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BUTLER,SHELDON& COMPANY 



'^dUx-*7r'5^v^,o-o. qo 




HARVARD COLLEGE 
LIBRARY 




GIFT OF THE 

GRADUATE SCHOOL 
OF EDUCATION 



f 






^ 



) 



3 2044 097 017 313 



ELEMENTARY PHYSICS 



BY 

ELROY M. AVERY, Ph.D., LL.D. 

AUTHOR OF A SBBOES OF FHY8ICAI1 SCOENCB TEXT-BOOKS 



BUTLER, SHELDON & COMPANY, 

NEW YORK, PHILADELPHIA, CHICAGO. 






c . 



'"■"•; 



AVERY'S PHYSICAL .SCIENCE SERIES. 



FIRST LESSONS IN PHYSICAL SCIENCE. 

FOR USE IN GRAMMAR SCHOOLS. 

(By Dr. Avbry and Prof. Sinnott.) 



ELEMENTARY PHYSICS. 
A SHORT COURSE FOR HIGH SCHOOLS. 



SCHOOL PHYSICS. 
FOR HIGH SCHOOLS AND ACADEMIES. 



ELEMENTS OF CHEMISTRY. 



COMPLETE CHEMISTRY. 



" The Complete Chemistry " contains " The Elements of Chem- 
istry/' with an additional chapter on Hydrocarbons in Series, or 
Organic Chemistry. It can be used in the same class with " The 
Elements of Chemistry. " 



COPTBIQHT, 1897, BY 

SHELDON AND COMPANY. 
6 

■'*• ••h-=-f^n F^CiH THE 



':;.Tio*f 



C^j 



M 



' I ,'".',- r 



PREFACE. 



This book has been prepared because of a belief that it 
was needed and would be welcomed. More specifically, 
the hook is an attempt to meet the wants of schools that 
cannot give to the study the time required for the com- 
pletion of the author's larger work, and yet demand a 
book that is scientifically accurate and '"up to date," No 
efifort has been spared by author or publishers to make it 
worthy of the place it is intended to fill. Especial care 
has been taken to provide simple teaching experiments 
that do not l-eqmre expensive apparatus, and a good sup- 
ply of well-adapted laboratory exercises. The author 
trusts that these efforts will meet with the approval of 
those who use the book* 

It is not expected that every pupil will solve every 
problem or perform all of the laboratory work indicated 
in the "Exercises-" The pupil should do as much as 
possible^ but the good judgment of the wise teacher must 
be called upon to determine how much, and to select just 
what is best adapted to the needs and capacity of each 
member of his class. No aothor can. make a comfortable 
Procrustean bedstead, and there can be no satisfactory 
substitute for the living teacher, 

8 



4 PREFACE. 

Much of the matter in this book is wholly new, and 
some of the apparatus described was designed expressly 
for it. Especial acknowledgment is due to Miss Emma 
Hogan, assistant principal of the Woodland Hills Avenue 
School of Cleveland, to Mrs. Alton H. Smith, and to Mrs. 
Elroy M. Avery, for aid in the revision of copy. 
. Teachers using this book are advised to ask the Ziegler 
Electric Company, 141 Franklin Street, Boston, Mass., for 
a copy of their catalogue of scientific apparatus. 

The author will be glad to receive suggestions from 
teachers who use this book, and to answer any inquiries 
that they may make. He may be addressed at Cleveland, 
Ohio, 



CONTENTS. 



CHAPTER L — MATTER. 

L Domain of Fmybics ; Ditihioms of Mattbh ^ , * 7 

IL Properties of Matter , 10 

nL CONDITIONfl OF MaTT£R ....... 20 

CHAPTER n. — MECHANICS. 

I. Motion and Force .>>..*,. 29 

IL Work and Energy .....,,, 40 

in. Gravitation ,46 

IV. Falling Bopies - . . .40 

V. pENDULtJM p$ 

VI. Simple Machines 61 

VIL Mechanics of Liquids »..-.,, 72 

VIII. Mbcmakigb of Gabes &7 

CHAPTER m.— ACOUSTICS. 

I. Nature or SouTfo^ r^fo 69 

IL Velocitv, Reflection, and Refraction . , ♦ .107 

III. CBAKACTEJliaTlCS OF T0NK9 Ill 

IV. Co- Vibration 121 

V. Laws of Vibration 128 

6 



6 CONTENTa 

CHAPTER IV. — HEAT. 

PAGE 

L Natubk of Heat, Temperature, etc 134 

IL ProduCtiok ahd Traksferekce of Heat . . . .137 

ILL Effects of Heat 140 

IV. Measurement of Heat 140 

V. BSLATIOir BETWEEN HeAT AND WORK • . . .163 

CHAPTER v.— RADIANT ENERGY. 

L Nature of Radiation 157 

II. Light: Velocity and Intensity 158 

IIL Reflection of Radiant Energy 166 

IV. Refraction of Radiant Energy 175 

V. Spectra, Chromatics, etc. 186 

VL Interference, Diffraction, Polarization, etc. . .198 

Vn. A Few Optical Instruments 202 

chapter' VL— ELECTRICITY AND MAGNETISM. 

L General View : 

A. Static Electricity 208 

B. Current Electricity 220 

C. Magnetism 233 

IL Electric Generators, Electromagnetic Induction, etc. 248 

IIL Electrical Measurements 276 

IV. Some Applications of Electricity 283 

V. Electromagnetic Character of Radiation . . . 300 

APPENDIX 306 

INDEX 311 



CHAPTER L 



MATTER. 

I. THE STBUCTUEE, DIVISIOlSrS, Al^D CHAJ^GES 
OF MATTER. — FORCE, ETC. 

1. Physics, or Natural Philosophy, is the science of 
matter and energy. Science is classified knowledge, 
Matter is anything that *' takes up room." Energy is 
the power of doing work. We shall understand the 
meaning of 'these words better as we go on. 

(a) S^stanceif are the different kinds of matter, as water, wood, and 
BllreT. A b&d^ is any separate portion of matter, as a book, a table, or 
a star- M atte r is in desti- ucti ble. 

Structure of Matter. 

Experiment i, — Heat the mercury in the bulb of a common ther- 
mometer. The bulb remains full, but the liquid rises in the tube- 
There seems to be more mercury than there was before. How can 
this be? T lie re must be a greater number of particles, the particles 
must be larger, or the^ mmt be farther apart 

Experiment 3, — Make a common goose-quill pop-gun. Notice that, 
when you use it, the air confined between the two wads is made to 
occupy about half the space it did before. The air particles are re- 
ductjd in size or in number^ or are crowded together more closely* 
Ptrhaps the matter of which a body ts made does not actually Jill all the 
space that the body $eem$ to occupy* 

2* Structure of Matter, — Many facts indicate that mat- 
ter is not continuous ; that any part of it that we can per- 
ceive is a group of very small particles ; that no two of 

7 



8 ELEMENTARY PHYSIOS. 

these are in actual contact ; and that the minute particles 
of each group are held together by certain forces. 

3. Divisions of Matter. — Matter appears to us as masses. 
Masses are made up of molecules, and, in nearly every case, 
molecules are made up of atoms. 

4. An Atom is the smallest quantity of matter that can 
enter into chemical combination, thus forming a molecule. 
It is the chemical unit of matter, and is considered indi- 
visible. There are more than seventy kinds of atoms now 
known. The study of atoms belongs to chemistry rather 
than to physics. 

5. A Molecule is a quantity of matter so small that it can- 
not be divided without changing its nature. It is the physi- 
cal unit of matter, and can be divided only by a chemical 
process. Molecules are believed to be in ceaseless motion. 

(a) If a drop of water could be magnified until it appeared to be 
as large as the earth on which we live, each molecule in the drop thus 
magnified would still look smaller than a base-ball. Even in dense 
solids, molecules are separated by spaces that are large as compared 
to their own size. It is probable that the distance between two mole- 
cules is several times the diameter of a molecule. Some molecules are 
very complex. The common sugar molecule contains forty-five atoms 
of three kinds. There are innumerable kinds of molecules. The 
nature of the molecule determines the nature of the substance. 

6. A Mass is a group of molecules. 

7. Forms of Motion. — It is probable that each of these 
three divisions of matter has its own form or mode of 
motion. The motion of a mass is often called molar or 
mechanical motion. The motion of a bullet is an example. 
The motion of the molecules in a mass constitutes heat. If 
a bullet strikes a target, the shock that destroys the molar 
motion of the bullet increases the vibration of the mole- 



DIVISIONS OF MATTER. ft 

cales of which the bullet is composed- These molecular 
vibrations constitute heatp The motion o£ atoms within 
the molecule has not been proved, 

(a) Fancy a million fliea surrounrted by a shell. If each fly repre- 
sents a molecule, the contents of the shell represent a mass. Imagine 
this shell to be thrDwn through the air. The motion of the shell I'ep- 
reaents molar motion. As the shell is moving through the air, the flies 
are moving slowly among themselves within the shell. This motion 
of the flies represents molecular motion^ and is a very dilTei-ent thing 
from the motion of the shell. When the shell strikes the ground, the 
raolar motion is destroyed, but the molecular motions are increased, 
for the flies ai'e set in much more rapid motion by the shock. This is 
just about what happens when a hullet is fired against u target. 

8* Physical and Chemical Changes* — -Any hange that 
alters the constitution of the molecule, and thus affects the 
identity of the substance, is a chemical change. The burn- 
ing of a candle or the rusting of iron is a chemical change. 
Any change in matter that does not alter the constitution 
of the molecule is ^physical change^ Heating or magnet- 
izing a piece of iron is a physical change; the iron remains 
iron, 

9. Phenomena, etc, — Any directly observed change iu 
matter is a phenoinenon, A supposition (or scientific 
guess) advanced in explanation of phenomena is an hy- 
pothesis. The value of an hypothesis increases with the 
variety of the phenomena for which it offers an exclusive 
explanation. As this variety increases, the hypothesis rises 
to the rank of a theory. When the theory has acquired so 
high a degree of probability that it is aeeepted by the 
judicious as an estahliii^hed truth, i.e., when it is easier 
for men to believe it than to doubt it, it becomes a law^ 
e,g., the law of gravitation. "Law means a rule which 
we have always found to hold good, and which we expect 
always will hold good." 



10 ELEMENTARY PHYSICS. . ' 

10. Force. — Force signifies the immediate cause that pro- 
duces^ or tends to produce^ a change in the velocity or the 
direction of motion of a body ; i.e., a push or a pulL 



1. What is science? 

2. What is matter? 

3. What is energy? 

4. What is physics? 

5. What is a substance? 

6. What is a body? 

7. Do you think that matter is continuous or not, and why? 

8. Define the several divisions of matter. 

9. State the diiference between mechanical and molecular motion. 

10. Give an original illustration of a physical and of a chemical 
change. 

11. What is the diiference between an hypothesis and a theory ? 

12. What is a physical phenomenon? 



n. THE PROPEETIES OF MATTER. 

11. Properties of Matter. — Any quality that belongs to 
matter^ or is characteristic of it, is called a property of mat- 
ter. Any property that can be shown without a chemical 
change is a physical property. 

12. Extension is that property of matter by virtue of 
which it occupies space. It has reference to length, 
breadth, and thickness. 

13. Measurement of Extension. — There are two linear 
units in use in this country, — the English yard and the 
international meter. From these are derived units of 
area and of volume. 

. (a) It is assumed that the pupil is familiar with the units of 
weights and measures of both the English and the metric systems. 



THE PROPERTIES OF MATTER. 



11 



B 



The scientific unit of length is the centimeter, the one-hundredth 
part of the meter. See Fig. 1. 

BXBRCISBS. 

1. With a yardstick, measure the length of your class-room. 

2. Compute the equivalent of ^ that length in 
meters and decimals thereof. 

3. With a meter stick, measure the length of 
your class-room, and compare the result with that 
obtained by computation. 

4. With a meter stick, measure the door of your 
class-room, and make an outline sketch thereof, 
using the scale of 1 : 20. 

5. With a yardstick, measure the width of your 
class-room. Draw a ground plan of the room, 
using the scale of one inch to the yard. 

6. Make the necessary measurements and com- 
pute the capacity of the room (a) in cubic feet, 
(b) in cubic meters, (c) in gallons, (r/) in liters. 

7. With the meter stick, measure the length of 
this leaf of your book. Place the stick on its edge 
so as to bring the graduation as close as possible 
to the object to be measured. Bring, not the end 
of the rod, but one of the centimeter marks, even 
with one end of the leaf, and from the stick read 
the length of the page accurately to 0.1 mm. You 
can divide the smallest division on the scale into 
tenths by the eye. 

8. Make two fine marks with a sharp knife on 
a table-top or other board, as far apart as is con- 
venient, the distance being more than a meter. 
Measure as accurately as possible the distance be- 
tween the marks, estimating fractions of milli- 
meters to tenths, and expressing the results in 
meters. Do this ten times. Measure the same 
distance in inches, estimating fractions of the smallest division on the 
scale to tenths. Express these results in inches and decimals of an 
inch. Do this ten times. Divide the average number of inches by 
the average number of meters; the quotient will he the number of 
inches in a meter. Express in millimeters the measures that you took 



*L . - 
w _ _ 



■J 

^ 1 

J ! . ^ 

J: 

-] itf 



5 



3 



Fig. 1. 




12 ELEMENTARY PHYSICS. 

in meters, and divide the average namber of millimeters by the aver- 
age number of inches; the quotient will be the number of millimeters 
in an inch. 

9. With the graduate, i.e., a glass vessel graduated to 
cubic centimetei-s, measure 250 cu. cm. of water and 
pour it into* the liter measure. See how often you can 
repeat the work without overflowipg the measure. It 
will require careful attention to tell just when the water- 
level reaches the required mark. The liquid climbs up 
the sides of the glass, so that it is difficult to tell where 
the water-level really is. The eye of the observer should 
be placed on the level of the required mark on the grad- 
uate. 

j.,Q^^ 10. Compute the number of cubic centimeters in a 

quart. Test your result by the actual measurement of 
water or of diy sand. 

14. Mass and Weight. — The mass of a body is its 
quantity of matter. The weight of a body t«, in general 
terms^ the measure of the earth's attraction for it. The 
mass of a given body is constant; its weight is not. 

(a) If the given body could be carried to the moon, its weight there 
would be the measure of the attraction existing between the body and 
the moon. The mass of the given body would be the same as it was 
on the earth, but its weight would be less. 

(b) The word " mass " is here used with a meaning different from 
that employed in § 6. This double use of the word is unfortunate. 

15. Units of Mass and Weight. — The English unit of 
mass is the quantity of matter contained in the avoirdupois 
pound. The international unit of mass is the kilogram. 
For many scientific uses, this unit is too large ; and the 
gram, which is the one-thousandth part of the kilogram, 
is generally used. The units of weight measure the 
attractions of the earth for the units of mass, and receive 
the same names. Under like conditions, a comparison of 
weights may be substituted for a comparison of masses, 
since at any one place the weight varies as the mass. 



THE PROPERTIES OF MATl^ER. 18 

(a) The mass of a gram wag intended to be, a ad is very nearly, 
equal to the quantitj of matter in one cubic centimeter of distilled 
water at the temperature of i^ C* 

BXERCISiBS. 

1. Provide an iron ball an inch or two in diameter ^ a base-ball, and 
a croquet-ball. Measure the mass of each of the three balls in English 
units. 

2. Determine^ iu international units, the ma^ of a nickel 5-cent 
coin ; of the iron balL 

3. Place a meter stick on the table, and by its edge place two rec- 
tangular wooden blocks (crayon boxes will answer for rough work). 
Place the croquet-ball between the blocks. Move the blocks as near 
each other as possible with the ball between them, keeping one face 
of each block in contact with the straight edge of the meter stick. 
What is the diameter of the ball? 

4. (a) In similar manner, measure the diameter of the base-ball* 
(b) On paper, draw a circle of that diaii;eter. (c) With a sharp pen- 
knife, cut out the circle ; pass the base-ball through the hole* 

5. {a) Compute the number of cubic centimeters of water that will 
weigh as much as the iron balh (See Exercise 2.) (b) Place the iron 
ball in a tumbler or beaker tilled with water; catch and measure in 
the graduate the water that runs over, (c) From this measure, deter- 
mine the volume (cubic centimeters) of the ball. 

6. If alcohol is 0.8 times as heavy as water, how much will 1,250 
en. cm. of alcohol weigh? 

7. Using international units, weigh a dry, clean bottle. Fill tha 
bottle with cold water, wipe its outside surface dry, and weigh the 
filled bottle. From the weight of the water, determine the capacity 
of the bottle. Test the result by measurement with the graduate. 

8. Wtiat part of a liter of water is 250 grams of water? 

&. If sulphuric acid is 1.8 times as heavy as water, what weight of 
the acid will a liter flask contain ? 

10. Weigh each of iiye bullets at least three times. For each bul- 
let take the average of the several weighings as the true weight. Com- 
bine these several averages to iind the weight of the average bullet* 
Count the bullets in a cupfuL Multiply the weight of the average 
bullet by the number of bullets, and compare the result with the mass 
of all the bullets as determined by weighing them together. 




14 ELEMENTARY PHYSICS. 

Inertia. 

Ezperiment 3. — Upon the tip of the forefinger of the left hand, 
place a common calling-card. Upon this card, and directly over the 
finger, place a cent. With the nail of the middle finger of the right 

hand let a sudden blow or "snap" 
be given to the card. A few trials 
will enable you to perform the ex- 
periment so as to drive the card away, 
and leave the coin resting upon the 
finger. Repeat the experiment with 
the variation of a bullet for the cent, 
and the open top of a bottle for the 
Fia. 3. finger-tip. 

Ezperiment 4. — Suspend an iron ball weighing at least 10 pounds 
by a long, stout string from a firm support. Safety-valve weights 
may be bought for a few cents a pound, and answer admirably for 
many such purposes. Tie a string strong enough to carry a weight of 
several pounds to the ball, and with sudden motion pull the ball hori- 
zontally. If the pull is sudden enough, the: string will break without 
giving much motion to the ball. Replace the stout stiing by a thread, 
,and by a series of gentle, well-cimed pulls, set the ball swinging. 
When it is in rapid motion, try to stop that motion by a single pull 
on the thread. It will be seen that the ball can go ahead as well as 
hang back, 

16. Inertia signijiea the tendency of matter at rest to 
remain at rest, and of matter in motion to move with uni- 
form velocity in a straight line. 

Porosity. 

Experiments. — Pour 30 cu. cm. of water into a long test-tube. 
Carefully add 20 cu. cm. of strong alcohol, holding the tube so that 
the latter may run down its side and rest upon the water without 
mixing with it. Gently bring the tube into a vertical position, mark 
the height of the liquid in the tube, close the mouth of the tube with 
the thumb, and thoroughly shake the two liquids together. Notice 
again the height of the liquid contents of the tube. It looks as if 
some of the water and some of the alcohol had been forced into the 
same space, in spite of the impenetrability of matter. 



THE PROPERTIES OF MATTER 15 

Experiment 6. — Fill a glass tumbler with large shot or peas, and 
then see how much well-dried sand or salt you can add. Perhaps 
what happens here is analogous to what happened in Experiment 5. 

17. Porosity is that property of matter by virtue of which 
spaces exist between the molecules, A body does not com- 
pletely fill the space it seems to occupy. 

As a result of this, it sometimes seems 0^2.OsO 

as if two bodies were in the same space ^2A_J^A^ 

at the same time. The molecules of oOo(fjo(^^ 

one body fit into the spaces between 0°0°0°C 

the molecules of the other body. AOaQsOs, 

noDoCX > 

(a) When iron is heated, the molecules are « , 

pushed further apart, the pores are enlarged, 
and we say that the iron has expanded. When a piece of iron or lead 
is hammered, it is made smaller, because the molecules are forced 
nearer together, thus reducing the size of the pores. Cavities or cells, 
like those of bread or sponge, are not properly called pores. 

18. Strain and Stress. — Any change in the shape or size 
or volume of a solid is called a strain. Thus, if a mass of 
metal becomes compressed, or bent, or twisted, or distorted 
in any way^ it is said to experience a strain. The force 
that produces a strain is called a stress. 

Elasticity. 

Experiment 7. — Squeeze a rubber ball. Stretch a rubber band. 
Stretch a spiral spring. Bend a thin strip of steel, wood, or whale- 
bone. In each case the volume or form is restored to its initial condition 
when the distorting force ceases to act, 

19. Elasticity is that property of matter by virtue of which 
bodies resume their original form or size when that form or 
size has been changed by any external force. There is an 
elasticity of volume, and an elasticity of form or figure. 
The former is peculiarly a property of gases and liquids ; 
the latter, of solids. 



16 ELEMENTARY PHYSICS. 

(a) The elasticity of a body may be developed by pressure, by 
pulling, by bending, or by twisting. 

Molecular Attraction. 

Experiment 8. — Dip a finger into water. Upon removing it, notice 
that it is wet, that water adheres to it. Hold the finger pointing 
downward, and notice that a drop of water gathers at the finger-tip. 
That drop is composed of many particles that cling together, or cohere. 
Something makes the water particles cling to each other and to the finger, 
in spite of the force of gravity. 

Experiment 9. — Cut a lead bullet so as to present two flat, clean 
surfaces. Pi'ess the two parts together with a slight twisting motion. 
They will cling together. 

Experiment 10. -^ Take a sheet of gold leaf in your fingers, and 
try to pick the metal off with the fingers of the other hand. Some 0/ 
the gold will stick to your fingers, 

20. Cohesion and Adhesion. — Cohesion is the force that 
holds together like molecules; adhesion is the force that holds 
together unlike molecules. 

(a) This force acts only at insensible (molecular) distances. Let 
the parts of a body be separated by a sensible distance, and we say 
that the body is broken. If the molecules of the parts can again be 
brought within molecular distance of each other, cohesion will again 
act, and hold them there. This may be done by simple pressure, as 
in the cases of wax, freshly cut lead, broken ice, and many powders ; 
it may be done by welding or melting, as in the case of iron. 

21. Hardness is that property of matter hy virtus of which 
some bodies resist any attempt to force a passage between 
their particles. The relative hardness of two substances 
is determined by finding out which of them will scratch 
the other ; e.g., we know that glass is harder than copper 
because it will scratch copper. 

Tenacity. 

Experiment xx. — Cut several strips of manilla paper about 5 by 
25 cm. Turn each end of each strip over, and fasten the edges 



THE PROPERTIES OF MATTER. 



It 



with glue so as to make a good hem at each eod. In the loop at one 
end of the paper strip insert a a tout rod the length of which exceeds 
the width of the paper strip. Fasten this rod hy a stout string or 
wii^ bail to a nail in a board or table-top. Siniilarly fasten the other 
end of the atrip to the hook of a good spring-balancCi held as shown 
in Fig, 5. Pull steadily with the balance and in a line with its length, 
so as to avoid, as far as possible, all friction of the sliding bar to 
which tlie hook is attached* Watch the index of the balance all the 
time, looking directly down upon it so as to avoid the error of parallax. 
Continue to pull until the paper breaks. Be careful that the recoil 
of the hook does not injure your hands. Repeat the experiment 




Fro, 6. 



with several similar strips, recording after each test the maximum 
reading of the index. If the index does not rest over the zero mark 
when the balance is in a horizontal position, the pro[ier correction 
should be made for each reading taken. The average of the^e several 
readings will be a fair expression of the sirenjjih of the paper. Make a 
similar series of teats with similar strips of paper twice as wide» 
Compare the two average lesults- Compute the strength of a strip 
2.2 cm. wide, and esppri mentally verify the result. 

22, Tenacity is that property of matter hy virtue of which 
gome bodies resist a force tending to pull their particles 
asimder- 

(a) Like hardness and other characteristic properties of matter, 
tenacity is a variety of cohesion. For any given material, it has been 



18 ELEMENTARY PHYSICS. 

found that tenacity is proportional to area of cross-section; e.g., a rod 
with a sectional area of a square inch will carry twice as great a load 
as a rod of the same material with a sectional area of a half square 
inch ; a rod 10 cm. iu diameter will carry four times as great a load 
as a similar rod 5 cm. in diameter. 

SXBRCISBS. 

1. Name some property of matter not mentioned in the text. 

2. Can any substance exist without extension? 

3. How many inches are there in a meter ? 

4. Which is the larger, a liter or a cubic decimeter? 

5. Which is variable, the mass of a given body or its weight ? 
Why? 

6. What is the relation between a cubic centimeter and a 
milliliter? 

7. What is a gram? 

8. Can an atom be destroyed? 

9. Which is the natural condition of matter, rest or motion? 

10. On what property of matter does compressibility depend ? 

11. If you thrust a knitting-needle into a mass of dough, is the 
hole thus made a pore ? What is a pore ? 

12. It may be said that strain and stress are related as cause and 
effect. Which is cause, and which is effect ? 

13. If you have made a series of careful measurements, each of 
which differs a little from all the others, what is the safest one to 
adopt ? 

14. What is the length of a full line as printed in this book ? 
Place the graduated edge (not the side) of the decimeter rule on the 
paper, with some plainly visible mark, £is 0.5 or 1 cm. (not the end of 
the rule), at one end of the printed line. Always use a rule in this 
way for accurate measurements. 

15. Tightly pinch the leaves of this book (inside the covers) 
fcetween two small blocks that come flush with them at the top. 
Remove some of the leaves so that those that remain make a layer 
just 1 cm. thick. Count the leaves, and compute in decimals of a 
millimeter the thickness of an average leaf of this book. 

16. Determine the gauge numbers of four pieces of wire. Use the 
notches around the edge of the steel plate (Fig. 6), and not the larger 
circular openings at the inner end of the notches. Introduce the 
wire into the slit which admits it with a very slight pressure, and 



THIi PROPERTIES OF MAriER. 



19 




Fig. Ci, 



note the nmnbar correaponding to that slit. Be sure that the wire is 
i\ot rusty, diity, or bruised at the poiiit wiiere it is gauged* It is 
convenient to buy audi 
wire wound on spools. 

17. Wind 25 turns 
of No. 30 ajinealed wire 
around a cylinder an 
inch or more in diame- 
ter, being careful that 
the successiv^e turns are 
as close as possible to 
each other. Measure the 
total width of the wire 
band on the cylinder, 
and compute the diam- 
eter of No- 30 wire. 
Compare your result 
with the table giveu in 
the appendix:. 

18. With the outside 
calipeiiSi measure the diameter of the iron ball used in Exercise 1 
on page 13. Compare the result then obtained and recorded in your 

notebook with that now found. 

19. Measure tlie diameter and lengtii of a 
small cylinder. If, by measuring the rod at 
short intervals with the calipers^ you find 
that ita diameter is not uniform, use the aver- 
age of your several measurements, (a) Com- 
pute the surface area of the cylinder. 
(h) Compute the Yolumc of the cylinder. 

20. fileasui^ the length, and the inside and outside diameters of 
a metal tube. If you have no inside calipers, 

bend a piece of annealed wire into a V^shape, and 

use that. (<x) Compute the total surface area of 

the tube, {h) Compute the volume of metal in the 

tube, (c) Test your result by the displacement of water, aa you did 

in Exercise o on page IS, 

21. (a) With the inside calipers, measure the diameter of the 
tumbler on the ini^ido, at the bottom and at lite top. From these 
measurements determine the average diameter of the tumbler. Place 




Fio. 7. 



Fm. 8. 



20 ELEMBHTABY PHYSICS. 

a straightedge (e.g., a ruler) across the top of the tumbler in the line 
of a diameter. Measure the pei-pendicular distance from the bottom 
of the tumbler to the under side of the straightedge. Compute the 
capacity of the tumbler in cubic centimeters, (h) Fill the tumbler 
with water and pour the water into the graduate, and thus test the 
accuracy of your previous measurements and computation. 



III. THE THREE CONDITIONS OF MATTER, ETC. 

23. Conditions of Matter. — Matter exists in three conr 
ditions or forms^ — the solid^ the liquid^ and the ae'riform. 
Gases and vapors are aeriform (i.e., having the form of 
air). Liquids and aeriform bodies are fluids. 

24. A Solid 18 a body whose molecules change their rela- 
tive positions with difficulty. Such bodies have a strong 
tendency to retain any form that may be given to them, 
and can sustain pressure without being supported at the 
sides. 

25. A Fluid is a body whose molecules easily change 
their relative positions. Fluids cannot sustain pressure 
without being supported at the sides. 

Note. — Review Experiment 8. 

26. A Liquid is a body whose molecules easily change their 
relative positions^ yet tend to cling together. Such bodies 
adapt themselves to the form of the vessel containing 
them, but do not retain that form when the restraining 
force is removed. Their free surfaces are always hori- 
zontal. Water is the best type of liquids. 

27. An Aeriform Body is one whose molecules easily 
change their relative positions^ and tend to separate from 
each other almost indefinitely. Gases remain aeriform 
under ordinary conditions, while vapors resume the solid 



THE THREE CONDITIONS OF MATTER. 



21 



or liquid form at ordinary temperatures. Atmospheric 
air is the most familiar type of aeriform bodies. 

2S. Changes of Condition. — Many substances, like iron 
and gold and water, may be made to exist in all of these three 
forms by suitable adjustments of temperature and pressure. 
The identity of ice, water, and steam is familiar to all- 

(a) Experiiiients with electric discharges in high vacuums have 
given results that many persons think prove the existence of a fourth 
condition of matter. For matter in this extremely thin or ftttenuated 
form, t^e name **nMliaut matter" has been ppopc^ed. 

Solution. 

Experiment ra. — Into a tumbler hall full of water, drop a few lumps 
of sugar. Stir the eon tents of the glass until the solid disappears > 

Experiment 13, — Mix 50 g. of pulverized ammonium nitrate and 
25 g. of pulveri:Eed ammouium chloride (sal-itninioniac). Put the mix- 
ture into 75 cu. cm. of cold water in a tumbler, and stir the substances 
together with a small testrtube containing a little cold water. Xotice 
that the solids disappear. Carefully observe the condition of the 
water in the test-tube, 

29. Solution is the transformation of matter from the solid 
or gaseous form to the liquid form hy means of a liquid 
called the solvent or menstruum* The process is essentially 
a chiinge o-f niolecular condition. When the change is 
from the solid to the liquid form, there is an absorption 
of heat and a fall of temperature, as is seen in freezing 
mixtures. The solution of a gas iu a liquid is accom- 
panied by a release of heat and a rise of temperature. 
When the solvent has dissolved as much of a given sub- 
stance as it can, the sohdion is said to be saturated, 

EXBRCISBS, 

1. What 13 the difference between a fluid and a liquid? 

2, Are triolecules of waler larger or smaller than those of steam? 
Give a reason for your answer. 



22 



ELEMENTARY PHYSICa 



8. Are intermolecular spaces greater in water or in steam? Give a 
reason for your answer. 

4. Considered with reference to the three conditions of matter, are 
cohesion and iieat cooperative, or antagonistic ? 

5. Ammonia gas is very largely soluble in water. Will such a solu- 
tion of the ammonia warm or cool the water? Refer by number to 
the paragraph of this book that contains a statement that supports 
your answer. 

6. Fill a clear glass tumbler with fresh hydrant or well water. Fill 
a similar vessel with water that has recently been well boiled. Set 
both in a moderately warm, quiet place, and let them stand over night. 
Examine the walls of the two tumblers, and account for the diffei-euce 
in their appearance. 

Superficial Films. 

Experiment 14. — Fill a tumbler brimming full of water. With a 
pipette (Fig. 9), or a pen-filler, add more water, drop by drop and 
patiently, until the water in the tumbler is actually 
heaped up higher than the edges of the glass. Try to 
imagine an invisible skin stretched over the liquid sur- 
face to keep it from overflowing the edge of the tumbler. 

30. Superficial Films. — Every liquid may 
be regarded as bounded by a superficial film. 
This film is physically different from the in- 
terior of the liquid mass, and is a seat of 
energy* Two of the properties of these films 
are called surface viscosity and surface tension. 

f^Q. a Surface Viscosity. 

Experiment 15. — Carefully place a fine sewing needle npon the 
surface of water. With care, and perhaps repetition, the needle may 
be made to float. If you have serious 
trouble in making it float, draw it between 
the fingers or wipe it with an oily cloth. A 
hair-pin bent slightly near the tips may be 
used to lower the needle so that neither end shall touch the water be- 
fore the other. Closely examine the surface of the water. Notice 
that the neetUe rests in a little depression or bed, just as it would il 
the surface of the water was a thin skin or membrane. 




Fig. 10. 



THE THREE CONDITIONS OF MATTER* 



n 



3L Surface Viscosity. — Tka superficial film of a liquid 
ts, atf a Tuie^ comparatively hard to move or breaks 

(a) A solution of soap in water had greater surface viscosity than 
has pure water, hence its aclaptability to the formation of bubblea^ 
The surface vjauoaity of alcoboL is very feeble. A rough sea ia some- 
times smoothed by [>ouniig oil upon it. The new surface is compara- 
tively rigid, and less easily broken into surf. 

Surface Tension. 

Expfrrltnent i6. — Float two sewing needles an the surf ace of water 
about a quarter of an inch apart, and lt;t a drop of alcohol fall upon 
the water between them, Notice that tlie needles separate as if they 
Lad been supported on a stretched membrane^ and the membrane had 
been cut so that its parts might 8e2:iarate, each carrying its needle with 
it. 

Experiment t?, — Blow a soap-bubble without detaching it fi-om the 
pipe or tube. Leave the tube ope n» atjd notice that the film contracts, 
diminishing the size of the bubble, and expelhug some of the air from 
it. The current of air from the interior of the bubble may be made 
to deflect the flame of a candle. 

32. Surface Tension, — Experiments ^low i:\\\it a liquid 
surface (as the surface that separates water from «tr, or oil 
from water^ is in a stffte of teuHiori Kinitlar to that of a 
membrane stretched equally in all directions. Pure water 
has a surface tension hic^her than that of any other sub- 
stance that is liqnitl at nnlinary temperatures, except mer- 
cury; hence the mixture of any other liquid with water 
lessens the surface tension of the water, as in EKp^ii- 
inent 16< 

(rt) The exterior and interior surf aces of a soap-bubble act like two 
she e ts of i ndi a-r i ib be r s tretc h e d e q uatl y i u 1 e n gth an d hre ei d th . The i r 
tendency to contract forces air from the interior of the bubble^ as in 
Experiment 17. 

{f}) If a roughened wire ring is dipped into a strong solution of 
Castile soap, to which glyceriii has been added^ a plans film will he 
found sti-etched n cross it To such a ring, tie a loop of thread and 



24 



ELEMENTARY PHYSICS. 





Fig. 12. 



secure another film, as shown in Fig. 11. With a hot wire, puncture 
the film inside the tliread loop, aud the tension of the film will pull 

the thread outward in 

all directions, as shown 

in Fig. 12. 

Capillary Attraction. 
Experiment i8. — 

Partly fill a thin, clean 

beaker (or tumbler) 

with water, and a sim- 
ilar one with clean 

mercury. Notice that 

the upper surfaces of 

the two liquids are 

level except at the edges 
near the glass. Notice, further, that the water is lifted at the edge by 
the glass, and that the mercury is depressed. 

Experiment 19. — Support a clean glass rod verti- 
cally in the water, and notice that the liquid is lifted 
by the rod, as shown in Fig. 13. Remove the rod. 
Notice that it is wet. Wipe the rod dry, and place it 
similarly in the mercury. Notice that this liquid is 
depressed by the rod. Remove the rod, and notice 
that it was not wetted by the mercury. 

Smear the glass rod with oil, and place it in the 
water, as before. Notice that the water is depressed 
^^^s^s^^^^ thereby. Remove the rod, and notice that it is not 
FiQ. 13. wetted by the water. 

33. Capillary Attraction. — The phenomena just noticed 
depend largely upon surface tension, and illustrate what 
is called capillary attraction. The truth suggested by our 
experiments is general: All liquids that wet the sides of 
solids placed in them will be lifted^ while those that do not 
will be pushed down. 

Capillary Tubes. 

Experiment 20. — Wet the inner surfaces of several clean glass tubes 
of small and different diameters (1 mm. and less) to remove the ad- 




THE THREE CONDITIONS OF MATTEE. 



25 



hering air-film. Support tke tubes vertically in pure 
wafer. Notice that the water rises in the tubes, 
as shown in Fig. 14 j that^ the less the diameter 
of the tube, the greater the elevation of the water; 
and that the free surface of the water in the tube is 
concave. 

Remove the tubes, and similarly support them 
in clean mercury. Notice that the mercury is de^ 
presfied lu the tubes; that, the less the diameter of 
the tube, the greater the depiessioEi j and that the 
free surface of the mercury in the tubes is eonveat, 

34, Capillary Tubes* — The effect of a capillary tube 
upon a liquid is due to the surface teusiou of the liquid. 
This tension produces an upward pulL where the liquid 
surface is concave, and a downward pressure where the 
liquid surface is convex, 

(a) Familiar illustrations of capillary action are numerous, such as 
the action of blotting-paper, aponges, lamp-wicks, etc- 




Fig. 14, 



Diffusion. 

Experiment at . — Wet the inner surface of a clear tani bier or beaker 
with strong ammonia water, leaving a few drops of the liquid in the 

bottom. Cover ifc with a 
sheet of writing paper, 
^Moisten the inner sur- 
face of a like vessel with 
fttrong hydrochloric (mu- 
riatic) acid. Invert the 
second vessel over the 
firstj mouth to mouth, so 
that the contents of ttie 
two vessels shall he sepa- 
rated only by tlae paj>er. 
Each vessel is filled with 
Fig. 15, an invisible gas. Remove 

^ the paper, and notice tfiat 

the invisible gases quickly diffuse iuto each other and form a dense 
cloud* 




26 



ELEMENTARY PHYSICS. 






35. Diffusion. — The gradual and spontaneous mixing of 
two fluids that are placed in contact is called diffusion. It 
takes place even in opposition to the force of gravity. It 
is explained only by the motions and attractions of the 
molecules 'of the two fluids. 

(a) Even with our most powerful microscopes, we cannot follow 
these motions or detect any currents. The motions are molecular, 
not molar. 

36. Kinetic Theory of Gases. — A perfect gas consists of 
free, elastic molecules in constant and rapid motion. Each 

molecule moves in a 
• • • -> straight line and with a 

uniform velocity until it 
strikes another molecule 
or the vessel in which 
the gas is contained. 
When these molecules 
encounter each other, 
they behave much as 
billiard balls would do 
if no energy was lost in 
their collisions. Each 
molecule travels a very 
small distance between 
one encounter and an- 
other, so that it is every 
now and then changing its velocity both in magnitude 
and direction. The magnitude of the velocity may be 
computed; one direction is just as likely as any other. 
Figure 16 represents the path that a molecule might 
travel in passing through a group of fixed molecules. It 
may help you to get a correct idea of the motion of a 
molecule, although, in fact, all of the molecules are in 




Fig. ic. 



THE THREE CONDITIONS OF MATTER. 



27 



motion as well as the one that is represented by the open 
circle* 

(a) It will be noticed that the di:Sfusion of gases, as illustrated in 
Experiment 21, is a necessary consequence of these molecular motions* 
The blows upon the walls of the contaitiing vessels are so numerous, 
that their total effect is a continuous, constant force or pressure. The 
paLh of a njolecule between any two successive colli sious is called its 
free path, 

EXBRCISBS. 

1* Why can yOu not blow a soap- bubble with pure water? 
2» Why can you not float a 20-penny nail on water as you can a 
fine needle? 

3. To svhat geoiuetrical truth does the surface tension of a soap- 
bubble give an illustration ? 

4. In Experiment 19, we saw that mercury is depressed by a glass 
rod placed iu it. How can you determiue whether a clean strip of 
tin or ziuc will lift or depress mercury? 

5. What kind of motion is illustrated by the diffusion of two 
gases into each other? 

ti. State the kinetic theory of gases- 

7* Is the free path of a molecule of steam greater or less than the 
free path of a molecule of liquid wflter? Wliy ? 

8. Carefully heat a tumbler, and half fill it with boiling water. 
Cover it with cardboard- Invert a second 
tumbler over the first. Watch the apparatus 
for a few minutes. If you notice any change 
in the appearance of the upper tumbler, find 
out whether it is clue to a change in llie inner 
or the outer surface of the gla#^s. What prop- 
erty of the cardboard is thus illustrated? 

9. Make of Ko. 124 iron wire a skoloton of a 
square pyramid with edges 5 cm. long, and ^^^- ^^' 
attach a handle, as shown in Fig. 17, Also make two wire rings 
6 cm. in diameter and with wire handles. Make a soap-bubble solu- 
tion as follows: Dissolve 5 g. of Castile soap, in line shavings, in 
200 cu, cm. of warm water, recently boiled, shaking the mixture from 
time to time. When the soap is dissolved, allow the solution to stand 
for several liours. Pour off the clear liquid, and to it add 125 cu. cm. 
of good glycerin, shaking the two thoroughly together. 




28 ELEMENTARY PHYSICS. 

(a) Slip a piece of rubber tubing over the shank of a glass funnel 
about 10 cu\. across the top. Dip the edges of the funnel into the 
solution, catch a film, and blow as large a bubble as you can. 

(b) Blow a bubble with a comtnou day pipe. Detach it from the 
pipe, and catch it on one of the iron rings. Bring the other ring into 
contact with the bubble on the other side, and draw the bubble into 
cylindrical form. 

(c) Immerse the pyramidal frame into the solution, and try to 
secure a film on each side, thus forming a hollow, regular penta- 
hedron. 



CHAPTER n, 

MECHAiaCS: MASS FH7SICS. 

L MOTION AND FORCE. 

37. Mechanics is the branch of phym^m that treata of 
forces and their effects^ 

38. Motioay Velocity, and Acceleration. — Motion is change 
of pomition. Velocity is rate of motion; its magnitude is 
expressed by saying tliat it is such a diBtaiice in such a 
time, as ten miles an hour, or one meter a second. Ve- 
locity may be uniform or variable- A variable velocity is 
accelerated or retarded. The change of velocity per vmit of 
time (^.^., the rate of change of velocity) i& called accelera- 
tion. The acceleration is positive ( + ) if the velocity is 
accelerated, and negative ( — ) if the velocity is retarded. 

(a) A body passing over unit of apace in unit of time has uuit 
velocity. The velocity per second multiplied by the number of 
seconds measures the distance traversed in any given time by a body 
moving with a uniform velocity. Representing these functions by 
/ for di stall ce^ v for velocity per second, and t for time counted in 
seconds, we Lave 

l = vt (1) ^ 

From tJiis fuiidamental formula we derive algebraically the fol- 
lowing : — 



I 



p = -j and f = — 
t y 

If two of these values are known, they may be substituted in one of 
these formulas, and the third value obtained thence. If a body moves 

29 



30 ELEMENTARY PHYSICS. 

at the rate of 50 feet per second for 12 seconds, and the distance 
traversed is desired, formula (1) is applicable : — 

1 = i?f =: 50 X 12 = 600, the number of feet 

Note. — It is assumed that the pupil understands the easy manipu- 
lations of a simple algebraic equation. If he does not, the teacher 
should explain to him such as he finds in this bouk. 

(6) Represent uniform increase of velocity (i.e., a constant accel- 
eration) by a. In / seconds, a body starting from rest will have 
acquired a velocity represented by at, 

V = at (2) 

This is the formula for a body starting from a state of rest, and hav- 
ing a unifor.mly accelerated velocity. Half the sum of the initial aud 
the final velocities is the average velocity. In the case now under 
consideration, the initial velocity was zero, and the final velocity was 
at; therefore, the average velocity of a body starting from rest, and 

gaining a velocity uniformly accelerated for t seconds, is "*" or } at. 

The average velocity multiplied by the number of time-units equals 
the distance traversed ; therefore, 1= i at xt, or 

l = iat^. (3) 

Equating the values of t in equations (2) and (3), we may deduce 
the following: — 

(c) To find the distance passed over in any particular unit of time, 
it may be necessary to subtract the distance traversed in f — 1 units, 
from the distance traversed in t units, the whole time. Representing 
this distance traversed in a single time-unit by /', we have 

/' = ia<2-ia(<-l)«; 
therefore, /' = J a(2 / - 1). (">) 

Example : Suppose that a body moving with a uniformly accelerated 
velocity starts from rest and passes over 7 meters in the first second. 
How far does it move in the next 3 seconds? If the body moves 
7 meters in the first second under the conditions stated, its average 
velocity for that second is 7 meters, and its velocity at the end of 
that time is 14 meters. All of this velocity is gained in this single 



MOTION AND JOECE 



31 



second ; hence ^ a = 14, Starting from rest, it moves 4 seconds j 
hence, t = 4. Substituting these vahies in forniiila (3), 

l = im^ = \ X 14 X 16 = 112, 

the distance passed over in 4 seconds. From this, subtract the dia- 
tance passed over in the first second, and we have 105, the number 
of meters passed over in the other 3 seconds, as called for. This 
solution illustrates the method of applying physical formulas to 
physical problems, 

39* Momeatum. — The result of the action of a force upon 
a body depends upon the mass of the body as well as upon 
its velocity* If m represents the mass of the body, and t? 
its velocity, the product, mu, will represent its quantity of 
motion* This product is called momentum. 

(a) The momentum of a hody having a mass of 20 pounds aud a 
velocity of 15 feet is twice as great as that of a body having a mass of 
5 pounds and a velocity of 30 feet. The unit of inomentuin has no 
naine* 

40. Laws of Motion, — The following propositions are 
known as Newton's Laws of Motion:—* 

(1) Every body continues in its state of rest or of uniform 
motion in a straight line unle&s compelled to change that state 
by an external force^ 

(2) Every change of motion (momentum^ is in the direction 
of the force impressed^ and is proportionate to it, 

(3) Action and reaction are equal and opposite in direc- 
tion. 

EXERCISES. 

1, Find the momentum of a 5(K)-pound ball moving 500 feet a 
second, 

2, By falliug a certain time^ a 20Opound ball has acquired a 
velocity of ^2L6 feet, What i» its momentum ? 

3, A boat that is moving at the rate of 5 miles au hour weighs 4 
tons ; another that is moving at tlie rate of 10 miles au hour weighs 2 
tous» How do their momenta compare? 



82 ELEMENTARY PHYSICS. 

4. What kind of motion is caused by a single, constant force 1 
Illustrate your answer. 

5. A stone weighing 12 ounces is thrown with a velocity of 1,320 
feet per minute. An ounce ball is shot with a velocity of 15 miles 
per minute. Find the ratio between their momenta. 

6. An iceberg of 50,000 tons moves with a velocity of 2 miles an 
hour. An avalanche of 10,000 tons of snow descends with a velocity 
of 10 miles an hour. Which has the greater momentum? 

7. Two bodies weighing respectively 25 and 40 pounds have equal 
momenta. The first has a velocity of 60 feet a second. What is the 
velocity of the other ? 

8. Two balls have equal momenta. The first weighs 100 Kg., and 
moves with a velocity of 20 m. a second. The other moves with a 
velocity of 500 m. a second. What is its weight ? 

9. A railway train moves at the rate of 40 miles an hour. Express 
its velocity per second in feet. 

10. If the mean distance of the earth from the sun is 92,390,000 
miles, and it requires 16 minutes 36 seconds for a ray of light to pass 
over the diameter of the earth's orbit, what is the velocity of light 
expressed in miles per second ? 

41. Units of Force. — The gravity unit of force is the 
weight of any standard unit of mass^ as the kilogram or 
pound. The absolute unit of force is the force that^ acting 
for unit of time upon unit of mas$^ will produce unit of 
acceleration (i.e., change of velocity^. 

(a) The foot-pound-second (F.P.S.) unit of force is the force that, 
applied to one pound of matter for one second, will produce an accel- 
eration of one foot per second. It is called a poundal. The centi- 
meter-gram-second (C.G.S.) unit of force is the force that, acting for 
one second upon a mass of one gram, produces an acceleration of one 
centimeter per second. It is called a dyne* The poundal and the 
dyne are absolute units and are invariable in value. 

(b) A force is measured in poundals or dynes by multiplying the 
number of units of mass moved by the number representing the accel- 
eration produced, only such units being used as are indicated by the 
initials F.P.S. or C.G.S. respectively. The acceleration may be de- 
termined by dividing the total velocity that the force has produced 
by the number of seconds that the force has acted. 

r 

V 



MOTION AND PORCE. 



33 



(c) The simplest way of measuring a force is to use a dyuainoiii- 
eter, of which the spring-balance (Fig. 18) is a faiuiliar exajuple* 
The dynamometer may be graduated in pounds, grams, 
poundals, or dynes. 

BXBRGISSS. 





1. A railway train 120 yardy long moves at the rate of 
30 miles an hour. How long will it take to pass completely 
over a bridge 120 feet long? 

2. At the sea-level at New York a force of 23 pounds ^^Bt= 
equals how many poundals? (Se^ § 68*) An». SOi^ 

3. Under the same conditiotirt, a force of 5 Kg. eqnala 
how many dynes? (See § 68.) An$. i,mO,mO, 

4. A poundal equals how mauy dynes? 

5. Compare the momentum of a 64-pound cannon ball 
moving with a velocity of 1,300 feet per second, with that 
of an ounce bullet moving witk a velocity of 400 yarda per 
second. 

6. What property of matter is illustrated in the removal 
of dust from a carpet by beating ? Fro, is. 

42. Graphic Representation of Forces- — Forces matf he 
represented by lines^ the point of application determining 
one end of the line, the direction of the force determining 
the direction of the line, and the magnitude of the force 
determining the length of the line. 

(a) It will be noticed that these three elements of a force are 
the ones that define a line. By drawing the line ag above in- 
dicated, the units of force being numerically equal to the units 

of length, we have a complete graphic 
representation of the given force. 
The unit of length adopted in any 
such representation may he deter- 
mined by convenience ] but, the scale 
once determined, it must be adhered 

> ^ to throughout the problem. Thus, 

-piQ, 19. the diagi'am represents two forces 

applied at the point J?. These forces 

act at right angles to each other. The airow heads indicate that the 

forces represented act from B toward -^1 and C respectively. The 

D 



84 ELEMENTARY PHYSICS. 

force that acts in the dii-ection, BA^ being 20 lbs., and the force acting 
in the dii*ection, BC, being 40 lbs., the line, BA, must be one-half as 
long as BC. The scale adopted being 1 mm. to the pound, the smaller 
force will be represented by a line 2 cm. long and the gi-eater force 
by a line 4 cm. long. 

43. Resultant. — Motion may be produced by the joint 
action of two or more forces. The single force that will 
produce an effect like that of the component forces acting 
together is called the resultant. The single force that, act- 
ing with the component forces, will keep the body at rest 
is called the equilibrant. The resultant and the equilibrant 
of any set of component forces are equal in magnitude, and 
opposite in direction. 

The point of application, direction, and magnitude of 
each of the component forces being given, the direction 
and magnitude of the resultant are found by a method 
known as the "composition of forces." 

Composition of Forces. 

Experiment aa. — Suspend two similar spring-balances from any 
convenient support, as shown in Fig. 20. From the wooden rod 
carried by their hooks, suspend a known weight Be sure that the 

dynamometers hang vertical, and 
i^3 therefore parallel. Record the 
readings of A and B. Carefully 
B measure the distances CD and DE, 
and record them. If the dyna- 
mometers are accurate, the work 
^^ has been carefully done, and the 
weight of the rod is inconsiderable, 
the results should show that 

TT = ^ + A and that 1 = ^. 

^ «A ^ CD 

Fio. 20. 

If the weight of the rod is con- 
siderable, place the rod in the hooks, and notice the readings of the 
dynamometers. Then hang the weight from the rod, and let A and 



I 



MOTION AND FORCE. 85 

B represent the increcute in the readings of the dynamometers. .The 
result should be as given above. 

44. Composition of Forces. — Forces may be compounded 
in several ways, the more important of which are the fol- 
lowing : — 

(1) When the component forces act in the same direction 
and along the same line. The magnitude of the resultant is 
then the sum of the given forces. Example : Rowing a boat 
down-stream. 

(2) When the component forces act in opposite directions 
and along the same line. The magnitude of the resultant is 
then the difference between the given forces. Motion will 
be produced in the dii-ection of the greater force. Ex- 
ample: Rowing a boat up-stream. 

(3) The resultant of two forces that act in the same direc- 
tion along parallel lines has a magnitude equal to the sum of 
the magnitudes of the components^ and its point of applicor 
tion divides the line joining the points of application of the 
components inversely as (he magnitudes of said components. 
This principle is iflustfated by Experiment 22. 

(4) When two equal parallel forces act at different points 
on a body and in opposite directions^ the arrangement consti- 
tutes what is called a couple. It produces rotary motion^ 
and the components can have no resultant, 

(5) When the component forces have a given point of 
application (i.e., when they are ^^ concurring forces ^^^ and 
act at an angle with each other^ as when a boat is rowed 
across a stream^ the resultant may be ascertained by the 
^^parallelogram of forces.'^ 

Parallelogram of Forces. 

Experiment 23. — Support two spring-balances, B and C, from P 
and S, two nails in the frame of the blackboard. Hook them, with 
a third dynamometer, D, into a small ring, Z, as shown in Fig. 21. 



36 



ELEMENTARY PHYSICS. 



Pull«8teadi1y on / in some downward direction. Mark on the board 
the deuters of the rings, Z and /, and record the readings of the 
three dynamometei-s. Remove the apparatus, and through the points 
indicated draw on the board t!ie lines ZP^ ZS, and ZI. Using any 
convenient scale, lay off the lines ZE, ZA, and Zf, proportional to 
the readings of the respective dynamometers. Complete the parallelo- 




Pig. 21. 



gram, ZETA. Draw the diagonal, ZT, measure its length, and 
determine the magnitude that it represents according to the scale 
adopted. If the work has been accurately done, ZI and ZT will be 
equal in value, and form a straight line. ZT is the resultant, and 
Zr is the equilibrant, of the components, ZE and ZA . Place the 
apparatus horizontal and repeat the work. 

45. Parallelogram of Forces. — In the diagram, let AB 
and AC represent two forces acting upon the point, A, 



MOTION AKD FORCE. 



37 




Tio, 22L 



Draw the two dotted lines to 
complete the parallelogram. 
From A, the point of applica- 
tion, draw the diagonal, AD. 
This diagonal will be a com-- 
plete graphic representation of 
the resultant, li two foices, 
siieh as those represented in the diagi-ani, act aimultrtne- 
oualy upon a body at A^ that body will move over the 
path repreiiented by AI>^ and come to rest at D. 

(«) If more than two forces coucuri tha resiiUaiit of any two may 
be combiDed with a third, their resultant with a fourth, and so on- 

Tlie ' last diagonal will represent the 
resultant of the given fotcea. As is 
indicated by Fig. 2Sj it is not neces- 
sary that all of the forces act in the 
same plarie, 

(6) Tiie converse of the composition 
of forces, i*e., the proce»s of Jinding ih^ 
components to which the gken forve is 
equivalent is called the resolution of forces. 
Represent the given force by a line ; on this line as a diagonal, con- 
struct a parallelogram. The two sides of the parallelogram that meet 
at either end of the diagonal will represent the component forces. 
An infinite number of such parallelograms may l>e constructed on 
a single diagonal unless some condition is added to make the prob- 
lem definite. 




FjO). 23k 




Fro. 24. 
Reaction. 



Experiment 34**— Make a railway of two wooden strips 1^ inches 
by J inch, and about 6 feet long, fastened together by three or five 
crosspieces, as shown in Fig. 24. The distance between the rails 



88 ELEMENTARY PHYSICS. 

should be about an inch. Place the railway on a board, and fasten 
down the middle crosspiece with a screw. Spring up the ends, and 
support them by books or wooden blocks. At the toy shop, get 
several large glass marbles, or other elastic balls, and place them 
on the middle of the railway. Bring one ball to the highest point of 
the track, and let it roll down against the others. Ball No. 1 gives its 
motion to No. 2, and comes to rest ; No. 2 gives it to No. 3, and in 
turn comes to rest The energy is thus passed through the line to 
No. 7, which is driven some distance on the up grade, as to the posi> 
tion shown by the dotted line at 8. Repeat the experiment after 
replacing the middle ball by a lead ball of the same size. 

Experiment 25. — From any convenient support, as the door frame, 
hang two bags of shot or of sand by strings of equal length and so 
that they will just touch each other. They should be of equal weight. 
If one is drawn aside and let fall against the other, both will move 
forward, but only half as far as the first would had it met no resist- 
ance. The gain of momentum by the second is due to the action of 
the first. It is equal to the loss of momentum by the first, which loss 
is due to the reaction of the second. If the experiment is repeated 
with elastic balls (glass or ivory), it will be found that the first ball 
will give the whole of its motion to the second, and remain still after 
striking. The balls may be suspended by gluing a narrow strip of 
leather to each, leaving a little loop at the middle of the strip for the 
fastening of the string. 

46. Elasticity and Reaction. — The effects of action and 
reaction are modified largely by elasticity, but never so as 
to destroy their equality. 

47. Reflected Motion i% the motion 'produced in a body by 
the reaction between it and another body against which it 
strikes. A ball rebounding from the wall of a house or 
from the cushion of a billiard table is an example of 
reflected motion. 

(a) The angle, ABD, included between the direction of the moving 
body before it strikes the reflecting surface, and a perpendicular to 
that surface drawn from the point of contact, is called the angle of 
incidence. The angle between the perpendicular and the direction of 
the moving body after striking is called the angle of reflection. 



MOTION AND FORCE, 89 

48. Law of Reflected Motion. — When the bodies are per- 
fectly elastic^ the angle of incidence is equal to the angle of 
reflection^ and lies in the same plane. When the elaHiielty 
of the bodies is imperfect^ the angle of reflection is greater 
than the angle of incidence. 

(a) If a glass or ivory ball is shot from A (Fig. ^5) against an 
elastic surface at 5, the center of the aeniicircle^ it will be reflected 
back to C, making the angles, ABD iintl CBD, equal. If the ball or 
the body at B is not perfectly elastic (e.g., if a lead hul] is used)^ the 
angle of reflection will be greater than the angle ot incidence. 




Fig. 2j, 

49. Curvilinear Motion. — When a bill at the end of a 
string is whirled around the hand, there is a pull on the 
string. The ball is pulled from the straight path which it 
tends to follow in accordance with the first law of motion, 
and is thus compelled to move in a curved line. There 
are evidently two forces involved in the production of such 
a motion. The resistance offered by the body to its deflec- 
tion from a rectilinear path is due to its inertia, and is 
commonly called by the ill-chosen name, "centrifugal 
force." From this point of view, centrifugal force may he 
defined as the reaction of a moving body against the force 
that makes it move in a curved path, 

(a) Examples and effects of this so-called centrifugal force may he 
suggested as follows: the water flying from a revolving grlivdHtone, 
erosion of river-beds, a pail of water whirled in a vertical circle, the 



40 ELEMENTARY PHYSICS. 

inward leaning of the circus horse and rider, elongation of the equa- 
torial diameter of the earth, etc 



1. Represent graphically the resultant of two forces, 100 and 150 
pounds respectiyely, exerted by two men pulling a weight in the same 
direction . Determine its value. 

2. In similar manner, represent the resultant of the same forces 
wliea the men pull in opposite directions. Determine its value. 

3. Suppose an attempt is made to row a boat at the rate of 4 miles 
an hour directly across a stream flowing at the rate of 3 miles an hoar. 
Determine the direction and velocity of the boat. 

4. A flag is drawn steadily downward 64 feet from the masthead of 
a moving ship. During the same time, the ship moves forward 24 feet. 
Represent the direction and length of the actual path of the flag. 

5. A sailor climbs a mast at the rate of 3 feet a second. The ship 
is sailing at the rate of 12 feet a second. Over what space does he 
actually move during 20 seconds ? 

6. A force of 1,000 dynes acts on a certain mass for one second, and 
gives it a velocity of 20 cm. per second. What is the mass in grams ? 

Arts, 50. 

7. A constant force, acting on a mass of 12 g. for one second, gives 
it a velocity of 6 cm. per second. Find the force in dynes. 

8. A force of 490 dynes acts on a mass of 70 g. for one second. 
What velocity will be produced? Ans. 7 cm. per second. 

9. Draw two lines bisecting each other at right angles, and mark 
the ends of the lines to represent the cardinal points of the compass, 
as in a map. From the intersection of the two lines draw another 
line to represent the velocity of a United States cruiser steaming south 
of southeast at the rate of 19 miles an hour. Determine the rate of 
the southerly and the easterly motions of the ship. Record on your 
dia<;ram the scale used. 



II. WORK AND ENERGY. 

50. Work. — In physical science, the word " work" siffni- 
fies the overcoming of resistance of any kind. Work implies 
a change of position, and is independent of the time taken 
to do it. When a force moves a body, it is said to do work 



WORK AND ENERGY. 41 

on that body. When the expansive force of steam presses 
against the piston of an engine and overcomes the resist- 
ance, i.e,, when it moves the pistoriy it does work. 

(a) A man who is suppoi-ting (not lifting) a heavy weight may be 
putting forth great effort, but he is not doing work. 

51. Units of Work. — Four work-units are in use ; viz., 
the foot-pound and the kilogrammeter (gravitation units), 
and the foot-poundal and the erg (absolute units). 

(1) The foot-pound is the amount of work required to raise 
one pound one foot high against the force of gravity, 

(2) The kilogrammeter is the amount of work required to 
raise one kilogram one meter high against the force of gravity, 

(3) The foot-poundal is the amount of work done by a force 
of one poundal in producing a displacement of one foot. The 
number of foot-pounds multiplied by the number of feet 
in the acceleration due to gravity (§ 68) equals the num- 
ber of foot-poundals ; thus, at New York, a foot-pound is 
equivalent to 32.16 foot-poundals. 

(4) The erg is the amount of work done hy a force of one 
dyne producing a displacement of one centimeter. Since there 
are 980,000 dynes in the weight of one kilogram of matter 
at New York, a kilogrammeter there equals 98,000,000 ergs. 
A foot-poundal is equivalent to 421,402 ergs; a foot-pound 
is equivalent to 32.16 times that many ergs. 

(a) To get a numerical estimate of work done, we multiply the 
number of units of force by the number of units of displacement : — 

Work done =fl. 

Since the resistance overcome is numerically equal to the force acting, 
the work done may be computed by multiplying, in a similar manner, 
the resistance by the space : — 

Work done = wl. 

In this formula, w represents the ivpistance; and U the length or dis- 
tance. When the body is simply lilted against the force of gravity, 



42 ELEMENTARY PHYSICS; 

w represents weight. A weight of 25 poands raised 3 feet, or one 
of 3 pounds raised 25 feet, represents 75 foot-pounds. A weight of 
15 kilograms raised 10 meters represents 150 kilogram meters. 

62. Activity and Horse-Power. — In measuring work 
done, no consideration is given to the time taken. In 
considering an engine or other agent that is to do the 
work, the time required is a very important thing. The 
activity of an agent is the rate at which it can do work^ and 
is measured hy the work it can do in unit time. The unit in 
most common use for the measurement of activity is the horse- 
power. It represents the ability to do 650 foot-pounds per 

second, 

jj-j^ ^pounds xfeet 

' "" 550 X seconds' 

(a) The practical unit of electrical activity is the watt. One horse- 
power equals 746 watts. 

63. Energy is the power of doing work. Energy of mo- 
tion is called kinetic energy ; energy of position is called 
potential energy. 

(a) A falling weight or running stream possesses energy of motion. 
Before the weight began to fall, it had the power of dohig work by 
reason of its elevated position with reference to the earth. When the 
water of the running stream was at rest in the lake among the hiils, 
it had a power of doing work, an energy that was not possessed by the 
waters of the pond in the valley below. 

(6) Kinetic and potential energies are convertible each into the 
other. Imagine a ball thrown upward with a velocity that will keep 
it in motion for two seconds. At the end of one second it has lost 
some of its velocity, and hence some of its kinetic energy; but it has 
gained an elevated position, and has, therefore, acquired some poten- 
tial energy. At the end of another second it has no velocity, and, 
therefore, no kinetic energy. But the energy with which the ball 
began its upward flight has not been annihilated ; it has been wholly 
converted into potential energy. If we ignore the disappearance (not 
loss) of the energy expended in overcoming the resistance of the air, 



WORK AND ENERGY. 



48 




the ball would, when permitted to fall, reach the level from which it 
started with undiminished velocity and kinetic energy. 

