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PRINCIPLES OF PHYSICS

FRANK M. GILLEY

CHBUBA HiaH\BCHOOI.

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Boston

ALLYN AND BACON
1901

TfHE NEW Yjr\K
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J. a Cufhing & Co. - Berwick &
Norwood Mam. U.S.A.

PREFACE.

In addition to acknowledgments made in the text, the author
desires to express his thanks to many who have assisted him
in the preparation of this work; more especially to Charles D.
Jenkins, Massachusetts State Inspector of Gas Metres and
Illuminating Gas, for suggestions in Photometry; to F. C.
Morton, in Steam Engines and Friction ; to N. H. Black, Rox-
bury Latin School, apparatus in Conjugate Foci; to I. 0.
Palmer, Newton High School, apparatus for Composition of
Forces ; the Westinghouse Air Brake Company, in Coefficient
of Friction. Mr. I. 0. Palmer and Mr. E. P. Churchill have
read portions of the manuscript, and Mr. C. B. Hersey has read
the manuscript and proofs of the entire book.

While the great body of scientific literature has been drawn
upon for suggestions, the author would mention the works of
John Perry and S. P. Thompson as particularly helpful.

J ChBLSBA, BfX88.,

August, 1901.

I
I

FRANK M. GILLEY.

iil

REFERENCE BOOKS.

Carhart's University Physics.

Watson's Text-Book of Physics,

Ame's Laboratory Manual.

Trowbridge's What is Electricity f

How Two Boys made their own Electrical Apparatus,

Taylor's Optics of Photography,

Orford's Lens Grinding.

Bottone's Wireless Telegraphy.

Lodge's Signalling without Wires.

C. V. Boy's Soap Bubbles,

Perry's Spinning Tops.

Avery's A. B. C. of Dynamo Design.

Ayrton's Practical Electricity.

Thompson's Elementary Lessons in Electricity and Magnetism.

Thompson's Light, Visible and Invisible.

The following journals contain articles of interest to students of
Physics : —

American Machinist. Scientific American.

Electrical Beview. American Electrician.

Model Engineer and Amateur Electrician.

The following are a few of the many firms that issue trade catalogues
containing instructive illustrations and descriptions : —

Carbonindum Co., Pittsburg, Pa.

Bausch & Lomb, Rochester, N.Y. ) _. _ _ ,

„_ - ^ /Ml 1 J /v } Binocular Telescopes.

Warner & Swazey, Cleveland, O. i

Nat. Tufts Meter Co., Boston, Mass. Photometer.

Economy Hot-air Engine, 4 Oliver St., Boston, Mass. 1 „ , . -, .
„.,-,. t:, . %, XT xr 1 \ Hot-air Engines,

Rider Ericson Engine Co., New York. i

Holoplane Glass Co., New York.

Luxfer Prim Co., Boston, Mass.

General Electric Co.

Westinghouse Electric Co.

The address of many others are in the various scientific papers.

CONTENTS.

OHAFTBB PAGK

L Density — Specific Gravity. (Exercises 1-7) . . 1

II. Pressure -; . . . 19

IlL Liquids and Gases. (Exercises 8-11) . . . . 34

IV. Forces. (Exercise 12) . , 66

V. Friction. (Exercise 13) 76

VL Parallel Forces. (Exercises 14, 16) . . . . 86

VII. Machines — Pulleys 99

VIII. Work. (Exercises 16, 17) 107

IX. Centre of Gravity. (Exercise 18) . . . .119

X. Weight and Mass 130

XI. Velocity. (Exercise 19) 140

Xn. Elasticity. (Exercises 20-23) 162

XIU. Heat. (Exercise 24) 176

XIV. Thermometers. (Exercises 25-29) . . . . 190

XV. Evaporation and Boiling. (Exercises 30-33) . 212

XVI. Expansion of Gases — Law -of Charles. (Exercises

34,35) 236

XVII. Thermodynamics. (Exercise 36) 244

XVIIL Light — Reflection. (Exercises 37, 38) ... 264

XIX. Light — Refraction. (Exercises 39-47) . . . 276

XX. Lenses. (Exercises 48-54) 298

XXL Curved Mirrors. (Exercises 66, 66) .... 326

XXII. Dispersion of Light 331

XXIIL Photometry. (Exercise 57) 340

XXIV. Optical Instruments 348

XXV. Sound. (Exercise* 68-60) 362

XXVI. Electricity — Magnets. (Exercises 61-64) . . 382

XXVII. Batteries. (Exercises 65, 66) 404

XXVIII. Magnetic Action of Electric Current. (Exercises

67, 68) 424

XXIX. Measurement of Electric Current .... 433

XXX. Ohm^s Law — Resistance. (Exercise 69) . . . 443

XXXI. Measurement of Resistance. (Exercises 70, 71) . 469

XXXn. Internal Resistance of Batteries — Grouping of

Cells — Storage Cells. (Exercises 72, 73) . . 468
v

vi coNTByrs.

OHAPTIB PACK

XXXIII. Blbctromagkbts — Induced Curbbnts — Dynamos

AND Motors — The Induction Coil. (Exercises

74-80) 482

XXXIV. Signalling through Ocean Cables .... 612
XXXV. Practical Applications of Electricity , 616

Appendix 53X

Index 546

LIST OF EXERCISES

CORRESPONDING TO THOSE REQUIRED FOR ADMISSION
TO HARVARD COLLEGE.

(NomeralB at the left of the page, not preceded by S, refer to Exercises.)

MECHANICS AND HYDROSTATICS.
1. Weight of Unit Volume of a Substance

2. Lifting Effect of Water upon a Body entirely immersed in it
8. Specific Gravity of a Solid Body that will sink in Water .
4. Weight of Water displaced by a Floating Body .
1 16. Specific Gravity by Flotation Method ....

6, 6. Specific Gravity of a Block of Wood by Use of a Sinker 16, 16

7. §46. Specific Gravity of a Liquid : Two Methods . 17, 36

12. Parallelogram of Forces 66

18 a. Friction between Solid Bodies (on a level) .... 76
18 6. Coefficient of Friction (by sliding on incline) .... 80

14. The Straight Lever : First Class 85

14. Levers of the Second and Third Classes 85

14. Force exerted at the Fulcrum of a Lever 85

App. Errors of a Spring-balance 536

18. Centre of Gravity and Weight of a Lever . . . . .126

LIGHT.

87. Images in a Plane Mirror 266

89. Index of Refraction of Water 277

41. Index of Refraction of Glass 285

48. Focal Length of a Converging Lens 300

60. Conjugate Foci of a Lens • 309

54. Shape and Size of a Real Image formed by a Lens . .320

§361. Virtual Image formed by a Lens 323

56. Images formed by a Convex Cylindrical Mirror .... 326
§ 356. Images formed by a Concave Cylindrical Mirror . . .328
§380. Use of Rumford Photometer 345

LIST OF EXERCISES.

Vll

MECHANICS.

8. Specific Gravity of a Liquid by balancing Columns
9 a, b. § 49. Compressibility of Air : Boyle^s Law

10. Density of Air

17. Four Forces at Right Angles in One Plane

§ 148. Comparison of Masses by Acceleration-test .

19. Action and Reaction : Elastic Collision
§ 180. Elastic Collision continued ; Inelastic Collision

20. Elasticity : Stretching . . .

21. BreakingHStrength of a Wire ....
§ 188. Comparison of Wires in Breaking Tests
22 a. Elasticity : Bending ; Effect of Varying Load
22 b. Elasticity : Bending ; Effect of Varying Dimensions
23. Elasticity ; Twisting '. .

. 34
37, 39, 40

. 43

. 116

. 130

. 156

. 169

. 162

. 164

. 166

. 168

. 170

. 173

HEAT.

Linear Expansion of a Solid 184

26. Testing a Mercury Thermometer .191

29. Determination of the Dew-point 208

31 b. Specific Heat of a Solid 222

32. Latent Heat of Melting 227

33. Latent Heat of Vaporization .231

84. Increase of Volume of a Gas heated at Constant Pressure . . 237
35. Increase of Pressure of a Gas heated at Constant Volume . . 242

SOUND.

68. Velocity of Sound in Open Air 369

69. Number of Vibrations of a Tuning-fork 370

§421. Wave-length of Sound 375

ELECTRICITY AND MAGNETISM.

61. Lines of Force near a Bar Magnet 386

§§460-463. Study of a Single-fluid Galvanic Cell .... 404

66. Study of a Two-fluid Galvanic Cell 418

68. Lines of Force about a Galvanoscope 426

69 (I). Resistance of Wires by Substitution : Various Lengths . 447
69 (II). Resistance of Wires by Substitution : Cross-section and

Multiple Arc .448

70. Resistance by Wheatstone's Bridge: Specific Resistance of

Copper 465

71. Temi)erature-coefficient of Resistance in Copper . 467

72. §§ 540, 541. Battery Resistance 468

Viii LIST OF EXERCISES.

PAOI

§§668-660. Putting together the Parts of a Telegraph Key and

Sounder 483

76. Putting together the Parts of a Small Motor .... 497

78. Putting together the Parts of a Small Dynamo .... 602

ADDITIONAL EXERCISES.

BZIRCI8I

11. Pressure in a Liquid due to its Weight 62

16. Moments of a Force 91

16. Inclined Plane 109

26 a, b. Temperatures corresponding to Pressure of Steam . 196, 198

27. Testing a Thermometer for Points between 0° and 100° C. . 204

28. Effect of Dissolved Substances on the Freezing-point of Water 206

30. Boiling-points of Liquids 216

31 a. Specific Heat of a Solid 221

36. Weight and Volume of a Gas 244

38. Mirrors at Right Angles 272

40. Critical Angle of Water 280

42. Critical Angle of Glass 288

43. Law of Internal Reflection 293

44. Index of Refraction of Glass by Parallax 294

46. Path of a Ray through Glass having Parallel Sides . . .296

46. Path of a Ray through a Prism 296

47. Measurement of Angle of Minimum Deviation .... 297
49. Measurement of Curvature of Lenses 306

61. Real Conjugate Foci — Parallax Method 314

62. Virtual Foci 316

63. Relative Size of Object and Image 317

66. Principal Focus of a Concave Mirror 329

67. Photometry 343

60. Overtones in Strings 378

62. Effects of Heat on a Magnet 397

63. The Simple Pendulum 399

04. Distribution of Magnetism in a Magnet — Vibration Method . 402

66. Study of a Simple Cell 411

67. Magnetic Action of a Current .' 426

73. Storage Batteries — Polarization 477

74. Current induced by a Bar Magnet 486

76. Current induced by an Electromagnet 494

77. Lines of Force in the Armature of Dynamo or Motor . . 500

79. Principle of the Induction Coil b(H)

80. Thermo-electricity 6()u

PRINCIPLES OF PHYSICS,

CHAPTER I.
DEKSITT. — SPEOIPIO GRAVITT.

1. Physics is the study of those laws of nature that govern
the forms of substances and their movements. These laws, so
far as they are known, were discovered originally by experi-
ment. Every one knows that when water gets very cold it
freezes, and when it gets very hot it boils. An experiment
will show exactly how cold it must be to freeze or how hot it
must be to boil under different pressures. The process of ex-
perimenting is simply that of testing some principle to find
out exactly what its limitations are.

It is necessary, then, at the very outset, to distinguish be-
tween the ordinary and the scientific ideas of such matters.
For example, the terms hard and soft, which are accurate
enough for everyday use, need definite qualification when used
in science. Steel is commonly called hard ; yet an armor plate
will splash like water when struck by a projectile from a mod-
em cannon. Similarly, in scientific language it is not enough
to say that a body moves fast or slow, that it is heavy or ligM;
we must measure its speed or its weight, and know exactly
how fast it moves or how heavy it is. The student of Physics
should learn, first of all, to use such words with precise scien-
tific meaning. He must realize that the common meaning of

2 PRINCIPLES OF PHYSICS.

these words includes only a few degrees along the middle of
the scale, while science uses the entire scale.

2. An Experiment is an effort to determine the answer to a
question. Since the whole field of Physics is to measure pre-
cisely things that we estimate vaguely every day, its whole
value lies in its accuracy. From every process of an experi-
ment comes a certain unchangeable result. The results of an
experiment have a definite meaning in every case, and if the
experiment has been properly conducted, they tell the student
what he wishes to know ; otherwise they will tell him some-
thing else. He must therefore have clearly in view the end he
is seeking, and know the exact value of every step he takes
towards it. Accuracy is equally necessary in conducting the
experiment and in interpreting the results.

3. Metric System of Measurement. — A decimal system of
weights and measures, called the Metric System, is commonly
used in experiments in Physics, as it is easier to attain a high
degree of accuracy with it than with the English system.

Examine a meter stick. Count the number of spaces that
are a little larger than the diameter of a lead pencil. Notice
that the meter is several inches — about a finger's length —
longer than a yard. To be exact, a meter = 39.37 inches. This
number (which need not be committed to memory) is to be
used in changing from one scale to the other, i.e, from inches
to meters and from meters to inches. On the meter stick
there are one hundred divisions, somewhat larger than the
diameter of a lead pencil. One of these divisions is there-
fore one one-hundredth of a meter. Just as we call the
hundredth of a dollar a cent, the hundredth of a meter is
called a centimeter. The abbreviation for, or short way of
writing, 'centimeter' is to use the letters cm. In like man-
ner, m. stands for meter. One meter contains one hundred
centimeters.

DENSITY. — SPECIFIC GRAVITY. 3

Measure in centimeters the diameter of a nickel ; the length
and breadth of your book ; the length of a pencil.

4. Length. — Try to measure exactly the diameter of a cent
piece ; of a dime. Express the amount in tenths of a centi-
meter, as near as can be guessed. In scientific work this is
called estimating. As the tenth of a cent is called a mill, so
the tenth of a centimeter is called a millimeter. The abbre-
viation for millimeter is mm. One centimeter equals how
many millimeters ? What is the number of millimeters in a
meter? Compare with the number of mills in a dollar.
Make up a table as follows: —

So many millimeters make a centimeter
So many centimeters make a meter

This is the table of length.

A piece of paper 20 cm. by 12 cm. has an area of 20 x 12,
or 240, square centimeters; written, for ^brevity, 240 sq. cm.
Find the area of a leaf of the note-book.

5. Volume. — What is the volume of a cube 10 cm. on an
edge ? How many little cubes 1 cm. on each edge could be
laid in a column 10 cm. long ? How many of these columns
must be placed side by side to make the width 10 cm. ? How
many little cubes in all have been so far used ? How many
of the large squares formed must be piled one on top of the
other to make the pile 10 cm. high ? How many of the little
cubes in the whole pile? The volume of the pile is called
a liter. Of course it may be put into any shape, and will
still have the same volume, — one liter, — and contain the
same number of cubic centimeters.

In working problems, be sure to change all the dimensions
in a question to the same unit; that is, to have all the
numbers millimeters, centimeters, or meters before multi-
plying.

PRINCIPLES OF PHYSICS.

Problems.

1. What is the height in meters of a raan 5 ft. 11 in. tall?

2. How many meters long is a 600-iuch fish line ?

3. In 2.5 m. how many centimeters?

4. 500 cm. = how many meters ?

5. 0.01 m. equals how many centimeters ?

6. 15 cm. equals how many meters?

7. In 30 cm. how many millimeters ?

8. A pole measuring 750 mm. is how many meters long?

9. A boy 5 ft. tall is how high in millimeters?

10. If a postal card is 14 cm. long and 0 cm. broad, what is its area?

11. A board, area 300 sq. cm., is 15 cm. long ; what is its breadth ?

12. Find the area of a strip of paper 1.5 cm. wide and 40 m. long.

13. Find the area of a strip of board 2 mm. wide and 6.5 m. long.

14. How many liters in a tank 50 cm. wide, 30 cm. deep, and
100 cm. long?

15. Give the volume, in cubic centimeters, of a box 00 cm. long,
50 cm. wide, 10 cm. deep. How many liters of milk would the box
hold?

16. If a cubical reservoir is 6 m. on each edge, what numl)er of
liters will it hold?

17. A cubic centimeter of water weighs approximately one gram ;
how many grams of water in a liter ?

18. What is the volume of 3500 grams of water? of 9750 grams
of water?

19. If a box 8 cm. by 4 cm. by 10.5 cm. were filled with water,
what would the contents weigh ?

6. Density is the weight of a unit volume. Where grams
and centimeters are used, density is a number giving the
weight, in grams, of one cubic centimeter. When pounds
and cubic feet are used, density gives the weight, in pounds,
of one cubic foot.

DEN 8lTr.— SPECIFIC GMAVITr.

Exercise 1.

DENSITY OF A SOUD.

Apparatus: A 250-gram spring balance; centimeter rule; block of pine,
spruce, oak, ash, whitewood, ebony, lignum yitse, or other wood. No
two dimensions of the block should be alike, and in any one dimension
there should be measurable variation in different parts of the block.

Find the dimensions of a rectangular block, making several meas-
urements of the height, width, and length. Record the measurements
on a skeleton diagram (Fig. 1). Find
the average height by adding all
the heights, -4J5, CD, etc., and divid-
ing by the number of measurements
taken. In the same way find the
average length and width. Multiply
these three average dimensions to-
gether to find the volume.

In measuring, the graduated edge
of the rule should be placed directly

upon the block, and the reading made in centimeters and tenths. Try
to estimate to tenths of a millimeter. As the entry in the note-book
is to be in centimeters, tenths of a millimeter would be written in

the hundredths' place. Do not measure
from the very end of the rule, for the
corner is apt to be worn. Figure 2
shows the correct position for the meas-
uring* rule. The reading is one centi-
meter, six-tenths, and perhaps six-
tenths of a tenth, or six hundredths.
This would be written 1.66 cm.
Find the weight of the block in grams, and compute the weight of
one cubic centimeter of it. If the dimensions of the block are 4 cm.,
6.1 cm., and 6.2 cm., the volume is 126 cc. (cubic centimeters), if we
omit the figures in the product (which is 126.48) that are beyond the
limit of accuracy of the measurement. If the block weighs 200 grams,
one cubic centimeter would weigh ^ of 200 = 1.58 g.

Illlllill

iiihiiiliiiili,

Fig. 2.

7. Experiments on Density. — Find the density of a cylinder,
a half cylinder, or a hexagonal prism, such as may be obtained

6 PRINCIPLKS OF PHYSICS.

from a set of drawing models. Find the density of a hard
brick, and also of a soft burned brick. (Have them weighed
at the nearest grocer's, if they are too heavy for the scales in
the laboratory.) Find the size and weiglit of different kinds
of bricks. Compute their density. Soak them in water, weigh
again, and compute the density. The best bricks absorb the
least water. Change pounds to grams by multiplying by 453.5,
which is the number of grams in a pound. Find tlie weight
of one cubic centimeter of each brick. Find the density in the
P^nglish system, i,e. the weight of one cubic foot. The dimen-
sions, if measured in centimeters, are to be changed to feet by
dividing by 30.5, — the number of centimeters in a foot.

8. Formula for Density. — To find the density of a bcxly,
or, what is the same thing, to find the weight of one cubic
centimeter of it, we divide the weiglit by the number of cubic
centimeters in the body. The density of a lump that has a
volume of 6 cubic centimeters and weighs 30 grams is ^ of 30,
or 5. The rule, then, is : —

Density equaU toeiglit divided by volume ,

Density = S^-
' ^ Volume

Abbreviating by using the first letter of each word for the
whole word, we have the formula,

9. Formula for Weight. — Knowing the density and the vol-
ume of a body, the weight is found by multiplication. The
weight of a body the density of which is 3 grams and the
volume 5 centimeters, is 3 x 5 = 15 grams.

Density times volume equals weight.

DV= W.

DENSITY. — SPECIFIC GRAVITY. 7

10. Fofnmla for Yoliime. — Suppose we wish to know the size
(volume) of a lamp, the density of which is 3, and the weight
15 grams. As density is the weight of one cubic centimeter,
the number of cubic centimeters in the lump will equal the
number of times that 3 is contained in 15, or 5.

To find the volume, divide the iveighi by the density.

Problems.

1. If a rectangular block, 5 cm. by 6 cm. by 20 cm., weighs 500 g.,
what is the weight of 1 cc. ? What is its density ?

2. What is the weight of the contents of a box 8 cm. by 12 cm.
by 30 cm., when filled with water? when filled with mercury, den-
sity = 13.6 ? when filled with kerosene, density = .8 ?

3. What does 1 cc. of mercury weigh? How much does a lit.er of
mercury weigh ? a liter of kerosene ?

4. What is the density of a block of marble 1 m. by .3 m. by .2 in.,
weighing 16,200 g.? What is the weight of 50 cc. of the same
marble ?

5. If a cube of zinc 4 cm. on an edge weighs 448 g., what does
1 cc. weigh? What is its density? How much would a block of
zinc 5 cm. by 3 cm. by 2 cm. weigh? How many cubic centimeters
in a block of zinc weighing 28 g. ?

6. How large is a piece of glass, weight = 100 g., density = 2.5 ?

7. What is the volume of 14 g. of zinc, density = 7 ?

8. How much space is taken up by 900 g. of coal, density = 1.5?

9. What is the size of a piece of pure gold, density = 19.4, weight
= 500 g. ? What is the size of a rock, density = 5, weight = 30 g. ?

10. What is the weight of 6.5 cc. of lead, density = 11.5?

U. What is the weight of a glass paper-weight 1 cm. thick, 8 cm.
long, and 12 cm. wide, density = 2.5?

12. Give the size of a 400 g. lead sinker, density = 11.4.

.13. How. many grams of sulphuric acid, density = 1.8, can be put
in a box 8 cm. by 4 cm. by 3 cm. ?

8 PRINCIPLES OF PHTSICS.

14. What is the density of a lump of wood containing 600 cc,
weight = 400 g. ? How much does 1 cc. of it weigh ?

15. How big is a lump of cork, weight = 100 g., density = .25 ?
What is the weight of 1 cc. of this cork ?

16. Find the weight of 1 liter of tin, density = 7.3.

17. What is the weight of 1 cc. of a body, 5 cm. by 4 cm. by
3 cm., weight = 80 g. ? Compute its density.

18. Compute the size of a piece of wood, weight = 80 g., den-
sity = J.

Bxeroise 2.

EFFECT OF WATEB ON A SOLID THAT SINKS.

Apparatus: Overflow can or 8team boiler; catch bucket; weighted block;
spring balance or platform scales, reading to 250 g.

Fill the overflow can. When dropping stops, slowly lower the
block into the water. Catch the overflow in the bucket, and weigh.
Also weigh the empty bucket, and find how many grams of water
overflowed. Measure the block, and compute its volume. Weigh the
block in air, then in water, and find the loss of weight. Ah one cubic
centimeter of water weighs one gram, a sinking body displaces as
many grams of water as there are cubic centimeters of volume in the
body.

When finding, by a spring balance, the weight in water of a sub-
stance that sinks, do not allow any part of the balance to touch the
water.

11. Experiments on Volume. — Describe a method of finding
the volume of an irregular lump. Describe another method of
finding the size or volume of an irregular body, by using a
spring balance and a dish of water.

Find the volume of pieces of marble, sulphur, coal, and glass,
by one or both of these methods. How does the weight of a
rock in water compare with the weight in air? Bodies in
water appear to lose weight. They are buoyed up by a force
equal to what ? Can a man lift a greater load under water
than he could lift in the air?

DENSITY. — SPECIFIC GRAVITY.

Problems.

1. A piece of rock weighs 25 g. in air and 15 g. in water ; what is
its volume ? Calculate its density. How does this compare with the
volume of the block in cubic centimeters?

2. Find the weight of one cubic centimeter of platinum, density
= 22.

3. Find the weight of a block of platinum that has the volume of
a liter.

4. A lump weighs 40 g. in air and 32 g. in water ; find its volume.
Find its loss of weight in water. How much water would run over
if the lump were immersed in a dish full of water?

5. Compute the density of a lump of ore 2 cm. by 4 cm. by
1 cm., weighing 25 g.

6. Find the weight of a liter of milk, density = 1.03.

7. If a body 10 cm. long, 3 cm. wide, and 6 cm. thick weighs 500 g.
in water, how much will it weigh in air?

Exercise 3.

SPECIFIC GBAVITT OF A BODT THAT SINKS IN WATEB.

Apparatus : A 250-gram spring balance ; a piece of sulphur, coal, glass (a
bottle, for instance), marble, iron, brass, or lead.

Find the density of one of these substances. Weigh in air ; then
in water. Compute the volume, and divide the weight by the volume.
Suppose a lump weighs 15 g. in air and 10 g. in water; the loss of
weight, or the buoyant effect, is 5 g. It must, therefore, displace 5 g.
of water; and as 5 g. of water have a volume of 5 cc, the lump, also,
has a volume of 5 cc. The density, or the weight of one cubic centi-
meter, is one-fifth of 15 g., or 3 g. The lump is three times as heavy
as water. The specific gravity of the lump, then, is 3.

12. Specific Gravity tells how many times heavier a body is
than an equal bulk of water.

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DENSITY. — SPECIFIC GRAVITY. 11

Problems.

1. If a substance has a density of 6, what is the weight of 1 oc of
it? What is its specific grayitj? What is its density in the English
system?

2. Calculate the specific gravity of a piece of ore weighing 40 g.
in air and 25 g. in water. Of a stone weighing 14 pounds in air and
8 1 pounds in water. What is the density in the metric system ?

3. A body weighs 12 g. in air and 8 g. in water ; find its size,
density, and the weight of 1 cc. of it. How many times heavier than
water is it ? What is its specific gravity ?

4. A rock weighs 80 g. in air and 60 g. in water; what is its
specific gravity, size, and density? If put in a full pail of water,
what would happen ?

5. If it takes twelve men to lift a rock on land and nine men to
hoist it when under water, what is its specific gravity ? What is its
density? Can you tell its size? Why not?

6. A body of rectang^ular form is 8 cm. by 5 cm. by 10 cm., and
weiglis 500 g. ; find its density. If it were immersed in a dish full
of water, how much water would run over?

7. What is the density of a substance of which .25 liter weighs
200 g.?

8. A lump has a specific gravity of 3.5 ; what is its weight per
cubic centimeter ? its density ? If it weighs 70 g. in air, what is its
volume ? How much, then, is it buoyed up in water ? What would it
weigh in water?

9. A piece of stone weighing 127 g. in water and 234 g. in air is
put in a full dish of water; how much water runs over?

10. Find the volume of a body, weight = 80 g., density = 5.

11. Find the weight of a body, volume = 60, density = 10.5.

12. Find the size of a lump, weight = 200 g., density = 1.5.

13. What is the size of a lump of cork, density = .25, weight =
300 g.?

14. If 32 cc. of a substance weigh 128 g., what is its specific
gravity?

PRINCIPLES OF PHYSICS.

15. Specific Gravity by Flotation. — To iind the density of a
substance we must know its weight and volume ; to find its
specific gravity we must find the weight of the substance and
the weight of an equal volume of water. How was this done
with a solid that sank in water?

Bxerolse 4.
8PECIFI0 GBAVITT OP A BODT THAT FLOATS.

Apparatus : A stick of one square centimeter cross-section, marked length-
wise in centimeters, and loaded at the lower end so as to float upright ; a
Jar of water ; an overflow can.

Weigh the stick. Place the stick in the jar of water; measure
and record the number of divisions above the water line and the
number below. As each section of the stick is a cubic centimeter,
the stick displaces as many grams of water as there are sections
of the stick under water. Compare this with the
weight of the stick, and record the relation between
the weight of a floating body and the volume im-
mersed. Put a gram weight on top of the stick ; try
a two-gram, then a five-gram weight. Place an object
of unknown weight on the stick, and determine its
weight.

The volume of the stick is in this case the number
of divisions. These are counted, and the number re-
corded. How can the weight of one cubic centimeter
be found ?

Weigh some larger object that will float (not neces-
sarily of any regular shape); weigh also the water
displaced by lowering it into an overflow can, and
compare the two readings. Record as follows: —

Fig. 3.

Weight of object =

Weight of bucket to catch water overflowing =
Weight of bucket and overflow =

Amount of water displaced =

How much water does a floating body displace ?

DENSITY. — SPECIFIC GRAVITY.

Refill the overflow can, and find the volume of the object by weigh-
ing the water that flows over when the object is pushed under the
surface. Find the density, i.e. the weight of one cubic centimeter.
What does a body that sinks, or is made to sink, displace?

16. Density of a Body that Floats. — Find the density or spe-
cific gravity of a cylindrical rod. It can
best be kept upright by a frame holding two
rings, as in Fig. 4. Mark the water level.
Remove the stick, measure, and record : —

Length under water =
Whole length =

While the stick probably does not have
a cross-section of one square centimeter, yet
it floats exactly as far down in the water as
would a stick of the same wood, of the same
length, with a cross-section of one square centimeter, or any
other diameter. The length under water, then, represents the
weight, and the whole length, the volume.

j^ > _ Weight _^ Length under water
^ ™ Volume "" Whole length

By this method the density of any volume that floats is
quickly determined. A piece of cork, a stick of paraffin (a
candle), a block of ice, and a piece of pure gum rubber, if
obtainable, may be tried.

How many times larger is the part of an iceberg under
water than the part above water? What solid has the least
density ? Is charcoal lighter or heavier than water ? Does
it float or sink ?

Fig. 4.

17. Measurement of Displacement. — A tall glass jar, or a stu-
dent lamp-chimney closed at the neck by a cork and supported

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DENSITY. — SPECIFIC GRAVITY.

8. A lamp, volume = 60 cc, weight = 40 g., is put in a full dish
of water; how much runs over? Does the body sink or float? What
is its density ?

9. If, in jar A, Fig. 6, the reading of the water level is 15 cc, in
B the level is 45 cc, and in C the level is 55 cc, what is the weight,
volume, and weight per cubic centimeter of the body.

lO. If a cake of soap, 8 cm. by 5 cm. by 3 cm., density = .96, is put
in a full basin of water, how much water overflows ?

18. Displacement and Loss of Weight — The volume of a
body that sinks has as many cubic centimeters as the number
of grams' loss in water. A body that floats loses all its weight
without being wholly under water. But, unless the body
sinks, or, as in the case of a floating body, is made to sink, it
cannot displace its volume of water. For every cubic centi-
meter of water displaced there is a buoyant effect of one gram.

Exercise 6.

SPECIFIC GEAVITY BY IMMERSION.

ApparattLS : Block of wood; spring balance; jar of water; small pulley
attached to a vertical rod, which is fastened to a heavy cross-piece of
wood resting on the edges of the jar.

Weigh the block of wood, find its
volume by measurement, and record.
By means of the pulley, draw the
block down into the water (Fig. 7).
Record the force required to make
the block sink, and compare with the
difference i^etween the volume and
the weight. What is the force tend-
ing to buoy the block up, when im-
mersed? W^hat force beside the pull
of the balance tends to hold the block
down ? If the block weighed 40 g. in
air and required a pull of 60 g. to sink
it, how large was the block ?

PRINCIPLES OF PHYSICS.

Bxeroise 6.
IMMEB8I0N BT USE OF A 8INKSB.

Apparatus : Spring balance ; block of wood ; sinker ; jar of water.

Weigh the sinker ; attach it to the block, and weigh the two in
water (Fig. 8). Record as follows : —

Weight of sinker in air =

Weight of sinker and block in water =
Loss of weight of sinker =

Add the loss of weight of the sinker to the
weight in air, and compare with the volume.

19. Volume and Loss of Weight — The

volume of a body in cubic centimeters

equals the loss of weight in grams, in

water. The block in water loses its own

weight and makes the sinker appear to lose

F««- 8. some.

A block weighs, in air, 200 g. ; a sinker, in air, 80 g. ; block

and sinker, in water, 40 g. What is the total loss of weight ?

What is the volume of the block ? Knowing the weight and

volume, find the density.

^ .^ Weight
^^"^^'y = VohISi'

but, since the volume as found by use of a sinker equals the
weight of the body plus the loss of weight of sinker.

Weight

Density =

Weight -f- loss of weight of sinker

Problems.

1. A piece of wood weighs, in air, 160 g. ; a sinker weighs, in water,
200 g. ; the wood and sinker, in water, weigh 100 g. Find the volume
and density of the wood. ^

DENSITY. — SPECIFIC GRAVITY. 17

2. What is the density of a substance that weighs 60 g. in air,
which, put in water, attached to 40 g. of metal, weighs 15 g. ?

3. A ten-pound anchor draws a fifteen-pound piece of wood under-
neath the water ; a force of four {>ounds brings them to the surface
together. What is the density of the wood ?

4. A lump of ore weighs 35 g. in air and 25 g. in water ; find its
loss in water, and its volume.

Bzercise 7.

BEHSITT AKD SPECIFIC GBAVITT OF A LIQUID. CAFAGITT OF A

BOTTLE.

Apparatus: Glass bottle with stopper; 250-gram spring balance; kerosene
oil or sulphate of copper solution.

Weigh the empty glass bottle and stopper. Fill the bottle with
water, and weigh. The latter weight should be within the capacity
of a 250-gram spring balance. From the fact that a cubic centimeter
of water weighs one gram, calculate the volume of liquid held by the
bottle. Fill the bottle with kerosene oil or sulphate of copper solu-
tion, and find the number of grams of liquid held by the bottle. Cal-
culate the weight of one cubic centimeter of the liquid, by dividing
the weight by the volume.

Problems.

1. An empty can weighs 200 g. ; when full of water, it weighs
600 g.; how large is the can? How many cubic centimeters of milk
will it hold ? If it weighs 612.8 g. when filled with milk, how many
grams of milk does it hold? What does 1 cc. of milk weigh? What
13 the density of milk ?

2. How much water does a cubic centimeter of lead displace?
How much, then, is it buoyed up in water ? What is its loss of weight
in water?

3. How much does 1 cc. of lead weigh in water, its density being
11.4? How much does 1 cc. of aluminum, density 2.6, weigh in water?
Which is the better for the keel of a boat? Which is the better for
tb9 body and deck?

18 PRINCIPLES OF PHYSICS.

4. A bottle weighs, when empty, 70 g. ; filled with water, 210 g. ;
how many cubic centimeters of a liquid does it hold? Filled with
nitric acid it weighs 196 g. ; find the weight of one cubic centimeter of
the acid. What is the density of the acid?

5. A bottle weighs, empty, 100 g. ; filled with water, 900 g. ; what
is the capacity of the bottle? How many cubic centimeters of mer-
cury, density 13.6, will it hold? Ilow many grams of mercury will it
hold ? Ilow many grams of oil, density .8'2, will it hold?

6. A perfume bottle, empty, weighs 80 g. ; filled with water, 280 g. ;
filled with perfume (alcohol), 250 g. Ilow large is the bottle, t.*.
what is its capacity ? What is the specific gravity of the perfume ?

7. The same bottle, filled with chloroform, weighs 380 g. ; find the
specific gravity of chloroform.

8. A bottle full of water weighs 180 g. ; empty, weighs 30 g.; what
is its capacity ? Some dry pieces of rock ai-e put in ; the bottle and
rock weigh 300 g. The bottle is then filled with water, and found to
weigh 450 g. Find the volume of water added, the volume or size of
the fragments of rock, and the density of the rock.

9. Tell how to find the specific gravity of sand.

10. A piece of oak 9 cm. long, 5.5 cm. wide, and 4.5 cm. thick,
weighs 189.4 g. ; what is its density? How much water will it dis-
place? Will it sink or float? If it were placed in water, how much
of its volume would be under water? How much would be out of
water?

11. How large a weight must be placed on top of the piece of oak
of Problem 1 to make the top of the block just level with the surface
of the water? If a block of cherry, density = .5, of the same size as
the block of oak, were floated in water, would it take a larger or
smaller weight to sink the block of cherry to the level of the water, •
than to sink the block of oak? How large a weight must be used?

12. If a lead! sinker weighs 60 g. in air and 54.7 g. in water, what
is its specific gravity? What is its loss of weight? its displacement?*
its volume ?

13. What is the buoyant effect of the water on the sinker of Prob-
lem 12? What would be the buoyant effect of alcohol, density = .8?
Would this sinker float or sink in mercury, density = 13.6 ?

CHAPTER 11.
PSESSUEE.

20. Force, or pressure, is a push or a poll. If a body is
stationary, a force applied to it tends to start it in motion ; or,
if the body is already moving, the force tends to stop it, to
make it go faster, or change the direction of its motion.

In moving a train, when does the locomotive push, and
when does it pull ? Does a horse push or pull on the collar ?
on the wagon to which he is attached ? A Japanese carpenter
uses his saw and plane in a way opposite to ours ; does he
push or pull them ? In Holland, the dogs that move the milk
carts are often hitched directly under the cart ; do they push
or pull?

21. To set a Body in Motion, a force must be applied outside
the body. It is the resistance of the rails that enables a loco-
motive to move ahead. When the track is slippery, the driv-
ing wheels slip round on the rails, and the locomotive stands
still. That the force is applied outside a moving body is
clearly indicated by the fact that, in rowing, limber oars are
bent in the direction in which the boat moves, showing that
the water presses against the blades in that direction. If a
row of boys were standing on a frozen pond, and another boy
taied to move himself along by pulling on the line, the boys in
the line would feel that they were pushing him.

If a boy standing in a basket pulls on the handles, does he
lift himself from the ground ? Can other persons standing on
the ground yaise him by pulling upward on the handles?
Suppose that. during a. calm the helmsman should blow on the

20 PRINCIPLES OF PHYSICS.

sails of his boat with a pair of bellows, as he might on the
sails of a toy boat in a tub, would the boat move as a toy one
would ?

22. Weight is the downward force a body exerts because of
its apparent attraction by the earth.

If you hold a piece of iron or a book in your hand, you must
press upward, — that is, exert an upward force, — to balance the
downward force exerted by the iron or the book. This down-
ward force, which is not exactly understood, appears to be an
attraction exerted by the earth.

23. Weight of Air. — Air is a gas, and is free to move in any
direction. The fact that it remains enveloping the earth, in-
stead of flying off into space, shows that it is subject to the
earth's attraction, — that is, it has weight. Since it has weight,
it must exert a force downward. Imagine grapes piled many
feet deep; where in the pile will the grapes be most com-
pressed? This downward pressure of the atmosphere is
easily shown.

24. Transmission of Pressure. — Put a piece of paper over
the mouth of a bottle filled with water, and invert the bottle.
If the paper itself held the water in the bottle, could the paper
be flat ? Put water in a large rubber cloth, and notice that
the cloth bulges downward under the weight of the water.
In place of paper, tie cloth over the mouth of the bottle, and
repeat the experiment. Fill with water, and invert, a small
bore tube, closed at one end, thus making a long, narrow^bottle.

When a bottle, or any other object, is pressed into a dish of
water^ the water transmits the pressure in every direction. If
the dish is weak, the sides may give way, or the bottom be
forced out ; otherwise, the water escapes upward. In driving
many sticks of wood or piles into soft ground, the downward
pressure exerted by the last ones often causes an upward press-
ure in the ground sufficient to lift those previously driven.

PRESSURE. 21

Fill a bottle with water; cover the mouth with paper; in-
vert the bottle, place it mouth down in a dish of water, and
remove the paper (Fig. 9). The downward pressure of air on
the surface of the water in the dish causes an upward pressure
in the bottle. This upward pressure keeps the water in the
bottle. In place of a bottle, fill a tube, one end of which is

J^'-B- 9- Fig, 10.

covered with thin rubber (R, Fig. 10). The air pressure on the
glass cannot be observed, as the strength of the glass prevents
any bulging.

25. Suction. — A common attempt to explain the results of
various experiments with water, is to call the force that holds
the water in place suction. To determine how powerful that
force is, put the empty tube, rubber down, on the surface of
the water in the dish. Notice if any more force is needed
to lift the tube from the water than is needed to lift it from
the table.

26. Unbalanced Force. — To make a body move, a force must
be applied from outside the body; but if two equal forces
in opposite directions be applied, the body will not be moved
by these forces. Therefore, if one force be observed to act
on a body, and the body does not move, then there must be
another force equal in amount acting in an opposite direction.
In order, then, to set an object in motion there must be an
unbalanced outside force, or pressure.

PBINC1PLE8 OF PHYSICS.

F\g. 1 1.

Fill a glass tube (Fig. 11) with
water to the level BC. The air press-
ure on B, being balanced by an equal
air pressure on C, does not tend to
move the column of water. Cover B
with the thumb, and partially remove
the air from A^ by the mouth. The
air pressure on C has been lessened,
but the air pressure is kept from
acting on B. With B uncovered,
lessen the pressure on C. The press-
ure on B- is now unbalanced and
forces the water down B and up the
arm AC.

Fig. 12.

27. Magdeburgh Hemispheres are two brass cups, fitting
together, with a joint made air-tight by tallow (Fig. 12). A
valve permits air to be exhausted or
admitted at will. Exhaust the air, and
try to pull the hemispheres apart. Admit
the air, and try it again. Exhaust the air
again, and admit it while pulling. When
the hemispheres are full of air, the inside and outside pressures
are balanced. When the air is exhausted, there is no inside
pressure, and the outside forces, all pressing inward, hold the
^ ^ cups together. An "eight-
in-one " apparatus even better
serves the purpose of this
experiment. Push in the
piston, close the valve, and
pull on the handles. Open
the valve while still pulling.

n^^

'''«'^' 28. Air Pressure. -^ If A

and B (Fig. 13) are two pieces of wood, what are the direc-
tions of the two forces acting on them to hold them together ?

PRESSUBE.

•ww/////mmz

Rg. 14,

To pull A and B apart, forces greater than the pressure exerted
by the clamp must be used.

Figure 14 shows a "vacuum-tipped arrow" pressed
a^inst a board, to expel the air from beneath the rubber.
What force would be required to pull
the arrow from the board ? How can
it be taken off without using this _
force ? ^

Dip the end of an open tube into a '~
dish of water (Fig. 15). Why does
not the air, pressing down on the sur-
face of the water in the dish, force the
water up higher in the tube? Notice that the air presses
down in the tube. What pressures are balanced ? Lessen the
pressure in the tube, by removing some
of the air, with the mouth. The out-
side air pressure on the surface of the
water in the dish is no longer bal-
anced, and causes the water to move
up the tube. On sucking a liquid
through a straw, what makes the liquid
rise ? How high can air pressure raise
Fig. 1 5. a liquid ?

29. How Air Pressure acts. — Make a large hole in the
bottom of a tin can. Place the can on the plate of an air-
pump, using tallow to make an air-tight ^^^^->s
joint. Put an apple on the top of the can ( J
(Fig. 16). The apple, being pushed by
equal pressures of air above and below,
is not moved. Exhaust the air from the
can. This removes one of these pressures *^' '
and leaves the other free to act. What pressure is unbalanced ?
Tie a sheet of rubber over the mouth of the can, and try the
effect of exhausting the air.

PRINCIPLES OF PHYSICS.

If the two springs shown in Fig. 17 press on an apple
from above and below with equal force, the apple will not be

pushed down into the can. But
when the lower spring is removed
(Fig. 18), the pressure above is
unbalanced and is free to act.

In various forms of cash carriers,
air is exhausted from one end of
a pipe. Explain how an object is
then made to traverse the pipe.
A pneumatic railway was operated
on this principle for a short time in Glasgow. In preserving
fruit in glass jars, the liquid, at the time of sealing, fills the
jar ; when cool, the liquid contracts, and a space is left at the
top of the jar. What is there in this space ? What enters, if
an opening is made under the rubber ring ? Why does the top
then unscrew more easily ?

30. Elasticity. — Such substances as steel, glass, wood, India
rubber, and paper, when bent or compressed, tend to return to
their original form. This is due to a quality called elasticity.
Wet clay, putty, and such materials are not elastic. A
billiard ball dropped on a steel floor will rebound to practically
the height from which it is dropped. If both substances were
perfectly elastic, it would rebound the entire distance.

Is air elastic ? Squeeze a tennis ball, or push down and re-
lease the piston of a bicycle pump, while preventing the air
from escaping. A pneumatic tire is inflated by pumping in
from three to five times as much air as the tire would hold if
open to the air. Does the pressure exerted by the air in the tire
increase as more air is pumped in ? What can you say about
the effect that a decrease of volume has on the pressure of a gas ?
Remember how much air is pressed into a tire. What makes
the water come out of a so-called siphon of carbonated water,
when the valve is opened ? What pressure is unbalanced ?

PRESSURE.

31. Yolume and Pressure of Gas. — Fasten the stem of a toy
balloon air tight into an open end of a soKjalled one-eighth inch
gas valve, F, Fig. 19. The other end of the valve screws into
a bit of pipe, T, the lower end of which is to be fixed in a
wooden base, B. Open the
valve, F, blow air into the
balloon, close the valve,
screw on the base, place
under the receiver of an air-
pnmp, and exhaust the air.
The tube P connects with
the air-pump. Why did not
the pressure of air in the
balloon cause expansion be-
fore exhaustion ? Admit air
to the receiver, and explain
the action of the balloon.

A piece of the inner tube of a bicycle tire may take the place
of the toy balloon and stand. The tube should be half filled
with air and tied tightly at the ends. It may be kept off the
pump-plate by raising it on a pasteboard box.

The statement regarding volume and pressure of gas is
called, after its discoverer, Boyle^s Law,

Pig. 19.

32. Measurement of Air Pressure. — When a bottle full* of
water is inverted in a shallow dish of water, the air pressure
on the surface of the water in the dish holds up the water
in the bottle. To measure this air pressure, we have only to
find out how high a column of water it will hold up. This
could be done, if the bottle were long enough to let the water
rise as high as the air pressure could push it. Mercury, being
heavier than water, is more convenient to use for this pux-
pose, as the column need not be so high. Mercury weighs
13.6 times as much as water; therefore the column held up
by the air pressure is 13.6 times as short.

PRINCIPLES OF PHYSICS.

33. The Mercury Column. — Fill with mercury a heavy glass
tube, 36 or more inches long, closed at one end (A, Fig. 20).
The bore of the tube should be two or three
millimeters. Hold a finger over the open
end; invert the tube (as -B), and place the
end in a dish of mercury. Release the mer-
cury in the tube, and let the column come
to rest (C). Measure the height (h) of the
mercury above the surface of the liquid in
the dish. Record, with date and hour. What
holds the mercury up in the tube ? Why is
it not held up higher ?
What is there in the
tube above the mer-
cury? Before answering, tip the tube
as in Fig. 21, and explain what happens.
In moving the tube to this position, does
the mercury rise? Place a stick hori-
zontally behind the tube in C, Fig. 20,
at the level of the mercury ; incline the
tube, and determine whether the mercury rises or falls.
Attach paper to the back of the tube, so that it extends two
inches above and below the level of
the mercury. Mark lines for inches
,1., 11 and tenths, and read and record the

/ Z[D^^ II height twice each day.

Fig. 22.

34. To vary the Pressure on the

surface of the mercury in the dish,
insert the same or a similar glass tube
into a rubber stopper, as in Fig. 22.
Slide the stopper, S, a little toward
the closed end of the tube. Fill the
tube and the rubber pipe, B, with
mercury. Put mercury in the jar, J.

PRESSURE.

Invert the glass tube, holding the mouth of the rubber pipe
upward, a.nd place it in the jar. Press in the stopper, and
read the height of the mercury. Increase the pressure on the
surface of the mercury, by blowing at T or by the use of a
bicycle pump. Suck air from T, or use an air-pump.

T may be attached to the air-pump in connection with the
receiver in which the rubber balloon was placed (Fig. 19),
and the experiment may be repeated. In place of a balloon,
a long test-tube, tt, half filled with water and inverted in a

Fig. 23.

dish of water, can be used (Fig. 23). The test-tube should
have a paper scale attached, or be marked with a cross-pencil.
Read the height of the mercury and the length of the air
column in the test-tube. The pressure on the air in the test-
tube is nearly the same as that on the mercury, being only less
in proportion as the column of water is shorter and lighter
than the mercury column. Exhaust the air till the height of
the mercury is reduced one-half, and measure the volume of
air in the test-tube. See how far the mercury can be made to
fall. Notice the action of the air in the test-tube. Allow air
to enter, and note how far the water rises in the test-tube.
Was all the air exhausted from the receiver ? What deter-
mines this ? Did the mercury fall to the level of the mercury

28 PRINCIPLES OF PUYSICS.

in the jar ? Place a bumed-out incandescent lamp, tip down,
in a dish of mercury or water, and tile ofif the end of the tip.
Does the liquid entirely fill the bulb ?

85. The Barometer. — A space where there is no air — for

instance, the space above the mercury in the glass tube in
the last exi)eriment — is called a vacuum, A glass tube over
thirty inches long, closed at one end, filled with mercury, and
inverted in an open dish of mercury measures, by the height
of the column of mercury, the pressure of the air. This in-
strument is called a barometer {i.e. pressure measurer).

When we say that one point on a mountain is 1000 feet
higher than another, do we mean that the road up the mountain
is 1000 feet long? The height of the mercury column in the
barometer, or, as is said for short, the height of the barometer,
at the s(»a level averages al)Out 30 inches, or 76 cm. Would
the baronietc^r stand higher or lower on Mt. Washington ? In
th(i l)ottoni of a mine ? At the level of the Dead Sea ?

Ln ascending from the sea level, there is less and less air
above to press down on the surface of mercury in the barome-
t(?r. The mercury column therefore falls. On Pike's Peak or
Mt. IManc, the height of the mercury column is about one-half
the height at sea level. The fall is one inch for 945 feet of
ascent. What would the barometer read at Denver, 5000 feet
aVove the sea level ? What is the difference between the
barometer readings at the base and the top of the Eiffel Tower,
1000 feet high ? What is a balloon doing when a barometer
in the car falls ? In a barometer, cross-section one square cen-
tim(5ter, how many cubic centimeters of mercury are in the
tul)e at the sea level ? Mercury weighs 13.6 times as much as
water ; what is the weight of the mercury column in the tube ?
What, then, is the average pressure of air in grams per square
centimeter, at the sea level ? How high is the column in a
water barometer ? If a mercury barometer falls one inch, how
much would a water barometer fall ?

PRE88UBE.

The Weather Bureau reports give as the height of the
barometer at a place above the level of the sea, not the actual
reading, but what would be the reading at that place if a shaft
were dug down to the level of the sea and the barometer low-
ered there and then read. This can be calculated when the
height of the place above the sea level is known.

36. Water lifted by Air Pressure. — In the apparatus shown
in Fig. 24, why does not the pressure of the air on the water
in the dish force water up the tube ? Raise the piston, thus
reducing the air pressure in the tube.
The air pressure on the water in the dish
is no longer balanced, and forces water
up the tube. If the piston was started
from the surface of the water, and lifted,
how far would the water rise, if the ap-
paratus were in New York? How far
would mercury rise ? How far would oil
rise, density = .85 ? glycerine, density =
1.26 ? sulphuric acid, density = 1.8 ? If
the piston be raised so high that the water
is no longer driven up, what would there '**

be between the level of water in the tube and the bottom of
the piston? If this experiment were tried also at Denver,
would the column be a different height from the one in New
York? If the experiment were tried on different days at
the same place, would the liquid always rise to the same
height ?

37. Lifting Pomp. — Water usually contains some dissolved
air, which expands when the pressure on the water is reduced.
How would the use of boiled water (containing no air) affect
the height to which the water column could be raised ? In
the tube (Fig. 24), the liquid falls again as soon as the piston
is pushed down. Make a hole through the piston ; put a trap

PRINCIPLES OF PHYSICS.

or valve on the top of the hole. Fix firmly in the bottom of
the tu\ie 2L plug of wood, or cork, having a hole covered on
the upper part by a valve opening upwards. Water can go up
through the valves, but not down.

Fit the base of a student lamp chimney with a plug having
a half-inch hole, covered by a piece of thin leather nearly as
large as the j)lug (Fig. 25). The leather
is held by a tack at one side. The pis-
ton is made of a single piece of wood,
j)ierced by as large a hole as its diame-
ter will permit. It should be made a
trifle smaller than the bore of the chim-
ney, and be wound with soft white string
till it is a loose fit. Place the base of
the chimney in a dish of water, and work
the piston. The apparatus operates as
a lifting pump. What forces the water
through the lower valve ? How high
can that force drive it ? Study the
pump, and make diagrams showing the
position of the valves when the piston
is ascending, and again when it is de-
scending. How high can the water be
raised when above the upper valve ? In case water is to be
pumped up 200 feet, where must the upper valve be, at the
highest part of the stroke ? Owing to the leakage of valves
and to dissolved air in the water, instead of 34 feet, 20 feet is
the practical limit for the distance of the piston above the
water in a well. What would this height be if mercury
were pumped ? If oil, density = .8, were pumped ? While
the model jmmp is full of water, raise it from the dish,
and continue })umping. Explain why bubbles of air enter
the lower valve. With metal pipe and tight-fitting valves
and piston, the apparatus would be a primitive form of air-
pump.

Fig. 2B.

PBESSUBE.

Fig. 26.

38. Cartesian Diver. — Nearly fill a small glass bottle with
water ; invert quickly in a dish of water. If the bottle does
not sink at a slight blow, and slowly rise to the surface, remove
the bottle, and add or take out water, as needed. Cover the
* mouth of the bottle with the finger, and re-
move to a narrow jar. Fill the jar with water
(Fig. 26), and tie sheet rubber over the top.
If the jar is narrow, the palm of the hand
may take the place of the rubber. Press on
the rubber, and note what the bottle does, and
any change of level of water in it. Remove
the pressure. How can the bottle and the air
in it be made to displace less water? By
what is a body in water buoyed up ? Is the
buoyancy of the bottle increased or decreased
by compressing the air in it? This appa-
ratus is called a Cartesian diver.

Place a bottle containing a Cartesian diver under the re-
ceiver of an air-pump. Exhaust the air a little, and then
admit air. Repeat, exhausting more
air each time. Explain the change
of level of the diver, and the rising
and sinking. Try a piece of hard
wood in place of the diver. What
change in density is there ?

39. Force-pump. — If the piston-
rod of a lifting pump is made to pass
through a tight-fitting cover, and an
opening anywhere above the piston
is connected with a pipe, water can
be forced or driven by the piston to
a height depending only on the force
applied to the piston and on the
However, in force-pumps it is usual

Rg. 27.

strength of the pump.

PRINCIPLES OF PHYSICS.

Ut iriakft the pi«t<m solid, and place the upper valve at the
n\tU in tfi« tul)e through which the water leaves the pump,
HM nSumw in Figure 27, page 31.

Makn diagrams of a force-pump, with the piston ascending,
Mu\ with tlifl piston descending. What makes the water rise*
ihroMgli tfi<j lower valve? How high could the lower valve be
nU/V^ tfi« \m^^\ of the liquid in the reservoir, in pumping
Uii^vvMvy 7 waU5r ? oil, density = .8 ?

40. Siphon. — Reread section 36, and then look at the appar
mim wliown in Fig. 24, page 29. Suppose the straight tube in
Fl^. 24 w<M'<i n^phwjcHl by a bent tube with a weighted piston,
fin whown in Fig. 28. The pressure exerted by the air in the
\M\f^ \n in part removed by the weighted piston. Turn the
f/UlKi tip tifiiil a little water is over the piston; then replace
Urn tiibn, and pull the j)iston down. The water acts as a pack-
ing, and even if the piston does not fit,
the water leaks slower than air. Work
the piston up and down a few times, or
turn the tube up and fill it with water.
For all practical purposes, the piston is
now made of water. This piston of
water is drawn down by its weight, just
as th(i first piston was, and in the same
way it lessens the pressure of air in the
tube. The atmospheric pressure on the
water in the dish is no longer balanced,
and drives the water up the short arm.
How high can the bend be above the
lovnl of the wat(ir in the tank, when the barometer is 76 cm. ?
I low high can the bond be, if mercury is siphoned? If the
long arm be phuMid in the tank, what happens ? Which would
oxnrt more pnmHure, the liquid in the long or in the short arm ?
I low high do(m water rise in a siphon placed empty in a tank ?
How should the length of the short arm be measured ? What

Fff. 20.

PRESSURE.

is the effect of making an opening at the bend ? at a point in
the long arm at the level of the water in the tank ? Can water
be siphoned over a hill 100 feet high ? What is the effect of
lengthening the long arm ?

41. Experiments with Siphons — Make a siphon in the form
represented in Fig. 29, using a rubber tube, and raise and lower

v^:^

Fig. 30.

n£. 29.

the opening. Partly close the opening, and try to find out
how high the water spurts from different levels.

Raise and lower one of a pair of tanks, connected by a
siphon, as represented in Fig. 30. Remove
the siphon. Does it empty itself ? Why ?

Under what conditions will a siphon fail
to work ? Consider the comparative lengths
of the short and the long arms, the pressure
of air, and the possibility of leaks in the
bends.

42. Intermittent Siphon. — Remove the
bottom of a bottle; put a siphon through
the stopper. Place it where water will
drip into it from a faucet or tank, as in
Fig. 31. Explain what happens. Read the
encyclopedia on "Tantalus cup" and "Intermittent springs."
How could a sewer be flushed at regular intervals ?

CU AVTKR III.

LIQUIDS AND OASES.

Bxerolse 8.

MI^MdlirMi (4IIAVITY Of A LIQUID. BALAHCDTe OOLinan.

■iliinnuluit \¥fti mImnh liiltoN, roiiiiiu!t<Ml by rubber tubing with a three-way
hilii. (|«n.rMitblv iif iiiHt(il), hi Mio third arm of which is attached a short
iiilflfi.! ImIm, ( liiHdil l)v M I'liiK i (HnIi of water; dish of some saline mixture.
I !(«' |«lii^ iiiiiy tin »t kIhmm tiibo rloMid at oii(5 eud.

I it( ifldHM tiilid I ( l«'lK. nif) (lipH into pure water; the glass tube B

Ht|iM imIm II hmIIiim iiiiiiliiiK, Hiioli liH c.oininon Bali or sulphate of copper.

(hwiMJVH iJin pliiM, ^/, iiiiil ilraw Mi« air from the three-way tube, T,

iiiiMl thi^ li<itii(lH rise nearly to the top of A

(f HIM I //. Pinch tight the short rubber tube

)HI0 iinivr thi) opon ond, and insert the plug G.

Nnwlodtin^ ih«5 nffect of capillarity (section

VM, piv^ii (II), incMisure the height at which

luvdh li(|ui(l MtandH in the tube above the

lovid hi thn dinh. Record these lengths on a

dhi^rain in th(5 note-book. The liquid in B

Im ivh many iimoH heavier than the water in

i A ttM th« hmgih of the liquid in 5 is con-

!/? iainod timoH in the length of the water in .4.

j SuppoMn tho liMigth of the watei in A =70 cm.,

j and of tho licpiid in B = 50 cm. Then the

t^ H k^^dl litpiid in B ih Jg, or 1.4, times as heavy as

I ■■■■ J 6^ ?« watt^r, and 1.4 is the specific gravity of the

Hg. 32. liquid in B, Its density is also 1.4 grams

per cubic centimeter.

Find, in this way, the specific gravity of kerosene, mercury, and

brine.

iL.

jjffnn^ jLiri' qas^.

i£ rmnter iniiiiir mop^ sbmec cnpsr -IJtt stat "i«JM*<'iM* a: T. xbc

i^ Tua^ £ JLsise i. rimgTgif,. sad jpkiiil ~til^ Tmntt a: tite
Bmhc BBC 'Ott i»?igir n. ^at^L tzzk:.^

f; ^ a a iHTB

BM^I

laiiMJJiiiieli

"^♦-ae.

1. 15iiifr ik|iiic It f. F^ 2£: »npt ^ wsft l cohnnx of jcat 5«' nx-
iqp^ sue life «ra»<!r ix. ^ im;i»: #* «l m^ wumt. » uuic Me Xttt famrmr

7i A jmmi at cuirtiL^ u oraur liqujar tiiTOK<!i. lan piMF cne
lamad it water tift otutr i»- ii«*;reu*7 Wiusl fioimm. j^ tu^ iugHs: '
HwF nott^- \ta0at lu^ite^''

1L 'VTiuc; ji. tb«- tft^i^eflK ^m^it* gc i. bqiuL. if & eoimm: of it
f JL Fjj^. £f ctouiiftr :5r -ni. jtM^^ Uat «eT<e. a: lye iiquic il iat ojol.

If L difrersu :

86 PRINCIPLES OF PHYSICS.

44. Volume and Displacement. — If a lump weighs five grams
in air and three grams in water, the volume is two cubic centi-
meters. The lump loses two grams of weight when weighed in
water, because it pushes aside, or displaces, two grams of water.
Since one gram of water takes up one cubic centimeter of
space, the size, or volume, of the lump must be two cubic cen-
timeters. Suppose the same lump is weighed in oil ; the loss
of weight is less than in water. The lump displaces two cubic
centimeters in oil; but oil is lighter than water, and the two
cubic centimeters of oil displaced weigh less than two grams.
It is not buoyed up as much ; that is, it does not lose as much
weight in oil as in water. A match, made heavy by a small
pin, floats in water and sinks in oil.

45. Specific Gravity of a Liquid by Immersion of a Solid. —

Weigh a lump in air, then in water, and then in the liquid of
which we wish to find the specific gravity. Suppose the loss
of weight in water is 40 g. ; then the volume of the lump is
40 cc. In oil this lump displaces 40 cc, but h)se8 only 32 g. of
weight ; therefore, 40 cc. of oil must weigh 32 g. ; and 1 cc. of
oil weighs |^ = .8 g. What we have done is to divide the
loss of weight in the liquid to be measured by the loss of
weight in water.

Problems.

1. A piece of rock weighs 200 g. in air, 130 g. in water. What is
the specific gravity of a liquid in which it weighs 120 g. ?

2. A lump of metal weighs 22 g. in air, 16 g. in water, and 17 g.
in another liquid. What is the density of the other liquid ?

3. What is the size of a lump of aluminum that weighs 52 g. in
air and 32 g. in water? IIow much room does the lump take up?
How much of any li(pii(l would it displace? IIow many grams of
oil, density = .8, would it displace? of acid, density = 1.5? IIow
much weight would it apparently lose in these liquids? What- is
its weight in these liquids?

LIQUIDS AKB GASES.

4S. Boy]e*B Lbw. — If the escape of air from a bicycle pomp
is preyented, the air within is pushed into a smaller space,
or is oompressedj by forcing in the piston. The greater the
pressure applied to the piston, the smaller becomes the volume
of air. When the pressure is removed, the air expands, and
the piston returns to its former position. The volume, or size,
of a mass of gas decreases a£ the pressure on it increases
(see section 31, page 25). This fact, from the name of its
discoverer, is called Boyle's Law.

(*)

flm»4Tg^ TBAM MM AXKOBPHZBX.

Apparatus: Two glass tabes, one of which miHt he (A) of nniform bore, and
may be closed by a damp and a robber washer; thick-walled robber
tobing; mercory. The glass tabes are attached to boards, which slide in
grooves on an oprig^t sopport, and are held by damps in any position.

Close A (Fig. 34) at c, by the clamp and rubber washer.
A with R, which is open at
the upper end, by means of the
thick-walled rubber tubing, B.

Case f, — While in the po-
sition indicated in I, Fig. 34,
pour mercury in at i2, and
open e so that air may escape.
Close c Bead the length of
the air column in A, making
sore to read from c to the top
of the curved surface of the
mercury. Call this length the
volume, V. Bead the height
of the barometer in the room,
and record. As x and y (I,
Fig. 34) are at the same level,
the air in .4 is under the same
pressure as that in the room,
and this pressure is indicated
by the barometer. Fig. 34.

CouDect

PRINCIPLES OF PHYSICS.

Case //. — Raise R 20 cm. or more (II, Fig. 34). The volume of
the air in A becomes smaller, and this new volume, 7,, is the distance
from c to X. The air in A is under greater pressure, for it is submit-
ted not only to the pressure of the air in the room, which presses on
the mercury in /2, but also to the column of mercury between the
levels X and ;/. Call this diiference of level, h.

Case IlL — Raise R (Fig. 34) higher than in Case II, and repeat
the readings. Continue till the greatest possible diiference exists
between x and y.

Arrange the observations as in the following table: —

Baromktbr
B

Prkaritrr

-fi + A-
p

VoLtTMR
V

PxV

Cwe I ...

Case II . . .

Case III . . .

—

Case IV . . .

CaseV . . .

B is the height of the barometer in centimeters, and if the experi-
ment is performed quickly, — that is, within an hour, — the air press-
ure is not likely to change much, and the barometer reading will be
the same for all cases ; h is the difference of level of mercury in the
two arms; 5 + A is the total pressure, P, on the air in A, Multiply
the total pressure, P, by the corresponding volume K, and put the
result in the column PT.

Considering the results in the last column, how do the first two or
three figures in each result appear ?

47. A Constant. — When the computations in each one of a
series of experiments give practically the same result in all
cases, the result is called a constant. Many of the tables in
the Appendix are made u}) of physical constants.

LIQUIDS AND OASES.

Exercise 9.

(2)) FBBS8UBS8 LESS THAN AN ATM08PHEBB.

Return to Case I, page 37. Lower R or raise A (Fig. 35). The
pressure on the air in ^ is now less than that of
the atmosphere. Measure the air column in A and
the distance, h, between the levels of mercury, x and
y. Repeat several times, till the greatest possible
difference of level is obtained. Arrange the results
in a table, remembering that the pressure column
is B — h; h is the difference between the levels
of the mercury columns, and must be subtracted
from the barometer reading to get the pressure of
the air in ^.

48. Formula. — Starting with a given amount
of gas, and keeping the temperature un-
changed, the pressure, P, multiplied by the
volume at that pressure, always equals a con-
stant. More briefly, P xV= K, K standing
for some number. Changing the pressure to
Ply the volume changes ; call this new volume
Fi. Then, as we have seen in the .experi-
ment, Pj X Fi = K. These products are equal
to each other.

Pressure now times the volume now = anotlier pressure times
the new volume.

This can be abbreviated as P x F= Pi x Fi.

Fig. 35.

Problems.

1. The volume of a balloon is 400 cc, the pressure on it is that of
the atmosphere, barometer = 76 cm. What will the volume become
when the pressure is 38 cm.? Ans. F, = 800.

In this example, 400 cc. = F, 76 cm. = P, 38 cm. = Pi. Substituting,

PxF=Pi xFi,
76 X 400 = 38 X Fi,
38 Fi = 30400 ; therefore Fi = 800.

40 PRINCIPLES OF PHYSICS.

2. One hundred cubic feet of air under a pressure of one atmos-
phere has the pressure increased to 20 atmospheres. What does the
volume become? Ans, V\ = 5 cubic feet.

1 X 100 = 20 X Fi.

3. The volume of a mass of gas is 150 cc, the barometer stands
at 76 cm. What is the barometer when the volume is 100 cc. ?

Ans, P^ = 108 cm.

4. P = 40 cc, V = 110 cc, Pi = 100 cm., Fj = what?

5. P = what, when V = 24, if P^ = 200 when Fj = 96?

6. A tank is filled with air, compressed to 1800 pounds to the
square inch. The volume of the tank is 2 cubic feet. The air, before
compression, was under a pressure of 15 pounds to the square inch
(the average pressure at the sea level). How many cubic feet of air
were compressed in the tank?

7. In a certain compressed-air system for operating railway
switches, the air is under a pressure of 95 pounds per square inch.
What volume of air at this pressure will have a volume of 190 cubic
feet, when subjected to merely the atmospheric pressure of 15 pounds
per square inch ? -4 n«. 30 cubic feet.

8. For operating calcium lights, oxygen is sold in steel cylinders
under a pressure one hundred times as great as that of the atmos-
phere. When one-half of the gas has escaped, what is the pressure
in a cylinder?

Disregard the half that has escaped, and think only of the original,
and find the volume of the half that remains.

9. If the cylinder in the last problem holds five cubic feet, and
if it should burst, how much space would the oxygen then fill ?

10. The Pintsch system of car-lighting employs oil gas; cylinders
having a capacity of four cubic feet are used, filled with gas under a
pressure of 13 atmospheres. How much gas do they hqjd when full ?
What is the pressure on the cylinders ?

49. Experiment for Air Pressure Greater than an Atmosphere.
— In the year 1772, when Robert Boyle was studying the
"spring of the air/' flexible rubber tubing had not been

LIQUIDS AND GASES.

Fig. 36.

invented; so he had to use an apparatus made entirely

of glass, like Fig. 36. This was a bent tube,

closed at the short end, supported on a stand. \ /

Unlike the apparatus used in Exercise 9, page 37,

it cannot well be used for pressure less than the

atmosphere. To repeat the experiment as Boyle

did it, there is needed, in addition, two or three

pounds of mercury, and a wooden base, with raised

edges, to catch any mercury that is spilled. Rings

cut from a rubber tube may be used to mark the

levels of the mercury.

Pour in mercury till the tube is filled above the
bend. The level need not be the same in both arms.
Slip on rubber rings at the level of the mercury in
each arm. Add more mercury, till the long arm is one-third
or one-half full. Mark the new levels
of the mercury in both arms by rings,
as before. Then nearly fill the long
arm with mercury. Pour out the
mercury, and lay the tube down flat
on a table. Put a block or box
against the bend, as shown in Fig. 37.
i Make a diagram like Fig. 37 in the
[ note-book. Measure the distances ^i,
I ^2) ''8> — the heights of the mercury
"t I in the long arm above the bend, —
I and tti, 02, ttg, — the heights of the
lijjj mercury in the short arm above the
i bend ; c is the total height of the short
arm. The volume of the air in the
first case is c — ai. The pressure is
the height of the barometer plus the
] amount that ^i is higher than Oj ; the
total pressure, then, is barometer -f
(hi'-ai). This total pressure, P, on the air in the short

ft.

i?v^-^

•if \r

Fig. 37.

PHINC'IPLES OF PHT8IC8.

Hakomktkk

h-a

Total Pkemuu

BAK. + (A-a)

TOLUlfE

Px V

arm Ih ilut air })reHKiire as read by the barometer plus the un-
balatHMul iiHercniry cxjlumn in the long arm (^i — Oi). Becord
tliiiH :

riiHi' II

CUMI' III

Mi'loni n'lnovin^' tlio rubber rings, compute the values for
\\\{\ IilhI. ('.ohiiiin in tlie table, and if the products are widely
(IilT<?n'nt, n'jx'at iho ni(«i8urements.

ftO. Limitations of Boyle's Law. — Boyle's Law is approxi-
inati'ly Iriui for all ^aH('» at temperatures far above the point
wIm'mi thi-y (Jill b<^ li(iu<»fi<Ml. As the temperature is reduced,
a KaH in coinincHKi'd at a greater rate than might be expected,
and near Mm point wIm'jo the gas becomes a liquid, the con-
liiMiMiiiion Ih vr.ry much more rapid than Boyle's Law would
in(li('at;<t.

Problems.

//. A ihiy wIhiu ilu; barrjumUn- rc.adH 75 cm., mercury is poured into
an a|»|uira(.iiH liko Vyr^. 2)7: //, — 0 cm., and a^ = 4 cm. How much
^wwSiw Ih \\w. prcHHiin; on Uh; air in the short arm than the atmos-
phi'iii' .pn'HMun^V An». 2cm.

h. What. Ih \\\k\ total prcHHun)? A^is. 76+2 cm.

rt. If V. liO cm., what in the volume of the air in the short arm?

Am, 20 - 4 = 16 cm.

//. Hnpp(m<< mercury is ])ourp(l in the long arm till it stands 50 cm.
ftbovp that in the nhort arm. The total pressure is now 76 + 50 cm.,
or 150 cm. What is the volume in the short arm?

P X F = P, X Vy

70 X 10 = 150 X Vy Find Vy

LIQUIDS AND GASES.

Exercise 10.

DENSITY OF AIS.

Apparatus: A sensitiye platform scale; a two-liter bottle, fitted with a rubber
stopper that is bored to admit a gas valve with a corrugated tip (Fig. !)8) »
the valve and stopper made air-tight
with tallow or glycerine ; a cradle (Fig.
39) to hold the bottle on the sensitive
platform scale.^

Fig. 38.

Fig. 35,

Find the capacity of the bottle, by

weighing it when empty, and again

when filled with water. The number

of grams of water it holds is its volume in cubic centimeters. Mark

this number on the bottle. Exhaust the air from the bottle, and

record the amount of air exhausted.

If all the air could be exhausted from the bottle,
the capacity of the bottle would show the number
of cubic centimeters of air exhausted. But since
an ordinary air-pump must leave an appreciable
amount of air in the bottle, and any process that

would exhaust practically all

the air would be slow and

tedious, the following appa-
ratus is used to measure the

amount of air drawn from

the bottle.

The bottle is connected

with the air-pump, by the

tube Bf as shown in Fig. 40.

7* is a three-way connection ;

Hy a glass tube one meter

long, resting in a dish of mer-
cury. The rubber tubes, A

and B, are of sufiicient length

to allow the bottle and pump

to be in convenient positions

on the floor or on a table or Fig. 40.

1 From a number of platform scales, the most sensitive may be selected by
loading them in turn with weights of a kilogram or more in each pan. Balance

44 PRINCIPLES OF PHYSICS.

shelf. C is a bottle that acts as a trap to catch mercury, in case the
tube H is accidentally raised during the exhaustion. P connects
with the air-pump. The trap C is not needed, provided the gauge is
90 or 100 cm. deep, and not more than half filled with mercury.
Instead of C and //, a U-shaped tube, used as a pressure or vacuum
gauge (A/, Fig. 214, page 242) is convenient.

Exhaust the air so far as possible. Read the barometer and the
height of the mercury in H, * and calculate the amount of air taken
from the bottle. Suppose the barometer reading was 76 cm., the
gauge reading in Hj 70 cm. All the air was not exhausted, or the
mercury in H would have risen to 76 cm. ; ^ of the air was pumped
out. Find the number of cubic centimeters of air pumped out, by
multiplying the capacity of the bottle — for instance, 2200 cc. — by Jg.
This gives 2026 cc. The accuracy of the weighing is not sufficient to
make the 6, or perhaps even the 26, of any account. Call the amount
of the air 2020 cc.

Close the valve, disconnect the bottle, and weigh it. Open the

the pans by adding bits of wood or chalk, if needed ; then note what distance
the sliding weight must be moved to make the pointer move one division
while the pans are swinging a little. For this experiment a scale should be
found that indicates a change of one-tenth gram in weight.

^ A large pump exhausts more quickly. Put the bottle on the scale and
counterpoise, having the sliding weight near the four-gram or five-gram
mark. Without changing tlie weights, attach the bottle to A, and let one
pupil operate the pump with strokes the full length of the cylinder, two others
measure the height of the mercury column in H, and another turn the valve,
V, at the moment of reading. One of the two pupils measuring the height
in // keeps the meter stick exactly at the level of the mercury in the dish.
Place the bottle on the scales, and move the sliding weight till exact balance
is obtained. Record the weight as X (the weight of bottle and valve) H- the
reading of the sliding weight in grams and tenths of a gram. Admit air, and
get the balance by moving the sliding weight. Record as X+ slider reading.
Read the barometer and thermometer. The exercise is rapidly repeated by
a large number of pupils, the bottle, as soon as the air is admitted and the
weighing made, being given to another pupil. Divide the difference in the
weighings — an amount between one and four grams — by the amount of air,
and record the weight of one cubic centimeter of air at the observed barom-
eter and thermometer readings. It would prove instructive to fill the bottle
with coal gas, hydrogen, or carbonic acid gas. The first two gases should
be passed into the inverted and unstoppered bottle by a tube reaching to the
bottom. With carbonic acid gas, the bottle must be filled mouth up. Pass
the gas for fifteen minutes.

LIQUIDS AND GASES. 45

valve, and record the increase of weight. Find the weight of one
cubic centimeter of air.

51. The Weight of Air. — Weigh an incandescent lamp; one
having a broken filament is as useful as a new one. Then, tile
till air is admitted, letting the tilings fall in the scale-pan.
Weigh the lamp and the filings. The experiment is made less
tedious if most of the tip is filed away before the first weigh-
ing is made. Of course the filings made before the first weigh-
ing are thrown away.

Problems.

1. In £xercise 10, page 43, if the barometer reads 74 cm., and the
gauge reads 72 cm., what proportion of the air has been pumped from
the bottle?

2. What is the reading of the gauge when half the air is ex-
hausted ?

3. If one cubic centimeter of dry air, at 20° Centigrade, barometer
= 76 cm., weighs .0012 g., what is the weight of one liter of air ?

4. A pneumatic tire has a capacity of 4200 cc. ; what weight of
air does it hold? (Use data of third problem.)

5. If air is pumped in to 45 pounds to the square inch (that is,
3 atmospheres in addition to the one atmosphere already in it), what
additional weight is there in the tire ?

6. Does a bicycle weigh more or less when the tires are blown
up hard?

7. One cubic centimeter of mercury weighs 13.98 g., one cubic
centimeter of air, as in Problem 3, weighs .0012 g. ; how many times
heavier than air is mercury ?

8. When the air pressure holds up a column of mercury in the
barometer 76 c, what is the pressure per square centimeter? Figure
the weight of a column of mercury 76 cm. long and 1 cm. square.

9. A body is buoyed up by the weight of the air it displaces. Find
the volume of 140 g. of zinc (density = 7). How many cubic centi-
meters of air does it displace? What is the weight of that air?
How much lighter does the zinc appear to be in air than in a vacuum ?

46 PHlSilPLKS OF PHYSICS.

10. How long \\^ a oi^lumn of air that weighs as much as a column
of iiuM'oury 70 oin. loug« I oiu. squai^? Divide the result of Problem
H by tho weiglit of I iH\ of air.

Thla 1h the height of the si^ called '^homogeneous atmosphere/* If the
air did not become thinner at higher altitudes, it would not extend so far
aH it really lioeH, and the height — of course an imaginary one — would be
about tive mllea,

XX, If a lump of gold (density = 19.3) is balanced against a lump
of aluminum (dennity = 2.7), which occupies the greater amount of
Bpaoe, and which ia buoyed up the more? What would happen if
the Hoalea were put under the ivoeiver of an air-pump and the air
exhauHted V

12. Which dlsplaoejj the more air, a pound of feathers or a pound
of gold ? in which case would you get the greater amount of feathers
in a pound, when weighed, balanced against iron weights, in air or
in a vacuum?

13. From the following data, calculate the density of air : —

Capacity of bottle. 2000 cc;

Barometer, 75 c. ;

Height of mercury in gauge, 72 c. ;

Weight of bottle, air exhausted, A' + 1.9 g. ;

Weight of bottle, air admitted, A' + 4.1 g.

14. IIow large is a bottle that holds .5 g. of air?

15. A toy balloon has a volume of 400 cc. ; how much is it buoyed
up by the air it displaces? IIow much can the balloon and contained
gas weigh and the balloon still float?

16. Some one has proposed an air-ship or balloon of thin sheet
steel, made air-tight. The air is supposed to be exhausted. If the
volume is 000,000,000 cc, what is the buoyant effect? How much
can the balloon and its load weigh, and the balloon yet float? What
would be the tendency of the air pressure on the thin covering?

17. A Whitehead torpedo weighs, in air, 522,000 g. ; in water it
weighs 250 g. ; how large is it? If the propeller does not operate,
will it sink or float? On the longest run possible, 32,000 g. of air
escapes to drive the little engine ; the torpedo is 32,000 g. lighter
than when launched. If it misses its mark, will it sink or float?
How many cubic centimeters will float out of water?

LIQUIDS ASD GASES. 47

62. Air-pumps. — The ordinary lifting pump (Fig. 25, page
30) acts as an air-pamp, before the water in the well or cis-
tern is drawn up to the piston. The first few strokes pump
air removing the downward pressure on the water in the
pipe. This allows the pressure of the air on the water out-
side the pipe, being no longer balanced, to force water up the
pipe, past the valves. When such a pump is made especially
for pumping air, the piston is packed with leather, string
saturated with tallow, or metallic rings fitting in grooves in
the piston. These rings spring out and prevent leakage. The
valves are often made of oiled silk, which is much lighter and
more air-tight than leather.

It is impossible to pump all, or even nearly all, the air out
of a bottle or globe with this kind of a pump. When the
piston descends, the air, being compressed, lifts the upper
valve and passes out. When the piston is raised again, the
air in the receiver expands and fills both the receiver and the
pump cylinder. Suppose C, in Fig. 41, page 48, holds one
liter of air, and R four liters. Then the four liters of air in
R, after one stroke, occupy five liters of space, and the entire
amount of air in C — one liter, or one-fifth of the original
total amount of air — is removed at the first stroke, and four-
fifths remain behind. The second stroke removes one-fifth of
the remainder.

53. Rate of Exhaustion. — Draw a line, AB, of any length, in
the note-book. Take away one-fifth of this, and make another
line the length of the re- ^ ^

mainder. Repeat this ten ^""■"""■"■^^^"— ~"""^""-""
or more times. Notice that the actual amount removed
decreases each time, and that even after a hundred or more
of these diminutions, an appreciable amount remains. In an
air-pump, the leakage of air into the pump increases as the
air is pumped out. After a certain number of strokes, air
leaks in as fast as it is pumped out.

PRINCIPLES OF PHYSICS.

54. Exhausting by Air-pumps. — By a three-way tube, connect
enclosed barometer, B, Fig. 41, with the tube leading to the
receiver, K The height of B measures the pressure of the air
in the receiver, i?. Taking full strokes with the pump, notice
the relative amount B falls at the end of each stroke. If B
falls one-fifth of its first reading, one-fifth of the air has been
removed. Try a small receiver at R, or, if necessary, discon-
nect R at D and let the pump exhaust the air out of the con-
necting pipes and barometer bottle merely, so that the volumes
of the cylinder, C, and the space to be exhausted are equal.
This will be the case when B falls to half its height in one

Fig. 41.

stroke. At the next stroke, one-half of the remaining air, or
one-fourth of the original amount, is removed.

Air-pumps of immense size are used to remove the air from
the " condenser " of condensing steam engines, such as are used
now cm all large steamers. The vacuum gauge on one of these
engines is a bent, flattened tube, fastened at one end. The other
end moves a pointer, or needle, over a scale. Increasing press-
ure inside the tube tends to straighten it. On decreasing the
pressure, the spring of the tube makes it bend, or curl up again.

Close a piece of thin-walled rubber tubing at one end with a
cork or plug of wood. Connect the open end with a water
main. Lay the pipe in a sharp curve, and turn on the water.
What does the pressure do to the tube?

LIQUIDS AND GASES.

55. Degree of Exhaustion. — By attaching a U-pressure tube, or
an enclosed barometer to the receiver of an air-pump, as shown
in Fig. 41, and exhausting the air, the number of inches that
the column B drops is indicated on the scale. If all the air is
pumped out, the gauge reads 30 inches. Since the water con-
densed in the condenser is at a temperature of about 50° Centi-
grade, the vapor exerts a certain amount of pressure (see Exer-
cise 26, page 196). Considering this steanr pressure, 27 inches
or more is a good vacuum; this means that the vacuum is as
good as when |^ of the air is exhausted from a vessel or bottle.

When the enclosed barometer (Fig. 41) is used to determine the
degree of exhaustion, all connections should be made with thick-
walled tubing to prevent collapse. Blow into A to determine
what pressure can be exerted by the lungs. Then suck the air
out ; as much as half a vacuum can be obtained by some persons.

56. A Liquid Piston of water or mercury offers many advan-
tages. Figure 42 is a rough diagram of the form invented by

Sprengel. Connect the tube ^ to a faucet,
and turn on the water. The water, in
passing by the side tube, breaks up into
drops. Each drop acts as a piston, and
takes some air from B be-
hind. The tube connected
to C should be a foot or more
long. Air and water mixed
will pass out of D into the
dish, and water or
mercury will rise in
E, showing that air
is pumped from E,

This form of pump
is much used for
exhausting the air
from the bulb of incandescent lamps. For this purpose it is
made in the form shown in Fig. 43. A millionth, or less, of

ng. 42.

rig. 43.

W PRINCIPLES OF PHYSICS.

le original air is left in the bulb before it is sealed off.
reissler tubes require a little less exhaustion, and Crookes
nd Rontgen-ray tubes require still more.

67. Qeissler's Mercury Pump. — If a barometer tube, more

Ithan 30 inches long, is filled with mercury (sec-
tion 33, page 26) and inverted in a dish of mer-
cury, the space above the mercury in the tube is
nearly a perfect vacuum. If the mercury was
boiled in the barometer tube before inverting, there
is in it a little mercury vapor, but almost no
air. If a barometer tube is made with a bulb
at the closed end {B, Fig. 44), the bulb may be
sealed off after the tube is filled and inverted.
This will leave an almost perfect vacuum in
the bulb.

Fig. 44.

68. Practical Forms of Geissler's Pump. — In the Boyle's law
apparatus (Fig. 34, page 37), loosen the cap over the tube on the
left-hand slide. Raise the open tube till the mercury drives out
all the air and begins to run
out under the cap. Screw
down the cap, and lower the
right-hand tube till the level
of the mercury in it is 80 cm.
or more below the cap. The
space under the cap is a good
vacuum.

An air-pump made on this
principle is shown in Fig. 45.
-^ is an incandescent lamp;
A and B are valves. Close A,
open B, and raise C; air is
driven out of R. Close jB,
open A, and lower C; mercury 0*45.

runs out of R, and the air of

LIQUIDS AND GASES. 51

the incandescent lamp L expands and part flows to R, Close
Aj open By ^nd raise C; air from B is expelled. Repeat, till
the air in 2/ is practically all exhausted. Then turn a current
on the filament in Ly thereby heating it and driving off the
gases in its pores, and seal the bulb off, while working the
pump. Crookes and Bontgen-ray tubes are often exhausted
on pumps of this type.

59. Exhausting by Condensation. — An interesting, though
not very practical, way of obtaining a good ^ j^

vacuum is to condense all the air in the glass ^"N /^~>^

bulb, B, Fig. 46, by pouring liquid hydrogen ^^^ ^^

over it The air condenses as a solid on the ^'« *^

inside of B, completely leaving A. The small tube between
A and B is then sealed off.

60. Pressnre in a Liquid due to its Weight — Like all other
substances, liquids exert a downward pressure, due to their
weight, or apparent attraction by the earth. It is not down-
ward pressure, however, that bursts a dam, or makes water
spurt up through a leak in the bottom of a boat, but a sideways
or upward pressure caused by the downward pressure.

61. Downward Pressure. — Tie sheet rubber over one end of
a glass tube (a atudent lamp-chimney, for instance), and hold
the open end up. Fill the tube a quarter full of water ; notice
the sag of the rubber. Pour in more and more water, till the
tube is full. Any increase of pressure is shown by the in-
creased bulging of the rubber. Does the pressure increase
with the depth of the water in the tube? The same experi-
ment may be tried by holding the hand over the bottom of
a lamp-chimney while water is being poured in at the top.

62. Sideways and Upward Pressure. — Unless there were
enormous sideways pressure exerted by a liquid in a deep

PRINCIPLES OF PHYSICS.

tanky there would be no need of strong hoops. The upward
pressure in a liquid is shown by pushing down
into a dish of water a glass tube with thin
rubber tied over the lower end. Any movement
of the rubber may easily be made apparent by a
straw reaching from the rubber to the top.
Press a tin can, having a hole in the bottom,
down into a dish of water (Fig. 47). Does the

Rg. 47.

water exert upward pressure *

I3Z

Exercise 11.

PBSssuBS nr a liquid due to its wsieHT.

Apparatus: A smaU-bore glass thistle tube, the mouth covered with sheet
rubber, aud connected by rubber tubing to a small-bore glass tube contain-
iug a drop of colored ink; a large battery jar full of water; a student
lamp-chimney, stopped at one end with a cork. The water in the jar should
be at the temperature of the room.

Case I. — Push the thistle tube, G (Fig. 48), to different depths in
the jar of water. The pressure on the rubber
acix>8S the niouth of the thistle tube is indi-
cated by the jx)sition of the drop of ink in the
level tul>e, L What effect does the depth of
water have on the amount of pressure ?

Case IL — Try the experiment, using the
chimney, filled with water, in place of the jar.

Case III, — Replace the apparatus by an- /\
other, in which the gauge at G can be turned Ct
iu any direction without raising or lowering

the rubber. Immerse the gauge and turn in differ-
ent directions. Does the drop of ink in / indicate
any difference of pressure in different directions?

Case IV. — Place the closed end of the lamp-
chinmey above the face of the gauge, as in Fig. 49,
noticing any variations of pressure. Note also
that when the face of the gauge is under the
closed end of the lamp-chimney, as at ^, the
depth of the water immediately over it is much
Pig- 49« less than when it is at B,

ng.48.

LIQUIDS AXD GASES.

Case V. — Fill the chimney with water, and invert it OTer the face
of the gauge, as in Fig. 50.

Case VI. — With the form of gauge used in Case I, push the
gauge up into the chimney, which is inverted and full of water
(Fig. 51), noting any variations of pressure. At what point is the

^^^U;

Fig. 50.

n«. 51.

pressure iuside the chimney the same as in the open air ? At what
point is the pressure less? How long would the chimney have to be,
80 that the gauge could be pushed up to a point where there would
be no pressure? Where would that point be if the liquid were
mercury?

63. Relation of Pressure to Depth. — These experiments show
that pressure increases with the depth of the liquid ; that at a
given point below the surface of the liquid open to the air, the
pressure is the same in all directions, and is the same whether
a solid or a hollow vessel, as in Case IV, or a column of enclosed
liquid, as in Case V, is above the gauge. The pressure of the
liquid at its surface (L, Fig. 51) is zero, and the pressure inside
the tube of water at the same level is also zero. For although
the gauge inside the tube, when at the level Z/, is under a
column of water, the depth of the gauge below the level L of
the surface of the water open to the air (or the free surface, as
it is called) is zero. The pressure is nothing at that level.
By pushing the gauge up into the water above the level L, the
pressure becomes less than at L. What is the pressure on
the gauge at L anywhere in the room outside the dish ? A

PRINCIPLES OF PHYSICS.

pressure of one atmosphere = 76 cm. of mercury, more or less, as
shown by the barometer. This pressure becomes less and less
as the gauge is moved up in the tube. If the chimney reached
fifty feet above the level L, would it stay filled with water ?

64. Average D^th. — A liquid exerts pressure due to its
weight. As a liquid is free to move in every direction, unless
hindered by the walls of the vessel, it exerts
pressure in every direction. Figure 52 shows a
can 1 cm. wide, 1 cm. broad, and 6 cm. long. It
^ — ICl^ holds 6 cc. of water, or 6 g. The pressure on the
bottom equals 6 g. The pressure at the level A
is 1 gram on 1 sq. cm. of surface. What is the
pressure at B? At C? At Z>? At ^? At F?
Consider 1 sq. cm. of the side, as SA. The
J) — pgi- pressure at S is zero; at A, 1 gram per
square centimeter. The average pressure is
zero plus one divided by two, or .5 g. The press-
ure on one square centimeter of the side, as A By is

Fig. 52 ■*• "^ '^ = 1.5 g. The usual way of expressing this

is to say that the pressure per square centimeter equals the
average depth. On the section AB just mentioned, the depth
of ^1 is 1 cm., the depth of 5 is 2 cm. The average depth is

?-t-? = 1 5 cm , and the average pressure over the section AB

2 *

is 1.5 g. What is the average depth of the other sections ?

What is the pressure on each?

65. Calculation of Pressures. — In all problems relating to
the pressure of liquids due to the weight of the liquid, the
following should be kept in mind : —

The total pressure in grams on a ?u>rizonlcd surface equals
the area in square centimeters tim^ the depth in centimeters.

The total pressure in grams on a vertical or slant surface equals
the area in square centim^eters times the average depth in centimeters.

LIQUIDS AND GASES, 55

These rules hold for water, the weight of which is one gram
per cubic centimeter, or nearly that. If mercury is the liquid,
tlie pressure is 13.6 times as great as for water.

Problems.

X. a. Find the pressure on the sides of a box 6 cm. by 8 cm. by

4 cm. deep.

0 + 4
The average pressure = the average depth = ——- = 2 g. per square

centimeter. The area of one small side, 6 cm. x 4 cm. = 20 sq. cm.
The total pressure on the side = the area x the average depth

= 20 X 2 = 40 g.

b. Find, in the same way, the pressure on a large side. Ans. 64 g.

c. Find the total pressure on the bottom, ^rw. 5x8x4 = 160 g.

2. In the top of a square box (Fig. 53), a
square tube 2 cm. by 2 cm. by 6 cm. high is
attached. The box is open where the tube is
attached, so that pouring water in tlie tube fills
the box and the tube. The box is 8 cm. by 10 cm.
by 5 era. deep.

a. Find the average pressure per square centi-
meter on the side A. ' ^'2- ^^•

The depth of the top of ^ is 6 cm., that is, the top edge of ^ is 6 cm.
below the level of the water in the tube. The depth of the bottom of A

is 6 -I- 5 = 11 cm. The average depth is "*" = 8.5 cm. The average

pressure per square centimeter on A is 8.6 g.

b. Find the total pressure on A by multiplying the area of A by
the average depth, 8.5 cm. ^n«. 8 x 5 x 8.5 = 340 g.

c. Find the total pressure on B, A ns. 425 g.

d. Find the average depth of D. .4ris. 3 c.

e. Find the total pressure on side D. A ns, 36 g.
/ Find the area of the top, C, of the box.

g. Find the area of the bottom of the box.

h. Find the pressure per square centimeter on the bottom, under
the tube.

56 PRINCIPLES OF PHYSICS.

u On what does presHure in a liquid depend ?

Ans. Depth below the free surface.
j\ Is the pressure at any part of the bottom any more or less than
right under the tube ?

k. What is the pressure on the bottom ?

Ans. Area 80 x depth 11 = 880 g.
/. What is the upward pressure on C ?

Ans, Area 70 x depth 6 = 466 g.
m. Find the difference between the pressures on the bottom and
on C.

n. What is the total weight of water in the tube and can ?

Am. 424 g.
3. Figure 54 is a tank 6 cm. by 6 cm. by 4 cm. deep. Out of the
top rises a tube 20 cm. long.

a. Find the pressure per square centimeter at the
bottom. Ans. 24 g.

b. What is the pressure per square centimeter at the
top of the box V

c. Does the diameter of the tube have any effect on
the pressure on the base ?

4. What are the pressures in Problem 3, if the liquid
is kerosene, density = .8 ?

5. A cubical box, 10 cm. on an edge, has a pipe, filled

Fig. 54. ^^^^ water, rising 80 cm. from the top. What is the

pressure per square centimeter on the bottom ? What is

the total pressure on the bottom? What is the average pressure on

a side of the box? What is the total pressure on a side of the box?

6. Find the pressure per square centimeter on the side of a canal
50 cm. below the surface of the water.

7. What is the pressure, near the keel, on a vessel drawing 600 cm. ?

8. What is the pressure at the bottom of an ocean 750,000 cm,
deep?

Neglect the increase in density of the water as the depth increases.
Water is slightly compressible.

9. A submarine boat sinks 1200 cm. below the surface of the
water; what is the pressure per square centimeter on the sides of
the boat?

LIQUIDS AND GA8E8. 57

10. The air in a diver's suit is pumped in under pressure at the
top, and escapes from the lower part of the suit. The pressure of
the air in the suit must equal that of the water outside. What is
the pressure 1500 cm. below the surface of the water?

11. The pressure of water in a street main or in a pipe in a house
service depends on the depth below the surface of the water in the
reservoir, or the difference in level. The size of the reservoir has no
influence on the pressure. If the water pressure at a certain point
is 2000 g. per square centimeter, how much higher is the surface of
the water in the reservoir?

12. K one atmosphere of pressure sustains a column of mercury
76 cm. high, or a column of water 1033 cm., what is the pressure of
an atmosphere, in grams, per square centimeter ?

13. An atmosphere equals 14.7, or nearly 15, pounds per square
inch, and this pressure holds up or balances a column of water about
34 feet high. (To find the exact amount, reduce 1033 cm. to feet.)
What is the pressure in pounds per square inch 34 feet under the
surface of a lake ? 68 feet under the surface ?

14. What is the difference of level between a place where the water
pressure is 45 pounds per square inch and the level of the reservoir?

15. If the water pressure in a town is 170 pounds, how high is the
reservoir above the town ?

66. Pressure and Weight — The bases of the dishes A, B,
and C (Fig. 55) are the same size, and the dishes have the
same depth.. Which

holds the most water ? V^ y I I J I

Which the least? Dis- X ^ X I ^ I X^X

regarding the weights p-g* 55

of the dishes, which

weighs the most when filled with water? The depth being
the same in all three, how does the pressure per square centi-
meter on the bases compare? Since the areas of all three
bases are equal, how do the total pressures on the bases com-
pare ? Not considering the weights of the dishes themselves,
the pressure that J5, when filled with water, exerts on the
table^ exactly equals the pressure of the water on the base.

PRINCIPLEa OF PHYSICS.

Ay full of water, weighs more and C less than the pressure on
the bases of the dishes. This paradox seems clear, if we
notice that the slanting sides of A help to hold up some of
the water, and the sides of C hold down some, as it were.

67. Pressure and Depth. — Why does not the water in a
kettle drive the water out of the nose ? Pressure depends on
depth only. In Fig. 6G, the weight of the
f' large amount of water in the large arm D
does not force the water out of the small
arm F, because the height ED equals the
height EF, The pressure at -K to the
right, due to the column of water DE, is
exactly equal to the pressure to the left,
due to the column FE, These pressures
balance. " Water seeks its level," because
a higher level at one point means a greater depth and a greater
pressure in all directions under the point of a higher level.
This greater pressure causes a flow of liquid till the surface of
the liquid is at the same level everywhere.

^ — E-

Flg. 5«.

68. A Body buoyed up in a Liquid. — Experiments have
shown that a body is buoyed up by a force equal to the weight
of tlie liquid it displaces. A cube, C
(Fig. 57), is 4 cm. on each edge. The vol-
ume is 64 cc. The loss of weight in water
is 04 g. Wliy is the cube buoyed up ? The
top of the cube is 6 cm. below the surface ;
the pressure per square centimeter at that
deptli is i^g.'y the area of the top of C is
16 sq. cm. The total downward pressure,
SAy is 6 X 16 = 96 g. The area of the bot-
tom of C is also 16 sq. cm. ; but the depth
is now SD, which is 10 cm., and the pressure per square centi-
meter is 10 g. The total upward pressure on the bottom
is 10 X 16 = 160 g. The difference between the downward

- t :

Fig. 57.

LIQUIDS AND GASES. 59

pressure on the top, 96 g., and the upward pressure on the
tiottom, 160 g., is 160 — 96 = 64 g. ; 64 ec. is the volume of
the cube. Work out the figure, if the cube is 20 cm. under
water, SA is 20 cm., and SD is 24 cm. Does the loss of
weight of an immersed body depend on the depth below the
surface ?

