileo, but it
remained for that great
observer to find that
a pendulum always took approximately the same time
for a swing, whether that swing was long or short, if the
pendulum remained the same length. Galileo, sitting in a
cathedral when the chandelier was set swinging, observed
that when almost at rest, one swing or vibration took the
same time that one vibration took when making a long
swing. The distance or length from point of rest to one.
end of the swing is the amplitude. The amplitude is the
length of the swing from the position of rest (see AB in
the figure). The swing from one point back to the same
point going in the same direction is a double vibration.
The swing from one side to the other is a single vibration
and is one-half a double vibration. The time of the pen-
dulum is the time of a single vibration. If the time is one
second, it is called a seconds pendulum. The laws of the
pendulum are:

FIG. 29.

DYNAMICS 39

1. The time of the pendulum is very nearly independent
of its amplitude, if the amplitude is only a small part of
the arc of a circle.

2. The time of a pendulum is proportional to the square
root of its length.

3. The time of a pendulum is inversely proportional to
the square root of the acceleration due to gravity.

4. The time of a pendulum is independent of its mass.

These laws are expressed in the formula t = "A/-;

t = time; / = length; g = acceleration due to gravity.

Solve this formula for g in terms of the other values.
The chief use of the pendulum is to measure time.

Before the use of the pendulum became general the sun-
dial and the sand hour-glass were used. Examine the
escapement of a clock and see how the pendulum is applied.
Substitute in the formula t = 1 and find the length of the
seconds pendulum. Compare this with the master-clock
in the office.

CHAPTER III
MECHANICS OF FLUIDS

THE most commonly accepted theory, that all matter
is made up of molecules, has been mentioned in Chapter I.
It is supposed that the spaces between the molecules are
large compared to the size of the molecules, and that the
particles themselves are therefore not in contact but are
continually in motion and bounce against one another.
If the molecules are fixed so that they vibrate in one
place, the body will not change its form and is a solid.
A solid is a body which retains a definite form and volume.

In some bodies the molecules are supposed to be free to
move about from place to place and, as they strike one
another and rebound, they move about from place to place.
The body will not hold a definite form but will flow and
take the shape of the containing vessel. Such a body is
a liquid. A liquid is a body which takes the shape of the
containing vessel but maintains a definite volume. At
ordinary temperatures water and mercury are examples
of liquids. In both of these cases the cohesion between
the molecules holds them together so that they keep a
fixed volume. In some bodies the molecules repel with a
force greater than that of cohesion and the particles get
as far apart as possible. Such a body will have no definite
fixed volume but will expand until it is distributed through-
out, or fills the containing vessel. Such a body is gas.
Hydrogen, oxygen, and air are examples.

The three states of matter are solid, liquid, and gaseous.
The last two are often combined and called fluid. The
characteristic of a fluid is the ease with which its parts

MECHANICS OF FLUIDS

slide over each other and it changes its shape, namely, its
mobility, If at a certain temperature a body be part
liquid and part gaseous, the latter part is not considered a
gas but is called vapor. Many substances may exist in
all three states of matter depending upon the condition of
temperature. Water may be put in an ice box in the form
of a solid. At ordinary temperatures it is a liquid while
at higher temperatures it becomes steam, an invisible gas.
At ordinary temperatures water exposed in an open vessel
will slowly evaporate. It then takes the form of vapor.

A gas may be compressed. When a pneumatic tire is
filled, several cubic feet of air may be compressed to one
cubic foot. If the pressure is removed it will expand
again. Liquids are almost incompressible, even under
enormous pressures, and on the other hand when the pres-
sure is removed they do not expand. Aside from this
difference, liquids and gases may be treated much alike.
This chapter is to present the mechanics of fluids.

In Fig. 30, suppose a and b are two cylinders of the
same size, one fitted by a block of wood while the other is
filled with water. Each is
fitted with a piston, and
suppose in each case the
piston has an area of 50
square inches. Neglect
the weight of piston, wood,
water, etc., in each case,
and suppose a force of 500
pounds is applied to each
piston. This would be a

pressure of 10 pounds to

, , .1 j • j.u In b pressure on the bottom only.

the square inch and in the In a ^ressure on the sides also.

case of b would be trans-
mitted to the end- of the cylinder and there exert a pressure

FIG. 30.

APPLIED PHYSICS

equal to 10 pounds per square inch. In a there would be
the same pressure of 10 pounds per square inch on the bot-
tom of the cylinder, but since the molecules are free to move
and slide over each other, they will press out on the sides
of the cylinder and the pressure of 10 pounds per square
inch will also be transmitted to the sides. If a pipe be
tapped into the sides of a and a pressure gauge put on, it
will be found that, neglecting, the weight of the water,
the pressure is the same at every inch of surface.

Every boy knows that the pressure applied to the water
at a pumping station is transmitted through the pipes
which make many turns and presses outward at any
point. If a hole is made in the water pipe at any point,
pressure will be required to keep the water in. Pascal
summed this up in the following law: " The pressure
per unit area exerted anywhere on a confined liquid is
transmitted undiminished in all directions and acts with
the same force on all surfaces at right angles to those
surfaces." This principle is made use of in the hydraulic
press.

In Fig. 31, a is a piston having a cross section of 1
square inch. When this is raised valve / opens and

water flows in to fill its
place. As a is pressed
down, valve / closes and
valve c opens allowing
the water to flow into the
large cylinder, and if a
is pressed down with a
force of one pound, this
pressure will be transmit-
ted to every square inch

ILb.

FIG. 31.

The pressure on the pistons is pro- of area jn tne large pis.
portional to the area or in proportion
to the square of the diameter. ton 6. li this has an

MECHANICS OF FLUIDS

area of 100 square inches the total pressure will be 100
pounds.

The small piston is usually worked by a lever and
may have a pressure of 500 pounds per square inch in
which case the large piston would receive a pressure of
500 pounds per square inch or a total force of 50,000
pounds.

It is evident that the lower part of a fluid must support
the portions of the fluid that rest upon it. The weight
due to gravity must cause pressure in the fluid. This pres-
sure is transmitted in all directions. Suppose a and 6,
Fig. 32, are two cylinders of the same size at the bottom,
connected by pipe c. If
water is poured in until
both are filled to near the
top the water will stand
at the same level in both.
The fluid is at rest and
the pressure at c is the
same from each side or
there would be a flow of
water. If we consider a
small particle of water at
/, the pressure must be

FIG. 32.

the same in opposite directions or the particle would
move in the direction of the unbalanced force. At d,
the water is exerting a downward pressure in the pipe
e, and at the foot of the pipe the pressure is transmitted
in all directions and presses up on the cylinder head the
same amount that it presses up to support the water at
the same level at / in a.

As the pressure is balanced at c, the pressure per square
inch is the same in each cylinder and the pressure on
the bottom of a is the same as the pressure of b. In a

44 APPLIED PHYSICS

fluid at rest, the pressure at any point is independent of
the size and shape of the containing vessel but depends upon
the depth of the fluid only. A dam 10 feet high and 50
feet long holding back the Atlantic ocean has the same
pressure to withstand as a dam the same size forming
part of the side of a salt water canal. If you suppose
that the pressure depends upon the quantity of water
present, rather than the depth, go home and watch the
tea kettle boil and wonder why the great weight of water
in the body of the kettle does not more than balance the
small quantity in the spout and make it all run out.

In Fig. 32, a and b each have an area of one square
foot, the total pressure is the same. The pressure is equal
to the weight of the water in b. To find the force on
a surface, multiply together the area of the surface, its
depth, and the weight of unit volume of the liquid. A
cubic foot of water weighs 62J pounds. A cubic centi-
meter weighs 1 gram.

If in Fig. 32 a has an area of one square foot and
the depth is 10 feet, what is the force on a when the
vessel is filled with water? What is the pressure per
square inch? Find the same for b. Since there is so much
more water pressing on b from where does the extra
force on a come? If a hole were drilled in d, would the
water run out? Why? Draw a diagram of a lawn hose
attached to the bottom of a water-tower to show that
pressure due to weight of fluid may be in any direction.

In a high-level water storage tank, suppose the level of
the water to be 60 feet above the level of the first floor of
your school building and a one-inch pipe to run from the
storage tank to the level leading into a closed steel tank
heater. What would be the pressure per square inch?
Would it be any different if the storage tank extended
down full size to the school level? A certain little town in

MECHANICS OF 'FLUIDS 45

Michigan which had no water-works put in a town pump
and put up a large tank, such as the railroads use, on
posts the height of the second floor. A two-inch pipe
ran from this to the street level and a hydrant was put in.
They expected to attach a hose to the hydrant and the
"great weight of water" in the tank would throw a stream
over any three-story building in town. Did it work?

The plumber uses the approximate rule that there is a
pressure of one pound per square inch for every two feet
in depth of water. What is the error of this rule at a
depth of 34 feet below the surface? A steam boiler must
be tested to a pressure higher than the steam pressure it
is to carry. If a new boiler is to be tested to a pressure of
500 pounds, would it be safe to fire up and run the steam
pressure to 500 pounds? It is filled full of water and then
a small force pump is attached and the pressure of 500
pounds per square inch is exerted in the force pump
cylinder. What pressure is exerted in the boiler? Why?
If it breaks, would there be an explosion? Why?

If a fish were 34 feet below the surface of the water,
what pressure per square inch would he have to sustain?
Why does this not crush him? Would the pressure vary
if the fluid had less weight per cubic foot or more weight
per cubic foot? Air is a fluid much lighter per cubic foot
than water. The enormous quantity of air above the
surface of the earth must exert a considerable pressure
upon the earth. Did you ever notice this pressure? From
the time of Adam until the time of Torricelli, men paid
little attention to the pressure of the air. Before this
time it had been observed that when a tube was placed
with one end in water, as in Fig. 33, and the piston with-
drawn, the water would follow it. It was also found that
the water would follow about 34 feet and could not be
raised any farther. Mercury is 13.6 times heavier than

APPLIED PHYSICS

water, and when mercury replaced the water it would
rise to a height of only 29.9 inches.

Torricelli, in 1643, filled a glass tube more than 30 inches
long with mercury. He then inverted it in a cup of mercury,
as in Fig. 34. The mercury fell from
the end of the tube and stood about
29.5 inches above that in the cup. He
believed the mercury in the tube pressed
down enough to equal the pressure of
the air on the same area in the cup. To
prove this he carried the tube up on a
mountain and found the mercury in the
tube settled down still lower. ^
The space above the mercury
containing nothing but a little
mercury vapor is called a Tor-
ricellian vacuum. The pres-
sure on the mercury surface
in the cup is due to the weight
of the air above it just as the
pressure on the boy at the
bottom of the heap in a foot
ball game is due to the weight
of the boys on top.

There is a popular impres-
sion that mercury rises in the
barometer tube, or water un-
der the piston, etc, because of
suction. What is incorrectly called suction is
due entirely to pressure outside. A simple dem-
onstration of this is shown in Fig. 35. A ba-
rometer tube, or Torricellian tube, is placed inside
a long air-tight guinea and feather tube. The
mercury stands at about 29 inches. If this is placed on

FIG. 33.

FIG. 34.

MECHANICS OF FLUIDS

the air pump and part of the air exhausted
the mercury in the tube falls. This shows
that pressure on the
mercury in the open
test tube, not suction,
held the column of
mercury up. If the air
pump is a good one,
the mercury will fall to
almost the same level
as that in the test
tube.

The reading of a
barometer depends up-
on the weight of the
mercury and upon the
pressure of the air. If
the temperature of
mercury is changed its
density changes, hence
to compare readings in
different places the
mercury must be at
the same temperature.
For convenience the
freezing point 0°C is
taken as normal tem-
perature. If the mer-
cury is warmer than
this, it has expanded
FIG. 36. — Standard and a small quantity
must be subtracted.

The pressure of the air depends upon the
layers of air above the instrument, so if

FIG. 35.

When air is
removed from
the large tube
the mercury
in the Torri-
cellian tube
falls, showing
that the mer-
cury is sup-
ported by
pressure with-
out, not by
"suction."

48 APPLIED PHYSICS

the elevation is changed, the pressure is changed. Sea-
level is taken as standard level, hence if the instrument
is above sea-level a small quantity must be added to the
reading. These are taken from tables and the correct
reading is said to be reduced to sea-level. When readings
taken in different places are compared, it is found that
they differ. A line drawn on a map through places of
equal pressure is called an isobaric line or an isobar. A
region of low-pressure is called a low or cyclonic area.
The air flows in from all directions toward such an area,
forming a whirlpool of air. These cyclonic areas in the
United States whirl counterclockwise. They are con-
tinually crossing the country from the west, following
well denned paths, and the weather forecaster is able to
predict the weather conditions for about 24 hours ahead,
because of his knowledge of the action of these lows. The
nearest United States weather bureau will furnish any
school with weather maps. A series of them should be
studied.

Problems

1. What is the force on the bottom of a vertical tank 34 feet
deep and one foot square, filled with water? What is the pressure
on each square inch of the bottom? Mercury is 13.6 times as heavy
as water, how deep must a tank of mercury be to give the same pres-
sure per square inch? What is the pressure in pounds per square inch
when the barometer stands 30 inches?

2. In the condensing engine the degree of vacuum in the condens-
ing chamber is expressed in pounds below atmosphere or in inches
of mercury below atmosphere. On a day when the barometer stands
at 30 inches and the condensing chamber is reduced to ^ the pressure
of the atmosphere the engineer calls it 20 inches of vacuum or 8.9
pounds vacuum. The pressure in the chamber would then be 10 inches
or about 4.9 pounds per square inch. When the barometer stands
at 29 inches what is the pressure inside in inches and the vacuum in
pounds when the vacuum gauge reads 10 inches? 14 5 inches? 26
inches? 34 inches? Is the last one possible? Why?

MECHANICS OF FLUIDS

In Fig. 37 is shown a lift pump, sometimes called a
suction pump. The piston (6) is lifted by means of the
pump handle and this removes the air pressure in the
cylinder above the valve (a). The pressure below (a)
raises that valve and the water runs into the cylinder.
Notice that suction can never raise water. If the air
pressure on the water outside of the pump were removed,
the water would not flow through (a). Piston (b) is

FIG. 38.

stopped and valve (a) closes, and as (b) is pushed down
the water flows through b. The next stroke lifts it out
of the cylinder. If suction pulled the water up, then there
would l)e no limit to the height at which the cylinder
could be placed above the water in the well. When the
water barometer stands at 34 feet, the cylinder must be
placed a little lower than that, as the valves cannot be
made to work perfectly air-tight. Could a city pumping
station be located more than 34 feet above the level of
5

APPLIED PHYSICS

a lake from which the water is drawn? Why? Air has no
tenacity such as wire would have. The air is removed from
many buildings by so-called " suction fans." If the air has
no tenacity, why does the air rush into the stacks leading
from a room to the fan when the fan is started. Suppose you
were to pump mercury out of a well, how high could you
place a cylinder above the mercury and still have it work?

The force pump in Fig. 38 fills its cylinder in the same
way but the top of the cylinder is closed and packed at (t),
and on the up stroke the water is forced into the air chamber
(/). The air is compressed and its elastic tension forces
the water out through the pipe in a steady flow.

In Fig. 39, the siphon is shown. So long as the siphon
is empty no water will flow from the vessel (6) . If the
^_-_^=^_-_-__- -_- ^-^ -_===^ tube is filled with water

it is evident that the air
pressure is the same at
(6) and at (d) , but on the
right between (c) and (d)
the water column (a) is
pressing down and its
pressure is subtracted
from that of the air. On
the left, the water col-
umn (h) is pressing down
and its pressure is sub-
tracted from that of the
air. The result is un-
equal at (c); there is an
unbalanced pressure
toward the longer column
FIG. 39. which pushes the water

through the tube. If
(c) were more than 34 feet above (6), the siphon would

MECHANICS OF FLUIDS 51

not work, as the air pressure would not lift the water to
the bend in the tube.

In gases the molecules are supposed to be far apart
and to move with great velocity. Each moves in a straight
line until it collides with another molecule or with the
wall of the containing vessel, when it rebounds in another
direction. The path from one collision to another is the
Free Path, and its length will depend upon the number of
molecules in a given space and their velocity. It is sup-
posed that the velocity of the hydrogen molecule, under
normal pressure and temperature (N.T.P.) conditions, is
about one mile per second. At the same temperature the
oxygen molecule has only one fourth as great a velocity,
but as its mass is 16 times as great it has the same kinetic
energy. If a gas is confined in a cylinder with an air-
tight piston working freely on one end, the molecules
will continually strike this and rebound. There will be
a pressure exerted against the piston. If the gas is com-
pressed more molecules will strike the piston and the
pressure is increased. This force, which the gas exerts
in trying to expand, is its elastic tension. It is supposed
that the number of molecules is very great and that their
bombardment is continuous. When a cannon ball is
forced out of a gun by the pressure of the expanding gases
behind it, the molecules in bounding and rebounding must
have an enormous velocity.

The pupils in any room are continually breathing out
C02 into the room. This gas is heavier than air. If it
were inert and the molecules not moving, it would all
settle to the bottom of the room and remain as a distinct
layer. Illuminating gas being lighter than air would
rise to the top of the room, and there would be a layer
of carbondioxide at the bottom, gas at the top, and air
between. But the molecules of each gas are moving with

52 APPLIED PHYSICS

great velocity, and when they come to the edge of the gas
many of them are carried on through and soon the gases
are completely and uniformly mixed. This process is called
diffusion. The lighter gases have the higher velocities,
and hence diffuse more rapidly than the heavier ones.
It is by the rate of diffusion that the molecular velocity
is measured.

The molecule of oxygen weighs sixteen times that of
hydrogen, and it is found that a cubic foot of oxygen weighs
sixteen times as much as a cubic foot of hydrogen. This'
fact is sometimes used to explain the low barometer when
the air contains a large amount of water vapor. The
molecular weight of oxygen is 32; that of nitrogen is 28.
Water (H20) has a molecular weight of only 18. If a
cubic foot of gas at a given temperature and pressure
always contains the same number of molecules, it is evident
that if some of these are replaced by lighter ones the gas
will not weigh so much per cubic foot. The effect will
be the same as removing some of the heavy players from
a football team and replacing them by lighter ones. The
combined weight of the team will be less. When mole-
cules of water vapor replace some of the oxygen and nitro-
gen, the pressure of the air will be less and the barometer
will stand lower.

When solids go into the solution they disappear as
visible solids. The molecules have become separated and
move about in the solution much as gas molecules move
about. Two solutions placed in contact will mingle by
diffusion, as gases do. If two solutions are separated by
membranes, it is found that the molecules will pass through
and the solution will mix. This is osmosis. Two solu-
tions will pass through at different rates. Many of the
membranes of the body allow dissolved substances to
pass through by osmosis. These are called semi-permeable

MECHANICS OF FLUIDS 53

membranes. The semi-permeable membranes of the plant
cells at the tips of roots allow water to pass into the plant
and thus increase the pressure, helping the sap to rise to
the top of the trees. Such pressure is osmotic pressure.

The molecular theory of gases would lead us to suppose
that if pressure were applied to a gas the molecules would
be crowded together and in a given volume there would
be more molecules. If the pressure on a given quantity
of gas were doubled, the gas would be compressed to one
half its first volume and there would be twice as many
molecules striking the same area in the containing vessel
and the elastic tension would be doubled. This fact was
discovered and experimentally proved by Robert Boyle
and stated as Boyle's Law: " At constant temperature
the volume of a given quantity of gas is inversely propor-
tional to the pressure upon it." If a cubic foot of air at
atmospheric pressure is pumped into a bicycle tire so that
the pressure becomes two atmospheres, that is, 15 pounds
more than the atmosphere, the volume will be one-half a
cubic foot.

Pressure gauges are made to read either in absolute
pressure or in pounds pressure above that of the atmos-
phere. Absolute pressure is the pressure above zero.
Steam pressure is usually given as the number of pounds
above the atmospheric pressure. In the condensing engine
a chamber is used in which the pressure- is less than one
atmosphere. Such a partial vacuum is measured by a
vacuum gauge. The pressure of the atmosphere is about
29 inches of mercury. The vacuum gauge is so arranged
that it reads, in inches of mercury, or in pounds the
amount the pressure has been reduced below atmospheric
pressure.

A common form of gauge is shown in Figs. 40 and 41.

The curved tube A, Fig. 40, is flattened slightly and

APPLIED PHYSICS

tends to straighten out, just as your garden hose does,
when pressure is applied to the inside through the tap.
This moves the pointer across the dial.

The air pump may be used for compressing air or for
exhausting the air from a chamber and producing a vacuum.

In the latter the piston and
valves are arranged in a manner
similar to those of the water
pump already considered, except
that in good pumps the valves
are arranged to work mechani-
cally as the pressure of the air
soon becomes too small to work
them. Suppose an air pump to
be so constructed that the cylin-
der is one-third as large as the
chamber from which the air is to
be removed. As the piston is
lifted, the air of the chamber
expands to follow the piston;
one-third is added to the volume,
and the air expands from i to f
its first volume. One-fourth of
the air is therefore removed from
the chamber. The next stroke re-
moves one-fourth of the remain-
der. Therefore, after each stroke

there remains in the receiver f of the quantity present at
the beginning of the stroke. After the tenth stroke there-
fore, there would remain (f)10 of the beginning quantity
of gas. A little consideration will show that an air pump
cannot produce a perfect vacuum. Examine the dash
pot of a large Corliss Engine, and explain how the air pres-
sure is made to close the cylinder valves quickly.

FIG. 40.

The curved tube A is flat-
tened slightly and tends to
straighten out, just as your
garden hose does, when pres-
sure is applied to the inside
through the tap. This moves
the pointer across the dial.

MECHANICS OF FLUIDS

TECHNICAL
HIOH- SCHOOL

FIG. 41. — Pressure and Vacuum Gauges.

These read in pounds per square inch above or below the pressure
of the atmosphere. The two lower dials read the pressure in the con-
densing chambers. Why does the vacuum scale run to 15 only?

At the surface of any liquid, a thin layer of molecules is
under tension so that it acts like a thin elastic membrane
stretched over the surface. It will be seen in Fig. 42 that
a molecule at the center of a very small circle with its
centre at the surface will be attracted by the molecules

APPLIED PHYSICS

near it in quadrants (6) and (c), and there will be no mole-
cules in (d) and (a) to balance this force. Hence the surface
will be stretched. This is called surface tension. A fine
steel needle may be supported by the surface tension of
water.

In Fig. 43, water is shown in contact with glass. Here
in the circle drawn, a molecule of water near the glass is
attracted by the glass in quadrants (a) and (6), which is
greater than the attraction of the water in (c), and the

an
H

1=HI

FIG. 42.