(c) The pendulum affords a good illustration of kinetic and poten- 
tial energy, their equivalence and 
convertibility. When the pendulum 
hangs at rest in a vertical position, as 
Pa, it has no energy at all. K we 
draw the pendulum aside to b, we 
raise it through the space, ak ; that is, 
we do work upon it, and endow it 
with potential energy. As it swings 
through its arc, the two types of 
energy vary from all potential at b or 
c, to all kinetic at a. At every in- 
stant, and at every point of the arc, 
the sum of the kinetic and potential 
energies (K,E. + P.E,) is an unvarying 
quantity, always equal to the energy originally spent in swinging it 
from a to b. 

Velocity and Energy. 

Experiment 26. — Into a pail full of moist clay or stiff mortar, drop 
a bullet fi'om the height of one yard. Notice the depth to which the 
bullet penetrates. Drop the bullet from a height of four yards. Ic 
will strike the clay with twice the velocity, and penetrate four times 
as far as it did before. This suggests that perhaps an increase in 
the velocity of a given body increases the energy of that body more 
rapidly than it increases the momentum. 

64. Kinetic Energy Measured. — The energy of a mpv- 
ing body may be measured by the units used in measuring 
work ; i.e., in units of force and displacement. Neither 
the direction of the motion, nor the manner of expendi- 
ture, changes the amount of onergy expanded. We may, 
therefore, find to what vertical height the- given velocity 
would lift the body (§ 70), and thus determine its energy 
in foot-pounds or kilogrammeters. 

(a) Representing the weight of a body by w, and the vertical 
height to which its velocity can carry it by I, it is evident that the 



44 ELEMENTARY PHYSICS. 

kinetic energy can do to x / units of work. From the formulas for 
falling bodies (§ 69), we may derive the following : — 

in which g represents the acceleration due to gravity, i.e., 33.16 feet or 
080 cm. Substituting this value of / in the equation given above, 
we have 

Kinetic Energy — ^. 

If to is measured in pounds and v in feet, this measures the energy 
in foot-pounds ; if to is measured in kilograms and v in meters, it 
measures the energy in kilogrammeters. 

(b) From Newton's second law of motion (§ 40) it follows that a 
force may be measured by the momentum it produces. Representing 
force by/, mass by m, and acceleration by a, we have 

f = ma. 

But the measurement of work (§ 51, a) introduces the additional 
factor, /, representing the number of units of displacement. Intro- 
ducing this factor into the equation above, we have, for work or 
kinetic energy, 

K.E.=Jl = mal. 
In § 38 (b) we have 

^ = ^' 
2a 

Substituting this value of / in the second member of the equation 
above, we have 

K.E,=Jl = '^=imv\ 

If m is measured in pounds and v in feet, this formula gives a 
numerical expression for foot-poundals ; if m is measured in grams 
and V in centimeters, it gives that expression for ergs. 

55. Potential Energy Measured. — In the case of a body 
raised above the surface of the earth, its potential energy 
may be measured, 

(1) In gravitation units, by the product w x h, 

(2) In absolute units, by the product m x h x ff. 



WORK A«D ENERGY. 



m 



56* ConserYation of Energy, — Except for friction and 
the resiatance o£ the air, a swinging pendulum would 
oscillate forever. Energy is withdrawn from the pendu- 
lum to overcome these impediments, but the energy thus 
withdrawn is not destroyed. What becomes of it will be 
seen when we study heat. The truth is that energy is as 
indestructible as matter 3 this is what is meant by the ^''con* 
servation of energyJ"' 

SXEROISBS. 

L What is the horse-power of an engine that will raise 8,250 
poiuida 1T5 feet in 4 miuutesV 

2. A ball weighing 192*90 poumis is rolled with a velocity of 100 
feet a second. How much energy has it? An&. 30,000 foot-pounda» 

3. A projectile weighing 50 Kg. ia thrown obliquely upward with 
a velocity of 19.0 m. How much kinetic energy h-is it? 

4* What is tlje horse-power of an engine that can raitje 1^500 
pounds 2,376 feet in 3 minutes? Ans. 36 H.P. 

5, A cuhic foot of water weighs about 02 i ponnds. What is the 
liorse-power of an engirje that can raise 300 cubic feet of water every 
uiinute from a mine 132 feet deep? 

0. A body weighing 100 pounds moves with a velocity of 20 miles 
per hour. Find its kinetic energy. 

7. How long will it take a ^-horse-power engine to raise 5 tons 
100 feet? 

8. How far can a 2-hoi-se-power engine raise 5 tons in 30 sec- 
onds? 

9. What is the boi-se-power of an engine that can do 1,650,000 
foot-pounds of work in a minute ? 

10. What ia the horse-power of an engine that can raise 2,370 
pounds 1,000 feet in 2 minutes? 

IL A railway car weighs 10 ton^. Fi-om a state of rest it is moved 
50 feet, when it is moving at the rate of 3 milea an hour. If tlie 
resistances from frictioi^ etc., are 8 pounds per ton, how many foot- 
pounds of work have been expended upon the car? (First find the 
work done in overcoming friction, etc-, through 50 feet, which is 50 
footpounds X 10 X 8. To this, add the work done in giving the car 
kinetic energy.) 

12. Determiue, by the composition of forces, whether three con- 



46 



ELEMhNTARY PHYSICS. 



earring forces with magnitades of d, 6, and 12 pounds, respectively, 
can be in equilibrium. 

13. Explain why a soap-bubble blown at one end of a tube con- 
tracts, and forces a current of air out of the other end of the tube. 



III. GRAVITATION, ETC. 

57. Gravitatioii. — Every particle of matter in the uni- 
verse lias an attraction for every other particle. This 
attractive force is called gravitation. 

58. Law of Gravitatioii. — The mutual attraction between 
two bodies varies directly as the product of their masses^ and 
inversely as the square of the distance between their centers 
of mass. For example, doubling this product doubles the 
attraction ; doubling the distance quarters the attraction ; 
doubling both the product and the distance halves the 
attraction. 

59. Gravity. — The attraction between the earth and 
bodies upon or near its surface is a form of gravitation 

that is commonly called gravity. 
Its measure is weight. Its direc- 
tion is that of the plumb line, 
vertical. 

60. The Weight of a terrestrial 
object is the measure of the attrac- 
tion between it and the earth. The 
weight of a body at one place on 
the surface of the earth may differ 
from its weight at another place, 
because the earth is not a per- 
fect sphere and its density is not 
Fig. 27. uniform. 




p 



GRAVITATION if 

61. Lav of Weight. — Bodies weigh most at the surface 
of the earth^ For bodies in the earth's crm^t^ the welcfM 
varies approximately as the distance from the center. For 
bodies above the earth's surface^ the weight varies inversely 
as the square of the distance from the center. 

62. Center of Mass. — A body's center of mass is a 
point the distance of which from any plane is equal to 
the average distance of the whole masis from the same 
plane. The same point may he the center of gravity. 

(a) The center of gravity may be considered the point of applica- 
tion of the resultant of many equal and parallel forces, one of which 
acts upon each particle of the body. 

(6) In a fi'eely falling body, no matter how irregular iU fonn or 
how nearly indescrihable the curvea made by any of its projecting 
parte, the line of dlrec^ioti in which the center of ma«3 moves ia a 
vertical line* 

(c) In some bodies, as a ring or box or hollow sphere or cask^ the 
center of Enass does not lie in the matter of which the body is com- 
posed, 

63. The Base. — The side on which a body rests is called 
its base. If the body ia supported on legs, as a chair, tlie 
base is the polygon formed by joining the points of support. 

64. Equilibrium, — A body supported at a single point 
will rest in equilibrium when a vertical line passing through 
its center of mass, i.e., the line of direction, also passes 
through the point of support- A body supported on a 
sui-face will rest in equilibrium when the line of direction 
(§ 62, b} falls within its base. The center of mass will be 
supported when it coincides with the point of support, or 
is in the same vertical line with it. When the center of 
mass is supported, the whole body ia supported and rests 
in a state of equilibrium. 

(a) When a body is supported in such a way that a slight diaplaee- 
inent raises ite center of maes, it ia said to be in ttahle equilibrium. 



48 



ELEMENTARY PHYSICS. 



When such a displacement lowers the center of mass, the body is 
said to be in unstable equilibrium. When sucli a displacement neither 
raises nor lowers the center of mass, the body is said to be in neutral 
or indifferent equilibrium, 

(jb) The stability of a body is measured by the amount of work 
that must be done to overturn it. This amount may be increased by 
enlarging the base, or by lowering the center of mass, or both. 

(c) When the body rests uix)n a point, as does the sphere, or upon 
a line, as does the cylinder, a very slight force is sufficient to move it, 
no elevation of the center of mass being necessary. 

BXBRCISBS. 

1. Suppose the earth to be solid. How far below the surface 
would a 10-pound ball weigh only 4 pounds?. 

Solution. — As the weight is to be reduced six tenths, it must be 
carried 0.6 of the way to the center. 

Ans. 4,000 miles x 0.6 = 2,400 miles. 

2. On the same supposition, what would a body weighing 550 
pounds on the surface of the earth weigh 3,000 miles below the sur- 
face? Ans. 137 J pounds. 

3. Two bodies attract each other with a certain force when they 
are 75 m. apart. How many times will the attraction be increased 
when they are 50 m. apart? Ans. 2\. 

4. Why does a person stand less firmly when his feet are parallel 
and close together than when they are more grace- 
fully placed ? 

5. Why can a child walk more easily with a 
cane than without? 

6. Why will a book placed on a desk-lid stay 
there, while a marble will roll off ? 

7. Why is a ton of stone on a wagon less 
likely to npset than a ton of hay similarly placed ? 

8. Why have the Egyptian pyramids great 
stability ? 

9. A boy placed a step-ladder as shown in 
Fig. 28, and it stood. Why? He then climbed to its top, and it fell. 

Why? 

10. Drive small tacks into the frame of a slate at adjacent corners. 
Tie the middle of a stout thread to one of the tacks. Fasten a small 
weight to one end of the thread, and support the apparatus from the 




^f 



Fig. 28. 



TAiLlNG BODIES, 49 

ctber end. Mark on the slate the direction in whkh the thread 
crosses it. Similarly support the skte by the other tack, and mark 
the direction of tlie thread by another Hue- Place the iiiteraection of 
the two lines over the end of the fingerj and aee if the slate is hal- 
aticed. The point tliu.s located appi'oxiiuately represents what? 

11. Cut a rectangle from cardboard. Draw its two diagonals. 
Balance the cardboard to see how near the center of mass coincides 
with the center of area. Can the center of mass lie on the surface 
of snch a body ? 

12. Drive a wire nail into a vertical support, and cut off the head 
of the naiL Bore several holes tlirough an irregnlarly shaped board 
near its edges. Using one of tlieae holes, hang the board on tlie naiL 
From the nail^ hang a chalked plumb line. When the plumb line has 
come to rest, " snap "it so as to make a vertical line on tbe board. 
Change the pnaiLion of the board, the nail pa^ssjng through another of 
the holes. Clialk the line, suspend and **snap" aa before. Place the 
intersection of tlie two chalk lines over the etid of the finjijer, and see if 
the board then balances. Using another hole, similarly chalk another 
line, and see if the three lines have a common point of intersection. 

13. Cut a piece of board 20" long, a" wide at one end, and 7'' 
wide at the other end. Find a point on the surface of the board 
as near as possible to the center of mB^s^ and over it paste a patch of 
black paper one inch in diameter. On the satne side of the board, 
and a foot or so from the other paper, paste a patch of red paper 
about 2" in diameter- Toss the board up edgewise in the open air, 
so that it will turn end over end, carefully observing the motion of 
the two paper patches relative to each other. Kecord and explain 
what you see. 



; IV. PALLmG BODIES, 

65* Freely Falling Bodies- — Wheii a body is left unanp- 
ported and free to move under the influence of the foree 
of gravity and without any resistance, it is a freely falling 
body. 

(n) If we ignore the Tesbtance of the air, the laws for falling 
bodies may, without seiisible error, be considered the same as fur 
uniformly accelerated motion. 



50 



BLEMENTART PHYSICS. 



Compariaon of Velocities. 

Szperimeiit 27. — From the upper window, drop simultaneously 
an iron and a wooden ball of the same size. Be careful that your 
fingers do not *♦ stick " to one ball longer than to the other. Notice 
that the two baUs of different weight strike the ground at practically 
the same time. 

66. Velocities of Falling Bodies. — When a feather and 

a cent are dropped from the same height, the cent reaches 

the ground first. This is because the feather meets with 

laore resistance from the air in proportion to its 

A mass. The resistance may be avoided by drop- 

A ping them in a glass tube from which the air has 

Vr been removed. The resistances may be neaily 

equalized by making the two falling bodies of 

the same size and shape but of different weights, 

as in the preceding experiment. 

(a) When water falls over a high precipice, the resist- 
ance of the air breaks part of it into spray before it 
reaches the bottom. In a vacuum, water falls as a solid 
as may be shown with a water-hammer, an instrument 
made by partly filling a stout glass tube with water, boil- 
ing the water that the steam may expel the air, and seal- 
ing the tube. 




Fig. 29. 



Impeded Fall. 



Experiment 28. — Tack a strip of wood half an inch square to the 
straight edge of a plank 16 feet long. Fasten metal strips an inch 
wide to the sides of the wooden strip so as to make a double-track way 
which should be straight and smooth. Divide the edge of the plank 
on one side of the track into 16 foot-spaces, plainly marked. Raise 
one end of the plank a foot higher than the other. Place a glass or 
an iron ball at the top of the inclined track. Notice how often the 
class-room clock ticks in a second. Place a finger on top of the ball, 
thus holding it ready for a start. Repeat the word " tick " in unison 
with the clock until you "feel" the rhythm of its swing, and, just at 
the moment of a " tick," lift the finger from the ball, which will begin 
to roll down the track. Notice and record the position of the ball at 



PALLING BODIES- 



SI 



the end of succe^ive seconds. To locate the ball at the end of the 
allotled peviod, place on the upper side of the half-iuch stiip a \YOoden 
bbck just wide enough to hold iU position, and just thick enough to 
produce an easily audible click when struck by the ball. By trial, 
place this block so that the tick and the click shall coincide. Repeat 
your observation 3j and averaj^^e the resnlts of similar trials* The 
greater the number of carefully conducted trials, the more valuable 
will be your averages. 

The ball will roll down the inclined plane ^ about 1 foot in the first 
second, 4 feet in 2 seconds, 9 feet in 3 seconds, 16 feet in 4 seconds, 
etc. The average resnlts may he tabulated as follows : — 



Vuinber o/ 


Spaces fallen 


Veiocities at the End 


Total Nuntber &/ 


Eevondi. 


mch Second. 


qf each Second. 


Spaces fallen. 


1 


1 


2 


1 


2 


d 


4 


i 


»' 


5 





d 


* 


7 


8 


15 . 


t 


2^-1 


2t 


r* 



Representing the Telocity gained each second (acceleration) by a, 
and, consequently, the value of each of our spaces by } a, we have, 
from the above, the already familiar formulas^ T = ia(2£ — 1); 
V = at\ and I = ^al^ (see § 38). 

67. Unimpeded Fall. — By giving a greater inclination 
tn the plane uaed in Experiment 28, the ball will roll more 
rapidly ; when the plane becomes yertical, we may say that 
the ball becomes a freely falling body. Our unit of space 
hhA now become 16.08 feet, or 490 centimeters. The ball 
will fall this distance during the first second, three times 
this distance during the next second, five times this dis- 
tance during third second, and so on. 

6S> Acceleration Due to Gravity^^In tlij^ latitude of 
New York, a freely falling body gains a velocity of 32.16 
feet, or 980 centimeters, during the first second of its falL 
It makes a like gain of velocity dining each subsequent 
second of its fall. This distance is, therefore, called the 



52 ELEMENTARY PHYSICS. 

acceleration due to gravity^ and is generally represented by 
the letter g. 

69. Formulas for Falling Bodies. — The foruiulas for 
freely falling bodies may be derived from those for uni- 
formly accelerated motion (§ 38) by substituting the deH- 
iiite quantity, g, for the indefinite quantity, a. Hence, we 
have for bodies starting from rest : — 

(1) v^gt. 

(2)/' =1/7(2^-1). 

(a) For bodies rolling down an inclined plane, these formulas may 
be made applicable by multiplying the value of g by the ratio between 
the height and the length of the plane. 

{b) None of these formulas involve any expressio*n for mass, thus 
indicating that the velocity of a falling body is not aflFected by its mass. 

70. Laws of Falling Bodies.— For bodies starting from 
rest, these formulas may be translated as follows : — 

(1) The velocity of a freely falling body at the end of any 
second of its descent is equal to 32.16 feet (980 cm,') multi" 
plied by the number of the second, 

(2) The distance traversed by a freely falling body dur- 
ing any second of its descent is equal to 16,08 feet (490 cm,) 
multiplied by one less than twice the number of the second. 

(3) The distance traversed by a freely falling body dur- 
ing any number of seconds is equal to 16.08 feet (490 cjn,) 
multiplied by the square of the number of seconds, 

(a) A body may be thrown downward as well as dropped. In sucii 
a case the effecf of the throw must be added to tlie effect of gravity. 

v = gt-^ V; Z'=^J5r(2/-l)+ F; l=lgt^+ Vt, 

When a body is thrown vertically upward, the time of the ascent may 
be found by dividing the initial velocity by the acceleration of gravity. 



]i 



FALLING BODIES. ' SS 

Projectiles. 

Experiment ag — From a strip of wood shaped like a meter stick 
or coTtimoii lath, cut a piece about 10 cm. long. Cut equal uotches at 
two corners^ a and Cj as shown in Fig< ^0. Nail the middle of this 
piece across the. eud of the rest of the lath, thus makiDg a T-abaped 
form* Clamp the o titer end of the lotiyf leg firmly in a vise so that 
thj edge flfij and the corresponding edge of the lojig piece, shall be 
horizontal and several feet above a level floor. Place lead bullets at 
a and €. Strike the long piece a sharp, hori- 
zontal blow near the crosspiece. One of 
the bullets will be shot horizontally, and the 
other will be dropped nearly vertically. 
Will the bullets strike the floor at the same 

time? Repeat the expei'iment several times, and do not expect more 
than approximate agi^einents* 

71. Projectiles^ — Every projectile is acted upon by fin 
impulsive force aiul the force of gravity* The path of 
a projectile is a parabolic curve, the resultant of these 
forces. 

EXERCISBS. 

1. What will be the velocity of a body after it has fallen 4 seconds? 
Soltdion : — v^gl^ 32.16 x 4 ^ 128.64. A ns. 128.64 feet, 

2, A body falls for several seconds. During one of these seconds 
it passes over 53(1.(14 feet. Which one is it? 

SoltjUion: — V-\g{2l- 1) 

530.64 ^ ie,OS X (2 t~l); .-.^^17. 

A ns, 17th second. 

3i A body wa=3 projected vertically apward with a velocity of 93,48 
feat. How high did it rise? 

l = iffi^^ 16.08 X t> = U4 J2. A ns. IUJ2 feet j 

4. How far will a body fall during the third second of its fall? 

5. How far will a body fall in 10 seconds? Atiu, IfiOS feet* 

6. How far in ^ second? Am. 4,02 feet. 

7. How far will a body fall during the first second and a hal£ of 
its fall? 



64 ELEMENTARY PHYSICS. 

8. A stone is thrown horizontally from the top of a tower 257.28 
feet high, with a velocity of 60 feet a second. Where will it strike 
the ground? Ans. 240 feet from the tower. 

9. A body was five seconds rolling down an inclined plane, and 
passed over 7 feet during the first second. Give (a) the entire space 
passed over, and (b) the final velocity. 

10. A body falls freely for 6 seconds. What is the space traversed 
' during the last two seconds of its fall? 

11. From the frame of a small pulley running with little friction 
suspend a weight of about 2 pounds. Place the wheel of the pulley 
so that it will run on a No. 10 wire tightly stretched between opposite 
sides of the room, one end of the wire being a little higher than the 
other. The wire may be tightened with a turnbuckle. Just above 
the wire, and parallel with it, stretch a cord. From the upper end 
of the wire start the pulley with its load, and note the point where it 
is at the end of 3 seconds. If the distance traversed in the 3 seconds 
is not at least 9 feet, increase the inclination of the wire. Mark the 
point where the pulley is at the end of. the third second by a strip of 
paper hung from the cord so that its lower end will be struck by the 
top of the pulley as it passes. Mark the point on the cord above 
the starting point of the pulley by tying a tliread there. Divide the 
intervening distance into 9 equal parts. Hang similar paper strips 
from the cord, at distances of 5 such equal parts and of 8 such equal 
parts above the strip already hung, and of 7 such equal parts and 16 
such equal parts below it. 

Swing the pendulum that vibrates seconds. As its thread passes a 
vertical line on the wooden support drawn downward from the needle, 
start the pulley, and see if it taps the successive strips as the pendu- 
lum successively passes the vertical line. If the weight carried by 
the pulley is of iron, the weight and the pendulum-bob may be simul- 
taneously released as in Exercise 1. 

Note. — A good Atwood machine is an expensive piece of apparatus, 
and unfortunately many schools and laboratories have none. If any 
particular school is thus equipped, the teacher should provide for its 
use in the verification of the laws of falling bodies, the approximate 
determination of the acceleration due to gravity, etc. 

12. From a rectangular wooden block about 30 x 23 x 4 cm., cut 
a semi-cycloid, thus shaping the piece marked B in Fig. 31. Cut a 
groove in the curved edge, and fasten the block against the black- 
board so that its long edge shall be vertical. A small ball that has 



THE PE^DtXCM. 



rolled clown the cycloidal path wiD b* projected witli * eoostut 

horizontal velocity and will acqaire aa »eeekfai«i TWtkal rttloalj. 

Let one of two pupils working together a4JQFL hj t^peated trials, m 

ruler so that the projected hall will just touch it, and thence det^TmiDe 

and n*ark the poiut passed over br 

the center of the ball. In this way 

locate points sufScientlY nnmerous \o 

plot on the blackboard the path d^ 

scribed by tlie center of tlie projected 

ball. From the center of the IjoII at 

the lowest point of its cydoidal path 

draw a horizontal line, and mark off 

a number of equal spaces npon iL 

These will repr&^nt the horizontal 

motiotm of the hall in equal in terrain 

of time. From eacb division on this 

liuBj draw a vertical line, /, to the 

plotted path, and measure the lengths 

of the?« lines. They represent the 

spaces fallen in the several interrala 

of time. 8how that, for each interval of time, I — W, k being some 

constant, if the horizontal intervals are made equal to the horiieontal 

speed of the ball per second, k will equal } g. 




FlU.31. 



Y. THE PENDTJUJiL 



72. A Simple Pendulum h a Mingle material particle 

supported by a line without weighty and capable of o»c':i* 
latlmj ahmit a fixed point. Siicb a pendulum has a 
theoretical but not an aetual existence. Its properties 
may be approximately determined by experiinentiiig with 
a small lead ball suspended by a fine thread. 

(a) Cut a builet halfway through* Tie a knot in the end of the 
tbi-eadj pliice the knot in the cut in the bullet, and, with a blow, close 
the lead upon it, 

(b) When the pendulum is drawn from its vertical position, as 
from. JV to Jl/, the force of gravity, MG, is resolved into two coinpo- 



66 



ELKMENTART FHTSICS. 




i'-a 



Fio 32. 



nents, one of wliich, A/C, produces pressare at the point of support, 
while the other, 3///, acts at right angles to it, producing motion 

toward N. As the pendulum approaches 
Ny its kinetic energy inci-eases. This 
energy carries the weight beyond N to- 
ward O, with transformation of energy 
and continued motion as explained in 
§ 53 (c). 

73. Definitions. — The motion 
from one extremity of the arc 
through which a pendulum swings 
to the other is called an oscillation. 
The time occupied in moving over 
this arc is called the time or period 
of oscillation. The angle measured 
by half this arc is called the ampli- 
tude of oscillation. The trip from 

M to is an oscillation. The angle, 

MAN^ is the amplitude of oscillation. 

(a) The motion from M to O and back 
agani, one " swing-swang," is sometimes called 
a "complete vibration." The time occupied by 
the round trip, or the time between its passage 
through any point and its next passage in the 
same direction through the same point, is some- 
times called a "complete period." 

Laws of the Pendulum. 

Experiment 30 — Suspend three lead bullets 
and a small iron ball as shown in the accom- 
panying figure. The lengths of the threads, 
measured between the points of support and the 
centers of the balls, should be as 1 : } : }; e.g., 
1 yard, 9 inches, and 4 inches respectively. 
Sec one of the pendulums swinging through a small arc, and count 
the oscillations made in 10 seconds. Set the same pendulum swing- 




FiG. 33. 



THE PENDULUM. 57 

iug through a somewhat larger arc, and count the oscillations as be* 
fore. Record and compare results- Repeat the experiments with 
each of the pendulums, recording and comparing results in each case. 
Note the effect of amplitude or of mass on the period of oscillation. 

From your notes, or by fresh experiment, determine the period of 
each pendulum, and observe the relation between the period of oscil- 
lation and the length of the pendulum. 

Place a magnet under the iron ball, so that when the latter swings 
it will just clear the end of the magnet. Swing the iron pendulum, 
and count the oscillations made in 10 seconds. The attraction of the 
magnet being added to that of the earth, the acceleration is increased 
and the period is lessened. 

74. Laws^of the Pendulum. — When tbe amplitude of 
oscillation is small, the period of oscillation depends mainly 
upon the length of the pendulum and the acceleration due 
to gravity. 

The following laws are consistent with the results of 
numberless experiments: — 

(1) At any given place^ the oscillations of a given pendu- 
lum are isochronous^ i.e., are made in equal periods. 

(2) The period of oi^cillation is independent of the mate- 
rial or the mass of the pendulum. 

(3) The period of oscillation varies directly as the square 
root of the length. 

(4) Tlie period of oscillation varies inversely as the square 
root of the acceleration. 

75. The Compound Pendulum. — Any pendulum other 
than the simple or ideal pendulum is a compound pendulum. 
In its most common form, it consists of a slender rod, 
flexible at the top, and carrying at the bottom a heavy 
mass of metal known as the boh. 

76. The Seconds Pendulum. — At any given place y a sec- 
onds pendulum is one that makes a single oscillation in a 
second. At the sea-level, its length is about 39 inches 



68 



ELEMENTARY PHYSICS. 



at the eqaatoFf and about 39.2 inches near the poles. Its 
value at the sea-level at New York may be found by mak- 
ing t = 1, and g = 980.19 cm., in the formula 



t = 7r\-. 



9 

and solving the equation for the value of I. 

(«) The Greek letter ir represents the ratio between the diameter 
and the circumference of a circle. See Appendix 1. 




Center of Oscillation. 

Experiment 31. — Drive a small wire nail through^ a flat board of 
any form, at some point near its edge, as shown in Fig. 34. Hold the 
ends of the wire by the finger and thumb, and allow the board to hang 
in a vertical plane. Fasten a small bullet to the 
end of a thread, and pass the thread over the wire 
so that the bullet hangs close to the board. Move 
the hand that supports the wire horizontally and in 
the plane of the board. Board and bullet will swing 
as pendulums. If one swings more rapidly than' the 
other, lengthen or shorten the string until they swing 
together. With the thread at this length, and board 
and bullet hanging in equilibrium, mark the point 
on the board opposite the center of the ball. Hold- 
ing the board by the wire as before, move it with 
varied, sudden, and irregular motions in the plane of the board. The 
bullet will not quit the marked place on the board. 

77. Centers of Suspension and Oscillation. — In every 
pendulum not simple, the parts near the center of suspen- 
sion tend to move faster than those further away, and 
force the latter to move more rapidly than they otherwise 
would. Between these, there is a particle that moves, of 
its own accord, at the rate forced upon the others. This 
particle fulfills all the conditions of a simple pendulum 
that has the period of the compound pendulum. Its posi- 
tion is called the center of oscillation or percussion. 



Fig. 34. 



THE PENDULUM. 



m 



fa) Fig, 35 repi-esents a wooden bar, suspended so as to 
have freedom of motion aljout the point S, which thus be- 
comes the center of suspension, G indicates the center of 
mass, and the center of oscillation, S and O are inter- 
changeable ; i»e,, if the pendulum is auspeiidtid from its 
center of oscillation, the rKjriod remains the siarae. 

(6) If we consider the length of the compound pendulum 
to be the distance between the centers of suspension and 
oscilJation, all the laws of the simple pendulum become ap> 
plicabte to the compound peudulum. 



BXERCISBS. 



IN^OTE* — Take 39.1 inches or 99.33 centimeters 
length of a seconds pendulum. 



the 



*0 



'0 



Fm. 3S. 



No. 


rit<;nBS. 


0«C(i.i^Titi)fe. 


PKitmD. 


NcL 


Cm. 


OSOTLLATIONH. 


PKfciau. 


1 


? 


20 per miu. 


? 


11 


9S.33 




? 


2 


? 


30 « . 


? 


12 


? 




2 sec. 


3 


ao 


? 


? 


13 


? 




2 min. 


4 


16 


? 


? 


14 


24.83 




? 


5 


7 


? 


} sec. 


15 


? 


8 per sec. 


? 


6 


? 


? 


^min. 


IS 


397,32 




7 


7 


30.37 


? per min. 


? 


17 


11,03 




? 


8 


? 


10 « 


? 


18 


? 




10 sec. 


9 


10 


7 per sec. 


? 


19 


2,483 25 




? 


10 


? 


1 per rain. 


? 


20 


? 




4 sec. 



21. Ho w wi 1 1 th e period!? o f osci 11a ti on o f two pen d ul u m e? c ot ti pare, 
their lengths being 4 feet and 49 feet respectively? Am. As 2 : 7* 

22. Of two pendnhims, one makcR 70 oscillations a minute, the 
other, 80 oscillations a minute. How do their lengths compare ? 

Aus. As 0i:49, 

23. If one pendulum is 4 timea as long aa another, what are their 
relative periods of oscillation ? 

24. The length of a seconds pendulum being 39.1 inches^ what 
must be the length of a pendulum to oscillate in ^ second? 

25. How long must a peuduluni be to oscillate (a) once in 8 sec- 
onds? {b) In} second? 



60 



ELEMENTARY PHYSICS. 



26. Set up a pendulum of length as great as you can conveniently. 
Set up another that oscillates just twice as often in a given time. 
Determine the ratio between the lengths of the two pendulums. 
Shorten the shoi*ter pendulum until it oscillates three times as fast 
as the other. Determine the relative lengths as before. Shorten the 
shorter pendulum again until it oscillates four times as fast, and fiud 
the ratio as before. In your notebook, record the data obtained, using 
the following form, and placing the ascertained ratios in the places of 
jt, y, andz; — 

Relative 
Lengths. 

1 

X 

y 

z 

f 

.* 







Fig. 36. 



Can you see any law or rule governing in such 
cases? Try, without experiment, to put the proper 
figures in the places of the two interrogation points. 
27. On a stout thread, fasten 5 or 6 lead bullets 
at successive intervals of 10 cm., and suspend the 
combination as a pendulum. Swing it as a pendu- 
lum. Does the string retain its rectilinear form 
while the compound pendulum is oscillating? Ac- 
count for any observed difference in this respect between 
this pendulum and those previously used. 

28. Through the laboratory meter stick or a similar 
atrip of wood, drill or burn a small hole 3 cm. from one 
end. Using this as a center of suspension, locate the 
center of oscillation. Determine the real length of the 
nH3ter-8tick pendulum. Suspend a bullet by a single 
tl»read, and adjust its length so that it will swing with 
the same period as the meter-stick pendulum. Compare 
the length of this pendulum with the distance between the 
centers of suspension and oscillation of the other pen- 
dulum. 

20. Remove the dial of a clock, and study the move- 
ments of the escapement (mn in Fig. 30), and of the 



SIMPLE MACHINES. 61 

escapement wheel, R, What does it enable the lifted weights or the 
coiled spring of the clock to do to the pendulum ? What does it en- ' 
able the pendulum to do to the weights or the spring? What would 
happen to the weights or to the spring if the escapement should be 
suddenly removed? What would happen to the pendulum if the 
escapement should be removed? How many times must the pendulum 
oscillate that the escapement wheel may turn around once ? 




VI. SIMPLE MACHINES. 

78. Machines. — In mechanics^ the word ^^ machine^' sig- 
nifies an instrument for the 
conversion of motion or the 
transference of energ I/, Thus, 
a machine may be designed 
to convert rapid motion into 
slow motion ; e.g.^ a crowbar. 

(a) No machine can create or F 37 

increase energy. In fact the use of 

a machine is accompanied by a waste of the energy that is needed to 
overcome the resistances of friction, the air, etc. 

79. Weight and Power. — The action of a machine in- 
volves two forces, called the weight and the power. The 
power signifies the magnitude of the force that acts upon 
one part of the machine ; the weight signifies the magni- 
tude of the force exerted by another part of the machine upon 
some external resistance. The general problem relating tq 
machines is to find the ratio between power an(i weig];^t; 
i.e., to determine the "mechanical advj^ntf^gq '' of the 
machine. 

80. General Laws of Machines. — In every machine, 
the work done by the power equals the work done on 
the weight. 



62 ELEMENTARY PHYSICS. 

(1) The power multiplied by the distance throitgh which 
it moves equaU the weight multiplied by the distance through 
which it moves : PI = WV. 

(2) The power multiplied by its velocity equals the weight 
multiplied by its velocity : Pv = Wv'. 

81. Efficiency of Machines. — The ratio that the useful 
work done by the machine bears to the total work done on the 
machine is called the efficiency of the machine. If this ratio 
could be brought up to unity, we should have a perfect 
machine, — the impossible thing that would supply " per- 
petual motion." 

(a) Whenever ve find that a machine does less work than was 
done upon it, we should bear in mind that the missing energy has 
not been destroyed. Mechanical energy has betMi transformed into 
molecular energy, and exists somewhere in the form of heat. 

82. Friction is the resistance that a moving body meets 
from the surface on which it moves^ and may be rolling or 
sliding. It is due partly to the adhesion of bodies, but 
more largely to their roughness. Even highly polished 
surfaces have minute irregularities, and when two such 
surfaces come into contact, the projections of one fall into 
the depressions of the other. When one slides over the 
other, energy is required to break off the projections or 
to lift the body out of the depressions. 

(a) Friction is generally lessened by polishing and lubricating the 
surfaces that move upon each other, and often by making the two 
bodies of different material. 

83. A Lever is an inflexible bar freely movable about a 
fixed axis called the fulcrum. Every lever is said to have 
two arras. The power arm is the perpendicular distance 
from the fulcrum to the line in which the power acts; 
the weight arm is the perpendicular distance fi-ora the 
fulcrum to the line in which the weight acts. If the 



SIMPLE ILACHINES, 



63 



arms are not in the same straigbt line, the lever is eiilled 

a bent lever, 

(a) There are three classes of levers, depending upon the relatiTe 
positions of power, weight, and f ulcnim. If the f alcrum i^ between 
the power and weight (PFW), tlie 
lever is of the first class (Fig» 36) j 
if the weight is between the other 
two {PWF), the lever is of the 
Siecond class; if the power is be- 
tween the other two (WPF), the 
lever is of the Ihird class. 



P* 



Fig. 3S. 



84, Hecbanical Advantage of the lever. — With a lever^ 
a given power will support a weight as man^ tivies a» great 

as itself as the pouter arm is times as long as the weight 
arm- 

(a) II the power arm is twice as long as the weight arm^ the 
power will move twice as fast and twice as far as the weight does, 
i,e,, the ratio between the arms is the same as the ratio between 
the velocities or distances traversed. The power multiplied by the 
power arm equals the weight multiplied by tlie weight arm. 

Note. — Tn all experimental work^ the lever shoaM be loaded so 
as to be in equilibrium befoie the povier and weight are applied. It 
is to be noticed that, when we i*i>eak of the power multiplied by the 
power arm, we refer to the abstract nmnbers representing the power 
and power arm. We cannot multiply pounds by fpet> bul w*e cati 
multiply the number of pounds by the number of feet. 

85. The Moment of a Force with respect to a given point 
is its tendencg to produce rotation about that pointy and is 
measured bi/ the product of the numbers representing respec- 
tivelg the magnitude of the force and the perpendicular dis- 
tance between the given point and the line of the force, 

(«) In the case of the lever represented in Fig. 38» the weight arm 
is 8 mm., and the power arm is iiO mm. Suppose that the piower is 
4 grams and represent the weight by x. Then the moment of the 
force acting on the power arm will be represented by (1 x 30 — ) 120, 
and the moment of the force acting on the weight arm by S :r. 



64 



ELEMENTAKY PHYSICS. 




Fig. 39. 



86. The Balance is essentially a lever of the first class^ 
having equal arms. The beam carries a pan at each end, 

— one for the weights 
used, the other for the 
article to be weighed. 

(a) Dishonest dealers some- 
times use balances with arms 
of unequal lengths. The true 
weight may be found by 
weighing the aHicle first on 
one side and then on the 
other, and finding the square 
root of the product of the two 
false weights. Another way 
is to place the article to be 
weighed in one pan, and counterpoise it, as with shot or sand placed 
in the other pan. Remove the article, and place known weights in 
the pan until they balance the shot or sand in the other pan. These 
known weights will represent the true weight of the article in ques- 
tion. 

BXBRCISBS. 

1. If a power of 50 pounds acting upon any kind of machine 
moves 15 feet, (a) how far can it move a weight of 250 pounds? 
(h) How great a load can it move 75 feet? 

2. If a power of 100 pounds acting upon a machine moves with 
a velocity of 10 feet per second, (a) to how great a load can it give a 
velocity of 125 feet per second? Q)) With what velocity can it move 
a load of 200 pounds? 

3. A lever is 10 feet long with its fulcrum in the middle. A power 
of 50 pounds is applied at one end. (a) IIow great a load at the other 
end can it support? (6) How great a load can it lift? 

Ans. (b) Anything less than 50 pounds. 

4. The power arm of a lever is 10 feet. The weight arm is 5 feet. 
(a) How long will the lever be if it is of the first class? (b) If it is 
of the second class? (c) If it is of the third class? 

5. A bar 12 feet long is to be used as a lever, keeping the weight 
3 feet from the fulcrum, (a) What class or classes of levers may it 
represent? (b) What weight can a power of 10 pounds support in 
each case? 



SIMPLE MACHINES. 



# 



0. The length of a lever is 10 feeb. Four feet from the fulcrum 
and at the end of thafc arm is a weight of 40 pounds \ two feet from 
the faleruiUj on the same eide, ig a weight of 1,000 pounds* What 
:force at the other end will counterbalance hotli weights? 

AnB. 360 pounds. 

7. The length of a lever is 8 feet, and its fulcrum is in the center, 
A force of 10 pounds acts at one end ; 1 foot from it is another of 
100 pouuds; 3 feet from the other end is a force of 100 pounds. The 
direction of all the forces is downwards Where must a downward 
force of 80 pounds be applied to balance the lever? 

Arts, 3 feet from the fulcrum. 

8, The length of a lever is 3 feet, Whei^ must the fnlcmm be 
plactid so that a weight of 200 pounds at one end shall be balanced 
by 40 pounds at the other end? 

9. lu one pan of a false balance^ a roll of hutter weighs 1 pound 
9 ounces; in the other, 2 pounds 4 ounces. Find the true weight, 

10, A and B, at opposite ends of a bar feet long, carry a weight 
of 300 pounds suspended between them. A's strength being twice as 
great as B'Sj where should the weight be hung ? 




:ilUUd11flillSJNlJJEEnJt![rIJ3ail^'^fl11E[[[!?eiilLljJiaLllllQ!2H^ 



Fig, 40. 



11, Support a wooden bar, preferably giaduated (the yardstick or 
the meter rod will answer adniirably)^ by a pin and clevis at the 
middle of its lengtli, a.s shown in Fig, 40, Pnt the bar in equilibrium 
(as in all such experimental cases), and provide stops 2 or 3 inches 
below each end of the bar to limit its oscillations. Support equal 
and known weij^hts by thread loops at equal distances from the mid* 
die of the lever, and compare the reading of the dynamometer with 
the sum of the siispfinded weights* Do they agree? If not, why not? 
Make the necessary correotioa. 



66 



ELEMENTARY PHYSICS. 



yilWirii^m,, 



12. Modify the apparatus used in Exercise 11 by removing the 
dynamometer and adding a counterpoise, as shown in Fig. 41. Re- 
place the weight at A with one 
twice as heavy, and shift its posi- 
tion until the bar is in equilibrium. 
Note the distances of C and B from 
O. Using either form of appai-a- 
tus, load the two arms of the lever 
with weights of varying ratios, and 
note the agreement or disagree- 
ment of your results with the sev- 
eral statements made in §§ 80 and 
84. 

13. Take two points at slightly 
different distances from O, the f ul* 
crum of the balance-beam. Sus- 
pend an unknown weight from one of these points, and counterpoise 
it with known weights at the other point so taken. Verify the state- 
ments made in § 86 (a). 

14. From one of the points taken as directed in Exercise 12, sus- 
pend a tin can, and put the lever in equilibrium. From the other of 
those two points, suspend a body of unknown weight, and find its true 
weight by the process of double weighing, as described in § 86 (a). 

87. The Wheel and Axle consists of a wheel united to a 
cylinder in such a way that they may turn together on a 
common axis. 






FiQ. 42. 



Fig. 43. 



(a) It is not necessary that an entire wheel be present, a single 
spoke or radius being sufficient for the application of the power, as in 
the case of the windlass (Fig. 43) or the capstan (Fig. 44). 



SIMPLE MACHINES. 



67 



(b) The advantage of the wheel and axle may be increased by 
combining several, so that the axle of the first may act on the wheel 
of the second, and so on, as shown in Fig. 45. 





Fig. 44. 



F.G. 45. 



88. Mechanical Advantage of the Wheel and Axle. — 
The mechanical advantage of this machine equals the ratio 
between the radii^ diameters^ or circumferences of the wheel 
and of the axle. 





Fig. 46. 



Fig. 47. 



89. A Pulley is a wheel having a grooved rim for carrying 
a rope or other line^ and turning on an axis carried in a 
frame^ called a pulley block. The pulley is fixed if the 
block is stationary (Fig. 46) ; the pulley is movable if the 
block moves during the action of the power (Fig. 47). 



68 



ELEMENTARY PHYSICS. 




(a) Combinations of pulleys are 
made in great variety. In the forms 
most commonly used, one continuous 
cord passes around all the pulleys. Fre- 
quently two or more sheaves are mounted 
in the same block and turn on the same 
axis, as in the common block and tackle, 
shown in Fig. 48. 

90. Mechanical Advantage of 
the Pulley. — With the ordinary 
arrangement of pulleys, like the 
block and tackle, a given power 
will support a weight as many 
times as great as itself as there are 
parts of the cord supporting the 
movable block. 

FiG. 48. W= P xn. 

(a) In expeiiments to determine the mechanical advantage of a 
system of pulleys, as in all sin)ilar experiments, see that the apparatus 
is in equilibrium before applying P and W. 

91. An Inclined Plane is a smooth^ hard, inflexible sur- 
face^ inclined so as to make an 
oblique angle with the horizon, 

(a) When a body is placed on 
an inclined plane, the gravity pull 
is resolved into two component 
forces. One of these acts perpen- 
dicularly to the plane, producing 
pressure on it, the other compo- 
nent tending to produce motion 
down the plane. To resist this last-mentioned tendency, and thus to 
hold the body in its position, a force may be applied in three ways : — 

(1) In a direction parallel to the length of the plane. 

(2) In a direction parallel to the base of the plane; i.e., horizontal. 

(3) In a direction parallel to neither the length nor the base. 




Fig. 49. 




SIMPLE MACHINES. 69 

92. Mechanical Advantage of the Inclined Plane. — 
(1) When a given power acts parallel 
to an inclined plane^ it will support a 
weight as many times as great as it- 
self as the length of the plane is times 
as great as its vertical height. 

(2) When a given power acts hori- 
zontally^ it will support a weight as ^®^^' 
many times as great as itself as the hori- 
zontal base of the plane is times as great as its vertical height. 

(a) When the power acts in a direction parallel to neither the 
length nor the base, no law can be given. 

BXBRCISRS. 

1. The pilot wheel of a boat is 3 feet in diameter; the axle, 6 
inches. The resistance of the rudder is 180 pounds. What power 
applied to the wheel will move the rudder ? 

2. Four men are hoisting an anchor of 1 ton weight. The barrel 
of the capstan is 8 inches in diameter. The circle described by the 
handspikes is 6 feet 8 inches in diameter. How great a pressure 
must each of the men exert? 

3. A capstan whose barrel has a diameter of 14 inches is worked 
by two handspikes, each 7 feet long. At the end of each handspike 
a man pushes with a force of 30 pounds ; 2 feet from the end of each 
bands(>ike a man pushes with a force of 40 pounds. Required the 
effect produced by the four men. 

4. With a fixed pulley, what power will support a weight of 50 
pounds? 

5. With a movable pulley, what power will support a weight of 
50 pounds ? 

6. With block and tackle, the fixed block having four sheaves and 
the movable block having three, what weight may be snpported by a 
power of 75 pounds ? K an allowance of i is made for friction and 
rigidity of ropes, what is the maximum weight that may be thus 
supported ? 

7. With a system of ^yq movable pulleys, one end of the rope 
being attached to the fixed block, what power will raise a ton ? 



70 



ELEMENTARY PHYSICS. 



8. If, in the system mentioned in Exercise 7, the rope is attached 
to the movable block, what power will raise a ton ? If an allowance 
of 25 per cent is made for friction and rigidity of ropes, what power 
will be required ? 

9. How great a power will be required to support a ball weighing 
40 pounds on an inclined plane whose length is 8 times its height ? 

10. The base of an inclined plane is 10 feet ; the height is 3 feet. 
What force, acting parallel to' the base, will balance a weight of 2 tons ? 

93. A Wedge is a triangular prism of hard material, 
fitted to be driven between objects that are to be sepa- 
rated, or into, anything that is to be split. It 
18 simply a movable inclined plane^ or two such 
planes united at their bases. The power is 
generally applied in repeated blows on the 
thick end or " head." For a wedge thus used, 
no law of any practical value can be given, 
further than that, with a given thickness, the 
longer the wedge, the greater the mechanical 
advantage. 

94. A Screw is a cijlinder^ generally of wood or metal^ 
with a spiral ridye (the thread) winding about its circum- 




Fig. 51. 





Fig. 52. 



Fig. 53. 



ference. The thread works in a nut, within which there is 
a corresponding spiral groove to receive the thread. 



SIMPLE MACHINES. 



n 



(a) The power is generally applied by a wheel or a lever, a ad 
moves through the circumference of a circle. The distance between 
two consecutive turns of any continuous thread, measured iu tlio 
direction of the axis of the screw, is called the^i^;A ufihescreaj. 

95. Mechanical Advantage of the Screw. — With ih& 
screw^ a given power will support a weiyJil a& many times 
as great as itself as the circumference described bjf Ute power 
is times as great as the pitch of the screw. 

96. Compound Machines. — When any two or more of 
tliese simple machines are combined, the mecli finical ad- 
vantage may be found by computing the effect of each 
separately, and then compounding them^ or by finding 
the weight that the given power will support, using the 
first machine alone, considering the result as a new power 
acting upon the second machine, and so on. 



EXERCISES. 

1. A bookbinder has a press, the screw of which has a pitch o! \ of 
an inch. The nut is worked by a lever that describes a circuuifeience 
of 8 feet. How great a pressure will a power of 15 pounds applied at 
the end of the lever produce, the loss by friction being equivalent to 
240 pounds? 

2. A screw has eleven threads for every inch in length. Tf the lever 
is 8 inches long, the power 50 pounds, and friction nlisoibs i of the 
energy used, what resistance may be overcome by it ? 

3. A screw with threads 1 J inches apart is driven by !i lev^er ij feet 
long. What is the mechanical advantage of the appaiatus? 

4. At the top of an inclined plane that rise=i 1 foot iu 20 is a 
wheel and axle. The radius of the wheel is 2^ feet; radius of axle, 
4i inches. What load may be lifted by a boy who liaiis tht; wheel 
with a force of 25 pounds? 

5. In moving a building, the horse is harnessed to tU** end of a 
lever 7 feet long, acting on a capstan barrel 11 indies in. diameter. 
On the ban'el winds a rope belonging to a system of 2 ii:^ed and 3 
movable pulleys. What force will be exerted by 500 ponmls power, 
allowing J for loss by friction ? 

6. Experimentally determine the ratio of power to weight with 



72 



ELEMENTARY PHYSICS. 



pulleys arranged as shown in Fig. 64. The 
pulleys and the cord should be strong enough 
to carry a load of KiO pounds. 




7. Determine the loss due to friction and to 
the rigidity of the ropes used in Exercise 6. 

8. Experimentally determine the ratio be- 
tween P and H^ with pulleys arranged as shown 
in Fig. 55. Determine the law of such a com- 
bination. 




Fig. 65. 



VII. THE MECHANICS OF LIQUIDS. 

97. Compressibility and Elasticity of Liquids. — Liquids 
are nearly incompressible. When the pressure is removed, 
the liquids regain their former volume, showing thus 
their perfect elasticity. The practical incompressibility of 
liquids is of great mechanical importance. 

Liquid Pressure. 

Experiment 32. — Tie a piece of thin sheet rubber (such as you can 
get from the druggist or dentist, or from a broken toy balioou) over 

the large end of a lamp^him- 
ney. Reinforce the other 
end by winding upon it a 
dozen turns of wrapping 
twine, and fit it with a fine- 
grained cork or rubber stop- 
per through which passes 
snugly a bit of glass tubing. 
Connect the glass tubing and a supported funnel by two or three feet 
of rubber tubing. Fill the apparatus with water, loosening the cork 




F1066. 



THE MECHANICS OF LIQUIDS. 73 

for a moment to allow the escape of air. See that the funnel is still 
half fuU of water and elevated above the chimney. Notice the effect of 
the water pressure on tlie sheet rubber. Hold the chimney in various 
positions, keeping the ceirter of the sheet rubber at a uniform distance 
below the level of the funnel, and notice whether the elastic sheet is 
stretched more or less when the liquid pressure upon it is horizontal, 
upward, or downward. Then try it at varying distances below the 
level of the water in the funnel, and determine whether such vertical 
distance or " head " has any relation to the pressure. 

98. Transmission of Pressure. — Fluids transmit preB- 
surea in every direction, 

(a) Figure 57 represents a number of balls placed in a vessel. 
Imagine these balls to have perfect freedom of motion and perfect 
elasticity. It is evident that if a downward pressure, say of 10 grams, 
is applied to 2, it will force 5 and 4 toward the left, and 6, 7, and 8 
toward the right, thus forming lateral pressure. Tliis motion of 5 
will force 1 upward, and 9 downward, etc. Owing 
to the perfect elasticity and freedom of motion, 
there will be no loss, and the several balls will 
be moved just as if the original pressure had 
been applied directly to each one. The pres- 
sure will be thus transmitted to all of the balls 
without loss, and the total pressure exerted on 
the sides of the vessel will equal 10 grams mul- 
tiplied by the number of balls that touch the sides. It makes no dif- 
ference with the result whether the pressure exerted by 2 was the 
result of its own weight only, this weight together with the weight of 
overlying balls, or both of these with still additional pressure. 

(b) Disregarding viscosity, we may consider a fluid to be made up 
of molecules having the perfect elasticity and freedom of motion 
assumed for the balls just discussed. Hence, when pressure is applied 
to one or more of the molecules of a fluid, the pressure will be trans- 
mitted as now explained. 

99. Pascars Law. — Pressure exerted anywhere upon a 
liquid inclosed in a vessel is transmitted undiminished in all 
directions^ and acts with the same force upon all equal sur- 
facesy and in a direction at right angles to those surfaces. 




71 



ELEMENTARY PHYSICS. 




^^ 



Fig. 58. 



(a) Provida two communicating tubes 
of unequal sectional area. When water 
is poured into these, it will stand at the 
same height in both tubes, — a fact 
which of itself partly coufii*ms the law 
al>ove given. If the smaller piston has 
an area of 1 sq. cm., and the larger pis- 
ton an area of 16 sq. cm., a weight of 
1 Kg. may be made to support a weight 
of 16 Kg. 

100. The Hydraulic Press. — 

Pascal's law finds an important 



application in the hydraulic press, in the more common 
forms of which the pressure of a piston operated by a lever 







Fig. 59. 



THE MECHANICS OF LIQUIDS. 



75 



is transmitted through a pipe to a piston of larger area. 
Tho piess is represented in Fig. 59. 

(a) If the power arm of the lever is ten times as long as the weight 
arm, a power of 50 Kg. will exert a pressure of 51)0 Kg. upon the 
water beneath the piston, a. If this piston has a sectional area of 
1 sq. cm., and the piston, C, has an area of 500 sq. cm., then the pres- 
sure of 500 Kg. exerted by the small piston will produce a pressure 
of 500 Kg. X 500 or 250,000 Kg. upon the lower surface of the large 
piston. 

Downward Pressure. 

Experiment 33. — Into a U-tube, pour enough mercury to fill each 
arm to the depth of 3 or 4 cm. Place the U-tube upon a table, and 
hold it upright by any convenient means. Back of it, and resting 
against it, stand a card having a horizontal line, a, drawn on it to 
mark the level of the mercury in the two arms of the tube. To one 
arm, attach the neck of a funnel by means of a bit of rubber tubing. 
The funnel may be held by the 
ring of a retort stand. Pour water 
slowly into the funnel until it is 
nearly full, and mark the level of 
the water by a suspended weight 
or other means. In one arm, the 
mercury will be depressed below 
the line marked on the card; in 
the other arm, it will be raised 
above it an equal distance. Mark 
these two mercury levels by dotted 
horizontal lines on the card. Re- 
move the funnel and replace it by 
a funnel- or thistle-tube, making 
the connection by means of a per- 
forated cork. Pour water into the .t 
funnel-tube until it stands at the 
level indicated by the suspended 
weight, being careful that no air is 
confined in the tubes* Although much less water is in the funnel-tube 
than was in the funnel, it forces the mercury into the position indi- 
cated by the dotted lines on the card. The downward pressure of the 
Arater in each case is measured by a mercury column with a height, ce, 




Fio. 60. 



76 



ELEMENTARY PHYSICS. 



equal to the vertical distance between the two dotted lines. The 
same principle may be strikingly illustrated by using Pascal vases, 
which may be obtained from dealers in scientific apparatus. 

101. Liquid Pressure Due to Gravity. — The downward 
pressure catised by the weight of a liquid is independent 
of the shape of the containing vessel and of the qv/intity of 
the liquid. It is proportional to the depth of the liquid and 
the area of the base. 

Upward Pressure. 

Experiment 34. — Make a smaU hole in the bottom of a tin fruit- 
can or similar vessel. Push the can downward into water until the 
open mouth of the can is " near the water's edge." The liquid will 
spurt upward through the hole in a little jet. Why? 

Experiment 35. — Get a lamp-chimney, preferably cylindrical. 
With a diamond or a steel glass-cutter, 
cut a disk of window glass a little 
larger than the cross-section of the 
lamp-chimney. Pour some fine emeiy 
powder on the disk, and rub one end 
of the. chimney upon it, thus grinding 
them until they fit accurately. With 
wax, fasten a thread to the center of 
the giound surface of the disk, and 
draw Uiat surface against the ground 
end of the chimney. Holding the 
chimney in the hand, or supporting it 
in any convenient way, place it in 
water as shown in Fig. 61. The up- 
ward pressure of the water will hold 
the disk in place. Pour water carefully 
into the tube; the disk will fall as 

soon as the weight of the water in the chimney, plus the weight of 

the disk, exceeds the upward pressure of the water. 

102. Rules for Liquid Pressure. 

(1) To find the downward or the upward pressure on any 
submerged horizontal surface, find the weight of an imaginary 




Fig. 61. 



THE MECHANICS OF LIQUIDS. 77 

column of the given liquid^ the base of which is the same as 
the given surface^ and the altitude of which is the same as 
the depth of the given surface below the surface of the liquid. 
(2) To find the pressure upon any vertical surface^ find 
the weight of an imaginary column of the liquid^ the base of 
which is the same as the given surface^ and the altitude of 
which is the same as the depth of the center of the given 
surface below the surface of the liquid. 

(a) A cubic foot of water weighs 62.42 pounds, or about 1,000 
ouuces. 

Liquid Level. 

Experiment 36. — To the cork used in Experiment 32, fit a piece of 
glass tubing about 2 feet long. Holding the chimney on the table-top 
with this glass tube upright, fill the apparatus with water. Does the 
water stand at a higher level in the funnel, or in the tube ? Raise and 
lower the funnel, and for each position notice the relation between the 
liquid levels in the funnel and in the tube. 

103. Communicating Vessels. — When a liquid is placed 
in one or more of several open vessels that communicate 
with each other, it will not come to rest until it stands at 
the same height in all of the vessels, "Water seeks its 
level." The principle is illustrated, on a large scale, in 
the system of pipes by which water is distributed in cities. 

BXBRCISBS. 

1. What will be the pressure on a dam in 20 feet of water, the dam 
being 30 feet long? 

2. What will be the pressure on a dam in 6 m. of water, the dam 
being 10 m. long? 

3. Find the pressure on one side of a cistern 5 feet square and 12 
feet high, filled with water. 

4. Find the pressure on one side of a ♦cistern 2 m. square and 4 m. 
high, filled with water. 

5. A cylindrical vessel having a base of a square yard is filled with 
water to the depth of two yards. What pressure is exerted upon the 

5? 



78 ELEMENTARY PHYSICS. 

6. A cylindrical vessel having a base of a squat-e meter is ^V.ed 
with water to the depth of two meters. What pressure is exerted upon 
the base? 

7. What will be the upward pressure upon a horizontal plate a foot 
square at a depth of 25 feet of water? 

8. What will be the upward pressure upon a horizontal plate 
30 cm. square at a depth of 8 m. of water? 

9. A squai-e board with a surface ot 9 square feet is pressed against 
the bottom of the vertical wall of a cistern in wliich the water is 8^ 
feet deep. What pressure does tlie water exert ujion tlie board ? 

10. The lever of a hydraulic press is C fest long, the piston rod 
being 1 foot from the fulcrum. The area of the tube is half a 
square inch; that of the cylinder is 100 square inches. Find the 
weight that may be raised by a force of 75 pounds. 

11. Cut the bottoms from a large bottle, and from another bottle of 
about equal height but much less diameter. Close their mouths by 
corks perforated by bits of glass tubing. Support the bottomless 
bottles by thrusting their necks downward through two holes bored 
in the top of a box. With rubber tubing, connect the glass tubes 
that pass through the corks, making thus two communicating vessels. 
Half fill the bottles with water, and mark the liquid level on each 
bottle. Pour a measured quantity of oil into the smaller bottle until 
it forms a layer several centimeters thick. The water-levels have 
been changed. Pour measured quantities of the oil into the other 
bottle until the water is restored to its marked levels. How do the 
thicknesses of the two oil layers compare ? How do the volumes of 
the two oil layers compare ? 

Principle of Archimedes. 

Experiment 37. — Suspend a stone or a brick by a slender cord or a 
fine wire from the hook of a spring-balance, and note the reading of 
the scale. Then itnmerse the load thus suspended in water and again 
note the reading. Transfer the load to a strong brine, and note (lie 
reading. Transfer the load to kerosene, and note again the reading. 
It seems as if the liquids help to support the stone, with a force of 
vailing magnitude. 

Experiment 38. — From one end of a scale-beam, suspend a cylin- 
drical metal bucket, 6, with a solid cylinder, a, that fits accurately 
'•^to it hanging below. Counterpoise with weights (shot or sand) in 



THE MECHANICS OF LIQUIDS. 



79 



the opposite scale-pan. Immerse a in water, and the counterpoise 
will descend, as if a hud lost some of its weight. Carefully fill b with 
water. It will hold exactly the quantity displaced by a. Equilibrium 
will be restored. 




Fia. 62. 

Experiment 39. — For rough work, a spring-balance may take the 
place of the beam-balance; a tin pail may take the place of 6; a 
piece of stone suspended beneath the pail by strings tied to the ears 
of the pail may take the place of a ; a larger tin pail filled with water 
and set in a tin pan may take the place of the vessel of water shown 
in Fig. 62. Note the weight of the smaller pail, with and without 
the suspended stone. Lower the apparatus so that the stone shall be 
immersed in the water, and note the reading of the scale. Determine 
the loss of weight resulting from the immersion of the stone. The 
volume of water forced from the pail and caught in the pan is equal 
to what other volume? Remove the pan, immerse the stone as before, 
pour the water from the pan into the upper pail, and note the read- 
ing of the scale. To what other reading is it equal ? To what is the 
weight of the water displaced by the stone equal? 

Experiment 40. — Modify the experiment again as follows : Instead 
of the suspended bucket, b, place a tumbler upon the scale-pan." In- 
stead of the cylinder, a, suspend any convenient solid heavier than 



80 



ELEMENTARY PHYSICS. 



water, as a potato. Counterpoise the tumbler and the potato with 
weights in the other scale-pan. Provide an overflow-can by inserting 
a spout about 6 cm. long and 7 or 8 mm. in diameter in the side of a 
vessel (as a tin fruit-can) about an inch below the top of the can. 
This spout should slope slightly downward. Fill the can with water 
and catch the overflow from the spout in a cup. Throw away the 
water thus caught. Wait a minute for the spout to stop dripping and 
then carefully immerse the potato in the water of the can, catching in 
the cup eveiy drop of water that overflows. Wait a minute for the 
spout to stop dripping. The equilibrium of the balance is destroyed, 
but it may be restored by pouring into the tumbler the water that was 
displaced by the potato and caught in the cup. 

104. Archimedes' Principle. — A body is buoyed up by a 
force equal to the weight of the fluid that it displaces. 
Hence the apparent weight of a body in a fluid (e.g., 
water or air) is less than its true weight. This buoyant 
effect is often spoken of as a *' loss of weight." 

(a) When a solid is immersed in a fluid, it displaces its own vol- 
ume of the fluid. Imagine a solid cube one centimeter on each edge 
to be immersed in water so that its upper face shall be level and one 
centimeter below the surface of the liquid, as shown in Fig. 63. The 
lateral pressm-es upon any two opposite vertical surfaces of the cube, 
as a and 6, are clearly equal and opposite. They have no tendency to 

move the solid. The vertical pres- 
sures on the other two faces, c and «?, 
are not equal. The upper face sus- 
tains a pressure equal to the weight of 
a column of water having a base one 
centimeter square (i.e., the face, d) 
and an altitude equal to the distance, 
dn. This imaginary column of water 
has a volume of one cubic centimeter, 
and a weight of one gram. The down- 
ward pressure on d is one gram. As 
the face, c, has the same area and is at 
twice the depth, the upward pressure upon it is two grams. The re- 
sultant of the two vertical and opposite forces acting on the cube is 
an upward pressure of one gram ; i.e., the cube is partly supported by 




Fig. 63. 



THE MECHANICS OF LIQUIDS. 81 

a buoyant force of one gram, which is the weight of the cubic centi- 
meter of water that it displaces. No matter what the depth to which 
the block is immersed, this net upward pressure, or buoyant effect, is 

always the same. 

Flotation. 

Experiment 41. — Place the tin can mentioned in Experiment 40 
upon one scale-pan, and fill it with water, some of which will overflow 
through the spout. Do not let any of the water fall upon the scale- 
pan. When the spout has ceased dripping, countei'poise the vessel of 
water with weights in the other scale-pan. Place a floating body on 
the water. This will destroy the equilibrium, but water will overflow 
through the spout until the equilibrium is restored. This shows that 
the floating body has displaced its own weight of water. 

105. Floating Bodies. — A floating body will sink in a 
liquid until it displaces a weight of the liquid equal to its 
own weight. 

(a) When a solid is immersed in a liquid, the buoyant effect of the 
liquid (§104) may exceed the weight of the body; then the body 
rises to the surface and floats. When buoyancy and weight are equal 
and opposite, their resultant is zero, and the body is in equilibrium in 
any part of the liquid. When the weight exceeds the buoyancy, the 
body sinks. In any case, Archimedes* principle is strictly true. 

BXBRCISBS. 