69. A Body haoyed up in Air. — A body in air is buoyed up
by the weight of the air it displaces. A cubic centimeter of
air at ordinary temperature at the sea level weighs about
.0012 g. How much heavier would a cube 100 cm. on an edge
be in a vacuum than in air ? A balloon of silk or a soap-bubble,
filled with hydrogen or coal gas, rises because the weight of the
balloon or bubble is less than the weight of the air displaced.

The air pressure increases the further we go toward the centre
of the earth (see section 35, page 28). At the sea level, the
pressure of the atmosphere per square centimeter is 1033, or
about 1000 grams. As water is about 800 times as heavy as
air, it is necessary to descend 800 cm. in air to get the same
increase in pressure that would be obtained by descending
one centimeter in water. A barometer, if taken from the level
of the bottom of a balloon to that of the top, registers the
difference in pressure that makes the balloon float.

Problems.

1. A vertical tube, DB (Fig. 58), 30 cm. long, is connected with the
side of a tank. ^ is 5 cm. above C, and ^ C is 25 cm. The tank and
pipe are filled with water, and open to the air at D.

Pressure depends on depth below the free surface.
The free surface here is 2>. Find the pressure per
square centimeter at the level of A ; also at B and at
C How far is C below the opening at Z) ?

Ans. Pressure at A, 10 g.; at ^, 30g. ; at C, 35 g.
C is 35 cm. below Z).

2. Suppose DB (Fig. 58) is 30 cm.; AB, 15 cm.;

BC, 20 cm. Find the pressure per square centimeter Fig. 58.

•E

60 PRINCIPLES OF PHYSICS.

at tho level oi A ; of B\ of C. Would these pressures be increased
if the tube DB had a greater diameter?

3. JCF (Fig. 50) is 20 cm. \HF, 30 cm. ; and FG, 10 cm.
a. What are the pressures at the level of //, E, F, and 6*?

h. If the tank and tube are filled with water, will the pressure at
// be greater or less than at E ?

c. If, after the can and tube are filled, a sheet of
rubber is tied over E, will the rubber bulge in or out?

d. If an opening is made in H, would water run
in or out?

e. What holds the water up to the level oi HI

f. If E were 50 feet below H, what would happen
to the water? What pressure would the top at H

liave to resist, and from what source would the pressure come?

4. The story is told of a little schoolboy in Holland who thrust his
arm into a small opening in a dike and stopped the flow of water,
thus preventing the opening from growing larger and causing an
inundation. Suppose the distance below the level of the North Sea
was 150 cm.; what pressure per square centimeter did he have to
withstand? How could a little boy hold back the whole North Sea?

5. Compare the difficulty in stopping the flow of water from a
large and from a small opening in a water-pipe or faucet. Why are
large pipes made thicker than small ones ?

6. Why does a bicycle tire need reenforcement with strong cloth
to withstand the same pressure that the rubber tube connecting the
pump easily stands ?

70. Forced Pressure of Liq^iids and Gases. — The pressure
exerted by liquids and gases is not always due to their
weight. Water driven by the piston of a force pump or
syringe, and air pumped into a bicycle tire, owe but a small
fraction of their pressures to their own weight. The pressure
on the piston is transmitted in every direction.

Stretch a rubber band by two pins or matches placed inside
the band. What shape does the band take? Use three or
four, or any number of pins, all pushing out equally. How
many must be used to make the band assume the form of a

LKfUIDS AND OASES. 61

circle ? A flexible tube under pressure from the inside always
takes such a form that a cross-section is a eircle. Look at u
rubber hose carrying water under pressure. Close one end of
a thin-walled rubber tube, and blow into the other end. A
rubber band is a small section cut from a large, thin rubber tube.
In how many directions must pressure be applied from the
inside of the band outward to make it take a circular shape ?
Why are boilers made round, instead of square ?

71. Distribution of Pressure. — From a study of the experi-
ments mentioned above, or by pressing on any part of a bicycle
tire, one is led to believe that pressure in a liquid or a gas is
exerted equally in all directions. A soap-bubble is almost a
perfect sphere. Any greater pressure of the air inside, in one
direction more than another, would make the bubble bulge out
at some part. The following experiment shows that the film
of a soap-bubble exerts pressure : —

Blow a soap-bubble with a large pipe. Hold the month of
the pipe toward a candle-flame. The air inside the bubble is
under pressure, and blows out the flame.

Blow into a tube having a diameter of \ inch ; I

hold one finger over the other end of the tube. 1 1

Blow in at c. Fig. 60, and try to keep the piston I

D in. (The piston fits much closer than the dia- ||| |||ij3

gram represents.) Exactly the same pressure 111 Jillll

per square centimeter was applied tp the finger pig, go,
closing the small tube and to the piston D, but
the total pressure on D was greater, because there are in it
more square centimeters for the pressure to act on.

72. Hydrostatic Bellows. — Lay an inner tube of a bicycle
tire on the table in the form of a U. Place a large drawing-
board on the tube, and blow in the opening of the tire. See
how great a weight can be raised. A person can stand on the
board and lift himself. This apparatus is known as the
Hydrostatic bellows.

PRINCIPLES OF PHy^8ICS.

Fig. 61.

Set the apparatus (Fig. 61) on a stand, and find the largest
weight that can be lifted by the piston Z>, by blowing in the
tube c. Calculate the area of the piston. Find what the
pressure of the air is, by testing with the en-
closed form of barometer (Fig. 41, page 48), or
by using a U-shaped mercury gauge (3f, Fig. 214,
page 242). Remember that each centimeter the
mercury is made to rise measures a pressure of
13.6 g. per square centimeter. How nearly does
the computed total pressure on the piston com-
pare with the weight raised? Of course the
weight of the piston itself and the friction cause some appar-
ent loss. Attach a stout rubber tube to c, and connect with a
bicycle pump. Which has the greater total pressure, the piston
D or the piston of the pump ? Which has the greater area ?

73. Efficiency of Pistons. — Connect c. Fig. 62, by a heavy
rubber tube to a small bicycle pump, or, preferably, to the pump
described in Section 34, page 27. In the former case, see that
the connection is made to the opening on the pump marked
" exit." The pump is then used as a force-pump. How great
a weight can be lifted by the piston
Z>? There is, of course, a large
amount of friction in both pistons;
and &ince the effective lifting i)ower
of D will not be as many times greater
than the force down on ^ as the sur-
face of D is times greater than that
of A, the pressure on A should be
tested by a s])ring balance, S.

Suj)pose D is twenty-five times as
large as A. Then any pressure ex-
erted on A — for instance, 10 pounds
— is transmitted to D, and the total pressure on Z> is 25 x 10
pounds = 250 pounds. However, any force applied to the
handle of -4, as registered by S, is not all effective. A little

Fig. 62.

LIQUIDS AND GASES. 68

is lost in friction betvreen A and the sides of the pump.

Again, at D, there is a further loss from the same cause. A

pressure of 10 pounds on the handle Ay instead of balancing

250 pounds at Z>, may balance 200 pounds. The efficiency

200
of the machine is -— = .80, or 80 per cent. If a liquid, such

as water, alcohol, or oil, is used in the experiment (Fig. 62),
in place of air or steam, the friction of each piston is from
one to five per cent of the force on it.

In all problems, disregard friction for the present.

74. Elevators. — Pistons, such as Z>, Fig. 62, are made several
feet in diameter and twenty or more feet long. The piston D
is sometimes used as shown in the diagram, to raise loads from
one story of a building to another. More often the piston, by
means of connecting pulleys and ropes, raises or lowers a car
rapidly, while the piston itself has a slow movement. Water
is almost always used to move the piston D. Figure 62, then,
is the simplest form of the hydraulic elevator.

75. Hydraulic Press. — Set the cylinder and piston, Z), in a
rectangular frame of iron (Fig. 63). Place a cork, E, on Z>, or
on pieces of wood or metal resting on D, The top of the cork
should nearly or quite reach the iron frame.
Connect a rubber tube to c and blow into it.
Replace the cork by an English walnut, and
try to crack the nut. A bicycle pump con-
nected with the tube gives higher pressure.
This (Fig. 63) is the simplest form of a hy-
draulic press, which is used to compress cot- p. gj
ton into compact bales, to press metal into

various shapes with dies, to punch holes in steel plates for
steam boilers, and, in fact, for any work where enormous press-
ures are required, and where the slow motion of the piston is
no disadvantage. Properly, the term hydraulic should be ap-
plied to this press only when water is used in the cylinder.

64 PRINCIPLES OF PHYSICS.

Problems.

1. The area of D, Fig. 0*2, is fA) Hquare inches ; the area of ^4 is 1
square inch. The pressure on A is 12 i>ounds ; what is the total press-
ure on Z) ?

2. What is the pressure per square inch on D ?

3. How many times larger must D be than A, so that a pressure of
20 pounds on A will lift or balance 240 pounds on Z)V

4. If 60 pounds on D balances 2 pounds on Aj what relation does
the size of D bear to that of A ?

5. If the water in a street main has a pressure of 40 pounds per square
inch, what pressure is D capable of exerting, if the area of D is 100
square inches ?

76. Surface Films of Liquids. — Dip a glass rod in water.
Examine the shape of the surface of the liquid next to the

glass rod and the sides of the jar (Fig. 64). Lift

the rod out of the water. How much water

clings to the rod? Try the same experiment,

using mercury in place of water. Try tubes of

small bore instead of the rod. Try a still

smaller glass tube, made by heating one of the

Fig. 64. small tubes a few inches from the end, and

drawing it out quickly. Color the water with ink, to make

it visible. The water rises higher in the smaller tube.

77. Experiment. — Draw out a fine ^^__^ ^ ^
tube, Cy from a larger tube, A (Fig. ^ ^
65). Hold a match near X. As soon
as the fine tube bends, change the po-
sition of the tul)e till a complete
bend, like B, is obtained. Pour mer-
cury into B. Notice the depression
in the small tube. *

78. Capillarity. — Water wets the surface of glass; they
attract one another. Mercury and glass repel each other, and

LIQUIDS AND GASES. 65

the surface of mercury in a narrow tube is convex. As these
phenomena are noticeable in the case of small tubes, the name
capillarity (from the Latin, capillus, * a hair ') is used. The
baiometer column of mercury is slightly depressed by capil-
larity.

Water, oil, etc., fill the spaces between the threads of cloth
or wicking. If a few drops of water are added to a tumbler
level full, this force of capillarity prevents overflow.

Tarnished metals are not wet by mercury. Show, by a
drawing, the shape of the surface of mercury into which
a piece of tarnished metal has been put. Zinc, or any other
metal, freshly cleaned by dipping in acid, can be wet by mer-
cury. Show the form of surface between zinc and mercury.

Problems.

1. Assuming that a 34-ft. head of water gives a pressure of 15
pounds to the square inch, or one atmosphere, as it is called, how
many atmospheres of pressure are there 1700 cm. below the surface
of a lake?

An$, 50, in addition to the pressure of the air itself on the surface
of the lake.

2. If 200 CO. of air at the level of the lake are under a pressure of
one atmosphere, what would the volume become 1700 feet below the
surface, where the total pressure is 51 atmospheres ?

3. The water pressure in a city water main is 80 pounds per square
inch; the diameter of the piston of an elevator is 10 inches, and the
area of the piston is 78 square inches. How heavy a load can the
elevator lift under pressure from the water main, disregarding fric-
tion? Taking the friction loss as 30 per cent, what load can be
lifted?

4. What must be the area of the piston of an elevator or hydraulic
jack to raise one end of a car weighing 10 tons, the pressure of water
being 200 pounds to the square inch ? (The jack lifts half the weight
of the car, of 5 tons. This equals 10,000 pounds. How many square
inches, each having a pressure of 200 pounds, must the piston have
to give a total foree of 10,000 pounds?)

CHAPTER IV.
FOBOES.

Bxerolse 12.
001CP08ITION OF FOBOSS.

Apparatus : Three 2000-gram spring balances ; adjustable clamps ; fish-line.

Tie two spring balances, .1 and By Fig. UO, to opposite ends of a

piece of fish-line. Hold Ji in the hand, or fasten it to a clamp. Pull

^'1 till one tliousand or more grains are registeretl on the two balances.
If tlie balances are liocurat^s thoy will l>oth register the same
O pull in grams. The pulls am in opposite directions, and ara
^ exactly equal.

Tie a loop in the end of the line, and through the loop
pass another piece of line (Fig. 67). Connect the balances
C and I), Pull (* and D till .1 n^gisters the same pull as
before. To hold the balunctvs in place, tie stout strings to
their rings. Hold the strings by the cams of clamps that
slip over the edge of the table.
Adjust the pull of A by loov^n- g

ing the cam and moving .4 by

Fig. 66. the string attached to the ring,
till it reads the same as before.

Then rotate the cam to fasten the string.

Record the readings. The result of the

pulls of C and D is exactly the same as if

the single foi*ce By dirtwtly opiH>site in

direction to ^l, rt»placed C and /). The

single force B is called the retfultant of

the forces C and 7). and the forces C Fig. 67.

and D are called compouents. The sum

of the forces C and D is greater than the single force B,
To see if this is always so, make the angle Itetween C and Dt

COMPOSITION OF FORCES.

Wge as possible. The limit is reached (Fig. 68, 1) when the force
^hich has been registered at A cannot be obtained by C and D
pulled oat to the limit of the scale. Make diagrams of the general
directions of the forces in Fig. 68, recording the readings of the
Wances. It will be noticed that the sum of the component forces C

C^ ^ C^^D

n. in. IV.

Fig. 68.

and D is always greater than the resultant or single force that can be
substituted for them. The sum of the components decreases as the
angle between them becomes smaller, till their sum, when the angle
between the forces is very small, as in Fig. 68, IV, is only slightly
greater than the resultant.

If two boys pull on a sled, one boy toward the east and the other
toward the north, the sled will move in a direction somewhat between
east and north, — in the direction of the resultant of the two forces
applied. If the boy pulling north pulls hard, and the other boy pulls
gently in an easterly direction, the sled wiU move a little east of north,
but nearly north ; for the resultant is always somewhere between the
two components, and its direction is nearer
to that of the greater component.

Arrange the apparatus about as shown in
Fig. 69. See that no balance registers less
than 1000 g. Place a sheet of paper under
the lines, with its centre near E. Tap the
balances, or jar the table slightly, so that
the effect of friction is eliminated. Press
the line down at E and at ^ . If the line
does not almost touch the paper, put a note-
book underneath the paper. With a sharp-
pointed pencil, held vertical, mark along on
both sides of the string near A and E. The dotted lines (Fig. 69)
indicate where the fine pencil marks are to be made; they are, of

Fig. «9,

PRINCIPLES OF PHYSICS.

course, closer to the fish-line than is shown in the figure. Mark EC
and ED in the same way. On A E record the pull of the balance E.
On the other lines, record the pulls of the balances attached to them,
llemove the paper. Make a fine mark, freehand, between the two
parallel lines at E^ and also at A, Draw a line through the marks
just made, using a ruler. This line will represent the direction of
A E. In the same way locate and draw CE and DE. If they meet
in a point, the work has been well done. The three lines represent
the three forces in direction only. To make the lines represent the
pull of each balance, mark o£E spaces, centimeters, for instance, on
each line, making a space for each 200 g. of pull. If the pull of ^4^
is 1400 g., then AE is 7 cm. long. Erase the ends of each line not
marked off into spaces.

Repeat the exercise, varying as much as possible the angles between
the forces. Have the balances register as nearly as possible the full
amount of the scale.

79. Parallelogram of Forces. — In Fig. 70, AE represents
1400 g., and DE 1600 g. Make a parallelogram by drawing a
line through D parallel * to EA, and another line through A
parallel to ED. These new lines cross at F, Draw the diag-
onal EF, Is the direction of EF opposite to EC? Measure
the numbers of centimeters in EF, and call each centimeter
200 g. ; what is the force represented by EF ? Is it equal to
CE? Exact correspondence may not be obtained, through
errors in the balances and slight inaccuracies in the work.

1 To draw a Line parallel to Another. — To draw a

line through z parallel to xy

(Fig. I), place a card with

its edge coinciding with the

line xy (Fig. II), and bring

a ruler close up to the end

of the card. Now, holding

the ruler in place, the edge

of the card is always parallel

to xy, no matter how far up

or down the ruler the card
is moved. Slide the card up, till its edge touches z. Draw a line along the
edge of the card, passing through z. This line is parallel to xy.

Fig. I.

Fig. II.

COMPOSITION OF FORCES.

Fig. 70.

A and D have been taken as the components. The force
EFy which could replace A and D, is the resultant of those
forces. CE, the force which
balances A and D, is called
the equUibraiU. How do the
resultant and equilibrant
compare in direction ? how
in magnitude? If A and
C are considered compo-
nents, ED is the equili-
brant. Complete the par-
allelogram, having AE and
CE as two sides. Its diag-
onal represents the result-
ant of A and C. Compare
it with DE. Take C and D
as the components, com-
plete the parallelogram, and study the diagonal, as before.

A boat is rowed across a river at the rate of four miles an
hour ; the current is two miles an hour. Find the path taken
by the boat, as follows : Draw two lines, representing the river
bank, of any length, four centimeters apart. Draw a perpen-
dicular between them, to show the course the boat would have
taken had there been no current. Measure down two centi-
meters on one of the lines representing the bank. Draw the
diagonal. What is the path of the boat?

If the wind blows ten miles an hour from the east, and a
bicyclist rides north ten miles an hour, from what direction
does the wind seem to him to come ? (From the noi-theast.)
With what apparent velocity does it blow ?

Does a flag on a moving boat ever indicate the real direction
of the wind ? If the wind is blowing from the north, a yacht,
in order to go north, sails first to the northwest and then tacks
and sails northeast. Why does the wind apparently shift
during the tacking ?

PRINCIPLES OF PHYSICS,

80. Direction and Amount of Resultant. — A force of 4 g.
pulls north (N) and another of 3 g. pulls east (J^ on the
object 0 (Fig. 71, I). What single force can be substituted
for these, and what is its direction ? Draw a line north and
another east from 0. Use arrow-heads to show the direction

II.

Fig. 7

of the forces. Make ON four units long and OE three units
(II). The units may be any convenient length, one centi-
meter, for instance. Complete the parallelogram (III).

Draw the diagonal OF, starting from 0 (IV). This diag-
onal represents the resultant in direction and amount. Find
the number of units of length in the diagonal. It is 5.

When the angle between the components is a right angle,
the amount of the resultant is easily computed. FE=0N=i4,
OE = 3. In a right triangle, the square of the hypothenuse
OF equals the sum of the squares of the other sides, OE
and FE.

4«=16

3« = _9

The square root of 25 is 5, and 5 is the number of units of
force in the resultant OF,

Problems.

1. Find, by drawing, the resultant of a force north of 4 pounds
and one east of 2 pounds.

COMPOSITION OF FORCES. 71

2. Find the same by computation. Ans. R = Vl8 = 4.2 +.

3. Find the resultant of forces 6 north and 5 southeast. Use a
diagram. What force would balance these two? Should it be called
a resultant or an equilibrant ? '

4. Compute the resultant of forces 5 and 12 at right angles.

5. Forces of 300 and 5C0 pounds can be brought to bear on a
stump. What is the direction of these forces, to make the resultant
as large as possible ? As small as possible ?

6. Find, by drawing, the resultant of forces 5 and 3 at an angle of
30°; 45°; 60°; 90°; 120°. In which case is the resultant the greatest?
How great can the resultant of these forces be ? How small ? If the
angle between the forces is 180°, — that is, if they pull directly oppo-
site, — what is the resultant ?

7. If an arc light is suspended over the centre of a street by a wire
rope attached to two posts, one on each side of the street, explain why
the rope will break long before it can be pulled tight enough to be
straight. Could the rope, without any weight attached, be pulled
straight? Try the experiment, using string. Sight along the string.

81. Three or More Forces. — It will be noticed that, in all the
cases of the composition of forces, the two components and the
equilibrant meet at a point ; that is to say, they are not par-
allel. The resultant can also be found of three or more forces
meeting at a point.

If a dozen horses, each hitched by a separate rope, draw a
light building on rollers, no two horses pull in exactly the
same direction; yet the twelve forces
have a resultant — a single force that
could replace the twelve forces. Sup-

pose three horses, A, B, and C (Fig. 72), ""

pull the house H, To find the resultant

of these forces, think of only A and B, ng. 72.

Cover up the line C for the moment,

and find the resultant of A and B ; call it R, Rub out A and

Bj and uncover C. There are now two forces tending to move

H, one force C, the other R, Find the resultant of R and G.

This is the resultant of, or the single force that could be sub-

PRINCIPLES OF PHYSICS.

Fig. 73.

stituted for, A, By and C, In a similar manner any number of
forces may be compounded.

82. Resolution of Forces. — A single force can be replaced by,
or resolved into, any number of forces, just as a single force

can replace two or more forces
acting on a point, or as one
strong boy can take the place of
a number of boys pulling a
double runner.
A and C (Fig. 76) are two
posts; a force, R, is applied to the rope connecting them.
This one force R causes two forces, one. Ally pulling A to the
right ; the other, //C, pulling C to the left. When one force,
like Ry causes two or more forces, we say that R is resolved
into the other forces.

83. To Resolve a Force. — Resolve a force of 3 pounds into
two forces, one of 5 pounds, making an angle of 30® with the
given force. Draw tlie line

IIR (Fig. 74, I), represent- ^^11.11 ^
ing, by three divisions, the
force of three pounds. As
the next step, make an
angle of 30° at //, as shown
in 11, Fig. 74. Draw 7/0,
five divisions. Since the
resultant is always between
the forces, the other com-
ponent must be on the other side of the resultant. Connect R
and O; draw DR parallel to 7/(7, and HD parallel to CR
(Fig. 74, III). 777> is the other component. The divisions
used in laying off HR and HC must be all of the same length.
See how many divisions can be found in HD, The number
of these divisions will be the number of pounds in the com-
ponent 777).

Fig. 74.

COMPOSITION OF FORCES.

Problems.

1. Resolve a force of 5 pounds into two forces, one of 3 pounds,
making an angle of 30° with the other ; what is the other force ?

2. Resolve a force of 5 pounds into two forces, one, at an angle
of 45® with the 5-pound force, having an intensity of 1 pound.

3. Resolve a force of 4 pounds into two forces, one being 0 pounds
and making an angle of 90® with the given force ; find the other.

4. A force of 3 pounds is resolved into two forces ; one is 5 pounds,
making an angle of 60° with the given force ; what is the other V

84. Direction of Force. — A strip AB (Fig. 75), fastened on
the table, represents a track rail. C is a ruler, driven along

->-£

F1«. 75.

Fig. 76*.

by a force applied at F in the direction of the arrow. C can
move only in the direction of its length. A sharp point on the
end of F prevents its slipping on (7.
Vary the experiment, as in Fig. 76,
where a string, F, is shown attached to a
pin at (7. The force has the same direc-
tion as before. G may be a car or a
boat. Sideways motion in the direction
CD is prevented by the flange of the
wheels or by the keel. Supposing there
is no friction between C and AB^ or that
it is very small, the force F is resolved /
into two components. One is (7jE7, as is
shown by the fact that the boat or car moves in that direction.
The other component is (7i>, perpendicular to AB, Test this
by laying the ruler C (Fig. 77) on a sheet of paper. Push a

Fig. 77.

74 PRINCIPLES OF PHYSICS.

pencil in the direction indicated by F, Prevent any sideways
movement of the pencil by the finger at G, Provided there is
little friction between the pencil and C, the motion of C will
be in direction of (7Z>, perpetidicidar to the surface of C.
The pressure on a surface where there is no friction is always
perpendicular to the surface.

85. A Keel is a thin board, held vertically, that prevents the
sideways movement of a boat. It answers the same purpose

as the flange of a car-wheel. A keel is
usually attached to the centre of a boat.
Occasionally it is held some distance to
the side, as in Fig. 78. The sail and
the keel form a wedge, like HDC, Fig.

Fig. 78. rj^

86. An Ice-boat may sail Faster than the Wind. — The fric-
tion between polished steel and ice is small. It is easily
computed from the measurements of the height and horizontal
distance (section 96, page 81) of an icy hill on which a sled
just keeps sliding.

DCHy Fig. 79, is a wedge; HC is longer than HD. See
that the edges are rubbed smooth and polished with graphite.
Press against the wedge with a rounded
piece of metal, W, in a direction at '^^^^^^^^^^^^
right angles to A and B. TT, in moving HI ^y^^

then the forward motion of the ice- Fig. 79.

the distance J/Z>, drives the wedge the " \y^ |
distance HC, If HB = 3, and HC^ 4, ^ \^

boat is four miles for every three miles

the wind blows in the direction DH, Though there is some

loss, the boat will go faster than the wind. However, in

sailing before the wind, — that is, in the direction in which

the wind blows, — the boat moves a little slowet than the

wind.

COMPOSITION OF FORCES.

87. Why a Boat sails into the Wind.— The pressure of the
wind on a slanting sail is not exerted in the direction in which
the wind blows, but nearly perpendicu-
lar to the sail. Suppose a force, TT,
Fig. 80, is applied by a pointed stick
that does not slip along the sail, S-,
the boat will move stern wards, or from
A to B. But if a breeze strikes the
sail in the direction W, the boat moves
forward. The action is somewhat the
same as if a lot of rubber balls were thrown in the direction W
and in bounding off from the sail caused a pressure on it per-
pendicular to the surface.

The fact that the wind pressure is perpendicular to the sail
is perhaps more clearly seen in the case of the old-fashioned
kite. The wind blowing horizontally strikes the inclined
surface of the kite a glancing blow. If the pressure on the
kite is in the direction of the wind, then the kite-string must
pull in exactly the opposite direction to the wind; that is,
horizontally. This is not so ; every boy knows that the string
is very nearly perpendicular to the
surface of the kite. The pressure
exerted by the wind must be oppo-
site in direction to the pull of the
string, and therefore must be per-
pendicular to the surface.

The wind blowing in the direction
WE, Fig. 81, causes at any point, E,
a pressure, ED, nearly perpendicular
to the sail. This force ED is re-
solved into two forces, one, EG, which moves the boat very
slowly sideways, and another, EH, which drives the boat
forward. In the case of the ice-boat, there is no slip nor any
sideways movement toward G.

CHAPTER V.

FEIOTIOH.

88. Surface Resistance. — We all know that a sled draws
easier over snow than over gravel or an iron rail, and that a
loaded sled pulls harder than an empty one. The resistance
caused by one surface sliding over another and tending to stop
the body is called Friction,

Exercise 13.

(a) COEFFICIENT OF FBICTION. - First Method.

Apparatus : Board having a smooth surface ; wooden box, to the bottom of
which three small pieces of wood or metal are glued, like runners of a
sled ; a 2000-gram spring balance, and various weights. Sandpaper the sur-
face of the board and round the three projections on which the box slides.

Weigh the box, containing a certain load. Place the board in a
horizontal position (Fig. 82). Find how many grams' pull is re-
quired to keep the box slowly sliding. The friction on starting is

greater, but this is to be en-
tirely neglected; what is to
be measured is the friction
P, 32, resistance while the box is

moving. The box will stick
a little in places where the friction is greatest, but several trials should
be made and the average taken as the friction resistance. It is easier
to read the balance if the board is drawn under the box than if the
box is pulled over the board.

The pressure between the surfaces of the board and box equals the
weight of the box and its contents. Find how much of the pull reg-
istered by the spring was required for each gram of pressure between
the surfaces. For instance, if the weight is 400 g. and the pull to
make it slide is 100 g., then the puU for 1 g. is ^ as much, \^= 0.25.

FRICTION. 77

Increase or decrease the load in the box. Does the pull, or force,
required to make the box slide vary? Make a statement showing
what effect increased pressure has on the friction. Does the friction
increase as the weight or pressure between the surfaces is increased ?
Compute the friction caused by each gram of weiglit for each case ; in
other words, find the force required to make one gram slide. Use as
small a spring balance as will register the load without the pointer
striking the bottom of the scale. Vary the weight again, and ret>eat.

89. Formula for Coefficient of Friction. — The force required
to make one gram slide on a horizontal surface is called the co-
efficient of friction. It is found by dividing the force required
to make the body slide by the weight. In shorter form,

Coefficient of friction = ^^^ •
Weight

Find the coefficient of friction between metal and wooden
surfaces ; between rubber and leather, using both the smooth
and the rough sides of the leather. Try the effect of unplaned
surfaces. Rub together two pieces of wood, — matches, for
instance. Cover them with blacklead (rubbing with a soft
lead pencil will answer) ; rub them together again, and notice
that the friction is less. Oil, graphite, tallow, etc., used to
reduce friction, are called lubricants,

90. Effect of the Load. — The values obtained for the coeffi-
cient of friction will be found to vary somewhat. Yet the
coefficient of friction is nearly the same for light and heavy
loads. The following law is approximately true: Tlie coeffi-
cient of friction is independent of the load. What is meant by
this ? Does increase of load in a sleigh increase the friction ?
Does it increase the coefficient of friction ?

If the pull indicated by the spring balance in Fig. 82 is
200 g., and the load, W, is 1000 g., what is the coefficient
of friction ? (tWtf = -^O.) What is the force required to
make a load of only one gram slide ? (.20.)

78 PRINCIPLES OF PHYSICS.

91. Effect of the Surface. — If the coefficient of friction,
that is, the force required to make one gram slide, is the same
for large and for small loads, it follows that the coefficient
of friction is practically independent of the size of the sur-
faces in contact. Suppose two blocks, each weighing one gram,
have the same surface. The same force is required to move
them, whether they are side by side or piled one oi\ top of
the other. The coefficient of friction is therefore nearly the
same, whether the sliding surface is large or small. The
usual way of stating this is: TJie coefficient of friction is inde-
pendent of the surface,

92. Exceptions. — These two laws are really two ways of
stating one law. They hold only while the surfaces are un-
changed as the body slides along. Very heavy loads may cut
and roughen the surface and so increase the friction. A sled-
runner as thin as a knife would cut into the ice and draw very
hard. The sliding surfaces should be large enough to prevent
one cutting into the other ; else the friction will be increased.

93. Advantag^es of Friction. — Friction is useful at times.
Without it, standing on the side of a hill would be impossible ;
a locomotive could not draw a train, nor could the train, once
in motion, be stopped by putting on the brakes; a bicycle
would slip sideways, and its wheels, though made to turn,
would not send it ahead ; a knot in a string would slip. In
most cases, however, friction is a disadvantage, and the work
done in overcoming it is all wasted.

Find the force needed to make a loaded car slide on a board
when the wheels are wedged or blocked so that they cannot
turn. Let the wheels turn freely, and again find the force.
Friction is reduced by making the load smaller, by using hard,
smooth surfaces, and by flooding them with oil. The use of
wheels diminishes the loss due to friction. A carriage wheel
thirty-six inches in diameter, for example, has an axle one inch *

FRICTION. 79

in diameter, on which it turns. The circumference of the
wheel, and consequently the carriage itself, travels thirty-six
times as far in one revolution as the bearing on the axle,
where the rubbing friction occurs ; so that the force of friction
has to be overcome through only ^ the distance ; and, besides,
the bearing and axles are made smooth and oiled.

Problems.
In the following problems, consider that the surfaces are horizontal.

1. A pull of 40 pounds is requhed to make 200 pounds slide.

What force is needed to make a weight of 1 pound slide, and what

is the coefficient of friction ? >« 40 oa

Arts, — = .20.
200

2. The coefficient of friction between two metal surfaces, well
lubricated, is sometimes as low as .03. What force must be applied
to make a one-pound weight slide ? What force to make 600 pounds
slide? Ans. .03 lb. ; 600 x .03 = 18 lbs.

3. If the weight is doubled, what is the effect on the friction?
What is the effect on the coefficient of friction?

Ans. About double; almost none.

4. Compute the coefficient of friction between two pieces of wood,
the pull being 44 pounds, and the pressure between them 88 pounds.

5. Compute the coefficient of friction, if a pull of 6 pounds is
needed to make a body weighing 30 pounds slide.

6. Cast-iron on cast-iron has a coefficient of friction of .15. What
force must be used to overcome the friction of a 32-pound lump? "

7. If two horses pull 3 tons of coal on a sled, how many horses
should be attached to pull 6 tons ?

8. What is the effect of making the runners twice as wide ?

94. Effect of Speed. — The coefficient of friction becomes less
as the speed is increased. A locomotive engineer, in stopping
a train at full speed, turns sufficient air pressure into the cylin-
ders under each car to drive the piston and to force the brake-
shoe firmly against the wheels. As the train slows down, the
coefficient of friction increases, and the wheels are sometimes
gripped fast by the brake-shoe and made to slide on the track.

PRINCIPLES OF PHYSICS.

To lessen the pressure and to keep the wheels from sliding,
the engineer turns off the high pressure and then turns on a
lower pressure. He is careful not to grip the wheels so hard
that they stop turning and slide on the rails ; for as soon as
the wheels begin to slide, the friction between them and the
rail is lessened, and the train cannot be stopped so quickly.
The wheels are held on the track by the weight of the train ;
but the brake-shoes can be forced against the wheels with a
much greater pressure. In case this is done, the wheels stop
sliding against the brake-shoe and slide along the rails.

Exercise 13.
ib) COEFFICIENT OF FBICTION. - Second Method.

Apparatus : The same as for Exercise 13, page 76.

Raise one end of the board till the loaded box, W (Fig. 83), slides
down slowly after it is
once started. Measure the
height, hy and the horizon-
tal distance, d. Divide h
by (f. Change the weights
in the box. In each case _, ^.

Fig. 83.

vary the height, A, till the

box just continues to slide after it is once started by the hand.

Record as follows : —

h
d

Case I. Box empty

Case IT. Box lightly loaded

Case III. Box with added weight

Case IV. Box heavily loaded

Case V. Box lightly loaded

Case VI. Box empty

FRICTION.

Let each case be an average of several trials. The values in the
last column ifvill be found to vary a little. How do they compare
with the values for coefficient of friction, as found by the First

Method (page 76) ? The value - is the coefficient of friction. Is it

the same for light and heavy loads?

95. The Coefficient of Friction is the force, or pull, required
to make a body slide when the pressure between the surfaces
is one gram or one pound. Of course, the force and the press-
ure must be measured in the same unit.

Coefficient of friction = ^"^°^ ^^1"^^^*^ ^ make body slide

Pressure between surfaces

or, letting F stand for force and P for pressure, the formula

becomes „

96. Resolution of the Force. — Study Fig. 84. The incline
AB is changed till the weight keeps sliding at a uniform

velocity. The force F driving the body down the slant
is then just equal to the friction. The weight of the
body, TT, is a force acting on it and pulling it down. This
force W may be resolved, or split up, into two forces, — P,

82 PBINCIPLXa OF PHYSICS.

the pressure perpendicular to the surface, and F^ the force
tending to make the bodj slide down the incline. (See sec-
tion 82.) The pressure P on the slant is
always less than the wei^t, and becomes
less and less as the slant becomes greater.
On a horizontal plane the pressure equals
the weight. When the slant becomes

straight up and down, as ABj Fig. 85, the

c vamX) pressure of W perpendicular to AB is
zero.

The perpendicular pressure P and the
Hg. 85. force F (Fig. 84), tending to make the

'^ body slide down, can be measured directly.

Attach spring balances F and P to the weight Wj as shown
in Fig. 86. Do not let W touch
the incline. There is now no fric-
tion, and F just balances the force,
or component, necessary to drive
W down the slant, and P balances
the perpendicular pressure that
would be exerted against the in-
cline. Start with FW horizontal.
F reads zero, and P equals the '*

weight. Lower P, keeping the strings at right angles;
becomes less and F increases.

97. Computation of the Coefficient of Friction.— In Fig. 84
(page 81) we do not know the lengths of F and P directly.
Study the little triangles made by F, P, and W. Make and
letter a card or paper model of Fig. 84. Cut out the little
triangles. Ai)ply one little triangle to the other, and notice
that they are exactly equal in every respect. Apply the angles,
or corners, of the little triangle to the large triangle ABC,
and find which corners fit. The little triangles are models of
the large one. Measure the short side, DF, of the little tri-

FRICTION. 83

angle, and the side P. DF stands for the force necessary to
overcome friction and make the body slide. P stands for the
pressure between the surfaces. Write out as follows : —

Force to make body slide _ DF
Pressure between surfaces "" P '

Find what the value is, and call it the coefficient of friction.
Find the side of the large triangle corresponding to DF-, it
will be found to be BC, or h (the height of the incline). Then
find the side of the large triangle corresponding to P; it is AC,
or d. Measure h and d, and find the value of h divided by d ;

that is, — As might be expected, this gives the same result
d

as dividing DF by P. It is much more easy and accurate to
measure, in the first place, the height h and the length d, than
to cut out the little triangles and measure them.

The coefficient of friction between the surfaces is found by
adjusting the slant till the body just keeps moving when
started, and then measuring the height h and the distance d,
and dividing h by d.

Problems.

1. If, in Fig. 84, A = 4, rf = 20, and the body just slides, find the
coefficient of friction. What force is required to pull the body along
the same surface in a horizontal plane, if the body weighs 1 pound ?
If it weighs 200 pounds?

2. If BC (Fig. 84) = 120 feet; AC= 1200 feet, what must be the
coefficient of friction between the weight and the incline, so that the
body will not slide? Ans. A little more than ^ffy.

3. If the coefficient of friction between two surfaces equals .3, and
a body slides on the incline, what must be the height and the hori-
zontal length of the incline? Ans. Height, 3; horizontal length, 10.

4. Find the coefficients of friction, when the dimensions of the
incline are : —

a. Height = 40, horizontal length = 800.

h. Height = 60, horizontal length = 1200.

c. Height = 12, horizontal length = 20.

d. Height = 1, horizontal length = 40.

84 rsurciPJLEs or rHTSics.

SL T&ae B SL mcrmi^ of w&Ddi ti&e bociaocklal length is dO. Find
tiK hai^ ixL each, of thi& foIlQwiii^ tsaiKS^ if Ha^ bodj just slides : —

c When idbe- co^ficffiid: of fnenkML is }.
i. Wben difr eoeificoeiLti of fnetnom is X
ff. Wh«i tihi* eoelfioMiti of frirtioa is A,

98. TifiitJMi if tke Ijtvs. — In tice case of smooth snrf aces,
especially ol metal, inorieasmg the weight or piessure between
the sarfaees increases the fri%!tioci. so that doobling the press-
ure pretty nearly doables the force required to make it slide.
But the frictioa caused by a one-gram pressure is about the
same whether the laid is light or heavy, just as we might say
the fare per passenger oa a train is the same^ whether one or
one hundred travel. In actual experiments^ one often finds that
the coefficients of friction vary with the load, and may cite the
instance of a heavily loaded sled coasting further than a light
sled- The laws of friction are only approximate. In Exercise
13, the empty box required a steeper slant than the loaded box.
Stilly the laws that the coefficient of friction is independent of
the weight and area of sliding surface are sufficiently accurate
to be very useful. Suppose the coefficient does vary from .14
to .16 by changing the load ; the mechanical engineer considers
these practically the same^ for the difference is much less than
would be caused if the surface were roughened or if oil were
applied. The laws and rules that engineers use are often only
approximate.

CHAPTER VI.
FASALLEL FOBGES.

99. The Resultant of two forces meeting at a point and mak-
ing a large angle is small (Exercise 12, page 66), As the
angle is reduced — that is, as the forces become more nearly
parallel — the resultant increases. When the forces are par-
allel, and pull in the same direction, the residtant force that
could replace them is equal to their sum.

Exercise 14.

(a) PARALLEL FORCES NOT MEETIHG AT A POINT. -Pint Method.

Apparatus: Stick or meter rule; 2000-gram balances; fish-line; adjustable
clamps to hold balances in position.

Tie a string, 6 inches or more long, to the ring of each balance.
To the hooks, tie pieces of string having loops to slide over the stick,
AB, Fig. 87. The strings,

C, C, C are held at any
point by clamps that slide
on the edge of the table.
Make the pull on E 1500
to 2000 grams. Adjust the
pulls on A and B till all
three strings are parallel to
each other and perpendicu-
lar to the stick AB, Over-
come friction by tapping
AB while making adjust-
ments of the balances.

Try several cases, vary-
ing the distances AE and
EB. Make diagrams; re-

Fig. 87.

86 PRINCIPLES OF PHY8IC8.

cord the distances AE and EB^ and the forces exerted at each point.
Keep tlie following questions in mind, and try to determine the
answers: How does the sum of A and B compare with J?? What
must be the value of a single force, i2, applied at E^ to replace A
and B and balance the equilibrant E ? The resultant /?, therefore,
always being opposite E, where is the resultant applied when A and
B are equal? Nearer which force is the resultant applied when
A and B are unequal? These questions may be answered by letting
two boys, A and B, carry the ends of a stick on which is hung a
basket. Where must the basket be hung for A to carry one-half the
load? one-fourth the load?

100. Conclusions. — In each case of equilibrium (Fig. 87),
multiply the force at A by the distance AE ; also multiply the
force at B by the distance BE, How do the products com-
pare ? In a case where the force at A is three times that at B,
how many times as long as AE is BE ? See if the following
conclusions can be drawn from the exercise : —

The resultant of parallel forces in the same direction equala

their sum.
Hie resultant is always sometvJiere between the cmnpojients.
TJie resultajit is always nearest the greater force.
If one comj)onent is a certain number of times the other, then

the second component is just as many times farther on one

side of the res^dtant.
One component times its distance from the restdtant equals the

other component times its distance from the resultant.

By the word distance is meant the shortest distance from
the line of the force to the point where the resultant is ap-
plied. Stating each case of equilibrium you have recorded in
the note-book, show how nearly the conclusions given above
apply.

Parallel forces are studied more completely in the exercise
on page 88, where the board. Fig. 89, may be thought of as a
widened form of the stick AB in Fig. 87.

PAEALLKT. FOBCEB. «7

X. Two hones poll at A (Fig. SS)^ one borae polk at B. Wbese an
AB must the wagon be attached, or where must Ihe resiiltaiit be a^
plied? As the force A is twice the force ^ m ^

B must be twice as far from the resiiltaiit A. j^

as A. DiTide AB into three parts, and I T

locate the resultant. ^« n

2. Let AB, Fig. 88, be ten feet lo^, and the force ax A equal 2,
and at B equal S. Where is the Tesnhant appiiedV How large v^ n'i

3. Where must a load be hung on a four-foot stic^ so thai a bor at
one end of the stick will carry one^hird di the load ?

4. K ^ (Fig. 87, page 85) = 15 pounds, and ^ = 5 pounds, how
large \a At A and B together must equal 15 pounds. If BE equals
4 feet, how long is AEt

5. A (Fig. 88) = 5 pounds, B = 7 pounds; fdid where the resultant
of these forces is applied.

5 + 7 = 12. Diride AB into 12 parts. Besahant is &^e drriBians from
which comiwnent ?

6. A bar is suspended by ropes, A and B. fig. §8. The rope B is
weak and likely to break under a load of 40 pounds. On what part
of the bar is it safe for an acrobat weig^iing 120 pounds to hang?

7. When a steam ndler weighing twelve tons has gone one-fifth of
the length of a bridge-^mn, what proportion of the wei^t is borne
by the support at each end of the span ?

8. Suppose Fig. 88 represents a ladder used as a staging by painters.
When a painter is on the ladder, the pull on rope A is 120 pounds,
and on B is 20 pounds. What is the weight of the painter? How
many feet from i4 is he, if AB = 12 feet?

In this problem, we will not consider the weight of the ladder, which
is very small.

9. One end of a car is supported by a two-axled track. The axles
are four feet apart The motor is geared to one axle, and it is de-
sired that this axle carry three-fourths of the load, so that the motor
wheels may not slip. On what part of the track does the car rest?
Make a diagram.

PRiyCIPLES OF PHYSICS.

14.

(&) TMMALLEL

MOT ■llTIWe AT A FQOIT.-

Apparatiu : The ezmeise on page 85 may be profitablj repeated, using the
foOowing apparatus: a square board, baring forty-oixie holes, in seTen
rmrs. one inch apart, with a border round the board, and extending a
fittle below it : fiah-Iine, used as a string : three 2000-grani ^ring balances:
damps ; marbles ; wire pegs fitting the holes in the board.

Part /. Lav the board on four or fire marbles. Insert three pegs
in holes in one line. Adjust the poll on the balances, holding, by
adjustable clamps, the strings attached to the
rings Cj. C^ Cg, Make the forces snch that
they are applied in parallel directions and along
the lines of holes in the board, as shown in Fig.
80. Cut out a square of paper ruled with cross
lines (Fig. 90). Make three points to represent
the position of the pegs. Draw arrows showing
the directions of the forces, and on each arrow
mark the number of grams' pull that force has.
Try seyeral cases, changing the positions of A,
E, and B, making them
different distances apart,
and changing the row of
holes, but always keep-
ing them in a straight
line. Record each case
on a separate piece of
squared paper, and paste in note-book. Study
the results. Disregarding the errors of the
balances, the two components A and B,
when added, are equal to the equilibrant E. Another way of stating
this is: the sum of the north forces equals the sum of the south
forces.

Part IL Taking any one of the cases of equilibrium in Part I.,
move one of the pegs to different holes along the line of the string, —
that is, along the line in which the force acts, as, for instance, in
Fig. 91, where the peg A has been moved from its position in Fig. 89.
See if the board is in equilibrium, when the forces Ay Ey and B have

Fig. 90.

PARALLEL FORCES.

the same intensity they had before. Try moving another peg along
the line of the string attached to the peg. Suppose ^ is to be moved.
Any point in the end row of holes may be tried. ^

While anywhere in this row, B is always four
spaces from the row of holes in which E is.
Another way of saying this is: the line of
direction of the force B is four spaces from the
line of direction of the force E.

It will be seen that a force has the same
effect, if applied or attached at any point along
the line on which the force acts. If the line
A C were extended in each direction, the peg A
could be placed anywhere along that line, and,
if the three forces were unchanged, the board
would still be in equilibrium, — that is, it would

not move nor twist.

i k

• 'E

. B
• •

Fig. 91.

Fig. 92.

A force, then, can
be applied anywhere along the line of
direction of the force, and always pro-
duce the same effect.

Part II L Try the effect of turning
the board as in Fig. 92. Keep the strings
parallel, by sliding the clamps along the
edge of the table. Adjust the positions
of the strings in the clamps, till the same
forces as before are applied. Is the
board in equilibrium? Move one peg
out of the straight line AEB\ equi-
librium cannot be had with the same
forces.

Problems.

1. What changes can be made in the point of application of a force
so as not to disturb the equilibrium of the case recorded in Exercise
14? What changes cannot be made ?

In Fig. 91, the strings could be fastened to the board at any point
in its length and yet not cause the board to move or the forces acting
on ^, ^, and D to change.

2. Force A^ Fig. 87, page 85, is 8 pounds ; £ is 4 pounds ; what is
force E2 Ans. 12 lbs.

90 PRINCIPLES OF PHYSICS.

3. Nearer which force is E applied? Ana, Nearer A,

4. Suppose A = 20 pounds and C = 34 pounds what does B equal?

Ans, 34 - 20 = 14 lbs.

5. How must the forces A and B compare, if the resultant R is
halfway between them?

101. Translation and Rotation. — When a force is applied to
a ball or a top, it sometimes is set moving without any twisting
or spinning. It then has a motion of translation merely ; that
is, a movement from one place to another, without turning or
rotating. The ball or top can be set spinning or rotating with-
out moving from one place to another. It is then said to have
a motion of rotation. Both motions often exist at the same
time, as when a ball is pitched or a bullet sent from a rifle, —
advancing and at the same time twisting.

102. Moments of a Force. — In the various cases we have
been studying, the forces were in equilibrium. They were

balanced in such a way that they
tended neither to move the body along
nor to make it rotate. The following
experiments show the tendency of a
force to make a body turn about a

Fig. 93. P°'°*-

Study the force required to lift the
cover of a book. First, apply a force in the direction of A,
Fig. 93 ; then of B, H is the turning-point. To raise the
cover, the same moment of force is required, whether the force
is applied in the direction A or B.

A door is hinged at H (Fig. 94). By means of a spring

balance, find how much jj

pull it takes to move the (ftl

door slowly, exerting the

pull first at Aj then at -^

(7, and afterward at B. ^'''- ^^'

It takes the same moment in all cases, but the force required

in a direction near to that of B is very large, and becomes

n^^Tx,

PARALLEL FORCES. 91

necessarily larger as its direction is more nearly parallel to
the door.

By moment of a force is meant the tendency the force has to
make a body turn or twist about a point.

103. Value of a Moment of a Force. — The vahie of the mo-
ment, or the twisting power of a force, is found by multiplying
the force by the distance of the force from the turning-point.
The distance is always the shortest that can be measured from
the line of the force to the turning-point.

A certain moment is needed to make the cover (Fig. 93)
"turn about H-, but since the distance from H to the line B
is very small, — that is, the leverage is so small, — a large
force must be applied at B to have the same moment, or turn-
ing effect, as a much smaller force at A,

Exercise 15.

MOMENTS OF A FOBCE.

Apparatus: A piece of wood about a foot long, one inch wide, and one-half
inch thick, bored at intervals with holes that fit the pegs used in Exercise
14; a pin slightly smaller than these, to be used as a pivot; a board that
can be clamped to the table, in which this pin should be set ; spring balances
and cord, as in Exercise 14.

Pivot the stick by the middle hole on the pivot-pin, C, and exert two
forces, as in Fig. 95, one of them, A , at right angles to the stick. Record
the forces on a diagram representing
the arrangement used. The mo-
ment of the force B must equal the
moment of the force Ay for the
moments tend to make the stick
turn in opposite directions, one just
balancing the other ; but the force
B is the greater. The shortest dis-
tance from C to the line of the force
A ia AC. Multiply that distance
by the force exerted at A. Mul-
tiply the force B by the shortest fig. 9«.

PRINCIPLES OF PHYSICS.

distance from C to the line of the force B, This line is produced in
Fig. 96. CD is the shortest distance from C (the turning-point) to

the line of the force B, The shortest

■^ >0 distance is always a perpendicular

one. Since a force can be applied

at any point in the line of its direction without

changing any condition, the force applied at B

has exactly the same effect as if applied at D.

Try other cases, with forces applied at dif-
ferent points on the line ABCj and at different
angles. In every case the moment of A equals
numerically the moment of B, Find the mo-
ments of A and B

Fig. 96. jj^ gj^^jjj ^jj^g^ Q^^

see how nearly they are equal.

Pivot the stick at ^, as in Fig. 97.
Find the moments of the forces D and E
about the point A. Measure from the
turning-point A to the line of the force.
As shown in Fig. 97, ADis this distance
for the force D, AE \s the distance from
A to the line of the force E. Compute the
moments. Are they numerically equal ?

Fig. 97.

104. Positive and Negative Directions. — Take any case of
equilibrium. Suppose, for example, that in Figure 89, page
88, the force ^ = 1800g, ^ = 1200g, 5=:600g. Consider
the point A fixed, as if a pin were driven through it into the
table, so that the board revolves about A, if it revolves at all.
Holding A, give a little extra pull to E, The board turns in
the direction of the hands of a clock, or, as it is called, in a
plus, or positive, direction. Force B will be found to make
the board turn, or rotate, in the opposite, or anti-clockwise,
direction, called a minus, or negative, direction.

The moment of the force E about A = 1800 x 2 = 3600
The moment of the force B about A=s 600x — 6 = — 3600

The sum of the moments is zera

PARALLEL FORCES. 93

Or, put a pin through a bit of cross-ruled paper, on which
this case has been represented (as in Fig. 90). Hold the pin
fast ; the pin is the turning-point. With the sharp point of a
pencil give a push at -& in the direction of the force E, as
indicated by the arrow.

105. The Sum of the Momeiits. — When a body is in equilib-
rium, that is, when it does not move, consider any point the
turning-point, and the moments of all the forces about that
point, added together, are equal to zero. This must be so,
because if the sum were not equal to zero, the moments would
not balance and the body would rotate.

Next, consider E (Fig. 98) the turning-point.

The moment of the force A is positive: 1200 x 2= 2400
The moment of the force B is negative : 600 x — 4= —2400

As before, the sum of the moments equals zero, and the board
has no tendency to twist about the point E, Notice that the
force acting on E does not tend to

cause rotation about the point ^; 1200 eoo

there is no moment to the force E; \ f

why ? How far is the line of the ••1«|«««1
force ^ f rom the point ^?Ina^-^ I ^

similar manner, consider B the turn- ^^

ing-point, and take the moments ^'«- ^8-

about B.

Take a point outside of the board as the turning-point. To
explain this, let us consider the point D (Fig. 98), although
any other point, however remote, would serve as well.

Moment of ^ = 1800 x 4 = 7200

Moment of ^ = 1200 x - 2 = - 2400

Moment of 5= 600x-8=- 4800 - 7200

The sum of the moments about any point whatever, near or
distant, would still equal zero.

94 PRINCIPLES OF PHYSICS.

Problems.

1. What must be the force at Ay Fig. 99, to balance the others?
What is its direction ?

I % f I 1 ' 2- 1° ^he preceding problem, find the force

JL Forces^ and C, added together, equal forced.
C

i»^oo a^«<^ ^' ^ X 5 = 30 X 3.

^ t Y T - * ^- ^n i-ne preceaing proDiem, Und the force

A T ^ at /I by taking moments about B, -4x2 = 12x3.

T A = what ? Xext, find A by taking moments

^^^^ about C. ^

Fig. 99.

In taking the moments about J5, the force of
30 has no moment, because there is no distance between the turning-
point and the line of the force B.

3. Find the force at C, Fig. 100. Take moments about A.
80 X 2 = C X 5. Find the force at A by taking moments about C.
80 X 3 = /I X 5. Prove the work by adding A and C; the sum
should equal 80.

A B C ^ B c

~T \

80 S6

Fijr. 100. Rg. 101.

4. Find the forces A and C, Fig. 101.

5. A weightless beam is supported at 5, Fig. 102. On the end A

is hung a six-pound weight. How

heavy a fish hung at C will balance ? ^_..-P._C
^ri . , fit % ^ % % %

What is the pressure on the sup- | £^

port B?

6. A meter stick is balanced at its p. , qj.
centre. On one end is hung a two-
pound weight. How far on the other side of the balancing point must
three pounds of tea be placed to balance the two-pound weight ?

7. One end of a 6-foot fishing-rod is held in the left hand; the
right hand grasps it 1.5 feet from the same end. Neglecting the
weight of the rod, what force must be applied by the right hand to
raise a one-pound fish from the water? How much must the left hand
press down ? Add the downward push of the left hand and the weight

PARALLEL FORCES. 95

of the fish. How does this sum compare with the pressure on the
right hand? ^»s, 4 lbs.; 3 lbs.

8. A stick, AB, floats east and west in the water. At A there is a
force north of 20 pounds ; four feet from A there is a force south of
50 pounds. What force will keep the stick from moving? Where
must that force be applied?

9. A crowbar, A C, Fig. 103, is pivoted at B ; what must be the
downward pressure at A to raise
a weight of 200 pounds at C? If

the bar is pivoted at C and the , [ [ [ [ | |
weight placed at B, what must be ^ ' I I I I I
the upward pull on ^ ? If the
bar is pivoted at A and the weight ^*«- 'O^-

is at C, what upward force must be exerted at B ?

10. A bat is 34 inches long; the left hand holds one end fixed;
the right hand grasps the bat 10 inches from the endj and moves 14
feet a second. How fast does the free end of the bat move ?

106. The Lever. — In problem 9, the bar is called a lever,
and is the simplest form of a machine. When the support is
at B, Fig. 103, the point B does not move ; that point is called
the fulcrum. When C is the support, that point does not move ;
C is then the fulcrum. The fulcrum in a machine is a point
that is considered not to move. We say considered, because,
in the case of a fishing-pole, either hand may be held station-
ary, and may, therefore, be the fulcrum. Both hands may also
move at the same time; but, for the purposes of calculating
the forces, either point may be considered as stationary, and
that is the point about which the moments are taken.

Suppose, in Fig. 103, that the left hand at C is stationary,
and the right hand, grasping the bar at B, moves, the fish being
attached to A. Which moves the faster, the right hand or the
fish? At which point is the greater pressure exerted? A
large force at B, moving a small distance, raises a small weight
at A through a large distance. Use a pencil or pen-holder for
the lever, and a bunch of keys for the weight.

96 PRINCIPLES OF PHYSICS.

107. Weiglit and Power. — A flat stick, or rule (Fig. 104) is
supported on a pivot through F, At equal distances from F

are pins, on which weights can be

.^JSu 5 ^ hung. Put four equal weights one

I ^ » ' ' ' I ' >i space from the fulcrum, or balanc-
ing point, F, and see if one weight,
four spaces on the other side of
- the fulcrum, will balance them.

pi^ ,04, Call the four weights, TT; and call

the distance of the point of sus-
pension from F, the weight arm, w (in this case, one division
of the stick). Call tlie other force P, and the distance of the
force P from F, the power arm, p. Four times one (that is, the
weight times the weight arm) equals one times four (the power
times the power arm). In shorter form this is written

Wxw = Pxp,
but is always read as

weigJU times weight arm = power times patoer arm.

Raise and lower the power arm, p (Fig. 104), touching it at
the point where P is applied. Do the same with the weight
arm, touching it where W is applied. The power travels four
times as fast as the weight. To raise the weight, W, one inch,
the power must move through a distance of four inches. In
this case, a weight four times as great as the power is raised.

108. Power and Speed. — This principle is used in making
machines to raise a small weight rapidly; for instance, to
strike a blow with an axe or hammer at a higher speed than
the hand can be moved. The power and the weight change
places in such a case. The power applied, for example, one
division from F, in moving one inch, causes the weight to move
four inches — four times as fast.

Place three weights two divisions from F, and find where

PARALLEL FORCES. 97

two weights will balance. Try other cases, testing the law
TF X w = P X p.

What is gained in power is lost in speed, and what is gained in
speed is lost in power is an old-fashioned way of stating this
law. In the case shown in Fig. 104, there is a gain in power, —
that is, the power moves a greater weight than itself, — but
there is a loss in speed, for the weight moves slower than the
power.

When a machine of any kind, as, for instance, the lever in
Fig. 104, is in motion, the power moves over as much greater
distance than the weight as the power arm is longer than the
weight arm. The formula

Wxw = P xp
can then be read as

weight times weight distance = power times power distance ;

or, the weight multiplied by the distance through which it
moves equals the power times the distance through which it
moves. Always measure from the fulcrum to find the weight
distance and the power distance.

109. Formula for Problems on Machines. — The same formula,
or law, Wxw = Pxpf holds for all problems on machines.
In solving questions, first decide what point is the fulcrum.
Always measure from it to where the weight is applied, in
order to get the length of the weight arm. Find the length of
the power arm in a like manner. In some problems, it is
better, instead of finding the weight arm and power arm, to
get the distances the weight and power move in the same time.

Problems.

1. Suppose Wf in Fig. 104, page 96, is 18 pounds, and is six divi-
sions from F; P is two divisions from F. How large is the power?
Which travels the greater distance ?

98 PBISCIPLES OF PHY8IC8.

2. Where should the power and weight be applied so that the
weight may move two-thirds as fast as the power?

3. A weight of 60 poonds is 4 inches on one side of the fulcrum ;
what power must be applied 5 inches on the other side to lift the
weight ?

4. A fisherman grasps the handle of a 9-foot fish-pole in his left
hand ; his right hand is 1 foot from the same end. If he holds the left
hand still and moves his right hand 1 inch, how far does the tip
move ? Disregarding the weight of the pole, what weight at the end
of the pole would a force of 4 pounds exerted by the right hand
lift ? If the right hand is held stationary and the left hand lowered
1 inch, how far does the point of the pole rise ?

Ans. 9 in.; J lb.; 8 in.

5. In a pair of shears for cutting metal, the handle is always longer
than the blade. >Vhich moves the faster, the power or the weight V
Is there a gain in power or speed ? From the centre of the bolt on
which the sheai*s turn, to the handle whei'e the power is applied, is 8
inches ; from the bolt to the end of the blade is 2 inches ; let a force
of 5 pounds be applied to the handle, what is the force of the blade at
the'end? Ans. 20 lbs.

6. The handles of a pair of nippers for cutting wire are 10 inches
long ; the cutting edge is J inch from the bolt, or pin. What force
must be put on the handle to exert a force of 400 pounds on the edge ?

7. At which end of a pair of scissors must a force be applied to
cause a greater force at the other end?

8. In a nut cracker, where is the fulcrum? If ACy Fig. 105, is
12 inches, and AB 3 inches, what pressure at B
would be exerted by 6 pounds acting on C?
What would be the pressure if B were 1 inch
from A ?

^''' '°** 9. If J5 is 4 inches from A, AC = 6 inches,

and the power acting at 5 is 6 ounces, what is the pressure on C ?

10. If a man shovelling snow holds the end of the handle in the
left hand, which hand exerts the greater force?

CHAPTER VII.
MAOHnrES. —PULLETS.

110. A Combination of Pulleys (Fig. 106) is a modified form
of the lever. A rope is wound around the large pulley, and
another around the small pulley. Pull on
A. Which moves the faster, A ox B^l
F is the fulcrum. The radius of the
large circle is the power arm, if A is the
power ; the weight is at J5, and the weight
arm is the radius of the little circle.

A model of this pulley is made by slip-
ping a spool, S, Fig. 107, on a piece of
wood or pencil, sharpened at both ends.
A string is wound around the spool, and
another around the pencil. Hold the
ends of the pencil between the thumb and forefinger.

the fulcrum.

By means of the simple form
of straight lever. Fig. 103, page
95, a weight can be lifted a short
distance. Using pulleys, the dis-
tance depends only on the length
Fig. 107. of the ropes coiled around them.

Fig. 106.

FF'\s

C''/^

^'//

111. Study of the Pulley as a Machine. — Fasten a car (ap-
paratus of Exercise 16, page 109) to a table, so that the forward
axle hangs over the edge. Let Fig. 106 represent the wheel of
the car. Tie a stout linen string, A, to the wheel. For this
purpose the rim is grooved, and through the edge of the wheel,
to the groove, a hole is bored. Fasten another thread, Bj to

^\-^^^

100

PRINCIPLES OF PHYSICS.

the shaft. Wind the strings a few times around in opposite
directions. Put a 2000-gram balance at J5, and a 250-gram
balance at A, Fasten to the floor the ring of the balance joined
to B. Apply different forces at A, Record the readings of
both balances. Divide the readings of A by the correspond-
ing readings of B. Divide the diameter of the wheel by the
diameter of the axle. The radius is really the length of the
arm of the lever, but the diameter is always twice the radius,
and if the diameters of both are used, the result is the same
as if the radii had been used instead.

Move B (Fig. 106) one inch; how far does A move? On
which rope would you apply a force to obtain a gain in speed ?
a gain in power ? Try the effect of applying forces not par-
allel. A given force at A always has the same moment, or
turning effect ; for no matter in what direction A is pulled, the
distance from the fulcrum to the line of
the force is always the radius of the circle,
and all the radii of a circle are equal.

112. Crank and Axle. — Sometimes one
of the pulleys is replaced by a simple
lever or crank. Suppose that in Fig. 108
all but one of the spokes of the wheel
were removed. If a handle were attached
to the one remaining spoke, at right an-
gles to it, and to the plane in which the
wheel revolved, the machine would be a
crank and axle.

Fig. 108.

Problems.

1. If the handle of a clothes-wringer is 10 inches from the axis,
the rubber roll is 2 inches in diameter, and a force of 30 pounds is
exerted on the handle, what is the force on the surface of the rubber
roll? Ans. 300 lbs.

Notice that 2 inches is the diameter of the axle, and 10 inches the
radius of the circle in which the crank moves. Either double 12, when

MACHINES. — PULLEYS. 101

the power and weight ann are as 20 to 2 ; or halve 2, in which case the
two arms of the lever are as 10 to 1. The proportion is the same in both
cases. That there is a gain in power in the wringer can be shown by
trying to hold back with one hand a piece of cloth from passing through
the rollers, while taming the crank with the other hand. If the rolls are
screwed tightly together, as they are when wringing clothes, there is a
large loss from friction.

2. The crank on a grindstone turned by hand is 12 inches long,
and the diameter of the stone is 30 inches. When a force of 60
pounds is put on the crank at right angles to its radius, what force
can be exerted on the rim of the stone by a knife that is being
ground? Ans. 48 lbs.

3. A crank and axle is used to raise buckets of earth weighing 50
pounds. The diameter of the axle is 6 inches. What power must be
applied to the crank, which is 15 inches long ?

Remember that the radius of the axle is 3 inches.

4. How many times larger than the axle must the large pulley in
Fig. 106 be, so that 40 pounds at A can raise 50 pounds at ZJ ?

5. If a belt travelling 1000 feet a minute passes over an axle that
is 2 inches in diameter, what must be the size of the emery wheel, so
that points on its rim travel a mile a minute ?

6. The diameter of a grindstone is 24 inches. The crank is driven
by foot power, and has a radius of 2 inches.
How many times greater is the radius of the
grindstone ? How many times faster does a point
on the rim of the wheel travel than a point on
the end of the crank? What force must be
applied perpendicular to the crank, to give a
force of 30 pounds on the rim of the stone ?

7. Why is a force that is applied as shown in
Fig. 109, less effective than one at right angles to
the crank? Fig. 1 09.

8. The blade of a screw-driver is J inch wide ; the handle is 1 inch
in diameter. Applying a force of 6 pounds to turn the handle, what
is the force tending to turn the screw ? Ans, 24 lbs.

9. Why can a screw be driven harder, or the head even twisted off,
by using a screw-driyer in a bit brace ?

102

PRINCIPLES OF PHYSICS.

113. Movable Pulley. — When a load is supported by two or
more strings, ropes, or chains, its weight is divided between
them. Support the handle of a pail by two
balances, A and B, Use at first a pail that
has a plain wire handle. The sum of the
pulls on the balances always equals the weight
of the pail. Raise B, As the pull on B in-
creases, that on A decreases. Substitute a
pail with a wooden handle stinrng on the wire
(Fig. 110). The pulls on A and B are each
about half the weight. The handle sei-ves as
a movable pulley. In this form of machine
there is a gain in power. Raise B one foot ;
how far is the pail raised ? In what do you
find a loss corresponding to the gain in power? The size of the
pulley has no effect on the power, except that there is slightly
less loss by friction in a large pulley than in a small one.

Fig. no.

114. Fixed Pulley. — The axles of the car used in Exercise
16, page 109, answer well as pulleys, and have almost no fric-
tion. Screw or clamp
a car. A, to a block,
and fasten the block
to a table (as in Fig.
111). For the weight,
Wf use another car
with a load, which
may be tied in. Raise
the car, and read the
balance.

Correction should
be made for the error _. . .

rtg. II

due to using the bal-
ance in an inverted position. This is determined by hanging
it from another spring balance, and pulling down till the upper

MACHINES. — PULLEYS.

103

balance shows that the force exerted is that which is to be
used iu the experiment. If the lower balance reads the same
as the upper, there is no error ; if not, the amount of the dif-
ference should be used in correcting the readings. (See exer-
cise on errors in a spring balance, Appendix, page 536.)

The arrangement in Fig. Ill comprises a fixed pulley only.
Fixed pulleys change the direction of a force. Is there any
gain or loss in power or in speed ?

116. Combinations of Pulleys. — Try the combinations shown
in Figs. 112, 113, and 114. In Fig. 114 there are three strings
pulling up. There is the same pull on every part of the

Rg. 112.

Fig. 113.

strings, since the pulleys all turn easily. Read the balances at
A and P. A force of one pound applied as a power at P is
in reality exerted three times on the weight. Therefore the
weight, Wy is three times the power. Move P an inch ; how
far does TTmove ? Does the law P x p = W x w, still hold ?
In the combinations of both Figs. 113 and 114, two ropes

104

PRINCIPLES OF PHYSICS.

support the movable pulley. W is twice P, The upper fixed
pulley iu Fig. 113 serves to change the direction of the string.
The weight moved is as many times the power applied as
the number of ropes attached to the weight. In practice,
there is some loss from friction.

Problems.

1. What power in Fig. 115 is re-
quired to lift a weight of 120 pounds
at Wl

Count the number of ropes support-
ing the weight.

Ans, 40 lbs., and a little more, to
overcome friction.

2. How many ropes support the
weight in Fig. 116? How many
times greater is W than P? How
many times faster than W does P
move?

3. Sketch a system of pulleys
where W is five times the power;
six times the power.

4. How great a force must a hy-
draulic piston apply at W (Fig. 116) to lift an elevator weighing 3000
pounds, attached to P? How many times faster does the elevator
move than the piston ? How long must the cylinder, in which the
piston moves, be, if the elevator has to travel 120 feet ? What is the
total downward force which the upper pulley exerts upon its support?

Turn the diagram upside down, and count the number of ropes run-
ning through the pulley in question. The pull on each rope is the same.

116. Gear of Bicycles. — The diameter of the rear, or driving,
wheel of a bicycle is usually 28 inches ; occasionally 26 or 30.
By the expression " 70 gear " is meant such a combination of
gears (pulleys having teeth) that the rim of the rear wheel —
and consequently the bicycle itself — goes as far in one revolu-

Flg. 115.

Fig. 116.

MACHINES. — PULLEYS. 1 05

tion of the pedals as a wheel 70 inches in diameter would go
in one revolution. The small rear wheel of a bicycle goes
round as many times more than the pedals as the gear on the
crank-shaft is times larger, or has times more teeth, than the
gear on the rear wheel. If the rear wheel has an 8-tooth gear
and the crank-shaft a 24-tooth gear, then the rear wheel turns
^, or three times as fast.

Problems.

1. Find the gear of a bicycle, if the diameter of the back wheel is
28 inches, the number of teeth on the same is 9, and if there are 27
teeth in the crank-shaft gear (called sprocket). .4ns. ^ x 28 = 84.

2. Find the gear of the wheel described in Problem 1, if the
diameter of the rear wheel is increased to 30 inches. Ans, 90.

3. Measure the diameter of the rear wheel, count the number of
teeth in the gears, or sprockets, and compute the gear of any bicycle
at hand. (Mark one tooth with chalk, calling it number one, and
count around to it.)

117. Speed Gearing. — Place a bicycle upside down, and
support it firmly, with the rear wheel free to turn. Attach a
2000-gram balance to the rim of the rear wheel and another to
the shaft of the pedal. Fasten or hold firm the first balance,
and exert a force of 2000 g. perpendicular to the crank.
Record the readings of the balances, the diameter of the rear
wheel, the length of the crank, and the number of teeth in
each sprocket. Calculate the gear of the wheel. This number
is the diameter of a wheel that will go as far in one turn as
the bicycle is sent by one turn of the crank. Half this
diameter gives the radius. How many times greater is this
radius than the length of the crank ?

The gain in speed may be found by comparing the gears of
the bicycle with the length of the crank ; for instance, if the
gear is 70 and the crank 7 inches long, the bicycle travels five
times as fast as the foot moves. For this gain in speed, what

106 PRINCIPLES OF PHYSICS.

is the loss in power ? Why cannot you ride up as steep a hill
as you can walk up ?

How many times greater is the pull measured by the spring
balance on the pedal shaft than the pull on the rim of the
wheel ? It is this pull, or push, on the rim df the wheel that
sends the bicycle along.

Move the crank one inch, and measure how far the rim of
the rear wheel travels. This is the gain in speed.

118. Pulleys and Belts. — Power is usually transmitted from
one part of a factory to another by belts of leather. An engine
or water wheel drives a long rod, called the main shaft, and on
this there are pulleys of various sizes.

Arrange several cars on blocks fastened to a board, so that
the bodies of the cars are vertical. Belt a little engine, or a
water or electric motor to the groove on the wheel of the end
car, using a piece of white string for a belt. By a loop of
string, connect the axle of this wheel with the groove on the
wheel of the next car. In the same way, belt the axle of the
second car to a wheel of the third car. On the last axle wind
a few turns of string, and fasten a weight to the string. Start
the motor. Which runs the faster, the motor or the weight ?
Is there a gain in power or in speed ? Such a gearing as this
is used in cutting or planing metal, which must be done at a
slow speed, or the cutting tool becomes hot, and dulls. It is
used also for lifting heavy weights. Eemove the engine or
motor, and turn the axle of the last car by hand. What part
of the train of wheels turns fastest ?

Emery wheels, circular saws, and wood-working tools must
travel at a high rate of speed. Make a diagram showing how,
by belts and pulleys, this speed can be obtained.

CHAPTER VIII.
WOEK.

119. Resistance. — To do work, a body must be kept in
motion where there is resistance. Resistance may be of sev-
eral kinds: friction; inertia, that is, the resistance an object
offers when started or stopped; the resistance a substance
offers when cut or broken ; some forms of resistance that are
to be studied under Electricity and Heat ; and the resistance
a body offers to being lifted. When a body moves against any
of these forms of resistance, it does work.

Does a spinning top do any work ? The point bores a hole
in the floor, and the surface fans and sets the air in motion a
little, and the top at last stops. In a vacuum, a top with a
hardened peg would revolve a long time on a smooth surface ;
or a grindstone could be mounted so that it would revolve an
indefinite length of time; but the grindstone would do no
work. If a knife were pressed on the grindstone, the motion
would be resisted and work done.

120. Unit of Work. — A body resists being lifted, because
it is apparently attracted by the earth. One pound raised one
foot is said to require one foot-pound of work. In the metric
system, the unit of work often used is the work done in raising
one gram one centimeter. Remember that work is measured
by the force required to make a body move, or, more briefly,
work equals force times distance,

W=fd.
107

108 PBINCIPLE8 OF PHYSICS.

121. Relation of Force and Distance. — It is easier to roll a
barrel of flour up an inclined plane from the sidewalk into
a wagon than it is to lift the weight straight up. In rolling
the barrel up the incline, the force applied is comparatively
small, — smaller than that needed to lift the barrel, — but the
distance is large. To lift the barrel up calls for more force,
but the distance is much less than before. Then, since work
equals force times distance, the amount of work done is the
same in either case. In the experimental study of the inclined
plank, or plane, by the use of a car, the friction is so much
reduced by the wheels that it may be neglected.

Problems.

1. How much work is done in lifting 1 pound 2 feet ? In lifting
3 pounds 5 feet? One-half a pound 30 feet?

2. How much work do you do in walking upstairs, 20 feet rise ?

3. How much work is required to lift a 500-pound hammer
30 feet?

4. If one pound = 454 g., and one foot = about 30 cm., how many
gram-centimeters in a foot-pound ?

5. How much work is needed in gram-centimeters to lift Ig.
1 cm.? To lift 5g. 4 cm.? To lift 10 cc. of water 42 cm.?

6. How much work is done in pumping 40 liters of water 50 m.
high?

7. What amount of work is required to raise a ton of coal 3000
feet from the bottom of a mine?

8. If in walking a person rises at each step ^ foot, how mnch
work is done in this way by a person weighing 150 pounds ?

9. How much work is done in pulling a 200-pound sled 40 feet
along a level road ? Can this be found until the friction resistance is
known ? If the pull to make the sled move is 22 pounds, how much
work is done ?

10. Find the force required to draw a 500-pound sled, with iron
runners, over iron street-car rails, the coefficient of friction being .3.
How much work is done in pulling the sled 20 feet ?

WORK. 109

Exercise 16.

INCLINED PLANE.

Apparatuis : Board ; car with a weight ; spring balance.

Lay a board, A B, Fig. 117, in a slanting position from the table to
the top of a box. Weigh a car with a load. The pull required to
draw the car up the in-
cline is measured by a ^^^^^
spring balance. The zero ^X^^f^^Y
point of the balance
should be recorded for
the slant used, and the
correction, if appreciable,
should be used in making
the computations. To de-
termine whether friction

is a large part of the resistance overcome in pulling up the car, record
the pull when the car is moving down the incline. The average of
the two pulls is the force that would be required to make the car go
up the slant if there were no friction. As this friction is very small,
it is best disregarded. Use as small a balance as possible ; if the pull
is less than 250 g., use a 250 g. balance. If the car were a horse-car,
the horses would have to walk from A to J5 to draw the car the dis-
tance AB^ and the work done would be the distance AB times the
amount of the pull. Calling AB the slant, the work done = slant
times pull. If IT were a load of coal, it could have been wheeled
from -4 to C with very little work, and then raised vertically to B,
The work performed is the weight, W, times the distance moved or
raised, which is CB, The work performed is therefore the weight
times CB. Calling CB the height, ^, the work performed is VF x //.
Compare the work done in pulling the car up the slant with the work
performed in lifting the car straight up from C to B,

Repeat the experiment with different loads and different slants.
What would the pull become if the slant were increased ? If it were
increased so as to be almost vertical ?

122. The Mechanical Advantage in the Inclined Plane is that a
small force, such as may be exerted by a man or a horse, can,

110 PBINCIPLES OF PHYSICS.

if the slant is gradual, move a heavier load than can possibly
be directly lifted by the same force. On the slant, while the
pull is less than the weight of the load, the distance the load
travels is greater than when it is lifted straight up. The work
done in either way is the same; the choice of method is a
mere matter of convenience.

123. Formula. — As the work is the same, whether the load
be pulled up the slant or lifted up vertically, we can wi-ite that
the pull times the slant distance = weight times the height ;

or PxS=Wxh.

Since slant distance equals power distance, and height equals
weight distance, this formula may be written : —

P xp=Wx w.
Power X power distance = tveight x weight distance

is the law that applies to all machines.

In this equation, if any three quantities are known, the
fourth can be found. If the slant = 30 feet, the height = 10
feet, and the load = 2400 pounds, what is the pull ? Writing
down the formula,

PS = Why

then erasing S and writing 30 in its place, writing 10 for h
and 2400 for W, we have

P X 30 = 2400 X 10,
30 P= 2400,
P= 800.

Problems.

1. What is the slant length of a plane on which a 50-pound pull
moves 800 pounds, when the height of the slant is 20 feet?

2. What weight can be moved on a rise of 1 foot in 25, with a pull
of 40 pounds?

WORK. Ill

3. On a rise of two feet in one hundred (called a two per cent
grade), what pull must a locomotive exert to draw ten cars, each with
a load weighing 25 tons, friction being disregarded ?

4. On a rise of three feet in one hundred (the steepest allowable
on a really good road), what is the force needed to move a 1200-pound
wagon up the hill, if we disregard friction ?

5. How great a load can, by a force of 120 pounds, be kept from
rolling down a 12 per cent grade (i.e, a fall of 12 feet in 100) ?

6. If a mountain railway has a rise of one foot in three, what force
is needed to move a car and passengers, weighing 10,000 pounds, up
the track?

7. Find the height of an incline 1000 feet long on which an 80-
pound pull moves 600 pounds.

8. An electric car on a hill is attached to a dynamometer (which
is practically a huge spring balance). The dynamometer reads 900
pounds, and the car weighs 6000 pounds. What is the grade? What
is the rise in 100 feet of slant?

124. The Wedge. — Instead of pulling a load up a slant, the
slant may be pushed under the load. For the purpose of rais-
ing the weight W, Fig. 118, an inclined plane, called a wedge,
is forced under the weight. In this case, the power by suc-
cessive blows is applied to
drive the wedge in a dis-
tance, AC. The work done
is Power x AC, or,

Power X horizontal distance.

The load, be it a safe or a
chimney or a lump of stone,
is raised the distance BC
The work performed is TT x BC, or Wxh. The work accom-
plished in raising the load must equal, disregarding friction,
the work expended in driving in the wedge.

Force x AC = Weight x BC

Fig. I

112 PRINCIPLES OF PHYSICS.

If a wedge is 10 inches long and 1 inch thick, and is driven
by a blow of 300 pounds, what weight does it lift ? In prac-
tice, something is lost in friction, and the weight lifted will
be much less than the computed amount. If
the wedge be used for splitting, it is usually
j^ a double inclined plane (Fig. 119). The
J^ power distance is AC, and the work dis-
^'^' "^- tance is BE. That is, by forcing the wedge

through a distance AC, a log is split open a distance BE.

Problems.

1. In a wedge 12 inches long, what must be the thickness (BE,
Fig. 119) for a blow of 150 pounds to cause a splitting force of 2000
pounds ?

2. On a grade of one in twelve, how much must a horse hold back
to keep a 3000- pound wagon from running away ?

3. On what grade can a horse move a load of 2400 pounds, if he is
capable of pulling 400 pounds ?

125. The Screw. — Examine and make a rough drawing of a
bolt having ten turns, or threads, to the inch. Rub the point
of a pencil on one side of the bolt. Lay the page of the note-
book over this, and rub the paper with the side of a pencil. A
tracing like Fig. 120 is left on the

paper. Lay off one inch from AtoB, 1^ i i i i i i i i t ? i i i
and count the number of ridges be- I j

tween those two points. The first *^ Fig.Tao.

ridge, in beginning at A, is not

counted, just as in timing a pendulum for a minute, the
observer does not count "one" at the beginning of the first
swing. Make tracings of the threads of other screws, microm-
eter calipers, iron clamps, etc.

126. The Power of the Screw as a machine comes from the
very long and slim wedge that is wound around it as a thread.

WORK.

113

Cut out a paper wedge thirty times as long as it is thick at
one end ; wind this around a pencil. Try to print the mark of
a medal on the page of a note-book, by
pressing with the fingers. Force the
medal in, using a clamp (Fig. 121).
Make a tracing of the thread, and
count the number of ridges in one
inch. Suppose the number is ten;
then, in one turn, the screw moves for-
ward -jiy of an inch. Call this the
weight, or work distance. If the diam-
eter of the handle is 2 inches, and the
power is applied at the ends of the
handle, the power in one revolution
acts over a distance that is a circle 2 ng. 121.

inches in diameter. The power dis-
tance, the circumference of this circle = 2 x 3| inches = 6f
inches, or about 6.3 inches. In case the power applied is 20
pounds, by substituting the formula,

Wxw = Pxpy
Wx^ = 20 X 6.3,

W= 1260 poimds,

the force that would be applied by the screw in case there were
no friction ; but more than three-quarters of the force is lost
in overcoming friction. This loss is more or less useful, be-
cause this friction keeps the screw from turning backward of
itself.

127. Power compared with Speed. — Set a nut, N, Fig. 122,
in a board, C Tie a 20-pound weight, W, to the lower end of
the bolt, B. E is Si rod or wrench attached to the head of the
bolt. The spring balance is so placed that DE = 3^ inches.
This distance is taken for convenience in computation. The
circle in which E turns = 3^ x 2 x 3| = 22 inches. Suppose

114

PRISCIPLES OF PHYSICS.

the bolt has ten threads to the inch ; then the work distance in
one revolution, or the height that W is raised, equals ^^ inch.

Read the spring bal-
^ ance as ^ is slowly

turned, keeping the
string at E perpendic-
ular to DjE?. The spring
balance measures the
power applied. Calcu-
late what weight should
be lifted without fric-
tion, and compare with
the weight actually-
raised. In one revolu-
tion, how far does the
IKunt E move ? (Ans, 22 inches.) In one revolution, how far
dws the weight rise ? (Ans. ^ inch.) How many times faster
does the power move than the weight ? (Ans, 220.)

Fig. 122.

128. Couples.— Two tugs, E and TF, Fig. 123, press with
equal force against a steamer, S, which is not working its own
engines. E pushes at the bow toward the east, and W at the
stern toward the west. The effect is to
turn the steamer around without moving her
to a different place. What would be the
effect if she worked one propeller. A, to
drive her backward, and the other, jB, to
drive her forward ?

Lay a pencil on a smooth surface. Try to
make it turn round on its short axis by
applying one force. Apply two equal forces, in opposite direc-
tions, at the ends of the pencil. Make a diagram of the forces.

129. Two Equal Parallel Forces in opposite directions cannot
have a resultant. If they are applied at the same point, as in

WORK. 115

a tug-of-war, there is no motion whatever. If they are applied
some distance apart, as in Fig. 123, there is still no resultant ;
the body does not move away, it rotates. In that case the two
forces form a couple, A couple is two equal and parallel forces
in opposite directions applied some distance apart. A couple
tends only to make a body rotate.

130. Moment of a Couple. — At two points, 10 feet apart,
on a beam are two forces, each 50 pounds, one north, the
other south. Take A, B, or C, or any point in the line or out of
it as the turning-point. The moments of 50
the force in any case will be 500. This is ^

the same as 50 x 10. The moment of a p S. 1

couple = one force times the distance be- I

tween the two forces. A couple cannot 50

be balanced by a single force. In stopping ^'^' ' ^*'

a spinning top by holding a finger against its side two forces

are applied, one where the finger touches, the other at the peg

of the top. Imagine the top whirling in space, as the earth

does. How would it respond to the touch of the finger applied

as before.

131. A Single Force cannot balance a Couple, but a second
couple can do so, if it tends to make the body rotate in the oppo-
site direction. Take hold of the handle of a broom and twist
it, to make, it turn to the right with one hand, and to the left
with the other. Repeat, grasping the larger part of the broom
with one hand. If the broom does not turn, the moment of
the couples exerted by the hands are equal ; but the forces are
by no means equal in the latter case. Two small forces, acting
as a couple, and applied a great distance apart, produce the
same moment as larger forces applied a short distance apart.
The forces of one couple may be parallel to or make any angle
with the forces of the other couple, provided they are all in
the same plane. In the following exercise, the forces of one
couple are at right angles to the forces of the other couple.

116

PRINCIPLES OF PHYSICS.

Exercise 17.

COUPLES.

Apparatus : Board used in Exercise 14, page 118 ; four 2000-gram, spring bal-
auces; fish-liue; clamps; marbles; pegs.

Place the board on the marbles, insert pegs, and apply forces A, B,
C, and D (Fig. 125) at such points that the couple of CD tends to
rotate the board in a direction opposite to that given it by the couple
^ AB. Vary the tension on the bal-

ances till the forces lie along lines
of the board. Notice that C = Dy

C^-

-•O-

'F^-

■^D

Fig. 125.

moments about G, note that both

also the moments about some point in which there is no peg.

other cases, with the pegs in different positions.

and ^ = J5, as should be the case
with couples. What is a couple ?
Record forces and directions on
cross-ruled paper. Take, in turn,
each peg as the turning-point, and
find the moments of the forces,
remembering that an anti-clock-
wise movement is negative. See
if the sum of the moments equals
zero. Force A has no moment
about E. Why? In taking the
C and B have no moment. Find

Try

24 In

-*fC

132. Calculation of Couples. — A bracket, ABC, Fig. 126, is
screwed to the wall at A and B, which are ten inches apart.
Neglecting the weight of the
bracket, if 360 pounds are
placed at (7, what is the hori-
zontal pull on A? Supposing
the force exerted at A breaks
the screw; the bracket falls,
turning on 5 as a pivot. The
moment of 360 pounds at C
about the point 5 = 260 x 24,
exerted by the screw is J. x 10.

Fig. 126.

The moment of the force

WORK.

117

3ft

360 X 24 = ^ X 10.

^==864.

If tlie screw cannot stand this strain, the bracket falls. Make
a model of such a bracket, with B as the turning-point, and
attach spring balances at A and C. Multiply force A by the
distance AB, and see how this product compares with the
product of the force C times the distance AO.

A door, three feet wide (Fig. 127), is
suspended by hinges, A and B, six feet

apart. The door weighs 200 pounds. What

is the force tending to pull the hinge A

out from the wall ? There is a downward

force on both hinges. This can have no

direct effect in pulling hinge A away from,

or pushing hinge B into, the wall. The

door is symmetrical, and the downward

force of its weight may be considered

as applied at the centre of the door.

Imagine a strong bolt passing through

B, and study the tendency that the forces

applied to the door have, to make it turn

about jB. In other words, take the mo-
ments about B, The hinge A pulls

toward the wall. The moment of this force equals Ax 6.

moment of the weight of the door is 200 x 1.5.

The

^x 6 = 200x1.5.

How

How far is the line of the force at A from the point B ?
far is the force of 200 from the point B ?

Make up several problems similar to the above, and solve
them.

Problems.

1. If a gate 12 feet long, weighing 300 pounds, is held up by hinges
3 feet apart, what lathe honzontal force on the hinges?

Ans. 600 lbs.

118 PRINCIPLES OF PHYSIC 8.

2. If a boy weighing 120 pounds stands on the very end of the
gate, what additional pull is there on the upper hinge?

3. K the pull needed to keep a wagon moving uniformly on a level
road equals .01 of its weight, what is the pull in drawing a wagon
weighing 2000 pounds? . How much work is done in moving it 600
feet?

4. A tool is pressed on a grindstone with a force of 20 pounds ;
the coefficient of friction is .3. What is the friction force? How
much work is done in one revolution, if the circumference of the
stone is 8 feet ?

5. In a hydrostatic press, if the distances moved by the pistons
are as 1 to 800, how many times greater is the total pressure on the
large piston ?

6. Which of two bicycle pumps, one i inch in diameter, the other
1 inch in diameter, can pump up a bicycle tire the harder ?

7. Is the coefficient of friction large or small when a body is
slippery ? Explain the use of sand on a rail, and rosin on a violin
bow.

8. If a force of 10 pounds just moves one surface over another,
the pressure between them being 100 pounds, what force would be
required if the pressure were increased to 200 pounds ? What force
would be required if the coefficient of friction were 3 times as great,
the pressure remaining 100 pounds?

9. If the coefficient of friction is .25 between the driving wheels
of a locomotive and the rail, what must be the weight of the locomo-
tive to exert a pull of 10 tons ?

10. If the coefficient of friction is .25, make a diagram of an inclined
plane down which the locomotive would start to slide, the wheels
being prevented from turning.

11. In the case of equilibrium represented by Fig. 125, are the
forces C and D large when C and D are far apart, as shown, or when
they are near together?

CHAPTER IX.
OENTEE OF GRAVITY.

133. Action of Gravitation. — The earth exerts its downward
attraction on each little particle of a body, — a block of wood,
for example. If the block is cut into small bits, each bit falls
(in a vacuum) as rapidly as the whole block. The forces of
the earth's attraction act downward in parallel lines. All
these parallel forces may be replaced by one force, called the
resultant — in this case the weight of the body. To make the
block fall down as the earth makes it fall, and without making
the block turn round in any direction, this force must be
applied at a certain point, which we shall call the centre of
gravity.

134. Centre of Mass, or Centre of Gravity. — Hold the card or
board AB, Fig. 128, I, by a pin near the corner A, On the
same pin hang a thread,
to which a weight is at- -4

tached. The centre of
gravity is somewhere un-
der the line AC, Mark
a line on the card where
the thread touches. Re-
move the pin and place
it in some other part of
the card — near the cor-
ner D, for instance. Let the card and plumb line DC hang
freely, as before. Mark the line DC on the card (Fig. 128, II).
Where the two lines marked on the card cross, insert the pin.

119

120

PRINCIPLES OF PHYSICS.

Turn the card to different positions. It remains in any posi-
tion in which it is put. The card behaves just as if all its
mass, or weight, were concentrated at the point G. This point
is called the centre of mass, or centre of gravity. Set the card
spinning. Does it shake the hand holding the pin ? Make a
hole about a centimeter from G, and insert the pin. Does the
card stay in any position in which it is put, or does it turn
and the point G move as low as possible. Set the card spin-
ning, and notice the shaking of the support. This shaking is

caused by the card trying
to revolve about its centre
of gravity.

A wheel or any revolving
part of a machine shakes
its bearings, unless it re-
volves about its centre of
gravity. Weights are often added to an unbalanced wheel to
make its centre of gravity in line with the bearings.

Find, in a similar manner, the centre of gravity of pieces of
board shaped like A, B, and O, Fig. 129. It will be found to
be outside of the body itself, in some cases. For instance, the
centre of gravity of a ring is inside the ring. If fine wires are
attached to the ring D, Fig. 130, in the directions
taken by plumb lines hung as in Fig. 128, the
centre of gravity will be at the point where they
cross, and, if supported at that point, the ring
will rest in any position in which it is placed.

135. The Line of Direction. — When a body falls, although,
under some conditions, it may turn and twist, still its centre
of gravity goes down in a straight line toward the centre of
the earth. This line is called the line of direction. It is the
direction in which a plumb line hangs. In Fig. 128, when the
card is suspended at A, AC is the line of direction ; when sus-
pended at Df DC is the line of direction.

CENTRE OF GRAVITY. 121

136. The Base. — Since a body acts as if all its weight were
concentrated at the centre of gravity, there must be some sup-
port under the centre of gravity to keep the body from falling.
The base on which a body rests is all the space that would be
included inside a string wound round all its supports. The
base of a three-cornered stool is a triangle, and the three points
give as good a support as a triangle of solid wood.

What is the base of an ordinary chair ? of a tricycle ? of a
barrel of flour standing on end ? of a person standing on one
foot ? of a person standing on both feet ? of a bicycle ?

137. Equilibrium. — A body tumbles over when its centre of
gravity is not over the base. Another way of saying this, is to
say that a body falls when its line of direction passes outside
of the base. A block of wood or a brick, lying on its side, is
hard to tip over. If it is tipped a little and released, it returns
to its place.

138. Stable Equilibrium. — Make a diagram of a block, show-
ing the position of its centre of gravity. Tip the block, keep-
ing the edge on the table. Notice that the centre of gravity
rises as the block is tipped. The block is said to be in stable
equilibrium, because, when it is tilted, the centre of gravity
rises. Now, since the earth's attraction tends to bring the
centre of gravity as low down as possible, a body, when re-
leased, if it has not been tipped too far, at once falls back to
its former position. Compare the amount of tipping necessary
to make the block tumble over when it is lying on its side,
with that required to make it tumble over when it is resting
on its end.

139. Unstable Equilibrium. — A pencil balanced on its point,
a man on stilts, a bicycle rider, have unstable equilibrium.
The least disturbance tends to make them fall. Their centres
of gravity are at the highest point possible above their bases,
and the bases have no size, being merely points or lines. The

122

PRINCIPLES OF PHYSICS.

Fig. 131.

least disturbance tends to move the centre of gravity from
over the base, and the body falls. By changing the point of
support and placing it under the centre of gravity, bodies in
unstable equilibrium are kept from falling.

140. Raising the Centre of Gravity. — Cut a block of wood in
the form of ABCD, Fig. 131. Change the slant at which the

block leans, or vary the height till
the centre of gravity is just inside
the base. A slight tip causes the
block to tumble over. The block
represents, in exaggerated form, the
Leaning Tower at Pisa, Italy. Sup-
port the block by a wire through a
hole at /S, and show that S is the
centre of gravity. Put another story,
EF, on the tower. This raises the
centre of gravity, and the line of

direction falls outside the base. Does the tower tip over?

Find the point by which the tower can be supported so as

to balance in any position.

141. The Most Stable Equilibrium of all is that in which the
support is above the centre of
gravity, as in a swing or a
pendulum. To make a body
that appears to balance on a
needle-point, A, Fig. 132, fasten
a wire to a cork, O; attach a
weight, Wy to the lower end of
the wire. Does the apparatus
balance on the point A ? Where
is the centre of gravity ? By
disturbing W, is the centre of
gravity raised or lowered ? Why will a pencil, weighted with
a knife, as in Fig. 133, balance on the finger ?

Fig. 133.

CENTRE OF GRAVITY.

123

Such forms of the pendulum as a hammock or a swing are
in stable equilibrium. Why? Show by a diagram how a
bicycle could be balanced on a wire, after removing the tire,
of course. Bolt a bar of steel to the frame of the machine,
and let the bar extend down and under the wire and carry a
heavy weight. Instead of building roads in a rough country,
freight is sometimes carried in boxes suspended from a car
that nins on a single overhead wire. Fold a card in the form
of a V. Invert, and suspend it from a wire. Imagine each
side loaded with passengers or freight. The loss by friction is
reduced by wheels running on the supporting wire. This form
of track and cars has often been suggested. In what kind of
equilibrium is it?

142. Centre of Buoyancy. — In boats, the centre of gravity
becomes an important consideration. In most boats the centre
of gravity is low down, as G, Fig. 134,
because of the heavy lead keel. Imagine
all the weight concentrated at G. The
forces that buoy the boat have likewise a
point, B, where they might be considered
as concentrated, called the centre of buoy-
ancy. This may be thought of as the point
of support. This being above the centre
of gravity, as in Fig. 134, the
boat is in stable equilibrium,
and will right itself if tipped
so that the sails strike the water.
"^ It is as if the weight G were
hung from the point B\ when
swung to one side or the other,
it falls again to the perpendicu-
lar position, like a pendulum. A
match, having a pin for a keel (Fig. 135), represents this type
of boat. Increasing the distance EG in Fig. 134, makes

Fig. 134

Fig. 135.

124

PRINCIPLES OF PHYSICS.

the boat more stable, or more "stiff." Loading the deck,
sending men aloft, or taking out ballast or heavy freight from
the bottom of the boat, raises the centre of gravity. What
effect does this have on the stability of the boat ?

The flat, or skimming-dish, type of boat (Fig. 136, I), is
more common in shallow waters. A flat block of wood (Fig.
136, II) may represent this type. The
centre of gravity may be at G, and the
centre of buoyancy somewhere below (?,
perhaps at B, The centre of gravity is
then practically above the support. The
boat is in unstable equilibrium, and tips
a little, as shown in III. The centre
of gravity is unchanged in position at
G. The centre of buoyancy shifts over
to C, since more of that part of the boat
falls below the water-line than before,
and is buoyed up by the water. Re-
member that a floating body is always
buoyed up by a force equal to the weight
of the water it displaces. The two
forces, one at G pulling downward and
the other at C pushing upward, form a
couple that tends to right the boat.

II.

143. Neutral EquUibrium. — Roll a
sphere in any direction. What com-
mon objects are spheres ? Roll a barrel
or a cylinder (a pencil, for instance) on its side. The centre
of gravity is neither raised nor lowered. No amount of push-
ing tips it over. It simply revolves, and remains in the posi-
tion in which it is left. A cylinder or sphere has neutral
equilibrium. If a body is supported at the centre of gravity,
in what kind of equilibrium is it? Why? What class of
objects have neutral equilibrium?

CENTRE OF GRAVITY.

125

144. Fall of the Centre of Gravity. — When a body falls, its
centre of gravity falls. Fasten a weight, W, Fig. 137, to one
side of a round berry box.
Make a hole, O, through
the centre of the top, and
another at the centre of
gravity, G, This last may
be found by the method of
Section 134. Place the box
on an incline, in position

A. The box appears to roll Fig. 13 r*
up the incline. The centre

of gravity does fall as the box moves from position A to
position B.

Make two little holes, C and 2), one in each end of an q^^.
Blow out the contents. Stop up D with gummed paper. Drop

in lead shot and a little

liquid glue. Keep the
Q^^ in an upright posi-
tion {A, Fig. 138) for
twenty-four hours. Then
try to put the Q^g down
on its side; it at once
stands upright again.
The centre of gravity in B, Fig. 138, is not over the support
S. The centre of gravity ^

falls, being nearer to the f^ =======3

table in position A. \^ S

E, Fig. 139, represents a
curved piece of wood, carry-
ing a long straw, S. When the centre of gravity, 6r, falls, the
straw stands upright.
Measure the distances from the centres of gravity in A and

B, Fig. 138, to the table. In which case is the distance the
greater ? Make a diagram of an inkstand that will not tip over.