Water adheres to clean glass. If
the glass be oiled what is the result?

surface of the water rises in a curve near the glass. If a
small tube is used, as in Fig. 43, the water will rise in the
glass tube.

If the tube is very small (a capillary tube), the water will
rise a considerable height. The absorption of ink by a
blotter or the rising of oil in the wick of a lamp are familiar
examples of capillarity. If the attraction of the mole-
cules of the liquid in the quadrant (c) is greater than that
of the molecules in (a) and (6), as is the case with mercury
and glass, the surface is depressed as in Fig. 44.

In Fig. 45, suppose a cube one foot on each edge be
placed with its upper surface parallel to the surface of
the water and two feet below it, the downward pressure
on the upper surface would then be 125 pounds, and the

MECHANICS OF FLUIDS

upward pressure on the lower surface would be 187.5. The

difference between these two would be 62.5 pounds and is

acting against gravity. The cube would appear to lose in

weight by the amount of

62.5 pounds, an amount

equal to the weight of a

cube of water of the same

size. This excess of up-
ward pressure is called

buoyancy. Archimedes

stated the principle of

buoyancy as follows: "A

body immersed in a fluid will lose in weight an amount equal

to the weight of the fluid displaced.''

This principle of Archimedes applies also to any body in

air; it is lifted or loses by an amount equal to the weight

of air displaced. A
sphere weighed in air
and then in a vacuum
will weigh more in the
latter case. Suppose a
pound of lead and a
pound of feathers are
each weighed in air and
then weighed in a vacu-
um, would the weight
be the same? Would a
balloon rise in a vacu-
um? Why does a bal-
loon rise to a certain
height and then not go

" any higher. If a bal-

loon be closed air-tight,

why will it burst when it reaches a high altitude?

58 APPLIED PHYSICS

A body lighter than a fluid in which it is immersed will
be lifted by a force equal to the weight displaced and will
rise and float at the surface, displacing fluid equal to its
weight. How many cubic feet of water will a 500-ton ship
displace? Why does a row boat sink deeper into the water
when a person steps into it? If the person weighs 151.5
pounds, how much water will the boat displace due to his
being in it? Why will a good egg sink in fresh water and
float in salt water?

The specific gravity of a body is the ratio between its
weight and the weight of an equal volume of water. If
the cube in Fig. 20 were cast-iron, it would weigh 450
pounds when weighed in air. Weighed in water the weight
would be 387.5; the loss of weight is 62.5 pounds. The
specific gravity then is 450 -4- 62.5 or 7.2.

In using the metric system it is customary to use the
term density instead of specific gravity. Density is the
quantity of matter per unit volume usually expressed in
grams per cubic centimeter. The gram is the weight of
one cubic centimeter of water. Hence, if we take one
cubic centimeter of cast-iron, which is 7.2 times as heavy
as water, it will weigh 7.2 grams. Specific gravity and
density in the metric system are numerically the same.
The specific gravity of a few substances is given in the fol-
lowing table.

The density of most substances will vary in different
samples and will differ somewhat from these figures.

Substance
Ash (dry)

Specific gravity or
density per cu. cm.

0.70

Weight, pounds
per cubic foot.

43.7

Ash (green)

. . 0.84

528

Acetic Acid

1 062

664

Alcohol

0.80

50.

Aluminium . ,

. 2.65 .

. 165.6

MECHANICS OF FLUIDS 59

Beech 0.69 to .852 53.2

Cedar 0.561 35.

Cork 0.24 15.

Copper (cast) 8.81 550.6

Copper (sheet) 8.88 555.

Brass 8.38 to 8.44 527.5

Gold 19.50 1218.8

Hydrochloric acid 1.22 75.2

Iron (wrought) 7.68 to 7.78

Iron (cast) 7.20 to 7.24 449.

Lead 11.36 709.7

Lignum Vitoe 1.33 83.3

Maple 0.75 46.

Mercury 13.6 850.

Milk 1.032 64.5

Nitric Acid 1.22 to 1.56

Oak 0.85 to 1.17

Pine 0.46 to 0.60

Platinum 21.5 1348.8

Sea water (about) 1.03 64.4

Silver 10.5 656.3

Spruce 0.5 31.2

Steel 7.84 490.

Sulphuric acid 1.84 115.1

Tin (cast) 7.29 455.8

Walnut 0.67 41.6

Water 1.00 62.5

Zinc (cast) 6.9 431.3

The principle of Archimedes furnishes an easy method
of finding the specific gravity of a solid which is insoluble
in water. The body is weighed in air and then in water.
As a body loses in weight, an amount equal to the weight
of water is displaced, and the loss is the weight of an equal
amount of water. Divide the weight in air by the loss of
weight in water and the result is the specific gravity. If
the solid be lighter than water, a sinker is tied on to sub-
merge it. Explain the mathematics in this case. The
specific gravity or density of a solid may be found if its

60 APPLIED PHYSICS

shape is such that its volume can be measured by getting
its volume in cubic centimeters and dividing the weight
in grams by the volume in cubic centimeters. Why is
this equal to the specific gravity?

The specific gravity of a liquid may be found by filling
a bottle with water and weighing it, then with a given
liquid and weighing it again. The weight of the liquid
divided by the weight of the same volume of water gives
the specific gravity.

The hydrometer is a glass tube terminating at its lower
end in a bulb filled with shot or mercury to cause the tube
to float in a vertical position. A floating body displaces a
weight of liquid equal to its own weight. If the hydrom-
eter is placed in water it will sink to some certain point;
this point is marked 1. If it be placed in a lighter liquid
it will have to sink deeper to displace its weight. A scale
is marked on the tube so that when placed in any liquid,
the mark at the surface of the liquid indicates the specific
gravity.

Problems

1. Explain the principle on which the so-called suction pump acts.

2. Explain the action of a siphon.

3. Can a perfect vacuum be produced with an air pump?

4. In what respects is the pressure of the atmosphere similar to
the pressure of a liquid?

5. How high a column of liquid, whose specific gravity is 2, will
the pressure of the atmosphere support?

6. How is the pressure of the atmosphere measured?

7. How is the degree of a vacuum in a vessel measured?

8. An oak timber is 4"X 6" X 12'. What is its weight? If
floating on water, what portion of its volume will be submerged?

9. A barge 12 feet wide and 30 feet long with vertical sides is float-
ing in fresh water. An elephant is led onto the barge, and when all
is still it is found that the barge has settled 2 inches deeper than it
was before. How much does the elephant weigh?

10. An irregular casting weighs, in air, 1047.6 pounds, and in water,

MECHANICS OF FLUIDS 61

922.6 pounds. What is its volume? What is its specific gravity?
What kind of metal is it?

11. Will a piece of solid steel float on water? Will a steel boat
float on water? Will a piece of solid steel float on mercury? Why?

12. A vat in the shape of a cube 3 feet on an edge is filled with
mercury. What is the total pressure on the bottom and the total
pressure on one side?

13. When the barometer stands at 30 inches, what is the pressure
of the atmosphere per square inch, when the barometer is 28.9 inches?

14. In making the casting for the base of a dynamo, the top of
the riser is 24 inches above the base of the casting. When first poured,
what is the pressure per square inch at the action of the casting. If
in the above problem the riser has a height of 12 inches above a given
point of the top of a casting and the specific gravity of sand is 1.8
what pressure per square inch must be applied to the surface of the
sand to keep it from lifting or "blowing"? Work this problem men-
tally, getting only the approximate result by the method used in the
foundry.

CHAPTER IV
STRENGTH OF MATERIALS

ELASTICITY has been denned as the resistance a body
offers to change its shape or volume, or the tendency a
body has to return to its original shape after being dis-
torted. If distorted beyond a certain point a body will
take a permanent " set," that is, fail to return to its first
form. This point is called the elastic limit. A force tending
to produce change of form or volume in a body is a stress.
Any resulting distortion which takes place is a strain.
Within the elastic limit the strain is proportional to the
stress. In designing machines, bridges, buildings, etc., it be-
comes necessary to know the strength of the materials used,
up to the elastic limit, and to make them of such a size and
shape that the greatest stress they will ever be subjected to
will not produce a strain coming anywhere near to the
elastic limit. If a given rod in a bridge must support a
given pull when the bridge is carrying its greatest load, the
rod is usually large enough and of such material that the
stress will not exceed one-fourth or one-fifth of the stress
which would strain it to the elastic limit. This is said to
give a " safety" factor of four or five.

The term " stress" is here used to mean the total force
causing the distortion, not the more specific meaning of
the term, namely, force per unit area. In the same way
the word strain is used to denote the total distortion.

Stresses are classified according to the kind of strain
they produce, as follows: tensile or pulling stress; trans-

STRENGTH OF MATERIALS 63

verse or bending stress; compression or pushing stress;
shearing or cutting stress; tortional or twisting stress. A
wire carrying a load is under tensile stress, a column sup-
porting part of a building is under compression. The
piston rod of an engine is alternately under tension and
compression. The rod used to turn the head of a jack-
screw is under bending stress. A rivet holding together
the plates of a boiler or the crank pin in an engine are
subject to shearing stress. The shaft transmitting power
in a shop is under tortional stress.

The tensile strength of any material is the resistance it
offers to being torn apart. The tensile strength of any
body is proportional to its minimum cross section. To
find the tensile strength of any body it is necessary to know
its tensile strength per square unit area and multiply this
by the area of the smallest cross section of the body. The
tensile strength of such metals as iron depends upon the
treatment they have received. Samples of metals to be
tested are placed in machines capable of pulling the samples
apart and arranged to measure the stress at which the
samples break. This is called the ultimate strength or
the breaking stress, and when divided by the cross section
of the samples gives the breaking stress per unit cross
section. Tables giving the ultimate strength or breaking
stress per square inch for the common materials will be
found in any engineering hand book.

If the load is to be repeatedly applied suddenly the usual
engineering practice is to use a safety factor of about 10.
An example of such loading is the piston rod of a recipro-
cating engine. If the variations in load are to be gradually
applied, 5 is usually considered a safe factor. The ultimate
tensile strength of a few metals in pounds per square inch
is as follows. It must be remembered that great variation
is found in different samples.

APPLIED PHYSICS

Breaking stress in thousand pounds per square inch

Brass cast 15 to 20

Copper 20 to 30

Iron cast 15 to 20

Iron wrought 40 to 50

Steel axle 70 to 90

Steel machine 50 to 75

Steel tool 90 to 150

Steel Vanadium 100 to 200

What force will probably be required to pull apart a
3-inch rod of soft steel? What size machine steel rod will be
required to carry safely a gradually applied load of ten tons?

In the case of chains the form of the links has much to
do with the load the chain will lift before breaking. The
Lufkins Iron and Steel Co. publish tables giving the break-
ing stress for their chains in pounds for each size rod used
in making the links from ft to 3 inches.

The shearing strength of any body is the resistance it
offers to being cut in two. Fig. 46 shows a body subject

FIG. 46. — Single Shear.

FIG. 47. — Double Shear.

to a single shear. Fig. 47 shows a body subject to a double
shear. The ultimate shearing strength is proportional to
the cross section. Under most circumstances the stress
required to shear a body in double shear is twice that
required to shear a body in a single shear. But it has been
found by experiment that iron and steel rivets will give
way under double shear at about 1.8 times their ultimate
strength in single shear.

In case wood is subjected to shear, the force required

STRENGTH OF MATERIALS 65

to cut it will be much less if the stress is applied parallel
to the grain than if it is applied across it.

The average shearing strength of a few materials, in
pounds per square inch cross section, follows. In determin-
ing the cross section needed to carry a given load, or in
finding what safe load a body of a given cross section will
carry, use a safety factor of 10 if the load is to be repeatedly
applied suddenly, or a safety factor of four or five if the
load is to be gradually applied.

Shearing strength in thousand pounds per square inch

Iron cast 16 to 30

Iron wrought 40 to 60

Iron rivets 30 to 50

Oak (parallel to grain) 500 to 800 pounds

Oak (across the grain)0 4 to 6 thousand

Steel 40 to 80

In the forge shop is a machine for cutting off bar iron.
The hand lever has a force arm of 6 feet and a weight arm
of 3 inches. This operates the cutting arm with a force
arm of two feet and a weight arm of 3 inches. What force
must be applied to shear a T% square bar of wrought iron?
If the cutting arm swings on a f-inch bolt of wrought iron
in double shear, how large a bar would it be safe to cut
with the machine?

The crushing strength of materials is the resistance to
a force tending to compress it. If the length of a column
is not greater than five times its diameter or its least
thickness when rectangular, it is called a short column.
For such a column the crushing strength resists compres-
sion only. If the length is greater than five times the
least diameter, we have compression and bending com-
bined.

If the ultimate crushing strength of brick be taken at
6

66 APPLIED PHYSICS

800 pounds per square inch, what load will a brick founda-
tion 8 inches square carry with safety factor of six?

For a long column (one from 5 to 40 times as long as its
least diameter) the compression strength combined with
the bending will depend upon the shape of the cross sec-
tion as well as its size. A constant depending upon the
shape of the cross section must be used with the above
values. Such constants determined by experiment for
solid round and rectangular, hollow round and rectangular,
angle, cross, and T beams will be found in any engineering
hand book.

Transverse strength of materials is the resistance the
material offers to being broken by bending.

If a beam or rod is rigidly supported at one end and free
at the other it is called cantilever. The rod used to turn
the head of a jack-screw would be considered cantilever.

It will be remembered that the force applied is the stress,
while the amount of distortion is the strain. The archi-
tect or the machinist sometimes meets the problem of
transverse strength in a form which requires him to com-
pute what size rod or beam will be required to carry a given
load without the resulting strain exceeding a specified
amount: sometimes he is required to find what safe work-
ing load a beam will support.

It has been found that if a beam is supported at the ends
and loaded in the middle the strain is proportional to the
load and to the cube of the length and inversely propor-
tional to the breadth and to the cube of the depth.

That is S = k -=r-

d?b

As indicated in Fig. 48, w = load, I = length between
supports, d = depth, b = breadth of beam, and k = a
constant which depends upon the material used and must

STRENGTH OF MATERIALS 67

be determined by experiments; s = bend or displace-
ment.

If a beam of a given size is found to bend one-eighth of
an inch with a certain load it will, if everything else re-
mains the same, bend one-

quarter inch under twice the. . — — ^— — ^ - &

load. If the load remains |j< l _ H_l d

the same as the first, while
the breadth be doubled, it

will bend only one-half as ,0 How

much or one-sixteenth inch, may the load be placed? The

while if the depth be doubled ^ *""

it will bend only one-eighth

as much or one sixty-fourth inch. If the length or clear

span be doubled, the bend will be eight times as much.

The value of a constant for a given material is determined
by experiment. If W is given in pounds, deflection or bend
in inches, span in feet, breadth and depth in inches, the
following constants are given in the engineering table by
Troutwine.*

Oak ....................................... 00023

Hickory ................................... 00016

White pine ................................ 00032

Cast-iron .................................. 000027

How much will an oak beam 8X8 inches resting on
supports 6 feet apart bend under a load of 2000 pounds at
its center? In building practice it is considered that a
beam should not bend more than ?V inch per foot of length.

* For other values the reader is referred to Troutwine's Hand-
book for 1908, page 484.

68 APPLIED PHYSICS

Problems

1. Why is the rod of a tension member in a bridge truss "upset"
before the thread is cut?

2. What load will probably be required to break a 1-inch round
rod of wrought-iron?

3. What load will be required to crush a short rod of machine steel
1 inch in diameter? If a groove -J- inch deep is cut around the rod, what
load will be required to crush it?

4. The screw of a jack-screw is f inch in diameter, 8 pitch, square
thread, and made of machine steel.

If the crushing strength of machinery steel is taken as 60,000 pounds
per square inch and its shearing strength is 52,000 pounds per square
inch, what must be the length of the thread on the screw in order that
it may sustain the full crushing load of the steel?

5. What is the maximum load such a screw will sustain?

6. On what diameter do you base the figures for crushing and
shearing strength? Why?

7. If the shearing strength of cast-iron is taken as 16,000 pounds per
square inch, what must be the length of the thread in the base in order
that it 'may sustain the full crushing load of steel?

8. On what diameter do you base the figure? Why?

Note. The shearing area in the above need not be figured on the
incline of the thread.

9. At a radius of 6 inches, how much force must be applied to the
lever in order to raise the full load, supposing that 50% of the power
is lost in friction?

10. What load will such a jack raise if the thread in the cast-iron
base is f inch long?

11. What proportions would you recommend for a jack-screw that
is to raise twenty-five tons? Why?

CHAPTER V
SOUND

IF a person in a boat in the middle of a pond drops a
stone into the water, a series of waves is started which
will spread in circles until it reaches the edge or dies out.
If a series of chips are placed on the water they will be
caused to dance up and down but will not be carried for-
ward. The particles of water, that is, the molecules,
dance up and down in the same way and are not carried
forward. The same thing may be seen in a field of ripen-
ing wheat on a windy day. A wave starts at one side of
the field and moves across to the other side. Any one
head of wheat moves back and forth, yet the wave motion
moves forward. Suppose an elastic ball, capable of expand-
ing and contracting, were fastened in the middle of this
room by elastic strings running out in every direction to
all sides and edges of the room and all stretched. If the
ball were suddenly to expand, an impulse would be sent
out in every direction to the sides of the room. When it
contracted, an impulse in the opposite direction would be
sent out in all directions. This is a wave motion, and
the front of any wave will be the surface of the sphere.
A wave motion or vibration of the frequency (number per
second) which will be received by the ear, is sound. .

For the transmission of sound the student will readily
recognize that three things are necessary, a vibrating body
to start the disturbance, some substance in which the
wave motion may travel, and a receiving instrument
capable of detecting the waves or vibrations.

70 APPLIED PHYSICS

If one end of a rope be held in the hand and given a
sudden jerk side wise, it will be set into vibration. These
vibrations will be at right angles to the length of the rope
and will, for that reason, be called transverse vibrations.
In the case of the rubber bands holding the ball, the vibra-
tions were parallel to the length of the band and hence
would be called longitudinal vibrations. In case of air
vibrating, the air has no tensile strength to hold it together ;
hence there can be no transverse vibration, as one mole-
cule would not pull the next one after it. A vibration in
air is set up when a few molecules are pressed forward
and crowded against the next ones. This compresses the air
at one point, and its elasticity causes the molecules in the
front of the disturbance to leap forward and those in the
rear to rebound. At a given point in the air we would have
molecules crowded together and then separated more than
the average or a condensation or rarefaction, and these
would move forward as the waves in the water did and we
would have a wave motion. The frequency is the number
of vibrations per second, and the wave length is the dis-
tance from a point on one wave to the corresponding point
on the next wave.

As a wave moves forward by the successive crowding
of the molecules, we would expect to find that it took time
for a disturbance to travel a given distance. This is con-
firmed by the experience of every one who has had his eyes
open at all. If you have watched a train at some dis-
tance you have noticed that the escaping steam can be seen
before the sound of the whistle is heard. The flash of a
gun will be seen before the sound of the report is heard.

This is because it takes the sound some time to travel
the distance between the gun and the ear. The velocity
of the sound has been measured by several methods and
it is found to be about. 1087 feet or 331.4 meters per second

SOUND

at 0° C., that is 32° F. It is found that the velocity varies
directly as the square root of the elasticity, and inversely
as the square root of the density of the medium in which
the wave moves. Since oxygen is 16 times as dense as
hydrogen, at the same temperature and pressure the veloc-
ity of sound will be four times as great in hydrogen as in
oxygen. Temperature changes produce changes both in
elasticity and density of air, and therefore in velocity of
sound. A rise in temperature of 1° C. increases the veloc-
ity of sound .6 meter or about 2 feet per second. What
would be the velocity at 20° C.? 2 X 20 = 40 feet increase.

1087 + 40 = 1127 feet velocity.

When

Suppose a bell is vibrating 256 times per second,
it has been vibrating for one
second when the velocity is 1087
feet per second, the first wave
sent out would be 1087 feet
from the bell, and between that
point and the bell the whole
256 waves will be found. If it
were possible to take a snapshot
of the series, we would have
256 waves arranged in order.
The length of one of these
waves will be 1087 -f- 256 or
4.24 feet. A little considera-
tion will make it evident that
if N = frequency, / = wave
length and v = velocity in feet seems to come from a center

npr sproTiH V - NJ beyond the reflecting surface.

Id, V - 1ML Thfi ppho from a wall Qr the

FIG. 49.

When a wave strikes a flat echo in the forest are ex-
surface it is reflected as in Fig. amPles-
49 and appears to come from a new center. This reflected

APPLIED PHYSICS

s — *•= — ;____-- — -

1 VC_==__----

l^a

FIG. 50.

When the air column
is adjusted to one-
fourth the wave length
produced by the fork,
a loud resonance is

heard.

sound is an echo. If the echo of a gunshot is heard in
five seconds when reflected from a cliff, how far away
is the cliff, temperature being 20° C.?

If a tuning fork vibrating with a given frequency be held
above an air column whose length can be changed, as in

Fig. 50, and then the length
can be adjusted so that, while
the fork is vibrating from (a)
to (b), the condensation started
at the fork downward from (a)
has time to travel down to (c)
and back to (6) exactly as the
fork is ready to start back
from (6) to (a), we will have
the reflected condensation and
the condensation of the fork

together, and the sound will be very loud. The movement
of the fork from (a) to (b) is one-half a vibration; if the
condensations are to occur at the same time, the distance
from (a) to (c) and back to (a) must be one-half a wave-
length in air; that is, the length of the air column must be
one-quarter wave-length.

If the length of the air column be increased by one-half
a wave-length in air, the reflected wave will come back
one and one-half-waves behind the fork and will again
strengthen the sound. When a vibration is reinforced in
this way, it is called resonance. The air column is called a
resonating air column. This principle is taken advantage
of in many musical instruments as will be seen when the
student studies them. Perhaps the best example is the
pipe organ.

Exactly the opposite of resonance will happen if two
sounds be produced so that one tends to produce a con-
densation at the same time the other tends to produce a

SOUND

rare faction. Then the two will strike a given particle of
air at the same time and no movement will take place.
One will destroy the effect of the other or interfere with
it; hence interference takes place. This may be illustrated
by slowly revolving the fork arranged before the resonating
tube, as in Fig. 50.