1. How much weight will a cubic decimeter of iron lose when 
placed in water? 

2. How much weight will it lose in a liquid 13.6 times as heavy as 
water ? 

3. If the cubic decimeter of iron weighs only 7,780 g., what does 
your answer to Exercise 2 signify? 

4. How much weight will a cubic foot of stone lose in water ? 

5. If 100 cu. cm. of lead weighs 1,135 g., what will it weigh in water? 

6. If a brass ball weighs 83.8 g. in air, and 73.8 g. in water, what 
is its volume ? 

7. A cubical vessel 20 cm. on an edge has fitted into its top a tube 
2 cm. square and 10 cm. high. Box and tube being filled with water, 
(a) what is the weight of the water? (b) What is the liquid pres- 
sure on the bottom of the vessel? (c) If the weight and pressure 
differ, explain the difference. 



82 



KLKMENTARY PHYSICS. 



106. Density. — The density (or specific gravity^ of a sub- 
stance is the ratio between the weight of any volume of the 
substance and the weight of a like volume of som>e other 
substance taken as a standard. For solids and liquids, the 
standard is distilled water at its temperature of maximum 
density (4° C. or 39.2° F.); for gases and vapors, the stan- 
dards are hydrogen and air, each under a barometric pres- 
sure of 76 centimeters, and at the temperature of 0° C. 
The term " density "has nearly displaced " specific gravity" 
in scientific works. 

(a) To illustrate, in the simplest way, what is meant by density, 
suppose that 1 cu. cm. of marble weighs 2.7 g. Since 1 cu. cm. of 
water weighs 1 g., the marble is 2.7 times as heavy as water, volume 
for volume. In shorter phrase, the density of marble is 2.7. To avoid 
the difficulty of obtaining just a unit volume of the substance, the 
principle of Archimedes is utilized, as will be illustrated. 

107. To Find the Density of a Solid Heavier than 
Water. — The most common way of determining the 

density of such a body, 
if it is insoluble in 
water, is to find its 
weight in air (w') ; find 
its weight when im* 
mersed in water (w'); 
divide the weight in air 
by the loss of weight in 
water. 




D = 



V) 



Fig. 64. 



W — W^ 



(a) This method is illustrated by the following example: — 

(1) Weight of the solid in air (w) 113.4 g. 

/2) « " " " " water (w') 79.14 g. 

/3\ u « equal bulk of water (w — w') . . . 34.26 g. 
(4) Density " the solid (l)-^(3) 3.31 



1 



THE MECHANICS OF LIQUIDS. 



83 



(b) Hydrometers are convenient for this purpose. Some of them 
are of constant volume, and others are of constant weight. The 
Nicholson hydrometer of constant volume is a hol- 
low cylinder carrying at its lower end a basket, d, 
heavy enough to ke6p the apparatus upright in 
water. At the top of the cylinder is a vertical rod 
carrying a pan, a, for holding weights, etc. The 
whole apparatus must be lighter than water, so 
that a certain weight ( W) must be put into the 
pan to sink the apparatus to a fixed point marked 
on the rod (as c). The given body, which must 
weigh less than W, is placed in the pan, and enough 
weights (u?) added to sink the point, c, to the water- 
line. It is evident that the weight of the given 
body is W — to. The given body is now taken from 
the pan and placed m the basket, when additional 
weights, Xy must be added to sink the point, c, to 
the water-line. 




FiQ. 05. 



108. To Find the Density of a Solid Lighter than Water. 
— Fasten to it another body heavy enough to sink it in 
water. Find the loss of weight for the combined mass 
when weighed in the water. Do the same for the heavy 
body. Subtract the loss of the heavy body from the loss 
of the combined mass. Divide the weight of the given 
body by this difference. 



109. To Find the Density of a Solid Soluble in Water. — 
Determine the density of the given solid with reference 
to some liquid, the density (J) of which is known, and 
in which the solid is not soluble. Multiply the result 
(obtained by any of the processes previously described) by 
the density of the liquid used. 



i> = 



wd 

•• • I > 



Si 



ELEMENTARY PHYSICS. 



110. To Find the Density of a Liquid. — There are sev- 
eral methods of liiiding the density of a liquid, but the 
priuciple in each is thiit ali*eady given. 

(a) Four of these methods are given here ; others will be found in 

the Exercises. 

(1) Weigh a flask, first, empty ; next, full of water ; then, full of the 

given liquid. Subtract the weight of the empty flask from the other 

two weights; the results represent the 
weights of equal volumes of the given 
substance and of the standard. Divide 
as before. A flask of known weight, 
graduated to measure 100 or 1,000 grams 
or grains of water, is called a specific- 
gravity flask. Its use avoids the first 
and second weighings above mentioned, 
aad simplifies the work of division. 

(2) Find the loss of weight of any 
insoluble solid in water and in the given 
tiquid. Divide the latter loss by the 
former. A solid thus used is called a 
specijic-gravily bulb. 

(3) The Fahrenheit hydrometer of constant volume is made of 
glass, the bulb at the bottom being loaded with 
mercury or shot. Its weight (W) being accu- 
rately determined, the instrument :s placed in 
water, and a weight (w) sufficient to sink a marked 
point on the rod to the water-line is placed in the 
pan. The weight of water displaced by the in- 
strument z=:W -\-w. The hydrometer is then re- 
moved, wiped dry, and placed in the given liquid. 
A weight (x) sufficient to sink the hydrometer to 
the marked point is placed in the pan. (Fig. 66.) 

(4) As generally made, a hydrometer of con- 
stant weight consists of a glass tube near the 
bottom of which are two bulbs. The lower and 
smaller bulb is loaded with mercury or shot. The tube and upper 
bulb contain air. The point to which it sinks when placed in water is 





Fig. 67. 



THE MECHANICS OF LIQUIDS. 85 

marked zero. The tube is graduated, tlie scale being arbitrary, aud 
varying with the purpose for which the instrument is intended. Such 
hydrometers are used to determine the degree of concentration of 
certain liquids, as acids, alcohols, niilk, solutions of sugar, etc. Ac- 
cording to their uses they are tnown as acidometers, alcoholometers, 
lactometers, saccharometers, etc. (Fig. 67.) 

Note. — The density of an aeriform body is found by comparing 
the weights of equal volumes of the standard (air or hydrogen) and 
of the given substance. The method is much like that first given 
for liquids. 'I'he deterniination of the density of gases presents many 
practical difficulties which cannot be considered in this place. 

111. Water Power. — An elevated body of water is a 
storehouse of potential energy. As the water runs to 
a lower level, it may be made to turn a wheel, and thus 
to move machinery, etc., a good illustration of the con- 
version of potential into kinetic energy. 

(a) "Water-wheels are of different kinds, their relative advantages 

depending upon the natui*e of the water-supply and of the work to be 

done. 

BXBRCISBS. 

Note. — Be on the alert to' recognize Archimedes' Principle in 
disguise. Consider the weight of watir 02j pounds per cubic foot. 

1. A piece of metal weighing 52.35 g. in air is placed in a cup 
filled with water. The overflowing water weighs 6 g. What is the 
density of the metal? 

2. A solid weighing 695 g. in air loses 83 g. when weighed in 
water. What is its density? 

3. A 1,000-grain bottle holds 708 grains of benzoline. Find the 
density of the benzoline. 

4. A solid that weighs 2.4554 ounces in air, weighs only 2.0778 
ounces in water. Find its density. 

5. A specimen of gold that weighs 4.6764 g. in air, loses 0.2447 g. 
weight when weighed in water. Find its density. 

6. A ball weighing 970 grains, weighs in water 895 grains, iv 
alcohol 910 grains. Find the density of the alcohol. 

7. Calculate the density of sea water from the following data : — 

Weight of bottle empty 3.5305 g. 

^ « filled with distilled water . . 7.6722 g. 

« « « sea ** . . 7.7819 g. 



86 ELEMENTARY PHYSICS. 

8. Determine the density of a piece of wood from the following 
data: weight of wood in air, 4 g. ; weight of sinker, 10 g. ; weight of 
wood and sinker under water, 8.5 g. ; density of sinker, 10.5. 

9. A lump of ice weighing 8 pounds is fastened to IG pounds of 
lead. In water, the lead alone weighs 14.6 pounds, while the lead 
and ice weigh 13.712 pounds. Find the density of the ice. 

10. A weight of 1,000 grains will sink a certain Nicholson hydrom- 
eter to a mark on the rod carrying the pan. A piece of hrass plus 40 
grains will sink it to the same mark. When the brass is taken from 
the pan and placed in the basket, it requires 160 grains in the pan to 
sink the hydrometer to the same mark on the rod. Find the density 
of the brass. 

11. A Fahrenheit hydrometer, which weighs 2,000 grains, requires 
1,000 grains in the pan to sink it to a certain depth in water. It 
requires 3,400 grains in the pan to sink it to the same depth in sulphuric 
acid. Find the density of the acid. 

12. A hollow ball of iron weighs 1 Kg. What must be its least 
volume to float on water ? 

13. Rock-salt is soluble. in water, and insoluble in naphtha. Deter- 
mine the density of a specimen of rock-salt. 

14. Make a rod of white pine or other light wood, just 1 cm. square 
and about 30 cm. long. In one end, bore a hole, and pound in enough 
sheet lead to make the rod stand on end when floated in water and 
with about half of it immersed. Fill the rest of the cavity with 
putty, and dip the rod into hot paraffin. Graduate one side of the 
rod to millimeters, with the zero of the scale at the loaded end. 
Place the rod in water, and read from the scale the depth to which 
it sinks. Using it as a hydrometer of constant weight, determine 
the density of alcohol, and of a 20-per-cent solution of common 
salt. 

15. Paste a strip of writing paper around the upper end of the rod 
used in Exercise 14, one edge of the paper overlapping the end of the 
stick so as to make a small cup. Float the rod as before, and place 
enough shot or sand in the cup to bring one of the graduations exactly 
to the water-level. Add successively weights of 1 g., 2 g., 3 g., etc., 
and at each addition, note how much the rod sinks. Record the 
teachings of the experiment. 

16. Provide a bottle that will hold two or three ounces of water, 
and that has a ground-glass stopper; a thread with which to suspend 
the bottle ; a cloth with which to wipe the bottle j a delicate spring- 



THE MECHANICS OF GASES. 87 

balance; water; kerosene. Without any other apparatus or supplies, 
determine the density of the kerosene. 

17. Fill a bottle like that used in Exercise 16 with water, and put 
the stopper firmly into place. Without removing the stopper or add- 
ing to your material, determine the density of the kerosene. 

18. Get a glass U-tube with an internal diameter of 8 or 10 mm. 
and having arms that are close together and about 50 cm. long (see 
Fig. 60); a meter stick graduated to railliineters; a small funnel for 
pouring liquids into the U-tube; some support that will hold the 
U-tube upright; water; kerosene. Without additional material, de- 
termine the density of the kerosene. 



VIII. THE MECHANICS OF GASES. 

112. Pneumatics is the branch of physics that treats of the 
mechanical properties of gases^ and describes the machines 
that depend for their action chiefly on the pressure and 
elasticity of air. 

(a) As water was taken as the type of liquids, so atmospheric air 
will be taken as the type of gases. All statements made in Section 
VII. concerning fluids, apply to gases as well as to liquids. 

Note. — It is taken for granted that the school has an air-pump, 
an instrument that will soon be described, and the simpler pieces of 
apparatus that generally accompany it. 

Weight of Air. 

Experiment 42. — On a delicate balance, care- 
fully weigh a tliin glass or metal vessel that will 
hold several liters, and that may be closed by a 
stopcock. Pump the air from the vessel, close the 
stopcock, remove the vessel from the pump and 
carefully weigh it again. Its loss of weight meas- 
ures the weight of the air removed. Fig. G8. 

Experiment 43. — Fill a tumbler with water, place a slip of thick 
paper over its mouth and hold it there while the tumbler is inverted; 




88 



ELEMENTARY PHYSICS. 




Fig. 69. 



the water will be supported when the hand is 
removed from the card. 

Experiment 44. — To the lamp-chimney ap- 
paratus used in Experiment 32, connect a thick- 
walled rubber tube, and partly exhaust the 
air with the air-pump or by suction. Hold 
the chimney in different positions, and notice 
that the pressure that pushes in the rubber 
diaphragm is exerted equally in all directions. 
Any change of pressure will be shown by a 
change in the form of the rubber cup. 

Experiment 45. — The Magdeburg hemispheres are accurately fit- 
ting, metallic vessels, generally three or four inches in diameter. 
Their edges are provided with project- 
ing lips, and fit one another au*-tight ; 
the lips prevent sidewise slipping. 
Grease the edges to make sure of a 
tight joint, fit the hemispheres to each 
other, and exhaust the air with a 
pump. Close the stopcock, remove 
the hemispheres from the pump, at- 
tach the second handle, and, holding 
the hemispheres in different positions, 
tiy to pull them apart. When you 
are sure that the pressure that holds 
them together is exerted in all direc- 
tions, place them under the receiver 
(i.e., the bell-glass) of the air-pump, 
and exhaust the air from around 
them. The pressure seems to be re- 
moved, for the hemispheres fall apart 
of their own weight. 

113. The Air. — These experiments show that air has 
weighty that it exerts great pressure at the surface of the 
earthy and that this pressure is transmitted equally in all 
direc'ions. Under ordinary conditions, a liter of air weighs 
about 1.3 grams; a cubic foot weighs about an ounce and 
a quarter. 




Fig. 70. 



THE MECHANICS OF GASES. 



89 



Atmospheric Pressure. 

£zperimeiit 46. — Into one end of a piece of stout glass tubing about 
1 m. long, and with a bore of about 1 cm., closely press a good cork or 
rubber stopper. Fill the tube with water; close the open end with 
tlie forefinger; invert Uie tube over lh.> water-bath, and, when the 
end is under water, remove the 
finger. Note whether the water 
falls away from the corked end 
of the tube. Loosen or remove 
the cork, and note the result. 

Experiment 47. — Fill with 
mercury a stout glass, tube 
closed at one end and about 
50 cm. long; a long "ignition 
tube " will answer. Invert it 
at the mercury-bath as shown 
in Fig. 71. Note whether the 
mercuiy falls away from the 
closed end of the tube. 

Experiment 48. — Select a 
stout glass tube about 80 cm. 
long, several millimeters in in- 
ternal diameter, and closed at 
one end. Twist a piece of 
paper into the shape of a hollow cone, and using it as a funnel, fill 
the tube with mercury. With an iron wire, remove any air-bubbles 
that you see in the tube. Close the open end with the finger, and 
invert the tube at the mercury-bath, as shown in Fig. 71. When the 
finger is removed, the mercury falls away from the upper end of the 
tube, and finally comes to rest at a height of about 30 inches (or 76 
cm.) above the level of the mercury in the bath, leaving a vacuum at 
the upper end of the Jube. This is known as Torricelli's Experiment. 

Experiment 49. — Modify the last exj>eriment by selecting a tube 
open at both ends. .Thoroughly soak in water such a membrane as 
comes tied over the stoppers of perfume bottles, and tie it tightly over 
one end of the tube. When the membrane is thoroughly dry, fill the 
Uihe with niercuiy, and invert it «it the mercury-bath as before. After 
measuring the height of the supported liquid column, prick a pinhole 
through the membrane, and notice what takes place. 




Fig. 71. 



9D 



ELEMENTARY PHYSICS. 



114. Atmospheric Pressure. — These experiment show 
that the pressure of the atmosphere may support a liquid 
column of great weight. This pressure at the sea-level is 
approximately 1,033.3 grams per square centimeter,^ or 14.7 
pounds per square inch. For rough work or " in round 
numbers," it is often said that this pressure, which is called 
an atmosphere, is a kilogram per square centimeter, or 
fifteen pounds per square inch. 

(a) Pascal carried a Torricellian tube (see Experiment 48) to the 
top of a mountain, and there found that the mercury column was 
three inches shorter, showing that, as the weight of the atmospheric 
column diminishes, the counterbalanced column of mercury also di- 
minishes. 

115. The Barometer. — A Torricellian tuhe^ firmly fixed 
^ to an upright support and properly graduated^ 

constitutes a mercurial barometer. The zero of 

En the scale is at the surface of the mercury in 
jf the cistern. 
^ (o) When scientific accuracy is required, the height of 

the barometer is corrected for temperature, for variations 
of gravity, for capillarity, for expansion of the scale, for 
elevation above sea-level, etc. 

(6) Observation shows frequent variations in the 
barometric readings. Some slight changes are found to 
be periodic, but the greater changes follow no known 
law. The utility of a barometer depends largely upon the 
fact that these irregular variations correspowl to chinges in 
the atmospheric pressure, and, therefore, signal coming mete- 
orological changes, The falling of the mercury generally 
[g-^ indicates the approach of foul weather; a sudden fall 
Wtf denotes the coming of a storm. The rising of the 
!• mercury indicates the approach of fair weather or the 

"clearing up" of a storm. 



^ 



:i 



FiQ. 72. 



EXERCISES. 



1. Give the pressure of the air upon a man the surface of whose 
20 square feet. 



THE MECHANICS OF GASES. 



91 



2. What is the weight of the air in a room 30 by 20 by 10 feet ? 

3. How much weight does a cubic foot of wood lose when weighed 
in air ? 

4. (a) What is the pressure on the upper surface of a Saratoga 
trunk 2 J by 3J feet? (b) How happens it that the owner can open 
the trunk ? 

5. (a) What effect would it have upon the height of the barometric 
column if the barometer tube was enlarged until it had a sectional 
area of 1 sq. cm. ? 

6. An empty toy balloon weighs 5 g. When filled with 10 1. of 
hydrogen, what load can it lift? A liter of hydrogen weighs 0.0896 g. 

Elastic Force. 

Experiment 50. — Tightly close the opening of a toy balloon, foot- 
ball, or other rubber bag, only partly filled with air. PL-xce it under 
the receiver of an air-pump, as shown in tlie 
accompanying figure, and exhaust the air from 
the receiver. The flexible wall of the bag will 
be pushed back by the innumerable impacts of 
the moving molecules against the confining sur- 
face. The observed phenomenon is in strict 
accord with the kinetic theory of gases, § 36. 

Experiment 51. — For the rubber bag used in 
Experiment 50, substitute successively a dish 
containing soap-bubbles, and a bottle with its 
mouth opening under water in a tumbler. Exhaust the air as be- 
fore, and notice the effect of the molecular impacts on the liquid 
walls of the confined air. 

116. Elastic Force of Gases. — The elastic force of a ga% 
supports and equals the pressure upon it. 




Km 



Relation of Volume to Pressure. 

Experiment 52. — Provide two glass tubes connected by stout rubber 
tubing and carried by a vertical stand as shown in Fig. 74. The left- 
hand tube, Bj may be about 30 cm. long and 5 mm. in diameter, and 
must be closed at the upper end. The right-hand tube, C, should !>« 
of greater diameter, open at the upper end, and arranged so that it 
may slide up and down by the side of the vertical scale. Pour mercury 



92 



ELEMENTARY PHYSICS. 




into C, thus confiniug in B a quantity of air on which the experiment 
is to be made. The volume of tliis confined air under varying pres- 
sure will be proportional to the length of the tube which it occupies. 
Slide C up or down until the mercury stands at the same level in B 
and C The air confined in B is under a pressure of one atmosphere. 
Read directly from the scale the length of the tube tliat it occupies 
and make a record of it. For .the sake of illustra- 
tion, suppose that it occupies 5 spaces. Note the 
rea<]ing of the barometer at the time of the ex- 
periment ; suppose this, to be 76 cm. Make the 
record that the confined air, under a pressure of 
76 cm. of mercury, occupies 5 volumes. Then 
raise Cythus increasing the pi-essure on the air 
in B. When the vertical distance between the 
levels of the mercury in B and C is one-fourth 
the height of the barometric column, the pressure 
upon the confined air will be { atmospheres, or 
95 cm. of mercury; the elastic force of the con- 
fined air just supports this pressure, and must, 
therefore, be \ atmospheres. Reading from the 
scale, it will be seen that the confined air meas- 
ures only 4 volumes; i.e., f as nmch as it did under a pressure of 
one atmosphere. Then raise C until the vertical distance between the 
two surfaces of the mercury is half the height of the barometric col- 
umn; the confined air is under a pressure of | atrnospheres (114 
cm.) ; its volume is | what it was under a pressure of one atmosphei-e, 
i.e., 3} volumes. Again, raise C until the vertical distance between 
the two surfaces of the mercury is equal to the height of the barometric 
column ; the confined air is now under a pressure. of two atmospheres 
(152 cm.) ; its volume is \ what it was under a pressure of one atmos- 
phere, i.e., 2i volumes. Arrange the data in the following form, and 
complete the table : — 

Volumes. 
5 
4 

n 

117. Boyle's Law. — When the temperature remains 
constant, the volume of a ga% varies inversely as the pres- 



Fig. 74. 



Pressures, 

76 

95 
114 
152 



Products. 

380 

? 

? 

? 



THE MECHANICS OF GASES. 93 

sure upon it; i.e., the product of the volume of the gas 
by its pressure is constant, 

(a) Later experiments have shown that Boyle's law is only 
approximately true, and that all gases deviate from it as they near 
the point of liquefaction. This law is often called Mariotte's. 

BZBRCISBS. 

1. Under ordinai*y conditions, a certain quantity of air measures 
one liter. Under what conditious can it be made to occupy (a) 500 
cu. cm.? {b) 2,000 cu. cm.? 

2. Into what space must we compress (a) a liter of air to double its 
elastic force? (6) Two liters of hydrogen? 

3. A barometer standing at 30 inches is placed in a closed vesseL 
How umch of the air in the vessel must be removed that the mercury 
may fall to 15 inches? 

4. A vertical tube, closed at the lower end, has at its upper end a 
frictionless piston that has an area of 1 square inch. The weight of 
this piston is 5 pounds,' and it cohfiues 2\ cubic inches of diy steam. 
(a) What is the elastic force of the confined steam? (6) If the 
piston is loaded^' witk a weight of 10 pounds, what will be the 
volume of the confined steam? 

5. Mercury stands at the same level in both arms of the apparatus 
shown in Fig. 74. The barometer rises, and thereupon is noticed a 
difference in the heights of the two mercury columns. In which arm 
does the mercury stand the higher ? Why ? 

Siphon. 

Ezperlment 53. — Place a pail of clean water on the table, and an 
empty water pail on the floor. Place one end of a piece of thick- 
walled rubber tubing, about a yard long, in the water. Hold the 
other end of the tubing below the level of the table-top, and fill the 
tube with water by suction. Notice the transfer of water from one 
pail to the other. Be careful that the flexible walls of the tubing do 
not close upon each other at the edge of the upper pail, and thus cut 
off the flow. 

Experiment 54. — Change the positions of the pails, placing the 
one containing water on the table. Gradually lower the rubber tub- 
ing into the water, allowing air to escape from the upper end as water 



9i 



ELEMENTARY PHYSICS. 



enters at the lower end. When the tube is filled with water, pinch one 
end of it tightly, and carry it below the level of the table-top. Raise 
and lower this end of the tubing to see if the distance of the opening 
below the edge of the upper pail has anything to do with the rate of 
flow. 

118. The Siphon is essentially a tube with unequal arms^ 
used to carry liquids from one levels over an elevation^ to 
a lower level by means of atmospheric pressure. The flow- 
will continue until the 
5j .^^^^^^^_^ ^c liquids stand at the same 

level, or until air enters 
the tube at the end of 
the shoiter arm. 

(a) The vertical distance 
from the level of the upper 
liquid to the highest point 
of the.tube {ah) is the length 
of one arm ; the vertical dis- 
tance from the highest point 
of the tube to the lower end 
of the tube, or to the level 
of the liquid into which it 
dips (erf), is the length of the 
other arm. The second of 
these must exceed the first. 
Consider the horizontal layer of molecules in the tube at the levels, 
a and d. The atmospheric pressures, whether direct or transmitted 
by the liquids in accordance with Pascal's law, will be upward and 
equal ; represent them by p. The weight of the water in the short 
arm produces a downward pressure at a ; represent this by to. The 
resultant of these forces acting at a is jo — w. Silnilarly, the weight 
of the water in the long arm produces a downward pressure at rf; 
represent this by to'. The resultant of these forces acting at rf is 
p — w'. These two resultants act against each other, p — w being 
the greater. The resultant of these resultants is their difference; 
(p — w) — (p — u/) = w' — w. Thus we see that the liquid is pushed 
through the tube by a resultant force equal to the weight of a liquid 




Fig. 76. 



THE MECHANICS OF GASES. 



96 



column whose height is the difference between the two arms of the 
siphon. 

(ft) If the downward liquid pressure at a is as great as the atmos- 
pheric pressure, the liquid will not flow. Hence, the elevation over 
which water is to be siphoned must be less than 34 feet. 



Pumps. 

Experiment 55. — Every one knows that a liquid may be sucked up 
through a straw or other tube. Modify the familiar experiment by 
passhig a glass tube snugly through the cork of a bottle. Fill the 
bottle with water, and close it with the perforated cork. Be sure that 
no air is left in the bottle. The tube should dip an inch or so into 
the water. Try to suck water from the bottle. 

119. The Lift Pump or suction-pump consists of a cylin- 
der or barrel, a piston, two valves, and a suction-pipe, the 
lower end of which dips below the 
surface of the liquid to be raised. 
The piston works practically air-tight 
in the cylinder, and has an outlet- 
valve that opens upward. The inlet- 
valve is at the upper end of the 
suction-pipe, and also opens upward. 



(a) When the piston is drawn upward, 
its valve is closed by the pressure of the 
air above, and a partial vacuum is formed 
in the cylinder below. The elastic force of 
the air in the cylinder being thus reduced, 
the atmospheric pressure forces water up the 
suction-pipe, driving the air above it through 
the lower valve. When the piston is pushed 
down, the inlet-valve is closed, and the con- 
fined air escapes through the outlet-valve. 
As the piston continues its work, the air is gradually removed from 
the cylinder and suction-pipe, and the transmitted pressure of the 
atmosphere pushes the water up to take its place and to restore the 
disturbed equilibrium. Owing to mechanical imperfections, the prac- 
tical limit for a pump lifting water by suction is about 28 vertical feet. 




96 



ELEMENTARY I'llYSlCS. 



120. The Force Pump. — The operation of the force- 
pump is similar to that of the suction-pump. The outlet- 
valve generally opens from the cylin- 
der, the piston being made solid, as 
shown in the accompanying figure. 

(a) When the piston is forced down, the 
iiilet-valve is closed, the water being forced 
through the other valve into the discharge-pipe. 
When next the piston is raised, the outlet- 
valve is closed, preventing the return of the 
water above it, while atmospheric pressure 
forces more water from below into the barrel. 

For the pui*pose of securing steadiness for 
the stream as it issues from the delivery-pipe, 
the water usually passes into an air-chamber. 
The elasticity of the confined and compressed 
air largely takes up the pulsating effect due to 
the successive pushes of the piston, and forces 
the water from the nozzle of the delivery-pipe 
in a continuous stream. 







Fig. 77. 



121. The Air Pump is an instrument for removing a gas 
from a closed vessel. Figure 78 shows the essential parts 
of one of the many forms. 

(a) The glass receiver, /?, fits accurately upon the ground plate. 
The edge of the receiver is often greased to insure an air-tight joint. 
The -inlet-valve, v, may be carried by a rod that passes through the 
piston, P. The outlet-valve, v', is in the piston. Of course, the 
valves and all sliding parts must work au*-tight. A down-stroke of 
the piston carries down the valve-rod, and closes v ; the elastic force 
of the air in C opens v\ and some of the confined air escapes. The 
next up-stroke of the piston closes u', lifts the valve-rod, and opens v. 
The upward motion of the valve-rod is closely limited by a shoulder 
near its upper end, the piston sliding upon the rod during the greater 
part of its up-and-down movements. The air that passes up through 
v' is forced out through an opening (preferably closed by a valve) at 
the top of the cylinder. The air in t and R is thus gradually removed. 
As only a fractional part of this residual air is removed at each 



THE MECHANICS OF GASES. 



97 



stroke, a perfect vacuum is out of the question ; moreover, there is a 
limit arising from the unavoidable imperfections of the apparatus. 
The glass vessel, F, contains a gauge to indicate the degi'ee of rare- 
faction obtained. A stopcock at S, when turned one way, cuts off 
communication between C and R, thus reducing the risk that air will 
reenter the receiver ; when turned the other way, it readmits air to R. 




Fig. 78. 

122. The Condensing Pump is an instrument for com- 
pressing a gas into a closed vessel, as in pumping air into 
a pneumatic tire of a bicycle. 

(a) It differs from the air-pump chiefly in that the valves are made 
strong enough to endure high pressures, and that they open toward 
the receiver. 

BXBRCISES. 

1. If a ILft-pump can just raise water 28 feet, how 
high can it raise alcohol having a density of 0.8 ? 

2. Water is to be taken over a ridge 12.5 m. higher 
than the surface of the water, (a) Can it be done 
with a siphon? Why? (6) With a lift-pump ? Why? 
(c) With a force-pump? Why? 

3. Will a given siphon carry water over a given 
elevation more rapidly at the top, or at the bottom, of 
a mountain ? Why ? 

4. The "sucker" consists of a circular piece of 

H 




Fig. 79. 



98 ELEMENTABT FUYSICS. 

thick leather with a string attached to its middle. Being soaked 
thoroughly in water, it is firmly pressed apon a flat stone to drive out 
all air from between the leather and the stone. Unless the stone is 
too heavy^ it may be lifted by the string. Is the stone really pulled 
up, or pushed up? £xplain your answer. 

• 5. Partly fill two bottles with water. Connect them by a bent tube 
that fita closely into the mouth of one, and loosely into the month of 
the other. Place the bottles under the receiver 
of the air-pump, and exhaust the air. Note 
and record what takes place. Admit air to the 
receiver. Note and record what takes place. 
Write an explanation of the phenomena. 

6. Fill a test-tube with water and invert it 
in a tambler of water. With a pen-filler, intro- 
duce a few drops of sulphuric ether, a very vola- 
tile and extremely inflammable liquid, into the 
test-tube. The ether will rise to the top of the tube. Place the tum- 
bler and the test-tube under the receiver and exhaust the air. The 
water in the test-tube falls. Readmit air to the receiver, and note the 
contents of the test-tube. Record your conclusions concerning the 
effect of pressure upon the molecular condition of sulphuric ether. 

7. With a short piece of rubber tubing, connect the short arms of 
two L-shaped glass tubes, and set up the apparatus as a siphon. 
While the water is flowing, perforate the rubber wall between the 
glass tubes. Note and explain the effect. 




CHAPTER III. 



ACOUSTICS: MASS PHYSICS. 
I. THE NATURE OF SOUND, ETC. 

123. Sound is a mode of motion that is capable of affect- 
ing the auditory nerve* 

Cause of Sound. 

Sxperiment 56. — Sound a tuning-fork and just touch a water sur- 
face with one of its prongs. Notice the spray. 

£xperiment 57. — Grasp one end of a straight spring made of 
hickory or steel in one end of a vise, 
as sliown in Fig. 81. Pluck the free 
end of the spring so as to produce a 
vibratoiy motion. If the spring is 
long enough, the vibrations may be 
seen. Lower the spring in the vise 
to shorten the vibrating paii; of the 
rod, and pluck it again. The vibra- 
tions are reduced in amplitude, and 
increased in rapidity. Continued 
shortening of the spring will render 
the vibrations invisible and audible; 
they are lost to the eye, but revealed 
to the ear. 




Fig. 81. 



124. Sound is caused by the 
rapid vibrations of a material 
body. All sounds may be 
traced to such vibrations. Bodies that emit sounds are 
called sonorous. 

99 



100 ELEMENTARY PHYSICS. 



Wind or Wave? 

Experiment 58. — Provide a tube four or five yards long, and about 
four inches in diameter. A few lengths of common spout from the 
tinner's will answer. Furnish it with a funnel-shaped piece, having 
an opening about au inch in diameter. Place the tube on a table with 
a candle flame opposite the opening at B. With a book, strike a 




Fig. 8*J. 

sharp blow upon the table opposite tlie opening at A. The flame will 
be agitated and perhaps blown out. Something went from A to B. 
Did it go through the tube ? 

Experiment 59. — Close the opening at A and repeat the experi- 
ment; the flame is not put out. Remove the tube and repeat the 
blow ; the flame is not put out. 

Experiment 60. — Dissolve as much petassjum nitrate (saltpeter) 
as you can in half a cupful of hot water. Soak a piece of blotting- 
paper in this liquid and dry it. This "touch-paper" burns with 
much smoke but no flame. Burn the paper in the tube near A, fill- 
ing that end of the tube with smoke. Repeat Experiment 58. No 
smoke issues at B ; it was not a wind that passed through the tube. 

125. Propagation of Sound. — Sound is ordinarily propa- 
gated through the air. Tracing the sound from its source 
to the ear of the hearer, we may say that the first layer of 
air is struck by the vibrating body. The particles of this 
layer give their motion to the particles of the next layer, 
and so on until the particles of the last layer strike upon 
the drum of the ear. ^ - ■ . 

(a) This idea is beautifully illustrated by Professor Tyndall. He 
imagines five boys placed in a row, as.shpwn in Fig. 83. "I suddenly 
push A ; A pushes B and regains his upright position; B pushes C; 
C pushes D; D pushes E; each boy, after the transmission of the 
push, becoming himself erect. E, having nobody in front, is thrown 



THE NATURE OF SOUND. 



101 




forward. Had he been standing on the edge of a precipice, he 

would have fallen over; had he stood in contact with a window, he 

would have broken the 

glass; had he been close 

to a drumhead, he would 

have shaken the drum. 

We could thus transmit 

a push through a row 

of a hundred boys, each 

particular boy, however, 

only swaying to and fro. 

Thus also we send sound 

through the air, and pj^ 33 

shake the drum of a 

distant ear, while each particular particle of the air concerned in the 

transmission of the pulse makes only a small oscillation." 

The Medium of Sound. 

Experiment 6i. — Provide a wooden rod about half an inch square 
and five or six feet long. . Place one end of this rod (preferably made 
of light, dry pine) against the panel of a door; hold the rod hori- 
zontal, and place the handle of a vibrating tuning-fork against the 
other end. Notice the sound given out by the panel. The common 
"string telephone " is a more familiar illustration of the transmission 
of sound by a solid. 

126. Sound Media. — Any elastic substance may he the 
medium for the transmission of sound. Liquids and solids 
are better conductors of sound than gases are. The 
scratching of a pin may be heard through a long wooden 
beam ; and the gentle tap of a hammer, through a water- 
pipe a mile or more in length. 

Vibratory Motion. 

Sxpsriment 62. — Grip one end of the meter stick in a vise, .as 
shown in Fig. 81. Pluck the free end, and notice that the vibrating 
end returns periodically to the starting point. Suspend a lead bullet 
by a long thread, swing it as a pendulum, and notice that the ball 
returns periodically to the starting point. Swing the ball as a conical 



102 ELEMENTARY PHYSICS. 

penduliunt aod notice that the ball, moving in a circular path, returns 
periodically to the starting point. 

Sxperiment 63. — Fasten an elastic cord to a ball, or buy a *^ return 
ball ** at a toy shop. Hold the end of the cord iu one hand, and, with 
the other hand, pull the ball down and let it go. The ball swings up 
and down iu the direction of the length of the cord. Notice that the 
speed of the ball varies much as does that of a common pendulum, 
and that the ball returns periodically to the starting point. 

127. Vibrations. — When the parts of a body move so 
that each retui*ns periodically to its initial position, the 
body is said to be in vibiution. Z%e motion made in the 
interval between two successive passages in the same direction 
through any position is called a vibration. 

(a) A vibration corresponds to a double or " complete " oscillation. 
When the movement is comparatively slow, as that of a pendulum, 
the term "oscillation" is commonly used; the term "vibration" is 
generally confined to rapid movements, like those of a sounding 
body. 

Pendular Motion. 

Experiment 64. — Let a pupil take a ball-and-thread pendulum to 
the further side of the room, and swing the ball in a circular path, 
thus forming a conical pendnlum. When the speed of the ball has 
become uniform, count the swings that the ball makes around the 
circle in 30 seconds. Then place your eye on a level with the ball and 
observe it; i.e., look at the ball along a line 
of sight that is in th^ plane of the circle. 
The hall will appear to move from side to side 
in a straight line that coincides with a diameter 
of the circle, and to vary its velocity as a com- 
mon pendulum does. Next, swing the same 
ball as a common pendulum, and count the 
vibrations that it makes in 30 seconds. A 
conical pendulum and a common pendulum 
of the same length have the same period. 
When the common pendulum is viewed from 
beneath, i.e., when the line of sight is in the plane of vibration as 
before, the ball again appears to move in a straight line and with a 




THE NATURE OF SOUND. 105 

like varying velocity. This apparent motion and its relation to the 
real motion are very interesting and instructive. Let the circle shown 
in Fig. 84 represent the path described by the conical pendulum ; then 
i?vill the diameter, AG, represent the apparent rectilinear path. Sup- 
pose that the ball goes around the ^cle in two seconds. Divide the 
circumference into any number of equal parts, as 12. The ball will 
move over each of these equals arcs in ^ of a second. To one who is 
looking at this motion in the plane of the paper, the ball appears to 
go from Ato B while it really goes from ^ to 6 ; it appears to go from 
-B to C while it really goes from 6 to c ; etc. When the ball is at rf, it 
is moving across the line of sight, and, therefore, appears to have its 
greatest velocity, just as a common pendulum does, at the middle of 
its arc. When it is at A or G, it is moving in the line of sight, and, 
therefore, appears to be at rest, although it is really moving with its 
uniform velocity. From a study of the figure, it will be seen that the 
ball appears to go from A ix) G and back in the two seconds in which 
it really goes around the circle. The unequal lengths, AB, BC, . . . 
FG, give a fair idea of the varying speed of a common pendulum. 

128. Simple Harmonic Motion. — If, while a particle 
moves in the circumference of a circle with uniform ve- 
locity, a point moves along a fixed diameter of the circle 
so as always to be at the foot of a perpendicular drawn 
from the particle to the diameter, as described in Experi- 
ment 64, the motion of the point along the diameter is 
called a simple harmonic motion. The radius of the circle, 
or the distance from the middle to the extremity of the 
swing, is called the amplitude of vibration ; the time inter- 
vening between two passages of the particle in the same 
direction through any point is called the period of vibra- 
tion. 

Transverse Waves. 

Experiment 65. — Drop a pebble into a tub of water. Waves will 
be seen moving on the surface of the water from the center of dis- 
turbance, and in concentric circles, toward the sides of the tub. A 
small cork floating on the surface rises and falls with the water, but 
is not carried along by the advancing waves of troughs and crests. 



104 



ELEMENTARY PHYSICS. 



Sxperiment 66. ~ Tie one end of a fiof t cotton rope about 20 feet 
long to a fixed support, and hold the other end in the hand. Move 
the hand up and down with a quick, sudden motion, so as to set up a 




Pig. 85. 

series of waves in the rope, as shown in Fig. 85, in which each 
curved line may be considered an instantaneous photograph of a rope 
thus shaken. 

129. Waves of Crests and Troughs. — In the familiar 
waves of water, ropes, carpets, etc., the motion of each 
material particle is vibratory, not progressive ; to and fro 
across the line in which the wave advances, i.e., ti'ans- 
verse. It is also a simply harmonic motion. The only 
thing that has an onward movement is the wave^ which is 
only a form or change in the relative positions of the par- 
ticles of the undulating substance, 

(a) By fixing a pencil at the end of a lath firmly held at the other 
end, and vibrating in a horizontal plane, the pencil may be made to 
mark a nearly straight line, ah, on a sheet of paper or cardboard. By 
moving tlie paper while the rod is vibrating, the pencil may be made 
to trace a sinusoidal curve or w^avy line like that shown in Fig. 86. 




Fio. 86. 

The distance from crest to crest (1 to 5), or from trough to trough 
(3 to 7), or from any point to the next point at which the vibrating 
])article was in the same stage*'of vibration or in the same phase 
(.4 to 4, or 2 to 6, or 4 to B), is called a wave-length. Evidently, the 
disturbance, i.e., the wave, advances just one wave-length in the time 
required for one vibration ; this time is called the vibration-period. 



THE NATURE OF SOUND. 



106 



Fig. 87. 



Longitadinal Waves. 

Experiment 67. — Make a spiral spring about 12 feet long by 
closely winding No. 18 spring-brass wire on a rod about half an inch 
in diameter. Fasten one end of the spiral to a hook on the wall, or 
clamp it in a vise, and tie short pieces of brightn^olored strings into 
several of the coils. Holding 
the other end of the spiral in 
the hand, insert a finger-nail or 
knife-blade between two turns 
of the wire near the hand, and 
pull one of them further from 
the other. Suddenly release the coil, and a pulse will run along the 
spiral. Each coil swings to and fro, the coils being crowded closely 
together at one place, and more widely separated at another. 

Experiment 68. — Tightly tie a sheet of writing paper over the 
large end of the tube used in Experiment 58, and hold a candle fiame 
in front of the small end. Tap the paper diaphragm, and notice the 
consequent flickering of the flame. 

130. Waves of Condensation and Rarefaction. — The 
advancing paper diaphragm or other vibrating body 
crowds the layers of air immediately in its front, thus 
setting up a condensation or push along the length of the 
lube, as explained in § 125. When the paper swings with 




Fig. 88. 

it3 pendulum-like motion in the opposite direction, the 
nearest layers of air follow it, thus setting up a rarefac- 
tion. As the paper diaphragm continues to vibrate, a 
series of condensations and rarefactions is sent along the 
tube, as shown in Fig. 88, which compare with Fig. 84. 



106 BLEMENTART PHYSICS. • 

The air particles are crowded onusnally at A and (?, 
where their velocity is the least, and are separated more 
widely at D, where their velocity is greatest Just as a 
water wave consists of two parts, a crest and a trough, 
so a Bound wave comusts of two parts^ a condensation and 
a rarefaction. The particles in a sound wave move with 
simple harmonic motion forward and backward in the line 
of propagation, and not across it. The vibrations are 
longitudinal, not transverse. 

(a) A series of complete sound waves, such as would be set up 
in the open air, consists of alternate condensations and rarefactions 
advancing in the form of concentric spherical shells, at the common 
center of which is the sounding body. Any radius of the sphere is 
a line of propagation of the sound. 

(b) The distance from any point to the next point that is in the 
same phase, as from condensation to condensation or from rarefaction 
to rarefaction, is a wave-length. The wave advances one wave-length 
in the time required for one vibration, or in a wave-period. 

(c) A sinusoidal curve like that shown in Fig. 86 is commonly 
used to represent a sound wave. The parts above the horizontal line 
represent condensations, while the parts below that line represent 
rarefactions. The curve is merely a symbol for the sound wave, not 
a picture of oue. 



1 . State clearly the difference between a transverse and a longitu- 
dinal wave. Illustrate. 

2. The velocity of sound being given as 1,145 feet per second, what 
is the wave-length of a tone due to 458 vibrations per second ? 

3. It is a common experiment for one of two boys in swimming 
to hold his head under water while another at a distance strikes 
two stones together under water. The loudness of the sound heard 
by* the first boy is painful and sometimes injurious, even when the 
distance is so great that the sound would be scarcely heard in the 
air. Explain. 

4. If a blow is struck with a hammer upon one end of a long iron 
pipe, a listener at the other end may hear two sounds instead of one. 



I • 



VELOCITY, REFLECTION, AND REFRACTION. 



107 



6. What is the difference between an oscillation and a vibration ? 

6. What is the difference between a motion of translation and one 
of vibration ? Illostrate. 

7. Cut a slit 1 mm. x 2 cm. in a postal card. Place a ruler below 
Fig. 86, and parallel with the printed lines. Place the edge of the 
card against the edge of the ruler, so that the slit shall be at right 
angles to the line, AB, at its end ; i.e., so that ah may be seen through 
the slit. Slide the card with steady motion toward the right and 
along the edge of the ruler, ob- 
serving the apparent motion of 
the short black line up and down 
the slit. How does that appar- 
ent motion compare with the 
simple harmonic motion of the 
pendulum ? 

8. Mount a Crova disk about 
30 cm. in diameter upon the 
spindle of a whirling-table. Tho 
disk may be bought for fifty 
cents or less. Hold a card with 
a narrow slit about 10 cm. long 
close to the disk, and so that 
the slit is parallel to the radius 
of the disk. Rotate the disk and watch the slit. The apparent mo- 
tion of the dots along the slit indicate the way in which air particles 
actually move in a sound wave. 




Fig. 89. 



11. VELOCITY, REFLECTION, AND REFEACTION 
OF SOUND. 

131. The Velocity of Sound depends upon two considera- 
tions, — the elasticity and the density of the medium. 
It varies directly a% the square root of the elasticity^ and 
inversely as the square root of the density. 

(a) The velocity of the wave motion may he found hy multiplying 
the wave-length by the number of vibrations per second, or the wave- 
length may be found by dividing the velocity by the number of vibra- 
tions. 



108 ELEBfENTARY PHYSICS. 

(b) Carefnl experiment has established the fact that the velocity of 
sound in air at the freezing temperature (0° C. or 32^ F.) is about 332 m., 
or 1,090 feet per second. Oxygen is sixteen times as dense as hydro- 
gen. Under the same pressui-e, the elasticity is the same; hence, 
sound travels four times as fast in hydrogen as it does in oxygen. 
A change of pressure on a gas will change elasticity and density 
equally, and, therefore, will not affect the velocity of sound trans- 
mitted by the fas. If a confined portion of any gas is heated, its 
elasticity is inci'eased without any change of density. Hence, a rise 
of temperature without barometric change increases the velocity of 
sound in the air. The added velocity is about 0.6 m., or 2 feet for 
each degree that the centigrade thermometer rises; or 0.33 ni. or 
1.12 feet for each degree that the Fahrenheit thermometer rises. 

(c) Owing to the high elasticity of liquids and so^ds as compared 
with their densities, they transmit sound with great velocities. In 
water at 8° C, sound travels at the rate of 4,708 feet per second ; in 
glass, the velocity is 14,850 feet, and in iron it is 16,820 feet ; in lead, 
a metal of high density and low elasticity, the velocity of sound is 
4,030 feet per second. 

Reflection. 

Experiment 69. — Repeat Experiment 66, and notice that the waves 
successively started by the hand are turned back at the other end of 
the rope and uieet the advancing waves. 

Experiment 70. — Slip the loops at the ends of the wire spiral used 
in Experiment 67 over hooks screwed into the sides of two boxes. 
Separate the boxes so as to support and slightly stretch the spiral, 
fastening the boxes by nailing them down or by loading them with 
sand. Start a pulse in the spiral, and notice that the wave runs to 
the other end, is turned back or reproduced in the same medium, 
moves along the spiral to its starting point, and so continues its jour- 
neys to and fro until its energy is 
dissipated. It looks as though a 
wave motion might be reflected as 
well as a motion of translation. 




Experiment 71. — Hold a lamp 
reflector or other large concave 
mirror directly facing the su:*, fo 
Fig. 90. as to bring the rays of light to a 



VELOCITY, Reflection, and refraction. 



109: 



focus. Move a piece of paper until you find the place where a spot 
ou the paper is tnost briiliautly illuminated by the reflected rays, and 
measure the distance of this focus, F, from A, the center of the re- 
flector (see Fig. 90). At some point, W, between F and C, the center 
of curvature of the reflector, hang a loud-ticking watch, and hunt for 
the point, X, at which the ear can most distinctly hear the ticking. 
Use a glass funnel as an ear-trumpet. Keep watch and ear in these 
positions, and have the reflector removed. The ticking will become 
less distinct or wholly inaudible. 

132. Reflection of Sound. — When a sound wave strikes 
an obstacle, it is reflected in obedience to the principle 
given in § 47. 

(a) Sound waves starting from a point, as F, may be twice reflected, 
as shown in Fig. 91, and thus made to 
converge at another point, as F'. By 
such means, the ticking of a watch may 
be made audible at a distance of two or 
three hundred feet. Two reflectors no 
placed are said to be conjugate to eadh other. 
This principle uiiderlies the phenomena 
of some whispering galleries. 




133. An Echo is a sound re- 



FiG. 91. 



peated by reflection so as to be heard again at its source. 

(a) The time interval between a sound and its echo is the time 
required for a sound to travel twice the space interval between tiie 
source of the sound and the reflecting body. Re^nembering that at 
the ordinary temperature sound travels about 1,120 feet a second, and 
supposing a person to pronounce five syllables in a second, it will be 
seen that the echoing surface should be about 112 feet distant. If it 
is nearer than this, the reflected sound will return before the articula- 
tion is complete and confusedly blend with it. 



Refraction. 

Experiment 72. — Fill with carbon dioxide a large rubber toy bal- 
loon or other double-convex lens having easily flexible walls. Sus- 
pend a watch, and place yourself so that you can just hear its ticking. 



110 



ELEMENTARY PHYSICS. 




Fig. 92. 



Have the gas-filled lens moved back and forth in the line between 
watch and ear until the ticking is much more plainly heard. Use a 

glass-funnel as an ear- 
trumpet. 

134. Refraction of 
Sound. — The lines of 
propagation of sound 
are ordinarily diver- 
gent. When sound 
waves pass obliquely 
from one medium to 
another of difiFe^ent 
density, the line of propagation is bent, as will be more 
fully explained in the chapter on radiant energy. Thi% 
bending of the lines of propagation is called refraction. 

BXBRCISBS. 

1. If 18 seconds intervene between the flash and report of a gun, 
what is its distance, the temperH-ture being 0° C? 

2. Steam was seen to escape from the whistle of a locomotive, and 
the sound was heard 7 seconds later. The temperature being 15° C, 
how far was the locomotive from the observer? 

3. What is the length of sound waves propagated through air at a 
temperature of 15° C. by a tuning-fork that vibrates 224 times per 
second? 

4. Determine the temperature of the air when the velocity of sound 
is 1,150 feet per second. 

5. Why will an open hand or a palm-leaf fan held back of the ear 
often aid a partly deaf person in hearing a speaker? 

6. A shot is fired before a cliff and the echo heard 6 seconds lat«r. 
The temperature being 15° C, determine the distance of the cliff. 

7. Taking the velocity of sound as 332 m., determine the length of 
the waves produced by a body vibrating 830 times per second. 

8. When the velocity of sound is 1,128 feet, determine the rate of 
vibration of the vocal cords of a man whose voice sets up waves 12 
feet long. 

9. Why does sound travel more rapidly through the iron of a pipe 
than it does through the air contained in the pipe? 



CHARACTERISTICS OF TONES. 



Ill 



10. From the cyclopedia, cull the story of the prison built by Dio- 
nysius, the Syracusan tyrant, and explain its, remarkable acoustic 
properties. 

11. On opposite sides of the center of a disk of cardboard about 
15 inches in diameter, cut out two sectors, as shown in Fig. 93. 
Mount the disk on a whirling-table. Sit beside tlie apparatus, so as 
to turn the driving wheel with one hand, and with the other hold a 
toy trumpet so that its axis shall be inclined to the surface of the 
disk, about midway between center and circumference. Rotate the 
disk steadily and sound the 
trumpet at the same time. 
Let other pupils take posi- 
tions in a distant pai*t of 
the room, as indicated by 
the law of reflected motion, 
so that the sound waves from 
the trumpet reflected by the 
disk will reach their ears. 
When the sectors pass before 
the mouth of the trumpet, 
the sound will become softer, and when the cardboard reflector 
passes, the sound will become stronger. Record a description and 
explanation of the exercise. 




Fig. 93. 



ni. CHARACTERISTICS OF TONES. 

135. Differences in Tones. — Sound waves differ in 
respect to amplitude, length, and form. Variations in 
amplitude correspond to differences in intensity or loud- 
ness ; differences in wave-length correspond to differences 
in pitch ; differences in wave-form correspond to differences 
in timbre or musical quality. 



Intensity and Amplitude. 

Experiment 73. — Set a tuning-fork in feeble vibration by striking 
it gently; the sound that you hear will be faint. Strike the fork a 
harder blow; its prongs will vibrate with gteater energy and ampli- 



112 ELEMENTARY PHYSICS. 

tude, and the sound will be louder. For a similar experiment, pluck 
the string of a guitar. 

136. Intensity and Amplitude. — The intensity of a sound 
depends primarily upon the energy of vibration of the sono- 
rous body^ and thence on the amplitude of the vibrating 
particles of the sound medium. The greater the ampli- 
tude, the greater the energy and the louder the sound. 

Intensity and Distance. 

Experiment 74. — Whisper into one end of a length (50 feet) of 
garden hose. A person listening with his ear at the other end of the 
hose can distinctly hear what is said although the sound is inaudible 
to a person holding the middle of the hose. 

137. Intensity and Distance. — In the open air, a sound 
wave expands as a spherical shell, distributing its energy 
over a gradually increasing area, and correspondingly les- 
sening the energy per unit of area. Hence, the intensity 
of sound varies inversely as the square of the distance 
from the sonorous body. This law is true only when the 
distance is so great that the sounding body may be con- 
sidered a center from which the sound waves proceed. 

(a) If the sound wave is not allowed to expand as a spherical 
shell, its energy cailnot be thus diffused and its intensity will be 
conserved. Hence, the efficiency of speaking-tubes and speaking- 
trumpets. 

Intensity and Area. 

Experiment 75. — Strike a tuning-fork held in the hand. Notice 
the feeble sound. Strike the fork again and place the end of the 
handle upon a table. The loudness of the sound heard is remark- 
ably increased. 

Experiment 76. — Strike the fork and hold it near the ear, counting 
the number of seconds that you can hear it. Strike the fork again 
with equal force; place the end of the handle on the table and count 
the number of seconds that you can hear it. 



CHARACTERISTICS OF TONES. 



113 



138. Intensity and Area. — When the sonorous body has a 
large surface^ its vibrations set up well-marked condensations 
and rarefactions^ and the consequent sound is correspond- 
ingly intense. , 

(a) In the piano, violin, guitar, etc., the sound is due more to the 
vibrations of the bodies that carry the strings than to the vibrations 
of the strings themselves. The strings are too thin to impart enough 
motion to the air to be sensible at any considerable distance; but as 
they vibrate, their tremors are carried by the bridges to the sounding 
apparatus with which they are connected. These larger surfaces throw 
larger masses of air into vibration and thus gi'eatly intensify the sound. 
It necessarily follows that the energy of the vibrating body is sooner 
exhausted. 

Pitch. 

Experiment 77. — Draw a 
finger-nail across the tips of 
the teeth of a comb, slowly 
the fii*st time and rapidly the 
second time. Notice the dif- 
ference in the pitch of the 
sounds produced. 

Experiment 78. — From a 
piece of stiff cardboard, cut 
a disk 8} inches in diameter. 
From the same center, draw 
four circles with radii of 2J 
inches, 2| inches, 3 J inches, 
and 3 J inches, respectively. 
Divide the inner of these cir- 
cumferences into 24 equal 
parts, the second into 30, the 
third into 36, and the fourth 
into 48. At each division, 
punch a ^^-inch (5 mm.) 
bole. Cut a hole at the cen- 
ter and mount the perforated disk on the spindle of a whirling-table, 
and you have a simple form of the siren. Rotate the disk slowly, blow- 
ing meanwhile through a tube of about ^^g-inch bore, the nozzle of the 




Fig. 94. 



114 ELEMENTARY PHYSICS. 

tube being held opposite the interior ring of holes. As each succes- 
sive hole comes before the end of the tube,^a puff of air goes through 
the disk. As the speed of the disk increases, the puffs become 
more frequent, and finally blend into a whizzing sound in which the 
ear can detect a smooth tone. As the disk is given an increasing 
velocity, this tone rises in pitch. With a given rate of rotation of the 
apparatus, the pitch will rise as the tube is moved outward in succes- 
sion from the inner to the outer circle of perforations. 

139. Pitch is the characteristic of a sound or tone hy which 
it is recognized as high or low. It depends upon the rapidity 
of the vibrations by which the sound is produced ; the more 
rapid the vibrations, the higher the pitch. 

(a) One of the easiest ways of determining the number of vibra- 
tions that correspond to a given tone is to run the siren-disk at the 
speed that gives a tone of like pitch ; the product of the number of 
revolutions of the disk per second, and the number of holes in the 
cu-cle used is the vibration-number sought Dividing the velocity of 
sound by the vibration-number gives the wave-length. The less the 
wave-length, the higher the pitch. 

Q)) Some persons are unable to hear low sounds that are distinctly 
audible to most persons ; some are unable to recognize sounds of high 
pitch that are easily heard by others. The lower limit for most per- 
sons is probably represented by about 30 vibrations per second ; the 
upper limit by about 40,000. A tone produced by more than 4,000 
vibrations per second has little musical value. 

(c) The approach of a sounding body to a listening ear is equiva- 
lent to increasing the vibration-number; the opposite is true when the 
sounding body recedes from the ear. 

140. An Interval is the difference or distance in pitch 
between two tones and is described by the ratio between the 
vibration-numbers tf the tivo tones. Thus, the interval of 
an octave is represented by the ratio 2 : 1 ; a fifths 3 : 2 ; a 
fourth^ 4 : 3; a major thirds 5:4; and a minor thirds 6 : 6, 

141. A Musical Scale is a definite, standard series of tones 
for artistic purposes, and lying within a limiting interval. 
In modern music, this limiting interval is the octave. 



CHARACTERISTICS OF TONES. 115 

142. The Diatonic Scale. — Starting from any tone, arbi- 
trarily chosen and called the keynote, the interval of an 
octave may be traversed by seven definite steps, thus giv- 
ing a series of eight tones that are very pleasing to the 
ear. The eighth tone of this group becomes the first 
tone (i.e., the keynote) of the group or octave above. 
This familiar series of eight tones is called the gamuts or 
the major diatonic scale. The series may be repeated in 
either direction to the limits of audible pitch. The names 
and relative vibration-numbers of these tones, and the in- 
tervals between them, are as follows: — 



i 



tj=i^ 



^*- 



Relative names 12345678 

Absolute names ..'... Cg D, Eg Fg G3 A3 B3 C4 

Syllables do re mi fa sol la si do 

Relative vihratioiv^umbers . . 24 27 30 32 36 40 45 48 

Vibration-ratios 1 f f J f f ¥ 2 



Intervals |j^jj|Y|i{ 

(a) The initial tone or keynote of such a series may have any 
number of vibrations, and whatever pitch is assigned to C, the num- 
ber of vibrations of any tone may be found by multiplying the vibra- 
tion-number for C by the vibration-ratios given above. Physicists 
assign to Cg, sometimes called middle C, 256 vibrations per second 
(256 = 2^). Musicians and makers of musical instruments in this 
country and Europe have adopted the "international pitch," which 
gives for standard ^4,, 435 vibrations per second. This corresponds 
to 258.6 vibrations for Cg. 

(b) The octave is the interval most readily produced by the human 
voice, and seems to have a foundation in nature. When three tones 
with vibration-numbers as 4:5:6 are sounded together (e.g., C, E, 
G)j SL new quality seems to be added, and the combination produces 
a very pleasing sensation. The tones are in harmony, or in accord 
with each other. Siich simultaneous sounding of three or more con- 



116 ELEMENTARY PHYSICS. 

cordant tones constitutes a chords of which there ' are several kinds. 
The three tones above mentioned (i.e.) C, E, G) constitute a major 
chord, 

143. Chromatic Scale. — Twenty-four different scales are 
ordinarily used in music. They require no fewer than 
seventy-two tonei within the limit of an octave. To use 
so many tones in each octave of keyed instruments, such 
as the piano and organ, is a practical impossibility. As 
many of these tones differ from each other but little, musi- 
cians have agreed to make a compromise, and. to divide 
the octave into twelve equal intervals, called semi-tones. 
The series of thirteen semi-tones separated by the twelve 
equal intervals^ constitutes the modem chromatic scale, 

(a) The eight tones nearest those already described are named as 
we have already designated them, while the five interpolated tones, 
corresponding to the black keys on the piano keyboard, are called 
sharps of the tones immediately below them, or Jlats of the tones next 
above them. The compromising process between theory and practice, 
or the principle by which the octave is divided into twelve equal 
intervals, is called equal temperament. In this system, the only perfect 
interval is tlie octave, and all chords are slightly "oat of tune." 
The intei-val in this scale is \'*J = 1.05946. 

Tones and Overtones. 

Experiment 79. — Bow or pluck the string of a sonometer near its 
end, thus setting it in vibration as a whole. The string will have the 



t 



-^^^3? i ^"^'^^^^j 



Fig. 95. 



appearance of a single spindle as shown in Fig. 95, and will sound 
tlie lowest tone that it is capable of producing. Lightly touch the 
wire at its middle point with the tip of the finger or the beard of 
a quill; the wire will vibrate in halves (Fig. 96) and sound a tone an 
octave above that previously heard. You may even hear both tones at 



CHARACTERISTICS OF TONES. 



117 



the same time. The point of apparent rest between the vibrating 
segments is called a node. Again cause the string to vibrate and touch 
it at one-third its length. The vibrating string divides into thirds, 



^;^£ga ^g 



Fig. 96. 



as shown in Fig. 97, and emits a tone that the trained ear recognizes 
as the fifth of the octave above tliat first sounded. Probably both 
sounds will be heard at the same time. The string should be touched 
at n and bowled at v, as shown in Figs. 96 and 97. 




Fig. 97. 

144. Fundamental Tones and Overtones. — The tone that 
is sounded Tyy a body vibrating as a whole^ i.e,^ the loiveH 
tone that such a body can produce^ is called its fundamental 
or primary tone. The tones produced by the vibrating seg- 
ments of sonorous bodies are called overtones,, partial tonest^ 
or harmonics. The partial tones are named first, second. 



118 ELEMENTARY PHYSICS. 

third, etc., in the order of their vibration-numbers, begin- 
ning with the fundamental. The interval from the funda- 
mental to the first overtone is an octave ; to the second, 
an octave and a fifth ; to the third, two octaves, etc. 

(a) It is customary to regard both ends of the string as nodes. 
.The points of greatest vibration, midway between the nodes, are 
called anti-nodes. If little A-shaped riders, made of slips of paper 
bent in the middle, are placed on a string, and the string is then 
made to vibrate in segments, the riders at the nodes will remain in 
position while those at the anti-nodes will be thrown off as shown 
in Fig. 97. 

145. Quality or Timbre is the characteristic by which 
we distinguish one tone from another of the same intensity 
and pitch. The middle (7 of a piano is different from the 
same tone of an organ, and any tone of a flute is distin- 
guishable from any tone of a violin. The physical basis of 
quality is wave-form^ and is due to the number, relative 

. intensities, and relative phases of the overtones that 
accompany the fundamental. 

(a) The well-trained ear can detect several tones when a piano- 
key is struck. In other words, the sound of a vibrating piano-wii-e 
is compound. The sound of a tuning-fork is a fairly good example 
of a simple sound. 

(h) Figure 98 represents the compounding of a fundamental with its 
second overtone. The fundamental is represented by the dotted line 

while the resultant 
compound tone is rep- 
resented by the con- 
tinuous line ADD'B, 
Such combinations 
may be made in almost endless variety, each combination represent- 
ing a compound tone that varies from all of the others. 

146. The Graphic Method of studying sounds is largely 
used and may be briefly explained : Suppose a sheet of 
smoked paper fastened upon the surface of a cylinder that 



Fig. 98. 



CHARACTERISTICS OF TONES. 



119 



is so mounted that, when it is turned by a crank, the screw 
cut upon the axis moves the cylinder endwise, as shown 
in Fig. 99. Such an in- 
strument is called a 
vibroBcope. 

(a) When a style attached 
to a vibrating tuning-fork 
just touches the paper, and 
the crank is turned, the vibra- 
tions will be traced in the 
form of a sinusoidal spiral 
upon the smoked surface, the 
amplitude, length, and form 
of each wave being truth- 
fully recorded. By counting 
the number of waves traced 

in one second, we obtain directly the vibration-number of the fork. 
The wave-forms that correspond even to a very complex tone may 
thus be secured for study or illustration. Such a record may be 




Fig. 99. 



Fig. 100. 

written parallel with that of a tuning-fork of known frequency (i.e., 
vibration-number), as in Fig. 100, and comparative study thus facili- 
tated. 

147. The Optical Method of studying sounds, like the 
graphic, has the advantage of being independent of the 
sense of hearing. When a steady flame is viewed by its 
reflection in a rotating mirror, it appears as a luminous 
ribbon of uniform width. If the flame is pulsating, the 
edge of the ribbon will become indentated in a very re- 
markable manner. A series of sonorous waves may be 
conducted by a tube to one side of the dividing membrane 
of a "manometric capsule," J?, the other side of which is 
connected with a gas supply and a gas jet. Tlie waves 



120 



ELEMENTARY PHYSICS. 