Flg»J38.

Fig. 139.

126 PRINCIPLES OF PHYSICS.

Bxercise 18.

CENTSE OF GBAYITT.

Apparatus : 2000-g. balance ; objects weighing 600 g. to 2000 g. ; a lever of
irregular shape, or a piece of board loaded at one end by a piece of wood
or a clamp.

Weigh the lever. Attach a weight ( W, Fig. 140) by a string to a
screw in the end of the lever. Balance the lever on a pencil, and
mark the spot, A, on which it balances. Record the distance AB and

Fig. 140. Fig. 141.

the amount of the weight W, The downward force of W tends to
make the lever rotate in a direction opposite to the hands of a clock.
To balance another force, the weight of the lever must act as if applied
somewhere to the right of A (as at C, Fig. 141). Then W y. AB -
AC y. weight of lever (call the amount L).

Wy AB=ACxL
AC=^Y^.

Balance the lever alone on the pencil, and record distance J52),

Fig. 142. Compare this with

^j^^^^^^mY^mmmmmmm ^| + ^4 ^ obtained above. For

•S r *^^ purposes of computation, where

^'^' ' ^^' may the weight of a lever, or of

any body, be considered as concentrated ?

At B, Fig. 143, hang a body, X, of which the weight is to be
found; find the balancing-point E. Consider E as the fulcrum,
or turning-point ; find the value

JC X BE = L X EC '^"- " "^

Y _L X EC
^-^BE~'
Repeat both cases, hanging
weights from the other end of the board. A weight may be hung at
each end, and the value of one unknown may be calculated.

CENTRE OF GRAVITY.

127

Problems.

1. UW (Fig. 140, p. 126) = 1000 g.y AB = 40 cm., weight of lever
= 800 g., where does the lever alone balance ?

1000 X 40 = 800 X -4 C. -4C=60. The lever balances and has its
centre of gravity, or mass, at 60 + 40, or 90 cm., from the end B.

2. A pole 20 feet long weighs 126 lbs. When a 30-pound bag of
meal is hung on one end, the balancing- point is 3 feet from the same
end. Find the point where the pole alone would balance.

3. A stick weighing 7 pounds balances 3 feet from the end A ;
how much weight must be put on A to make the whole balance at a
point 2 feet from the same end?

4. A hammer weighing 12 ounces balances 14 inches from the
handle end. What does a fish weigh, which, when tied to the end of
the handle, makes the whole balance at a point 6 inches from the end ?

145. Levers. — Let C be the centre of gravity of the lever

AB, Fig. 144, which weighs 12 pounds. The force L, which

may be considered for

purposes of computation

as applied to O, is the

weight of the lever, 12

pounds. Let BC equal

20; BE, the distance of

the balancing-point from B when the weights W and Y are

acting on B and A, equals 15 ; AE equals 19.5 ; W equals 30.

Find Y. Make a new
diagram (Fig. 145), put-
ting the numbers in their
places. Calling E the ful-
crum, or turning-point,
the moment of 30 about
that point is 30 x 15 =

450. The force 12 is 5 away from E, the moment is 12 x 5 = 60.

The force Y is 19.5 away from E, the moment is 19.5 Y, As

^19^5 »J

12
Fig. 145.

128

PRINCIPLES OF PHYSICS.

U- 2 ^vJ

14
Fig. 146.

¥¥

these last two tend to make the board turn to the right, their
sum,

19.5 r+60 = 450

19.5 r=390
Y= 20.

A lever weighing 14 pounds has its centre of gravity 3 feet
from A (Fig. 146). At A is hung 10 pounds; at B, two feet to

the right of C, is hung 2 pounds.
Find the centre of gravity of the
whole. Suppose this point is at
E, at a distance d to the right
of C. Consider E the balancing-
point.

10 X (3 -h d) + 14d = 2 (2 - cZ)
30 + 10 d + 14 f? = 4 - 2 (Z
26 (Z = - 26
d = -l.
The negative value shows that the supposition that the
balancing-point was to the right of C is incorrect, and that
the balancing-point is one foot to the left of C. Assume that
to be the point, and see if the sum of the moments about it is
equal to zero.

Another way to deal with such problems is to take the
moments about one end, as A, remembering that at E there
must be a force upward equal to the sum of 10, 14, and 2.

146. Bodies that are not Uniform in Cross-section. — An iron
mast is made of three pieces, 20, 16, and 10 feet long. The
first piece weighs 80
pounds, the second 60,
and the third 40. Find
the centre of gravity of
the mast. As each sec-
tion is uniform, its cen-
tre of gravity is at its

-20-

-16-

-8—? ♦-S

-10-

Fig. 147.

CENTRE OF GRAVITY. 129

centre. To support the mast at a distance d to the right of
Ay there must be an upward force equal to the sum of the
downward forces (80 + 60 + 40 = 180). The moment of this
force is 180 x d. This tends to make it swing upward on A
(Fig. 147). The moments of the separate forces tend to make
the pole swing in the opposite direction around A,

80x10= 800

60 X 28 = 1680

40x41=1640

4120

This must be equal to 180 d,

180 d = 4120

d = 22.8+,
the number of feet to the right of A,

Problems.

1. Find the centre of gravity of a spindle composed of three sec-
tions, the first 8 cm. long, weighing 25 g. ; the second, 6 cm. long,
weighing 30 g. ; the third, 12 cm. long, weighing 20 g.

Taking the moments about the left-hand end, we have
25 X 4 =
30 X 11 =

20 X 20 =

Find the sum of the products.

At the centre of gravity, a distance d from the end, a force of
(25 -I- 30 + 20) must be applied. Find d, Ans. d = 11.

2. Three weights, 4 g., 12 g., and 10 g., are hung on a weightless
stick 20 cm. long. The 4 g. and 10 g. weights are at the ends of the
stick ; the 12 g. weight is 6 cm. from the 4 g. weight. Where does
the stick balance?

Taking the moments about the left end, where the force of 4 g. is
applied, this force has no turning effect.

(12 X 6; + (10 X 20) = d X (4 + 12 + 10). Ans. d = 10.4.

CHAPTER X.
WEIGHT AND MASS.

147. Mass means amount of matter. If we wish to know, in
a general way, how much there is in a box or package, there
are three ways of finding out. Measuring the size and measur-
ing the weight are two familiar ways. By measuring the size,
the merchant knows how much molasses, grain, or ice cream
he is selling to his customers ; in fact, almost all liquids and
gases, and some solids, are measured and sold by volume, or
bulk. Similarly, when we ask for a certain amount of sugar,
the grocer measures the amount by weighing it. In each of
these cases we are buying a certain amount of matter, or, as
the scientist says, a certain mass.

In addition to measuring the volume or weighing a body to
find its mass, there is a third way. A wagon piled full of
boxes looks heavy ; but if it starts easily when the horses pull
it, the boxes are either empty or tilled with something that
contains a small amount of matter. An empty barrel is made
to roll or stop by a slight push. The mass or amount of matter
that a body contains can be measured by the resistance it
offers to being started or stopped.

148. Comparison of Masses. — Select two cars that run easily.
Arrange them as shown in Fig. 148. W is a grooved wheel,
five inches in diameter, turning on a machine screw in a piece
of board. The board is clamped to the table. Fasten the
end of a rubber cord to a screw in the centre of the upper
edge of the box of each car. The whole length of the cord
may be two feet or more. Pull the cars away from the wheel

130

WEIGHT AND MASS. 131

Wj thereby stretching the cord. If one end of the cord is

stretched a little tighter than the other, the wheel revolves,

distributing the tension

evenly between the two

ends of the cord. Load

one car. Let both cars

stai-t together, and notice

which car first reaches a

mark, M, six inches or jt

more from the wheel W. Fig. 1 48.

Stop the cars before they

strike the wheel. Load more heavily the car that gets first to

the mark M, When the two ears are loaded so that they both

reach the line M at the same instant, weigh each car. Provided

the wheels run loosely on their centres, it is unnecessary to tip

the board to overcome friction, since the friction is small.

A locomotive engineer can tell, by the speed with which his
train starts up, if a car has been detached from the train ; for
equal forces pushing for the same time on equal masses impart
to them the same speed.

149. Change in Weight. — Bodies weigh less near the equator
than they do near the poles of the earth. This is because the
surface of the earth is a little farther from the centre at the
equator than it is at the poles. Besides this, the centrifugal
force (see section 159, p. 138), due to the rotation of the earth
on its axis, tends to make a body at the equator fly from the
earth, like mud from a revolving wheel. If the earth revolved
seventeen times as fast as it does, its centrifugal force would
be greater than the force of gravity, and bodies actually would
fly from its surface. The variation in weight of a body carried
from the equator to one of the poles is about one pound in two
hundred. A mass weighing 199 pounds at the equator would
weigh 200 pounds at either pole. This diflFerence could be de-
tected only by a spring balance of some sort, as weights would

132 PRINCIPLES OF PHYSICS.

gain or lose, when carried from place to place, equally with
the object weighed.

160. Weight as a Measure of Mass. — If sufficient weight, a
mass of rock, for instance, were put on a spring balance to
make it read 200 pounds at either the north or the south pole,
and the balance, with its load, were carried toward the equator,
the spring would gradually shorten, and finally read about 199
pounds. The mass of the rock would be unchanged. The
springs of a wagon would be nearer together at the poles of
the earth than in the neighborhood of the equator. The differ-
ence, of course, would be slight, but it could be made evident
by using some multiplying device.

A box of candy weighs a pound, let us say. Take this box
to the surface of the moon ; there would be just as much candy,
— that is, the same mass or amount of matter, — and it would
do just as much sweetening, although its weight would be only
one-sixth of what it was on the earth's surface, because the
moon is a smaller body and attracts objects on its surface less
powerfully. Take the same box to the sun's surface; the
amount of matter would remain the same, but the weight
would be 27^ pounds. The sun is a much larger body than
the earth, and there is more matter in it to attract an object
on its surface. On the surface of Vesta, one of the smaller
planets, the box would weigh only one-thirtieth of a pound.

While the weight of this pound box of candy, which we will
call a pound mass, varies with the attraction on this mass,
being greater on the sun and less on the moon and smaller
planets, yet .the force required to set it moving in a horizontal
direction, in a given time, at a certain speed, would be the
same in each case. A regulation baseball weighs nine ounces.
On the sun its weight would be 27^ x 9 ounces ; on Vesta,
■^jj of 9 ounces. The weight varies ; still, the force required
to pitch this ball with the same swiftness is the same in all
cases, for the mass does not change.

WEIGHT AND MASS. 133

Mass can be measured by weight, as long as weight is con-
stant, or practically so, as on the earth. Outside of the influ-
ence of the force of gravitation a body would have no weight,
but its mass would remain unchanged.

151. Attractive Force of Different Planets. — The speed, or
velocity, acquired by a freely falling body depends on the
attraction exerted upon it. On the earth, the velocity of a
falling body, while varying in different places, at the end of
one second is about 32 feet, or 980 cm., per second. The
velocity at the end of one second's fall is 27^ times this on
the sun's surface, or 880 feet per second, — the velocity of a
rifle ball. The attraction of the moon for bodies on its surface
is about one-sixth that at the surface of the earth. A falling
body at the end of one second, on the moon, has a velocity of
about 5 feet a second, and would fall 2^ feet in the first second.
A person on the moon could jump six times as high as on the
earth. On the surface of Vesta the attraction is one-thirtieth
of that on the earth's surface. In one second a falling body
would drop about six inches, and have a velocity of one foot a
second. Human beings cannot exist there, for its attraction is
insufficient to retain an atmosphere for any length of time. If
they could exist, they would be able to carry 30 times as many
bricks or jump 30 times as high as on the earth.

162. Mass and Weight. — The mass of a body, then, — that
is, the amount of matter which it contains, — does not change,
but the weight of the body depends entirely on the particular
planet, or part of the planet, in which the body happens to be.
Although the same mass has different weights in different
latitudes, it always has the same weight at any particular
latitude. It is on this account that we are able to use the
convenient method of comparing masses by weighing them.
Mass is the amount of matter a body contains. Weight is the
force of attraction pulling down on this mass. The mass
remains the same everywhere ; its weight varies.

134 PRINCIPLES OF PHYSICS.

153. Measurement of the Earth's Attraction. — The metric
unit of mass is the amount of matter contained in a cubic
centimeter of water at a temperature of 40° C. In practice,
mass is measured by himps of brass, iron, or any metal, which
are made to conform to a standard unit — a lump of platinimi
kept by the government. Since, the weight of any mass de-
pends on the attractive force of the earth, the weight is meas-
ured by measuring that attractive force. The greater this
force is, the faster it will pull a body toward the earth. It is
conveniently measured, therefore, in terms of the velocity of a
falling body, and expressed by the velocity such a body acquires
in a second. On the surface of the earth this is about 32 feet,*
or 980 cm., varying from 978 cm. at the equator to 983 at the
poles. Since it is troublesome to measure exactly the velocity a
falling body acquires in one second, or even the distance it falls
in one second, various ways have been devised to dilute, as it
were, the force of gravity and make a body fall more slowly, so
that its velocity can be accurately measured. Galileo increased
the time of fall by making a ball roll down a hill or incline.

164. Measurement of Velocity. — If the height BC (Fig. 149)
is one foot, this one foot is the distance the body really falls in

going the length of the hill AB,
Then, if AB equals 10 feet, the
body goes 10 feet in falling one
foot, and gets up speed one-tenth
as quickly as if it were falling
straight down. Let a heavy mar-
ble or steel ball roll down the groove in a matched board for
one second, and measure the distance it goes. Start it again,
and let it roll two seconds. Notice that the distance gone
over in two seconds, in starting at rest, is much more than two
times the distance gone in the first second.

1 Change feet to centimeters, by multiplying by 12, to reduce to inches, and
then by 2.54, because there are 2.54 cm. in an inch.

WEIGHT AND MASS. 135

This method, first used in the study of falling bodies by
Gralileo, does not give accurate results, because of the friction
of the board and the energy needed to make the ball roll
around.

155. Vibration of a Pendulum. — A much more accurate way
of measuring the earth's attraction is to measure the length of
a simple pendulum and the time of one vibration. A pendu-
lum is a falling body (at least the bob, or weight, is), and it
moves up and down a sort of double inclined plane. The path
is slightly curved, and the weight slides down one hill and up
the other, repeating this many times, since the friction of the
support is almost nothing and the resistance of the air is slight,
because the pendulum moves slowly. By counting the number
of vibrations for a long time, the exact time of one vibration
is calculated. From this and the length of the pendulum, the
velocity acquired in one second by a freely falling
body is estimated. (See section 455, page 399.)

To show that the rate of vibration of a pendulum
depends on the downward force acting on it, suspend
a weight of about 50 g., B, Fig. 150, by a thread one-
fourth of a meter long. Set it vibrating, and count
the number of vibrations per minute. Attach a rubber
thread, R, fastening it at A. Set B vibrating, and
count the number of vibrations for one minute. In-
crease the tension on R, if possible, to three times the
weight of jB, as shown by a spring balance at A. If R
is very long, the pull exerted by it will be nearly
parallel with the earth's pull. Suppose B weighs
50 g., — that is, the earth's attraction, or downward
pull, is 50 g. This was the downward pull on B when
its vibrations were counted without R attached. Make Fig.'^so.
the pull of R, as shown by the spring balance, 150 g.
Then the total pull on B is 200 g., or four times what it was
at first. The pull of the elastic has the same effect on the

136 PRINCIPLES OF PHYSICS.

pendulum as if the latter were swinging on a planet heavier
than the earth. Find the number of vibrations in a minute.
They should be twice as many as before. Increase the down-
ward pull to nine times as much as at firsts and the number of
vibrations will be three times as great.

A pendulum, if carried to different parts of the earth's sur-
face, vibrates at different rates. A pendulum clock that keeps
correct time at any one place gains time on being carried
toward the pole, because the pendulum beats faster. It is
easy to count the number of vibrations it makes and to meas-
ure its length. In this way the force of the earth's attraction
is computed. A pendulum clock that keeps exact time at the
equator gains nearly four minutes a day if taken to one of the
poles. The discovery that the earth's attraction varies in dif-
ferent places was made in 1671, when a clock, taken from
Paris to Cayenne, near the equator, lost over two minutes a
day till its pendulum was shortened.

156. Mass considered apart from Weight. — If we could take
a piece of rock so far off into space that the attraction of the
earth or any planet would be reduced to
little or nothing, we could then experi-
ment on it as a mass of matter having no
weight. Instead of doing this, the weight
of a body, or its downward attraction, can
be neutralized by floating it in water or
suspending it by a long thread. Of course
the water offers resistance to the motion of
anything in it, while a very long suspend-

r^i ^ „ ing thread, for the purpose of the experi-

' — ' . nient, is no practical hindrance.

As long as the body A, Fig. 151, is moved
a short distance in a horizontal direction, there is practically
no resistance outside of A itself to stop it. Give a little pull
to the string B, and notice how quickly A begins to start. Pay

WEIGHT AND MASS.

137

no attention to the pendulous motion set up, because we are
seeking only the force required to start A, or to set it in
motion. Try to start A more quickly, and see how strong a
string at B can be broken.

157. Setting a Body in Motion. — Suspend a weight. A, Fig.

152, by a string, C, that is but little more than strong enough

to support A. Fasten a similar string,

B, to A and to a stick, D, B is not

long enough to reach to the floor. By

pulling down gently on B, C will be

broken, because the pull on C is the

weight of A plus the pull given to B.

Pull down quickly on B, using, if need

be, the stick D to give a quick pull,

and notice that B breaks. Replace

B with a string strong enough to hold

up several times the weight of A, If

the downward pull on B is quick

enough, B will be broken in every

case. The reason for this is that C

stretches a little without breaking, but A resists being set in

motion, and this resistance causes the forces to accumulate, as

it were, below A, and breaks
B before it can act suffi-
ciently on A to break C.
A bullet, if thrown by the
-^ hands, shatters a window-
pane, but if shot from a gun
it is likely to cut a clean
hole. The glass, being elas-
tic, can give a little without
breaking; and as it resists

being set in motion so quickly, the bullet cuts its way through

before the glass some distance from it is bent far enough to

Fig. 152.

Fig. I 53:

138 PRINCIPLES OF PHY8IC8.

break. A candle can be shot through a board without splitting
the board.

A oanl may be snapped out from under a cent, because the
resistAuoe of the cent to being started quickly is greater than
the friction that would make it move with the card. Place a
iiathead screw, S, Fig. 153, on a sheet of paper. Strike down
sharply on the paper at A, thereby pulling out the paper with-
out disturbing the screw.

158. The Resistance a Body offers to being set in Motion may.
be very little, if the starting is slow ; or it may be very great,
many times the weight of the body, if the starting is quick
enough. To stop a body quickly requires a greater force than
to stop it slowly. The shorter the space of time in which a
body is stopped, the greater the force necessary to stop it.
Sand driven by a blast of steam or air makes little impression
on paper or on the flesh of the hand, for they yield a little
and stop the flying grains of sand more slowly than does a
piece of glass or hard steel. These substances are rapidly cut
by the sand blast.

159. Centrifugal Force. — Tie a spool to the end of an elastic
string and swing it in a circle. The spool pulls harder and

harder on the string, stretching it more

b(^oJ^- >-c the faster it is swung. In Fig. 154, A

represents the elastic string, and B the
spool. If A should break, B would go off
in a straight line except for the down-
ward pull of gravity. As long as the
elastic holds, however, it pulls against
Rg. is4w *^^^ tendency and makes the spool swing

in a circle. The fact that the spool does
have an outward pull is shown by the stretching of the elastic.
Every point of a revolving wheel has this same tendency to
pull away from the centre. Flywheels, grindstones, and

WEIGHT AND MASS. 139

emery wheels fly to pieces when turned too rapidly, because
the speed makes the outward pull too strong for the stone or
iron to resist ; that is, the parts of the wheel tend so strongly
to move in a straight line that the iron or stone is not strong
enough to pull them into the circular motion. In Fig. 154, BC*
is the path the body tends to take, and BD the path the body
is made to take by the pull of the string toward A.

160. Inertia. — A body resists being set in motion, or being
stopped, or being pulled out of a straight line in which it is
moving and made to revolve in a circle. The resistance the
body offers in these cases to being started or stopped, or pulled
out of Us line of motion is said to be due to its inertia. If a
three-pound mass and a one-pound mass are moving at the
same velocity, then the three-pound mass has three times as
much inertia as the one-pound mass. The one-pound mass, for
instance, has the same inertia if moving at a certain speed,
whether it is on the earth and has weight, or is far away
and has no weight. It would have inertia anywhere and
everywhere.

CHAPTER XL
VELOCITY.

161. Average Speed. — A man walks 4 miles an hour for 5
hours. The distance, or space, he goes over is 20 miles, for 20
equals 4 times 5. At one part of the journey he may have
gone at a faster speed, or velocity, than at another, but he
averaged 4 miles an hour.

162. Distance. — To find the distance, or space, passed over
by a moving body, multiply the average velocity by the time.
In a shorter form, this may be written

Space = average velocity multiplied by time,

or, letting 8 stand for space, or distance, v for average velocity,

and t for time,

8=V xt

Problems.

1. If a body moves at an average velocity of 4 cm. a second for 20
seconds, how far does it go? Ans. 80cm.

2. What is the average velocity of a railroad train that goes 480
miles in 420 minutes ? Find the distance it goes in one minute.

Ans, 1.14+ miles a minute.

3. How long does it take a steamer to go 6000 miles if it averages
22 miles an hour? Ans. 272+ hours.

163. Average Velocity. — On a uniformly increasing rate of

wages a man earns at first 50 cents a day, and later $1.00 a

day. His average earnings per day are found by adding

f 0.50 and f 1.00, and dividing by 2. This gives $0.76 as

the average.

140

VELOCITY. 141

When a train is slackening speed its velocity is not uniform,
but is growing slower and slower each successive second. For
example, if its velocity at one moment is 8 feet a second, but
at the end of several seconds is reduced to 4 feet a second, its
average velocity is (8 + 4) divided by 2.

164. Formula for Average Velocity. — The average velocity
is found by adding the velocity at the start and the velocity at
the end of the observation and dividing by 2 : —

Average velocity = velocity at end plus velocity at start^

As before, write v for average velocity ; write Vq for velocity
at the beginning, or initial velocity, and Vi for velocity at
the end of the observation, or final velocity. Putting these
abbreviations for the rule above, we have the short way of
writing it: —

-?;i + -?;o

Read this as

v = (v sub one + v sub naught) divided by 2 ;
also as

Average velocity = (JincU + initial velocity) divided by 2.

In becoming familiar with any new formula, practise reciting
and writing it in both the long way and the short way.
Vq and Vi are sometimes read "v-oh," "v-eye."

Notice that the three different v's stand for different veloci-
ties. To distinguish the three different v's, they might be
printed of different colors or sizes, or, as here, have some dis-
tinguishing mark added. Vq does not necessarily mean that
the velocity is zero, although any one of the velocities may be
zero. For instance, if a body starts from rest, the initial
velocity is zero; if, at the end of the observation, the body
comes to rest^ the final velocity equals zero.

142 PRINCIPLES OF PHYSICS.

Problems.

1. A train at the top of an incline is going at the rate of 30 miles
an hour ; at the bottom it is going at the rate of 70 miles an hour.
What is the average speed down the incline ? j 70 + 30 _ ^

2 ~

2. What is the average velocity of a sled down a part of a hill, if
the velocity at the beginning is 4 feet a second and at the end is 20
feet a second? Ans, 12 feet a second.

3. If initial velocity (that is, velocity at the beginning of the obser-
vation) is 30 feet a second, and the body comes to rest, what is the

average velocity ? v= — ^^—. Ans, 15.

4. Find the average velocity of a sled in passing over a patch of
ground, if the velocity at the beginning was 30 feet a second and at
the end was 6 feet a second. Awt, 18 feet a second.

166. Fonnula for Distance. — In the formula S ^V x t, sub-
stitute the expression for average velocity,

v=!!L±iLo.
2

Then s^h±^Y

This may be read :

Distance equals average velocity times time.

Call this important Formula No. 1.

A train is moving at a rate of 80 feet a second ; in the course
of 40 seconds it is slowed down by the brakes to 20 feet a
second. How far does it go in the 40 seconds ? Substitute, in
Formula No. 1,

The initial velocity, v© = 80
Final velocity, Vi = 20
« = 40
^20 -f 80\ gQ ^ ^ 50 X 40 = 2000 feet.

After the answer to the above problem is known, it may be
worked to find the time, assuming that the time is unknown.

•=(-

VELOCITY. 143

Other problems may be made from this one by assuming that
the initial velocity or the final velocity is unknown.

Problems.

1. If a body, starting from rest, in 10 seconds is moving at the rate
of 50 feet a second, how far does it go? Ans. 250 feet.

2. How long does it take a train moving 30 feet a second to stop
in a distance of 400 feet? Ans, 26.6 seconds.

3. A body goes 80 feet in 5 seconds and then has a velocity of
10 feet a second; what was the initial velocity?

4. A bullet is stopped in ^J^j second after penetrating two feet into
a wooden block. What was the velocity of the bullet when it struck?

Make up problems similar to the above and solve them. Work
them backward.

166. Acceleration. — If a body is moving, at one instant, 10
feet a second, and at another instant 30 feet a second, the gain
in velocity is 30 - 10 = 20. Or,

Gain in velocity equals the final velocity minus the initial

velocity ; or,

Gain in velocity equals v^ —Vq.

But what we usually wish to know is the gain in velocity in

one second. Suppose five seconds elapsed; then the gain in

velocity in one second is J of 20 = 4.

Gain in velocity in one second = (final velocity— initial velocity)
• divided by the time.

Gain in velocity per second = ^ ~ ^'

The gain in velocity per second is called the acceleration,
and the abbreviation for it is the letter a. The formula then
becomes

t
Call this Formula No. 2.

If the body is stopping, there is a loss of velocity. The
gain in velocity in such a case is a minus quantity.

144 PRINCIPLES OF PHYSICS.

Problems.

1. Wliat is the gain in velocity per second, if the initial velocity
cMluals G feet a second and the final velocity equals 21 feet a second,
and the time is 5 seconds ? What is the acceleration ?

2. Wliat is the acceleration of a train, if the initial velocity is 45
feet a second and the final velocity is 15 feet a second, the time being
(I seconds? Ans. —5.

3. I'j, = 80 cm. a second ; rj = 24 ; t = S; a = what ? What is the
gain in velocity j>er second ? Arts, — 7.

4. Find the final velocity if i'^ = 26, / = 2, a = 12. Ans, 50.
Make up a few problems, solve them, and also work them backward.

167. Combination of Formulas. — The two fundamental for-
mulas for moving bodies first studied are

■=c^>

y. (1)

a^ViJILHo. (2)

Any problems involving distance, time, acceleration, initial
velocity, and final velocity can be solved by these formulas.
It is more convenient to combine the two formulas and obtain
other formulas that have fewer letters. The work of obtain-
ing these new formulas is a process of algebra.

168. Elimination of t. — This is done by any of the methods
used in algebra, — substitution, addition, subtraction, etc.^ In
this special case, as Ms in the numerator of one formula and
in the denominator of the other, multiply the two equations

(1) and (2).

1 liCt some pupils try one method, some try another.

VELOCITY. 145

Cancel the t and multiply the parentheses together; then
multiply both sides by 2.

Problems.
1. Initial velocity = 10.
Final velocity = 30.
Distance = 5.
What is the acceleration ?

2 X 5 X a = (30)2 _ (io)2,

^ 900 - 100 ftf.
« = ^^— = 80.

2. Initial velocity = 20 ; final velocity = 24 ; s = 8 ; a = what?

Ans. 11.

3. What must be the velocity of a ball, if it has an acceleration of
2 feet a second, and after 5 seconds has a velocity of 18 feet a second,
and goes 65 feet ?

Evidently, s = 65, a = 2, i'q = 18. Atis. v^ = 8.

4. A car starts up an incline at a velocity of 16 feet a second ; its
acceleration is —2 feet a second. After going 39 feet, what is its
velocity? Ans. 10 feet a second.

5. A cannon is 30 feet long ; at the instant the powder explodes,
the velocity of the projectile is, of course, zero ; the muzzle velocity is
2500 feet a second. What is the acceleration? Ans. 104,000.

8 = 30, vo = 0, vi = 2500. In this problem, the pressure of explo-
sion, and consequently the gain in velocity inside the cannon, is assumed
to be constant, though this is not strictly true.

6. From the data in the preceding problem, find how long it takes
the projectile to leave the cannon after explosion. Use the formula

g _ '^i + ^0 ^^ ^n.9. < = jf^^ seconds.

169. Elimination of Vq and Vj. — From the fundamental
formulas

s = Vl±3>^t and a^^^l^l^,
2 t

146 PRINCIPLES OF PHYSICS.

two others can be obtained: one by getting rid of, that is,
eliminating, Vq; the other, by eliminating v,. The latter
formula is a particularly useful one. Try to eliminate Vi
from the two equations above, and obtain the formula

When solving the following problems, practise substitution in
this formula.

Problems.

1. A sled starts down a hill with a velocity of 3 feet a second ; the
acceleration is 2 feet a second. Find the distance it goes in 5 seconds.

*=^^ + (3x5)
= 25 + 15 = 40 feet.

2. A railway train moving 10 feet a second starts down an in-
cline ; the increase in velocity is 1 foot per second. Find the distance
it goes in 30 seconds. Ans, 750 feet.

3. The initial velocity is 10 cm. a second ; the acceleration is 10.
Find the distance traversed in 3 seconds.

4. Call the initial velocity 0 ; that is, the body starts from rest.

Show that the formula becomes s = —.

5. Use this formula to find the distance a body falls from rest in

3 seconds, when a = 32 feet. Ans, 144 feet.

6. Find the distance a weight falls in 4 seconds ; in 2 seconds ; in
2J seconds ; in 1 J seconds ; in 5 seconds.

7. Find how much time is required for a body to fall 64 feet,
when a = 32 feet. Ans, 2 seconds.

8. How high is a tower, if a bullet takes IJ seconds to fall to the
ground? Ans, 36 feet.

9. How long would a body take to fall to the ground from a
balloon 900 feet above the surface of the earth? Ans. 7i seconds.

10. How long does it take for a weight to fall 16 feet? 1 foot?

4 feet? 400 feet? J foot?

VELOCITY. 147

11. A baseball is thrown straight up in the air. A person starts
to count seconds as it begins to fall. In 3 seconds it reaches the
ground. How high up did the ball go ?

12. As an icicle melts, two drops of water fall, the first ^ of a
second before the other. How far apart are they when the second
one falls? Ans. ^ foot.

13. Using the metric system, acceleration = 980 cm. Find the
number of centimeters a body falls in 6 seconds ; } second.

170. Acceleration of Falling Bodies. — The acceleration, or

gain in velocity, made by a falling body in 1 second is about

32 -h feet, or 980 cm., varying a little on different parts of

the earth's surface. A falling body every second increases

its speed by about 32 feet. The exact amount of increase

in any place where experiments are conducted is well worth

knowing, and is best obtained by finding the distance a body

falls in a measured time, and then computing by the formula

at*
«=■--. The difficulty is in measuring the time accurately.

In sections 154 and 155 there are described several methods
(the inclined plane, the pendulum, etc.) of so "diluting" the
attraction of the earth and increasing the time of fall that an
accurate measure of time can be made. From this the velocity
gained per second on the acceleration is computed.

171. The Dyne. — Since the weight of a lump of any sub-
stance varies in different parts of the world, the weight of a
body — that is, the downward force it exerts because of the
attraction of the earth upon it — cannot be used as an accurate
standard in scientific work.

Make a cube of wood, 1 cm. on an edge. If this does not
weigh a gram, bore a small hole in it and put in one or more
shot, as needed to bring the weight to 1 g. Close the hole
with paraffin. Suspend the cube by a long thread. The
block contains the same amount of matter as is contained in

148 PRINCIPLES OF PHYSICS.

a cubic centimeter of water and occupies the same amount of
space.

The force that pushing for one second on this mass gives it
a velocity of 1 cm. a second is the same the universe over.
This force is called a dyne — a word coined by scientists from
a Greek word like it, meaning force.

172. The Dyne compared with the Gram Force. — A dyne,
then, is a force, that, acting on a gram mass for one second,
gives it a velocity of 1 cm. a second. But this little block
weighs a gram ; how, then, does the gram force compare with
the dyne ? In one second, one dyne would give this one gram
a velocity of 1 cm. a second. Suppose the block is dropped
out of the window. At the end of one second it has a velocity
of about 980 cm. a second, — a little less at the equator, a little
more at the poles. The force of the earth's attraction on it —
a force that we call a gram force, or a gram — is 980 times that
of a dyne. There are from 978 to 981 dynes in a gram, accord-
ing to the locality in which the gram force is measured.

A dyne force is extremely small. The weight of a mosquito
can be scarcely felt, but it is a dyne, or more.

Problems.

1. What is the velocity acquired by a mass of 1 g. acted on by a
force of 1 dyne for 3 seconds? Ans. 3 cm. per second.

2. What is the velocity acquired by a mass of 6 g. acted on by a
force of 1 dyne for 1 second ? Ans. I cm. per second.

3. What is the velocity acquired by a mass of 4 g. acted on by a
force of 12 dynes for 3 seconds ? ^ ^ 12x^ ^ g ^^ ^^^^

4. Find the speed a 1-gram lump attains if a force of 1 dyne acts
on it for 1 second ; for 4 seconds.

A ns, 1 cm. per second ; 4 cm. per second.

5. Find the velocity a force of 6 dynes gives to a mass of 2 g. in
3 seconds. Ans, 9 cm. per second.

VELOCITY, 149

173. Velocity in Tenns of Force and Time. — The velocity is
made greater by increasing the force. The greater the force
applied to a boat, the quicker it starts ; the longer the force
acts, the greater the velocity, or speed, attained. In these two
ways, then, by increasing the force and the time of applying
that force, more velocity is acquired. But by increasing the
mass to be moved, the velocity gained is made less. A heavy
train gets up speed slowly.

Velocity equals force multiplied by time and divided by mass ;

ft
or, V = !^.

In this formula, m stands for grams of mass, t for time in
seconds, v for velocity in centimeters per second, and / for
the force in dynes.

Problems.

1. What velocity will a force of 8 dynes give to 2 g. in 12

seconds? ^ = §_2^. Ans. 48 cm. per second.

2 ^

2. How fast will a bullet, weighing 10 g., go, after being pushed
by a force of 20 dynes for 6 seconds? Ans. 12 cm. per second.

3. What force is required to give 100 g. a velocity of 20,000 cm. a
second in ^ of a second ?

Substituting, 20,000 = -^ ^ A ; then /= 100,000,000. The answer is
in dynes ; change this to grams by dividing by 980 or 1000.

4. How long must 20 dynes act on 80 g. to give a velocity of
120cm. a second?

120 = — . t = 480 seconds.

From each of the above questions make others, letting each quan- .
tity in turn be the unknown one. For instance, Problem 1 might
become : How long does it take a force of 8 dynes to make 2 g. move
with a velocity of 48 cm. per second ?

160

PRINCIPLES OF PHYSICS.

Id Problems 5 to 14, inclusive, below, find the value of the unknown
quantity.

DYNK8

10.

11.

2000

12.

13.

14.

980

15. What force is always nearly 980 dynes ?

174. Conversion of Grams to D3rnes. — If a force is given in
grams, change to dynes by multiplying by 980 before substi-
tuting in the formula. If the answer is required in grams,
divide the number of dynes by 980.

175. Formula for Force. — The formula for acceleration, as
shown in section 166, is

If the initial velocity is zero, that is, if the body starts from
rest, Vq = 0, then Vq, being zero, drops out, and the formula

becomes a=— • Since there is now only one v in the for-

VELOCITY. 151

mula, there is no need of any mark to distinguish it from any
other V. Therefore, instead of Vi, let us write v. The for-
mula then is

a = —
t

Multiply both sides by t ; then v = (jU. Substitute aty which
is the value of v, in place of v in the following formula : —

1;=—; then

at = —' Cancel the fs :
m

a = ^, or f=::ma,

an important formula in considering projectiles, throwing and
stopping a baseball, starting and stopping a railway train, etc.

Problems.

1. Find the force in dynes that will give 40 g. an acceleration of
10cm. a second. /= 40 x 10. Ans, 400.

2. What force must be applied to a mass of 200 g. to cause the
body to go 3 cm. per second faster each second ? Ans, 600.

3. What is the gain in velocity per second caused by a force of
24 dynes on 4g.? Ans. 6cm. per second.

4. If the acceleration of a falling body is 980 cm. per second, how
many dynes is the force that the earth exerts on a gram mass ?

5. An artesian well spouts a stream of water 25 feet high ; what is
the velocity of the water at the mouth of the pipe? Acceleration = 32.
Use the formula 2a8=v^ (section 168). Ans, v=iO feet per second.

6. If the diameter of the jet of water of Problem 5 is 3i inches,
the cross-section is about 11 square inches. (Calculate it.) How
many cubic inches of water will flow per second ? Find the number
of gallons of water per second by dividing by the number of cubic
inches of water in a gallon.

162 PRINCIPLES OF PHYSICS,

176. Multiply the formula, section 1G8, page 145,

by f=ma

term by term.^ Then 2 a«/= mav^

which is another important formula in studying projectiles, etc.

177. An Erg. — In section 119, work was deiined as making
a body move against resistance, and formulated as Force times
distance through ichich the force acts. This is what is meant
by fs. Therefore fs in the formula stands for work that has
been done or can be done. The other side of the equation,

exactly equal to fs, is the expression ^^— This latter repre-

sents the work a moving body can do when it stops. Since
the force is measured in dynes and the distance in centi-
meters, the work is measured in dyne-centimeters. A dyne-
centimeter is usually call(»d an erg. This is the work done by
pushing or pulling a distance of 1 cm. with a force of 1 dyne.
If there are 980 dynes in a gram force, how many dyne-centi-
meters are there in a gram-centimeter? How many ergs?
What energy does a 20-gram rifle ball have when moving

10 cm. a second? Substituting in the formula ^^, we get

?^-~^ = 1000 dyne-centimeters, or ergs.

Square the velocity, multiply by the mass, and divide by 2.
fs can be read as "force times distance through which the
force acts.*'

1 To be convinced that this is possible, consider the two equations

2 = 2,

3 = 3.

The equality is not destroyed by multiplying the first two and the last two
terms together ; for then 6 = 0.

VELOCITY. 153

Suppose the question is : What force must be used to stop
tbe ball in 1 cm. ? Then, / x 1 = 1000, and / is 1000 dynes. If
tbe body moved 5 cm. while stopping, then s = 5, and / x 5 =
1000 ; /= 200. The force required over the longer distance
is only one-fifth as great as before.

Problems.

1. Find the energy of :

a. A 20-gram bullet going 60,000 cm. a second.

6. A 300-gram baseball moving 1500 cm. a second.

c. A 6,000,000-gram electric car moving 600 cm. a second.

d. A 50-gram weight moving 5 cm. a second.

e. A 500-gram hammer moving 600 cm. a second.

2. Find the force required to stop each body in Problem 1, in
1 cm. ; in 2 cm. ; in 10 cm. ; in 1000 cm. ; in .001 cm.

Notice that the force required increases enormously if the body is
stopped in a short space. Why is the blow of a hammer on a solid,
unyielding body more severe than on a flimsy stick ?

3. Find the force required to stop each body in Problem 1, in
3 cm.; in 4cm.; in 500cm.; in .005cm.

4. a. What is the energy of a 60-gram arrow moving 200 cm. a
second? Ans, 1,200,000 dyne-centimeters, or ergs.

b. What force is required to stop it in 1 cm. ?

Ans. 1,200,000 dynes.

c. What force is required to stop it in 30cm.? Ans. 40,000 dynes.

d. What force must the string have applied to the arrow to set it
goins at a velocity of 200 cm. a second, the string moving 30 cm. ?

Ans, 40,000 dynes.

5. a. A force acts in the barrel of a rifle 60 cm. long ; the bullet is
20 g., and its velocity on leaving the muzzle is 60,000 cm. a second.
What is its energy? Ans. 36,000,000,000 ergs.

b. What is the average force exerted by the powder on the bullet ?

Ans. f- 600,000,000 dynes.

Since the barrel is 60 cm. long, s = 60, / x 60 = 36,000,000,000.
Change the force to grams, by dividing the answer by 080.

154 PRINCIPLES OF PHYSICS.

6, A 3(KVgrain ball is thrown with a velocity of 1200 cm. a second.
Find :

a. Its energy.

6. How much work it can do in stopping.

r. AVhat the force is with which it presses on the catcher's hands
when he stops it gradually in 20 cm. (The catcher moves his hands
back.)

7. A bicycle and rider weigh 50,000 g. They move at a speed of
1 (KK) 0 m . a secon d. Find ;

<i. Tlje energy. Ans. 25,000,000,000 ergs.

A. The force necessary to stop them in 1 meter.

0. The force necessary to stop them in 10 cm.

//. The foi*ce necessary to stop them in 10 meters.

8. How high up a hill could the same rider coast?

Since the energy is 25,000,000,000 dyne-centimeters, and the gram is
080 times as great as the dyne, the energy in gram-centimeters will be
,Jo as nwxQh, or, roughly, 25,000,000, and this will raise 50,000 g.,
^ftftW^ <-'>"•» ^1' 250 cm.

9. A 1-gram mass moves with a velocity of 4 cm. a second. Find :

a. Its energy.

b. The amount of force that will stop it in 1 cm.

c. Tlie amount of force that will stop it in 10 cm.

d. The height to which this energy will lift it.

10. Find:

a. The energy of 1 g. moving 1 cm. a second.

b. The energy of 1 g. moving 2 cm. a second.

c. The energy of 1 g. moving 3 cm. a second.

d. What effect does doubling tlie velocity have on the energy?

11. By use of smokeless powder and better cannon, the velocity of
projectiles has been increased during the last century three to five
times. How much has the energy of the moving projectile been
increased ?

12. a. How many times greater is the energy of a train moving
100 miles an hour than that of one moving 50 miles an hour?

Ans, 4: times greater.

b. If the force that the brakes can exert to stop each train is the

VELOCITY. 155

same^ how much farther will the first train go, with the brakes on,

than the second ? Ans. A times as far.

c. State the objection to a railroad speed of 200 miles an hour.

13. Which has the greater energy, and which will strike the harder

blow, a 100-pound shot having a velocity of 600 feet a second, or a

10-pound shot moving 2400 feet a second ?

This illustrates the relative effectiveness of the artillery of the Revolu-
tion and of the present day.

178. Reaction. — If a person sitting in a swing throws a
heavy weight in a horizontal direction, the swing starts to
move in the opposite direction. If a man jumps from the
bow of a light boat to a wharf, the boat moves backward a
little. From a heavy boat, a person can jump ashore without
causing any perceptible motion to the boat. If one were to
jump from successively lighter boats, the same effort to jump
would appear to affect him less and the boat more. A gun
"kicks," or moves backward, at the same instant that the
bullet is being driven forward. Newton states this in his
second law of motion: To every action there is an equal and
opposite reaction.

179. Momentum of a. Body. — In every instance the lighter
body has the greater velocity. If the gun and the bullet were
of the same weight, the velocity of the gun and the bullet
would be equal. It has been found that even when the bullet
and the rifle have different velocities and different masses, the
mass of the rifle times its velocity backward equals the mass
of the bullet times its velocity. Suppose the bullet in a toy
cannon weighs 1 gram and the cannon weighs 100 g. On
firing the powder, the bullet has 100 times as much velocity
forward as the cannon has in the opposite direction. The
mass of the cannon times its velocity equals the mass of bullet
times its velocity. Mass times velocity (or m times v, or mv)
is called the momentum of a body. The word " momentum "
expresses something about a moving body that is more imaginary
than real, but it is a convenient term to use in some problems.

156 PRINCIPLES OF PHYSICS.

For experiments in momenta, boats in water or cars on a
track have too much friction, and there is too much difficulty
in measuring the velocity. Experiments can be made, how-*
ever, with bodies suspended as are A and 5, Fig. 165. Sup-
pose a spring on A, which is pressing against B, is
let go. A and B will separate. The larger ball, B,
acquires the less velocity, and swings a shorter dis-
tance than A, In fact, we must assume, what is dif-
ficult to prove, that the velocity the pendulum A ot B
A^^ has at the lowest point of the swing is proportional
^5[^5 to the length of the swing it makes. This is nearly
Fig. 155. true, if the swing is not too great. If either A or B
swings 20 cm. before or after reaching the lowest
point of the swing, then the velocity at the lowest point is
twice as great as if the swing has been 10 cm. Instead, there-
fore, of trying to measure directly the velocities of the bodies
A and B before and after they strike, we have only to find the
distance each swings before and after they strike.

Bzeroise 10.

ACTION AND BEACTION.

Apparatus : Two ivory or wooden balls, one larger than the other ; meter rod
on base-board ; two swinging stops, fitted to board, and arranged so that
by pulling a string both balls are released at the same instant ; a board
8 inches wide and 12 inches long, with bevelled edges, and some means of
supporting it six or more feet above the table ; linen thread for suspensions.

Pass the thread through the holes
in the balls and over the support at C
and D (Fig. 156). Make the distance
between C and D such that A and B
just touch. The distance between C
and D equals the radius of A plus the
radius of B, Adjust the height of A
and B so that their centres are on the
same horizontal level. This can be Fig. IS0,

done by tying knots in the suspensions to shorten them*

VELOCITT. 157

C€ue I. ^— Record in a note-book on a diagram (Fig. 157) : Ist, the
distance, BC, that B is drawn back; 2d, the distance, BF, that B
goes after collision; 3d, the distance AE^ that A goes after collision.

Record the two points on the meter rod that are uuder the
centres of A and B, Record these, as well as all other measurements,
on a diagram like Fig. 157, in note-book. Draw B back 20 cm.,
holding it in position by the stop. Release,
and try to slide a block of wood, holding a ^

card, so that the centre of B at its point of ©"

farthest swing to the left is just in line F^ — l—AB

with the card. Bring A to rest, and repeat pig, 1 57.

the trial, changing the position of the card,

if necessary. Record on diagram the position of B and the distance
it swings^ from B to F, While doing this, pay no attention to the
distance A swings. Then, in the same way, find how far A swings
from -4 to ^. Weigh A , to determine its mass in grams ; weigh B,
Before collision. A, being at rest, has no momentum. The weight,
or mass, of B times the distance, BC, that it swings may be called its
momentum before striking A, This is the momentum before colli-
sion. At that instant B gives up, as it were, a part of its momentum
to -4. Compute the momentum of A after collision ; then of B. Mul-
tiply the mass of A by the distance it swings, and the mass of B by
the distance it swings after collision. Add these two products to-
gether, and see how nearly the total momentum before collision
equals the total momentum after collision. As we have assumed that
the velocity of a pendulum at the lowest point of its swing depends
on the distance it swings before reaching the lowest point, the dis-
tances we have recorded represent velocities. Representing the mass
of A by the letter A and the mass of B by the letter i5, does

B X distance BC =(Bx distance BF) + (^ x distance A E),
Momentum before striking = momentum after striking ?

Case II, — Pull A back 30 cm., and let it strike B at rest. Make a

j> r» diagram (Fig. 158), and record on it the

' ' /^ /^ position from which A starts and the

(B ®\J!/ \l) distance AE. Record also the position

""' p' I ' of -B before collision and the positions

B and A after collision and the distances

they move. On striking B, A not only gives up all its momentum,

168 PMIXCIPLES OF PHYSICS.

but chore than it has, and goes in debt for that extra amount, and
on this account swings backward with a velocity that carries it
to t\ The momentum before collision = A x distance A E, The
momentum after collision = (B x distance BC) -{Ax distance A F).
The sign of this last product is a minus one. Either for the reason
»t«t^ l^fore^ or because A and B after collision have velocities in
op(H>site directions, the momentum of one body must be a negative
one.

(V«» !Ff. — Draw A and B back 15 to 25 cm., and release them at
exactly the same instant. A and B need not be drawn back the same

distance. Record on diagram like Fig.
H A B ^7 159 the distances, EA and BC, that

(^.-. -C/Ti -ZlT) -** and B go before striking together;

p^ I u-_^ »^ also the distances, AF and BK, they go
Fig. 159. after rebounding. Mark the weights

on the outlines of A and B in the dia-
gram. If A is very much lighter than B and is not drawn back a
greater distance, then B may not fly back after striking, but may
continue on.

Compute the momentum of each ball before striking. As they are
moving in opposite directions, one value will be plus and the other
minus. Call the momentum plus if the body moves to the right.
Find the total momentum before collision by adding the momentum
of A (a plus value) to the momentum of B (a minus value). If
^ = 100 g., B = 200 g., i4£ = 30 cm., BC = 20 cm., then the momen-
tum of A is

+ 100 X 30 = 3000,

the momentum of 5 is - 200 x 20 = - 4000,

and the algebraic sum is — 1000.

Compute the total momentum after collision. If A moves toward
Ff then its momentum is minus; if toward K, its momentum is plus.
Add the two values just as you would in algebra, and call the result
the momentum after collision. How do the momenta before and
after collision compare ? While these should be the same, the errors
in measurement may maVe them differ by several hundred units.
Even that amount is not large compared with the momentum of
one of the balls, for instance (200 x 20 = 4000).

A(t>

VELOCITY. 159

180. Inelastic Balls. — Wooden or ivory balls are more or
less elastic. To make them inelastic (that is, so there is no
bounce), put a band of putty around

one ball. Figure 160 shows it around

B. Draw back Ato E and release. J J A i

Measure the distance the balls go © ©v)"

after collision; this distance will j, —

be the same for both, since they pig. ico.
will be held together by the putty.

The total momentum before striking = mass A x distance AE.

The total momentum after striking = (masses A-\- B and

putty) X distance BC,

181. Recoil. — If a person standing in the bow of a boat
throws weights forward, he will cause the boat to move back-
ward. If he throws them backward from the stern, the boat
will move forward. There is an instance reported of a man-
of-war pursuing another and losing ground with every shot
fired from her bow guns, while the other, firing from the stern,
finally gained enough to enable her to escape. If a vessel,
complete, weighs 50 tons (100,000 pounds), and a 100-pound
shot leaves the muzzle of the gun with a velocity of 800
feet a second, how much is the speed of the ship increased
or decreased. The process is:

100,000 v = 100x800;

V = .8 feet per second.

The shot, then, has an instantaneous tendency to decrease the
speed of the vessel .8 feet per second; that is, if the ship
were sailing .8 feet per second, the recoil of the shot would
bring her to a standstill. Continued and rapid firing from
a vessel's guns in the direction in which she sails would per-
ceptibly retard her progress.
Make examples similar to the above.

160 PRINCIPLES OF PHY8IC8.

Problems.

1. A toy cannon weighing 200 g. is suspended by a long string.
On firing, a 10-gram bullet has, at the mouth of the cannon, a velocity
of 5000 cm. a second. What is the velocity of the cannon backward ?

The formula is mv = m^v^, or the mass times the velocity of one
part (the bullet) = the mass times the velocity of the other part.
200 V = 5000 X 10. Ans. v = 250 cm. a second.

2. A cannon is mounted on a car; both together weigh 10,000
pounds. If the velocity backward is 2.5 feet a second just after firing,
what is the velocity of the projectile weighing 20 pounds?

Ans. 1250 feet a second.

3. A form of lifeboat is driven by the reaction caused by pumping
water out of a pipe at the stern. If the boat weighs 20,000 pounds,
and the pumps send 2500 pounds of water per minute sternward with
a velocity of 60 feet a second, what is the velocity the boat would
gain in 1 minute, supposing there is no resistance whatever to the
movement of the boat? Ans. 7\ feet per second.

There is, of course, much resistance offered by the water, etc., and the
velocity given above would not be obtained. Such a boat has little
machinery to break down, but is very inefficient, because it requires a
large boiler and pump to drive the boat at a slow speed.

4. A ball weighing 150 g. is moving 20 cm. a second, and strikes
another ball, weighing 200 g., at rest. The first ball flies back with a
velocity of 4 cm. a second. Find the velocity of the second ball.

Ans. 19 cm. a second.

The smaller ball not only gives all the momentum it has, but gives up
more and acquires velocity backward.

Momentum before striking = momentum after striking.
160 X 20 = - (160 X 4) + 200 v.

5. A, Fig. 159, p. 158, weighs 50 g., and swings 30cm. before col-
lision; B weighs 150 g., and swings 25 cm. before collision. After
collision A swings back 35 cm.; how far does B swing?

Letting D represent the distance B swings,

(60 X 30) - (160 X 25) = - (60 x 36) -|- 150 Z) ;
Z> = - 3.3 to the left.

VELOCITY, 161

182. Momentum, starting from Zero. — The experiment of
Exercise 19, page 156, maybe varied
by using flat boards, each sus-
pended by four strings or wires.
Place a coiled spring, tied with a
thread, between the boards. When
the thread is burned, A and B
swing apart (Fig. 161), the smaller
mass, A, having the greater ve- p.
locity. The momentum of ^ =

the momentum of B, In this case the momentum before start-
ing is zero, for neither pendulum was moving.

183. Examples of Reaction. — A powerful stream of water
from a fire-hose causes such a reaction that the united strength
of two men is needed to direct the stream. In a small hand-
hose the reaction can be felt as the water is turned on sud-
denly. Lawn sprinklers are driven by the reaction force
given the pipe by the water as it acquires velocity in coming
out of the nozzle.

This principle can be easily demonstrated by means of a
glass tube with a rubber tube attached to each end. Connect
one rubber tube with a faucet and allow the glass tube to fill
slowly with water. When the tube is full, opening the faucet
suddenly will jnake it swing backward.

CHAPTER XIL
ELASTIOITY.

Exercise 20.

8TSETGHING.

(o o]-4.

Apparatus: A coil of more or less elastic wire, such as No. 90 brass, iron,
steel, bronze, or aluminum; clamps; spring balance; a light pointer a
foot or more long ; a scale ; an upright board, with a vertical groove in
which a clamp can slide freely.

Fasten one clamp to the top of the board (-4, Fig. 162). Double
a piece of wire of any convenient length more than two meters,
and attach the loop to the clamp. Pass the two free ends of the
wire through two holes near one end of the pointer and through
the clamps B and C. Fasten the clamp B to the wire, as shown in
the figure. Fasten the clamp C to the wire in such a
position that the tip of the pointer is nearly at the
top of the scale. Below C attach a spring balance
or a scale-pan, D. Adjust the clamp C in the
groove. The pointer is now adjusted to act as a
lever. B is its fulcrum, and if BS is 10 times 5C,
a vertical motion at C is magnified 10 times at S.

Determine the error of the balance for the posi-
tion in which it is to be used (see section 114,
page 102), and use the error in
correcting results. Record the
reading of »S? with no pull on
A C. With the balance D apply
a 200-g. force to ^C; i-ead <S^.
Lift 7), and find the zero load
reading of S again. Then apply
400 g^ 600 g., 800 g., etc., remov-
ing the load each time to get
the reading for no load. Cease
to increase the load when the
162

Pig. 162.

ELASTICITY. 168

pointer does not return to the fii'st reading. Measure the diameter
of the wire.i When the wire begins to stretch permanently, its elastic
limit has been passed, and any further increase in the force applied
merely increases the permanent stretching. This, of course, makes
the wire grow smaller in cross-section, just as a piece of candy, when
" pulled," grows longer, but smaller in diameter.

Find the elastic limit of soft copper, aluminum, or brass wire. The
wire can be made soft, if not already so, by drawing it quickly through
a hot flame. Fasten one end of the wire to a clamp on the edge of a
table ; to the other end of the wire attach a spring balance. Put a
paper pointer on the wire near the balance, and mark its position,
with chalk, on the table. Measure the diameter of the wire. Stretch
the wire by successively increasing forces. After each stretching,
release the wire and mark the zero point. Notice the amount of
permanent stretching. Try the same experiment with fuse wire,
which is made largely of lead or tin. It will be found to have very
slight elasticity.

From the data in this exercise, what has been determined about :

1. The effect that doubling the load has on the stretching ?

2. The effect of hardness on elasticity ?

184. Experiments on Stretching. — Compare soft annealed
iron wire and spring steel wire, or hard spring brass and
annealed brass. Compute the amount the wire stretches under
a given load, remembering that the pointer magnifies the
stretching. Look in a table of the areas of circles in the
Appendix, find the area of the cross-section of the wire used,
and calculate how many of these wires together would equal
1 sq. cm. If you wanted to stretch a wire with a cross-section
of 1 sq. cm. to the same extent you stretched the No. 30 wire,
how much greater force would you have to use ?

185. Young's Modulus. — When comparing the behavior of
two different wires, it is convenient to know how much a

^ In case there are several pieces of apparatus, put a different kind of wire
in each. The pupils may, in rotation, test the stretching of different speci-
mens in a short time.

164 PRINCIPLES OF PHYSICS.

piece of 1 sq. cm. cross-section and 1 cm. long would stretch
or compress if a force of 1 g. were applied at the ends A and B

^ ^ (Fig. 163). Another way of stating the problem

is : What force must be applied to A and B to
make it stretch so much as to double its length ?

Fiff 163 "^^^^ ^^ absolutely impossible, but the number of

grams necessary to do it, if it were possible,

can be calculated. The number is a large one, and varies for

different kinds of metal ; it is known as Toung^s Modulus, or

measure of elasticity,

186. Stretching. — We have found that doubling the force
applied to a wire produces double the amount of stretching ;
and, evidently, doubling the area of cross-section of a wire
decreases the amount of stretching by one-half. Further, a
wire 2 m. long will stretch twice as much as a wire 1 m.
long under the influence of the same pull, for each half of
the longer wire will stretch as much as the shorter one. Wires
of different materials stretch different amounts.

187. Breaking Strength. — The strength of materials used in
houses, ships, bicycles, and bridges must be known, or they
would be built so heavy as to be clumsy, or so light as to
be dangerous. Test the breaking strength, or the force required
to break pieces of twine, thread, fishline, and fine wire.

Exercise 21.

BEEAKING 8TSENGTH.

Apparatus: A testing-machine, consisting of an extensible frame, a wedge,
spring balance of 2000 g. capacity, ratchet, and crank, arranged as shown
in Fig. 164; wires of brass, copper, aluminum, and soft iron (No. 27 is a
useful size). The wire, stretched by the crank and ratchet, moves the
frame and registers on the spring balance the pull used. As the frame
moves, the wedge W drops down and holds it, when the wire breaks,
preventing the recoil of the balance. The rings xx. Fig. 164, are attached
to the frame and are stationary.

Select a piece of wire without sharp bends or kinks. Wind one
end three times around the end of the frame in whidt "■dge W

ELASTICITY. 166

(Fig. 164) fits. Fasten the other end to the axle of the ratchet.
Insert the wedge, as shown ; set the pawl to engage the ratchet wheel.
Slowly turn the handle. K the wedge does not follow the movement
of the movable frame, put a small weight on top of it. When the
wire breaks, the wedge holds the hook of the balance from flying
back. Record the reading of the balance. Take hold of the movable
frame and release and lift out the wedge. Let the frame go back
slowly. Make several trials, using each time a fresh piece of wire.
The average is approximately the breaking strength of the wire used.
Measure the diameter of a fresh piece of wire with a micrometer
caliper. Calculate the area of the cross-section. The rule is : Square
the diameter, and multiply by J tt, or by .785. For instance, if a wire

T-O-qh^ "■«" >o

measured .5 mm. (this may be written .05 cm., the square of this =
.0025), thus multiplying by .785, we have as the area .00196, or about
.002 sq. cm., or about -^^ of a square centimeter. Suppose the break-
ing strength of a wire of this diameter is 12 kg. The strength of a
wire having an area of 1 sq. cm. cross-section would be 500 times as
great, or 6000 kg. To find the breaking strength per square centi-
meter, divide the breaking strength of the wire used by the area of its

cross-section. --— = 6000.
.002

188. Experiments on Breaking. — Compare the breaking
strengths of other kinds of wire, strings, etc. Notice that
violin strings are often stretched to the breaking point. For
sounding great depths in the ocean, Lord Kelvin first used
piano wire. Which do you find the stronger for pieces of the
same length and weight, piano wire or string ? Kecently piano
wire has been used in kite flying. Compare the strength of

166 PRINCIPLES OF PHYSICS.

steel wire with that of soft iron wire. Soften a piece of brass
or hard-drawn copper wire, and compare its breaking strength
with that of an unannealed piece. Measure the diameter
before and after breaking. The wire may be annealed by
heating it slightly with a candle. Some idea of the amount
of permanent stretching, or elongation, is found by marking
with an ink pencil several places 20 cm. or more apart.
Measure the length between two of these marks between
which the wire does not happen to break.

189. Strength of Fine Wire. — If of two wires of the same
material, one has twice the diameter of the other and four
times the cross-section, it might be expected to stand four
times the pull before breaking. Such, however, is not always
the case ; because, as a wire is drawn finer and finer, the metal
becomes stronger. A rope of fine wire is stronger than a rod
made of the same amount of metal. The separate strands of a
wire rope should be capable of stretching a little before break-
ing. Before the most tightly stretched strand receives a pull
big enough to break it, it stretches a little, and the other
strands receive their share of the load. In well made rope
all strands are wound equally tight.

Problems.

1. If No. 20 copper wire breaks at 28 pounds, how much should a
No. 10 wire stand?

As the diameters (see Table, page 539) are in the proportion of nearly

1()2 IQQ

3 to 10, the amount of metal in the second is — -, or — -^ or 11 times as
great. The larger wire will break at somewhat less than 11 x 28 pounds.

2. A piece of No. 24 iron wire breaks at 22 pounds ; what should
No. 30 wire break at ?

3. Compare the strength of two similar wires, one .1 of an inch
and the other .3 of an inch in diameter.

4. How many times stronger is a rod .7 cm. diameter than a simi-
lar one .2 cm. diameter? Ans. ^ — 12.1.

ELASTICITY. 167

190. Factor of Safety. — In the construction of bridges, ma-
chinery, etc., enough material must be used so that the strength
at any spot is always much greater than the force that is to be
applied there, greater even than any force that would cause
it to be permanently stretched. Enough metal, wood, or other
material is used to withstand a force from 4 times (in the
case of metal) to 20 times (in the case of wood) as great as is
ever to be applied. When a beam breaks at 4 times the work-
ing load, we say that the factor of safety is 4.

191. Bending. — Support a match on two other matches, as
in A, Fig. 165. Press on the centre with the butt of a lead-
pencil, and notice the bending. Try the

effect of doubling the width by using two '° "a ^

matches joined together, laid flatwise, as ^ <

in B, Work a little glue into the opening

between the two matches; on drying, the ^S ^^

two act as one piece of wood. Try the

bending of this, first on its side and then

on its edge. Shave a match down to the shape of C. Try the

bending of this on its side ; then on its edges. Try the effect

of reducing by one-half the distance between the supports.

Which is the stiffer, or resists the downward pressure more,
a board on its side or on its edge? Why are iron or wood
floor beams laid on their edges and not on their sides ? Set a
bit of card 2 cm. wide and 6 cm. long on edge, on
[L jC*-^ two supports. Apply a slight force to make it
'^ ^ bend downward. Notice that it bends somewhat

Fig. I 66.

sideways, and as a result sags down. Bend a strip
of card to the shape a cross-section of which is like Aj Fig.
166 ; test its stiffness. The horizontal part hinders the verti-
cal part from bending sideways.

Why is a bicycle frame that is built of tubing stiffer than
one of solid rod of the same weight ? Compare the stiffness
of a paper mailing tube, a straw, and a tin tube, and the same

168 PRINCIPLES OF PHYSICS.

materials in flat section. Explain why a T-rail (B, Fig. 166) is
less likely to bend than the same amount of steel in a flat rail
(C, Fig. 166).

192. A Support, or ** Girder/' forming part of a bridge or the
floor of a building, is sometimes supported merely at the ends,
as the match is in Fig. 165, A. In other cases, one or both
ends are rigidly fastened, thus increasing the stiffness. The
timbers supporting the floors of modern houses are deeper
than those used in old-fashioned houses. In which are the
floors the more springy?

The laws of bending are most easily studied with beams
free to move at both ends.

Exercise 22.

(a) BENDING.

Apparatus : A wooden rod somewhat more than a meter in length and about
V2 inch square ; two triangular supports ; a micrometer screw (3f, Fig. 167),
so placed that it can be screwed down to touch a tack in the centre of
the rod ; weights of from 100 to 500 grams ; any convenient arrangement
for suspending weights from the centre of the rod. The tack and microm-
eter screw are connected with a battery, the circuit of which also includes
a bell ; a sounder, lamp, or galvanometer may be used instead of a bell.

Case L — Screw down M until the fluttering action of the bell

shows that contact is just made
between the end of the mi-
crometer screw and the tack.
Read the micrometer, and call
this the reading with no load.
Put a 100-g. load, W, on the
rod, and read the micrometer.
Turn the micrometer screw
back and remove the load.
Fig. 167. Find the reading at zero load

again. In the same way find

the reading when there is a load of 200 g., of 300 g., of 400 g., of 500 g.

In each case remove the weights and find the reading with no load,

ELASTICITY.

169

always remembering first to turn the micrometer screw back far
enough so that the tack will not touch it when the load is removed.
If a square metal rod is substituted for wood, the tack becomes
unnecessary, and V-shaped supports of metal are used, the binding
post being on one of these.

Arrange results in a table, as follows : —

Load

Reading
with load

Rbadino

NO load

Average
no load
bradino

Deflection

FOR 100-GBAM

load

The average no-load reading is the average of readings without
load, before and after the load has been added in each trial.

Fig. 168.

193. Process of Bending. — To show what really takes place
when a rod bends, lay a long rubber eraser on a page of the
note-book and mark its outline with a sharp
pencil. Bend the rubber and tie a string
around it to hold it. Make another tracing
in the note-book. Measure the length of
the side C (Fig. 168) by laying a strip of
paper on it. Lay off this distance in the book and see how it
compares with the original length of the eraser. In the same
way measure the length of the side D. Notice that the con-
vex side is lengthened and the concave side is shortened.

When a rod is bent, the forces at any point in the rod tend
to pull the fibres apart in the upper half of the rod and to
push them together, or compress them, in the lower half. The
problem is somewhat like the horizontal forces on the hinges
of a door (section 132, page 116), where the upper hinge is pulled
apart and the lower hinge is compressed. If the door had
hinges along its entire side, instead of one at the top and
another at the bottom, the analogy would be still closer.

170 PRiyCIPLES OF PHYSICS.

Sappo^ a beam or stick (Pig. 169; has a small section cut
ooty aod rods or hinges {1 to 6) are inserted. If the rod is

supported at the ends SS, and
^I r' forces FF are applied to bend

J tj_^ 7 it downward, ^ 5, and ^ will

1^ c 3 )t I be stretched, and resisting the

W 5^4^ 1 Stretching will tend to hold the

fe r ^ * '' ' " ^ lower parts of the stick together ;

^ *^ ^» -^r and ^ will be compressed

and will tend to push or keep
apart the upper half of the stick, as the arrows indicate. The
leverai^e of / and 6 is much greater than that of 3 and 4, In-
creasing the thickness of a stick a little increases its stiffness
a great deal. Consequently, if 3 and 4 were removed and
placed near / and 6, the rod would be much stiffer. Does this
suggest the reason why a tube is stiffer than a rod of the same
weight ?

Exercise 22.

(2>) BEKDnie.

Apparatus : The same as for Exercise 22 (a), page 168.

Case II. — Place the supports, SS (Fig. 169), 50 cm. apart; use
weights of 500, 1000, 1500, and 2000 g., and make the readings as in
Case I. Notice how much halving the length of the rod affects the
amount of bending for the same load. If it becomes one-eighth as
much, that is, makes the rod eight times as stiff, what relation does
its increase bear to the decrease of length? How
many 2*8 multiplied together make 8?

Case III. — Using weights of from 200 g. to 1000 g.,
test the stiffness of a stick (A, Fig. 170) double the
width of the one used in Case II.

Case IV. — Set the stick used in the preceding case
on edge, as B, Fig. 170. Use weights of from 500 g.
to 2000 g., and find what effect making the thickness

twice as great has on the amount of bending, or p. j^^

stiffness.

ELASTICITT. 171

Compare the various results, and record the conclusions reached,
trying to find what connection there is between : —

1. Increase of bending and change of load.

2. Increase of bending and change of length.

3. Increase of bending and change of width.

4. Increase of bending and change of thickness.

194. Formula for Bendii^. — Combining these conclusions,
we have: —

Bending or deflection equals ^^ X (length)^ ^.^^^

(thickness)' x width
some number, which varies with the kind of rod used.

D = — X some number, which varies with the kind of

rod used.

What has been studied in this exercise is the stiffness, and
not the breaking strength, of a rod. The laws are not the
same. Making a rod twice as thick makes it eight times as
stiff, but only four times as strong, and doubling the length
makes it one-half as strong.

Problems.

1. A floor sags, or bends, ^ cm. with a load of 100 pounds. What
would be the sag if loaded in the same spot with a ton weight?

A m. 2 cm.

2. The tip of a stout flsh-pole, held horizontally, bends 2 inches
when a one-half pound downward pull is exerted on the tip. What
is the load on the tip when the rod bends 7 inches? Ans. IJ pounds.

3. A brook is bridged by a long plank, 10 inches from the surface
of the water. If 20 pounds at the centre make it sag one inch, what
is the greatest weight that can pass over the bridge without sinking
it in the water?

4. How much would the plank in Problem 3 bend under a load of
20 pounds, if it were made twice as wide ? If made four and one-half
times as wide? one-half as wide? Ans. } inch ; J inch ; 2 inches.

5. The same bridge is made one-half as wide; what effect does
this have on the bending? Ans. It bends twice as much.

172 PRINCIPLES OF PHYSICS.

6. How will the bending of two similar boards in a plank walk
compare, if the cross supports are put 2 feet apart under one board
and 5 feet apart under the other ?

Ans. As 2' is to 5', or as 8 is to 125.

7. A beam 3 inches thick will bend how many times as much as
one 6 inches thick, supposing that all other conditions are the same ?
as one 9 inches thick ? Ans. 8 times ; 27 times.

8. If a pine stick 1 inch thick, 2 inches wide, and 6 feet long bends
.1 inch when a load of 20 pounds is suspended at its centre, how much
would a plank of the same material, 3 inches thick, 8 inches wide, and
20 feet long, bend under a load of 400 pounds ?

This can be solved in several ways. First, consider only the difference
in the thickness, then in the length, etc. Another way is to write out the
question as follows : —

A stick 1 inch thick, 2 Inches wide, 6 feet long, load 20, bends .1.

A stick 3 inches thick, 8 inches wide, 20 feet long, load 400, bends how
much?

The thickness of the second makes it bend ^ as much as the first.

The width of the second makes it bend ) as much.

208 ins 1000
The length of the second makes it bend — = -^ r= ±lliir as much.

* 68 88 27

The load of the second makes it bend ^ as much.
Therefore the bending of the second stick is the amount the first bends,
.1, multiplied by all these numbers, or

27 8 27 20

9. If a beam 6 feet long, 3 inches broad, 2 inches thick, under a
certain load bends 2J inches, how much would a similar beam, 30 feet
long, 5 inches wide, and 8 inches thick, bend in sustaining a load one
hundred times as great ?

.„..».(f)\8.(?)\2,. ■

195. Twisting. — Hold a match by the ends, and try to twist
it. Cut away some of the wood, reducing the breadth and
thickness by one-half, and again twist it. The following exer-
cise shows how the twisting of a rod or beam is affected by
increasing the load, the length, and the thickness.

ELASTICITY.

173

Exercise 23.

TWISHNO.

Apparattis : A rod I inch in diameter, clamped firmly to a table at A, Fig. 171,
and fastened at B to a i-inch rod ; pointers, C, />, E^ Fy and &, all of which,
except E and F^ must be equally distant from each other ; a grooved disk,
6 inches in diameter, at the end of the i-inch rod, to which disk are
applied forces tending to twist the rod ; spring balances, arranged as shown
in the figure, to measure the forces ; a graduated circle on a support behind
each pointer, so that the pointer marks the zero point on the scale ; supports
like Fig. 172 placed at intervals under the rods.

Record the reading of each pointer at no load. Apply a load of
500 g. at each balance. Record the position of each pointer. The

Fig 171.

difference between the readings of C and D is the amount the part
between C and D has twisted.

How does the twist of the length CE compare with that of CD ?
Remove the load and read the positions of the pointers.
Apply forces of 1000, 1500, and 2000 g. to each balance.
What effect does doubling the forces have on the amount
of twist? For the same force, how many times as much
twist takes place between C and D as in an equal length
{FG) of the larger rod? Is it about sixteen times as
much? The larger rod has twice the diameter, and 16 is
the fourth power of 2. Therefore the twisting of shafts
of the same material is greater in the smaller shaft and decreases
as the fourth power of the diameters.

Fig. I 72.

174 PRINCIPLES OF PHYSICS.

196. Conclusions. — From the exercise, we see that —

1. Twisting increases with the length.

2. Twisting increases with the moment of force applied. It is
easy to see that forces of 100 g. 10 cm. apart have the same
effect as forces of 50 g. 20 cm. apart. The moment of the
forces is the same.

3. Twisting increases as the diameter decreases. The increase
is as the decrease of the fourth power of the diameter.

Problems.

1. Compare the twist of a bicycle spoke 1 cm. long with that of
one 30 cm. long.

2. How many times as much does a rod twist if the twisting
moment is increased five times?

3. If a shaft 1 inch in diameter is replaced by one 3 inches in
diameter, and the same forces are applied, how many times is the
twisting angle decreased ? A ns, 3* = 81.

4. How would the amount of twist in two propeller shafts 3 inches
and 20 inches in diameter compare, if the same twisting moment were
applied to each ?

CHAPTER XIII.
HEAT.

197. Heat is a condition of a body. The hotter the body,
the faster the little particles of which it is composed move
hack and forth. They do not move at all in the sense of
going from one end of a rod to the other, but approach and
recede without passing one another. The hotter a body is, the
more violently they strike one another.

Three dishes are filled with water, that in one as hot as can
be borne by the hand, that in the second as warm as the room,
and that in the third ice-cold. The water in the second, if
left standing fifteen minutes, will be near enough to the tem-
perature of the room. Put one hand in the first dish for a
minute, and then in the second ; how does the water in the
latter feel ? Put the other hand in the third dish, and after-
ward in the second ; how does the water in this dish feel to
that hand ?

The sense of touch, for several reasons, gives little idea
about the heat of a substance. For instance, in the experi-
ment the water- in the first dish feels warm, because it gives
heat to the hand; and when this hand, warmed by contact
with the hot water, is placed in the second, heat is absorbed by
the water from the hand, and the feeling of cold is produced.
In the same way, when the hand that was chilled in the ice-
cold water is placed in the second dish, it absorbs heat from
the water, which consequently feels warm.

A body that can give heat to another body is said to be of a
higher temperature. A body is of a lower temperature when
it can receive heat from another body.

175

176 PRINCIPLES OF PHYSICS.

198. Distinction between Temperature and Quantity of Heat. —
If a red-hot nail is dropped into a bucket of boiling water, the
nail is cooled, showing that it is of a higher temperature than
the water. But the water actually contains more heat, — that
is, a greater quantity of heat, — as is shown by the fact that it
gives off more heat in cooling, and warms the room much more
than the red-hot nail.

199. Conduction. — We speak of heat as moving, or travel-
ling through a substance. If one end of an iron bar is put in
the fire, in time the other end becomes warm. The heat is
carried, or travels, through the iron. This is called conduction.
The motion of the little particles of a body is very small in
the case of a solid. The transfer of heat from one part of a
body to another is like the movement of a bend along a rope.
Give a quick swing to one end of a long clothes-line ; the dis-
turbance will travel to the other end.

Twist the ends of two wires, one copper and one iron, around

the end of a glass rod or of a pipe-stem ; or, if the ends are of

about the same diameter, they may be held

together by a smaller wire, as in Fig. 173.

The length of each piece should be four

inches or more. Run the drip from a

lighted candle on the full length of A, B,

and C Support on a ring-stand, and heat

Pj^ ,73 at D. After a few minutes the wax will

cease melting. Note how far on each rod

the wax has melted. Which apparently conducts heat the

best ? Why can a glass-blower hold one end of a tube in his

hand, while the other is held in the flame, for as long a time

as he pleases ?

Examine a " soldering iron." It is a lump of copper with
an iron handle, which is less likely to break than a copper
handle. What other advantage is there in the iron handle?
Why is it difficult to solder a large lump of or*

HEAT. 177

200. Condttctors of Heat — If pieces of wood, lead, iron, and
glass are left in a room for half an hour, — long enough for
them all to reach the same temperature, that of the room
itself, — they will seem to the touch to vary somewhat in
temperature. This is because one conducts heat away from
the hand faster than another. A loaf of bread and the pan in
which it is baked are of the same temperature just as they
come from the oven ; but the pan feels hotter, because it con-
ducts heat to the hand more rapidly than the bread does. In
winter, why does an iron fence feel colder than a wooden one ?
How can the hand bear the hot air from a baker's oven when
the bricks are hot enough to cause a burn? Wrap paper
around a metal pipe or bolt, or attach a label to the bottom of
an iron kettle, and try to burn the paper. Paper wrapped
about a piece of wood and exposed to a flame scorches at once.
Metal, being a better conductor, carries off the heat so fast
that the paper is kept comparatively cool. Lead may be
melted or water boiled in a box made by folding up the
corners of a thin sheet of paper of good quality. This experi-
ment is more difficult, but the paper may be kept from scorch-
ing by shaking the box. Water can be almost entirely boiled
away from over a lump of ice without melting the ice, if the
ice is weighted at the bottom of a test-tube and the water
heated above the weight. How does the conductivity of
liquids for heat compare with that of solids?

201. Liquid Conductors of Heat. — Liquids and gases are poor
conductors of heat. A long time would be needed to heat a
dish of water, if the heat were applied at the top. Nearly fill
a beaker with water. Drop in a piece of the lead of a copying
pencil, and apply a gentle heat. The water near the flame is
warmed, expands, and thus becomes lighter and rises. Cold
water flows down to take its place. Repeat the experiment;
instead of colored lead, use sawdust, which also will show the
direction of the currents of liquid.

178

PRINCIPLES OF PHYSICS.

202. Convection. — Fill a tube, bent as in Fig. 174, with col-
ored water. Suspend it in a jar of clear water. Heat one
side of the tube, and observe the movement of
the colored water.

Soak paper or cloth in a solution of one
part nitrate of potassium to twenty parts of
water. Roll into the form of a taper. Ignite,
and by aid of the smoke, study the air cur-
rents in a room.

Just as a crowd buying tickets is more
quickly served by passing in line, instead of
having the persons in the rear receive and
send messages to the ticket-seller through the
intervening crowd, so a liquid or gas is more
quickly heated by having each particle in turn go to the heated
surface and receive heat. And just as one person can pur-
chase tickets for a number, so it is unnecessary for each par-
ticle in every case to go to the heated surface, for those particles
that do go become strongly heated, and, on rising, mix with
and share their heat with other particles. This process of dis-
tributing heat is called convection.

Fig. 174.

203. Radiation. — If a hot object is held above the hand, the
heat is felt, although the transference of heat is not by either
conduction or convection. Hold the hand on a lighted incan-
descent lamp ; then turn out the light. Could the glass have
cooled as quickly as the heat disappeared? Was the heat the
hand received transmitted by conduction through the glass?
Within the bulb of an incandescent lamp there is practically
no air ; yet the heat comes from the filament across the empty
space as the heat of the sun comes to the earth. This method
of transmitting heat is called radiation, because the path is a
radius, that is, a straight line. Scientists believe that all
space is filled with a weightless, elastic * ^n called,

which vibrates, and sends along hei Aions.

HEAT,

179

Try an incandescent lamp which is dim from use. Air has,
perhaps, leaked in a little, and by convection heat is carried
from the hot filament to the glass. Place an incandescent
lamp under water, and turn on the current ; is the heat felt ?
Turn out the lamp ; has the water been much warmed.

204. Effect of Surface on Radiation. — Fill a bright tin or
nickelled brass can with water that has been heated to nearly
100® C* Place a thermometer
in it, and read the tempera-
ture every minute or half min-
ute. Plot temperatures up-
ward, and time in minutes to
the right, and draw the curve,
as in Fig. 175. Repeat, using
a can painted black, and plot
the curve. Which radiates
heat more rapidly ? Should a
stove be nickelled or black-
ened? Should a coffee-pot,
in which coffee is to be kept
hot, be black or bright? Clouds retard radiation. Why does
the earth cool less on a cloudy night than on a clear night ?
In what kind of weather may frosts be expected?

The conditions can be reversed, and the bright and blackened
cans filled with cold water, and the temperatures taken regu-
larly as before. For rapid work, place the cans in the sun-
shine. Good absorbers are good radiators. Some heat is lost
by convection when the cooling experiment is done in the air.
Notice that the filament of an incandescent lamp cools less
rapidly in the vacuum that exists when the lamp is new than
in many lamps that have been burned a long time, and into
which a little air has leaked.

minutes
Fig. 175.

1 The water may be dipped from a large panful that has been heated before
the beginning of the exi)eriment.

180

PBINCIPLE8 OF PHYSICS.

206. Effect of Heat on the Size of Substances. — Invert a flask
or test-tube, fitted with a long tube inserted in the stopper,
and place the open end of the tube in a tumbler
of colored water (Fig. 176). The water may be
colored by scraping the lead of a copying pencil
into it. Heat the flask with the hand ; cool the
flask by blowing upon it. Heat the flask with a
burner, and allow it to cool.

Remove the stopper from the flask. Fill the
flask with colored water, and replace stopper and
tube, so that the liquid stands some distance up
in the tube, as in Fig. 177. Heat the flask, but
not to the boiling-point. Allow it to
cool, mfU'king the heights of the liquid
in the tube, by a label or a Cross
pencil. What happens to a dish full
of cold water, when heated ? Which
must be the lighter, cold or warm
water? Of two liquids of different
densities, which floats ? In summer, fish stay in
the cooler parts of lakes; why are they not
of toner found near the surface at that season?
Why does a heated liquid rise?

Repeat the experiment, using test-tubes of the
same size, in place of the flask, Fig. 176, one filled
with water, the other with a different liquid, — Fig. 177.
alcohol, for instance, — and determine if the rate
of expansion is the same.

Fig. I 76.

206. Maximum Density of Water. — One cubic centimeter of
water weighs a gram exactly at the temperature at which water
is most dense. To find this point, that of the mcmmum density
of water, fill the metal can, C, Fig. 178, with water. The
lower part of the can should be wrapped with doth, to prevent
absorption of heat from the room. Pa y B, with

BEAT.

181

ice and salt. Read the thermometers, 7\ and T^, at frequent
intervals, until both are constant. Which thermometer first
shows a change? How low does it
go? Why does the cold water fall
at first ? How cold can the water in
a deep lake become at the bottom of
the lake ? The water cooled by the
ice and salt in the basket, B, con-
tracts, becomes denser, and sinks.

When, however, the water has cooled |» T^

to about 4° C, it does not continue
to contract and become denser on fur-
ther cooling, but instead it expands,
grows lighter, and rises to the top.

Do 100 cc. of water at 50° C. weigh more or less than 100 g. ?
Do 100 cc. of ice-cold water weigh more or less than 100 g. ?
Which is the more buoyant, water at 3° C. or at 0° C. ? How
cold will water in the bottom of a pitcher half-filled with ice
become on a warm day ? In testing the freezing-point of a
thermometer, what error would there be if the bulb were left
in the water below the ice, without stirring ?

Fig. 178.

207. Coefficient of Expansion. — The metal rod, R, Fig. 179,
— that of a ring-stand, for example, — is supported horizon-
tally; one end rests on the
pin to which the pointer,
PP, is attached by sealing-
wax. The pin rests on
the glass plate, O, or on
* any smooth, hard surface,
which is levelled by boards
or books ; the rod R does
not touch the glass plate.
Push the ring-stand, D, toward the pointer, PP, and record
the direction of the movement of the pointer. Heat the rod ;

Fig. 179.

182 PRIXCIPLES OF PHYSICS.

Then let it cool. Drop some water on it Were the rod to
IrDgthen an amount equal to the circumference of the pin, the
pointer would describe a complete circle. The pin may be
measured by a micrometer caliper, the circumference computed,
and the expansion of the kkI calculated from the part of the
circle through which the pointer moved. If the pointer moved
throufirh half a circle, the expansion was half the circumference
of the pin.

The numbers given in books to express expansion are called
otejficiehfs of exjyansion. and they mean the amount a rod one
centimeter long would expand for one degree of increase in
temperature.

208. Linear Expansion. — Metals do not all expand at the
same rate. Lay a strip of copper, | inch wide, ^^ inch thick,
and 12 inches long, over a similar strip of iron. Make a small

hole in the two, every quarter of an

inch, by driving an awl or sharp nail

Pj^ ,gQ through both. Put small tacks in the

holes, and hammer down the points.

Fig. 180 shows a portion of the two strips, after riveting.

Hold one end with pliers, and heat. Copper expands more

than iron, so the riveted strips will curve when heated.

Wood swells when wet. A thin board, wet on one side, will
warp. Measure the length of two opposite sides of an oblong
rubber eraser. Cut two strips of paper, the exact length of
the eraser, and gum them on opposite sides of it, attaching the
paper only at one end. Bend the rubber, and notice what
change there is in the length of the sides.

209. Examples of Expansion. — Metallic thermometers and
some forms of heat regulators, or thermostats, are made of two
metals riveted or soldered together. A balance wheel of a
watch expands in warm weather, grows larger, swings slower,
and the watch loses time ; but if another metal, which expands
faster, be fastened to the rim, the halves of the rim, which are

HEAT. 183

fastened only at one end, are made to curve in toward the
centre of the wheel when the temperature is increased. A bal-
ance wheel of two metals, skilfully designed, vibrates at the
same rate, whether hot or cold. As the wheel grows warmer
and expands, its tendency is to swing slower, like a lengthened
pendulum. This is compensated for, because the unequal ex-
pansion of the two metals of which the rim of the balance
wheel is made, causes a part of the rim, which is free to move,
to bend in toward the centre. This action tends to shorten the
pendulum and make the wheel vibrate faster.

210. Micrometers. — As metals expand comparatively little,
the increase of length due to a change of temperature must be
magnified in some way, so as to be read easily. Micrometers
and levers have been used for this purpose, A micrometer meas-
ures the increase in length in the same way that a micrometer-
caliper measures thickness.

Practice finding, by a micrometer, the diameter of wires, the
thickness of paper, sheet metal, and glass plates. Set the
micrometer for the following readings : 1 mm., .02 mm., 6 mm.
3.02 mm.

An English binding-post may be studied as a rough model of
a micrometer (Fig. 181). Count the number
of threads in half an inch. Common binding- ^

posts have thirty-two to the inch ; one thread
to the millimeter is to be preferred. Hold the
nut, Nj and turn the head, H, one whole rev- p.

Q olution. How far

^.f" J fl- does the point A advance? How
A ! vww«^) many revolutions must H be turned

foT

to advance A one inch ?
13 S BDE, Fig. 182, is a wooden frame.
A hole is made in E and a milled
nut (like N, Fig. 181) is pressed in
Fig. 182. . firmly. A circle of cardboard, C, is

184 PRINCIPLES OF PHYSICS.

glued to H. Mark any number of divisions on C, ten or one
hundred, for instance. On E fasten a little scale of cardboard,
S, which is marked off into thirty-seconds of an inch. Place
S so that the zero on (7, when close to S, is opposite one of
the marks on S. Turn the screw till it touches B, and if the
zero on C is not close to S, file away B, Practice measuring.
If the circle C is divided into ten parts, turning C one division
moves the point A one-tenth of one-thirty-second of an inch,
or -^ of an inch.

In measuring the expansion of a rod, we use a micrometer

somewhat similar to Fig.
183. BB is removed to
permit the rod to touch
the end of the screw, and
Z> is of a shape suitable
to be clamped to a sup-
^, , „, port. If the screw has ten

Fig. 183. \

threads to a centimeter,
that is, one to a millimeter, one whole turn of the screw moves
the point forward or back one-tenth of a centimeter, or one
millimeter. If the dial attached to the screw is divided into
one hundred divisions, turning the screw so that the dial moves
one division, moves the point y^ of a millimeter.

Exercise 24.

COEFFICIENT OF EXPANSION.

Apparatus : A rod of glass, aluminum, brass, zinc, or iron, one-fourth inch in
diameter and about 60 cm. long, i)ointed at the ends, and inserted through
corks in the ends of a steam jacket, which rests on supports not s^own in
Fig. 184 ; a base, with metal upright near each end, one to hold a micrometer
screw, M, the other to hold a metal stop, A ; a steam can (see Fig. 186,
page 191) . The micrometer screw should have a friction rachet, or a handle,
F, of small diameter, that will slip in the fingers when a certain pressure
is applied. This handle acts as a friction slip, and prevents the micrometer
from being screwed up harder at one time than another.

Turn back M; slip a knife blade in front of AT, to push the rod, R,
toward A. Read the thermometer in the room. Screw up M till the

5E .J _j,

3C R

^^j jF

iinriiXr

Fig. 184.

HJr^T. 185

frictionHslip acts. Read the dial, and make a drawing of it in the
position read. Note the mark on the scale, Z, that coincides with
the edge of the dial.
Turn back M two full _ .?

turns. Connect 5 with
the steam can by a thin
rubber tube. Lead the
drip from Z) by a
tube to a dish. Read
the barometer. The
temperature of the rod is assumed to be that of the steam. Determine
that from the barometer reading (section 226, page 201). For in-
stance, if the barometer is 76 cm., the temperature of the steam not
confined is 100° C. After steam has been coming from D for two
minutes, turn the screw M up slowly, till contact is shown by the
slipping of F. Read the dial, and turn M back a little. Repeat until
the reading is constant, and make a drawing of the dial, recording
also the scale reading on L, which is marked in millimeters.

Suppose that at the beginning the temperature = 20°, the reading
on Z is 4 mm., and the dial, where it touched L, reads 60 (that is,
1% of a millimeter) ; and that at a temperature of 100°, L reads 5,
and the dial 40. Then the difference in length of the rod was
5.40 mm. — 4.60 mm = .90 mm. This is .09 cm. We use centi-
meters, since the coefficient of linear expansion is the amount that
one centimeter of metal expands for 1° C. The coefficient of ex-
pansion in this case equals .09 divided by 60, — since a one-centi-
meter rod would expand one-sixtieth as much as the one used, — and
divided also by 80, the rise in temperature, since the expansion for
1° would be one-eightieth as much as for 80°. Then

Coefficient of expansion, that is, the amount a sec- qq

tion of the rod 1 cm, long expands when warmed = aq \^ go

= .000018

In this way find the coefficients of expansion of glass and of one or
more metals. To repeat quickly the reading with the same rod, or to
cool the jacket for another rod, attach the rubber tube connected with
S (Fig. 184) to a funnel or faucet, and let cold water run through the
jacket, around the rod, and through D into a dish, in which there is a

186 PRINCIPLES OF PHYSICS.

theriMometer. After two minutes read this thermometer. When the '
thermometer no longer falls, record the temperature, which is that of
the rod. Turn up the micrometer screw, and record the reading. In
this manner, several readings may be taken in an hour.

Problems.

1. A meter of brass at 20^ C. is how long at 30° C, if the coefficient
of expansion of brass = .000018?

2. A copper wire stretches across a river 1000 feet. How much
longer is the wire at 25° C. than when it was put up in winter at
- 10° C. ? Does the wire sag as much in winter as in summer? (Con-
sult tables for coefficients, in Appendix.)

3. The outer rings of heavy cannon are shrunk on. When made,
the rings are smaller than the tube or the other rings that they are
intended to surround. How can they be made large enough to fit?
The sheets of iron of which a boiler is made are fastened with hot
rivets. Do they become looser or tighter as they cool? Why is a
space left between the ends of rails on a steam railroad ?

4. How much does a bridge of iron, 1000 feet long, increase in
length when warmed from - 10° to 20° C?

This problem is done exactly as if the length were 1000 cm., and
the result is read as centimeters or feet, according to the problem.

5. Which contracts the faster per degree, iron or glass ? If the
leading-ill wires of an incandescent lamp be made of iron, what hap-
pens as the glass and iron cool down from the high temperature at
which tliey must be sealed? Find, in the table in the Appendix, a
metal better suited and one less suited to this purpose.

6. In the left-hand pan of a delicate balance is a mass of 50 g.
This is counterpoised by weights on the right-hand pan. The sun
falls on the left arm of the balance. Does the mass appear to weigh
more or less than before ?

7. If, in turning a piece of iron, the metal is heated to 60° C, and
measures 3 cm. in diameter, how much too small will it be, or how
much will it shrink, when cooled to 20° C?

Accurate work on metal sometimes is made with an error of less
than .001 mm.

HEAT. 187

8. If the temperature of an iron steam pipe 600 feet long is raised
from 10° C. to 120° C. when steam is admitted, how much does it
lengthen? • '

9. Calculate the coefficient of expansion of lead, if the length at
0° C. = 150 cm., at 90° C. = 150.37 cm.

10. If 10° C. is the average temperature of the three days before
a road is laid of 40-foot iron rails, how much space should be left
between the ends, that they may not touch in summer (temperature
= 25° C. ? Consider the rails fastened firmly at their eastern ends, if
the road runs in that direction, so that all the expansion appears at
the western ends.

U. What will be the effect of cold on a piano, if tightening a
string or wire raises the pitch ?

211. Expansion of Rails. — When lengths of a mile or more
of street car rails are welded together, as has been done on a
few roads, no provision is made for expansion, and the rails
do not expand and contract. Suppose a rail, when warmed a
certain amount, expands one-tenth of an inch. As much force
would be exerted by this rail in attempting to expand as would
have to be applied to stretch it one-tenth of an inch without
any change in temperature (see section 186, page 164). The
force required to prevent an expansion of one-tenth of an inch,
when the rail is heated, is as much as would have to be applied
to stretch it one-tenth of an inch, there being no change of
temperature. The rails are nailed to cross-pieces, and are so
firmly imbedded in the paving that the force tending to pro-
duce expansion due to ordinary changes of temperature is
more than counteracted.

212. Cubical Expansion. — In Exercise 24, page 184, the
lengthening or linear expansion of a solid was measured.
The rod, however, grew broader and thicker also. In the
case of a liquid, confined like mercury in a thermometer, the
expansion can take place (disregarding for a moment the ex-
pansion of the glass) only lengthwise. As there is little or

188

PRINCIPLES OF PHYSICS.

no increase or expansion in breadth and thickness, the entire
increase must be indicated by movement in the direction of
length.

In considering how much greater the entire expansion (cubi-
cal expansion) of a body in all directions is than the expansion
in length merely, assume that a cube 10 cm. on an edge ex-
pands 1 cm. in length, breadth, and thickness. Suppose ABC
(I, Fig. 185) is the cube before expansion. The increase in
length adds a piece 1 cm. thick, covering B (II). Adding the

U UI

Fig. 185.

same amount to the width and thickness, the expanded cube
appears as abc (HI), where the increase in all directions, or
the cubical expansion, is three times the increase in length,
or the linear expansion. But we know that after a cube has
expanded it is still a cube, and does not lack the little pieces
needed to make aho a perfect cube. Adding those little pieces
(IV, Fig. 185), the cubical expansion is a little more than
three times the linear.

In the case of a solid, however, the expansion of a 10 cm.
cube for 100° increase in temperature is about the thickness of
two leaves of this book. Fit two sheets of paper on the faces,
-4, JB, C, of a 10 cm. cube, such as the model cube used in teach-
ing the metric system, or on a box having nearly the same
dimensions, and determine whether or not the little pieces are
needed to complete the cube, as they were in obOi Tig. 185.
In this qase they are too small to measun

HEAT, 189

213. Cubical Expansion by Computation. — Let us compute
the volume of a cube 1 cm. ou an edge. The volume is
1 X 1 X 1 = 1 cc. If warmed 100°, the increase in length is
between y^^ and y^^^ of a centimeter. Of course, the cube
has expanded equally in all directions. The dimensions now
are 1.002 at the most.

The volume = 1.002 x 1.002 x 1.002 = 1.006009002.

All figures beyond the 6 must be disregarded, for they are too
small to be of any account. Practically, the volume is 1.006,
and the increase in volume, or the cubical expansion, equals
.006, which is three times .002, the linear expansion.

Suppose a cube 100 cm. on an edge increase to one 101 cm.
Cube 100, that is, find 100 x 100 x 100. Cube 101, and show
that the cubical increase is practically three times the linear
increase.

Problems.

1. How many times as much room does a lump of iron 10 cm. by
10 cm. by 50 cm. take up at 80° C. as at 20° C. ?

2. What metal would have a greater expansion than iron ? a less
expansion ?

3. Give a reason, other than the great brittleness of glass, why,
when suddenly heated, a thick piece of glass cracks more easily than
a metal.

4. Why is a pendulum rod of wood better than one of brass ?

5. If a brass pendulum is 100 cm. long at 20° C. ; what is its length
at35°C.?

6. Why do long lines of iron pipe screwed together have loops in
them every few hundred feet V

CHAPTER XIV.
THEBMOMETEBS.

214. Measurement of Temperature. — As expansion, or in-
crease in size, is the most common effect of heat, it may be
used to measure temperature. For measuring most tempera-
tures, solids expand too little and gases expand too much. Of
liquids, water freezes and does not vary in volume uniformly ;
alcohol, though not easily frozen and useful for determining
low temperatures, boils at a lower temperature than water;
mercury is generally used.

215. Construction of a Thermometer. — A flask and tube
like that shown in Fig. 177, page 180, filled with mercury or
alcohol, or even with water, could be used as a thermometer.
But if the tube and flask are made of one piece of glass, the
thermometer is more lasting and reliable. The flask, or bulb,
can be made on the end of the glass tube. To make a model
thermometer, first close the end of a tube. This is done by
heating the end of the tube and touching the hot end with
another. Continue heating, and pull gently on the pieces of
glass; the hottest part draws out fine, melts, and seals the
tube. By repeatedly heating the tube and blowing into it, a
large bulb can be made. While the bulb is still warm, put the
open end of the tube into a dish of mercury. As the air in
the bulb cools, the mercury rises and partly tills the bulb.
Holding the open end up, re-heat the bulb till the mercury
boils, and then replace the mouth of the tube in the mercury
dish. After several trials a tube can be filled a little distance
up the stem. When this is warmed, the mercury rises higher
in the stem. The glass expands, too, but not so rapidly as

100

THERMOMETERS.