Sound waves, as we have shown, are longitudinal, but
for convenience they may be represented as in Fig. 51.
Let the full line represent one wave series and the dotted
line represent a second one, starting both, as at a, but of
different frequency. Then if they start together or in the
same phase, that is, the same part of the wave at the same

FIG. 51.

time, one will gain on the other and soon we will find them
as at 6, exactly opposite each other, that is, in opposite
phase, so that one tends to produce a rarefaction at the
same time that the other tends to produce condensation.
The result would be mutual destruction or no sound at
all. This is called interference. A little later we will find
them as at d, where one has gained a complete vibration
on the other and both are in the same phase, that is, both
tend to produce condensation at the same time and place.
The result is a condensation which effects the ear very
strongly and the sound seems loud. The combined sound
is first loud and then less so, the loud stages being called
beats.
When a pendulum is vibrating, the distance from its

74 APPLIED PHYSICS

point of rest to one end of its swing is its amplitude. When
a bell or string or other sounding body is vibrating, if its
amplitude is small, it strikes the air with little force and the
amplitude of each particle of air is small; while, if it is set
in motion with a greater amplitude, it strikes the air with
more force and the air is more strongly effected. The
latter sound is louder than the first; loudness depends upon
the amplitude of vibration.

A pendulum has a fixed time of vibrating which is inde-
pendent of the amplitude. The same thing is nearly
true of any vibrating body, such as a bell, a tuning fork, a
plate, or wire.

Most vibrations have a definite frequency. It is well
known that if a vibrating wire is tightened so as to increase
its frequency, the sound will be of a higher pitch. Pitch
depends upon frequency.

If a sound contains a mixture of a lot of vibrations of
different frequency some of which are not periodic, it is
called a noise. Such would result from clapping the hands
or stamping the feet. If the vibration is regular, or periodic,
the sound is a musical tone.

We have noted that the pitch of a tone depends upon the
frequency or number of vibrations per second. The
ratio of the frequencies of two tones is called a musical
interval. If the ratio is 1, the tones are in unison: f,
a fifth; |, a fourth; {, major third; If, a half tone;
2, an octave. Four tones whose frequencies are in the
ratio of 4, 5, 6, 8, are a major cord.

Probably every student is familiar with the diatonic
scale, a series of eight notes known as do, re, mi, fa, sol, la,
si, do. The first one (do) may start with any frequency.
The others have a fixed ratio to its frequency. The
physicist starts with a key note of 256. There are several
musical standards at present. The most common one is the

SOUND 75

international pitch, using a key note, C, of 261 vibrations.
The following table will show how the scale is built up.

The tempered scale, while of great importance in music,
is omitted here, as other things seem to have a stronger
claim on the time of the student in a one-year course of
physics in a secondary school.

SCALE

Number... 12345678
Letter ....C D E F G A B C

Name do re me fa sol la si do

Ratio 1C 9/8C 5/4C 4/3C 3/2C 5/3C 15/8C 2C

1st octave . 256 288 320 3411 334 426f 480 512

2nd octave. 512 576 640 682f 768 853J 960 1024

Interval ... 9/8 10/9 16/15 9/8 10/9 9/8 16/15

We have now discussed loudness and pitch and must
consider one other important characteristic of sound —
quality. If the organ pipe is blown gently, its column of
air will be set vibrating as one unit, that is, in one segment.
The tone which will be the lowest that pipe ever produces,
is called its fundamental tone. If blown a little harder, a
much higher pitch will be given. This is due to the air
column being broken up into segments and caused to
vibrate in parts instead of a whole. By blowing carefully,
the air in the pipe may be set in motion so that it produces
both tones at the same time and both may be readily
detected by the ear. The sound given out when both are
produced is very different from either one alone. It is
said to have different quality. The higher tone is an
over-tone. The quality of a tone depends upon the over-
tones present. Certain over-tones produce, with a funda-
mental, pleasant effect on the ear and give a rich, full
tone, while some are unpleasant and discordant. The
same note C sounded on the organ, the flute, the violin,

76 APPLIED PHYSICS

and the piano are of the same frequency, but the different
over-tones in them give them a very different quality or
timber. Helmholtz analyzed sounds, and then, by strik-
ing tuning-forks, produced all the same over-tones found in
a given note; in this way he could reproduce or imitate
the tones of different instruments so closely that he could
deceive the ear.

The wire as a vibrating body is used in so many musical
instruments that it is well to understand the laws govern-
ing the vibration frequency of stretched wires. It is found
by experiment that if a wire is vibrated, either by a violin
bow or by plucking it with the fingers, it gives out a certain
tone, and if the middle point is held so that each half
vibrates as a half length, the pitch will be the octave of
the first tone, that is, the frequency is doubled. It is
found that if the tension remains constant the vibration
frequency is inversely proportional to the length. If a
wire under a fixed tension sounds middle C (256) when
its length is 60 cm., what length must it be to sound G
(384)? The tension and length remaining constant, the
vibration number varies inversely as the diameter. The
length and diameter being constant, the vibration number
varies directly as the square root of the tension.

An interesting application of sound vibration is found
in the talking machine. There are several on the market,
but all work on the same principle as the first one invented
by Thomas A. Edison. A cylinder or disk of wax is re-
volved while a sharp needle point carried on a thin flexible
steel plate scratches its surface. Any sound collected in
the funnel will set the plate vibrating and the needle will
trace these vibrations in the wax. The cylinder is moved
forward by means of a screw, so that a helix is traced its
entire length. A needle with a blunt point is substituted
in place of the sharp one and the cylinder is turned again.

MOLECULES 77

This time the hills and hollows in the wax will cause the
needle and the steel diaphragm to vibrate exactly as it
did before, and the sound will be reproduced so accurately
that even a dog will recognize his master's voice. It was
said of the Chicago Stock Yards that they saved every
part of the pig but the squeal; now they pickle the squeal
and hand it out at the five-cent theaters.

Problems

1. What is the length of the sound wave in air produced by a tuning
fork vibrating 320 times per second, the temperature being 20°?

2. If a bell be struck by a hammer the sound gradually dies away.
Explain.

3. Why is the pitch of a sound produced by a phonograph raised
by increasing the speed of the cylinder?

4. A siren has 24 holes in the disk and makes 1000 revolutions per
minute. What is the frequency of the tone?

5. A string stretched by a force of 25 pounds sounds the note E.
What tension must it have to sound the C below?

6. What are the three characteristics of sound?

7. What law of strings does the violin player follow with his left
hand?

8. Will the pitch of an organ pipe be raised or lowered by a rise in
temperature? Of a piano?

CHAPTER VI
LIGHT

THE universal law — that every particle of matter in the
universe attracts every other particle in the universe with
a force inversely proportional to the square of the distance
between their centers and directly proportional to the
product of their masses — enables us to compute the force
of gravitation between any two bodies. Beyond this law,
stated in a single sentence, how much does man know about
the force of gravity?

The earth is held to the sun by an enormous force.
What are the invisible bands holding the earth with the
strength of steel and yet perfectly elastic? Is the force
a pull from the front or a push from behind? How long
does it take this force to reach out to the earth and harness
it to the solar system? Has the action of this force a
definite speed or is it instantaneous? The earth attracts
an iron casting with the same force, whether or not air,
wood, or any other known substance is between them. Are
there any substances which would cut off gravity? Up to
the present time we know almost nothing about this most
common force. What little we do know about gravita-
tion was discovered and announced by Sir Isaac Newton.

Newton also spent much time in investigating light.
At the time he lived, about as much was known of it
as is now known about gravitation. Newton asked the
question, " What is light? " " How fast does it move? "
" How does it travel from one point to another? " Al-

LIGHT 79

though Newton made the first observations which finally
led to the discovery of the nature of light, he thought
that it consisted of small white particles, which he called
corpuscles, thrown out by some body, such as the sun,
and flying through space until some of them came in con-
tact with the eye and enabled one to see.

We harness Niagara Falls and develop electric power to
light and turn the wheels of several cities. Coal comes
from plants which lived thousands of years ago. Plants
will grow only in sunlight; this is stored up energy, and,
whether in coal or in water, power comes from the sun.
If on a clear day a surface is held up at right angles to the
sun's rays, it receives about two and one-half horse-power
per square yard. How is all this energy transmitted from
the sun to the earth? It is now known that there are
many wave motions or vibrations transmitted through a
medium called ether. These waves vary, from exceedingly
short ones, so small that if they are visible it would take
a powerful microscope to see them, up to a mile long.
Sound waves are longitudinal while these are transverse.
Sound waves are in the air or some kind of matter, while
these are in ether only. When these ether vibrations are
of such length that they will be detected by the eye they
are called light. Light will pass through a perfect vacuum
while sound will not, showing that they do not and can not
travel through the same media. Light will pass through
glass not as a vibration of the glass but of the ether which
fills the spaces among the molecules of glass.

Until the time of Roemer, only a hundred years before
the colonies signed the Declaration of Independence, the
question of the speed of light was not answered. Roemer
was observing the eclipse of one of the moons of Jupiter.
He determined the time it took the moon to go once around
Jupiter and computed the time of each eclipse for a year.

80 APPLIED PHYSICS

Then he observed that the eclipse fell behind his schedule
and this continued for six months and then began to gain
until it caught up to his computed time in six months.

We might compare this to a fact observed on Lake
Michigan. At one of the lighthouses at a dangerous
point there is a fog whistle which is blown by machinery
once each minute. Suppose a person in a boat at this
point hears the whistle blow at exactly 10 o'clock and then
rows directly out from the shore two miles in a half hour.
Would he hear the whistle at 10:30 o'clock? Why does
he hear it about 10 seconds past 10:30? What does this

FIG. 52.

Roemer found that light from Jupiter took about seventeen
minutes to travel from a to 6. This is about 186,000 miles per
second. The fastest railroad train would require for the same
distance about 350 years if it ran without stop.

10 seconds represent? Now he rows back to shore in
another half hour and hears the whistle at 11 o'clock.
Why did it first lose and then gain on its schedule of blow-
ing each minute?

In Fig. 52 the earth was at (a) when Roemer made his first
computations, and when the earth was at (6), six months
later, the eclipses were about 1000 seconds slow. He
reasoned, therefore, that it took light 1000 seconds longer
to travel from Jupiter to (b) than from Jupiter to (a) as
the distance from the earth to the sun is 93,000,000 miles,
the distance from (a) to (6) is 186,000,000 miles, which

LIGHT 81

gives a velocity of 186,000 miles per second for light. It is
now possible to measure the velocity of light by several
other methods and results agree quite closely with the
above value. It is found that in such substances as glass
the velocity is slower than in space.

This velocity is so great that it is difficult to realize it.
Light travels a distance equal to a little more than seven
times around the world at the equator in one second. If a
race were to take place between a wave of light and the far-
famed 20th Century Limited train, the " Limited" might
have a start of one year of twelve months on a straight
way without a stop, and then the ray of light could catch
the train in a little less than three seconds.

When a piece of iron is placed in the forge and heated,
its molecules soon become so disturbed that they start
vibrations in the ether. When these vibrations are of
high frequency the iron is incandescent and emits light.
This process of sending out waves of ether is radiation and
may be either heat or light waves. The usual source of
light waves is some substance heated to incandescence.
The glowworm and the firefly in some way yet unknown to
man are able to emit light without heat.

When light is traveling out from any source, the wave
front if undisturbed is spherical. A beam of light is the
path from a point of the source to some other point and
consists of a series of small elements of the successive waves.
This line of travel, if the medium is alike all the way, is a
straight line. If it were not, one could not sight a gun and
the surveyor could not run a line with the transit.

Since light travels in straight lines, it is evident that if
light be radiating from a point, and some object is placed
so that it stops part of the rays, the space behind the object
will be without light from the given source.

This space from which light is excluded is called a shadow.
7

APPLIED PHYSICS

If a screen be held up behind the object a cross section of
the shadow will be obtained, which is often incorrectly
called a shadow.

Fig. 53 and 54 show the difference between the shadow
formed when the light is from a point and when it is from

an object with a consider-
able size. Fig. 54 shows
the position of the sun,
earth, and moon, so that
the moon will pass through
the shadow of the earth
and be eclipsed.

The experience of the
race has taught us to be-
lieve that under ordinary
conditions light travels in straight lines.

Note. Attention should be called to the fact that this
statement is only approximately true. If the student
takes an advanced course in physics, he will find that
because of the short wave-length of light, the statement,
that light travels in straight lines in a uniform medium,

FIG. 53.

Shadow when the light is from a
point.

FIG. 54.
Shadow when the light is from a large surface.

is satisfactory for a high school course in physics. Let the
student look through a thin fine cloth toward a bright light,
or let him put a thumb mark on polished brass and look
in it at the reflection of a bright light. The students who
are especially interested might then be referred to Prestons'
"Theory of Light."

LIGHT

When light radiating from a point is received by the
eye, we at once assume that the object from which it comes
is at that point. As a result of this, the eye is often deceived.
If light from an object in front of a plane mirror strikes
the mirror, it is reflected so that the angle of incidence
equals the angle of reflection. Angle of incidence is the
angle between the ray of light striking the mirror and the
line perpendicular to the mirror at the point of incidence.
The angle between the same perpendicular and the re-
flected ray is called the angle of reflection. This causes
the light to appear to be diverging from a point or object
as far back of the mirror as the object is in front, as in
Fig. 55. This may be
proved both mathe-
matically and experi-
mentally. The image
formed in a plane mir-
ror is a virtual image,
as no rays of light actu-
ally converge at the
point where the image

appears to be, but only Looking in a good plane mirror the

eye is deceived. An image appears to
be back of the mirror as far as the object

Image

FIG. 55.

appear to do so. If a

person stands before a js m front

plane mirror, the image

is as far back of the mirror as the object is in front, and

is virtual.

Intensity of illumination is defined as the quantity of
light energy per unit area. Even a child knows that to get
more light on its page the book is brought nearer the source
of light. This may be studied quantitatively as follows:
suppose a light be placed at the center of a hollow sphere,
the energy sent out is distributed over the inner surface
of the sphere; if it is placed at the center of a sphere

APPLIED PHYSICS

.with twice as great a diameter, the same energy is spread
over the surface four times as large, since the surface of
the sphere varies as the square of the diameter.

In Fig. 56, suppose a screen be held at a distance of one
foot from a source of light, and a square, one inch on the
edge, be cut out. If a screen be held up parallel to the first,
and two feet from the source of light, the energy which
was received on the square of card cut out now passes
through the hole and is spread over a surface four times
as large as the opening in the first card. One ounce of
butter will be four times as thick spread on one slice
of bread as it will be if spread over four slices of bread of
the same size. We are now ready to state the law that the

FIG. 56.

At two feet a giyen amount of light covers four times as
much surface as at one foot.

intensity of illumination varies inversely as the square of the
distance from the source of light. Ten feet from a given
lamp the illumination is 1/100 as intense as it would be
one foot from the same lamp. If two sources of light are
to be compared, they are placed so that they shine on oppo-
site sides of a card, and the card so adjusted that the in-
tensity of illumination is the same on both sides. Then we
may state that the intensities of two sources of light are
directly proportional to the squares of the distance at
which they give equal illumination. To measure the
power of any light some unit must be used. The one most

LIGHT 85

commonly used is a sperm candle weighing £ pound and
burning at the rate of 120 grains per hour. This is called
one candle-power, and when we say that a light is 60 candle-
power, we mean that it emits as much light as 60 standard
candles. In making the measurement, a paper screen is
used with a grease spot near its center. If light shines
on only one side of the paper the spot will be dark on the
one side and bright on the other. If the card be equally
illuminated on both sides the spot will almost disappear.
Sometimes two mirrors are used in order to see both sides
at the same time. In measuring a certain light a standard
candle is placed on one side of the screen and the light to
be measured on the other. It is found that when the card
is equally illuminated on both sides, the candle is 15 inches
from the screen and the other light is 60 inches from the
screen. Then to compute the candle-power we have, by
the law of intensity,

1 152 _!_

x ~ 602 °r 16

From which x = 16 candle-power.

The reflection of light in a plane mirror has already been
discussed. Reflection of light from a rough surface fol-
lows the same law, but owing to the large number of small
surfaces, the light is sent out in all directions and is called
diffused light. It is by means of diffused light that we see
objects.

It has been found by experiment and measurement that
the velocity of light is less in -glass, water, diamonds, etc.,
than it is in air, and that it is a little less in air than in a
space free from air. Such substances are called optically
dense. It is supposed that ether pervades these substances
but that the molecules of the substances interfere with the
speed of the ether vibrations. A substance like glass, which

APPLIED PHYSICS

will let them through, is called transparent, while a sub-
stance such as iron, which will stop them, is opaque; and
one which will let part of the rays through but diffuse
them so that the object cannot be seen, such as frosted
glass, is translucent. If a series of wave fronts, as shown
in Fig. 57, not perpendicular to the surface, enters a piece
of glass, one side of a wave front (a) will enter the glass
before the side (c) reaches it, and it will be retarded so

FIG. 57.

When light passes from one medium to another it is bent or refracted
at the surface.

that (c) will run around it, and the direction of the wave
will be changed and its path through the glass is a new
straight line. When the wave reaches the other side of
the. plate and is about to emerge from the glass the side
(6) gets out first, and on account of its greater velocity
runs ahead of (d), so that the direction of the ray of light
is changed again and takes another straight line. If the
two surfaces of the glass are parallel, the change in veloc-
ity and therefore the change in direction of the ray of

LIGHT 87

light is the same at each side and the emergent ray is
parallel to the entrant ray. The angle x between the
ray and the perpendicular is the angle of incidence, the
angle y between the ray and the perpendicular is the angle
of refraction. The change in direction of light rays at
the surface of a substance is refraction.

This refraction leads to many familiar deceptions of the
eye. A stick thrust into clear water appears bent at the
surface. Objects under water seem to be lifted toward
the surface. When in bathing, your feet seem to be nearer
to you than they are. The bottom of the lake seems to
run out level, but when you wade out it becomes deeper.

The veolcity of a light is always the same in a given
substance and the refraction of light depends upon the
velocity, that also may be measured. When light passes
from a vacuum into a substance, an examination of Fig. 57
will show that the angle of incidence is greater than the
angle of refraction ; (x is greater than y) when light passes
from a vacuum into a substance. The sine of the angle of
incidence divided by the sine of the angle of refraction is
the absolute index of refraction. When light passes from
one medium to another, the sine of the angle of inci-
dence divided by the sine of the angle of refraction is the
relative index of refraction. This is usually written

sin i

: — U

sin r

In general, when light passes from a rarer to a denser
medium, it is bent toward the perpendicular. When it
passes from a denser to a rarer medium it is bent from the
perpendicular.

The index of refraction for a few substances is as follows :
Water 1.33, Crown glass 1.52, Flint glass about 1.62,
Diamond 2.47.

APPLIED PHYSICS

In Fig. 58 a ray of light is incident at (o), coming from a
dense medium to a rarer. In that case (r) is larger than (i)
and as the incident ray swings toward (a1) the refracted
ray will move toward the surface and (r) becomes 90°. If
the incident ray x moves farther toward the surface, as at
(a1), the refracted ray cannot follow the law of refraction
any farther and is then all reflected from the surface as

from the plane mirror and is
said to be totally reflected.
The angle of incidence, when
the angle of refraction is 90°,
is the critical angle. When
the critical angle is passed
the ray is totally reflected;
such a reflecting surface is
the best reflector known.
The sparkle and glow of the
diamond is largely due to
the fact that its index of refraction is large, and therefore
light soon passes the critical angle and is totally reflected.
If white light be passed through a glass prism, as in Fig.
59, it is twice refracted in the same direction, and, besides
its deviation from the origi-
nal direction, it is found to
be dispersed, that is, sep-
arated into different colors.
These colors correspond to
light of different wave-
lengths, much as pitch in
sound depend upon differ-
ent wave-lengths. The red,
which is least refracted, is
the longest, about .000081
cm. ; the violet, which is the most refracted, is the shortest

FIG. 58.

FIG. 59.

White light passed through a
prism is twice refracted in the same
direction and is separated (dis-
persed) into the colors of the rain-

LIGHT

or .000033 cm. It is customary to speak of seven colors
in the solar spectrum — red, orange, yellow, green, blue,
indigo, violet. It is now known that these seven may be
made by properly combining red, green, and violet. The
primary colors then are red, green, and violet. Between
the extremes there are thousands of wave-lengths which
cause these colors to shade into each other in an endless
number of shades. The color of light then depends upon
its wave-length, while the color of a body depends upon
the color of light it reflects. If a body reflects only red
and absorbs all other colors it is red. A piece of glass so
colored that it will only transmit blue light is blue. Some
artificial lights are lacking in one or more colors. When
this is the case, objects will not appear to be their cor-
rect colors under these lights. For instance, the mercury
vapor arc has no red in its light. If you will go to the
engine room in the evening and stand under the mercury
vapor arc you will see a peculiar change. The lips are
red and hence reflect only red light; there is no red in
this light and hence the lips reflect no light at all and
appear black.

In Fig. 59 the ray of light is twice bent toward the base
or thicker side of the prism. If two such prisms are placed
base to base and then
ground until each face is
part of the surface of a
sphere, a double convex
lens would be produced,
and rays striking the sur-
face would be twice bent
toward the center and
brought to a point. If
parallel rays strike the
lens, as in Fig. 60, the point F, at which they focus, is the

FIG. 60.

Parallel rays of light brought to a
point (focus) F, by means of a con-
vex lens. The burning glass is an
example.

90 APPLIED PHYSICS

principal focus; 0 is the optical center; OF is the axis and
OF is the focal length (/.)

In the back of the eye there is a layer of rods and cones
each forming an end of a fiber of the optic nerve. It is
supposed that these are of three kinds, one set responding
to red light, one to green and one to violet light. If all
are stimulated at once the effect is that of white light. If
a proper mixture of the red ones and the violet ones is stim-
ulated, the sensation given to the brain is that of a yellow
light. The most common form of color-blindness is called
red-blind. It is probably because the red rods and cones
are 'either defective or inactive. They cannot distinguish
red from the other colors.

A beautiful effect produced by separating white light
into its colors is seen in the rainbow, when the sun is
shining low in the heavens on one side and rain is falling
on the opposite side; the light entering the drops of water
is reflected to the eye from the back side of the sphere,
and is refracted at the surface so that the colors are sepa-
rated. Standing at the brink of Niagara one may often
see the complete circle in the mist.

When light is twice refracted in the same direction
through a prism or a lens, the light is bent from a straight
line and also separated into colors. A
convex lens will focus the light from an
object, but the colors will focus at differ-
ent points and the image will not be
FIG. 61. sharp. When the red is in the focus

T , , every object will be surrounded by a

Lens made of ^ J

two kinds of glass, band of rainbow colors. This is called
tojocus all colors chromatic aberration and would be unde-
sirable in a camera. Photographs of
most of our neighbors would not look natural if each had
his head surrounded by a halo. It is found that crown

LIGHT 91

and flint glass, having the same dispersive power, do not
have the same refractive power. A lens built up of two
kinds of glass in the proper proportions will focus all colors
alike and is called achromatic (without color). A section
of such a lens is shown in Fig. 61.