Fig. 101. 



set up vibrations in the 
membrane and pulsa- 
tions in the flame. 
When the pulsating 
flame is observed by 
its reflection in the ro- 
tating mirror, M, there 
is an appearance known 
as a manometric flame. 
Each projection of this 
image -corresponds to 
the condensation of a 
sound wave, and each 
depression to the rare- 
faction. 



(rt) Figure 102 represents the flame produced by the simple tone of 
a tuning-fork. Figure 103 
corresponds to the tone of a 
fork that is an octave higher, 
twice as many tongues being 
crowded into the same space. 
Figure 104 represents the ap- 
pearance caused by blending 1 




Fig. 102. 




the tones of the two forks. The alter- 
nate condensations sent out 
by the fork of higher pitch 
unite with the condenser 
tions sent out by the fork of 
lower pitch, thus making the 
flame jump higher by their 
combined action on the diapliragm. 



1. Tf a musical sound is 
due to 144 vibrations, to how 
many vibrations will its 
"^fth, and octave, re- 
be due ? 



(Miiii/jiMMM 



Fia. 104. 



CO- VIBRATION. 121 

2. If a tone is produced by 264 vibrations per second, what number 
will represent the vibrations of the tone a fifth above its octave ? 

Ans. 792. 

3. A given tone is found to be in unison with the tone emitted by 
the inner row of holes of the siren descnbed in Ex^ieriment 78 when 
the disk is turned at the uniform rate of 640 times in 30 seconds. 
Assigning 256 vibrations for middle C, name the given tone. 

4. Is there any difference in the pitch of a locomotive-whistle when 
the locomotive is standing still, when it is rapidly approaching the 
observer, and when it is rapidly moving from him? If so, describe 
and explain it. 

5. If an observer should approach a sounding organ-pipe with the 
velocity of sound, what would be the effect upon the pitch of the tone? 

6. If an observer should recede from the source of a musical 
tone with a velocity a little less than that of sound, what would 
be the effect upon the pitch of the tone? 

7. Suppose that when an orchestra has nearly finished a per- 
formance, an observer should move away from the orchestra with a 
velocity twice that of sound. Describe his relation to the sounds 
previously executed by the orchestra. 

8. Bow a sonometer-string vigorously, and while it is sounding 
lessen the tension. Explain the discordant groan-like sound that is 
produced. 

9. Make another disk for the siren used in Experiment 78, making 
eight circles of holes, each. circle having, in order, the number of holes' 
indicated by the illative vibration-numbers given in § 142. Put this 
disk upon the whirling-table and rotate it at such a uniform speed 
that the puffs made by the inner circle of twenty-four holes shall give 
a smooth musical tone. Move the nozzle of the tube through which 
you blow over the several circles in succession and name the familiar 
series of tones that you hear. 



IV. CO-VIBRATION. 

Coincident Waves. 

Experiment 8o. — Vary Experiment 69 by timing the movements of 
the hand so that an advancing crest shall meet a returning trough 
near the middle of the rope. The rope particles at this point, being 
thus simultaneously acted upon by opposite forces, will remain at rest 



122 EXEMENTARY PHTSIC& 

or nearly so. The resultant will be the difference of the components. 
TlkuSj one ware atirjf be made io deslroy another wave. 

148. Comddeiit Waves. — Just as, when one crest coin* 
eides with another, the wave has an increased height, and 
when a crest coincides with an equal trough, the wave 
disappears, so, when a condensation coincides with another 
condensation, the actual motions of the particles of the 
sound medium are increased, and, when a condensation 
coincides with a rarefaction, said motions are reduced or 
desti*oyed. Such increased resultant motions of the mate- 
rial particles imply an increased loudness of the sound. 
Such diminished i*esultant motions imply an enfeebled 
sound or perhaps silence. 

Sympathetic Vibrations. 

Experiment 8i. — Repeat Experiment 4, and vary it by setting the 
heavy pendulum in motion by the cumulative action of well-tiuied 
puffs of air from the mouth or from a hand-bellows. 

Experiment 82. — Suspend several pendulums from a frame as 
shown in Fig. 33. Make two of equal length, so that they will vi- 
brate at the same rate. Be sure that they will thus vibrate. The 
other pendulums are to be of different lengths. Set a in vibration. 
The swinging of a will produce slight vibrations in the frame, which 
will, in turn, transmit them to the other pendulums. As the succes- 
sive impulses thus imparted by a keep time with the vibrations of 6, 
this energy accumulates in b, which is soon set in perceptible vibration. 
As these impulses do not keep time with the vibrations of the other 
pendulums, there can be no such marked accumulation of energy in 
them, for many of the impulses will act in opposition to the motions 
produced by previous impulses, and thus weaken if not destroy them. 

Experiment 83. — Tune the two strings of a sonometer to perfect 
unison. Place two or three paper "riders" upon one of the strings, 
and gently bow the* other. The " riders " will be dismounted from 
tlie .first string, even if the vibrations of the second string are not 
audible. The vibrant energy was carried from one string through 
the bridges of the sonometer to the other string and there accumu- 
lated. Change the tension of one of the strings, thus destroying the 



CO-VIBRATIOX. 



123 



unison, and try to repeat the experiment, 
thetic vibrations are not produced. 



Notice that the sympa- 




Fig. 105. 

Experiment 84. — Place two mounted tuning-forks that are in 
perfect unison several feet apart, and with the openings of their 
resonant boxes facing each other. Sound one of the forks, and 
notice its pitch. After a sec- 
ond or two, touch the prongs 
to stop their motion. It will 
be found that the second fork 
is giving forth a sound of the 
same pitch as that originally 
produced by the first fork. 
The successive pulses were 
transmitted by the interven- 
ing air. With wax, fasten a 
small weight to one of the 
prongs of the secon<l fork. 
An attempt to repeat the ex- 
periment will fail. 




F.Q. 106. 



149. Sympathetic Vibrations, — The last few experi- 
ments show that sound may produce motion. The most 
important feature now to be noticed is that the sonorous 
body accumulates only the 'particular hind of vibration that it 
is capable of producing. 

Resonance. 

Experiment 85. — Hold a vibrating tuning-fork over the mouth of 
I cylindrical jar about 15 or 18 inches deep, and notice the feebleness 



124 



ELEMENTARY PHYSICS. 



of the sound. Pour in water, as shown in Fig. 107, and notice that, 
when the liquid reaches a certain level, the sound suddenly be- 
comes much louder. The 
"water has shortened the air- 
column until it is able to 
vibrate in unison with tlie 
fork. If more water is 
added, the sound will be- 
come weaker. If a fork of 
different pitch is used, the 
length of the air-column 
must be changed, said length 
being about one-fourth the 
length of (he wave produced 
by the fork. 

150. Resonance. — The 
increase of %ound by the 
sympathetic vibrations of 
a body other than that by 
which it was originally 
produced is called reho- 
nance. The apparatus 
used to produce such an effect is called a resonator. 

(a) Resonance occurs in connection with all sound, and is care- 
fully utilized in musical instruments. Sounding-boards like that of 
the piano, and diaphragms like those of the phonograph and tele- 
phone, are sensitive to any vibratory motion within tlie limits of 
ordinary audition. 

(b) Hehnholtz constructed a series of resonators, each one of 
which responds powerfully to a single tone 
of certain pitch or wave-length. They are 
metallic vessels, nearly spherical, having 
an opening, as at A in Fig. 108, for the 
admission of tlie sound waves. The funnel- 
shaped projection at B has a small open- 
ing, and is inserted in the outer ear of the 
observer. Such resonators are largely used 
in the analysis of complex tones. Fig. 108, 




Fig. 107. 




CO-VIBRATION. 



125 



Interference. 

Experiment 86. — Hold a vibrating tuning-fork near the ear, and 
slowly turn it between the fingers. During a single complete rota- 
tion, four positions of full sound and four positions of silence will be 
found. When a side of the fork is parallel to the ear, the sound is 
plainly audible ; when a corner of a prong is turned toward the eai* 
the waves from one prong destroy the waves started by the other. 

Experiment 87. — Hold a vibrating tuning-fork at the mouth of 
a resonator, and slowly turn it upon its axis. Notice that, in certain 
positions of the fork, 
its tone is nearly in- 
audible. While the 
tube is in one of 
these positions, slip 
a paper tube over 
one of the prongs, as 
shown in Fig. 109, 
being careful not to 
touch it. The sound 
will be restored, be- 
cause the interfering 
sound has been re- 
moved. Wlien, by 
removing the paper 
tube, we restore the 
sound of the second 
prong, we demon- 
strate the almost 
paradoxical fact that sound added to sound • may produce silence. 
See § 148. 

151. Interference. — As the words are generally used, 
the interference of sound Bignifies the union of two or more 
systems of sound craves in such a way as to weaken or de- 
stroy the sound. It is the leading chai-acteristic property 

of wave motion. 

Beats. 

Experiment 88. — Simultaneously sound two large tuning-forks that 
are in unison, and notice that the sound is as smooth as if only one 




F.G. 109. 



126 ELEMENTARY PHYSICS. 

fork was sounding. Load one of the prongs of one of the forks with 
wax, sound both forks, and notice that the sound is not smooth, but 
that a series of palpitations or beats is easily perceptible. 

Ezperiment 89. — In a quiet room, strike simultaneously one of the 
lower white keys of a piano, and the adjoining black key. A similar 
series of beats will be heard. 

152. Beats. — The peculiar pulsation arising from the 
suecesiive reinforcement and interference of two tones differ- 
ing slightly in pitch is called a beat. 

(a) If two tuning-forks, A and B, vibrating respectively 255 and 
256 times a second, are set in vibration at the. same time, the first 
result will be an intensity of sound greater than that of either. After 
half a second, B having gained half a vibration upon A, the waves 
will meet in opposite phases, and the sound will be weakened or 
destroyed. At the end of the second, we shall have another reinforce- 
ment; at the middle of the next second, another interference. The 
number of beats per second equals the difference of the two vibration- 
numbers. 

153. Noise and Music. — A noise is a sound so complex 
that the ordinary powers of the ear fail to resolve it into 
its constituent tones. A simple tone is incapable of reso- 
lution, by reason of its simplicity. A combination of 
sounds that may be easily resolved into simple tones is 
a musical sound. The distinction is often difficult. 

BXBRCISBS. 

1. How can a deaf person determine whether a given tone is simple 
or compound ? 

2. If two tuning-forks, vibrating respectively 256 and 259 times 
per second, are simultaneously sounded near each other, what phe- 
nomena will follow? 

3. A musical string, known to vibrate 400 times a second, gives a 
certain tone. A second string, sounded a moment later, seems to 
give the same tone. When sounded, together, two beats per second 
are noticeable. Are the strings in unison ? If not, what is the rate 
of vibration of the second string? 



CO-VIBRATION. 127 

4. A tuning-fork produces a strong resonance when held over a jar 
15 inches long, (a) Find the wave-length of the fork, (b) Find 
the wave-period. Assume a temperature of 15° C. 

5. A tuning-fork held over a tall glass jar, into which water is 
slowly poured, receives its maximum reinforcement of sound when 
the resonant aii*-column is 64.8 cm. long. Assuming that the fork is 
accurately tuned to give an exact number of vibrations per second, 
noting the fact that the thermometer records a temperature of 16° C, 
and keeping in mind the probability of slight experimental error, 
determine the vibration-number of the fork. Ans. 132. 

6. One of two tuning-forks, each tuned to 512 vibrations per 
second, is loaded with wax. The forks are simultaneously sounded, 
and 20 distinct beats are heard in 10 seconds. What is the vibration- 
number of the loaded fork ? 

7. Figure 110 represents two series of sound waves traveling together. 
The full line represents one series and the dotted line another. What 




Fig. 110. 

phenomenon would result from such a combination of tones as is here 
represented? Describe the condition of affairs as represented at Ay 
B, and C respectively. 

8. Stretch a string horizontally between two fixed supports. From 
this string suspend two bullet pendulnms by threads about a meter 
long. Swing one of these pendulums across tlie diiection of the hori- 
zontal string. Describe and explain the result that you think the 
exercise was intended to bring to your notice. 

9. Remove the cover from a piano, depress the pedal so as to lift 
the dampers from all the wires, hold the lips near the wires, and sing 
the vowel, a, with the sound it has in "fate," and prolong the tone. 
Listen for the sympathetic response of the piano. Repeat the experi- 
ment, singing the same vowel with the sound it has in "father," and 
then the vowel, o, with the sound it has in " tone." 

10. Get a glass tube about J of an inch in diameter and 12 inches 
long. Into this tube thrust a neatly fitting cork. Move the cork with 
a ramrod until, by trial, you have adjusted the tube for maximum 




128 ELEMENTARY PHYSICS. 

resonance with a tuning-fork, e.g., one marked "Philharmonic A.** 
Support the tube with its mouth close to 
the disk of the siren shown in Fig. 94, and 
facing one of the circles of holes. Hold 
the nozzle of the tube on the other side 
of the disk and just opposite the mouth of 
the resonant tube. Turn the disk with 
gradually increasing speed, and blow air 
°' • through the tube. When the sound is 

at its maximum, the siren-tone will be in unison with the tone of the 
fork by which the resonant tube was tuned. Determine the vibration- 
number of the fork. 

11. Support a wooden rod about an inch square and three feet long 
with its lower end resting upon the cover of a music-box that is sound- 
ing. Wrap the music-box in cotton-wool and manifold layera of 
woolen cloth, until no sound from the box can be heard. Carefully 
balance a guitar or violin upon the top end of the rod. Describe and 
explain the consequent phenomenon. 



y. THE LAWS OF VIBRATIOK 

154. Vibrations of Strings, — The transverse vibrations 
of strings are the most important of the vibrations that 
give rise to musical tones, and may be conveniently studied 
with the aid of a sonometer. (See Fig. 105.) 

(a) When used for the production of musical tones, strings are 
fastened at their ends, stretched to proper tension, and then made to 
vibrate by bowing, as in the violin ; by plucking, as in the guitar or 
banjo; or by striking them with a light hammer, as in the piano 
or dulcimer. The manner of producing the vibrations has little effect 
upon the tone, which is chiefly determined by the length, diameter, 
density, and tension of the string itself. 

Laws of Vibrations of Strings. 

Experiment 90. — Remove the sliding bridge of the sonometer, 
stretch one of the strings and pluck or bow it near its end. Notice 
the pitch of the tone. Place the sliding bridge at the middle of the 



THE LAWS OF VIBRATION. 129 

scale on the sonometer box so as to halve the length of the string; 
then bow as before. Notice that the pitch of the tone is an octave 
higher. 

Experiment 91. — Stretch, with unequal and known tension, two 
wires of the same diameter and material, and, with the movable 
bridge, shorten the wire that carries the smaller weight until it 
sounds in unison with the other. Notice that the lengths of the 
strings vary as the square roots of the weights or tensions. The 
length of the string is the distance between the edges of the sup- 
porting bridges. 

Note. — By similarly using two iron wires of different diameters, 
and under equal tension, a third fact may be developed ; a like experi- 
ment with a brass and a steel wire of the same diameter may develop 
a fourth fact. 

155. Laws of Vibrations of Strings. — Countless experi- 
ments have established the following facts relative to 
musical strings: — 

(1) Other conditions being alike, the vibration-numbers 
vary inversely as the lengths. 

(2) Other conditions being alike, the vibration-numbers 
vary directly as the square roots of the tensions, 

(3) Other conditions being alike, the vibration-numbers 
vary inversely as the diameters, 

(4) Other conditions being alike, the vibration-numbers 
vary inversely as the square roots of the densities. 

(a) The third and fourth laws may be consolidated as follows : — 
Other conditions being alike^ the vibration-numbers vary inversely as 
the square roots of the weights per linear unit. 

Air-Columns. 

Experiment 92. — Make a reed-pipe by cutting a piece of wheat 
straw eight inches (20 cm.) long so as to have a knot at one end. 
At r, about an inch from the knot, cut inward about a quarter of the 
straw's diameter; turn the knife-blade flat and draw it toward the 
knot. The strip, rr', thus raised is a reed; the straw itself is a reed- 
pipe. When the reed is placed in the mouth, the lips firmly closed 



130 ELEMENTARY PHYSICS. 

around the straw between r and s and the breath diiven through the 
apparatus, the reed vibrates and produces vibrations in the air-column 
of the pipe. Notice the pitch of the tone thus produced. Cut off 



4 



Fig. 112. 

two inches from the end of the pipe at s. Blow through the pipe 
as before and notice that the pitch is raised. Cut off two inches 
more, sound the pipe, and notice that the pitch is still higher. 

156. Vibrations of Air-Columns, — Experiments 85 and 
91 show that when gases are confined in tubes they may- 
be made to vibrate as sonorous bodies. The air-column 
may be set in vibration by a vibrating tongue, as in the 
reed-pipe of Experiment 91, or in reed instruments like 
the melodeon, accordion, clarinet, etc., or by the fluttering 
of air particles driven against the edge of an opening in 
a tube, as in the whistle, fife, flute, or organ-pipe. 

(a) Whatever the way of producing the vibrations, the dimensions 
of the air-column itself determine the tone. In Experiment 91, we 
saw that the air-column, and not the straw tongue, determined the 
pitch. 

Laws of Vibrations of Air-Columns. 

Experiment 93. — Fit a cork loosely as a piston iuto the end of a 
glass tube about 2 cm. in diameter and 30 cm. long. Blow across the 
open end of the tube so as to produce a steady tone. It may be more 
easy to do this if you use a mouthpiece made by flattening the end 
of a piece of brass tubing. Notice the pitch of the tone produced, 
and measure the length of the air-column in the tube. By trial, 
determine the lengths of the air-columns that will give the tones of 
the gamut, and compare the relative lengths with the relative vibra- 
tion-numbers given in § 142. 

Experiment 94. — Provide two glass tubes of the same diameter 
(about 2.5 cm.), one being half as long as the other (e.g., 10 cm. and 
20 cm.). Blow across the end of the longer tube so as to produce its 
lowest tone while the other end of the tube is open. Notice the pitch. 



THE LAWS OF VIBRATION. 131 

Stop one end of the shorter tube with the hand, and blow across the 
open end so as to produce the lowest tone. Notice that the pitch of 
the short stopped-pipe is the same as that of the long open-pipe. Of 
course, if the school is provided with an assortment of organ-pipes, or 
of Quincke's acoustic tubes (as is desirable), it is better to use them. 

157, Laws of Vibrations of Air-Columns, — (1) The vi- 
hratiorirnumbers of air-columns vary inversely as their lengths. 

(2) The pitch of a closed-pipe is an octave below that of 
an open-pipe of equal length. 

(a) The two ends of an open-pipe sounding its fundamental are 
the middle points of ventral segments; the middle of tlie pipe is a 
node. The length of the air-column is half the wave-length. In the 
stopped-pipe sounding its fundamental, the node is at the end, and 
the length of the air-column is a fourth of the wave-length. 

(6) If a hole is made in the side of a pipe at a point occupied by 
a node, the point is at once changed to the middle of a ventral seg- 
ment, and there is a corresponding change of pitch. This action is 
familiarly shown in the fife and flute. 

158. The Vibrations of Rods may be transverse, longi- 
tudinal, or torsional. Transverse vibrations are famil- 
iarly illustrated in the music-box, jews'-harp, tuning-fork, 
etc. By clasping a vertical glass tube with one hand, and 
rubbing the upper half with a wetted cloth held in the 
other, it is possible to produce longitudinal vibrations that 
will shatter the lower part of the tube. If a violin-bow is 
drawn around a rod that is clamped at one end, the rod 
will twist and untwist with vibrations that are as isochro- 
nous as those of a tuning-fork, emitting a tone a little 
lower than that produced by longitudinal vibrations of tlie 
same rod having the same number of segmental divisions. 

Vibrations of Plates. 

Experiment 95. — Support, as shown in Fig. 113, a glass or brass 
plate, square or round, and strew it evenly with fine sand. Place the 
finger at any point on the edge of the plate (e.g., at the middle of 



132 



ELEMENTARY PHYSICS. 




Fig. 113. 



one side) so as to form a node there, and draw a violin-bow at a point 
properly chosen (e.g., near the adjacent comer). The sand imme- 
diately begins to dance on the 
plate and arrange itself along 
nodal lines. By changing the 
nodal points and bowing prop- 
erly, other sand-figures may be 
produced, one of which is shown 
iu Fig. 113. 

, 159. Vibrations of Plates. 

— The arrangementof nodal 
lines in the Cbladni figures 
just illustrated is deter- 
mined by the relative posi- 
tions of the point that is 
bowed and the point that is 
touched with the finger. The figures may be produced in 
great variety. As th^ complexity of the figures produced 
on a given plate increases, the pitch of the corresponding 
tone rises, the same figure always answering to the same tone. 

Vibrations of Bells. 

Experiment 96. — Draw a vio- 
lin-bow across the edge of a large 
goblet nearly full of water on the 
surface of which cork dust or 
powdered sulphur has been evenly 
sifted. When this glass bell sounds 
its fundamental toue, it vibrates 
in four segments, and the sui-face 
of the water tells the story by a 
record like that shown in Fig. 114. 
A few vigorous strokes of the bow 
would set up vibrations of ampli- 
tude sufficient to break the bell. 

160. Vibrations of Bells. — Just as a tuning-fork may 
be looked upon as a rod bent into a U-shape, so a bell 




Fig 114. 



THE LAWS OF VIBRATION. 133 

may be considered as a disk bent into a cup shape. Like a 
disk, it sounds its fundamental tone when vibrating in 
four segments, and the number of segments is always 
even. 



1. A musical string vibrates 200 times a second. State what takes 
place when the string is lengthened or shortened with no change of 
tension ; and what change takes place when the tension is made more 
or less, the length remaining the same. 

2. A certain string vibrates 100 times a second, (a) Find the 
vibratipn-nuraber of a similar string, twice as long, stretched by the 
same weight, (b) Of one that is half as long. 

3. A string sounding C, is 18 inches long. Must it be lengthened 
or shortened and how much to give the tone D^ ? 

4. A sonometer string is stretched by a load of 16 pounds. What 
load must be given to it so that it may sound a tone an octave lower? 

5. A tube open at both ends is to produce a tone coiTesponding to 
32 vibrations per second. Taking the velocity of sound as 1,120 feet, 
find the length of the tube. If the number of vibrations is 4,480, find 
the length of the tube. 

6. Find the length of an organ-pipe the waves of which are four 
feet long, the pipe being open at both ends. Find the length, the 
pipe being closed at one end. 

7. What will be the relative vibration-numbers of two strings of 
equal length, diameter, and tension, one being made of catgut and 
the other of brass, the density of brass being nine times that of catgut? 

8. Bring the siren into unison with a tuning-fork. Turning the 
wheel regularly for 10 seconds at the rate that gives unison, determine 
the number of puffs per second, and thus determine the vibration- 
number of the fork. 



CHAPTER IV. 

HEAT: MOLECULAR PHYSICS. 
I. NATURE OF HEAT, TEMPERATURE, ETC. 

161. Heat is a form of energy into which all other forms 
of energi) are convertible. It consists in the agitation of the 
molecules of matter^ and is generally recognized by the sensa- 
tion of warmth to tvhich it gives rise. 

162. The Temperature of a body is its state considered 
with reference to its ability to communicate heat to other 
bodies. When two bodies are brought together, there is a 
tendency toward an equalization of temperature. The 
one that gives the greater amount of heat has the higher 
temperature. 

(a) Water flows from a point of high to one of low level. Electrifi- 
cation flows from a point of high to one of low potential. Ileat flows 
from a point of high to one of low temperature. 

(6) An addition of heat may increase the velocity of the molecular 
motion or it may do another kind of work. When a hody receives 
heat, its temperature generally rises, but sometimes a change of con- 
dition results instead. When a body gives up heat, its temperature 
falls or its physical condition changes. 

An Effect of Heat. 

Experiment 97. — Connect, by a perforated cork, a piece of glass 
tubing about 50 cm. long to a Florence flask. Put water that has 
been colored with red ink into the apparatus so that it partly Alls the 
upright tube. Mark the level of the water in the tube by a rubber 
band or in some other convenient way. Immerse the flask in hot 
water and carefully observe the level of the water in the tube. 

ia4 



NATURE OF HEAT, TEMPERATURE, ETC. 



135 



163. Expansion. — Experiment 97 shows that one effect 
of heating a body is to increase its volume. This expan- 
sion is due to the increase of the molecular motions ; the 
amount of the expansion is definitely related to the increase 
of temperature. 

164. A Thermometer is an instrument for measuring tem- 
peratures. In its most common form, it consists of a liquid- 
filled bulb and a tube of uniform bore, as illustrated in 
Experiment 97. The liquid generally used is mercury or 
alcohol. The upper part of the tube is freed 
from air and sealed by fusion. A scale of 
equal parts is added for the measurement 
of the rise or fall of the liquid in the tube. 

(a) An air thermometer consists essentially of a 
large glass bulb at the upper end of a tube of small 
but uniform bore, the lower end of which dips into 
colored water. Any slight change of temperature 
affects the elastic force of the air in the bulb and 
changes the height of the liquid column. It is a 
thermoscope rather than a thermometer; i.e., it en- 
ables^us to detect slight changes of temperature rather than to meas- 
ure temperatures. 

(ft) The differential thermometer shows the 
difference in temperature of two neighboring places 
by the expansion of air in one of the two bulbs 
that are connected by a bent glass tube containing 
some liquid not easily volatile. 

(c) Mercury freezes at about — 39° C. For 
temperatures lower than - 38° C, an alcohol ther- 
mometer is generally used. Mercury boils at 
about 350° C. Temperatures higher than 300° C. 
are generally measured by the expansion of a 
metal rod or b}^ using an air thermometer with 
a porcelain or platinum bulb. 

{(l) In every thermometer there are two fixed 
points, called the freezing-point and the boiling-point. The first of 
these indicates the temperature of melting ice ; the other, the tem- 




FiG. 115. 




Fio. 116. 



136 



ELEMENTARY PHYSICS. 



peratore of steam as it escapes from water boiling under the ordinary 
atmospheric pressure (76 cm. of mercury). The distance between 
these tixed points is divided into equal parts according to different 
scales. The two scales chiefly used in this country are the centigrade 
(or Celsius) and Fahrenheit's. For these scales, the fixed points, 
determined as just explained, are marked as follows : — 



Centigrade. 


Fahrenheit 


0° 


32° 


100** 


212° 



Fio. 117. 



Freezing-point, 
Boiling-point, 

The tube between these two points is divided into 100 
equal parts for the centigrade scale, and into 180 for Fah- 
renheit's. Either scale may be extended beyond either 
fixed point as far as is desired. The divisions below zero 
are considered negative ; e.g., — 10° signifies 10 degrees 
below zero. The scales are designated by their respec- 
tive initial letters, as 5° C, or 41° F. Unless otherwise 
stated, the thermometer readings given in this book are 
in centigrade degrees. 

Since 0° C. corresponds to 32° F., and an interval of 1 
centigrade degree equals an interval of 1.8 Fahrenheit 
degrees, we may reduce centigrade readings to Fahrenheit readings 
by multiplying the number of centigrade degrees by 1.8 and adding 
32. Similarly, we may reduce Fahrenheit degrees to centigrade de- 
grees by subtracting 32 from the number of Fahrenheit degrees and 
dividing the remainder by 1.8. 

165. Absolute Zero of Temperature. — The temperature 
at which the molecular motions constituting heat wholly cease 
is called the absolute zero. It has never been reached, but 
theoretical considerations indicate that it is 273° below the 
centigrade zero. 

(a) Absolute temperatures are obtained by adding 273 to the read- 
ings of a centigrade thermometer, or 460 to the readings of a Fahren- 
heit thermometer. 

EXERCISES. 

1. The difference between the temperatures of two bodies is 36 
Fahrenheit degrees. Express the difference in centigrade degrees. 

2. The difference between the temperatures of two bodies is 35 
centigrade degrees. Express the difference in Fahrenheit degrees. 



PRODUCTION AND TRANSFERENCE OF HEAT, ETC. 137 

3. (a) Express the temperature 68^ F. in the centigrade scale. 
(h) Express the temperature 20° C. in the Fahrenheit scale. 

4. What is the corresponding centigrade reading for 50° F. ? 

5. Suppose that one of the flat faces of a tin can was painted with 
a mixture of lampblack and oil, the opposite face of the can being 
left bright ; that the can thus preparisd was filled with hot water and 
hung between the bulbs of a differential thermometer with the painted 
side facing one of the bulbs ; and that the liquid moved toward the 
bulb that was opposite the bright face of the can. What inference 
would you draw concerning the effect of the paint on the facility with 
which tin at a given temperature emits heat? 

0. Suppose that when the Florence flask used in Experiment 97 
was immersed in hot water, the level of the liquid in the tube fell a 
little before it began to rise. How would you explain such an effect? 

7. Describe very briefly the molecular agitations of a body at a 
temperature of — 273°. 

8. What is the absolute temperature of this room at this time? 



II. THE PRODUCTION AND TRANSFERENCE OF 
HEAT, ETC. 

166, Sources of Heat. — The sun is the great source of 
thermal energy, but man is able to transform other forms 
of energy into heat. 

Transformations of Energy. 

Experiment 98. — Rub a metal button on the floor or carpet. It 
soon becomes uncomfortably warm. 

Experiment 99. — Place a nail or coin on an anvil or stone and 
hammer it vigorously. It soon becomes too hot to handle. In this 
way, blacksmiths sometimes heat iron rods to redness. 

Experiment 100. — Cut a thin slice from a stick of phosphorus 
under water. Carry the slice on the knife-blade, and press it between 
the folds of a handkerchief to dry it. Moving it again upon the knife- 
blade, place it upon a brick. Carefully place a single crystal of iodine 
upon the phosphorus. Some of the potential energy of chemical sepa- 
ration will be transformed into the kinetic energy of heat. 



138 ELEMENTARY PHYSICS. 

167. Production of Heat — The experiments just given 
illustrate some of the methods by which other forms of 
energy are transformed into heat. Such transformations 
are continually taking place, and the attention has only to 
be called to the subject that they may be recognized. 

Diffusion of Heat. 

Experiment loi. — Thrust an iron poker into the fire. The end of 
the poker that is held in the hand soon grows warm. The rod has 
been heated through its whole length, and there is a gradual rise of 
temperature from the end held in the hand to the end that is in the 
fire. Hold the hand over the stove, and it is warmed by the ascending 
current of heated air. Hold the hand in front of the stove and, in 
some way that we shall understand better by and by, it is warmed. 

168. Diffusion of Heat. — Heat is transferred from one 
point to another in two ways, conduction and convection, 

(rt) It is often said that heat is transferred in a third way, viz., by 
radiation. What is sometimes called radiant heat will be considered 
in the next chapter. 

Conductivity of SoUds. 

£z]>eriment 102. — Instead of the iron poker used in Experiment 
101, use a glass rod or a wooden stick. The end in the fire may be 
melted or burned without rendering the other end uncomfortably 
warm. 

Experiment 103. — Put a silver and a German-silver spoon into the 
saiiie vessel of hot water. The handle of the former will become 
hot much sooner than that of the latter. 

Experiment 104. — Provide two stout wires, one of iron and one of 
copper, each 40 or 50 cm. long. Twist them together for about 
10 cm., and spread the untwisted parts so as to form a fork with a 
twisted handle. Dip the prongs of the fork into melted paraffin wax, 
thus coating them. Balance the fork on a coverless crayon box, and 
place a lamp flame under the overhanging handle. Notice which 
prong melts its wax coat to the greater distance. 

169. Conduction is the mode by which heat is transmitted 
from points of high temperature to points of low temperature 



PRODUCTION AND TRANSFERENCE OF HEAT, ETC. 139 

"by pasBingfrom one particle to the next particle. The con- 
duction of the heat is very gradual and as rapid through 
a crooked as through a sti-aight bar. 

(a) The power of conducting heat is called thennal conductivity. 
Among solids, metals are the best conductors both of heat and of 
electricity. Of the metals, silver and copper are the best, and German- 
silver and bismuth the poorest. 



Conductivity of Liquids. 

Experiment 105. — Fasten a piece of ice at the bottom of an ignition 
tube. A loosely wound coil of soft wire that snugly fits the tube 
will hold it in place. Cover the ice to the depth of several inches 
with water. Hold the tube obliquely, and apply the flame of a lamp 
below the upper part of the water. The water there may be made 
to boil without melting the ice below. Instead of using ice and 
water, pack the tube full of moist snow if you can get it. 

170. Conductivity of Fluids. — Water has a very low- 
conductivity, a fact that applies to liquids generally. The 
one marked exception to this rule is 
the liquid metal, mercury. The con- 
ductivity of copper is about five hun- 
dred times that of water. Gases have 
still less, if any, thermal conductivity. 

Fluid Currents caused by Heat. 

Experiment 106. — With a lamp chimney 
or other large glass tube, a perforated cork, 
two pieces of glass tubing 4 and 15 inches 
long respectively, a bit of rubber tubing, a 
small lamp or a candle, and two coverless 
crayon boxes, arrange apparatus as shown 
in Fig. 118. Partly fill the apparatus with ^^ jjg 

water, and add a small quantity of fine 

paper raspings, or of a paste made by moistening some aniline dye 
with a drop of water. Carefully heat the tube, as shown in the figure, 
and explain any observed movement of the water. 




140 ELEMENTARY PHYSICS. 

Experiment 107. — Cut a sqnare of stiff writing paper, 15 cm. on 
each edge, and draw its diagonals. From the four corners, cut the 
paper along the diagonals to within 1.5 cm. of the middle of the 
square. From the corners, bring four alternate paper tips together 
and thi-ust a pin through them and the middle of the square and into 
the end of a penholder or lead pencil. Hold the paper wind-wheel 
thus made over a stove or metal plate that is very hot, the woodea 
handle being vertical and above the paper. One of the components 
into which the force of the ascending current of heated air is resolved 
sets the wheel in rotation. 

171. Convection* — When a portion of a fluid is heated 
above the temperature of the surrounding portions, it 
expands and rises, the cooler and heavier portions of 
the fluid rushing in from the sides and descending from 
higher points. In this way, all the fluid becomes heated. 
This mode of transferring heat hy the mechanical motion of 
heated fluids is called convection^ and the currents thus 
established are called convection currents. 

(a) Convection currents are applied to the heating of houses, etc., 
by hot^water pipes or hot-air furnaces, and constitute the basis of the 
most common forms of house and mine ventilation, the draft of 
chinmeys, etc. The Gulf Stream and the trade-winds are grand con- 
vection currents. 



III. EFFECTS OF HEAT. 

172. Expansion is the first visible effect of heat upon 

bodies. 

Ezpansion of Solids. 

Experiment xo8. — Provide a ring (or a sheet of tin with a hole cut 
in it) and a metal ball that, at the ordinary temperature, will just 
pass through the opening. Heat the ball and it will no longer pass 
through. 

Experiment 109. — Support a slender flat iron bar about 50 cm. 
long upon two blocks as shown in Fig. 119. Place a heavy weight 



EFFECTS OF HEAT. 141 

upon one end of the rod, as at ^, and a glass plate under the other 
end, as at B. (Instead of the block and weight at A, that end of 
the rod may be gripped in a vise.) Stick the point of a fine sewing 
needle into a straw pointer, and place the needle between the glass 
plate and the iron rod so that if 
the rod moves lengthwise it will P^*vl 

roll the needle along the plate ^.^^ b\/ >I 

and move the end of the straw ^^5|^^^"^^^^""^SBh^ 
pointer along a graduated arc JHH^^^H^^^^^^^ll^ 
on a piece of cardboai'd placed ^ l|||H|Bi^^3^ ^J^^B||^p- 
as shown in the figure. Heat ^^ ^^L_ "fc ''•— ^ ■ ■ ^^^r 
the rod with a Bun sen burner yj^ j29. 

or an alcohol lamp. The rod 

expands, rolls the needle, and moves the pointer along the scale. 
Remove the lamp ; as the rod cools, the pointer comes back to its 
original position. 

173. Expansion of Solids. — Almost without exception, 
solids expand when heated and contract when cooled, the 
amount of expansion varying with the increase of the 
temperature and the nature of the substance. 

(a) The energy of the expansion and contraction of solids is very 
great and enables many industrial applications. 

Expansion of Fluids. 

Experiment no. — Close by fusion one end of each of three similar 
glass tubes, 15 or 20 cm. long. Put water into one, alcohol into 
another, and glycerin into the third, using equal quantities of the 
liquids. Place the three tubes in a vessel of hot water and notice 
that the liquids expand unequally. 

Experiment in. — Close a bottle with a cock through which passes 
a glass tube of small bore and about 30 cm. long. Warm the bottle ' 
between the hands, and place a drop of ink at the end of the tube. 
As the air in the bottle contracts, the ink will move down the tube, 
forming a liquid index. By heating or cooling the bottle, the index 
may be made to move up or down. 

Experiment 112. — Pour recently boiled water into the apparatus 
used in Experiment 111, until the tube is half full. Pack the bottle 



142 ELEMENTARY PHYSICS. 

ill a mixture of salt and finely broken ice. Observe the liquid level 
in the tube. The water contracts, then expands, then freezes and 
expands. 

174. Expansion of Fluids* — Liquids and gases expand, 
when heated, and contract when cooled, the amount of 
expansion varying with the increase of temperature. In. 
tlie case of liquids, the amount of expansion also varies 
with the nature of the substance. The rate of expansion 
is practically the same for all gases, and greater than it is 
for solids or liquids. 

(a) Substances that crystallize on cooling, expand as they approach 
the temperature of solidification; i.e., a given quantity of matter 
occupies more space when it has a crystalline structure than it does 
when it has a liquid form. Ice is a good example of such a sub- 
stance. 

175. Coefficient of Expansion. — The elongation per unit 
of length for each degree that the temperature is raised 
above 0®, is called the coefficient of linear expansion. Simi- 
larly, the increase in volume per unit of volume for a change 
of one degree of the temperature^ is called the coefficient of 
cubical expansion, 

(a) For solids, the coefficient is nearly constant for different tem- 
peratures. For liquids, the coefficient is more variable. .For gases 
under constant pressure, the coefficient is nearly constant, with a 
value of ^}j or 0.00366. As water is heated from 0° to 4*^, it gradu- 
ally contracts, so that 4° is the temperature of maximum density for 
water. As the temperature is raised above 4°, the water expands, 
slightly at first, but more and more rapidly as it approaches the 
boiling-point. 

EXERCISES. 

1. Why does oil-cloth on a cold floor feel colder to bare feet than 
carpet does, both being at the same temperature ? 

2. Why is water heated more quickly when placed over a fire than 
when placed under one? 



EFFECTS OF HEAT. 143 

3. Why do wheelwrights heat the tires of wheels before setting 
them? 

4. Why is at least one end of a long iron bridge generally sup- 
ported upon rollers ? 

5. What is the temperature of the surface water of a pond that is 
just about to freeze ? Of the water at the bottom of the pond ? 

6. A certain quantity of gas is measured at 0°. To what tempera- 
ture must it be heated, the pressure being constant, so that its volume 
may be doubled ? 

7. A mass of air at 0°, and under an atmospheric pressure of 30 
inches, me'asures 100 cubic inches; what will be its volume at 40°, 
under a pressure of 28 inches ? 

Solution: — First suppose the pressure to change from 30 inches 
to 28 inches. The air will expand, the two volumes being in the 
ratio of 28 to 30 (§ 117). 100 cu. in. x f f = 107| cu. in. Next, sup- 
pose the temperature to change from 0° to 40°. The expansion will 
be -^^ of the vohime at 0°; the volume of the air at 40° will be 
1^^ times its volume at 0°. 

107f X US\ = 122|ff Ans, 122||f cu. in. 

A Iternate Solution : — 28 : 30 > ^ r.r. 

273 : 273 + 40 f ••^"" = ^- 

8. At 150°, what will be the volume of a gas that measures 10 cu. 
cm. at 15°? 

273 + 15 : 273 + 150 : : 10 : x. Ans. 14.69 cu. cm. 

9. K 100 cu. cm. of hydrogen is measured at 100°, what will be 
the volume of the gas at — 100°? Ans, 46.37 cu. cm. 

10. A gas measures 98 cu. cm. at 185° F. What will it measure 
at 10° C. under the same pressure? Ans. 11 Al cu. cm. 

11. A liter of air is measured at 0° and 760 mm. What volume 
will it occupy at 740 mm. and 15.5°? Ans. 1,085.34 cu. cm. 

12. The bulb and tube of an air thermometer were filled with boil- 
ing water. The bulb being placed in water that contained ice, the 
level of the water in the tube fell for a time and then rose. Explain. 

Liquefaction. 

Experiment ii'a. — Place snow or finely broken ice and a thermome- 
ter in a vessel of water. The thermome^r will fall to the freezing- 
point, but no further. Apply heat, so as to melt the ice very slowly, 
and stir the mixture constantly. The temperature does not rise until 



144 ELEMENTARY PHYSICS. 

all of the ice is melted, or it rises so little that we may feel sure that 
there would be no rise if each particle of water could be kept in con- 
tact with a particle of ice. 

Experiment 114. — Put a little water into a beaker, and determine 
its temperatui'e. Add a small quantity of sodium sulphate, and stir 
with a thermometer. Notice the fall of temperature during the 
process of solution. Repeat Experiment 13. 

176. The Liquefaction of a solid is effected by fusion 
or by solution. In either case, heat is required to over- 
come the force of cohesion, and disappears in the process. 

(a) The action of freezing-mixtures, e.g., one weight of salt and 
two or three of snow or pounded ice, depends upon the fact that heat 
is absorbed or disappears in the solution of solids. 

Solidification. 

Experiment 1x5. — Place a thermometer in a small glass vessel 
containing water at 30^ and a second thermometer in a large bath of 
mercury at — 10°. Immerae the glass vessel in the mercury. The 
temperature of the water gradually falls to 0°, when the water begins 
to freeze and its temperature becomes constant. The temperature of 
the mercury rises while the water is freezing. 

177. Solidification. — When a liquid changes to a solid, 
the energy that was employed in maintaining freedom of 
molecular motion against the force of cohesion is released 
and appears as heat. The amount of heat that reappears 
during solidification is the same as that which disappears 
during liquefaction. 

Melting-Point. 

- Experiment xi6. — Close one end of a small glass tube by fusion. 
Place the tube in hot water and drop small bits of paraffin wax into 
the tube until it is filled. Notice that the melted wax is transparent. 
Remove the tube from the water, and, as the wax solidifies, notice 
any change in transparency or volume. With rubber bands, or in 
any other convenient way, fasten the tube to a thermometer and place 
both in a beaker of cool water. Gradually heat the water, stirring it 
with the thermometer, and carefully noting the temperature at which 



EFFECTS OF HEAT. 145 

the wax becomes transparent, i,e,y melts. Allow the water to cool, 
and carefully note the temperature at which the wax becomes opaque. 
Find the mean of the two temperatures and record it as the melting- 
point of paraffin wax. 

178. Laws of Fusion. — (1) A solid begins to melt at a 
certain temperature that is invariable for a given substance 
under constant pressure. This temperature is called the 
melting-point of that substance. In cooling^ such liquids 
solidify at the melting-point, 

(2) The temperature of a melting solid or of d solidify- 
ing liquid remains at the melting-point until the change 
of condition is completed, 

(3) Substances that contract on melting^ as ice does^ have 
their melting-points lowered by pressure^ and vice versa, 

(a) It is possible to reduce the temperature of a liquid below the 
melting-point without solidification, but when solidification does 
begin, the temperature quickly rises to the melting-point. 

Vaporization. 

Experiment 117. — Wet a block of wood and place a watch-crystal 
upon it. A film of water may be seen under the central part of the 
glass. Half fill the crystal with sulphuric ether, and evaporate it 
rapidly by blowing over its surface a stream of air from a small 
bellows. So much heat disappears that the watch-crystal is frozen to 
the wooden block. 

179. Vaporization is the process of converting a substance^ 
especially a liquid^ into a vapor. This change of condition 
may be effected by an addition of heat, or by a diminution 
of pressure, or both. When it takes place slowly and 
quietly, the process is called evaporation. When it takes 
place so rapidly that the liquid mass is visibly agitated by 
the formation of vapor bubbles within it, the process is 
called ebullition. The heat that produces the change of 
condition disappears in the process. 




146 ELEMENTARY PHYSICS. 

180. Condensation. — The liquefaction of gases and va- 
pors is effected by a withdrawal of heat or by an increase 
of pressure, or both. In either case, the energy that was 
employed in maintaining the aeriform condition is released 
and appears as heat. The amount of heat that reappears 
during liquefaction is the same as that which disappears 
during vaporization. 

Boiling-Point 

Experiment ii8. — In a beaker half full of water, place a thermom- 
eter and a test-tube half filled with ether. Heat the 
water. When the thermometer shows a temperature of 
about 60°, the ether will begin to boil. The water will 
not boil until the temperature rises to 100®. The tem- 
perature will not rise beyond this point. 

Experiment iig. — When the water used in Experi- 

F 120 i"ent 118 has partly cooled, dissolve in it as much 

common salt as possible, heat it again, and notice that 

it does not boil until the temperature is noticeably higher than 

before. 

181. Laws of Ebullition. — (1) A liquid begins to boil 
at a temperature that is invariable for a given substance 
under constant conditions. This temperature is called the 
boiling-point of that substance. In cooling^ such vapors 
liquefy at the boiling-point. 

(2) The temperature of the boiling liquid or of the lique- 
fying vapor remains at the boiling-point ^ntil the change of 
condition is completed. 

(3) An increase of pressure raises the boiling-pointy and 
vice versa. 

(4) The solution of a salt in a liquid raises its boiling- 
pointy additional energy being required to overcome the cohe- 
sion involved in the solution, 

(a) It is possible to heat water above its true boiling-point without 
ebullition, by confining the steam and thus increasing the pressure, 



EFFECTS OF HEAT. 



14? 



but when the pressure is relieved, the superheated vapor immediately 
expauds and its temperature is reduced. 

(b) A drop of water on a smooth metal surface at a high tempera- 
ture may rest upon a cushion of its own vapor, without coming into 
contact with the metal. A liquid in this spheroidal stale is at a tem- 
I)erature below its boiling-point. When the metal cools so that the 
vapor pressure will not support the globule, the liquid comes into 
contact with the metal surface, and is converted into steam with great 
rapidity. Many boiler explosions are due to such cause*. 

(c) Whenever the boiling-point of a substance is lower than its 
melting-point, the substance vaporizes directly without previous lique- 
faction. Such a change is called sublimation. Carbon dioxide sub- 
limes under any pressure less than three atmospheres. Iodine sublimes 
at pressures less than 00 mm. of mercury, and ice cannot be melted at a 
pressure of less than 4.6 mm. 

Distillation. 

Experiment 120. — Pai-tly fill with strong brine a Florence flask, the 
cork of which carries a delivery-tube and a thermometer. Pass the 
delivery-tube through a 
** water jacket," J, kept 
cool substantially as 
shown in Fig. 121. 
Heat the liquid in the 
flask until it just boils, 
and taste the distilled 
water that collects in R, 

182. Distillation is 
the process of sepa- 
rating, by volatili- 
zation and subse- 
quent condensation, 
a liquid from other matter with which it has been associated. 
It depends upon the fact that the dififerent substances vola- 
tilize at different temperatures, and is used for various pur- 




FiQ. 121. 



(n) The most common distillation process consists in placing the 
distillable liquid in a metal retort, generally made of copper. When 



148 ELEMENTARY PHYSICS. 

heat is applied, vapors rise into the movable head' of the retort, the' 
Deck of which is connected with a spiral tube called the worm. 

The worm being kept cool 
by flowing water, the vapors 
of the more easily volatile 
constituents of the liquid 
pass into it, are condensed, 
and make their exit as a 
liquid, while the solid and 
non-volatile liquid constitu- 
^^' ^^' ents remain behind in the 

retort. The whole apparatus is called a still. 




^5^^ 



BXBRCISS8. 

1. For the extraction of gelatin from bones by the action of hot 
water, a higher temperature than 100® is required. How may the 
water be heated sufficiently for such purposes ? 

2. In sugar refiuing, it is desirable to evaporate the liquid at a 
temperature considerably lower than 100^ Indicate a way in which 
this may be done. 

3. Solid type-metal floats on melted type-metal. Does melted type- 
metal expand or contract on solidifying? 

4. At the sunnnit of Mount Washington, water boils at a tempera- 
ture of about 94**; at the summit of Mont Blanc, at 86°; at the level 
of the Dead Sea, at 101°. Explain these differences. 

5. If the smooth, dry surfaces of two pieces of ice are pressed 
together for a few seconds, the pieces will be frozen together when the 
pressure is removed. Explain this result, which is called regelation. 

6. How may searwater be made fit for drinking? 

7. A drop of water may be placed on a very hot platinum plate, 
and the plate so held that a candle-flame may be seen between the 
water and the plate. Explain. 

8. On a day when the doors and windows are closed, ascertain the 
temperature of the class-room near the ceiling and near the floor. 
Record your observations and explain any difference that you find. 

9. On a day when the air in the class-room is warmer than that 
outside, stand an outer door slightly ajar, and with a candle-flame 
seek for inward and outward air-currents. If you find them, explain 
their production and show that they have an important relation to 
artificial ventilation. 



THE MEASUREMENT OF HEAT. 149 

10. Determine the boiling-point of a saturated solution of saltpeter. 

11. A copper wire is passed around a block of ice and made to 
carry a heavy weight. The wire slowly cuts its way through the ice, 
which freezes up again behind the advancing wire. Explain the 
melting in front of the wire, and the freezing behind it. 



IV. THE MEASUREMENT OF HEAT. 

183. Calorimetry is the process of measuring the 
amount of heat that a body absorbs or gives out in 
passing through a change of temperature or a change 
of physical condition. 

184. A Thermal Unit, or a heat-unit, is the quantity 
of heat required to raise the temperature of unit mass of 
water one degree. The unit most commonly used is the 
quantity of heat required to raise the temperature of one 
gram of water from 0° to 1°. This water-gram-degree unit 
is called a therm^ or a small calory. 

(a) A large calory is the quantity of heat required to raise the 
temperature of a kilogram of water from O*' to 1°. Unless otherwise 
specified, the calory mentioned in this book is the small calory. 

185. Latent Heat. — In considering changes of condition 
of matter, we have spoken of the disappearance and re- 
appearance of heat. When heat thus disappears, molec- 
ular kinetic energy is transformed into the potential form ; 
when it reappears, the reverse transformation takes place. 
Because this molecular kinetic energy affects temperature, 
it is called sensible heat. Because this molecular potential 
energy does not affect temperature, it is called latent heat. 

Latent Heat of Fusion. 

Experiment 121. — Add a kilogram of finely broken ice (0°) to a 
kilogi'ain of water at 80^ The ice will melt, and the temperature of 



150 ELEMENTARY PHYSICS. 

the two kilograms of water will be aboat 0°. The 80,000 calories 
given out by the hot water were used in simply melting the ice. 

186. The Latent Heat of Fusion of a mbstance is the 
quantity of heat that is required to melt orie gram of the 
substance without raising its temperature. The latent heat 
of fusion of ice is about eighty calories. 

(a) The heat required to melt any weight of ice would warm 80 
times that weight of water one degree, or the same weight of water 
80 degrees, provided there was no change of physical condition. 

Latent Heat of Vaporization. 

Experiment laa. — To the end of the delivery-tube of a Florence 
flask containing water, attach a " trap " like that shown in Fig. 123, 
so that the water that condenses in the delivery-tube may be retained 
in the trap. (Instead of using the trap, the delivery-tube may be kept 
hot by a steam jacket, for which purpose the apparatus shown in 
Fig. 121 may be easily adapted.) Boil the water, and when steam 
passes rapidly from a, the lower tube of the trap, dip a into a beaker of 
known weight and containing water of known weight and tem- 
perature. The temperature of the water in the beaker should 
be considerably lower than that of the room, and the end of the 
tube that leads steam from the trap to the beaker should not 
dip into the water so much that the condensation of the steam 
may not be plainly heard. The beaker should be covered with 
a piece of cardboard, perforated for the admission of the tube, a, 
and of the thermometer, and should be shielded from the heat 
„ of the lamp and flask. After the flow of steam has been con- 
J23 tinned for some time, remove the beaker, stir its contents with 
the thermometer thoroughly, and take the temperature quickly 
but carefully. Ascertain the exact increase in the weight of the water 
in the beaker, and compute the amount of heat derived from the con- 
densation of each gram of stem. Suppose that at the beginning of 
the experiment the water in the beaker weighed 400 g., and had a 
temperature of 0°, and that at the end of the experiment the weight 
was 420 g., and the temperature 30°. The 400 g. of water received 
12,000 calories that came from the 20 g. of steam. In cooling from 
100'' to 30°, the condensed steam parted with 1,400 calories. The 
remaining 10,600 calories came from the latent heat of the steam; 



THE MEASUREMENT OF HEAT. 151 

i.e., each gram of steam at 100^ gave out 530 calories in condensing 
to water at the same temperature. This result is subject to correc- 
tion for radiation, absorption, etc. 

187. The Latent Heat of Vaporization of a sttbstance is 
the quantity of heat that is required to vaporize one gram 
of that substance without raising its temperature. The 
latent heat of the vaporization of water is about 537 
calories. 

(a) The heat required to vaporize any weight of water would warm 
537 times that weight of water one degree, or n times that weight 

537 
of water degrees, provided there was no change of physical con- 
dition. 

188. The Specific Heat of a substance is the ratio between 
the amount of heat required to raise the temperature of any 
weight of that substance one degree^ and the amount of heat 
required to raise the temperature of the same weight of water 
one degree. It indicates the number of calories absorbed 
or emitted by one gram of that substance while under- 
going a change of one degree of terapemture. 

(a) The specific heat of hydrogen is 3.409 ; of ice, 0.505 ; of steam, 
0.48; of oxygen, 0.2175; of iron, 0.1138; of lead, 0.0314. Water in 
its liquid form has a higher specific heat than any other known 
substance except hydrogen. 

189. The Thermal Capacity of a body is the number of 
calories required to raise the temperature one degree. It 
is the product of the mass into the specific heat, and has 
direct reference to the amount of heat the body absorbs 
or gives out in passing through a given range of tem- 
perature. 

EXERCISES. 

1. One kilogram of water at 40°, 2 Kg. at 30^ 3 Kg. at 20°, and 
4 Kg. at 10°, are thoroughly mixed. Find the temperature of the 
mixtui-e. Am. 2P°. 



152 ELEMENTARY PHYSICS. 

2. One pound of mercury at 20® was mixed with one pound of 
water at 0**, and the temperature of the mixture was 0.634°. Calcu- 
late the specific heat of mercury. 

3. What weight of water at 86® will just melt 15 pounds of ice 
at 0®? Ans, 14.117 pounds. 

4. What weight of water at 95° will jast melt 10 pounds of ice 
at - 10°? Ans. 8.947 pounds. 

5. How many grams of ice at 0° can be melted by 1 g. of steam at 
100°? ^n,s. 7.96 grams. 

6. What temperature will be obtained by condensing 10 g. of 
steam at 100° in 1 Kg. of water at 0°? Ans. 6.3°+. 

7. If 200 g. of iron at 300° is plunged into 1 Kg. of water at 0°, 
what will be the resulting temperature? Ans. 6.67°. 



Solution : — 



Specific heat, 1 

Weight, 1,000 
Change of temperature, x 



Water. Iron. 
0.1138 
200 
300 -ar 



1,000 a: = 6,828- 22.76 ar 

8. A pound of sulphur can melt only one-fifth as much ice as a 
pound of water at the same temperature. What does this show con- 
cerning the specific heats of water and sulphur ? 

9. Tubs of water are sometimes placed in cellars to "keep the 
frost away " from vegetables, the freezing-point of which is a little 
below 0°. Explain the effect of the water in this respect. 

10. The cylinder of a pump that forces air into the pneumatic tire 
of a bicycle is heated in the process. Explain. 

11. Pour quickly, and through the shortest possible air space, 1.5 
Kg. of mercury at 100°, into 500 g. of water at 0°. Stir the liquids 
thoroughly together with a thermometer, and, from the resultant tem- 
perature, determine the specific heat of mercury. 

12. Place small and similar balls made severally of iron, copper, 
tin, lead, and bismuth, in a bath of linseed oil, and heat them to a 
temperature of 180°, or 200°. When they have all had time to acquire 
the temperature of the bath, wipe them dry, place them upon a cake 
of beeswax or paraffin wax about half an inch thick, and, from what 
you see, arrange the five metals in the order of their several s{>ecifio 
heats. 



THE RELATION BETWEEN HEAT AND WORK. 153 



V THE RELATION BETWEEN HEAT AND WORK. 

Mechanical Effect of Heat. 

Experiment 123. — Pass a bent glass tube through the air-tight cork 
of a flask half full of water, and let it dip beneath the surface of the 
water. Heat the flask. The heat will raise 
some of the water to the end of the tube. 

190. Heat and Mechanical En- 
ergy. — When heat is produced, 
some other kind of energy disap- 
pears, and vice versa. The most 
important of these transformations 
are those between heat and me- 
chanical energy. We are able to 
effect a total conversion of me- 
chanical energy into heat, bat we 
are not able to bring about a total 
conversion of heat into mechani- 
cal energy. 

191. Joule's Principle. — The disappearance of a definite 
amount of mechanical energy is accompanied by the produc- 
tion of an equivalent amount of heat. 

192. The Mechanical Equivalent of Heat signifies the 
numerical relation between work-units and equivalent heat- 
units. 

(a) The quantity of heat that will raise the temperature of one 
pound of water one Fahrenheit degree is equivalent to about 778 foot- 
pounds. For centigrade degrees the equivalent is 1.8 times as great, 
or about 1,400 foot-pounds. For centigrade degrees the equivalent of 
a calory is about 427 gram-meters, or 4.2 x 10'' ergs. 

193. The Heat Equivalent of Chemical Union is of 
practical importance in determining the values of dif- 




FiG. 124. 



154 



ELEMENTARY PHYSICS. 



ferent faels. For example, the combustion of a gram of 
pure carbon develops 8,080 calories. 

(a) The relative values of the several fuels mentioned are as 
follows : — 



Hydrogen . 
Petroleum 



34,462 

i2,aoo 



Carbon 8,080 

Alcohol 6,850 



In each case, the figures indicate that the combustion of a given 
weight of the substance in oxygen yields heat enough to warm so 
many times the same weight of water one centigrade degree, or 1.8 
times that many Fahrenheit degrees. 

194. The Steam-Engine is a powerful device for utiliz- 
ing the energy involved in the elasticity and expansive 

force of steam as a mo- 
I I tive power. It is a real 

heat-engine, transforming 
heat into mechanical en- 
ergy. Its fundamentally 
impoi-tant parts are the 
cylinder, piston, and slide- 
valve, represented in Figs. 
125 and 126, in which the 
steam-chest is represented 
as being at a distance 
from the cylinder, simply 
for the purpose of making 
clear the communicating steam passages. The piston, P, 
is moved to and fro in the cylinder by the pressure of the 
steam which is applied to its two faces alternately. This 
alternate application of the steam pressure is effected by 
the slide-valve, inclosed in a steam-chest, and moved by 
the valve-rod, R. The slide-valve covers the exhaust- 
port, iV, and one of the other two ports, A and B. 




Fig. 125. 



THE RELATION BETWEEN HEAT AND WORK. 



155 



(a) Steam from the boiler enters the steam-chest at M, When 
the valve is in position, as shown in Fig. 125, " live " steam passes 
through the induction-port. A, 
into the cylinder, and pushes the 
piston, as indicated by the arrows^ 
f)rcing out the "dead" or ex- 
h lust steam by the eduction-port, 
/>, and the exhaust-port, N, As 
tiie piston nears the end of its 
journey in this direction, the 
valve-rod, /?, is moved by an " ec- 
centric," or other device, and 
shifts the valve into position, as 
shown in Fig. 126. This move- 
ment of the slide-valve changes B 
to an induction-port, by which 
"live" steam is admitted to the 
other face of the piston, pressing 
it in the direction indicated by the arrow, and forcing the "dead" 
steam out through A and N, Then the slide-valve is pushed back to 
its former position by the rod, /?, and the alternating movement of the 
piston thus continued. The piston-rod and the valve-rod work through 
steam-tight packing boxes. 

Good steam-engines are now easily accessible from nearly every 
school, and should be studied in detail, and by direct inspection. 
The action of the pitman, the crank, the crank-shaft, the fly-wheel, 
and the dead-points may be illustrated by almost any sewing- 
machine. A model showing the movements of the several parts may 
be bought for two or three dollars, and is desirable. 




Fig. 126. 



EXERCISES. 



1. If a cannon ball weighing 192.96 pounds, and moving with a 
velocity of 2,000 feet per second, could be suddenly stopped and all its 
kinetic energy converted into heat, to what temperature would that 
h3at warm 100 pounds of ice-cold water ? 



Solution:— K.E,:=^ = 



wv^ 192.96 X 20002 



= 12,000,000, the number 



2g 64.32 

of foot-pounds. Division of the number of foot-pounds by 778 gives 
the number of heat-units (pound-Fahrenheit) developed. This number 



156 ELEMENTARY PHYSICS. 

divided by 100 gives the number of heat-units for each pound of the 
water, and consequently the number of Fahrenheit degrees that it will 
raise the temperature. This, added to 32°, the initial temperature, 
will give the temperature called for. 

2. A steam-engine raises 8,540 Kg. to a height of 50 m. How 
many calories are thus expended ? 

3. One gram of hydrogen is burned in oxygen. To what tempera- 
ture would a kilogram of water at 0° be raised by the combustion ? 

4. From what height must a block of ice at 0° fall that the heat 
generated by its collision with the earth would just melt it if all of 
the heat was utilized for that purpose ? 

5. Show that to raise the temperature of a pound of iron from 0° 
to 100® requires more energy than to raise 7 tons of iron a foot high. 

6. To what height could a ton weight be raised by utilizing all 
the heat produced by bui-niug 5 pounds of pure carbon ? 

Ans. 28,280 feet 



CHAPTER V. 

RADIANT ENERGY: ETHER PHYSICS. 
I. NATURE OF RADIATIOK 

195. The Ether. — Physicists generally are of the opin- 
ion that all space is filled with an incompressible medium 
of extreme tenuity and elasticity. Thi% hypothetical me-- 
dium is called the ether. See § 9. 

(a) The ether is regarded as an incompressible substance pervade 
ing all space and penetrating between the molecules of all ordinary 
matter wliich are embedded in it and connected with one another by 
its means. 

196. Radiant Energy. — Since the ether fills all inter- 
molecular spaces, the vibrating molecules of a body must 
communicate their motion to it. The ether-waves thus 
produced are propagafed with a velocity of about 186,000 
miles per second. When they strike a body, they may 
communicate their energy to the molecules of that body, 
and thus increase the total energy of that body. The 
transference of energy hy means of periodic disturbances in 
the ether (without regard to the precise nature of those .dis- 
turbances^ is called radiation. The energy thus transferred 
is called radiant energy. 

197. A Ray is a line along which radiant energy is propa- 
gated; i.e., the straight line perpendicular to the wave- 
front. A collection of parallel rays is called a beam. A 
collection of converging or diverging rays is called a 
pencil. 

167 



16a ELEMENTARY PHYSICS. 

(a) The expressions rays, beams, and pencils, are traces of an 
exploded theory. So far as they pertain to the wave theory, they are 
convenient conceptions, nothing more. 

198. Incident Radiation may be transmitted, reflected, 
or. absorbed by the body upon which it falls. When a 
body absorbs radiant energy, it is heated thereby. 

Recognition of Radiant Energy. 

Experiment 124. — Take a white-hot poker into a dark room. You 
readily attribute the heat and light to the energy radiated by the 
poker. The light gradually becomes reddish, and finally fades from 
view. There is a continuous change from the emission of white light 
and much heat to that of no light and less heat. 

199. Radiant Energy is Recognized by its phenomena, 
which may be classified as luminous, thermal, and chemi- 
cal. 

(a) Not even in theory can we assign limits to the length of the 
ether undulations. Some of these waves are competent to excite the 
optic nerve and to produce vision ; some are not. The difference is 
one of wave-length only. Most of the properties and phenomena of 
radiant energy are most conveniently studied by luminous effects, 
which constitute the chief subject-matter of this chapter. 



n. LIGHT: VELOCITY JlSD INTENSITY. 