191

the mercury. Repeat the experiment described in section
205, Fig. 177, noticing what happens when the heat is first
applied. A fall of the liquid in the tube shows that the glass
expands, the flask becomes larger, and more liquid flows down
into it. In a moment the liquid in the flask begins to warm,
and, as the rate of expansion of the liquid is greater than that
of the glass, it rises in the tube.

216. The Standard Temperatures generally used in fixing the
scale of a thermometer are : (1) the freezing-point of water, or
the melting-point of ice (though exactly the same temperature,
the melting-point is more convenient to use) ; (2) the boiling-
point of pure water under the pressure of one atmosphere, that
is, when the barometer reads 76 cm. : (3) the melting-points of
various chemical salts.

Exercise 25.

TESTIKO A THERMOMETER FOR 0° AND 100° G.

Apparatus : Steam can (Fig. 186) ; mercury thermometer; beaker or tin can.

Place the thermometer to be marked or to be tested in a beaker or
tin can full of snow or fine ice. Keep the snow or ice well up to the
height of the mercury, and notice the reading
when the mercury stops falling ; or, if the tem-
perature be unmarked, make a
little scratch with a file at the fl
height of the mercury, and call ^waterloils
this point " ice melts " ( Fig. 1 87) .
Remove the thermometer; warm
it with the hand, and insert it in
the long top of the steam can
(Fig. 186). Stop the pipe in
the side of the can, and allow
steam to escape freely from the
pipe in the long top. Read the
thermometer when the mercury
has ceased to rise; also read
the barometer. If convenient,
Fig. 186. push the thermometer down Fig. 187.

ice melts

i ice and salt

192 PRINCIPLES OF PHYSICS.

into the boiling water, and read the temperature. The boiling-point
used as a standard temperature is that of the steam. On the
unmarked thermometer mark with a file the level of the mercury,
and call that the boiling-point (Fig. 187). If the bore of the tube
is uniform, the space between the marks " ice melts " and " water
boils " can be divided into any number of convenient equal distances,
called degrees. On the centigrade ^ thermometer, " ice melts " is called
zero, and " water boils," 100 degrees. The space between tlui two is
divided into 100 parts, or degrees.

These experiments servo to test the thermometer under a pressure
of about one atmosphere.

217. The Zero Point is not the point of no heat; there are
lower temperatures, as every one knows. Fahrenheit chose the
point reached by the mercury in ice and salt as the zero point,
thinking that this gave the greatest possible cold. It was an
unfortunate choice, because the melting-point of ice and salt,
or ice and other substances, is difficult to determine. Lower
temperatures than zero Fahrenheit are common. He divided
the space between " ice melts " and " water boils " into 180° on
his scale. There were thirty-two of these divisions in the space
between the melting-point of ice and that of ice and salt.

tPrt/tH

icf

218. Fahrenheit and Centigrade. — The differ-
ence between a Fahrenheit and a centigrade
thermometer consists only in the marking of the
scale, and both scales are sometimes made on
one thermometer. If the boiling-point in the
100 Fahrenheit scale is 180° above "ice melts" (Fig.
188), and if the melting-point of ice is 32°
above that of ice and salt, — the zero of the
...J.. Fahrenheit scale, — how many degrees from
'"^"'''' " zero to the boiling-point ? (180° + 32° = 2 12°.)
midmii There being 180° from the melting-point
^ (usually called the freezing-point) to the boil-

Fig. 188. ing-point in the Fahrenheit scale, and only 100

^ Centigrade means 100 steps, or di*"

THERMOMETERS, 193

degrees in the centigrade scale, it follows that 180 Fahrenheit
divisions equal 100 centigrade divisions. Divide both these
numbers by 20 ; then 9 Fahrenheit degrees equal 5 centigrade
degrees. If a Fahrenheit thermometer shows a rise of 18 de-
grees, how many degrees does a centigrade thermometer rise ?
A fall of 30 degrees on the centigrade scale would be registered
by how many degrees Fahrenheit ?

The minus sign applied to temperature means below zero.
— 10° C. is read " minus 10 degrees centigrade," or " 10 degrees
below zero centigrade," or "10 degrees below the melting-point
of ice." So, in the same way, — 5° F. means 5 degrees below
the Fahrenheit zero.

Every Fahrenheit temperature is reckoned, not from the
freezing-point, but from a point wrongly thought to be the
greatest cold possible, — 32° lower. Starting from this low
point, all Fahrenheit temperatures are 32° larger than they
would be if the freezing-point were the zero.

219. To change a Fahrenheit Temperature to a Centigrade,
first, subtract 32. The reason for this is evident, if it is
remembered that, while there are 180 divisions from the freez-
ing-point to the boiling-point on the Fahrenheit scale, the
number of degrees marked on the boiling-point is 212, or 32
more than 180°. Suppose the temperature be 68° F. Subtract
32; 68-32 = 36. These are still Fahrenheit degrees, of
which nine equal five centigrade degrees. Multiply by f ;
36 X I = 20° centigrade. Change to centigrade: 212° F.;
0°F.; 150° F.; 50° F.; -10°F.; 32° F.

In changing from centigrade to Fahrenheit temperatures,
exactly the reverse operations should be employed. For
instance, in changing 20° centigrade to Fahrenheit, first, mul-
tiply by I; 20 X I = 36. Add 32 ; 36 + 32 = 68° F.

Change 100° C. to F. ; 0° C. ; 40° C. Change - 40° F. to C. ;
1000°F. to C. Change -40°C. to F.; 12° F. to C; -20C.
to F.

194

PRINCIPLES OF PHYSICS.

^00"-

Cent.

(>?».J

Comparison of Fahrenheit and Centigrade Scales. — As-
sume the space on a thermometer tube between the freezing

and boiling points to be any con-
venient distance, as four or five
inches. Make, on one side of a
line, the Fahrenheit scale, and on
the other side, the centigrade scale
(Fig. 189). On the Fahrenheit side
measure down thirty-two spaces
from " ice melts," and locate the zero
point.

There could be, of course, any
number of arbitrary scales. The Reaumur scale, still used
a little, calls the freezing-point 0°, and the boiling-point 80°.

"^ice melta
Fig. 1 89.

221. How to vary the Boiling-point. — In studying the ther-
mometer, we assumed that the barometer read 76 cm. when the
mark indicating the boiling-point was made ; that is, that the
pressure on the surface of the water was equal to one atmos-
phere. The following experiment shows the effect, on the
boiling-point, of variations of this pressure.

Boil a little water vigorously in a test-tube, and while the
water is still boiling, stop the test-tube with a one-hole rubber
stopper, coated with glycerine and plugged with a glass rod or
a closed glass tube. Place the test-tube, mouth down, in a
dish of water (Fig. 190), so that if there is
any leakage it will be of water, and not of
air. Cool the test-tube by blowing on it,
then by pouring cold water on it. What
effect does this have on the water inside the
tube ? Notice anything collecting on the
inner surface of the test-tube. Pour on cold
water until bubbles cease to form ; then note
the temperature of the water in the test-
tube. Take the test-tube out of the disli

THERMOMETERS. 195

and raise and lower it quickly, to get the hammer-like sound
of the water. What causes this ? What is the bubble made
of that forms under the water when the tube is lowered
quickly? Take the test-tube out of the dish of water, and
remove the glass plug. What enters the tube ? What must
have been the pressure on the water in the tube before the
plug was removed? Try to get the water-hammer effect.
Repeat the experiment from the beginning, but hold the
mouth of the test-tube under water when removing the plug.
When the water is first boiled the steam carries off the air
from the tube. If the stopper fits tightly, or is held under
water, no air can enter. At that stage the pressure of the
steam is the same .as that of the outside air. The effect of
the cold water on the steam pressure may be determined by
considering what happened when the plug was removed under
water. The water-hammer effect comes from there being no air
to cushion the water as it strikes the bottom of the test-tube.

222. Pleasure of Steam. — If, instead of the plug, a glass tube
80 cm. long is insei'ted in the stopper, the variation of
pressure inside the test-tube can be studied. Boil the
water in the test-tube, insert the stopper, and continue
boiling till steam comes from the end of the long tube.
Then invert the test-tube, with the end of the long tube
in a cup of mercury (Fig. 191). With the barometer
reading compare the greatest height to which the mer-
cury rises. Touch the test-tube from time to time
to form an idea of its temperature. If the barom-
eter reads 76 cm., and the mercury rises 60 cm. from
the cup, then the pressure of steam in the test-tube
(76 cm. — 60 cm.) is 16 cm., or a pressure equal to that
of a column of mercury 16 cm. high.

Temperatures corresponding to pressure of steam may
be read by a thennometer inserted in a modified form
of this apparatus, as shown in Fig. 192. E\g. i9i.

li¥

PBLSCIPLES OF PHYSICS.

Szercise 26.

v4i' TSMFSE4TUXXS OQBXBSPOHDDre TO FBBSSUBE OF STEAM.-
Fint Method.

.<y,:\: •%•?>»* A Tif*t-<ube, held in & tetort clamp; stopper for test-tube i)er-
(vxTAicvi wixh ihwe hv^les, one for m gljiss plug, another for a thermometer,
r, Fis:. Ift2, and the third for a long bent tube, JJ, reach-
ing doun to a cup of mercury. Put small pieces of
nnsbrick in the water to make it boil steadily. The
test-tube may be covered with asbestos, except a section
in which to watch the boiling.

Ixnl the wat^r in the test-tube, with the thermom-
eior and the tube to the mercury cup in place.
>Yhon the water has boiled for half a minute insert
the glass plug and remove the lamp. Record, at
intervals of one or two minutes, the reading of
if the thermometer and the height of the mercury
ixUunin.

In this method the tube. H (Fig. 192), is full of
air» since steam is allowed to escape through the
lu>le in which the plug fit^ and is not forced through
// lo drive the air out. Owing to the volume of air
in //. which expands and exerts some pressure, the
boiling oejises Wfore the temperature falls near
zero. When the boiling ceases the experiment is
^Fig. 1 92. finished. Record as follows : —

Tkmpkratirk

Hkuuit of

Mkroiry GAr«K

Height or

Barometer

Pressurb in

Test-Tubk

b -h.

Calculate h — k in each set of readings, and plot on coordinate
paper in any convenient form. For example, let spaces to the right
represent pressm-e, and spaces upward temperature. The plot may

THEBM0METEB8.

197

well be on a larger scale
than shown in Fig. 193.
One point is shown by the
cross.

b
76

b-h
76

Pressure in centimeters of mercury
Fig. 193.

The point is on the 100°
temperature line and on the
76° pressure line. Where
these liues intersect is the
point P, Locate the other
points, and draw a curve
connecting them. Practice reading off boiling-points for different
pressures.

Find the change in pressure from 100° down to 95°, for the nearest
temperature recorded to 95°. Divide the change in pressure thus
obtained by the number of degrees* fall in temperature. For
example ; —

PBESBinuE IN Test-Tube

Tempbratube

760 mm.
634 mm.

100°
95°

The fall in pressure on the boiling water is 760 — 634 mm., i.e.
126 mm. for 5° change in temperature. For 1° change the fall in
pressure is 4^, which equals 25 mm.

In the same manner find the change of pressure per degree for the
change of temperature between 95° and 90°, and so on for every five
degrees down to the lowest temperature recorded.

The pressure on the water in the test-tube, where A = 0, is the pres-
sure as read on the barometer. What is the temperature? What is
the pressure of steam in the test-tube when the thermometer reads 85° ?

Suppose the test-tube is cooled so that its temperature drops
regularly, does the pressure fall regularly ? This is the same as ask-
ing if the mercury in Hy Fig. 192, rises regularly.

198

PRINCIPLES OF PHYSICS.

Exercise 26.

(b) TEMPEBATUEES OOEEESPONDIKO TO PEESSUBE OF STEAM. -
Second Method.

Apparatus ^ ; A glass tube, aboat 60 cm. long and 2 cm. in diameter ; a rubber
stopper fitting this tube, in which is inserted a smaller tube of medium
thick glass, 80 to 90 cm. long and 4 mm. in diameter, closed at one end and
filled with mercury to within 1 cm. of the top ; cup of mercury ; varnished
tin pan; thermometer; clamp; ring-stand; a funnel, attached to a third
glass tube ; asbestos shield for the large glass tube.

Close, with the finger, the open end of the small tube containing

the mercury, and invert several times, to remove air bubbles. Fill
to the top with water, and invert a few times. Cover the
open end with a cork drilled half through, insert through
the rubber stopper of the
larger glass tube, as in Fig.
194, and place in a rack till
needed. Before the labora-
tory exercise is to be done,
again fill the inner tube with
water and invert till the ab-
senceof airbubbles is assured,
thus making a barometer, B,
Fig. 195; then place, still
inverted, in the cup of mer-
cury. Set this in the var-
nished tin pan, D. The

thermometer, T, is hung on the stand,

to which is attached the clamp, C,

holding the outer tube. The shorter

ring-stands of the chemical laboratory

would rest on the table and the appa-
ratus project down below, the cup and

dish resting on a box on the floor.

Place the funnel, F, in the apparatus,

with its glass tube reaching to the

bottom of the outer glass tube, or

D=0

Fig. I 94.

1 ThVee or four pupils can work with one piece of apparatus : one holds a
meter stick at the level of the mercury in the dish * * M«d8 the height

THERMOMETERS.

199

jacket, J. Pour in a little cold water and then, at once, a large amount
of boiling water. At first, the cold water mixes a little with the hot,
and prevents the glass from cracking ; but it is soon displaced by the
hot water, the excess flowing into the pan, D, below. Nearly surround
the jacket with an asbestos shield. Record many series of readings,
taking the readings of the thermometer and mercury columns at the
same instant. Continue to take readings every few minutes, until the
temperature of the water in the jacket has fallen to that of the room.
Ice water may be poured in, or fine ice added, and a few readings
taken near zero.

As the water cools, the steam generated in the barometer tube
condenses and the pressure exerted by the steam decreases. The
mercury in the barometer, B, is pressed down less and less by the
steam vapor, and accordingly rises higher and higher. Record the
temperature of the room and the height of a standard barometer.
The more slowly the water cools, the less likely are the water and the
water vapor in the barometer tube to be warmer than the thermome-
ter. Record in note-book as follows : —

Tkmpebatcrb

Heioht op Mercury
h

Barometer

Pressure of Water Vapor

IN Barometer Tubs

h-h

Plot the temperature and pressure of the water vapor, in colored
pencil or ink, on the same paper used in the First Method for the first
plot. The fall in pressure for one degree may be found as in the
First Method. For pressures greater than one atmosphere, the special
steam boiler used in the engine experiments, p. 257, and a U-shaped
mercury gauge are convenient.

Was there any difference in the readings of the standard barometer
and the barometer, containing a little water, used in this exercise?

of the mercury column ; another reads the thermometer ; and still another
Tecords the observations. The experiment can be repeated several times in
an hour, and each pupil take his turn in making the different observations.

200 PRINCIPLES OF PHYSICS.

What happened to the water, when hot water was poured in the
jacket ? What was the pressure on the water at the top of the mer-
cury column before the hot water was poured in the jacket? After
it was poured in? On what part of a mountain would water boil at
the lowest temperature ? In what part of a mine ?

The boiling-points of ether, alcohol, etc., under different pressures
can be found in the same way as those of water,

223. Vacuum Pans and Digesters. — If water is boiled away
from syrup in an open pan, the sugar that is left will not be
granulated; if water is boiled away from milk the milk will
be cooked. How ai'e granulated sugar and condensed milk
made? How are fruits dried quickly without cooking? A
vacuum pan is a closed kettle, from which the air or steam
is removed by a pump. Milk heated in such a pan to 70° C. is
not cooked, though the water boils away, leaving the milk
condensed.

In various manufacturing processes many substances must
be raised to a temperature higher than 100° C. In some cases
this must be done in a closed kettle which is called a digestor.
The boiling point of the water or other liquid in it is raised
above 100° C. as the liquid boils and its vapor exerts pressure.
The utmost limit to which the pressure of steam in a boiler
can be raised is reached when the boiling-point rises to the
temperature at which iron begins to be red, and therefore
weaker.

224. Boiling. — From the reading of the barometer tube con-
taining a little water, in the preceding section, it is seen that
the vapor of a liquid always exerts some pressure, — more at
greater temperatures. When the vapor pressure of a liquid is
greater than the pressure upon its surface, then the liquid under
the surface begins to turn into vapor, bubbles of vapor form
and rise, and the liquid boils. In the process of boiling, bubbles
form in any part of the liquid, usually near the surface that is
heated by a lamp or a fire.

THERMOMETERS. 201

226. Evaporation. — Water that is not boiling disappears in
time. Place under the receiver of an air-pump a dish of water
that has just ceased boiling, and exhaust the air, but not rapidly
enough to make the water boil. A dense fog fills the receiver,
and condenses on the sides. This is the process of evaporation,
which takes place only at the surface of a liquid, but at all
temperatures, more rapidly at higher than at lower tempera-
tures. Even snow and ice evaporate and waste away in cold
weather. Evaporation is more rapid under low pressure.

226. Corrections for Pressure in Testing a Thermometer. — In

Exercise 25 (page 191), the thermometer was tested under a
pressure of one atmosphere, or 76 cm. of mercury. At or about
this pressure, a variation of 2.7 cm. in the barometer reading
causes a change of one degree in the boiling-point. Therefore,
if the barometer reading was not exactly 76 cm. when the ther-
mometer was tested, corrections must be made for the varia-
tion. If the thermometer reads 100.2° in steam, when the
barometer reading is 77.2 cm., the thermometer would have
read lower with the barometer at 76 cm. As 2.7 cm. change
in pressure causes 1° change in the boiling-point, and in this
case the change is 77.2 cm. — 76 cm. = 1.2 cm., the thermome-

1.2
ter would read 27 of a degree lower, or .4° lower, with the

barometer at 76 cm. The true 100° point is .4° lower than
100.2°, or 100.2° - ,4°, which is 99.8°. At or near the boiling-
point the thermometer reads .2° too low. To correct readings
in this part of the scale, .2° should be added. The bore of the
tube varies in size in different parts of the thermometer, and
for very accurate work the true 50°, 25°, and 75° points need
to be known.

Following out the rule that 2.7 cm. change in the barometer
causes a change of 1° in the boiling-point, a fall of 100° would
seem to indicate a fall in the barometer of only 27 cm. But
the barometer must fall 76 cm. to indicate no air pressure.

202

PRINCIPLES OF PHYSICS.

Therefore the rule holds only at or near 100° C. Above
100°, a change of 1° in the boiling-point is caused by over
2.7 cm. change in pressure.

Study the readings and the curve obtained in Fig. 193,
page 197, and notice that farther down on the thermometer
scale 1° change is caused by much less than 2.7 cm. fall in
pressure.

Suppose the lowest temperature reached by the thermometer
in melting ice is — .3° ; then the true zero point is at — .3°.
The thermometer in that part of the scale reads too low by
.3, and all readings near the zero mark must be increased by
adding .3 to the reading.

Problems.

1. At half an atmosphere (barometer 38 cm.)^ what is the boiling-
point? (Consult curve.)

2. If a thermometer in steam reads 99° (barometer 76 cm.), what
is the true 100° point and correction?

3. If the reading in melting ice is 2°, what is the correction ?

4. If the reading in melting ice is — .1°, what must be done to a
low reading of the thermometer ?

5. Find the true 100° point, the correction, and the correction to
be used for low temperatures in the following thermometers : —

Reading in Steam

Centimeter Reading
OF Barometer

Reading in
Melting Ice

101.3°

78.4

.3°

100.9°

75.2

-.1°

98.2°

~.4o

99.8°

76.8

.0^

100.2°

.2°

100.1°

75.8

-.2^

99.4°

74.4

.1°

THERMOMETERS. 203

6. Unless exact points in other parts of the scale are obtained,
the corrections to be applied in the middle of the scale may be taken
as the average of the 100° and the zero corrections. If thermometer
a reads 98**, what is the temperature V If a reads - 5° ? If a reads
45°? If c reads 90°? If 6 reads 104° ?

Practical Working of a Thermometer. — When a ther-
mometer is cooling from a high temperature, the glass of
the bulb does not contract at once and the zero-point changes
slightly. Re^ietermine the zero-point. The column of mer-
cury in the stem should be heated to the same temperature as
the bulb before a reading is taken. Find what difference
there is in the reading when the bulb only is in steam and
when the whole column of mercury is in steam. The stem of
a thermometer is usually sealed with no air above the mercury.
Invert an all-glass thermometer, tap the top gently on a soft
board, and watch the thread of mercury run to the top. Which
is the more sensitive — that is, which will show the greatest
difference in length of the thread of mercury for a given change
in temperature — a thermometer with a large bulb or one with
a small bulb ? One with a small bore or one with a large bore ?

228. Melting-points. — The melting-point of ice, made by
freezing pure water, is fairly constant, varying only a few
thousandths of a degree. Solid ice, for instance, melts at a
little lower temperature than slush formed by carefully stir-
ring water that is slowly freezing. The melting-points of
many crystalline substances other than ice are also fairly
constant when theusubstances are pure. Of these, crystallized
sodium sulphate melts at 32.5"* C. ; sodium thiosulphate (the
'hypo' of the. photographer), at 48.1° C. ; and barium hydrox-
ide at 78® C. Many other points of the scale between 0° and
100® may be found and marked on a thermometer stem by
using other salts.

The following exercise shows a simple method of calibrating
a thermometer from two other points : —

204 PRINCIPLES OF PHYSICS.

Exercise 2*7 A

TESTING A THEBMOMETEB FOB POINTS BETWEEN C* AND 100° C.

Apparatus: Test-tubes, 1 inch by 6 inches; wide-mouthed bottles; cotton
wool; pans of hot water; thermometer; recrystallized sodium sulphate
and sodium thiosulphate. These salts are prepared from the commercial
salts by melting, in a graniteware pan, five or more pounds of the salt to
be purified with one-third its volume of water. After a few hours' cooling,
remove the crystals. Put these in another pan, melt as before, and recrys-
tallize ; then put in glass jars.

Expose a portion of the crystallized sodium sulphate to the air and
dry it. Mix 10 parts of the crystallized salt, powdered as fine as
granulated sugar, with 1 part of the dry salt. Fill a test-tube half
full of the mixture. Heat over a Bunsen burner till the mixture
begins to melt and appear like slush. Add about one-tenth as much
of the un melted mixture. Place the test-tube in a bottle lined with
cotton wool. Set the bottle in a pan of water at about 50° C. Wash
carefully the bulb of a thermometer, wipe it dry, insert it in the test-
tube, and stir the mixture with it. Record the reading.

A large number of thermometers may be tested in turn in the same
mixture. When the mixture is nearly melted, place the bottle in a
bath of water a few degrees below 32.5° C. At this temperature the
sodium sulphate recrystallizes. (The word freezes is used exclusively
for the crystallizing of water as it turns into ice or snow.) More
thermometers may be tested as the substance crystallizes. The tem-
perature remains constant during the melting and the solidifying, if
some of both the dry and crystallized form of sodium sulphate are
present.

229. The 32.5° C. Point. — The melting-point of crystallized
sodium sulphate is always the same (that is, constant), pro-
vided the salt is pure. Just as the zero point of a thermome-
ter is determined with great accuracy by noting its reading in
melting ice, so the 32.5° C. point is determined by the reading
of the thermometer in melting sodium sulphate.

In a similar way, find the true 48.1° point, in a bath of melt-

1 This Exercise was outlined hy Mr. J. B. Churchill, who diacovered that
many chemical compounds have definite melting-points.

THERMOMETERS.

206

ing sodium thiosulphate crystals. Be careful to wash each
thermometer before inserting it in a testing-bath, since very
small impurities alter the melting-point. Barium hydroxide
crystals have a melting-point of 78** C.

230. Effect of Pressure on the Melting-point of Ice. — A con-
siderable pressure can be applied to ice without apparently
changing the melting-point. Snow that is at the freezing-point
is made into a snowball by pounding, and by continued pi'cs-
sure becomes a block of ice.

Apply a heavy pressure to ice by a fine wire, to which a
weight is hung. Support the ice on two
ring-stands or boxes (Fig. 196). Over the
ice pass a loop of fine wire, to which a
weight equal to the breaking strength of
the wire, is hung. The wire will not break,
because the weight will be distributed
between the two sides of the loop. When
the wire has passed completely through,
notice that, while the ice has been melting a little all thee tinier,
the two pieces have frozen together solidly. Und(»r the j)r(^s-
sure of the wire the ice melted ; in doing so, it absorlxid heat
and lowered to a fraction of a degree below zero the temp(;raiure
of the water formed. This water, escaping from under the
wire, was no longer pressed upon, and froze at once.

Enormous pressures reduce the melting-point of ice very
little, though enough to allow glaciers to flow and tin? snow to
settle down and become ice under the pressure of more and
more snow which falls on top. The ice-cap on Greenland and
other Arctic lands is formed in this way from accumulations
of snow. The ice slowly flows to the water's edge and breaks
off as huge icebergs. As they are formed of snow, what must
be the melting-point of icebergs ?

231. Freezing-points. — The fresh water of rivers and lakes
in winter freezes long before the salt water of the ocean. Salt

Fig. 196.

206 PRINCIPLES OF PHYSICS.

melts the ice from a sidewalk, unless the weather is extremely
cold. Pure water melts and freezes at 0® C. Almost all sub-
stances in a pure state have a definite melting-point. Some
substances, such as cast iron and platinum, have high melt-
ing-points ; others, such as mercury, alcohol, and air, have low
melting-points.

Bzercise 28.

EFFECT OF DISSOLVED SUBSTANCES ON THE FBEEZINO-POINT OF

WATEB.

Apparatus: A beaker, or tin can; one-inch test-tubes; thermometer; salt;
snow or fine ice ; five per cent, seven per cent, and ten per cent solutions
of common salt. Other salts may be tried.^

Fill the can half full of a mixture of ice and salt. Test the zero
point of the thermometer in ice. Find the lowest temperature of the
ice and salt mixture. If necessary, make an opening in the ice and salt
mixture and put in a test-tube containing 2 inches of a solution of
salt. Insert the thermometer, and stir. Record the temperature
every minute; try to read to tenths of a degree. Remember that
about once in ten readings the mercury column is likely to be on a
whole number of degrees.

Plot the results, as in Fig. 197. Vertical spaces represent degrees ;
horizontal spaces, minutes. The curve
may be somewhat like A BCD. AB
shows the cooling down to the freezing-
point. What is happening during the
time from 5 to C? Why does the tem-
perature again begin to fall at C?
What effect does the amount of the dis-
solved substance have on the freezing-
Fig. 197. point?

Dew-point. — In the warm, muggy days of summer,
drops of water appear on the surface of a cold dish. This
water does not come through the sides of the dish ; what is its
source ?

1 Let each pupil make one set of observations of either pure water or one
of the salt solutions. Compare the results.

THERMOMETERS.

207

Thoroughly moisten a piece of muslin and suspend it from
a board. Let the muslin reach well down into a test-tube of
water, held in a wooden
stand inside a glass jar
{A, Fig. 198). The board,
W, which should be well
greased on its lower side,
prevents any change of air
in the jar. Set up a similar
apparatus, JB, omitting the jar. Cover another jar, C, in which
a dish D of calcium chloride or strong sulphuric acid has
been placed. The cover, W, is made air-tight with tallow. After
a time, the level of the water in the tube in A will gradually fall
a little. Most of the water will disappear from B, because the
air around it is continually changing and absorbing water.

233. Air saturated with Moisture. — Fill a bright calorimeter
or tin can half full of ice water, or ice and salt, making it suffi-
ciently cold so that moisture is deposited on it from the air in
the room. Wipe off the moisture and hold the calorimeter in
C, Fig. 198. No moisture is deposited. The air in C is dry.
Then hold the calorimeter in A, first removing the muslin.
Moisture will be deposited on the bright surface. Remove the
calorimeter and allow it to warm so that moisture from the air
in the room will not be deposited, then replace in A, Moisture
will condense on the cold surface. The air in A is saturated
with moisture, while the air of the room is only partly saturated.

Air or an empty space can hold in an invisible form an
amount of water depending on the temperature. The air is
very seldom saturated with all the moisture it can hold. Dur-
ing a long rain or fog, it becomes saturated ; in such an atmos-
phere, water does not evaporate from wet clothing. The air in
A is saturated, and, on being cooled, is unable to hold all the
moisture. The air in C is dry, and would deposit no moisture,
no matter to how low a temperature it might be cooled.

208 PRINCIPLES OF PHYSICS.

Exercise 29.
THE TEMPEBATUBE AT WHICH MOISTUBE IS DEPOSITED.

Apparatus : A bright calorimeter ; a thermometer ; a bent strip of zinc.

Fill the calorimeter, C, Fig. 199, half full of water. Suspend the
thermometer, T, in it. Add ice water, or ice and salt,
and stir continually by moving the bent strip of zinc, S,
up and down in the water. Be careful not to breathe on
C. Watch for the first sign of moisture deposited. An
easy way to tell when moisture appears is to stand toward
the light, and place a page of print facing C. When the
reflection of the letters becomes blurred, the moisture has

Fig. 1 99.

begun to gather. Read the thermometer. At this point,
stop adding ice, stir until the moisture disappears, and read the ther-
mometer again. These two readings should not be more than a
degree apart. The dew-point at the time of the experiment is the
average of these two readings. Record the temperature of the room
and of the outside air, and the condition of the weather. Copy in
note-book the report of the nearest Weather Bureau station for the
day on which the experiment is performed.

On repeating the experiment, the temperature of the water in C
should be reduced at once to within two degrees of the dew-point
just obtained, and then the liquid cooled gradually till the moisture
appears. It is instructive to take the dew-point in various parts of
the building, in the cellar, and out of doors. These observations
should be made about the same time, since the dew-point often varies
greatly in a short time.

234. The Capacity of the Air for holding Moisture increases
rapidly with the temperature. At the freezing-point of water,
a cubic foot of air, when saturated, holds about .1 g. of water,
that is, about one drop. For each 10° rise in temperature, the
amount of water in a saturated space nearly doubles. At
40° C, one cubic foot of air can hold about 1.3 g., that is,
about 1.3 cc, of water. A cubic foot of saturated air, if cooled
to 0° C, deposits 1.3 - .1, or 1.2 g. of wi '^mg, the

capacity of the air to hold moisture %ially

THERMOMETERS. 209

a point is reached where the air can hold only what moisture
it has. It is then at the dew-point. Any further lowering of
temperature causes some of the moisture to be deposited as
rain, fog, or dew ; or if the temperature is below 0® C, as snow
or hail. On the other hand, saturated air becomes dry by
warming ; not that it has any less moisture, but its capacity
for holding moisture is increased and it absorbs, or evaporates,
moisture from any source, — from vegetation, the surface of
water, or damp cloth. During the process of evaporation, an im-
mense amount of heat is absorbed. (See section 257, page 2.*K).)

235. Wet-bulb and Dry-bulb Thermometers. — Suspend two
thermometers, A and B, Fig. 200, some distance apart. Tie to
the bulb of A some muslin in the form of a wick, _

long enough to reach into a dish of water, W.
Before moistening the muslin, notice that both
thermometers read alike. Fill the dish, W, and
moisten the muslin with water that has been
standing long enough to have the same tempera-
ture as the room. . Record, each minute, the tem-
perature of ^ and -B, as long as there is any change.
Then fan the thermometers, and continue the ob-
servations till there is no change in either ther-
mometer. In the meantime, the dew-point should l>e taken by
the method of Exercise 29 (page 208).

The wet bulb is cooled by the evaporation of water from the
muslin, and its temperature falls to some point between that
of the air and the dew-point. The data in the table on page
539 of the Appendix are the results of experiments. The first
column contains the temperatures of the dry bulb; the second
column, a number corresponding to each dry-bulb temperature.
This number is used in multiplying the difference between the
wet-bulb and dry-bulb reading, to give the number of degrees
the dew-point is below the temperature of the air, as read
by the dry bulb.

210

PRINCIPLES OF PHYSICS.

When the dew-point is in the neighborhood of 0**C., the
results of this method do not agree exactly with those of
Exercise 29.

Problems.

1. If the dry bulb reads 20° and the wet bulb 15°, what is the dew-
point?

20 — 15 = 6° ; the wet bulb is 6° lower than the temperature of the air.
The dew-point is still lower. Look in Appendix, page 539, for 20° ; next
to it is the number 1.8. 6 x 1.8 = 9 ; therefore the dew-point is 9° below
20° C. ; that is, 20 - 9 = 11°, the dew-point.

2. Find the dew-point, when the thermometers read as follows : —

Rradino

OF Dry Bulb

Reading of Wbt Bulb

Sensible Temperature. — The reading of the wet bulb is
practically the temperature that the air feels to us ; that is, it
is the senidble temperature. Dry air feels cool, because of the
cooling effect of evaporation of the perspiration from the skin.
Set TT, Fig. 200, page 209, in a glass jar that reaches above
the bulb. Cover the top of the jar tightly, and half an hour
later read A and B. The evaporation ceases as soon as the air
in the jar becomes saturated. The bulb is no longer cooled,
and registers the same as B does ; that is, it registers the tem-
perature of the surrounding air.

237. Formation of Rain. — Air, by expansion, does work and
becomes cooled (section 266, page 24^^^ a mass of

THERMOMETERS. 211

air rises ; it expands, and does work in pushing away the air
around, and cools 1**C. for every 100 meters, or 300 feet, it
rises. This is one reason why the air is cool afhigh eleva-
tions. Should the cooling bring the temperature below the
dew-point, a part of the moisture is condensed as rain or snow,
and falls.

Instead of trying to take a mass of gas up to a great height,
the same result can be attained by removing the pressure by
an air-pump. Leave a tumbler of warm water under the
receiver of an air-pump for a few minutes; the air soon
becomes saturated. Remove the tumbler and see that the
receiver is dry on the inside. Exhaust the air rapidly ; the air
expands, is cooled, and a dense fog appears. Open the inlet ;
the air in the receiver is compressed and warmed, and the fog
disappears.

Problems.

1. Why is the dew-point on the ocean always nearly as high as the
temperature of the air?

2. On a rainy day, why do wet clothes dry near a stove ?

3. Why should a thermometer be protected from rain if reliable
indications of temperature are desired ?

4. Why does moisture form on a mirror when the mirror is
breathed on? What would happen if the mirror were as warm as
the breath?

5. Does a high dew-point indicate a comfortable or an uncom-
fortable day?

CHAPTER XV.

EVAPORATION AND BOILING.

238. Dissolved Air in Water. — Set aside, in a warm place,
two tumblers, one of freshly drawn water, and the other filled
with water that has been boiled and cooled. From time to
time look for the formation of bubbles. In which tumbler
are there bubbles of air clinging to the sides of the glass?
Which has the pleasanter taste, boiled or unboiled water?
Heat slowly a test-tube or flask of freshly drawn water; do
not let it reach the boiling-point. Notice the small bubbles
that form all through the liquid and on the sides of the test-
tube. These bubbles are composed of the air that was dis-
solved in the water. They rise slowly, because they are small,
and do not change much in size as they rise.

289. Evaporation. — As the temperature of the water in the
test-tube approaches the boiling-point, hold a bright metal
surface (C, Fig. 201) for an instant near the
mouth of the test-tube. The metal surface
may be a nickelled calorimeter in which
there is cold water; but it should not be
cold enough to condense moisture from the
air of the room. Instead of the metal sur-
face, a plate of glass may be used. The
moisture deposited comes from the surf(Ke
of the liquid in the test-tube, and is noticed
even at low temperatures, provided the metal
or glass, C, is much colder than the water in
the test-tube.

This process of a liquid turning sP udled

212

Fig. 201.

EVAPOEATION AND BOILING. 213

evaporation. It takes place at all temperatures, but only at
the surface of the liquid ; even in cold weather, snow wastes
away by evaporation. It takes place more rapidly at high
than at low temperatures. The effect of pressure is shown by
placing a flask of warm water under the receiver of an air-
pump and exhausting the air, but not carrying the exhaustion
far enough to make the water boil. Evaporation takes place
most rapidly at low pressures.

240. Boiling. — To study the phenomena of boiling, it is
better to begin again with cold water. Review the phenom-
ena noted in studying the boiling-point. Often, before the
air bubbles have entirely escaped, one or more large bubbles
form over the surface of the glass heated by the flame and at
once collapse. There is a clicking, or singing, sound. As the
water becomes warmer, these large bubbles, which are of
steam, rise into the cold liquid above, and there condense,
warming the liquid. Watch the level of the water in the
test-tube as the steam bubbles are formed and condense. As
a bubble of steam is formed it lifts the water. The bubble of
steam condenses; the water falls, and, having nothing to
cushion it, strikes a sharp blow, which gives rise to the click-
ing, or singing, sound, and is, in fact, a water-hammer. The
process going on is a steam heating plant on a small scale.
Steam generated at the heated surfojce rises and is condensed
by the colder liquid above. This upper layer of liquid soon
becomes warmed to the boiling-point, and the bubbles of steam,
not being condensed, escape into the air. The liquid is then
said to boil.

241. Pressure of Steam Bubbles. — Watching the bubbles of
steam at the stage in the heating when they immediately con-
dense, what has a little bubble to do as it turns into a large
bubble of steam ? It has to make room for itself. It, then, or
its vapor, must exert enough pressure to lift the column of

214

PRINCIPLES OF PHYSICS.

water above it and the air above that. In a shallow vessel
the pressure caused by the depth of the water is comparatively
small ; but the air pressure on the surface of the water at the
sea level is, on the average, equal to that caused by a column
of mercury 76 cm. high, or 15 pounds to the square inch, or
1000 g. per square centimeter. If the atmospheric pressure is
less, then the vapor pressure of the little drop of water that is
about to turn into steam does not need to be so great, and
therefore the water does not need to be heated to so high a
temperature to cause it to have sufficient pressure to lift the
water and the atmosphere above it and to expand into steam
bubbles. At 100° C, — the boiling-point of water when the
barometer is 76 cm., — 1 cc. of water forms about 1700 cc. of
steam.

Consult the results of the experiment on relation of pressure
to the boiling-point (Exercise 26, page 198). Select from them
one set of readings at a high temperature and another at a low
temperature, and arrange as follows : —

Barombtrb

PRB88CRB

Barometer ~/r

76
76

32.7
74.3

43.3
1.7

85°
20<»

In the first column is given the height of the barometer ; in
the second column, the height of a barometer in which a little
water floats on the mercury. The reason the mercury column
in this second tube does not stand as high as the other is that
the water vapor on top exerts some pressure. The pressure of
this vapor increases with the temperature. At 100** C. (a tem-
perature that we could give by supplying the jacket with
steam or hot brine), the vapor pressure would drive all the
mercury out of the tube and balance the atmospheric pressure
without the help of a column of mercury. The third column

EVAPORATION AND BOILING.

215

gives the amount of the depression caused by the pressure of
the water vapor. This column shows the pressures exerted
by water vapor at temperatures of 85** and 20** C. Other
liquids give different results.

Boiling takes place when the vapor pressure of a liquid is
greater than the pressure on the liquid.

In Exercise 26, page 196, it was suggested that fire-brick
(many other substances would do as well) be put in the water
to insure boiling. The temperature of water, especially if it
has no air dissolved in it, rises a little above the boiling-point,
and then the water boils violently and throws the liquid
The liquid is said to bump.

Absorption of Heat in Evaporation and Solution. — Heat
is absorbed when a liquid evaporates or a substance dissolves.
The following is one way of measuring differences in
temperature : —

Through the rubber stoppers of two test-tubes insert a small-
bore glass tube, bent in the shape indicated in Fig. 202, and
carrying an index of colored water at /. The sensitiveness is
increased by using large test-
tubes with a very small-bore
glass tube. Breathe on one test-
tube; hold the hand on one;
apply water a little warmer than
the room. What happens at
first. Blow on one test-tube;
does the movement of the index indicate that evaporation
absorbs heat?

Place the apparatus in two dishes of water, as in Fig. 202.
When the index has ceased to move, stir salt or ammonium
nitrate in A, Does the solution absorb heat ? Empty A and
By and refill with boiling water. Place burners under each,
and as soon as the index is at rest, add salt to A. When boil-
ing begins again, which is the warmer, ^ or -B ?

Fig. 202.

216

PRiyCIPLES OF PHYSICS.

Exercise 30.

BOILIHG-POIHTS 0? WATER SOLUTIOHS AHD 0? OTHER LXQUISS.

Apparatus: Test-tabes 1 inch by 8 inches; thermometers reading to 120° C;
riDg-stands and clamps ; the test-tabes may be fitted with two4iole robber
stoppers.

Fill the test-tabes one-third full, putting common grain alcohol
(ethvl alcohol) into one, wood spirit (methyl alcohol) into a second,
a strong solution of calcium chloride into a third, and

yn 1 pure water into several others. Suspend the test-

.||. tubes by ring-stand clamps, as in Fig. 203. On the
^\X II base of each ring-stand put a number and the name of
S the substance in the test-tube. Put a thermometer in
^ each test-tube, and boil the liquid. Record the tem-
perature of each liquid when it boils. Add a little
alcohol to one of the test-tubes of pure water; sugar
to another ; and salt to another. When the solutions
boil, again read the thermometers in these tubes. Add
more alcohol, sugar, and salt, and find the boiling-points again. A
large amount of sugar, one-third or one-half the bulk of water, should
be added to the tube of water in which the boiling-point of the sugar
solution is to be determined.

Fig 203.

243. Distillation. — In the experiments on boiling and evap-
oration it may have been noticed that while the water was
sometimes cloudy, the condensed steam was clear.

Into a boiler or kettle put water and either salt or sugar.
Boil, and allow the steam to condense in a can or tumbler. A,
Fig. 204, and to drip into B. A
may be held with a cloth. Is the
condensed water salt or sweet ?

With the exception of liquids
boiling below 100° C, any mixture
of water on boiling gives off steam
that condenses to pure water.
Rain, being the condensation of
water vapor evaporated from plants,
bodies of water, and the soil, is also perfectly pure, excepting

Fig. 204.

EVAPORATION AND BOILING.

217

a few minute impurities it may wash out of the atmosphere in
falling to the ground.

Beplace the metal rod of the linear expansion apparatus
(pi^ 185) by a long glass or metal tube, as in Fig. 205. Pass
in cold water at B, and run a rubber tube from ^ to a sink or
jar. The jacket of the
condenser is supported
in an inclined position
by a clamp on a ring-
stand. This forms a
simple model of a still
and condeuser.

By burning one pound ^''" ^°^'

of coal, ten pounds of water, more or less, are turned into
steam. The water into which the steam condenses is pure,
and is fully as wholesome as spring or well water, though it
does not taste as good. On long sea voyages, either a sufficient
supply of fresh water must be carried or the salt water must
be distilled. Every bit of space on a vessel is valuable. Is it
more economical of space to carry fresh water or to carry coal
to be used in a still ?

244. Difference between Evaporation and Boiling. — Define
boiling. How does it differ from evaporation ? Any liquid,
when boiling, turns into vapor by bubbles of steam rising
from the hot surface of the boiler and by evaporation from
the surface of the liquid. In a given time more water
can be turned into steam by boiling than by evaporation.
Engineers say that a pound of coal evaporates ten pounds
of water, when they really mean boils and evaporates. The
word evaporate has usually this meaning in mechanics.

SMS. Distillation of Alcohol, etc. — In the dipper used for
heating the metal in the exercise on specific heat (page 221),
put cider, or a mixture of alcohol and water, or a dilute solu-

218

PRINCIPLES OF PHYSICS.

tion of molasses and water that has been allowed to ferment
some, but not enough to turn the alcohol into vinegar. With
a one-hole rubber stopper and flexible tubing connect the dipper

with the condenser. Heat the
water in the boiler nearly to
boiling. Then, and not till
then, put the apparatus in place,
as in Fig. 206. Nearly close
the opening S, and turn the gas
down so low that the water in
the boiler does not quite boil.
See if the liquid dripping from
^^«- ^°*' the glass tube in the condenser

will burn. Alcohol, having a boiling-point of 78.5** C, boils
before the water with which it is mixed. However, it carries
with it a little water vapor, for water vaporizes rapidly at
80° C. without boiling, and a mixture of alcohol and water is
condensed in the glass tube. Redistilling this product would
increase the proportion of alcohol in the distillate.

Crude petroleum is composed of many substances of different
boiling-points. As the crude oil is slowly heated one sub-
stance after another comes off in turn, each at a higher boiling-
point, and is condensed in a tube, which for convenience is
usually made into a coil and called a worm.

Mercury mixes with lead, zinc, tin, and other metals. It is
best purified by distillation.

246. A Heat Unit, or Calorie. — The amount of heat required
to warm 1 g. of water V C. is called a heat unit or calorie.
How many heat units are required to warm 1 g. of water
6** C. ? (6 heat units.) How much heat is absorbed by 5 g.
of water in rising 6® in temperature ? (5 x 6 = 30 heat units.)
How much heat is given out by 40 g. of water in cooling
25** C. ? How many heat units are needed to raise the tem-
perature of 1 liter of water from 10** to 50** C. ?

EVAPORATION AND BOILING. 219

947. Mixiiigr Waters of Different Temperatures. — Find the
exact size of a small tin box, to be used as a measure, holding
100 to 120 g. Weigh the box empty ; then fill with water and
weigh. The difference in the two weights is the number of
cubic centimeters the box holds. Find the temperature of a
dish of hot water, and that of a dish of cold water. Fill the
measure with the hot water, and empty into a calorimeter,
which may be a large tin can or a glass beaker. Pour in a
measure of the cold water. Stir with a thermometer, and
record the temperature. How does the temperature of the
mixture compare with that of the hot water? with that of
the cold water ? How many degrees did the temperature of the
cold water rise? How many degrees did the temperature of
the hot water fall ? Find the number of heat units given out
by the hot water in cooling, by multiplying the weight by the
fall in temperature. Find the heat units absorbed by the cold
water.

Bepeat the experiment, using two measures of hot water to
one of cold, or two measures of cold water to one of hot. In
which case would the temperature be the higher ?

Assuming that there is no loss or gain of heat from the
outside, the amount of heat lost by the hot water must equal
the heat gained by the cold water. Suppose 50 g. of water at
80® C. and 200 g. of water at 5° C. were stirred together, what
was the temperature of the mixture ? Call this t If the hot
water cooled from 80° to t, or (80 — t) degrees, the heat given
out was the weight, 50, times (80— «). If the cold water warmed
up from 6^ to «, or (* — 5), the heat absorbed was 200 (t — 5).
The hot water must have lost as much heat as the cold water
absorbed; therefore

200 (< - 5) = 50 (80 - t)
200 1 - 1000 = 4000 - 50 1
250 1 = 5000
t = 20^

so PRINCIPLES OF PHYSICS.

tssume that tr, = weight of hot water,

ti = temperature of hot water,

tc = weight of cold water,

fo = temperature of cold water.

Then, using lett-ers, the rule, Weight of cold tjoater times rise in
WihijH'iwUtre = \0ei4j1kt of hot water times fall in temperature,

IT X (f - fo) = «-, («, — e).

Using this formula, or the method illustrated above, solve
the following

Problema.

1. If 25 g, of wat-er at O^C. and 40 g. at 24° C. are stirred together,
Mhttt is the t-emperature? Ans. 14.8°.

Sulx»titutiug, we have

25(f-0) = 40(24-0
25« = 960-40^
a. How much water at 100° C. must be mixed with 200 g. at 12° C.
to make the mixture SS'^C? Ans. 83+ g.

Here f = dS\ au<t if,, the weight of the hot water, is the unknown
iiuantity.

IT, {100 - SS) = 200 (S8 - 12)

62 ic = 5400.

a. To what t<»mperature are 150 g. of hot tea at 95° C. cooled, by
thb aiUUtiou of HO g. of milk at 20° C? Assume that 1 g. of these
hquiiU alv^iiul^a one heat unit in warming 1°C.

4. Kuowiug the temperature of the mixture in Problem 1, assume
that au>' one ol lite other values is unknown, and solve the problem.

Make other problems from those given above.

248. The Amount of Heat absorbed by Different Substances

varies considerably. It is well known that a bottle of hot
water will do more heating than the same weight of brick of
the same temperature. The following exercise shows how
various substances compare with water in the amount of heat
absorbed b}' 1 g, when warmed V,

EVAPORATION AND BOILING. 221

Exercise 81.

(a) SPECIFIC HEAT OF A SOLID. -First Method.

Apparatus: A calorimeter; a dish for hot water; thermometers; a strip
of copper, lead, zinc, alamioam, or iron (sheet tio), 2 ioches wide aod loog
enough to weigh 120 to 150 g., rolled in a coil, with a wire looped through a
hole in the coil for conyenieQce in handling. A tin can may be used instead
of the calorimeter, and may be cut down by a pair of shears till the water
it holds is of the same weight as the coil of metal used.

Heat the coil of metal by standing it in a dish of hot water, in
which there is a thermometer. Into the calorimeter pour a weight of
cold water equal to the weight of the coil, and take the temperature.
Take the temperature of the hot water, remove the coil of metal, and
at once place it in the calorimeter. Add the cold water, and stir.
After the thermometer in the calorimeter ceases to rise, record the
temperature. Record somewhat as follows: —

Temperature of cold water = 10°.
Weight of cold water = 150 g.

Temperature of coil = 100°.

Temperature of mixture = 18°.
Weight of coil = 150 g.

The number of heat units absorbed by the water = weight times
(^ ~ ^a» **^* temperature of mixture — temperature of cold water) ; 150
(18 — 10) = 1200 heat units. This must equal the number of heat
units given out by the metal. Multiply the weight of the coil by the
number of degrees fall in temperature; 150 (100 — 18) = 12300.
This is evidently larger than the number of heat units given out by
the coil and absorbed by the water. Divide the number of heat units
really given out by the number of heat units the metal, on account of
its weight and fall in temperature, might be expected to give out.

249. Specific Heat. — We have divided the amount of heat
the water absorbs (the same amount that is given out by the
metal in cooling) by the number of grams of metal times the
fall in temperature in centigrade degrees. The quotient is
the amount of heat given out by 1 g. of the substance in cool-
ing I**. This is called the specific heat, which is the number of

222 PRINCIPLES OF PHYSICS.

heat units required to warm 1 g. of a substance V C. Only
approximate values for the specific heat may be obtained by
the method described above. The following exercise gives
more accurate results.

Bxeroise 81.

(2>) 8PE0IFI0 HEAT OF A SOLID. - Second Method.

Apparatus: Steam can; dipper; thermometer; calorimeter; rubber tubing ;
copper or aluminum wire clippings.

Half fill the steam can with water, and light a burner under it.
Stop up the side tube by slipping over it a bit of rubber tubing in
which is inserted a pencil end. Take approximately 500 g. of lead, or
300 g. of copper or aluminum wire clippings. Measure the amount
in a small tin can, which may be cut down by shears to the desired
size. Pour the metal into the dipper, which fits into the steam can,
and cover the mouth of the dipper with a piece of wood or thick
pasteboard, through a hole in which the thermometer has been
inserted. Zinc, iron, or marble will do as well as any of the metals
mentioned above. The exact amount of the substance used is not
important, but enough must be taken to cover at least the bulb of the
thermometer in the dipi>er. Sufticient cold water should be put in
the calorimeter so that the final temperature of the mixture is about
that of the room.

Stir the metal in the dipper from time to time. Weigh the empty
calorimeter. Turn down the burner till steam escai^s in a small
quantity around the rim of the dipix^r. When the temperature has
ceased to rise, readiug 100° C. or a little less (often two or three
degrees less), record the reading. Remove the thermometer and
allow it to cool to 40° or 50° C. Measure about 100 g. of water at
10° C. or less, and \x>\it it into the calorimeter. In warm weather the
water may he taken from a large pan or bucket containing ice. Wipe
the outside of the calorimeter ; weigh the calorimeter and water, and
insert the thermometer. Read to a tenth of a deg^'ee. The calorimeter
should not be touched with the hand after the temperature is taken.
Pour in the heated metal from the dipper. Stir the mixture with the
thermometer, and record the temperature when it l>ecomes fixed.
Weigh the calorimeter and mixture. Compute the specific heat of
the metal.

EVAPORATION AND BOILING. 223

As a model showing how computations should be made, compute
the specific heat of sulphur from the following data : —

Calorimeter, 50 g.

Specific heat of calorimeter, .1.

Calorimeter and water, 245 g.

Calorimeter, water, and sulphur, 465 g.

t^ (temperature of water in calorimeter before adding sulphur), 8^ C.

t (temperature of sulphur), 98^

fi (temperature of mixture), 23°.

Water used (245 - 50), 195 g.

The calorimeter is always heated where the liquid touches it, and
is nearly of the same temperature as the liquid. But, as a calorimeter
of brass or iron (tinned) hsis a specific heat of .1, — that is, in warm-
ing absorbs one-tenth as much heat as the same weight of water would
when warmed the same number of degrees, — a calorimeter weighing
50 g. absorbs as much heat as 50 x A, or 5 g. of water. The problem
is the same as if a calorimeter of no weight and 200 g. of water had
been used. We write : —

Water (195 g. + water equivalent of calorimeter, 5 g.) = 200 g.
Weight of sulphur (465 - 245) . . . . = 220 g.
Rise of temperature of cold water (23° - 8° C.) . = 15°.
Fall of temperature of sulphur (98° - 23°) . . = 75°.

Amount of heat given out by sul-
phur in cooling, 220 x 75 x «
(the specific heat of sulphur).
3000 = 16500 s

* = !"%%

s = .18.

The specific heat of sulphur is .18. How much heat warms a gram
of it 1°C.? If 100 g. of sulphur at 80° and 100 g. of water at 10° are
mixed, nearer which temperature will the temperature of the mixture
be? Why?

250. Calculation of Temperature. — Calculate the temperature
by substituting in the rule : —

Weight of water times rise in temperature = weight of solid times
fall in temperature times specific heat of solid.

Amount of heat absorbed by
cold water, 200 x 15

224 PRINCIPLES OF PHYSICS.

Let w = weight of water,

(o = temperature of water,
ti = temperature of mixture,
t = temperature of solid,
Wi = weight of solid,
8 = specijfic heat of solid.

The abovo nde is expressed by the formula: —

w X {('i — (o) = Wi (t — ii) fi.

Having found /„ tlu» temperature of the mixture, assume
that tlio weight of Hul])]nir or of water or the temperature of
sulpliur or of wator is unknown, and work out four problems,
finding tho vahie of the unknown quantity in each case.

Whon wator is niixiHl witli water, « = 1 in the formula
alK)vo, whioh boiMunea

w (t, - W = tv, (/ - t,).
Why is i» =e 1 ? What is the a|)ocific heat of water ?

Problems.

1. IKH) g. of WAtor At mr And LHH) g. of wAter At lO"" will be of what
li^mp^rAtur« whf^n inixcti?

ft. Find to whAt tonii^'rAtim^ a pah of tHX) g. of boiling water
(Ur* = Vrt oniv) is lowoitni hy lh<» Addition of 4(X) g. of water at 2(rC.

S. How much wAtf»r At 4iV C\ must U» put with 200 g. at 15** C. to
t«Akf» \\\p mi\t\nt» *i»V'C\?

4^ WhAt nui5t tvo thf^ tonii^rAturt^ of 120 g. of water to cool to
JUV (\ A dij«h tvnlAiidng aiM> g. of WAtor At tkV 1\?

S. WhAt AnuMnU of ioiMN^Ul \vAti»r wiU <hx»I a 2*V) g. tumbler from
^y K\ to ^» ^\ ^?i|>*H^it\o hoAt of glA58 ^ .17) ?

•^ WhAt \5 th<» tf*«i^vrAtw«>j» of l(^> g, of mAH>l<', if when mixed
with rt.% ji. of wAtf^r At ^^v*C. ih^ nuxui«>j» i5 *r C (»pecifie heal of
m^U^ -r .;?t>?

tv U xrtH'n A l<v-)^v:im lum^^ of plAtinum (»p^6e iMil « JDtt^ k
t<AWn frH%m A f«v»>A«v Mu\ y\\\\^^c^\ i«to 10 g. of
tWrm^%ttH*t'r»r v\,'«^> to ^iLM l\. xx hM xkhs fh<» tomr

EVAPORATION AND BOILING. 225

8. What reading on the centigrade scale corresponds to — 70° on
the Fahrenheit? Change 55° C. to F.; - 22° C. to F.; 4°F. to C;
-8°F. toC; -8°C. toF.

9, A thermometer reads — .8° in melting ice, and 99.6° in steam
(bar. = 74.5 cm.) ; find zero and 100° corrections and the true 100°
point.

10. A fall of 1° C. in the boiling-point is caused by the reduction
of atmospheric pressure due to an elevation of about 960 ft. How
hot is boiling water at Denver, 5000 ft. above the sea level ?

11. The difference between the boiling-point of water at the base
of a mountain and that at the summit is 2.5° C. ; what is the height
of the mountain ? Why must the boiling-point at the base and that
at the summit be taken at the same time ? What besides change of
elevation could cause a change in the air pressure ?

12. How high would a mercury barometer stand if the boiling-
point of water was 99° C. ? 102° C? 75° C? 50° C?

251. Number of Heat Units required to melt One Gram of Ice.

— Put 200 g. of ice water at 0° C. in a metal dish (a tin
can or a tarnished calorimeter), and heat over a small flame.
Record the temperature each half-minute. If the thermometer
rise 5** a minute, then 1000 heat units are absorbed each min-
ute. Pour out the water and put in 200 g. of dry ice ; stir
constantly, and note the time it takes the ice to melt. Find
how long it took to warm the 200 g. of water one degree,
and how many times longer it took just to melt 200 g. of ice
at 0** C. into ice water at 0° C. Exactly as many times longer
would be needed to melt only 1 g. of ice as to warm 1 g. of
water 1®. One gram of water warmed 1° takes one heat unit,
and the number of times longer required to melt the ice is,
roughly estimated, the number of heat units required to melt
1 g. of ice. Ice water at 0° C. is no warmer and no colder than
ice at 0° C. just before it melts.

252. Latent Heat of Melting. — Heat is required to melt the
ice without causing any change in the temperature. The

226 PRINCIPLES OF PHYSICS.

number of heat units required to melt, one gram of ice is
called the latent heat of melting (latent means hidden). The
heat used in melting gives no indication on the thermometer,
but does work, in changing the state from solid to liquid.
The heat thus stored up is given out again when the liquid
freezes.

Find the melting-point of salt and water, by a thermometer
in a mixture of ice and salt. Use plenty of salt. Pour in
water. When the thermometer registers as low as 10**, remove
the unmelted ice and place in the liquid a test-tube containing
ice water and a second thermometer. As the water freezes in
the test-tube, note the rise of temperature of the salt water.
Leaving out of account, for the present, the effect of dissolved
substances on the melting, explain the influence of lakes and
rivers on climate, due to the heat absorbed in melting ice and
snow in the spring, and the heat given out in freezing in the
early winter.

853. Another Method of finding the Number of Heat Units
required to melt One Oram of Ice. — The number of heat units
required to melt 1 g. of ice may be found by adding water of
various temi)eratures to the same weight of ice, and repeating
the experiment until a temperature of watt^r is found that will
just melt an ei|ual amount of ice. Then the number of heat
units given out by one gram of hot water in cooling to zero
will be the number of heat units absorbeil and rendered latent
in melting one gram of ice. It may be more convenient not
to take exactly 50 or 80 or 100 g. of either iin* or water, but
the exact weight must be known. If the weights of water and
ice and the temperature of the water are so chi>sen that the
ice is not only melted, but the whole mixture is warmed to
about the temiH»rature of the rix)m, the results will be more
exact, since the heat absorbeil from the roi>m by the ice and
cold water will be balanced by the heat given out to the room
by the hot water.

EVAPORATION AND BOILING. 227

Bxerciae 32.

HUKBEB OF HEAT UVUS BSQinBED TO MELT ONE OEAM OF
IGE.—LATEHT HEAT OF WATEB.

.^pparatu$: Calorimeter; thermometer; crashed ice; dipper holding aboat
300 g. The pieces of ice should be smaller than walnats.^

Weigh the calorimeter. Pour in about 300 g. of water at a tem-
perature of 75° to 80**. Weigh calorimeter and water together and
place the thermometer in it. Stir the water in the calorimeter. Read
the thermometer to tenths of a degree, and, after wiping the calorime-
ter, put in nearly all the ice. Stir again, until the melting is complete.
Record the temperature of Vie mixture. Find the weight of the
mixture. If there is much ice remaining when the water has cooled
to l(f C, remove the ice with a small strainer, taking as little water
as possible.

Weight of hot water = weight of calorimeter and water less weight

of calorimeter.

Weight of ice added = weight of entire mixture less weight of

calorimeter and water.

The hot water, in cooling down, gives out as many heat units as
the number of grams times the number of degrees fall in temperature.
This heat does two things : it melts the ice, and it warms the melted
ice water to the temperature of the mixture.

Call / the number of heat units required to melt 1 g. of ice.

Weight of water times fall in degrees = weight of ice times I + weight
of ice water times rise in degrees from 0° to temperature of mixture.

This may be written

W (t — t{) = W^l + W^ty,

if we let w = weight of water,

t = temperature of water,
^1 = temperature of mixture,
w^ = weight of ice.

To the weight of hot water add the weight of the calorimeter times
the specific heat of it.

1 Before the exercise the crushed ice should be placed in boxes holding
about 12S g. each. The water may be heated in large dishes, and is most con-
veniently distributed to the pupils by means of a dipper holding 300 g.

228 PRINCIPLES OF PHYSICS.

Problems.

1. How many heat units are required to melt 100 g. of ice ? half a
gram? 4.5 g.? 400 g.?

2. Calling the latent heat of ice 80, how many heat units will be
absorbed in melting 60 g. of ice?

3. Which absorbs more heat, melting a gram of ice or warming a
gram of ice water to 50° C. ?

4. What amount of water at 80° C. must be put with 1 g. of ice at
0° C. to make the mixture 0° C. when the ice is melted ?

854. Solution of Problems on Latent Heat — By using the
formula on page 227, many problems relating to the melting
of ice can be solved by substitution. For example, find the
tempemture to which the addition of 40 g. of ice will bring
150 g. of water at 90^ C. Here the t^ of the mixture is unknown.

w(t — ti) = wil -f- wA
150 (90 - /,) = (40 X 80) + 40/,
13500-150/1 = 3200 + 40/,
-190/, = - 10300
/, = 54^

As water does not usually remain liquid at a lower tempera-
ture than 0* C, a minus result obtaineil for the temperature of
the mixture indicates that all the ice did not melt in lowering
the mixture to 0**. If 40 g. of ice at 0^ C. are put with 60 g.
of water at 50"* C, calculate /, of mixture.

00 (50 - /,) = (40 X 80) + 40 /,
/, = -r.

The mixture will be 0** and a little ice unmelted.

Problema.

1. Find the temperature of 25 g. of iee at 0^> and ^g. of water

aiao".

2. How many grams of ice at 0^ C. must b« put with 200 g. of
water at W C. to lower the temperature to 10^ C?

EVAPORATION AND BOILING. 229

3. What is the temperature of iced tea, if 20 g. of ice at 0° C. are
stirred into 150 g. of tea at 100° C. ?

4. A tin can weighs 200 g. (specific heat of iron = .1). It is
wanned to 40° C, and dry snow at 0° is put in ; how much snow
melts?

5. In using a large calorimeter in determining the latent heat of
water, one-third of the metal was touched by the water or ice. If the
calorimeter weighed 120 g. (specific heat = .1), to what weight of
water was the part of the calorimeter in use equivalent?

6. From the following data calculate the latent heat of melting
of ice:

Calorimeter, 100 g. (specific heat = .1).
Calorimeter and water, 190 g.
Calorimeter, water, and ice, 245 g.
Temperature of water, 60° C.
t^, temperature of mixture, 10° C.

255. Practical Applications of Latent Heat. — Why does ice
cool more than the same weight of ice water ? What should be
the temperature of an ice chest ? What the temperature of the
waste water ? If this is as cold as the ice, how has the food
in the chest been chilled ? How much waste water, in addi-
tion to the regular flow^ comes from an ice chest after 3000
grams of water at 20° C. is put in to cool ?

An interesting experiment is the testing of the melting-point
of ice cream and the freezing-point of milk and strong lemon-
ade. Place the lemonade or milk in a test-tube inserted in a
mixture of ice and salt. Explain why a packing of ice does
not keep a can of ice cream from melting. What should be
the packing, to prevent melting of the cream ? Wrapping the
ice in a cloth before placing it in an ice chest makes the ice
last longer, but the chest is not cooled ; why ?

How low may the temperature fall during a rain? How
high could it rise during a snowstorm ? Why do the lakes
and rivers freeze up before the harbors on the seacoast?

230 PRINCIPLES OF PHYSICS.

What is the result of spreading salt on an icy walk ? How
low must the temperature be for the salt to have no effect on
the ice ? If the melting-point of ice and salt is — 17** C, how
cold must the weather be, if salt does not thaw the ice on an
electric car track ? If a person stands in water from ice melted
in this way, are his feet likely to freeze ?

256. Latent Heat of Vaporization. — Compare the time taken
to warm water from 0° to 100° C. with that required to boil it
away. The latter takes over live times as long. How many
heat units are absorbed in warming one gram of water from 0**
to 100® C. ? Then, roughly, how many heat units are taken up
by the water at 100° C. in turning into steam at the same tem-
perature ? This heat, not indicated by any movement of the
thermometer, is called the latent heat of steamy or the latent heat
of vaporization,

257. Vaporization is the process of turning a liquid into
vapor, or steam, and takes place as evaporation or boiling.
Let water evaporate on the hand. Into a porous cup, a bat-
tery cup, or a flower pot, pour water that has acquired the
temperature of the room, and insert a thermometer. What
caused tlie difference between the readings of the wet-bulb
thermometer and the dry-bulb thermometer? Both evapora-
tion and boiling absorb heat, and exactly the same amount
of heat is given out when the vapor condenses again into a
liquid.

258. Cooling by Evaporation. — In India, water for drinking
purposes is often put in porous jars. Some of the water oozes
through the pores and evaporates. What effect does this have
on the temperature of the water? Why does a person feel
chilled when standing in the wind, on a summer day, after
taking violent exercise or being wet in any way?

EVAPORATION AND BOILING. 231

In the Carr^ ice machine, a flask of water is connected with
an air-pump, as in Fig. 207. The air is exhausted, the pressure
falls, and boiling begins. This ab-
sorbs heat and lowers the tempera-
ture till 0** C. is reached, when part
of the water freezes, the remainder
boiling away. The result is quicker
and more certain if the vapor, on
leaving the flask, passes into a tank '*'

of sulphuric acid and is absorbed. Under the slight pressure
exerted on the surface of the water, the evaporation is rapid.
We have seen that evaporation is hastened by heat and
decreased pressure.

To evaporate, or boil away, a gram of water requires more
heat than is required to evaporate a gram of any other liquid.
Into a known amount of cold water pass steam. The amount
of heat absorbed by the water in getting warm equals the
amount of heat given out by the steam in condensing and then
cooling from 100° to the temperature of the mixture. The
steam has a certain supply of heat to give out when it con-
denses into water at 100° C. But the steam, in condensing,
becomes water at 100° C. This water cools down as it mixes
with the cold water, and gives out more heat.

Exercise 33.

LATENT HEAT OF VAPOBIZATION.

Apparatus : Calorimeter ; steam can ; thermometer ; rubber tubing ; dipper
holding about 200 cc. ; glass tube, A, Fig. 208.

Fill the steam can about one-fourth full of water, and heat. While
the water is beating, weigh the calorimeter. From a dish of water
that has been cooled by ice or snow pour into the calorimeter about
200 g. of water, using the dipper. Weigh the calorimeter and water.
To shorten the time of the exercise, hot water may be put in the steam
can. Screw the cover on loosely, to prevent its sticking. When

S3 &

232 PRINCIPLES OF PHYSICS.

steam has passed long enough to heat Uioroughly the rubber and
bent tube, A, Fig. 208 (that is, when not more than six or seven drops
of water per minute pass with the steam), stir the water, which should

be 10° C. or less, in the calo-

rimeter, and read the ther-
mometer. Raise A by holding
a pencil under the bend ; slide
the calorimeter along on a
block of wood, and let the
tube, i4, drop into the water.
The end of the tube should
'** not be more than 2 or 3 cm.

below the surface. Place a sheet of wood, cardboard, or paper be-
tween the boiler and the calorimeter. Take roughly the length of time
steam is passed in. Stir ; when the thermometer reads between 50° and
60° C. remove the calorimeter and stir till the temperature is constant.
Weigh calorimeter, water, and condensed steam. To the weight of
the water add the weight of that part of the calorimeter touched by
the water times the specific heat of the metal of which the calorimeter
is made. Find the weight of added steam.

I^t / represent the number of heat units given out by 1 g. of steam
at 100° C. in condensing to water at 100° C. But this condensed
steam at 100° C. cools down from 100° to the temperature of the
mixture (t^), or to 100° - /j degrees. The steam warms the cold water
in two ways, first in condensing, and then in cooling.

weight of steam

weight of steam x

fall in degrees

( 100° - <i)

' weight of cold water x
number of degrees rise

Let s = weight of steam, and of course of condensed steam.

w = weight of cold water -|- water equivalent of calorimeter.
t = temperature of steam (near 100° C).
<j = temperature of mixture.
(q = temperature of cold water.

The above equation can be written,

(8 Xl)+8(t-t,) =w(t,-tf,).

Calculate /, the latent heat of vaporization of steam, at 100^«

EVAPORATION AND BOILING. 233

As the weight of the steam is small (from 15 to 25 g.), any error
in weighing the calorimeter and water before or after adding the
steam, or any water carried into the calorimeter with the steam, or
any water spattered out by the steam as it bubbles in, will make the
results obtained disagree ; for an error of 1 g. in 15 is over 6 per cent.
It is not necessary to use a steam trap. To find the error due to
water brought over with the steam, catch and weigh the water that
drips from the tube, i4, for a length of time equal to that during
which steam was passed into the calorimeter.^ To do this, turn A so
that the steam blows out in a horizontal direction, and place a tin
cover to catch the drops of water. To obtain the real weight of the
steam, subtract this weight of water from the number of grams of
steam apparently added to the calorimeter.

Effects of Latent Heat of Vaporization. — The return
water from a steam radiator is often as warm as the steam j
where does the heat come from that warms the room ? This
water returns to the boiler at as high a temperature as the
steam that leaves the boiler ; what does the heat generated by
the fire do? Water evaporating at any temperature absorbs
as much heat as would raise it to boiling and boil it all away ;
why does sprinkling cool a brick pavement ? Vast quantities
of water evaporate from the leaves of all plants and trees;
why is not the heat so intense at noon in a country covered
with trees and vegetation as in a desert ?

Problems.

1. Calling the latent heat of steam 540 (that is, 1 g. of water at
100° C. in changing into steam at lOO^'C. absorbs about 540 heat
units), calculate the amount of heat required to boil away 40 g. of
water at 100° C.

2.- Find the number of heat units required to warm 40 g. of water
atO°C. to 100° C. I Find the number of heat units needed to turn
40 g. of ice water into steam at 100° C.

1 This error may be determined by the teacher or by one pupil.

2S4 PRINCIPLES OF PHYSICS.

3. How many heat units are given out by 25 g. of steam in con-
densing? How many by 25 g. of water at 100° C. in cooling to
50° C. ? What is the total amount of heat, if 25 g. of steam are con-
densed and cooled to 50° C. ?

4. Find the true 100° point and zero point of a thermometer that
reads 1° in ^melting ice and 100.2° in steam (barometer = 76.4 cm.).
What is the temperature of a liquid in which this thermometer
reads 3° ? 98°?

5. A thermometer reads 99.2°, when the barometer is 75.4 ; what
would the thermometer read if the barometer column were 76.2 cm.
high?

6. What is a heat unit ? How many heat units are absorbed by 1 g.
of ice in melting? How many heat units are required to melt 150 g.
of ice ?

7. If 84 g. of water cool from 50° C. to 25° C, what is the number
of heat units given out? How many heat units does 1 g. of water
absorb in warming from 10° to 25° C.? Then how many grams of
water at 10° C. must be put with 84 g. of water at 50° C. to make the
mixture 25° C?

8. What is meant by the statement that the specific heat of anti-
mony is .05? How umch heat is given out by 300 g. of that metal in
cooling from 95° to 30° C? How much water at 5°C. mixed with
300 g. of antimony at 95° C. will make the mixture 30° C. ?

9. How much heat is given out by 20 g. of steam in condensing?
If the temperature of steam was 10<P, what is the temperature of
the condensed steam? How many heat units can the condensed
steam give out in cooling to 30° C?

10. Steam at 100° C. is admitted to an iron pipe at 20° C. weighing
10,000 g. How many heat units will be required to warm the pipe to
100° (specific heat of iron = .1) ? How many grams of steam are con-
densed in doing this ?

11. If two boxes of the same size and weight, one containing ice
and the other ice water, are placed in pails of warm water, just alike,
will there be any difference in the temperature of the water in the
pails? Why?

12. The Norwegian cooking box and the Aladdin stove are con-
structed on the principle that after food has been heated to a tem-

EVAPORATION AND BOILING. 235

perature at which cooking begins, do farther heat is needed to cook
for a length of time, except to replace what heat escapes by convec-
tion and radiation. With what kind of substance should the box or
stove be covered ?

13. The space between the double waUs of an ice house is filled
with shavings or sawdust Is convection retarded? Which is the
poorer conductor of heat, a block of solid wood or sawdust? How are
the walls of a refrigerator constructed ?

14. The specific heat of ice is .5. If 20,000 g. of ice are exposed
for a long time to a temperature of '60° C, how much heat will be
absorbed by the ice before melting begins? If a piece of ice, say
10 g., at — 30** C, is dropped into a dish of ice-cold water, will there
be more or less ice?

CHAPTER XVI.
EXPANSION OP GASES. -LAW OP CHARLES.

260. Expansion of Gases. — All gases expand at the same
rate when heated. Gases expand more than liquids or solids
(see section 205, page 180). To find the expansion of a gas,
it is more convenient and more accurate to measure the entire
(that is, the cubical) expansion in a tube where the total
expansion takes place only in one direction, than to measure
the increase in diameter of a rubber balloon or sphere.

Half fill a long test-tube and invert it in a dish of water.
Let this stand for some time. Mark the level of the water in
the tube with a Cross pencil. The temperature of the air in
the tube is about that of the room. Warm the air in the tube
a little. The tube grows a little larger when heated, but this
increase is so small that we may say that the entire expansion
of the air takes place in one direction only. To get rid of the
water vapor and the weight of the column of water in the tube,
^ consider the apparatus shown in

diameter throughout. A perfectly
fitting piston moves in the tube
without any friction. As gases expand so much more than any
solid of which the tube may be made, let us neglect the error
made by not allowing for the change in volume of the tube at
different temperatures. The length from the closed end to the
piston, P, may be taken as the volume of the air, or as repre-
senting this volume. When the distance TP has doubled, the
volume of air has doubled.

Suppose the piston is at P when the tube is embedded in

236

SXPANSIOy OF GASES. — LAW OF CHARLES. 237

?^ > then the temperature of the air in the tube is 0** C. and
^^ volume is TP. When the tube is heated to 100° C. in
f^^am, the piston moves to F*. The distance from P to P*
^^ the increase in volume. What we wish to know is how
*^Hch one cubic centimeter of air would expand for one degree
^^e in temperature. The original length was more tlian 1 cm.
^d the rise in temperature was 100°, instead of 1°. Divide,
then, the increase in volume by the original length and by the
dumber of degrees rise in temperature. If the length of the
air column at 0° was 50 cm. and the rise in temperature was
100°, the increase in length must be divided by (50 x 100) to
get the amount 1 cm. would expand when warmed 1° C. The
amount that 1 cm. expands for 1° rise in temperature is called
the coefficient of expansion. Remember that, as all the expan-
sion in width and thickness must be in the direction of the
length, the cubical expansion is what is measured m this case.

-steam 200'

Exercise 34.

COEFFICIENT OF EXPANSION OF AIB.

ApparcUtts: A glass tube, 50 cm. long, the bore 1 mm. or less in diameter,
filled with dry air or gas; a drop of mercury in the tube, about 17 cm. from
the closed end, as an index p a piece of rule, to which the tube is clamped ;
a dish of snow or of ice and water ; a steam boiler.

Place the rule and tube vertically in the dish of ice and
water. Read the position of the lower part
of the mercury index. Place it in a bath
of steam, using the extended cover of the
steam boiler, as in testing a thermometer
(Fig. 186, page 191). Record the reading
of the index in steam. From the barom-
eter reading calculate the temperature of
the steam. Record the reading of the end
of the tube (A, Fig. 211). The difference
between the readings at A and B gives the
original volume of air at 0° C. The differ-
ence between the readings at B and D is j± \jA.
Fig. 210. the increase in volume for 100° rise in Fig. 211.

iceO'C

238 PRINCIPLES OF PHYSICS.

temperature (or nearly that). The increase in volume of 1 cm. is the
increase divided by the length AB, To find the increase for 1^ rise
in temperature, divide by 100.

In this way, calculate the coefficient of expansion of air, which

Increase in length

Length at 0° x degrees rise in temperature

As the air pressure does not change perceptibly during the time of
the exercise, the result is the coefficient of expansion of air at con-
stant pressure. Since all gases have the same rate of expansion, the
word gas may now be substituted for air.^

261. Law of Charles. — A body of gas for each degree it is
warmed above 0° C. increases ^^ of the volume measured at
0° C, and decreases to the same extent on cooling. This fact,
or law, is called, from the name of its discoverer, the Law of
Charles.

A balloon filled with gas at 0° C. is just doubled in volume,
if heated to 273° C. Suppose a mass of gas to be cooled
steadily. For every degree below 0°C. that it is cooled it
contracts ^|j of its original volume. Suppose that the gas
did not condense into a liquid at — 40° C, or — 80** C, or
— 180** C, or at any low temperature, how much must the gas
be cooled to have no volume at all ? As it loses y|^ of its
volume when cooled 1**, to lose the whole volume, or ^^j, it
must be cooled 273° below zero centigrade, or to — 273** C.

Of course, matter cannot be destroyed, and all gases become
liquid at some low temperature, when the rate of contraction
is slow. But all gases do contract at a rate that, if carried far
enough, points to a temperature — 273** C, where they would

1 It is instructive for one member of the class to measure a tube filled with
coal gas, hydrogen, or carbonic acid gas. The result obtained by good work-
ers is .00.')06, or g^. In case a much larger number is obtained, the results
and the tube are to be rejected, because of moisture in the gas. As water in
turning to steam increanes in volume over 1700 times, a very minute amount
of water vapor in the tube causes a large additional movement of the mercury
index.

EXPANSION OF GASES. — LAW OF CHARLES. 239

have no Yolmne as gases. The electrical resistance of wires
decreases in much the same ratio, and the decrease is at such
a rate that if the wires could be cooled to — 273° C, they
would haye no resistance whatever, and a fine wire could
carry, without heating, any amount of current. Such a plan
has been proposed by Elihu Thomson.

Point of Absolutely No Heat. — This point, -273** C, is
indicated in other ways as the point of no heat, — that is, of
the greatest cold possible, — and is probably the temperature
of distant space ; it is called the absolute zero. Yet Fahren-
heit chose the zero of his scale at what he thought w£^ the
point of greatest cold.

^•»-

-^73"-

ice meltt

273*

Absolute Scale. — The left-hand scale in Fig. 212 repre-
sents the standard temperatures on a centigrade scale; the
right-hand scale rep-
resents what is called lOOH — water boilt -r- 573*
the absolute scale, so
called because the
zero is at the point
of absolutely no heat.
JN^otice that the "ice
melts" point is 273°
in the absolute scale
and 0° in the centi-
grade scale. To change from centigrade to absolute, add
273°.

As shown in the following table (p. 240), 273 cc. of gas at
0° C. or at 273° of the absolute scale have different volumes at
different temperatures.

As the volume increases, the absolute temperature increases
at the same rate. Therefore we may say that the volume of a
mass of gas varies as the absolute temperature. This is another
way of stating the Law of Charles (section 261).

. point ofmo heat J— 0^ or absolute cold
Fig. 212.

240

PRINCIPLES OF PHYSICS.

Volume in

Temperature on

Tempbraturr on

GuBio Centimbtbhs.

Centiorade Scale

Abbolutb Scale.

271

-2°

272

-P

272

273

0°

273

274

1°

274

275

278

3°

276

A balloon of gas, if taken from a room at 5° C. and left in a
room at 30° C, does not, as can be seen, increase six times in
volume. Change the temperatures to absolute scale. The
lower temperature becomes 273 -f 5 = 278° ; the higher be-
comes 273 + 30 = 303°. Then the size of the balloon is as
many times greater in the warm room as 303 is times larger
than 278. Call the volume of gas in the balloon at first
1000 cc. ; then write

1000^278
V 303'
and find the value of v

Problems.

1. If 300 cubic feet of air is cooled from 20° to - 40° C, what does
the volume become?

2. Sixty cubic feet of air at 20° has what volume at the melting
point of platinum (4000° C.)?

3. Change 100° C. to the absolute scale ; 0° C. ; - 273° C; 500° C. ;
- 10° C.

4. Change the following absolute temperatures to centigrade:
500°; 50°; 0°; 273°. Why are tliere no minus temperatures in the
absolute scale? What scale must be used in order that the volume
of a gas may be proportional to the temperature ?

264. Air Thermometer. — The length of the air column be-
tween Tand /, Fig. 213, at 0°C., is 40 cm. ; what is the tem-
perature when the distance is 60 cm. ? 100 cm. ? 20 cm. ?

EXPANSION OF GASES, — LAW OF CHARLES. 241

Express the temperatures first in absolute degrees and after-
ward change to centigrade degrees, by subtracting 273. Why
with the apparatus, 77, can lower temperatures be read than
with a mercury thermometer ? T/rep- j

resents an air thermometer. ' " "^^^

For measuring very high tempera- ng. 213.

tures, the tube is made of porcelain, and it is then called a
pyrometer. Often there is a large bulb at T, and instead of
measuring the expansion of air by the movement of the index,
J, the increase of pressure (made by a pump, for instance)
required to keep / in a certain place is read on a mercury
gauge and the temperature calculated. (See Exercise 35,
page 242.)

Problems.

1. A balloon holds 30,000 cubic feet of coal gas. The gas is passed
in at 15°C. By the heat of the sun the gas is warmed to 25° C. What
is the volume ?

2. A gas company measures its gas at 25° C, and the meter regis-
ters for a month 1,000,000 cubic feet. The gas is chilled to 10° C.
before passing through the customers' meters. How much gas is
registered ?

3. A balloon, capacity 600,000 liters, is filled with air heated to
80° C. by a stove; what space does the air occupy on cooling to 20° C?
Which is the heavier, the balloon filled with hot or cold air? Why
does it rise when filled with hot air?

4. The air in a chimney is heated to 273° C, while the surrounding
air is 0°C.; what does the volume of a cubic centimeter of air become
after entering the chimney ?

5. If 1 cc. of air at 0° (bar.= 76 cm.) weighs .0012 g., what does
1 CO. of heated air in the chimney weigh?

6. If the chimney is 3000 cm. high, what does a cohunn of air
1 sq. cm. inside the chimney weigh? What does a similar column of
air outside weigh ?

7. What is the tendency of the air in the chimney to rise, expressed
in grams per square centimeter? What is the effect of making the
chimney taller or shorter ?

242 PRINCIPLES OF PHYSICS.

Bzercise 35.^

INCBEASE OF PBESSUBE OF A OAS WHEN HEATED, BUT NOT
ALLOWED TO EXPAND.

Apparatus : Glass tube, closed at one end, with an index (I, Fig. 214) ;
U-shape mercury gauge ; compression pump (a bicycle pump having a valve
is excellent) ; three lengths of rubber tubing, connecting a three-way brass
connection to the glass tube, the mercury gauge, and the pump, as shown
in Fig. 214.

Cool the tube, T, to 0° C, and record the whole length of the tube,
and also the distance from the open end to the inner part of the
. index. Then, with the tube in steam, measure

/=Or^^B the distance from the open end to the inner

\) II part of the index, 7. These measurements, as

/ UJJ in Exercise 34, are used to determine the ex-

11 IL^J^rp-Q pansion of air for 1° rise in temperature. If
I ^ the air in the tube be pushed upon, or com-

pressed, till the index is driven back to the
Fig. 214.

position it had at 0° C, the increase of press-

ure over that of the atmosphere can be measured by the U-tube
mercury gauge, M,

The opening to the mercury gauge, M, or manometer, is nearly
closed, to prevent rapid oscillation of the mercury. The tube, T, is
in steam, and the pressure is increased until the index, /, is driven
back to the position it had when the tube was in ice. The difference
in the level of the mercury in M gives the increase in pressure over
that of the atmosphere on the air in 77. This increase of pressure is
caused by warming the air about 100°.

The coefficient of increase of pressure at constant volume is the
increase of pressure for 1° rise. Divide the increase of pressure by
the rise in temperature, and the coefficient is obtained. The result is
almost the same as the coefficient for increase of volume under con-
stant pressure. Starting from 0°, each degree of rise causes jfy in-
crease in pressure.

Boyle's Law is readily tested by this apparatus. The tube, T, is at
the temperature of the room. Varying pressures above and below

1 This Exercise is quickly performed with that on the Law of Charles,
page 237.

EXPANSION OF OASES. — LAW OF CHARLES. 243

the atmosphere are applied by the pump, the pressures read at Jf,
and the volumes of air calculated by the measurements of the index
position.

Problems.

1. Place a bicycle tire, filled to 50 pounds' pressure to the square
inch at 0° C, in the sun, and warm it to 30° C. ; what is the increase
of pressure ? As the tire was filled with air at atmospheric pressure
(15 pounds to the square inch) before j)umping, the total pressure
was 65 pounds.

2. The air in the cylinder of a hot-air engine at atmospheric press-
ure (15 pounds to the square inch) is at 0° C. What is the increase
of pressure when warmed to 60° C. ? when warmed to 273° C?

CHAPTER XVII.

THEBHODTNAMIOS.

266. Cooling: by Expansion. — Compressing a gas develops
heat. This is shown by the warming of a bicycle pump sup-
plying air under pressure to a bicycle tire. It is shown also
by the ignition of a substance in the piston of a fire syringe.
Phice tinder in a cup-shaped piston, Fig. 215, A,

[Push the piston down as rapidly as possible in
the cylinder, B. Do this with one strong push,
^ and remove the piston at once. The air in the
cylinder is heated by compression to a tempera-
Fi 215 *^^^ above the kindling point of the tinder, which
is therefore set on fire. The air is warmed be-
cause work is done on it. On the other hand, a gas, in expand-
ing, is cooled by doing work, whether a piston is pushed, or
the air of the atmosphere is pushed away in front of the
escaping gas.

Bxercise 36.

WEIGHT AND VOLUME OF A OAS.

Apparatus : Platform KcaleH ; capHulo of compressed carbonic acid gaH ; clamp,
to open capsule ; rubber bag of a football ; jar ; tube.

Record the weight of the capsule as a: + a number of grams and
tenths of a gram, as registered by the slider of the balance. To do this,
put enough pieces of chalk or weights in the right-hand
pan to obtain a balancing with the slider between four
and five grams. Notice the temperature of the capsule,
and of the tube, T, Fig. 'JIO, through which the gas
is to flow when the capsule, T, is pushed on to T,
Find the space taken up by the material of the rubber
bag by pressing it, em])tied of air, into a full jar of
water, taking care that no water enters the bag. Re- Fig. 216.

244

THERMOD YNAMICS. 245

move the bag. The unfilled space at the top of the jar equals the
space taken up by the bag itself. This space need not be measuied.
Put the mouth of the bag over the opening, 0. Turn down the screw
cap, A Ay forcing the capsule on to the tube, T. As soon as the gas
has escaped, remove the screw cap and notice the temperatures of
C and T, A flake of solid carbonic acid gas is often seen by removing
the capsule and looking near the opening of the tube, T. Pinch the
mouth of the rubber bag and press it under the surface of the water
in the jar. The water that runs over this time is the volume of the
gas in the bag. Measure roughly the volume of this water. This is
the volume of the gas that came from the capsule.

The capacity of the capsule (Exercise 7, page 17) is found by
weighing the capsule empty and again when filled with water. To
fill it with water, hold the open end under a stream of water, and
strike the opening repeatedly with the finger. The difference between
the weights of the capsule empty and filled with water is the volume,
or capacity. The loss of weight due to the escape of gas represents
the weight of gas the capsule contained. Find the weight of one
cubic centimeter of the gas by dividing the loss in weight of the cap-
sule by the volume of the gas, and compare this value with that for
air (Exercise 10, page 43).

266. Work done by Ezpandingr Gases. — A large amount of
work was done by the gas in expanding and lifting away the
atmosphere, which has a pressure of a little more than 1000 g.
per square centimeter. The energy for doing this was obtained
by absorbing heat, in part from the walls of the capsule in
which the gas was compressed, and in part from the tube, T,
and from the gas itself. That is, the gas is cooled by expan-
sion, but is not so much cooled as it would have been had it
not taken so much heat from the metal surfaces in contact with
it. Of course, if the bagful of gas were pumped back into the
capsule and compressed to its original volume, just as much
heat would be generated.

Steam or any gas, in pushing the piston of an engine, ex-
pands and becomes chilled. Air at 50 to 80 pounds to the
square inch pressure, and at ordinary temperatures, 20° C, for

246 PRINCIPLES OF PHYSICS.

instance, after driving an engine, is cooled below the freezing-
point, and has been used to keep a refrigerator cool.

267. The Ice Machine consists of a steam engine, which drives
a pump to compress the gas. This gas is usually ammonia,
sometimes carbonic acid gas. Air could be used, although very
inefficiently. The gas, on compression, is warmed, just as is
air that is compressed in a bicycle pump. If the gas be allowed
to expand at once, it falls to the original pressure and tempera-
ture. Instead of doing that, the gas, heated by compression,
is first cooled by cold water. Ammonia gas is easily liquefied
by pressure and cooling in this way. When the cooled gas is
allowed to expand, it absorbs heat, and the temperature is
reduced far below 0° C. The gas then flows back to the pump
and is used over again.

268. A Refrig^erating: Plant in its simplest form could consist
of a powerful bicycle pump, P, Fig. 217, forcing air into a long
tube, which is cooled by water, WW. At 0 the gas is allowed

n WW AAA

■ =s

Fig. 2 1 7.

to expand into a tube, S. The air, compressed by the pump
and consequently heated, is cooled to the temperature of the
water, WW, On expanding, it cools still more. If the com-
pression is carried to 2000 pounds per square inch, and the
compressed air, cooled somewhat at WW, is still further cooled
by letting some of the air escaping at 0 blow on the tube, AAA,
the gas issuing from 0 grows gradually colder and colder, till
a portion of it liquefies. In practice, the pipe is coiled, and
the air is first compressed a little (100 to 300 pounds' pressure) ;
it is then cooled and compressed under a pressure of from 2000
to 3000 pounds ; cooled again by water, and then allowed to

THERMODYNAMICS. 247

expand. A part of the expanding air still further cools some
of the unexpanded air^ which, in turn expanding, is cooled
enough to condense and become a liquid.

Recently, Pictet, using apparatus not unlike Fig. 217, has
liquefied air with a bicycle pump, using pressures of less than
60 pounds to the square inch. The cooling effect at AAA was
brought about by using liquid air on the tube at that point to
start with.

269. Uses of Compressed Gas. — Slip pressure tubing over the
end of r. Fig. 216, page 244, and connect with the boiler of a
toy engine. Operate the engine by the gas from the capsule.
The motive power of a Whitehead torpedo is an engine driven
by gas from a tube of liquefied carbonic acid. Precautions are
taken, in carbonic acid gas and air motors, to prevent the
engines freezing up. The exhaust air is so cold that it chills
the engine and pipes, and moisture from the surrounding air is
condensed and frozen solid. This is prevented by heating the
compressed air before it enters the engine.

270. Heat derived from Work. — Mix sulphuric acid and water.
Pour water on a lump of quicklime ; the quicklime should be
obtained fresh, from a brick-mason or plasterer. In a few min-
utes thrust a match into the lime. Almost all chemical action,
of which these and the more common processes of burning oils
and other fuel are examples, produces heat. Touch a strip of
sheet lead, such as plumbers use, and notice its temperature.
Lay it on a block of iron and hammer it hard with a few quick
blows; then quickly touch the lead. Hammer a nail into a
piece of hard wood and immediately touch the nail.

271. Number of Heat Units produced by One Gram-centimeter
of Work. — Fig. 218 represents a test-tube containing mercury.
Through the rubber stopper a thermometer is inserted, marked
to tenths of a degree. An ordinary glass thermometer, with

248 PRINCIPLES OF PHYSICS.

large spaces for degrees, may be used. Knowing the weight
of mercury, the amount of work done and destroyed, as it
were, every time the tube is turned upside down,
equals the weight of mercury times the distance, d.
Fig. 218. To find what becomes of the work, read the
temperature, wrap the tube in several layers of cloth,
and turn it upside down 100 times, rapidly, and read
the temperature again. The work done in turning the
tube once = w x d. For 100 strokes, the work done
is 100 K'(/. All this work is turned into heat, and this
^^ heat warms the glass, the mercury, and also the air.
Fig. 218. unless the tube is completely surrounded by a non-
conducting substance. As the specific heat of mer-
cury is about ^^, the mercury is warmed up 30 times as much
as an eciual weight of water. One gram falling 1 cm. does
1 gram-centimeter of work, and this experiment can be made
to give, very roughly, the number of heat units produced by
1 gram-centimeter of work. Forty-two thousand gram-centi-
meters of work give approximately one heat unit.

272. Examples of Heat derived from Work. — A gram in fall-
ing 42,000 cm. could do how much work ? If the substance be
water, how much would it be warmed ? If iron, specific heat
.11, how much would it be warmed ? Does a gram of iron in
falling 1 cm. do any more work than a gram of water ? How
far would a gram of water have to fall to be warmed 1° C. ?
to be raised from 0° to 100° ? to be turned into steam ?
Assume, in these questions, that all the heat is absorbed by
the water, although such is not always the case.

Explain why the wooden sheathing on the interior of iron-
clads, during the war between China and Japan, was often set
on fire by shells that struck the armor. Why is it that a
blacksmith can bring a piece of iron to a red heat. by pound-
ing it with a hammer ? Why does a lead bullet sometimes
melt on striking a stone or plate of iron ? A meteor is a floaty

THERMOD YNAMICS. 249

ing mass, which is cold before striking the earth's atmosphere
and losing its motion ; why does it become warm ? In bend-
ing a wire back and forth, is any work used up ? Into what
is the work changed ? The old way of making a fire was to
strike together a piece of flint and a piece of steel. The sparks
fell on and set fire to a box of scorched linen, which was called
tinder. In grinding hardened steel tools that would be soft-
ened by heat, why is the stone flooded with water ?

273. Work derived from Heat. — We have seen that there
are two methods of producing heat: one, where some chemi-
cal action takes place; the other, where work or the power
of doing work is destroyed, as when a moving body is
stopped or a substance is forcibly cut or bent or twisted or
rubbed over another body, — that is, by friction. The heat-
ing of bearings, moving shafts, brake-shoes, drills, and other
tools, and the different operations of lighting a fire by the
friction of wood upon wood, are illustrations of the fact that
motion destroyed produces heat. While, by 43,000 centimeter-
gram units of work, 1 g. of water is heated 1° C. (or, in English
units, 778 foot-pounds ^ of work warm 1 pound of water 1° F.)
and all the work is turned into heat, the reverse process, that
is, using heat to produce work, is not economical. For, while
1 heat unit ought to give 43,000 gram-centimeters of work
(should lift, for instance, 1 g. 43,000 cm.), it will, with the
best steam or gas engines, give about 8000 centimeter-grams of
work, or about one-fifth of what it apparently ought to give.
The other four-fifths is not lost, but stays as heat, and is not
converted into work.

A mass that weighs 1 g. on the earth would weigh 21\ g. on
the surface of the sun. So that on the sun more work is
required to lift a body a given distance, and a body in falling
does more work, or gives out more heat, than on the earth —
just 21\ times as much. If it cooled down as fast as it gave

> This was first measured by Joule.

250

PRINCIPLES OF PHYSICS.

out heat, after a few thousand years the sun would be no
longer a sun, providing us with warmth and light. But a
little cooling, too slight to be noticed by us, causes a con-
traction of its surface, which falls in toward the centre, and
being stopped, produces so much heat that several million
years may pass before the sun is too cold to keep the earth
warm enough for people to live on.

274. Condensation of Steam. — The cost of animal power led
inventors, over a century and a half ago, to apply the expan-
sive power of steam to the driving of machinery. When water
is boiled in a flask the air is driven out by the steam. If the
flask is then stoppered and cooled, the steam condenses, and
the pressure of the atmosphere, no longer balanced by the
pressure of air or steam within, often crushes the flask. The
story is told of a milkman who, when scalding a large can with
boiling water, emptied the can and drove in the stopper tight.
In a few minutes the can was flattened out. Solder the cap of
a gallon oil can and provide a short piece of rubber tube that
fits over the nose of the can. The rubber tube is closed by a
bit of glass tube sealed at one end. Remove
the tube. Warm the can a little and put the
nose under water. When half a cup of water
has been forced into the can set it over a
burner. When the steam has passed freely
for a minute, close the nose of the can with

U^ the rubber tube and plug. Remove the can
from the flame. The condensation of the
steam in the can may be hastened by drench-
ing with water.

Connect the pressure gauge of mercury, 6?,

Fig. 219, with a test-tube containing a little

water. Remove the plug, P, and boil the

water. Insert the plug and pour cold water on the test-tube.

Heat the water again.

Fig. 219.

THERMODYNAMICS.

251

275. Kewcomen's Engine. — Replace the liquid piston of
mercury (Fig. 219) by a solid piston (Fig. 220). On boiling
the water the piston is forced up. The steam is then con-
densed by cooling the test-tube, and the air pressure,
15 pounds to the square inch, drives down the piston
and moves any machinery (the handle of a pump, for
instance) attached to the piston rod.