APPLICATION OF LENSES TO OPTICAL INSTRUMENTS

The eye (Fig. 62) is a small camera. A ball about one
inch in diameter has an opening in front at which the crys-

Colored
Diaphram

Cornea

FIG. 62.
Section of the human eye.

talline lens is placed, and a sensitive coat composed of nerve
endings at the back, upon which the real image is formed.
An object in front of the eye reflects light, which enters
through the pupil of the eye and is focused in a real, in-
verted image on the retina by the crystalline lens. The
distance from the front to the back of the eye cannot be
changed, so when objects are at different distances the
accommodation is made by changing the curvature of the
lens by means of the muscle surrounding it. When the
eyeball becomes too long, so that the image is formed before
reaching the retina, only near objects can be seen dis-

APPLIED PHYSICS

tinctly, and distant objects are blurred. Such an eye is
near-sighted (myopic) . The defect is corrected by concave
glasses.

In the laboratory five possible positions were found for
the convex lens.

1. When the object is beyond 2/, the image is real,
inverted, smaller. This is the position used in the camera
for taking all ordinary pictures. See Fig. 63.

FIG. 63.

2. When the object is between / and 2/ the image is
beyond 2/, real, inverted, and larger than the object. This
is the position used in the projection lantern. The slide
is placed in the lantern at a distance a little greater than
If, the image being formed on the screen enlarged and
inverted, as in Fig. 64.

FIG. 64. — Projection lantern or moving-picture machine.

In. front of a powerful light a lens, as in setting 4, throws almost
parallel rays through the slide or film. A convex lens in position 2 is
then used to form a large image upon the screen. If sixteen or more
per second are thrown on the screen the impression of one upon the eye
lasts until the next is presented and the result appears to be a continu-
ous moving picture.

LIGHT

3. When the object is at 2/ the image. is at 2/, inverted
and real. This is the position used in taking a life-sized
picture with the camera.

4. When the object is at /, the rays diverging from it
upon the lens leave the lens in a parallel beam of light.
This is used in the dark lantern to throw a strong beam of

FIG. 65. — Compound Microscope.

A mirror reflects light upward through the semi-transparent object
Oi. A convex lens converges the rays of light toward Oz, but another
convex lens in the eyepiece converges them to a real image 03. A
convex lens is used as a simple microscope to cause the rays of light
coming from this image to appear to come from the targe virtual
image 04.

APPLIED PHYSICS

light to a considerable distance by placing the light at /.
The same setting is used in the condensing lens of the pro-
jection lantern to throw a strong light upon the slide.

5. When the object is between / and the lens no real
image is formed, but by looking through the lens a virtual,
enlarged image is seen. This is used in the simple micro-
scope and in the reading glass, or the eyepiece in a tele-
scope, as lens 6, Fig. 66.

FIG. 66. — Telescope.

The telescope uses a convex lens for the object glass and forms a
real inverted image, just as the camera does. This is sometimes
reinverted by a second convex lens and then seen through a simple
microscope.

The compound microscope is composed of two parts:
a convex lens, set as in a projection lantern, forms an en-
larged real image in the barrel of the microscope. The
eyepiece is a simple microscope used to enlarge this image
again.

FIG. 67. — Opera Glass.

In the opera glass a convex lens deflects the rays of light toward
an image (6). A concave lens is interposed so that the rays do not
focus but a'ppear to the eye to come from point (&')• The result is
to bring the object apparently near without inverting it.

LIGHT

FIG. 68. FIG. 69.

Optical disk, showing reflection of light in mirrors.

When light is reflected by a plane mirror the angle of
incidence is equal to the angle of reflection and right and
left are reversed. (Figs. 68 and 69.)

FiG 70. FIG. 71.

Optical disk, showing reflection of light in mirrors.

The concave mirror focuses parallel rays at a point called
the principle focus (Fig. 70). The convex mirror tends to
diverge light reflected from its surface (Fig. 71).

APPLIED PHYSICS

FIG. 72. FIG. 73.

Optical disk, showing effect of refraction of light.

Light passing from air to glass is partly reflected and
partly refracted toward the perpendicular (Fig. 72). Light
passing from glass to air is bent from the perpendicular
(Fig. 73).

FIG. 74. FIG. 75.

Optical disk, showing effect of refraction of light.

Rays of light parallel to the principle axis of a convex
lens meet at the principle focus (Fig. 74). Rays of light
diverging from a distance equal to the focal length upon a
convex lens, leave as parallel rays (Fig. 75).

LIGHT

FIG. 76. FIG. 77.

Optical disk, showing reflection and refraction of light.

The concave lens tends to diverge light passing through
it (Fig. 76). Fig. 77 shows how light passes through the
drop of rain when a rainbow is formed.

FIG. 78. FIG. 79.

Optical disk, showing reflection and refraction of light.

The total reflection or right angle prism is often used in
optical instruments. The light strikes at greater than the
critical angle (Fig. 78).

A semi-circular tank of glass may be used to show the
refraction of light at the surface of a liquid.
8

CHAPTER VII
HEAT

ALL scientists agree that heat is a form of energy. It is
supposed to be motion of the molecules composing mat-
ter. The molecules according to the general accepted
theory are not in a state of rest but are moving and vibrat-
ing back and forth, some slowly, some rapidly. If the
motion is slow the body feels cold, if the motion is rapid
the body feels warm. Due to its inertia any body in mo-
tion possesses energy, hence it is considered that heat is
a form of kinetic energy. Heat may be readily transformed
into vibration of ether, like light vibrations, except that
the waves are longer, when it behaves, in most respects,
exactly as light waves do. It is in this form that heat
travels from the sun to the earth. Radiant heat may be
changed back to molecular vibrations when it becomes
kinetic energy.

The term temperature is used to indicate that a body is
hot or cold. It indicates whether the molecules of the
body have a high speed or a low speed. A hot body has a
high temperature while a cold body has a low temperature.
When a body receives heat from any source, its temperature
rises; when it loses heat its temperature falls. It is a
common mistake to suppose that temperature is a measure
of the quantity of heat a body possesses.

A teapot full of water may have the same temperature
as the water in Lake Erie, yet the quantity of heat in Lake
Erie is much greater than the quantity of heat in the tea-

HEAT

Boiling 212C
Point-H2O

_1QO

pot full of water. If the teapot is heated to the boiling
temperature, its quantity of heat is increased, but the
total quantity of heat energy it possesses is much less than
the quantity of heat energy possessed by the lake at a
lower temperature.

The method of measuring temperature and of measuring
the quantity of heat present in a body are very different.
For measuring temperature the ther-
mometer is generally used. A long,
thin, glass tube with a bulb at one
end is partly filled with mercury.
The space above the mercury must
contain no air. If the mercury is
heated it expands in proportion to
the change in temperature. In the
Fahrenheit scale, the one generally
used in this country, the point where
the mercury stands when the bulb is
surrounded by melting ice is marked
32°. The point where the mercury
stands when placed in steam over boil-
ing water under the pressure of air
at sea-level is marked 212°. The space
between them is then divided into 180
equal parts. The centigrade scale has
the same two fixed points marked 0°
and 100° respectively and the space
between divided into 100 equal
spaces. If these two scales be
placed side by side, as in Fig. 80, it
is evident that 0° C. is the same as
32° F. and that 100* C. is the
same as 212° F., also that 180° F.
covers the same space as 100° C. Therefore 1° F. is the

FIG. 80.

100 APPLIED PHYSICS

same as f ° C. To change 20° C. to Fahrenheit, 20 X I =
36° F. above the freezing point. 36° + 32° = 78° F. All
changes must be computed above the freezing point. To
change 104° F. to C., 104° - 32° = 72° F. above freezing
point. 72 X I =• 40° C.

Heat cannot be measured in pounds or quarts as sub-
stances are, but must be measured by the effect it pro-
duces. It is found that the quantity of heat required to raise
the temperature of one unit of water one degree is almost
the same at any point between the freezing and boiling
points, that is, it takes almost the same quantity of
heat to raise the temperature of one gram of water from
2° C.to 3° C. that is required to raise the temperature from
75° to 76° C. Therefore the quantity of heat required
to raise one gram of water 1° C. is taken as the metric
unit of heat and is called the calory. This unit is very
small. When a large quantity of heat is to be measured a
larger unit, known as a great calory or kilogram calory, is
used. This is the quantity of heat required to raise the
temperature of one kilogram of water 1° C. It is equal to
1000 gram calories and is approximately equal to 4 B.T.U.'s.
In the English system the quantity of heat required to
raise the temperature of one pound of water 1° F. is
taken as the unit and is called one British Thermal Unit.
(B.T.U.)

Suppose we take a vessel partly filled with water at the
freezing temperature. If the vessel be placed on the stove,
and heat applied, the millions of molecules at first moving
slowly will begin to move faster as the heat is transferred
to them. Their kinetic energy increases and the tem-
perature rises. After reaching a certain temperature
the molecules, in addition to their rapid movement, also
move farther apart and their paths are longer between
bumps. As the molecules move farther apart, the space

HEAT 101

occupied by the water becomes larger and the body
expands.

If we take a block of ice at a temperature of — 10° C.
and apply heat while a thermometer is in contact with it, we
will find that the temperature rises until the thermometer
stands at 0° C. and will then become stationary. ' As soon
as this temperature is reached, the ice begins to melt and
the heat applied instead of raising the temperature is all
used up to produce the change of state from solid to liquid.
The temperature of the liquid will remain at 0° until the
ice is all melted. If more heat is now applied to the water
its temperature will gradually rise, until, if it is in an open
vessel at sea level, its temperature reaches 100° C. No
matter how much heat is applied to the water the reading
of the thermometer will remain stationary at 100° C. and
cannot be made to rise higher. The molecules have been
set into such rapid motion that the attractive forces can
no longer hold them and they tend to separate. The
liquid changes to a gas, that is, steam, and the heat is
being used to produce this change.

The heat that is used in changing a solid to a liquid or a
liquid to a gas is called latent heat. The portion of heat
that produces change in temperature may be detected by
the sense of feeling and is therefore called sensible heat.
Changes in volume have also been taking place in the
water. While the ice is being heated from -10° to 0° the
ice expands slowly. At the point of melting, the water
at 0° occupies about f the volume of the ice at 0°. The
water contracts until it reaches 4° C., after which it expands
almost uniformly until it reaches 100°. Nearly all sub-
stances expand as heat is applied to them.

We have noted the following effects produced by heat :

1. It increases the rate of motion of the molecules as
indicated by the rise of temperature.

102 APPLIED PHYSICS

2. It increases the length of the paths and the distance
between the molecules, causing the body to expand and
occupy more space.

3. It overcomes the force of cohesion, changes the state
of a matter from a solid to a liquid and from a liquid to a gas.

The heat used in changing a solid to a liquid is called
the latent heat of fusion. It has been found by experi-
ment that to change one gram of ice at 0° C. to water at
the same temperature, requires 80 calories. Hence we
say that latent heat of fusion of ice is 80. Expressed in
the English system the latent heat is 144 B.T.U., which
means that 144 B.T.U. are required to change one pound of
ice to water without changing its temperature.

The latent heat of steam is the heat required to change
water to steam without changing its temperature. In the
metric system this is 537, that is, to change one gram of
water to steam at atmospheric pressure requires 537
calories. To change one pound of water to steam at
212° F. takes 966 B.T.U. ; in other words, to change one
pound of boiling water to steam at 212° F. requires 966
times as much heat as is needed to heat one pound of
water from 62° to 63° F.

You perhaps have never considered the process of freez-
ing as a heat producing process, but it is. When one pound
of Lake Erie water freezes, the 144 B.T.U. it contained as
latent heat are given out to the air and help to keep the
temperature of Cleveland mild in winter. This same pound
of ice placed in your refrigerator must take in 144 B.T.U.
in order to melt, and takes it from the surrounding sub-
stances and cools the meat and butter. The same ice
may be packed around a can containing cream. Salt
mixed with the ice will cause it to melt and it must have
its latent heat from somewhere ; so it takes it from the cream
and you have ice cream for dinner.

HEAT 103

The calory has been defined as the quantity of heat
required to warm 1 gram of water 1° C. If we warm one
gram of brass 1° C., it will not require as much heat.
Suppose we take two vessels exactly alike, each containing
the same amount of water at 20° C., and in one of them
place a brass ball weighing 526.3 grams and at a temper-
ature of 100° C.; we find that it warms the water to 60° C.
If then we pour boiling water at 100° C. into the other,
taking care to add only enough to warm the water to the
same temperature, 60°, we will then find that we have added
only 50 grams of water. As each vessel was alike and
contained the same amount of water and was warmed from
20° to 60°, each must have received the same amount of
heat. The brass and the hot water are each cooled the
same amount, from 100° to 60°. It took 526.3 grams of
brass to furnish the same amount of heat as given out by
50 grams of water, .095 as much water as brass. Hence
the same weight of brass gives out only .095 as much heat
as water when cooled through the same number of degrees.
The specific heat of a body is the ratio between the amount
of heat required to warm the body through 1° and the heat
required to warm an equal weight of water 1°. When we
say that the. specific heat of iron is .1138 we mean that to
warm any weight of iron 1° requires only .1138 as much
heat as would be required to warm the same weight
of water 1°. The amount of heat to warm 1 gram of
water 1° C. is one calory and .1138 of that would be .1138
of a calory, hence the specific heat of a substance is often
defined as the number of calories required to heat one
gram of a substance 1°C. Both definitions are the same.
The specific heat of a few substances is given below:

Aluminum 22

Brass 094

Copper 095

104 APPLIED PHYSICS

Iron 1138

Mercury 038

Lead 031

Ice , 5

Air (at constant pressure) 2375

Hydrogen (at constant pressure) 3.4

Steam (at constant pressure) 48

What difference would it make in the rate of warming
up in the spring and cooling in the fall if Lake Erie were
iron instead of water? Which is the best foot-warmer for
a long cold ride — soap stone, hot water bottle, or a flat
iron? Why?

When heat is applied to a metal, one of the effects is to
cause molecules to vibrate faster and increase the length
of their paths crowding the other molecules back and making
the total space occupied by the body larger. The rate of
expansion is not the same for different metals. The frac-
tion of its length which a body expands while its temperature
is raised 1°, or the expansion of unit length for one degree
change in temperature is the coefficient of linear expansion.

The following coefficients are given per degree Centi-
grade. Since the Fahrenheit degree is I of the Centigrade
degree these may be changed to the Fahrenheit by multi-
plying by f.

Aluminum 0000222

Brass 0000187

Glass 0000083

Iron 0000112

Platinum 0000088

Steel : 0000013 (tempered)

Steel 0000011 (untempered)

The Hippodrome has put in a steam pipe 400 feet long,
and to allow for expansion " expansion collars" are put in.
Each of these allows the end of the next pipe to slip with-
in it, giving 1 J inches free play. How many of these must

HEAT 105

be put in to allow for a range in temperature from 32° F.
to 232° F?

Examine the balance wheel of a watch, the pendulum -of a
clock, and the thermostat, to see how the different rates
of expansion for two metals are applied.

Why should the pattern to be used in the foundry be
made larger than the finished casting
is to be? The melting point for brass
is 1020° C. and for iron from 1500° C.
to 1600° C. Figure out a general rule
to give to the pattern maker, who may
be working in your shop some day,
regarding the allowance to be made
for shrinking in casting each of the
above metals.

Why do castings often " warp " in
cooling? Why is platinum the only
metal which can be successfully sealed
in glass?

If a bar of iron is heated it will ex-
pand in width and thickness as well
as in length. As these expansions are
all small the corners are neglected
and the coefficient of the cubical ex-
pansion is taken as three times the
linear expansion.

If a gas is confined in a cylinder with a movable piston
fitted so that it moves easily but yet is air tight, any ex-
pansion of the gas will force the piston back against the
pressure of the air and we will have the gas expand-
ing under constant pressure. We will find that the
expansion of all gases follows the same law and that
each expands ^ of its volume at 0° C., if the pressure
remains constant, or that the pressure changes ??? of

106

APPLIED PHYSICS

its pressure at 0° C. if the volume is kept constant. If a
gas is cooled while the pressure is constant, it will con-
tract STS of its volume at 0° C. for every degree change
in temperature. If it were to keep this up while it was
cooled from 0° C. to -273° C. its volume would decrease
to 0. For this reason -273° is taken as absolute 0. The
law then may be stated that at constant pressure the volume
of a gas is proportional to its absolute temperature, or at
constant volume the pressure of a gas is proportional to its
absolute temperature. This is known as the Law of Charles
and holds for all gases except when they are near their
point of liquefaction.

Fig. 81 shows a simple form of apparatus for demonstrat-
ing the Law of Charles. Tube a contains dry air, and by

adjusting b so that the
mercury is at the same
level in a and b the
confined gas is at a
pressure of one atmos-
phere. By rilling the
jacket first with ice, then with cold water, hot water,
and last with steam, the volume or length of a} which is
proportional to volume, may be taken at , temperatures
from 0° to 100° C. The results plotted as Fig. 82 give
a line crossing zero volume at a point very near -273 C.

-273 °C.

-200'

-100°

FIG. 82.

Temp.C.

Problems

1. How many 1^-inch expansion collars must be put into a 700-foot
steam pipe to allow for a range of temperature of 200° F.?

2. The pattern maker allows i inch per foot for shrinkage in making
a pattern for cast-iron if the melting point of iron is 2075° F. how much
of this is for contraction and how much for machining?

3. If the melting temperature of brass is 1692° F. how much must
be allowed for shrinkage in making patterns for brass casting? How
much for aluminum castings, melting temperature being 1157° F.

HEAT 107

4. Why is platinum always used where a metal must be sealed into
glass to make an air-tight joint?

5. How much steam will be required at 212° F to melt a ton of ice
at 32° F.?

If one pound of coal yields 11,000 B. T. U., and one half is lost in radia-
tion, how many pounds will be required to melt 100 pounds of ice at
32° F. and change it to steam at 212° F.?

6. If 1000 pounds of water enter the boiler of a locomotive and
leave the engine as exhaust steam, how many B.T.U's do they carry
away as latent heat?

CHAPTER VIII
ENGINES

WE have noted that heat is a form of kinetic energy.
Every boy has observed that, when a hammer strikes a
piece of iron, mechanical energy is changed to heat. Elec-
trical energy is changed to heat in the electric lamp, and
stored chemical energy is changed to heat in the firebox
when coal or any fuel is burned. The question arises, can
the process be reversed — can heat energy be changed
into mechanical energy for doing useful work? For answer,
ask yourself what runs the steam-engine, the gas-engine,
or the hot-air engine.

THE STEAM-ENGINE

When a vessel of cold water is placed over a fire the water
at the bottom in contact with the heated portion of metal
is warmed. This causes the water to expand and there-
fore becomes lighter. It is then pushed up by the heavier
cold water which flows in to take its place. This circu-
lation, known as convection currents, is kept up until the
whole mass of water is heated. We have already learned
that heat makes the molecules of water move about or
bound to and fro faster. Some of them will move so fast
that they will jump through the surface into the air. This
is evaporation and takes place more rapidly as the tempera-
ture rises. The pressure of the air normally is 14.7 pounds.
When the particles of water get to moving so rapidly that
their pressure trying to jump out is equal to the pressure
of air on the surface, they will escape rapidly and force the

108

ENGINES 109

air back. The temperature at which they do this is the
boiling point. It is evident that as the pressure is increased
the speed with which the molecules move before they will
jump out must be greater, that is the temperature must be
higher. The boiling point of a liquid is the temperature at
which its vapor tension is equal to the applied pressure.
The boiling point of water at normal pressure is 212° F.
The boiling point in the boiler of a Lake Shore locomotive
running at 200 pounds is about 387 F. While at a height
of three and one-half miles above sea level, where the pres-
sure of the the air is 7f rpounds per square inch, the boiling
point is only 180° F.

One cubic foot of water weighs 62J pounds, but one pound
of water changed to steam at the pressure of the atmosphere
occupies 26.4 cubic ft., that is, the 62| pounds would
occupy 1650 cubic ft., at a pressure of 14.7 pounds per
square inch. If water in a closed boiler is heated the space
will soon be filled with steam and the pressure will rise.
The pressure rises until a balance occurs, then the par-
ticles of steam condensing to water are equal to the par-
ticles of water jumping off. The space contains all the
steam it will hold at the given temperature. Any increase
of pressure will cause some of it to condense and any
decrease in temperature will cause some of the steam to
condense. This is called saturated steam. Boiler steam in
contact with water is always saturated steam. If the same
steam is conducted to a chamber separated from the water
and heated above the boiling point corresponding to its
pressure, it is called superheated steam.

We are now ready to study the steam-engine. Examine
the engine in the laboratory and draw a section of the
working parts. Compare with Fig. 83.

Live steam from the boiler is admitted to the steam
chest through pipe a. In the position shown the steam

110

APPLIED PHYSICS

passes through port b to the left or head end of the piston
and pushes it along. The exhaust steam in the right or
crank end of the cylinder is driven out through the port e

FIG. 83. — Slide valve steam-engine.

to the exhaust pipe c. As the stroke progresses the valve
is moved by the eccentric so that it closes the port 6, not
admitting any more steam to the left end of the cylinder.

FIG. 84. — Section model of a slide valve steam-engine.

The continued motion of the valve then releases the steam
in the head end of the cylinder to the exhaust, and admission
at the other end takes place and live steam rushes in to

ENGINES 111

push the piston back. Opening the port for live steam is
called ''admission"; closing the live steam port is "cut
off." Opening the exhaust port is " release " ; closing
the exhaust port is " exhaust closure." The valves are
usually set so that the admission takes place a fraction of
a second before the piston reaches the end of its stroke in
order that the space may. be filled with live steam when
the return stroke begins: this is called " lead."

The horse-power of a steam-engine is rated by two
methods. One is called the delivered or brake horse-
power and is measured by the Prony brake as already
described. This measures the actual delivered horse-power.
The other method is by means of the indicator card. If
the pressure on the piston were the same as boiler pressure
throughout the length of the stroke, the horse-power would
evidently be the total pressure tending to move the piston
multiplied by the distance the piston moves per minute,
divided by 33,000. The total pressure tending to move the
piston is the difference between the pressure per square
inch on the live side and the back pressure per square inch
on the exhaust side multiplied by the piston area in square
inches. In practice however it is not advisable to admit
live steam from the boiler throughout the stroke. It is
far more economical to admit steam at boiler pressure for
part of the stroke (from one third to one-half of the length
of the stroke) and then have the valve "cut off," that is,
close the entry port. The inclosed steam then continues
to push the piston along for the rest of the stroke, expanding
as it does so. During this part of the stroke no more
energy is added to the steam cylinder. The steam is
expanding and doing work at the expense of its own tem-
perature. Energy which would be carried away as heat
is saved for useful work. It is advisable to have the steam
enter the cylinder as hot as possible and leave it as cool as

112

APPLIED PHYSICS

PencC

possible. The compound engine allows this expansion and
consequent drop in temperature to take place twice or
even four times in the quadruple expansion engine. While
this expansion is taking place the pressure drops and the
average pressure during the stroke must be used in com-
puting the horse-power.