200. Light. — The portion of radiant energy that is capable 
of producing the effect of vision constitutes light, 

(a) The longest ether-wave yet recognized is 3,000 x 10'^ cm. ; the 
shortest is 18.5 x 10"* cm. .These wave-lengths correspond respectively 
to vibration-frequencies of lOx 10^^ and 1,622 x 10^*, a range of mora 
than seven octaves. The radiations that constitute light lie within 
the comparatively narrow limits of 7.6 x 10-* cm. and 3.9 x 10** cm. 
These wave-lengths correspond to vibration-frequencies of 392 x 10'^ 
«^nd 757 X lO^*, a range of little more than one octave. 



LIGHT: VELOCITY AND INTENSITY. 159 

201. Visible Bodies are visible because of the light that 
they send to the eye of the observer. This is true whether 
the body shines by its own or another's light, i.e., whether 
it is self-luminous like a " live " coal, or illuminated like a 
" dead " coal. 

Note. — For many experiments in light, a darkened room is desir- 
able. The windows should be provided with opaque curtains so 
arranged that the sunlight may be quickly and completely excluded 
from the class-room. 

Rectilinear Propagation. 

Experiment 125. — Provide five blocks IJ x 2J x 3J inches, and 
three other pieces of wood each J x 3 J x 4 inches. Place three postal 
cards one over the other on a board and perforate them with a stout 
needle about half an inch from the middle of one end. Pare off the 
rough edges of the holes with a sharp knife, and again pass the needle 
through each hole to make its edge smooth and even. Stand one of 
the postal cards on end against a vertical 1} x 3} inch face of one of 
the blocks, and back it with one of the } inch strips. Nail the strip 
and the card to the block. Make two more such screens. Place the 
three screens parallel to each other and with their blocks sepa- 
rated by two of the other blocks ; the screens will be 5 inches apart. 
Pass a thread through the holes in the screens and carefully put it 
under tension to be sure that the perforations are in a straight line. 
If necessary, adjust the screens for that purpose. Remove the thread 
without disturbing the adjustment. On the exterior block, place a 
lighted candle of such length that its flame is at the height of the 
perforations in the cards. Place eye and candle so that the flame 
may be seen through the screen perforations. Move one of the screens 
a little so that the three holes are not in a straight line; the candle- 
flame cannot be seen as it was before. 

202. Radiant Energy is Propagated along straight lines 
when the medium is homogeneous^ i,e.^ when it has a uniform 
composition and density. 

203. Transparency, etc. — Transparent bodies, as glass, 
transmit light so freely that objects may be seen through 
them distinctly. Translucent bodies, as oiled paper, 



160 



ELEMENTARY PUYSiCS. 



transmit light so imperfectly that objects seen through 
them appear indistinct. Opaque bodies cut off the light 
entirely, and prevent objects from being seen through 
them. No sharp line of separation can be drawn between 

these classes. 

Shadows. 

Ezperiment ia6. — Coat with asphaltuni varnish the lower half of 
the outer surface of the chimney of a lamp that has a large flat flame. 
At the height of the flame, scrape the varnish from a spot 3 or 4 mm. 
in diameter. Place the chimney on the lighted lamp with the clear 
spot oppasite the middle of a screen of light-colored paper and about 
2 m. from it. Instead of being varnished, the chimney may be 
smoked, or surrounded by a hollow cylinder of asbestos paper in 
which a hole has been cut at the proper height. Hang a croquet ball 
midway between the lamp and the screen. If the room is not dark- 
ened, place the ball 
and the screen be- 
tween the lamp and 
the window. Prick a 
pin-hole through the 
darkened section of 
the screen and look 
through it toward 
the lamp. From the 
further side of the 
screen, prick a series of such holes about an inch apart and in a 
straight line, looking through each hole before another is pricked. 
When you have pricked a hole through which you can see the lumi- 
nous spot on the lamp-chimney, examine the other side of the screen 
and notice that the pin-hole is outside the darkened section. 

Experiment 127. — Replace the chimney used in Experiment 126 
by one that is clear, and see that the side of the flame is turned 
toward the ball. Examine the darkened section on the screen and 
notice that its central disk is equally dark hi all its parts, and 
surrounded by a ring of varying darkness. Beginning at the middle 
of the disk, prick pin-holes as before, examining each in succession, 
and avoiding those pricked in Experiment 126. Notice that you 
cannot see the flame through any hole in the central disk, that you 




Fio. 127. 



LIGHT: VELOCITY AND INTENSITY. 



161 



can see part of the flame through any hole in the annular space, 
and that you can see the whole of the flame through any hole outside 
the annular space. 




Fio. 128. 



204. A Shadow is the darkened space from which an 
opaque body cuts off light. If the source of light has con- 
siderable magnitude there will be a region of complete 
shadow, called the umbra, surrounded by a partial shadow, 
called the penumbra. No light enters the umbra; the 
penumbra receives light from a luminous surface. 

205. An Image is an optical counterpart of an object and 
may be formed in several ways. When the light actually 
comes from the image to the eye, the image is real. Such 
an image may be received on a screen. When the light 
seems to come from the image to the eye but does not, 
the image is virtual. All virtual images are optical illu- 
sions. 

Inverted Images. 

Experiment 128. — Place the opened end of an empty tin fruit-can 
upon a hot stove and leave it there just long enough to melt off the 
mutilated cover. Make a good-sized nail-hole at the center of the other 
end. Cover the nail-hole with tin-foil, and the other end of the can 
with thin tracing cloth or paper. Prick a pin-hole in the tin-foil, and 
turn it toward a candle-flame. Upon the paper may be seen an 
inverted image the size of which will depend upon the distance of 
the flame from the pin-hole. The image will be seen more plainly 
if the room is darkened, or a dark cloth used (after the manner of a 
photographer) to shut the outside light from the eyes and the screen. 



162 



ELEMENTARY PHYSICS. 



206. Images by Apertures. — If light from a highly 
luminous body is admitted through a small hole to a 
darkened room, and there received upon a white screen, 
it will form an inverted image of the object. 




FiGi 129. 



(a) As the rays are straight lines, they cross at the aperture ; hence, 
the inversion of the image. The darkened room constitutes a camera 
ohscura of simple form. The image of the school playground at recess 
is very interesting, and is easily produced. 

207. The Velocity of Light is about 186,000 miles 
(3 X 10^^ cm.) per second. For terrestrial distances, the 
passage of light is, therefore, practically instantaneous. 

(a) The nearest of Jupiter's satellites passes within the shadow 
of that planet at equal intervals. But, as observed from the earth, 

the intervals are 
not equal, they 
being longer while 
the earth is passing 
from E to E' than 
they are while the 
earth is passing over 
the other half of its 



® 




Fio. 130. 



orbit, E' to E, Observations show that it requires 16 min. 36 sec. for 
light to pass over the diameter of the earth's orbit, from E to E\ 
This distance being approximately known, the velocity of light 



LIGHT: VELOCITY AND INTENSITY. 



163 



is easily computed. The velocity of light has been measured by 
other meaus, giving results that agree substantially with that above 
recorded. 

Intensity of Illumination. 

Experiment 129. — Make three cardboard screens, A, B, and C, 
respectively 5 cm., 12 cm., and 17 cm. on a side. Draw a line parallel 
to each edge of B and C, and at a distance of 1 cm. therefrom, 
thus inscribing squares 10 cm. and 15 cm. on a side. Divide the 
smaller inscribed square into four squares, each the size of Ay and 
the larger inscribed square into nine such squares. Mount the three 
screens so that they stand upright with their middle points at the 
height of the cleared spot on the lamp-chimney used in Experiment 




Fig. 131. 



126. The screens may be conveniently supported by soft-wood rods, 
each having a fine slit sawed in one end and a sewing-needle thrust 
halfway into the other end. Place A about 30 cm. from the chimney. 
Set C parallel to A and at such a distance that the shadow of A just 
covers its nine squares. Then place B so that the shadow of A 
just covers its four squares. Determine the relative distances of ^ , J5, 
and C from the source of light. Remove A and notice that the light 
that previously fell upon it now falls upon B. Remove the second 
screen and notice that the light that previously fell upon A and B 
now falls upon C •• 

208. The Intensity of Radiation that falls upon a sur- 
face — 

(1) Varies inversely as the square of the distance between 
this surface and the source of radiation. 

(2) Varies with the angle that the incident radiation 



164 



ELEMENTARY PHYSICS. 



makes with this surface^ being at a maximum when the 
surface is perpendicular to the direction of propagation. 

(a) In Experiment 129, the light that fell upon A was diffused 
over four times the area at B, at twice the distance ; and nine times 
the area at C, at three times the distance. With the same quantity 
of light diffused over nine times the area, the intensity of the illumi- 
nation, i.e., the quantity of light per unit of surface, is only \ as great. 

Photometry. 

Experiment 130. — Arrange apparatus in a darkened room as shown 
in Fig. 132, where S represents a screen of white paper or cardboard. 




Fio. 132. 



and iJ, a small rod placed upright a few inches from S (a cheap pen 
and pen-holder, or a lead pencil lield by a bit of wax on the table will 
answer) . On the table-top, draw a line through the foot of R and 
perpendicular to the lower edge of .S. Place the candle. on one side 
of this line and about 20 inches from S. Place the lamp on the other 
side of the line and at such a distance that the two shadows upon iS 
nearly touch and are of equal darkness. The two flames should be 
at the same level and at equal angular distances from the line drawn 
on the table-top. The flat lamp-wick should stand diagonally to i>. 
If the distance from / to Z is twice that from c to C, then L is four 
times as powerful a light as C ; if the distance is three times as far, 
L is nine times as powerful. Apparatus thus used constitutes a 
Rumford photometer. 

Experiment 131. — Drop some melted paraffin upon a piece of 
^''avy unglazed white paper, making a spot about an inch in diameter. 



LIGHT: VELOCITY AND INTENSITY. 165 

Remove the excess of paraffin with a knife, and heat the spot with a 
flat-iron or can of water. Support the paper as a vertical screen. 
Place a lighted standard candle (see § 208) at one end of a table, and 
a lamp or gas-flame at the ot^ier eiid. Place the screen between 
them, and ai-range the pieces so that the middle points of the caudle- 
flame, the translucent disk, and the lamp-flame are in a straight line 
that is perpendicular to the screen. ^ If the lamp-flame is flat, set it 
diagonally to the screen. Move the screen along the line between the 
candle and the lamp until its two sides are equally illuminated ; i.e., 
until the paraffined spot is invisible, or as nearly so as possible. Find 
the ratio between the distances of candle and lamp from the screen, 
and square the ratio to find the candle-power of the lamp. Appara- 
tus thus used constitutes a Bunsen photometer, 

209. Photometry is the measurement of the relative 
amounts of light emitted by different sources. The stand- 
ard in general use is the light given by a sperm candle 
(of the size known as *' sixes") when burning 120 grains 
per hour. The result is expressed by saying that the light 
tested has so many candle-power. 

BXBRCISBS. 

1. Describe the shadow cast by a wooden ball (a) when the source 
of light is a luminous point ; (5) when the source of light is a white- 
hot iron ball smaller than the wooden ball ; (c) when it is of the 
same size ; (d) when it is larger. 

2. Do sound waves or water waves the more closely resemble waves 
of light? Why? 

3. A coin is held 5 feet from a wall and parallel to it. A lumi- 
nous point, 15 inches from the coin, throws a shadow of it upon the 
wall. How does the size of the shadow compare with that of the 
coin ? 

4. An opaque screen, 3 inches square, is held 12 inches in front of 
one eye; the other eye is shut; the screen is parallel with a wall 100 
feet distant. What area on the wall may be concealed by the screen ? 

5. A standard candle is 2 feet and a lamp is 6 feet from a wall. 
The shadow^ that they cast on the wall are of equal intensity. What 
is the candle-power of the lamp? 

6. An electric arc lamp 100 feet north of me and one 200 feet south 



166 



ELEMENTARY PHYSICS. 



of me niuminate opposite sides of a sheet of paper in my hand and 
rendek' invisible a grease spot on the paper. How do the illuminating 
powers ot the lamps compare V 

7. If you hold a sheet of paper with a greased spot on it between 
you and the light, the spot will look lighter than the rest of the sheet. 
Why is this? 

8. If you hold the sheet in front of you when you are turned away 
from the light, the spot will look darker than the rest of the sheet. 
Why is this? 

9. Study the shadows cast by an electric arc lamp, and write a 
very brief description of the penumbra of the shadows. 



ni. REFLECTION OE RADIAItTT ENERGY. 

A Simple Reflector. 

Experiment 132. — About two feet from an air or other sensitive 
thermometer, place an inverted flower-pot. Midway between the two, 

place a board or glass screen 
that reaches frojn the t^ble 
to a height of several inches 
above the bulb of the ther- 
mometer. Upon the flower- 
pot, place a very hot brick. 
Notice that the heat of the 
brick has little effect upon 
the thermometer. Then 
hold a sheet of tin-plate 
over the screen so that en- 
ergy radiated obliquely up- 
ward from the brick may be reflected obliquely downward toward the 
thermometer. By properly adjusting the position of the reflector, 
the thermometer may be quickly affected. 

210. Reflection of Radiant Energy is the sending hack of 
incident ether -waves by the surface on which they fall irito 
the medium from which they come. The reflection may be 
irregular or regular. 




Fig. 133. 



REFLECTION OF RADIANT ENERGY. 



167 



(a) The reflection of radiant energy may be thus explained : Con- 
sider a beam of light as made up of a number of etiier-waves moving 
forward in the air and side by side, as represented by the rays A, B, 
and C Imagine a plane, MN, normal to these rays, attached to the 
waves and moving forward with them. Such a plane is called a wave- 
frimU It moves forward in a straight line, and is always perpendicular 
to the line of propagation. As the wave-front advances beyond A/iV, 
the ray, A^ strikes the reflecting surface, RS^ and is turned back into 




Fig. 134. 

the air. By the time that the ray, C, arrives at P, the ray, i4, trav- 
eling with unchanged speed, has passed over the distance, A/0, equal 
to the distance, NP. This changes the direction of the plane that is 
attached to the waves, and sets it in the new position indicated by 
OP. Lines drawn from A/, Q, and P, perpendicular to OP, will rep- 
resent tiie new direction of propagation, i.e., the paths of reflected 
rays. From Fig. 134, it may easily be proved that the angles of inci- 
dence and of reflection are equal. 

Note. — The class-room 
should be provided with a 
porte-luniiere, which con- 
sists of a plane mirror so 
mounted and fitted with ad- 
justing appliances that the 
direction of tiie light re- 
flected from the mirror may 
.be easily controlled. The 
mirror is placed on the out- 
side of the shutter of a 
darkened window and oper- 
ated frotn within, sunlight 
being reflected through the 
aperture in the shutter. 
The accompanying figure represents a form that may be used with a 
variety o£ accessories for projection. 




Fig. 136. 



1C8 



ELEMENTARY PHYSIC& 



Irregnlar Reflection. 

Experiment 133. — Let a beam of light pass through an opening in 
the shutter of a darkened room, and fall upon a sheet of drawing 
paper lying on the table-top. The light will be scattered, and will 
illuminate the room. With a hand mirror, reflect the beam down- 
wai*d into a tumbler of water into which a teaspoonf ul of milk has 
been stirred. The milky water will scatter the light, and illuminate 
the room as if it was self-luminous. 



211. Irregular Reflection or 
Diffusion results from the inci- 
dence of radiant energy upon 
an irregular surface, as is illus- 
trated by Fig. 136. Bodies are 
made visible to the eye mainly by 
the light that they thus diffuse. 




Fig. 136. 



Regular Reflection. 

Experiment 134. — Repeat Experiment 133, allowing the beam of 
light to fall upon a miiTor instead of drawing paper. Most of the 
light will be reflected in a definite direction, and will brilliantly 
illuminate a small part of the inclosing wall. Reflect the beam down- 
ward into a tumbler of clear water ; the tumbler will be visible but 
the room will not be illuminated as it was by the milky water. 

212. Regular Reflection re- 
sults from the incidence of 
radiant energy upon a polished 
surface. When a beam of light 
falls upon a mirror, the greater 
part of it is reflected in a defi- 
nite direction as is illustrated 
by Fig. 137, and forms an image of the object from which 

it came. 

Law of Reflection. 

Experiment 135. — Provide a semicircle of soft wood about 25 cm. 
in diameter, and on its upper surface draw radii at intervals of 10°. 




FiQ. 137. 




KEFLECTION OF RADIANT ENERGY. 1G9 

Fasten a bit of looking-glass about 1x2 cm. at A and facing the 
curved edge of the board. The glass should be set in a notch cut in 
the boai'd so that the silvered back of the mirror coincides with the 
diameter of the semicircle, and the middle of the mirror with the cen- 
ter of the semicircle. To the curved edge of the board, fasten a 
bright metal band that has a row of 17 holes each 4 or 5 mm. in 
diameter, so that one of the holes will be 
at the outer end of each radius marked 
on the board. Number the holes each 
way from the middle one. Hold the 
board so that you can look through the „ -go 

hole marked toward the mirror and 
the window, and notice the image of that hole. Identify the hole by 
sticking a pin upright in front of it. The incident ray strikes the 
mirror perpendicularly and is reflected back along the same line ; the 
angle of incidence is zero. The image of any other hole can be seen, 
not in this way, but through the hole that bears the corresponding 
number, i.e., at an equal angular distance from the radius that is per- 
pendicular to the mirror. 

213. Law of the Reflection of Radiant Energy. — The 
angle of incidence and the angle of reflection are equals and 
lie in the same plane. 

214. Apparent Direction of Bodies. — Every point of a 
visible object sends a cone of light to the eye. The pupil 
of the eye is the base of the cone. The point always 
appears at the real or apparent apex of the cone. If the 
path of the light from the point in question to the eye 
is straight, the apparent position of the point is its real 
position. If the path is bent by reflection, or in any other 
manner, the point appears to be in the direction of the 
light as it enters the eye. 

Plane Mirrors. 

Experiment 136. — Place a jar of water 10 or 15 cm. back of a pane 
of glass placed upright on a table in a dark room. Hold a lighted 
caudle at the same distance in front of the glass. The jar will be 



170 



ELEMENTARY PHYSICS. 



seen by light transmitted through the glass. Ad image of the candle 
will be formed by light reflected by the glass. The image will be 
seen in the jar, giving the appearance of a candle burning in water. 
The same effect may be produced in the evening by partly raising a 
window, and holding the jar on the outside and the candle on the 
inside. This experiment suggests an explanation of many optical 
illusions. 



215. Plane Mirrors. 




Fig. 139. 



— If an object is placed before a 
plane mirror, a virtual image ap- 
pears behind the mirror. Each 
point of this image seems to be as 
far behind the mirror as the cor- 
responding point of the object is 
in front of the mirror. Hence, 
images seen in still, clear water 
are inverted. 



(a) In Fig. 139, ABE and ACD rep- 
resent two luminous rays proceeding from 
A and reflected by the plane mirror, MR. 

From the figure, it may be proved geometrically that A IB is & right 

angle, and that al = AI, 

(h) The "construction for the image" is performed by locating 

the images of a number of well-chosen 

points in the surface of the object. 

In Fig. 140, OB represents an arrow 

in front of the mirror, MR, From 

the ends of the arrow, draw OC and 

BD perpendicular to the face of the 

mirror, and prolong them indefinitely. 

Take oC equal to OC and bD equal to 

BD. Join and b. The image is 

virtual, erect (i.e., not inverted), and 

of the same size as the object. 





Fig. 140. 



Foci. 



Experiment 137. — Let a small beam of light fall perpendicularly 
upon a concave mirror. Strike two blackboard erasers togetlier iu 



REFLECTION OF RADIANT ENERGY. 



171 



front of the mirror, and notice that the light converges at a point 
not far from the mirror. 

216. A Focus is a point at which light converges, in 
which case it is called a real focus ; or it is a point from 
which light appears to proceed, in which case it is called 
a virtual focus. 

217. Concave Mirrors are generally spherical; i.e., the 
reflecting surface is a small part of the inner surface of a 
spherical shell. A concave mirror increases the conver- 
gence or decreases the divergence of light that falls 
upon it. ' . ' 

(a) C, the center of the sphere, is the center of curvature of MR, 
the mirror. A, the middle point of the mir- 
ror, is called the center or vertex of the mirror. 
Any straight line passing through C to or 
from the mirror is called an axis of the mir- 
ror. ACX, the axis that passes through 
A , is called the principal axis ; all other axes 
are called secondary axes. The angle, MCR, 
is called the aperture of the mirror. Fig. 141. 

218. The Foci of Concave Mirrors may be in front of the 
mirror, in which case they are real; or they may be behind 
the mirror, in which case they are virtvM, 

(a) The location of these foci gives rise to several cases : — 

(1) When the incident rays are 
practically parallel to the principal 
axis (e.g., the sun's rays), they will 
be reflected, as shown in Fig. 142, 
to a focus at F, midway between 
C and A. This focus of rays par- 
allel to the principal axis is called 
the principal focus of the mirror. 
The distance, FA, is called the 
principal focal length, or distance of the mirror. 

(2) When the rays diverge from the center of curvature, the 
i-a^ant point and the focus coincide. 





Fig. 142. 



172 



ELEMENTARY PHYSICS, 




Fio. 143. 



(3) When the rays diverge from a point beyond the center of 
curvature, as from B, the focus is at a distance from the mirror 

greater than that of the 
v^ principal focus, and less 

than that of the center of 
curvature, as shown in 
Fig. 143. 

(4) When the rays di- 
verge from a point at a 
distance from the mirror 
greater than that of the 
principal focus and less 
than that of the center of curvature, we have the converse of the third 
case. If the radiant point is at b (Fig. 143), the focus falls at B. 
Foci that are thus interchangeable are called conjugate foci, 

(5) When the rays diverge from a point at a distance from the 
mirror less than that of the principal focus, the reflected rays diverge 
as if from a point back of the 
mirror. This point, 6, is a 
virtual focus. 

(6) When the rays diverge 
from the principal focus, the 
reflected rays are parallel and 
there is no focus, real or vir- 
tual. This is the converse of 
the first case. 

(6) The convergence of parallel rays at the principal focus is only 
approximately true with a spherical mirror ; it is strictly true with a 
parabolic mirror. In order that the difference between the spherical 
and the parabolic mirror may be reduced to a minimum, the aperture 
of the former should be small. The light from a luminous point at 
the focus of a parabolic mirror is reflected in truly parallel lines. The 
headlights of railway locomotives are thus constructed. Parabolic 
mirrors would be more common if they were less expensive. 




— ~£^6 



Concave Mirror Images. 

Experiment 138. — Place a concave mirror facing the sun, and hold 
a bit of paper so that its illumination by the reflected light is of the 
greatest intensity obtainable, thus locating the principal focus of the 



REFLECTION OF RADIANT ENERGY. 



178 



mirror. Measure this focal distance. In front of the mirror, and at 
a distance greater than once and less than twice the focal distance, 
place a candle-flame. Place a tracing cloth or oiledrpaper screen 
back of the candle, and, with a blackened card, shield it from the 
direct light of the candle. Adjost the positions of the candle and 
the screen until a good image of the former is projected on the latter. 

219. Images formed by Concave Mirrors consist of the 
conjugate foci of the several points in the surface of the 
object presented to the mirror and may, therefore, be real 
or virtual. The " construction " may be easily performed 
by selecting a few determinative points, as the ends of an 
arrow, and determining their foci. 

(a) The focus of each point chosen may be determined by tracing 
two rays from the point, and locating their real or apparent inter- 
section after reflection by the mirror. The two rays most convenient 
for this purpose are the one that lies along the axis of the point, and 
the one that lies parallel to the 

principal axis t^ the mirror. \. . X^M^ 

The first of these is reflected ^'" 
back upon itself, and the focus 
must, therefore, lie in that 
line. The other is reflected 
through the principal focus, 
and the construction of equal 
angles of incidence and reflec- 
tion is, therefore, unnecessary. The process is illustrated in Fig. 145. 
Following the order of the cases discussed in § 217, it will be found 
that: — 

(1) When the incident rays are practically parallel (e.g., solar 
rays), the image is at the principal focus. 

(2) When the object is at the center of curvature, the image is 
real, inverted, of the same size as the object, and at the center of 
curvature. 

(3) When the object is at a distance from the mirror somewhat 
greater than the center of curvature, as beyond C, the image is real, 
inverted, smaller than the object, and at a distance from the mirror 
greater than that of F and less than that of C. 

(4) When the object is at a distance from the mmor greater than 




174 



ELEMENTABT PHYSICS. 




that of F and less than that of C, the image is real, inverted, larger 
than the object, and beyond C, as in Fig. 146. This is the converse 

of the third case. 

(5) When (he object is at a distance 
from the mirror less than that of /% 
the image is virtual, erect, and larger 
than the object. 

(6) When the object is at a dis- 
tance from the mirror equal to that of 
F, the reflected rays are parallel and 
no image is formed. This is the con- 

Fio. 146. verse of the first case. 

220. A Convex Mirror is generally a part of the outer 
surface of a spherical shell. It increases the divergence, 
or decreases the conver- 
gence, of light that falls 
upon it. 

(rt) The foci are virtual; 
the principal focus is midway 
between the center of the 
mirror and the center of cur- 
vature. The foci may be 
located and the images deter- 
mined by processes similar 
to those used for concave 
mirrors, as is illustrated by 
Fig. 147. Such an image is 
erect, diminished, and vir- 
tual. Fio. 147. 




~2-C 



BXSRCISES. 

1. Copy Fig. 140, and add lines to show that the rays that form the 
image for the right eye of the observer are different from the rays that 
form the image for the left eye. 

2. With a radius of 4 cm., describe ten arcs of small aperture to 
represent the sections of spherical concave mirrors. Mark the centera 
of curvature, and the principal foci, and draw the principal axes. Find 
the conjugate foci for points in the principal axis designated as fol- 



REFRACTION OF RADIANT ENERGY. 175 

lows : (a) At a distance of 1 cm. from the mirror ; (b) 2 cm. from 
the mirror ; (c) 3 cm. from the mirror; (rf) 4 cm. from the mirror; 
(e) 6 cm. from the mirror. Make five similar constructions for points 
not in the principal axis. Notice that each effect is in consequence of 
the equality between the angle of incidence and the angle of reflection. 

3. Rays parallel to the principal axis fall upon a convex mkror. 
Draw a diagram to show the course of the reflected rays. 

4. When the sun is 30** above the horizon, its image is seen in a 
tranquil pool. What is the angle of reflection ? 

5. Given three points, A, B, and C, not in a straight line. Show, 
by a diagram, how to place a plane miiTor at C so that light proceed- 
ing from A shall be reflected to B. 

6. With a thread or fine rubber band, fasten a piece of looking- 
glass about 5 X 10 cm. to the vertical face of a rectangular wooden 
block. Balance the block and mirror upon a rule so that the face of 
the mirror crosses the rule at its middle. Place the eye so that the 
further end of the rule may be seen by looking obliquely downward 
and over the upper edge of the mirror. If the block back of the 
mirror is visible, move the mirror up until it conceals the top of the 
block, or use a thinner block. Adjust the mirror so that the further 
end of the image of the rule as seen in the mirror coincides with the 
end of the rule as seen over the mirror. The length of the rule is 
now perpendicular to the face of the mirror. Look at the images of 
the several divisions of the scale in front of the mirror and notice the 
distance of each image back of the miiTor. 

7. Place a cardboard screen close behind a candle-flame. Hold a 
concave mirror so that a shai*p image of the flame is projected on the 
screen, making image and Came coincide as nearly as possible. Image 
and flame will be nearly at the center of curvature of the mirror. 
Describe the image. Determine the focal length of the mirror. 



IV. REFRACTION OF RADIANT ENERGY. 
Simple Refractors. 

Experiment 139. — Hold a double-convex lens in the sun's rays, so 
that the bright focus on the side opposite the sun shall fall upon 
some easily combustible material like the tip of a friction-match. A 
spectacle-glass will answer, but a larger lens, like that of a reading- 



176 



ELEMENTARY PHYSICS. 



glass, is desirable; the larger the lens, the better. Compare the 
effect of holding clean white paper at the focus, and of holding there 
the same paper after it has been smeared with lampblack. A leus 
thus used is called a burning-glass. 

Experiment 140. — Place a coin on the bottom of a tin pan. Rest 
the head against the edge of a shelf or other fixed support, close oue 
eye, and have the pan adjusted so that its side just hides the coin 
from view. Have water carefully poured into tlie pan until the coin 
is visible. The light coming from the coin to the eye is bent down 
somewhere and somehow. Measure the depth of the water in the 
pan. Empty and .wipe the pan. Repeat the experiment using kero- 
sene instead of water, and compare the depth of the two liquids. 

. 221. Refraction of Radiant Energy siffnifies a retarda^ 
tion of the ether-waves^ and may be manifested hy a change 
of direction. Part of the light that falls on the surface of 
a transparent body enters it, and generally pursues therein 
a changed direction. This part is said to be refracted. 

(a) There is a change of direction, i.e., the radiant energy is 
deviated, when it falls obliquely upon the interface that separates 
two media, as air and water, and passes from one to the other ; or 
when it passes through a medium the density of which is not uniform, 
as the atmosphere. 

(b) In Fig. 148, LA represents a ray of light propagated in air, 

falling obliquely upon the surface of 
water at .4, and deviated by the 
water from AE to AK, Draw CZ> 
perpendicular to the refracting sur- 
face at tlie point of incidence. LA C 
is the angle of incidence; KAD, the 
angle of refraction; and KAE, the 
angle of deviation. From ^ as a cen- 
ter and with unity as a radius, describe 
a circle, and draw mn and pq perpen- 
dicular to CD, Then mn is the sine 
of the angle of incidence ; pq is the 
sine of the angle of refraction. 

(c) For any two media, the quotient arising from dividing the sine 
of the angle of incidence by the sine of the angle of refraction is con- 




FiQ. 148. 



BEFR ACTION OF RADIANT ENERGY. 



177 



stant, and is called the index of refraction. For ordinary purposes, 
the index of refraction of gases may be neglected ; the index of re- 
fraction for light passing from air may be considered as 1 J for water ; 
IJ for crown-glass ; and If/ for flint-glass. 

(d) The determination of the direction of the refracted ray may be 
illustrated as follows : Let LA represent a ray passing from air 
into water at A. Through A, 

draw CD perpendicular to the L 

refracting surface. The index 
of refraction for the two media 
is |. From ^ as a center and 
with radii that are to each other 
as 4 : 3, draw concentric circles. 
Prolong LA to E, From v, the 
intersection of ^^ with the 
circumference of the inner cir- 
cle, draw vp parallel to CD. 
Through p, the intersection of 
this line with the circumfer- 
ence of the outer circle, draw 
AK, the line sought. 

(e) The refraction of radiant energy may be thus explained : Con- 
sider the case of light passing from air into glass. The velocity of 
light in glass is less than it is in air. When a beam of light, as repre- 
sented by the rays A, B, and C, moves forward in the air, the wave- 
front, MNy continues 
parallel to itself and 
moves forward in a 
straight line. As the 
wave-front advances 
beyond MN, the ray, 
A, enters the glass, 
while B and C are still 
in the air. The ad- 
vance of A in the glass 
is retarded by the 
glass so that, while C 
is passing in air from 
N to P, A traverses 
the shorter path, MO. 





Fio. 160. 



178 ELEMENTARY PHYSICS. 

This retardation of A and the corresponding retardation of B change 
the direction of the plane that is attached to the waves, and set it in 
the new position indicated by 0I\ All of the rays haying entered 
the glass, the wave-front again moves forward in a straight coui*se, 
normal to OPj representing the new direction of propagation. In 
passing into the glass the direction of the beam was changed, a direct 
result of a change of speed at the surface of the glass. The beam was 
bent toward a perpendicular to the bounding surface, RS. When the 
beam emerges from the glass, similar changes will take place in in- 
verse order, and the beam will be bent from the perpendicular to the 
refracting surface. 

222. The Laws of Refraction. — (1) When radiant energy 
passes obliquely from one medium to another of greater refrac- 
tive power ^ the rays are bent^ at the point of incidence^ toward 
a line that is perpendicular to the surface that separates the 
two media. 

(2) When radiant energy passes obliquely from one me- 
dium to another of less refractive power^ the rays are bent 
from the perpendicular. 

223. Total Reflection. — When the angle of incidence 
exceeds what is called the critical angle^ a ray of light can- 
not pass from a medium of higher to one of lower refrac- 
tive power, as from glass or water to air; it will be totally 
reflected and not refracted. The critical angle for water 
and air is about 48 J^ ; for crown-glass and air, about 41". 

Refraction by Plates. 

Experiment 141. — Draw a straight line of such length that it ex- 
tends both ways beyond the ends of a piece of thick plate-glass placed 
upon it. Look obliquely through the glass and from the side of the 
line, and notice the apparent displacement of the pai*t of the line seen 
through the plate. 

224. Refraction by Plates. — When radiant energy passes 
through a medium bounded by parallel planes, the refrac- 



KEFRACTION OF RADIANT ENERGY. 



179 



tions at the two surfaces are equal and contrary in direc- 
tion. The direction after pass- 
ing through the plate is parallel 
to the direction before entering 
the plate ; the rat^s merely suffer 
lateral aberration. 




Fig. 161. 



225. A Prism is a transparent 
body with two refracting sur- 
faces that lie in intersecting 
planes. The angle formed by these planes is called the 
refracting angle. 

(a) If a thin book, partly open, stands on end on a table, it repre- 
sents a prism, the covers of the book representing the refracting sur- 
faces and including the refracting angle. The table-top is perpen- 
dicular to the sides of the 
prism and, therefore, rep- 
resents a principal plane. 
The triangular base of 
the book represents a 
principal section of the 
prism. Let jnno represent 
the principal section of a 
prism. A ray of light 
from L is refracted at a 
and b. An object seen" 
through a prism seems to 
be moved in the direction 
of the refracting angle ; the rays are bent away from the refracting 
angle. 

226. A Lens is a transparent body the two refracting 
surfaces of which are curved, or one of which is curved 
and the other plane. Lenses are generally made of crown- 
glass which is free from lead, or of flint-glass which con- 
tains lead and has greater refractive power. The curved 
surfaces are generally spherical. 




Fig. 152. 



180 



ELEMENTARY PHYSICS. 



. (a) Lenses are convergiDg or diverging. Each of these two classes 
has three varieties : — 



(1) Double-convex*, 

(2) Plano-convex, 

(3) Meniscos, 



Thicker at the middle than at the edges ; 
converging. 




Fio. 153. 



The double-convex (biconvex, or magnifying) lens may be taken as 
the type of these ; its effects may be considered as produced by two 
prisms with their bases in contact. 



(4) Double-coyicave, 

(5) Plaiio-coacave, 

(6) Concavo-cgnvex, 



Thinner at the middle than at the edges ; ' 
diverging. 



The double-concave (biconcave) lens may be taken as the type of 

these ; its effects may be considered as produced by two prisms with 

their refracting edges in contact. 

(6) A double-convex lens may be described as the part common to 

two spheres that intersect .each other. The centers of the limiting 

spherical surfaces, 
as c and C, are the 
centers of curvature. 
The straight line, 
XY^ passing through 
*" the centers of cuwa- 
ture is the principal 
axis of the lens. In 
the piano-lenses, the 
principal axis is a 
line drawn from the 




FiQ. 154. 



center of curvature normal to the plane surface. A point on the 
principal axis so taken that rays passing through it pierce parallel 



REFRACTION OF RADIANT ENERGY. 



181 



elements of the refracting surfaces is called the optical center, A ray 
passing through the optical center suffers no change of direction 
other than a slight lateral aberration that may be disregarded. Any 
straight line, other than the principal axis, passing through the opti- 
cal center is a secondary axis. 

(c) To trace a ray through a lens, we have only to apply the prin- 
ciples already explained. For example, let LN represent a glass bi- 
convex lens (index of refraction, |) with centers of curvature at C and 
C, and AB, the incident ray. From JS as a center, draw the arcs, mn 
and op, making the ratio of their radii equal to the index of refraction, 
i.e., 2 : 3. Draw the normal, C'B. Draw st parallel to C'B. Draw 
the straight line tBDy ; BD is the path of the ray through the lens. 




From Z) as a center, draw the arcs, uv and wx, using the same radii 
as for mn and op. Draw the normal, CD. Draw yz parallel to CD. 
Draw DzA'f the path of the ray after emergence. 



Focus of Convex Lens. 

Experiment 142. — Hold one of the large lenses of an opera glass 
or of an optical lantern in the sun's rays. Notice the converging 
pencil formed by the light (after passing through the lens) as it 
passes through air made dusty by striking together two blackboard 
erasers. The focus and its distance from the lens may be seen. 
Measure the distance from the lens to its focus. 

227. The Foci of Convex Lenses may be determined 
experimentally, but some of their properties are more 
conveniently studied by the diagrammatical tracing of 



182 ELEMENTARY PHYSICS. 

rays. To locate the focus for light diverging from any 
point, it is necessary to determine the point of intersec- 
tion of two emergent rays. The problem is much sim- 
plified by considering the axis that passes through the 
point of divergence as the path of one of these rays. 

(a) Experimental work with convex lenses develop frequent analo- 
gies to the phenomena of concave mirrors, and give rise to several 
cases as follows : — 

(1) When the incident rays are parallel to the principal axis, their 
focus is called the principal focva. With a biconvex lens of crown- 
glass (index of refraction, |) the principal focus is at the center of 
curvature, i.e., the focal length of the lens is equal to the radius of 
curvature. With a plano-convex lens, the focal length is twice the 
radius of cui*vature. In either case, the focus is real. 

(2) When the incident rays diverge from a point more than twice 
the focal distance from the lens, a real focus is formed on the other 
side of the lens, and at a distance greater than the focal length and 
less than twice the focal lengtli. (See A and A', Fig. 155.) 

(3) When the incident rays diverge from a point at twice the focal 
distance from the lens, a real focus is formed on the other side of the 
lens and at the same distance from it. These two points, as c and d 
in Fig. 155, are called secondary foci. 

(4) When the incident rays diverge from a point distant from the 
lens more than the focal length and less than twice the focal length, 
a real focus is formed on the other side of the lens and at a distance 

. greater than twice the focal length . This is the converse of the second 
case. Two foci that are thus interchangeable, like A and A' in Fig. 
155, are called conjugate foci. The secondary foci are conjugate. 

(5) When the incident rays diverge from the principal focus, the 
emergent rays will be parallel, and no focus, real or virtual, will be 
formed. This is the converse of the first case. 

(6) When the incident rays diverge from a point nearer *the lens 
than the principal focus, the emergent rays are still diverging, and 
a virtual focus is formed back of the radiant point. 

(7) When the incident rays are converging, a real focus is formed 
on the other side of the lens at a distance less than the focal length. 
This is the converse of the sixth case. 

(6) Each pupil should draw a figure to illustrate each of the fore- 
going cases. 



REFRACTION OF RADIANT ENERGY. 



183 



The Foci of Concave Lenses may be located by 
processes already studied. Such lenses have their centers 
of curvature, their primary and secondary axes, and their 
optical centers the same as convex lenses. 

(a) Experimental work with concave lenses develop frequent analo- 
gies to the phenomena of convex mirrors, and give rise to several 
cases as follows : — 

(1) When the incident rays are parallel to the principal axis, the 
emergent rays diverge as if they came from a virtual focus, which is 
called the principal focus. With a biconcave lens of glass (index of 
refraction, l), the principal focus is at the center of curvature. With 
a plano-concave lens, the focal length is twice the radius of curvature. 

(2) When the incident rays are diverging, the focus is virtual and 
at a distance from the lens less than the focal length. As the radiant 
point approaches the lens, the focus also approaches the lens. 

(3) When the incident rays are converging, the effects are varied 
according to the degree of convergence. If the point of convergence 
is nearer the lens than the principal focus, a real focus will be formed 
at a distance greater than the focal length of the lens. If the point of 
convergence is at the principal focus, the emergent rays will be paral- 
lel, and no focus will be formed. If the point of convergence is further 
from the lens than the principal focus, a virtual focus will be formed. 

(b) Each pupil should draw a figure to illustrate each of the fore- 
going cases. 




v» 



yfi 






''''niillllliiiiiljjiiiiiyiiiiiiijijiil^ 



'■;■".*■ -! ::r*--^_ 



KmhW 



Fig. my. 



Images. 

Experiment 143. — Place a* candle, a convex lens of known focal 
length (see Experiment 142), and a screen in line as shown in Fig. 15G, 



184 ELEMENTARY PHYSICS. 

the distance of the candle from the lens being a little greater than 
the focal length of the lens. Adjust the position of the bcreeu until 
a sharply defined image of the candle is projected upon it. Place the 
eye back of the screen and have the screen removed; the inverted 
image may be seen suspended in mid-air. Burn touch-paper under 
the image, and notice its projection on the sci-een of smoke. Replace 
the screen first used. 

Experiment 144. — With candle and screen in positions as described 
in Experiment 143, adjust the position of the lens so that the flame 
and the image of the flame ai*e of the same size. IVleasure the dis- 
tance of the screen from the candle, and compare a quarter of that 
distance with the focal length of the lens. 

229. Images formed by Lenses consist of the conjugate 
foci of the several points in the surface of the object pre- 
sented to the lens and may, therefore, be real or virtual. 
The construction for such images is closely analogous to 
the process used for images formed by mirrors. 

(a) The focus of each point chosen may be determined by tracing 
two rays from the point, and locating their real or apparent intersec- 
tion after emerging from the lens. The two rays most convenient 
for this purpose are the one that lies along the secondary axis of the 



A 






J 


C "^ — 


.^... l^ \ 1;^^ / ^ 


1 


[__ --—^ Xj 



Fig. 167. 

point, and the one that lies parallel to the principal axis of the lens. 
For example, from A and E, extremities of an arrow, draw the sec- 
ondary axes, A Oa and EOe. From A, draw AB parallel to the prin- 
cipal axis, XY, Determine the direction of BD by construction. 
From Z>, draw the path of the emergent ray through the principal 



REFRACTION OF RADIANT ENERGY. 185 

focus, F, It intersects the secondary axis at a, the conjugate focus of 
the radiant point, A, In similar manner, the conjugate focus of the 
point, E, may be located at e. The points, a and e, mark the extremi- 
ties of the image of the object, A E, 

(h) An examination of Fig. 157 shows that the linear dimensions 
of object and image are directly as their respective distances from the 
center of the lens ; they will be virtual or real, erect or inverted, ac- 
cording as they are on the same side of the lens, or on opposite sides. 

EXERCISES. 

1. Remembering the varying density of the earth's atmosphere, 
draw a diagram showing that the sun may be seen before it has 
astronomically risen, and after the true sunset, i.e., after it has dipped 
below the western horizon. 

2. Draw circles so that parts of their circumferences may repre- 
sent the curved surface of a meniscus, a biconcave, and a concavo- 
convex lens. 

3. Construct the critical angle for air and water. 

4. Show how a beam of light may be bent at a right angle by a 
glass prism. 

5. Trace a ray through a biconvex lens for the location of its 
principal focus. 

6. Trace a ray through a biconcave lens for the location of its 
principal focus. 

7. Through what point does the line joining the conjugate foci 
of a convex lens always pass ? 

8. (a) The focal distance of a convex lens being C inches, deter- 
mine the position of the conjugate focus of a point 12 inches from the 
lens. (6) 18 inches from the lens. 

9. The focal distance of a convex lens is 30 cm. Find the con- 
jugate focus for a point 15 cm. from the lens. 

10. If an object is placed at twice the focal distance of a convex 
lens, how will the lengtli of the image compare with the length of the 
object ? 

11. Focus a spy-glass or small telescope on an object a mile or more 
distant. The rays coming from the object to the eye will be practi- 
cally parallel. Place a lens, the focal length of which yon are to 
measure, in front of the telescope. Place a small-type newspaper- 
clipping on a piece of cardboard, and look at it through the telescope 
and lens. Adjust the position of the cardboard so that the printing 



186 



ELEMENTARY PHYSICS. 



appears distinct. Measure the distance of the cardboard from the 
lens. Obtain the average of several such trials. Record a discussion 
of the proposition that this average distance is the focal length of the 
lens. 



V. SPECTRA, CHROMATICS, ETC. 

Analysis. 

Experiment 145. — Admit a sunbeam through a small opening in 
the shutter of a darkened room. In the path of the beam, place a 
prism, as shown in Fig. 158. Instead of the colorless image ot* the 




Fig. 158. 

sun at E, there appears upon the white screen a many-colored band 
changing gradually from red at the lower end, through all the colore 
of the rainbow, to violet at the upper end. 

230. Dispersion. — The separation of differently colored 
rays hy refraction is called dispersion. Experiment 145 
shows that white or colorless light, like that of the sun, 
is a mixture of radiations of varying color, and that they 
may be separated because of their varying refrangibility. 

(a) The differences in deviation arise from differences of wave- 
""ength, the angle of deviation increasing as the wave-length diminishes. 



SPECTRA, CHROMATICS, ETC. 



187 




(5) A converging lens brings the focus of violet rays nearer the 
lens than it does the focus of red rays, because of their 
greater refrangibility. The images formed by such lenses 
are, therefore, often fringed with color. This difference in 
the deviation of differently colored rays is called chromatic aber- 
ration, A compound lens, like that shown in Fig. 159, is 
called achromatic because it forms an image that is nearly 
free from the fringe of color. Fig. 169. 

231. Spectra. — The many-colored image of the sun pro- 
jected on the screen in Experiment 145 is called a spectrum. 
As the differently colored images of the sun overlap, the 
spectrum thus produced is an impure spectrum. 

(a) These prismatic colore are generally described as violet, indigo, 
blue, green, yellow, orange, and red. The initial letters of these terms 
form the meaningless, mnemonic word " vibgyor." 

Synthesis. 

Experiment 146. — Let light that has been dispersed by a prism 
fall upon an achromatic convex lens as shown in Fig. 160. It will 
be refracted to a focus and recombined to form white light. Hold 




Fig. 160. 

a card between the prism and the lens so as to cut off the red light, 
and notice the focus of what remains. Similarly cut off the violet 
light, and again notice the focus of what remains. A concave mirror 
may be used to reflect the light to a focus instead of using the lens as 
above described. 



188 ELEMENTARY PHYSICS. 



The Composition of White Light. — We have now 
shown, by analysis and by synthesis, that white light is 
composed of the prismatic colors. 

Color. 

Experiment 147. — Gradually raise the temperature of a platinum 
wire by an electric current. The first radiations emitted are those of 
" obscure heat " ; i.e., they affect the nerves of general sensation only. 
As the temperature continues to rise, waves of shorter and shorter 
wave-length are added, while those previously emitted are increased in 
amplitude. The wire successively appears red, orange, and yellow and 
then becomes white hot, the light emitted being exceedingly complex. 

233. Color is a property of lights and depends upon wave- 
length. Thus, the relation between color and light is the 
same as that between pitch and sound. 

(a) The wave-lengths that correspond to the several prismatic 
colors as they appear in the solar spectrum are as follows : — 

Violet, 4,059 Green, 5,271 Orange, 6,972 

Indigo (violet-blue), 4,383 Yellow, 6,808 Red, 7,000 
Blue (cyan-), 4,960 

These magnitudes are for the middle points of the several colors, and 
represent ten-million tl is of a millimeter. Light of only one wave- 
length is said to be monochromatic or homogeneous. 

(h) An incandescent body emits radiations with wave-lengths that 
grade imperceptibly from values less to values greater than any of 
those given above. When the wave-lengths are much less or much 
greater than those above given, the radiation is incapable of exciting 
vision. The visible spectrum occupies only one of the seven or more 
octaves of the full spectrum. The invisible spectra (ultra-violet and 
infra-red) have been explored with delicate thermoscopes, by pho- 
tography, etc. 

Color of Bodies. 

Experiment 148. — Paint threQ narrow strips of cardboard, one 
vermilion-red, one emerald-green, and the otlier aniline-violet. Be 
sure that the coats are thick enough thoroughly to hide the cardboard. 
When dry, hold the red strip in the red of the solar spectrum; it 
-appears red. Move it slowly through the orange and yellow ; it grows 



SPECTUA, CHROMATICS, ETC. 189 

gradually darker. In the green and colors beyond, it appears black. 
Repeat the experiment with the other two strips, and carefully notice 
the effects. 

Experiment 149. — Make a loosely wound ball of candle-wick ; soak 
it in a strong solution of common salt and water ; squeeze most of the 
brine out of the ball ; place the ball in a plate, and pour alcohol over 
it. Take it into a dark room and ignite it. Examine objects of dif- 
ferent colors, as strips of ribbon or cloth, by this yellow light. Only 
yellow objects will have their usual appearance. 

234. The Color of a Body depends upon the light that the 
body reflects or transmits to the eye. Some bodies have a 
power that may be described as selective absorption, re- 
flecting or transmitting light of certain wave-lengths, and 
absorbing the othei-s. If the light incident upon a body 
has only the wave-lengths that the body absorbs, the body 
can send no light to the eye and, therefore, appeai-s black. 

(a) A red ribbon is red because it reflects li^ht of the particular 
wave-length that corresponds to the sensation of redness, and absorbs 
the rest. A white ribbon is white because it reflects the same propor- 
tion of all the light that constitutes sunlight. A piece of blue glass 
is blue because it transmits or reflects light of the particular wave- 
length that corresponds, to the sensation of blueness, and absorbs the 
rest. Glass that absorbs none of the incident light is colorless. 

235. Complementary Colors are 
any two colors the blending of which 
produces white light. If the colors 
of the solar spectrum are divided 
into two parts and the colors in 
each part are blended, each re- 
sultant color evidently has what 
the other needs to make white 
light. Either of such colors is said 
to be complementary to the other. ^'° ^^^* 

(a) Any two colors standing opposite each other in Fig. 161 are 
complementary to each other. If such colors are blended, the result- 




190 ELEMENTARY PHYSICS. 

ant is white light; if any two alternate colors are blended, the result- 
ant will be the color that appears between them in the figure. 

Pigments. 

Experiment 150. — With a yellow-colored crayon, draw a broad 
mark on the blackboard. Along the same line, draw a similar mark, 
with a blue crayon. Also mix a small quantity of chrome-yellow 
with a like quantity of some ultramariue-blue pigment. The blend- 
ing of blue and yellow colors gives a white ; the blending of yellow 
and blue pigments gives a green. 



Mixing Pigments is a very different thing from 
mixing coloi*s. In the majority of cases, the scattering of 
incident light takes place not only at the surface of bodies 
but also at distances below the surface. In the case of 
pigments, most of the scattered light comes from below 
the surface. In Experiment 160, the yellow pigment re- 
moved most of the violet, indigo, and blue by such absorp- 
tion. The blue pigment. similarly removed most of the 
yellow, orange, and red. The radiations that escaped 
both were of the particular wave-length that constitutes 
green: — 

The Rainbow. 

Experiment 151. — Fill a glass bulb with clear water. Cut a circular 
opening (somewhat smaller than the bulb) in a large sheet of card- 
board. Reflect a sunbeam into a darkened room so that it shall pass 
through the opening in the cardboard and fall upon the water-filled 
bulb. Adjust the position of the bulb until circular spectra are thrown 
by the bulb back upon the cardboard screen. 

237. A Rainbow is a solar spectrum formed hy water' 
drops. 

(a) The center of the circle of which the rainbow forms a part is 
in the prolongation of a line drawn from the sun through the eye of 
the observer. This line is called the axis of the how. 




SPECTRA, CHROMATICS, ETC. 191 

The rays of sunlight incident upon the rain-drops are refracted as 
they enter the drop, internally reflected, and chromatically dispersed. 
The drop at V has an angular distance of 40° from EO, the axis of 
the bow, and sends only violet rays to the eye at E, Other drops, at 
the same angular distance from EO^ send 
violet light to the eye and, therefore, form 
a violet-colored circular arc of which V 
is the radius of curvature. Similarly, the 
angle of deviation for red rays is such 
that the drop, /?, at an angular distance 
of 42° from EO, sends red rays to the eye 
of the observer. Other drops at the same 
angular distance send red light to the eye 
and, therefore, form a red-colored circular yiq i62 

arc, of which OR is the radius of curva- 
ture. The primaiy bow, therefore, has an angular width of 2°, the 
other prismatic colors ranging in regular order between the violet 
and the red. 

(c) Sometimes a secondary bow is visible outside the primary and 
with the colors in reversed order. This bow involves two reflections 
within each drop, as shown at R and V. 



Pure Spectra. 

Experiment 152. — Cut a very narrow slit, 2 or 3 cm. long, in a 
piece of tin or of tin-foil, and fasten the sheet over the opening in the 
shutter of a darkened room so that the slit shall be horizontal. The 
porte-lumiere (Fig. 135) may be provided with a disk with an adjust- 
able slit that is very convenient for such purposes as this. Hold 
a prism about 1.5 m. from the slit and with its edges horizontal. 
Looking through the prism at the slit, turn the prism about its axis 
until the colored image of the slit is at the least angular distance from 
the slit itself. The colors of the image will show with a greater dis- 
tinctness than before observed. 

238. A Pure Spectrum is made up of a succession of 
colored images with little or no overlapping. The first 
requisite in preventing the overlapping is that the slit 
be very narrow. 



192 



ELEBiENTARY PHYSICS. 



(a) A spectroscope is an instrument used to produce a spectrum of 
tiie light from any source, and for its study. It affords a delicate 

meaus of chemical 
analysis and is one 
of the most powerful 
aids to modern 
science. In one of its 
simple forms it con- 
sists of, — 

(1) A collimator, 
C, a tube with an ad- 
justable slit with par- 
allel edges at the outer 
end through which the 
light entera, and at the 
other end a coUimating lens that brings the rays into a parallel beam. 

(2) A prism, P, or a series of prisms, that receives the radiation 
from C, and disperses it, thus forming a spectrum. 

(3) A telescope, T, through which the magnified image of the spec- 
trum is viewed. The spectrum is received directly upon the retina of 
the eye and may be distinctly seen even when the radiation is feeble. 

A pocket form of the spectroscope, so often called direct-vision spec- 
troscopCf is not very expensive, and may be made to atiswer for the 
purpose of this book. 




Fig. 163. 



Spectrum Analysis. 

Experiment 153. — Examine a candle-flame with a spectroscope, 
and notice that the colored spectrum is continuous through all the 
prismatic colors. Evidently, the radiation is extremely complex. 

Experiment 154. — Dip a platinum wire or a strip of asbestos into 
a solution of sodium chloride (common salt), and hold it in the almost 
colorless flame of a Bunsen burner or an alcohol lamp. The sodium 
vapor colors the flame yellow. Examine this sodium flame with a 
spectroscope, and notice that the spectrum consists of a bright yellow 
line instead of the continuous multi-colored band. 

239. Spectrum Analysis. — Certain substances yield 
colored flames, the yellow of sodium, the lilac of potas- 
sium, etc., being familiar. The vapors of such substances 



SPECTRA, CHROMATICS, ETC. 193 

yield characteristic spectra that may be used for their 
identification. This method of analyzing composite radi- 
ations^ or of identifying substances by the spectra of their 
incandescent vapors^ is called spectrum analysis. 

(o) As a condition necessary for the production of the spectrum, 
the temperature must be so high that the substance to be examined 
will bo vaporized, diassociated, and made incandescent. Having 
mapped the spectra of all knov^n substances, the presence of new 
lines in any spectrum would indicate the presence of a substance 
previously unknown. The quantity of material required for such 
examination is exceedingly small, a hundred-millionth of a milli- 
gram of strontium giving the spectrum characteristic of that element. 

Dark-Line Spectrum. 

Experiment 155. — Remove the objective from an optical lantern 
(§ 251). From the lantern, send a beam of electric or calcium light 
through a narrow vertical slit in a screen. Beyond the screen, place 
a double convex lens to receive the light that passes through the slit. 
Beyond the lens, place a prism so as to throw a spectrum on a screen 
still beyond. Pla<Se a Bunsen burner or an alcohol lamp between the 
lantern and the slit and, in its almost colorless flame, hold a bit ot 
sodium. The metal will burn, giving an intense yellow to the flame. 
Notice that the yellow of the spectrum, instead of being more intensely 
illuminated, is marked by a dark hand. Then hold a piece of tin 
between the lantern and the flame and so as to cut off the light of the 
lantern from the upper part of the slit. The upper part of the slit 
is now traversed by light from the sodium-colored flame, and the 
lower part of the slit by light from both the lantern and the flame. 
The image of the slit is inverted, and two parallel spectra are thrown 
on the screen. One of these is the bright-line spectrum of sodium ; 
the other shows a dark line on a continuous spectrum. Notice that 
the bright line of one spectrum is in the same relative position 
as the dark line of the other spectrum, as if the sodium vapor ab- 
sorbed light of the same refrangibility as that which it emits. 

240. Kinds of Spectra. — A spectrum may be continuous 
or discontinuous; a discontinuous spectrum may be a 
bright-line spectrum or a dark-line spectrum. Dark-line 



194 



ELElffENTART PHYSICS. 



spectra are sometimes called reversed spectra, or absorp- 
tion spectra. 

241. The Fraunhofer Lines. — A spectrum of sunlight 
is crossed by dark lines, many hundreds of which have 
been counted and accurately mapped. The more conspic- 
uous of these dai-k lines are distinguished by letters of 




JM Oramg$ iVfaw Crw» Blm» 

Fig. 164. 

the alphabet, as shown in Fig. 164. A few of these dark 
lines in the solar spectrum are due to absorption in the 
earth's atmosphere, but by far the greater number originate 
in the selective absorption of the solar atmosphere itself. 

(a) Just as the D-line corresponds to sodium, so the greater num- 
ber of the Fraunhofer lines have been identified in the spectra of 
known terrestrial substances. The presence of at least thirty-six ele- 
ments in the sun's atmosphere has been thus established, the absent 
wave-frequencies indicating the identity of the absorbing media. 

242. Laws of Spectra. — (1) Incandescent solids and 
liquids give continuous spectra. This is true of vapors 
and gases also when they are under great pressures. The 
spectrum from the flame of a candle, of kerosene, or of 
illuminating gas is continuous, being due to the incan- 
descent carbon particles suspended in the flame. 

(2) Incandescent rarefied vapors and gases give discon- 
tinuous spectra consisting of colored bright lines or bands. 

(3) If light from an incandescent solid or liquid passes 
through a gas at a temperature lower than that of the incan- 
descent body^ the gas absorbs rays of the same degree of 
refrangibility as that of the rays that constitute its own 
spectrum. 



SPECTRA, CUROMATICS, ETC. 195 

Thermal Effects of Radiant Energy. 

Experiment 156. — Hold a pane of glass between the face and a 
hot stove; the glass shields the face from the heat of the stove. 
Hold tlie glass between the face and the sun; the glass does not 
shield the face from the heat of the sun. 

243. Thermal Effects may be detected throughout the 
length of the visible spectrum and beyond in each direc- 
tion, i.e., in the infra-red spectrum and in the ultra-violet 
spectrum. The infra-red or longer wave-length radiation 
is present in the spectrum from any hot body ; the ultra- 
violet or shorter wave-length radiation in that from a body 
at a high temperature, as the incandescent carbons of an 
arc electric light. 

(a) When radiant energy is consiilerjed with reference to its heating 
effects, it is sometimes erroneously called " radiant heat." Similarly, 
the radiation of the infra-red region is spoken of as " obscure heat." 

(b) Glass, water, watery vapor, and alum transmit light, but absorb 
nearly all of the energy of infrarred rays. A solution of iodine in 
carbon disulphide absorbs luminous and transmits infra-red rays. 

Absorption, etc. 

Experiment 157. — Focus a sunbeam on the clear glass bulb of an 
air thermometer, and notice the feeble effect produced. Coat the bulb 
with candle soot, and repeat the experiment. Notice the greatly in- 
creased effect. 

244. Radiation, Reflection, and Absorption. — Bodies 
differ greatly in absorbing power. A good absorber is a 
poor reflector. Lampblack is a substance of maximum 
absorbing and of minimum reflecting power. The emission 
and the absorption of radiant energy go hand in hand, good 
absorbers being good radiators, good reflectors being poor 
radiators, etc. 

245. Chemical Effects may be detected throughout the 
length of the visible spectrum and beyond in each direc- 



196 ELEMENTARY PHYSICS. 

tion. The chemical changes upon which ordinary pho- 
togmpliy depends are most stimulated by the violet and 
ulti-a- violet rays ; this, however, is not true of all chemical 
changes, and even infra-red photography has been accom- 
plished. 

(a) From one end of the spectrum to tlie other, the radiation differs 
intrinsically in wave-length only; the observed diversity of effect is 
due to the character of the surface upon which the radiation falls. 

246. Change of Vibration-Frequency. — When solutions 
of certain substances, such as sulphate of quinine, are 
exposed to ulti-a-violet radiation, the solutions lower the 
rate of vibration to that of an opalescent blue light. Thi% 
'property of lowering the vibration-frequency of ultra-violet 
radiation to the ranye of vision is called fluorescence. An- 
other class of substances, such as the sulphides of barium^ 
calcium, and strontium, are luminous when carried from 
sunlight into a dark room and, for a long time after, 
present the general appearance of a hot body cooling. 
This property of shining in the dark after exposure to light 
is called phosphorescence^ and has been utilized in the pro- 
duction of what are called '* luminous paints." The 
luminous rays of an electric arc may be absorbed by a 
solution of iodine in carbon disulphide, and the residual 
infra-red rays reflected or refracted to a focus. A piece 
of platinum or of charcoal at such a focus of non-luminous 
radiation may be heated to incandescence. This raiding 
of the vibration-frequency of infra-red radiation to the range 
of vision is called calorescence. 

EXERCISBS. 

1. Taking the velocity of light to be 186,000 miles per second 
and the wave-length of green light to be 0.00002 of an inch, how 
many waves per second beat upon the retina of an eye exposed to 
green light? 



SPECTRA, CHROMATICS, ETC. 197 

2. How may the chromatic aberration caused by a simple leos 
be corrected ? 

3. What name is given to the differential deviation by refraction 
of rays of different wave-frequencies ? 

4. Why is a rainbow never seen at noon ? 

5. Why do not the sun's rays heat the upper atmosphere of the 
earth as they pass through it ? 

6. Show that the glass walls and roof of a greenhouse are a trap 
for solar heat. 

7. Why is it oppressively warm wheii the sun shines after a sum- 
mer shower ? 

8. Why is there gi*eater probability of frost on a clear than on a 
cloudy night ? 

9. Explain the fact that the glass of a window may remain cold 
while the sun's radiations are pouring through it and heating objects 
in the room. 

10. How can you cut out the short-wave radiations of an arc elec- 
tric lamp ? How can you cut out the long-wave radiations ? 

11. Show that the watery vapor in the atmosphere acts as a blanket 
for terrestrial objects. 

12. Make a cubical metal vessel with edges of about 7 or 8 cm., 
and vertical faces made respectively of polislied brass, sheet lead, 
bright tin-plate, and tin-plate that has been coated with lampblack. 
Leave a small opening in the upper face. Such a vessel is called a 
Leslie cube. Fill it with water, and bring the temperature to 10°. 
Place the cube 3 or 4 cm. from an air thermometer or from one bulb 
of a differential thermometer, and note the effect upon the thermom- 
eter. Raise the temperature successively to 20", 30°, 40°, etc. ; bring 
it within the same distance of the thermometer, and note the effect 
in each case. Record a comparison of the readings of the mercury 
thermometer in the cube with the indications of the air thermometer, 
and a clear statement of the relation between them. 

13. Repeat one of the tests of Exercise 12, and then interpose a pane 
of window glass between the cube and the thermometer. Explain the 
effect produced by the screen. 

14. With the same apparatus, test the absorptive powers of tin-foil, 
lampblack, India-ink, and white-lead by successively coating the bulb 
of the air thermometer with such substances. 

15. Test the radiating powei-s of tin, lampblack, India-ink, and 
white-lead by successively turning faces of the Leslie cube thus coated 



198 ELEMENTARY PHYSICS. 

toward the bulb of the air thermometer, being careful that the tem- 
perature and the distance of the cube are the same in each instance. 
Try to find some relation between the absorbing powers and the radi- 
ating powers of these several substances. 



VI. INTERFERENCE, DIFFRACTION, POLARIZATION, 

ETC. 

Interference. 

Experiment 158. — In any convenient clamp, firmly press together 
the centers of two pieces of clean, thick plate-glass. Look obliquely 
at the glass, and a beautiful play of colors will be seen surrounding 
the point of greatest pressure. If the glass is illuminated by the 
monochromatic light of a sodium flame (see Experiment 149), yellow 
bands separated by dark bands will be seen. 