S76. Atmospheric or Vacuum Engine. — The work-
ing form of Newcomen's engine, which was never

used for anything but
pumping, is more like
Fig. 221. Suppose the
piston is at the bottom
of the cylinder. The
valve, F, is opened, and
steam from the boiler, B,
at a pressure of one or Fig. 220.
two pounds to the square
inch, forces the piston up. This
is easy, since the pump rod is
made heavy enough to lift the
pump handle and piston. V is
closed and D opened. Cold water
runs in from the tank, T, and con-
denses the steam. The atmos-
pheric pressure forces the piston
down, pulling the pump handle and
lifting the water in the well. D
ng.22i, is then closed, ^opened, and the

water runs out. E is closed, V
opened, and steam again enters to start a new stroke. Con-
siderable steam is wasted in warming up the cylinder, which
was chilled when the steam in it was condensed. This engine
is often called an atmospheric, or a vacuum, engine, since the

252

PRINCIPLES OF PHYSICS.

pressure of the atmosphere does the direct work of pumping.
In those days lK)ilers wtu-e sometimes made partly of wood,
and were not designed to stand liigh pressures.

277. The Condenser. — One day, after repairing a model of a
Newcomen engine, James Watt noticed the waste of heat in
cooling down the cylinder at each stroke, and
thought of condensing the steam in a separate
vessel. lie made a model something like Fig.
222. The valve, V, is oi)ened, and the piston
rises. V is closed and E opened. The steam
rushes into C, and is condensed by a jet of water
playing into C, or by the surface of the sides of
C, which are kept cool by cold water on tlie
(mtside. The condensed water and air are re-
moved by an air-pump con-

!3»

nected with O,

jj- ^ M^^ Watt used the "jet" form

IffO ^ ■/ \* of condenser, in which water

^^""^ ^^ ^^ is injected inside C. Nowa-

days the surface condenser, of
which tlie diagram shows a
model, is much used, es])ecially
in sea-going vessels, in which
the water from the condensed
steam is returned to the boiler,
to which salt water is injurious. To this improvement of
Watt — the separate condenser — may be credited, directly or
indirectly, most of the improvements in transportation and
manufactures of the last century.

>^=

Fig. 222.

278. Further Development of Newcomen's Eng^ine. — The en-
gines of Figs. 221 and 222 are single-acting; that is, steam
presses only on one side of the piston. At first the valves of
the Newcomen engine were turned by hand. Then levers and

THERMOD YNA MIC 8.

253

strings were connected with the pump handle or walking beam,
and the valves were moved by the engine itself. Watt further
improved the engine by different forms of valves and by
closing the top of the cylinder and admitting steam, first
above and then below the piston.

279. Cylindric Valves. — Many large engines have four valves
to each cylinder (Fig. 223). Draw this figure in the note-book.
Show C and D connected with the
boiler, and A and B connected with
the condenser. If D and B are open,
in which direction does the piston
move? Trace the path of the steam
to the piston by heavy arrows. Trace
the path of the steam from the piston
to the condenser by faint arrows.
Show by a diagram what happens
when A and C are open. Valves like
those shown in the diagram are simi-
lar to gas taps. Although valves simi-
lar to this are used in many engines, sliding valves are more
common.

Fig. 223.

280. Slide Valves. — The simplest, earliest, and still much-
used form of valve (especially on locomotives and small en-
gines) is shown in Fig. 224. Draw
the figure as shown, and trace the
path of the steam as it enters at aS,
passes by and around the slide
valve, F, and through the opening,
B, to the piston. The valve, V, is
an open iron box, which works
back and forth in another box that
opens into the cylinder through A
and B, Trace the exhaust from

Fig. 224.

254 PRINCIPLES OF PHT8IC8.

the piston through A, then under the valve F to ^, which
connects with a pipe vertical to the section
V shown.

Lj ^ Draw Fig. 224, omitting the valve, F,

and the piston, and the rods connected with
them. Cut out of paper the outlines of
the valve and piston (Fig. 225). Put these
Fig. 225. in place on the diagram, and place the

valve, (1) so that the steam makes the

piston rod move from A to B-, (2) so that the piston moves

from Bio A', and (3) so that no steam reaches the piston.

281. The Eccentric. — The valve is moved by a form of crank
called an eccentric. Bore a bole through a spool near the edge
(Fig. 226). Drive a nail, SS, through this
hole. Bend one end of a wire, i?, around
the spool. Hold SS in the fingers, and
turn. Let R rest in a groove in a piece
of wood, to guide it. How much does R
move back and forth in one revolution?
Compare this distance with twice the dis-

FIff 226.

tance the hole for SS is bored from the
centre. SS, in an engine, is the shaft, on which are the fly-
wheel and the crank to which the piston is attached.

282. Reversing Gear. — There must be two eccentrics, one set
just opposite to the other. In the first locomotives, designed
by Stephenson, there was a hook at the end of the rod R
(Fig. 226). To reverse, the engine was stopped, R was lifted,
and the hook of the rod from another eccentric, set just oppo-
site, was dropped on the valve rod.

Arrange two spools as in Fig. 227. The wires, R and i?,,
are connected to the ends of a link, LK, which is simply a
link of a chain. Let the loop end, F, of the valve rod slip
over one side of the link, LK, Move F to Lj and revolve 88 \

THERMOD YNAMICS.

255

V takes its motion from Ei. Move V to K-, the motion of
the valve rod is now controlled by R, and the engine runs in
the opposite direction.
Place V half-way be-
tween L and K] the
valve rod is not moved,
both ports are closed
by the valve, and the
engine stops. To make
the apparatus of Fig.
227 exactly similar to
the valve gear of an
engine in use, put the
spools near together; make Ei and E six inches or so long,
and twist them so that LK stands vertical. Locomotives,
and the engines of automobiles and steamboats have reversing
gear. Most other engines do not, and need but one eccentric.

Fig. 227.

iVj Vahe rod

The Governor, or regulator of the speed, of a stationary
engine regulates the speed by opening and closing a valve in
the steam pipe. Fasten a small weight on the middle of a
piece of string. Hold one end of the
string firmly in each hand, and make
the weight swing round rapidly. Notice
the force pulling the hands together.

The weights, WW, Fig. 228, are con-
nected by hinged strips to the shaft, A.
A belt from the engine shaft drives the
grooved pulley, D. A cannot move up
or down. As the speed increases, the
weights, WW, fly out and lift B, which
turns the valve, V, and partially shuts
. off the steam. In large engines, the
governor, different from this in form, is often in the fly-wheel,
and acts by varying the movement of the slide valve.

Rg. 228.

256 PRINCIPLES OF PUYSICS.

284. Expansion. — The most work may be obtained from
steam, especially if of high pressure (100 to 150 pounds to the
s(piai'e inch) by iwlniitting a little to the cylinder for one-fourth
of the stroke and then closing the opening. The steam ex-
pands during the remainder of the stroke, the pressure and
temperature gradually falling as the heat of the steam is turned
into the energy of motion, and the cylinder l)ecomes cooled.
It is often best to let the high pressure steam expand a little
in the cylinder of one engine, and then to drive a larger engine
by the expanded exhaust of the first engine. These two en-
gines, connected together, are known as a compound engine.

By varying the size of valve and the position of the eccen-
trics, the motion of the valves is shortened and steam is cut off
before the end of the stroke. During the remainder of the
stroke the steam expands and escapes finally at low pressure
into the air. On starting a locomotive, notice the sharp puifs
of exhaust steam. There is no expansion. After a minute the
engineer moves the link so that the valve rod is a little way
from the end of the link ; the steam is now used expansively,
and the puffs of escaping steam are less noisy.

285. A Working Model of a Condensing Engine. — The boiler,
7i, Fig. 229, supplies steam under pressure to the engine, E.
The steam pressure is shown by the mercury gauge, (?, and the
temperature of the steam is read by the thermometer, T. The
exhaust from the engine passes into the condenser, O, on which
water (not shown in the figure) is allowed to flow. The
pressure inside (, is less than that outside; the difference in
pressures, as shown by //, is called by steam engineers the
" vacuum." It is only a partial vacuum, in good condensers
being less than \l of a perfect vacuum. The vacuum is shown
by the gauge, 77, and the temperature by T\ The air and con-
densed water are ])nniped from C by the aspirator, A. Discon-
nect the engine at 7", and let the exhaust pass into the air.
Notice the temperature of the exhaust steam. The heat lost

THERMOD YNAMICS.

257

in the engine is in part used up in keeping the metal of the
engine warm, and is in part turned into work.

Connect F with C (Fig. 229), being sure that all joints are
tight. Washers of thick brown paper or rubber rings serve as
packing to make the screw tops air-tight. Keep C cool by run-
ning water on it. Run water from the faucet through the
aspirator pump, A, until a partial vacuum is shown by H. By
the use of the condensers, the back pressure of the atmosphere
(15 pounds to the square inch) is removed ; the steam in C is

Fig 229.

much below 100** C. The steam now does more work in the
engines and is cooled more, as can be seen by reading T'.

The engines in ocean steamers and all of the best large sta-
tionary engines are provided with condensers, because the steam
can do more work when it pushes the piston against a partial
vacuum than when it pushes against the atmospheric pressure.
Ocean steamers must have condensers, because they use the same
fresh water over and over again. Salt water injures boilers.

One cubic inch of water at atmospheric pressure forms seven-
teen hundred cubic inches (about a cubic foot) of steam.

The most common forms of gas meter are double slide valve

268 PRINCIPLES OF PHYSICS.

engines. The pistons are circular disks of metal on the bot-
toms of oil silk bags. The only work done is to move the
meter dial.

286. ITon-condensing Engines. — Locomotive engines and
many small engines have no condensers. Such engines, called
non-condensiiig, can be recognized by the puff of exhaust steam
given into the air as the piston reaches each end of the cylin-
der. How many puffs does a locomotive give for every revo-
lution of the driving wheels ?

287. Compressed Air. — Force air, with a large double valve
bicycle pump, into an engine. Power is transmitted by com-
pressed air through a long pipe, as in signal systems and in
mining. Air in tanks, compressed to 2000 pounds to the
square inch, is used in propelling street cars.

288. Steam Turbines. — The backward and forward move-
ment of the piston and piston-rod jars and shakes the founder
tion of the engines, and the piston cannot well move more than
1200 feet a minute. Parsons and l)e Laval have perfected
forms of engines that are driven by jets of steam striking
against the blades of a wheel. The number of revolutions is
from 3000 to 30,000 a minute, and there is no jar. A small
engine develops an enormous power. A speed of over 40 miles
an hour has been made by a torpedo destroyer driven by
Parsons turbines.

289. Horse-power. — Steam engines first replaced horses
largely for pumping. The first question asked regarding an
engine was. How many horses can it replace ? Watt, after
some test with horses, decided to call the work of one horse
equal to lifting 33,000 pounds one foot in a minute ; that is,
33,000 foot-pounds of work. This, however, is more than an
average horse can do for any length of time, unless strongly
urged.

THERMODYNAMICS. 259

Problems.

1. What horse-power is required to raise a 500-pound bucket of
coal 30 feet a second ?

30 X 60 = 1800 feet a minute. 1800 x 600 = 900,000 foot-pounds.
This divided by 33,000 gives the number of horse- power.

2. How many horse-power can be developed by a waterfall 80 feet
high over which flows 600 cubic feet a minute ?

1 cubic foot of water weighs 62.5 pounds.
600 X 62.5 x80_
33,000
Multiply the result obtained by 75 per cent, the efficiency of a good
water-wheel.

3. What must be the power of an engine to pump 600 gallons of
water an hour, 50 .feet high? (One gallon of water weighs 8.4
pounds.)

4. Make up and solve problems similar to Problems 1-3.

5. Find the amount of water and the height pumped by the nearest
water-works or steam fire-engine, and compute its horse-power.

890. Measttrement of Horse-power. — Suppose S, Fig. 230, is
the shaft of a steam, gas, or hot-air engine, a windmill, or a
water or electric motor, of which we
wish to find the power. A and B

are spring balances at the ends of a ^j^^^-^ob^^ B

string or rope wound one or more ^
times about the shaft. Let the shaft
turn in the direction indicated by the ^ .^

•^ Fig. 230.

arrow. Pull A and B apart till the

engine or motor is doing as much work as it can without slow-
ing down too much. If the pull on B is 1500 g. and on A is
600 g., then the force exerted by the string on the shaft is
900 g. Find how far the surface of the shaft travels in one
minute. Suppose the diameter is f of an inch; the circum-
ference is 3|, or ^, times this, or about 2 inches, one-sixth
of a foot. Hold a revolution counter against the end of S for

260

PRINCIPLES OF PHYSICS.

a minute. If the number of revolutions is 1800, the surface
of the shaft, in one minute, goes J^^^, or 300 feet. Nine
hundred grams is nearly two pounds (1 pound = 454 g.). A
force of 2 pounds exerted for 300 feet = 600 foot-pounds. If
the time is one minute, the horse-power is ^I^qq.

The work is absorbed by the string and shaft and turned
into heat. For larger motors, the string, or band of leather,
is laid over a large pulley, and water is sometimes used to
carry away the heat generated.

291. Amount of Power obtained from Coal. — One pound of
coal in a good boiler turns 10 pounds of water into steam.
The consumption of steam per horse-power per hour varies
from a hundred or more pounds in small engines to eleven in
the best large pumping engines. Ocean steamers use about 15
pounds of water. The best engines turn to motion gnly one-
sixth of the heat of the coal. The best gas engines convert
one-fifth of the heat into useful work.

292. Hot-air Engines. — A steam, gas, or hot-air engine is a
machine for causing the energy of heat to produce motion.

Air or any gas, when heated, expands, if free
to do so (see Exercise 35, page 242). If the
air is confined, the pressure rises. This in-
crease of pressure is made use of in driving
the piston of a hot-air or gas engine.

A hot-air engine, in its simplest form, is
shown in Fig. 231. A fine wire, passing
easily through a hole in a rubber stopper of a
test-tube, is attached to a piston-head or to a
hollow can, T, which does not touch the sides
of the test-tube. The lower part of the test-
tube, A, is heated, and the upper part, B, is
kept cool by loss of heat to the air or water
surrounding that part. The pressure gauge, G, indicates any
change of pressure in AB. Before applying heat, move T up

Fig. 23 I .

THERMO D YNAMIC8.

261

and down. Notice that the slight change of level in the water
or mercury in O is due to the room taken up by the piston-rod
as it is pushed in the test-tube. As T is pushed down, most
of the air in the test-tube is driven up to B. As T is raised,
the air goes down toward A. Heat A, and loosen the stopper
and replace it. Move the transfer piston, T, up and down.
As T is raised, the cold air at B goes down and is heated,
exerts greater pressure, and tries to expand, as is shown by
the level of the liquid in G. When T is lowered, the hot air
moves to By is cooled, contracts, and exerts less pressure.

Problems.

1. Assume that a 34-foot head of water gives 15 pounds' pressure
to the square inch ; what is the difference of pressure due to the
movement of T, Fig. 231, if the level of water in G varies 2 feet?

Ans. A of 15 pounds to the square inch = about .9.

2. If a column of mercury 76 cm. high exerts a pressure of 1000 g.
per square centimeter, what is the difference of pressure in AB^ Fig.
231, as Tis moved, if the mercury in G varies 3 cm. in height?

Ans. /^ X 1000 = 39+ grams per square centimeter.

How the Hot-air Engine Works. —
In place of the pressure gauge, connect a
cylinder, O, Fig 232, in which there is a
piston, P. On moving T to B, the increase
of pressure in AB drives the piston P up,
and the rod /2 by a crank turns the shaft S
and fly-wheel F. On the other end of the
shaft, a crank moves the transfer piston, T,
down to A. The air, driven from A to B,
is cooled, and the pressure falls, and the
pressure of the atmosphere on P helps
to drive it down. Very little power is
used to move the air back and forth be-
tween the hot and cold parts of the tube.

Fig. 232.

262

PRINCIPLES OF PHYSICS.

It is the piston P that does the work, while T merely shifts
the air.

This form of engine, invented by Ericsson (who bailt the
first Matiitor), has been improved, and is mach used for pump-
ing water and running small machinery. The same air is used
over again ; there is no possibility of explosion ; there are no
valves. The engine is started by giving a turn to the fly-wheel
after the fire has been burning a few minutes.

Fig. 233.

Gas Engines. — As the differences of pressure in a hot-
air engine are small, a piston of large size must be used. For
five horse-power and upward, it is best to use fresh changes
of air in the cylinder, and to heat the air by burning or ex-
ploding in it oil or gas. It then becomes a gas engine.
Make a hole in the side of a long tin can by driving in a nail
Select a cork, C, Fig 233, that fits loosely.

I I . Close A with the thumb, remove the cork,

I [^ and holding the tube mouth down, let a fine
jet of hydrogen or coal gas blow into the
mouth of the tube for a few seconds. In-
sert the cork, hold the tube in a horizontal position, and apply
a light at A. The mixture of air and gas bums rapidly (ex-
plodes), and heat generated makes the gases expand.

295. Two-cycle Engines. — In the simplest form of gas
engine (the two-cycle), as the piston, C, Fig. 234, begins its
stroke, a mixture of air
and gas is drawn in at
A. Before the piston has
moved far, the mixture is
lighted by a flame brought
near A, The explosion
drives 0 and turns the
wheel, R As C passes by
Ef the expanded gas escapes,

Fig. 234.

The momentum of the fly-wheel
drives the piston back for another stroke.

THERMODYNAMICS. 263

296. Four-cycle Engines. — In most gas engines, the mixture
of air and gas is drawn in during one stroke (1), compressed
on the return stroke (2), and exploded as the piston starts the
next stroke (3), and on the return (4) the burnt gases are
driven out. As there are four movements, or strokes, of the
piston for one explosion, this is called a four-cycle engine.

Gas engines using gas or the vapor of gasoline are made
from one-half up to one thousand horse-power.

CHAPTER XVIII.
LIGHT. -EEFLEOTION.

297. Nature of Light. — We know that light is not matter,
because it does not fill space. If the shutters and doors of a
room that is full of sunlight are closed, the light is shut out.
Why is it not in the same way shut in ? What does this prove
about the nature of light ? What other facts do you think of
that prove the same thing ?

Though not substance, light has certain very real physical
effects. It not only enables us to see, and so gives us knowl-
edge of color, but it has much to do with the actual creation
and destruction of color. Why is the grass growing under a
log or a stone almost colorless ? Why do housekeepers pull
down the curtains to save the carpets and wall-paper? To
most plants it gives the color of leaves and flowers, and is,
indeed, a very necessity of life to them, as it is also to most
animals. To other forms of vegetable and animal life it is
fatal. Why are sunny rooms more healthful than dark ones ?
Why is not mould found on the roof as often as in the cellar ?

It is generally believed that light is vibration of ether, the
substance that fills space even where there is no air. This
vibration is a series of wave-like motions, much like waves in
water, and travels with great swiftness, at a rate of about
186,000 miles a second. Have you ever noticed any difference
in speed between light and sound ? If there were men on the
North Star who could by any means see the inhabitants of the
United States, they would see us engaged in the beginning
of the Civil War. Why could they not see more recent
events ?

264

LIGHT. — EEFLECTION.

398. Reflection. — On looking in a plane, or flat j mirror,
objects appear much the same as when they are viewed
directly. Stand in front of a mirror j and walk toward it and
then away from it ; notice what the reflection, or image, api^ears
to do. Move the right hand, and notice which hand the image
appears to move, A line stretched from yourself in the direc*
tion of your linage in the mirror, wonld make what angle with
the mirror ? Notice that a line to the image of another person
seema to you to make more of a slant directioo with the mirror,
though the other person ^s image comes to him perpendicularly
from the mirror. Suppose two or more persons draw lines on
the ground pointing to a tree ; the lines, if prolonged, will meet
at the tree.

299. Location of a Point by Sight-lines, — Place a large sheet
of paper flat on the table j draw a line across the centre of the
sheet, and place
the lower edge of
a small mirror on
t h is 1 i ne, as sho wn
in Big. 2:^5. Sup-
port the mirror in
an upright post*
tion, fastening it
by rubber bands
to a block of
wood. Place ^
pin in front of
the mirror, as
shown in the
figure* Wherever you stand in front of the mirror, an image,
or reflection, of the pin is seen in the mirror. Two or more
persona, some distance apart, at Aj B^ and C, for iustanee,
aim at the image of the pin they see in the mirror. To find
where the image is^ lay a ruler at ^j and point it toward the

Fig S35.

266

PBINCIPLES OF PHYSICS.

refleetioiL Draw a line along the edge that points to the reflect
tion of the pm. He move the niler, and look along the lincp
with the eye almost at the level of the paperj and see if tiif
line really points to the image of the pin seen in the mlraji
If not, erase the line^ and try again. In the same way, mM
lines from B and C pointing to the im^e of the pin Lu the
mirror. If the mirror is moved accidentally^ replace it, and be
sure that the lines from A^ B^ and C point as desired,

Kemove the mirror, and continue the lines, /t, B^ and Cy till
they cross. Draw a line from the pin across the line marking
the position of the edge of the mirror, perpendicular to it, and
see if the line passes through the intersection of the lines A,
B, and C How far behind a mirror does the image of a point
appear to be ? ^Vhen the position of the image of the pin cau
be located accurately by this method, repeat the exercise as
follows : —

Exercise 37,

LOCATION OF All IMAGE IK A PLANE MIEEOE.

Apparatui t Plane mirror ; rubber bauds, fagtemtig the mirror iti an upHglit
position to a, block of wood ; largie sheet of paper ; pin. fl

Draw a triangle, ABC^ Fig, 236| in front of the mirror^ Insert ^
pin at B, or place a block of wood, marked with a vertical line, so that

the lower end of
the line touches B.
Sight along a ruler
pointed jit t
image of B,- a;
draw a line along
the edge of the
ruler. The ruler
may be placed in
any position in
front of the mi
ror. Wherever y^
move in front of
rift 335. the mirror you

Lier

LIGHT— REFLECTION, 267

the image of the pin B. Point the ruler, not at B, but at the image
yon see in the glass. Call the line drawn along the edge of the ruler
a sight-line. Remove the ruler, and look along the surface of the
paper, to see if the line really points to the image of the pin in the
mirror. K not, erase the line and make a new trial. Mark the letter
B on all lines that point to the image of B. Of these lines, one may
point perpendicularly to the mirror, and at least two should be at a
considerable slant. Remove the mirror and continue the lines till
they cross. Do they meet in a point ? How far behind the mirror is
this point? How far is B in front of the mirror?

Place the pin, or marked block, at A, and replace the mirror.
Draw lines along the edge of a ruler pointing to the image of A,
making different angles with the mirror, and letter each one of these
sight-lines A, In a like manner draw sigh twines pointing to the
image of a pin at C, Remove the mirror, continue sight-lines Aj and
locate the image of ^. In the same way locate the image of the pin
at C, Connect the images of the points A, B, and C, and compare
the figure in form and size with A BC itself.

Where does the image in a plane mirror appear to be ? If a rod
stands 4 feet in front of a mirror, and you wish to place a second rod
behind the mirror, so that when the mirror is removed the second
rod will look just like the image of the first rod, how large must the
second rod be, and where must it be placed ? Locate a pin at B and
another behind the mirror where you think, from the conclusions of
the experiment, that the image of the first pin must be. Look at the
image, and, without moving the head, remove the mirror.

300. Parallax. — There is another way of locating images,
or points of images, that can be used in this and other experi-
ments. Hold two pencils, one behind the other. Move the
head sideways, back and forth, and notice which pencil moves
the slower, or, in other words, notice which appears to move in
the same direction in which your head moves. From the
window of a moving train the distant hill seems to be going
along slowly in the same direction as the train, while the tele-
graph poles seem to pass swiftly in the opposite direction. If
a tree and a chimney appear to move together, they are close
to one another ; then they are said to have no parallax. But

268 PRINCIPLES OF PHYSICS.

if the tree and the chimney do not seem to move together, as
we move back and forth, they have parallax.

Almost every one has used unconsciously the method of
parallax. Which of two branches of a tree is the nearer?
Walk back and forth and see which moves the faster. If
you have forgotten whether the nearer or the farther object
moves the faster, set the two pencils in line again and find out.
Does a wire touch a tree ? Move about and see if the wire
and the tree appear to move together. Practise till you are
sure you can tell by parallax whether or not two objects are
near together.

301. Location of an Image by Parallax. — Place a pin at ^4,
Fig. 236, and behind the mirror move a long pin, supported
by a piece of cork, till the long pin, seen over the mirror,
moves with the image of the first pin, and seems to stay -with
the image, no matter how you move your head. Mark the
position of the long pin behind the mirror, and compare with
the result obtained by the sight-lines.

Suppose you wish to locate the image of an object or of
three or more points of an object in a plane mirror. Remem-
ber that a point in the image is as far behind the mirror as
that point of the object is in front. From each point of the
object draw a perpendicular to the mirror, and continue the
line behind the mirror, measuring on the line to a point
as far behind as the point in the object is in front of the
mirror.

In this way locate by drawing the image of an arrow, CD^

Fig. 237, in a mirror,

^ C^ — ^D^ ^ IfO"^ ^~/iL ^ -^A placing the arrow

A^f ^ at different distances

from the mirror. Draw

the image of the arrow

GH in the mirror EF. What would be the image of LM in

the mirror IK?

Fig. 237.

LIGHT. — REFLECTION. 269

302. Apparent Positions of Images. — In walking near a
mirror a person sees his own image approach ; in what direc-
tion is he going? A man passing down an avenue sees his
own image apparently coming into the avenue from a cross
street ; how must a mirror be placed in a corner store to give
this illusion ? What apparent effect on the depth of a store
does a rear wall entirely of mirror-glass have? How can a
store be made to look wider?

Stand before a mirror in which you can see your full height
(the glass windows of a laboratory case may do). Let another
person place a bit of paper on the mirror where the image of
your forehead appears to be, and a second bit of paper at the
apparent position of your feet. Measure the distance between
the pieces of paper and compare this with your height. Move
nearer to and farther away from the mirror, to see what effect
distance has upon the height of your image. In case a large
mirror is not available, use a smaller one, and find the smallest
height of mirror in which the whole of your head can be seen.

303. Incident and Reflected Rays. —Let A, Fig 238, be a
point, and / be the image of that point in the mirror, MM.
As light moves in straight

lines, the ray AD (called /'^

the incident ray), after re- /

flection from the mirror, ^ ^

becomes DL (called the re-
flected ray). Compare the
distance AD-\-DL with the
distance IL. Which would
go the greater distance, a
ball thrown from / to L, or
one thrown from A to D
and from D bounced, or reflected, to L ? The image, /, it will
be seen, is apparently as far from L as the light has to go in
its way to the mirror at D, and from D to L. Draw a perpen-

•M

270

PRLSCIPLES OF PHTSICB.

dicular, DX (call it a normal^ — normals are nothing more noi
less than perpendiculars) ; measure the angle, LDN, and com-
jiare it with the angle, ADN. What is the law connecting the
angle of incidence and the angle of reflection ?

Test your conclusion in this way : Arrange the mirror and

paper as in section
2<)9, page 265. Draw
a line, AB, Fig. 239,
at any angle. Draw
a line, BC, as the con-
tinuation of the re-
flection of AB, Mark
the edge of the mir-
ror on the paper.
Draw a perpendicular,
BN. What name has
such a line in physics ?
Cut with a sharp
knife along AB and
BC. Crease the pa^^r at BN, and compare the angle of inci-
dence, ABX, with the angle of reflection, 2^0,

Print a word — ** school,'' for instance — in large letters on
a card. Hold the card toward a mirror ; in the note-book draw
the word as it appears in the mirror. Hold a picture toward
a mirror and describe the image.

Fig. 239.

304. The Brightness of a Reflection depends upon the angle

at which the light strikes the
mirror. Hold a candle over a cup
of water and look almost perpen-
dicularly down at the reflection.
Holding the candle at the same
distance from the cup, but almost
on a level with the water, view the reflection. Decide in which
case the image is the brighter.

F«g. 240.

LIGHT. — REFLECTION.

271

lold a mirror, M^ Fig. 240, vertically near a bright light, L

Fay of sunlight is preferable to a candle). Turn the mirror

Ithe direction of the arrow, and follow the motion of the

lection as the mirror is turned through a right augle (90^)

f the position Mi. Which moves faster, the refieetion or the

lirror? In turning the mirror through a right angle, what

igle does the rejected ray go through ?

305, Location of an Image by Shadows. — Arrange a mirror as
|m section 209, page 2t>5, using a caudle for the object. Mark
the edge of the mirror and the position of the candle on the
paper on which they rest. At any points some distance apart,
as A am] By Fig.
241, place tall
pins* as nearly
vertical as possi-
ble. Look at the
shadows the pin
at B appears to
cast- One, which
may be called
the direct shadow^
goes to the mir-
ror and is re-
flected in the path
BCD* Do not consider this at all» but trace on paper the other
shadow, BEy which appears to be caused by a candle you see
in the mirror. Trace a similar shadow for the pin at A.
Kemove the mirror, and continue the lines till they meet behind
tbe mirror. Place a candle on this point* and notice if the
real candle behind the mirror line casta the same shadow lines
that tlie image candle cast before the mirror was removed.

Fif. 341.

306, Reflectioua in Two Mirrors. — Lay two pieces- of mirror
I OD a table, end to end. Slowly lift the outer ends. How many

272

PRINCIPLES OF PHYSICS.

reflections of the face can be seen. Replace the mirrors, and
lower or raise them slightly, until the image of a pencil held
in various positions over and nearly parallel to the mirrors does
not look bent at the edge where the two pieces of mirror join.
LiH)k along the surface of the mirrors, and see if they form, as
it were, one flat mirror.

Exercise 38.

MUtSOSS AT BIGHT ANGLES.

Apparatus: Two mirrors, each arranged on a block of wood, as in Exer-
cise l^f and set at right angles on a sheet of paper, as shown in Fig. 242.

Draw an arrow, A B, Fig. 242, between the mirrors. Place a pin at
the head of the arrow, and by three sight-lines locate an image of

the pin behind M.
Then, in the same
way, locate another
image behind My
Locate a third im-
age somewhere be-
hind both. Draw
lines at the edges
of the mirrors. Put
the pin at the other
end of the arrow,
and locate the three

Fig 242

. images. Having the
position of the ends of the arrow, draw the three images of the
arrow. The record of the exercise can be made as follows : —

Lay down a sheet of paper in the note-book, with one corner near
the binding. Place two mirrors, M and 3/j, on the edges at this
corner, letting the mirrors touch ; remove the paper, and mark the
edge of the mirrors. On this diagram make the record of this exercise.

Write a word on a card. Hold it toward M, and describe the
reflection; then hold it toward 3/p and describe the reflection.
Finally, hold the card in the position of the arrow AB. The first
two images were reversed, being reflected once only. The third image
looks like the writing itself, and is reflected twice, first from one

LIGHT, — REFLECTION. 273

irror and then from the other. Push a card over the face of the

irror M, toward the intersection of the mirrors. What images are

>vered up when the card is entirely in front oi Ml When only

artly in front of M ? Try the same with My The third image is

eflected from one mirror to the other, and then to the eye.

Replace the arrow, ^Z^, by a cork or spool, colored red on one side,
blue on the other. (Instead of being colored, the cork may be marked
A on one side and B on the other.) Let the red side face one mirror
and the blue side the other. Bring the mirrors a little nearer together,
making the angle less than a right angle. What does the third image
appear to do ? Make the angle 60% and count the images ; then 30°.
Does the angle bear any relation to the number of images ? Notice
that the images seen in one mirror are red, then blue, and so on; If
the red face is toward Af , the first image in M is red ; the next image
is blue, and, as the blue side faces away from M, the light from the
blue sfde must be reflected fiirst from the other mirror. My

How many images can you see in two large mirrors that are par-
allel? Hold a card, on which the word " on " is written, between the
mirrors, placed at different angles, and notice which images are
reversed and which are direct, that is, which images spell *' on,'* and
which spell "no."

307. Images in Parallel Mirrors. — Keep in mind that an
image in a plane mirror appears as far away from the observer
as the light fi*om the object

has to travel before reach- . P \

ing the eye, and find the I j

position of images of an !

object between parallel mir- pj^ 243 ^

rors. M and My, Fig. 243,

are parallel mirrors 10 feet apart. Four feet from M stands
a card, O, with the word " Moon " printed in red on the side
toward 3f, and "Moon" printed in blue on the other side.
The first image in 3f is 4 feet behind 3f ; the first image in
Ml is 6 feet behind My, The second image in M is blue, and
is not reversed. The light travels from C to 3fi 6 feet, and
from Jlfi to Jf 10 feet more (as in Fig. 244, I) before reflectix)n

274 PRINCIPLES OF PHT8IC8.

\^h^

to the observer. The image, therefore, appears 10 -h 6, or 16,
feet behind M. In the same way, the light from C goes to M

4 feet, and thence,
after reflection, 10
feet to Ml (Fig. 244,
II), before it is re-
j^ /- Jf, If n. M, fle^jted to the eye.

"**^^' The second image

behind Mi appears 14 feet behind the mirror Jfj. Locate two
more images behind each mirror. The images in M, including
the first, are; respectively, 4 feet, 16 feet, 24 feet, and 36 feet
behind the mirror; those in Mi are, respectively, 6 feet, 14 feet,
26 feet, and 34 feet behind the mirror.

A man stands 10 feet away from and facing a mirror; a
second mirror is 20 feet behind him, and enough out of the
exact parallel so that he can see several images of himself.
How far behind the mirrors do his reflections appear ? Find
three in each mirror. In which do the image of the man face
him? Account for the fact that as a man walks toward a
mirror his image approaches him.

Place a photograph halfway between parallel mirrors, 4
feet apart, facing one of them; locate four images of the
picture side of the photograph. If two parallel sides of a
room 24 feet wide are mirrors, and an arc light is hung 8 feet
from one wall, where do the nearest two images seen in each
mirror appear to be ?

308. Kaleidoscope. — Place two mirrors facing each other and
meeting at an angle of 60°. Push a pencil between them. Put
sev(iral coins, beads, or bits of colored paper between them,
and note the appearance of the reflections. This forms a
kaleidoscope, the construction of which is somewhat like Fig.
245. The mirrors meet at an angle of 60° (one-sixth of a
circumference), or at an angle that is one-fifth, one-seventh,
or any other even division of a circle. The end of a kaleido-

IIGBT. — REFLECTION.

276

Fig MS.

scope is made of two layers of glass, with beads between them j
the outer layer is usually of ground glass. A coveriug is
wrapped araiind the
mirrors J coveriug the
open space between
the edges of the mir-
rors. The observer
looks iu at the open
end. On turning the
apparatus the beads
fall into different ar-
rangements, which
are reflected as sym-
metrical figures.

Place three mirrors as in Fig. 246, facing inward. Hold

theiu in place by rubber bandsj and examine the reflections of

a bright object at the end B. Looking

in at A^ notice that a set of images is

formed in each corner. What is the

angle of the mirrors ? A triangular

Fjg- 245. 60° prism of the form AB is covered

with paper, except the ends. On the

end B make a figure or letter with ink. Holding the prism so

that tlie end B is well lighted, look in at the end A^ to the

three corners of B, in turn. The inner surfaces of the glass

sides of the prism act as mirrors, and the light is said to be

internally reflected. It will be noticed that the image farthest

from the object is faintest. This is because the last image

has been reflected several times, and has lost light at each

reflection.

CHAPTER XIX.

UOHT. — BEFRAOnOlf .

309. Refraction by Water. — Hold a pointer or a pencil in a
jar of water, perpendicular to the surface. Look down througli
the water at the part of, the pencil under water. Slant the
pencil a little ; then more and more. Notice that it looks as

if it were bent or broken at the sur-
^^^ face of the water.
^ ^^' In a pan, close to one side, put a

\^' bright coin, O, Fig. 247. Stand in

^ ""^ such a position that looking along

Pj^ 247. ^^ *^® ^^^^ ^s barely out of sight.

Keep the head in the same position
while some one pours water into the dish until the coin be-
comes visible. Obviously, the coin is not moved. To see
where the change of direction of the light from the coin
occurs, place in a battery jar. Fig. 248, an
apparatus consisting of a vertical strip of
board nailed to a heavy cross-piece, which
rests on the edge of the jar. At B, which I
is about a centimeter below the lower edge
of the cross-piece, with a double-pointed
tack fasten a piece of wire solder, ABC.
Straighten the part AB; fasten A to the Fig. 248.

board. Fill the jar with water to B. Look
down from such a position that AB appears end on, or as a
point only. Bend BC till AB and BC look like one straight
line. Mark roughly the water-line, and remove the apparatus
from the jar. The light travels in a straight line in water or
in air ; but in passing from water to air the direction changes.

276

^ LIGHT, —REFRACTION^

Repeat the experiment once or twice^ and in one trial let the
part AB have a eonsiderable slant (as in Fig. 248)^ 4o° or more
f Tom the perpendicular. The more the ray of light repre-
sented by AB slants in water, the more the ray is bent on
leaving the water.

Exercise 39,

INDEX OF EEFBACnOlV OF WATEK.

Appar^tm: Battery jar; pins; ahBet of paper ; centj meter ml©; thin board
nailed to a heavy crosa-piece of wood.

Stick a bright pin. A, Fig, 249, near the lower corner of the board,
and put the board in the battery jar. Fill the jar nearly to the top
with water, and mark the
water-line by pin a B and C.
Add or take out water, or
tip the jar by placing a few
thicknesses of card under the
bcjttotti^ till B and C are wet,
but not covered by the water*
Look into the jar on a level
with the water. When prop-
erly adjusted, the water just
shiiit^s up on each side of
the pin, without covering the
topt as in Fig. 250, where
the pin B is shown touching
the surface of the water^
W W. Standing on one side,
near C (Fig. 210), look down
into the jar in a slanting
tlirection at the pin, A.
Keeping tlie head steady, put
a pin (Z>) in the board a little abo^e the water*

F.g. J4«

If thia pin does not
eover the iniage of ^4, move the head un-
W til it does. Put another pin. £, exactly
■ in line with D and the image of .4.
Remove the board, wipe off the water,
and hammer in the pins tightly; see that they are straight. Lay a

278

PBISCIPLES OF fBTSlCa.

Fif. 251.

sheet of unsind white p*per oTer ihm pins. Break the paper when

the piDS touch, and pre^s it down to Ihe bovd. Lay a ruler cloee to

the pins BC, and draw a line with a sharp

pencil, held vertkaUy (Fig. 251). This

line is the water surface. From the water

surface the light went in a straight line to

D and B- Lflf a ruler against D and £,

and draw a line from E through D to the

water-line at F. The bending of the light

took place on leaving the water at F\ bat

in the water, from AtoFy the path of the

light from ^4 was straight. Draw FA.

The path of light from the pin .-1 was to F, and thence along the line

through D and E to the eye of the obaerver.

Remove the paper and lay it flat on the table. Erect a normal,

FNy Fig. 252. This is a line perpendicular to the water surface.

With F as a centre, and any radius, draw a circle. From S draw a

perpendicular to the normal, and an-
other from I to K. Measure SH and

IK, DiYide SH by IK.

Repeat the exercise, looking into

the water at different angles. In one

case have FE nearly horizonti^. How

for

Fig. 252.

near alike are the values of -—

different slants ? The number is a con-
stant, and is called the inde^ of refrac-
tion of water. The abbro?iation for
index of refraction is n.

Instead of drawing a circle in Fig.
252, it is sufficient to measure off from F equal lengths on the ray AF
in water and on the rays FE in air. Place the corner of a strip of
paper at F, and lay the edge along FE, Choosing
some convenient length, the longer the better,
mark the point S on the drawing and on the strip
of paper. Then, on FA lay off the same length,
/F. To avoid confusion, it may be well to erasf
so much of the lines FE and FA as project beyond
8 and 7. For drawing lines, use a hard pencQi

Fig. 253.

LIGHT. — REFRACTION.

279

cut to a wide, sharp edge, shaped like a chisel. Hold the pencil
vertical, the flat side of the point against the ruler.

To obtain a right angle for use in drawing perpendiculars, fold a
sheet of paper, ABC, Fig. 253, with the crease at B. Make the
edge» AB, coincide with BC. The comer JB is a right angle.

810. Effect of Refraction on Vision. — If a man at E, Fig.
261, looked at a fish in the water at A, the fish would appear
to be in the line, EF, prolonged below the surface. How should
a spear be thxown to strike the fish ? In what position should
the fish be so that such a change of direction need not be
made? Point a long needle perpendicular to the surface of
water in a dish at an object in the bottom; push the needle
down and see if the aim was good. A fish at A sees the fish-
erman at jE? as if he were somewhere in the line AF, extended
above the water.

811. Apparent Depth of Water. — Rule a card (Ay Fig. 254) with
heavy lines, 3 mm. apart. Lower it into a jar of water. Look
into the water almost vertically,

and notice the apparent shorten-
ing of the card and the crowding
together of the lines. Although
an object, viewed by looking
straight down into the water, does
not appear bent sideways appre-
ciably, yet it looks much short-
ened. The bottom of a vessel

containing water appears to be nearer the surface than does
the bottom of an empty vessel. To one looking at a pond
some distance away, the shoaling effect is much greater than
from a nearer point of view, and the bottom of the pond
appears but very little below the surface. Some distance
away from the shore the water may be deeper than near the
shore, and yet look shallower.
Wind paper around the jar (Fig. 254). With the head a

*=rt

Fig. 254.

280

PRINCIPLES OF PHYSICS.

conTcnient distance from the jar, look in a direction nearly
parallel to the surface of the water, and pass the card, ^, in
and out of the water. Repeat the experiment, using a card
ruled like B.

Fig 255.

312. Critical Angle. — A ray of light that enters or leaves

the surface of water in a perpendicular, or normal, direction is

not bent. The ray, NF, Fig. 255,

would continue as FK after entering

the water. The greater the angle

that the ray makes with the normal

FK, the more it will be refracted on

leaving the water. This holds true

up to a certain angle, which is the

largest that a ray can make with the

normal and still pass out of the liquid.

A i-ay (LF) striking the surface at

this angle is refracted so as just to skim the surface (as FC).

The following exercise determines the value of this angle for

water.

Eixercise 40.

CRITICAL ANGLE OF WATER.

Apparatus : Battery jar ; pan or dish in which the jar may stand ; candle ;
metal or wooden screen ; sheet of metal, to cover about three-quarters of
the diameter of the jar. Make the jar as nearly level as possible, and
partly cover it with the metal, as shown in Fig. 256, bending the metal at
F, so as to come about a millimeter below the surface of the water. This
prevents the upward curve in the surface of the water at the edge of the
cover.

Fill the jar with water and set it
in the pan. Place the screen, H,
so it will reach exactly to the top of
the jar. Place the lighted candle,
C, between H and the jar, a little
to one side. Wet a piece of paper,
half as large as a postage-stamp,
and place it in the position /. Look

Fig. 256.

LIGHT. — REFRACTION. 281

down through the water near F, and see /. Slide the paper, a little at
a time, up toward the position L, and lower the head so that finally the
line of sight is almost horizontal from the eye to F. Adjust the paper
at L so that its lower edge only can be clearly seen. Place a wet piece
of paper at /, and try to see it by looking in at any angle through the
water near F. The lower edge of L and any point below can be seen.

Measure MF, from the edge of the jar to F, and ML, from M to the
lower edge of the paper at L, Draw a line, MC, Fig. 257, and lay off
the length, MF, on it. Lay a sheet of paper
with its edge to MC and its corner at M,
and draw a pei-pendicular, ML, making
ML the distance measured from M to L
on the side of the jar. Draw a perpen-
dicular, a normal, FN; draw FL. The
angle, a, Fig. 257, is the greatest angle a
ray in water can make with the perpen- -j 257

dicular and yet escape from the water.

How is the ray, iVF, refracted? How is a ray from any point
between L and N refracted at F?

As any ray from / to F, Fig. 257, cannot pass out of the water, the
angle, LFN, is called the critical angle of water. Measure the angle
with a protractor. For another method of measuring the angle, see
Appendix, page 536. To see what becomes of a ray striking the
surface of the water at an angle greater than the critical angle,
remove H and the caudle, and look upward at the surface. Move ./,
and see if the reflection moves. Replace / by the candle, and see
it reflected from the surface near F.

As the light from any position between M and L, Fig. 257, cannot
pass out of the water, all the light practically is reflected. This is
called the total reflection.

Light from / is partly reflected. Light from a candle at / is seen
by looking up in about the direction of H, and is partly refracted, for
a bright piece of wet paper at / is seen by looking down into the jar.
Of course, where the light is partly reflected and partly refracted,
neither image can be as bright as one totally reflected. It will be
noticed, in looking down through the surface of the water, that / is
brighter than L, since, as the critical angle is approached, more and
more light is reflected back into the water, and less is refracted and
leaves the water.

282 PRINCIPLES OF PHYSICS.

813. Velocity of Light through Space. — The moons of Jupiter
were noticed, 200 years ago, to pass behind the planet once in
42 hours 28 minutes 36 seconds, when the earth was nearest
the planet. As the earth in revolving around the sun went
away from Jupiter, the time for one revolution of Jupiter's
moon increased. The difference, about 16^ minutes, is the
time light takes to go a distance equal to the diameter of the
earth's orbit. The difference between the shortest and longest
distance from the corner of a building to a point on a merry-
go-round is equal to the diameter of the circle in which the
point goes. The distance across the earth's orbit is about
186,000,000 miles. How fast does light go in a minute ? in a
second ?

314. The Ether. — There can be no air or other gas for a
large portion of the distance from the earth to any heavenly
body. Yet the heat and light of the sun reach the earth.
They pass through a vacuum. Witness the heat and light
from the filament of an incandescent lamp passing through
the inside of the globe, which is exhausted so that only one-
millionth of the original air remains. That which transmits
light can have almost no weight or mass, and must be very
elastic. Exactly what it is that transmits light across space
or through a vacuum is not known. It is called the ether,

315. Velocity of Light in Dense Substances. — Light travels
a kittle slower in air than it does in space where there is no
air. In more dense bodies — water, glass, etc. — light travels
much more slowly, and for this reason it is refracted.

316. Why Light is Bent or Refracted. — A company of soldiers
always marches straight ahead ; that is, at right angles to the
line of front. Let AB, Fig. 258, represent a company of men
marching on a level field, in the direction indicated by the
arrowheads. Below EF the ground is rough, and the rate, or

LIGHT. — REFRACTION.

288

velocity, at which they can go is reduced. While the man at
C is walking slowly over the rough ground to G, the man at
D goes at full speed to H, OK
is the direction the company now
marches — a line which is more
nearly perpendicular to EF than
was the original direction. If the
company march in the opposite
direction, after leaving the rough
ground they would go in the direc-
tion CA, or at a greater angle with
the perpendicular. Now, imagine
AB is the front of a wave of light

moving rapidly in air. In a liquid or solid where the velocity
is less, the path is bent, or refracted, to a direction more
nearly perpendicular to the refracting surface. Remember
that light entering the surface of a more dense medium is bent
toward the perpendicular (normal), and on leaving is bent from
the perpendicular.

317. Angles of Incidence and Refraction. — Calling the index
of refraction of water ^, or 1.33, draw the path of a ray strik-
ing the surface in air at 45®. An
angle of 45® is easily drawn by
folding a sheet of paper, starting
the crease at a corner, and making
the adjacent edges meet. Draw
CF, Fig. 259, making the angle
NFC=:45\ This we will call
the angle of incidence, i. With
i^ as a centre, draw a circle, or
such portions of a circle as are
shown in Fig. 259. AB repre-
sents the water surface. Draw
CD perpendicular to NF, Divide OD into four parts. On

284 PRINCIPLES OF PHYSICS.

the lower arc of the circle shown in Fig. 259, find the point,
H, from which a perpendicular drawn to FM is equal to three
of the parts of CD. Draw FH, the ray after refraction. Call
the a,ngle, HFEy the angle of refraction, r.

Problems.

1. Find, by drawing, the direction of the refracted ray in water,
when the incident ray in air is 30° from the normal ^ ; 60° from the
normal ; almost 90° from the normal.

2. Assume the incident ray is 90° from the normal ; it will then
be BF, in Fig. 259. In this case, BF is to be divided into four parts,
and three of them laid off below from the normal to the circle. What
name can be given to the angle r in this problem ?

3. If the ray in water, HF, Fig. 259, makes an angle of 30° with
the normal, find the direction of the ray in air. Make r = 30°.
Divide HE into three parts, and find what perpendicular line from
the normal, as DC, is four times as long as one of these parts.

4. Try to trace a ray in water when r = 60°, and show that the
construction is impossible. What happens to the ray?

5. Can a ray making in water an angle r = 45° be refracted and
leave the water? Construct the diagram. In this problem the angle
r is very nearly what angle ?

318. The Effect of Glass upon Light may be first studied with
a piece of plate glass. This may be 10 cm. by 7.5 cm. by .7 cm.,
with at least one edge ground straight and polished. One
short edge may be left rough ground. Lay the glass flat on a
printed page and tilt it, raising first one edge and then another.
Stand the glass, edge down ; look through the upper edge, and
tilt the end. Which moves the image most out of place, a
thin piece of glass or a thick piece ? Hold the plate 16 or
20cm. from the face; look through at a book on the table,
and tilt the plate in various directions. Hold a pencil behind

1 Bejpnning at a corner of a sheet of paper, fold over the edge until the
right angle is divided into three equal parts. One of these is 30?; two, 60°.

LIGHT. — REFRACTION.

285

tine plate, and look toward the plate in a slanting direction.
Show, by a drawing, how the pencil looks. Look at the pencil
tbrough the edge of the glass. In what position does the
pencil look unbroken? Does a ruler aimed in a slanting
direction through a thick glass window really point at a
mark?

The index of refraction of glass is found by a method simi-
lar to that for water.

Exercise 41.

INDEX OF BEFBAGTION OF GLASS.

Apparatus : Glass plate ; sheet of paper ; pins.

Lay the glass plate, G, Fig. 260, on the sheet of paper. Place a
pin at A J or, hetter, make a mark with black or red ink at A, Using
the pin, look through the edge, DE,
and (keeping the head a foot away
from DE) move till the pin, seen
over the glass, is directly in line with
the part of the pin seen through the
glass. Move the head slowly toward
E, and, when the image seen through
the glass has moved a considerable
distance, place another pin at 5, cov-
ering the image of the pin A. B
should be well down toward E,

Move the head a little, right and left, and notice the image of A
move back and forth past the pin B. It is well to place a book or
block on (?, to hide the part of the pin, A, that projects above the
plate. Hold the head so that B covers the image of A , and place a
third pin at C, covering both ; that is, the pin C alone is seen, because
B and the image of A are exactly behind C and are hidden by it.
With a sharp pencil draw a line on the paper along the edge DE ;
make a little circle around each of the pins, A, B, and C, and remove
the pins and plate glass. Where the plate was, write the word " glass "
faintly in large letters.

Using the corner of a sheet of paper, draw the perpendicular, or
normal, BN, Fig. 261. Lay the sheet of paper used for a square with

Fig, 260.

286

PRINCIPLES OF PHYSICS.

one edge on BE and with the corner at B, Draw along the edge,
extending the line NB to J/. With jB as a centre, and any radius,

the longer the better, draw either a
whole circle or the portions shown
in Fig. 261. Draw GH and FK per-
peudicular to iVAf. Measure GH
and FK, and divide FA' by GH,
The quotient is the index of refrac-
tion of the glass.

The setting of B and C (Fig. 260)
to cover the image of ^4 is made
more exact if a colored ink-mark
is made at Ay instead of using the
pin.

Repeat, placing the pin By Fig. 260, at different distances from E,
Perform the experiment once with B almost at E,
Compare the indices of refraction obtained at
different angles.

See what effect, if any, a greater length of glass
has on the index of refraction. To do this, put
the pin or ink-mark on one end, and use the other
end to look through. If one edge {LEy Fig. 262) is rough, an ink-
mark. Ay on that edge is seen perfectly through the clear edge RD.

Fig. 26

L
A

nz\.

Fig. 262.

319. Variation of Index of Refraction. — Crown glass bends a
ray of light less — that is, has a smaller index of refraction —
than glass made with lead, known as flint glass. Lead glass
is denser. With different varieties of glass the index of refrac-
tion varies from about 1.5 to 1.7 The index of refraction of
the diamond is nearly 2.5.

The index of refraction of glass can
be found by the method described by
using any piece of glass (of course, a
thick piece is best), if one edge only is
straight and fairly clear. A piece of an
old plate glass window may be tried. So
long as the edge DE, Fig. 263; is as good

LIGHT. — REFRACTION. 287

as can be cut with a diamond, the irregularity of the remainder
is of no consequence. Place a pin at A^ or make a mark with
ink, and proceed to locate the pins B and C, as before.

Problems.

1. Construct the path of a ray of light in glass (index of refrac-
tion = 1.5), when the incident ray in air makes an angle of 45° with
the normal.

The same construction holds as in Fig. 259, page 283, excepting
that the index of refraction of glass is 1.5, or |. DC, therefore, must
be divided into three parts, and a line equal to two of them laid off
from the normal to cut the circle, like HE.

2. Construct the refracted ray in glass, when the ray in air makes
an angle of 30° with the normal ; 60° with the normal ; almost 90°
with the normal.

3. Let the angle of incidence in air be 90°. Divide FK, Fig. 261,
into three parts, and lay off GH equal to two of these parts. What
name can be given to this angle of refraction? Is the critical angle of
glass smaller or larger than that of water ?

4. The index of refraction of the diamond is 2.5 or more. Make a
diagram showing the path of the ray in the diamond, if the incident
ray in air is 45°; 30°; 60°; almost 90°; 90°. The index of refraction
is conveniently written |.

5. Make a diagram showing the path of rays in the diamond which
strike the surface, making an angle of 15° with the normal; making
an angle of 30° with the normal.

6. What is the critical angle of the diamond ? Measure the angle
with a protractor in the last diagram of Problem 4, or compute its
value as in Appendix, page 536.

7. Find the path of a ray in air, which in glass makes an angle of
30° with the normal ; 15°. (To get 15°, fold in halves a piece of paper
cut to an angle of 30°.)

8. Try to find the path of a ray in air if the ray in glass makes
45° with the normal ; 60° with the normal. Which of these is totally
reflected ?

iS8

PRiyCIPLES OF PHYSICS.

SMK CoHiparison of the Refraction of a Liquid and of Glass.—
Half fill with water, with water
and oil, or with bisulphide of car-
bon, a flat-sided bottle of the same
width as the glass plate of section
318, page 284. Lay the bottle on
the glass plate, as in Fig. 264^ and
look at the pin, P, from different
positions, through the liquid and
the glass plate at the same time.
Determine which has the greater
^ * '^ index of refraction.

Exercise 42.

THS CRITICAL ANGLE OF GLASS.

Af^imrMrudt ; A ^Iass pl^te, with one edge groand ; a narrow strip of label, or
Uutoru slide binder, fixed on the glass as shown in Fig. 265.

Stiiud ftioiujr n window, and look into the edge of the plate, just
l^ikit tho UlvU towani the corner of the opposite long edge and the
jjixnxnd iHlgi* ( Fijj.
*.V»C^V Notiiv that
tho i»\nor suvfjui^ oi
tho jjnnxnd jjliu^s tHlg\»
KH>ks dark. Turn
tho plato slowly, Si>
as to UH>k nion* alonv:
tho odj;:\\ 1U\ Fiij.
LHUk in tho dilution
of tho arrow. Tho
odi:^^ liH>ks briijht
from C up to the
point J", when* the
imago of tho corner
L is stvn. Move the

Fig. 265.

sharp iwint of a pencil along the edge from C till it just enters the
image of the dark corner, L. The pencil will be somewhere near x.
Make a mark on the label at this point. Lay the plate on the note-

N- — -^

LIOffT. — REFRACTION. 289

book. Mark the ontline, and letter as in the figure. Draw a line

from Z. to X. At x erect Nx perpendicular to BC, In ^ ^

the angle, LxN, write : '* This is the greatest angle a

ray can make with the perpendicular to the surface of

the glass and yet be refracted and come out. This is

the critical angle.** Measure the angle by a protractor,

or calculate its value, as in Appendix, page 536.

The critical angle of ordinary glass is 42^°; it is
less for the denser kinds. Rg. 266.

321. Total Internal Reflection. — Cut out a piece of colored or
printed paper the size of the glass plate used in Exercise 41,
page 285. Lay the plate on the paper. Exactly cover the
plate with another piece of paper. Look in at any edge
of the glass, at an angle of 30° from the paper. Can the
colore'd paper be seen ? Move a pencil close to the opposite

edge. The pencil is seen reflected
in the lower inner surface of the
plate by a person looking in at
A, Fig. 267. The colored paper
underneath the glass is invisible,
because light, entering from under-
neath, is refracted, and, if it strikes the edge toward A at all, it
does so at an angle greater than the critical angle and is totally
reflected away from the observer ; for, on removing the paper
on top, and looking down through the top side, the colored
paper can be seen reflected directly through the glass or in the
inner sides of the edges.

Remove the paper from underneath the glass. Slide the paper
up to the edge next P, and look down toward P on a slant
through the top. Notice that the paper is invisible. Slide
it under the edge, and then it is seen double, — first, through
the glass directly, and second, reflected from the inner surface
of the edge.

322. Internal Reflection in a Prism. — ^BC, Fig. 268, is a
glass prism having a right angle at B. The ray 1, in striking

■

290 PRINCIPLES OF PHYSICS.

the surface, AC, perpendicularly, is not bent, and on reaching
AB is totally reflected, because the angle of incidence is 45®.

The ray on reaching BC is
again totally reflected, and
passes out of the glass in the
g opposite direction to which it
entered. Ray 2 is reflected
in the same manner. What
^ happens to the image in this
experiment ? With the excep-
^C tion of a small amount of light

Fig. 268. lost by reflection as the rays

enter the prism, and of a still
smaller amount absorbed by the glass, the whole of the light
is reflected. A right-angled prism is for this reason superior
to a silvered mirror ; and further, the image made by a
silvered mirror is somewhat indistinct, as can be seen by the
following experiment.

323. Reflections from the Surfaces of a Plane Mirror. — Hold a
pencil to the surface of a glass plate, and try to see one reflec-
tion from the surface, and another from
the inner surface. Do the same with a %^ / ^ /i

thick plate mirror; no light now passes

through the glass. The first image, 1, Fig. \
269, is faint, as only a little light is re-

Fig. 269,

fleeted from the surface of the glass. No. ^
is bright, being reflected from the silvering on the back of the
mirror. All of the light does not escape at 2, for a little is
reflected back by the inner surface to the silvered surface,
where it is reflected and leaves as No. S. A part of this is
reflected back and gives rise, on leaving, to a fourth image, etc.
Each successive image becomes fainter, and the fourth, fifth,
sixth, and so on, are usually not bright enough to be seen.
For accurate work, a mirror as shown in Fig. 269 is entirely

LIGHT. — EEFBACTION.

291

onsuited, because of the number of reflections ; while a totally
reflecting prism (Fig. 268) gives but one image at full brilliancy.

324. Reflections from the Inner Surfaces of a Glass Plate. — Mark
a letter A on the ground edge of the plate glass used in the
experiment in section 318, page
284. Look in the opposite edge,
in the direction of the arrow. Fig.
270. Notice the images of A
totally reflected from the inner
surface of the sides. Tip the
plate, and notice how many reflec-
tions can be seen. Why are some
of them upside down? (Com-
pare section 307, page 273.) The last images, seen by tipping
the plate considerably, are faint, because they have been
reflected many times, criss-cross, from one side to the other,
and have gone through a greater thickness of glass. Make a
diagram showing the appearance of the reflections.

Fig. 270.

325. Internal Reflection in a Glass Rod. — If a straight piece of
glass tubing or rod and a curved piece are each heated at one
end (at A and C, Fig. 271), in a non-lumi-
^^ nous Bunsen flame, the sides will not be
illuminated, but the ends, B and D, will
be bright from the light that travels, by
total internal reflection, from the red-hot
^ ends. In place of being heated, A and C
F»g. 271. ^^y ^® ^^^^ close to a bright light, shield-

ing the eyes from the light by the hand
Notice the light in B and D. Can any be

grasping the rod.
seen in the sides ?

CD is a form used to light an object under the microscope.
The light at C is kept entirely from the observer, except what
comes out at Z>.

2K PRISCIPLS8 OF PHT8IC8.

SK. Ite A9f^ of iBtenud Reflection. — The critical angle of
c.As> is 42t^ or lessL A raj of light in glass striking the
$..;rfA^ie 43 a:iv greAt^er angle is totally reflected. Set a right-
aagled prism, ABC, Fig. 272, on the note-
book. Mark the outline of the prism.
On the face of the prism, AC, near the
paper, make an ink mark, Z>, and con-
tinue the mark down to the paper. Lay
a ruler on the paper, and, keeping the
edge of the ruler perpendicular to AB^
Ig more it till it points at the ink-mark, D.
Draw XE along the edge of the ruler.
See if this line really points toward D.
lA\>k in :.he i^ide Bi\ The line XE is seen reflected from the
ir.r.oT fAoo of .10. l>raw a line, HF, pointing at the reflection.
HF ^x\a :V.e n^rieotion should appear to be in one straight line.
Kor.iovo tViO prism. Continue XE. It will pass through D,
lxv;u;se XK ontors the glass perpendicularly and is not re-
fnu u\i or Ivut. ED strikes the inner face of AC at an angle
of 4o\ This is irroater than the critical angle. The ray ED
is thon^fort^ totally reflected to F. Since DF is perpendicular
to 1K\ the ray does not suffer refraction, but continues in the
same straijjht line to //,

To prove that the ray ED is totally reflected, replace the
prism, and, Kx^king in the face ACy try to see NE or FH.
riaiv a bUx^k on each side of XE so that the light from N
can go only in the direction XE. Can XE be seen by looking
in any direction in the side AC f If the ray of light XE does
not come out at all from the surface of AC, it must be totally
reflected. Holding the prism with its face AB in front of a
printed page, look in at the face BC. Is the image reversed
or inverted ? Is the image bright ? All the light entering
the prism perpendicularly to the surface AB is totally reflected.
A little light is lost by reflection from the surface AB, and a
little from absorption by the glass. Like any other mirror.

LIGHT. — REFRACTION,

293

the inner surface of AG reverses any picture, making right
appear left and left appear right. The reversion of the image
is often used in the preparation of illustrations by photography.
The image that is formed by reflection in a right-angled prism
is entirely free from any color fringes. Hold the edge B or
the face AC toward the eye. Objects seen through the prism
are tinged on the edges by the colors of the spectrum.

B«

Exercise 43.

LAW OP INTEBNAL BEPLECTION.

Apparatus: The glass plate used in section 318, page 284. On the clear edge
make a fine mark with red ink {A^ Fig. 273) ; on one of the long edges
make a black mark {B)t about one or two centimeters from the corner.

Lay the plate down or hold it in the hand, and look in the edge
at C; notice the red mark, A, the black mark, B, seen through the
plate, and the reflection of B in the edge. Move the
head or turn the plate till the reflection of B covers A

A, and make a mark at C that will hide both. Lay
the plate on paper, draw a line along the edge on
which A is, and locate the points, A, B, and C. Con-
nect A and B, and A and C. Draw a perpendicular at
A, and see how the angle of incidence compares with Fig. 273.
the angle of reflection.

327. Shoaling Effect of Water by Par-
allax.— The bottom of a tank or pond
looks nearer the top than it really is.
The place at which the bottom appears to
be can be located by the method of paral-
lax. Ay Fig. 274, is a mark on the bottom
of a jar or tank. By closing one eye, the
observer looking from C can see the mark,
A, as if it were the continuation of a pin
at B. Move the head back and forth, and
if B does not move exactly with A raise
or lower B. When there is no parallax.

PEmCTPLES OF PBTSICS.

— that is, when A and B move together^ — the pin at B is
at the level at which the bottom of the jar appears to be.

On account of the thickness of the side of tlie jar, an exact
setting is hard to make. The oxpsriment can be easily per-
formedj howevcTj with a glasa plate.

Exercleo 44.

ilTBEX OF EEFEACTIOK OF GLASS BY PAEALLAX,

Appar^hti: A glass pl:itp, with one of ilie short edges roughened firgponnd;
a pin in a eardlMurd support. On the ground edge of the glasa make a ^tie
line with ink, as rIjowu in ibe figure.

Lay the plat^ on the table and look at the image of the line through
the opposite short edge^ Place the pin on the cardboard tsupport, aa
shown in Fig. 275, so that the piti s^ims to be a continuation ul the

Fig 275.

line. The observer ehould look in at the edge perpendicularly, throng^]
the edge opposite the line. More the head a little from right to left,
and change the position of the pin till it moves with the line. The
image of the line is nearer the observer than the line itself, for tlje
image is at th** point where the pin stands. To one lookitig through
the edge, the plate nppf>ars to be only as long as from the edge next
the observer to the pin

LIGHT. -^ REFRACTION. 295

As the index of refraction of glass is greater than that of water,
the shoaling effect is also greater. The length of the glass plate
divided by the distance from the side next the obseiTer to the pin
gives the index of refraction of glass.

Bzercise 45.
PATH OP A BAT THBOUGH GLASS HAYING PABALLEL SIDES.

ApparatiLs : Glass plate ; sheet of paper ; pins.

Lay the glass plate on a sheet of paper. At A, Fig. 276, place a
pin, or mark with ink on the edge of the plate. Place a pin at B^ so
that a line from B to A will be at an angle of
45°, or less, with the edge of the plate. Lay a book • ^
or block on the plate to hide the top of the pins
when looking in the edge EF, Move the head
till the image of A, seen through the glass, covers

the image of B, Place pins at C and 2>, so that ^ D*

D covers C and the images of A and J5. The four

pins will then look in line. Make a little circle '**

around each pin to mark its position, and draw a line along the edges

of the plate. Remove the plate and trace the course of the light froui

B to D. Is the direction of a ray of light changed by passing through

a refracting substance having parallel sides?

A prism is made of a substance that refracts, and has two plane
surfaces that are not parallel. Look through a prism. In what
way do things look different? Try a 30° prism and then a 60°
prism; which gives the greater effect? What other way is there to
change the direction of light?

Exercise 46.

PATH OP A BAT THBOUGH A PBISM.

Apparatus : A 30°, 46°, or 60° prism ; pins ; sheet of paper. The third side
of the prism, BC, Fig. 277, if not rough, should be roughened for a centi-
meter or two from the end on which it rests, by rubbing on another piece
of glass, on which is a little moist carborundum powder.

Place the prism upright on the sheet of paper. Look through the
prism at pins placed at D and E, Fig. 277, and move the head till
they are in line. Then place pins at G and F, the latter quite near
the prism, so that all four pins look in line. In that case the pin at

296 PRINCIPLES OF PHYSICS.

G hides the others. With a sharp pencil mark the edges AB and A C
of the pvism. Remove the prism, and draw
•S through ED to the line AB, and through GF

to the line A C. What must have been the path
of the ray in the glass ?
_ #D Replace the prism, see that the pins appear in

line, and look through the prism from the other
side, behind E, The light from G goes in exactly
the opposite direction over the path already drawn.
Repeat the exercise, placing E and D so that
•■^ the line ED makes different angles with the line

AR. Try a prism having a different angle at A,

^Q 328. Tracing the Path of a Ray. — The

Fi 277 P^*^ ^^ ^ ^'^^ "^^y ^® traced by the direc-

tions taken by the shadow of a pin or a wire.
The pin D, Fig. 278, stuck through a sheet
of paper, casts a shadow from a gas or elec-
tric light or a candle at L, If the light is
much above the level of the table, raise one
edge of the board on which the paper rests
till the pin, D, casts a long shadow. The
prism ABC is put in such a position that
the shadow falls on the prism near the
angle. A, Mark the edges of the prism,
and draw a line in the shadow on both sides of the prism.
Remove the prism and mark by a dotted line the shadow of
the pin.

329. Deviation. — Perform the experiment with the shadow
coming more in the direction of E, Fig. 279, and again with
the shadow coming from F, See how nearly
parallel E and F can be to the line, AB, and
still have the shadow visible on the other
side of the prism. The change of direction
of a ray, on passing through a prism, is
Fig. 279. called deviation.

LIGHT. — REFRACTION. 297

330. Tlie Angle of Bfinimum Deviation. — Look through a

prism at a bright light; rotate the prism, first to the right, then

"to the left The image moves from and toward the light itself.

-A.t one point in the rotation of the prism the image stops

approaching the light and begins to move away. The prism

then is at the position where the ray of light passing through

the prism is least bent. The light appears to be turned through

a smaller angle than in any other position of the prism. This

is called the angle of least bendingy or of minimum deviation.

The angle of minimum deviation, or the angle of least change
of direction, is the angle at which a prism is placed for many
experiments in light.

Bzercise 47.
MBASUBEMEKT OP ANGLE OF MIKIMTrM DEYIATIOIT.

Apparatus : A glass prism on a sheet of psLper ; pin.

Let the shadow of a pin at D, Fig. 280, strike the prism near the
corner A. Turn the prism slowly back and forth on ^ as a centre or
pivot. Notice the direction of the shadow on
the side A C, and make a mark where the
shadow appears least turned toward C, Turn
the prism again, to be sure that the mark is
on the line of the shadow when it is least
bent. Draw a line along the edges of the
prism and in the shadows. Remove the
prism and indicate the shadow not already
marked by making a dotted line, EH. The angle between FG and
the dotted line is the amount the ray, DE, is bent, and is the angle
of minimum deviation.

At the angle of minimum deviation the incident ray DE makes the
same angle with the normal toAB that the ray FG, coming out of the
prism, makes with the normal to ^4 C.

CHAPTER XX.
LENSES.

1 ,

"7^ N>

*,._J

V V

-J.^-

\dA

Fig. 281

331. Combinations of Prisms. — Bearing in mind which prism

— one of 30° or one of 00°— bends
a ray the more, determine what
will be the paths of parallel rays
after passing the prisms A, B, C,
and A Fig. 281. As A and D
have a greater angle than B and
C, the sides of B and C being
more neai^ly parallel, rays 1 and 4
will be bent a great deal, rays 2 and 3 a less amount, and all
the rays will nearly meet and cross at a point, F,

Arrange two 60° prisms at A and D, and two 30° prisms at
B and C. Let sunlight or light from a lamp three or four feet
away fall on the prisms. Describe the appearance of the light
after refraction by the prisms.

Glass having one side moulded into prisms is much used in
the windows of deep rooms. The prisms either bend (refract)
or totally reflect light that ordinarily falls on the floor near the
window, and send this light where it is needed, — in the back
of the room.

332. A Lens. — A poly prism (many prisms) consists
of a piece of glass on one side of which a number of
plane faces have been ground, making a number of
prisms. Employ this as in Fig. 281, and see if there
is a point where the light bent by all the prisms comes
together. If the number of prisms were increased
very many times in Fig. 281, or in the polyprism, the

298

Fig. 282.

LENSES. 299

little plane surfaces, or flat places, would become so many that
they would run into each other, and form a curved surface,
as in Fig. 282. This is a lens,

333. Focus of a Lens. — To find the position of the point
where parallel rays or rays from a distant object cross, after
passing through a lens thickest at the centre, vary the distance
of the lens from a card until the image of the sun or of a
distant light is as sharp and clear as possible. Stand in the
darker part of a room, and hold one side of the lens toward a
window. Move the card until the picture of the objects out of
doors are clear and distinct on the card. Measure roughly the
distance from the card to the lens.

The rays of light which enter a lens from a distant object
are nearly parallel, and for experiments in light can be con-
sidered as perfectly parallel.

334. Principal Focus. — If the sun is shining, hold the lens
with one side toward the sun and bring a piece of printed
paper toward the lens on the other side. Find the place where
the bright spot caused by the lens is as small and sharp as
possible. Hold the finger a moment at this point. Keep all
light from reaching the finger or the paper, except what passes
through the lens. Try to ignite the printed paper. Practically
all the light and heat from the sun that reach the lens are
brought together at the bright spot. Some lenses bring
together enough heat to set fire to wood or paper. This spot
is called the focusy a word that in Latin means " fireplace."

In Fig. 283, F is the principal focus, so called because it is
the focus of rays parallel before passing
through the lens. The distance from F^
F to the centre of the lens is called the
principal focal distance, or, for brevity,
the principal focus, or the focus. '^'*' ^®^*

The easiest method for measuring this distance is described
in the following exercise.

PRINCIFLE8 OF FHY8IC3.

Exercise 4B.

FEIMCIFAI FOCUS OF A LEHS TEAT 15 THICKEE AT THl CEFim
XSAH AX THE EB&ES.

Afp9fmtmM ■ A km held hy rubber bands in a bolder, arranged to slide on %
neier stkk, whkb is fagteaed Uy a bai^eboard, as sliown hi Fig. Ml
anotb&f bolder to i»i|q>ort irertli;^l|^ a card.

M^kod L — Ftaee the baud Id such & position that a piGiureof a
dkUnt tree or chimney is formed on the screen, S, Move the screen
to and from the lens till the branches of the tiees or the bricks of the
chimney look sharp and clear. When the bricks can be couixtedj the
foctia k 6ud to be sharp. Measure the rliJ^tanee fron* S to tlie leDB,

Move the lens, start over again, and make a new setting- Record the '
distance in each case* The average of several measurements is the
principal focal length of the lens, and is represented bj the letter F.
If the screen, 5, were removed after the picture was focussed, and
a plate of glass or paper covered with a substance affected by light
were put at S, all light being shaded from B except what passed
through the lens, the picture would be permanently recorded, that
is, photographed. (See section 384, page 349.)

How does the picture, or image, on the screen, S, Fig, 284, compare
with the objects in color, position, and size? When the aunt's rays
are focusaed on a paper, what is the little bright spot the image of ?
Instead of a whole lens, try a piece — half a lens or lees. How does
the picture differ in size, position, colors, or brilliancy ? The elfect of
a piece of a lens is obtained by covering a part of the original lens by

LENSES. 801

a card. Cover the upper half; then the lower half. Make circular,
square, oblong, and triangular holes in cards, and cover the lens with
them in turn. What is the effect upon the image ?

Method IL By Parallax. — Remove the screen at S, Fig. 284, and
fasten across the face of the support, 5, half covering the opening, a
piece of thick card. Put a pin in the card, as ^ o

shown in Fig. 285. With the head near A, Fig. ^

284, and about a foot from S, look at the pin
and the image of a distant tree or chimney seen
through the lens. The image is of course upside
down, as it appears on the card at S. Move the
head right and left, and, if the pin and chimney
do not keep together, move the lens toward or
away from the pin till a point is found where
there is no parallax.

Should there be any diflBculty in making a good setting, practise
with a pencil and a wire, both black. Stand the two in spools, placing
one spool behind the other. Hide the spools by a dark-covered book,
and try to decide by parallax which is the nearer. If there is still
difficulty in adjusting the position of the pin, the support S can be
moved until there is a sharp image on the little strip of card, and then
moved nearer to and farther away from the lens, while the observer
all the time keeps moving his head and watching the pin and image.
The head must be kept far enough from S so that the pin can be easily
seen. If necessary, write a word on the back of S and always stand
so that the writing can be seen clearly. The head will then be far
enough away to see the pin distinctly. A vertical mark on the back
of the strip of card at S is sometimes used instead of the pin.

Make several settings of the pin at the position of no parallax, and
measure from the pin to the lens. Average the readings.

The parallax method is the more accurate way of finding the focal
length of a lens.

Examine a lens of short focus (four or five inches) and one of
longer focus (seven or eight inches) . Roughly determine the focus
of each. What difference is there in the appearance of them? Which
one gives the brighter picture? Which the larger picture?

835. Image made by a Small Opening. — Instead of a lens,
use a sheet of paper perforated by a pinhole. Get an image

"P>K

302 PRINCIPLES OF PHYSICa.

of a candle or lamp. Examine the form and size of the image.
The brighter the light, the farther the pinhole can be from
the screen on which the image is formed. Move the pinhole
toward the screen, and note the effect on the image. The dis-
tance between them may be varied from a
, g few inches to several feet.
S To account for the inversion of the image,
construct a diagram like Fig. 286, where C
takes the place of the candle. The light
Pj from the tip, d, passes through the opening

in A, and reaches the screen, aS, at the point
/, and light from d reaches no other part of the screen. Light
froii) e goes to g,

336. Comparison of Image made by a Small Opening with that
made by a Lens. — The image made by a small opening, like
the image made by a lens, is inverted. The image formed by
a lens is much the brighter. To determine why, return to the
arrangement in Fig. 286. Place A a foot or more from the
candle, and S two or three inches from A, Make a second
hole in A; a third; then a lot of little holes in A near to-
gether. Each one forms an image of the candle on S. Place
a lens over the holes in A, and move the screen, S, slowly away
from a position close behind A till the images overlap. How
does the brightness of the image compare with that formed by
a single hole ? If the opening in A is as large as the lens, the
illumination on S becomes bright, but, being formed by an
immense number of little images overlapping, is indistinct
and only a patch of bright light on S.

One of the Jidvantages of a lens over a small opening is in
the sliar])ness and brightness of the image formed; for all the
images that are formed by all the little openings that could
fill up a space as large as the lens are made by the lens to
overlap.

On a clear day use the sun's rays in place of a light at C,

LENSES.

303

Tig. 286. The hole in A can now be made very small. The
advantage of a small opening is that the distances may be
varied at will, without making the image less sharp and dis-
tinct. Using a lens, the screen, S, must be placed at some
particular distance, this distance depending on the lens and
its distance from the object, C,

337. Different Kinds of Lenses. — The surfaces of lenses are
always parts of spheres ; other curves are too difficult to grind.
In Fig. 287, a, c, and e are
thicker at the middle, and
give a picture of a distant
object on a screen ; b, d, and
/ are thicker at the edge,
and cannot, when used alone,
make a picture on a screen.
The first three tend to bring
rays of light together; the
others tend to scatter the
rays; a does not always
have the two surfaces parts
of equal-sized spheres.

The names of these lenses,
which represent all the varie- ^ig. 287.

ties possible, are given merely
for reference. Far-sighted
persons wear glasses of a or
c; near-sighted persons wear b. The different varieties are
used together for photographic, microscopic, and telescopic
lenses. A single lens does not give a perfectly clear image.
Try a lens of large diameter, thick at the middle. Notice
that with no position of the screen is the image perfectly
clear. Very many combinations of lenses have been devised
to obviate this imperfection. A lens can be made of any
transparent substance — ice, quartz, water, a diamond, etc.

a. double convex.

b. double concave.

c. plano-convex.

d. plano-concave.
6. concavo-convex.
/. convexo-concave.

804 PRINCIPLES OF PHYSICS.

Make a hole a little smaller than the lens in a piece of card-
board. Put any one of the first three kinds of lenses (a, c, or e)
over the hole, and try to throw the image of the sun or a lamp
on a screen. Trace the direction of the light by smoke or chalk
dust. Place the lens at different distances from the screen.
Then use a lens like 6, d, or /. The patch of light grows
larger, the greater the distance from the lens, and at no dis-
tance from the lens is the light brought together.

Of the lenses, a, c, and e act like two prisms with their bases

together (A, Fig.
288); 6, d, and
/ act like two
prisms with their
edges together
(B, Fig. 288).
Fig. 288. " ^ Parallel rays of

light, after pass-
ing through, are spread apart as R and S, and seem to come
from a point F, which is called the focus.

A drop of water, the round top of a glass stopper, and a
flask filled with water are convex lenses of great thickness for
the radius of curvature of the surfaces. A plano-convex water
lens can be made by filling a watch glass with water; two
placed together under water, filled, and removed, form a
double convex lens.

338. Focus of a Concave Lens. — This point cannot be found
by the simple method of throwing a ])icture on a screen. Con-
cave lenses, of which h, d, and/. Fig. 287, are types, have no
real focus ; the point F, in B, Fig. 288, is called a virtual focus.
They cannot bring together the sun's rays and burn paper;
they cannot, used alone, form a picture that can be thrown on
a card or screen. The effect such lenses have when placed in
front of the lens of the eye will be ex])lained under " Optical
Instruments." Opticians usually judge of the focus of a con-

LENSES. 305

cave lens by trying it with a convex lens. If a six-inch focus
convex lens applied to a concave lens makes it look and act
like a piece of plate glass, the concave lens has a focal length
of — 6 inches.

339. The Centre and the Radius of Curvature. — The centre of
the sphere of which the surface of a lens is a part is called the
centre of curvature. The radius of the sphere is called the
radius of curvature. Draw a curve showing what you think is
the curvature of a lens you are using, and compare with the
result obtained by the following method.

Exercise 49.
XEASUBEMENT OP CUBYATUBE OP LENSES.

ApparatiLs : Double convex lens.

Draw a part of a circle with dividers, or with a pencil held by a
loop of thread to a pin. Cut out a piece like Fig. 289, and put the
curve on one face of the lens. Try a segment
of a circle of 3-inch radius, and one of 8-inch
radius. At Ay Fig. 290, the paper segment, or

template, T, has a greater radius than the

surface of the lens, A, At B the seg-
ment, 5, has a smaller radius than the

surface of the lens, B, Record the

radius of T, adding the statement, " too

large " ; record the radius of S as " too
Fig. 289. small." After a second trial, the fit

may be so close that the template and
lens must be held toward the light, to determine whether the two
agree. Record the number of the lens, its focus, and the radii of
curvature of each side. More exact results may be obtained by using
a set of templates of sheet metal.

840. Principal Axis and Oblique Axis. — A line drawn through
a lens, L, Fig. 291, from the centre of curvature of each
face, C, C, is called the principal axis. An oblique axis.

306 PRINCIPLES OF PHYSICS.

X, Xi, Fig. 291, is any line making an angle with C, C", and
passing through the centre of the lens. For exact work, the
line X, Xi should be taken as passing
through the optical centre, — a point
that in a double convex lens is exactly
or nearly at the centre of the lens.

Fig. 291.

341. Image Distance and Object Dis-
tance. — Set a lamp against the wall at
one side of a window. Hold a lens in
front of the window. Move a sheet of
paper toward or away from the lens
till the image of the distant buildings or landscape is clear
and sharp on the paper. The distance from the paper to the
lens is the principal focal length. How far away must the
paper be moved to focus the lamp on it? Which is the
shorter, the focus of a near object or one far away ? Kepeat,
with the lamp three or four times the focal length from the
lens, then with the lamp nearer and nearer. Does the focus
for nearer objects increase in length ? What effect does bring-
ing the object nearer the lens have on the size of the image ?
Suppose the lens in Fig. 292 is 60 inches from an object, J., and
the image, B, is 12 inches
from the lens. Would the . ^^

■•(>H

principal focus be greater U. ~-'A*

1 1 -.^ . 1 r> C5 object distance

or less than 12 inches? M '^^,„„^,.

Try the experiment, using a ^^^^ ^

convex lens. (The num- Fig. 292.

bers given in this section

are chosen merely for convenience in explanation ; with a 10-
inch focus lens these exact numbers will be obtained.) How
does the size of the image compare with the size of the object ?
Which is the farther from the lens, the object or the image?
As long as the object is at A, can a distinct image be formed
on the screen in any other position than B ?

LENSES. 807

The distance from the lens to the object, which may be a
candle or other light, is called the object distance ; the distance
from the lens to the screen is called the image distance,

342. Conjugate Foci. — Interchange the object and screen,
putting the candle or other light at B, Fig. 292, and the screen
at A. Is a sharp image formed on the screen ? Which is the
larger, the object or the image ? Is the object distance or the
image distance the greater ? These distances, 12 inches and 60
inches, go together, if the lens has a focus of 10 inches ; and
when one of the distances from the lens is 12 inches, the other
must be 60 inches, no more and no less.

Set the screen 15 inches from the lens, and move the candle.
When the candle is 30 inches from the lens, a clear image is
formed. Interchange the object and image. While one dis-
tance is 30 inches, can the other distance be more or less than
15 inches ? The distances 15 inches and 30 inches go together.
By making either the image distance or the object distance
from the lens a given distance, — which may be any distance
greater than the principal focus, — there will be found another
distance that goes with the given distance. An indefinite
number of sets, or pairs, of image and object distances, like 60
inches and 12 inches, or 15 inches and 30 inches, can be found.
Whatever the object distance, or the distance that the object
at A, Fig. 292, is from the lens, there is one, and only one,
image distance at which the image is formed on the screen at
B. These two distances go together, and an object placed at
one distance has its focus at the other distance. They are
called conjugate foci.

A conjugate focus is always larger than what? How short
can a conjugate focus be ? What is the length of the focus
that is conjugate to it ? These two last questions may be put
in this way : How near can an object be held to a lens to form
aij image ? how far away will the image be ?
- The abbreviations, D^ for object distance, and Z>< for image

308 PRINCIPLES OF PHYSICS.

distance, are often used. F usually stands for principal focus,
and / and /i are sometimes used for object distance and image
distance, respectively.

t-^<} — -■--- — )

343. Conjugate Foci Interchangeable. — Instead of interchang-
ing the object and image, as in section 342, the same result

may be obtained in a sim-
pler manner.

Move the lens toward A

When the lens is 12 inches

^ from A (Fig. 293), the

'** image of the object at A

will be focussed on the screen at By and the image distance,

the distance from the lens to B, will be 60 inches.

Place a light at B, Fig. 294, about one and a half times the
focal length from the lens. If the lens has a focus of 6 inches,
let the distance from the lens to 5 be from 8 to 10 inches.
By the side of B place a screen. Place another at A, where
the image of B is focussed.
Place a second light at ^, d U

and move the screens, but ^| f\ |^

without changing their A \/ b

distances from the lens,

o -^ • Fig. 294.

so that the image of B is

formed on the screen at A, and the image of A is formed on
the screen at J5. Cover up A ; then B, Are both images in
focus ? What name is given to the distances of A and B from
the lens ? (They are called object distance and image distance,
but what name includes them both ?) On which screen is the
image the larger ? Which image is the brighter ?

Problems.

1. How far from a wall must a 6-inch lens be held to cast a distinct
image of a distant tree ?

2. A lens and the image formed by it on a screen are 8 inches
apart. Can you tell if the lens has an 8-inch focus, without knowing

LENSES. 309

where the object is? Where is the object if the lens has an 8-inch
focus?

3. The image of a distant object is focussed on a screen. The
object, a boat, for instance, rapidly approaches ; what must be done
to keep the image sharp?

4. A lens has a focus of 5 inches ; what is its focus for parallel
rays?

5. Make two dots, one a centimeter above the other, on the left-
hand page of the note-book. Draw lines through these points across
the page toward a point 20 feet or more away. Sight along the edge
of a ruler, as in the exercise on plane mirrors. Are the lines on the
note-book apparently parallel? What is the focus of a lens for
parallel rays?

6. If a point of light is placed at the principal focus of a lens,
6 inches away from a 6-inch focus lens and 10 inches away from a
10-inch focus lens, what will be the direction of the rays after passing
through the lenses ?

7. A lamp, 20 cm. from a lens, is focussed on a screen 30 cm. dis-
tant from the lens. What kind of foci are 20 cm. and 30 cm. ? If
the lamp and screen are not moved, what other position can the lens
have and yet focus a distinct image?

8. How many sets of conjugate foci does a lens have?

Exercise 50.^

(a) BELATION BETWEEN THE CONJUGATE FOCI OF A LENS. -First

Method.

Apparattu : Meter stick on baseboard, as in Exercise 48 ; lens holder; screen
holder ; a lens ; metal support covered with netting.

Find the focus of a lens on the holder, L, Fig. 295, by the screen
method, getting a clear, sharp image on the card, S, of a far-away tree
or chimney. Call the distance from the lens to S the principal focus.
Take an average of three settings. In place of the distant object find
the focus of a light, a meter or more away, or of the window sash.
Record the distances from the lens to the screen, and from the lens to

1 Begin all laboratory exercises by finding the focal length of the lens used.

810

PHINCIPLES OF PHYSWS.

the light or window* Remember in all exercises with lenses to measuFe
always from the lens, unless otherwise directed. Find a focus of a
light 60 cm* away from the lens; then 30 cm. away. Do all thii

Fig. 395.

rapidly. How does the focus of near objects compare with the prin-
cipal focus? Which liaa the longer fociL^j an object 1 m. or 2
away ?

The object, 0, Fig, 295, may be a candle or an incandescent lamp
or a gas flame. In using these^ measure from the lens to the wiek or
the filament of the lamp. Jt is better to use a gas flame or ii keroaem
larap» which should he provided with a tin or iron shade on the si
of the chimney facing the lens^ and a vertical slit in the tin or iro]
covered with netting. The meshes of the netting are treated as tl
object in focussingj and the leus is moved till a sharp image of the
meshes h formed* The object distance sliould be measured froin
the netting to the lens.

Place the object at 0^ Fig, 295, near the end of the meter sticl
Move L toward 5 till the image of the netting is distinct on
^ v Measure the image and object

■0-

distances. Call the object dis-_
tance D^ and the image dlstano
Ai and record two or thi'ee selj
tings on a diagrara like Fi^
296. In every case record aid

Fig. 29fi.
tlie whole distance from the screen to the object,

NoWj instead of interchanging the object and image by actual]
moving them, slide the lens near the object (Fig, 207), and nn

LENSES.

311

-0---H

the object and image distances of several settings in the new position.
The lens is now near the object, and the image is a large one. Meas-
ure and record.

The screen, S, which has been
at the extreme end of the meter
rod, is now moved 20 cm. nearer
the light; two positions of Z,
one near the object and the '^'*' 2^^*

other near the screen, making a sharp image on S, are found, and
distances measured and recorded as before. Call these measurements
the second sett

Repeat the experiment, placing the screen 30 cm., 35 cm., 40 cm.,
45 cm., 50 cm., 55 cm., 60 cm., etc., from the end, ending the experi-
ment only when the screen is so close that with no position of the
lens can an image be focussed.

Consider now the two sets of measurements of the first position of
the screen. How does the image distance in Fig. 296 compare with
the object distance in Fig. 297? How does the object distance in
Fig. 296 compare with the image distance in Fig. 297? The two
small values are practically the same, and so are the two large ones.
Which is the larger, the principal focus or these distances ?

Replace the apparatus as in Fig. 296, and without disturbing the
lens, let the screen and lamp change places. There will be a large
image formed on the screen, as in Fig. 297. The position of the
screen and the position of the light or object are interchangeable.
Look at any other set of measurements you have. The same dis-
tances do not occur at all. The two distances — that is, the Do and
the Di — of the first set go together, and are the conjugate foci. In
each case, what are these distances greater than ?

Record in a table, as follows : —

Isfcset
2d set

DuiTA^ei: uir Object

Image Dia-

312

PRINCIPLES OF PHY8IC8.

Id the column headed — , put the numbers obtained by dividing 1

1
by the object distances. The column — • contains the numbers ob-
tained by dividing 1 by the image distance in each set. Express the
numbers in these columns as decimals. For the next column, jr—t —t
add the values of -^ and '^. Finally, in the last column put the

value of — , that is, 1 divided by the principal focus expressed as a
F

decimal. Suppose that in one case Z), = 30 and A = 10. The table
would be filled out as follows : —

1st set

Total
D18TANCB

/>.

.033

-L + -L

.133

Here the last column is not filled.

344. Formula for Conjugate Fed. — As the numbers in the
last column are practically equal to those in the column before,
we may say that 1 divided by the object distance added to 1
divided by the image distance, equals 1 divided by the princi-
pal focus. That is : —

1 + 1 = 1
Z>, A F'

a formula which is approximately true. As it does not matter
which of the two measurements from the lens is called the
object distance or the image distance, and as these distances
are conjugate foci, the letters / and /i, respectively, are used,
for D. and Df, The formula becomes

1+1 =1.

/ /, F
This is exactly the same as the other formula, and either
may be used.

LENSES. 313

Exercise 50.

(6) SELATION BETWEEN THE CONJUGATE FOCI OF A LENS. — Second

Method.

Apparatus : That shown in Fig. 295, page 310.

Ccue L — Stai-ting with the screen 80 cm. from the object, take sets
of readings, as in Exercise 50 a. Find, finally, the nearest position of
the screen and object where a distinct image can be formed. How do
the object and image distances now compare? Is the total distance
from object to image four times the focal length of the lens ?

Case II. — Find the distance between the object and the screen,
when the object distance equals the image distance.

Compare with the principal focus. If D,, and Z)< are each 12 cm.,
find F. How far is the screen from 0? How does the size of the
image compare with the size of the object? What distance from an
object 4 inches long must a 7-inch focus lens be placed, so that the
image also may be 4 inches long?

Problems.

1. If the object distance is 4 cm. and the image distance 6 cm.,
what is the focus of the lens ?

1 + 1 = 1
4 6 F

6F+4F=24

10F = 24

F = 2.4

2. How far away must the screen be held from a 10-inch focus
lens to give a clear picture of a window 40 inches away ?

40 A 10
102)< + 400 = 40A
30 A = 400
A = 13.3.

The screen must be held 13.3 inches from the lens.

314 PBiyCIPLES OF PHYSICS.

3. If the object distance is 20 cm. and the image distance is 30 cm.,
what is the principal focus ?

4. Ilow far away from a wall is a lens of 12-inch focus that throws
a sharp picture of the wall on a card 20 inches from the lens?

5. If F=5 inches, and one conjugate focus is 15 inches, what is
the other?

6. The principal focus = 6 inches ; /j = 12 inches ; /= what?

7. A = 6; A = 8; F = what?

8. Z>o= 12; F=4; A = what?

9. How could the focus of a lens be found in a small room, by the
aid of a candle and a meter stick ? (Compare Problem 7.)

Exercise 51.

HEAL CONJUGATE FOCI. - PABALLAX METHOD.

Apparatus : Apparatus shown in Fig. 21)5, page 310. Instead of the light at
0, use a pin or card having a vertical mark on it, as the object. Replace
tbe screen at <$ by a pin or vertical line on a small strip of card. Tbe line
is on the side of the card toward the observer, whose eye is at a convenient
distance from S, ou the side away from the lens.

Proceed exactly as in finding the principal focus (Method II., page
301), the only difference being that the object viewed is a near one.
Locate the position of the image when the object is 60 or 70 cm.
away from the lens.

Place the object a little farther than its focal length away from the
lens ; notice that the image is very large, or cannot be seen at all.
Bring the object nearer than the focal length ; an image is seen. Is
it erect or inverted? Is it a real image ? ' By this is meant, is it an
image that really exists, — one that can be thrown on a card ? To try
this, place a candle about half the focal length from the lens, and try
to find a position where an image is formed on the card. Consider
how the focus (in this case we mean the conjugate focus) of a lens
increases as the object is brought nearer the lens. The image is
formed farther and farther away. When the object is at the principal
focus of the lens, the rays, after passing through the lens, are parallel,
and go in directions opposite to the arrows in Fig. 283, page 299.
Those rays never come together, and therefore do not form a picture.

Any image, real or virtual, formed in any way, whether by lenses
or mirrors, can be located by the method of parallax.

LENSES. 315

345. Magnifying Power of a Cylindrical Glass Tube. — The
bore of a thermometer appears to be larger than it is. Place a
pin or a bit of wood, just large enough to fill the bore of a tube,
— that of a broken thermometer will do, — so that a part pro-
jects beyond the tube. Roughly estimate how much the cylin-
drical lens, which is the tube itself, magnifies. Does the bore
or the thread of mercury look longer because of the magnifying
power of the cylindrical tube ? What kind of lenses make an
object look broader, as well as longer ?

346. Virtual Foci. — In Fig. 298, an object is placed at/,
nearer the lens than the principal focus, F. Were the lens re-
moved, a ray of light would continue

in a straight line to A and beyond.
The lens bends or refracts the ray so
that the direction is toward B, The
image will appear to be somewhere in
the line Bfi, — at/i, for instance, which
is the point from which the light
seems to come. While the points / ^. ^^^

^ -' Fig. 298.

and /i are conjugate foci, the posi-
tions are not interchangeable. If the object is placed at /i,
the image is not formed at/.

Exercise 52.

VIBTUAL FOCI.

Apparatus : Meter support, lens holder, and two screen holders ; lens, prefer-
ably a half-lens ; pins or cards.

Place the half of a lens, L, Fig. 299, in a holder at the end of a
meter stick. 0 is a pin or vertical mark on a card, which is placed
about half the focal length from L. / is a tall pin or a vertical mark
on a card. A tall card at / (carrying a vertical mark on the upper
part only) is best, since it is easily moved sideways, to make / and 0
appear in the same line; I should be seen only over the lens; for if

316

PRINCIPLES OF PHYSICS.

object
dutanee
<.

image distance

Fig. 299.

any part of it can be seen through the lens, it is sometimes confused
with the image of 0 seen through the lens. The pin or mark, /, must
be so high that it can be seen over the lens by the observer looking
from a position at ^, a foot or more from
the lens.

With the head at A, look through the
lens and see 0 — that is, the image of 0»
Where is this image? To answer this
question, slide / sidewise in its holder till,
as seen over the lens, it appears to be a
continuation of 0. Move the head from
right to left. If / and 0 do not move
together, bring / closer to or move it farther away from O, Move
the head sidewise. If 0 and I do not keep in one continuous line,
change the position of / till there is no parallax between 0 seen
through the lens and / seen over the lens. / is then located at the
image of 0. The image is not really formed there ; it cannot be thrown
on a card or screen. But to the eye at A the image of the object 0 ap-
pears to be at /. It is a virtual image. The rule for the measurement
of object and image distances holds in this case : always measure from
the lens to the object and from the lens to the image, as shown by the
figure. Starting with 0 about half the focal length away from the
lens, set / so that there is no parallax, and record the object and image
distances. Move 0 half a centimeter at a time, making new settings
of 7. Arrange the readings as follows : —

Objbgt Distanok

Imagb Dibtanob

_1_
A

In one part only does this table differ from the one on page 311 ;
this table — is subtracted from — . In the other exercise the ob'
was on one side of the lens and the image on the other ; in this e

LENSES.

317

ciae they are both on the same side of the lens. The position of the
image has changed from one side of the lens to the other, and the
image distance becomes a minus value. Compare the change of sign
in transposing a quantity from one side of an equation to another.

347. Relative Size of Object and Image. — Thus far, in study-
ing the image formed by a lens, more attention has been paid
to the object and image distances, or, as they were called, the
conjugate foci, than to the relative size of the object and the
image. The problem to be considered is, why the image or
picture of an object is sometimes larger and sometimes smaller
tlian the object itself. We have found (section 343, page 308)
that when the lens is near the object, the object is smaller than
the image.

Exercise 53. .

BELATIVE SIZE OF OBJECT AND IMAGE.

Apparatus : The same as shown in Fig. 295, page 310, arranged as in Fig. 300.

The width of the opening in 0, Fig. 300, is called the size of the
object. Move the lens till the image of 0, cast on 5, is distinct
Measure the width of the image, /,
and call this the size of the image.
Measure and record the distance from
Z to 0 (the object distance) and from
Lto I (the image distance). Record
also the total distance from 0 to /;
this answers as a check on the other

measurements, because it must equal the sum of Do and A* Record
the principal focus of the lens. Arrange the results as follows : —

DiSTAlfCB BETWEEN

Object and Image

i>.