The indicator is a device for finding this mean effective
pressure and at ttie same time showing the setting of the
valves of the engine.

Fig. 85 shows part of the mechanism of the indicator. A
tap is made in each end of the cylinder. This tap at one

end of the cylinder is
then connected to pipe
at the bottom of the
indicator. The steam
forces the piston (6)
whose area is \ inch up
against a spring and in
doing so carries pencil

(d) up a distance
proportional to the
amount of pressure.
If, while the cylinder

(e) stands still steam
is alternately ad-
mitted and withdrawn from the indicator, the pencil traces
the straight vertical line. The cylinder (e) is carried on a
pivot and connected with a string to the piston rod of the
engine, so that it revolves back and forth as the piston rod
makes its stroke. If no steam is admitted to the indicator
while the cylinder revolves, the pencil will trace the hori-
zontal line (y) . If both these take place at the same time
while the engine is working, the pencil will trace a curve
representing the two variables, the one on the vertical or

FIG. 85. — Steam indicator.

ENGINES 113

(x) axis being proportional to the pressure pushing the
piston, and the one on the horizontal axis being propor-
tional to the movement of the piston on its stroke or in
proportion to the volume behind the piston.

Such a card for the head end of a Corliss engine is shown
in Fig. 86. A is point of admission taking place just as the
piston is at the end of its
stroke and the line rises
along the vertical line to
B. B C is the steam line,
steam at boiler pressure
being admitted. C is the
point of " cut off ." From
C to D the steam is work- ,-,

r IG. oO.

ing expansively. CD is

the expansion line, and during this time pressure and temp-
erature are falling. D is the release, EF is the back press-
ure line during exhaust, F is exhaust closure. This takes
place before the piston reaches the end of its stroke in order
to confine enough of the exhaust steam to cushion the recip-
rocating parts of the engine which may weigh several hun-
dred pounds and would soon pound the engine to pieces
if their rapid motion were not stopped against this elastic
cushion of steam. The line FA is the compression line
showing the rise of pressure as the parts are cushioned.

To find the horse-power: The springs commonly used
for the indicator are so made that the figure is drawn to
scale 1 inch to 80 pounds or 1 to 100 or 1 to 120, etc. If
the average altitude of the figure between the steam and
expansion line for one side of the stroke and the back pres-
sure line on the other side of the stroke is used and multi-
plied by the scale of the spring, the result is the mean

effective pressure. Then we have H =

114

APPLIED PHYSICS

Where H = Horse-power

L = Length of stroke in feet
P = Mean effective pressure
A = Area of piston in square inches
N = Number of times steam pressure is applied to
the piston per minute or in the steam-engine twice the
R.P.M. The result is called the indicated horse-power and
is always somewhat larger than the brake horse-power.

FIG. 87.

Steam indicator, piston, extra springs, reducing wheel, and a card
or diagram taken on a 400-horse-power Corliss engine.

The efficiency of the best reciprocating engines is a
little below 15% and of the best locomotive about 10%.
That is, of all the stored energy in the form of fuel put in,
only about 10% is delivered as useful work. About 70%
is lost in the form of heat losses which cannot be recovered.

In an indicator card the average height is .812 inches;
spring 40 was used; LOO R.P.M.; stroke 30 inches; piston
diameter 15 inches. What is the indicated horse-power?

ENGINES 115

2 X 40 = 80 scale of spring used
80 X .812 = 64.96 Ibs. Mean effective pressure
100 X 2 = 200 times steam is admitted
30 -f- 12 = 2| ft. stroke
(15)2 X .7854 = 176.7 square inches area of piston

PLAN 64.96 X 2j X 176.7 X 200

In an indicator card the average height is .642 inch;
spring 30; 200 r.p.m.; piston diameter 9 inches; stroke
15 inches. What is the indicated horse-power?

1. Divide Fig. 49 into ten spaces, measure the altitude of each, and
get the average height. If it was taken with spring 30 and the engine
was running 150 R.P.M., diameter of piston 10 inches, length of stroke
30 inches, what is the indicated horse -power?

2. Average height of indicator card is .45 inch, spring 60 was used,
diameter of piston 18 inches, stroke 30 inches, 300 R.P.M. What is
the horse-power?

STEAM TURBINES

There are at present on the market three types of turbine
engines, DeLaval, Westinghouse-Parsons, and the Curtis
turbine. As the Curtis turbine in a measure combines
the other two we will describe that one only. In the Curtis
turbine the parts shown in Fig. 88 are arranged in the
circumference of a circle. The moving blades (6.6.) are
carried on the circumference of a wheel. An observer at
the center looking out would have the view shown here.
The steam expanding through nozzles at a. a. comes with
great velocity to the moving blades 6. These are driven
forward, not by steam pressure but by the kinetic energy
of its impact. The second row of blades (c) is held sta-
tionary to change the direction of the steam so that it will
strike the next row of moving blades the same as it did
the first. The steam is carried through a large number of

116

APPLIED PHYSICS

these rows of blades. As the steam expands, the circum-
ference of successive rows is increased by placing them on

Moving
.Blades

Stationary
Blades

Moving
Blades

FIG. 88.

circles of larger diameter. The turbine is not reversible
and works at its best efficiency when running at high

speed for a long continued
run. They occupy much
less space than reciprocat-
ing engines of the same
horse-power. These facts
combine to make them
valuable for ocean steam-
ship service.

• 'iC^pM The turbine works at its

best efficiency when the
steam is expanded and
moving at high speed. On
FIG. 89. — De Laval turbine, with a th th r han(j the recipro-
single set of blades. . ...

eating engine works at its

highest efficiency when the steam is at high pressure. The

ENGINES 117

efficiency of the best reciprocating compound engines is
almost 14% and that of the best turbines about 15%.

The Subway power plant of New York has recently
installed turbines between the condensing chamber and
the low-pressure cylinder of the compound reciprocating
engines and found the combined efficiency 22.3%. They
have almost doubled the power output of their plant with-
out increasing the floor space or the amount of coal used.
This is the greatest advance in steam engineering in recent
years. .

The horse-power of a turbine cannot be taken by indi-
cator card, hence the rated horse-power is the brake or
delivered horse-power.

THE GAS-ENGINE

The gas-engine is a heat engine. In the " four-cycle "
engine shown in Fig. 90, the piston on its down stroke
draws in a mixture of explosive gas, either gas, gasoline
vapor, alcohol vapor, or coal oil vapor, mixed with the proper
proportion of air. On the return this gas is compressed,
and then the spark at the spark plug (a) explodes the
mixture. The heat generated causes the gases to expand
and push the piston down. On the next return stroke the
exhaust valve is mechanically opened and the gases are
driven out ready for the next- cycle. It will be seen that
there are two revolutions or four strokes to each explosion.
In the two-cycle engine there is an explosion for each revo-
lution or two strokes.

Fig .91 is a section of a three-port valveless two-cycle
engine. When the piston is near the top of its stroke the
explosive mixture is drawn in at a, passing to the air-tight
crank case. This is somewhat compressed on the down
stroke. The exhaust port is at c, and opens slightly
before the port d is uncovered. When the piston is at

118

APPLIED PHYSICS

the lower end of its stroke the burned out gases pass out
at c and the mixture from the crank case passes in at d.
A baffle plate or deflector prevents its blowing across and

FIG. 91. — Three-port,
valveless, two-cycle gas-
engine.

FIG. 90. — Four-cycle gas-engine.

out at the exhaust. The return stroke compresses the
gas ready for the explosion. An explosion takes place at
each revolution or every two cycles.

The explosive mixture is a gas and is a gas after the
explosion. The chemical change does not produce any

ENGINES

119

great change in volume such as would result when a solid
changes to a gas, as in explosion of gunpowder. The tem-

FIQ. 92.

Gas-engine, with carburettor, built by a
high-school boy.

perature however is changed through a wide range and,
since the volume is expanded ^fs of its volume at freezing
point for each degree Centigrade, it expands violently.
This is strictly a heat engine and the hotter it can be run
the more efficiently it will work. The limit to the tem-
perature is set by the temperature at which the moving
parts will work and can be lubricated.

For finding the horse-power of a gas-engine the most
accurate method is the Prony brake. A special form of

120 APPLIED PHYSICS

indicator is also used to find the mean effective pressure
and this is substituted in the formula

= 33,000

The following formulas are commonly used and are
approximately accurate. The Association of Licensed
Automobile Manufacturers use the formula

D2 N D = Diameter of cylinder, in inches
2.5 N = Number of cylinders

This gives the horse-power only at full speed. Find the
horse-power of 4-cylinder engine with 4-inch cylinders.

H.P. = — -—— = 25.6 horse-power
2.5

A formula often used is

SCAN

H.P.

12000

S = stroke in inches
C= number of cylinders
A= piston area
N= number R.P.M.

HOT-AIR ENGINE

The hot-air engine has no valves nor ports. A confined
quantity of gas is alternately heated and cooled. The re-
sulting expansion and contraction cause changes in pres-
sure which run the engine. It does not work very efficiently,
but, because of its simplicity and slight care needed, is
much used to run farm pumps. In Fig. 93, heat is ap-
plied at c, a is the working piston fitting tightly in the
cylinder, b is the displacer fitting loosely. The air becomes

ENGINES

121

heated and forces a out to position shown in section. The
displacer is moved over to positions forcing the air out to

FIG. 93. — Section of hot-air engine.

end d. Here it is cooled, and its contraction allows the
outside atmospheric pressure to force the piston back to
position /.

FIG. 94.

The hot-air engine of which section is shown in Fig. 93.
are no valves and few parts to keep in order.

There

122 APPLIED PHYSICS

Since heat may be changed to other forms of energy and
other forms of energy may be changed to heat energy, it
must be that a certain amount of heat is equivalent to a
foot-pound of energy. Just before our Civil War, an Eng-
lishman, J. P. Joule, after several years of measurements,
found that one B.T.U. is equal to 778 foot-pounds of energy.
This means that in the metric system, one kilogram calory
of heat is equal to 427 kilogram meters of energy. The
water of Niagara Falls changes its kinetic energy to heat,
and by means of the heat equivalent, it is possible to com-
pute the rise in temperature due to the descent of the water.

If a one-pound weight were allowed to fall freely 778
feet, it would have, at the moment of striking, 778 foot-
pounds of kinetic energy. This changed to heat would
be 1 B.T.U.

A good grade of coal, such as pocahontas, yields, when
burned, about 14,000 B.T.U's per pound. Suppose one
pound of coal (14,000 heat value) be used under a boiler
and the steam be used to run an engine. The 14,000
B.T.U's are equivalent to 14,000 X 778 or 10,892,000 foot-
pounds. If the combination is working at 10% efficiency
this would mean a yield of 1,089,200 foot-pounds of work
or the equivalent of one horse-power for 33 minutes.

How many pounds of such coal would be required to
melt one ton of ice at 32° F. and change it to steam at
212° F. if 25 % of the heat is lost?

If air weighs .08 pound per cubic foot, how much coal
would be required to warm the air of a room 30 X 50 X 15
feet 70° F.?

Heat energy may be carried from one point to another
by three different methods. If one end of an iron rod is
heated in the forge the other end soon becomes too hot
to handle. This method of transmitting heat by one
molecule heating the next one is conduction. A glass rod

ENGINES 123

may be held in the hand while the end a few inches away
is melted. If rods of silver, copper, iron, and brass are
heated at one end, the heat will not travel along them at
equal rates. Most of the metals are good conductors.
Silver and copper are the best, while iron is not so good
and glass is almost a non-conductor and air and water are
very poor conductors of heat. A copper boiler is better
than an iron one for boiling the clothes as it will conduct
the heat better. For the same reason a copper teakettle
is better than an iron one.

When air is heated it expands and is therefore lighter
than cooler air. If the air in one part of the room is heated
it will be forced up by the heavier air crowding in to take
its place. If a lighted match is held over a radiator, rising
currents of air will be found. Near the floor, currents of
air toward the radiator, and near the top of the room
currents of air away from the radiator will be shown. These
are convection currents. The draft of a chimney, the air
rising in a hot air furnace, the trade winds and nearly all
our terrestrial winds are convection currents. The hot
water heater is a good example of heat transmission by
convection currents.

In the last two paragraphs, we found that heat is carried
from one place to another along a continuous solid by con-
duction and from one place to another by convection cur-
rents, as in the hot water heater when water is heated in the
boiler by contact and then carried along by convection cur-
rents to heat radiator by actual contact. We know that
heat is brought to us from the sun, that it travels through
space where there is no matter to carry it either by conduc-
tion or convection. We know that it travels with great
velocity and that it comes through the window without
warming the glass. This is called radiant heat and is sup-
posed to be waves in ether, as light is, with a longer wave

124 APPLIED PHYSICS

length. Radiant heat, as waves of ether, travels on with
the velocity of light until it collides with some surface
which is able to change it to the ordinary form of heat.
If radiant heat from the sun strikes a black rough sub-
stance like iron, it is changed to kinetic heat. This is
called absorption. If the waves strike a polished surface
like a mirror they are reflected and pass out again to
space. A black suit is hotter in summer than a light
colored one because it absorbs a greater quantity of the
radiant heat striking upon it. Explain how a greenhouse
traps the heat from the sun. Explain why the mountain
climber on top of Mt. Shasta must cover every part of his
face or it will be seriously blistered, while the snow never
melts. Why is the upper air so cold while radiant heat
is coming from the sun to the earth? Why does the
radiant heat of the sun fail to reach the earth on a cloudy
day? Why do we get our early frosts only on clear
nights?

We have discussed the change of radiant heat to sensible
heat; is the process ever reversed? A glowing grate,
glowing coals, or a hot iron will send out radiant heat and
in so doing will be cooled. It is found by experiment
that a hot body with a black rough surface will radiate
its heat much more rapidly than a polished surface. A
good radiator is also a good absorber and a poor radiator
is also a poor absorber. A black kettle will heat more
quickly than a polished one and then when set aside with
hot water in it will cool more quickly. A bright polished
teapot will keep the tea hot on the table longer than the
dingy iron one. This is because the surface is a poor
radiator although the silver is a good conductor.

Laying aside art and beauty, the nickel and polish on
your heating stove might better be replaced with black
iron rough surfaces, as they are better radiators. Why does

ENGINES

125

snow under a dirty black cover melt before the clear white
article does?

Freshly fallen snow is a poor conductor of heat because
it has much air confined in the small spaces, and air is a
non-conductor where
it cannot set up con-
vection currents.
Loosely woven wool-
en goods are poor
conductors for the
same reason. In hot
countries closely
woven white goods
are worn as they re-
flect the heat from
without and conduct
the heat from the
body.

Study the following
and be prepared to
report on them in
class. Hot air fur-
naces, steam heating, hot water heat, ice plant, blast fur-
nace, and foundry.

In Fig. 95, transmission of heat by convection currents is
shown as applied to the hot air furnace. The fire on the
grate in the fire-box heats the gases inside the fire-box to
a high temperature. This causes them to expand, and as
cold air is heavier than hot air, a " draught " is caused.
In other words, the greater pressure of the cold air forces
the smoke up the chimney. The air inside the jacket of
the furnace is heated and convection currents are setup
through the hot air pipes to the rooms above.

FIG. 95. — Section of hot air furnace.

CHAPTER IX
MAGNETISM AND ELECTRICITY

EVERY boy knows that steel treated in a certain way
becomes a magnet. If the blade of a knife is stroked by a
permanent magnet, it in turn becomes a magnet and
will then attract pieces of iron and steel. We will find later
that there are other ways of producing the same result.
A kind of iron ore, called lodestone (leading stone), possesses
the same property of holding small particles of iron. It
was early found that magnets, suspended so that they were
free to swing toward any part of the horizon, come to rest
with one end pointing toward the north or nearly north.
This end is called the North Pole. The opposite end is
the South Pole.

If one magnet be free to turn and a second is brought
near it, the north pole of one will attract the south pole
of the other and repel the north pole. Like magnetic
poles repel, and unlike poles attract each other.

If a long bar of hard steel or a knitting needle be mag-
netized, and dipped in filings, a point near each end will
hold a large bunch of filings, while the middle will hold
none. These strongest points are the poles. If a piece
of soft steel be brought near a magnet it becomes a strong
magnet, but loses its magnetism as soon as the magnet is
removed, while hard steel will hold it. If a magnet is
placed on a drawing board and a sheet of paper be placed
over it and fine iron filings sifted on the paper, they will
arrange themselves in lines as shown in the figures below.

126

MAGNETISM AND ELECTRICITY

127

Where the unlike poles are presented the lines will
appear as in Fig. 96. If the like poles are toward each other

fol

FIG. 96.

FIG. 97.

FIG. 98.

the lines run as in Fig. 97, while for a single magnet they
run as in Fig. 98. The space filled with these lines around
a magnet is called the magnetic field.

128

APPLIED PHYSICS

The lines of force shown by iron filings in Fig. 96 run
between a North and a South pole. These lines seem to
act like stretched rubber bands pulling the poles together
but the lines repel each other laterally. When two N-
poles are presented in Fig. 97 this lateral repulsion causes
the poles to repel each other.

The lines are alike at each pole so far as the filings show
them but later study with electrical apparatus will show

FIG. 99.

FIG. 100.

that they have direction; therefore they are assumed to
pass from the N-pole around through space to the S-pole.

Soft iron within the field becomes a magnet by induc-
tion. Note how the lines crowd together in order to pass
through the soft iron rather than through air. The soft
iron is more "permeable" than air.

Pieces of iron or steel brought within the magnetic field
become magnets and are attracted, as in Figs. 99 and 100.
These also show the lines of force to be gathered in more
thickly by soft iron as they find it easier to pass through

MAGNETISM AND ELECTRICITY 129

iron than through air. The electrician says the soft iron
is more permeable than air. Glass, paper, wood, and many
other substances brought within the magnetic field are not
affected by it and apparently produce no effect on the field,
as the lines seem to run through them as well as through
the air. A few substances such as antimony and bismuth
are repelled by a magnet. We will find, as we take up
the study of electricity, a very close relationship between
electricity and magnetism, and the facts about magnets
will constantly be used in the study of electricity.

THEORY

The statements of the last few paragraphs are observed
facts. The statements made in this paragraph are pure
theory used to explain those facts and may be changed
any day. There are now several other theories about
equally as good and you must feel free to accept this theory
or some other, or to reject all of them as you choose. We
feel that the next few years may see some discoveries which
will reveal the true nature of magnetism and electricity.
It is supposed that in a piece of steel, each molecule is a
magnet with a north pole and a south pole. If the mole-
cules are arranged without any order, some one way, some
another, like a mob, the north poles of some are balanced
by the south poles of others and the pieces of steel will
show no magnetism. Let a magnet be brought near and
the molecules will line up like a column of well-drilled
soldiers, and all of the north poles will be in one direction
and all of the south poles in the other direction, and the
whole piece will show at one end a north pole and at the
other a south pole. In the middle the poles will balance
each other, but, if the magnet is broken, each half will
be found to be a magnet. A piece of hard steel will hold
its molecules lined up and hence hold its magnetism, while
10

130 APPLIED PHYSICS

a piece of soft steel will let them rearrange themselves so
that it will not hold its magnetism.

The ether in the space surrounding a magnet is supposed
to be under a strain, and this strain reveals itself in the so-
called lines of force shown by the iron filings near a magnet.
These lines of force are said to begin at the north pole and
pass around to the south pole, then through the magnet
to the place of beginning. They act as stretched rubber
bands which tend to shrink to zero length. They repel each
other laterally and try to get as far apart as they can. How
nicely this explains the attraction of unlike poles and the re-
pulsion between like poles of Figs. 97 and 98. But do not
forget that this is theory and so far has never been proved.

The earth is a great magnet. When iron filings are
placed near a bar magnet each piece of steel arranges itself
with its length in one of the lines of force. .A magnetic
needle free to turn does the same thing in the earth's
field. We say the needle points north. This is not strictly
true. The north magnetic pole and the geographic North
Pole found by Peary are not at the same place. The mag-
netic pole is about 1000 miles south of the North Pole, at
latitude 70° North, longitude 97° West, north of Hudson
Bay. The needle does not always point in the same direc-
tion but slowly changes its direction through a long period
of years and then swings back again. A needle free to
move in a vertical plane will not remain horizontal but
will " dip," that is, its north end will drop down. At the
magnetic pole the needle stands in a vertical line.

ELECTRICITY

At the present time scientists do not know what elec-
tricity is. Electricians know a few things about it and may
know some day what it is. It is closely related to light
on one hand and magnetism on the other, and these things

MAGNETISM AND ELECTRICITY 131

lead us to think that it may be some kind of disturbance
or strain in the ether, or it may be something always ac-
companied by a strain in ether. If this strain is com-
municated to one part of a body made of certain material,
such as copper, the electricity is distributed to all parts of
the surface. Such a substance is called a conductor and
the electric strain while being transmitted is called an
electric current.

We have mapped the magnetic field around a magnet
and have seen how something which we call lines of force
fills the space near a magnet. If a loop of wire or any
conductor of electricity is placed within this field some of
the lines of force will pass through the loop; we might say
they link with the conductor. If by any means the number
of lines of force linking through the loop of the conductor
is changed, an electric current is set up. We may cause
this change in the number of lines of force in several ways,
by revolving the loop of the wire, by moving the loop, or by
moving the magnet. The result is the same in all cases.
That is, if a conducting circuit be placed in a magnetic
field, and by any means whatever the lines of force thread-
ing through it be changed, an electric pressure is caused in
the circuit, and the electric pressure is proportional to the
rate of change of the number of lines of force.

The terms, pressure and current, have much the same
relation to electricity that they have to water pressure
and flow of water. When considering fluids, the pressure
was found to be proportional to the depth. If a long
horizontal pipe be tapped into the bottom of a water-tower
or stand pipe and the opposite end be left open the flow
of water depends upon the pressure and the size of the
pipe, that is, upon the resistance it offers to the current.
The pressure gauge also shows a fall in pressure from the
end at the tower along the pipe to the open end. The rate

132

APPLIED PHYSICS

of flow is the same in all parts of the pipe but the pressure
falls. The same terms, pressure and current, are applied
to electricity. The pressure may also be called potential,
Electro-Motive Force, or (E.M.F.). The fall in potential
along a conductor may be called line drop or difference in
potential. In discussing the loop of wire it is important
to state that the pressure is proportional to the rate of
change in the number of lines of force; the current depends
both upon the pressure and the opposition to its flow or
resistance.