247. Interference of Light. — We have seen that two 
wave-motions may combine in such a way as to neutralize 
each other (§ 151), and that such an interference is a 
peculiarity of wave-motion. The fact that light may thus 
neutralize light is strong confirmation of the wave-theory. 

(a) III the historical experiment of which Experiment 158 is a 

modification, a plano-convex lens of little curvature was pressed upon 

a flat piece of glass. When looked at from 

I above, the center of the lens thus used is 

--.^ ya^c^^.^^ surrounded by rainbow-like bands of color, 

\ m^,n^^^mmi^u^ known as Newton rings. Of the light 

-J, -«- that falls vertically upon the lens, some is 

reflected at the curved surface, and some 

from the upper surface of the plate under the lens. These latter rays 

have to traverse twice the wedge-shaped film of air between the lens 

and the plate. Whenever the thickness of the air-film is such that 

the two sets of reflected waves unite in opposite phases, interference 

is the result. If the apparatus is observed by white light, and the 

red rays are destroyed at a certain distance from the center of the 

lens, the color perceived at thai distance will be complementary to 

the destroyed red, and will form a circular green band. If the appa- 



INTERFERENCE, DIFFRACTION, POLARIZATION. 199 




Fig 



ratus is observed by red light, a dark ring will appear at the same 
distance. At another distance from the center of the lens, the violet 
rays will be destroyed, and the circular band seen at that distance 
will be due to the combination of the other constituent rays of the 
light used. 

(6) Interference colors similarly produced by reflection are often 
seen in soap-bubbles, in small quantities of oil that have been spread 
over large sheets of water, in mica, selenite, ice, and other crystals. 

(c) If a beam of monochromatic light is passed through a nar- 
row slit and received upon a screen in a dark room, a series of alter- 
n.itely light and dark bands 
or " fringes " is seen ; if white 
light is employed, a series of 
colored spectra is obtained. 
As the primary and secondary 
waves cut each other, they 
unite at some points, crest with crest, and, at other points, crest with 
trough. At the latter points, we have interference of light with the 
effects of colors produced thereby. Such interference phenomena con- 
stitute what is called diffraction. The halos sometimes seen around the 
sun and moon and street lamps are due to diffraction of light by 

watery globules in the atmosphere. 

Polarization. 

Experiment 159. — While 
looking through the plates of 
a pair of tourmaline tongs, 
turn one of the plates in its 
wire support. The intensity 
of the light transmitted will vary as the plate is turned. When little 
or no light is transmitted, the plates are said to be " crossed." 

Experiment 160. — Write 
your name on a sheet of 
paper, and cover it with a 
crystal of Iceland spar. The 
lines will appear double, as 
shown in Fig. 168. Place 
the crystal over a dot on the 
paper, hold the eye directly 
over the dot, and slowly turn 




Fig. 167. 




Fig. 168. 



200 ELEMENTARY PHYSICS. 

the crystal around; one of the two images of the dot will revolve 
ahout the other image. Pnck a pin-hole through a card, and hold 
the card against one side of the crystal, look through the crystal at 
the pin-hole, and rotate the crystal as before. 

Bzperiment i6x. — Look through one of the plates of the tourmaline 
tongs (Fig. 167) at the two images of the dot formed by the double 
refi*action of the Iceland spar, as described in Experiment 160. One 
of the images will be much fainter than the other. Turn the tourma- 
line plate slowly around, and notice that one image grows fainter and 
the other brighter, the maximum brightness of one being simultane- 
ous with the extinction of the other. 

248. Polarizatioii of Light. -^ Common white light em- 
braces not only an indefinite number of wave-lengths, but 
also an indefinite number of modes of vibration. A trans- 
verse wave is capable of assuming a particular side or 
direction; a longitudinal wave is not. When a rope is 
shatken as described in Experiment 66, the vibrations of 
the wave thus produced lie in a vertical plane ; when the 
hand is moved horizontally, the vibrations lie in a hori- 
zontal plane. In like manner, a single row of ether 
particles engaged in propagating a linear transverse wave 
may describe any one of a variety of paths, each being 
perpendicular to the line of propagation of the radiation. 
For example, each particle may vibrate in a 
straight line, parallel to the wave-front and 
indifferently in any plane about the line of 
propagation, as represented in Fig. 169. If 
Fia. 109. all the ether particles in the row under con- 
sideration successively vibrate along lines lying in the 
same plane, the radiation is said to be plane-polarized, 
and the wave thus constituted is called a plane-polarized 
wave. A change by which the transverse vibrations of 
luminous waves are limited to a single direction is called 
polarization of light. This change may be produced in 
several ways. 




INTERFERENCE, DIFFRACriON, POLARIZATION. 201 




(a) Light may be polarized by reflection from the surface of glass, 
water, and other non-metallic substances ; by transmission through a 
series of transparent plates of glass placed in parallel position ; and 
by double refraction, as in the case of Iceland spar, or of a plate cut 
in a certain way from a tourmaline crystal. A prism of Iceland spar 
prepared in such a way that one beam of polarized light is totally 
reflected and extinguished, while the other beam passes through as 
polarized light, is called a Nicol prism, Nicol prisms and tourmaline 
plates are largely used in experiments with polarized light. 

(6) Light that has passed through a tourmaline plate, or been 
otherwise polarized, differs so much from ordinary light that it may 
be stopped by a similar plate, as was seen in Experiment 159. For 
the sake of simplicity, imagine the indifferently placed planes of 
vibration, as represented in Fig. 169, to be resolved into two that lie 
at right angles to each other, as shown 
in Fig. 170. Then the action of the 
first tourmaline plate may be compared 
to that of a vertical-bar grating that 
allows the vibrations in a vertical 
plane to pass, but absorbs the vibra- 
tions that lie in a horizontal plane. Evidently, the vibrations that 
pass one such gi*ating, as T, will pass others similarly placed, but will 
be stopped by one that is crossed, as at V, The part of the beam 
that lies between T and T represents plane-polarized light. 

(c) An instrument for producing and testing polarized light is 

called a polariscope, one 
form of which is repre- 
sented in the accompany- 
ing figure. Whatever its 
form, the instrument con- 
sists of two characteristic 
parts ; one, used to produce 
polarization and called the 
polarizer, as the glass re- 
flector at a, the other, used 
to test or to study the 
polarized light and called 
the analyzer, as the Nicol 
prlsTo at c. Apparatus that serves for either of these purposes will 
serve for the other. 




Fig. 171. 



202 ELEMENTARY PHYSICS. 

VIL A FEW OPTICAL INSTRUMENTS. 

The Eye. 

Experiment x6a. — Close one eye and try to thread a needle. Bend 
a stout wire at a right angle, and try to pass one end of it through a 
ring held at arm's length, one eye being closed. 

Experiment 163. — Prick a pin-hole in a card, hold it near the eye, 
and look through the pin-hole at a pin held at arm's length. As the 
pin is slowly moved toward the eye, the visual angle (§ 248, c) in- 
creases and the pin seems to grow larger. 

249. The Human Eye, optically considered, is an ar- 
rangement for projecting inverted, real images upon a 
screen made of nerve filaments. 

(a) The most essential parts of this instrument are contained in 
the eyeball, a nearly spherical body, about an inch in diameter, and 
capable of being turned considerably in its socket by the action of 
various muscles. The greater part of the outer coat is tough and 

opaque, and is called the white of 
the eye or the sclerotic coat, S; 
the front part of this coat is a hard, 
transparent structure called the cor- 
nea, C. The inner coat is the retina, 
Ri an expansion of the optic nerve 
which enters the eyeball from be- 
hind. These coats form a camera 
filled with solid and liquid refractive 
media. The crystalline lens, L, a 
solid biconvex body, is suspended in 
this camera and directly in the axis 
of vision; it tends to flatten with age. With its capsule, it divides 
the eye into two compartments, and is chiefly instrumental in bring- 
ing the rays of light to a focus on the retina. The larger compart- 
ment of the eyeball is filled with a transparent jelly-like substance, F, 
the vitreous humor. The compartment between the cornea and the 
lens is filled with a more watery liquid, the aqueous humor, and is 
partly divided into anterior and posterior chambers by an annular 
curtain, /, called the iris. 




A FEW OPTICAL INSTRUMENTS. 203 

(b) Without our consciousness, the muscular action of the eye 
changes the curvature of the crystalline lens so that rays from near 
or distant objects may be focused on the retina. Instead of moving 
the screen, the refractive power of the lens is changed. This power of 
"accommodation," or automatic adjustment for distance, is limited. 
For instance, when a book is held close to the face, the rays from the 
letters are so divergent that the eyQ cannot focus them upon the 
retina. When the power of accommodation for distance is abnor- 
mally defective, the owner of the eye is said to be near-sighted, or 
far-sighted, or old-sighted. In the first case, the remedy is in concave 
glasses ; in either of the other two cases, the remedy is in convex 
glasses. At the point where the optic nerve and its central artery 
enter the eyeball, the retina lacks the visual functions; this part of 
the retina is called the blind spot, 

(c) The estimation of distances by the eye is a matter of judgment 
and is chiefly based upon experience. This experience relates to the 
amount of muscular effort exerted in adjusting the eye for distinct 
vision, and in turning the two eyes inward so that their axes meet at 
the object, thus forming the optical angle (see Experiment 162) ; to the 
comparison of the angle formed by lines drawn from the extremities 
of the object to either eye and called the vuual angle with the visual 
angle subtended by objects of known size and distance; and to the 
observfition of changes of color and brightness produced by the varying 
thickness of the air through which the object is viewed. 

(d) The estimation of the size of distant objects is also a matter 
of judgment, based upon the known or supposed distance of the object. 
The ratio between the size of object and image equals the ratio be- 
tween the distance of each from the lens, and the mind unconsciously 
bases its conclusions on this fact. 

250. A Microscope consuls of a lens or a combination of 
lenses used to observe small objects^ often so minute as to 
be invisible to the unaided eye. Its magnifying power is 
the ratio between the length of the object and the length 
of its observed image. 

(a) The simple microscope is generally a single convex lens. The 
object is placed between the lens and its principal focus. The lens 
increases the visual angle. The image is virtual, erect, and magni- 
fied. 



204 



ELEMENTAKY THYSICS. 



(6) The compound microscope consists essentially of two lenses or 
systems of lenses. One of these, 0, called the objective, is of short 

focus. The object, AB, being placed 
slightly beyond the principal focus, a 
real image, cd, magnified and inverted 
is formed. The other lens, E, called 
the eyepiece or ocular, is so placed that 
the image, cd, lies between it and its 
focus» A magnified, virtual image of 
the real image, cc/, is formed by the 
eyepiece and seen by the obsei-ver at ah. 
Eyepiece and objective are placed at 
opposite ends of sliding tubes, and so 
that they may be easily adjusted for 
distinct vision. 

251. A Telescope is an instru- 
ment designed for the observation 
of distant objects^ and consists 
essentially of an objective for the 
formation of an image of the ob- 
ject and of an eyepiece for mag- 
nifying this image. The optical 
parts are generally set in a tube 
so arranged that the distance between the objective and 
the eyepiece may be adjusted for distinct vision. A tele- 
scope is refracting if its objective is a convex lens, and 
reflecting if its objective is a concave mirror. If it was 
designed for the observation of terrestrial objects, it is 
called a terrestrial telescope ; if for the observation of 
celestial objects, it is called an astronomical telescope. Its 
magnifying power depends upon the ratio between the 
focal length of the objective and that of the eyepiece, and 
may be changed by changing one eyepiece for another. 

(a) The astronomical refractor consists essentially of a large convex 
lens objective of long focus, and a convex lens eyepiece of short focus. 
The real image formed by the objective is magnified by the eyepiece^ 




A FEW OPTICAL V INSTRUMENTS. 



206 



as in the case of the compound microscope. The objective of a reflect' 
ing telescope is a concave mirror, technically called a speculum, 

(b) The spy-glass or terrestrial telescope avoids the inversion of the 
image by the interposition of two double-convex lenses. 

(c) The Galilean telescope has a double-concave eye-lens that inter- 
cepts the rays before they reach the focus of the objective. The rays 




Fig. 174. 

from A, converging after refraction by 0, are rendered diverging by 
C The image, ab, is erect and very near. Two Galilean telescopes 
placed side by side constitute an opera-glass. 



Optical Projection. 

Experiment 164. — Reflect a horizontal beam of sunlight into a 
darkened room. In its path, place a piece of smoked glass on which 
you have traced the representation of an arrow, AB (Fig. 175), or 
written your auto- 
graph. Be sure that 
every stroke of the 
pencil has cut 
through the lamp- 
black and exposed 
the glass beneath. 
Place a convex lens 
beyond the pane of 
glass, as at L, so 
that rays that pass through the transparent tracings may be refracted 
by it, as shown in the figure. It is evident that an image will be 
formed at the foci of the lens. If a screen, SS, is held at the positions 
of these foci, a and 6, the image will appear clearly cut and bright. 
If the screen is held nearer the lens or further from it, as at S' or 
5", the picture will be blurred. The porte-lumiere and slide-holding 
disk shown in Fig. 135 are very convenient for this purpose. 




206 



ELEMENTARY PHYSICS. 



252. The Optical Lantern is an instrument for project- 
ing on a screen magnified images of transparent photo- 
graphs, paintings, drawings, etc. 

(a) The light is placed at the common focus of a concave mirror, 
and of a convex lens, Z, called the condenser. A powerful beam of liglit 
is thus thrown upon aft, the transparent object, technically termed a 
slide. A compound objective, m, is placed at a little more than its 
focal distance beyond the slide. A real, inverted, magnified image of 
the picture is thus projected upon the screen, S. The tube carrying 
m is adjustable, so that the foci may be made to fall upon the screen. 




Fig. 176. 

and thus render the image distinct. By inverting the slide, the image 
is seen right side up. An optical lantern is often called a magic 
lantern. Two matched lanterns placed so that their images coincide 
constitute a stereopticon, 

EXERCISES. 

1. In a good light, press together two pieces of clean plate-glass 
with a clamp at their centers, and explain the appearance of colorr in 
the glass. 

2. Spring a clothes-pin upon each of three corners of the glass 
plates used in Exercise 1, and support the plates by an iron clamp at 
the fourth corner. Let a beam of sunlight from the port-lumi^re fall 
upon the face of the plate so as to make the angle of incidence 45°. 
Receive the beam reflected from the plate upon a convex lens so that 
an image of the opening in the shutter will be projected on the screen. 



A FEW OPTICAL INSTRUMENTS. 207 

Vary the pressure at the clamp, and explain the change of colors on 
the screen. 

3. While a friend is looking intently at a distant object, look 
obliquely into his eye, holding a candle-flame on the other side of it. 
If the flame is properly held, three images of it will be seen ; one 
erect and bright, reflected from the cornea; another erect and less 
bright, reflected from the anterior surface of the crystalline lens ; and 
a third, inverted, reflected from the posterior surface of the lens. 
When the eye that is being studied changes its aajustment for the 
observation of an object held near it, the first image of the candle- 
flame is unchanged, while the second and third become smaller, the 
change being greater in the second than in the third. 

4. Close the left eye and look steadily at the cross below, holding 
the book about a foot from the face. The dotwis plainly visible as weU 



as the cross. Keep the eye fixed on the cross and move the book 
slowly toward the face. When the image of the dot falls on the 
" blind spot " of the eye, the dot disappears. Hold the book in this 
position for a moment and see if the changing convexity of the 
crystalline lens throws the image of the dot off the blind spot: making 
the dot again visible. 



CHAPTER VI. 

£L£CTRICITY AND BIAGKETISM. 
(^Ether Physics continued.) 

L GENERAL VIEW- 



A. Static Electricity. 
• 
253. Electricity is the common cause of a large variet f 
of phenomena, including apparent attractions and repul- 
sions of matter, heating, luminous and magnetic effects, 
chemical decomposition, etc. 

(a) The tnie nature of elec- 
tricity is not yet well understood. 
Little more can be said at this 
point than that it in the agent 
upon which certain phenomena 
depend, and that it behaves like 
an incompressible fluid filling all 
space and entangled in the lumi- 
niferous ether. 

Electrical Attraction. 

Experiment 165. — Cut a num- 
ber of pith-balls about 1 cm. in 
diameter. Whittle them nearly 
round, and finish by rolling them 
between the palms of the hands. 
Fig. 177. Cover one of these balls with 

gold leaf, suspend it by a silk 
fiber, and call it an electric pendulum. Briskly i*ub a stout stick of 
sealing-wax with flannel, and bring it near the electric pendulum. 

208 





STATIC ELECTRICITY. 209 

Notice the attraction. The sealing-wax and flannel should be dry 
and warm. 

Experiment i66. — Rub a glass rod or tube (a long ignition-tube 
will answer) with a silk pad. The eifect may be increased by smear- 
ing lard on one side of the 
pad and applying a coat of 
the amalgam that may be 
scraped from bits of a bro- 
ken looking-glass. Small 
scraps of paper and other 
light bodies may be simi- 
larly attracted. The glass 
and silk should be dry and 
warm. Take like precau- 
tion in all experiments with „ ^„„ 
... , . .\. Fig. 178. 
static electricity. 

254. Electrification. — Bodies that are endowed with 
the power of attracting other bodies, as just illustrated, 
are said to be electrified. Any substance may be electri- 
fied by suitable means. The state or condition thus 
established is called electrification^ and may be brought 
about in a variety of ways. 

Electrical Conductivity. 

Experiment 167. — Support a meter stick upon a glass tumbler. 
Bring an electrified glass rod to one end of the stick, and hold some 
small pieces of gold leaf or of paper a few centimeters under the other 
end of the stick. The gold leaf or the paper will be attracted and 
repelled by the stick as it previously was by the glass itself. The 
electrification passed along the stick from end to end. 

255. Conductors and Insulators. — Substances that easily 
permit the transference of electrification along them are mid 
to be good conductors. No substance is so good a con- 
ductor as not to offer some resistance to the trans ff^i% 
Substances that offer very great resistances are called 
insulators^ or non-conductors. A conductor supported by 



4 



210 



ELEMENTARY PHYSICS. 



an insulator is said to be insulated. An insulated body that 
is electrified is said to have a charge^ or to be charged. 

(a) lu the following table, the substances named are arranged iu 
the order of conductivity : — 



Conductors. 


Salt water. 


Paper. 


Glass. 


Metals. 


Linen. 


Silk. 


Sealing-wax. 


Graphite. 


Cotton. 


Indiarrubber. 


Vulcanite. 


Acids. 


Dry wood. 


Porcelain. 


Insulators. 



(h) The fact that a conductor in the air may be insulated shows 
that air is a non-conductor. Dry air is a very good insulator, but 
moist air is a fairly good conductor. All experiments in static elec- 
tricity are, therefore, more successfully performed in clear, cold 
weather when the atmosphere is dry. 

(c) A medium intervening between two electrified bodies, i.e., a 
substance, solid, liquid, or gaseous, through or across which electric 
force is acting, is called a dielectric. 



Kinds of Electrification. 

Experiment x68. — Suspend several pith-balls by fine linen threads 
from an insulating support, and touch the m 
with an electrified rod. The rod repels the 
balls, and the balls repel each other. 

Experiment 169. — Bring an electrified 
glass rod near a pith-ball electroscope as 
before, and notice that, after contact, the 
ball is actively repelled. Similarly charge 
a second ball with an electrified rod of 
sealing-wax. Bring the two balls near 
each other, and notice their mutual attrac- 
tion. Charge the two balls as before. 
Bring the glass rod near the ball that is 
repelled by the sealing-wax, and notice the 
attraction. Bring the sealing-wax near the 
ball that is repelled by the glass rod, and notice the attraction. 

256. Opposite Electrifications. — Electrification may be 
manifested by repulsion as well as by attraction, and is 




Fig. 179. 



STATIC ELECTRICITY. 



211 



of two kinds, opposite in character. The electrification 
developed by rubbing glass with silk is called positive; 
that developed by rubbing sealing-wax with flannel k 
called negative. Bodies similarly electrifie(} repel each 
other ; bodies oppositely electrified attract each other, 

(a) The statement that there are two kinds of electrification does 
not necessarily imply that there are two kinds of eleptricity. It is, 
however, very convenient to speak of one kind of electrification as 
caused by a charge of one kind of electricity, and the other kind of 
electrification as caused* by a charge of an opposite kind of electricity. 

(b) The electrification of the rubbed body is equal in amount to 
that of the body with which it is rubbed, but opposite to it in 
character. 

257. Electrification by Conduction is. the process of charg- 
ing a body by putting it in contact with an electrified body. 
The charge thus produced is of , the same kind as that of 
the communicating body. 

258. The Electroscope is an instrument for detecting and 
testing electrification^ The elec- 
tric pendulum constitutes a sim- 
ple and efficient electroscope. 

(a) The gold-leaf electroscope rep- 
resented in Fi^. 180 is a common form 
of a more sensitive instrument. A 
metallic rod passes through the cork 
of a glass vessel, and terminates on 
the outside in a ball or a disk. The 
lower end of a rod carries two strips 
of gold leaf or of aluminium-foil that 
hang parallel and close together. 
When an electrified object is brought 
near the knob or into contact with it, 
the metal strips below become simi- 
larly charged and are, therefore, mutually repelled. The pupil can 
make one, using a glass fruit-jar or other bottle. 




FtG. 180. 



212 



ELEMENTABY PHYSICS. 



(6) A proof-plane (Fig. 181) may be made by cementing a cent or 
a disk of gilt paper to the end of a thin insulating handle, as a glass 

tube, and will be found very conven- 
ient in carrying a charge from an 
electrified body to an electroscope. 

259. Electrical Units. — There 
are two systems of electrical 
uuits, one set being based upon 
the attraction or repulsion ex- 
erted between two quantities of 
electrification, and the other up- 
on the force exerted between 
two magnet poles. Units of the former set are called 
electrostatic; those of the latter, electromagnetic. Distinc- 
tive names have not yet been adopted for the electi-ostatic 
units. 




The Electrostatic Unit of Quantity is the quantity 
of electrification that exerts through the ait a force of one 
dyne on a similar quantity at a distance of one centimeter. 
The force may be attractive or repulsive. 

261. Law of Electric Action. — 
The force that is mutually exerted 
between two charges varies directly 
as the product of the charges, and 
inversely as the square of the dis- 
tance between them. 

Distribution of the Charge. 

Experiment 170. — Make a conical bag 
of linen, supported, as shown in Fig. 182, 
by an insulated metal hoop five or six Fio. 182. 

inches in diameter. Electrify the bag. 

A long silk thread extending each way from the apex of the cone will 
^nable you to turn the bag inside out without discharging it. Test 




STATIC KLECTRICmr. 213 

the inside and outside of the bag, using the proof-plane. Tom the 
bag and repeat the test. Whichever surface of the linen is external, 
no electrification can be found upon the inside of the bag. 

Experiment 171. — Prick a pinhole at each end of an egg. and blow 
out the contents of the shell. Paste tin-foil or Dutch-leaf smoothly 
over the entire sui*face of the empty shelL Pass a white silk thread 
through a light ring, and fasten its two ends with wax near the ends 
of the shell, so that the shell may be suspended with its greater diame- 
ter horizontal, or support it in this position on an egg-glass. Charge 
this insulated egg-shell couductor. With a proof-plane, carry a charge 
from the side of the conductor to the knob of the gold-leaf electro- 
scope, and notice the degree of diyergeiioe of the leaves. In like 
manner, carry a charge from the smaller end of the couductor, and 
notice the greater diyergence of the leaves. 

Experiment 172. — Cement the end of a small glass tube to the 
middle of a pin, and hold the head of the pin against the koob of a 
charged gold-leaf electroscope. Observe the collapse of the leaves. 

262. Distribution of the Charge. -=— The charge lies wholly 
upon the outer surface. The amount of electrification per 
unit of surface is called the surface density. Whenever a 
charge is communicated to a conductor, the electrification 
distributes itself over the surface of the conductor until it 
reaches a condition of equilibrium. It is greatest where 
the curvature is the greatest ; on a sphere, the density is 
uniform ; on an egg-shaped conductor, it is greatest at the 
smaller end. 

(rt) Since any charge is self-repulsive, there must be, at every point 
of the surface of a charged conductor, au outward pressure against the 
surrounding dielectric. When the density becomes about a hundred 
electrostatic units per square centimeter, the electrification cannot be 
retained upon the conductor, and sparks -fly into the suiTounding air. 
The disc|)arge takes place most readily where the density is the great- 
est i i.e., where the curvature is the greatest, as at a point. Since the 
air in contact with such a point is similarly electrified, and, therefore, 
repelled, an air-current passes from the point, and the charge is dissi- 
pated by convection. 



214 ELEMENTARY PHYSICS. 

(b) Many pieces of apparatus for use with static electricity, made 
of wood and neatly covered with tin-foil put on with flour-paste, will 
prove as good conductors as if made wholly of metal. 

263. Process of Electrification. — When two dissimilar 
substances are brought into contact and then separated^ they 
are equally and oppositely electrified. 

(a) If the substances are pgor conductors, they must be rubbed 
together. If the substances are good conductors, the opposite and 
equal electrifications flow to the point last in contact^ and pass by 
conduction from one to the other ; the resultant is zero. 

264. Electrical Field and Lines of Force. — The space 
surrounding an electrified body and through which the elec^ 
trical force acts is called an electrical field of force. We 
raay imagine lines drawn in this field, each indicating 
the direction in which a unit of electrification would move 
if placed in the field. 

(a) To " map " an electrical field and to show the relative intensity 
of different parts of it, it has been agreed that one line shall be drawn 
through each square centimeter of surface for each dyne of force 
exerted in the field. Try to imagine two electrified bodies as im- 
mersed in an electrical field of force, and connected by elastic lines of 
force that tend to shorten and that are self -repel lent. 

265. Potential. — In a general way, it may be said that 
potential represents degree of electrification^ or that it is 
the relative condition of a conductor that determines the 
direction of a transfer of electrification to it or from it. 

, (a) An electrostatic unit difference of potential exists between two 
points when an erg of work is involved in moving unit charge from one 
point to the other, 

(b) As the sea-level is taken as the zero from which altitudes are 
measured, so the surface of the earth is taken as the zero of electric 
potential. As water tends to flow from highet to lower levels, and 
as heat tends to flow from places of higher to places of lower tempera- 
ture, so electrification tends to flow from places of higher to places of 



STATIC ELECTRICmr. 215 

lower potential iiutil an equalization is reached. In the latter case, 
the flow is called a current of electricity. 

(c) Surfaces throughout which the potential is everywhere the 
same are called equipotential surfaces. If any two points in such a 
surface were to be joined by a conductor, no flow of electrification 
would take place. 

266. Electromotive Force. — If two conductors at dif- 
ferent potentials are connected by a wire, a transfer of 
electrification will take place until the difference of poten- 
tial disappears. Whatever its nature^ the agency that tends 
to produce such a tranter is called electromotive force. 

Electrostatic Induction. 

Experiment 173. — Electrify a glass rod by rubbing it with silk, and 
bring it near the electroscope but without making contact. The 
leaves diverge. When the rod is removed, the leaves fall together. 
Bepeat the experiment, holding a glass plate between the rod and the 
electroscope. 

Experiment 174. — Bring a metallic sphere positively charged near 
an insulated cylindrical conductor with hemispherical ends and 
provided with pith-ball and 
linen-thread electroscopes as ^««£ » 

divergence of the pith-balls ^M^\^^^^^^^^^^^^^^^^^\ 
shows electrification at the ' ^ * 

ends but not at the middle yiq. 183. 

of the conductor. With the 

proof-plane and gold-leaf electroscope, examine the condition of the' 
conductor at the points A^ B, and w, and compare your results with 
the representations in the figure. Remove the sphere from the vicinity 
of the conductor, or discharge it by touching it with the hand. All 
signs of electrification on the conductor disappear, showing that the 
charges at A and B were opposite and equal. 

Note. — Instead of the sphere, C, you may use the egg-shell con- 
ductor used in Experiment 171. The cylindrical conductor may be 
replaced by two such conductors that are in contact, end to end. See 
§ 262 (6). 



216 ELEMENTARY PHYSICS. 

Ezperimeiit 175. — Electrify the insulated couductor, ^IB, as in Ex- 
perimeut 174. Touch it with the fiuger, thus connecting it with the 
earth and making it of indefinite length ; its positive electrification is 
so diffused as to be insensible. Remove first the finger and then the 
electiified sphere. The negative electrification, being no longer held 
at A by the attraction of the positive electrification at C, diffuses 
itself over the cylinder, and the balls at each end of the cylinder 
diverge, all being charged negatively. 

Ezperiment 176: — From a horizontal rod, suspend two egg-shell 
conductors by silk threads as described in Experiment 171. Be sure 
that the shells are in contact end to end. Bring an electrified glass 
rod near one of them, and slide the loop of the other along the support- 
ing rod until the shells are about 10 cm. apart. Then hold the electri- 
fied rod between the shells. It will attract one and repel the other, 
showing that they are oppositely electrified. 

267. Electrification by Induction. — Whenever an elec- 
trified body is brought into the vicinity of an unelectrified 
conductor, the unelectrified conductor becomes electrified. 
A dissimilar electrification appears on the side nearer the 
electrifying conductor, and similar electrification upon the 
further side. Electrification produced in this way^ by the 
influence of an electrified body and without contact with it^ 
is called electrification by induction. An induced charge is 
opposite in kind to the charge of the inducing body. 

(a) The amount of inductive effect that takes place across an inter- 
vening mediumtdepends, in a considerable degree, upon the nature of 
that medium. 

268. The Capacity of a conductor is the amount of electri- 
fication required to raise its potential from zero to unity ^ i.e., 
the ratio of its charge to its potential. 

(a) The unit of capacity is the capacity of a conductor that requires 
unit quantity to produce unit difference of potential; it is called a 
farad; one-millionth of a farad is called a microfarad. 



STATIC ELECTRICITY. 217 

Condensers. 

Experiment 177. — Spread a sheet of tin-foil upon a pane of glass 
supported on a tumbler. Charge the tin-foil by repeated sparks from 
the electrophorus (§ 313) until it will receive no moi*e. Count the 
number of sparks that the tin-foil will receive. 

Experiment 178. — Lay a sheet of tin-foil upon the table so that it 
will be in electrical connection with the earth. Over it place the glass 
and foil used in Experiment 177. Charge the upper sheet as lief ore, 
and notice that it will receive a much greater number of sparks. Touch 
the lower sheet of tin-foil with a finger of one hand, and the upper 
sheet with a finger of the other hand, thus discharging the apparatus. 
A pricking sensation will be caused by the discharge. 

269. A Condenser is a device for increasing the electrical 
density without increasing the potential, i.e., for accumu- 
lating a large charge with a small electromotive force. In 
its simplest form it consists of a pair of conductors slightly 
separated by a dielectric. If one of these conductors is 
connected to earth, it requires a much larger quantity of 
electrification to raise the potential of the other from zero 
to unity, i.e., the capacity of the other is greatly increased. 
The smaller the distance between the conducting surfaces, 
the greater the capacity of the condenser. 

(a) The nature of the dielectric has a great effect on the capacity 
of the condenser. For instance, changing the dielectric from air to 
ebonite more than doubles the capacity of the con- 
denser. Condensers of the flat type (Fig. 184), con- 
sisting of tin-foil conductors separated by thin, flat 
dielectric sheets (usually of mica), are much used. 
To obtain large area, and hence great capacity, they Fra. 184. 

are arranged alternately in two series. 

(b) The most common and, for many purposes, the most conven- 
ient form' of condenser is the Leyden jar. This consists of a glass jar 
coated within and without for about two-thirds its height with tin- 
foil, and a metallic rod that communicates with the inner coat, and 
terminates above in a knob or a disk. The jar may be a smooth, thin 
tumbler of good glass, and the tin-foil may be put on with flour-paste. 




213 ELEMENTARY PHYSICS. 

The knob may be carried at the upper end of a wire, the lower end of 
which is wound into a flat coil that rests on the foil at the bottom of 
the tumbler. The coil may be fastened in position with hot sealing- 
wax. Evidently, it may be considered as a flat condenser rolled into 
cylindrical form. The phenomenon of electrifi- 
cation pertains to the dielectric and not to the 
conducting plates. The metallic coats simply 
provide the means for the prompt discharge of 
the superficial layers of the molecules of the 
dielectric. A number of Leyden jars having 
their coats connected constitutes an electric hat- 
tcry. 

(c) The jar may be charged by holding it in 
the hand as shown in Fig. 185, or otherwise 
placing the outer coat in electrical connection 
with the earth, and bringing the knob into con- 
:i^~' tact with a charged body. If the outer coat is 

Fig. 185. insulated so that the repelled electrification can- 

not pass to the earth, the jar cannot be very 
highly charged. To discharge the jar, pass a stout wire through a 
piece of rubber tubing and bend it into^a V shape, or, in some other 
way, provide the wire with an insulating handle. Bring one end of 
the wire into contact with the outer coat, and then bring the other 
end into contact with the knob. It is well to provide the wire " dis- 
charger " with metal balls at the ends. 

270. Nature of Electricity. — According to the general 
belief of physicists, electricity is a form of matter rather 
than a form of energy. A full discussion of the nature of 
electricity is beyond the province of this book, but it is 
safe for us to say that electricity is that which is transferred 
from one body to another in the process of electrifying them. 

271. Theory of Electrification. — When electricity is 
transferred from one body to another and the bodies are 
separated (see § .263) against their mutual attraction, the 
intervening medium is thrown into a state of stmin indi- 
cated by the lines of force. This state of strain in the die- 
lectric constitutes electrification. Whatever the real nature 



STATIC ELECTRICITY. 213 

of electricity, electrification results from work done^ and is a 
form of potential energy. 



1. How can you show that there are two opposite kinds of electri- 
fication ? 

2. How would you test the kind of electrification of an electrified 
body? 

3. Why is it desirable that a glass rod used for electrification be 
warmer than the atmosphere of the room where it is used ? 

4. (a) Having a metal globe positively electrified, how could you 
with it negatively electrify a dozen globes of equal size without affect- 
ing the charge of the first? (6) How could you charge positively one 
of the dozen without affecting the charge of the first V 

5. When a pin or needle is held with its point near the knob of a 
charged gold-leaf electroscope, the leaves quickly collapse. Explain. 

6. A Leyden jar standing on a plate of glass cannot be highly 
charged. Why ? 

7. Will you receive a greater shock by touching the knob of a 
charged Leyden jar when it is held in the hand or when it is standing 
on a sheet of glass? Explain. 

8. Quickly pass a rubber comb through the hair and determine 
whether the electrification of the comb is positive or negative. 

9. Show that an electric charge is self-repulsive by blowing a soap- 
bubble on a metal pipe and then electrify- 
ing it. Compare the change in the size of 
the bubble with that noticed in Experi- 
ment 17. 

10. Twist some tissue paper into a loose 
roll about six inches long. Stick a pin 
through the middle of the roll into, a verti- 
cal support. Present an electrified rod to 
one end of the roll, and thus cause the roll 
to turn about the pin as a horizontal axis. 
Give this piece of apparatus a scientific _, 
name. 

11. Prepare two wire stirrups, A and B, like that shown in Fig. 186, 
and suspend them by silk threads. Electrify two glass rods by rub- 
bing them with silk, and place them in the stirrups. Bring A near 
B, Notice the repulsion. Kepeat the experiment with two sticks of 




220 ELEMENTARY PHYSICS. 

sealing-wax that have been electrified by rubbing with flannel. Notice 
the repulsion. Place an electrified glass rod iu A y and an electrified 
stick of sealing-wax in B. Notice the attraction. Give the law illus- 
trated by these experiments. 

12. Place a gold-leaf electroscope inside an insulated tin pail and 
electrify the pail. Describe and explain the indications given by the 
electroscope. 

13. Insulate a tin pail, and run a fine wire from its edge to the knob 
of an electroscope. Suspend a metal ball by a silk thread, electrify 
it, and lower it into the pail without contact. Notice and account for 
the divergence of the leaves of the electroscope. Touch the pail with 
a finger. Notice and account for the collapse of the leaves. Remove 
the finger and withdraw the ball. Notice and account for the diver- 
gence of the leaves. If the ball is negatively charged, what is the 
final charge of the electroscope ? 

B. Current Electricity. 

Preliminary. 

Experiment 179. — Partly fill a tumbler with a solution made by 
slowly pouring one part of sulphuric acid into ten parts of water. 
Place a strip of zinc, 2 x 10 cm., in the tumbler of dilute acid, and 
notice the bubbles that rise. Apply a flame to them as they reach the 
surface of the liquid, and notice that they burn with slight puffs. 
Hydrogen is evolved by the chemical action between the zinc and the 
acid. 

Experiment 180. — Take the metal strip from the tumbler of acid 

and, wliile it is yet wet, rub thereon a few drops of mercury, thus 

amalgamating the zinc* The amalgamated surface 

will have the appearance of polished silver. Replace 

the zinc in the acid, and notice that no bubbles are 

given off. Place a copper strip, 2 x 10 cm., in the 

solution, being careful that it does not touch the 

zinc. No bubbles appear on either the copper or 

the zinc. Bring the strips together at their upper 

ends as shown in Fig. 187. Bubbles now arise from 

the copper. Connect the metals above the liquid 

Fig. 187. y^y ^ piece of copper wire, about No. 18. The same 

results are observed. 




CURRENT ELECTRICITY. 221 

Note. — Always make such connections secure, metal to metal, and 
with large area of contact. Each metal strip may be bent at the top 
so as to clasp the edge of the tumbler, leaving the part on the inside 
long enough to reach very nearly to the bottom. 

Experiment i8i. — Solder a wire 50 cm. long to each of the metal 
strips used in Experiment 180. Place the strips' in the acid, and bring 
the free ends of the wires into contact with the tongue, one above and 
one below it, being sure that there is no acid on the wires. A bitter, 
biting taste is felt. Make sure that this taste disappears when either 
strip is removed from the solution, when either wire is disconnected 
from the tongue, or when the circuit is broken at any point. Notice 
that the hydrogen bubbles cling tenaciously to the copper, and that, 
by this " polarization of -the cell," its electrical power is much dimin- 
ished. 

272. Suspicion. — It seems as though a metallic contact 
is necessary to bring about this phenomenon of bubbles 
on the copper. We have a complete circuit of materials, 
copper strip, wire, zinc strip, and acid. Perhaps we do not 
see all that is talking place in the system. 

Voltaic Cell and Electric Current. 

Experiment 182. — Put the cover of a tin spice-box into a fire and 
thoroughly melt the tin coating from the iron plate. Use the cover 
thus prepared as a mold for casting a zinc plate 6 mm. thick. While 
the zinc is still liquid, embed in it the bent end of a wire about 30 or 
40 cm. long. When the zinc has cooled, 

remove it from the mold and straighten i r-^g J 

the wire, which should project from the 
edge of the plate as shown in Fig. 188. 
Smooth the rough edges of the zinc with a file, and amalgamate it. 

Invert a common tumbler on a square board of soft pine, about 
1.5 cm. thick, and large enough to serve as a cover for it. Run a 
pencil around the edge of the tumbler and draw the diagonals of the 
inscribed and circumscribed squares, as shown in Fig. 189. Bore 
holes as shown at a, b, c, and d just large enough to admit an electric 
(arc) light carbon. Cut four such carbons to lengths that are equal 
and less than the depth of the tnmbler. If the carbons are copper- 
ooated, dissolve t- e copper with nitric acid from all of the rod except 



222 



ELEMENTAHY PHYSICS. 



1.5 cm. at the upper end. Insert one end of each carbon into one of 
the holes, and connect the four carbons by a copper wire as shown in 
Fig. 190. Pass the wire of the zinc plate through a small hole at the 
middle of the board, so that the plate may be suspended in the tum- 





Fia. 189. 



Fig. 190. 



bier, as shown in Fig. 191. Wedge the wire in place. Be careful that 
this wire does not touch the wire from the carbons on the top of the 
cover. Insulated wire may be used for supporting the zinc, the end that 
is to be embedded in the zinc being scraped bare before the casting. 
Prepare a solution as follows : slowly pour f67 cu. cm. of sulphuric 

acid into 500 cu. cm. of water, and 
let the mixture cool. Dissolve 115g. 
of potassium dichromate (bichro- 
mate of potash) in 335 cu. cm. of 
boiling water, and pour the hot solu- 
tion into the dilute acid. When 
this liquid is cool, fill the tumbler 
about two-thirds full with it, and 
place the carbons and zinc therein. 
Adjust the height of the plate as 
shown in Fig. 191, and be sure that 
the zinc does not touch any of the 
carbons. The zinc and carbon 
should be kept in the fluid no longer 
than is necessary. It is well to pro- 
vide a second tumbler in which to 
drain them. Each pupil should make at least one of these cells; 
he will find three or four of them very useful. 




Fig. 191. 



CURRENT ELECTRICITY. 



223 



Hold the two wires of this or of some other good cell, end to end, 
over a compass-needle and parallel to its length, as shown in Fig. 192. 
No change appears. Bring the two ends of the wu*e into contact, and 




Fia. 192. 

thus close the circuit. The needle instantly flies around as though it 
was trying to place itself at right angles to the wire. Break the cir- 
cuit, and the needle swings back to its north and south position. 
Twist the wires together, and bend the conductor into a loop so that 
the current passes above the needle in one direction and beneath the 
needle in the other direction. The deflection of the needle will be 
greater than before. If the wire is formed into a loop that makes 
several turns about the needle, the deflection will be still greater. 
Notice the direction in which the north-seeking end of the needle 
tui-ns. Reverse the cell connections, and notice that the needle 
deflects in the opposite direction. See Experiment 192. 

273. Certainty. — We are now sure that sometliing 
unusual is going on in the wire. This something is called 
a current of electricity. The contain- 
ing vessel^ the plates^ and the exciting 
liquid constitute a voltaic cell. 

(a) There is a difference of potential be- 
tween the plates, and the chemical action 
between the liquid and one or both of the 
plates, or some other cause, tends to maintain 
that difference. 

274. Direction of Current. — We 
cannot conceive a current without ^^' ^^ 
direction. The actual direction of current-flow is not 
known, but, for the sake of convenience and uiiifoiniitj'. 
electricians assume that the cun*ent flows from the carbon 




224 ELEMENTARY PHYSICS. 

through the wire to the zinc, and from the zinc through 
the liquid to the carbon. 

275. Plates, Poles, etc. — The entire path traversed by 
the current, including liquids as well as solids, is called 
the circuit. The plate that is the more vigorously acted 
upon by the liquid is called the positive plate ; the other 
is called the negative plate. The free end of the wire 
attached to the negative plate is called the positive pole 
or electrode; that of the wii-e attached to the positive 
plate is called the negative pole or electrode. In any part 
of an electric circuit, a point from which the current flows 
is called positive (4-) and a point toward which the cur- 
rent flows is called negative (— ). When the two elec- 
trodes are joined, the circuit is closed; when they are 
separated, the circuit is broken. 

(a) When several cells 
are connected so that the 
positive plate of one is joined 
to the negative plate of the 
next, as zinc to carhon, and 
so on, as shown in Fig. 194, 
they are said to be grouped 
or joined in series. When all 
of the positive plates are 

connected on one side, and all of the negative plates are connected on 

the other side, as shown 

in Fig. 195, the cells 

are said to be joined in 

parallel, or in multiple 

arc, A number of cells 

joined in either way is 

called a voltaic battery. 




T^^JT" Tco^ 



Fig. 194. 




Note. — The repre- Fio. 195. "" 

sentation of the zinc 

and carbon plates, as at Z and C in Fig. 194, is the conventional way 
of representing a voltaic cell. 



CURRENT ELECTRICITY. 



225 



Resistance. 

Bzperiment 183. — Provide a flat piece of soft pine wood about 
10 cm. square and 3 cm. thick, and 
wind on evenly one layer of No. 16 
cotton-covered or insulated copper wire 
covering the greater part of the block. 
Secure the two ends of the wire by 
double-pointed tacks. Place a small 
pocket compass upon the block thus 
wound, and turn the block until the 
coils of the wire are parallel to the ^®' '^* 

needle when the circuit is open. Pass a current through the coil, 
quickly notice how much the needle has been deflected, and break the 
circuit. The instrument you have made is called a galvanoscope. 

Experiment 184. — Interpose 20 feet of No. 30 (or finer) iron wire 
in the circuit of a voltaic cell. Connect it so that the current will 
flow from the carbon through the galvanoscope, through the iron 





J 



R^tBTANCLE O^^FfON *m£ 



FiQ. 197. 

wire, and back to the cell. In other words, connect the wire and 
galvanoscope in series. The deflection will he less than before. Keep 
the current on just long enough to read the galvanoscope. 

276. Resistance* — The property of a conductor^ hy virtue 
of which the passage of an electric current through it is 
diminished^ and part of the electric energy is transformed 
into heat, is called resistance. Nothing is known of its 
nature, but it pertains to all substances. 

Q 



226 ELEMENTARY PHYSICS. 

(a) Any material device, such as a coil of wire, introduced into 
an electric circuit on account of the resistance that it offers to the 
passage of the current, is called a resistance. 

(b) The ohm is the practical unit of resistance. It is the resistance 
of a column of pure niercuiy one squaie millimeter in cross-section, 
and 108.3 centimeters long, and at a temperature of 0^. A thousand 
feet of No. 10 copper wire, or 9.3 feet of No. 30 copper wire, has 
a resistance of very nearly an ohm, — an important " rough and 
ready " standard. A million phms is called a megohm ; one-millionth 
of an ohm is called a microhm. 

Laws of Resistance. 

Experiment 185. — Provide 20 feet of No. 30 iron wire, 20 feet of 
No. 30 copper wire, 60 feet of No. 30 iron wire, and 20 feet of No. 20 

iron wire. Repeat Experiment 
20 FT. Ng 30. IRON ~"!L »:» 184 with each of these wires, in 

20 FT. NO. 36. COPPER ~""* 2 ^-P ' 

each case noting the deflection of 



eo FT. NO. 80. IRON 



20 FT. Na 20, (RON 



t\& 




the galvanoscope, G. 

Each wire may be coiled on a 
board, care being taken that adja- 
cent coils do not touch. Coiled or 
Fio. 198. uncoiled, the wires may be con- 

- . nected as in Fig. 198, and the free 

end of F touched at 1, 2, 3, and 4 successively. Give the cell a 
moment's rest between successive contacts. 

277. Laws of Resistance: — 

(1) Other things being equal, the resistance of a condtictor 
is directly proportional to its length. 

(2) Other things being equal, the resistance of a conductor 
is inversely proportional to its area of cross-section. 

(3) Other things being equ^l, the resistance of a wire de- 
pends upon the material of which it is made. 

(a) The resistance of metals is raised, and the resistance of carbon 
is lowered by heating. At a given temperature, resistance is directly 
proportional to a constant that is different for different substances. 
This lonstant, A", is called the specific resistance or the resistivity of 



CURRENT ELECTRICITY, 



227,. 



the material. Resistivity is the reciprocal of conductivity. Tables of 
resistances, etc., are given in the appendix. 

Note. — In many respects, it is convenient to compare the flow of - 
electrification through a wire to the flow of water through a horizontal 
pipe. Such a comparison yields the following analogues : — > 



Functions, 

Pressure. 
Quantity. 
Rate of flow. 

Resistance. 

Work. 

Rate of work. 



Hydraulic Units.' 

Head in feet. 

Pound. 

Pounds per second. 

No definite unit. * * 
Foot-pound. * 
Foot-pounds per second, 
or horse-power. 



Electromagnetic Units. 

Volt. 

Coulomb. 

Coulombs per second,^ 

or ampere. 
Ohm. 
Joule. 
Volt-ampere, or watt 



278. The Volt. -^ Hydraulic pressure might be called 
water-moving force; electrical pressure is called electro- 
motive force (E.M.F.). . The practical unit of electromotive 
force is called the volt ; it is a^lmost the same as the electri- 
cal pressure of a cell consisting of a copper and a zinc- 
plate immersed in a solution of zinc sulphate. 

(a) Although differeii6e of |)otential is measured in volts, it is a- 
different thing from etectromotive force. The electromotive force of 
a circuit is the total electrical pressure existing therein, while the 
difference of potential is merely the difference of electrical pressure 
between two points on the circuit. A generator of electricity for arc 
lights may have an electromotive force of 3,000 volts, while the dif- 
ference of potential between the terminals of an arc lamp in the cir 
cuit is only 45 volts. 

279. The Ampere. — The unit of rate of flow^ or current 
strength^ is the ampere^ which may be defined as the cur- 
rent flowing per second through a wire having a resistance 
of one ohm, and between the ends of which a potential 
difference of one volt i^ maintained. A thousandth of an 
ampere is a milliampere. 



228 ELEMENTARY PHYSICS. 

260. Ohm's Law. — Representing current strength by 
(7, voltage, i.e., electromotive force, by E^ and resistance 
by i2, the numerical relations of these functions of an 
electrical current are expressed by the formula, 

C7=4orJS?=(7xi2, or i2 = ^. 

Any two of these being known, the third may be found. 

(a) Applied to an eliectric generator (as a dynamo or a voltaic cell), 
we may represent the resistance of the external cii'cuit by R and the 
internal resistance of the generator itself by r. Then 



r + R 

Thus, if the E.M.F. of a chromic acid cell is 2 volts, the internal 
resistance of the cell is 1.5 ohms, and the wire resistance is 0.5 ohms, 

^-1.5 + 0.5"- ^* 
The current strength will be 1 ampere. 

SMI. The Coulomb is the quantity of electrification car- 
ried past any point by a 1-ampere current in one second. 
The unit is rather large for practical purposes, and is but 
little used. 

282. The Joule is the electrical unit of worh^ and repre- 
sents the energy of one coulomb delivered under a pres- 
sure of one volt. 

Joules = volts X coulombs. 

283. The Watt is the unit of electrical activity or power^ 
and represents the rate of working in a circuit when the 
electromotive force is one volt and the current is one 
ampere. One horse-power equals 746 watts. 

Watts = volts X amperes. 



CURRENT ELECTRICmr. 229 

(a) Representing algebraically the defioition of the watt^ we have 

ir=JSxC. (1) 

Substituting, in this equation, the value of E given iu § 2d0, we have 

W = RxC*. (2) 

Substituting, in the same equation, the value of C given in § 280, we 
have 

W = ^. (3) 

Heating Condnctora. 

Experiment z86. — Join equal lengths of iron wires of different 
sizes end to end, and pass a gradually increasing current through 
them. The smallest wire will be most heated. 

Experiment 187. — Join, end to end, equal lengths of iron and cop- 
per wires of the same size, and increase the current that passes through 
them until the iron wire is red-hot. Ascertain the thermal condition 
of the copper wire. 

284. Distribution of Heat. — The heat developed in any 
part of an electric circuit is proportional to the resistance of 
that part of the circuity or to the fall of potential through 
that part of the circuit. 

285. Shunts. — When part of a circuit consists of two 
branches, each branch is said to be a shunt to the other. 




The current flowing through such a circuit will divide, 
part of it going one way, and the other part the other 
way. 



230 ELEMENTARY ^ PHYSICS. 

(a) The current that flows through the branches will be inversely 
proportional to the respective resistances of the branches. Suppose 
that the branch that carries the galvanometer, G, has a resistance of 
900 ohms, and that the branch that carries the >coil, 5, has a resist- 
ance of 100 ohms. Then 0.9 of the current will flow tlirough Sy and 
0.1 through G, 

(h) The introduction of a shunt lessens the resistance of the cir- 
cuit. In a case like that above specified, the resistance of the part be- 
tween a and h will be less than that of either of its branches, thus : — 

R = ^^ ^ ^^^ = 90, the number of ohms. 
900 + 100 ' 

BXERCISB8. 

1. What is the resistance of a No. 10 copper wire, 1,000 feet long? 
(Consult the table in the appendix.) 

2. Wliat is the resistance of 750 feet of iron wire, No. 8? 

3. What is the resistance of 6,050 feet of copper wire. No. 25 ? 

4. A copper wire is carrying a 5-ampere current. The resistance 
of this wire is 2 ohms. 

(a) How many volts are necessary to force the cmTent through the 
wire? 

Solution: — E = C X 72 = 5 x 2 = 10, the number of volts. 

(b) How much energy is consumed in the wire? 

S<aution: — W = E x C = 10 x 5 = 50, the number of watts; or 
WzzR X C^= 2 X 25 = 50, the number of watts. 

5. An incandescence lamp is connected with an electric generator 
(dynamo) 300 feet away by a No. 18 copper wire that is carrying a 
1-ampere current. A fine coil galvanoscope would show differences in 
potential between the ends of the two wires running to the lamp, and 
between the two terminals of the lamp itself. What is the loss volt- 
age due to the line ? 

Solution : — The table of resistances given in the appendix shows 
that the resistance of the 600 feet of wire is 3.83466 ohms. 

E=C X R = l X 3.83466 = 3.83466, the number of volts. 

If the lamp took 1 ampere at 100 volts, the line loss would be nearly 
3.8 per cent. 



CURRENT ELECTRICITY. 231 

6. What would be the proper size of- copper wire to supply a group 
ot lamps 400 feet away, and taking 15 amperes, so that the line loss 
shall be 2 volts? 

Solution : — The resistance of the line would be, 

/e = ^ = ;^ = 0.1333, the number of ohms. 
C 15 * 

its resistance in ohms per foot must be (0.1333 -?- 800 =) 0.0001666, 
and the resistance per 1,000 feet, 0.1666 ohms. From the table, we 
find that No. 2 is the nearest size of wire. 

7. The wire loss of an electric motor is 156 watts. If the resist- 
ance of the motor is 2 ohms, what current flows? 

Solution : — 

W=Rx (y; C = yj^ = 8.83, the number of amperes. 

8. How many foot-pounds per minute equal a watt ? Ans. 44.236. 

9. How many horse-power will be absorbed by a circuit of arc 
lamps, taking 9.6 amperes at 2,900 volts pressure? 

Ans. 37.32 H.P., nearly. 

10. A group of incandescence lamps absorbs 21 amperes. The line 
loss is limited to 1.5 volts. 

(a) What is the resistance of the line? Ans. 0.07143 ohm. 

(b) How many watts are lost? Am, Shb watts. 

11. What mechanical horse-power is necessary for 50 incandescence 
lamps, each taking 0.5 ampere at 110 volts, allowing 10 per cent loss 
for transformation from mechanical into electrical energy? 

Ans. 4.09 H.P. 

12. What energy is absorbed by a coil of wire of 23 ohms resist- 
ance, through which a current of 3.5 amperes is flowing? 

Ans. 281.75 watts. 

13. Wind four or five layers of No. 20 insulated copper wire upon the 
edge of a board 25 cm. square. Slip the wire from the board and tie 
together the several turns of the wire at the corners of the rectangle. 
Bend one end of the wire into a hook and solder it to the middle of the 
pointed half of a sewing-needle as shown at m in Fig. 200. Straighten 
the other end at a right angle, as shown at n. Bend a narrow sfrip of 
brass at a right angle, and in on^ arm make an indentation that will 
liold a globule of mercury, f Support the brass L with the indented 
arm horizontal, and from, it hang the wire rectangle. A globule of 



232 



ELEMENTARY PHYSICS. 




Fig. 200. 



mercury insures a good condition at m, and the straightened part of 
the wire dips into a cup of mercury at n. Adjust the form of the sup> 
porting hook so that two sides of the rectangle are horizontal, and 

place the face of the rectangle in a 
north and south plane. Pass the 
current of a battery of 3 cells 
through the apparatus, and notice 
that the rectangle turns into an 
east and west plane. Reverse the 
current and notice the effect. Make 
a record of this motion of the wire 
rectangle, and reserve it for future 
study. 

14. Wind four or five layers of 
No. 20 insulated copper wire upon 
the edge of a board 10 x 20 cm. 
Slip the wire from the boards 
and tie as directed in Exercise 13, 
Place this coil in the circuit be- 
tween the battery and the mercury 
cup at n, Fig. 200. Call the larger wire rectangle -4, and the smaller 
one B, Hold B with one of its 20 cm. sides vertical and near one 
side of A . Record the effect as manifested by the motion of A, when 
the current flows upward through the adjacent sides of the two 
rectangles; when the current flows downward through both; and 
when it flows upward in one and downward in the other. Formulate 
a general expression of the action of parallel cunents upon each 
other, (a) When they flow in the same direction, {b) When they 
flow in opposite directions. The consid- 
eration of the interaction between cur- 
rents as herein illustrated constitutes the 
subject-matter of electrodynamics, 

15. Wind some No. 16 insulated copper 
wire into a close spiral about 4 cm. in 
diameter and 15 cm. long. Bend its ends 
as indicated in Fig. 201. Put it into the 
cii'cuit of the battery as directed for the 
rectangle of Exercise 13 and hold a bar magnet near one of its ends. 
Trace the current through the solenoid, 

16. Pass two stout copper wires separately through a cork about 



^ 



D 



Fig. 201. 



MAGNETISM. 233 

2 cm. in diameter. About 2 cm. from the smaller end of the cork, 
conDect the copper wires with a short piece of very fine iron wire. 
Wrap the edge of a strip of paper about 5 cm. wide around the cork 
so as to make a paper cup with the irou wire inside. Fill the cup 
with fine gunpowder, and close the other end with a cork or a paper 
cap. Place this torpedo at a safe distance, connect it by stout copper 
wires to a voltaic battery, and send through the wires a current that 
will heat the iron wire and explode the torpedo. State some indus- 
trial application of electricity that is illustrated by this exercise. Cut 
the leading wires at three or four points and join them with short 
pieces of fine iron wire. Tie the fuse of a fire-cracker around each 
piece of iron wire, and send a current that shall ignite all of the 
fuses. 

C. Magnetism. 

Artificial Magnets. 

Experiment x88. — Wrap a piece of writing paper around a large 
iron nail, leaving the ends of the nail bare. Wind fifteen or twenty 
turns of stout insulated copper wu*e around this paper wrapper. Put 
this spiral into the circuit of a voltaic cell, and dip the nail into iron 
filings. Some of the filings will cling to the ends of the nail in a 
remarkable manner. Upon breaking the circuit, the nail instantly 
loses its newly acquired power, and drops the iron filings. 

Experiment 189. — Draw a sewing-needle four or five times from 
eye to point across one end of the nail used in Experiment 188, while 
the current is flowing through the wire wound upon it. Dip the 
needle into iron filings. Some of the filings will cling to each end 
of the needle. 

Experiment 190. — Break the tangs from a few flat, worn-out files. 
Smooth the ends and sides of the files on a grind-stone. Get some 
good-natured dynamo tender to magnetize these hard-steel bars, and 
three or four stout knitting-needles. You can magnetize the needles 
yourself by winding upon them successively, evenly, and from end 
to end, a layer of insulated No. 20 wire, and sending a current from a 
voltaic battery through the wire. Freely suspend these permanent 
magnets at a considerable distance from each other and so that each 
can turn in a horizontal plane. The knitting-needles may be thrust 
through two corners of triangular pieces of paper to the third corner 
of which the end of a horse-hair is fastened by wax. The heavier 




234 ELEMENTARY PHYSICS. 

magnets may be placed in stout paper stirrups similarly supported, or 

they may be floated upon water, as shown in Fig. 202. The magnets 

will come to rest in a north and south line, 

-^ Mark the north-seeking end of each magnet 

= so that it may be distinguished from the 

other. 

286. A Magnet is a hody that has 

Fio. 202. ^^^ property of attracting iron or steely 

and that^ when freely suspended^ tends 

to take a definite position^ pointing approximately north and 

south. 

(a) One of the most valuable iron ores is called magnetite (Fe^O^). 
Occasional specimens of magnetite attract ii'on. Such a specimen is 
called a lodestone. It is a natural magnet. 

(b) Artificial magnets have all the properties of natural magnets, 
and are more powerful and convenient. They may be temporary or 
permanent. Temporary magnets are made by passing electric cur- 
rents around soft iron, as in Experiment 188, and are called electro- 
magnets. Permanent magnets are made of hardened steel, as in 
Experiment 189. The most common form of artificial magnets ai-e 
the bar magnet and the horseshoe magnet. The first of these, is a 
straight bar of iron or steel; the second is U-shaped, as shown in 
Fig. 203. A piece of iron placed across 

the two ends of a horseshoe magnet is 
called an armature. The process of mak- 
ing a magnet is called magnetization, 

(c) It appears that matter is subject to fig. 20a 
the magnetic force as universally as it is to 

the force of gravitation. Substances that are attracted, as iron is, are 
called paramagnetic, or magnetic; substances that are repelled, as 
bismuth is, are called diamagnetic. 

287. Magnetic Poles. — We have seen that when a bar 
magnet is dipped into iron filings, the magnetic effect is 
greatest at the ends of the bar, that it diminishes rapidly 
toward the middle, at which point no filings are sustained, 
and that the ends of the freely suspended magnet point 




MAGNETISM. 235 

toward the poles of the earth. It is common to put a 
distinguishing mark on the end that turns toward the 
north, and to call it the marked, north-seeking, or -f- pole. 
The other end is called the unmarked, south-seeking, or 
— pole. The line that joins the poles of a freely suspended 
magnet is called the magnetic axis. A unit magnetic pole 
is a pole that exerts a force of one dyne upon a like pole 
at a distance of one centimeter. 

(a) A unit magnetic pole, i.e., a pole of unit strength, is sometimes 
said to be of unit magnetic mass. 

Magnetic Needles. 

Experiment 191. — Re^Seat Experiment 15 using the sewing-needle 
of Experiment 189. The needle will assume a north and south 
position. 

Experiment 192. — Straighten a piece of watchnspring about 15 cm. 
long by drawing it between thumb and finger. Heat the middle of 
this steel bar to redness in a flame and bend 
it double. Bend the ends back into a line 
with each other, as shown in Fig. 204. Mag- 
netize each end separately and oppositely. 
. Wind a waxed thread around the short bend yiq. 204 

at the middle to form a socket, and balance 

the needle upon the point of a sewing-needle thrust into a cork. A 
little filing, clipping, or loading with wax may be necessary to make 
it balance. The needle will point north and south. 

Experiment 193. — Pass a knitting-needle through a small cork 
from end to end and so that the cork shall be at the middle of the 
needle. Thrust a sewing-needle or half of a knitting-needle througli 
the cork at right angles to the knitting-needle, to serve as an axis of 
support. Place the ends of the axis upon the edges of two glass 
goblets or other convenient objects. Push the knitting-needle through 
the cork until it balances upon the axis like a scale-beam. Magnetize 
the knitting-needle, and notice that the marked end seems to have 
become heavier. 




ELEMENTARY PHYSICS. 



288. Magnetic Needles. — A small bar magnet suspended 
in stuih a manner as to allow it to assume its chosen position 
relative to the earth is a magnetic needle. 

(a) If the needle turns freely in a horizontal plane, it is a hori- 
zontal needle ; e.g., the mariner's or the surveyor's compass. If it turns 

freely in a vertical plane, it constitutes 
a dipping-needle (Fig. 205). Two mag- 
nets fastened to a eouimon axis, and 
with their poles reyei*sed, constitute an 
astatic needle (Fig. 206). An astatic 
needle assumes no panticular direction 
with respect to tije earth if the two 
needles are equally magnetized. 





Fio. 206. 



Fig. 206. 



Magnetic Field. 

Experiment 194. — Lay a bar magnet on the table between two 
wooden strips of the same thickness as the magnet. Cover the magnet 
with a sheet of paper or cardboard, or a plate of glass. With a dredge- 
box or muslin bag, sprinkle uniformly over the plate the finest filings 
of wrought iron that you can obtain. Gently tap the plate to facili- 
tate the movement of the filings. They will arrange themselves in 
lines that seem to proceed from the poles, to curve outward through 
the air, and to complete their circuit through the magnet, as shown 
in Fig. 207. Freely suspend a short magnet (e.g., a piece of a mag- 
netized sewing-needle supported by a silk fiber) just above the 
filings, and move it into different positions. At every point, the 
magnet will place itself parallel to a tangent to the curves, with its 
marked end always pointing in the same direction relative to the 



MAGNETISM. 



237 







W^mmimi 



Fia. 207. 



Experiment 195. — Similarly map out the "magnetic phantom** 
curves when the oi>nosite poles of two bar magnets are brought near 
each other. The res-i^t will be like that represented in Fig. 208. The 
lines from one magnet seem to interlock with those from the other ud 
if by mutual attraction. 



m 




Fia. 208. 



E^tperiment 196. — Similarly produce the phantom when the like 
poles of two bar magnets are brought near each other. The result 



238 ELEMENTARY PHYSICS. 

will be like that repi^eseuted in Fig. 209. The lines now seem to 
repel each other. 