I>i

RlZB OF

Object

Size of
Image

Size of Object
Size of Image

318 PRINCIPLES OF PHYSICS.

Place S in turn 80, 70, 60, and 50 centimeters from 0, and make and
record all measurements as above. Remove 0. Find the principal focus
of the lens. Point the meter support toward a window. Focus the
window sash. Measure the object distance, that from the lens to the
window. The size of the object is taken as the width of the window.
Divide the object distance by the image distance, and put the result in

the column — -. Divide the size of the object by the size of the

image, and record in the column headed ^^^ ^ ^ 3^^ . In each case,

size of image

is the object as many times larger than the image as the object dis-
tance is times the image distance ?

A screen of ground glass, since light passes through it, is sometimes
preferred to cardboard at S, Fig. 300. Prepare a piece as shown in
appendix, page 536, and use it instead of the card. View the image
on the ground glass, first from one side, then from the other. What
advantage does the ground glass have?

Replace the wire netting at 0 by a lantern slide or a magic lantern
transparency. How must the slide be placed to give an erect image ?
To give one that is not reversed, right and left? Arrange the lens
and screen so as to form a small image of a lantern slide. Compare
its brightness with an image as large as you can produce. To do this,
put the screen far away, and the lens a little more than its focal length
from the lantern slide.

348. Size of Image. — The image of an object (a candle, C,
Fig. 301, for instance) formed through a small aperture, is
always inverted. The triangles Ade and Agf
.g are similar. If the distance AS (the image
S distance) is twice AC, then gf, the image, is
twice de, the object. Draw a similar diagram,
making AS three times as long as AC, and
Fi£ 301. ^^^ whether or not gf is three times de. In

another diagram, place the object several
times as far from A SiS S is. Why is the image of the sun,
formed through a short-focus lens, so small? Focus sharply
the image of the sun, using a spectacle lens of 160 or 315
inch focus.

«PH<

LENSES.

319

If the distance of the aperture, A,
Fig. 302, from the object is fixed, the
size of the image depends entirely on
the distance of the screen from the
opening at A. The size of the image
at any point depends on the distance
between the two diverging lines at the

right of the aperture, A.

Fig. 302.

At m, the image

Fig. 303.

is small ; at r, it is much larger.

Again, let the distance from the screen
to the object be fixed. This is often the
case when photographing in a room or
narrow street. Fig. 303 shows the aper-
ture near the object. The result is a large
image at t A long-focus lens can replace
A. A smaller picture is obtained by the

aperture. A, Fig. 304, near to the screen, w,

A short-focus lens must be used at A if

the aperture is removed.

The image of a candle flame one inch

high is 60 cm. from a lens. The candle

is 30 cm. from the lens. What is the

size of the image ? The formula is

object distance size of object ^ _ ^ u«;^fl,r A 0

,-J -— = - -—-^ — , or, more briefly, 77 = —

image distance size of image A m

0 stands for the size of the object, and m for the size of the
image. Substituting,

30 1

60"

Fig. 304.

— = - ; m = 2 inches.

Problems.

1. Find the size of an image 40 cm. from a lens, if a 3-cm. object
is 60 cm. from the lens. Ans. 2 cm.

2. Using a 6-inch focus lens, the image of an 80-foot tower is 4
inches high on the ground glass of the camera. How far distant is

320 PRLSCIPLES OF PHYSICS.

the tower from the lens? (The object is a distant one, and the image
is formed at the (Minciple focus, 6 inches from the lens.)

Atis, 120 feet

3. What is the ^ range " of, or how far away from a fort is, an
enemy's warship 400 feet long, if a 6-inch lens gives a 3-inch picture?

4. How tall is a tree 500 feet away, if the picture formed by a
4-iuch lens is .S of an inch?

5. What must be the object and image distances, when a picture
and the object are of the same size ?

6. Take the sun s distance as 93,000,000 miles. Its image formed
by a small opening 108 inches from a card measures 1 inch. Calcu-
late the diameter of the sun.

349. Large Image formed by a Lena. — In the previous ex-
periments, the object was small, — much smaller than is
generally looked at through lenses. The following method
may be used in studying an image of considerable size formed
by an ordinary lens.

Rxerclse 54.
BSAL DIAGE FOSMSD BT A LENS.

Apparatus : Lens ; sheet of paper ; lens holder ; candle.

Draw on the paper {AB, Fig. 305), near one end, an arrow 10 cm.
long. Number five points on the arrow, which represent the different
positions of the object.

Hold the lens in the lens holder by rubber bands, as in the pre-
ceding exercises, and place the holder so that the lens is from one

and a half to two times its focal
length from the arrow ; that is,
if the lens has a focus of 12 cm.
place it from 18 to 24 cm. from
the centre of the arrow. Place
a short candle on the point L
'^ Move the screen on the other

side of the lens to a position where the image of the candle is sharp.
Mark a point on the paper under the centre of the lens, which is not
to be moved during the exercise. Make a point under the tip of the
image of the candle flame, and number it I^ Move the candle to

LENSES. 321

point £ on the arrow ; focus the image on the screen, and mark the
point Ij. In the same way locate the position of the images of points
5, 4, and 5. Connect the points of the image, Ij, Ig, l^ T^, and T^.
This line will be considerably curved. The image is not what photog-
raphers call flat. In taking pictures, the lens is usually composed
of several lenses, and the combination of them gives a much straighter
picture of the arrow, or a flatter field, than the lens used in the exercise.

Remove the lens and screen. Draw lines from 1 to Ij, from S to
Ijj, etc. These will pass nearly through the centre of the lens.

Review the experiment with images formed by a small opening
without any lens (section 335, page 301). The lens just used was,
of course, many times larger than a pinhole; more light passed
through, giving a brighter image.

Unless a room is darkened, the image of an object in the room is
faint. If candles are placed at the numbered points on the object,
0, Fig. 306, the outline or the image of that object is a row of bright
candle flames. Make 0 20 cm. or more long. Vary the distance
of the screen, 5, from the
lens, L, In no position are x ^
all the images formed on S
in focus. Replace 5 by six '" a

cards held upright in holders. J- - I ] S

Set each card so that the im- V

age of one candle is sharply
focussed on it. If £ is an ^'>
ordinary double convex lens, p. j^^

the line connecting the posi-
tions of the images will be curved. Remove the cards, bend S in the
same curved form, and focus all the images on it at once. The six can-
dles are six points of light on the object, 0. Keeping the screen, 5, flat,
move it toward and away from the lens, and notice the changes in
the size of the image. Just how large the image is depends on the
distances of the object and the image from the lens; but a clear
image is formed only at one distance from the lens for any particular
object distance. These distances are conjugate foci. Measure the
object and image distances and compare with the sizes of the object
and image. Measure the distances and the sizes of the object and
image in one case where the lens is twice its focal length from the
centre of 0,

822 PRINCIPLES OF PHYSICS.

Bring the screen, 5, near the lens. Move the screen slowly away
and notice the overlapping circles of light, a circle for each candle
flame. Farther away, these circles contract, till at the conjugate focus
for the distances OL they become distinct images of the candles.

Problems.

1. A 6-inch focus lens is placed 20 inches from a light ; how far

from the lens is the image formed ? In the formula - + - = —,/*= 6,

A f ^
/= 20; substitute, and find the value for/,.

2. In the preceding problem, if the object is 12 inches wide, how
wide is the image?

3. In a room 10 feet wide, a lens 4 feet from a window casts a
sharp image of the window sash on the other side of the room. Find
the focuH of the lens. Notice that the conjugate foci must be 4 and
12 feet.

4. If the window in Problem 3 is 3 feet wide, what is the width of
the image?

5. If a camera is placed 100 feet from a tower 40 feet high, what
is the height of the tx)wer in the picture, the lens having a focal
length of 7 inches? The picture of the tower is as much smaller
than the tower itself as the image distance, 7 inches, is smaller than
the object distance, 100 feet. For the picture to be smaller, must
the camera be moved nearer or farther away from the tower?

350. Location of the Image by the Parallax Method. — A more
accurate, hut difficult, method of locating the positions of the
images of the i)oints i, ^, 3, 4j and 5, Fig. 305, is exactly the
same as that described in Exercise 51, page 314. To locate by
the parallax method the conjugate foci of five points of the
arrow in Fig. 305, put a pin at point /, or a card having a ver-
tical mark over 1, On the other side of the lens, toward B,
another pin, supported by a thin slice of cork, or a short card
having a vertical mark, is moved about until an observer stand-
ing somewhere near B sees the farther pin at point / through
the lens, in line with the movable pin. Move the head, and if the
image seen through the lens and the pin at point 1 move together,

LENSES. 323

that is, have no parallax, press the movable pin down to mark
on the paper the position of the image of point 1 of the arrow.
Draw a little circle around the point made by the movable pin
and letter it Ii. Take the pin or card from point 1 of the
arrow and place it on point 2. Locate the image of this in
the same manner, and proceed to find the image points of S, 4,
and 6. The eye must be a foot or more from the pin nearest
it The fact that we are dealing with conjugate foci is made
evident, if the observer stands near Ay placing the pin at point
1 of the arrow, and varying the position of a movable pin
between the lens and B till there is no parallax. The common
mistake in this exercise is that the observer stands too near
the lens. In case the observer has difficulty, if he is at B,
another person may stand at A, and both at the same time can
determine if the setting is exact. The corresponding image
and object points are to be connected, and the lengths of the
object and image measured, precisely as in the last exercise,
where a candle was used.

351. Virtual Image formed by a Lens. — When an object is
held nearer the lens than the principal focus, the image cannot
be focussed on a screen, yet an image can be seen by the eye.
Such an image is virtual. (See section 346, page 315.) From
Fig. 299, page 316, it will be noticed that the observer is on
one side of the lens, and both the object and image are on the
other side. In Exercise 52, a very small image was formed, —
that of a small wire or pin. For the purpose of studying a
larger image, place the lens at one
end of a sheet of paper. Make a
mark under the centre of the lens, L,
Fig. 307, which is held in the holder
used in Exercise 50 on conjugate foci.
At a distance from L of about two- ' pjg. 307.

thirds of the focal length of the lens,
draw an arrow, iJ, from 3 to 5 cm. long, and make three or

824 PRINCIPLES OF PHYSICS.

five points on it. At point 1 place a pin. With the head near
A and a foot or more from L, look through the lens at the pin.
On the paper near AB, Fig. 307, place a screen holder carry-
ing a card (Fig. 308). The card faces the lens, and has marked
on the surface a vertical line. From the bottom
to the upper edge of the lens this line is dotted
faintly; the upper part of the line is heavy.
The dotted portion serves to mark the position
of the line, and yet cannot be seen through the

Fig. 308. ^®^s SO as to confuse the observer. The heavy

portion is seen over the lens. Change the posi-
tion of the card till there is no parallax between the pin and the
heavy line on the card. Mark the position of the base of the
line on the paper and letter it /i. In the same way locate
the other image points. Remove the lens. Draw lines through
1 and /i, 2 and /j, etc. Do they pass through the centre of the
lens?

Connect the points /i, /j, etc., by a curved line. Measure
the distance from /i to /j; this is the length of the image.
Measure the distance of the image from
the lens, taking the distance from a straight
line connecting /, and I^, Fig. 309, paying
no attention to the curved shape of the
image. LC is the image distance, and
LD the object distance. Divide the image
distance by the object distance, and divide '*' ^°^'

the length of the image by the length of the object. The
image is as much larger than the object as the image is
farther away from the lens than the object.

CHAPTER XXI.
OTJBYED MIBBOBS.

352. Convex Blirrors. — Look in a convex mirror, such as the
back of a spoon, the side of a silver pitcher, a highly polished
piece of pipe, or a bright tin can. Hold the mirror, if it be
a cylindrical one, such as a piece of pipe or a can, first with
the axis horizontal, then vertical. The effects are somewhat
amusing; and, while the subject is comparatively unimpor-
tant, yet convex and concave mirrors afford a review of the
principles that underlie the formation of images in plane
mirrors.

353. Centre of Curvature. — First of all, find the centre of
curvature ; that is, the centre of the circle of which the surface
is a part. Suppose a boy stood in front of a cylindrical pillar
trying to throw a rubber ball so that after striking the pillar
it would bound back to him. In what direction must he throw
it ? So as to strike perpendicularly, or, as we say, normally, to
the surface ? Were the pillar of paper and the ball heavy, the
ball would break the paper and pass through the centre of
curvature. A rubber ball thrown along one of the spokes of a
wheel bounces back from the hub in the same direction. The
centre of curvature of the hub must lie somewhere on the line
of the spokes.

354. Centre of Curvature of a Convex
Blirror. — Set a convex mirror, 3f, Fig.
310, on a sheet of paper. Mark the edge.
Lay a ruler in the position AB, so that its
reflection is a continuation of itself. The Fig. 3io.

326

326 PRINCIPLES OF PHYSICS.

ruler and the reflection lie in a straight line, which is a normal
to the circular surface of M. With the ruler some distance
away, as at DE, arrange as before, and draw another normal.
Remove the mirror, and continue the normals till they cross
at the centre of curvature, C Replace the mirror, and in
the same way draw with the ruler one more normal, at least.
Remove the mirror and continue this normal. If it pass
through the intersection of AB and DEy the point C, the
centre of curvature, has been accurately determined.

Exercise 55.
LOCATION OF AN IMAGE IN A CONVEX MISSOS.

Apparatus: Convex mirror, radius 5 cm. ; sheet of paper ; pins.

Method /. By Sight Lines. — Mark the edge of the mirror on a
sheet of paper. One centimeter from the mirror draw an arrow 2 cm.
long (2, e, 3, Fig. 311). Place a pin at point 1, or put
over point 1 a block with a vertical mark. Draw three
lines pointing to the image of the pin or the vertical
mark, using the edge of the ruler as before. Let the
three lines be as far apart as possible. Number each of
the three lines " 1." Remove the mirror and continue the
lines, locating the head of the arrow where the lines cross. Place the
pin or block at point 2^ and locate its image in the same way ; locate
also the image of point S.

Repeat on another sheet of paper, having the arrow 3 cm. long and
2 cm. away from the mirror ; and again, with the arrow 3 cm. long
and 5 cm. away.

Study the diagrams. Is the image the same size as the object, or
smaller or larger ? Is the image reversed, right for left, as in a plane
mirror ? Hold a plane mirror in front of the arrow.

Place a spool or a cork or a card marked in squares in front of a
convex mirror. Which lines are shortened? On which side of a
plane mirror is the image always formed ? On which side of a convex
mirror? Is the image curved? Does it curve the same way as the
mirror ?

CURVED MIRRORS.

327

Method II, By Construclion. — From the data obtained by this
experiment, it is now possible to construct the position of an image
by drawing. Draw a portion of a circle with a
radius of 3 cm., representing the mirror, il/, Fig.
312. Two centimeters in front of the mirror
draw an arrow 4 cm. long. Number the arrow
i, 2y S. The light from point 1 in the line A C
normal to the surface is reflected in the same
line. To a person standing at ^, or anywhere
on the line CA in front of the mirror, the image
of point 1 appears to be somewhere in the line
AC. Rays of light come off from the point 1 in every direction.
Take one ray, ID. Draw the normal CDN. The ray is reflected
at the same angle at which it strikes ; that is, the angle BDN equals
the angle 1 DN. To a person standing at B, the image of point 1
appears to be in the line BD or BD lengthened. The observer at A
sees the image somewhere in the line A C. The point of the image
must lie at the intersection of A C and DE, or at E. In a similar
way, locate the images of points 2 and 3. Connect the images of
7, ^, and 3, marking the head of the arrow. Do not have the point D
too far from the centre of the mirror.

Method III. By Angles. — Another way of locating the image of a
point ill a convex mirror is shown in Fig. 313. 0 is an object, or one
point in an object, in front of the mirror, M,
Two rays are drawn from 0 to the mirror.
Where these rays touch the mirror, normals,
CN and CN^, are drawn. See that the re-
flected ray. By makes the same angle with N
that the ray from 0 did. In a similar man-
ner draw G. Continue B and G back be-
hind the mirror till they meet at Ey which
is the position of the image of O. Test the
accuracy of your drawing by laying a ruler or the edge of a sheet of
paper on 0 and C (the centre of curvature). E should lie in the
line OC.

Method IV. By Parallax. — At the point O, Fig. 313, place a pin
or a block with a vertical mark on it. Behind the mirror move a
tall pin or wire till there is no parallax between it and the image of
the pin at O, The tall pin will then be over the point E.

Fig. 313.

328 PRINCIPLES OF PUY8IC8.

355. Concave Bfirrors, for almost all practical purposes, are
parts of spheres, or are of nearly that form. The inside of a
spoon or ladle and the front surface of a concave lens are good
examples of concave mirrors. As concave mirrors of spherical
form are expensive, a cylindrical form, such as the section of
a piece of pipe, is often used; but the cylindrical form cannot
throw a picture on a screen.

The following experiments, described with reference to a
concave cylindrical mirror, are equally well adapted to a
spherical concave mirror, of which one, at least, should be in
every laboratory.

356. Image in a Cylindrical Concave Mirror. — Trim a card till
the end is 2 or 2.5 cm. wide. Lay the card down and turn up

the short edge 1 cm. Make marks or letters

at A and B, Fig. 314, one red, the other blue.

Set the mirror on a sheet of paper and mark

the edge of the mirror. Place the lettered

edge of the card, which is the object, close to

fig. 31^. ^YiQ mirror. Pull the card 5 cm. away, and

mark its position by a line under the lettered edge. Does the

image have the same direction as the object? Is the image

formed in front of or behind the mirror ?

Point the ruler at the image of the corner of the card near A.
Draw a line along the edge of the ruler. This line points to
the image of the corner. Draw another sight line pointing to
the same image. Continue these lines, removing the mirror if
necessary. The image, if formed behind the mirror, cannot be
thrown on a screen, and is therefore unreal, or, as we say,
virtual. Place the lettered end of the card 1 cm. away, and
repeat. Which image is the larger ? How far away from the
mirror is the object, when the image is indistinct, the red or
blue mark appearing to spread across the mirror ? Mark this
position of the card. Withdrawing the card still farther,
determine whether the image is reversed or not.

CURVED MIRRORS. 329

Exercise 56.
FBINCIPAL FOCUS OF A GOKCAYE MIBSOS.

Apparatus : Concave mirror ; sheet of paper ; lamp.

Set the mirror on the paper, with the concave side toward a lamp,
L, Fig. 315, which is 5 or 6 feet away. L is so far away that the
point F, where the reflected rays from the mirror, My meet, is, for
practical purposes, the principal focus.
This point, F, will be where the light /t^
streaks that appear on the paper cross / '\

each other ; it is also the brightest point. I / ^

The focal distance is so short that the M
light several feet away has the same Fig. sis.

focus that rays from a very distant ob-
ject — the sun, for instance — would have. Measure the focal distance
and compare it with the distance of the card from the screen in
section 356, page 328, where the colored letters appeared to extend
away across the mirror. Cover up the edge of the mirror with a card
held vertically. Notice that some rays are cut off, which, on reflection,
did not pass through the principal focus F, In fact, F is the focus
only for rays that are reflected by a small strip of the centre of the
mirror. The mirror is of circular or spherical form. Just as lenses
do not have the same focus for rays passing the edge and the centre
of the lens, because the surfaces of lenses are circular in shape — that
is, are parts of spheres — so circular mirrors have the same fault.

Place the lettered edge of the card shown in Fig. 314 so it will
face the concave mirror of which the focus was measured. Move the
card back and forth till the edge facing the mirror is of the same size
as the image. On the paper mark the edge of the mirror and the edge
of the card. Measure the distance of the card from the mirror. If
the radius of curvature is 2 inches, how does this distance compare
with the distance of an object from the mirror when the image and
object are of the same size?

Place the edge of the card, A B, halfway between the focus and the
centre of curvature, and determine whether the image is magnified or
not. Place the card a distance from the mirror somewhere beyond the
centre of curvature ; what can be said of the size of the image ? With
reference to a concave mirror, where must an object be placed so as to
be magnified ?

330

PRINCIPLES OF PHYSICS.

Determine the position of the image of a pin halfway between the
focus and the centre of curvature, by drawing two or more sight lines
pointing at the image of the pin in the mirror. Determine the posi-
tion of the image in the same way when the object is farther away
from the mirror than the centre of curvature.

357. A Mirror in the Form of a Parabola (Fig. 316) is straighter
at A and B than at the centre, and such a mirror brings all
parallel rays, as C and Z), to the focus, Fy whether the rays are
A^ iiear the centre, as D, or far away from

the centre, as C If a bright light is
placed at F, the rays, after reflection, are
parallel. Search-lights, much used in the
navy, are made in this way, with a power-
ful electric arc light at F. The reflected
rays can be made fairly parallel. By
moving the light a little nearer the mirror,
^^ the rays C and D diverge slightly, but are

F«g. 3ie. go powerful that by means of them a book

may be easily read at night by a person five miles away. Hold
a candle in a darkened room at the focus of a concave spherical
mirror, and examine the circle of reflected light several feet
away.

CHAPTER XXII.
DI8PEB8I0V OF LIGHT.

358. The Spectrum. — Look through a prism at a bright
object or light. A triangular bottle or tank filled with water,
or a glass prism of any angle, will cause the objects to appear
colored, — red on one side and blue on the other. A prism of
60^ displaces the image more than a prism of smaller angle,
and at the same time colors the image more. On a clear, sun-
shiny day try the following experiment : —

Hold a prism, having one face ground rough, in the sun's
ray, and turn the prism till the refracted and colored light falls
on a white surface. Partially close the shutters and blinds,
and, if possible, shut out all light except that passing through
the prism. Cover one face of the prism with paper, except
a slit one millimeter wide, extending nearly the whole length.
Support the prism with one edge down, and place it where the
sun shines upon the slit Adjust so that a band of colored
light falls on a wall or screen of cloth or paper.

Make a diagram like Fig. 317, on an enlarged scale, and
locate the yellow, green, and blue, as well as the violet and
red. Show the relative width of
the colors, using colored crayons
if possible. Violet light is bent
or refracted more than blue, and
blue more than green, and so on
to the least refracted rays that can
be seen — the red. Beyond the ^

red there are heat rays invisible

to the eye, and beyond the violet there are other invisible rays
that esert chemical action, — that will blacken silver paper,

331

332 PRINCIPLES OF PHYSICS.

for instance. All the visible rays exert chemical action, — a
very little in the red, more in the green, and still more toward
the violet. The colors into which white light is decomposed
form what is called the specti*um.

359. Dispersion of Light. — The separation of the colors is
due to different amounts of refraction ; violet, being refracted
more than red, is separated from that color. This separation is
called dispersion.

360. Composition of Light. — Hold a second prism of the
same angle, with its edge up, in the light that passes through
the first prism. The colored rays, which by the first prism
were spread out, are now bent back again and brought together
and form a patch of white light. Hold a lens in the path of
the colored rays, and bring the rays to a focus on a screen.
Here, too, they recombine and produce white light. Keflect
the colored rays on a white wall or ceiling. Rapidly tilt the
mirror back and forth a little. The impression given to the
eye is that the colors overlap and mix, and a streak of white
light is seen, except at the ends, where a little color appears.
White light, as will be seen from these experiments, is com-
posed of a number of colors.

361. Color. — The colors of the spectrum of any solid heated
white hot are always the same. Whether the white light
entering the prism comes from an arc light, a piece of lime
heated by an oxhydrogen flame, an incandescent lamp, a gas
flame, a candle, or the sun, a spectrum containing all the colors,
from red to violet, is formed. An arc light gives strong blue
and violet, while a gas flame is richer in red and yellow than
in the colors toward the violet end. While, for convenience, a
few names only are given to the colors, there is really an
unlimited number of them. In the red there are different
shades, verging to orange and then to yellow, and, in the varle-

DISPERSIOy OF LIGHT. 383

ties of blue and violet, an intermediate one of indigo is some>
times named. The colors then would be red, oramgej yeSoiD,
greeriy Utie, indigo, and violeL

It might be expected that the colors of the spectrum could
be seen in nature ; but no rose is exactly the color of any part
of the red of the spectrum; grass and leaves are never the
same green as the spectrum color ; and the blue of the sky is
far from being like what we call blue in the spectrum. With
some difficulty can artificial colors be found that imitate the
colors of the spectrum.

362. lOxtiire of Colors. — Return to the spectrum, Fig. 317,
page 331. Hold a lens in front of S and bring the colors to a
focus, making a spot of white light. Between the lens and the
prism move a card so as to cut off the red. The spot changes
to a color composed of all the spectrum colors except red.
Move the card, cutting off the red and yellow ; then cut off the
red, yellow, and green. Repeat, beginning to shade the violet
and blue. Cut off the central colors, yellow and green, by a
match or pencil. If the pencil is held close to the prism, more
of the expanding rays are cut off. The color of the spot is now
caused by the mixture of certain proportions of red and violet.

By combining different spectrum colors of different intensi-
ties, any known color or shade of color may be produced ; the
variety is endless. WTiite, which is a combination of all the
colors of the spectrum, can be mixed with any one color or
set of colors. Black, which is the absence of all color, also
produces many shades in combination; grays are white and
black, chocolates are red and black.

In all this work, colored lights, not colored paints, have been
mixed. The. colored lights, or the light sensations, are min-
gled, and produce the effect on the eye of a compound color.
On a whirling apparatus, overlapping disks of different colors
give, when rotated rapidly, a variety of shades, depending on
the colors of the disks and the amount of them used. Here

334

PRINCIPLES OF PHYSICS.

colored paints are mixed. The spectrum colors, properly ar-
ranged on the disks, produce the effect of white with a grayish
tinge; for it is difficult to obtain paints or dyes that are
exactly like the pure colors of the spectrum. But, since gray
is a mixture of white and black, while black is the absence of
all color, the experiment is convincing. White is a combina-
tion of colors.

Orange and green produce, upon the eye, the effect of yel-
low; but it is impossible to produce green by mixing any
two pure colored lights.

363. Mixing Colors. — Place on a black surface any two
pieces of colored paper ; for instance, yellow or red at Y, and
blue at B (Fig. 318). Hold a glass plate as shown in the figure.
Looking from the position A toward Y) move or tip the plate
till the yellow through the glass and the blue reflected from
the surface of the glass are seen at the same time. If the
colors are pure, the resulting color is a dull white. Raise or
lower the plate, so that the proportion of the two colors varies.
The resulting color is yellowish or bluish, according to the
position of the plate. A position can be
found where neither the yellow nor the
blue predominate ; the result is then a
gray white. As the plate is tilted so
that the light from B strikes the glass
in a direction more nearly parallel to
the surface, a greater amount of blue
light is reflected. Whatever light is
not reflected is absorbed by the glass
or is refracted and passes through the
glass to the other side. Try other
combinations of colored papers. This
^'**''®* experiment illustrates the statement

that the amount of light reflected from a surface varies with
the angle of incidence.

DISPERSION OF LIGHT. 335

364. Absorption of Colors. — Hold sheets of glass or gelatine
of various colors in the path of the spectrum. Blue glass ab-
sorbs, or stops, all the light except the blue and violet. Ruby
glass, such as is used for the windows of photogi'aphic dark
rooms or for dark-room lanterns, absorbs all except the yellow
and red. Since most photographic plates are little affected by
yellow and red light, a room is made photographically dark by
orange or ruby glass windows, although the eye can see and
distinguish objects by red or yellow light. Colored glass for
railway signals is tested in this way. A good red glass, held
in the path of a spectrum, allows no green or blue to pass
through it. Tanks used for projection or flat-sided glass bot-
tles, filled with solutions, such as permanganate of potash, bi-
chromate of potash, and copper sulphate and ammonia, and
various colored dyes, such as red ink, can be used to absorb
various parts of the spectrum.

Try the effect of a glass or liquid that absorbs all but the
yellow and red, and a blue glass or a blue liquid, such as the
copper ammonia solution just mentioned. Arrange them so
that the light must pass through both. The light is some-
times completely shut off, or a part of the green only is seen.
The yellow glass does not absorb the green ; neither does
the blue glass absorb the green. It can be seen now why
a mixture of yellow and blue paints makes a green paint.
Place a piece of yellow paper or cloth in the spectrum. Where
the yellow, red, and green lights fall, the paper has those
shades ; it absorbs the blue and violet, reflecting the other
colors to the eye. Try red, blue, and other colored materials.
A blue ribbon looks black in yellow light, for the ribbon re-
flects blue, violet, and a little green light, and absorbs the rest
of the spectrum. Since green is not absorbed by either a yel-
low or a blue paint or dye, the mixture reflects only green to
the eye, and therefore looks green. The same principle holds in
mixing other colored paints. Remember that it is the reflected
colors of objects, not the absorbed colors, that come to the eye.

336

PRINCIPLES OF PHYSICS.

365. Achromatisqi. — Look through a lens of short focus and
of considerable diameter. Objects appear fringed with the
colors of the spectrum. This effect is obtained even with a
lens of six-inch focus, by holding one edge close to the eye and
looking at something bright. Focus sharply on a screen the
image of a bright light. The spectrum coloring is present in
every part of image, but is probably not evident to the eye.
Move the lens nearer the screen ; the image becomes not only
blurred, but colored yellow or red on the outer part. Move
the lens farther away ; the outer part is colored blue.

366. Achromatic Lenses. — If the same experiments are tried
with a photographic lens or the front lens of an opera glass or
telescope, the fringes of color will be very slight, if found at
all. Such lenses are called achromatic (without color). The
focus, however, for the simplest forms of lenses is not the
same for all colored lights.

367. Effect of Dispersion on the Focus of a Lens. — Allow the
sun's rays to pass through a lens, Z, Fig. 319. The rays

cross near F, the principal focus.
Hold a card at F; move it
toward A a little. The circle
of light on the card grows
larger and is fringed on the
outside with yellow. Move

the card toward B; the fringe changes to blue.

Construct Fig. 320 in the note-book. Draw, in order, the

lens ; the path of the blue rays, with heavy or blue lines, and

mark the focus on the blue rays;

the path of the red rays, with

dotted or red lines, and mark their

focus. Explain why the circle of

light on a card held at A, Fig. 319,

is bordered with red, and why with

blue at B, Which kind of light is bent or refracted the most,

Pig. 319.

Fig. 320.

DISPERSION OF LIGHT. 337

yellow or blue ? Inside the border of the circle, the spectrum
colors are recombined much the same as in section 360, page
331, where a lens was used to bring the scattered colors of
the spectrum together to form a white light.

Looking at Fig. 321, we see why the image of a light or
brightly illuminated object appears to be surrounded with
red or yellow
when the lens is

near the screen. £eamo/ white ught
If the screen
is anywhere be-
tween the focus Beam 0/ white light

of red and the ^ "^^^j}

lens, as at ABy Fig. 321.

the image re-
ceives red and yellow on the outer part. If the screen is at
CD, violet and blue fringe the outer part of the image. Now,
a lens is composed of an immense number of prisms and pro-
duces the same effect as the prism in Fig. 321.

368. Achromatic Prisms. — Up to the time of Sir Isaac
Newton, and for a long time afterward, lenses of considerable
size were ground and polished for the front lenses, or object
glasses, of telescopes. As large lenses collect, or concentrate,
most light, the images of faint stars can be more clearly seen
when magnified to a greater size by lenses held in front of the
eye, called eye-pieces. But it was found that the larger lenses
and higher magnifying eye-pieces gave images blurred with
the spectrum colors. The lenses were not achromatic. This
difficulty is less in long focus lenses, and these were tried
with a little better success. Newton gave up the problem,
and large concave mirrors were tried. Since all colored light
is reflected at the same angle, there is no blurring of the
image due to the separation of light into the prismatic colors.
Lenses used to form an image of the sun, for instance, produce

388 PRINCIPLES OF PHYSICS.

a red image (see Fig. 321) at a position nearer the lens than the
principal focus, and a violet image farthest away, and images
in the other colors between the two. The problem of making
these colored images lap over one another, that is, to make
them come to a focus at the same point, was solved by DoUand.
He first made an achromatic prism. Try his experiment.

369. DoUand's Experiment. — Look through a glass prism
of small angle (about 24°); the edges of all objects appear
colored. Pass a ray of sunlight through the prism ; the ray
is not only bent (refracted) out of its path, but the different
colors are refracted different amounts, and the white light is
spread out (dispersed) into the colors of the spectrum. Try
the same experiment with a water prism of about 40°. This
angle is chosen because a water prism of 40° disperses the
spectrum as much as a glass prism of 24°. Stated roughly,
crown glass has a dispersion nearly double that of water. The
bending effect — that is, the refraction — of glass is by no
means double that of water. The index of refraction of water
is 1.33, of crown glass 1.52, — only about one-seventh greater.
Place the glass prism on the water prism, bringing them
closer together than in Fig. 322. Look through both. If the
observer is at A, an object at B appears bent
or deviated, but is not colored. Pass a ray of
sunlight through the two prisms. The water
prism is of large angle. It bends the ray con-
siderably, and separates the colors to a certain
Fig. 322. extent. The glass prism, being placed with

its edge in the opposite direction, bends the rays back; but,
as it is a much smaller prism, it does not bend them entirely
back. The separation of the colors (the dispersion) is the
same for the large water prism and the small glass prism.
The two prisms are so placed that one tends to separate the
colors in one direction, and the other tends to separate the
colors in the other direction. The result is that white light

DISPERSION OF LIGHT.

889

is not spread out and separated into the prismatic colors by
the two prisms used together. Wet the glass, and the prisms
will stick together. Place
the glass on the water
prism, with the glass prism
a little above. Hold them
in the sunlight. Light now
passes through the glass
alone, through the two
prisms, and through the
water prism alone. The prisms are at P (Fig. 323). The colors
at A are in the opposite order from those at B and are of the
same length. At C the colors are recombined and form a color-
less patch of light. Yet C is not in the line of the ray of the
sunlight.

Fig. 323.

370. Crown and Flint Glass Lens. — Because of the incon-
venience of water lenses, Dolland studied different kinds of
glass. He found that flint or lead glass had a slightly greater
refracting power and nearly double the dispersion of ordinary
(crown) glass. The water prism or lens was replaced by one
of crown glass ; the other prism or lens, made of flint
glass, was of smaller angle or less curvature. The
latter was a concave lens, as if two prisms were
placed with the edges together (Fig. 324). The lead
or flint glass lens, though of less bending power than
Fig. 324. *^® crown glass lens, has the same dispersive power ;
that is, it separates the colors of white light almost
exactly as much as the crown glass lens. However, since the
crown glass lens has a much greater curvature, and con-
sequently shorter focal length, it bends the rays more; the
concave flint glass of less curvature bends them back. As a
result, the rays of all colors are bent, and yet come to the
same focus.

CHAPTER XXIII.

PHOTOMETRY.

371. Standard of Light. — We have standards of length that
vary but slightly, or practically not at all ; a metal rule does
not change in length unless the temperature changes. Our
standards of weight are lumps of metal ; these can be made
one like another, and they do not change, that is, do not become
heavier or lighter. The standard of light is not so satisfactory.
In England and America, the standard is the light given by a
sperm candle burning 120 grains, or 7.7 grams, per hour. The
candles weigh one-sixth of a pound, and are made uniform.
The amount of light vaiies with the shape of the candle, the
amount of charring of the wick, the temperature and purity of
the air, and the centring of the wick. It is supposed that the
amount of light is proportional to the weight of the candle
burned. This is not exactly true, but in default of a better
standard,^ the candle is still used. A variation of more than
five per cent in the rate of burning makes an unreliable test,
and is thrown out; the extremes of time of burning for 20
grains, are 9 minutes 30 seconds and 10 minutes 30 seconds.

372. Photometry. — As the candle was formerly almost ex-
clusively used, and to-day is very generally used the world
over, the illuminating power of any substitute, whether oil, gas,
or electricity, is expressed by the number of candles the light
can displace. The measurement of the light of any lamp — that
is, the determination of the number of standard candles that
would give as much light as the lamp — is called Photometry,

1 For other standards, see Dibdin's Practical Photometry,
340

PHOTOMETRY. 341

373. Diffusion of Light. — Lights are not tested by looking at
them, but at some objects illuminated by them. The amount
of light falling on an object varies with the distance from the
source of light. A book held close to a light cuts off nearly half
of the light given out. Held farther and farther away, the book
cuts off less and less light. The amount of light the book stops,
or cuts off, is the amount that falls on and illuminates the book.

Darken the room somewhat. Place a screen four feet from
a light. Hold a book two feet from the light. Measure the
size of the shadow and the size of the book. How many times
larger than the book is the shadow ? How much farther away
from the light ? A certain amount of light fell on the book,
and the same amount, when the book is removed, falls on the
space that was occupied by the shadow, which was four times
as large as the book. The shadow was twice as long and twice
as broad. This is strictly true only when the source of light
is a point. The light on the screen at double the distance of
the book from the light is only one-fourth as strong as the
light on the book. Place the screen three feet from the light
and the book one foot from the light. Measure the shadow ;
it is nine times as large as the book. The screen, three times
as far away, receives only one-ninth as much light as it would
receive if it were one foot away from the light. The farther
away, the less light. At twice the distance, one-fourth the
light, and at three times the distance, one-ninth the light,
would fall on the screen.

In changing from a strong to a weak light for reading, we
unconsciously try to go nearer the weaker light, so that the
page will be as well illuminated as before. While such a test
may tell which is the stronger light, the results are inaccurate.
We must compare the two lights at the same instant.

374. Law of Diffusion of Light. — The illumination, or amount
of light that falls on an object^ diminishes as the square of the
distance increases.

342 PRINCIPLES OF PBY8IC8.

375. Principle of the Photometer. — Make a spot of grease or
oil in the centre of a sheet of heavy unsized paper, such as
drawing paper of fine grain. Oil soaJcs through easily, but if
tallow or wax is applied, the paper should be heated. Hold
the paper toward a window. Which is the brighter, the plain
paper, or the grease spot ? Stand with the back to the win-
dow, and look at the paper ; which is the brighter now ? Set
up two candles, a meter or more apart. Hold the paper be-
tween them so that the light from the candles falls on opposite
sides. When the paper is nearer one candle than the other,
on which side does the spot look bright ? Which side receives
the more light ? Can you place the paper where the spot dis-
appears, or, if it does not disappear entirely, where the spots
on the two sides look equally dark or bright ?

376. Bunseo's Photometer. — Place a paper, on which there
is a grease spot, Z>, Fig. 325, usually called a disk, in a support
which is fitted with inclined mirrors, M, 3/i, so that the two

sides of the disk, reflected in
^^ **^ the mirrors, can be seen at

&' the same time. The disk
must be moved near one of
the two lights which are to
be compared, L and Z^i, until
the spot disappears, or until the reflections of the two sides
look alike. Practise making the setting, and measure the dis-
tances LD and LiD. How do these compare? Ordinary can-
dles vary from moment to moment, and so the distances from
the screen to the candles will vary somewhat.

For practice in setting the disk, remove it and the support
carrying the mirrors. Take it between two windows, and
revolve it, all the time watching the reflections of the sides of
the disk in the mirrors. With some disks, the spots can be
made to disappear; but, even if this is impossible, a good
setting is made when the two sides of the disk look alike.

Fig. 325.

PHOTOMETRY. 343

The Bunsen disk is often in a box painted a dull black, and the
openings in the ends are large enough to let in light from the
candle and lamp to be tested, but not large enough to let much
stray light from the room fall on the disk. Boards or boxes
painted black, or covered with black velvet, are placed behind
the candle and lamp, so that no light can be reflected on
the disk.

Exercise 57.
PHOTOMETST.

Apparatus : A Bunsen photometer, which is two meter rods on flat supports,
end to end, and a box containing disk and inclined mirrors, placed on the
meter rods; a candle at one end of the rods and two candles at the other
end. Allow the candles to burn a moment, till the flames are as nearly
equal as possible.

Move the box till the appearance of the disk indicates that the sides
of the disk are equally illuminated. Make a diagram (not to scale)
like Fig. 326, and record the distance,
a, of the single candle from the disk,
and the distance, 6, of the two candles
from the disk. Move the disk some

distance to the right or the left, and ^'^' ^^^'

reset. Measure again the distances from the disk to the candles.
Repeat several times. Average the values of a, and also the values
of 6. Square the values of a and 6, and divide h^ by a^. How near
does the quotient come to the number 2?

Place one candle at L and three candles at Lj, and repeat the
exercise. Is the square of h three times the square of a ? Try four
candles at L and one candle at L^ Multiply the distance h by itself;
is the product four times as large as a multiplied by a?

877. Formula for Bunsen Photometry. — Test the following
formula : —

(Distance of light L)' _ candle power of L
(Distance of light Z^)* candle power of Li

344 PRISCIPLES OF PHYSICS.

The shorter form is : —

g* _ e. p. of Z
6* c. p. of Li*

a being the distance of L from the disk in the experiment,
b the distance of Zq from the disk.

378. Candle Power. — As candles do not all bom at the saiKi€
rate, some give more light than others, and a candle may lye
burning brightly one moment and dim considerably the nex^
owing to the varying shape and size of the wick. In the
experiments, we assume that all the candles give the same
amount of light This is not so ; but by averaging a number
of readings taken at frequent intervals, the result approaches
nearly what would be obtained with uniform candles. Com-
mon paraffin candles are suitable for the experiments.
Standard candles are expensive, and they, too, vary in their
rate of burning. In practical work, the standard candle is
supported on one end of a balance, and the time is taken for
the burning of 10 grains (.67 grams). This is exactly five
minutes, if the candle has an even cup, neither too dry nor
filled with sperm, and the wick is properly curved, of uniform
diameter; and glowing red at the end, and is burning 120 grains
an hour, at which rate it is supposed to give one candle of light,
and is called a legal candle.

379. Use of the Formula in testing Lights. — Almost always,
the practical question in photometry is: What is the candle
power of a certain light ? Returning to the apparatus of Ex-
ercise 57, page 343, balance a gas or kerosene flame against a
candle, preferably a standard candle. Suppose that L (Fig.
326) is a standard candle; it gives 1 candle power of light.
Ordinary candles are often of a little less, but will do for
experiment. Suppose a = 20 cm. and 6 = 50 cm. Required,
the candle power of the light. Substituting in the foripula,
we have

PHOTOMETRY 346

20* 1

-— = -> where x is the c. p. of the light tested.

o(r X

400 1

2500 X
400a; = 2500,

a? = 6 J candles.

Mea43ure and compute the candle power of a kerosene or gas
flame, first, with the wide part of the flame facing the disk, and
then with the edge facing the disk. Which position gives the
more light ?

The candle power of gas flame is the light given when the
gas is burning at the rate of 5 cubic feet per hour, or calculated
to this rate. We cannot burn oil gas, for example, much faster
than between 1 and 2 feet per hour, 1 foot giving, say, 12
candles. Such oil gas would be rated at 60 candle power,
meaning that 5 cubic feet burned an hour in suitable burners
would give 60 candle power.

Find the candle power of a Welsbach burner, an Argand
burner, an incandescent lamp, or an acetylene flame. The low
form of Bunsen burner can be fitted with lava tips, using from
1 to 6 cubic feet of gas an hour. The air opening must be
tightly closed by rubber tube or wet paper tied around it.

880. Rttmford's Method. — The shadow photometer of Count
Kumford was one of the first successful attempts to measure
light. Shadows of two lights are compared, and one light is
moved nearer or farther away from the wall or screen on which
the shadows fall, until they look equally dark. The object
casting the shadow may be a pencil a few inches from a sheet
of paper. The lights to be compared are so placed that the
shadows are near together. The screen receives the same
amount of light from each light when the shadows are equally
dark. The distances are measured from the lights to the screen,
and the same formula is used as in the Bunsen photometer.

846 PRINCIPLES OF PHYSICS.

The Rumford method is not used in practical work. Light
from a window or from lights other than those being tested
interferes seriously with the accuracy of this method.

Problems.

1. If a standard candle is 50 cm. and a gas flame 300 cm. from the

disk of a Bunsen photometer when the spot disappears, what is the

QAAa
candle power of the gas flame? Ana, = 36 c. p*

2. A candle 40 cm. from the disk balances an incandescent lamp
120 cm. from the disk. Compute the candle power.

3. When a balance is obtained with a candle 30 cm. and an arc
light 500 cm. from the disk, what is the candle power of the arc light?

4. In the preceding problem, if a newspaper replaces the disk, which
side of the paper is the brighter ?

5. How far away is a 25 c. p. gas flame, to give the same illumina-
tion as a candle 2 feet away?

Substitute in the formula.

ft2 2o
100 = 62. J = what?

6. Wishing to compare a gas and an arc light, a man moves about
till he finds a position where the shadows cast by a cane look alike.
The distance from the gas is 10 feet, and from the arc light 50 feet.
How many times more light does the arc give than the gas?

7. How far away must a 16 c. p. gas flame be, to illuminate a book
as well as a candle 1 foot away does ?

Substituting, K = ^- ^^ = 1^- 6 = what?

8. How far away must a 400 c. p. arc light be, to throw as much
light on a sign as a 9 c. p. lamp 4 feet away ?

9. In a Bunsen photometer, a standard candle is 30 inches from
the disk ; a lamp is 70 inches from the disk. Find the candle power
of the lamp.

PHOTOMETRY. 347

381. Candle Power of Various Lights. — A gas flame of flat
form, burning 5 cubic feet of gas an hour, has a candle power
of from 16 to 2^^ according to the quality of the gas. The
Argand burner consists of little holes in a ring ; the flame is
circular, and gives about the same candle power as the ordinary
flat flame. The Welsbach consists of thin gauze of oxides of
rare metals in the form of an inverted bag. The gauze is
heated by a Bunsen flame. Three cubic feet of gas an hour
in one of these burners give 40 to 100 candle power.

Acetylene gas in \ foot burners gives 24 candle power.

Incandescent electric lights seldom give the candle power
marked on them. The light given by them increases very
rapidly with a slight increase of current. After some use, the
filament allows less current to pass through, and they give
less light, unless the pressure of the current is increased.
Incandescent lights are usually intended to give 16 candle
power of light, although they are made of from a fraction of a
candle power to 1000 candle power.

Arc lamps, using from six to ten amperes, vary from 300 to
800 candle power. Eight to ten ampere lamps are 2000 candle
power, nominal. This is supposed to have been obtained by
measuring an arc which gave 500 candle power, and adding up
the measurements of the four sides. Arc lamps cannot well
be made to take less than three amperes ; and the light of any
arc becomes reduced to almost nothing if the carbons come too
close together.

CHAPTER XXIV.
OPTICAL nrSTBUMENTS.

382. Picture formed by a Lens. — Review Exercises 48, 60,
and 53 till the following statements regarding lenses are clearly
in mind; —

Conjugate foci for real images are always greater than the
principal focus.

The focus for distant objects is the principal focus.

As an object is brought nearer a lens, the focus (conjugate)
is farther and farther away.

The difference in size between the object and image depends
on their distances from the lens.

By the use of the apparatus of Exercise 48, page 300, draw on
a screen the outline of the image of a building, by marking
with a pencil the outlines seen on the screen. On the drawing,
which may be kept in the note-book, put the focus of the lens,
and, if known, the distance and size of the object. If these
measurements cannot be made conveniently, use, in place of a
building, the window as the object, and mark the outline of
the window sash on the screen. In this case, record both the
principal focus of the lens and the distance from the lens to
the image of the sash. Why is this distance slightly greater
than the principal focus?

383. Principle of the Camera. — Expose a bit of silver paper,
an inch or two square, to the light of the window. In time
the paper darkens. Focus the sun's rays on another piece of
silver paper. The image of the sun — a little round bright

348

OPTICAL INSTRUMENTS. 349

spot — is where all the sun^s rays that came through the entire
lens are concentrated. The paper is darkened almost instantly
at this spot. On another piece of paper, focus the image of a
building or of the window frame. Probably long before the
faint light coming through the lens and forming the picture
produces any visible effect, the light which comes from all
directions around the lens and falls on the paper will com-
pletely blacken it.

Repeat the experiment, covering the silver paper and lens
by a pasteboard box blackened on the inside with shellac and
lampblack. Make a hole in the end oi the box, in front of the
lens. See that no light enters except through the lens. If
the building, tree, or window serving as the object is very
bright, in some minutes a distinct outline of the picture will
be visible.

384. Photographic Camera. — In practice, the instrument used
in taking pictures, called a cameray does not differ essentially
from the arrangement just described. A screen of ground
glass is moved toward or away from the lens till the picture
is sharp. The ground glass is then removed, and in exactly
the same place is put the photographic plate. This consists of
a mixture of a silver compound, spread on a glass plate or
celluloid sheet. It is more sensitive than the silver paper used
above. The light is allowed to pass through the lens for from
a fraction of a second to many minutes, the length of time
depending on the lens, the brightness of the object photo-
graphed, and the sensitive plate. The image does not appear
at all until the plate is put in a mixture of chemicals called a
developer. All light excepting that passing through the lens
is kept from reaching the plate, which is virtually in a box
entirely dark except the lens opening. The sides of the box
are made flexible, because the distance between the lens and
the screen, or sensitive plate, must be changed when the object
is brought nearer the lens. While a fairly good picture can be

350 PRINCIPLES OF PHYSICS.

taken by the very inexpensive lenses used in the experiment,
yet it is difficult to adjust the focus ; because to the eye, being
most affected by red, yellow, and green rays, the focus will
appear to be (see Fig. 320) at the crossing of the red rays.
But the focus for the blue and violet rays, which affect the
plate, is at the point nearer the lens, and these rays will not
be in focus where the plate is placed. The focus of the rays
that affect the sensitive plate is shorter than the focus of the
rays that affect the eye. A picture taken by the simple lens
used is likely to be a little out of focus, or blurred. Photo-
graphic lenses, even when called "single lenses," almost in-
variably consist of a convex lens of crown glass and a slightly
concave lens of flint glass, except in the cheaper forms of fixed
focus cameras. A combination may be made to have the same
focus for all colored rays, and is called achromatic (see section
370, Fig. 324).

385. Defects in Single Lenses. — It may have been noticed
there is difficulty in finding a position where the image made
by a lens on a screen is perfectly sharp. As has been stated,
for convenience in manufacture the surfaces of all lenses are
parts of spheres. To study the defect in lenses
caused by the spherical curvature of the sur-
faces, fasten a card, CC, Fig. 327, to the front
of a lens of 1^ or 2 inches diameter and of short
focus (2 inches). Make two openings in the
card, about as large as a pencil, one close to the
edge of the lens, the other over the centre. Focus
the image of the filament of an incandescent lamp
or of an opening in a card in front of a bright
lamp, allowing the light to pass only through the opening.
By in front of the centre of the lens. Cover B and open A.
The image is no longer distinct, and the screen must be
moved nearer the lens. If possible, measure the focus for
the rays through A and the rays through B. Is a lens of

OPTICAL INSTRUMENTS. 351

the same focus for rays that pass through the centre and the
edge?

386. Spherical Aberration. — The defect in lenses, arising
from the spherical shape of the surfaces, is called spherical
aberration. In the very large lenses, 20, 30, or 40 inches in
diameter, used in telescopes, it is possible so to change the cur-
vature of the lens as to remove this defect. The work is done
largely by rubbing the surface of the glass with the hand.
Several years were spent in perfecting the lenses for Lick and
Yerkes telescopes, at great expense. In lenses for ordinary
telescopes and photograph cameras, spherical aberration is
avoided by placing a small opening somewhere in the path
of the rays,^ or by combining different lenses.

In photographic lenses, a small opening (in S Fig. 328), called
a stopy is placed a little in front of the lens. The light from
the centre of the object 0 cannot pass ^

through the margin of the lens. Rays form-
ing the central portion of the image must
pass through the centre of the lens, while
rays from 1 and 3, forming the margin of
the image, must pass through the opposite
margin of the lens. The image of point 1
of the object 0 is formed entirely from
rays that pass the lower margin of L, P'«" ^^s.

387. Use of Lenses of Different Foci. — Arrange lenses of dif-
ferent foci in lens holders, and focus them all on a sheet of
paper, placed at a considerable distance from a window. Com-
pare the sizes of the pictures and the foci of the lenses (see
section 348, Fig. 303). If it were impossible to go very near a
building, how could a large picture of it be taken, — by a long-
focus or a short-focus lens ? If a camera can be placed only
in a narrow street, so near a building that the picture of it

i Examine diagrams of lenses in a photographic catalogue.

352

PRINCIPLES OF PHYSICS.

more than covers the size of the plate used, which lens should
be substituted, that a picture of the entire building may be
taken, — a longer or a shorter focus lens ? *

388. Focal Length of Combination of Lenses. — Put two lenses
of the same focal length together, and find the focal length of
the combination. Put two lenses of different focus together,
and repeat. Try a concave and a convex lens together ; let the
convex lens have the shorter focus.

Review or repeat the experiment on real image formed by
a lens (Exercise 54, page 320). An ordinary convex lens re-
quires a curved screen, in order to
bring the image of a large object to
an etjually sharp focus in all its parts.
The image of the arrow in Fig. 306
was found to be very much curved.

The lenses, A and L^ (Fig. 329), in
the front of the eye act like one lens.
Z/j, however, can be made flatter or
more convex at will. When flatter, the
focus is longer. The image formed by
the lens is received on a curved screen,
RRy sensitive to light, called the retina,
A curved screen is the best form on
which to receive pictures of very large
objects.

Fig. 329.

r*, the cornoa.
RR, th(> rutina.
JV, tho optic norve.
X,, a<)UoouR humor.
7^, tho crystalline lens.
Z^, vitreous humor.
ii, tho iris diaphragm.
5, the blind spot.
y^ the yellow spot.

389. Accommodation. — From the experiments on conjugate
foci, it was found that the focus of near objects was greater
than the principal focus, and the nearer the object, the longer
the focus. For near objects, then, the distance from the lenses
Li and L^ to the screen, or retina, RR, needs to be increased,

1 The Optics of Photography and Photographic Lenses^ by J. Traill Taylor,
and Lens Work for Amateurs^ by Orford, give simple and interesting; iiifdr-
mation on Lenses.

OPTICAL IN8TBUMENTS. 353

or the lens Lf made more conyex, that is, of shorter focus.
The change of focus of the lens L^ (called the crystalline lens)
is called accommodatiotiy and is done by changing the curvature
of the lens Lf,

390. Concave Lenses. — In near-sighted persons, the eyeball
is elongated; the distance from the lenses to the retina is
greater than the focal length (Fig. 330). Place a short-focus
lens a little farther from a screen than

the focal length ; the image of an object is
blurred, as it is in a near-sighted eye when
distant objects are viewed. Move the ob-
ject, a candle, for instance, near the lens. p. ^^
A point is found where the image is sharp.
The conjugate focus of near objects is greater than the prin-
cipal focus, and, for objects near enough, their focus will equal
the distance from the lenses to the retina, and the image will
be sharp ; that is, the person will see near objects distinctly.
A thickened lens, L^ Fig. 329, also causes near-sightedness.

Remove the candle to a distance. The image is no longer
sharp ; the lens, just as in the near-sighted eye, is too far away
from the screen or retina. Make the lens have a longer focus
by placing a suitable concave lens in front of it. The con-
cave lens may be one of the glasses worn by- a near-sighted
person. After a few trials, the convex lens used can be set a
distance a little greater than the focus for a sharp image, and
the sharpness restored by applying the concave lens.

391. Convex Lenses. — In most " far-sighted " eyes, the power
is wanting to make the crystalline lens more convex for near
objects. The lenses of the eye must be made of shorter focus
by placing a convex lens in front. Hold a lens a distance
equal to its focal length from a screen. A clear image of a
distant object is formed. Bring a bright object — a candle
for instance — within two or three feet. The conjugate focus

854 PRINCIPLES OF PHYSICS.

of this is greater than the principal focus. A dear image
would be formed somewhere behind the screen. Let us sup-
l>ose the screen is immovable, as in the case of the eye. The
f(H5us must be made shorter. This is done by placing a convex
hm in front of the other. Far-sighted persons, in looking at
near objwts, wear convex lenses. Near-sighted persons can
JMH) near objects unaided ; for distant objects they must wear
(H)ncave lenses.

398. Simple Microscope. — Review section 351, Virtual Image
fonned by a Lens (page 323). It was seen that both the
objo^'t and the image were on the same side of the lens;

that the image was larger than the object, and was virtual

oouUl not bo foeussed on a screen. Hold any convex lens near
a page of print. Bring the lens slowly away. In what posi-
tion is the image the largest? Try a lens of different focus;
which magnifies the more ? Sometimes two or three lenses are
(jombined. Use two or more lenses, placed close together, and
determine whether they magnify more or less than one lens
alone. What may be said of the focus of two lenses used
together ? Reading glasses are convex lenses several inches in
diameter, used to magnify print.

393. Telescope. — Focus the image of the landscape on a
card. Use two lenses, side by side, of the same focus, but of
different diameters ; or use lenses of the same diameter, and
cut down the diameter of one by covering it partly with a card
having a hole one-half the diameter of the lens. This prac-
tically makes one lens smaller. The images, however, made
by these lenses are of exactly the same size ; the one formed
by the larger lens is brighter, for more light goes through the
larger opening.

Try two lenses of the same size and different foci; which
gives the larger image? Which the brighter image? In
section 387, it was shown that when the distance from the

OPTICAL INSTRUMENTS. 856

object to the opening or aperture through which a picture is

formed cannot be changed, then the only way to obtain a large

image is to place the screen farther away from the opening.

The distance between the earth and any heavenly body — sun,

moon, or stars — is always enormous. Even when they are

nearest the earth, their images, which are of course formed at

the principal focus of a lens, are very small. For telescopes,

lenses of long focus are used, to make this image as large as

possible, and because it is easier to make and perfect long-focus

lenses, especially if they are of large diameter. To make the

image bright, the lenses rmist be of

large diameter. The greatest expense

is incurred in increasing the diameter.

The image is so small that it must

be magnified by a simple microscope, ^

called an eye-piece. This is a short- ^^'' ^^''

focus lens, or combination of lenses, E, Fig. 331, held near the

real image at F. The observer is at -4.

A simple microscope, when used to magnify print, is called
a reading glass; when used to magnify a real image it is called
an eye-piece,

394. Construction of a Model Telescope. — At one end of a
meter support, pointed out of a window, place a long-focus
lens, Ly Fig. 331, in a lens holder. Find the principal focus, F,
by moving a bit of tissue or oiled paper in a support till a
sharply-defined image is formed. The image can be seen from
either side. A little behind this place a short-focus lens, E,
called the eye-piece. Look through E. The inverted image at
F is seen magnified. Vary the distance of E till the image is
sharp. Remove the paper. The image that was formed on the
paper is now formed in the air at the same place, and this
image is magnified by the eye-piece, E, just as the image on the
paper was. A telescope, in its simplest form, consists of a
long-focus lens, L, called the objectivey and a short-focus lens.

356 PRINCIPLES OF PHY8IC8.

E, called the eye-piece, used as a simple microscope. A real
image is formed at the principal focus, F, and this ims^e is
magnified by the eye-piece.

If E and L were placed in tubes, blackened on the inside,
I. ,,-■ one tube sliding in the other so that the

y I ^^ distance between E and L could be varied,

we should have a rough model of a telescope
»^«-332. ^pig 332^ YoT practical use, the lensL

should be achromatic.

395. The Magnifying Power of a Telescope may be found by
counting the number of bricks in a wall (seen with only one eye)
that seem to be overlapped by one brick seen with the other
eye through the telescope. The magnifying power is nearly
equal to the focal length of L divided by the focal length of E.
Determine these lengths and compute the magnifying power.
If the focus of j& is 2 inches, and the focus of L is 20
inches, then the telescope magnifies ^, or 10 times, and an ob-
ject viewed through the telescope appears ten times as large as
it appears to the naked eye.

The largest telescope is at the Yerkes Observatory. The
lenses at L are 40 inches in diameter and have a focal length
of about 60 feet.

For use in the laboratory or in astronomical work, the in-
verted image is no inconvenience. At sea, the telescopes used
have such a combination of lenses in the tube between L
and E that the inverted image formed by the object lens is
brought to a second focus and rein verted and made erect.

By the use of two mirrors (see section 322, totally reflecting
prisms), a telescope can be shortened to one-third its usual
length. Besides this, the mirrors reverse the image and make
it appear right side up. This form is convenient to carry, and
is displacing the common form of operorglass and field-glass.

396. Compound Microscope. — In studying pin-hole pictures
(see section 335, page 301, and section 348, page 318), it was

OPTICAL INSTRUMENTS. 357

found that moving the opening or lens nearer the object gave
a larger image or picture. Bring a lens near a lamp. Adjust
the distance (which must be greater than the principal focus),
till the image of the lamp is sharply defined on the wall. The
object being near the lens (section 347), the image distance is
increased and is much larger than the object distance. The
image is larger than the object. This image can be still fur-
ther magnified by a short-focus lens as a simple microscope.

397. Model of a Compound Microscope. — Illuminate a piece
of wire netting, 0, Fig. 333. Place a lens, L, called an objec-
tive, of one-inch or two-inch focus, a little
more than its focal length from the object, 0. ^ f\ A

Find the position of the conjugate focus. Do o ^ p

this by moving a piece of oiled paper back S

and forth till the image is sharply focussed «• 333.

on the screen, S. The object, 0, may be any brightly illumi-
nated object, as a card, on which numbers or letters have been
marked, or a microscope slide. Examine the image on the
screen, S, by looking at it through the eye-piece, E. Eemove
the screen. The magnified image is still seen through E. In
fact, the image is formed by L at S, whether the screen, S, is
there or not. The image at S is larger than the object, and
is still further magnified by the eye-piece. In photographing
small objects (micro-photography), the sensitive plate is placed
at Sf and no eye-piece is then used.

The real image formed at the principal focus of a telescope
is much smaller than the object. In a compound microscope,
the real image is larger than the object. In both instruments,
the real images appear magnified to the eye looking at them
through the eye-piece, or simple microscope.

The compound microscope was less useful than the simple
microscope until the introduction of achromatic lenses for the
objective, about the year 1840. Soon after, the discovery of
gernjs and bacteria began.

358

PRINCIPLES OF PHYSICS.

Fig. 334.

The Magic Lantern and other lamps for projection are
arranged as in Fig. 334. The object at D — a diagram or picture

on glasS) a lantern slide, or a
small piece of apparatus —
is lighted by the sun's rays
reflected by a mirror. The
screen, S, is a white wall or
curtain. The relative sizes
of the object and image de-
pend on their distances from the lens. When an oil lamp,
a lime light, or an arc light is used, the object is made as
bright as possible
by a reflector be-
hind the light, or
a large short-focus
lens in front.
Usually both are
used, as in Fig.
335. The light
from the lamp is
reflected by the
mirror, M, and re- ^^'' ^^*'

fracted by the lens C upon the object, a6, which of course is
pai-tly transparent. The lens I brings the rays from ab to
a focus on the screen, S, making the image, AB.

Problems.

1. The object distance in a magic lantern is 4 inches ; the distance
from the lens to the screen is 40 inches ; how many times larger than
the object is the image ? ^n5. 10 times.

4 inches and 40 inches are conjugate foci. Substitute in the

formula, -- = ^ 4- --, and find the value of F, the principal focus.
^ / /i

2. In a lecture roo?n, the curtain is 30 feet from the lantern ; the
object is a picture two inches high on a lantern slide. How high will

OPTICAL INSTRUMENTS. 359

the image on the screen be, if the lens is 1 foot from the lantern
slide ? If it is 2 feet from the lantern slide ?

3. In taking a picture of a building, which is always the greater,
the object distance or the image distance ?

4. In projecting a picture with a lantern, is the object distance or
the image distance the greater?

5. The objective lens, L (Fig. 333), of a compound microscope is
1 inch focus, the object, O, is 1.1 inches away ; how far from the lens is the

image formed? j^+^ = j /+ 1.1 = 1.1 x/ jL/=l.l /= 11 inches.

How many times is the image magnified? If the eye-piece magni-
fies this image 20 times, how many times does the object appear to
be magnified?

6. If the objective in the preceding problem is .1 inch focus, and
is .09 inch from the object, compute the conjugate focus and find the
magnification.

7. The focal length of the objective of the Yerkes telescope being
60 feet, what would be the diameter ef the moon's disk on a sheet of
paper held at that distance from the lens? The moon's diameter is
about 2200 miles and its distance from the earth 240,000 miles.

399. Experiments with a Model of a Magic Lantern. — The
experiments on conjugate foci and real image formed by a lens
have apparatus which represents the magic lantern in its
simplest form. The object, however, is usually not a flame,
but is strongly illuminated by a flame or in some other way.
If a large lens is at hand (one of 4 to 6 inches in diameter is
best), try the following experiments, after shutting out most
of the light from the room : —

1. Hold a lantern slide, transparency, or photographic negative in
the sun's rays or in a bright light. Place the lens as in Fig. 295,
page 310, but somewhat more than its focal length from the object.
The object replaces the netting at O. Shade the screen as much as
possible from all light, except that coming through the lens.

360 PRINCIPLES OF PHYSICS.

2. In the light near a window hold an engraving or a bunch of
flowers. With the lens cast an image on a sheet of paper a few feet
away.

3. Let a person stand near a window where the sun shines on the
face, if possible, and bring a picture of the face to a sharp focus on a
sheet of paper held in the shade. If there are shutters, close them all
except one. The lens and screen can then be held near the wall and
in comparative darkness, and the image formed, while faint, will be
seen easily.

400. Stereoscopes. — Make a red mark on one side of a card,
and on the other side a blue mark. Hold the card with an
edge toward the face, about 10 inches away. Close first one
eye and then the other. In looking at any point, we see more
of the left-hand side of it with the left eye, and more of the
right-hand side of it with the right eye. When looked at with
both eyes, an object has a solid appearance, which is lacking
when viewed with one eye. An ordinary picture or photo-
graph, especially of a near object, does not appear solid or
lifelike, because both eyes see the same picture. If, however,
two photographs are taken with the lenses several inches apart,
we have two pictures almost the same; but one appears as
the landscape or building would have looked to one eye, and
the other as it would have looked to the other eye. If the
pictures are placed near together, so that the left-hand picture
can be seen by the left eye, and the right-hand picture by the
right eye, the impression given to the brain is the same as the
object itself would have given.

A model of a simple stereoscope is constructed as follows :
Make a circle and a cross, 5 inches apart, on a sheet of
paper. Hold two 20° prisms, one in front of each eye, with
the edges pointing toward each other, and look at the marks
on the paper. These can be made to appear to overlap. The
same experiment may be shown with two lenses, which, of
course, are prisms of many angles combined. Look at the
letters A and B, one red, the other blue, placed three-eighths of

OPTICAL INSTRUMENTS. 361

an inch apart. Hold two convex lenses side by side, one over
each letter. Bring the lens away from the paper slowly till
the letters seem to overlap.

In looking at a near object, the eyes are turned toward each
other, and by the amount of the turning we judge of distance.
In this we are also aided by the necessary movement of the
muscles of the eye, which change the shape of the crystalline
lens so as to bring an object in focus.

CHAPTER XXV.
SOUND.

401. Vibration. — Clamp a meter stick on a table (Fig. 336).

Pull the end A up or down a little, and let it go. The regular

movements are almost slow enough to be counted. Reclamp the

C stick so that the length

tCTN ^^ from A to the clamp is a

Fig. 336.

few inches less than it was
the first time. Bend A
again. The motion of the
stick is more rapid. Make
the length AC still less.
When the length is three
or four inches, the movements are not only too rapid to count,
but they can be seen only with difficulty. A sound, however, is
heard, which is of higher and higher pitch as AC is shortened.
The stick is a sort of pendulum, and obeys practically the same
laws as the pendulum. The movements of the stick to and fro
are just as fast, or just as many times per second, whether the
stick moves over a large or a small distance. So, just like the
vibrating pendulum of Exercise 63, page 399, any vibrating
body, whether it produces sound or not, makes approximately
the same number of vibrations or movements back and forth,
whether the movement, or amplitude, is over a large space or
a small one. There is, however, a difference in the loudness
of the sound, the sound becoming fainter as the amplitude
of the vibration grows less.

402. Rate of Vibration. — Repeat the experiment, using other
strips of wood, brass, iron, or even a glass tube. They will

362

SOUND. 868

give different notes, or pitches, for the same length, because
the size, shape, and materials vary ; but for any one strip, the
pitch becomes higher when the strip is shortened. As the
shorter strip vibrates faster and the pitch of the sound rises,
we may say that pitch depends on the number of vibrations
per second, or, as it is called, the rate of vibration.

403. Transverse Vibrations. — Fasten one end of a rubber
thread, three feet or more long (or better, a spiral of brass wire
of still greater length), to a support. Hold the other end in
the hand. Move the hand up and down at a rate that makes
the whole thread curve upward and then down. The vibra-
tions are at right angles to the length, and are like those of a
tuning fork or the strings of a violin or other stringed instru-
ment. All these are pendulums. Strings are double pendu-
lums, since they are fastened at both ends. The vibrations at
right angles to the length of the vibrating body are called
transverse.

404. Point of No Vibration, or Node. — Give a clothesline or
a long spiral of wire, fastened at F and held at H, a sudden
troughlike depression (I, Fig. 337). The trough runs along to
F, and is reflected, coming back as a crest jj „
(II) ; then it is again reflected from ^ as a S — "^T
trough, and so on. For these experiments,

a rope hanging vertically, such as that in a ^

hand-elevator, is better than a rope sus- ^^'

pended horizontally. By raising and lower- '"'«• ^^^•

ing H at the proper rate, the whole line first rises and then
falls. The rope or spiral vibrates as a whole.

^ What really happens is this : A long trough,

passing from H to F, is reflected as a crest ;

^ this crest coming back is reflected from ^ as a

"*" trough. BymovingJTupanddowntwiceasfast,

rig. 338. ^Yie trough of a second wave is sent toward F,

PRINCIPLES OF PHYSICS.

and meets the first, reflected as a crest, at N, Fig. 338. The
crest tries to pull the particles of rope upward, the trough tries
to pull them downward. The result is no motion at N, just as
if the rope were tied there. N is called a node (meaning
knot). An instant later the rope takes the form shown in
^ ^ Fig. 339. This is repeated, one half of the

y" N. y rope going up while the other half goes

-a x,_^ down. The rope vibrates in halves, and, as

^ — ^ seen by the quicker motion of the hand, the

Fig. 339. vibrations are doubled. By moving the

hand still more quickly, the rope is made to vibrate in thirds,

fourths, etc.

In a long, narrow box, half filled with water, such waves may
be set up by pushing a large stick quickly in and out of one end.

405. Longitudinal Vibrations. — Fasten several pieces of
gummed label along an elastic cord. Hold one end of the
cord firmly in the hand, and with the other hand take hold of
the cord a short distance from the first hand, and pull in the
direction of the length of the cord and then let go. In case a
long spiral of wire is used, fasten a few bits of string at inter-
vals along its length. The stretching will travel back and forth
on the cord or spiral. These lengthenings and shortenings
which travel back and forth are called longitudinal vibrations.
Hold a glass or metal rod at its centre, and stroke it from the
centre toward one end with a rag covered with rosin or wet
with water. The high note heard is caused by the lengthening
and shortening (the longitudinal vibrations) of the rod. This
note is much higher in pitch than that caused by transverse
vibrations, which are set up by plucking or striking the rod.

406. Torsional Vibrations. — There is a third kind of vibra-
tion (torsional), like the twisting and untwisting of a string on
which a weight hangs. A metal or glass rod may be thrown
into torsional vibrations by turning on it a tightly fitting cork
or rubber stopper.

SOUND. 366

407. Medium of Transmission. — Sound must have some
medium — a gas^ a liquid, or a solid — to transmit the vibra-
tion.

Set a dish filled with cotton wool on the receiver of an air-
pump. Lay a dollar watch on the wool. Cover with the re-
ceiver and listen to the ticking. Exhaust the air and listen.
Let in the air and listen again.^

In transmitting sound, the vibrations of the air are longi-
tudinal. (Compare section 405.) If two boards are struck
together, or an inflated paper bag is struck and burst, the air
near by is pushed together or condensed, and the condensation
travels away, spreading and growing weaker. This condensa-
tion is followed closely by a rarefaction (that is, the air is under
less pressure), just as when a stone is thrown into a pond
and causes a crest of a wave, which is followed by a trough.
That the air does not move bodily in carrying the sound of
the blow of the boards (BB, Fig. 340) is shown by striking
them together before one end of a large pipe, such as is used
for rain conductors. Notice the movement of a candle flame,
C. Fill the pipe with ^

smoke made by burn- ■ ' ; v^ ah

*' ,^ S m o k e ^

mg paper or cotton i i ■

cloth saturated with a ^

solution of nitrate of 'g J^o.

potassium and dried. A paper or pasteboard cone on the end

of the pipe, near the candle, will so concentrate the effect of the

wave passing through the air as to put out the candle. A wave

or disturbance travels from one end of the pipe to the other.

The air itself does not move bodily from the boards to the

candle flame, for the smoke is not blown completely out of the

tube, if at all.

The explosion of a powder magazine destroys buildings and

breaks windows at a great distance, although the smoke of a

1 Suggested by W. H. Snyder of Worcester Academy.

366

PRINCIPLES OF PHYSICS.

bonfire near the magazine is not carried along ; but an explo-
sion does cause a current of air. The condensation is followed
by a rarefaction, as the hot gases generated by the explosion
cool down and contract. The rarefaction (which is another
name for contraction), following close behind the condensation
produced at the beginning of the explosion, reaches a building
and causes a lessened air pressure outside, and the windows
and walls, which were blown in a little at first, are then
blown out.

408. A Musical Sound consists of a succession of waves that
come to the ear with regularity. Set a wheel in rapid rotation
by winding a string on the axle and pulling it off quickly.

Direct a jet of air to a row of evenly spaced holes on a disk,
called a siren (Fig. 341). A musical sound is leard. Repeat
the experiment, using a row of holes unevenly
spaced. Examine a tracing made by the prong
of a tuning-fork (Exercise 59, page 370), and
notice the regularity of the rate of vibration.

The vibrations must be rapid (about thirty
per second) to be felt as a musical sound, instead
of a succession of separate noises. Above thirty
thousand to forty thousand vibrations per second — sounds of
a pitch that can be made by a very short whistle or a short bar
of thick steel — are heard only by the lower animals and insects.

Fig. 341.

409. Sympathetic Vibrations. — From a string, AB, Fig. 342,
suspend two pendulums, C and E, of equal length, and another,
D, somewhat longer or shorter. Set
C swinging. Little by little E is
set going by the swaying of the
supporting string, AB. The other
pendulum, /), is at first set in mo-
tion, and then stopped. E, being
of the same length as C, has the

Rg. 342.

SOUND. 867

same rate of vibration ; the swayings given to AB gradually
set E in motion, always helping it along and increasing its
swing. In the same way, a "swing" or a battering ram can be
set in motion by a succession of gentle pushes applied at just
the right time, so that each push helps and does not hinder the
swinging. The vibrations of E are sympathetic. In the case
of D, however, the rate of vibration is different. At first the
pendulum D is started, but after a few
swings it gets out of step, so to speak, and ^
is stopped. ^

Clamp a hacksaw blade, GZ>, Fig. 343, at
its centre in a small vise. Start C vibrating, p ^^^^

and watch D. If the two ends of the blade
have the same rate, D will be set vibrating. If the two ends
have not the same rate of vibration, D will be started and then
stopped.

Suppose A and B, Fig. 344, are tuning-forks of the same
pitch, or rate of vibration. Hold A firmly on a board or table.
Set B vibrating, and press its base for a
second on the table, and then stop Ji by
touching one of its prongs. Notice that
A has been set in motion. The vibra-
I ' ' — 1 tions of A are sympathetic. If the forks

Fig. 344. ^r® powerful, and mounted cm boxes

open at one end, and if the boxes are of
such size that the air column has the same rate of vibration
(section 422), the experiment can be performed with A and li
ten or more feet apart, and even though A and B both rent on
rubber tubing, so that the vibrations are not carried from one
box to the other through any solid, but must l>e carried through
the air itself.

Pieces of paper, furniture, and glassware all have different
rates of vibration, and are set vibrating sympathetically when
their particular note is sounded. Soldiers break ste]) on a
bridge, since any portion of the bridge, if it lias the same, or

368 PRINCIPLES OF PHYSICS.

nearly the same, rate of vibration as the regulation step, might
be set violently in motion and broken. Large vessels, especially
warships, which are somewhat top-heavy, are designed to have
a much slower rate of rolling than the slowest, and conse-
quently the highest, waves of the ocean. Otherwise, in a sea in
which the rate of the waves coincided with the roll of the vessel,
it would roll farther and farther, and perhaps roll over. (All
vessels may be considered as pendulums.)

410. Forced Vibrations. — Although a pendulum sways a cer-
tain number of times a second when left to itself, still, by taking
hold of the bob, it can be forced to swing either faster or slower.
It then has a forced vibration. Every object — a board, a pane
of glass, pieces of crockery, etc. — has its own rate of free vi-
bration ; but any one can be forced to vibrate at the rate of a
tuning-fork, by setting the fork in vibration and placing it on
the object. The sounding-board of a piano, the body of a violin,
or other stringed instrimient, gives some one note for each par-
ticular instrument, if lightly tapped, but is forced to vibrate at
the rate of any sounding tuning-fork that is placed upon it.
All the notes of stringed instruments, except, perhaps, the one
note just mentioned, are the results of forced vibrations of the
body of the instrument. A string or wire has too small a sur-
face to set the air into vibration enough to make a loud note.
The same wire, stretched between pins that are fastened to a
thin board, sets the board vibrating, and this, because of its
greater surface, sets the air vibrating more vigorously and
causes a loud note. A piano without a sounding-board, or a
violin body made of a rod of metal, would give comparatively
faint sounds.

411. Velocity of Sound. — The lightning flash of a distant
thunder-storm is seen long before the thunder is heard. The
bells of a fire-alarm system all strike at the same instant, but
a listener hears them one after another. The most distant is

SOUND. 369

heaxd last. A long procession marching to the music of a band
does not appear to keep step. Farther and farther from the
music, they are more and more out of step. Suppose the march
music is played so that 120 steps are made in one minute (that
is, two per second). If the line is very long, about 550 feet
back from the music, the procession will appear to be in time,
but just half out of step, for they hear the music half a beat
after it is played. Still farther away, about 1100 feet, they
appear to be exactly in step. It takes about one second for *
sound to travel this distance. A change in the density of the
air (read by the barometer) has no effect on the velocity of
sound. A rise in temperature increases the velocity.

The velocity of sound is greater in metals, increasing with
the elasticity and diminishing with the density. The sound of
a blow on a long line of fence or railroad track is heard through
the solid long before it is heard through the air. Sound travels
faster through water, also, than through air.

A system, better than wireless telegraphy, of signalling from
the shore to a vessel or from one vessel to another, at distances
of less than ten miles, consists of a powerful bell that can be
struck under water, by means of machinery in a lighthouse or
lightship. Even without the aid of a microphone receiver, the
sound is easily heard several miles by listening at the sides of
a vessel.

The velocity of sound in air can be found approximately by
the following method.

Exercise 58.
VELOCITY OF SOUND IN AIK.

Apparatus : Pendulum ; watch ; box ; hammer or stick.

Set up a pendulum that beats one-half seconds (Exercise 63,
page 399). This will be about 25 cm. long. One person, standing
near this, strikes the box with the hammer, keeping time with the
swings of the pendulum. A second person walks away, watching the
fall of the hammer and listening to the sound of the blows. At first

'370 PRINCIPLES OF PHYSICS.

the sound and the blow that causes it g^w more and more ''out of
step." When he is 400 feet away, they become somewhat in unison.
If he moves away till the sound is heard at the same instant that the
blow is struck, he of course really hears a blow at the instant the
succeeding blow is struck. Since the pendulum beats half seconds,
two times the distance between the observers is the velocity of sound
in air at whatever may be the temperature at the time. This experi-
ment should be made on a still day. Some of the earlier measurements
of the velocity of sound were made by determining the time between
the flash and the report of a cannon a mile or more away.

Exercise 59.
BATE OF VIBBATION OF A TUNIHO-FOBK.

Apparatus : Toniog-fork and peodulom, supported on a base.

A piece of steel, bent into the form of a deep U and held or fastened

at the centre of the bend, is a simple form of tuning-fork ; or two rods

like the one used in section 401, nailed at their

ends to a block of wood, B, Fig. 345, may be used.

' -^ Both prongs must have practically the same rate

Fig. 345. of vibration, or they will stop vibrating almost the

instant they are set in motion. To give any vol-
ume of sound for a number of seconds, a tuning-fork must be made
of steel and be hardened. As any fork that gives a musical sound
vibrates too fast to be counted by the eye, a fine wire or bristle is
attached to one prong. Smoke a piece of glass by drawing it slowly
through the flame of a gas burner, candle, or kerosene lamp. Lay the
glass in a frame, smoked side up, and adjust the fork in a clamp so
that the marker of fine wire just touches the smoked surface. Place
a short pendulum, having a wire that runs easily through a vertical
hole in the bob, so that the wire touches the smoked glass near the
marker attached to the fork. The pendulum swings in front of
the prongs of the fork. First set the pendulum swinging; then set
the fork vibrating by a well-rosined bow, and at once draw the frame
holding the smoked glass steadily but quickly across the fork. The
fine, wavelike trace made by the fork will be crossed by the larger
tracing made by the pendulum. Set the pendulum swinging and
count its vibrations for one minute. One-sixtieth of this number

SOUND. 371

gives the number of vibrations of the pendulum per second. Count
on the smoked glass the number of vibrations of the fork correspond-
ing to any number of swings of the pendulum, and compute the num-
ber of vibrations of the fork per second.^

Several sets of tracings may be recorded on the same plate by slid-
ing it along sideways, and so bringing a fresh surface under the bristle
and marker. When a good set of records is obtained, pour on the
smoked surface some negative varnish or spray with a fixative. Let
this dry, and print any desired number of copies on blue or other
photographic paper. Paste a copy in the note-book, with a diagram
of the apparatus and the calculation of the number of vibrations and
the pitch of the tuning-fork.

412. Chronograph. — For measuring small intervals of time,
in place of a smoked plate, a smoked cylinder turned by clock-
work is used. This is called a chronograph. A fine bristle
attached to one prong of a tuning-fork touches the smoked
surface. The fork is kept in continuous vibration by an elec-
tromagnet like the armature of an electric bell (section 563,
page 485). By pressing a key another pointer is moved by
another electromagnet, and made to touch the cylinder. The
time passed between the making of two such marks is com-
puted from the number of vibrations of the tuning-fork between
the two marks.

413. Sonometer. — A string fastened at both ends is a double
pendulum. On a screw or clamp, S, Fig. 346, wind a w4re.
Pass this over two V-shaped A c B
bridges of wood, A and B, A\ (\ j^
and also over a pulley, P. Si^ ' ' ^
Vary the weight attached

to the wire, and notice the | W \

effect on the pitch. Just ng. 346.

as an increase of tension, or pull, on a simple pendulum (sec-

^ This experiment should be performed by the teacher, if the time is
limited.

372 PRINCIPLES OF PHT8IC8.

tion 155) makes it vibrate faster, so an increase of tension of
the wire increases the number of vibrations and raises the
pitch. Four times the weight, W, doubles the niunber of
vibrations and raises the pitch one octave. Shorten the dis-
tance between A and B by sliding the movable bridge B, A
shorter pendulum vibrates faster, and the pitch rises. Try a
heavier wire ; with the same length of wire and tension, the
pitch is lower. State, in general terms, what effect a change
of length, tension, or weight of wires has on the pitch.

414. Harmony. — On a second sonometer (Fig. 346) stretch a
second wire, like the first, supported on two bridges, and under
an equal pull. See if the two wires are of the same pitch
when the length AB is the same in both. Shorten the length
AB in both sonometers to less than one-half of the length of
the board. Move the bridge on the second wire so that the
length is ^ the first. Make both wires sound. The two notes
sound well together ; they are in Jiarmony,

415. Discord. — Make the second wire, between A and B, of
a length f that of the other; J; f. Make both wires sound at
the same time. These are simple ratios. If the ratios were
not simple, but, for instance, like 17 to 10, the notes would
make a discord.

416. The Musical Scale, in its simplest form, is
composed of seven notes, thus ; —

C D E F O A B a

1 I f J f I ¥ 2

The numbers underneath have the following mean-
ing; Df for instance, has | as many vibrations per
second as C. E has J as many as C. Notice that
the numbers are the simplest possible. Assuming
that C has 264 vibrations per second, and the other
notes the corresponding numbers given in Fig. A, find

264

297

330

362

396

440

496

628

g.A.

SOUND. 37S

the increase in the number of vibrations between each two
notes ; that is, find the difference between C and D, D and E,
etc. The interval between E and F is about one-half that
between D and E, The interval EF is a half-tone. It will
be noticed that C has 528 vibrations a second, or twice as
many as O, one octave below. For each octave higher, the»
number given in Fig. A is doubled.

Problems.

1. What is the number of vibrations of D", which is two octaves
above /) = 297 ?

2. Find the number of vibrations of a note three octaves below
C = 264. -4715. 33 vibrations a second.

3. Find how many octaves above C = 264 is the limit of hearing,
40,000 vibrations a second.

To find this, keep doubling 264 till a number is found near 40,000.
The number of doublings is the number of octaves above C = 264
vibrations where sounds are audible. Higher numbers of vibrations
are not heard at all.

417. Apparent Variation of Pitch : Doppler's Principle. — If a

boat is anchored, and waves are coming at the rate of one per
second, the boat moves up and down once per second. If the
boat steams in the direction in which the waves go, a less num-
ber of waves per minute will reach the boat ; it will move up
and down less than once per second. If the boat travels as fast
as the waves in the direction they are going, it moves steadily
as in still water. Should the boat go in a direction against the
waves, it strikes more than one wave per second. Similarly,
the pitch of a sound depends on the number of vibrations that
reach the ear in a second. If an observer moves away from the
source of a sound, — a whistle, bell, etc., — a less number of
waves reach his ear each second, and the pitch as he hears it is
lower than the pitch of the sound. On approaching a sound
more waves a second are met, and the pitch, as heard by the

374 PRiyCIPLES OF PHYSICS.

person approaching, rises higher. How does the whistle of a
locomotive sound while it is approaching? while moving away ?
while just passing? If two bicycle riders have bells that are
of the same pitch, and one bicycle is not moving, why should a
bystander, hearing the two bells sounding, think that one bell
is of lower pitch than the other ?

418. Reflected Soand — A mountain, an iceberg, a vessel, or
a large building may reflect sound. A reflected sound is called
an echo. If the distance from a hill is known, the velocity of
sound can be roughly determined from the time that elapses
between the sound and its echo. On the other hand, knowing
the velocity of sound, the distance from a vessel or an iceberg
hidden by darkness or fog is estimated by the time between
the sound of a gun and its echo. Suppose the time that elapses
is 30 seconds The sound was 15 seconds in going to the ice-
berg, which is 15 x 1100 feet away, or about 3 miles. While
sound does not obey exactly the law of reflection as observed
in light, yet a whisper at a certain place in a room may be
reflected from a curved wall, and brought to a focus at a place
even at some distance, and plainly heard by a person standing
there This phenomenon is often noticed near arched bridges,
which are sometimes called echo bridges.

In a speaking-tube the sound waves are kept from spreading,
and by continual reflection are made to go, almost undiminished
in loudness, to the end of the tube. The sides of a trumpet or
megaphone reflect and send in one general direc-
tion a sound that would otherwise spread and be
inaudible a thousand feet or more away.

419. Resonance. — Imagine a pipe. Fig 347, closed
at D and containing a coil of spring wire. Give a
sudden push down at A (see section 405, page 364).
The push, or compression, in the spring travels
down rapidly, is reflected from the bottom, returns

SOUND.

375

to the top, and may reach the hand, if the timing is rightly
chosen, just as it is raised to the position of starting. Now
raise the hand, and a rarefaction travels down the spiral tube,
is reflected, and reaches the top of the tube as the hand returns
down to A.

420. Ware Length. — Starting from A, Fig. 348, the whole
motion of the hand to cover a complete vibration is down
and back (to the position of starting), then up and back.
Hold the hand horizontal, and go through the
motions indicated by the heavy and dotted lines
at Af at the same time repeating the words, " down
and back, up and back.'' Each one of these
four motions is done in the time required for a
condensation, or rarefaction, to travel once the
length of the closed pipe, AB. Therefore AB is
one-fourth of the distance the wave travels in one
complete vibration, which is called a wave length.
ABj then, is one-fourth a wave length ; or, a wave
length is four times AB, In the study of sound,
by dosed pipe is meant a pipe closed at one end, and open at
the other; by open pipe y one open at both ends.

Fig. 348.

Fig .J49.

421. Measurement of Wave Length. —
Fasten a tube in a clamp, C, Fig. 349.
Raise a jar of water until the length, AB,
is such that a vibrating tuning-fork held
over A sets the air in the tube in vibra-
tion, reenforcing the fork, and making
the loudest sound. As explained above,
the length, AB, is about one-fourth of the
wave length. Measure AB, and compute
the wave length given by the fork. Find
also the number of vibrations by dividing
1100 by the wave length. Increasing the

376 PRINCIPLES OF PHYSICS.

diameter of the pipe has the same effect, to a certain extent,
as lengthening the tube. For accurate work, the length of
the air column is taken as the length AB plus one-fourth the
diameter of the pipe.

Remove the tuning-fork, and blow gently across the mouth
of the tube at A j along with the rustling of the air may be
heard faintly the same note as that given by the fork alone.

422. Reenforcing Notes. — It is only when the rate of vibra-
tion of the air column, AB, Fig. 349, is the same as that of
the tuning-fork that the air column is set into sympathetic
vibrations and reenforces the sound of the fork. A sounding
board reenforces a note of any pitch; while an air column,
vibrating as a whole, reenforces only that particular note or
some overtone of it (section 426), of the same rate of vibration
as the air column itself. Practise blowing across closed pipes,
such as bottles, test-tubes, or keys. Notice that when the
diameters are the same, the shorter air column gives the higher
pitch. A bottle, especially a wide one, with a small opening,
used as a resonance tube, reenforces a much lower note than
would be expected from its length.

Problems.

1. Taking the velocity of sound in air as about 1100 feet a second,
find the number of vibrations of a fork reenforced by a closed pipe
1 foot long.

The wave length is four times this, or 4 feet. The fork makes a
complete vibration while the sound is travelling 4 feet. There are as
many vibrations in one second as there can be waves 4 feet long in
1100 feet. J-y^ = 275 vibrations per second.

2. Find the number of vibrations of forks reenforced by a column
of air 12 feet long, closed at one end ; 6 feet long ; i foot; J inch.

Ans. 22+; 45+; 550; 13,200.

3. How many vibrations in the note made by blowing a key, the
hole of which is J inch deep? -4fw. 13,200.

4. Assume other lengths for the resonance tube, and calculate the
pitches of forks reenforced by them.

SOUND,

377

5. A ttming-fork making 130 vibrations per second is reenforced
l>y a column of carbonic acid gas .5 m. long. Find the velocity of
aoond in this gas.

The wave length is 4 x .5m. = 2 m. Since there are 130 waves
per second sent out by the fork, the velocity = 130 x 2 m.

6. A fork making 256 vibrations a second is reenforced by a tube
1.25 m. long, fiUed with hydrogen gas. Find the velocity of sound in
hydrogen. Ans. 1280 m. per second.

423. Open Pipes. — These are open at both ends. Find the
length of an open pipe that reenforces the fork used in section
421. Vary the length by sliding over the open
tube a paper tube, T, as in Fig. 350, made by ^^

rolling paper tightly around the pipe.

Record the length of the complete pipe, and
compare with the length of the closed pipe that
reinforces the same fork. Blow across the end
of the pipe. A rustling sound is heard, of the
same pitch as the fork ; but there
is difficulty in making the air col-
umn give a full musical sound.

An open pipe has about twice
the length of a closed pipe of ng. ssa

the same pitch. In fact, any
open pipe has a node, or point of no vibration,
at the centre, Xy Fig. 351. The pijje acts much
as if a plug closed the pipe at X. (See section
Fig.iii, ^5j P2^€ ^^% which shows that there is a node
at X.) Pipes A (open) and B (closed) have
about the same pitch. The wave length of the sound is four
times the length of B and twice the length of A.

Problems.

1. What is the ware length of a note given out by an open pipe 10
feet long? What is the number of vibrations ?

Ant. 20f€et: ii|< = 55 vibrations.

378 PRiyciPLES OF physics.

2. What is the wave leugth of the note of an open pipe half a foot
long? Find the number of vibrations. Ans. Ifoot; 1100 vibrations.

3. Find the number of vibrations of a flute (which is practically
an open pipe), if the air column is 2 feet long.

4. How long must an open organ pipe be, to give a note of 550
vibrations a second ?

424. Fundamentals. — It is almost impossible to produce a

really musical sound by blowing across the end of an open pipe

like A, Fig. 3.51. Musical wind instruments, organ pipes, flutes,

flageolets, etc., have mouth-pieces more or less like M, Fig. 352.

Air blown in at M strikes the edse of the

l^ jy pipe at C, and vibrates between going into

the pipe and over the edge. The air in
Hg. 352. , . . , . ., . ^,

the pipe IS thus set in vibration. The

pipe is open at both ends; that is, at C and D. Cover the holes

in the sides of the pipe with gummed labels. Blow gently in

the mouth-piece. The note is the fundamental, or the lowest

given by that length of air column. Close D with the hand.

By blowing very gently, the fundamental of the closed pipe

will be sounded one octave lower than that of the open pipe.

A portion of the pipes of an organ are closed pipes, called

stopped pipes.

Bzercise 60.

OVEBTONES IN STRINGS.

Apparatus: Sonometer (Fig. 346).

Strike or bow the wire A B, Fig. 353. Diminish its length by one-
half ; the pitch rises an octave, there being twice the* number of
vibrations. Make the length AB the same

as at first ; touch the middle point, C, and ^ | a^ ^ y" y j.

bow or pluck the wire near the end B. ,-..-..

Fig. 353.

What is the note? Place a rider (a little

piece of paper in the form /\) on the wire between -4 and C. Touch
C and bow the wire near B. The paper rider jumps or is thrown off.
The string vibrates in halves at double the rate of the whole wire -^B.

SOUND. 879

The note olAB, vibrating as a whole, is called the fundamental The
note, when the string vibrates in halves, is the first overtone. The
vibrations are the same as, only more rapid than, those illustrated by
Fig. 338, section 404.

Touch the wire at 2>, Fig. 353, one-third of the length from B.
Place riders at E and between AE and ED. AE is one-third the
length of AB. Bow near B. Since the rider at E is not moved, there
is a point of no motion, or a node, at that point. The string now
vibrates in thirds, makes three times as many vibrations as the whole
string, and sounds a note between two and three octaves above the
fundamental. If the fundamental is C, the first overtone is C an
octave above ; the second overtone is G above that. In other words,
if we call the fundamental doy the first overtone is- do an octave higher;
the second overtone is the sol above. With care the wire may be
touched at E and bowed near B and yet made to vibrate in thirds.

Try the same experiment, dividing AB into four parts, then into
five parts, etc.

425. Overtones in Open Pipes. — Using a flageolet having the
side holes closed, blow gently and bring out the lowest note,
or fundamental. Blow a little harder. The pitch rises an
octave, giving the first overtone. When this occurred in a
stringed instrument, the string was found to be vibrating in
halves. Make a small opening through the
paper pasted over the hole nearest the mouth-
piece. The hole is about in the middle of the
tube. The first overtone now sounds easily ; I—

the fundamental is impossible. This shows ^i — j,v
that a node was formed at the centre of the
pipe -4, Fig. 354, when the fundamental sounded.
A node is where the sound waves are reflected.
When a hole is made halfway along the pipe,
as at B, the sound waves escape somewhat
through it, and a node is now no longer formed there, but
halfway between B and the ends. Blowing harder and more
suddenly brings out the third, the fourth, and even higher over-
tones. Open pipes have all the overtones, like vibrating strings.

jir

ng3 354rf

380 PRINCIPLES OF PHYSICS.

426. Overtones in Closed Pipes. — Close all the side holes in
one pipe. In another, push a tight-fitting piston halfway up,
thus making a closed pipe of half the length. Sound the
fundamental by blowing gently on both. Make them exactly
in tune by moving the piston. Bring out the overtones on
each by blowing harder. Notice that the open pipe has twice
as many overtones as the closed pipe. Find a note on a
piano in tune with the fundamental, or lowest note, of the
open and closed pipes. Call this do. Blow the first overtone
on the open pipe ; the note is do an octave above. This over-
tone cannot be obtained on the closed pipe. The overtone
first sounded on the closed pipe is sol of the octave above, the
very same note as the second overtone of the open pipe. In
the same way, study the higher overtones.

A more difficult method of determining the pitch of the
overtones is to move the bridge B of the sonometer (Fig. 346)
till the wire is in tune with the fundamental of the pipes, and
then sounding the overtones to find the length of wire in tune
with them.

l8t

Fundamental Overtone 2g 8d 4th 5tb
Rate of vibration, open pipes : 1 2 0 4 5 6

Rate of vibration, closed pipes : 1 3 5

Closed pipes include " stopped " organ pipes and the clario-
net. While the clarionet is open at the bell, or side hole, as
well as at the mouth-piece, still it acts like a closed pipe.

427. Quality of Sound. — Bow ohe string of the sonometer, or
blow gently on the organ pipe rying to bring out the funda-
mental, and then the first cv3r' ne. By practice, they can be
made evidently to sound toge^licr. When a note is played on
any instrument, not only is that note heard, but a large num-
ber of the overtones of that note. Of course, in closed pipes
half the overtones do not exist. In one kind of instrument
some overtones are loud and others weak. A musician playing
a violin brings out with the fundamental of each note a few of

SOUND. 381

the lower overtones. A poor player cannot sound a note with-
out its higher overtones, some of which discord and are harsh.
Quality of sound depends on what overtones sound with the
fundamental, and the relative loudness of those overtones.
The overtones of bells almost always discord with the funda-
mental. Closed pipes (the clarionet, of all the orchestral and
band instruments, is the only one which acts like a closed pipe)
have an entirely different quality of sound from open pipes.
We recognize voices and different instruments by the quality
of the sounds they produce. Two voices may sing the same
note equally loud; yet there is a difference in quality; one
brings out certain overtones louder than the other.

428. Interference of Sounds. — If two persons hold the ends
of a pole, in the middle of which a basket is hung, and one
person steps faster than the other, at one instant they are in
step and the basket rises and falls. A moment later they are
out of step ; one is rising and lifts the pole, at the same time
that the other lets his end of the pole drop a little. As a
result, the basket neither rises nor falls, the upward motion of
one interfering with the downward motion of the other. In
the same way, two sounds interfere and produce silence. Sound
two tuning-forks of exactly the same pitch ; the note, loud at
first, gradually dies away. Load a prong of one fork with a bit
of wax ; warm the fork to make the wax hold. Sound the two
forks and press them on a sounding-board. One fork is a little
slower in vibrating than the other. When both are in step,
the sound is loudest, but grows fainter as they fall out of step.