In Fig. 101 a magnetic field is shown with lines of
force running from north pole to south pole through a

rectangle of wire which
may be turned by a
crank. If the loop is re-
volved toward the right,
the number of lines of
force through it will fall
to zero. Then as the
loop revolves farther the

FIG. 101.
If the loop of wire revolves, the num-

ber of lines of force through
changed; in other words, it cuts the
lines of force. This cutting of the
lines of force develops an electrical pres-
sure. Since the invention of the Edi-
son dynamo in 1881, most of the elec-
tricity used is generated by this process.

lines of force will pass
it is through in the opposite
direction and increase
until all the lines run
through in the opposite
direction. They will fall
again to zero and in-
crease to the full number, as in the figure, when the rect-
angle has made a complete revolution. The effect would
be exactly the same if the loop of wire were held stationary
and the magnets revolved about the loop so that the lines
of force passed through the loop first in one direction and
then the other. We have said that the electric pressure
developed is proportional to the rate of change of the

MAGNETISM AND ELECTRICITY 133

number of lines of force. Careful observation of the
rectangle will show that the change of lines of force is
first one way and then the other, and both mathematical
demonstrations and experimental measurements show that
the electric pressure follows the same change as in Fig. 102,
that is, a pressure first in one direction and then the other
following wave lines as in Fig. 102. Such a current, first in
one direction and then the other, is called an alternating
current or A.C. If wires are connected to the ends of

FIG. 102. FIG. 103.

The pressure generated in the loop of Fig. 101 follows the sine curve
shown in Fig. 102. It is proportional to the rate of cutting lines of
force at each point of the revolution. The commutator changes the
direction of each negative loop as in Fig. 103.

the rectangle by slip rings and led away to form a circuit,
the .wire would carry A.C. electricity. Such a current is
used for ordinary incandescent lighting. We will later
study the advantages and disadvantages of A.C. distri-
bution.

If two pieces of copper are attached to the ends of a
loop and two brushes set to slide on the pieces of copper
as shown in Fig. 101, in such a way that just as the
current is about to reverse in the loop each brush slides over
onto the other piece of copper, the current in the outside
wire will flow in the same direction it did before and will be
like the line in Fig. 103. This current, since it is all in one

134

APPLIED PHYSICS

direction, is called a direct current or D.C. If more loops

are put on so that while
the current of one loop is
low, another loop is sup-
plying the needed pressure,
the curve becomes that of
Fig. 104 and we have a

D.C. generator such as is used to supply current for

motors and lights of this building.

The magnets supplying the lines of force are field magnets.

FIG. 104.

FIG. 105. — Dissectible Hand Dynamo.

The loop of wire is revolved at high speed (3500 R.P.M.) between
the poles of a strong magnet. A soft iron core insures a large number
of lines of force for the conductor to cut.

MAGNETISM AND ELECTRICITY 135

The pieces of copper for changing or commuting the cur-
rent to make it direct are the commutator.

The loop of wire in which the electric pressure is developed
is called the armature. Either field or armature may
be revolved. The electric pressure is commonly called

FIG. 106. — 300 Horse-power B.C. Dynamo.

One of two used at Technical High School, Cleveland. This ma-
chine makes 600 R.P.M., and at each revolution each conductor cuts
the lines in front of 14 poles.

electro-motive force or E.M.F. and is measured in volts
which we will define later. The quantity of current set
up is measured in amperes which we will also define later.

A magnetic needle comes to rest with its north pole
pointing almost north. If a wire carrying an electric
current is brought down near it and parallel to the needle

136

APPLIED PHYSICS

as in Fig. 107, the needle will swing from its former position
and come to rest at an angle to the wire. If the direction

v of the current in the wire is

reversed, the needle will be
deflected in the opposite di-
rection. We speak of the
direction of the current as
though we knew. Electric-
ity may be some sort of a
strain in ether and when
that strain is transmitted
from one point to another

FIG. 107.

The copper is non-magnetic, but
when a current of electricity flows
over the wire the needle tends to
turn at right angles to the wire.
This shows a magnetic field about
a current of electricity.

one

we call the connecting sub-
stance which distributed the
strain a conductor, and not knowing any better term to use,
we call the flow of electricity
a current. For convenience
in studying some of the ap-
plications we say the current
flows from the positive (+)
to the negative ( — ) side. It
must be understood that this
is only a convention, al-
though a useful one. With
the wire above the needle as

FIG. 108.
Concentric rings show the field

shown, if the right hand is

brought down with the palm

of the hand toward the wire around a wire carrying a current of

and the fingers pointing in

the direction of the current,

the extended thumb indicates which way the north end

of the needle will move.

The above results lead us to suppose that there is some
magnetic field around the wire when the current is flowing.

MAGNETISM AND ELECTRICITY 137

To test this we run the wire through a piece of paper and
scatter iron filings around it. When a current flows
though the wire, the filings arrange themselves in con-
centric rings about the wire as a center. These rings
show lines of force in the space about the current, Fig. 108.
Grasp the wire with the right hand with the thumb in the
direction of the current and the fingers will show the direc-
tion of the lines of force. Make a helix or coil of the
wire as in Fig. 109 and apply the same rule for grasping

FIG. 109.

the wire and we will find that the lines of force of each turn
of wire tend to strengthen those of the others. Grasp the
coil with the right hand with the fingers along the wires in
the direction of the current and the thumb will indicate
the north pole. When studying the magnetic field, it
was found that the lines of force pass through iron much
more readily than through air, and we find by experiment
that if a soft iron core be placed in the coil of Fig. 109, a
current which would before produce only a few lines of
force will produce a large number through the iron, and a
strong magnet will result, see Fig. 110. This is an electro

138

APPLIED PHYSICS

magnet. We shall now take up some of its applications,
which cover a large part of the field of applied electricity.
When a current of electricity flows through the wire
coil or helix described in the last paragraph, the coil be-
comes a magnet with a north pole and a south pole, like
any other magnet. When a core of soft steel is inserted
through the helix the strength of the magnet is greatly
increased, for the reason that the soft iron lets the lines of

force pass through more
readily than the same
space containing wood
or air or any other non-
magnetic substance.
Soft iron is more per-
meable than hard steel;
hence while the current
flows, the soft iron core
is a stronger magnet
than the hard steel. As
soon as the current is
turned off the soft iron
loses most of its mag-
netism. The Morse
telegraph instrument de-
pends upon this principle. A bar of soft iron is held in
place above an electro magnet by a spring. The electro
magnet is connected to a circuit from a distant station
where a current is furnished either by a dynamo or a
battery. As the earth is a good conductor the return
wire may be replaced by the earth. Any wire offers some
resistance to the flow of an electric current, so the cur-
rent carried by a wire for long distances is too small
to make the sounder work as well as it should. There-
fore, a relay is put in and acts as a key to work a local

FIG. 110.

MAGNETISM AND ELECTRICITY

139

140

APPLIED PHYSICS

MAGNETISM AND ELECTRICITY

141

circuit. The connection for the sending and receiving
station is then as in Fig. 114.

The key at Chicago is pressed and the current flows
through each relay on the circuit and each sounder is

FIG. 113. — Lifting Magnet.
Two tons of scrap iron are transferred at
each lift by this magnet.

pulled down and held as long as the sending key is pressed.
Dots and dashes are used to represent letters.

TEC HNICAL

spells Technical.

142

APPLIED PHYSICS

The door bell is also an application of the etactro magnet.
The circuit is wired as in Fig. 115. When the key or but-
ton K is pressed, the circuit is completed and the current
flows through the electro magnet m, pulling the armature
up and striking the bell. At the same time the circuit is
broken at 0, the current stops, m is no longer a magnet

FIG. 114. — Morse telegraph Circuit.

Chicago sending. Every time this key is pressed every relay and
every sounder on this line clicks the same signal.

and the soft iron armature falls back to B and the process
is repeated, ringing the bell as long as the button is pressed.
The contacts in K and 0 are likely to get dirty or covered
with oxide and prevent the working of the bell. They
should then be scraped clean. If the battery is composed
of dry cells, they will need replacing occasionally, or if a
sal-ammoniac battery is used, the solution will need renew-
ing when exhausted. Aside from this slight attention the
bell needs no care.

MAGNETISM AND ELECTRICITY

143

FIG. 115. — Electric Bell.l

We will now take up the study of another application

of the electro magnet, the motor, which is much in evi-

dence every day. In the instrument known as the

D'Arsonval galvanometer, a

coil of wire is suspended by

a tape of phosphor-bronze so

that the coil hangs between

the poles of a permanent

magnet with the axis of the

coil at right angles to the

lines of force of the field in

which it hangs, as in Fig.

116. A spring below the coil

serves as a conductor to com-

plete the circuit and also to

hold the coil in place. When

a current is sent through the coil it becomes a magnet,

according to the law of magnets ; the north pole is attracted

by the south pole of the permanent magnet and repelled

by the north pole. The
south pole of the coil is
pulled in the opposite
direction so that the
coil swings about in its
field, and the amount
of the deflection de-
pends on the strength
of the current. If the
current is strong enough
the coil will turn at

right angles to its first position or until its north pole is

toward the south pole of the magnet. If the current con-

tinues to flow in the same direction and the coil is turned

beyond this position, the magnetic drag will stop it and

FIG

144

APPLIED PHYSICS

FIG. 118.

The D' Arson val Galvanometer as used
in the D.C. Voltmeter. The movable
coil is carried on jewel bearings. The
scale is read in volts.

FIG. 117. — Galvanometer. I

The frame is a strong per-
manent magnet. The coil is
copper wire wound on a brass
frame. It is non-magnetic ex-
cept when a current of elec-
tricity passes through it, then
it indicates the current by
turning toward one side.

FIG. 119. — Section of the D'Arson-
val Galvanometer, used as a Voltmeter.

MAGNETISM AND ELECTRICITY

145

FIG. 120.
Weston Voltmeter and Ammeter, galvanometers with other names.

FIG. 121. — Switch Board.

Voltmeters and ammeters in use on a distributing switch board.
11

146

APPLIED PHYSICS

bring it back. If the current is reversed just as the
coil reaches the position where it would stop, the in-
ertia carries it beyond; the magnetism of the coil being

Potential '"
Coil*.

001

^V Spring

HH!

\\r\f\-Cmient

JO(T c°"

Lamps

Resistance

FIG. 122. — Direct Reading Wattmeter.

The current coil carries the current while the potential coil
carries a current proportional to the pressure. The reaction
between the two measures the product of the volts times the
amperes, thus it is read in watts.

reversed, the permanent magnet swings it on the rest
of the turn. If this were continued with a galva-
nometer, it would soon twist
off the supporting tape. By
putting the coil on bearings
and making the electric con-
nection through brushes and
commutator as in the dynamo
shown in Fig. 101, the cur-
rent is carried to the coil by
a sliding contact. The mag-
netism of the coil is reversed
at the proper time to keep it

FIG. 123. — Toy Motor.

Again the principle of the gomg and we have the prin_
galvanometer is applied, al- . ° .

though the name is changed, ciple of the common direct

current motor such as run
the street cars of the city.

MAGNETISM AND ELECTRICITY

147

Do not fail to note that in the electro magnet there
are two distinct circuits: the electric circuit, which is
of copper wire, with each turn insulated from the iron
core and also from the other
turns; and the magnetic cir-
cuit, which is of soft iron, and
should have as little air gape
as possible for the lines of force
to pass through, since iron will
allow many more lines of force
to pass for the same current
than will air.

The field magnets of the dy-
namo and of the motor are
usually electro magnets and in
the dynamo may be energized
by a current from the dynamo FIG. 124. — Series Dynamo,
itself (self excited) or by current

from another source (separately excited). When the
field of a dynamo is connected, as in Fig. 124, so that
the current all runs through the field, then through the
load and back to the other brush,
it is " series wound " and large wire
must be used. With the external
circuit open such a field has no
current through it, and if volts are
plotted on one axis and amperes on
the other the voltage starts at a
very low point, as a, Fig. 125. If
more load is now added to the ex-
ternal circuit by turning on more lamps, the voltage
builds up along the curved line ab. If the field is
connected so that the current opposes the residual mag-
netism, the series dynamo will fail to build up and

Amperes
FIG. 125.

148

APPLIED PHYSICS

will follow the dotted line ax. If a series dynamo fails
to "pick up" when the contacts are all tight, it is usually
necessary to reverse the field.

Battery, A pair
of lines for
each cell.

D.C. Dynamo
or Generator.

D.C. Motor.

A.C. Dynamo
or Generator.

Field of Shunt D.C.
Dynamo.

Field of Series
D.C. Dynamo.

Resistance Box.

M/WV&WW

Variable Resistance
or Rheostat.

Voltmeter.

Ammeter.

Galvanometer.

Transformer.

-O-

Incandescent Lamp. Arc Lamp.

FIG. 126. — Symbols Used in Electrical Diagrams.

MAGNETISM AND ELECTRICITY

149

In Fig. 127, the connection is shown for the " shunt
dynamo." Whenever an electric circuit is connected so
that the current may divide
and flow through two paths,
the connection is called shunt
or parallel. In the shunt
dynamo the current divides at
one brush, part going through
the field to the other brush
and part through the external
circuit back to the second
brush. If this generator be
run at a. constant speed, the
highest voltage will be reached

when there is no external load

, „ , . , FIG. 127. — Shunt Dynamo,

and all the current is used to

excite the field. As the external load is increased the
voltage will drop along the curved line ab, Fig. 128. Note
from this curve that the shunt machine fails completely
under too heavy a load. A resistance in series with the

Series

O Amperes
FIG. 128.

FIG. 129. — Compound Dynamo.

field must be put in to adjust the field strength as the load
is thrown in. For lighting and power purposes a con-
stant voltage, usually 110 or 220 or 500, is wanted at all
loads. In the series machine the voltage rises higher as
more lamps are thrown in, while in the shunt machine,
unless an operator stands constantly at the regulator to

150

APPLIED PHYSICS

regulate it, the voltage falls as more lights are cut in.
Fig. 129 shows a connection in common use where both

External Circuit

WWWWM

FIG. 130. — Short Shunt and Long Shunt,
Compound Dynamo.

series and shunt windings on the same magnets are used,
and one picks up as the other decreases so that the voltage

remains constant, as is shown by
the dotted line ab, Fig. 131. This
machine is self regulating and is
compound wound. The greater
part of the electric power gene-
rated and distributed to-day is
AC, but in order to define the
units used, we will now take up

__Compqund_

Amperes
FlG. 131.

a brief study of the chemical relation of the electric cur-
rent before studying the alternator and transformer.

THE CHEMICAL RELATION OF AN ELECTRICAL CURRENT

Experiments in the chemistry course have demonstrated
that pure water is a non-conductor of electric currents.
When a little H2S04 is added to the H20 in dilute solution
the electric current passes readily through it. Many salts
in solution produce the same effect. It is supposed that
when a salt is in the solution some of the molecules are
separated into atoms or groups of atoms, each with a small
quantity of electricity, together called ions. Until recently

MAGNETISM AND ELECTRICITY

151

this was mere theory with little to prove it, but within
the last year no less than six different experimenters have
actually measured the quantity of electricity carried on
the atom and the results by all these methods are about
the same. When an electric current passes through an
electrolyte (as the solu-
tion is called), these ions
pass across from one wire
to the other through the
solution and each carries
its little load of electric-
ity and dumps it just
as a laborer pushes his
wheelbarrow load of sand
and dumps it onto a pile.
A good union man will
push only a certain size
load and will refuse to
move if he has one extra FIG. 132. — Electrolytic Cell,
shovelful. These ions are When a current is forced through the
the best union men there 9ell,the electrolyte is broken up and Cu

is plated on the cathode,
are, as every univalent

atom carries exactly a certain amount of electricity, no
more, no less, and every divalent atom carries twice as
much and they never make a mistake.

When the ends of two wires connected to an electric
circuit are placed in an electrolyte the circuit is completed
through the solution and the ends are called the electrodes.
Sometimes they are called anode (the way in) and cathode
(the way out). The electrolytic cell of Fig. 132 is shown
connected to an electric circuit with pressure enough to
drive the current through the direction shown. The action
all appears at the electrodes and not in the solution between.
The Cu atom with its charge migrates to the plate C,

"^\

Annode
S04
At Plate
A

T—

ode
Deposited
onC

Sgi

MQ
-ivti

t^~"

152 APPLIED PHYSICS

where it gives up its charge and is deposited as copper on
the plate. The SCX ion migrates to the other plate and is
liberated at plate A . If A is of copper the sulphion radical
attacks it and forms Cu SCX. If A is a platinum plate the
sulphion ion will take H2 from the water and liberate O
at plate A.

If platinum plates are used and the electrolyte is H2SO4,
the H ion migrates to the cathode, deposits its charge
and is liberated as free hydrogen. The SCX ion migrates
to the other plate, and since it cannot act on platinum it
attacks the H2O, taking out H2, and forming H2SO4, liber-
ating O. The H2S04 therefore remains the same in quan-
tity while H2O is used.

Electro plating is done by the method shown above.
In Fig. 132, C will be copper plated. If the electrolyte is
a solution of silver salt and A is a silver bar, the plate
C will be silver plated. The silver and nickel plating
industry is of great commercial importance in the manu-
facturing world to-day. Much of the printing of to-day
is done by electrotype.

The type is set and an impression made in wax. The
face of the wax impression is covered by a thin layer of
graphite to make it conducting and then plated by a layer
of metal a little thicker than paper. This would be too
thin to use in the press, so it is " backed" by pouring on
melted type metal. The electrotype plates so made are
an exact copy of the type and may be used to print, while
the type is distributed and set up again.

We have pointed out that a univalent atom always
carries the same quantity of electricity. That is, the
quantity of an element deposited by a current passing
through an electrolyte is directly proportional to the
quantity of electricity passing through it. In dealing with
the flow of electricity, through an acid for instance, the

MAGNETISM AND ELECTRICITY 153

quantity of hydrogen deposited is independent of the
kind of acid and its concentration, but depends on the
quantity of electricity only. If the same quantity of
electricity is passed through different electrolytes the
quantity of the substance deposited is proportional to the
atomic weight for a univalent element. Each atom carries
the same quantity every time. This fact furnishes a
means of defining the unit current. The cathode is weighed,
and then after an electric current has been passed for a
given time, the increase in weight will indicate exactly how
much electricity has gone through the circuit. The Inter-
national Congress defined the ampere as: "The constant
current which will deposit 0.001118 grams of silver or
0.0003287 grams of copper in one second." This is 4.025
grams of silver per hour.

The same congress defined the ohm as "The resistance
offered to a constant current by a column of mercury at
the temperature of melting ice, 14.4521 grams in mass of
a constant cross section and 106.3 cm- m length."

It defined the volt as " That electric pressure which
will force a current of one ampere over a resistance of one
ohm."

A watt is the power to supply one ampere with a pres-
sure of one volt. These international units are those used
in common electric practice in this country. The unit
used in selling electricity is the kilowatt-hour, that is,
1000 watts for one hour (746 watts are equal to one horse-
power, that is, one kilowatt is equal to about 1.3 horse-
power).

BATTERIES

There are a large number of battery cells but we will
here consider only a few, the simplest voltaic cell and the
one representative of each of the types of cells in most com-

154 APPLIED PHYSICS

mon use. As the simple voltaic cell will be studied with some
care in the laboratory, this description may be brief. A
simple voltaic cell may be made of a glass of salt water, a
piece each of zinc, copper, and wire. Usually a diluted solu-
tion (about one part in twenty) of H2S04 is used. When
these are not connected a few bubbles will rise from the zinc.
If the zinc plate is amalgamated with mercury no action
will take place. If now the two strips are connected by
a conductor, bubbles will rise freely from the copper strip.
A test will show that these bubbles are hydrogen, that an
electric current is flowing along the wire, and that the zinc
is used up, that is, changed to ZnSO4. The electric current
is set up at the expense of the chemical energy. The action
of the ions is similar to that of the electrolitic cell described,
but in the opposite direction. If the zinc is not amal-
gamated, the action goes on at the zinc plate between points
of different degrees of purity independently of the electric
circuit. Such wasting of the zinc is called local action.

If undisturbed, hydrogen bubbles soon coat the copper
plate and oppose the flow of the current. Often this polar-
ization nearly stops the action of the battery.

OPEN CIRCUIT BATTERIES

There are two batteries (the NH4C1 cell and the dry
cell) in common use, which if used continuously for a short
time will polarize. If connected to a lamp or a small
motor they will work for a short time until the collection
of hydrogen stops the action. The battery must then
rest while the hydrogen disappears. On a door bell cir-
cuit which is closed only occasionally and then for a short
time such a cell is all right, and for that reason is called an
open circuit battery. The NH4C1, ammonium chloride or
sal-ammoniac cell, is made by placing in a glass jar a solu-
tion of NH4C1, and in this a carbon with a large fluted

MAGNETISM AND ELECTRICITY

155

surface and a heavy piece of zinc are placed. The large
surface of the carbon reduces the speed of polarization.
Often the carbon is hollow and packed with graphite and
MnC>2, to further absorb the hydrogen.

In the dry battery the zinc is the jacket of the cell and
the electrolyte is made into a paste and the whole sealed
by covering with wax. The basis is
usually NH4C1. If the cell is not used
it dries out until the resistance of the
paste becomes so large that no current
'flows. Until the zinc is used up, such a
cell may be renewed by injecting a weak
solution of NH4C1 or dilute HC1.

CLOSED CIRCUIT BATTERIES

The cells described in the last para-
graph work well on the open circuit sys-
tem, but in closed circuit work such as
running motors, small electric lights, or
for commercial telegraph work, polariza-
tion renders them useless. Polarization
is the deposit of hydrogen about one of
the electrodes. In several cells such
chemicals are used that some other sub-
stance is deposited and polarization is
prevented. Fig. 134 shows the gravity
cell used in commercial telegraph sys-
tems. A strip of copper is placed at
the bottom in a saturated solution of
CuSCX and near the top a heavy piece
of zinc is suspended in a dilute solution
of ZnSO4. The heavier solution is at
the bottom so that gravity retards dif-
fusion. Some of the molecules of the

FIG. 133. — Section
of a Dry Cell.