Fig. 209. 

289. Magnetic Field and Lines of Force. — The space 
surrounding a magnetised body andr through which the 
magnetic force acts is called a^ magnetic field. We may 
imagine lines drawn in the magnetic field, each indicating 
the direction in which a marked pole would move. Such 
lines are called magnetic lines of force. 

(a) The magnetic action that takes place in a magnetic field has 
been happily illustrated by supposing the lines of force to be stretched 
elastic threads that tend to shorten along their lengths, and that are 
self-repellent. This suggests that unlike poles ought to attract each 
other (see Fig. 208), and that like poles ought to repel each other 
(see Fig. 209). These lines of force are assumed to flow from the 
marked to the unmarked pole outside the magnet, and in the opposite 
direction inside the magnet, so as to form closed loops, or complete 
circuits. By agreement among physicists, as many lines are drawn 
through each square centimeter of surface as there are dynes in the 
force of that part of the field. 

(b) A number of lines of force traversing a magnetic field is called 
a flow ov flux of force. The unit of flux is called a weher, and repre- 
sents one line of force. The unit of strength offleld, or intensity offliLx^ 



MAGNETISM. 239 

u called a gauss^ and represents the number of lines of force per square 
centimeter. With a flux of 24,000 webers in 12 squai*e centimeters, the 
intensity of flux would be 2,000 gausses. A field is of unit strength 
when a unit magnetic pole placed in it is acted upon with a force of 
one dyne. 

Laws of Magnets. 

Experiment zgy. — Suspend one of the bar magnets at a consider- 
able distance from the others. Bring one end of another magnet held 
in the hand near one end of the suspended magnet, and notice the 
attraction or repulsion. Also notice the designations of the poles that 
are brought into proximity. Satisfy yourself that — 

N repels N, N attracts S, 

S repels S, S attracts N. 

290. Law of Magnetic Poles. — (1) Like magnetic poles 
repel each other; unlike magnetic poles attract each other. 

(2) The force exerted at different distances between two 
poles of the same magnetic mass is inversely proportional to 
the squares of the distances. 

(3) The force exerted at a given distance between two 
poles is directly proportional to the product of the magnetic 
masses of the poles. 

291. Magnetic Potential is essentially analogous to elec- 
trostatic potential. At any point, it is measured by the 
work done against the magnetic forces in moving a unit 
magnetic pole from an infinite distance to the given point. 
The difference of magnetic potential between two points is 
measured by the amount of work required to move a unit 
magnetic pole from one to the other. If this work is one 
erg, there is unit difference of potential between the two 
points. 

292. Magnetization. — Any magnetic substance is mag- 
netized by bringing it into contact with a magnet, or 
simply by placing it in a magnetic field. In the latter 



240 ELEMENTARY PHYSICS. 

cose, it is said to be magnetized by induction. The amount 
of magnetization developed . depends upon the nature of 
the substance and the strength of the field. 

(a) AVith a given field, iron receives the greatest amoant of mag- 
netization, steel coming next. As the magnetizing force increases, 
the magnetization produced also increases, rapidly at first but more 
' and more slowly. When the magnetization ceases to increase, the 
substance is said to be saturated, 

Theqry of Magnetization. 

Experiment 198. — Magnetize a piece of watch-spring about 10 cm. 
long, and ascertain how large a nail it will support. Break the magnet 
at its middle, and test the strength of magnetization of the two new 
poles developed at the point of fracture. 

Experiment igg. — Nearly fill a slender glass tube with steel filings, 
and close the ends of the tube with corks. Draw the marked pole of 
a strong magnet from the middle of the tube to one end, and the 
unmarked pole from the middle to the other end, and repeat the 
stroking several times. One end of the tube will attract and the other 
will repel the marked pole of a suspended magnetic needle ; i.e., the 
filled tube has become a magnet. Thoroughly shake up the filings ; 
the tube loses its magnetic properties, as if the actions of the many 
little magnets in the tube were neutralized through their indiscrimi- 
nate arrangement. 

293. Theory of Magnetic Polarization. — When a magnet 
is broken, each piece becomes a magnet, the newly developed 
poles being of strength nearly equal to that of the original 
poles. The subdivision of the magnet may be carried on 
indefinitely, and with like results. This suggests that 
the molecules of a mafjnetic substance are always magnets ; 
that the substance does not exhibit magnetic properties when 
the magnetic axes of the molecules are turned indifferently 
in every direction ; and that the process of magnetization 
consists in turning the molecules so that their magnetic axes 
point in the same direction. 



MAGNETISM. 241 

Kagnetic Properties of Electric Onrrents. 

Experiment aoo. — Dip a short part of a stout copper wire that is 
carrying a large current into fine iron filings. A cluster of the filings 
will cling to the wire. 

Experiment aoi. — Repeat Experiment 182, and test the accuracy of 
the following rules : — 

(1) To detei mine the direction of the deflection of the needle, hold 
the open right hand over or under the conducting wire, but so that the 
wire is between the hand and the needle, so that the palm of the hand 
is toward the needle, and so that the^ fingers point in the direction of 
the current; the marked end of the needle will turn in the direction of the 
extended thumb. 

(2) To determine the direction of the current, hold the open right 
hand over or under the conducting wire, but so that the wire is be- 
tween the hand and the needle, so that the palm of the hand is toward 
the needle, and so that the thumb is extended in the direction in which 
the marked end of the needle is deflected ; the fingers will point in the 
direction of the current. 

Note. — If you cannot obtain an electric-light or a trolley-wire 
current for the next experiment, connect a number of similar cells in 
parallel. Make the external circuit of very heavy wire, and have the 
paper in place around the wire, and the dredge-box ready. Close the 
circuit and perform the experiment quickly. 

Experiment aoa. — Around a vertical conductor carrying a heavy 
current, place a piece of paper, and sprinkle fine iron filings on tlie 
paper. Notice that the iron particles arrange thembeives in distinct 
circular whirls around the wire, as 
shown in Fig. 210. Hold the closed 
right hand ab that the extended thumb 
points in the direction of the current 
in the wire; then the fingers will in- 
dicate the direction of the lines of 
force in the surrounding field. Bend 
the upper part of the conducting wire, 
and pass it vertically downward through 
the paper. Sprinkle iron filings as be- 
fore. Notice that the magnetic lines 
of force arouUd the two parallel parts of the wire circle in opposite 
directions, clockwise in one case, and counter-clockwise in the other. 




242 



ELEMENTARY PHYSICS. 




Fig. 211. 



Szperinieiit 203. — Coil some No. 12 copper wire throngli holes in a 
board, as shown in Fig. 211, and pass a strong current through it. 

Sprinkle iron filings as before and 
note the effect. Such a coil of con- 
ducting wire, wound so as to afford 
a number of equal and parallel cir- 
cular electric circuits arranged npon 
a common axis, is called a solenoid. 

Experiment 204. — Wind the mid- 
dle part of about 3 meters of No. 20 
insulated copper wire around a rod 
about 1.5 cm. in diameter, forming 
thus a solenoid about 10 cm. long. 
Bring the ends of the wire along 
the axis of the solenoid, and bend 
them at right angles near the mid- 
dle. Solder small plates of sheet 
copper and amalgamated sheet zinc 

to the ends of the wire. Support the solenoid 

and plates by a large flat cork on the surface 

of dilute sulphuric acid, as shown in Fig. 212. 

The floating cell will take position so that the 

axis of the solenoid extends north and south. 

Test the ends of the solenoid for polarity, 

using a bar magnet for that purpose. 

Experiment 205. — ^Prepare a second solenoid 

similar to that described in Experiment 204, omitting the plates. 

Put it into an electric circuit, and use it as 

you did the bar magnet in Experiment 204. 

294. The Magnetic Character of 
an Electric Current has been shown 
by several experiments. The passage 
of an electric current through a sole- 
noid gives it many of the properties 
of a cylindrical bar magnet. 

(a) The polarity of the solenoidal magnet may be determined by 
holding it in the right hand so that the fingers point in the direction 





Fig. 213. 



MAGNETISM. 



243 



of the current ; then the extended thumb will point toward the marked 
or north-seeking pole of the magnet. 

(b) The influence to which these magnetic lines of force are due 
is called magnetomotive force (M.M.F.). The magnetomotive force of 
a magnetic circuit is directly proportional to the number of amperes 
iu the electric circuit surrounding it, and to the number of turns 
that the electric circuit makes around the magnetic circuit; i.e., 
the magnetomotive force is proportional to the ampere-turns. The unit 
of magnetomotive force is called a gilbert, and corresponds to 0.7958 
ampere-turns. 

Permeability. 

Experiment 206. — Place a strip of sheet iron in the solenoid of 
Experiment 203, as shown in Fig. 
214, and repeat that experiment. 
Notice that most of the lines of force 
are gathered into the iron and issue 
from its ends. Notice that the lines 
cui-ve outward and tend to return, 
forming closed loops or complete 
magnetic circuits. Change the iron 
from the inside of the solenoid to the 
outside, and repeat the experiment. 
Notice that the iron again gathers in 
the lines of force as if it offered an 
easier path for them. 




Fia. 214. 



295. Permeability. — Some substances are capable of 
receiving more lines of force than others with the same 
magnetomotive force. This relative capacity is called 
permeability. 

(a) Permeability is a ratio. For paramagnetic substances, it is 

greater than unity; for diamaj- 
netic substances it is less than 
unity. When a paramagnetic 
substance is placed in a uniform 
magnetic field, an increased num- 
ber of lines of force are crowded 
into it, as shown in Fig. 215. 
Fig. 215. When a diamagnetic substance is 




244 ELEMENTARY PHYSICS. 

placed in such a field, the number of lines that pass through it is 
diminished. 

(6) If a small compass is put into a glass bottle, an outside magnet 
will affect it, but if it is put into a hollow iron ball, an outside magnet 
will not affect it. Soft iron acts as a magnet screen because of its high 
permeahiliy. Watches are sometimes protected from magnetic influ- 
ence by soft iron shields in the shape of inside cases. i 

296. Reluctance and Reluctivity. — Like electric cur- 
rents, magnetic lines of force flow in the greatest quantity- 
through paths of least resistance. Magnetic resistance is 
called reluctance^ and its unit is the oentted. Specific mag- 
netic resistance (specific reluctance) is called reluctivity. 
Reluctivity is the reciprocal of permeability. 

(a) The relations of these magnetic units are expressed by the 
equation, — 

- gilberts 

oersteds 

Electromagnets. 

Experiment 207. — Make a helix about 15 cm. long by neatly wind- 
ing three layers of No. 18 insulated copper wire upon a rod about 
2 cm. in diameter. Remove the rod, pass a few threads through the 
opening of the helix, and tie them on the outside so as to hold the 
turns of wire in place. Put the helix into the circuit of a voltaic cell, . 
and bring it near a magnetic needle. The deflection of the needle 
shows the magnetic power of the helix. Nearly fill the opening in 
the helix with straight pieces of soft iron wire, and again test its 
magnetic power. The deflection of the needle will be much greater 
than before. 

297. An Electromagnet is a bar of iron magnetized by 
an electric current. 

(a) When the current was passed through thr helix used in Ex- 
periment 207, some of the lines of force leaked cut at the sides, as 
indicated by Fig. 216, and few of them extended from end to end. 
The soft iron core, by reason of its high permeability, diminished 
this leakage of lines of force, and greatly increased their number, 03 
n in Fig. 217. 



MAGNETISM. 



245 



(b) When an electromagnet is U-shaped, the coils around the two 
ends of the bent iron core are so wound that if the core should be 

straightened either coil would appear as a 
^\ I ^y^ continuation of the other, i.e., the current ^^ 






Fig. 218. 

would circle around the core in the same 
direction in the two coils, as is shown in p^^ 217 
Fig. 218. 

(c) If the iron of the magnet core is of commercial quality, it is 
not wholly demagnetized when the current is interrupted. The mag- 
netization thus retained after withdrawal from a magnetic field is 
called residual magnetism. 

298. Ampere's Theory of Magnetism. — As an electric 
current is surrounded by a whirl of lines of magnetic 
force, so we may conceive a magnetic line of force as 
surrounded by an electrical current- whirl. This would 
imply, as Ampere long ago suggested, that magnetism is 
simply a vortical electric current, and that a 
magnetic field is something like a whirlpool 
of electricity. 




(a) Fig. 219 represents a vertical conductor cariying 
an electric current, and surrounded by a magnetic line 
of force, which is in turn surrounded by electric whirls ; 
the magnetic line 0/ force is an electric vortex-ring, Tt is 
not difficult to conceive the vortex-ring as made up of ether whirls. 
Ampere's theory supposes that electric currents circle round the mole- 



Fio. 219; 



24G ELEMENTARY PHYSICS. 

cules of a magnetic substance, thereby polarizing them, and that when 
all the molecular magnetic axes face in the same direction the sub- 
stance is magnetically saturated. 

Terrestrial Magnetism. 

Experiment ao8. — Place a small dipping-needle over the marked 
end of a long, horizontal bar magnet, and move it slowly toward the 
other end of the bar, observing the changes in the position of the 
dipping-needle. Similar changes would be observed if you could 
carry the dipping-needle from far southern to far northern latitudes. 

Experiment aog. — Take a bar of very soft iron about 75 cm. long, 
and make sure by trial that its ends will not attract bits of soft iron. 
Then hold the bar in a meridian plane, and with its north end de- 
pressed below the horizon a number of degrees approximately corre- 
sponding to the latitude of the place of the experiment, i.e., give it the 
position of a dipping-needle. Tap the rod on its end with a mallet 
or wooden block, and test it for magnetic polarity. 

299. Terrestrial Magnetism. — The directive tendency 
of the compass, and other phenomena, show that the earth 
is surrounded by a magnetic field. In fact, these phe- 
nomena are such as might be expected if we knew that 
a bar magnet four or five thousand miles long extended 
nearly north and south through the earth's center. 

(a) The angle that the axis of a dipping-needle makes with a hori- 
zontal plane is called the inclination or dip of the needle. The dip is 
90° at the magnetic poles of the earth, and 0° at the magnetic equator, 
and, at any given place, does not differ greatly from the latitude. 
Lines passing through points on the earth's surface where the incli- 
nation has the same value are called isoclinic lines. The inclination 
of the needle is subject at most places to periodic changes. 

(6) The angle that the axis of a compass-needle makes with the 
geographical meridian at any place is called the declination or variation 
of the needle at that place. When the marked end of the needle lies 
east of the meridian, the variation is easterly, and vice versa. Lines 
drawn through places on the earth where the declination is the same 
arc called isotonic lines, as is shown in Fig. 220. The particular iso- 



MAGNETISM. 



247 



gonic line for which the declination is zero is called an agone or 
an agonic line. In 1890, the American agoue entered the United 
States near Charleston. It is 
slowly moving westward. The 
declination of the needle is sub- 
ject to both periodic and irregu- 
lar changes. 

(c) The magnetic intensity of 
the earth also varies from point 
to point at the same time, and 
from time to time at the same 
place. Lines drawn through 
places on the earth where the 
force of terrestrial magnetism is 
the same are called isodynamic 

^''^^' Fig. 220. 




1. What part of a magnet might properly be designated by the 
term " equator " ? 

2. Show that the influence of the earth's magnetism upon a mag- 
netic needle is merely directive. 

3. If a wire coil of 220 turns carries a 3-ampere current, what is its 
magnetomotive force? Ans. 829+ gilberts. 

4. Float a magnet on water. The float should be the lightest that 
will carry the load with safety, and the body of water should be so 
large that surface tension will not urge the float toward the side of 
the vessel. When the magnet is at rest near the middle of the liquid 
surface, determine the tendency of the magnet to drift toward the 
north or south. Repeat the experiment with a variety of magnets, 
and try to find one that always floats in one direction, i.e., one in which 
the marked pole is stronger or weaker than the other. If you cannot 
find such a magnet, strongly magnetize the blade of an old hack-saw, 
and test it on the float. If you have not yet found that for which 
you seek, break the blade in the middle, and test each half. If neces- 
sary to the success of your search, break one of the halves in two, and 
repeat the tests. Make very careful notes of any magnet that you 
find to have more magnetism of one kind than of the other. 

5. Map a magnetic field as in Experiment 194. Carefully remove 
the magnet and wooden strips. Over the filings, carefully place a sheet 



248 ELEMENTARY PHYSICS. 

of printing-paper that has been wet with a solution of tannin. Ovet 
this, place a sheet of heavy blotting-paper. Place a board on the 
blotting-paper and a weight on the board. When the printing-paper 
is removed, some of the iron filings will adhere to it. When the 
paper is dry, brush oil these filings. The ink-like markings on the 
paper make a permanent copy of the map. 



II. ELECTRIC GENERATORS, ELECTROMAGNETIC 
INDUCTION, ETC. 

Note. — The devices considered in the preceding section are inca- 
pable of producing a current adequate to the demands of the age in 
which we live. It is the pui-pose of this section to indicate how such 
currents are produced. 

300. Voltaic Cells are the most common " electric gen- 
erators," and have been devised in great variety. Some 
of them are dry, some have one liquid, and others have 
two. Some are constant and strong v\rhile they last, but 
require frequent renewals ; others are effective for short 
periods only, and require time for their own recovery. 
Each has its advantages and its disadvantages, so that one 
is the better for one purpose, and another for another. 

(a) When commercial zinc is used as one of the plates of a cell, 
much of the energy of the cell is wasted in what is known as local 
action. This is probably due to chemical action between particles of 
zinc and adjacent particles of carbon, iron, etc., that are present as 
impurities in the zinc. It is easy to imagine minute voltaic cells, the 
currents flowing in short circuits from the zinc through the liquid to 
the foreign particles, and thence back to the zinc. This local action 
is prevented by usin" pure zinc, or by amalgamating commercial zinc 
as in Experiment 180. 

(hi) The polarization of the cell, i.e., the accunuilation of the hydro- 
gen film on the negative plate, diminishes the available current by 
increasing the resistance of the circuit, and by setting up a counter 
electromotive force that may reduce, stop, or even reverse the flow of 
the current. The various devices for removing the hydrogen, or for 



ELECTRIC GENERATORS, ETC. 249 

preventing its accumulation, constitute the most essential differences 
between the different forms of cells. 

(c) A few forms of cells are mentioned ; it is impossible to give 
descriptions of all or many. The oxidation of hydrogen yields water- 

(1) T\\Q potassium dichromple cell (see Experiment 182) consists of 
zinc and carbon plates immersed in a solution of potassium dichro- 
mate in dilute sulphuric acid. The action of the sulphuric acid on 
the dichromate liberates chromic acid which oxidizes the hydrogen, 
and thus prevents polarization. This cell is very convenient for quick 
use, and valuable for '^all-around" work. It is sometimes called the 
Grenet cell. A similar cell tliat employs sodium dichromate instead of 
potassium, dichromate is more enduring in its action. A solution of 
chromic acid is much used and is more economical than either. 

(2) In the Grove cell, a cylindrical plate of zinc is immersed in 
dilute sulphuric acid, and carries a porous cup that contains strong 
nitric acid in which a platinum strip is immersed. The hydrogen 
evolved at the zinc plate is oxidized by the nitric acid. 

(3) The Bunsen cell differs from the Grove in a substitution of 
carbon for platinum, and in the larger size of the plates. Like the 
Grove cell, it is little used now, the fumes that come from the nitric 
acid being choking and corrosive. 

(4) In the Leclanche cell, a zinc rod is immersed in a saturated 
solution of ammonium chloride (sal-ammoniac). In this solution is 
also a porous cup that contains a bar of carbon tightly packed in a 
mixture of granular carbon and manganese dioxide. The hydrogen 
evolved is oxidized by the dioxide, but so slowly that the cell must be 
given frequent intervals of rest to recover from polarization. This 
cell is much used for working telephones, electric bells, etc., i.e., on 
circuits that are open most of the time. 

(5) The Daniell cell consists of a zinc plate immersed in dilute sul- 
phuric acid contained in a porous vessel outside of which is a perfo- 
rated copper plate surrounded by a solution of copper sulphate. The 
hydrogen is taken up by the sulphate before it reaches the copper 
plate. Polarization being wholly prevented, this cell is one of the 
most constant known. 

(6) The gravity cell is a modification of the Daniell. The liquids 
are kept separate by their different densities, thus dispensing with 
the porous cup. It is commonly used on closed circuits. This is the 
form of cell most used for telegraphic purposes. 

(jd) Every cell has an internal resistance that consists chiefly of the 



250 



ELEMENTARY PHYSICS. 



resistance of the liquid or liquids used. The voltage of the cell is 
largely taken up in overcoming this internal resistance, thus greatly 
lessening the energy available. Jl R \s the resistance of the circuit 
outside the cell, and r is the resistance of the cell itself, then Ohm's 
law becomes 

E 



C = 



r + R 



Refer to Fig. 193, and notice that the liquid prism between the plates 
is part of the circuit ; that when the plates are separated, the length 
of the liquid conductor, and the internal resistance of the cell, are in- 
creased (see § 277) ; that when one of the plates is lifted partly from 
the liquid, the area of cross-section is reduced, and the resistance 
increased. 

The Grouping of Cells. 

Experiment aio. — Upon each end of a 4-inch piece of soft, round 
iron rod 1 inch in diameter, drive a vulcanite or hard-wood collar 

about \\ inches in diameter. 
Upon the spool thus formed, 
wind about 6 feet of No. 8 in- 
sulated copper wire, being care- 
ful first to insulate the iron core 
with paper. Fasten a rectan- 
gular piece of soft iron, a, to a 
piece of whalebone, and support 
it, as shown in Fig. 221, over M, 
the electromagnet just described. 
Place M in the circuit of a battery of six or more similar cells joined 
in series. The whalebone magnetoscope will enable you to make a 
rough estimate of the pull of the electromagnet. Connect the cells of 
the battery in parallel, and repeat the experiment. 

Experiment 211. — Connect the terminals of a high resistance gal- 
van oscope to the poles of a single cell, and record the deflection of the 
needle. ' Next, put the galvanoscope in circuit with a battery of six 
similar cells joined in paiallel, and record the deflection of the needle. 
Then put the galvanoscope in circuit with a battery of the same cells 
joined in series, and record the deflection of the needle. From the 
records, determine which method of joining cells is most effective 
with a high external resistance. 




Fio. 221. 



ELECTRIC GENERATORS, ETC. 251 

301. Advantages of Grouping in Parallel. — Some of the 
foregoing experiments indicate what is a general truth, 
that, when the external resistance is small, the grouping 
of electric generators in parallel will give a greater cur- 
rent than will a series grouping of the same generators. 

« 
(a) With such a grouping, the available difference of potential 
between the terminals of the system is not increased, but the internal 
resistance is diminished. 

302. Advantages of Grouping in Series. — Our experi- 
ments also indicate that when the external resistance is 
great, the grouping of electric generators in series will 
give a greater current than will a parallel grouping of the 
same generators. 

(a) With such a grouping, the voltages of the several generators 
are added together for the total available difference of potential, and 
the internal resistances are added together for the total internal resist" 
ance of the system. 

(6) Having a given number of similar cells and a certain known 
external resistance, the maximum current may be obtained by joining 
the cells in such a way as to make the resistance of the battery as 
nearly equal as possible to the resistance of the external part of tlie 
circuit. 

BXERCISBS. 

1. Determine the current strength of a battery of 5 cells joined 
in parallel, each having an E.M.F. of 2 volts and an internal resistance 
of 0.5 ohm, (a) wheVi the external resistance is 0.1 ohm; (b) when 
the external resistance is 500 ohms. Ans. (a) 10 amperes. 

(ft) Nearly 0.004 ampere. 

2. Determine the current strength of a battery made up by coup- 
ling the same 5 cells in series, (a) when the external resistance is 0.1 
of an ohm ; (6) when the external resistance is 500 ohms. 

Ans. (a) 3.846 + amperes; (6) 0.0199 + of an ampere. 

3. Connect in parallel 8 voltaic cells, each having an E.M.F, of 2 
volts, and an internal resistance of 8 ohms, the total external resistance 
being 16 ohms. Determine the current strength. 

Aus. 0.1176 of an ampere. 



252 



ELEBiENTARY PHYSICS. 



4. Compute the current strength of the same 8 cells connected in 
series, the external resistance remaining the same. Ans, 0.2 ampere. 

5. Compute the current strength of the same 8 cells when joined 
in two rows, each row being a series of four cells, and the rows being 
joined in multiple arc, the external resistance remaining the same. 

Ans. 0.25 ampere. 

6. Each of ten given cells has an electromotive force of 1 volt and 
an internal resistance of 5 ohms. What is the current strength of a 
single cell, the external resistance being 0.001 of an ohm ? 

Arts, 0.19996+ ampere. 

7. The ten cells above mentioned are joined in parallel. The ex- 
ternal resistance is 0.001 of an ohm. What is the current strength of 
the battery? Ans. 1.996 + amperes. 

8. The ten cells above mentioned are joined in series, the external 
resistance remaining the same. What is the current strength of the 
battery? Ans, 0.19999 + ampere. 

9. What is the current strength given by one of the above-men- 
tioned cells when the external circuit has a resistance of 1,000 ohms? 

Ans, 0.00099502 ampere. 

10. AVhen the ten cells are joined in parallel with an external re- 
sistance of 1,000 ohms, what is the ampere yield of the battery? 

Ans. 0.0009995 ampere. 

11. When the ten cells are joined in series with an external resist- 
ance of 1,000 ohms, what is the current strength of the battery? 

Note. — Compare the results in Exercises 6, 7, and 8, in which we 
have a small external resistance. Then compare the results in Exer- 
cises 9, 10, and 11, in which we have a high extenial resistance. 




Fio. 222. 



Electromagnetic Induction. 
Experiment 212. — For a 
galvanoscope more delicate 
than any we have yet used, 
procure two soft pine blocks, 
4 cm. square and 2 cm. thick. 
On the square faces of each, 
nail or glue a thin piece of 
wood, 6 cm. square. (These 
pieces may be cut from a 
cigar box.) The channel 
around the edges of the 



ELECTRIC GENERATORS, ETC. 



253 



blocks will be 2 cm. wide and 1 cm. deep. Throngh the middle of 
each block, from face to face, bore a hole at least 1.5 cm. in diameter. 
Wind tlie grooves full of No. 36 insulated copper wire, and mount the 
blocks, A and B^ on a basel)oard with their opposing faces about 1 cm. 
apart, as shown in Fig. 222. Connect the wires of the two coils so 
that a current flowing through the wire will circle around the coils in 
the same direction ; Le., connect them in series. 

Straighten and magnetize four or five pieces of watch-spring each 
1.5 cm. long, and fasten them with thiu sliellac Tarnish to the back of 
a piece of looking-glass, 1.5 cm. square and as thin as you can get 
(see Fig. 223). From a support made of brass wire, suspend the mirror, 
Jl/, by a strand of silk, the lightest that will carry the load. A single 
silk fiber may be strong enough. The mirror when suspended should 
hang midway between the two coils, and directly Li line with the holes 
through the two coils. So adjust the base of the galvanoscope that 
the coils are parallel to the mirror when the latter is freely suspended 
between them, and protect the apparatus from air 
currents by a glass cover. A feeble current pass- 
ing through the coUs will deflect the delicately 
suspended needles, as was roughly illustrated in 
Experiment 182. By placing a bar magnet on the 
table so as partly to neutralize the directive t^^n- 
dency of tlie terrestrial magnetism, the sensitive- 
ness of the galvanoscope may be increased. 

Stick a pin into the end of the base-board and 
in line with the centers of the o])enings in the coils, 
as appears more plainly in Fig. 224. The eye may 
be so placed that the pin will cover its image in the 
mirror. The slightest deflection of the mirror will 
be manifested by the destruction of this coinci- 
dence. Indicate the polarity of the suspended magnets by marking 
the letters iV^and S near the edges of the base-board between the coils 
A and B, Put the galvanoscope into circuit with a single cell, and 
note the deflection of the min-or. Record on the base-board of the 
instrument the fact that "This instrument shows a deflection of the 
JVend of the needle toward the east when the zinc plate of a cell is con- 
nected with the free terminal of coil B*' (or of Ay as the case may be). 







V 


s\ 


1 


s 


51 


■ 1 


A' 


5 


r 


V 


tfl 



Fig. 223. 



Experiment 213. — Make a coil with many turns of Xo. 36 insulate<l 
copper wire, as shown at IT in Fig. 224. The coil should have an 



254 



ELEMENTARY PHYSICS. 



internal diameter of about 3 cm., and a cross-section area of at least 
1 sq. cm. Connect the terminals of the coil with the terminals of the 
galvanoscope. Level the galvanoscope, and see that its needle-mirror 
is freely suspended as dh'ected in the preceding experiment. Thrust 




Flo. 224. 



the end of a bar magnet at least X,o cm. in diameter into the coil, H, 
thus filling the coil with lines of .force. An electric pulse deflects the 
mirror of the galvanoscope. That the deflecting current was of mo- 
mentary duration is shown by the fact that the mirror returns to its 
first position. When it has come to rest, remove 
the magnet from the coil. The mirror is turned 
the other way and comes to rest as before, thus 
showing that the direction of the second current 
was opposite to that of the first, and that its dura- 
tion was but momentary. Repeat the experiment, 
making the motions of the magnet more rapid. 
Notice that the pulses are more marked than 
before. Repeat the experiment again, using a 
low resistance solenoid that carries a current of 
electricity, as shown in Fig. 225, instead of the 
bar magnet. Then place the solenoid inside the coil, /i, and break, 
and make the battery circuit. Place a soft iron rod inside the sole- 
noid and again break and make the circuit, noticing any increase in 
the deflections of the needle. 

That the galvanoscope may be free from disturbing magnetic 
influence, see that all knives, keys, watches, and other articles of iron 




Fig. 225. 




ELECTRIC GENERATORS, ETC. 255 

or steel are kept at a considerable distance from it, and that the coil, 
H, is so far removed that the maguet or the solenoid may not have 
any perceptible direct influence upon it. It will be well to wind the 
wire of the coil, Hy upon a spool. 

Experiment 214. — Place the coil, JT, in circuit with a telephone 
receiver instead of the galvanoscope. 
When the circuit of the solenoid is 
made or broken, a distinct click may 
be heard in the receiver, which is a 
delicate detector of pulses of elec- 
tricity. The telephone may be bought 
at a low price, or borrowed. ^^* 

303. Induced Currents. — When the number of mag- 
netic lines of force that pass through a closed coil of wire 
is changed, as in Experiment 213, pulses of electricity are 
generated in the coil. The rapidity with which the coil 
is filled with lines of force, or emptied, has a marked 
effect upon the intensity of the pulses generated. These 
momentary currents are said to be induced in the coil ; i.e.^ 
they are induced currents, 

304. Laws of Induced Currents. — (1) An increase in 
the number of the lines of force passing through a closed 
coil induces a current in one direction through the wire of 
the coil; a decrease in the number of the lines of force 
induces a current in the other direction. 

(2) The electromotive force of the induced currents de- 
pends upon the rapidity of change in the number of lines 
of force that pass through the coil. 

305. A Magneto is a device for inducing electric currents 
hi wire coils or bobbins^ by variations in the relative positions 
of the coils and of permanent magnets. 

(a) The fundamental process in the generation of electric currents 
from mechanical power consists in revolving closed conductors in a 
magnetic field in such a way as to vary the number of lines of force 
passing through tliem, i.e., by successively filling and emptying closed 



256 



ELEMEliTARY PHYSICS. 




coils. Tlie mechanical motion may move the coils, or the sonrce of 
the magnetic flux, or it may simply move a mass of iron that forms 
a ready path for the lines of force. The magneto is of historical in* 
terest, but it has been largely displaced by the more efficient dynamo, 
an electric generator that differs characteristically from the magneto 
in that the former employs a field of force due to the influence of 
electromagnets, while the latter utilizes permanent magnets. 

306. The Dynamo. — Suppose a single loop of wire to 
turn upon a horizontal axis, and between the opposite poles 
of two magnets, iVand S^ as shown in Fig. 227. When the 

loop stands in a vertical 
plane, as indicated by 
the heavy black line, the 
magnetic lines of force 
between the pole-pieces 
thread through the loop 
in the greatest possible 
number. When the loop 
has been turned until it lies in a horizontal plane, as indi- 
cated by the dotted lines in the figure, the lines of force 
run parallel to the plane of the loop, and none thread 
through it. During this quarter revolution of the loop, 
the number of lines of force that pass through the loop 
was decreasing, and an electric current was thereby in- 
duced in the loop, as indicated by the arrows. During the 
next quarter revolution of the loop, the number of lines of 
force threading the loop was increasing, but as they passed 
through the loop from the other side, the current induced 
in the loop had the same direction as before. During the 
next half revolution, the induced current will flow through 
the loop in the opposite direction. The current, therefore, 
reverses twice for each revolution of the loop. 

(a) The direct current dynamo consists essentially of three parts : 
an armature made of coils of wire, which may be revolved in a 



Fig. 227. 



ELECTRIC GENERATORS, ETC. 



267 



magnetic field ; a commutator for giving a uniform dii*ection to the 
alternating currents induced in the armature coils ; and a large elec- 
tromagnet for creating a magnetic fifeld. 

(6) Fig. 228 represents the Brush dynamo complete. A shaft runs 
through the machine from eud to end, carrying a pulley, P, at one end, 
a commutator, c, at the other end, and a wheel armature, R, at the mid- 
dle. The armature carries eight or more helices of insulated wire, H H, 
connected in pairs. As the shaft is turned by the action of the belt 
upon the pulley, the armature and the commutator are turned with it. 
The armature coils are thus carried rapidly across the four poles of 




Fig. 228. 

the field magnets, il/Af, traversing the iutenser parts of the magnetic 
field, and cutting the lines of force. 

(c) The alternator is a dynamo designed for the generation of 
alternating currents. It has collecting rings instead of a commutator, 
so that the current is delivered just as it is generated (§ 305), and a 
small direct current dynamo for energizing its field magnets, the pole- 
pieces of which are generally very numerous. Nikola Tesla has 
invented an oscillator that is a combined prime motor and electiic 
generator, and that produces alternating currents without rotary 
motion of the generating coils. 

3D7. An Armature is a soft iron cylinder or ring upon 
which coils of insulated copper wire have been wound and 
arranged for rapid rotation in a magnetic field. 



258 



ELEMENTARY PHYSICS. 



(a) By virtue of its greater magnetic permeability, the soft iron 
core of the armature increases the number of lines of force gathered 
into the space traversed by the coil, and thus increases the electric 
effect. The revolving coil is made of many turns of wire instead of a 
single loop, and the electromotive force generated by the revolution is 
correspondingly multiplied. 

(b) Armatures are of several distinct types, the chief of which are 
the drum or shuttle armature, and the ring armature. In the former, 
a cylindrical iron core is made of thin disks of soft iron insulated from 
each other, thus minimizing the "local" or "Foucault currents," 




Fig. 229. 



which are generated in the iron, absorbing energy and transforming 
it into heat. On the cylinder thus built up, many separate coils are 
wound lengthwise, as is shown in Fig. 229. These separate coils are 
joined in series, and the several junctions connected to insulated bars^ 

the extremities of which are 
grouped around the shaft of 
the armature, as shown at the 
left of the figure. Brass bands 
around the outside of the cylin- 
der hold the coils in place. 

(c) The ring armature con- 
sists of coils wound in grooves 
upon an annular core, as shown 
in Fig. 230, which represents a 
partly wound armature for a 
Brush dynamo. The core is 
laminated, i.e., built up by 
winding a thin ribbon of soft 
iron in successive layers, each 
layer being insulated from the 
next. Coils radially opposite are joined in series, and the terminals of 
each such pair are carried to the commutator. 




Fig. 2^0. 




ELECTRIC GENERATORS, ETC. 259 

308. A Commutator is a device for reversing the con- 
flections of armature coils at the moment when the current 
in the coils is reversed^ thus causing the induced currents 
to flow in the same direction in the external circuit. 

(a) A simple commutator for a single-coil armature consists of the 
two halves of a metal collar around the armature shaft, and two metal 
strips or "brushes." The two halves _^-,r--— 

of the collar, i.e., the "commutator ^'T^ 
segments," m and n, are separated from 
the shaft, a, tliat carries them by a bush- 
ing of insulating material, and are sepa- 
rated from each other, as shown in Fig. 
231. One end of the armature coil is 
connected with one segment, and the 
other end with the other segment. 

The brushes, bb\ are held by fixed 

Fig 231 
supports so that their free ends rest 

lightly on the segments. The points of contact are diametrically 
opposite. 

Consider b and 6' the terminals of the dynamo, and that they are 
connected by a wire that constitutes the external circuit. Remember 
that m and n are connected through the armature coil. Assume that 
the connections of the terminals of the armature coil with the commu- 
tator segments are such that current flows through the coil and passes 
out by way of n and b. As the armature is turned a little further, 
the current in the coil is reversed, and flows out through m instead 
of n. But the same rotation of the shaft that carries both the arma^ 
ture and the commutator has now brought m into contact with b so 
that the current continues to flow through 6, which thus remains the 
-f terminal as long as the shaft is turned in the direction indicated 
by the arrow. There are many different ways of connecting arma- 
ture coils with their comnmtators, each one of which may call for 
careful study. 

309. The Field Magnet. — The electromagnet that sup- 
plies the flux of force must have a current to excite it. 

(a) This current is sometimes supplied from an outside source, as 
is diagrammatically shown in Fig. 232. Such a dynamo is said tc 



260 



ELEMENTARY PHYSICS. 



be separately excited. Often , all of the current from the armature is 
canied around the coils of the field magnet, thus forming a series 




Fig. 2C2. 



Fig. 233. 



dynamo, as is shown in Fig. 233. Sometimes a part of the current 
from the armature is carried through a shunt circuit consisting of 
many turns of wire that is smaller than the wire of the main circuit, 




SNUNT CIACU4T 

Fig. 234. 




Fig. 235. 



as is shown in Fig. 234. Such a dynamo is said to be shunt wound. 
Sometimes, for purposes of regulation, the field magnet is encircled 



ELECTRIC GENERATORS, ETC. 



261 



by both series and shunt coils, as is shown in Fig. 235, or by either 
of those with a separately excited coil. Such a dynamo is said to be 
compound wound, 

(b) When the armature of a " self-exciting " dynamo, i.e., one that 
has not an exciting current from an external source, is put in motion, 
the feeble residual magnetism of the cores of the field magnets induces 
feeble currents in the armature coils. These currents flow around 
the magnets, intensifying their power, and thus increasing the E.M.F. 
of the machine. The current thus strengthened further energizes the 
field magnet. Thus, the machine " builds up " its current until the 
magnets are saturated. 

BXBRCISBS. 

1. What is an induced electric current ? How is it produced ? 

2. How are induced currents made continuous? 

3. Give some proof that the condition of a wire when it closes an 
electric circuit is different from the condition of the same wire when 
the circuit is open. 

4. Why are the field magnets of dynamos generally provided with 
iron cores ? 

5. What is the difference between a magneto and a dynamo ? 

6. When a dynamo is in operation, its field magnets are likely to 
become heated. Does this increase or diminish the efficiency of the 
machine, and why ? 

7. Given the two electrodes of a concealed voltaic battery, deter- 
mine which of the wires is connected to the zinc plate. 

8. Provide a glass tube of 
about 1 cm. internal diameter. 
Insert a wire in each end, and 
fill the tube with pieces of 
pounded electric light carbon. 
Pass a current from a cell 
through the apparatus, inter- 
posing a low resistance galvan- 
oscope. By means of a wooden 
rod, compress the powdered 
carbon. Why is the deflection 
largely increased? Why is a low 
resistance galvanoscope used ? 

9. To a vertical board clamp two magnet bobbins (see Exercise 10) 
joined in series, as shown in Fig. 236. Support one end of the arma- 




262 ELEMENTARY PHfSICS. 

ture, 6m, by an elastic band, ab. Pass a current through the bobbins, 
and no^ce the pull upon ab. Looking at the upper ends of the bob- 
bins, notice whether the cuiTeiit circles around the two bobbins in the 
same direction or not, as clockwise or counter-clockwise. Turn one 
of the bobbins upside down, changing the connections in this respect. 
Ascertain which connection gives the greater pull upon the armature, 
&m, and, with the bobbins thus joined, bring the movable soft iron 
yoke, cd, into position as shown in the figure. Explain why this im- 
proves the magnetic circuit, so that the upper armature is pulled 
harder than l>efore, and probably drawn down with a sharp click. 

10. Make two magnetoscopes like that shown in Fig. 221. Ordi- 
nary carriage-bolts about 7 cm. long may be used as the cores, and 
soft iron nuts may answer as the armatures. With the two magneto- 
scopes, a voltaic battery, and a supply of insulated No. 20 copper 
wire, arrange apparatus so that you can exchange telegraphic signals 
with another pupil at another table, or in another room. 

The Pulsating Current. 

Experiment 215. — Mount a metal clock-wheel upon wooden bear- 
ings, and solder to its axle a wire crank by which it may be turned. 

Provide two metal springs. The 
upper end of one should rest upon 
the toothed edge of the wheel, and 
" snap " from one tooth to the next 
as the wheel is turned, 'i'he upper 
end of the other should rest on 
the axle of the wheel. Consider the 
fixed ends of these springs as the 
terminals of this "interrupter." 
Fig 2^^^^ ^^^ ^^^ apparatus into the circuit 

! with a voltaic battery and the gal- 

vanioscope that has a coil of No. 16 wire. Turn the wheel, and notice 
the deflection of the needle. 

310. Alternating Currents have some peculiar properties 
largely due to the constantly fluctuating field of force that 
surrounds their conductors. The pulsating current pro- 
duced by the interrupter has many of the properties of the 
'"^ernating current, and will facilitate our investigations. 




ELECTRIC GENERATORS, ETC. 263 

(a) The current does not wholly cease when the sprmg of the 
interrupter snaps from tooth to tooth. As the circuit is broken, the 
encircling magnetic lines of force are decreased in number, and that 
very decrease tends to continue the current. In brief, the current does 
not have time wholly to die away before the spring is on the next 
tooth of the wheel. 

Self-induction. 

Experiment 216. — Double a piece of No. 24 insulated copper wire 

about 100 feet long, and wind it upon a wooden rod as shown in 

Figl 238. Join the ends of this wire in tiie series circuit of the 

apparatus aiTanged for Experiment 215. Turn the wheel of the 

interrupter rapidl}', and note the de- 

flection of the galvanoscope. Remove j I C C C C C C C C /^"l 

the No. 24 wii*e from the circuit, ' ^.^ 

, . , . Fio. 238. 

straighten it, and wind it upon an 

iron rod so as to form an electromagnet. Put this electromagnet into 
the circuit, and repeat the experiment. Notice that the deflection of 
the galvanoscope is less, and that the sparks at the wheel of the inter- 
rupter are greater than before. 

311. Self-induction. — When the number of lines of force 
in a coil is increasing^ an electromotive force opposite to that 
of the inducing current is established^ thus weakening the 
direct current; when the number is decreasing^ an electro- 
motive force that coincides in direction with that of the 
inducing current is established^ thus strengthening the direct 
current. 

(a) When the doubled wire of Experiment 216 was wound upon 
the rod, every part of it lay adjacent to another part that was carry- 
ing current in the opposite direction. The magnetic lines of force 
generated by one part neutralized the lines of force that circled (see 
Fig. 371) in the opposite direction around the adjacent part; i.e., the 
circuit was non-inductive. When the wire was straightened, the lines 
of force circled in the same direction around adjacent parts of the 
wire, and assisted each other in settinp: up an opposing, self-induced 
electromotive force that greatly weakened the current that produced 
them. 

(6) A coiled circuit is said to have a reactance. This reactance 



264 ELEMENTARY PHYSICS. 

has mach the effect of resistance, but it depends upon other considera- 
tions, chiefly the frequency of the pulsations, and upon a certain con- 
stant called the coefficient of self-induction. This coefficient depends 
upon the shape, coiling, and coring of the circuit and, in practice, is 
determined only by experiment. 

(c) As alternating currents are fluctuating in value, their measure 
must be that of averages. For a true alternating current, the numeri- 
cal relations may be represented thus : — 

E 



C = 



y/R^-{-(2irnLy 

in which R represents the ohmic resistance, n the frequency of alter- 
nation, and L the coefficient of self-induction. The expression 2 irnL 
represents the reactance. The apparent resistance, i.e., V/i^^.^Ow/iL)-*, 
is called the impedance^ and is measured in ohms. 

Transformers. 

Experiment 217. — Wind about twenty turns of No. 18 insulated 
copper wire around a J-inch iron rod, or (preferably) around a bundle 
of iron wires, and put the coil into circuit with a pulsating current. 
The lines of force inside the coil and in the core fluctuate in value 
with the current. On the outside of this coil, and carefully insulated 
from it, wind 300 or 400 feet of No. 28 insulated copper wire. Place 
one of the terminals of this outer or secondary coil above the tongue, 
and the other terminal below it. When the pulsating current flows 
through the inner or primary coil, currents are induced in the second- 
ary coil, and produce distinct shocks in the tongue. 

312. The Transformer. — By suitably winding and coring 
primary and secondary coils, an alternate current at one 
voltage may be received by the primary, and a current at 
a different voltage delivered from the secondary. When 
the primary is made of a few turns of large wire, and the 
secondaiy is made of many turns of small wire, the vol- 
tage is increased, and vice versa. Coih so wound and prop- 
erhj cored are called transformers. 

(a) Transformers are largely used when currents are to be carried 
fTftat distances. With a given line, the loss in watts is less with 



ELECTRIC GENERATORS, ETC. 



265 



a small current aud high voltage than it is with large curreni* and 
low voltage. High voltage currents enable the use of small conduc- 
tors; copper wire is expensive. When the electric energy is trans- 
formed from a current of low voltage and many amperes to one of 
high voltage and few amperes, the apparatus is called a " step-up *' 
transformer. Similarly, when the voltage is decreased, the apparatus 
is called a " step-down " transformer. 

313. The Induction Coil is a modification of the appa- 
ratus used iu Experiment 217, and is often called the 
Rhumkoi-ff coil. Receiving a large current of small 
electromotive force, it delivers a small current at a high 
pressure, sometimes hundreds of thousands of volts, i.e., it 
is a " step-up " transformer. 




Fio. 230. 



(a) In the diagram shown in Fig. 239, M represents a core of iron 
wires upon which is wound a primary coil of coarse wire that is in 
circuit with the voltaic battery, B, In this primary circuit, are a com- 
mutator, c, for changing the direction of the current, and an automatic 
interrupter, h, AVound upon the primary coil, and very carefully in- 
sulated from it, is a secondary coil made of very many turns of fine 
wire, the terminals of which are marked T V. If the coil is designed 
to give sparks between T and T'> the condenser, CC, is added. This 
consists of sheets of tin-foil separated by sheets of paraffined or shellac- 
varnished paper. The alternate sheets of tin-foil are joined in 
parallel; the two groups are connected to the primary circuit on 



266 



ELEMENTARY PHYSICS. 



opposite sides of the iuternipter. The condenser is generally placed 
ill the base that carries the coil. 

(6) A simple form of the induction coil is shown in Fig. 240. The 
current passes through the couimutator, c, up the post, A, through the 
adjusting screw, d, and across to the spring interrupter, 6, which rests 
against the end of c?, and is carded by another post. Tlience it passes 

.to the primary coil, 
magnetizing the iron 
core, and making its 
way back to the gen- 
erator. The iron core 
thus magnetized at- 
tracts the soft iron 
hammer at the end of 
the spring, thus break- 
ing the circuit at b. 
When the current is 
broken, the core is 
demagnetized, and the 
elasticity of the spring throws b against the end of d, again making 
the circuit. Thus the spring vibrates between the end of the core and 
the end of the screw, making and breaking the circuit with great 
rapidity, and inducing currents in the secondary coil. Owing to the 
permeability of the iron core, which intensifies the flux of force through 
the coils, and to the great number of turns in the wire of the secondary 
coil, the electromotive force of the induced currents is very high. 




High Potential Phenomena. 

Experiment 218. — Connect a voltaic battery with the primary of 
an induction coil. Bring the terminals of the secondary within a 
few millimeters of each other, and notice the rapid succession of 
sparks that strike across the gap filled with air, one of the best of 
insulators. With a good coil, plates of glass and other non-con- 
ductors may be thus perforated. We have not noticed this property 
of electricity before because we have not had a current of sufficiently 
high E.M.F. 

Experiment 219. — In a shallow tin pan (e.g., a common pie-tin), 
melt equal quantities of rosin and shellac. Stir the substances to- 
giithar, avoid ijnition and the formation of bubbles, and, when the 



ELECTRIC GENERATOBS, ETC. 



267 



tin is filled, sefc it aside to cool. Cut a disk of sheet tin a little less in 
diameter than the resin plate, and fasten a piece of sealiug-wax at its 
center for a handle. Solder a round button or other metal ball on the 
upper side of the disk and at its edge. Whip the resiu plate briskly 
with a catskin, or rub it with warm flannel. Place the tin disk upon 
the plate, and touch the former with a finger. Place a number of 
small bits of paper upon the disk. Lift the disk by its handle ; the 
charged paper bits are repelled. Bring a knuckle to the button ; an 
electric spark may be seen. The disk may be charged many times 
without repeating the excitation of the resinous plate. The apparatus 
may be improved by making the disk of wood, rounding its edge, and 
covering it smoothly with tin-foil. 

314. An Electxophorus consists of a plate of resinous 
material or of vulcanite resting on a metallic bed-piece, 
and a movable metallic cover provided with an insulating 
handle. 

(a) As the surface of the resin plate is uneven, the metallic cover 
touches it at but a few points ; 
as the material is non-con- 
ducting, scarcely any electrifi- 
cation passes from the former 
to the latter. The two disks 
and the thin layer of air 
between them constitute a 
condenser (§ 268). The neg- 
atively electrified resin plate 
acts by induction on the disk, 
holding positive electrification 
"bound " at its lower surface, 
and repelling the negative 
which escapes through the 
finger. When the plate thus 
charged is removed from the 
resin plate, the bound electri- 
fication is set free. -piQ. 241. 

315. Electric Machines for developing statical electrifi- 
cation in large quantities depend upon either friction or 



^A, 





268 ELEMENTARY PHYSICS. 

induction for their operation, and are made in great 
variety. 

(a) The frictional electric machine usually consists of a plate of 
glass, A^ which is revolved between stationary cushions, Z), the sur- 
faces of which are covered with amalgam. The parts of the plate 
thus positively electrified are successively brought between two me- 
tallic combs, F^ the pointed teeth of which nearly touch the plate. 
The prime conductor, P, is electrified by induction, the negative elec- 
tri6cation escaping by air-convection from the pointed teeth to the 
oppositely electrified plate, thus neutralizing its electrification and 




Fig. 242. 

leaving the prime conductor positively charged. The negative con- 
ductor, JV, that carries the cushions is generally connected to earth, 
as shown in Fig. 242. The potential energy of the electrification thus 
obtained is the equivalent of the kinetic energy expended in turning 
the crank, minus that transformed into heat. 

(6) The induction machines may almost be described as continuous 
electrophori. The Wimshurst machine (Fig. 243), which may be taken 
as a representative of the class, consists for the most part of two equal 
glass disks that revolve in opposite directions. Sector-shaped strips of 
tin-foil are fastened to the outer surfaces of the plates, and act as car- 
riers of electrification and, when opposite each other, as field plates or 
inductors. Two conductors are placed at right angles to each other, 
obliquely across the plates, one at the front and the other at the back. 



ELECTRIC GENERATORS, ETC. 



269 




The ends of these conductors carry tinsel brushes that lightly touch 
the sectors as they pass. 
The discharging circuit is 
provided with combs that 
face each plate, and that 
are connected with small 
Ley den jars. The dis- 
tance between the balls 
of the discharging circuit 
may be regulated by insu- 
lated handles. This ma- 
chine is almost wholly 
free from "weather trou- 
bles.*' 

The tin-foil strips or 
carriers on the rear plate 
of a Wimshurat machine 
are represented in Fig. 
244 by the outer row of 
strips ; those on the front 
plate, by the inner row. 
The diagonal conductor that faces the rear plate is represented by cd ; 
the one that faces the front plate, by ab. The strips from which the 

arrows proceed are charged posi- 
tively; the others, negatively. 
The strips at the top of the 
rear plate are represented in 
the diagram as being positively 
charged; those at the bottom 
as being negatively charged. 
These conditions are reversed 
for the front plate. The maxi- 
mum charge upon one of the^ 
tin-foil strips or carriers is rep- 
resented as six units. The oppo- 
site motions of the two plates 
are represented by the two large 
curved arrows. As the carrier 
a moves into the position shown 
in the diagram, it comes under the inductive influence of the posi- 



FiG. 243. 




Fig. 244. 



270 



ELEMENTARY PHYSICS. 



lively charged carrier opposite it on the rear plate. At this instant^ 
it touches the brush of the diagonal conductor, and a transfer of posi- 
tive electrification from a to 6 leaves the carrier at a negatively 
charged. At the same instant and in the same way, the carrier at b 
is positively charged. Similar effects are also produced in the carriers 
at c and d. Thus, the carriers of both plates come to m and n, the 
combs of the discharging circuit similarly charged, positively at «, 
and negatively at m. The inductive action of these carriers upon the 
discharging circuit electrifies its two sides oppositely. 



High Voltage Currents. 

Experiment aao. — Wind several turns of wire upon a piece of glass 
tubing inside of which is an unmagnetized sewing-needle. Discharge 
a I^eyden jar through the wire, and test the needle to see if it has been 
magnetized. 

Experiment aai. — Wind ten or more turns of insulated wire. No. 
22, on the outside of a thin glass tumbler, being careful that the 

turns do not touch each 
other. A coating of shel- 
lac varnish will help to 
hold the wire iu place. 
Wind a smaller coil of 
ten or twelve turns of 
similar wire, bringing 
one end of the wire up 
through the coil, and be- 
ing careful that it does 
not touch any of the con- 
volutions. Tip the two 
ends of thb wire with 
bullets, and adjust them so that they will be within about 1 cm. of 
each other. Place the second coil in the tumbler, as shown in Fig. 
245, and fill the tumbler with high-grade kerosene. Connect n, the 
lower end of the outer wire, with the tin pan of the electrophorus. 
Charge the disk of the electrophorus, and discharge it through m, the 
upper end of the outer coil. Notice the spark between the terminals of 
the inner coil. Support an iron rod inside the inner coil, being careful 
that it does not touch the wire. Repeat the experiment, and notice 




Fig. 245. 



ELECTRIC GENERATORS, ETC. 271 

that the " striking distance ** between the terminals of the inner coil 
may be increased. 

Experiment 222. — Connect one terminal of the outer coil of the 
apparatus used in Experiment 221 to a terminal of the secondary of 
an induction coil. Set the latter in operation, and discharge the other 
terminal of its secondary into the other terminal of the outer coil of 
the tumbler. Notice the series of sparks between the terminals of the 
inner coil of the tumbler, and that the sparks there keep step with 
those of the induction coil. 

316. Identity. — The experiments just given indicate 
the remarkable similarity between current electricity at 
high voltage, and static electricity. Many facts tend in- 
evitably to the conclusion that the two kinds of electricity 
are identical. 

317. Geissler and Crookes Tubes. — A Geissler tube con- 
sists of a closed glass vessel with platinum electrodes 
sealed into the glass, so that an electric discharge from an 
induction coil may be produced in a rarefied gas within the 
vessel. (See Fig. 249.) The rarefaction is about one two- 
hundredth of an atmosphere. The discharge produces a 
beautifully stratified light, the color of which depends 
upon the nature of the contained gas. If the exhaustion 
of the tube is continued to one-millionth of an atmosphere 
or beyond, the phenomena exhibited dliBfer from those of 
ordinary gases as much as those of gases diJBfer from those 
of solids or liquids. The tube is then called a Crookes 

tube. 

Nature of Electric Discharge. 

Experiment 223. — Let another pupil push a pin through a visiting 
card. Examine the card, and try to tell from which side of the card 
the perforation was made. Perforate the card by the spark of an 
induction coil, examine it carefully, and try to tell from which side 
the perforation was made. Similarly examine the perforations made 
in a card by the discharges of an electrio machine, and of a Ley den 
jar. What do you infer from your comparison of the perforations? 



272 



ELEMENTARY PHYSICS. 





Ezperimeiit 224. — Wind two or three layers of paper upon MN 

(Fig. 246), a bar of soft iron, 
and about fifty turns of No. 
22 insulated copper wire upon 
the papers Twist loops in the 
wire at A and B, Tip the 
ends of the wire with bullets, 
and bring them very near each 
other, as at C, Ground the 
wire at B, i.e., put it into elec- 
trical connection with the 
earth, and discharge the elec- 
trophorus or a Leyden jar into 
the loop at A, Notice the 

sparks at C, 
Fio. 246. 

Experiment 225. — Straighten 

the wire of Experiment 2*24, and bend it into a lorfg loop returning on 

itself as in Fig. 247. Adjust the knob terminals at c for the same 

distance as in Experiment 224. Grouud 6, and 

discharge the electrophorus or Leyde 

a, as before. You will find great 

getting a spark at c, and may not ] 

80 at all. Fig. 247. 

318. Oscillatory Discharge. — Recent investigations have 
done much to justify the statement that in an electric dis- 
charge the flow surges back and forth thousands of times in 
the brief interval measured by the duration of the spark. 

(a) The sparks between the knobs, as observed in Experiment 224, 
show that, for some reason, the electricity preferred the path through 
the air at C, with a resistance of millions of ohms, to the path through 
the wire coiled upon Af .V, with a resistance of only a small part of an 
ohm. If the flow was of the nature of a direct current, it would have 
passed in the greatest quantity through the path of least resistance. 
On the other hand, if the flow was that of an alternating current, it 
would be governed by the law given in § 310 (c), rather than by- 
Ohm's law. The experiments just given indicate that the paradoxi- 
cal choice of path was due to the impedance of the wire coiled around 
*he iron bar MN. Study of the mathematical expression for impe- 



Ground 6, and 

eyden jar into „j 

t diflSculty in OOOOOOOOOOOoi} 
; be able to do *| 



ELECTRIC GENERATORS, ETC. 273 

dance shows that the factor n is the only one that is great enough to 
account for the very great impedance noticed, and that it must repre- 
sent a frequency of alternation measured by hundreds of thousands. 

319. Atmospheric Electricity. — The surface of the earth 
is electrified. The electrical density varies greatly at 
different times and places. The origin of this electrifica- 
tion is not known with certainty. The clouds collect and 
concentrate the diffused electrification of the atmosphere. 

(a) Suppose a thousand spherical watery particles, each having a 
unit charge, to coalesce to form a water-drop. The diameter of this 
drop will be ten times that of a single particle, its electric capacity 
will be ten times as great, but its charge will be a thousand times as 
great ; in other words, its potential will be increased a hundred fold. 
The condensation and aggregation of charged vapor particles must result 
in the production of a very high potential. 

320. A Lightning Flash is simply a disruptive discharge 
between two surfaces oppositely and highly electrified. 
The discharge may be from cloud, to cloud, or from cloud 
to earth. Like the discharge of the Leyden jar, the light- 
ning flash is oscillatory. A lightning flash a kilometer 
long corresponds to a difference of potential of about thir- 
teen million electrostatic units. 

(a) The induced charge on the earth tends to accumulate on build- 
ings, trees, and other elevated objects, thus reducing the thickness of 
the dielectric, intensifying the attraction between the opposite elec- 
trifications, and increasing the liability of such elevated bodies. 

(b) The sound that follows a lightning flash constitutes thunde^ 
The sudden expansion and compression of the heated air along thb 
line of discharge is followed by a violent rush of air into the partial 
vacuum produced, thus causing the sound. One-fifth the number of 
oeconds that intervene between seeing the flash and hearing the roar 
approximately indicates the number of miles that the observer is from 
the discharge. 

Thermo-electricity. 

Experiment 226. — Twist together, end to end, an iron and a German- 
silver wire, and attach their free ends to the terminals of a galvano- 

T 



274 



ELEMENTAKY PHYSICS. 



scope. Heat the junction of the two wires. The deflection of the 
needle indicates that an electric current was generated. Cool the 
junction of the dissimilar metals with ice. The opposite deflection of 
the needle shows that the current now generated flows in the opposite 
direction. 

321. Thermo- electric Pile. — Two dissimilar metals joined 
and used as in Experiment 226 
constitute a thermo-electric pair. 
Antimony and bismuth ai*e the 
metals generally used for the 
purpose. Many such pairs con- 
nected in series and having 
their ends exposed constitute a 
thermo-electnc pile. Such a pile 
with conical reflectors is repre- 
sented in Fig. 248. When its 
terminals are connected to the 
terminals of a delicate galvano- 
scope, the combination consti- 
tutes a thermoscope of great sensitiveness. 

BXBRCISBS. 

1. Describe the electrophorus. 

2. Explain the action of the electrophorus. 

3. Sketch the connections of the induction coil. Explain the action 
of the automatic current interrupter. 

4. Attach a Geissler tube (Fig. 249) to the secondary terminals of 
an induction coil. Put the coil in operation, and notice the discharge 
through the tube, 
and the difference 
from its discharge 
through air. Meas- 
ure the maximum 
length of the spark 




Fig. 248. 



Fig. 249. 



obtainable with the coil, and compare it with the length of the long- 
est discharge that you can get through a Geissler tube. 

Present a magnet pole to the Geissler tube, and notice the deflection 



ELECTRIC GENERATORS, ETC. 



275 




of the discharge. Reverse the polarity of the primary of the indnction 
coil. Notice that the discharge is now deflected iu an opposite direo- 
tion. Study the discharge through the tuhe with reference to the 
different appearances of the two ends of the tube. Reverse the coll, 
and notice the corresponding reversal iu the positions of the violet 
tint i^d the scintillations. K yon have no iuductiou coil, use the 
Wimshurst machine. 

5. Suspend a tiu plate about 10 cm. square from each binding-post 
of the secondary of a strong 

induction coil, as shown iu 

Fig. 250. Let the plates 

hang parallel to each other 

and about 8 cm. apart. Start 

the coiL Darken -the. room, 

and hold a small Geissler 

tnbe in the electrostatic field 

of force between the plates, 

with the ends of the tube 

near but not touching them. 

The tube glows brightly. 

Touch the plates with the 

ends of the tube. Notice the increased brightness. Quickly lay the 

tube in a daik comer, and notice the after-glow. 

6. Grasp a 110-volt incandescence lamp firmly in the hand, keep- 
ing the fingers away from the brass cap. ' Let some one else charge 
the lamp with an electrophorus. Discharge the lamp by touching the 
brass cap, keeping an eye oa the filament. When the discharge takes 
place, the filament swings around the bulb as if it were sweeping off 
the charge from the surface of the glass and delivering it to the cap. 
As there is danger of breaking the filament, it is well to use an old 
lamp. Repeat the experiment in the dark, and notice the brilliant 
glow of the lamp when discharging. 

7. Connect the outside coating of a Leyden jar by a wire to one of 
the terminals of an induction coiL Bring the knob of the jar near 
the other terminal of the coil and allow sparks to pass between them 
for a minute. Remove the jar, and connect its two coatings with the 
fingers. A smart shock shows that the jar is charged. Bring the 
knob of the jar into contact with the free terminal of the coil instead 
of allowing the discharge to spark across. It will be found impossible 
thus to charge the jar. 



Fio. 250. 



276 



ELEMENTARY PHYSICS. 



8. Support two metal balls, a and b, between the terminals of an 
induction coil, put the coil in operation, and determine the limiting 
length of the discharge between the balls. Then connect a Leyden 
jar to the terminals, as shown in Fig. 251. Start the coil again, and 

notice that the spark will 
not strike across so long a 
gap, but that it is a much 
hotter, " fatter" spark. Open, 
the circuit at x, and insert 
the oil transformer used in 
Experiment 221. It will be 
found to work in a satis- 
FiG. 251. factory manner. 




ni. ELECTRICAL MEASUREMENTS. 

322. Electrical Units. — The practical, electromagnetic 
units in common use among electricians are derived as 
multiples and submultiples of the absolute, C.G.S. electro- 
static units. 

(a) The wonderful advance made in the last few years by electrical 
science is largely due to the adoption of definite electrical units, and 
the general practice of making exact electrical measurements. 

323. The Galvanometer is an instru- 
ment for determining the strength of an 
electric current by means of the deflec- 
tion of a magnetic needle around which 
the current flows. When a galvano- 
scope is provided with a scale so that 
the deflections of its needle may be 
measured, it becomes a galvanometer. 