429. Beats. — Variations of loudness of sound due to inter-
ference of two sounding bodies of slightly different pitch are
called beats. If two forks make, respectively, 263 and 264
vibrations per second, one beat a second is heard. Several
beats per second are not unpleasant. As the number increases,
the result is disagreeable — a discord, in fact. On becoming
very numerous, they are pleasant

CHAPTER XXVI.
ELEOTEIOITY. -MAGNETS.

430. Magnetic Attraction. — Try the effect of holding one
end of a magnet near the following substances in turn : lead
pipe, a brass screw, a silver dime, copper, an iron nail, a tin
dipper (iron thinly coated with tin), pieces of paper, glass, etc.
Is there any attraction between the magnet and these sub-
stances? Hold a magnet near a nickel five-cent piece, and
then near a bit of pure nickel. The coin is not pure nickel,
but contains a large amount of copper.

Place a few iron filings on a sheet of paper. Move a mag-
net underneath. Does the magnet act through the paper?
Place iron filings on glass, copper, brass, sheet lead, and thin
wood, in turn, and determine if the magnet attracts through
any of these substances. Try a piece of sheet iron one-eighth
of an inch thick. Is the attraction of the magnet for the iron
filings apparent through the iron ? What substance could be
used as a shield for magnetism ?

Hold a nail near iron filings. Push the nail into the filings;
then remove it Then put the nail into filings, as before, but

hold a magnet (3f, Fig. 355) near the nail.

A B Withdraw the nail, still holding the magnet

r -^^ _J T near it. Tap the nail. Remove the magnet

and tap the nail. A few bits of the filings
Fig. 355. wil^ cling to the nail. The softer the iron,

the less it will act like a magnet when the
magnet is taken away. Try small tacks in place of iron fil-
ings. How many does the nail hold at one end when the
magnet is close to the other? How many when the magnet
is removed and the nail given a slight tap with a pencil ?
. For the iron substitute a piece of hard steel, such as a heavy

ELECTRICITT. — MACXKT.'^s S^S

needle, a \At of watch spring, or a fragment of a moul haoksAW
blade. First see how many tacks the stool alono lifts, thou how
many when the magnet is held at one end, and thon how t\iany
alone after the ma^et is removed. Does tapping the stoi^l mak<^
it lose its power in the same degree that the iron nail did ?

431. Temporary and Permanent Magnets. — Iron noar a mag^
net becomes a magnet itself until the nmgnot is roniovofl.
The iron is a temporary magnet A piooo of stool, aftor thi^
magnet near it has been taken away, still rotaittH a larg^
portion of the power of attraction, and is callod a pprmnmni
m^agnet. Any form of hardened steel — old knife bladoH, oar-
penter's tools, files of all sorts, scissors, or noodlos — cati be
made into magnets. One way is to touch a piece of steel with
a magnet, or to bring it near a magnet.

Suppose we wish to make a magnet of a sewing needle.
Place the middle of the needle on the end B of the nmgnei/,
Fig. 355, page 382. Slide the needle so that its point totu?he»
B, and then pull the needle away. Place the middle of the
needle on the end A^ and slide it along till the eye of the
needle is at ^; then pull the needle away, Thii* may l>e
repeated several times. The needle will now fiiirmi mm
filings or tacks, and will cause a bit of iron, held near ii^ to
attract The needle is a permanent magnet,

432. Wluit A MMgaet win do if kit frm — Tie fine 5;ilk ihtf^fl
<m the middle edf the needle }n»i magnetii/^/L If ihp, weedle
does not liang in a hfmimiUtl fVnfi^f^um^ 9^hp Ptlmt^
the knot c* load fme «5md fA tli^e w^lh mf,h -^hk

till it dctts fiwinig hfmifmts^Uy. M^U <i^in^ ^^x
or ftaialliiiii fram at esaPi>M^. em tilie kin/vft^ Uy p-pf>,-^p:fvf,
its sflipjpwD)^ Faft-fteta) the fthnn'raH't f/y f»h^, u^>^r M^f'.
of a pattttftftoaordi h^x cm the cypim .^idA» ^ in f\c(. '*' *^'

356l Wftatft gjftiwwaJ. dii?ei»f,i<m ck)e^ f.h^, i^^acU^. f^k^ 6n <*Arrtir*i^
to wsaA? IM> sbE the swij^pendM needl<»s rv\M\<^ Ky diffAT«<*Yit. m<^i^v
» df tffl» dbsft poiikt in Che .^^on*'*^ diT(*,?*.f.i<'m ".^

384 PRINCIPLES OF PHYSICS.

Magnetize another needle (a short one) or a piece of watch

spring one inch long, and fasten it to the

— top of a bit of flat cork (Fig. 357). Float it

in a glass jar of water. What direction

Fig. 357. ^Q^g ^Yie needle take ? Hold a magnet near,

and then remove it. Does the floating needle point in the

same direction as before ?

433. Compasses. — A small piece of magnetized steel, sus-
pended on a fine point, or pivot, and enclosed in a box hav-
ing a glass cover, is more convenient to carry about than either
the apparatus shown in Fig. 356 or that of Fig. 357. All three
are compasses, although the name is usually applied to the
form where the needle is suspended on a pivot. Examine a
compass. Friction at the pivot is overcome by gently tapping
the compass. If the compass is moved, does the needle always
point in the same direction when it comes to rest ?

434. Effect of One Compass on Another : Law of Poles. — The

parts of a magnet where there is a large amount of attraction —
that is, where many iron fillings cling — are called poles. In
long magnets having two poles, the poles are near the ends.

In addition to the suspended needle previously used, arrange
another, which need not be attached to a support. Bring the
north-pointing end, or, as it is called, the north-seeking pole,
of one near the north-seeking pole of the other. The north-
seeking poles should be previously marked with paper or wax,
to distinguish them. Bring the south-seeking poles together.
For brevity, the word 7iorth is used instead of north-seeking,
and south instead of south-seeking ; but the longer expression
is the exact one, and should always be kept in mind. Put the
south pole of one needle near the north pole of the other. Fill
in the blank spaces in the following statements : —

Like poles

Unlike poles.. _

ELECTRICITY. —MAGNETS. 385

Magnetized needles on floating bits of cork may be tried, in
place of suspended needles. See how far apart the needles can
be placed and one still have an
appreciable effect on the other.
An amusing experiment is to
stick needles through bits of
cork, as in Fig. 358 ; first float
them with north poles above
water. Try what effect the
poles of the bar magnet have upon them.

435. How to tell the Poles of a Magnet. — Suspend the bar
magnet by a fine silk thread, well waxed. Mark the end that
points north. Which pole of the suspended needle does the
north pole of . the magnet repel ? Which pole of a magnet is
it that repels a south pole? Which attracts a south pole?
Try the effect of a piece of soft iron — a wood-screw, for in-
stance — on the poles of the suspended needle. Bring the iron
close up to the poles of the needle. As the needle is a magnet,
both of its poles attract soft iron. Attraction, then, does not
prove that a substance is a permanent magnet, because a mag-
net — both poles equally — will attract any form of soft iron.
Repulsion, however, can only take place between the like poles
of two magnets. To prove that a substance is a permanent
magnet, it must repel one pole of a magnet.

436. One Way of demagnetizing a Magnet. — It is often
troublesome to have a tool that is magnetized. If a pair of
scissors or shears, such as are used in cutting sheet metal,
.becomes magnetized, bits of iron and filings will.be picked up,
and the finer filings are hard to remove. One way of demag-
netizing, or taking the magnetism out of a magnet, — not the
best way, because the steel is softened by the process, — is
shown by the following experiment.

Magnetize a piece of watch spring. See how many tacks it

886 PRINCIPLES OF PHYSICS.

will lift. Pound it hard ; how many does it lift now ? Al-
though jarring causes a magnet to grow weaker, it never makes
it lose all its magnetism. Heat the watch spring to a bright
red color in a Bunsen flame. When it cools, try its effect on a
compass or a suspended needle. Does either end of the watch
spring repel a pole of the compass? How many tacks does it
lift now? Try to bend it. Does a file cut it easily? Try
the effect of bending and filing on a piece of watch spring cut
from a coil of spring.

437. Annealing and Hardening Steel. — On being raised to a
red heat and allowed to cool slowly, steel becomes soft. This
is called annealing. Cut several pieces of watch spring of
equal length, — one inch long, for instance. Do nothing to
one piece, except to straighten it. Anneal a piece. Raise a
third piece to a red heat, and, instead of allowing it to cool
slowly and become soft, drop it in water. To do this success-
fully, hold the piece of spring half an inch over some water.
Tip a Biinsen burner so that the flame plays on the spring.
When the spring is red hot, drop it in the water. By so doing,
the steel is cooled suddenly. Magnetize all three pieces of
steel. Which one is the strongest ? Which is the hardest ?
Try them with a file. The spring as made for a watch is not
hardened as much as the piece just treated. Which of the
three little magnets just made bends the least before breaking;
that is, which is the most brittle ?

Exercise 61.

LINES OF FORGE OF A MAGNET.

Apparatus : Numbered map^nets, I inch square, 2 inches long; smaU compass
I inch diameter; steel or iron filings of uniform size.

Part I, — Lay a sheet of paper with the longest edge pointing north.
Set a compasfl on one corner. Mark the outline of the compass. Re-
move the compaHS) and in the circle representing the outline of its
case draw an arrow pointing north. Letter the head of the arrow N,

ELECTRICITY. — MAGNETS. 887

Determine the north pole of a bar magnet ; the north pole is the one
that repels the north pole of the compass and attracts the south pole.
Record the number of the magnet, adding the words " the numbered
end " (or " unnumbered end," as the case may be) " is the north pole."
If the magnets are unnumbered, attach a label to the north end and
mark it N.

Place the magnet on the centre of the paper, the north pole point-
ing north. Mark the outline of the magnet. Remove it, and mark
the poles N and S on the outline. Replace the magnet. Lay the
compass close to the end of the north pole of the magnet. Move the
compass in the dii*ection in which it points, a distance about equal to
the length of the needle. Draw an arrow on the paper where the
compass just was, of course making the arrow point as the compass
did. Continue moving the compass in the direction in which the
needle points, and mark the track of the needle by arrows, as described
before. When the edge of the paper is reached, make a new line of
arrows, starting with the compass close to the north end of the mag-
net again, but a little to one side. The line formed by the little
arrows will probably be slightly curved. Trace similar lines, starting
with the compass at different points near the centre of the magnet.
These lines, which represent the successive directions of the compass
needle, which is continually moved in the direction in which it points,
are called lines of force. Draw a few on the other side of the magnet,
and at least one at the south pole of the magnet. The work of plot-
ting the lines of force in this exercise should be done with rapidity,
and no time should be wasted over elaborate drawing or extreme
exactness.

Part II. — Repeat the exercise on another sheet of paper, having
the south pole pointing north. The lines are traced as readily by
starting from a south as from a north pole ; but the pupil must re-
member to make all the arrows point as the compass points. Try
to find a point on the lines of force from the ends of the magnet
where the compass points indifferently in any direction.

Part III. — Place two magnets six or seven centimeters apart, with
the north poles pointing north. Pay particular attention to the lines
of force between the magnets. Do any lines oi force cross from one
magnet to the other ?

Part /F. — Place the magnets as in Part III., except that the north
pole of one magnet and the south pole of the other point north.

388 PRINCIPLES OF PHYSICS.

From these experiments, what can be said of the lines of force?
Do they attract or repel when they are in opposite directions, as in
Part III. ? When they are in the same direction ?

438. Tracing Lines of Force with Iron Filings. — Instead of a
compass, which has to be moved a little at a time to trace a line
of force, an immense number of small magnets or bits of iron,
which act like magnets while near a large magnet, may be
used. Sprinkle iron filings on a sheet of paper that covers a
magnet or magnets. The filings should be sprinkled from a
height of a foot above the paper, and may be sifted through
muslin, if desired. Tap the paper lightly with a pencil. There
are several ways of making a record of the lines of force in
which the filings set themselves. Drop a little wax from a
candle on the paper. When the wax hardens, put the paper
over a magnet, sprinkle on the filings, and melt the wax by
letting a flame play down on it. When the wax cools, it holds
the filings in place.

Photographic paper may be used in making a record of the
filings (see Appendix, page 535).

439. Plotting Lines of Force in Other Planes. — The lines of
force have been plotted thus far only in one plane. They exist
all around a magnet, as the action of a compass shows, whether
it be moved above or below.

Problems.

Plot the lines of force in Problems 1-12, keeping the paper hori-
zontal in all cases.

1. Bar magnet vertical.

2. Horseshoe magnet horizontal.

3. Horseshoe magnet vertical.

4. Horseshoe magnet horizontal ; a piece of soft iron (a large nail)
lying against one pole.

5. Two bar magnets parallel, the north and south poles side by
side. Have the magnets 2^ inches apart.

ELECTniCITT. — MAGNETS.

389

FIfif. 359.

6. Same as Problem 5, with two iron washers, piled
one on the other, and placed between the magnets, near
the ends, as in Fig. 359.

7. A bar magnet, Af, one pole lying near a curved
piece of soft iron. Ay Fig. 360.

8. A bar magnet lying 2 or 3 cm. from the iron,
in the position B, Fig. 360.

9. Two bar magnets, M and ilf. Fig. 361, in a
line, unlike poles, N and 5, 2 inches apart.

10. Place an iron washer, W, Fig. 361, between
Fig. 360. the magnets.

11. As pole pieces for the magnets, use the curved pieces of iron
mentioned in Problems 7 and 8 (^4 and B, Fig. 361).

12. A smaller magnet, L, Fig. 361, between the large magnets.
Pieces of brass or other non-magnetic
material keep the smaller magnet from M
swinging out of position. Make a sketch L_
showing the movement it tends to take.

13. Trace the lines of force of a mag- •—
uetized file or knife. Notice that the
handle end, which is left soft, has no [^
well-defined pole. The lines of force
are not crowded together around the
soft end of the file. I—

14. Try to magnetize a knitting- ^
needle, having a south pole in the centre Fig. 36 1.
and a north pole at each end. To do

this, touch the centre with the north pole of a magnet, and the ends
of the needle with a south pole. Try to make a still larger number
of poles in one piece of steel.

HI [H

440. Magnetic Screen. — Through what do lines of force
travel more easily than through air ? Try a large nail one-
half centimeter away from a bar magnet and parallel to it. A
line of force is considered to make a complete circuit, start-
ing out of the magnet at the north pole ; where does it go on
entering the south pole of a magnet? Do the iron filings

390 PRINCIPLES OF PHYSICS.

show the presence of many lines of force between the nail and
the magnet ? Looking at the lines of force of Problem 6, above
(Fig. 359), what can be said of the space in the centre of
the iron washers ? Are there many lines of force there ? Do
the filings dropped over that part arrange themselves in lines ?
Dip one end of a bar magnet in filings and hold it up. The
filings indicate pretty well the lines of force, except that the
weight of the filings makes them sag a little. Hold a large
piece of soft iron almost down on either pole of a magnet;
what do the lines of force do ? What can be suggested as a
magnetic screen ? A powerful magnet will affect a compass
fifty feet away. If, on modern warships, a compass is put
below decks, why will the same magnet outside the vessel fifty
feet away no longer affect it ?

441. Lines of Force in the Magnet. — Break or cut off a bit of

watch spring two inches long. If the spring is hardened by
heating it red and plunging it into water, it will break easily
in the fingers; if unhardened, it may be cut with shears.
Magnetize the piece and study its lines of force, or Jieldj as
they are called, with iron filings. Remove the paper. Break
the spring in two, separating the broken ends a little, and
fasten it to paper with paste or a little gum arabic. Cover it
with paper and sprinkle on filings. The lines of force lie within
the steel until it is broken, when they spread out, in passing
from one piece of the spring to the other. Break the pieces
into smaller pieces, and study the effect. Into bow many
little magnets can a single magnet be made?

442. Arrangement of Particles in a Magnet. — Seal at one end,
or stop with a bit of cork, a glass tube about 6 cm. long and
from 5 to 8 mm. in diameter. Fill it with iron or steel filings.
Close the other end with a cork, and stroke the tube with a
magnet, as in magnetizing a piece of steel. Begin at the
centre, and slide one pole of the magnet to one end of the tube ;

ELECTRICITY. — MA GNET8. 391

then slide the other pole from the middle of the tube to the
other end. Repeat several times, gently tapping the tube
meanwhile. Bring a compass or suspended needle near the
centre and the ends. Do the filings in the tube act like a
magnet ? Uncork the tube, pour the filings out, and put them
back again. Do they now act like a magnet, or do they attract
both ends of the compass indifferently ?

This experiment may be performed in even a simpler way.
Lay a sheet of paper on the poles of a powerful horseshoe
magnet. Drop on filings, and tap the paper till they arrange
themselves in the space between the poles. Lift the paper
gently away, and test with a compass. Shake the filings up
and test again.

443. One Theory of Magnetization is that every little particle
of iron and steel is a magnet. When all the north ends of the
particles point one way, the substance acts like a
magnet. On shaking the filings or jarring a piece
of soft iron, the particles of this soft iron, although
it is solid, turn around, and the north pole of one
particle attracts the south pole of another. This
is illustrated by the arrangements of bar magnets
in Fig. 362. A represents unlike poles together.
The attraction takes place largely between the magnets, and
the external attraction is very small.

Consider the question from the point of view of lines of
force. Place paper over the arrangement as Shown in A, and
sprinkle on filings. Trace the lines of force and remove the
paper. Arrange as in By and trace lines of force by filings on
another sheet of paper. The lines of force in A nearly all run
through the magnets, there being a complete circuit. Make a
diagram of A, and draw a few arrows showing the paths of the
lines of force through the magnets. Separate the magnets a
little, and trace lines of force by filings. Do the lines run in
large number from the north to the south poles ? In B the

■^s

i\r

N
N

s
s

Fig. 362.

892 PRINCIPLES OF PHYSICS.

lines of force can complete the circuit only by returning
through the air.

In a piece of hard steel the little particles are supposed to
turn around with some difficulty. Hard steel is magnetized
when the little particles are made to point in one direction.
Hard steel is more difficult to magnetize than soft iron ; but
when the magnetizing force is removed, some of the steel par-
ticles keep their positions, and the magnet is a permanent
magnet. Steel or iron lengthens slightly on being magnetized.

444. Hard Steel Magnets. — Magnets of tool steel, made in-
tensely hard by heating to redness, cooling in cold water, and
then magnetizing, retain their magnetism well, even though
they are left in any position or subjected to jarring. It is
well, however, to avoid dropping them or banging them together
hard. They are best magnetized, not by another magnet of
steel, but by an electromagnet, as will be described later.
Until the present century, steel magnets were magnetized by
pieces of magnetized iron ore. The ore, a compound of iron
called magnetite, is found in almost every part of the world,
and is always slightly magnetic. Some specimens, called
loadstone, are powerful magnets, and as such were formerly
used to magnetize pieces of steel for magnets of large size for
use in compasses. Electromagnets are more powerful, can be
made of any size, and are now always used. The strongest
magnets (permanent) for telephones, magnets, dynamos, etc.,
are made of steel containing a few per cent of tungsten. The
so-called steel used in bridges, rails, ships, and most machinery
does not harden on being cooled, nor does it make permanent
magnets of any great strength.

445. Direction in which a Compass Points. — A compass tends
to point in the direction of the line of force of a magnet near
it. Hold a compass over the centre of a magnet; then over
one of the ends of the magnet. Here one end of the compass

ELECTRICITY. — MAGNETS.

393;

Pig. 363.

Fig. 364.

points down a little. It would do so still more if the point
where the compass is suspended were not above its centre of
gravity. NS, Fig. 363, represents a bit ^-y-

of steel bent so that the supporting part y-^ — y T
on the needle point is high. A large |

force is needed to make NS tip much.
A suspended needle, in which the silk
suspending it is attached directly to the needle, as at the point
A, Fig. 364, tips readily in any direction, to adjust itself in the
line of a magnet. Disregarding for a moment the tendency of
the compass or suspended needle to tip when no magnets are
near, what else do you notice about its direc-
tion ? It points persistently toward a certain
point, — in most parts of the world, not directly
north, for by north we mean the direction
toward the imaginary pole or axis on which
the earth turns, the pole that Arctic ex-
plorers try so hard to reach, which is called
the north geographical pole. The meridians of longitude on a
map point to this pole. The pole star is almost exactly over
the north pole of the earth. This star is easily made out, be-
cause two stars in the Dipper constellation
point to it.

446. Magnetic and Geographical Poles. —

The compass points in one direction in a
place. This direction varies very slightly
from hour to hour. There is a steady
change of direction of about one degree west- g^^
ward in twelve years. Pass a brass wire
(NSy Fig. 365) through the centre of a ball
of twine or yarn. Let this represent the
earth, the wire being the prolongation of
the imaginary axis pointing nearly toward
the pole star. As nearly through the centre

Fig. 365.

394 PRINCIPLES OF PHYSICS.

as possible put a steel wire, ab, — a piece of knitting-needle, for
instance, — strongly magnetized. Let a be the south-seeking
pole of the magnet. Place ab so that a is about one-sixth of
the way from the pole to the equator. Hold a small compass
on different parts of the ball. Does the compass always point
north, — that is, to the north pole, to the pole star ? Are there
any places where the compass points to the north exactly?
If a compass were carried between N, the north geographical,
pole, and a, how would it point?

447. Angle of Declination. — Remember that in speaking of
the poles of a magnet, the terms north and south are abbrevi-
ations for north-seeking and south-seeking. The north, or north-
seeking, pole points toward a, a direction more or less that of
the north geographical pole. As like poles repel, the so-called
north magnetic pole at a is really a south-seeking pole, because
the north-seeking poles of magnets, suspended so they can tuni
freely (compasses, for instance), point toward it. The point a
is just within the Arctic circle, about one thousand miles from
the geographical north pole, and a little north of Baffin's Bay
All compasses on a line passing nearly through Charleston, S.C,
Cincinnati, Ohio, and a little to the west of Detroit, in the year
1900, pointed exactly to the north. At all places to the east
of this line, as at New York, the compass points several degrees
to the west of north ; and at places to the west of this line, the
compass points to the east of north. The angle between the
true north and the direction of the compass is called the decli-
nation of the needle. The angle of declination varies from 20®
at Halifax and 12° at Boston, to 8° at New York. The declina-
tion is affected by beds or mountains of iron ore.

448. Action of a Needle suspended over a Magnet. — Place a
magnet, SN, Fig. 366, on the table. Over the magnet, in
positions represented by the dots in the semicircle, hold a
short suspended needle. Reproduce Fig. 366 in the note-

ELECTRICITY. — MAGNETS. 395

book, adding arrows to indicate the position the suspended

needle takes in various parts of the dotted curve AB. Where

is the needle parallel to the magnet and

yet some distance from it? Where is

the suspended needle when near a pole / \

and pointing in the same direction as the / | ^ — -y^ \

magnet ?

Tie thread to the centre of an unmagnet- *'

ized knitting-needle. Balance the needle in a horizontal posi-
tion by putting gummed paper or sealing-wax on one end, or
by slipping the knot along. Put shellac or liquid glue on the
knot, and let it harden. Magnetize the needle, suspend it,
and let it come to rest. Which end points down, the north or
the south pole ? In which hemisphere do you live ? Draw a
diagram in the note-book. Mark the north end of the needle
in some way that will not increase its weight, — with colored
copying pencil, for instance. Remagnetize the needle so that
the unmarked end is a north pole. Suspend again, and notice
which end and which pole points down.

449. Dipping-needle. — The dipping-needle is merely a long
suspended needle free to set itself in a line of force of the
earth's magnetic field. As shown by the experiment (Fig. 336),
the needle is parallel to the magnet, about halfway between
its poles. As the needle approaches one pole, one end of the
suspended needle points down, or dipsy more and more, till at
a position A or B, Fig. 366^ it points in the line of the magnet.

If a suspended needle or a compass (which, when used for
the experiment in section 446, is called a dipping-needle) is
carried over the north magnetic pole at a, Fig. 365, the north-
seeking pole of the dipping-needle points straight down.

450. The Angle of Inclination between a level and a dipping-
needle varies in the United States from 60° at New Orleans to
pyer 70** in the northern tier of States, from Maine to Wash-

396 PRiyciPLES OF physics.

ington. What can be said of the dip in the southern hemi-
sphere, in Australia, in Cape Town, or in Chili ? The places
where the needle does not dip are, in some parts of the world,
a little south, and in other parts a little north, of the geographical
equator. Why ? The dip changes slightly from year to year.
Magnetize a steel ball half an inch in diameter. Let this
represent the earth. Move a small compass over the surface.
Where does the compass point to the centre of the ball?
Where does it point in a direction parallel to the magnetic
axis of the ball?

451. The Earth's Magnetism. — Jarring a piece of steel or a
bottle of filings, held apart from all magnets, lessens the mag-
netism. In magnetizing steel, a greater effect is produced by
jarring or striking it while near the magnet that magnetizes it.
Filings sprinkled on paper over a magnet, or filings enclosed
in a glass tube, easily adjust themselves in lines of force if
they are jarred. The particles take an end-to-end position, as
appears from the fact that a bar lengthens slightly when mag-
netized.

It can easily be seen that the earth's lines of force, or attrac-
tion, are fewer at any point on the earth's surface than the lines
of force of a magnet close to its poles ; for a compass a few
inches from a bar magnet appears to be almost completely
under the influence of the field, or lines of force, of the magnet.
There is a sim pie test for a magnet. It can magnetize, and make
another magnet. Hold a rod of iron (the rod of a ring-stand or
a stove poker may be used) pointing in the direction taken by
the dipping-needle. The rod is now in the direction of the
lines of force of the earth's magnetic field. Strike the rod
sharply with a hammer or a piece of iron. Hold the ends of
the rod, in turn, near the north pole of a compass. Is the rod
a magnet ? Does one end of the rod repel the north pole of
the compass ? Hold the rod with the other end pointing down
in the direction taken by the dipping-needle. Strike thQ rod|

ELECTRicrrr. — magnets. 897

and test it as before ; which end is now the north pole ? The
earth's magnetism is not strong enough to demagnetize and
magnetize hard steel ; but the rod or poker, being of iron not
perfectly soft or annealed, becomes a weak permanent magnet,
and yet is easily demagnetized and then magnetized in the
opposite direction by even the weak force of the earth's magnet-
ism. As the earth has magnetic poles and lines of forces, and
as it magnetizes iron, we conclude that the earth itself is a
magnet. The cause of the earth's magnetism is not known.
Beds of iron ore are magnetic. Bricks of a red or black color
are slightly magnetic. Iron rails running north and south,
iron bars or pipes in vertical position, — in fact, almost all
iron and steel, — in time become magnetized by the influence
of the earth's magnetism.

Exercise 62.

EFFECT OF HEAT ON A MAGNET.

Apparatus ; No. 16 soft iron wire ; No. 00 tacks ; compass ; Bunsen burner ;

magnet.

Place the wire, W, Fig. 367, on the magnet so that one end overlaps
the end of the magnet about 1 J inches. The wire is a temporary mag-
net. Find how many No. 00 tacks or

bits of wire 1 mm. long are held up at | ^ N\ W

the end of the wire. Heat the middle ^^^^^"^^^^

of the wire red hot ; how many tacks I

stay on? Let W cool, and repeat. Fig. 367.

Then try heating the tacks themselves.

Place three iron wires {A, Fig. 368), about 5 inches long, together
on a magnet, so that about 2 J inches overlap. Support the magnet
and compass a few inches above the table, using blocks of wood.

Heat the iron wires red hot at A . The

A lines of force pass through red-hot iron

1^ S I r^rt or steel no better than through wood,

^^ glass, etc. Since the presence of lines

Fig. 368 of force causes attraction, red-hot iron

is not attracted by the magnet. A

piece of iron below red heat offers a so much better path for line* of

398 PRINCIPLES OF PHYSICS.

force than does air, wood, etc., that the lines of force try to crowd
through the iron, and the iron is attracted and becomes a temporary
magnet. A permanent magnet loses its magnetism (becomes demag-
netized) on being heated red hot.

452. The Strength of Magnets, or lifting power, depends some-
what on the shape of the poles. In a horseshoe form, a magnet
will lift three or four times as much as a bar magnet. The

lifting power is greater with small ends. If the
load is gradually increased, much more can be applied
M than the magnet would have lifted at first. The
lifting power is easily measured by the method
shown in Fig. 369. A is any piece of iron, usually
called the armature. To it is connected a hook or
string, by which is held the brass bucket B.

Hold a magnet. My in a wooden clamp or in the

hand ; against M place A, so that B is half an inch

from the table. To B add water, sand, or shot till A is pulled

off. Weigh A, then B. See if the magnet will hold the same

weight if it is applied all at once.

The force required to pull a piece of soft iron from different
parts of the magnet gives some idea of the magnetic strength.

453. Distribution of Magnetism in a Magnet. — The lines of
force of a magnetized file or knife show that the handle end of
soft steel is a large pole of no very great strength at any one
point. The other pole is concentrated at the other end, where
the hardened steel is. The distribution of magnetism may be
studied in several ways.

Make a tracing of a magnet in the note-book. Find how
many No. 00 tacks can be strung one from the
other, at one end of the magnet, as in Fig.
370. Make a diagram in the note-book. Re-
move the tacks from the end, and try them at a
position 1 cm. from the end ; then at 2 cm. from ''

the end, and so on till every part of the magnet has been

ELECTRICITY. — MAGNETS. 899

tested. This method, although inaccurate, gives a general
idea of the strength of a magnet. A more accurate method is
the following.

454. The Strength of a Magnet at Any Point is proportional to
the square root of the weights lifted. For instance,

if 16 g. are lifted at the end and 9 g. a distance of 5^1 j
2 cm. from the end, then the strength at the end is to
the strength 2 cm. from the end as the square root of
16 is to the square root of 9, or as 4 is to 3 (Fig. 371).
A curve may be plotted by drawing lines perpendicu-
lar to the magnet, of lengths representing the square Fig. 371.
roots of the weights lifted.

455. The Compass as a Magnetic Pendulum is subject to the
same laws as the simple pendulum (section 155, page 135).

A simple pendulum is a weight hung on a fine thread. It is
really a falling body when it swings. It acts as if all its mass
were concentrated at the centre of the weight, or bob, as it is
called. The length of the pendulum is measured from the
point of support to the centre of the bob.

Bxercise 63.

THE SIMPLE PENDULUM.

Apparatus : Thread ; wax ; bobs of different sizes and weights ; support from
which a pendulum may be suspended.

Case /. — In the end of a piece of wood make a vertical slit. In
this insert the thread of a pendulum a meter long.^ Count the vibra-
tions as the bob pasvses the lowest point of its swing. The beginning
and end of the minutes may be marked by an electric bell or a signal
made by hand. Set the pendulum vibrating through an arc of about
30 cm. and count the vibrations for one minute and record. It is well
to practice counting a few times before making any record. In count-

1 Let the exact length be measured by several pupils and recorded by all.

400

PRINCIPLES OF PHYSICS.

ing at the first transit o£ the pendulum, say << Begin/' at the second
transit say " One." ^

Case II. — Repeat Case I., letting the pendulum swing in an arc of
10 cm. Does changing the length o£ the arc have an appreciable effect
on the number of swings ?

Case III. — Try bobs of different weights, of chalk, iron, wood.

Case IV, — Vary the length of the pendulum from 25 cm. to 400 cm.
What effect does a change of length have? Does doubling the length
halve the number of vibrations ? Record as follows : —

Length

Number of Vibrations

/Length

^Length x Number of Vibrations

Problems.

1. If a meter pendulum makes 60 vibrations a minute, how many
would a pendulum 25 m. long make ? Take the square root of the
lengths. The square root of 1 is 1. The square root of 25 is 5.
Remember that the longer pendulum must vibrate slower. A? = 12.

2. Find the number of vibrations of a pendulum J m. long ; J m. ;
16 m. ; 100 m. ; yi^ m. Ans. 120, 180, 15, 6, 600 vibrations.

3. Find the length of a pendulum that makes 4 vibrations a
minute. Write out as follows : —

A meter pendulum makes 60 vib. 60^ = 3600. 3600

What length of pendulum makes 4 vib. 4^ =z 16. 16

4. Find the length of a pendulum that vibrates 10 times a minute ;
40 times; 180 times; 120 times; 50 times; 5 times.

5. The pendulums of two clocks are made one of wood, the other
of brass. The second clock gains time in winter. Why? Which
must expand the more with a change of temperature, metal or wood ?

6. What should be done to a pendulum clock that gains time?
To one that loses time ?

1 The teacher should compare the results and have the class repeat the
exercise till there is an error of only one vibration.

ELECTRICITY. — MA GNETS. 401

456. Vibration of the Compass Needle. — In the last exercise,
when the downward force acting on the bob was increased, the
pendulum vibrated faster (section 155, page 135). Other forms
of experiment and mathematical calculations have shown that
when the pendulum vibrates twice as fast, the force acting upon
it is four times as great. Four is the square of two. The force
increases as the square of the increase in rate of vibration. To
verify this, hold a book at arm^s length in a horizontal position.
Swing the arm right and left slowly, counting "one, two,"
" one, two." Swing twice as fast, counting " one and, two and."
The force necessary to keep up the same arc of swing will seem
to be more than twice as much as before.

A vibrating compass needle is a kind of pendulum. The
attraction of the earth on the north-seeking pole is like a long
thread pulling always the same, much like the rubber elastic in
the pendulum experiment. The mass or inertia of the needle
keeps it swinging after the middle point has been passed.
Place a compass along a bar magnet at different positions. Set
the needle swinging, by shaking the compass. Where does the
needle vibrate the fastest ? Can a place be found where the
needle vibrates very slowly or not at all ? What is the strength
of the magnetic field at that point? A suspended needle
vibrates long enough so that its vibrations can be counted.

457. Law for testing the Strength of a Magnet. — The differ-
ence between the squares of vibration of a needle near a magnet
and a needle alone gives a number representing the strength of
the magnetism of the magnet near one pole. If the needle
alone makes twenty vibrations a minute, and at a point near
one pole of the magnet makes one hundred, squaring these
numbers we have 10,000 and 400. If the magnet and the earth
tend to make the needle point in the same direction, one force
assisting the other, then the force of the magnet is 9600, the
difference between the two numbers. If the magnet and the
earth oppose each other, add the numbers.

-A'

402 PRINCIPLES OF PHYSICS.

Exercise 64.

DISTSIBUTION OF MAGNETISM IN A MAGNET. YIBBATION
METHOD.

Apparatus : A magnet | inch square, 18 inches to 2 feet long, which need not
be hardened and may be magnetized on an electromagnet ; a small magnet
or suspended needle of h inch steel, h inch long, attached to a fibre of raw
silk ; a clamp from which the small magnet is suspended and to which the
long magnet can be clamped vertically. Before beginning the exercise,
make marks on the long magnet 5 cm. apart.

Attach the clamp which holds the bar magnet to a table in such a
position that the north pole, placed as shown in Fig. 372, will not
J attract the suspended needle out of the magnetic meridian ;
I that is, the suspended needle points north before the bar
magnet is placed in position, and the clamp must be
turned till putting the bar magnet in place does not pre-
vent the suspended needle from still pointing north. Set
the needle vibrating and count the vibrations for one
minute. Move the bar magnet up 5 cm. at a time, and
count the number of vibrations of the suspended needle at
each position.

Record the distance or distances from the end to posi-
tions where the suspended needle turns end for end.
Count the vibrations of the needle with the magnet re-
moved. In this way the strength of the earth's field, or
Fig. 372. rather the horizontal force or component of the earth's
field, may be compared with that of the magnet at any
point. Still, it is impossible, unless the experiment is done inside a
big box of iron, to have the needle under the influence of the magnet
alone. The needle is in the magnetic field both of the magnet and
of the earth, and the vibrations are more or less rapid than they would
be if the magnet alone affected the needle, according as the earth and
the magnet work together or against one another.

Perhaps the easiest way to plot the distribution of magnetism along
the bar magnet is to disregard for a moment the effect of the earth.
Record as in Fig. 373. NS is a line of convenient length drawn on
coordinate paper and representing the bar magnet; the divisions are
.5 cm., or less, apart. With any convenient scale, letting 1000 l»e
represented by 1 cm., or \ inch, or by one, two, or five divisions of

ELECTRICITY. — MAGNETS.

403

the section paper, lay off NA = 10,000. Locate B, C, and other points,
in the same way. I^t the curve cross the line NS at the point D,
where the needle is re-

Jfumberqf
vib. needle

versed, and lay off the
numbers of the second
column on the other side
of NS in all cases where
the needle is reversed. The
influence of the earth made
the needle vibrate faster
when the north pole was
near, and slower when the
south pole was near, than
would have been the case
if the forces of the magnet
alone had acted on the
needle.

(vib.)*
lOOOO

8100

iSOO

1600

30 900

4 16

Needle renened. at 28 cm.

50 2600

y-5 /..

Fig. 373.

458. Comparison of Two Magnets of the Same Length. — On a

meter stick pointing east and west place a compass, (7, Fig.
374, which points at right angles to the meter stick. File a
knitting-needle, cut a watch spring, or break a flat file, M\ to
the length of the bar magnet M. M' is the magnet to be com-
pared with M. First bring M so that its centre is from 30 to
50 cm. from C, — near enough to
make C deflect 10° or so. ' Find a
position where the second magnet,
M', with the same pole pointing
toward C that JIf has, attracts C as
much as M attracts it; C will then point as it did before any
magnets were brought near it. If M and M' have the same
magnetic moment, AC and BC will be equal in length.

459. The Magnetic Moment is the moment or turning force
exerted on a magnet when placed at right angles in a magnetic
field of unit strength. The term is a difficult one to explain,
and has no simple substitute. Magnetic strength may be used
in a general way for magnetic moment.

— ^ — -
c

Fig. 374.

CHAPTER XXVII.
BATTERIES.

460. Study of a Simple Cell. — Make a solution of sulphuric
acid one part, and water ten to twenty parts. Which is the
heavier, water or sulphuric acid? What happens when the
acid and water are mixed ? If the water is put into the acid,
the water, being lighter, remains on top, and between the two,
where mixing occurs, considerable heat is generated, — some-
times enough to spatter out the liquid or to crack the vessel
holding it ; therefore, always pour the acid into the water. In
a tumbler two-thirds full of the dilute acid place a strip of cop-
per. What is the effect ? Remove the copper and substitute
zinc. The bubbles of gas that come from the zinc are caught
by filling a test-tube or small bottle with dilute acid or water,
dropping in a small bit of zinc, and inverting the test-tube, the
mouth covered with paper, in a tumbler of the dilute acid.
The gas displaces the water, and fills the test-tube. Remove
it, and apply a lighted match to the mouth of the tube. The
gas is hydrogen.

To find what becomes of the zinc, add zinc to the solution
till no more bubbles come off. Evaporate a little of the solu-
tion. The crystalline solid is zinc sulphate. Zinc and sulphuric
acid produce hydrogen gas and zinc sulphate.

Put a strip of copper and one of zinc in the
acid ; from which do the bubbles come ? Touch
—I the zinc and copper together. Let them touch
/-j first under the liquid, then out of the liquid.
'-I From which do the bubbles now come ? In Fig.
^ 375, the bent strip is copper, the straight one
Fig. 375. zinc. Fill the test-tube with water, cover it with

404

BATTERIES.

paper J and Invert in the tumbler of dilute acid, pushing it
down over the copper. Make the copper touch the zinc. In
tliis way the gas from the copper alone is collected. Try to
light it with a flame. The gas is bydrogeUj exactly the same
ai that given off by the zinc,

46L Generation of the Electric Current — Replace the plain
strips by aume to wiiieh Na 24 or 20 insulated copper wires
(t,e, wires covered with cotton) have been soldered. Bend the

406

PRINCIPLES OF PflYSlCS.

ends of the wires together, being aure that the covering, or
insulation, is off of the ends of the wire. From which strip
do the bubbles come now ?

Place vertical I J, pointing north and south, a coil of insulated
copper wire of ten to fifteen tnrna (I*j Fig. 377). In the centre
place a compass
or suspended
needle ; it points
north, as does the
coil, The needle
need not neces-
sarily be in the
centre, though
the instrument

Fig, 377.

is somewhat more sensitive with the needle in that posi-
tion. To the ends of the coil, or to the binding-posts to
which the ends are attached^ fasten the wires from the zinc
and copper strips shown in Fig, 376. iRotice the effect upi
the needle. Interchange connections and note effect

A coil of wire with a suspended needle (II., Fig. 377), used
to detect a current of electricity, is called a galvaiioscope ; us*
to measure the cnrrent, it is called a galvmiometer.

462, Open and Closed Circuits. — Unless a wire from one strip
(Fig, 376) touches one binding-post and a wire from another

BATTERIES. 407

strip touches the other binding-post, the circuit is said to be
open, because there is an opening or gap in the path. When
connected so that there is a complete path by the wire from
one strip to the other, the circuit is said to be dosed. If a
compass is used, the instrument should be gently tapped to
overcome the friction of the needle support. From which strip
do the bubbles come ? Take one of the wires out of the bind-
ing-post ; what is the effect on the needle and the bubbles of
gas?

An electric current is said to flow when the circuit is closed.
Is there any connection between the current, the bubbles of
gas, and the deflection of the compass needle?

463. Effect of Mercury on Zinc. — Remove the zinc, taking
care not to bend it, and touch it to a small drop of mercury,
not much larger than the head of a pin. Rub the mercury
over the zinc, and if it does not spread over all that part of
the zinc that was in the liquid, put on a little more mercury.
It is very easy to get on too much, and make the zinc very
brittle. Replace the zinc, and leave the circuit open; are
there any bubbles ? If so, remove the zinc and rub it to
spread the mercury. Close the circuit, and note the deflection
of the needle. This may be more or less than before.

The copper strip should not have any mercury on it, and
should be bright.^ Mercury may be removed from the copper
strip by heating the strip in a Bunsen flame. If the copper is
not bright, wash it and rub with emery cloth. Replace it in
the tumbler, and notice its surface.

Set aside one piece of apparatus and let it remain connected
until the current ceases, taking readings whenever convenient.
Set aside a tumbler containing a strip of copper and a strip
of zinc coated with mercury, but with the wires disconnected.
Set aside a test-tube containing dilute sulphuric acid and a

1 In this experiment some pupil is likely to coat the copper strip with mer-
cury ; if this happens, each pupil should note the effect.

408 PRINCIPLES OF PHYSICS.

strip of zinc on which no mercury has been put, and another
test-tube containing the same solution and a strip of copper.
Examine them the next day.

464. Galvanic or Voltaic Cell. — Two metals, or a metal and a
carbon, in a solution of acid or salt is often called a Galvanic
Cell, or a Voltaic Cell, Galvani and Volta were two early
students of the phenomena of electricity.

465. Poles of a Battery. — The strips of metal of a cell are
called poles. One of these, the zinc pole, is the one consumed,
while the copper strip, or pole, is entirely unaffected. Zinc is
a fuel. Sheet zinc burns, if thrown on a coal fire, and either
zinc foil or a fine thread cut from a sheet of zinc with shears,
burns in a Bunsen flame. Likewise in the cell the zinc is con-
sumed. When a metal joins the two poles, a current of
electricity is spoken of as passing from one pole through the
metal, outside the tumbler, and back to the other pole, then
through the liquid in the tumbler to the first pole. Just what
electricity is, and whether a current of any kind actually
passes through the wire, need not now be considered. It is
convenient to think of the wire or metal connecting the two
poles as a conductor of electricity. The direction of the current
in a cell or battery, as it is supposed to flow, is easily remem-
bered after performing the experiment in the next section.

466. Direction of Current in a Cell. — C, Fig. 378, is a simple
__ cell of zinc (Zn), and copper (Cu),

C i — ^^ ^^ ^^ ^ solution of dilute sulphuric

14_-_-. If »•■•."-. -lI 2icid. Z) is a jar of sulphate of
iV ~ - ^ - H 1" .'-.'.? F| copper solution . A and B are two
01 -." :u »•..■_■ _"I3 copper strips or wires dipping into
y- - -' "■ '- -" - -I the solution. The zinc is amalga-

p. ^yg mated (that is, covered with mer-

cury), and the circuit is completed
by copper wires, as shown in the figure. From time to time

BATTERIES. 409

notice the appearance of A and B, When the zinc in the liquid
has disappeared, examine A and B; which has increased in
size? which has grown smaller? Does it seem that copper
has been carried in some way from one strip to the other ?

Reproduce Fig. 378 in the note-book, drawing arrows in the
liquid of D, to show the direction in which the copper from one
plate, or pole, in D is carried, as it were, through the liquid to
the other pole. Draw arrows near the connecting wires, to
show the direction of the current in them. Show, in the same
way, the direction of the current in cell C. Make a statement

thus ; The current leaves the cell from the pole and returns

by the pole. Use the words zinc, copper, to fill the blank

spaces.

467. Positive and Negative Poles of a Battery. — Almost any
two different metals in an acid solution make a galvanic cell ;
but whatever combination of metals is used in the cell C, Fig:
378, the current appears to leave the cell by the wire attached
to the pole that is not consumed, or eaten up, by the solution.
The current then passes through the connecting wire, which
may be wound into any shape, back to the pole that is con-
sumed, and thence through the liquid to the unconsumed pole.
This latter is sometimes called the positive pole, and the other
is called the negative pole. They are sometimes marked with
the plus and minus signs, as shown in Fig. 379. The use of
the terms positive and negative, or plus and minus, often leads
to confusion. In place of them, the terms consumed pole and
unconsum£d pole, or pole from which the current conies, may
be used.

468. Short-circuiting. — Pure zinc, or common zinc coated
with mercury, is very slowly dissolved in sulphuric acid or
other solution used in a battery, unless the zinc touches
another pole of metal or carbon within the liquid, or is con-
nected to the other pole by a wire outside. In the latter case,

410

PRINCIPLES OF PHYSICS.

Connecting

the current can be put to some use, and zinc is consumed only
when the circuit from pole to pole outside is complete or closed.
On open circuit, — that is, when there is
no conductor from one pole to the other,
— there is little or no consumption of zinc,
and no current flows. If a short piece of
wire joins the two poles in a jar under the
surface of the liquid, the current takes the
easier path and goes by the short wire,
and not through the long connecting wire
outside. The cell is short-circuited, and
does no useful work. The cell is also
short-circuited, if the two poles touch,
either inside or outside of the liquid.

Fig. 379.

469. Short-circuiting by Local Action. ~

Pure zinc is expensive, costing many times as much as common
zinc, which contains minute specks of iron, carbon, and other
substances. Notice the liquid in which a piece of common
zinc has dissolved. The impurities appear as black mud in
the bottom of the jar. These little bits of iron, carbon, etc.,
are really just so many poles pressing against the zinc, forming
so many short-circuited cells. Numerous little currents are set
up between the zinc and the bits of foreign substance, and none
of these currents pass through the wire to do useful work out-
side the cell. The zinc is short-circuited with these numerous
bits of iron and carbon, instead of with one large piece, and the
current from short circuits is always wasted. In the simple cell
of zinc and copper, before the zinc was amalgamated (covered
with mercury), there was a strong current flowing through the
wire connected with the copper strip. The copper, however,
did not touch the zinc and was not short-circuited. The zinc
was then consumed partly to furnish current flowing through
the liquid to the copper and thence through the outside circuit,
where it could be set to do useful work, and back to the zinc ;

BATTERIES. 411

and it was consumed partly to supply the useless local cur-
rents of the short circuits caused by the impurities on the
surface of the zinc.

470. Amalgamation. — Mercury does not dissolve the impuri-
ties of the zinc, but it does dissolve zinc Try to dissolve
bits of carbon, iron, and zinc in mercury. In a cell, the solu-
tion comes in contact only with the pure zinc dissolved in
the mercury. There is no short circuit (local action, it is
often called) on zinc that is consumed only to furnish current
actually going out of the cell. Even if the zinc is pure, one
part is usually denser or harder than another ; the soft parts
and dense parts act like different metals and more or less
short-circuiting, or local action, occurs all the time, till the
zinc is finally consumed. Amalgamation prevents this. Zinc
must be clean, or mercury will not wet, or amalgamate it.
Dipping the zinc in weak sulphuric acid cleans the surface
so that mercury can be rubbed into the surface with a rag. A
few per cent of mercury added to the zinc before casting is a
good way of amalgamating it ; but any excess of mercury in
the zinc or on the surface eats its way into every part and
makes the zinc brittle.

471. A Simple Cell is a combination of two metals in an acid.
Plates of zinc and copper, in a solution of dilute sulphuric acid,
are usually meant when the term simple cell is used.

Exercise 65.

STUDT OF A SIMPLE CELL WHILE OENEBATING A CTJBBENT
OF ELECTSICITT.

Apparatus : Glass tumbler ; battery stand ; dilute sulphuric acid ; strips of
copper and amalgamated zinc, 2cm. wide by 10cm. long; a galvanometer
of 100 or more turns ; a resistance of a No. 28 or 30 German silver wire or
manganin wire, to reduce the deflection of the needle to between 30 and 40
degrees. It is essential that the galvanometer needle come quickly to rest.
A fibre suspension is desirable (see Appendix, page 536).

412

PRINCIPLES OF PHYSICS.

Place the galvanometer coil pointing in the same direction as the
needle points. Clean the zinc and copper. Set up the cell and con-
nect each pole of the cell with a binding-post of the galvanometer.
Complete the circuit and read the deflection as soon as the needle
comes to rest. The deflection at the start is sometimes estimated by
averaging two swings. For instance, when the pointer vibrates be-
tween 30^ and 34 ^ could it come to rest at once, it would read about
32**. After a few seconds, the deflection decreases. Notice the sur-
faces of the copper and zinc the instant the needle comes to rest at
the lowest point. Shake off the bubbles of gas that form on the cop-
per, and watch the needle. Remove the copper strip, clean it, heat it
in Bunsen flame, and replace in the cell. When the bubbles form
again, rub the surface of the copper with a stick. Remove the cop-
per, wipe carefully, and replace. Try the effect of lifting the copper
out of the liquid and immediately replacing it. What three ways can
be suggested for keeping up the current of a simple cell? What
seems to cause the current to weaken ?

The bubbles of hydrogen gas that form on the copper are best

cleaned off by heating the strip in a Bunsen flame.
A ' ' /i If the thin film of oxide of copper formed by heating

is not rubbed off, the current remains at the highest

point for a minute or more.

Place two strips of clean copper in the cell. Note

the effect on the needle. Remove the copper, and see

what effect two strips of zinc have. Two pieces of the
p. 3gQ same metal, used as the poles of a battery, produce

no current. Place a strip of copper, -4, Fig. 380, and
a strip of zinc, jB, in the cell. Note the direction of the deflection
of the galvanometer. As soon as the copper is well coated with
hydrogen bubbles, replace the zinc by a strip of clean
copper, Z), Fig. 381. Does the needle show that the
direction of the current has changed ? The hydrogen
bubbles on the strip 4, Fig. 381, now set up a small
current in the opposite direction to that of the copper-
zinc cell, Fig. 380. As soon as the hydrogen bubbles
were formed on A , Fig. 380, they tended to set up a
current in the direction opposite to the current of
the cell as shown by the arrow; this weakened the Fig. 38 h

force of the cell.

BATTERIES. 413

472. Polarization. — When the zinc of a simple cell is amal-
gamated, bubbles of hydrogen gas rise only when the circuit is
closed and the current flows, and then from the copper pole
alone. The presence of the current is made evident by the
needle of the galvanometer. The needle did not point north
while the current flowed through the coil of the galvanometer.
The greater the deflection of the needle, the greater the cur-
rent. At first, before the bubbles collected on the copper plate,
the deflection of the needle, and consequently the current, was
the largest. As the bubbles covered the copper, the current
became less. Rubbing off the bubbles made the current
greater, until more bubbles were formed and covered the cop-
per again. The bubbles were small and formed a film over the
surface of the copper, which was then said to be polarized.

473. Effect of Hydrogen Bubbles on the Current. — The hydro-
gen lessens the current, for two reasons : first, because hydro-
gen is not a conductor of electricity; second, — and this is by
far the more important reason, — because the hydrogen film on
the copper tends to send a current in the opposite direction
(see Exercise 65); it opposes the current, exerting a back
pressure, or, as it is called, a counter-electromotive force. While
this back pressure is less than that caused by the zinc plate
connected with the copper, it is enough to lessen greatly the
available current of the cell. Of the hundreds of forms of
cells, or batteries, almost all have some device to remove the
hydrogen quickly or to prevent its formation. As the simple
cell (two metals in one liquid) has no means of ridding itself
of the hydrogen, it quickly polarizes.

474. Ways of reducing Polarization. — To prevent polariza-
tion, remove the hydrogen, or prevent its formation. More
power might be required to keep in motion some device to de-
polarize the copper plate of a simple cell by rubbing it, than
would be obtained from the cell itself. In the Smee cell, now

414 PRISCIPLES OF PHYSICS.

seldom used, the copper plate is replaced by one of sU^er, and
this is plated with platinum. The hydrogen collects in large
bubbles on the rough points of the platinum plating; these
rise and stir up the liquid, brushing away many of the small
bubbles. The common method of reducing or preventing polar-
ization consists in adding some chemical that unites with the
hydrogen gas as fast as it forms, or entirely prevents its
formation.

Repeat the experiment, Exercise 65, page 412. Record the
time necessary to complete polarization. Remove the copper
and dip it in a solution of sulphate of copper. Let it drain
for half a minute, then dry it completely over a burner, and
replace it in the cell. Does the current continue at the highest
point for a longer time than before? Try the experiment
with a cell of zinc and copper strips in a solution of CUSO4.
Set the cell away, and examine it after several hours.

475. Curve of Polarization of a Simple Cell. — Use as large a
plate of copper as possible, one having an area of 200 square
centimeters or more. Thoroughly heat it, and clean with fine
sandpai)er or emery cloth. Place it in the acid, but do not
make the final connection until ready to read the galva-
nometer. Read at least every minute, and, if possible, every
half minute, until the current has decre«ased and become con-
stant. Record the angles of deflection. Look in a table of
tangents of angles, and beside each angle of deflection record
the value of the tangent. Plot the results, letting horizontal
distances represent minutes, and vertical distances represent
tangents of deflections.

476. Two-fluid Cell. — Leave a strip of zinc in a solution of
sulphate of copper for a day or more. If the solution is still
colored blue, add more zinc and again let it stand. Pour off and
evaporate a little of the clear, colorless solution thus obtained ;
allow the sulphate of zinc to crystallize, and preserve it. The
reddish brown or black mud that forms on the zinc is

BATTERIES. 415

copper, or copper oxide. It could be fused on charcoal by the
blowpipe, and a globule of solid copper formed, which would
have the true copper color. Suppose we start with zinc and
sulphate of copper. In time we have copper and sulphate of
zinc. More briefly, zinc and sulphate of copper give copper and
sulphate of zinc ; or, in chemical abbreviation (Zn standing for
zinc, and Cu for copper : —

Zn + CUSO4 = Cu + ZnS04.

There is no hydrogen whatever formed.

477. Daniell Cell. — Dkniell intended to use sulphate of
copper instead of sulphuric acid, because nothing but copper
could then be deposited on the copper plate, and the deposited
copper would offer no resistance and would not exert a back
pressure, or counter-electromotive force, to the current as
hydrogen does ; there would be no polarization. But whil«
the substitution of sulphate of copper stopped the polarization,
the zinc, whether amalgamated or not, was rapidly destroyed
by local action on itself, zinc going into solution and copper
taking its place without producing any current in the wires
outside of the cell. To overcome this difficulty, the sulphate
of copper in the Daniell cell is kept away from the zinc by a
porous cup — a sort of cage, as it were.

478. The Gravity Cell is practically another form of the
Daniell cell, in which the zinc is placed in the top of the cell,
the copper and copper sulphate at the bottom. This form
(Fig. 382) consists of a sheet of copper or a coil =
of bare copper wire connected with an insulated l^\
wire that extends up through the liquid. The liZ^EJj;
zinc is supported in the upper part and sur- U - 1 - "
rounded by a solution of sulphate of zinc (shown |"J copper
in the cut by the light dotted lines). Crystals ^
of sulphate of copper are dropped in the jar. '*'
These dissolve, and, as the density of sulphate of copper solu-

416 PRINCIPLES OF PHYSICS.

tion can be kept greater than that of the sulphate of zinc, the
sulphate of copper solution (shown by the heavy short lines in
the figure) remains at the bottom of the jar, away from the zinc.

Instead of using sulphate of zinc at first, water with a little
sulphuric acid is used. This soon forms sulphate of zinc by
uniting with a portion of the zinc plate. The zinc is often
unamalgamated. In a week, the sulphate of copper diffuses
upward and attacks the zinc, unless the cell is on a closed
circuit, that is, furnishing current.

This cell is not suitable for intermittent work, — bells, burg-
lar alarms, etc. It has a high internal resistance ; that is, the
liquids between the copper and zinc are not good conductors
and the cell can give but a small current; it is therefore use-
less for telephones, electric lights, or motors, but is used for
telegraph and fire-alarm circuits, in which the current flows
practically constantly.

479. A Simple Form of Gravity Cell — Make some form of a
gravity cell. Leave it connected with a galvanoscope for a
time, or till the blue color disappears, and describe what hap-
pens to the plates, or the poles of zinc and copper. Figure 383

^y is a gravity cell, made of a bottle from which

the bottom has been cracked. Copper wire,

Cu, is cleaned of its insulation and twisted

^ into a coil. Where this wire passes through

the stopper, the insulation is not removed.

The bottle is held in a hole cut in the top of

-[} / a box. A piece of sheet zinc, to which a wire

^ is soldered, is placed as shown in the figure.

F'g 383 ^^^ water, a few crystals of sulphate of copper,

and a few drops of sulphuric acid, and connect A and B

together. Leave them connected for a day.

480. Porous Cup Form of Daniell Cell. — This form, usually
called the Daniell cell, has a low internal resistance. Make a

BATTERIES.

417

Ctt

iZm,

diagram in the note4xK)k like Fig. 384. First draw (?, the jar
of glass. In this is the porous cup, P. In the porous cup
is a sheet of copper, Cm, and a solution
of sulphate of copper. Outside the po-
rous cup is a strip or cylinder of zinc,
Zn. Water and a little acid (one part
of acid to 30 parts of water) is poused
in the glass jar outside of the porous
cup. The zinc is amalgamated. For
the cup, any form of unglazed earthen-
ware or crockery can be used The bowl
of a tobacco pipe, set on a lump made of
plaster of Paris and water, a flower-pot
with the hole stopped by a cork, a cup
or bowl taken from the pottery before the glaze is melted on,
are all practical forms of porous cups Fill the porous cup
with water, mark the level, and cover with a card. Notice the
level in a few hours. Fill the porous cup with sulphate of cop-
per and set it in a jar of water. Make the liquids of the same
level. Notice the liquids from time to time. How long before
the blue liquid begins unmistakably to come through the cup ?

Fig. 384.

481. Advantages of the Daniell Cell. — While a porous cup
prevents the liquids from mixing readily, and consequently
prevents the sulphate of copper from reaching and destroying
the zinc, very little increased resistance is offered to the flow
of the current. The pieces of the zinc and copper are of large .
size, and are much closer together than in the gravity cell.
Besides, sulphuric acid can be added to both solutions, and the
acid and the nearness of the plates reduces the resistance to
one-twentieth or one-thirtieth of the gravity form. Quite often
the zinc and sulphuric acid are put inside the porous cup, and
the sulphate of copper and a cylinder of sheet copper outside the
cup. Make a diagram of this arrangement. When the cell is
not in use, remove the porous cup

418 PRINCIPLES OF PHY8IC8.

Exercise GQ.

STUDT OF A DAHISLL CELL.

Apparatus : Porous cap ; tambler ; battery stand ; copper sulphate ; sulphuric
acid ; copper and zinc strips ; balance ; galvanometer.

Amalgamate the zinc thoroughly, using no excess of mercury.
Wash the zinc, dip it in boiling water, and let it dry. Wash and dry
the copper in the same m&nner. Weigh each with the connecting
wires to .1 g. or less. Have a few more crystals of sulphate of copper
than will dissolve in the solution. Set up the cell and connect the
wires from the copper and zinc to the terminals of the galvanometer.
Read the deflection of the needle, recording the number of degrees
and the time of observation. Before each reading tap the instrument
to overcome the friction of the needle support. This is unnecessary
if a fibre suspension is used in place of a pivot. Read the deflection
once a minute till there is no change ; then once every three minutes.
Continue this at least half an hour; from three to five hours is even
better. Be sure there are plenty of sulphate of copper crystals with
the copper plate. The zinc must be so well amalgamated that no
hydrogen bubbles come from it.

Remove the plates and wash them gently in running water ; then
dip them in boiling water for a few seconds. Remove them from
this, and hold them, if possible, two feet above a Bunsen flame;
they will dry at once. Weigh them carefully ; which one has gained
in weight? Which one has lost? Where does the zinc go that dis-
solves? From what does the copper come that is deposited on the
copper plate?

When the cell is set up fresh, some time is required for the solution
to soak through the pores of the porous cup. This process is hastened
by soaking the cups in dilute acid before the exercise.

. Set up two Daniell cells. Leave one on open circuit, the other short-
circuited. Examine them, after six hours or more. This form of
cell is useless where current is wanted for a few seconds at a time, as,
for instance, in ringing a bell or in other so-called open-circuit work ;
for, unless the cell is working all the time, sulphate of copper works
through the porous cup and attacks the zinc.

482. Chemical Action in Daniell and Gravity Cells. — Tbe

Daniell cell is used mostly in the laboratory. It is a constant

BATTERIES. 419

cell ; thai is, the current is uniform, because there is no polari-
zation. Hydrogen forming on the copper plate of the simple
cell causes polarization, thereby reducing the current. Copper
is deposited on the copper plate in the Daniell cell, and in the
gravity form too, and the plate merely increases in thickness,
and offers no opposition to the current. The chemical actions in
the Daniell and gravity cells may be divided into two stages.
The zinc and sulphuric acid give zinc sulphate and hydrogen.

Zn + H2SO4 = ZnS04 + Hj.

This takes place on the surface of the zinc. The hydrogen
does not escape, but is supposed to unite with the SO4 of a
neighboring particle of H2SO4. Of course, the new hydrogen
(Hj) repeats this process through a long chain till the surface
of the copper is reached ; then the last hydrogen particle (H2)
acts as follows :

Hydrogen and copper sulphate give sulphuric acid and copper,

H2 + CUSO4 = H2SO4 + Cu,

and the copper (Cu) is deposited on the copper plate, some-
times firmly, sometimes loosely.

483. Varieties of Cells or Batteries. — Hundreds of forms of
cells have been devised. The materials and design of a gal-
vanic cell are chosen principally with a view of preventing or
lessening polarization and reducing the internal resistance.
The sulphate of copper battery in the Daniell or gravity form
belongs to the class where polarization is prevented through
the deposition of a metal instead of hydrogen gas on the uncon-
sumed plate.

Study the polarization of cells composed of carbon and zinc
in dilute sulphuric acid (section 474, page 414). Try the effect
of brushing the carbon after the current fails. The hydrogen
fills the pores of the carbon, and can be removed best by some
chemical. Dip the carbon in a solution of bichromate of soda
and sulphuric acid. Let it drain, and replace it in the cell.

420 PRINCIPLES OF PHTSICa.

484. The Bichromate Cell, so called because the depolarizing
solution is bichromate of potash or soda, is the best form to
furnish a powerful current for a short time. The porous cup
contains a carbon pole in a solution of sulphuric acid and bichro-
mate of soda. The zinc is in a solution of one part sulphuric
acid to ten parts water. The bichromate solution may be pre-
pared by dissolving 200 g. of bichromate of sodium in a liter
of water, and adding 150 cc. or more of strong sulphuric acid.
Allow the mixture to cool.

Make a diagram of a bichromate cell, and label the parts.
The porous cup is not absolutely necessary if the cell is used
for only a few minutes at a time and if the zinc is removed
when the (^ell is not in use. The bichromate solution slowly
attacks and wastes the zinc, so the two-fluid form, with the
porous cup separating the fluids, is to be preferred. When
th(i bichromate solution is exhausted, the color changes from
red to green. The carbon poles may be matle cheaply from
half lengths (six inches) of an electric light cai'bon. If not
held in one of the clamps of the battery stand, a connecting
wire is attached as follows. Soak the end of each piece in
melted parafline for two or three minutes. Remove the pieces,
and rub the end with a lump of parafline. Scrape the insulation

y rrr-r\ fi'om six inches of No. 18 annunciator

1^^^'^^ wire, and wind the bare part around the

D paraffined end of the carbon (Fig. 385),
'^ C making the turns closer together than is
Rg. 385. shown in the figure. Twist the ends of

the wire A and B together, using pliers to draw the wire tight,
and make it come in close contact with the carbon surface.
Rub melted paraffine over the bare copper. C, the insulated end
of the wire, is of any convenient length, — a foot or more. In
time the solution in which the carbon is placed rises through
the pores, and, in spite of the paraffine, attacks the copper
wire, which then shows a green corrosion. Throw away the
carbon, as the contact between it and the copper is destroyed. ■

BATTERIES. 421

A small per cent of bisulphate of mercury — a pinch or two
stirred into the sulphuric acid solution — assists in making and
keeping the zinc amalgamated.

Almost all attempts to run street cars, launches, balloons,
and electric lights with primary batteries have been made with
the bichromate cell described. Primary cells or batteries furnish
current by consuming the zinc and solutions, and so these require
continual renewal. Secondary or storage batteries do not con-
sume the materials of which they are made, but merely give
out the current which was used in charging them. They must
be charged by passing through them the current from a dynamo
or primary battery (Exercise 73, page 477).

485. The LeclanchI Cell consists of a porous cup packed with
granulated black oxide of manganese around a rod or plate of
carbon ; outside the cup is a rod or plate of zinc. The solution
is chloride of ammonium (called sal ammoniac), five ounces to
a quart of water. Sometimes the porous cup is made of hollow
carbon, filled with the manganese. Another form has the man-
ganese pressed into blocks, which are held by rubber bands to
the carbon plate. In this form there is no porous cup, as its use
is merely to keep the pieces of manganese close to the carbon.
The oxide of manganese is the depolarizer. The cell, if kept
on closed circuit, readily polarizes or "runs down"; but when
the circuit is opened again the hydrogen on the
carbon pole is absorbed and destroyed by the
manganese, and the cell becomes as strong as
ever. This cell is used in almost all bell, gas-
lighting, and telephone circuits.

A similar form of cell, but without the depo-
larizer, is easily made fairly efficient. Make
holes in a piece of paraffined board, through p. ^^^

which the zinc, Zn, and the carbon, C, fit tight
(Fig. 386). The solution is the same as that described above.
Cpmiwon salt may take the place of the ammonium chloride.

422 PRINCIPLES OF PHYSICS.

The Leclanch^, in any form, is called an open-circuit bcUtery.
It is useful only on open-circuit work; that is, where the
current is flowing only for a few seconds at a time. It is
useless for power purposes, or for running electric lights. The
zinc need not be amalgamated, and it is not consumed when
the circuit is open.

486. Polarization of the Leclanchi Cell. — Study the polariza-
tion of carbon and zinc in a solution of sal ammoniac. Fix a
carbon rod in one clamp of the battery stand, and a strip of
zinc in the other. Put the cell in circuit with a galvanometer
of a large number of turns. Let the resistance in circuit be
four or five ohms. This may well be the resistance of the gal-
vanometer coil. Read the deflection every minute till the
current has dropped to a certain point and become steady.
Open the circuit for two or three minutes. Close the circuit
and take readings, as before. Repeat these operations several
times. Look in a table of tangents, and write down by the
side of each deflection of the needle the value of the tangent of
that angle. Plot a curve, having the horizontal spaces repre-
sent minutes and the vertical spaces represent the correspond-
ing values of the tangent of the angles recorded. The current
does not vary as the angle, but as the tangents of the angles.
What does the curve show about the constancy of the cell ?

In case a sal ammoniac cell, like that just described, will not
ring a bell, join two or more in series. This is done by con-
necting the carbon of one cell with the zinc of the next. Wires
connect the zinc of the first cell and the carbon of the last cell
with the bell. After the bell stops ringing, open the circuit,
and let the cells rest a few minutes. Then close the circuit
again through the bell.

487. Dry Batteries. — We might, perhaps, say that there are
no dry batteries, or at least none that are perfectly dry. The
various chemicals used in batteries are non-conductors when

BATTERIES. 423

dry. There must be some moisture to make the chemicals
good conductors, else the current could not pass in the cell be-
tween the poles. There are no really dry cells in use; they are
damp cells, with sufficient water for the passage of currents
between the poles in the cells. The water, in one form of dry
cell, is held absorbed by plaster of Paris.

Expose to the air for a day or more a diy piece of zinc chlo-
ride and a dry piece of calcium chloride. These tend to absorb
moisture from the air, and if mixed with the plaster, they pre-
vent the cell from becoming dry.

Make a model of a dry cell. Put a strip of zinc and a rod
of carbon in a glass jar made by cracking off the top of a bottle,
or in a wide-mouthed bottle. In the bottle put the following
mixture : oxide zinc, 1 part; chloride ammonium (usually called
sal ammoniac), 1 part ; dry plaster of Paris, 3 parts ; chloride
of zinc, 1 part ; water, 2 parts, — all by weight. The exact
proportions are not necessary.

to battery

Fig. 387.

CHAPTER XXVIII.
MAGNETIC ACTION OP ELECTEIC CUREENT.

488. Current Reverser. — Examine a current reverser (Fig.
387). Ay B, C, and D are binding-posts connected by wire
with mercury cups, E, F, O, and H, The battery terminals

are connected at opposite corners,
as at A and D. The wires, x and
2/, leading to the motor, bell, gal-
vanoscope, or any other electrical
apparatus, are connected with the
other opposite corners, B and C.
Make a diagram in the note-book,
showing the current reverser, bat-
tery, and X and y connected with
a coil of wire. Draw a line from E to F^ representing a bent
wire dipping in the mercury in E and F, Draw a line between
G and H, Suppose the current enters at A. Put numerous
arrow-heads on the wires to indicate the course of the current
back to the battery. Make another diagram in the same man-
ner, except that E is connected with O, and F with H. Study
the diagrams. Does this change alter the direction of the
current in the battery ? In the coil connected with x and y ?

489. Effect of a Current on a Compass. — Hold a wire running
in a north and south direction over a compass or suspended
needle. Send a current through the wire by connecting it with
a cell. What does the compass needle do? Hold the wire
under the compass. What happens now? A Daniell or
bichromate cell is the best for this experiment.

424

MAGNETIC ACTION OF ELECTRIC CURRENT. 425

Exercise 67.
MAGNETIC ACTION OF A CUSSENT.

Apparatus : Daniell cell ; current reverser ; wire ; compass.

Connect the battery, B, Fig. 388, with a current reverser, C, Lay
a wire flat on the table, in the form of a square, the sides 10 cm. or
more long, and connect it with C.
Arrange the square so that DE points
north. Arrange the connection be-
tween the mercury cups so that the
current flows north in DE.

Make a diagram of the whole appa-
ratus in the note-book, and indicate
the direction of the current by arrow-
heads drawn on the wires. Place a
compass over the sides of the square
in at least three places on each side. ^''' '®®*

Make arrow-heads on the diagram to show the positions taken by the

MRS

needle. Place the compass under the sides of
the square; show the positions taken by the
needle, representing the positions of the com-
pass needle above the wire by arrows crossing
Fig. 389. . it (83 Af and S above the wire, HI, in Fig. 389),

and positions of the needle under the wire by broken arrows (as R
and T),

Shift the wires in the current reverser, C Make a diagram, indi-
cating the direction of the current in the wire and the positions taken
by the compass needle. Always consider the current as leaving the
battery by the wire attached to the copper or carbon pole. The com-
pass needle sets itself in the lines of force which
surround the wire. These lines of forces are absent
when no current is flowing, for the needle is then
unaffected. Unless very powerful currents are sent
through the wire, DE, Fig. 388, the lines of force
would not be shown by iron filings.

/M7

490. Lines of Force about a Wire canying a b

Current. — Let AB, Fig. 390, be a vertical wire Fig. 390.

426 PRINCIPLES OF PHYSICS.

carrying a large eiirroiit. SS is a piece of paper slipped over
the wire and held horizontally. Iron filings dusted on the
paper arrange themselves in circles.

Bxeroise 68.

LIKES 0? FOBGE HI A COIL OF WISE OABBTINQ A OUBBSNT.

Apparatus: A coil of wire of Hmiill radius (the p^alvanoscope coil» I.» Fig. 377,
will aiiHwer if tlie (lirocaion of tlie wiren fn>m the binding-posts to the coil
are in sight); current reverser; Daniell or biohntmate cell; centimeter
rule; blt>ckH or boxes t<i Hupi>ort the rule in the centre of the coil.

Set the coil east and west (Fig. 301) ; it is now not to be considered
as a galvaiioscop(% but merely as a coil of wire, for a galvanoscope

coil points in the same direc-
tion as the suspended needle
or compass in it points be-
fore any current is passed
through tlie coil. Connect the
battery with the current re-
verser. Lead wires from it to
Fig. 391. * the binding-posts connecting

with the coil. Reproduce
Fig. 391, adding all connections, in the not<»-book. Set the currant
reverser so that the current flows in tlio top of the coil from east to
west. Mark an arrow-head on the diagram to show this. Start-
ing at the centre, move the compass south 2 cm. at a time, and
notice the direction of the needle and tlie rate at which it vibrates.
In whicli direction does the needle point when there is no currant
in the coil? What makes it point in that direction? How does
the needle point when it is inside tlie coil and the currant flows?
Which is the stronger, the effect of the earth, or of the current in the
coil? What can be said of the strength of the fleld, indicated by
the number of lines of force, at the place on the rule where the
needle not only refuses to vibrate, but points indifferantly in any
direction? Review Exercise 01, Part II., i)age 387.

Beginning at the centre, move the compass 2 cm. at a time toward
the north, and record on a diagram, as l)efore.

Reverse the current by the currant raverser. Make another dia-

MAGNETIC ACTION OF ELECTRIC CURRENT. 427

gram, and repeat all observations. Where is the effect of the coil
the greatest? If the needle away from the coil swings forty times
a minute, and in the centre of the coil swings four hundred times a
minute, how many times stronger is the field of the coil than the mag-
netic attraction of the earth at that point? Square 40 and 400, and
subtract, if the needle pointed north in
the coil. The difference compared with
the square of 40 gives the relative strength
due to the current in the coil.

Before studying the lines of force near
the sides, remove the rule and make dia-
grams representing the coil. First draw
an ellipse, H, Fig. 392, and add lines as

shown in /, J, K, till Fig. 393 is reached. Send the current through
the coil from east to west on the top. Hold a compass at Z), Fig. 394 ;
move it in the direction in which it points, and
trace out a line of force as in Fig. 394. Add
arrow-heads indicating the point of the needle.
Do the same at C, E, and F, and a few other
points. What is true of the general direction
of the needle inside the coil ? Outside the coil ?
Reverse the current, and record similar obser-
vations on a new diagram. In tracing the lines
of force at E and F, hold the compass box vertically, to allow the
needle to dip freely.

491. Multiplying the Effect of a Current. — Hold a wire car-
rying a current over and close to a compass. Slowly lift the
wire. Twist the wire into a circle of one turn just large
enough to slip over the compass. Have the circle of wire
point north. Try more turns. Try one turn of larger radius,
of 4 to 10 cm. Record the deflections, and state in each case
the relative rate of vibration of the needle. What effect does
a smaller circle of wire have on the lines of force at the centre
of the coil ? What effect does an increased number of turns
have? What is the effect of increasing the radius of the
coil ? of decreasing the number of turns ? A coil of small
diameter and a large number of 'turns must be used to show

428

PRINCIPLES OF PHYSICS.

the lines of force by means of filings; for they do not set
themselves in the lines of force as readily as does a compass,
in which friction is reduced by the needle-point support.

492. Lines of Force about a Magnetic Coil. — Wind a coil of
100 to 200 turns of No. 27 insulated wire, or finer wire. The
inside radius should be about 2 cm., the outside radius 4 cm.
This forms a more sensitive coil for a galvanoscope than

the one previously used.
Cut out pieces of card {A
and C, Fig. 395), having
slots to slip over the coil.
-D ^ D shows the coil in posi-
'^'*^' ^'** tion. The inner edges of

the cards overlap ; the outer edges are turned down, to form a
support. Connect the ends of the coil to a bichromate cell
or a hand dynamo. Sprinkle filings on the card, and tap it
lightly. Open the circuit by disconnecting one of the wires.
Remove the filings. Place a piece of iron inside the coil.
Sprinkle on filings, and notice the increase in the number of
the lines of force. The iron inside the coil acts like a magnet.
The coil alone, when current is flowing through it, is also a
magnet; but the presence of iron inside may increase the
number of lines of force — that is, the strength of the field —
thirty times or more.

493. Direction of Galvanoscope Needle. — We find, then, that,
as a compass needle tends to set itself in the lines of force, the
direction taken by the needle when in the centre of the coil is
a direction at right angles to the plane of the coil. If the
coil points north, the needle tends to point exactly east or
west. It seldom does this, because the lines of force of the
earth tend to make the needle point north.

Consider, for a moment, only the north pole of the needle
(Fig. 396). The force toward the north is that due to the

MAGNETIC ACTION OF ELECTRIC CURRENT. 429

earth's field. The force toward the west is that due to the

field of the eoiL Make a model of wood.

Bore a hole in the centre of a strip of wood ;

mark an arrow-head on one end. Drive a

wire nail part way into a board, and place

the strip on the nail. Attach two strings ^

to the end of the strip, and, if desired, put

spring balances on the strings. Pull one

north and the other west. Keep the north

pull a constant, — one hundred or more grams ^''' ^^'

all the time. Vary the pull west. What angle does the strip

make with the north, when the pulls are equal? Can the

strip be made to point west? The strip or the needle sets

itself in the direction of the resultant of the north and west

fcxees. If the current in the coil were reversed, the field of

the coil would tend to pull the point of the needle to the east.

fB Rule— Study the diagrams like Figs. 388
and 3Wy with a view of making a rule to predict the way
a ecMnposB points when near a coil or a wire carrying a cur-
rent of electricity. Cut out of paper an outliue of a man.
Mark the letter F on the face, and E and L on the right and
left arms, respectively. Place this paper man on the line
representing the wire, and let the face be toward the needle.
When the needle is underneath the wire, the figure faces
down ; when above, the figure faces up. See if your observa-
tions agree with Ampere a rule.

jhmagime yourself )ncim/ahfkg in tke aurr^.iU and Kith it,, and
lookmg at the needle : the north pole U deflected totcard the left

fK. App&cadoa <rf Ampte's Snle — You must imagine
yourself movin^z in the direction of the rnirrent. Voa mu:*t
face, or Itxjk. t^ivard the oeeiile. whether you hav»* to l<x>k up
or down or tideway a ; then the north pole of the compasii. or.

430 PRINCIPLES OF PHYSICS.

what is the same thing, the lines of force, will run to the left
hand. Test the winding, the direction of current^ and the
polarity of the ends of an electromagnet

An electromagnet is a coil of wire, usually wound on a piece
of iron or a bundle of iron wires (section 497, page 432).

Test the polarity of any coil used as an electromagnet. Does
Amp^re^s rule apply here ? Is a north pole formed at C, Fig.
397, if the current enters at -4? Draw
Fig. 397, putting an arrow, showing the
direction of the current, on each turn of

mj'

I wire. Mark C as north or south, as the

' case may be, and draw arrows at C and D

'^^^ to show the direction of the lines of force

generated by the coil. CD is supposed to be iron.

Make a similar diagram, supposing that the current enters
at B. Cut a paper arrow and wind it around your pencil so
that if a current flowed in the direction of the arrow, the point
of the pencil would be a south pole ; a north pole.

Problems.

1. How must the current go around a tree to make the roots a
north pole?

2. If a current goes around an iron pole in the same direction that
bicycle racers go around a track, what is the polarity of the base of
the pole?

3. If the polarity of the earth is caused by currents traversing its
surface parallel to the equator, is the direction east or west, to make
the pole near the geographical north pole a south-seeking pole?

4. A man stands under a trolley wire that runs north and south;
a compass held in his hand points toward the east; what is the
direction of the current in the trolley wire?

5. In many steamers, the return wire for all electric lights is the
metal hull of the vessel. If the vessel is sailing south, and a compass
held under an electric wire points nearly east, what is the direction of
the current?

MAGNETIC ACTION OF ELECTRIC CURRENT. 431

6. Mark arrows on a porous cup, showing a current which makes
the bottom a south pole.

7. If a current passes around the rim of a watch in the direction
in which the hands move, is the face or the back a north pole ?

8. In a street running north there is a puddle of water over the
electric car track. The tracks form the return wire for the current.
If a magnetized needle floated in the water points toward the west,
what is the direction of the current in the trolley wire? In the
tracks ?

9. What is the polarity of the point of a gimlet, if a current goes
around it in the direction in which it is turned to bore a hole ?

Fjg. 398.

496. Direction of a Current in the Liquid of a Cell. — Figure
398 is a form of Daniell cell in which the tube, T, connects
the glass funnel containing the copper and copper sulphate with
another containing zinc and sulphuric acid
solution. Connect the glass funnels to the
tube, T, by rubber tubing. The zinc and
copper are joined by a wire, as shown in
the figure. Hold a compass under the
tube near T, Is there a current flowing
in the liquid in the tube? Hold the
compass above the tube. A compass hav-
ing a fibre suspension, and, if possible, a
mirror (mirror galvanometer, section 592, page 514) may be
used. A bichromate cell (Fig. 399), in which ^ is a long,
narrow, paraffined box filled with bichromate solution, gives
a larger current than the Daniell cell. Place the compass box
(Fig. 377, II., page 406) over T, so that the needle points along
the box, T, The wires connecting the zinc and the carbon are
several feet long. What effect does making
and breaking the circuit have on the com-
pass needle? Try a small compass above
T] then below T,
What is the direction of the current in
Fig. 399. the liquid of a cell ? Hold the compass

432 PRINCIPLES OF PHYSICS.

under the wire connecting the zinc and the carbon, C, Fig. 399.
What is the direction of the current in the wire ?

497. Heftt produced by a Current of Electricity. — Connect the
wire from a large Dauiell or bichromate cell with a fine plati-
num wire (No. 36). Twist the platinum wire around the copper
terminals, leaving half an inch of platinum in circuit. Try a
longer length, six inches or more. Heat is always produced by
the passage of a current through a conductor, whether solid like
wire or carbon, or a liquid, such as any conducting solution, of
which the various solutions mentioned for battery use are a
few examples.

Fine iron wire will do for the experiment, but a platinum
wire is better, for several reasons ; one reason is that platinum
stands a high temperature before melting, though not so high a
temperature as carbon. The loop, or horseshoe, of an incandes-
cent lamp is invariably of carbon, and is practically infusible.

498. Electromagnets. — Any coil of wire carrying a current
acts like a magnet, and in fact is one. Soft inm inside the coil
offers a path for more lines of force than a permanent magnet
of steel, and becomes a powerful magnet. If a piece of steel is
placed inside the coil .and the current turned on, the steel does
not become as strongly magnetic as iron would. On 0}^)ening
the circuit, the current would no longer flow; but instead of
losing nearly all its magnetism, as soft iron would, the steel,
especially if it has been hardened, retains a considerable amount.
An electromagnet should therefore have a core of soft iron.

CHAPTER XXIX.
MEASlTfiEMEHT OF ELEOTBIO OUBSEHT.

^"^M^Mf^'

A a

F\g. 400.

499. Constrnction of an Electrolytic CelL — Remove the bot-
tom of a shallow, wide-mouthed bottle. Make two holes

through the cork, an inch apart, and draw
lead strips, A and B, Fig. 400, through them.
These should be ^ inch, or less, thick, \ inch
wide at the ends A and B^ and increasing in
width to I inch at the other ends. The holes
in the cork are made just large enough for
the ends A and B to pass through. Heat the
bottle gradually in the position shown in the
figure, and drop liquid paraffine on the cork.
Allow it to cool, and suspend it in a ring-stand.
Fill the bottle with water above the lead
strips. Attach to A and B wires leading from three or more
Daniell or bichromate cells in series (Fig. 401). The carbon
or copper of one cell is connected with the zinc of the next. The
wire, Ej from one carbon ter- ^

minal and the wire, Z>, from one " ""

zinc (Fig. 401), are to be con-
nected with A and B, Fig. 400.

500. Decomposition of Water.
— Scrape the ends of D and E,
twist one around A^ the other around B. Watch the lead strips
in the liquid. Add a few drops of sulphuric acid to the liquid.
Water, especially if pure, is a poor conductor. Most substances
dissolved in it increase its conductivity. Notice the appear-

433

Fig. 401,

434 PRINCIPLES OF PHYSICS.

ance of the lead strips. Fill test-tubes with water containing
a few drops of acid and invert them over the strips, as shown
in Fig. 400. Collect half a test-tube of the gas that forms
in larger amount. Raise the tube, sliding the thumb over the
mouth of it. Invert the tube, and apply a lighted match. The
gas is the same that comes from unamalgamated zinc or from
the copper in a simple cell. Into the gas collected in the other
tube thrust the glowing end of a splinter of wood. The wood
burns brighter, and often relights. The g£ls is oxygen.

Make a diagram of the apparatus in Fig. 400 and of that in
Fig. 401. By arrows show the direction of the current in every
part. From which lead strip is the hydrogen set free ? Does
the current enter or leave by it ? From which is the oxygen
set free ? In the simple cell, from which pole is the hydrogen
set free, where the current enters or where it leaves the cell ?

The sulphuric acid is not decomposed ; the gases come from
the water, which is decomposed, or split up, by the action of
the current. Carbon or platinum poles are often used in place
of lead. Many metals, such as zinc, copper, iron, and various
others, are not suitable, because the pole that gives off oxygen
is consumed in the process.

501. Acids and Alkalies. — Put a solution of sodium sulphate

(Na2S04) in a U-tube. A and By Fig. 402, are platinum or

carbon terminals connected with a cell by wires.

*%A BC In a test-tube drop litmus solution or the water

m JtI obtained by boiling red cabbage. Study the

V -y effect of an acid (sulphuric acid, for instance)

Fig,. 402. o^ ^ little of this solution in the test-tube. In

another tube try the effect of an alkali, such
as ammonia or caustic soda. What is the effect of sodium
sulphate on the coloring solution ? Make a diagram of Fig.
402, with the battery and connecting wires, and indicate the
direction of the current in every part. Add litmus to the
U-tube. Where is an acid formed ? An alkali ?

MEASUREMENT OF ELECTRIC CURRENT. 435

502. Electrolysis. — Any salt — common table salt, for in-
stance— gives similar results to those described above. If
a solution of acetate of lead is decomposed, metallic lead is
deposited on one pole; which one? Sulphate of copper is
decomposed in a similar manner. The decomposition of water
or ahy salt or acid and other substance is called electrolysis.
Aluminum and sodium are decomposed from solid compounds
containing those elements.

503. Electroplating. — Dip a piece of zinc in sulphate of cop-
per. Do the same with a piece of iron — a knife blade or a
nail. The reason for the deposition of copper on zinc in this
way was given in section 476, page 415. This form of plating
is not as h^rd and adherent as the method in section 466,
where one strip of copper was electroplated. The experiment
was there described for the purpose of showing a reason for
the statement that the current in a galvanic cell always flows
in a certain direction.

Ay Fig. 403, is a sheet of copper ; JK' is an uncoated electric
light carbon. Before putting it into the solution, which is
sulphate of copper, the carbon is black. Connect A with the
copper or carbon terminal of a cell, and K
with the zinc terminal. What forms on the C*^ 5^

carbon ? From where does the copper de-
posited come ? If any doubt exists, continue
the experiment until there is no doubt whether
the plate A is dissolved or not.

The pole, A, from which the copper is taken,
is called the anodes and K, on which it is de-
posited, is called the kathode.

In electroplating with silver, the anode. A, is a plate of pure
silver, and the solution is one of silver chloride dissolved in
potassium cyanide. In a similar way, for gold plating, A is
of pure gold and the solution is one of some compound of gold.
A nickel anode and a nickel solution deposit nickel. The
object to be plated at /^must be clean.

^^,c.,

436 PRINCIPLES OF PHT8IC8.

504. Electrotypes are made by depositing a coating of copper
on a mould of plaster or wax covered with graphite, which is
a form of carbon and a conductor of electricity. The mould is
made by pouring plaster of Paris or wax on the woodcut, page
of type, or other object. The deposit of copper removed from
the mould is thin, and is backed up with type metal.

505. Refinement of Metals by Electric Current — If the solution
in an electroplating bath is pure nickel, pure copper, or, in
fact, a solution of a pure metal of any kind that can be electri-
cally deposited, the anode may in many cases be impure.

The copper mined in Michigan, near Lake Superior, in the
form of metallic copper is very pure. In most other mines, the
copper, after reduction from the ores, contains silver, arsenic,
and sometimes gold. By depositing the copper as illustrated
in Fig. 403, where A is the impure block of metal, using pure
sulphate of copper, only pure copper is deposited on K, while
the impurities fall as mud to the bottom of the tank and are
recovered and sold. Not only is the deposited metal purer,
but the value of the gold and silver recovered from the mud
makes the process a paying one.

506. Chemical Method of measuring Current. — If the current
from a cell, or a number of cells in series, is first passed
through an apparatus for decomposing water, next through a
plating bath where copper is deposited, and then through
another bath, where another metal — silver, for instance — is
deposited, although there is the same current passing through
all, the weight of metal deposited will not be the same in all,
nor equal to the weight of the gas set free.

An accurate, but somewhat inconvenient, method of measur-
ing current is to weigh the copper plates, and, after allowing
the current to pass a known length of time, to weigh the plates
again. It is not necessary to weigh both plates, since the loss
of one equals the gain of the other; but, by weighing both,
errors may be detected.

MEASUREMENT OF ELECTRIC CURRENT. 437

In laboratories, current is sometimes measured by the amount
of silver or copper deposited. The Edison meter has plates of
zinc in a solution of sulphate of zinc.

507. An Ampire is the amount of electric current that, flow-
ing for one second,

deposits 0.001118 g. of silver,

" 0.000328 g. of copper,

« 0.000337 g. of zinc,

sets free 0.00001 g., or 0.11 cc, of hydrogen gas,

or " " 0.000083 g., or 0.059 cc, of oxygen gas.

508. Amount of Currents for Commercial Uses. — Incandescent
lamps of sixteen candle power take from one-half to one am-
pere of current. Arc lamps require from four to ten amperes ;
the large arcs used in search-lights or lighthouses require much
more. The current in motors varies according to the type and
the power. The motors on a street car sometimes take as high
as twenty-five or more amperes, when the car is full of passen-
gers. Bells, telegraph instruments, and signals use a small frac-
tion of an ampere of current. In the electrolysis of emery, for
the purpose of getting aluminum, one thousand amperes are used.
In electric welding of large masses, the current rises to thou-
sands of amperes. The current given in the treatment of disease
varies from two thousandths to ten thousandths of an ampere.

509. Calculation of a Current in Amperes. — A certain current
for a given time deposits a little more zinc than copper. In
the study of the Daniell cell (Exercise 66, page 418), unless
sensitive balances were used, the zinc loss and the copper gain
would appear to be the same. Any large excess in the loss of
zinc over the gain in weight of the copper was probably due to
local action on the zinc, which may have been imperfectly
amalgamated. Suppose the copper in the Daniell cell at the
beginning of the experiment weighed x -f 3.1 g., x being any
counter-balance for most of the weight of the copper plate,

438 PRINCIPLES OF PHYSICS.

and 3.1 g. the reading in the movable arm. Call the weight of
the copper, after 100 minutes' run, x -\- 4.3 g. The gain in
weight is 4.3 — 3.1 g. = 1.2 g. In one second, one ampere
deposits .000328 g. of copper ; in 100 x 60, or 6000, seconds,
it would deposit 6000 times as much, or nearly 1.97 g. But
1.2 g. were actually deposited. The current, then, was

— :^ .6 ampere.

Just as the same amount of water is used, whether one gal-
lon per hour is supplied for one hundred hours, or one hundred
gallons for one hour, so the same amount of metal is deposited
in an electroplating bath by one ampere running for one
hundred hours, as by one hundred amperes running for one
hour, there being one hundred ami^re-hours of current used.

Problems.

1. In a Daniell cell, the copper plate gains .7 g. in 30 minutes.
What is the current in amperes?

2. How many amperes are needed to deposit 100 g. of copper an
hour?

3. A deposit of .3 g. of silver is made in 2 hours. What is the
current ?

4. How many grams of zinc are deposited in a jar containing sul-
phate of zinc solution and plates of zinc, if a current of 5 amperes
flows for 10 hours?

5. In an Edison meter, the loss of one zinc plate, or the gain of the
other, is 2.31 g. How many amperes must flow for one hour, or for
how many hours must one ampere flow, to produce that change ?

6. An Edison meter is so arranged that y^^ of the current supplied
to electric lights or motor flows through the meter. Using the fig-
ures given in Problem 5, how many amperes for one hour flowed
through the main circuit?

7. In an apparatus for decomposing water, 40 cc. of hydrogen are
given off in a minute. What is the current?

8. How much current is required to produce 1000 cc. of hydrogen
gas in two minutes?

MEASUREMENT OF ELECTRIC CURRENT. 439

510. Study of a Galvanoscope. — A galvanoscope is a coil of
wire of any shape, usually placed north and south, and a sus-
pended magnetized needle or compass inside or near one side
of the coil. As shown in Exercise 68, any current in the coil
sets up lines of force running through the axis of the coil,
which axis of course is east and west. The needle tends to set
itself in these lines of force, either toward the east or the west,
according to the direction of the current in the coil. The
attraction of the earth acts on the needle, to make it point
north. The needle therefore takes up a compromise position,
as it were, neither north nor east perhaps, but part way be-
tween, the exact place depending on the relative strength of
the earth's magnetism and the coiPs magnetism. (See section
493, page 428.)

511. Magnetic Method of measuring Current. — To detect the
presence of very small currents, the coil is made small and of
many turns; but for the purpose of measuring currents in
ordinary use the coil is made of a diameter of 20 cm. or larger,
and the needle less than one-tenth the diameter of the coil.
The pointer on the needle may be of any length. This instru-
ment will detect strong currents, and is therefore a galvano-
scope, though not a sensitive one. The amount of current
flowing can be computed if the diameter of the coil, the num-
ber of turns of wire, and the angle of deflection of the needle
from the north and south line are known. The instrument,
when used to measure currents, is called a galvanometer.
Except for very small angles, doubling the current, while it
doubles the effect of the coil, does not double the deflection of
the needle.

512. Forces acting on the Needle. — AB, Fig. 404, is a door
hinged at A, Imagine that B — the handle where two strings,
N and W, are attached — is the north-seeking pole of a compass
needle. The south pole, which would extend to C, need not be

440 PRINCIPLES OF PHYSICS.

considered, since the attraction and repulsion on it would have
the same effect as the north and west pulls on the north pole,
B. N is the pull of the earth toward the north. W is the pull
of the coiPs lines of force tending to make the
needle point west. The north force, due to the
earth, is practically always the same in any
given place. The pull of the coil, W, varies with
the radius, the number of turns, and the cur-
rent in the coil. Try this experiment with a
light door that turns easily on its hinges. Make
and keep the north pull two pounds. Make
Fig. 404. *^® west pull one pound; notice the angles

through which the door turns. Double the
west pull, keeping the north pull two pounds, as before. Make
the west pull three pounds, then four pounds, five pounds, etc.
Is the angle of deflection of the door ten times as great for ten
pounds as it is for one pound ? Is it possible, within the
limits of a 32-pound balance, to make the door point exactly
west?

While the angle does not increase in proportion as the west
force is increased, the tangent of the angle does increase ex-
actly as the west force increases. If the angle of deflection
of a needle is increased from 30° to 60°, the current has not
merely doubled ; for the tangent of 30° = .577 and the tan-

1 7^
gent of 60° = 1.73, and ^ = 3.1 ; therefore the current is 3.1
.557

times as great. (See Appendix, page 540, for table.) In many

books the name ^ natural tangent ' is used.

If, as has just been said, the coil is large compared with the

length of the needle, the current passing through the coil can

be computed by the aid of a table of tangents. The instrument

is called a tangent galvanometer.

513. Formula for Tangent Galvanometer. — If the needle is at
the centre of the coil the formula is : —

Current

in
amperes

MEASUREMENT OF ELECTRIC CURRENT. 441

^ r 10 times earth's horizontal mag-

netic strength times radius

2 times 3.1416 times number of

turns

times tangent
of deflection.

^ /lO Hr\

tan a, is a shorter form.

The radius of a coil = 20 cm. = r.

Number of turns =5 = n.

ir, the number of times longer the circum-
ference is than the diameter of a circle =3^^, nearly.

The strength of the earth's magnetic field

in a horizontal plane =H=,17 (for Boston).

10 X. 17x20

2x3fx5

- = 1.08.

This is the value for the parenthesis above, and is computed
once for all. For Boston, the formula for this particular gal-
vanometer becomes

C= 1.08 tan a.

If a = 45^

tan a = 1,

then C = 1.08 x 1 = 1.08 amperes.

If a = 10^ tan 10* = .176,

C= 1.08 X .176 = .19 amperes.

In the Appendix are given the values for the horizontal in-
tensity of the earth's magnetism, for which the letter H is
used in the formula. Use the value for the nearest city men-
tioned in the table, and compute the value of the parenthesis for
a tangent galvanometer. If the connection admits of using a
different number of turns, make the computations for each
case. While the presence of iron in a building lessens or

442 PRINCIPLES OF PHYSICS.

increases H considerably, the error in using the number in the
tables will be less than that of many expensive direct reading
ammeters (instruments for measuring the current in amperes)
in commercial use.

Problems.

1. The ring of a tangent galvanometer is of 12 cm. radius; the
number of turns, 3 ; and the value of H for the place where it is used
is .16. Find the value of the parenthesis, substituting these values
in the formula (section 513). Ans. Nearly 1.02.

2. Find the current in this instrument, if the deflection is 30°;
45°; 60°. Ans. .59; 1.02; 1.76.

3. How many amperes are flowing, when the deflection is 10°?
How many when the deflection is 5°?

4.» In measuring currents accurately, the deflection should be as
near as possible to 45°, or at least between 30° and 60°. In selecting
a galvanometer to measure large currents, which is the better, a. large
or small diameter? a large or small number of turns?