The zinc container
is one electrode. It
is separated from
the carbon by a
paste containing
ammonium-chloride.
The carbon elec-
trode is packed in a
mixture of carbon
and manganese di-
oxide.

zinc sulphate are

156

APPLIED PHYSICS

ionized and the -SO4 ion migrates toward the zinc, deposits
its charge, and forms new ZnSCU, while the Zn ion migrates
toward the other electrode, meets the CuSO4 and displaces
a Cu ion. This migrates to the copper plate and is de-
posited as metallic copper, while its charge is given to the
copper electrode. As the cell is used the zinc "crowfoot" is
consumed, the solution of zinc sulphate becomes more
concentrated, the copper sulphate becomes dilute, and the
copper plate grows by deposit of pure copper. New

" blue rock " must be added
and the zinc sulphate solution
must be diluted to keep the
cell in good condition. To
prevent diffusion the circuit
must be kept closed.

The cell just described has
so many advantages in the
way of furnishing a constant
pressure, while being used to
furnish a constant current,
that a portable form is desired.
The result is the Daniel Cell.
FIG. 134. — Gravity Cell. Exactly the same materials are

This is a closed circuit cell, used, but the zinc is placed in
Used in telegraph work. a poroug ^ containing the

zinc sulphate and the cell may be carried about. The
action is the same as in the gravity cell.

The storage battery is one of great importance in the
present age of electricity. A home-made storage cell for
every boy is shown in Fig. 135. Any glass jar may be used.
A small one may be made in a ordinary drinking glass.
Two lead plates fastened by wires to the sides of a stick of
wood are suspended in a 10% to 20% solution of H2S04.
If A and B are connected to a suitable source of elec-

MAGNETISM AND ELECTRICITY

157

tricity a current will flow through the electrolyte and
hydrogen will escape at the negative plate, but the oxygen,
instead of escaping at the positive plates, unites with the
lead forming a brown-colored coat of PbC>2. After the
electrolysis has been carried on for a time the circuit may
be disconnected and a bell, if connected, will ring. Test will
show the current going through
the cell in the opposite direc-
tion. While the discharge is
going on the lead peroxide
formed during the charge is
reduced to soft sponge metallic
lead, while some lead sulphate
is formed on the other plate.
When the cell is charged again
the hydrogen reduces this lead
sulphate to spongy lead. Two
plates like those shown will
not take a very large charge,
as only a small amount of the
"active material" will be held
by each plate. After several
charges the cell will work bet-
ter than 'at first, as more of
the plate has been changed to
the active spongy form.

When the cell is being
charged, just as much electric-
ity comes out at the negative
plate as goes in at the positive
plate. No electricity is stored

FIG. 135. — Toy Storage Cell.

Forcing a current of electric-
ity through this cell stores up
chemical energy. This chemical
energy may afterwards be used to
generate an electric current.

in the cell, but some of the energy is retained as chemical
energy. When water runs down through a water-wheel as
much water comes out as goes in, but the wheel takes

158

APPLIED PHYSICS

some of the energy out. So the storage cell takes some
of the energy out but does not store the electricity.

The commercial storage cell has plates of lead bars (Fig.
136), between which are pockets, filled with a paste of the
active material, which increases the capacity but not the
voltage. The internal resistance is very small, hence a
storage battery must not be short circuited.

The lead gridiron plates have little rigidity and buckle
easily if they are heated very hot. If discharged or charged
too fast the plates heat and buckle, thus short circuiting
the cell and destroying it. The jars are glass or hard

rubber and easily broken. If
the battery is allowed to stand
discharged for a few weeks, the
lead sulphate formed on one
plate during discharge hardens
into a white layer which inter-
feres with the working of the
cell. Unless the cell is watched
and given the greatest care it
soon gets out of order. All con-
tacts and metal parts near the
battery must be lead covered,
to protect them from the fine
spray of H2SO4 which is carried
into the air by the escaping
gases.

FIG.

Storage

136. — Lead
Battery.

The lead grid plate con-
tains the paste of "active ma-
tenal" m its pockets.

Thomas A. Edison, after several years' constant effort
and thousands of experiments, nas produced a storage
battery which in many respects is far ahead of the lead
storage cell. The jar is of nickle plated steel, thus doing
away with breakage. The plates have a frame work of
steel which will not buckle even on short circuit. The
electrolyte is a solution of KOH, hence no corrosive fumes

MAGNETISM AND ELECTRICITY

159

are formed. One plate consists of a gridiron of steel with
a paste of iron oxide in the pockets. The other plate is a
frame work of steel carrying steel tubes about the size of
small lead pencils. These tubes are perforated and contain
alternate layers of nickel oxide and nickel, the nickel being
for the purpose of
making the mixture
conducting. Th.e
battery weighs about
half as much as the
lead battery of the
same capacity. It
is free from corro-
sive fumes, is almost
non-breakable, is not
injured by too rapid
discharge nor by
standing discharged.
Its rated efficiency
is not so high as that
of the lead battery,
but in practise it is
so difficult to keep
the lead battery in
good condition that
the actual working
efficiency is usually
higher. The pros-
pect is that the new
battery will largely
displace the old in a
few years. Parts are
shown in Fig. 137.

We have found that the definition of the volt leads us

FIG. 137. — Electrodes of the new Edison
Storage Cell.

One nickle plated steel plate contains iron
oxide in the pockets. In the other plate
perforated steel tubes contain nickel oxide.

160

APPLIED PHYSICS

at once to Ohm's law C = V/R, which may also be stated
V = CR also R = V/C. This gives us one of the commonly

used practical methods of

measuring

voltmeter

no v

resistance. The
and an ammeter

(g) | are connected over the resist-

ance as shown in Fig. 138.
A current is passed through
and the voltmeter and the
FIG. 138. ammeter readings are taken

Measuring resistance by the use as near the same time as pos-
of voltmeter and ammeter. ^^ Tfaen foy ohm>s ^

R = V/C. When V is in volts and C in amperes, R will be
in ohms. One of the common testing boxes which the
lineman carries with him is based on the principle of the
Wheatstone's bridge. To
understand this it will be
necessary to consider divided
circuits, which may be called
also parallel or shunt cir-
cuits.

In Fig. 139 consider two
resistances r\ and r2 in shunt
circuit, with a current C flow-
ing from A to B as shown by
the arrows, where c\ and c2 are the currents through r\ and
r2. The fall of the potential from A to B is V volts and
is the same by either path ; then C = ci + c2 but by Ohm's

V V V

law C = — ; Ci = — , and C2 = — ; substituting we have

FIG. 139.

Divided circuit, shunt circuit,
or resistances in parallel. Part
of the current flows over each
wire, the larger part in the wire
of least resistance.

V _ V 7
R TI r2

MAGNETISM AND ELECTRICITY

169

nected to the ends of the interrupter. When the inter-
rupter breaks the circuit the induced electricity, instead
of producing a spark, goes to charge the condenser, and as
the circuit is closed again the condenser is discharged,
helping to build up the current quickly. Hence both
changes take place more quickly and the secondary will
give a longer spark. See Fig. 145.

An extensively used modification of the induction coil
is the transformer. It is said that the reason the moon-
shiners of the Kentucky moun-
tains are still in existence is that
the roads are so bad and rail-
roads so few, they cannot get
their corn to market, but by
making it into whiskey the bulk
of the corn is so much reduced
that it is easy to carry out. After
getting it to market in this form
it is not considered good food for
horses. In the case of an alter-
nating current of electricity, such
as described on page 133, the cur-
rent may be reduced to small
amperage at high tension for
transportation, and then easily
transformed to large amperage
at low tension for ordinary use.
You may suppose that the elec-
tric lights in your home are connected with the power
plant of the Illuminating Company. They are not. They
are completely insulated. To supply 20 amperes at 110
volts to light 40 lamps, only one ampere at 2300 volts is
transmitted along the line. The line loss in transmitting
the one ampere is much less than it would be to transmit

FIG. 146. — Closed Core
Transformer.

170 APPLIED PHYSICS

the 20 amperes and the wire may be much smaller, and at
the present prices of copper that is a great item. How is
it done? By means of the transformer. Imagine an in-
duction coil with the core extended from one end, around
the outside of the coil to the other end, to form a complete
return circuit of soft iron for the lines of magnetic force,
and you have a good idea of the transformer. In one set
of windings there are 20 turns of small wire, for every
turn of large wire in the other winding. Either may be
used as the primary. Usually the small wire is connected
to the 2300-volt feed wires and the large wire to the light-
ing circuit. If there were no loss in transformation the ratio
of the voltages would then be 20/1 and that of the cur-
rents 1/20, that is, the watts (amperes times volts) would
be the same in both lines. In practise there is from 30 to
10% loss, although transformers have been built which
give 98% efficiency. The transformer will not work on a
direct current, as the secondary generates an E.M.F. only
during a change in the magnetic flux through the coil, and
this change takes place only while the current in the pri-
mary is either increasing or decreasing. The transformer is
used on the alternating current following the curve shown
on page 133. In common practise, the lighting transmis-
sion lines are 2300 volts and the current makes 60 cycles
or 120 alternations per second. For long distance trans-
mission high tensions are used. The Sanitary District of
Chicago generates power 38 miles from the city at 11,000
volts, steps it up to 66,000 volts, transmits it on bare
wires to Chicago and steps it down to 110 volts for use.
Some lines transmit power at 100,000 volts. In one of
our large cities a 2300 volt lighting wire fell across a tele-
phone wire and before the " trouble shooter " could locate
and correct it several people were killed by shocks from
telephones. It is important that wherever such lines cross

MAGNETISM AND ELECTRICITY 171

they should be protected by automatic devices which will
cut them out of the circuit if anything happens to the
line. A person with dry feet standing on a dry floor may
handle one side of a 2300 volt circuit with bare hands
without danger, but he must not ground the circuit or
connect the two lines through his body.

We are now ready to take a more complete survey of
the lighting system of a modern city. For street lighting,
the system still in common use is the open arc with the
lamps in series. Such lamps require about 45 volts for
each lamp and an average of 5 volts for line drop, making
50 volts for each lamp. 100 lamps are connected in series
and operated by 5,000 volts D.C. constant current dynamo.
The current for most cities is maintained at 6.6 amperes,
although some use 9.6 amperes. Such lights rate at 1,200
and 2,000 candle-power respectively. They should never
have been rated so high, as they actually give only from 375
to 450 candle-power. The demonstration with the lead
pencil arc has shown that, when turned on, the carbons
must be in contact and then drawn apart to "draw out
the arc." As the carbons are burned away under the
heat of the arc, one or both must be fed forward. Both
these movements are accomplished by means of the electro
magnet. The coils of large wire, S, Fig. 147, is in series
with the arc. The sliding brush, B, forms contact with
the brass rod carrying the upper carbon. When the key,
K, is opened the current flows through the coil, S, and
lifts the armature, pulling the upper carbon with it by
means of the loose clutch, A. The coil, C, is of small
wire with a high resistance and takes very little current
while the arc is short, but as the arc increases in length by
the burning of the carbons the resistance becomes greater.
The dynamo is all this time forcing a constant current
through the lamp so that the strength of the magnet, S,

172

APPLIED PHYSICS

FIG. 147.

stays the same, but the increasing resistance of the arc
drives more current through the coil, C, until it overcomes
the pull of the upper magnet and pulls the clutch down.

When the clutch, A,
strikes block, D, and takes
the horizontal position,
the rod slips through it
and the upper carbon is
said to "feed." The coil,
C, may be wound on the
outside of coil, S, but with
current in the opposite
direction to it, and the
result is the same.

In the open arc . de-
scribed above, the carbons

at the high temperature of the electric arc (about 3,500° C.)
are oxidized rapidly and must be replaced after about 8 hours.
In the inclosed arc, used in most of the newer lighting
systems, the arc is inclosed in an inner small glass globe
which fits rather closely about the carbons to prevent
much circulation of air. This globe soon becomes filled
with CO2 instead of O and the carbons are not consumed
so rapidly. The carbons in such a lamp will last from 150
to 200 hours, hence much of the expense of " trimming "
is saved.

In both the arcs described most of the light comes from
the pit formed in the positive carbon, as very little light
comes from the arc itself. A type of lamp now coming
into use is the flaming arc. The carbons are fed forward
at an angle. The carbons have been soaked in some salt,
usually calcium floride, or have a core composed of the
same salt. The heat of the arc vaporizes the salt and
the electricity is conducted on this incandescent gas. The

MAGNETISM AND ELECTRICITY 173

light is the color caused by the salt used and comes mostly
from the arc itself. They are often used two in series
on the 110 volt A.C. circuit.

For incandescent lighting, where the electricity is to be
used in the building, it is quite the common practice to
use 220 volt D.C. generator. The lamps are connected
in parallel, hence the voltage must remain constant while
each .lamp takes its own current, and the total current
used is the sum of the currents required for each lamp
turned on. Where the power must be transmitted for
long distances, such as required in lighting a large city
from one central plant, this would mean the transmission
of large currents. It is found that for a given wire the
loss due to heat in the line increases as the square of the
current, that is, double the current, and the line loss is
four times as large. The loss due to carrying a large
current is avoided by using an A.C. generator or alternator
and generating current at 2300 volts. This is transmitted
over well-insulated bare wires to the city block where it
is to be used and then stepped down by a transformer,
already described, to 110 volts and distributed to the house
for use.

The incandescent lamp used 'until recently has a small
filament of carbon inclosed in a vacuum within a bulb.
When the electric current, passes through, this filament is
heated to incandescence. The resistance of the carbon
decreases as the temperature increases. The carbon lamp
requires about 3J watts per candle-power. About 98%
of the power used is lost in heat. Recently filaments made
of the element tungsten have come into common use.
The resistance of this filament increases as the tempera-
ture rises. It requires about 1J watts per candle-power.
The long filament is fragile and must be handled with great
care. It is best to burn the lamp in a vertical position,

174 APPLIED PHYSICS

and even then it is found that the life of the lamp is short
if there is much vibration of the fixture. Where the voltage
is lower the filament does not need to have so high a resist-
ance and may be made shorter and thicker. For this
reason engineers are generally of the opinion that where
new buildings are being fitted for electric light it is better
to fit them for 40 volt lamps and transform the current
40 volts instead of 110. Where this has been tried the
lamps are showing high efficiency and long life. The
110 volt circuit is left because of the old carbon lamp.
Space forbids a detailed description of the Nernst lamp and
the Cooper Hewitt mercury vapor arc.

The complete circuit for the ordinary lighting circuit is
shown in Fig. 148. As shown, the house circuit is not
electrically connected to the power-house from which the
consumer buys power, but is completely insulated from it.
The only connection is the magnetic interlinking in the
transformer. For such a circuit the alternating current

shown by the curve on
Page 133, known as single
phase, is used.
FIG. 148. — Transformer Circuit. In considering a wave-

The line circuit is insulated from the motion and when speak-
house circuit. Both are wound on the . , , A r1

same iron core, and change in current mS about trie A.U.
in the primary generates the E.M.F. current already shown,
of the secondary. ,, , , .

we called a complete

wave a cycle. In the two-pole machine studied it required
a complete revolution of 360°. On a many-pole machine
the rotation from a north pole past a south pole and to the
position in front of the next north pole produces the same
electrical effect as a complete revolution of the two-pole
machine. It is, therefore, an electric cycle, and is con-
sidered electrically 360°. Phase refers to the position in
this cycle. If it has made one fourth of the cycle the phase

MAGNETISM AND ELECTRICITY

175

FIG. 149.

is 90 degrees. In the alternator it is common to have
the armature stationary and revolve the fields, as in Fig.
149. Suppose the coil
were spread out as coil V

a — b in that figure.
Some of the turns of
wire will be generat-
ing E.M.F. opposed to
the rest of the coil and
the back pressure will
prevent the coil from
generating as much
pressure as it should.
It was early found that
if the coil were crowd-
ed together, as at d,
all the turns of wire

would be in the same phase, that is, they would reach the
highest point of the curve at the same time and produce the
greatest result. But if the turns were crowded together this

way they would leave a large

fi \/2 \/s \/*\ / \ s part of the ring not sur-
rounded by wire; and to put
on more coils and connect
them together would only go
back to the wide-spread coil
a — 6. If separate coils be
put on equally spaced as

1, 2, 3, Fig. 149, the first is almost through the cycle when
the third is just starting it, that is, they are in different
phase and are really 120° apart on the electrical revolution.
In Fig. 150 the E.M.F. generated by each of the three coils
is shown by lines 1, 2, and 3. Add the three pressures at
any point of the curve and you will find the result zero.

FIG. 150.

176

APPLIED PHYSICS

The electrician who built the first alternator tried to
connect the coils in series and found they would not light

2300 Volts

110 V.

2300 Volts

110 V.

2300 Volts

110 V.

3 Phase 6 Wires

FIG. 151.

lamps while each coil separately would run electric
lights. Each coil may be used separately as in Fig. 151,
and each makes a satisfactory
lighting circuit. There are many
alternators in operation, fur-
nishing three separate circuits
at 2300 volts each. Such a 3
machine generates as much
electricity as three separate
machines would do. It takes
three times as much power to
run it as one set of c coils FIG. 152.

would require, but it takes no

more floor space in the power plant than one machine
with one set of coils would require.

If the three are connected together the result is like con-
necting three equal forces pulling at angles of 120°, as in
Fig. 152. The resultant of any two is equal to and opposite

MAGNETISM AND ELECTRICITY

177

tine

Phase 1

Common Connection
Phase 2

Line

FIG. 153.

to the third and the result of all three is exactly zero. Elec-
tricians have lately found out how to take advantage of this
to save wire. The three coils
of the alternator are connected
together at one end of each
and a wire from the other end
of each is run out across the
city (Fig. 153), and each run
through its lighting circuit,
and then after running through
its useful circuit are all con-
nected together. Each fur-
nishes its own circuit with its
full supply of current but,
when the three run together,
the result is zero, and no
return wire is needed. The wire may stop at the union

or be grounded as de-
sired. It will be seen
that the three wires
in this circuit operate
as many lights as the
six wires above. This
is the common three-
wire, three-phase sys-
tem of the present
time.

The Sanitary Dis-
trict of Chicago
develops about 60,000
horse-power at 66,000
FlG- 154< volts and transmits

Diagram showing coils and their cormec- it 34 miles to Chicago
tion m the armature of a three-phase ._ . .

alternator.

over three aluminium

178

APPLIED PHYSICS

conductors. The neutral wire at each end is grounded,
but under all ordinary conditions carries no current.

When studying the direct current generator and appli-
cation of the electro magnet a brief study of the direct
current motor was made. Refer to it and read it as a

part of this lesson. A
direct current genera-
tor may be used for a
motor. A small direct
current series motor
may be used on a sin-
gle phase A.C. circuit,
as the current reverses
the field at the same
time that it reverses in
the armature, but for
large motors this would
not work. In operat-
ing the D.C. motor,
the shunt type of con-
nection is generally
FIG. 155.

From a photograph of the station-
ary armature of the type of three-phase
alternator used to generate most of the
electricity used at the present tune.
Fig. 156 shows the revolving field for this
generator. The field is excited by a di-
rect current from a small D.C. dynamo
called the exciter. In Fig. 157 the
dynamo is shown assembled.

used, except in the
street car, where the
motor must start under
heavy load. In that
case series motor is
used. The winding of
the armature and of the

field is practically the

same as for a generator, and if the shunt motor were
belted to an engine and run up to speed it would act as a
generator. When running as a motor, however, the E.M.F.
is supplied by an outside source and drives the current
through the machine and the magnetic drag of the lines

MAGNETISM AND ELECTRICITY

179

of force pulls the armature around. The resistance of an
armature intended to operate on the 220-volt circuit is
usually only a fraction of an
ohm. Applying Ohm's law
would show an enormous cur-
rent, which would either blow
all fuses on the circuit or
burn out the insulation of
the armature. If the full
drop of potential is applied
while the motor is standing
still this would be the case,
but a starting box is con-
nected in series with the

armature and as the motor FIG. 156. - The Revolving Field.

is started the lever of the

starting box is moved over slowly. On the first notch

the resistance is all in series with the armature, and

holds down the cur-
rent. As the motor
gets up speed the lever
is moved over on the
successive contacts
until when the motor
has reached full speed
the resistance is all cut
out and the E.M.F.
is all applied to the
motor armature, Fig.
158. The resistance
is no longer needed be-

FIG. 157. — The Dynamo.

cause the motor run-
ning at speed is acting
as a dynamo and generating an E.M.F. in the direction

180

APPLIED PHYSICS

opposite to that applied, and this back pressure, which
is almost equal to that applied, keeps the current from
becoming large. In fact, if a motor were a perpetual-
motion machine, that is, an ideal machine running with-
out friction and doing no work, the counter E.M.F.
would be equal to that applied, and the current zero
a condition not reached in practice.

On every street car there is a controller for the motor-
man which contains a set
of contacts to control the
current through the rheo-
stat and motors beneath
the car. There are on
each car, connected to
the drivers by a spur
gear, either two or four
series motors. When the
controller is on the first
notch the motors are all
in series with the rheo-
stat. If run here long
much power is lost in
heat in the rheostat. The
next notches cut out re-
FIG. 158. sistance until the fourth

Wiring diagram for a D.C. Shunt M6tor. and fifth notch. Here

the resistance is all out

and the motors are in series and at half speed, but no
power is lost in heat in the resistance. The next notch
throws the motors in parallel and all the resistance of the
rheostat is thrown in again. The next successive notches
cut out the resistance until on the eighth notch all the
resistance is out and the full 550 volts is applied to the
motors in parallel, and the motor is furnishing its full

MAGNETISM AND ELECTRICITY

181

power. The ninth or last notch shunts the field. This
weakens the strength of the field magnets. On a level
track the car will then run at full speed, as the motor
armature must turn faster to cut as many lines of force
as before. Weakening the field makes the motor run
faster provided it is not too heavily loaded. Except in
starting, the car should be run on the running notches to
avoid loss in heat in the rheostat. If the controller is
thrown over too fast the circuit breaker is automatically

Main

FIG. 159.
Wiring diagram for a Series D.C. Motor.

released and protects the motors from burning out. Some
motormen are experts at starting a car smoothly and run-
ning in the running notches most of the time. Other
motormen are careless and cost the operating company far
too much for power wasted in the rheostat. Watch the
next motorman you ride with and see if he is using the
current intelligently or if he is wasting power and destroy-
ing equipment.

The recording watt-meter (Fig. 160) is practically a
little motor. To keep it from running too fast a brake

182

APPLIED PHYSICS

which acts in proportion to the speed must be used.
A mechanical brake would act too strongly when the
machine was standing still or running slowly and not
strongly enough when the meter is running rapidly.
In the bottom of the watt-meter shown, an aluminium
disk, run by the motor, revolves between the poles of

Armature.

FIG. 160. — The Recording Watt-meter.