(rt) The astatic galvanometer consists of an 
astatic needle supported by an untwisted fiber 
so tliat one of its needles is nearly in the center • 
of the coil through which the current passes while the other needle is 
just above the coil. When the deflections of the needle are less than 10** 




ELECTRICAL MEASUREMENTS. 277 

or 15°, they are very nearly proportional to the strengths of the currents 
thai produce them. A current that deflects the needle 6^ is about three 
times as strong as one that deflects it 2°. 

(6) The tangent galvanometer consists of a very short magnetic 
needle suspended so as to turn in a horizontal plane, and with its 
point of support at the center 
of a vertical hoop or coil of cop- 
per wire through which the 
current is passed. In use, the 
hoop is placed in the plane of 
the magnetic meridian, the cur- 
rent that is to be measured 
is sent through the hoop, and 
the deflection of the needle is 
read from the scale. The 
strength of the current is pro- 
portional to the tangent of the 
angle of deflection. The values 
of such tangents may be ob- ^ 
tained from a table of natural 
tangents. Such a table is given 
in the appendix. 

(c) Any sensitive galvanom- pj^ 253 

eter, the needle of which is 

directed by the earth's magnetism, and in which the frame on which 
the coils are wound is capable of being turned round a vertical axis, 
may be nsed as a sine galcanometer. The coils are set parallel to the 
needle (i.e., in the magnetic meridian). The current is then sent 
through the coils, deflecting the needle. The coil is then turned until 
it overtakes the needle, which once more lies parallel to the coil- The 
strength of the current is proportional to the sine of the angle tkrou^jk 
which the coU has been turned. The values of the sines may be ol>- 
tained from a table of natural sines. Such a table is given in the 
appendix. 

(ji) The mirror galvanometer has a very short needle ri^dly attach*?! 
to a small concave mirror that is sas{>ended by a delicate fiber in iLe 
center of a vertical coil of small diain^^ter. A beam of li^'Lt from a 
lamp passes through a small openin^^ under a nii'-limeter scale aV^jt a 
meter from the mirror, falls upon the mirror. a:.d is refie^-t^l back 
npou the scale. A current {jassing throu^^'u the coil turns tLe neoiie 




278 



ELEMENTARY PHYSICS. 



and its mirror, thus shifting the spot of light to the right or left. The 
apparatus was devised for use with the Atlantic cable, and is exceed- 
ingly sensitive. The current produced by dipping the point of a brass 
pin and the point of a steel needle into a drop of salt water, and 
closing the external circuit through this instrument, sends the spot of 
light swinging way across the scale. 




Fig. 264. 



(e) A galvanometer of low resistance, graduated for the direct 
measurement of electric currents and giving its readings- in amperes, 
is called an ammeter. Any galvanometer that is wound with wire of 
sufficient size safely to carry the current to be measured, and properly 
graduated, may be used as an ammeter. 

(/) If a galvanometer is put in a shunt circuit between two points 
of different potentials, current will pass through it, and the current 
thus passing, may be used to measure the difference of potential. A 
galvanometer of high resistance, graduated so as to indicate in volts 
the difference of potential between its terminals, is called a volt- 
meter. 

(jg) A specially constructed galvanometer is sometimes used to 
measure, in watts, the rate of working, or the electrical activity of the 
current. Such a device is called a wattmeter. Electric cun^ent being 
a merchantable commodity, it is often desirable to measure both the 



ELECTRICAL MEASUREMENTS. 



279 



rate at which the electrical energy is delivered and the time during 
which it is delivered, i.e., the number of watt-hours. This is accom- 
plished by a modification of 
the wattmeter. The current 
swings an armature coil with 
complete revolutions in the 
field of a stationary coil. 
These revolutions are counted 
by a registering apparatus 
that gives direct readings in 
watt-hours. 

(A) The resistance of a gal- 
vanometer should correspond 
to that of the rest of the cir- 
cuit; i.e., a high resistance 
galvanometer should be used 
on a high resistance circuit, 
and vice versa. 




Fig. 256. 




FiQ. 25G. 



324. Resistance Coils are made of wires of known resist- 
ance for use with galvanom- 
eters in measuring resistances. 
Insulated and doubled wires 
are wound upon spools, and 
the terminals of each spool 
connected to heavy brass 
blocks, A^ B, (7, etc., on the 
top of the box that carries 

the spools. This style of winding destroys the magnetic 

effects, and reduces 

the self-induction of 

the coils. 

(a) When the brass 
pings are inserted as 
shown in Fig. 256, the 
coils are short-circuited, 
hut when a plug is 
withdrawn the current Fia. 257. 




280 



ELEMENTARY PHYSICS. 



passes through the corresponding coil. Such coils with resistances of 
1, 2, 2, 5, 10, 10, 20, 50, 100, 100, 200, 500 ohms, etc., severally are 
connected to form a resistance-box as shown in Fig. 257. By with- 
drawing the proper plugs, one may throw into the circuit any resist- 
ance desired, from a single ohm up to the full capacity of the box. 

325. The Measurement of Resistance is made in several 
ways according to the nature and magnitude of the resist- 
ance. Much use is made of the following important prin- 
ciple : The fall of potential between two points on a conduc- 
tor is proportional to the resistance of the. conductor between 
those points. 

(a) We may observe a certain deflection of the galvanoscope with 
a wire of unknown resistance in the circuit. By removing such un- 
known resistance, and inserting known resistances until an equal 
deflection of the same galvanoscope with the same cell is obtained, 

we may determine the re- 
sistance of the wire first 
used. This naethod is called 
resistance measurement by 
substitution, 

(b) The method that has 
the most general applica- 
tion is that known as the 
Wheatstone bridge. In Fig. 
258, we have a quadrangle 
of resistances. The four 
conductors, m, n, p, and z, 
that form the sides are 
called the arms; the con- 
ductor that joins C and D and carries the galvanometer, G^ is called 
the bridge. The current divides at A^ and reunites at B. The fall 
of potential through n and ar is evidently the same as the fall through 
m and p. The resistances of the arras may be so adjusted that, when 
the bridge-circuit is closed at /T, there will be no deflection of the 
needle of G, Under such circumstances, C and D are at the same 
potent' j,l, and it may be shown that the resistances of the four arms 
" balance " by being in proportion, thus : — 

m:n:: p:x. 




Fig. 258. 



ELECTRICAL MEASUREMENTS. 281 

When three of these resistances are known, the other one may be 
calculated. 

(c) The best way of determining the internal resistance of a voltaic 
cell is to join two similar cells .in opposition to each other, so that 
they send no current of their own. Then measure their united resist- 
ance (as if it were the resistance of a wire), as just described. The 
resistance of one cell will be lialf that of the two. 

326. The Measurement of E.M.F., or of difference of 
potential, is generally made with a volt-meter, or by 
comparison with the E.M.F. of a standard cell. 

BXBRCISBS. 

1. A volt-meter that has a resistance of 26,000 ohms indicates 37 
volts, (a) What is the strength of the current? (b) What voltage 
would such an instrument indicate with a current of 3 niilliamperes? 

2. Two volt-meters, one of which has a resistance of 25,000 ohms, 
and the other a resistance of 15,000 ohms, are connected in series 
across 110 volts, (a) What current flows through the system? 
(b) What voltage does the first instrument indicate? (c) The second 
instrument? 

Ans, (a) 0.00275 ampere ; (b) 68.75 volts; (c) 41.25 volts. 

3. How many watts are taken by a station volt-meter that indicates 
110 volts and uses a 0.002-ampere current? 

4. A dynamo is run at 450 revolutions, developing a current of 
9.925 amperes. This current deflects the needle of a tangent galva- 
nometer 60^. When the speed of the dynamo is sufficiently increased, 
the galvanometer shows a deflection of 74°. What is the current 
developed at the higher speed? Ans. 20 amperes. 

5. Solder one end of a piece of No. 20 insulated copper wire, 50 cm. 
long, to one end of a piece of zinc 10 x 2.5 x 0.5 cm., and amalgamate 
the zinc. Solder a similar wire to a piece of sheet copper 10 x 10 cm. 
Put the zinc into a porous cup 4 or 5 cm. in diameter and 10 cm. deep, 
and fill the cup to the depth of 8 cm. with dilute sulphuric ac!d. Tut 
the copper plate into a glass vessel 7 or 8 cm. in diameter and 10 cm. 
deep, bending it slightly to fit the inner surface of the tumbler. Put 
the porous cup and its contents into the glass vessel, and fill the latter 
to the depth of 8 cm. with a saturated solution of copper sulphate. 
Connect the terminals of this Daniell cell with the terminals of a low 
resistance galvanoscope, and record, at intervals of 5 minutes for half 



282 



ELEMENTARY PHYSICS. 



an hour, the deflections of the needle. Ascertain whether the current 
strength is practically constant after the porous cup is wet through. 

6. To a table-top or other board, tack two stout metal strips, A C 
and BDy with a meter stick between them, as shown in Fig. 259. 
Tack a similar metal strip, EF^ 90 cm. long, in position as shown. 
Solder metal binding-posts at the ends of these strips, and at the 
middle of EF. The resistance of the strips is so small that it need 
not be considered. Tightly stretch a Grerman-silver wire. No. 26, over 
the face of the meter stick, and solder it to the faces of the metal 
strips at r and 8. One of the terminals of a sensitive galvanoscope is 
to be connected to EF\ the other galvanoscope wire is to make a 




Fia. 259. 



sliding contact with the German-silver wire, dividing it into two 
variable parts, m and p, Pat the apparatus into the circuit of a vol- 
taic cell, as shown in the figure. Interpose a conductor of unknown 
resistance at x and a known resistance of approximately equal 
value at n (the better this guess at the equality of resistances, the less 
the liability of error in the results attained). You have a Wheatstone 
bridge, easily comparable to that shown in Fig. 258. Make the slid- 
ing contact at a point on rs that causes a deflection to the right, and 
note its position on the meter scale ; find a position that causes a 
deflection to the left. As the point of contact at which the bridge 
will balance is between these points, it is easy to locate it definitely. 
When the contact is made at such a point on rs that there is no de- 
flection of the needle, read the values of m and p directly from the 
meter scale, and determine the resistance of x, llepeat the work with 



SOME APPLICATIONS OF ELECTRICITY. 



283 



two slightly different values for n, and take the average of the three 
computed values of x, 

Note. — In practice, the galvanoscope should be placed at a distance 
from the rest of the apparatus, the connecting wires being kept near 
together. 



IV. SOME applicatio:n^s of electricity. 

Incandescence Lighting. 

Experiment 227. — Place a few centimeters of No. 36 platinum wire 
across the terminals of a battery of several bichromate cells in series. 
The wire wiU be heated to incandescence, and may be melted. Lift 
one of the plates partly from the liquid, and notice the diminished 
brilliancy of the light emitted by the incandescent wire. By gradu- 
ally lowering the plate into the liquid as the cells weaken, the bril- 
liancy of the platinum wire may be kept nearly uniform. Notice the 
progressive oxidation of the wire. Try to continue the experiment 
until the wire breaks down by oxidation, noting the length of time 
taken. Repeat the work with No. 36 iron wire, and compare the 
lasting qualities of the two wires. 

327. Incandescence Lamps operate essentially on the prin- 
ciple illustrated in Experiment 227, the cur- 
rent being sent through some substance that, 
because of its high resistance, becomes in- 
tensely heated and brilliantly incandescent. 
The only suitable substance known for such a 
resistance is a carbon filament, which is en- 
closed in a glass bulb from which the air is 
exhausted to prevent combustion. The ends 
of the carbon filament are cemented to short 
platinum leading-in wires that are embedded 
in the glass by the fusion of the latter. 

(a) As incandescence lamps are generally connected in parallel, 
they require a heavy current at a comparatively low voltage. Such 
currents require large conductors that are generally made of copper. 
With lamps placed in parallel, the greater the number of lamps in use, 




Fig. 260. 



284 



ELEMENTARY PHYSICS. 



the less the resistance of the circuit. The current is usually operated 
at 110 volts, and each 16-c.p. lamp takes about 0.5 of an ampere. The 
expenditure is, therefore, nearly 3.5 watts per candle-power. 




Fig. 261. 

(b) Incandescence lamps are often placed on the secondary circuit 
of a " step-down " transformer, the primary circuit of which carries 
the high-voltage current of an alternator. The primary coils of 
several transformers may be put in series, or in multiple arc, as 
shown in Fig. 261. ' 

Caution. — In experimenting with an incandescence electric light- 
ing current, remember that a low 
resistance placed across the mains 
will receive an enormous current. 
IMany a galvauoscope and other 
piece of apparatus has been ruined 
in this way. Never " ground ** an 
electric lighting wire. 

328. The Voltaic Arc is the 
most brilliant luminous effect 
of an electric current. When 
carbon rods that form part of 
the circuit of a strong electric 
current are separated, the'r 
tips glow with a Irilliancj 
greater than that of any other 
light under human control, and 
the temperature of the inter- 
vening arc is unequaled hy 
that of any other source of 
artificial heat. 
Fig. 262. (a) When the carbons are sepa- 




SOME APPLICATIONS OF ELECTRICITY. 



285 



rated, the intervening layer of vaporized carbon becomes a con- 
ductor of very high resistance. The intense heat of the arc is due to 
the conversion of the energy of the current and not to combustion ; 
the arc may be produced in a vacuum where there could be no com- 
bustion. Tlie general appearance of the arc is shown in the accom- 
panying figure. Most of the light is radiated from the concave tip 
of the positive carbon. The 
arc may be studied by project- 
ing its image on a screen, or 
by looking at it through a 
piece of smoked glass or 
through several thicknesses of 
colored glass. 

329. The Arc Lamp is 

essentially a device for 
automatically separating 
the carbons when the 
current is turned on, for 
" feeding " the carbons 
together as they are 
burned away at their 
tips, and, in some cases, 
for short-circuiting the 
lamp in case of irregu- 
larity or accident. 

(a) Such lamps of from 
one to two thousand candle- 
power require a current of 
from 7 to 10 amperes, and 
have a potential difference be- 
tween the carbons of 45 to 
50 volts. They are generally 
operated in series, so that the current passes in succession through all 
the lamps on the circuit. As many as 125 such lamps have been 
thus worked on a single circuit. 




Fig. 263. 




286 ELEMENTARY PHYSICS. 

Electric Motors. 

Experiment 228. — Connect a small battery-motor (one may be 
bought for a dollar or less) to a number of cells joined iu series, and 

interpose a low resistance galvanoscope 
as indicated in Fig. 264. Hold the shaft 
of the motor to prevent its rotation, and 
note the reading of the galvanoscope. 
Then permit the motor shaft to revolve, 
and again note the reading of the gal- 
vanoscope. The resistance of the circuit 
seems to be greater when the armature 
is in motion than when it is at rest. 
Fio. 264. Dynamos and motors are often repre- 

sented by commutator circles and brushes, as in Fig. 264. 

330. An Electric Motor is a device for doing mechanical 
work at the expense of electric energy. As made for indus- 
trial use, it is generally similar to a dynamo in form and 
construction, and is often identical with it. 

(a) The current from a dynamo is' sent through the armature of 
the motor (the binding-posts of one machine being connected to the 
binding-posts of the other), and causes the mqtor armature to revolve 
in a direction opposite to that in which it wpuld revolve if the motor 
was acting as a dynamo. Any direct cuiTent dynamo will act as an 
efficient motor when it is supplied with a current of the same strength 
and potential as that which it yields when acting as a dynamo. The 
pulley on the armature shaft is belted or geared to other machinery. 

(6) The convenience, cleanliness, and economy of the electric motor 
have led to its common use for the operation of light macliinery, such 
as fly and ventilating fans, sewing-machines, lathes, printing-presses, 
etc. On the larger scale, the motor is used for the propulsion of 
sti-eet cars, and is even displacing the locomotive engine on some 
railways. As a generator and as a motor, the dynamo is revolution- 
izing more than one department of the industrial world. 

331. An Electric Bell consists mainly of an electromag- 
net, J5!, and a vibrating armature that carries a hammer, J?", 
that strikes a bell. One terminal of the magnet coils is con- 
nected to the binding-post, and the other terminal to the 



SOME APPLICATIONS OF ELECTRICITY. 



287 



flexible support of the 
armature. The arma- 
ture carries a spring 
that rests lightly 
against the tip of an 
adjustable screw at Q. 
This screw is con- 
nected to the other 
binding-post. The bell 
is connected to a bat- 
tery of two or three 
cells in series, a push- 
button, P, or some 
other device for closing the circuit being placed in the line. 

(a) When the circuit is closed by pushing the button at P, the 
magnet attracts the armature and causes the hammer to strike the 
bell. The continued action of the apparatus is like that of the vibra- 
tory interrupter of the induction coil, as explained in § 313 (6). 




Fig. 265. 




Fig. 266. 

Electrolysis. 

Experiment 229. — Arrange apparatus as shown in Fig. 266. The 
glass vessel may be made from a glass funnel, or by cutting the bottom 



288 ELEMENTARY PHYSICS. 

from a wide-mouthed bottle/ and may be supported in any convenient, 
way. The platinum electrodes should be about 2 cm. apart and cov- 
ered with water (HjO) to which a little sulphuric acid has been added 
to increase its conductivity. Fill two test-tubes with acidulated water, 
and invert them over the electrodes. When the circuit is closed, bub- 
bles of oxygen escape from the positive electrode, and bubbles of 
hydrogen from the negative. The volume of hydrogen thus collected 
will be about twice as gi'eat as that of the oxygen. When a sufficient 
quantity of the gases has been collected, they may be tested; the 
hydrogen, by bringing a lighted match to the mouth of the test-tube, 
whereupon the hydrogen will burn ; the oxygen, by thrusting a splin- 
ter with a glowing spark into the test-tube, whereupon the spark will 
kindle into a flame. If the gases thus separated are mixed, and an 
electric spark produced in the mixture, the ions will recombine with 
explosive violence. 

332. Electrolysis, etc. — The decomposition of a chemi- 
cal compound, called the electrolyte^ into its constituent 
parts, called tow«, by an electric current is called electroly- 
sis. When, for example, water is electrolyzed, the hydro- 
gen collects at the negative electrode, called the cathode ; 
such an ion is called a cation^ and is said to be electroposi- 
tive. The oxygen similarly collects at the positive elec- 
trode, called the anode ; such an ion is called an aniorij and 
is said to be electronegative. 

(a) In battery or in electrolytic bath, the metallic or electropositive 
ion is carried with the current through the electrolyte. Similarly, when 
a chemical salt is electrolyzed, the metallic base is carried to the cath- 
ode, while the acid constituent appears at the anode. The amount of 
chemical decomposition effected in a given electrolytic bath in a given 
time is proportional to the current strength. This principle has been 
utilized in devices for the commercial measurement of electric energy. 

Electrometallurgy. 
Experiment 230. — Fasten a copper wire to a silver coin, and a simi- 
lar wire to a piece of sheet copper of about equal size. Suspend 
the two pieces of metal in a tumbler containing a solution of copper 
sulphate. Connect the wire that carries the silver to the negative 



SOME APPLICATIONS OF ELECTRICITY. 289 

terminal of a strong battery of cells joined in parallel, and the other 
wire to the other terminal. Close the circuit, and notice that a firm, 
hard copper coating is deposited upon the silver. Reverse the current 
until the copper is removed from the silver. Then connect the cells of 
the batteiy in series, and notice that copper is deposited upon the silver 
as a spongy mass instead of a firm coating. 

333. Electrometallurgy is the art or the process of de- 
positing certain metals, such as gold, silver, and copper, 
from solutions of their compounds by the action of an elec- 
tric current. Its most important applications are electro- 
plating and electrotyping. Current for such processes is 
generally provided by specially constructed dynamos of low 
voltage. Such dynamos are called electroplating machines, 
or simply platers. 

Secondary Cells. 

Experiment 231. — Arrange apparatus as in Experiment 229. After 
the passage of the current for a few minutes, disconnect the battery 
and put a galvanoscope in its place. The deflection of the needle 
shows that the " water voltameter " is developing an electric current, 
and illustrating the reversibility of electrolytic action. 

334. A Secondary or Storage Battery is a combination 
of cells each of which consists essentially of two plates of 
metallic lead coated with red oxide of lead, and immersed 
in dilute sulphuric acid. When such a cell is " charged " 
by passing an electric current through it, the electrolysis 
of the liquid liberates oxygen and hydrogen. One of 
these ions peroxidizes the coating of one of the plates; 
the other ion reduces, i.e., deoxidizes, that of the other 
plate, thus storing up chemical energy to be given back 
as an electric current when the poles of the charged cell 
are connected, and the chemical action is reversed. Such 
a cell or battery is often called an accumulator. 

(a) In a charged secondary battery, the two plates are unlike, and 
the potential energy of chemical separation is converted into the 



290 



ELEMENTARY PHYSICS. 



kinetic energy of an electric current, just as with an ordinary or " pri- 
mary ** battery. When a secondary battery has run down, the passage 
of a current through it will restore the plates to their former effective 
condition ; when a primary battery has run down, a current will not 
thus restore the plates. 

(b) The condition of the plates of a charged secondary cell is 
closely analogous to that of the polarized plates of a primary cell. 
The ions have a tendency to reunite by virtue of their chemical affin- 
ity, and thus to set up an opposing E.M.F., as was illustrated in 
Experiment 231. 

Telegraph. 

Experiment 232. — Connect two telephone receivers, two batteries, 
and two keys as shown in Fig. 267. Both batteries are on open 
T 





Fig. 267. 

circuit. When the key is depressed at 2 or 3, and thus raised at 1 or 
4, clicks will be heard at T and R, Trace the path of tlie current in 
each case. It would be easy to devise a code of signals for communi- 
cation with such apparatus between two distant stations. 

Experiment 233. — Support a metal cylinder, C, upon an axle. Pivot 




Pia. 268. 



a metal bar at a (Fig. 268) so that the style, s, at its other end may 
rest upon the cylinder. Connect battery wires to the axle of the 



SOME APPLICATIONS OF ELECTRICITY. 



291 



cylinder, and at a, and interpose a key, K. Make a paste by boiling 
starch in water. Dissolve about 3 g. of potassiom iodide in 3 or 4 
cu. cm. of hot water, and add a little of the paste. Prepare a long 
ribbon of white paper, and soak it in the starch and iodide solution. 
While the paper is moist, fasten one end of it to a spool, 5, and turn 
the handle so as to draw the paper between the style and cylinder. 
While the pap^ is moving over the surface of C, make and break the 
circuit at /^ so as to inscribe a series of blue dots and dashes on the 
paper at $. With K at one station and 9 at another, it would be easy 
for a person at /^ to send a dot and dash message to a person at «. 
Consult the code of signals given in § 335, and, with your apparatus, 
write the word Morse, 

335. The Electromagnetic Telegraph is a device for 
transmitting intelligible messages at a distance by means 
of interrupted electric currents. It consists essentially 
of a line-wire or main conductor; a battery or dynamo 
for the generation of the current ; a transmitter or key ; 
and an electromagnetic receiving instrument. The sys* 
tern devised by Professor S. F. B. Morse about 1844 is still 
in general use. 

(a) The Morse code of signals is as follows : — 



a 

h 

C-- - 

d 


Lkttsbs, ktc. 

h 

/ 

tn 

n 


u 


Figures. 

2 

3 

4 


w 

X 


c- 


0' - 


y- -- 


5 


9 


P 

q 

r- -- " 


2 - 

5- 


6 

8 


t-- 


8 


f 


9 


j 


t — 


. 






To prevent confusion, a small space is left between successive letters, 
a longer one between words, and a still longer one between sentences, 
thus: — 



H e w i 1 1 



c o 



ten 




232 ELEMENTARY PHYSICS. 

(ft) A carefully iasulated wire connects the apparatus at the sev- 
eral stations. When the stations are far distant from each other, the 

ends of the line-wire are connected to 
large metallic plates buried in the 
earth (see Fig. 278), or otherwise 
"grounded." The current generator 
^generally consists of a dynamo, or of 
many gravity cells connected in series. 
The transmitter or key (Fig. 269) is 
Fig. 269. manipulated by the o[>erator for mak- 

ing and breaking the curi*ent at will. When it is not in use, the cir- 
cuit is closed at that station by the switch, s. In the early days of 
•telegraphy, a dot and dash record of the signals sent by the operator 
at the key was made by a register at the receiving station. The prin- 
ciple of this instrument is illustrated in Experiment 233. Such 
regis tei*s are little used nowadays, most operators reading by sound, 
i.e., determining the message from the clicks of a sounder, as will soon 
be explained. 

(c) In the Morse system, just described, a given wire can trans- 
mit only one message at a time. By what is known as the duplex 
system, a wire may be made to convey two messages, one each .way, 
at the same time, without conflict. By what is known as the quad- 
ruple! system, a wu*e may be made to carry four messages, two each 
way, at the same time. The multiplex system enables the sending of 
six or more messages in the same direction at one time. In the so- 
called i:apid system, the message is first prepared by punching a series 
of holes in a strip of paper, each peiioration or group of perforations 
representing a letter. This strip of paper is rapidly passed under 
metal points connected with the line-wire. At each perforation, a 
point passes through the paper and closes the circuit. At the other 
end of the line, a band of chemically prepared paper is drawn rapidly 
under a style connected with the line-wire. The current that is inter- 
rupted at the sending station makes a series of stains on the prepared 
paper at the receiving station, as is iUustrated in Experiment 2 ]3. 
As the transmission and recording are automatic, the messages may 
be sent in rapid succession. There are several telegraphic-printing 
systems, the object of which is to print the message directly upon 
paper as it is received. Facsimile teler/raphy has also been accom- 
plislied. In submarine telegraphy, the transmitted signals are made 
visible by a mirror galvanoscope (§ 323, d) used as a receiver. 



SOME APPUCATIONS OF ELECTRICITY. 



293 



The Sounder. 

Sxperiment 234. — Pat a key aud the apparatus shown in Fig. 236 
in series in the circoit of a voltaic cell. Kee^ng the Morse alphabet 
in mind, try to signal the word similarly used in Experiment 233. 
Ck>nsider a short intenral between two clicks to be a dot, and a 
longer interval to be 
a diish. 

336. The Sounder 

is a telegraphic re- 
ceiver consisting of 
an electromagnet, 
and a pivoted ar- 
mature that plays 
up and down be- ^ 
tween its stops as 
the circuit is alter- 
nately made and 

broken. The message is "read by sound,' 
clicks made by the armature. 




Fig. 270. 



i.e., from the 




Fig. 271. 



The Relay. 

Experiment 235. — Fasten a wire to the apparatus used in Experi- 
meut 234, so that when the armature descends, the free end of the 




294 ELEMENTARY THYSICS. 

wire will be dipped into mercury in the cup at c. Arrange apparatus 
as shown in Fig. 271, placing a sounder or a telephone receiver at Tl 
As the key is worked at K, the secondary or "local" circuit is made 
and broken at c, and clicks are produced by the instrument at T, 

337. The Relay. — With a long main line and many- 
instruments in circuit, the resistance may be so great 

as to render the 
main-battery 
current so fee- 
ble that it can- 
not operate the 
sounder with 
sufficient energy 
^'°-^^- to render the sig- 

nals distinctly audible. This diflBculty is met by intro- 
ducing a " local battery " and a " relay " at each station 
on the line. The relay is an electromagnet made of 
many turns of fine wire of which the terminals, a and 6, 
are connected with the main line. This magnet operated 
an armature lever, e, the end of which strikes against a 
metal contact-piece and thus closes the local circuit through 
the terminals, c and d. The " Westarn Union " standard 
relay has a resistance of 150 ohms. 

(a) The arrangement of instruments is best studied at a telegraph 
station, one or more of which may be found at almost any town 
or railway station. The general features of the " plant " are repre- 
sented by the diagram shown in Fig. 273. The pupil will probably 
find the key, sounder, and relay on a table, and the local battery, b, 
under the table. The keys being habitually closed, the current passes 
through all relays on the line, the current being continuous except 
when a message is being sent from some office. When an operator, 
in sending a message, opens his key, the breaking of the circuit 
demagnetizes the relays, and allows their springs to draw back the 
armature levers, e. This breaks each local circuit, and demagnetizes 
each sounder, the spring of which raises its armature. Things are 



SOME APPLICATIONS OF ELECTRICnT. 



295 



now as shown in the diagram, which 
also represents the condition of affairs 
at every other station on the line. 
When a message is sent from any sta- 
tion, each relay lever, e, acts as a key 
to its local circoit, it and the sounder 
armature working in correspondence 
with the motions of the key at the send- 
ing station. Of coarse, the message 
may be read from any sounder on the 
line. 

(ft) If the local circuit at New York 
(see Fig. 273) is lengthened so as to 
reach thence to Boston, and the local 
battery, ft, is increased to the size of a 
main battery, B (ground connections 
being made, of course), the relay at 
New York will transmit to Boston the 
message received from Cleveland. In 
such cases, the relay at New York be- 
comes a repeater. 




The Ucrophoiie. 

Experiment 236. — Put a telephone 
receiver in 
circuit with a 
battery and 
two electrio- 
light carbon 
pencils, as 
shown in Fig. 
274. Vary the 
resistance of 
the circuit by 
pressing the 
points of the 
pencils to- 




FiG. 274. 



gether, and notice the harsh, grating 
sound heard in the telephone. 




TiCL 273. 



296 



ELEMENTARY PHYSICS. 



338. The Microphone is an instrument for augmenting 
small sounds. Its action is based on the fact that when 
substances of low conductivity are placed in an electric 
circuit, the resistance of the circuit is diminished by even 
a very small pressure. 




Fig. 275. 



The Telephone is an instrument for the transmis- 
sion of articulate speech to a distant point by the agency of 
electric currents, 

(a) The Bell telephone receiver (see Fig. 226) is a niagnetoelectric 
device, and is represented in section by Fig. 275. -4 is a permanent 

bar magnet around one 
end of which is wound 
a coil, B, of carefully 
insulated fine copper 
wire. The terminals of 
B are connected to the 
binding-posts at D. A 
soft, flexible sheet-iron 
disk or diaphragm, E^ 
is held by a conical 
mouthpiece or ear trumpet across the face of By near to but not quite 
touching the end of ^4 . 

(6) Wlien a person speaks into the mouthpiece, the sound waves 
beat upon the diaphragm and cause it to vibrate. Each vibration of 
the diaphragm modifies the mag- 
netic circuit of the receiver, varying 
the lines of force that pass through 
B, and thus generating electric pulses 
in tlie wire when the circuit is closed. 
When E approaches B, a current 
flows in one direction ; when E 
moves the other way, the current 
flows in the opposite direction. 

(c) The cun*ents generated as 
just described may be sent through a similar instrument, at a consid- 
erable distance. As in the case of the telegraph, the earth may form 
a part of the circuit, but a return wire or complete metallic circuit is 




Fig. 276. 



SOME APPLICATIONS OF ELECTRICITY. 



297 



preferable. One of the insti-uments is used as a transmitter and the 
other as a receiver. The sound thus produced is feeble, but, when 
the receiving instrument is held close to the ear of the listener, the 
sound is clear, and the articulation remarkably distinct Conversation 
may be carried on between moderately distant stations with this appa- 
ratus, no batteiy being necessary. 

340. The Transmitter is a microphone adapted for the 
transmission of telephonic messages and, in general practice, 
is so used. 

(a) In the Blake transmitter, a diaphragm is supported back of 
a mouthpiece, as in the Bell telephone. Back of the center of the 
diaphragm is the point of a spring, m, that carries a small platinum 



LINE WIRE. 




ball that makes gentle contact with the diaphragm. Back of this 
is a spring, n, that is insulated from m, and that carries a carbon 
button, By that rests lightly against the platinum ball. The ball, the 
button, and the primary of an induction coil are put in series in 
the circuit of a voltaic battery, D, as shown in Fig. 277. The varia- 
tions in the resistance of this circuit, caused by the varyinjif pressure 
and surface contact between the platinum and the carbon, cause 
variations in the current that flows through the primary of the induc- 
tion coH, and thus induce currents in the secondary of the coiL These 
currents thus induced flow along the line-wire to the receiver at the 
other station, the connections being as shown in Fig. 277. Complete 
metallic circuits are preferable to earth connections, and are coming 
into general use. An electric bell is placed at each station. It is rung 
by a small magneto at the sending station for the purpose of ''calling 
up " the person at the other station. When the receiver, B, is lifted 



298 



ELEMENTARY PHYSICS. 



from the hook that carries it, as shown in Fig. 278, the upward motion 
of the hook cuts the magneto and the bells from the circuit, and com- 
pletes the connections substantially as 
^ shown in Fig. 277. 

(6) The long distance transmitter, 
represented in Fig. 278, differs from the 
Blake transmitter chiefly in the use of 
a carbon that is granular instead of hard, 
and in the use of two or three cells in- 
stead of one. 

(c) In most cities and villages, the 
telephones are connected by wires with 
a central station, called a telephone ex- 
change. Upon request by telephone, the 
attendant at the central station connects 
the line from any instrument with that 
running to any other instrument. Long 
distance telephony has been so nearly 
perfected that it is commo?i to carry on 
conversation between places as far dis- 
tant as Boston or Kew York and Chi- 
cago. 

341. A Lightning Rod is a metiil- 
lic conductor placed on a building 
as a protection from lightning. Its 
upper end should have several 
branches terminating in sharp 
points that are plated, or othei- 
wise protected from rust or corro- 
sion; it should be continuous and run to earth by the 
most direct path, avoiding sharp bends, and going deep 
enough to be sure of a good connection with a stratum 
that is always moist. Iron is as good as copper, and 
extent of surface* is of more importance than sectional 
area. 

(rt) When an electrified cloud floats over a building, the latter is 
oppositely electrified by induction. The electrification of the building 




Fig. 278. 



SOME APPLICATIONS OF ELECTRICITY, 299 

t from the pointed conductor, and tends to neutralize the eleo- 
trification of the cloud. Its action may proceed too slowly to keep 
down the rapidly rising potential of the cloud and to prevent the 
disruptive discharge, but even then the rod tends to protect the build- 
ing by offering a path of less resistance. The discharge does not 
always follow the path of least resistance, but the protection is 
probable. The discovery of the oscillatory character of the discharge 
has largely modified the character of the protection recommended. 

BXBRCISB8. 

1. A dynamo is feeding 16 arc lamps that have an average resist- 
ance of 4.56 ohms. The internal resistance of the dynamo is 10.55 
ohms. The resistance of the line-wire is inconsiderable. What 
current does the dynamo yield with an E.M.F. of 838.44 volts? 

Ans. 10.04 amperes. 

2. The current running through the carbon filament of an incan- 
descence lamp was found to be 1 ampere. The difference of potential 
between the two terminals of the lamp was found to be 30 volts. 
What was the resistance of the lamp? 

3. The resistance of the arc of an electric lamp is 3.8 ohms. The 
current strength is 10 amperes. What is the difference of potential 
between the carbon tips ? , Ans. 38 volts. 

4. The resistance of the arc lamp above mentioned, when the 
T^arbons are held together, is 0.62 ohm. When it is burning with 
normal arc and a 10-ampere current, what is the difference of potential 
between the terminals of the lamp? Ans. 44.2 volts. 

5. Upon trial, it was found that a dynamo that was known to have 
an internal resistance of 4.58 ohms developed a current of 157.5 volts 
and 17.5 amperes. What was the resistance of the external circuit? 

Ana. 4.42 ohms. 

6. Suppose that the armatures of two dynamos rotate at the same 
speed in fields of like intensity. The armatures differ only in that 
one has twice as many bobbins in series as the other. How will the 
dynamos compare in E.M.F. ? 

7. I have two telegraph sounders. One of them is made with a 
few turns of coarse wire; the other of many turns of fine wire. Try- 
ing them on a long line of great resistance, I find that one works 
satisfactorily while the other will not work at all. Which sounder 
works? Explain the difference in the results secured with the two 
instruments. 



300 ELEMENTARY PHYSICS. 

8. A telegraph line is to be operated between Boston and Chicago. 
The high resistance of so long a line requires a current of such high 
potential that there is great difficulty in maintaining the insulation. 
How may this difficulty be removed ? 



V. ELECTROMAGNETIC CHARACTER OF 
RADIATIOK 

342. Electromagnetic Waves. — Certain facts well known 
to physicists suggest with great force that there is some 
definite relation between electricity and light. It is pos- 
sible that the characteristic difference is in wave-length. 

(a) In recent years, Hertz and Tesla have experimented with these 
electromagnetic Waves, and have shown that they may be reflected, 
refracted, and polarized, and that they possess all the transmittive 
properties of radiant energy. They have also shown that their velocity 
is identical with that of light, and that indices of refraction are the 
same for electromagnetic waves as they are for the shorter waves that 
are familiarly recognized as radiant energy. 

343. The Hertz Experiments. — By methods that cannot 
be liere explained, Hertz, the first successfnl investigator 
in this field, was able to determine the periods of the 
electrical oscillations. To reduce the wave-length to con- 
venient values (say a meter or two), the oscillations were 
made rapid. 

Hertz found lihat non-conductors are transparent to the electric 
radiations, and that conductors act as reflectors. He found points of 
maximum and minimum disturbance corresponding to the loops and 
nodes of a vibrating string. The wave-lengths thus determined multi- 
plied by the frequency of vibration gave a velocity for electromagnetic 
wave propagation that is practicaVy the same as the velocity of light. 
Electromagnetic waves, that had passed through floors and walls, 
have been detected at a distance of hundreds of feet 



ELECTROMAGNETIC CHARACTER OF RADIATION. 301 

344. The Tesla Experiments. — By means of an oscUlator 
ill which the armature coils are shot, very rapidly and 
sbuttle^fashion, in and out of the magnetic field, Nikola 
Tesla generated alternating currents of higher frequency, 
potential, and regularity than any previously employed. 

(a) He has shown that such currents flow mostly on the outer sur- 
face of the conductor, as though ether vortices were rolled along the 
wire as a rubber band may be rolled along a pencil. He led a small 
cable around the walls of a room 40 x 80 feet in size, and connected 
its ends to the terminals of an oscillator. In the middle of the room 
he placed a coil-wound resonator, provided with two adjustable con- 
denser plates. By adjusting the condenser plates, the resonator was 
so attuned that the frequency of the induced current kept step with 
that of the cable current. When current from the oscillator was sent 
along the cable ai-ound the room, powerful sparks poured in dense 
streams across the space between the cymbal-like plates of the attuned 
condenser in the middle of the room. A potential difference of 
200,000 or 300,000 volts is easily developed in this way, and energy 
transmitted throuyhfree space, i.e., without any wire. 

345. Cathode Rays. — The gaseous molecules that strike 
the negatively charged electrode of a.Crookes tube become 
electrified and are thrown off. It is supposed that, in the 
high vacuum of the tube, many of the electrified molecules 
are actually projected without collision across the tube, 
striking the glass opposite the cathode. This stream of 
electrified particles constitutes the cathode rays, 

(a) The particles move in straight lines from the cathode, exert 
mechanical force, produce heat where they strike, are deflected by a 
magnet, and produce beautiful phosphorescent and fluorescent effects. 
Diamonds and rubies glow brightly when subjected to this discharge, 
tind the glass of the tubes fluoresces with a greenish color. The 
cathode rays of themselves are not luminous, but seem to be inti- 
mately connected with light. 

346. X Rays. — Roentgen discovered that rays from an 
excited Crookes tube produced fluorescence even when 



302 ELEMENTARY PHYSICS. 

opaque substances were interposed between the tube and 
llie fluorescent paper. 

(a) When he placed his hand between the shielded tube and the 
paper, he found that the effect penetrated the hand^ the flesh offering 
less resistance than the bones, and thus casting a shadow of the bones 
upon the paper. He then substituted a photographic plate for the 
fluorescent paper, and succeeded in photographing the bones of his 
hand. In experiments of this kind, the prepared photographic plate 
is placed in an ordiiiai-y plate-holder, a light-proof case with a cover of 
dense pasteboard or thin, hard rubber. The object to be photographed 
is placed upon this coyer as near as possible to the photographic plate, 
1)0 camera being used. If a hand or arm is to be photographed, a few 
bandages holding it to the plate-holder avoid movement during the 
period of exposure, reduce the personal fatigue, and do not interfere 
with the results obtained ; the bandages, plate-holder, etc., are trans- 
parent to the X rays. The plate is placed' a few inches from the 
Crookes tube, as shown in Fig. 279, which shows the arrangement of 
the several parts of the aj^paratus. 

Roentgen showed that the effect apparently proceeds from the tube 
in straight lines, like rays ; that .opacity to these rays increases with 
the thickness of the objects, and usually with their density. These 
'* rays " are invisible to the eye, and do not produce any heat effects ; 
they are incapable of reflection or refraction ; they cannot be polarized, 
and are not deflected by a magnet. They seem to originate where 
the cathode rays first strike an object. To the unknown cause of 
this new effect. Roentgen gave the name of ** X rays," suggesting, 
however, that they might be due to longitudinal ether-waves. 

347, The Electromagnetic Theory of Light. — Optical 
and electrical phenomena seem to call for media that have 
identical properties; i.e., they indicate that the medium 
of the one is identical with the medium of the other, and 
that to produce radiation, it is only necessary to produce 
electric oscillations of sufficiently short period. This 
theory of light as an electromagnetic disturbance was pro- 
pounded in 1865 by Maxwell; if recent investigations do 
not wholly establish it, they certainly give it very strong 
support. 



304 ELEMENTARY PHYSICS. 

(a) The theory that electromagnetic waves and light waves differ 
only in wave-length is winning its way among physicists. The 
" chasm " between them is growing narrower and narrower ; i.e., the 
length of the shortest electromagnetic wave known does not exceed 
the length of the longest infrarred wave known as much as it did a 
few years or months ago. Electromagnetic waves only six millimeters 
long have already (1897) been produced. The ability to produce and 
to recognize these " electrical waves ** underlies the art of wireless 
telegraphy, etc. 

848. Yesterday, To-day, To-morrow. — It seems fitting 
to suggest that constant study is the price of a clear under- 
standing of conditions that prevail in the domain of elec- 
tricity. "Its theoretical problems assume novel phases 
daily. Its old appliances ceaselessly give way to suc- 
cessors. Its methods of production, distribution, and 
utilization vary from year to year. Its influence on the 
times is ever deeper, yet one can never be quite sure into 
what part of the social or industrial system it is next to 
thrust a revolutionary force. Its fanciful dreams of yes- 
terday are the magnificent triumphs of to-morrow, and its 
advance toward domination in the twentieth century is as 
irresistible as that of steam in the nineteenth." 



APPENDIX. 



1. Mensarative, etc. 

v= 3.14159. 

Circumference of a circle = irD, 

Area of a circle = irRK 

Surface of a sphere = 4 irR^ = irD\ 

Volume of a sphere = J irR^ = J irD*. 

Meters x 3.2809 = feet. 

Feet X 0.3048 = meters. 

Inches x 2.54 = centimeters. 

Cubic inches x 16.386 = cubic centimeters. 

Cubic centimeters x 0.06103 = cubic inches. 

Kilograms x 2.2046 = pounds. 

Kilograrameters x 7.2331 = foot-pounds. 

2. Table of Resistivities. — Represent the length of a conducting 
wire measured in feet by /, its diameter measured in thousandths of 
an inch (mils) by rf, and its resistance measured in ohms by r. In the 
formula 

K represents a constant that depends upon the material of th6 wire 
and, for the substances considered, is as given in the following table 
of resistivities : — 



Silver . 9.84 

Copper 10.45 

Zinc 36.69 



Mercury 58.24 

Platinum 59.02 

Iron 63.35 



German-silver 128.29 

These values of K are computed for the temperature of 20®. Thus 
the resistance of 1,000 feet of No. 0000 copper wire at 20% is 
10.45 X 1,000 + 460* = 0.049 + ohms. 
X 306 



806 ELEMENTARY PHYSICS. 

3. Dimensions and Functions of Copper Wires.— In the table given 
on the next two pages, the second column gives the diameters in mils, 
i.e., thousandths of an inch ; the third column in millimeters. The 
fourth column gives the equivalent number of wires each one mil in 
diameter. By multiplying the numbers in the sixth column by 5.28, 
the resistances per mile may be found. The resistance for any other 
metal than copper may be found by multiplying the resistance given 
in the table by the ratio between the resistivity of copper and that 
of the given metal (see section 2). The resistances given in the 
table are for pure copper wire. Ordinary commercial copper wire has 
a lower conductivity than that of pure copper. Consequently, the 
resistances of such wires will be greater than those given in the table. 



APPENDIX. 



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308 



ELEMENTARY PHYSICS 



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APPENDIX. 



301) 



4. Table of Natural Tangents. 



Arc. 


Tangent. 


Aec. 


Tangent. 


Aec. 


Tangent. 


Aec. 


Tangent. 


0° 


0.000 


23° 


0.424 


46° 


1.036 


69° 


2.61 


1 


0.017 


24 


0.445 


47 


1.07 


70 


2.75 


2 


0.035 


25 


0.466 


48 


1.11 


71 


2.90 


3 


0.052 


26 


0.488 


49 


1.15 


72 


3.08 


4 


0.070 


27 


0.510 


50 


1.19. 


73 


3.27 


5 


0.087 


28 


0.532 


51 


1.23 


74 


3.49 


6 


0.105 


29 


0.554 


52 


1.28 


75 


3.73 


7 


0.123 


30 


0.577 


53 


1.33 


76 


4.01 


8 


0.141 


31 


0.601 


54 


1.38 


77 


4.33 


9 


0.158 


32 


0.625 


55 


1.43 


78 


4.70 


10 


0.176 


33 


0.649 


56 


1.48 


79 


5.14 


11 


0.194 


34 


0.675 


57 


1.54 


80 


5.67 


12 


0.218 


35 


0.700 


58 


"1.60 


81 


6.31 


13 


0.231 


36 


0.727 


59 


1.66 


82 


7.12 


14 


0.249 


37 


0.754 


60 


1.73 


83 


8.14 


15 


0.268 


38 


0.781 


61 


1.80 


84 


9.51 


16 


0.287 


39 


0.810 


62 


1.88 


85 


11.43 


17 


0.306 


40 


0.839 


63 


1.96 


86 


14.30 


18 


0.325 


41 


0.869 


64 


2.05 


87 


19.08 


19 


0.344 


42 


0.900 


65 


2.14 


88 


28.64 


20 


0.364 


43 


0.933 


66 


2.25 


89 


57.29 


21 


0.384 


44 


0.966 


67 


2.36 


90 


Infinite. 


22 


0.404 


45 


1.000 


68 


2.48 







810 



ELEMENTARY PHYSICS. 



S. Table of Natural Sines. 



Arc. 


SiNB. 


Abo. 


8lMB. 


Arc. 


SiNB. 


Arc. 


SlKB. 


(P 


0.000 


23*» 


0.391 


46** 


0.719 


69« 


0.934 


1 


0.017 


24 


0.407 


47. 


0.731 


70 


0.940 


2 


0.035 


25 


0.423 


48 


0I743 


71 


0.946 


3 


0052 


26 


0.438 


49 


0.755 


72 


0.951 


4 


0.070 


27 


0.454 


60 


0.766 


73 


0.956 


5 


0.087 


28 


0.469 


51 


0.777 


74 


0.961 


6 


0.105 


29 


0.485 


52 


0.788 


75 


0.966 


7 


0.122 


30 


0.500 


53 


0.799 


76 


0.970 


8 


0.139 


31 


0.515 


54 


0.809 


77 


0.974 


9 


0.156 


32 


0.530 


55 


0.819 


78 


9.978 


10 


0.174 


33 


0.545 


56 


0.829 


79 


0.982 


11 


0.191 


34 


0.559 


57 


0.839 


80 


0.985 


12 


0.208 


35 


0.574 


58 


0.848 


81 


0.9.88 


13 


. 0.225 


36 


0.588 


59 


0.857 


82 


0.990 


14 


0.242 


37 


0.602 


60 


0.866 


83 


0.993 


15 


0.259 


38 


0.616 


61 


0.875 


84 


0.995 


16 


0.276 


39 


0.629 


62 


0.883 


85 


0.996 


17 


0.292 


40 


0.643 


63 


0.891 


86 


0.998 


18 


0.309 


41 


0.656 


64 


0.899 


87 


0.999 


19 


0.326 


42 


0.669 


65 


0.906 


88 


0.999 


20 


0.342 


43 


0.682 


66 


0.914 


89 


0.999 


21 


0.358 


44 


0.695 


67 


0.921 


90 


1.000 


22 


0.375 


45 


0.707 


68 


0.927 







INDEX. 



Numbers refer to Pages unless otherwise indicated. 



Absolute unit of force, 32. 

zero, 136. 
Absorption of radiation, 195. 
Acceleration, 29. 

due to gravity, 51. 
Accumulator, Electric, 289. 
Achromatic lens, 187. 
Acoustics, 99. 
Activity, 42. 
Adhesion, 16. 
Aeriform body, 20. 
Agonic lines, 247. 
Air, 87, 88. 

Air columns. Vibratory, 130. 
Alternating currents, 262. 
Alternator, 257. 
Amalgamating zinc, 220. 
Ammeter, 278. 
Ampere, 227. 
Ampere's theory of magnetism, 

245. 
Ampere-turns, 243. 
Amplitude of oscillation, 56. 

of vibration, 103. 
Anion, 288. 
Anode, 288. 
Anti-nodes, 118. 
Archimedes, 78, 80. 
Arc lamps, 286. 
Armature of dynamo, 257. 

of magnet, 234. 
Astatic needle, 236. 



Atmospheric electricity, 278„ 

pressure, 89, 90. 
Atom, 8. 
Axis of lens, 180. 

of mirror, 171. 



Balance, 64. 
Barometer, 90. 
Base, 47. 

Beam of rays, 157. 
Beats, Acoustic, 126. 
Bells, Electric, 286. 

Vibrations of, 132. 
Blake transmitter, 297. 
Block and tackle, 6S, 
Body, 7. 

Boiling-point, 135, 146. 
Boyle's law, 92. 
Burning-glass, 176. 



Calipers, 19. 
Calorescence, 196. 
Calorimetry, 149. 
Calory, 149. 
Candle, Standard, 165. 
Capacity, Electrical, 216. 

Thermal, 151. 
Capillary attraction, 24. 

tubes, 25. 
Capstan, 67. 
Cathode, 288. 

rays, 301. 



311 



312 



ELEMENTARY PHYSICS. 



Numb€r» rtfw to PagM uhUm oUurwUe indicated. 



Cation, 288. 
Center of mass, 47. 
Centrifugal force, 39. 
C.G.S. units, 32. 
Cliarge, Electric, 210, 213. 
Chemical changes, 9. 

effects of electric current, 288. 

effects of radiation, 195. 
Chladni plates, 132. 
Chords, Musical, 116. 
Chromatic aberration, 187. 

scale, 116. 
Chromatics, 188. 
Coefficient of expansion, 142. 

of self-induction, 264. 
Cohesion, 16. 
Coincident waves, 121. 
Color, 188. 
Commutator, 259. 
Complementary colors, 189. 
Condensation of gas, 146. 
Conduction, Electric, 211. 

Thermal, 138. 
Conductivity, Electric, 209. 
Conjugate foci, 109, 172. 
Oonvection, 140. 

Electric, 213. 
Coulomb, 228. 
Co-vibration, 121. 
Critical angle, 178. 
Crookes tubes, 271. 
Crova disk, 107. 



Declination, Magnetic, 246. 
Density of matter, 82. 

Electric, 213. 
Diamagnetic, 234. 
Diatonic scale, 115. 
Dielectric, 210. 
Diffraction, 199. 
Diffusion of gases, 25. 

of heat, 138. 
Dip, Magnetic, 246. 



Dipping-needle, 236. 
Dispersion of light, 186. 
Distance, Estimation of, 203. 
Distillation, 147. 
Divisions of matter, 8. 
Double refraction, 199. 
Dynamo, 256. 
Dynamometer, 33. 
Dyne, 32. 



Ebullition, 145, 146. 

Echoes, 109. 

Efficiency of machines, 62. 

Elastic force of gases, 91. 

Elasticity, 15, 38. 

Electric action. Laws of, 212. 

bells, 286. 

capacity, 216. 

circuit, 224. 

condenser, 216. 

current, 221, 223, 255, 262. 

discharge, 272. 

field, 214. 

generators, 248. 

induction, 216. 

lighting, 283, 285. 

lines of force, 214. 

machines, 267. 

measurements, 276. 

pendulum, 208. 

units, 212, 276. 

waves, 300. 
Electricity, 208. 

Atmospheric, 273. 

Nature of, 218. 
Electricity, CuiTent, 220. 

Frictional, 208. 

Static, 208. 

Voltaic, 220. 
Electrification, 209, 210, 214, 218. 
Electrodes, 224. 
Electrodynamics, 232. 
Electrolysis, 288. 



INDEX. 



313 



Numb€r9 refer to Pages tmless othertoiae indicated. 



Electromagnet, 244. 
Electromagnetic induction, 255. 

radiation, 300. 

telegraph, 291. 

theory of light, 303. 

units, 212, 276. 

waves, 300. 
Electrometallurgy, 289. 
Electromotive force, 215, 281. 
Electrophorus, 267. 
Electroplating, 289. 
Electroscope, 211. 
Electrostatic units, 212. 
Electrotyping, 289. 
Energy, 7, 40, 42. 

Conservation of, 45. 

Measurement of, 44, 45. 

Radiant, 157. 
Equilibrant, 34. 
Equilibrium, 47. 
Equipotential surfaces, 215. 
Erg, 41. 
Ether, 157. 
Evaporation, 145. 
Expansion, 140. 
Extension, 11. 
Eye, The human, 202. 

P. 

Falling bodies, 49. 
Farad, 216. 
Field magnet, 259. 
Flats and sharps, 116. 
Flotation, 81. 
Fluid, 20. 
Fluorescence, 196. 
Flux of force, 238. . 
Focus, 109, 171, 181, 183. 
Foot-pound, 41. 
Foot-poundal, 41. 
Force, 10. 

Centrifugal, 39. 

Composition of, 35. 

Graphic representation of, 33. 



Force, Measurement of ^ 32. 

Moment of, 63. 

Parallelogram of, 35. 

Resolution of, 37. 
Foucault currents, 258. 
F.P.S. units, 32. 
Fraunhofer lines, 194. 
Freezing-point, 135. 
Friction, 62. 

Frictional electric machine, 268. 
Fundamental tones, 117. 
Fusion, 145. 

Latent heat of, 150. 

G. 

Galvanometer, 276. 

Galvanoscope, 225, 252. 

Gamut, 115. 

Gas, 20. 

Gases, Kinetic theory of, 26. 

Mechanics of, 87. 
Gauss, 239. 
Geissler tube, 271. 
Gilbert, 243. 
Graduate, 12. 
Gram, 13. 

Graphic study of sound, 108. 
Gravitation, 46. 
Gravity, 46. 

Center of, 47. 

unit of force, 32. 



Halo, 199. 
Hardness, 16. 
Harmonic motion, 103. 
Harmonics, 117. 
Hearing, 114. 
Heat, 8, 134. 

Diffusion of, 138. 

Latent, 149. 

Mechanical equivalent of, 153. 

Production of, 138. 

Sensible, 149. 



314 



ELEMENTARY PHYSICS. 



ITuniberB refer to Pages 

Heat, Specific, 151. 

units, 149. 
Hertz experiments, 300. 
Homogeneous light, I8d. 
Horse-power, 42. 
Hydraulic press, 74. 
Hydrometer, 84. 
Hypothesis, 9. 

I. 

Images, 161, 173, 184. 
Impedance, 264. 
Incandescence lighting, 283. 
Inclination, Magnetic, 246. 
Inclii^d plane, 68. 
Index of refraction, 177. 
Induced electric currents, 255. 
Induction coil, 265. 

Electric, 216. 

Electromagnetic, 252. 

M^tgnetic, 240. 

Self, 263. 
Inertia, 14. 

Center of, 47. 
Insulators, 209. 
Intensity of sound. 111, 112; 
Interference of radiation, 198. 

of sound, 125. 
Intervals, Musical, 114. 
Ions, 288. 
Isoclinic lines, 246. 
Isodynamic lines, 247. 
Isogonic lines, 246. 

J. 

Joule, 228. 

Joule's principle, 153. 



Kathode, see Cathode. 
Ration, sre Cation, 
keynote, 115. 
Kitogram, 12. 
Kilogrammeter, 41. 



unlsM oihervfise indietUed. 

Kinetic energy, 42, 43. 
theory of gases, 26. 



Law, 9. 
Lens, 179. 
Lever, 62. 
Leyden jar, 217. 
Lightr, 158. 

Analysis of, 186. 

Electromagnetic theory of, 303. 

Intensity of, 163. 

Velocity of, 162. 
Lightning, 273. 

rod, 298. 
Liquefaction, 144. 
Liquid, 20. 

Liquids, Mechanics of, 72. 
Local action, 248. 

currents, 258. 
Lodestone, 234.. 

M. 

Machines, 61. 

Efficiency of, 62. 

Laws of, 61. 
Magdeburg hemispheres, 88. 
Magic lantern, 206. 
Magnet, 234. 

Field, 259. 
Magnetic field, 236. 

lines of force, 238. 

needles, 236. 

phantom, 237. 

substances, 234. 
Magnetism, 233. 
Residual, 245. 
Magnetization, 234, 239. 
Magneto, 255. 
Magnetomotive force, 243. 
Magnifying glass, 203. 

power, 203. 
Manometric flames, 120. 
Mariotte law, 93. 



INDEX. 



315 



Nvmhera rtfer to Poqm wUs^s piherwiae indicated. 



Mass, 8, 12. 

Center of, 47. 
Matter, 7. 

Conditions of, 20. 

Divisions of, 8. 

Properties of, 11. 

Structure of, 7. 
Mechanical equivalent of heat, 153. 
Mechanics, 29. 
Megolim, 226. 
Melting-point, 144. 
Microfarad, 216. 
Microhm, 226. 
Microphone, 206. 
Microscope, 203. 
Milliampere, 227. 
Mirror, Concave, 171. 

Convex, 174. 

Plane, 170. 
Molecular attraction, 16. 

motion, 8. 
Molecules, 8. 
Moment of force, 63. 
Momentum, 31. 
Monochromatic light, 188. 
Morse alphabet, 291. 
Motion, 8, 29. 

Curvilinear, 39. 

Forms of, 8. 

Laws of, 31. 

Reflected, 38. 
Motors, Electric, 286. 
Multiple arc, 224, 251. 
Music and noise, 126. ' 
Musical intervals, 114. 

scale, 114. 

N. 

Natural philosophy, 7. 
Newton's laws of motion, 31. 

rings, 198. 
Nicol prism, 201. 
Nodes, 117. 
Noise and music, 126. 



Obscure heat, 195. 
Octave, 115. 
Oersted, 244. 
Ohm, 226. 
Ohm's law, 228. 
Opacity, 160. 
Opera glass, 205. 
Optical angle, 203. 

lantern, 206. 

study of sound, 119. 
Oscillation, Center of, 58. 

of pendulum, 56. 
Oscillatory electric discharge, 272. 
Overtones, 116. 



Paramagnetic, 234. ' 

Partial tones, 117. 

Pascal, 73. 

Pencil of rays, 157. 

Pendular motion, 102. 

Pendulum, 55. 

Penumbra, 161. 

Period of oscillation, 56, 57. 

of vibration, 103. 
Permeability, 243. 
Phenomenon, 9. 
Phosphorescence, 196. 
Photometry, 166. 
Physical changes, 9. 
Physics, 7. 
Piano scale, 116. 
Pigments, Mixing, 190. 
Pipe instruments, 131. 
Pitch of sounds, 113, 114. 
Plater, 289. 
Plates, Vibrations of, 132. 

of voltaic cell, 224. 
Pneumatics, 87. 
Polar iscope, 201. 
Polarization of cell, 248. 

Magnetic, 240. 

of radiation, 200, 300. 



816 



ELEMKNTARY PHYSICS. 



Kumbern refer to Pages unUw othertciae indicated. 



Poles, Magnetic, 234, 239. 

of voltaic cell, 224. 
Porosity, 14. 
Porte lumiftre, 167. 
Potential, Electric, 214, 281. 

energy ,\42, 44. 

Magnetic, 239. 
Poundal, 32. 
Power, 6V 

Pressure, Fluid, 73, 89. 
Prism, 179. 
Projectiles, 63. 
Proof- plane, 212. 
Properties of matter, 11. 
Pulley, 67, 72. 
Pumps, 96. 

Q. 

Quality of sound, 11& 



Radiant energy, 167. 

heat, 196. 
Radiation, 167. 

Intensity of, 163. 
Rainbow, 190. 
Ray, 157. 
Reactance, 263. 
Reaction, 38. 
Reflection of motion, 38. 

of radiation, 106, 195, 300. 

of sound, 109. 

Total, 178. 
Refraction, Double, 397, 399. 

Index of, 177. 

of radiation, 175, 300. 

of sound, 110. 
Regelation, 148. 
Relay, Telegraph, 294. 
Reluctance, 244. 
Reluctivity, 244. 
Repeater, Telegraph, 296. 
ResistaTice coils, 279. 

Electric, 226, 226, 249, 280. 



Resistance, Magnetic, d44« 
Resistivity, 2^7, 305. 
Resonance, Acoustic, 124. 
Resultant, 34. 
Rhumkorff coil, 265. 
Rods, Vibrations of, 1^1. 
Roentgen rays, 302. 



Scales, Musical, 114. 

Science, 7. 

Screw, 70. 

Secondary .isells, 289. 

Self-induction, 263. 

Shadows, 161. 

Sharps and flats, ll6. 

Shunt, '229. 

Sines, Natural, 310. 

Siphon, 98, 94. 

Siren, 113. 

Size, Estimation of, 203. 

Solenoid, 232, 242. 

Solid, 20. 

Solidification, 144. 

Solution, 21. 

Sonometer, 123. 

Sound, 99. 

Sounder, Telegraph, 293. 

Specific gravity, 83. 

heat, 151. 

magnetic resistance, 244. 

resistance, 22(^. 
Spectroscope,; 192. 
Spectrum, 187, 191, 193, 194. 

analysis, 192. 
Spheroidal state, 147. 
Spy-glass, 206. 
Stability, 48. 
Steam-engine, 164. 
Stereopticon, 206. 
Still, 148. 

SU)rage battery, 289. 
Strain ahd stress, 16. 
Strings, Vibratory, 128. 



INliEX. 



317 



Kumh^n r$ftt to PtigM unless otherwise indicated. 



Structure of matter, 7. 
Sublimation, 147. 
Substance, 7. 
Surface tension, 23. 

viscosity, 22. 
Sympathetic vibrations, 122. 



Tangents, Natural, 309. 
Telegraph, 21H, 304. 
Telephone, 255, 296. 
Telescope, 201. 
Temperament, 116. 
Temperature, 134. 

Absolute zero of, 136. 
Tenacity, 17. 

Terrestrial magnetism, 246. 
Tesla experiments, 301. 
Theory, 9. 
Therm, 149. 

Thermal effects of electric current, 
229. 

effects of radiation, 195. 

unit, 149. 
Thermo-electricity, 273. 
Thermometer, 135. 
Thermoscope, 135, 274. 
Thunder, 273. 
Timbre, 118. 
torpedo, 233. 
Torricelli, 89. 
Tourmaline tongs, 199. 
Transformer, 264. 
Transparency, 159. 



Umbra, 161. 



U. 

V. 

Vapor, 20. 
Vaporization, 146. 



Vaporization, Latent heat of, 161. 
Variation, Magnetic, 246. 
Velocity, 29. 

of sound, 107. 
Vibrations, 102, 128. 
Vibroscope, 119. 
Visual angle, 203. 
Volt, 227. 
Voltaic arc, 284. 

battei-y, 224, 250. 

cell, 221, 248. 
Voltmeter, 278. 

Water-hammer, 50. 
Water power, 85. 
Watt, 42, 228. 
Wattmeter, 278. 
Wave forms, HI, 118. 

length, 104, 188. 

motion, 100, 104. 
W^ber, 238. 
Wedge, 70. 
Weight, 12, 46, 61. , 

Law of, 47. 

Measurement of, 12. 
Wheatstone bridge, 280. 
Wheel and axle, 66. 
Wimshurst electric machine, 268. 
Windlass, 66. 
Wire gauge, 19. 

Table of dimensions, etc., 307. 
Wiring for electric lights, 283. 
Work, 40. 



X rays, 301. 



I Zinc, Amalgamation of, 220. 



F