This is practically a small motor in which the
number of revolutions depends upon the number of
kilowatt-hours of electrical energy used. A worm
gear moves the pointers which record the power
used.

a flat horseshoe magnet. Aluminium is non-magnetic,
but when the plate revolves it cuts the lines of force
and eddy currents are set up. These eddy currents are
in proportion to the rate of cutting lines of force and
therefore proportional to speed. The magnet reacts on
these and drags them back, acting as a brake. Read

MAGNETISM AND ELECTRICITY

183

the meter at home, then time it for an hour on a given
number of lamps, and see if it is running properly.

We have considered the direct current motor, its use
and control, but to be at all up to date we must consider
at least two types of A.C. motors. A few years ago one
of the leading scientific papers of our country published a
long article stating that the A.C. motor would probably
never be used except for a few special applications because
it would run at only
one speed and because
it was very unreliable at
that. Now they are in
common use for all pur-
poses. The use of the
two- and three-phase
current and the single
phase " split," so that it
becomes a two-phase
current, has brought
about this result. Fig.
161 represents a ring of
soft iron with a coil of wire connected to a single phase
A.C. generator furnishing 60 cycles.

A permanent magnet is mounted on a shaft so that it
may revolve within the ring. As the current through the
coil rises in one direction a north pole is built up at
the top of the ring; then it dies out and is built up at the
bottom of the ring as the current rises in the opposite
direction. This alternation takes place 120 times per
second. At one time it is repelling and at the other time
attracting the magnet. This action takes place so rapidly
that the tendency for the magnet to begin to rotate is
gone and the tendency to push it the other way appears
before the magnet has had time to start. The result is that

FIG. 161.

184

APPLIED PHYSICS

the magnet remains stationary. If, however, it is started
and run up to speed, that is, 60 revolutions per second
in either direction, the alternating field will give it a pull
or push in the same direction twice each revolution and
it will run as a constant speed motor. A permanent magnet
may be replaced by an electro magnet and the effect will
be the same. Such a motor is called a synchronous motor,
as it keeps step with the generator. It will not start itself
and if overloaded so that it falls behind the generator it

FIG. 162.

will stop. Such motors are of use where a number of
machines must run at exactly the same speed and that
speed be controlled from one point, the generator.

If we have a two-phase current with one 90° behind the
other, as in Fig. 162, and connect to two sets of coils wound
on a ring as in Fig. 162, we will have current, r, at its largest
value when s is zero, and we will have Ni as shown in the
ring at point A. One-eighth of a cycle later, r will have
fallen to half its value and s will have risen to half its value ;
the resultant will be N>2 pole half way between the two at
0. It will have reached that point by moving along the
ring from A to 0 as r has decreased gradually and s has
increased gradually. One-eighth of a cycle later r will

MAGNETISM AND ELECTRICITY

185

be zero and s will be at its highest point, resulting in a
north pole at N* at C. As the cycle continues the north
pole will slide along the ring, making the complete circuit.
As it passes the pole of the magnet it will give it a jerk
to bring it along with it, and as these impulses are all in
the same direction the magnet will start and we will have
a self -starting two-phase A.C. motor. The magnet may
be replaced by an electro magnet, electrically excited,
and the result will be the same. Instead of an elec-
tro magnet, that is, an armature excited from with-
out, place an iron core similar to the drum armature
with large copper bars placed in the slots around the cir-
cumference, as in Fig. 163, with the bars connected so that
they resemble a revolving wheel in the squirrel cage. If
this replaces the mag-
net in Fig. 162 it will
not be a magnet as
long as zero current
flows through the
coils of the ring. As
soon as the current is
turned on in the coils
on the ring the field
begins to run around
the ring. We have a
field revolving rapidly
around a closed cir- FlG- 163<

cuit loop of wire, and, , Squirrel Cage Rotor of the three-phase In-

auction Motor,
although that loop of

wire has no electric connection with any outside circuit,
the revolving field generates a large current in it and this
makes a magnet of the iron core, and the field acting on this
magnet drags it around and we have a self-starting variable
speed A.C. motor known as the induction motor. As elec-

186

APPLIED PHYSICS

tricians do not know which to call the armature nor which
to call the field, they avoid the difficulty by calling the
stationary part the stator and the rotating part the rotor.
The three-phase A.C. lends itself to this type of motor very
well indeed, as it requires only three wires for transmission
from alternator to motor and by placing the coils uniformly
produces a revolving field. Since a revolution means an
electric cycle, that is, from one pole past the opposite to
the like pole again, these may be placed along the ring to
give any speed desired. Such a motor has no sliding con-
tacts, so all commutator and ring troubles are eliminated.
A resistance is usually placed in the rotor to prevent too

1 IJV Tino Receiver Jffl

J" Id

WVVVWVW WAMAMA/

r TJ

Transmitter

FIG. 164. — Telephone circuit.

The transmitter changes sound waves to a fluctuating current of
electricity. These are changed at the receiver to sound, thus repro-
ducing words spoken at the transmitter.

large a current while the motor is getting up speed, and then
is automatically cut out by centrifugal force as soon as
the motor is up to speed. Many electric railways are now
adopting the three-phase induction motor for traction
purposes.

The telephone is an interesting application of the electric
current to the transmission of messages. In discussing
Ohm's law we found that if the applied E.M.F. remains
constant while the resistance of the circuit is changed, the
current changes accordingly.

MAGNETISM AND ELECTRICITY 187

If two pieces of carbon are placed in contact and an
electric current is sent through them, the resistance changes
with every change of pressure. The modern telephone
makes use of this fact. Fig. 164 shows a diagram of the
essential parts. The transmitter contains a space (A)
filled with small pieces of hard carbon between two plates
B and C. One of these plates, B, is at the base of the
mouthpiece and vibrates with every sound wave entering
the mouthpiece. This causes the pressure between the
carbon particles to vary with every vibration and this
causes the current in the primary circuit to fluctuate with
the same pulsations that the sound waves make. The pri-
mary runs through an induction coil, D, and as the induc-
tion takes place only with changes of current the secondary,
E, carries an exceedingly small current fluctuating with
every sound vibration; but it is not sound, it is only
fluctuating electric current, and would not affect the ear
except to shock it; so the receiver is used. It is a per-
manent magnet with a steel disc, G, placed in front of
one end of it. F is a coil of fine wire wound around the
magnet and connected to the line carrying the fluctuating
current from the transmitter. This varying current causes
the same changes in magnetism, and the steel plate, G,
reproduces the same vibrations in the air which were
received at the transmitter, B. The sound is not carried
along the wire but is changed to a fluctuating current of
electricity, and this is conducted along the wire and at
the receiver is changed back to sound.

Historically static electricity was known for hundreds
of years before any practical use was made of electricity
and for that reason is usually studied first. It has little
practical application and will be considered here very
briefly, not because of its value, but because most of the
boys are interested in it. The principal application is in

188 APPLIED PHYSICS

the condenser used in wireless telegraphy. At any time
some inventor may bring out a practical application which
will increase the importance, to the world, of static elec-
tricity; there are rumors that Edison has one now.

The Greeks knew that if amber (Greek electron) is
rubbed with silk some change takes place around it so
that it will attract small pieces of paper. This is the origin
of the name electricity. Later it was found that glass
rubbed with silk and wax rubbed with fur differed from
each other, and the former came to be called positive and
the latter negative electricity. Almost any two sub-
stances rubbed together will generate electricity but many
substances conduct the strain away so it is not detected.
When one kind of strain is developed an equal amount of
the opposite sign is also generated, that is, when glass is
rubbed with silk the positive strain is found on the glass
and an equal amount of negative electricity is found on the
silk. There is an impression that this electricity is differ-
ent from the electricity we have been studying generated
by dynamos or batteries. This is not correct; it is the
same kind of strain. When electricity is flowing along a
conductor it is called current electricity and when a body
is charged with electricity which is said to be standing
still it is called static electricity. When a condenser is
charged by a current it becomes static.

A little time spent experimenting with a glass rod, silk,
wool, and sealing wax will convince the student that like
electricities repel and -unlike charges attract each other.
If a glass jar is lined with tinfoil, and covered outside with
tinfoil, but the two coats left insulated by the glass and a
charge of electricity is communicated to one of the coats,
it will attract and hold in the other coat an equal amount
of the opposite kind and repel an equal amount of the like
kind, which will escape if given a chance. To charge a

MAGNETISM AND ELECTRICITY 189

Ley den jar, connect the outer coat to the earth and then
conduct either + or — electricity to the inner coat; the
repelled charge will flow to the earth and the bound charge
will remain. When charged, a large spark may be obtained
by connecting the two coats, so that the two phases of the
strain which are trying to get together may unite. A
Ley den jar may give a serious shock. If the glass is re-
placed by paraffined paper and the tinfoil is built up in
several layers, first a strip of tinfoil and then a strip of
the oiled paper etc., with every other strip of tinfoil con-
nected together at one end and to one pole, while the others
are connected together to the other pole, we have a con-
denser. Some form of condenser is much used in wire-
less telegraphy, as we shall see later.

A few experiments which every student should work at
home and which will lead to a thoughtful understanding
of static electricity are the following:

Rub a piece of glass with silk, bring it near some small
piece of paper, also bring it near a very small jet of water.
Can you explain what you see? Rub a piece of sealing
wax with wool or fur. Repeat the experiment you did
with the glass. Suspend two small pieces of pith by
silk thread and let them touch the electric wax. Explain
what you see. When they are electrified from the wax,
bring the glass near them.

Scuff your feet along on any wool rug and then touch the
gas pipe or any other grounded conductor. It takes several
thousand volts to produce a spark one-eighth of an inch
long — why did the spark produce no serious results? Let
some one else turn on the gas and you can light it with the
spark from your finger.

For testing static charges of electricity a gold leaf elec-
troscope is commonly used. As shown in Fig. 165, a flask
is fitted with a rod through the stopper and the upper end

190 APPLIED PHYSICS

terminates in a brass ball while the lower end supports
two pieces of gold-leaf. When this is charged the leaves
fly apart as shown in the figure because like charges repel.
To charge an electroscope by conduction, take a small
piece of metal carried on a hard rubber handle and after
rubbing it on a charged body touch it to
the ball of the electroscope. This will
charge the electroscope by conduction. To
charge by induction bring any charged
body near the ball and the like sign will
be repelled to the leaves while the unlike
sign will be attracted to the ball. Now
touch the ball with the finger and the re-
pelled charge will escape to the earth.
Remove the finger and then remove the
charged body and the leaves will stand
FIG. 165. — Elec- apart, the electroscope being charged with
troscope. ^e sjgn opposite to that of the inducing

the gold leaves .

diverge. Study the influence machine and report

on its operation. We found that when a
direct current was used in the primary of an induction
coil the secondary gave a high potential spark when the
primary current was interrupted. This discharge practi-
cally all occurs at the interruption of the primary.

A condenser connected to the terminals increases the
intensity or "fatness" of the spark. The discharge of a
condenser behaves like a spring carrying a heavy weight.
When stretched and released it bobs up and down, that
is, it vibrates, gradually coming to rest. The spark dis-
charge is similar. It oscillates, as shown in Figs. 166
and 167.

If the ends of the secondary be connected to the ends of
a Geissler tube, the discharge is found to be entirely differ-

MAGNETISM AND ELECTRICITY

191

FIG. 166.

The spark from a condenser
oscillates as shown above.

ent. The Geissler tube is a glass tube with platinum

terminals sealed into the ends and the air exhausted to

about 1/380 of an atmosphere. The discharge through

the tube becomes almost continuous and the gas left in

the tube glows with a brilliant

color which depends upon the

kind of gas remaining in the

tube. The light resembles

the Aurora display. It has

been used to a limited extent

in lighting buildings. The

Moore light on this principle

is now successfully used.

When the gas is exhausted
to about one-millionth of an

atmosphere the discharge undergoes another change dis-
covered by Sir William Crooks. A stream of electrified
particles called corpuscles is projected from the cathode
in straight lines until they meet the opposite side of the

tube and there cause it to
glow with a beautiful flores-
cence. These particles
cannot pass through the
glass and may be deflected
from their course by a mag-
net. Rontgen found that
when these particles of the
cathode rays strike on glass,
x-ray Field or better on a platinum

FIG. 167. screen placed in their path,

they give rise to a differ-
ent kind of ray or vibration, which he called the X-ray.
These rays will pass through glass, paper, cardboard,
wood, etc., but not through metal or bone. They will

192

APPLIED PHYSICS

affect the photographer's plate as light does, hence when
a photographer's plate is placed in a plate-holder or box
and the hand laid on the box and exposed to the X-ray,
the ray will pass through the flesh and the box but not
through the bones and a shadow picture of the bones and
any metal imbedded in the hand will be taken (Fig. 168).

As the X-ray does not
affect the eye, the shad-
ows cannot be seen by
the eye, but if a screen
coated with calcium
tungstate is placed back
of the hand it becomes
luminous where the
rays strike it and hence
the shadow picture of
the bones may be seen.
This is much used in
examining bone diseases
and imbedded bodies
such as bullets. The
X-ray is much used in
treatment of cancer and
similar diseases. It
should be used with
great care, as exposure to
the X-ray often causes
serious burns which are not felt at the time but develop
later and cause the flesh to slough away. The operator
continually exposed to the rays is protected by lead
shields which stop the X-rays.

The photographer can take a flash-light of moving object,
because the light from the burning powder is of such short
duration that during the time of exposure the object

FIG. 168.
X-ray picture of the Hand of a Child.

MAGNETISM AND ELECTRICITY 193

moved only an inappreciable distance. Recently a scientist
has taken a series of pictures of the splash when a weight
is dropped into water. It was soon found that for such a
rapid event as this, the flash-light was too slow and un-
certain, hence he used an electric spark. We think of
the electric spark from the condenser or Ley den jar as
being almost instantaneous. Investigation shows that
discharge or spark behaves much like a spring carrying a
weight. When the spring is stretched and released, it
goes beyond the point of rest and vibrates back and forth
until it gradually comes to rest. The spark from the con-
denser or Ley den jar does the same thing as though it
were a stretched spring. Possibly it is some form of strain
in ether. The frequency of the alternations of the dis-
charge depends upon several conditions but is often about
230 million per second. The conductor leading to the
spark gap has a current reversing 230 million times per
second. It is a well-known fact that a magnetic needle
near a wire carrying a current tends to turn at right angles
to the wire. If the current is reversed the needle swings in
the opposite direction. If this alternation takes place
230 million times per second, the needle would not have time
to keep up, but we can imagine a strain or impulse in the
ether sent out and reversed that many times per second.
This would be a wave motion in ether and would travel
out through space much as light waves do. These waves
were discovered by Professor Hertz and are called the
Hertzen rays. They always accompany an electric dis-
charge, are continually passing through space and through
your body. Some one may be telegraphing a message
through your body now, and you never know it. As these
waves cannot be seen, felt, nor heard, they were long undis-
covered. These senses of ours are very dull. We know
little about this world of ours ; we suspect a few things and
14

194 APPLIED PHYSICS

now and then some one finds out some new fact about
things about us. The eye can detect a few ether vibrations;
the others have existed all these hundreds of years and
now we have found only a few of them. Here we have a
poetry of motion surpassing any poetry ever written by
man, a machine so wonderful in its fine mechanism that
although the wisest men since the time of Adam have
been studying it, we have to admit to-day that there are
many of the parts we do not know how to use and that we
know only a little about our surroundings. The true
scientists can only wonder at the marvelous intelligence of
a being capable of making the working drawings and
constructing such a mechanism that man with all his
boasted powers of thought can understand only a little
of it.

To lead up to an understanding of the Hertzen ray we
will summarize a few vibrations with which we are already
familiar.

16 vibrations per second, lowest sound

32 vibrations per second, lowest musical tone

128 vibrations per second, man's conversational voice

512 to 256 vibrations per second, woman's conver-

. ,
sational voice

2000 vibrations per second, high soprano

4000 vibrations per second, highest musical tone

40,000 vibrations per second, highest audible sound

f Trillions vibrations per second, X-ray
Ether ' 2000 billion vibrations per second, photo-
vibrations: I graphic ray

750 to 400 billion vibrations per second

MAGNETISM AND ELECTRICITY

195

Violet
Indigo
Blue
Eye : Green
' Yellow
Orange
Red (about 33,000 to make one inch)

230 million vibrations per second Hertzen ray used in
wireless. (The frequency often becomes much less than

Spark Coil

FIG. 169.

Simple form of Marconi apparatus for wireless telegraphy. The
coherer is not very sensitive and is now replaced by a detector. Ether
at the sending station is vibrated by a spark. These waves travel
out as light waves do and set up electric vibration in the receiving
circuit.

this as the waves vary from a few feet to over a mile in
length.)

There are many forms of apparatus and many helpful
devices such as tuning coils, condensers, electrolytic inter-

196 APPLIED PHYSICS

rupters, electrolytic detectors, etc. But the essential
features of the Marconi system are shown in Fig. 169.
At the sending station an induction coil or transformer is
used to produce the high tension to cause a spark.

The discharge of the spark causes an oscillating current
in the aerial with a frequency of some 230 million oscilla-
tions per second. The frequency may be varied by the
size of the coil or transformer and capacity of the con-
denser. This pulsating charge in the wire will send out
vibrations of ether which travel out in all directions.. At
the receiving station a coherer is so connected that the
vibrations received by the aerial pass through it to the
earth. A variable capacity or else a tuning coil must be
used to make the receiving station of the same frequency
as the sending station, so that sympathetic vibrations will
be set up. For detailed description of all parts of the
apparatus the reader is referred to Popular Electricity
for 1910.

INDEX

Aeroplane, 25

A. C. Current, 133

A. C. Motor, 183, 184

Acceleration, 28

Acceleration formulas, 30

Air pressure, 46

Air pump, 54

Alternator, 175

Ammeter, 145

Ammonium chloride cell, 154

Ampere, 153

Amplitude, 39

Archimedes' principle, 57

Arc light, 171, 172

Armature, 135

Barometer, 46

Batteries, series or shunt, 161, 162

Boiling point, 109

Boyle's law, 53

Brake horse-power, 111

Buoyancy, 57

Calorimetry, 100
Candle-power, 85
Capillarity, 56
Cathode ray, 191
Center of gravity, 33
Centrifugal force, 34
Characteristic of dynamo, 147
Charles' law, 106
Chemical relation of electric

rent, 150, 151

Coefficient of expansion, 104
Coefficient of friction, 37
Color, 88
Commutator, 133

Compound dynamo, 149
Condenser, 188, 190
Conduction of heat, 122
Controller, 181
Convection currents, 123
Convex lens, 89
Critical angle, 88
Crook's tube, 191
Crushing strength, 65
Current of electricity, 131, 133
Curvilinear motion, 34
Cycle, 175

Daniel cell, 156

D. C. Current, 133

Delta connection, 177

Density, 58

Differential pulley, 19, 20

Diffusion, 52

Door bell, 142

Dry cell, 155

Dyne, 31

Echo, 71

Edison storage cell, 158
Efficiency, 6
Elasticity, 62
Electric bell, 143
Electric discharge, 192
Electrolytic cell, 151
Electro-magnetic relation, 136
cur- Electro-magnets, 137
Electro-plating, 152
Electroscope, 190
Equilibrium, 33
Ether vibrations, 79
Eye, 91
197

198

INDEX

Falling bodies formulas, 30

Field magnets, 134

Flaming arc, 173

Fluid, 40

Fluid pressure, 43

Foot-pound, 3

Force, 21

Frequency, 70

Galvanometer, 143
Gas, 40

Gas-engine, 117
Gas pressure, 51
Geissler tube, 191
Gravity, 32
Gravity cell, 156

Hertzen ray, 193
Hot-air engine, 121
Hydraulic press, 42
Hydrometer, 60
Hydrostatic paradox, 44

Inclined plane, 13
Inclosed arc, 173
Index of refraction, 87
Indicator, 112
Indicator card, 113
Indicated horse-power, 113
Induction coil, 166, 168
Induction motor, 185
Inertia, 22

Intensity of illumination, 83
Interference, 73

Joule, 122

Kinetic energy, 35
Kinetic theory of heat, 98

Latent heat, 101, 102

Laws of motion, 22

Laws of vibrating strings, 76

Lever, 6

Ley den jar, 189

Lifting magnets, 141
Light, 79
Liquid, 40
Loudness of sound, 74

Magnetic attraction and repulsion,

126

Magnetic field, 127
Measurement of force, 31
Mechanical equivalent, 122
Micrometer, 14
Microscope, 93
Momentum, 31
Motion, 21
Motor, 146, 179
Motor A. C., 184

Ohm, 153

Ohm's law, 160

Open circuit batteries, 154

Opera glass, 94

Optical disk, 95-97

Optical instruments, 92

Osmosis, 52

Parallelogram of forces, 23
Pascal's law, 42
Pendulum, 38
Phase, 175
Phonograph, 76
Photometry, 85
Pitch of sound, 75
Polarization, 154
Poles of magnet, 126
Post-office box, 165
Potential, 132
Potential energy, 35
Power transmission, 9
Pressure, 41
Pressure gauge, 53
Principle of machines, 5
Projection lantern, 92
Prony brake, 17
Pulley, 7
Pulley cone, 15

INDEX

199

Pump, 49

Quality of sound, 75

Radiation of heat, 122
Recording wattmeter, 181, 182
Reflection of light, 83
Refraction of light, 86
Resistance box, 164
Resonance, 72

Safety factor, 62

Saturated steam, 109

Screw, 14

Series dynamo, 147

Series motor, 181

Shadow, 81

Shearing strength, 64

Shunt circuit, 160

Shunt dynamo, 149

Simple dynamo, 132

Simple machines, 4

Siphon, 50

Slide valve engine, 110

Solid, 40

Specific gravity, 58

Specific heat, 103

Star connection, 177

Starting box, 180, 181

Static electricity, 187, 188

Steam engine, 110

Storage cell, 157, 158

Strain, 63

Stress, 62

Superheated steam, 109

Surface tension, 55

Switch board, 145

Symbols, 148

Telegraph, 142
Telephone, 186
Telescope, 94
Temperature, 99
Tensile strength, 63
Theory of magnetism, 129
Thermometers, 99
Three-phase A. C., 186
Torricellian tube, 46
Transformer, 169
Transmission of A. C., 133
Transmission of fluid pressure, 42
Transverse strength, 66
Turbine steam, 115

Units of force, 31

Velocity, 22
Velocity of light, 79
Velocity of sound, 70
Volt, 153
Voltmeter, 145
Voltmeter-ammeter method of

measuring resistance, 160
Wattmeter, 146, 182
Wave length, 71
Wave motion, 69
Weather map, 48
Weston differential pulley, 20
Wheatstone's bridge, 163
Wheel and axle, 7
Wireless telegraphy, 195
Work, 3

X-ray, 191, 192

YC 11428

578546

/ 2.

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