5. What kind of a tangent galvanometer should be selected to
measure small currents?

CHAPTER XXX.
OHM'S LAW.-EESISTAWOE.

614. Electromotive Force. — The amount of water or the
current that passes through a pipe depends on the pressure of
the water. In some such way, the current or amount of elec-
tricity that passes through a wire or any other conductor
depends on the pressure of the electric current, or, as it is
called, the electromotive force. This force is measured in volts.
A high electromotive force sends more current through a wird
than a small electromotive force can send. A Daniel 1 cell has
an electromotive force of a little more than one volt ; a bichro-
mate cell, about two volts. This means that the Daniell cell
tries with a force of one volt to send a current in a wire con-
necting the copper and zinc.

515. Effect of Size of Cell on Electromotive Force. — A, Fig.
405, is a large Daniell cell. (By "large" is usually meant a
cell of large plates, having considerable surface.) 5 is a small
cell. The jar may be of the same size
as A, or smaller; but the plates, or
poles, of zinc and copper are small
The copper pole may be the end of the
copper connecting-wire. O is the gal-
vanoscope. Connect as shown in the •
figure.

Make a diagram in the note-book,
and add arrows showing the way the current tries to go from
each cell. Does the galvanoscope indicate any current ?

What does this show about the tendencies of the currents

443

444 PRINCIPLES OF PHYSICS.

from the two cells? The electromotive force of a cell does
not depend at all on the size of the plates.

Replace 5 by a bichromate cell, either large or small. The
carbon is then in the position marked Cm, in Fig. 405, and is
connected with the copper of the Daniell cell at A. Is there
any current ? Which way does it flow ? Are the electromo-
tive forces of the two cells opposing? Which cell has the
greater electromotive force ?

Make a diagram like Fig. 405, and show by small arrows the
direction the current in A tends to take, and by larger arrows
the direction in the whole circuit.

516. Internal Resistance. — If the bichromate cell just used
is quite small, connect it alone with the galvanoscope. Note
the deflection. Disconnect the cell, and connect the large
Daniell cell with the galvanoscope. Which cell gives the
larger current? As the electromotive force of a bichromate
cell is much more than that of a Daniell, and as the few turn^
of copper wire in the galvanoscope are a slight obstacle to
the flow of the current, the cause of less current through the
bichromate cell must lie in the cell itself. The small poles
provide a smaller path through the liquid than is provided in
the larger cell, and therefore offer more internal resistance.
All conductors, whether metals like copper, etc., or liquids like
mercury, sulphuric acid, etc., offer resistance. A thread of mer-
cury about 106 cm. long and of 1 sq. mm. cross-section has a
resistance of 1 ohm. An electromotive force of 1 volt sends a
current of 1 ampere through 1 ohm resistance. Since resist-
ance is an obstacle to the current, increasing the resistance
decreases the current.

517. Ohm's Law. — The current in amperes equals the volts
divided by the ohms. This is Ohm's Law, and is abbreviated

c ^■

ohm's law. — resistance. 445

C stands for current in amperes ; E for electromotive force in
volts ; R for resistance in ohms.

This formula, C'= — , may be read as

Electromotive force

Current =

or Amperes =

Resistance

Volts
Ohms

There is no difference in meaning, and the expressions are
interchangeable.

If batteries are used, R includes the resistance of the liquids
of the cell (the internal resistance) and the resistance of all
connecting wires, etc., outside the cell (the external resistance).

Such expressions as *how much current' and 'what cur-
rent,' mean 'how many amperes'; the abbreviation for am-
peres is C, as shown above. ' Electromotive force,' ' number
of volts,' and ' voltage,' all mean the same thing ; E, or
E.M.F., is the abbreviation used. The number of ohms
resistance is expressed by R.

Problems.

1. How much current will an electromotive force of 2 volts send
through a resistance of 5 ohms? Ans. A ampere.

In this problem, 2 stands for E, 5 for jR, and we wish to find C.
Substitute in the formula : —

-f

C = -, or .4. The current is .4 ampere,
o

2. What must be the electromotive foree to send a current of
.4 ampere through 5 ohms resistance? Ans, 2 volts.

-f

2 = E.

446 PRINCIPLES OF PHYSICS.

3. What is the resistance in a circuit through which a current of
.4 ampere is sent by 2 volts electromotive force ?

4-1

p 10 X 2

R = 5,

4. Find the electromotive force required to pass 10 amperes through
5 ohms.

In this and the following problems the results are tested by work-
ing backward, as is done in Problems 2 and 3.

5. What current will 20 volts send through 15 ohms ?

6. What is the resistance, if the current is 12 amperes and the
voltage is 3 ?

7. One type of Edison incandescent lamp hasa resistance (hot) of
220 ohms; the electromotive force is 110 volts; how much current
flows through the lamp ?

8. An electromagnet has a resistance of 1.5 ohms; how many
volts are required to send a current of 6 amperes through it ?

9. Current = 100 ; resistance = 3 ; what is the E.M.F. ?

10. Resistance = 100; E.M.F. = 40; current = what?

11. C = 5; 72 = 20; E = what?

12. C = 200; E = 150; R = what?

518. Resistance — Substitution Method. — ^While the laws gov-
erning the resistance of wire of different sizes, lengths, and
connected in various combinations are almost obvious, they
may be proved. Using the analogy of the flow of water in
pipes, it seems reasonable that the resistance of ten feet of a
wire is ten times as much as of one foot of it ; and just as the
resistance of a pipe increases as the diameter is decreased, so
a small wire has greater resistance than a large one. ^

1 The method of working and the results obtained in this experiment
should be studied, although the actual work may be omitted, if necessary, to
make room for the more profitable study of the Wheatstone bridge, electrical
instruments, and the applications of electricity.

ohm's law. — RESISTANCE.

447

If a constant battery, such as a Daniell cell or an oxide of
copper cell, is connected with a long fine wire and a galvano-
scope, a smaller deflection is noticed than when only short
wires necessary for connections are used. The resistance of
the long fine wire reduces the current, and consequently the
deflection of the needle. If this wire is removed and another
wire of any metal or a rod of carbon is put in its place, and the
length of it in circuit, that is, the length through which the
current flows, is changed until the needle has the same deflec-
tion, then the original wire and the one substituted for it have
the same resistance.

Exercise 69.

RESISTANCE OF A GONDUGTOB.

Apparatus : Daniell cell ; current reverser ; galvanometer ; two triple binding-
posts ; German silver wire No. 30 and No. 28. If the porous cups of the cell
are soaked in water before the exercise, the cell becomes constant as soon
as set up.

Part L — Connect the copper leading-wires from the battery, B,
Fig. 406, to two opposite corners of the current reverser, C These
and the wires from the galvanometer,
G, to C, and to the binding-post, E,
should be as large as No. 18. Cut
from the coil of No. 28 wire a piece a
few centimeters longer than 200 cm.
Make a slight bend a centimeter from
the end; from this bend measure 200
cm., and make another bend. Connect
this wire, R, with the current reverser at
D and with the binding-post at E^ leaving
just 200 cm. in circuit between those
two points. In C, place the wires connecting the mercury cups, and
note the deflection of the galvanometer, the coils of which have been
set north and south. Read the deflection of the needle. Record all
these observations and the length and size of the wire, R (in this case.
No. 28). Take care that the wire, R, which' is uncovered, does not
cross itself at any point. Sufficient turns of the galvanometer (ten to
fifteen, for instance) should be in circuit to give a deflection of 45° to 60"^.

R
D

Fig. 406.

\ — I

448 PRINCIPLES OF PHYSICS.

Remove the No. 28 wire, and replace it by 200 cm. of No. 30 wire
of the same kind. (The numbers given to the sizes of wire are purely
arbitrary ; the larger numbers are wires of less diameter. See Appen-
dix, page 539.) Which allows the less amount of current to flow
through the circuit — that is, which has the greater resistance ?
Loosen the end of R in the binding-post, E. Make the part of R
between D and E 120 cm. ; record the deflections of the needle, as
before. If the deflection is not nearly the same as when 200 cm. of
No. 28 wire were in circuit, try a little greater or less length than 120
cm. of No. 30 wire at R, by loosening the binding-post and sliding
the wire along a few centimeters.

Part 11. — Connect with D and E, as shown in Fig. 407,
two 200-cm. lengths, /2, of the No. 30 wire. Record the
deflection. Remove tiie German silver wires from D and
E, and replace by a single No. 30 wire at R, putting 100 cm.
^ of it between D and E. Read the needle deflection of the
galvanometer as before. If the average deflection is not
«g. 407. ^j^g same, change the length of R.

519. Wires in Parallel or Multiple. — Two wires connected as
in Fig. 407 are said to be in parallel or multiple. The current
has an easier path between D and E (Fig. 407) through the
the two wires than through one. In fact, it is just twice as
easy. So two similar wires in parallel have one-half the resist-
ance of one. Three similar wires in parallel have one-third
the resistance of one.

520. Laws of Resistance. — The shorter a wire is, the less
resistance it has. Ten centimeters of wire have ten times as
much resistance as 1 cm., and five times as much as 2 cm. of
the same wire. This principle is often stated as, tlie resist-
ance of a conductor varies as the length.

In Part I. of Exercise 69, about 120 cm. of No. 30 wire has
the same resistance as 200 cm. of No. 28.

The diameter of No. 30 = .255 mm.
The diameter of No. 28 = .321 mm.

OHM'S LA W. — RESIST A NCE. 449

Measure the wires with a micrometer caliper. Wire is not
always drawn exactly to the diameters intended. In working
up the result of Part I., follow the method given here, substi-
tuting the actual numbers obtained by experiment. The diam-
eter of No. 28 is only a little more than that of No. 30, while
the resistance of No. 30 is much greater than of No. 28.

The square of .255 is .065.

The square of .321 is .103.

The square of the diameter of No. 30 is .065 ; the length used
was 120 cm. The square of the diameter of No. 28 is .103;
the length used was 200 cm. Is 200 about as many times
larger than 120 as .103 is times larger than .065?

The resistance of a conductor decreases as tfie square of the
diameter increases. If a wire has a resistance of one ohm, a
wire twice the diameter of the same length has less resist-
ance,— just one-fourth as much.

Problems.

1. How many times greater is the resistance of a wire 1 mm. in
diameter than one of the same length and similar material 2 mm. in
diameter? Ans, Four times greater.

2. The diameter of No. 18 wire is .04 inch, and of No. 30 .01 inch.
Of equal lengths of the same kind of wire, which has the greater
resistance ? How many times greater V A ns. Sixteen times greater.

3. Remembering that resistance increases with the length of a
conductor, find the resistance of 1000 feet of No. 30 copper wire, if 1
foot has a resistance of .1 ohm.

4. How many ohms resistance in 50 cm. of No. 28 copper wire, if
1 meter has a resistance of .22 ohms?

5. From the data in the preceding question compute the resistance
of 1 meter of No. 30 copper wire. The cross-section of No. 30 wire
compares with that of No. 28 wire as 65 is to 103.

The No. 30 wire has greater resistance. ^ x .22 = the resistance
of 1 meter of No. 30 wire.

450 PRINCIPLES OF PHYSICS.

6. If 1 meter of No. 30 German silver wire has 6.5 ohms resist-
ance, how much resistance would 40 cm. of the same wire have ?

German silver wire varies in resistance according to the proportion
of nickel in the alloy. The resistance given here holds for the ordi-
nary kind used in this country.

7. What is the resistance of 10 miles of No. 6 copper wire if 1000
feet have .41 ohm resistance?

8. There are six wires of No. 30 German silver, each 2 meters
long, and the resistance of each piece is 13 ohms. What is the fesist-
ance if they are joined in series? Ans. 6 x 13 = 78 ohms.

9. If the six wires of Problem 8 were made into one wire of the
same length, how many times as great would the cross-section be?
What would be the resistance?

10. What is the resistance if the six wires of Problem 8 are con-
nected in parallel ? Ans, J of 13 = 2.1 ohms.

11. Make a diagram showing the wires connected for series and
also for parallel, as indicated in Problems 8 and 10.

12. For street lighting arc lamps are connected in series. When
burning, each lamp offers a resistance of 6 ohms, neglecting the resists
ance of the line wire connecting the lamps, what is the resistance
of a 100-lamp circuit? a 50- lamp circuit?

13. In electric cars the incandescent lamps are often connected 5
in series. If each lamp has a resistance of 180 ohms, what is the;
resistance of the series of 5 lamps?

14. A dynamo supplies 1000 incandescent lamps in parallel, each
having a resistance of 50 ohms (hot), what is the resistance of the
circuit?

15. What is the resistance of a 10-ohm coil, a 50-ohm line wire, and
a 100-ohm lamp connected in series?

When different resistances are joined in series the resistance of the
whole is the sum of the separate resistances.

521. Resistances in Series. — Lay down three pins of the same
length, A, B, and C, in series. If connected with a battery
they will look as in Fig. 408. Here the current passes first

ohm's law. —resistance.

451

through A, then through B, and
then through C. The current has ^
the resistance of the three to over-
come. The resistance of A, B, and
C in series is greater than that
of one alone. How many times
greater is it?

z:p

rig. 408.

522. Resistances in Parallel. — Lay the pins down as if con-
nected in parallel (Fig. 409). The current from
the copper divides over three paths, A, B, and
C, a little current going by each. Each wire,
then, is less crowded, as it were, and offers
less resistance. How does the resistance of the
three wires connected as shown compare with
that of one alone? If C is cut, how does the
resistance of A and B in parallel compare with
that of A alone?

Fig. 409.

-► b

Fig. 410

523. Formula for computing Two Resistances in Parallel. —
When the resistances joined in parallel are not the same, the
rule for computing the resistance of the combination is compli-
cated; but where there are only ^ „

two resistances in parallel, as a — v | [^

-and 6, between the points E and
F, Fig. 410, the resistance is found
by multiplying the two resistances, and dividing by their
sum.

If a = 2 ohms, and 6 = 5 ohms, a and b multiplied = 10 ;
this divided by the sum of the resistances (2 4-5 = 7) is
10/7 = 1.3+ ohms between E and F. The rule is expressed
by the formula: —

Resistance of two wires in parallel, one of a ohms, the other
of b ohms, = — — .

452 PRINCIPLES OF PHYSICS.

ProblemB.

1. What is the combined resistance of a 5K)hm coil and a 10-ohm
coil in parallel ? Ans, 3.3+.

2. If 20 bells are connected in parallel, what is the resistance, if
each bell has a resistance of 2 ohms ?

3. If 2 bells, one of 5 ohms resistance and another of 2 ohms, are
joined in parallel, what is the resistance? Through which would the
greater current flow ?

4. If a wire of 50 ohms resistance is connected in parallel with
another of 25 ohms, what is the resistance of the circuit?

5. If 1 m. of German silver wire having a resistance of 6.5 ohms
is put in circuit with a battery and a galvanoscope, and a deflec-
tion of 20° is produced, what is the resistance of a coil of wire that
could replace the German silver wire, the deflection of the needle
being unchanged?

6. A little incandescent lamp is in circuit with a galvanoscope
and a battery ; the deflection is 6°, and the lamp does not light up ;
with 12 cm. of No. 30 German silver wire in place of the lamp, the
deflection is 6°; what is the resistance of the lamp "cold"? One
meter of No. 80 German silver wire has a resistance of 6.3 ohms.

7. Using greater battery power, the lamp of Problem 6 burns
bright, and the needle stands at 11°; when the lamp is replaced by
No. 30 German silver wire, the length is reduced to 6 cm. before the
needle stands at 11°; what is the resistance of the lamp "hot"?

8. The "hot" resistance of a 110-volt Edison lamp is 160 ohms;
what is the resistance of 10,000 connected in parallel? What is the
resistance of 500 of them in series?

9. If the resistance of the copper core of a small submarine cable is
1.7 ohms per 1000 feet, what is the resistance of a cable 500 miles long?

10. Compute the total resistance of an ocean cable 3000 miles long,
if the copper core has a resistance of .5 ohm per 1000 feet.

11. What current would be sent through the cable in the preceding
question if the electromotive force were 5 volts ?

12. Aluminum is much lighter than copper (look in the Table of
Densities on page 538, and find how many times lighter). For wires
of the same diameter, copper is the better conductor in the propor-
tion of 100 to 54. For which kind of wire can you pay the more per
pound, to obtain equally good conductors?

OHM'S LAW.— RESISTANCE. 453

524. Measurement of Current by an Ammeter. — The methods
of measurement by a tangent galvanometer, or the deposition
of a metal as before described, are accurate, but inconvenient
in rapid work. More convenient forms of galvanometers, called
ammeters, for measuring current in amperes, are so constructed
that the pull of the coils carrying the current is not resisted
by the earth's magnetism, for that force is comparatively
weak, and varies in different places, especially near masses of
iron.

525. One Form of Ammeter. — There are many forms of
ammeters. In one, the measure of the current is the amount a
spring is bent ; in another,, the distance a
pendulum is moved out of the perpendicu- fijoc^^^^^ V^^^^^
lar. The latter form is shown in Fig. 411.
A magnet, NS, is suspended on pivots at
its centre. A weight, W, makes the
centre of gravity below the pivots, and
therefore the pointer, P, is vertical and
points to zero on the scale, SS, unless a
current flows in the coils.

The coils, which are shown connected
to binding-posts, BB, are in a horizontal *^

plane. One turn is shown in the figure; more turns are often
used. The action of the coil may be illustrated by laying any
coil of wire flat on a table, with a compass placed in its centre
so that the dial is vertical, and passing a current through the
coil. Notice the movement of the needle.

The scale, SS, is marked off, or calibrated, by sending a cur-
rent through the instrument and a tangent galvanometer, or
another ammeter known to be correctly marked. Adjust the
resistance in the circuit till there is a current of one ampere,
for instance, as shown by the tangent galvanometer or standard
ammeter. Mark the position of P on the scale, and number
it ** 1." Change the resistance so that two amperes, three, four,

454

PRINCIPLES OF PHY8IC8.

etc., in turn pass through the instruments, and mark the scale
as before.

526. Test an Ammeter by comparison with a tangent galva-
nometer or a standard ammeter. As the ammeter to be tested
probably has a scale, record results as follows : —

^Scaudivisiona
Fig. 412.

527. Plotting the Current measured by an Ammeter. — An in-
teresting exercise is to plot the amperes and corresjKjnding

scale of divisions, as in Fig. 412. Sup-
pose the scale reading is 3.5 divisions
when the current is 2 amperes. A is the
point for these readings. Plot others,
and draw a curve through the points.
In using the instrument to measure cur-
rents, read the number of scale divisions.
Find this number on line X, and erect a

perpendicular to meet the curve. Then move horizontally to

the line F; the number of divisions on T is the number of

amperes.

The coil of an ammeter is usually of a few turns of large

wire. An ammeter therefore has a small resistance, — so small

that it can be neglected.

528. Voltmeters. — Suppose a very fine jet is attached to a
water pipe ; the height of the jet, in a rough way, is a meas-
ure of the pressure in the pipe, and the small current of water
flowing through the jet need not reduce the pressure on the
pipe. An instrument for measuring volts is called a voltmeter.
It differs from an ammeter in having many turns of wire in the

OHM'S LAW.

RESISTANCE.

455

coil ; the wire, being fine and of great length, has a high resist-
ance. Practically little current is consumed by a suitable volt-
meter, just as little water is used in the jet mentioned above.

A tangent galvanometer of high resistance and of many
turns of wire may be used to measure volts. The form shown
in Fig. 377, II., page 406, when used as a voltmeter, has a coil
of many turns around the needle.

One of the ways to mark the scale, or calibrate the voltmeter,
is to connect the terminals of the fine wire coil with a single
Daniell cell. This should be a large cell, so that its internal
resistance will be small compared with that of the coil of the
voltmeter. Make the position of the pointer 1.1. Then connect
with two cells in series. The pointer then stands at 2.2 volts ;
three cells in series gives 3.3 volts, etc. Test the electromotive
force of several kinds of cells on open circuit ; then again when
the cells are connected with a lamp, an electric motor, or a
bell. In measuring the voltage of a cell always join the termi-
nals of the voltmeter to the terminals of the cell.

629. Fall of Pressure, or Drop. — E, Fig. 413, is a reservoir of
water. T, T, T, T, are glass tubes fitted in the side openings
of a horizontal tube. Close
W and open K, Is the press-
ure at any point in the hori-
zontal pipe the full pressure
due to the height of water in
the reservoir? This illus-
trates the case of a voltmeter
connected directly with the
terminals, M and N^ of the
cell, L, Fig. 414. The en-
tire voltage, or electromotive

Ftg. 413.

force, of the cell is registered by the instrument. In the ques-
tion. How many volts does a cell give ? we mean the number
of volts on open circuit as in L.

456

PRINCIPLES OF PHYSICS.

Fig. 414.

Open Wy Fig. 413. Notice the height of the liquid in jg.
Join the poles of the battery by a short wire ( Q, Fig. 414), and

connect M and N with
the voltmeter. Although
the cell gives one volt,
for instance, that one
volt has to drive the cur-
rent through the liquid
of the cell. In the same
way, by opening W, the pressures at E, F, and O fall. The
pressure of the water is spent in driving the large mass of
liquid through the pipe to W,

By varying the length of a German silver wire in F, Fig. 414,
the voltmeter connected to M and N shows a varying voltage,
according to length of the wire between M and N. The electro-
motive force generated by the cell does not vary. It is spent
in part in overcoming the resistance of the liquid, and in part
in overcoming the resistance of the wire, and all the voltmeter
measures is that part of the voltage of the cell used in sending
the current through the wire.

Close W, Fig. 413, and attach a long tube to K, Notice the
increased pressure at E, Notice also the fall of pressure
between F, O, and H.

W ^

530. Fall of Pressure in a Wire. — The experiment suggested
by F, Fig. 414, is best performed as shown in Fig. 415. Con-
nect the cell, B, by copper ^

wires, not smaller than ^ \^y

No. 18, with the two strips
of copper, C and Z), which
are connected by a Ger-
man silver wire lying
along a meter stick. Con-

i. i. /-» 1 J- Fig. 415.

nect at C one wire leading

to the voltmeter, Fwi, and the other at A. The leading-wires

OHM 'S LA W. — BESI8TANCE. 457

from the battery and the copper strips, CD, have little resist-
ance, so that the voltmeter is practically connected at the poles
of the cell. To prove this, connect the voltmeter directly
with the cell, and compare the readings of the pointer. The
electromotive force of the battery at B may be one, two, or
more volts, according to the kind and number of cells connected
in series.

Suppose there is one cell at B and that its electromotive
force is one volt. Part of this electrical pressure is used or
destroyed in sending current through the liquid of the cell, and
the more current there is, the more the one volt generated
by the cell will be used up in the cell itself. Connect one end of
the Vm terminal at C, and the other end with the slider, which
can be moved along the meter stick on which the German
silver wire lies. Make contact with the slider at A, at different
positions along the wire. Does the voltage, or difference of
potential between C and A, depend on the length CA ? If, for
example, .5 of a volt is indicated between C and A, .5 of a volt
is required to drive the current then flowing through the
resistance of the length of wire, CA. Is more pressure required
to send the same current through CD ?

The loss of electrical pressure, the difference of potential,

the " drop " voltage, or the number of volts, between C and

A varies with the length of CA, Keep in mind the last

expression, "number of volts," although the others mean

exactly the same thing, and are much used. In the following

problems, remember that E is the abbreviation for all these

expressions. The methods of solution are exactly the same as

E
in section 517, and the same formula, C= — , holds.

Problems.

1. A battery of several cells supplies an incandescent lamp some
distance away ; the E.M.F. measured at the terminals of the battery
is 20 volts ; at the lamp terminals, 18 volts. What is the " drop " ?

Ans* 2 volts.

458 PRINCIPLES OF PHYSICS.

2. If the current in Problem 1 is 1 ampfere, what is the resistance

of the wires leading to the lamp? Ans, 1 = — ; /J = 2 ohms.

3. If the difference of potential between two points on a wire is 8
volts, and the resistance is 20 ohms, what is the current ?

4. If the drop in volts between a dynamo and the lamps supplied
by it with current is 3 volts, and the current is 50 amperes, what is
the resistance ?

5. If 1000 amperes pass through a conductor, and two points on it
are connected with a voltmeter which indicates 4 volts, what is the
resistance between those points?

6. How much "drop" is there on a line wire carrying a current of
10 amperes and having a resistance of 35 ohms?

CHAPTER XXXL

MEASUEEMEHT OF EESISTAKOE.

531. Detecting Small Currents. — A sensitive galTanoacope is
one that gives a uotict;abIe deflection for a small ciiiTeat.* The
coil in Fig. 416 sets up lines of forccj some of which pass through

Fig. 416,

its centre. The suspended needle tends to set itself in the
direction of these lines, turning east or west according to the

1 Tbe He»i^ for this a^nsitive ^alvanoseope la similar to that dcaedbed in
What i9 Siecfrif'ity/ by ^Ti^hri Trowbrirlge. See Appendix, page S^^ti.

459

460 PRINCIPLES OF PHYSICS.

direction of the current in the coil ; but the earth's field tends
to keep the needle pointing north and south. The effect of
the coil depends on : —

1. The number of turns of wire.

2. The distance of the wire from the needle.

3. The current in the coil.

As the fibre suspending the needle has little torsion, the very
least pull on the needle caused by the current in the coil would
make it point east and west, if the earth's magnetism did not pull
the needle toward the north and south direction. The earth's
pull on the needle is neutralized in one of two ways : by the
use of either a magnet to oppose and weaken the earth's mag-
netism, or an astatic combination for the needle.

532. Weakening the Effect of the Earth's Magnetism by a
Magnet. — Let the coil of Fig. 416 point north and south. If
a magnet is in the line with the coil, its north pole pointing
south, a position can be found, by moving the magnet toward
or away from the coil, where the magnet's field just neutral-
izes the action of the earth's field on the suspended needle.
Move the magnet away a little. The suspended needle is then
under a slight influence to point north, and a very small cur-
rent causes a large deflection. The slower the needle swings,
the more sensitive is the instrument.

633. Astatic Combination. — A second needle,
NSy Fig. 417, sometimes a little shorter than the
first, SN, is placed above the coil, on the same sup-
port that holds the lower needle. The two needles
are forced to turn together. If the two needles have
exactly the same strength, the combination points
indifferently in any direction. Usually one needle
is slightly stronger than the other. The combina-
tion points north, but acts like a needle in a very
Fig. 417. weak field. Notice the slow swing, and review

MEASUREMENT OF RESISTANCE.

461

the experiment Of section 457, p. 401. How can the strength
of magnetic fields be compared by a vibrating magnet ?

Pig. 418.

534. Points of Equal Pressure. — In a board cut two grooves,
CED and CFDy Fig. 418. Fill these grooves with mercury, and
connect at C and D with the poles of a battery, B, The cur-
rent at C divides, part passing by each
branch, just as a river divides in passing
around an island. Between E and F
there is a wire. Any current that flows
from E toF must pass through the coil
of the sensitive galvanoscope, G (section
531, page 459), and make its presence
known by the deflection of the needle.
Place E about halfway between C and
Z>. Move the terminal F toward Z>;
then toward C The reversal in the swing of the needle of the
galvanoscope shows that 2^ can be put in the mercury some-
where between C and D so that there will be no deflection of
the galvanometer and consequently no current flowing between
E and F, Find that point.

Push some of the mercury from x up to r. This is easily
done, if the mercury is contaminated with zinc, and somewhat
pasty. The current of electricity now finds an easy path
as far as E, and then a part of the
current, instead of continuing over x, a
narrow and therefore hard path, will
cross over to F, and thence by n to D,
unless F is moved up toward C, Fig. 419.
Tip the board, and make the thread
of mercury CED small, but uniform. Move E along, and find
the various positions of F where no current flows through the
cross wire.

Returning to the analogy of the river, were the river at x
narrowed as shown in Fig. 419, then a cross-cut canal would

462 PRINCIPLES OF PHYSICS.

have to be made with F near C, as shown in the figure, else a
current would pass from E to F, Whether a current of
electricity is flowing through the mercury channels or a current
of water is flowing round the island, there will be no current in
EF when the pressure or level at the points E and F are equal.
If the pressure at E is greater than at F, there will be a current
from E to F.

535. The Wheatstone Bridge. — Fit two double binding-post
stands on the ends of a meter stick support. Stretch different

wires — copper, German silver,
or iron — between the binding
posts, C and Z>, Fig. 420. Con-
nect a batteiy with C and Z>, the
wires e and / leading to the gal-
vanoscope, G, Touch the wires
e and /, leading from the galvano-
scope, anywhere along the wires joining C and D, until one
of the galvanoscope wires can be lifted and replaced without
affecting the needle of the galvanoscope. There is then no
current flowing between e and /. They are points of the
same potential, or equipotential points. In other words, there
is no voltage between e and /, the points where the galvano-
scope terminals touch, or a current would flow through the
wires connecting these points and affect the galvanoscope.
The voltage, or difference of potential, between C and /, equals
that between C and e, and the voltage between / and D equals
that between e and D.

Suppose the voltage beween Cand D is 1 volt and that //> = |
volt and Cf= | volt. In that case, fD would be one-third the
whole distance, and the resistance of n would be one-half the
resistance of m. The same must hold true of the other wire, x,

havine: one-half the resistance of r. Therefore - = -, as both
" m r

fractions equal ^. The same formula is true when / and e are
at any position between C and D. The numbers 1 and 2 are

MEASUREMENT OF RESISTANCE.

463

used merely to give a numerical illustration. If the lengths n
and m are measured, and the resistance of r, in ohms, is known,
then the resistance of x, the unknown, is computed.

Suppose no current flows through the galvanoscope when
m = 60 cm., n = 40 cm., r = 10 ohms. To find the resistance
of Xy substitute in

60 10

a = 6| ohms.

-Starting with a
B

536. Construction of a Slide Wire Bridge,
diagram of the form of Fig. 421, arrange
the apparatus as shown in Fig. 422.
Stretch a German silver wire between
C and Z>, Fig. 421, which are two bind-
ing-posts. The lower sides of Fig. 421
are now made straight. Connect a bat-
tery with C and D. A third binding-
post, E, connects the galvanoscope, G, 2l
known resistance, r, and the unknown resistance, x, which we

wish to measure, m, n, r, and x
are called the arms of the bridge.
A simple method of studying
out the connections is to draw
the form of the bridge, Fig. 421,
and then build up Fig. 422, step
by step, lettering each line and
point as it is added.
In the convenient form of the bridge shown in Fig. 423, the
triple connector E is merely
lengthened. The wires m and
n may be straight, as in Figs.
422 and 423, or curved, or
bent up double, as in Fig.
424.

In the short form of bridge

Fig. 422.

.fe

\y-

Fig. 423.

464 PRINCIPLES OF PHYSICS.

(Fig. 424), the meter wire is in two pieces, connected at its
centre by a heavy metal strip. As shown
in the figure, the arm, m, of the bridge would
be more than half a meter long, and n, the
remainder of the meter.

The bridge method of measuring resistance
was introduced by Sir Charles Wheatstone,
and named after him, although invented by
Christie.

Fig. 424. 537. Practice in Measurement. — Insert at a;.

Fig. 423, various pieces of No. 30 or No. 28
German silver wire, from ^ m. to 2 m. in length. At B put
a coil of known resistance or a resistance box, and pull
out plugs so that 2 to 3 ohms of resistance are in circuit.
Slide F along, and make contact with the meter wire for an
instant. If the galvanoscope needle is affected, move the
slider until contact can be made without causing a deflection
of the needle. If F is then near C or Z), decrease or increase
the resistance, R. The most accurate results are obtained if R
is such that there is a balance when F is near the centre of the
wire. Measure the resistance of one or more of the following:
telegraph sounder, hand telephone, electric bell, ammeter coil,
voltmeter coil, arc light carbon, incandescent lamp, electro-
magnets of any kind, armature of a dynamo or motor, primary
and secondary coils of an induction coil, a piece of fuse wire.
The measurement of resistance of liquids, except mercury,
requires some modification in the apparatus.

Problems.

1. Jf R = 10 ohms, m = 70 cm., and n = 30 cm., what is the resist-
^^<^^ofx? ^^^ 70^10 ^ = 4.3^hm8.

30 X

2. What is the resistance of a lamp at z, if plugs are removed from
a resistance box at R, indicating that there are 120 ohms at R;
m = 55 ; n = 45 ? • Ans, 98+ ohms.

MEASUREMENT OF RESISTANCE. 465

3. If -R = 25 ohms and a: = 50 ohms, how far from C will F be
when a balance is obtained? m is as many times shorter than n as
R is smaller than x ; m must be half as long as n.

4. jR = 4, m = 42, n = 58 ; find x,

5. If F is halfway between C and Z), how do R and x compare in
resistance ?

6. i2 = ^, m = 80, n = 20; what is x?

7. If jR = 1000, m = 25, and n = 75, what is the resistance of z?

8. If a resistance, x, to be measured is near 60 ohms, how much
resistance must be put in at R so that F may be near the centre of the
bridge when the galvanoscope shows a balance ?

Exercise 70.

COMPASISON OF BESISTANGE OF VABIOUS MATEBIALS.

Apparatus : A cell ; slide wire bridge ; sensitive galvanoscope ; resistance box
or separate resistance coils ; coil No. 30 covered copper wire, 10 m. long ; a
few meters of bare iron, brass, aluminum, platinum, or Glerman silver wire,
No. 30; a piece of fuse wire.

Method L — JR, Fig. 425, is a coil of copper wire ; a: is a piece of the
bare wire of one of the metals, to be
compared with copper. Change the
length of x till contact made by the
slider F at the middle of the meter
wire does not disturb the galvanoscope,
showing that a balance has been ob-
tained. Then copper is as many
times better conductor of electricity
as the coil R is longer than .t.

Method II. — Put the resistance box in circuit at jR, and at x put
the 10-meter coil of copper wire; measure its resistance. Measure
the resistance of wires of other materials. If all the wires measured
have the same diameter, the relative conductivity is well shown by
making a table showing the resistance of one meter of each kind of
wire.

638. Specific Resistance. — It is not always convenient to
have wires of the same diameter to compare. Therefore, in

466 PRINCIPLES OF PHYSICS.

practice, the resistance of a known length of a wire of known
diameter is measured on the bridge. The specific resistance,
that is, the resistance of a piece of wire of 1 sq. cm. cross-
section and 1 cm. long, is computed from the diameter and
resistance of the measured length.

Problems.

1. If 3 meters of copper wire, 1.12 mm. diameter, have a resistance
of .048 ohm, what resistance would a piece 1 cm. long have? What
is the area of the cross-section of this wire ?

2. How many wires like that in Problem 1 would it take to make
an area of 1 sq. cm.?

3. What would be the resistance of a copper wire 1 cm. long, having
a cross-section of 1 sq. cm. ?

4. If 25 m. of lead wire of 5.6 cm. diameter have a resistance of
.197 ohm, what is the resistance of wire of similar material 1 sq. cm.
cross-section and 1 cm. long? What is the specific resistance of lead?

5. If 1 m. of iron wire, having a diameter of 1.12 mm., has a re-
sistance of .16 ohm, what is the resistance of a meter of a, rod 3 cm.
in diameter?

6. If the resistance of 500 m. of a wire 3.36 mm. in diameter is 1.6
ohms, what is the resistance of 1 m. of the wire? What is the resist-
ance of a similar wire 1 m. long and one-half the diameter? three
times the diameter ?

539. Effect of Temperature on Resistance. — Insert pieces of
copper or iron wire of nearly the same diameter and length, at
R and x, Fig. 425, p. 465. Connect the battery and galvano-

scope as in measuring resistance, and get

y^ ^ a balance by moving F, Then warm x.

Does the resistance increase or decrease?
'*' * In circuit at x connect the lead of a pencil

(which is graphite, a form of carbon), having copper wire
tightly wound around the ends, for connection (Fig. 426). At
R, Fig. 425, put any resistance that can be varied, — a resist-

MEASUREMENT OF RESISTANCE. 467

ance box or a piece of German silver wire. Vary the resist-
ance at E until a balance is obtained near the centre of the
bridge. Then heat the carbon at x. What effect does heat
have on the resistance of carbon ?

Exercise 71.
TEHFEBATUBE COEFFICIENT OF BESISTANCE.

Apparatus: Cell; bridge; galvanoscope ; resistance box; steam boiler and
burner; ice; thermometer; coils of fine wire — copper, iron, Grerman sil-
ver, or manganin — wound on a tube ; dipper used in Exercise 222, page 31.

Measure the resistance of the ceil while in ice water; record the
temperature. Place the coil in boiling water ; measure the resistance
again.

The increase in resistance for one degree rise in temperature is of
course xizy oi the difference between the resistance of the wire hot
and the resistance cold, if the ice water is 0° and the boiling water
100°. Find the increase of resistance. Calculate the increase of resist-
ance for a wire having one ohm resistance. This value is called the
temperature coefficient of resistance.

Problems.

1. Suppose an aluminum wire has a resistance of 3.50 ohms at
0° C, and 3.64 at 100° C. The temperature coeflBcient is calculated as
follows :

The gain in resistance is 3.67 - 3.50 = .14.

14
For one degree rise in temperature this is - — = .0014. But this is
^ 100

the gain in resistance for a wire having a resistance of 3.50 ohms. A

1-ohm wire would have '^^ = .0004.
3.5

2. Find the temperature coefficient of platinum, if a wire at 5° C.
has a resistance of 10 ohms, and 90° a resistance of 12.4 ohms.

3. The temperature coefficient of nickel is .005 at 200° C. ; what
would be the resistance of a wire measuring 32 ohms at 20° C. ?

Ans, 60.8.

4. What would be the resistance of the same wire at 0° C ?

CHAPTER XXXII.

IKTEENAL EESISTANOE OF BATTEEIES. — GEOUPINO OF
0ELL8. — 8T0EA0E OELLS.

Exercise 72.

BESISTANCE OF BATTEBIES.

Apparatus : Daniell cells ; galvanometer of low resistance, i.e. having tye to
ten turns ; a resistance box or resistance coils.

Connect the Daniell cell with a sufficient number of turns of a gal-
vanometer. Decrease the area of the zinc plate in the liquid, by
raising it until one corner just dips below the surface. Replace the
zinc, and remove the copper plate slowly. Move the copper near to
the zinc ; then take it as far away as possible, reading the needle in
each case. We have considered the current as passing out through the
wire attached to the copper plate, and, after passing through
the wire of the galvanometer, returning to the cell and entering
the zinc plate. To complete the circuit, the current passes from the
zinc plate through the liquid to the copper. The resistance of the
liquid between the plates is called the interned resistance of the celL
Just as the resistance of a wire is increased in two ways, — by making
the wire longer or of less cross-section — so the internal resistance of
a battery is increased by making the distance between the plates
smaller. Replace the copper plate by a fine copper wire. Vary the
length of the wire in the liquid, and move it toward anfl away from
the zinc plate. This copper wire is a copper plate of very small area.

540. Cells joined in Parallel. — The resistance of batteries is
usually high, — too high to get as large a current as is often
desired. A large pump is capable of throwing a large amount
of water, and a large cell — that is, one having plates of large
area — can furnish a large current. Instead of increasing the

468

INTERNAL RESISTANCE OF BATTERIES.

469

Fig. 427.

size of the plates (beyond a certain size) to reduce the internal
resistance, the same effect is more con-
veniently produced by joining two or
more cells in parallel.

The cells in Fig. 427 are joined in
parallel. All the zincs are connected
to one wire, A, and all the coppers to
another wire, B. It does not matter
whether the plates are in three separate
jars, as shown in the figure, or in one
single jar. The zincs have the effect
of one large plate of zinc, and the electromotive force of the
battery is merely that of one cell.

Join two or more cells in parallel. The cells should be of
the same size and equal in every respect. Test them by cut-
ting out first one and then the other cell. This is done by
taking the zinc out of the liquid. Each cell alone should give
the same deflection on the galvanome-
ter. Note this deflection. Connect A
and B, Fig. 428, to a galvanometer, O,
through a resistance box, R. The cur-
rent is compelled to pass through any
resistance that is put in circuit by pull-
ing out plugs from R. First, put in all the plugs, so that the
box R offers no resistance. The cells are now on a low resist-
ance, practically short-circuited through the galvanometer. Re-
cord the deflection. Pull out plugs, so that there will be 5 ohms
in circuit ; then 10 ohms. On a low resistance, what effect does
connecting cells in parallel have on the amount of current ?

Fig. 428.

541. CeUs johied in Series. — To
join cells in series, connect the zinc
of one cell to the copper or carbon of
the next cell. Join two Daniell cells
in series with the resistance box and

Fig.jl29.

470 PRINCIPLES OF PHYSICS.

galvanometer, as in Fig. 429. Read the deflection with no resist-
ance in E ; then with 5 ohms in circuit ; then with 10 ohms.

542. Comparison of Cells joined in Series and in Parallel.—

Which method of connecting cells — in parallel or in series —
gives the greater current on a low external resistance ? On a
high external resistance ?

With no external resistance, do two cells in series give more
current than one cell did ? If an external circuit is of high
resistance, 100 to 1,000 ohms, ought cells to be connected in
a series or in parallel to give the strongest current ? If the
external resistance is small, a mere fraction of an ohm, how
should the cells be connected ? Try the effect of increasing
resistance by partly lifting the copper plate out of the liquid.
What effect does increase of resistance always have on the
current ?

543. The Internal Resistance of Cells joined in parallel is less
than that of one cell. A current of water encounters less
resistance in flowing through two or more pipes side by side
than in flowing through one alone. In the same way, there is
less resistance in cells connected in parallel than in one cell.
If the cells are all alike, then two cells in parallel have one-
half the internal resistance of one cell ; five cells in parallel
have one-fifth the internal resistance of one cell.

When cells are connected in series, the current, let us say,
passes through the liquid of the first cell and encounters resist-
ance ; the same current then passes through the second cell
and encounters more resistance there. When connected in
series, two cells have twice the internal resistance of one cell;
five cells have five times the internal resistance of one cell.

544. Electromotive Force, or Voltage, of Cells connected in
Parallel. — Test two or more cells separately on the voltmeter.
Connect them in parallel (Fig. 430, III.). A lot of pumps
taking water from the same pond and emptying into the

INTERNAL RESISTANCE OF BATTERIES.

471

water pipes of a town will not give any greater pressure than
one pump would, provided little or no water is allowed to flow
out of the pipes. The pumps so arranged (Fig. 430, IV.) may be
said to be connected in parallel. If all the hydrants in the city
are opened and the external resistance, that is, the resistarif c

2S, €^ Z» Cm Zm (M

3? A 3?^

BMtl

IV,

Fig. 430.

oatside of the pamps^ decreased, then they will send a ^f ater
current of water than one pump would. Assuming that the
cells are alike, ^ dectromotive force of ce!h in parallel U the
electromotive force of one ceU,

545. nectnnnotive Force <tf CeOa cimiieeted in SerlM. — Con-
nect the cells in series ('Fig. 430, I. j and test the volt,age. The
current paaaing through one cell gets the push, pressure, or
voltage, of one cell ; the same current then passes into a ser*ond
cell and receives the additional pressure or voltage of that pell ;
and so on. Compare IT., Fig. U^, where the onmm are in ^eriPH
and the pressure in the water mains is (^pater than rhat opven
by any one pump. Tlte f>]ect,rom,oth*p. forrp. or I'olttiQp, of »^p.n>t hi
series equals the electromotwe force of ove /^// muLtiptied fy*j tJie
of edU.

472 PRINCIPLES OF PHYSICS.

546. Measurement of Internal Resistance of a CelL — Try the

effect of increasing the resistance by partly raising the copper
plates from the liquid. What effect does increase of resistance
always have on the electromotive force of a cell or battery ?
Does a large cell have a higher electromotive force than a
small cell ? The voltage decreases very much with an increase
of current, and the internal resistance increases.

Short-circuit a Daniell cell through an ammeter. If the re-
sistance of the ammeter is low, the only resistance in circuit
worth considering is that of the cell itself. Suppose the cell
gives 3 amperes. Then, assuming that the electromotive force
of the cell is 1 volt, the formula

E 1

C= — becomes 3 = - , and i? = ^.

This is not an approved method of finding the internal re-
sistance of a cell, but is mentioned to make clear the fact that
a cell has internal resistance. In the following problems, the
voltage and internal resistance is assumed to remain unchanged,
whether a large or small current is flowing through them.

What current flows from a cell, having an E.M.F. of 1.5
volts and a resistance of 3 ohms, if the poles are connected by

E 15
a short wire, that is, short-circuited ? C=— = -^=.5 ampere.

M 3

If the same cell is connected with a wire having a resistance
of 2 ohms, how much current flows ? The formula becomes

C= ; r = internal resistance of the cell, and E = the ex-

■i K "IK,

ternal resistance. 0= — '■^-— = -^ = .3.
3-f-2 5

Problems.

1. What current can a " dry " cell of 1.5 volts and 1 ohm resistance
give on short circuit? Ans, 1.5 amperes.

2. What can the same cell give if the external resistance is 1 ohm?
2 ohms? 10 ohms? Ans. .75 ampere; .5 ampere; .13 ampere.

INTERNAL RESISTANCE OF BATTERIES, 473

3. If a cell, E.M.F. = 1 volt, r = 5 ohms, is connected with a 10-
ohm telegraph sounder, what is the current?

4. What current can a storage cell, E.M.F. = 2 volts, r — ^ ohm,
send through a .5 ohm incandescent lamp ?

5. If a bichromate cell having two volts and .2 ohm resistance, is
short-circuited, what is the current ?

6. If the cell of Problem 5 is connected with an electromagnet
having .1 ohm resistance, how much current flows through the
circuit?

7. If a dynamo furnishes a current of 200 volts electromotive
force, and its internal resistance is 3 ohms, how many amperes will it
send through a 20-ohm resistance ?

8. A Daniell cell, E.M.F. = 1 volt, r = .2 ohm, gives what current
on short circuit? On an external resistance of 100 ohms?

9. A gravity cell, E.M.F. = 1 volt, r = 5 ohms, gives what current
on short circuit? On a circuit of 100 ohms?

10. Study the results in Problems 8 and 9. Does there appear to
be any advantage in a low resistance cell like the Daniell over the
gravity form, which has a high. resistance?

547. Joining Cells in Parallel decreases the internal resistance
of the battery as a whole, and does not affect the voltage. A
battery of two similar cells in parallel has one-half the resist-
ance of one cell.

Problems.

1. Given 4 cells, each having a resistance of 2 ohms and an E.M.F.
of 1.5 volts; they are connected in parallel ; the internal resistance is
} or .5 ohm.

a. What is the current when the external resistance is zero ?

1 5
Arts, C = -^ = 3 amperes.
.5
h. Find the current on an external resistance of 1 ohm.
c. How much current flows, if the external resistance is \ ohm ?

Ans. 1.5 amperes.

2. If the cells of Problem 1 are connected with a telegraph
flounder having a resistance of 5 ohms, how much current can flow ?

474 PRINCIPLES OF PHY8IC8.

3. Ten Daniell cells, each having 1 volt and \ ohna internal resist-
ance, are joined in parallel. What is the current : —

a. If the external resistance is zero ?
6. If the battery is short-circuited ?

c. If the external resistance is A ol"» ?

d. If the external resistance is 1 ohm ?

4. How much current would the ten Daniell cells of Problem 3
send through a resistance of 1000 ohms?

5. How much current would five of the same cells in series send
through a resistance of 1000 ohms?

6. How much current would one of the cells of Problem 3 send
through 1000 ohms resistance ?

7. Is there much advantage in connecting cells in parallel on a
high external resistance?

8. Compute the current of one cell of Problem 3, on a resistance
of .05 ohm.

9. What current would five of these cells in parallel send through
the same resistance ?

10. Five bichromate cells, each having 2 volts and 3 ohms resist-
ance, are joined in parallel on an external resistance of half an ohm.
Find the current flowing.

11. What would one such bichromate cell give on the same
resistance?

12. Is there any advantage in using several cells in parallel when
the external resistance is low ?

13. If 20 oxide of copper cells, giving .8 volt each and having an
internal resistance of .02 ohm, are joined in parallel and connected
with an external resistance of 10 ohms, what is the current? If
connected with an external resistance of 2 ohms? If connected
with an external resistance of .01 ohm? If short-circuited?

648. High Electromotive Force from Batteries. — Cells in com-
mon use rarely have an electromotive force of even 2 volts.
When it is desired to have a source of electricity of more than
2 volts, cells are joined in series. John Trowbridge, at Cam-
bridge, Mass., has constructed a battery of twenty thousand

INTERNAL RESISTANCE OF BATTERIES. 475

small storage cells; when these are connected in series, the
battery has an electromotive force of twenty thousand times
2 volts, or 40,000 volts. Since the current passes through
all the cells in the series, the total internal resistance equals
the sum of the resistances of each cell. But as all the cells
joined together are usually of the same size and pattern, the
resistance of ten cells in series may be taken as ten times the
resistance of one cell.

549. Rules for a Battery of Cells in Series. — For a battery of
similar cells in series, we have the following rules ; —

The electromotive forcey or voltage, of the battery equals the
volts of one cell mvltiplied by the number of cells.

The internal resistance of the battery equals the internal resist-
ance of one cell multiplied by the number of cells.

It must not be supposed that the internal resistance of a cell
is an advantage. Connecting cells in series increases the
internal resistance in proportion to the number of cells, and
this cannot easily be prevented. To get a high electromotive
force from cells, they must be connected in series.

Problems.

1. Using Daniell cells, each having an electromotive force of 1 volt
and an internal resistance of .3 ohm, find the current in the following
combinations : —

a. One cell, short-circuited. Ana. C = - = 3.3 amperes.

•o

b. One cell, external resistance = 10 ohms.

c. Ten cells in series, short-circuited. Ans. C=—-^ — =3.3 amperes.

d. Ten cells in series, external resistance = 10 ohms. The voltage
is 10 X 1, or 10; the internal resistance is 10 x .3 =3 ohms. Then

C = -i^ = 12 = .77 amperes.
3 + 10 13 ^

e. Ten cells in series, external resistance = .1 ohm.

/. Five cells in series, connected with the terminals of an electro-
magnet, resistance = 2 ohms.

g. Three cells in series, external resistance = 8 ohms.

476 PRINCIPLES OF PHYSICS.

2. A Daniell cell tries to send a current from the copper, through
the wire, to the zinc. If two cells are set up with the zinc plates con-
nected by a wire and the copper plates similarly connected, do the
cells aid or oppose each other? Will there be any current through the
cells if both have the same electromotive force ?

3. Three cells are connected in series, but one of them is connected
so that its electromotive force opposes that of the other two. The
internal resistance of each cell = .3 ohm. What current will they
send through an external resistance of 1.1 ohms? Am. .5 ampere.

The voltage of the combination is 2 — 1, because the voltage of the
third cell opposes the other two. The fact that one cell is reversed
does not change its internal resistance. The total resistance is 3 x .3
ohm plus the external resistance 1.1. Therefore

2 — 1 1

the current = — — — - = - = .5.

(3 X .3) +1.1 2

4. A Bunsen cell (2 volts, 1 ohm internal resistance) and a Daniell
cell (internal resistance .4) are connected in opposition through an
external resistance of 3 ohms. Find the electromotive force of the
cells and the current.

E.M.F = 2-1.

Current = • ^ " ^

IH- .4 H- 3

5. What disadvantage is there in having one cell of a battery
connected in the wrong direction ? How does such a cell affect the
voltage and the internal resistance of the battery as a whole ?

6. State what current will be given by bichromate cells of 2 volts
and 3 ohms internal resistance each, connected as follows : —

a. One cell short-circuited. Arts, f ampere.

b. One cell, no external resistance. Ans, j ampere.

c. One cell, external resistance 10 ohms.

d. Six cells in series, external resistance 10 ohms.

e. Six cells in series, no external resistance.
/. Six cells in parallel, no external resistance.

g. Six cells in parallel, outside resistance .1 ohm.
h. Six cells in parallel, outside resistance 10 ohms.

7. When the outside resistance is large, which is the best method
of connecting cells, in series or in parallel ?

STOBAGE BATTERIES.

477

8. A bichromate cell (2 volts, 3.7 ohms internal resistance) and a
Daniell cell (internal resistance .3) are connected in series through an
external resistance of 11 ohms. Find the current. Ans. .2 ampere.

The electromotive force is 2 + 1 or 3 volts. The resistance is
3.7 + .3 + 11 or 15 ohms. Then

3
C = — = .2 ampere.
15

Exercise 73.

STOBAGE BATTEBIES - POLABIZATIOK.

Apparatus : Three or more Daniell or bichromate cells ; two galvanometers,
one of a few turns, used as a voltmeter, the other of many turns, used as
an ammeter ; lead sheets. Commercial forms of voltmeter and ammeter
may be used in place of the galvanometers.

Review section 499, page 433.

Join the three cells, B, B, B, in series (Fig. 431). Make the con-
nections as shown in the diagram, so that the current flows through
the ammeter or tangent
galvanometer, A, and a
storage or secondary cell,
5, which, in its simplest
form, consists of two lead
sheets in a solution of
weak sulphuric acid (one
part of acid to ten parts of
water), and diifers from Fig. 431.

the apparatus described in section 499, used in the decomposition of
water, only in the size of the plates. The other galvanometer or volt-
meter, Vm, should be connected with the lead plates of 5. The lead
plates may be as large as can be used in the largest battery jar, and
they should be within an inch of each other. Note the current and
the voltage at the terminals of the storage cell, 5.

At first the reading at Vm shows the number of volts required to
drive the current through the liquid in S. But soon the plates
polarize ; hydrogen gas comes from D, and oxygen from C ; the cur-
rent decreases, and the number of volts between C and D increases.
Notice the color of the lead plates. The one from which the oxygen

478 PRINCIPLES OF PHYSICS.

comes turns dark brown, and the gas comes in full quantity from that
plate only after it has darkened completely. At first — at least for a
second or two — no bubbles came from C. It was absorbing all the
gas as fast as formed, and on the surface the lead turns into a brown
compound of lead and oxygen.

Disconnect the cells at E and F. The voltage of the storage cell
falls a little ; record the amount. Connect E and F to the binding-
posts of a bell. The current flows from the cell in the opposite
direction, coming out by the wire attached to C, as shown by the gal-
vanometer at A, The color of the plate C changes as the cell S,
discharges its store of energy. The amount stored is small, because a
thin layer of the lead plate absorbed the gas generated.

Change the connections of C and D, making the current go in the
opposite direction through the cell S, D, being connected with F, is
now the plate where the current enters. D turns dark and absorbs
oxygen for a time, while C loses entirely its brown color and is
reduced to pure lead. By repeatedly discharging the cell and charg-
ing in the opposite direction, the surface of the lead becomes porous
to a greater and greater depth ; the cell is then able to store up a
greater amount of electrical energy. After the firat charging, the
brown coating is hardly thicker than a film of dust. In a few months
the plates may become entirely porous, if they are thin and enough
reversals of the current are made ; but it is not desirable to carry the
forming of the lead into the porous condition to such an extent, for
some unchanged lead must be left to serve as a conductor. When
the plates, by repeated reversals of the current, have been formed
deep enough to hold a good charge, the current, in charging, is there-
after always sent through the cell in the same direction, and the
depth of the porous coating no longer increases to any extent.

550. Forming a Storage Battery. — The process of forming
just described was invented by Plants, forty years ago. It
is tedious and expensive. About twenty years later, Faure ap-
plied oxides of lead to the lead plates. To the plate at which
the current enters on charging and leaves on discharging, he
applied a coating of red lead, and to the other plate a coating
of yellow lead, called litharge. A long charging changes all
the red lead to the brown peroxide, and the litharge to spongy

STORAGE BATTERIES. 479

metallic lead. The cell is then formed, and ready for use.
Reversal of current in charging is rarely used. Nearly all
storage cells in commercial use are made on Faure's plan or
some modification of it.

551. Kinds of Storage Batteries. — In one type of cell, lead
frames are cast around lumps of fused chloride of lead. The
plates are then formed as in the Faure type. The discharging
current should not be more than one ampere for 150 sq. cin. of
area of the plate that turns brown ; although if the life of the
cell is of no account, the discharge may be many times this.

Many other metals and combinations of metals have been
tried. Edison has perfected a storage cell in which the plate
corresponding to the zinc of the primary cell is of spongy iron
in a frame of iron; the plate corresponding to the copper or
carbon of a primary cell is a compound of nickel in an iron
frame. This cell is three times as light as the lead cell and
has none of its faults.

552. Efficiency of Storage Cells. — Storage cells made of lead,
in charging, require nearly 2.5 volts per cell to overcome the
electromotive force of the cell itself. The current on discharge
comes out of the cell at the same pole at which the current
entered on charging. After a short charge, the pressure of
the current in the storage cell rises to 2.5 volts, and tends to
stop the current. This polarization, as it was called in the
study of the simple galvanic cell, is put to good use when the
cell is discharged ; but on discharge the voltage falls at once
to nearly 2 volts. Therefore, even if exactly as many ampere-
hours flow out of the cell as are sent through it in charging,
the work that the cell can do on discharge is always less than
the work done in charging it. The efficiency of a storage cell

2
is not usually much more than -—, or 80 per cent, and is

usually much less. When the voltage on discharge drops
below 1.9, the cell should be recharged at once.

480 PRINCIPLES OF PHYSICS.

553. Charging a Storage CelL — For experimental purposes,
two or three small bichromate cells, each having an internal
resistance of J to 1 ohm and an electromotive force of 2 volts,
can be used to charge slowly a storage cell of considerable
surface. The two bichromate cells in series give 4 volts or
less. This electrical pressure sends a current through the
resistances of the cells and connecting wires and overcomes
the counter-electromotive force, as it is called, of the storage
cell. The voltage of the two bichromate cells in series is 4
volts. The voltage of the storage cell in opposition is 2.5
volts. 4 - 2.5 = 1.5 volts.

1.5

The amount of current =

Total resistance in circuit

554. The Resistance of the Storage Cell depends partly on the

amount of surface of the plates. While a primary cell of the

Daniell or bichromate type may have an

^1 internal resistance of \ ohm or more for a

jar of the size generally used in the labora-
tory, a storage cell in the same jar could
be made with an internal resistance of
less than ^ ohm, by increasing the num-
ber of the plates. Fig. 432 shows three
'' ' plates, a, a, a, connected with one wire, C,

and two plates, b, &, connected with D. Several plates are
thus joined together to form each pole, instead of using single
large plates.

Since the resistance of a storage cell charged by a battery or
by any other source can have a very low internal resistance,
immense currents can be drawn from it. A fine iron wire,
No. 30, while appreciably warmed by two or more bichromate
cells, is easily melted by a storage cell. Faure's invention was
designed to furnish currents for electrical welding.

Electromotive forces of more than a few volts are not ob-
tained conveniently from primary cells. A large number of
storage cells are charged in parallel or one at. a time by a few

STORAGE BATTERIES. 481

primary cells in series. When the desired number of storage
cells have been charged, they are connected in series.

Connecting large storage cells in parallel for large currents,
and small cells in series for high voltage, is now carried out
mostly in experimental work.

555. Storage Cells as Regulators. — Large batteries of many
cells in series are used in stations generating current for
electric light. During the daytime, or whenever the load is
not heavy, the batteries absorb the surplus current, and give it
out again in case an extreme number of lights or motors are
turned on, or in case the engines are stopped and current is no
longer generated by the dynamos.

CHAPTER XXXIII.

ELBOTBOMAOIETB, HDTTOED OUBSEVTS, DTVAMOS AID
M0T0B8, THE HDUOTIOH OOIL.

556. Electromagiiets. — Send a current throagh a coil of
wire. The coil attracts iron or steel; in fact, acts like a
magnet If the coil is wound around a bar of iron or a bundle
of iron wires, the number of lines of force generated by the cur-
rent may be thirty times as great as before. The iron core, if
the current is large, is a more powerful magnet than any per-
manent magnet made of steel. The coil and core form an
electromagnet. On breaking the current, the magnetism almost
completely disappears if the core is of soft iron. A piece of
hardened steel placed in a coil, if a current is turned on for an
instant, becomes permanently magnetized. A part of its mag-
netic strength is temporary, and exists only while current is
flowing in the coil around the steel, but it retains considerable
magnetism after the current is turned off and the coil removed.
In this way hardened steel is magnetized more strongly than
by rubbing it on a permanent magnet. The fact that an electro-
magnet attracts only while the current is flowing through the
coil is an essential principle of telegraph sounders, bells and
signals, and many other electrical devices.

557. Telegraph Sounder. — Suppose a galvanoscope in Chi-
cago were connected by long wires with a battery in New York.
The galvanoscope, if sensitive enough, would indicate a current
by the deflection of the needle. Reversing the current makes
the needle swing in the opposite direction. By letting various
combinations of movements of the needle to the right and left

ELECTROMA 0NET8.

488

stand for different letters, messages were formerly sent from
one part of Great Britain to another. About the same time,
Morse, in this country, had perfected a more practical instru-
ment, using an electromagnet. In its crudest form, it consists
of an electromagnet connected by wires with the station or
place from which the message is sent. Each time the circuit
is made, a curi'ent flows over the wires to an electromagnet in
the place where the message is received. The core of the elec-
tromagnet attracts a bit of iron, and keeps attracting it as
long as the current flows. On breaking the circuit, thereby
shutting off the current, the core of the electromagnet no
longer attracts, and the bit of iron (called the armature) falls
away or is pulled away by a weight or spring.

558. A Simple Model of the Telegraph Sounder is shown in
Fig. 433. B is the base of wood, and, as shown in the lower
part of the figure, is cut in at the ends so that the uprights D
and F are in line with the coil, CC,
This is the same coil that was used
in the galvanoscope, or one similar
to it. / is a core of iron, a car-
riage bolt, for instance, which screws
into a hole in the base; a is a piece
of iron, a nut, for instance, which
is tied or fastened to the rod, E.
E is of wood, and is cut away to make it as light as possi-
ble; it tilts on a pin, or needle, held in F. A sliding weight,
W, is placed so that a just rises from /when there is no cur-
rent flowing. The motion of E should be limited to an eighth
of an inch or less, by a nail in the end of E, which plays in a
slot in D. When the armature is attracted by /, A should not
be allowed to touch it, because the residual magnetism which
is left after the current stops sometimes holds A down. The
sound is increased by a piece of tin screwed in D, on which
the nail in E strikes.

Fig. 433.

484

PRINCIPLES OF PHYSICS.

559. Morse Alphabet — The armature held down for an in-
stant indicates a dot; if held for a longer time, a dash. In
Morse's original form of instrument, which was in general use
from its invention in 1837 until fifteen or twenty years ago,
the dots and dashes were made on a strip of paper, steadily
moved by heavy clockwork under the nail in E, After a time
telegraph operators could spell out the words by the clicks of
the instrument, without looking at the paper, and its use has
been generally abandoned.

560. A Simple Form of Key to make and break the circuit is
shown in Fig. 434. Two screws are
fastened in a block of wood. One
screw holds the connecting-wire, A-,
the other screw holds a strip of brass,
tin, or zinc, B, and the other connect-
ing-wire, C. By pressing B, the current has an unbroken path
from A to (7.

Fig. 434.

561. The Telegraphic Circuit. — Iron telegraph wire has a
resistance of about 10 ohms per mile. To do away with
the need of a return wire of 10,000 ohms between New York
and Chicago, plates of metal, E and E', are sunk in the

(fi^K--^

Key

Chicago

F\g. 435.

earth, and the circuits arranged as in Fig. 435. For a short
line, it is better to use a return wire, since the resistance be-
tween the plates and the earth is ten ohms or more. While

ELECTROMA GNEfS.

485

soil is not a good conductor, there is so much of it — the earth
is so large — that the resistance between E and E\ whether
they are one mile or one thousand miles apart, is almost the
same. Between A and B there are a thousand miles of wire.
Keys are always used in both the sending and receiving sta-
tions. Reproduce the figure, putting a key and battery in
circuit at Chicago. Keys are always kept closed, so the current
can flow, except when signals are sent.

562. Strength of the Current. — Count the number of turns in
the coil used on the model sounder. Fig. 433, and measure the
current required to bring down the armature and make a dis-
tinct soimd or tick. If there are 300 turns and the current is
.2 ampere, then the number of ampere turns is .2 times 300,
or 60.

On long lines, as the resistance is large, the current is small;
therefore the sounders must have coils with a large number of
turns. On the longest lines, as, for instance, between New
York and Omaha, relays are used every few hundred miles.
For example, sounder S' at Chicago, Fig. 435, could be made
to open and close the key of a new line running from Chicago
to some point farther on.

563. Electric Signals. — Electromagnets arranged somewhat
like the sounder in Fig. 433 are used to let a weighted hammer
drop on a church bell in a fire-
alarm system, or to let fall a
numbered disk in a hotel annun-
ciator, or a semaphore arm, or a
colored screen in railway sig-
nalling.

The principle of electric bells
and vibrating interrupters for pj ^^^

induction coils can be illustrated
by a modification of the telegraph sounder shown in Fig. 433,

tr^

486 PRINCIPLES OF PHYSICS.

in which the nail is replaced by a spring. The current
passes through the circuit only when the spring touches the
metal strip at the upper part of D, Fig. 436. The spring is
connected by a wire with the coil, and thence through a key or
button, back to the battery. As soon as the armature is
attracted, the circuit is broken at the point of the spring.
Draw a diagram of the circuit in a vibrating bell.

564. Uses of Electromagnets. — Powerful electromagnets are
used to hold drills against the deck or sides of iron ships ; to
remove an iron or steel splinter from the flesh ; to regulate the
movement of the carbons and the length of an arc in an arc
lamp ; to open a circuit in case an unsafe amount of current
flows. Most electrical inventions use electromagnets in some
way.

565. The Solenoid. — The lines of force inside a coil of wire
are stronger than outside. Count the number of vibrations

of a compass needle in the centre of a coil

^.]]^ ] c \-'-'^^ ^^ ^^^® (*^® galvanometer coil), and then

A some distance away. Iron is forced or

^ attracted into the position where the most

'■ * lines of force can pass through it. Send a

strong current through the coil, CC, Fig. 437, and hold a nail

as shown. The nail is sucked up into the coil. Breaking

the current makes the nail fall. Electric drills are made on

this principle. The coil used in this way is called a solenoid.

Exercise 74.

OXJBBENT INDUCED BT A BAS MAGNET.

Apparatus : Sensitive galvanoscope ; bar magnet ; coil of wire, which may be
similar to the one in the galvanoscope ; cell (Fig. 499).

The coil, C, Fig. 438, should be far enough from the galvanoscope,
Gf so that a slight movement of the magnet, NS, will have little or no

INDUCED CURRENTS. 487

effect on the needle before the connections at i> and E are made.
Make a diagram like Fig. 438, in the note-book. The arrow beside
the magnet indicates that the move-
ment of the galvanoscope needle is to
be noted as the north pole of NS is
pushed in the coil. Before connect-
ing the coil with the galvanoscope, "E^
determine from which wire, D or E, ^*«- *'••
current enters G when the marked end of the needle moves to the
right (or to the left). To do this, hold D in contact with a piece of
zinc, as in Fig. 439, and put the zinc and the copper wire E in slightly
acid water. We have in this figure a small, simple cell ; arrows on

the wires E and D indicate the direction of the current
i^ i^^ (see section 466, p. 408).
p|l--.[J_| If the galvanoscope is very sensitive, a deflection will

be shown when the copper and zinc are placed near to-
*■ ' gether on the tongue, and a piece of iron (a knife blade
or a nail) may be substituted for the zinc. Note whether the marked
end of the needle moves to the right or the left. It may move either
way according to the winding of the coil. Suppose it moves to the
right. As the current is always understood to leave a battery by the
unconsumed pole, — in this case copper, — the current passes from
the wire E to the galvanoscope. Then a movement of the needle to
the right indicates a current in E toward the galvanoscope; and a
movement to the left indicates a current from the galvanoscope toward
E, Of course a mere swinging of the needle need not indicate any
current. The direction of the current in D is always in the opposite
direction to that in E.

Case I. — Push the north pole of the magnet into the coil C, Fig. 438.
In which direction does the needle move ? The movement indicates the
direction of the current in the wire E. A current must flow into the
galvanoscope by one wire and out by the other wire. On your dia-
gram, put arrows at D and E and on the coil, C, to show the direction
of the current. In some way, the movement of the magnet into the
coil, C, has generated a current of electricity in it, and that current
has been carried some distance and has shown its presence by affecting
the needle of the galvanoscope. With longer wires, this current could
have been carried to greater distances. It could be utilized for a
variety of pui*poses, as will be explained in later sections. The

488 PRINOIBLES OF PHY8IC8.

current here is not caused by consumption of zinc, but by motion of
the magnet. It is called an induced current.

The current induced in the coil, C, sets up lines of force in the
coil, and poles appear at the faces of the coil. One face, or end,
acts as a north pole, and the other face as a south pole. The direc-
tion of the induced current in the coil is known from the swing
of the galvanoscope needle. Indicate clearly in your drawing which
wire goes over the coil, and which goes under it. Knowing the
direction of the induced current in the coil, and remembering Am-
pere's law regarding electromagnets, what pole is made on the face
of the coil nearest the magnet? Mark this on your diagram. It
will be a north pole, just like the north pole of your magnet. Now,
two north poles repel, and in pushing up the magnet against this
repulsion, work was done, and practically all of this work was turned
into an electric current that flowed in the coil, C, and the circuit
attached to it.

Instead of considering the pole of the magnet and the pole set up
on the face of the coil, draw the lines of force due to the magnet

(Fig. 440). The lines of force gener-
ated in the coil by the induced current
must pass through the coil in such a
way as to cause repulsion. In some
way, the coil and the magnet resist
being brought together, if the current
is allowed to flow through the coil. The
current is allowed to flow if the circuit
is closed by connecting D and E directly
p. ^ together or through some other outside

wire ; in this case, through the galvano-
scope. The experiment should be repeated several times. Wait for
the needle to come to rest before pushing the magnet in the coil.

Case II. — Insert the magnet slowly and wait for the needle to
come to rest. Remove the magnet. Note the movement of the
needle. Make diagrams, as in Case I.

Case III. — Thrust the south pole of the magnet into the coil.
Case IV. — Remove the south pole.

Case V. — Try the effect of moving the coil in one of the previous
cases, holding the magnet stationary.

Case VI. — Repeat one of the first four cases, moving the magnet

INDUCED CURRENTS. 489

very slowly. Then let the magnet remain inside the coil, and note
the effect.

The current flows, or is induced, in the coil only as long as the
magnet is being moved toward or away from the coil. While the
magnet is still, whether inside or outside of the coil, no current is
induced. And, further, the movement of the magnet causes an elec-
trical pressure of a certain number of volts at the ends D and E of
the coil. Naturally, no current can flow unless the ends are con-
nected directly together or through a wire outside. The more turns
of wire there are in the coil, the nearer these turns are to the magnet,
the faster the magnet is moved, and the stronger the magnet is, the
greater the number of volts induced in the coil. The current depends
on this voltage and the resistance of the complete circuit, including

wires connected with D and E, But Ohm's law, C =-^, does not hold
exactly.

How does the pole induced in the nearer face of the coil compare
with the pole of the magnet? When the north pole of the magnet is
brought toward the coil, a north pole is formed on the face of the
coil, and repels the magnet. This .force of repulsion in the exercise is
too slight to be noticed if the magnet is held in the hand. Study the
diagrams, and notice that there is always repulsion when the magnet
is moved toward the coil, and attraction when the magnet is taken
away from the coil. In fact, a pole of such polarity is formed on the
face of the coil nearest the magnet as always to resist the movement
of the magnet, whether it is brought up nearer or moved farther away
from the coil. The work in overcoming this resistance is turned into
the current of electricity in the coil.

566. Principle of the Dynamo. — The necessary motion of the
magnet may be kept up by hand, by a water wheel, a windmill,
a steam or gas engine. Such a machine for generating a cur-
rent is called a dynamo, and the coil and magnet is the sim-
plest form of that machine.

In more scientific language, instead of speaking of the move-
ment of a magnet toward and away from a coil of wire, the
wire is considered as sweeping through or cutting the lines of
force of the magnet.

490 PRINCIPLES OF PHYSICS.

567. Magneto-teleplioiie. — The telephone, in its simplest
form, consists of a magnet, NSy Fig.
441, a coil of wire wound round one
pole of the magnet, and a thin disk
of iron, D. The lines of force of
the magnet, XS, pass from the north
pole to the south pole, and only a few-
pass to the disk, D, on their way to
the south pole. When i> is in the position shown in Fig. 442,
a large number of lines of force pass into and through it.

Wind a coil of wiie around the end of a magnet. When D
is in the position shown in Fig. 441, many
lines of force pass through the wire ; but .<'^'^~S?yr^^

when D is moved to the position shown //^f^'" '^^->xX
in Fig. 442, fewer lines of force pass *^ \j;ij

through the wire ; they travel straight to J\ V-ix^ sf

the disk, through it to the edge, and then / / ^
through the air to the south pole, passing ^^ ^2.

around the coil of wire. Changing the
position of the disk, D, therefore causes some of the lines to
sweep through or cut through the coil of wire.

Place a small compass, C, Fig. 443, near the pole of a mag-
net, in about the position of a coil in a telephone. The needle
shows the direction of the lines of force at
nl jiv' ~~T\ that point. Move a disk of iron, D, toward

I 0 and away from the magnet. The move-

^. ment of the compass needle indicates a

movement of the lines of force. A coil of
wire would be cut by these lines of force,
aud a current of electricity would be gen-
erated in the wire.

Hold a thin disk, D, Fig. 444, at the edges.
Conuect with a galvanoscope the ends, a and , «• *^«
b, of the coil. Push the centre of the disk in, and then let it fly
out. Fig. 444 shows the north pole in the coil, but the south

'1^

IXDCCED CURREXTS. 491

pole may be used. Moving a wire and making it cat Hues of
force, as in Case V^ in Exercise 71, or making the lines of
force pass through the ooil, tends to induce a coirent in the coiL
The instaument shown in Fig. 444 is the simplest form of a
ms^neto-telephone. This form is used as a transmitta- on
short lines only. The disk, Z>. is made to Tibrate, in and oat,
by the air wares of the voice. As the disk goes in toward the
magnet, a eorrait in one direction is induced in the coil of
wire ; as the disk springs oat, a earrent in the opposite direc-
tion is induced. This instrament is a generator of alternating
currents, and is a simple form of dynama

568. Xltt Seccmiis iBstnwiit, or Seoemr, at A, Fig. 445, is

of the same construction. Each instrament is used, in turn, as a

^Far

F«.445.

transmitter to talk into and then as a receiver. While one
perscm talks at T, the transmitter, the listener holds the
receiTcr, Ry close to his ear. In both instruments, the disk of
sheet iron is always zXtneted more or less by the powerful
magnet near it.

568. Tkft Attkm itf tins Fonn of Telepiwc, used as a receiTer.
is as follows : —

Imagine a current to enter the coil by the wire a (Fig. 446V
Apply Ampere's rule. The current tends to
set up a north pole at the left, and a south pole ^^——-rny^ I >^
at the right, or north-pole end of the magnet a^-_--^J/\
The current is never strong enough to change ^
the polarity of the magnet, but only to weaken ***'

the north pole a little. The disk, Z>, is then less attracted,
and flies oat a little ; but another current follows, in the oppo-

492

PRINCIPLES OF PHYSICS.

site direction, entering at h. Reproduce Fig. 446, and mark
the direction of the current in the wire. The current now
tends to set up a north pole at the right end of the magnet,
where the north pole is already, and the result is that this
north pole becomes a little stronger, and attracts the disk, D, a
little more. The strengthening and weakening of the north
pole succeed each other every time the current alternates.

Since the disk, D, Fig. 445, vibrates at the same rate as the
tones of the person speaking before it, a current of the same
number of alternations is induced in the coil A, The alternat-
ing current goes through the wires to the receiver, i?, and
passes through the coil. By weakening and strengthening the
magnet. The disk at R is attracted more, and then less, at
the same rate, and reproduces the tones of the speaker at T.
Therefore, T is a dynamo, and generates the current of elec-
tricity. In R these currents produce motion in the disk; R
therefore acts as a motor. As the magnets used are permar
nent, the instruments are called magneto-telephones. All tele-
phone receivers now in use are of this type.

670. Commutation of Currents. — For many purposes, an al-
ternating current is not as useful as one that always flows in
the same direction, such as the current of
jEl II \\\ a cell. A machine that delivers a current,

/y. A flowing always in the same direction, is

called a direct-current dynamo, Now, the
movement of a magnet toward or away
from a coil, or, what is the same thing, the
movement of a coil toward or away from
a magnet, produces currents that vary in
direction, as often as the direction of the
Fig. 447. motion is changed.

Suppose a coil, Ey Fig. 447, is connected with a current
reverser. On pushing the north pole of the magnet toward
the coil, a current is induced in the coil.

INDUCED CURRENTS. 493

Copy the diagram, and trace the current in the wires, which
are connected with a lamp, an electromagnet, or a galvanoscope.
The top of the reverser is so placed that A is connected with
Cy and D with B, Change the current reverser, so that A is
connected with D, and C with B, Remove the magnet. A
current in the opposite direction is induced in the coil.

Make another diagram, showing the direction of the current
in the entire circuit. If a galvanoscope were in place of a
lamp, the movement of the needle would show that a current
of the same direction, that is, a direct current, passes through
the wire.

The current in the simple apparatus used will not be con-
stant in strength. It will fall away to nothing when the magnet
stops ; but whenever there is a current, although it alternates,
or changes in direction in the coil, the current will always have
the same direction in the wires. Of course, the current re-
verser must be changed every time the direction of the motion
of the magnet changes. The coil and the magnet make a
simple form of dynamo, and the current reverser serves as a
commutator.

571. The Armature. — In all practical forms of dynamos, the
coil or coils of wire in which the current is generated is called
the armature. In this the current is alternating, first in one
direction, then in the other.

572. Direct Current and Alternating Current Dynamos. — Con-
nect the galvanoscope directly with the coil. Move the magnet
in and out. Notice the slight to-and-fro movement of the
pointer, indicating an alternating current. Without a commu-
tator, the dynamo delivers an alternating current to the wires
connected with it, and is called an alternating dynamo or an
alternator. A similar machine, furnished with a commutator,
furnishes a current of always the same direction, and is called
a direct current dynamo.

494

PRiyCIPLES OF PHT8IC8.

573. Effect of Strength of Magnet. — The current indaced in

a single wire (Fig. 448) by moving it between the poles of a

powerful magnet is sufficient to cause a

noticeable deflection of a sensitive galvano-

scope, especially if a mirror is fastened to

the needle suspension and the movement

Qf a spot of light reflected by the mirror

r 448 ^ observed. A strong magnet naturally

has more lines of force, and a stronger

current is induced in a wire moved through those lines.

SxerciBe 75.
CUBBSHT UBUCKD BT AH ELEGTBOMAGHBT.

Apparatus : An electroma^et, which oijiy consist of a coil of wire, D, Fig.
449, connected with a batteiy, B ; coil of wire, C; an iron core, which may
be a piece of iron, a nail, screw, bolt, or, better, a bundle of iron wires ; a
galvanoscope, O.

First move the coil D toward the coil C, and then away from it.
Insert the iron core, and repeat The coil without the iron acts as a
weak electromagnet ; with the iron inserted
it is a powerful magnet Study the direc-
tions of the currents in the two coils.

Case L — Record which way the marked
end of the galvanoscope needle moves when
currents enter the binding-post E or F.
Make a diagram in the note-book. Trace
the winding, and on the outline of D make
an arrow showing the direction of the cur-
rent in D, Bring C and D near together.

Record the swing of the galvanoscope needle. Trace the direction of
the induced currents and indicate by an arrow on C. Are the cur-
rents in the two coils in the same or in opposite directions? Mark
the poles formed at the faces of the coils by the currents. Draw
arrows passing through the coils to represent the direction of the lines
of force in them.

Case II. — Make another diagram, representing the conditions
when the coils are moved away from each other. Try the effect of
iron in each coil. A current in D has no effect on C, if the coils are

Fig. 449.

DYNAMOS AND MOTORS.

496

both at rest. On bringing them together a current is induced in C,
in the opposite direction to that in D, When the coils are separated,
the induced current has the same direction as the current in D, The
direction of the induced current is always such as to oppose the force
tending to move the coils. The work required to do this is mostly
converted into electrical energy.

Case III. — Move one end of / across
the face of C. When does the current
reverse? Intensify the effect by using
iron in both coils.

Case IV, — Move one edge of the coil
C, Fig. 450, past the end of /. Study the
direction of the induced current, with the
view of discovering at what point the cur-
rent reverses.

Case V. — Arrange the coils as in Case I. or II., and move a piece
of soft iron before /. Notice the induced current.

Fig. 450.

574. A Dynamo consists of an electromagnet (D, Fig. 450,
for instance), called the field mcfjgnet, and a coil (C) in which

the current is induced or gen-
erated, called the at^mcUure,
Either the field magnet or the
armature moves. In some dy-
namos, whether direct or alter-
nating current machines, the
armature revolves; in others,
the field magnet revolves ; in a
few alternate-current dynamos,
both the armature and the field
magnet are stationary, while a
mass of soft iron with projec-
tions revolves in front of the
poles of the field magnet. This
last class is illustrated in Case V. of Exercise 75 ; see also
Fig. 444, page 490.
Place a small magnet between the unlike poles of two large

Fig. 451.

496

PRINCIPLES OF PHYSICS.

magnets. Notice the direction of the lines of force (Fig. 451).
Lay paper over the magnets, sift on iron filings, and make a
drawing or photographic print of the lines of force. In what
direction does the small magnet try to turn?

M "&.

Fig. 452.

676. Dynamos and Motors. — Send a strong current through

the coil of a D'Arsonval galvanometer (Fig. 480, page 515).

It will turn and set itself so that the
axis of the magnet and coil are in
the same line.

Let D, Fig. 452, be either a per-
manent or an electromagnet; the
latter is shown in the figure. C is
a suspended coil, with or without
an iron core, /. Send the current
through the coils in such directions

as to make poles as indicated. The coil C tends to rotate

in the direction of the arrow, and

to take the position shown in Fig.

453, and to stay in that position.

Suppose, however, as is likely, the '

momentum of the coil carries it a

little beyond, and the current at the

same time is reversed in the coil C,

by changing its connections with the battery. Then the end

G, Fig. 454, becomes a north pole, and the repulsion between
the two north poles keeps the coil,
C, turning. If the current in C is
reversed every time the axes of the
two coils are in line, and if there
is sufficient momentum to carry the
moving coil, C, over the dead point,
there will be continuous rotation. A
similar coil, like Z>, on the other side

of the armature (7, having its south pole facing C, would assist

in making C revolve.

Fig. 453.

Fig. 454*

DYNAMOS AND MOTORS.

497

Exerdae 76.
8TUBT OF SIMPLE 8IEMEHS DTHAKO OB MOTOR.

Apparatus : A brass frame fastened to a steel shaft ; a coil of wire, C, Fig.
455, slipped in the frame, the ^ids connected with A and J?, which are
pieces of brass tubing insulated from the shaft by a tube of fibre or rubber ;
brushes, B^ and 2?^, which can be moved up and down ; an electromagnet
or a permanent magnet; a galvanosoope.

Move one brush up, and make it bear on E. Make the other brush
bear on ^ . In this way one brush is always electrically connected
with one end of the coil
C, and the other brush is
always connected with the
other end of the coil.
Hold the permanent mag-
net near the coil. Connect
the brushes with the gal-
vanoscope. Revolve the
frame slowly. The to-and-
fro trembling motion of the
needle indicates an alter-
nating current in the coil.

Make an outline sketch
of Fig. 455, and show in
what position the coil is
when the current reverses.
Slide the brush holders up
and down till the brushes
bear on the half-circle parts
of A and E. Hold the mag-
net pointing through the
centre of the coil. Revolve

Fig. 455.

the coil. The contact of one brush shifts from the half of A to
the half of E ; the other brush making the opposite change at the
same instant that the current reverses in the coil.

The current in the brushes and the wires connecting is always in
the same direction — a direct current. The half circles on which the
brushes bear form the commutator. The effects are most powerful
when there is a bundle of iron wires in the coil, C

498

PBiyCLPLES OF PHYSICS.

576. Series Dyiumia — Keplace the permanent magnet of
Fig. 455 with an electromagnet connected with a battery. In

a practical dynamo, a part or
the whole of the cnrrent gener-
ated in the armatnre, C, is sent
through the coil of the electro-
magnet, MJf, Fig. 456. Con-
nected as shown in the figure,
all the current generated passes
a few tnms around the electro-
magnet, 3/J/, and through the
lamp, L. The armature and the
electromagnet, or " field," as it
is more often called, are now
connected in series. Fig. 456
represents a series dynamo.

Rg. 456.

577. Series Motor. — Connect a battery in that part of the
circuit indicated by L, Fig. 456. The armature turns, and the
machine becomes a motor. Reverse the battery connection,
thus sending the current through the motor in the opposite
direction. The motor still revolves in the same direction as
before. Although this motor operates on an alternating cur-
rent, it is hardly a practical form, and the armature and field
magnets heat rapidly, unless made of wires or sheets of iron.

In place of the horseshoe form of electromagnet, MM, Fig.
456, use a coil similar to C as the field magnet. Insert an iron
core and present one end to the coil. An alternating current,
such as is furnished for lighting in many towns, drives the
motor well. The current should be run first through a 32
candle power lamp as a resistance. Using the single coil as
a field magnet, first present one face of it, and then the other,
to the armature. This reverses the polarity of the field, just
as it would be reversed by changing the connections of the
field: the motor runs in the opposite direction.

DYNAMOS AND MOTORS.

499

Put the permanent magnet in place, of the electromagnet.
Revolve the armature, and note the deflection of the galvano-
scope in circuit at L. Remove the galvanoscope, and substitute
a powerful battery connected in such a way as to send the cur-
rent in the same direction as that previously generated. The
rotation of the armature is in the opposite direction to what it
was when used as a dynamo.

578. The Method of connecting the Field Magnet in Shunt is
shown in Fig. 457. Suppose the current comes from the brush
jBg. It divides, a part passing through the lamp, L, and the
remainder passing through
the electromagnet coil. All
the current finally unites at
the brush Bi. This is a shunt
dynamo.

Replace Z/ by a battery or
other source of current. The
machine now is a sh^lnt motor.
Reverse the battery connec-
tions. The motor still turns
in the same direction. In
order to make a motor run
in the opposite direction to
that in which it has been run-
ning, the current must be reversed in either the field magnet
or the armature, but not in both.

Dynamos that are required to supply a current of constant
strength, as for series arc lamps, are usually series wound.
For most other purposes they are shunt wound, and then they
furnish current of nearly the same pressure or voltage, whether
they are working at full load or generating only a little cur-
rent. Motors for electric cars, automobiles, and elevators are
series wound. For other uses, they aie almost always shunt
wound.

Fig. 457.

600

PRINCIPLES OF PHYSICS.

Exercise 77.

LINES OF FOBGE IN THE ABMATUEE OF A DTNAMO OB MOTOB.

S N

Fig. 458.

Fig. 459.

Apparatus : Bar magnets ; iron filings ; iron washers.

Plot, by any of the methods of section 438, the lines of force be-
tween two magnets. Fig. 458. Place an iron washer between the

poles, as in Fig. 459. The lines of
force pass from the north pole of the
magnet into the ring, and thence
through the ring to the south pole
of the other magnet. There are very few lines of force that cross
the air space, A, since the path through the iron is the easier one.

Replace the washer by another, cut
into four parts, C, D, Ey and F, Fig.
460. Notice that the lines of force
from N divide. Some cross to C, then
become invisible because they are in
the iron, are visible as they leap the gap between C and D, and

enter D, and again as they pass from
D to S, Make a sketch of Fig. 460,
showing the path of the lines of force,
using heavy lines in air and dotted
lines where they pass through the iron.
The arrangement of Fig. 460 is not used in dynamos or motors. It
is given here to show what must be the path of the lines of force in
the iron washer of Fig. 459.

579. Principle of the Gramme Ring. — Consider
two electromagnets, AB and CD, Fig. 461. Repro-
duce the figure in the note-book. Suppose the
current enters by E and F and leaves by G and
H. Find, by Ampere's law, the north and south
ends of the magnets ; mark them in the diagram.
Show by arrows a few of the lines of force of
each magnet, paying special attention to the space
between the magnets.

.1^%E

Fig. 460.

Fig. 461.

DYNAMOS AND MOTORS.

501

In Fig. 462, magnets similarly wound are represented as
bent into a circle. They are sometimes called horseshoe
magnets, because of the resemblance in shape to a horse-
shoe. In the note-book make a diagram like
Fig. 462, mark the poles, and indicate the
lines of force, still considering that the cur-
rent enters by E and F.

The two horseshoe magnets
represented in Fig. 463 f orip a
continuous ring of iron. As
before, show what poles ap-
pear between E and F and
between G and H, Trace the paths of the
lines of force. Leaving the iron at E and F,
the lines pass through the air, and enter the
ring at G and H.

580. The Gramme Ring Armature. — This form of dynamo

armature, named after its inventor, consists of

an iron ring wound with insulated copper wire

(Fig. 464). Imagine the rim of a wagon wheel

wound with a continuous length of wire,

the beginning and end of the winding being

joined together. By connecting E and F and

G and H, Fig. 463, we have the same result as ^•«' '^^'^*

in Fig. 464. At any number of points .on
the rim, equally^ distant from each other,
scrape the insulation oif and solder on a
short copper wire, A, E, C, and D, Fig.
465, and connect each with a section of the
commutator. Though the figure shows
four sections, the number varies from two
to more than a hundred.

For convenience in explanation, the ring

is shown in Fig. 466 with the commutator segments arranged

Fig. 465.

502

PRINCIPLES OF PHYSICS.

JNT

in a circle of larger diameter
thau the ring. This is a pos-
sible method of construction.
In fact, in one type of dynamo,
the insulation was taken off the
outer face of the wire on the rim
of the ring, and the brushes,
Bi, B2, rested directly on the
wire of the armature.

Study Fig. 466. What poles
are formed at A and C, sup-
posing the current to enter at
brush Bi ? Which way will.

jsr

Fig. 466.

the armature revolve ? As the
armature revolves, the brush
Bi is no longer in contact with
A, but is in contact with Z>, as
in Fig. 467. Current enters the
winding at D, and there divid-
ing, one-half goes through the
wire on each side, and unites
and passes out at brush B2.
What poles are formed at D
and E ? Why does the arma-
ture continue to revolve?
Make a drawing showing the position of the armature after each
quarter of a revolution.

Exercise 78.

STUDT OF A OBAHME BIKG MAGHINS.

Fig. 467.

Apparatus : Battery, or hand dynamo ; compass ; iron filings ; Gramme ring
machine, I., Fig. 468, having an armature revolving on a vertical axis; the
field magnet rests on a sapport, and is removable ; the commatator is on
the under side of the armature ; the armature rests on a pointed bearing
— ^ '^ easily lifted off; the brush holder, B, revolves on the base of the

DYNAMOS AND MOTOES.

503

Baft ibat fliipports tlw armature, and is removable. L, Fig, 4118* shows the
armature and muguet; 11. sbowa tiie commutator sections on the under uide
of the armatare ; 111. Eifiows the ap]>aFatuji with Ih© armature removed.

Lift the armature, Aj oil:', and set it aside. Send a current through
he Held ttiagnet coil, C\ Lay a sheat of paper over it, and itudy the

■

Fig. 468 1.

iiiea of force with iron filings. Remove the field inagnett and re-
place the ill mature. Connect the brushes with a battery or hand
pynanio, and send a current through the armature. Mount a card
Dver the armature, just out of contact with it. Sprinklt! on iron
iilings. Study the liiiefl of force of the armature, Reoiember that
the armature is an ejectromaguet. Set the armature revolving. I>o
the lines of force api>ear to change much ?

504 PRINCIPLES OF PHYSICS.

Suppose a permanent magnet, NS, Fig. 469, were revolved about
A, what would be the appearance of iron filings on a sheet
^ of paper held above it ?

When the Gramme ring armature revolves, do the poles
revolve? As the model armature has but four commutator
sections, there is a slight shift of the poles when the
brushes slide from one segment to another. Remove the
Fi ^ 460 P^-P^r ^'"d filings and use a compass. Turn the armature
slowly; the pole of the armature shifts a little, but flies
back as soon as the brushes move from one segment to another.

Holding the compass near the armature, try moving the brushes,
first with the armature at rest, and then with it in rotation.

Replace the field magnet. Send current through it alone, discon-
necting the armature. Trace the lines of force with filings. Why
are there almost no lines of force in the space in the centre of the
iron ring of the armature ? (See Fig. 459, page 500.) Now change
the connections, so that the current passes through both the field and
armature. Set the brushes as in Fig. 466, page 502. Test the lines of
force, and compare with Fig. 451, page 495. Does the armature turn ?
The motion of the armature may be studied in two ways. First, it
may be studied by considering the attraction and repulsion of the
armature poles for the field magnet poles. The armature, as already
stated, is an electromagnet. The brushes are so placed that the poles
formed are between the poles of the field magnet, as in Fig. 451.
The armature rotates ; but before the south pole of the armature has
turned round so as to be opposite the north pole of the field magnet,
the commutator has also turned, the current enters at a new point,
and the pole shifts back again.

It should be borne in mind that the idea of poles is an artificial
one, and only imperfectly illustrates the conditions that exist.

Another way of studying the subject is to consider the lines of
force of the field magnet and the armature. Placing the brushes as
in Fig. 466, we find, when a current is sent through both armature
and field, that the lines of force are disturbed, as in Fig. 451. Lines
of force always tend to take the shortest path. See how many of them
go out from the north pole of the large magnet to the south pole of
the little magnet (which represents the armature magnet), then
through the little magnet and out of its north pole, and thence into
the south pole of the field magnet.

DYNAMOS AND MOTORS. 505

The lines of force act like stretched elastic bands, and urge the
armature to turn and furnish a shorter path to bridge across the
space between the north and south poles of the field magnets.

Remove the electromagnet, and place bar magnets with north poles
on one side of the armature, and south poles on the other side. Send
a current through the armature. Turn the brush holder around to
find the position where the armature revolves best. Connect the
armature with a galvanometer. Revolve the armature.

The Gramme ring armature is here studied in detail, because it is
easy to understand. In practical machines, however, some different
form of winding in the armature is frequently used.

581. Almost all Direct-current Machines, when the armature
is made to turn, furnish current, and are dynamos. The same
machines, supplied with a direct current from any source, re-
volve and furnish power, and are motors. The field magnets
of a dynamo or motor are preferably electromagnets instead of
permanent magnets, since the electromagnets are easily ten
times as powerful as any permanent magnets could be.

In starting dynamos having electromagnets for the field, the
current at first generated in the armature has very little force
(electromotive force), because the iron of the field magnets
retains very little magnetism. But the slight current generated
in the armature passes around the field magnet coils, and makes
the field magnet a little stronger. Since the field magnet is
stronger, the armature current becomes stronger. This building-
up process keeps on (taking several minutes in large machines)
till the iron is about as strong an electromagnet as it can be.
In very small dynamos this building-up process may not take
place at all unless the armature is run at an enormous speed.

582. Siemens Armature. — Fig. 470 represents a Gramme
ring armature between two poles of a field magnet. When the
armature is made to revolve, a current flows in the wires of the
armature. One way of stating the cause of the current is to
say that the wires have currents induced in them because

506

PRINCIPLES OF PHYSICS.

they cut the lines of force of the magnets ; but in studying the
lines of force in such an instrument" as this (see Fig. 459, page

500), we find that there are
practically no lines of force in
the air space inside the ring.
Therefore the parts of the wire
on the inside of the coil are of
B^ ^' no use, because they have no

p'g- 470. lines to cut. In some machines

these parts of the wire are cut out, and the wire A (Fig. 470)
is joined to A', A' is joined to B, B to B', and so on all around
the ring, and the hole in the ring is sometimes filled with iron.
By this arrangement there are not so many wires that are idle,
that is, that produce no current. Almost all large direct-cur-
rent machines use some modification of this method, and are
really a development of the simple Siemens machine of Exer-
cise 76, page 497.

Exercise 70.

PBINCIPLE OF THE INDUCTION COIL.

Apparatus : Galvanoscope ; coils of wire, A and B, Fig. 471 ; bundles of iron
wires; a battery; a current reverser. Coil A is in circuit with the
galvanoscope; D, the cell of a battery, is connected through the current
reverser, C, to the coil, B.

As in Exercise 74, determine the movement of the needle when the
current enters the marked binding-post of the galvanoscope, G, Fig.
471. Make a diagram of the apparatus. Complete the circuit in
the coil B. From the movement of
the galvanoscope needle, determine the
direction of the induced current in A,
How does its direction compare with
that of the current in 5 ? Record this
on the diagram in the note-book, by
large arrows on A and B,

Place iron in the centre of the coils, as
in Fig. 450, page 495, and repeat the ex- '^''' *^ ' *

periment. After completing the circuit, wait till the needle comes to
rest. Break the circuit. How does the direction of the induced

THE INDUCTION COIL. 507

current in A compare with that in 5 ? While the current is flowing
in jB, bring it up to and then take it away from A. Holding the
coils close together, make the current in B ; then break it. Making
the current in B has the same effect as bringing B (while the current
flows in it) up to -4.

583. Primary and Secondary Circuits. — A coil of wire, B,
Fig. 471, for instance, when no current is flowing in it, sets up
no lines of force. On completing the circuit with the battery
or other source of current, as the current begins to flow and
increases, some of the lines of force formed by the coil B pass
through A, In studying the dynamo (section 566, page 489),
it was found that current is generated, or induced, in a wire if
lines of force are made to sweep through, or cut, the coil. In
this experiment, by closing the battery circuit, lines of force
sweep through the coil A. On breaking the circuit, they fade
away, and in doing so cut the copper wire in the opposite di-
rection. Making the circuit or an increase of current in the
coil B, is like bringing a magnet up to A, Breaking the cir-
cuit is like pulling the magnet away. Coil B is called the
primary coil; coil A, the secondary. The two coils, with the
iron core, constitute an induction coil, or transformer.

684. The Induction Coll. — Coil B, Fig. 471, should be of low
resistance, wound with No. 18 to 26 wire. Insert a bundle
of wires through the two coils. Replace -4 by a coil made
of great length of No. 36 gauge wire. Connect the wires from
A with metal plates. Hold a metal plate in each hand. Make
and break the battery circuit. The arrangement of two coils,
one of many turns used as a secondary, another of few turns
used as a primary, is called an induction coil. Suppose the
number of turns or length of wire in coil A is one thousand
times as great as in J5. Then the induced current in A will
have about one thousand times the voltage of the battery, D,

The high voltage currents required to operate X-ray tubes
or to send a signal in wireless telegraphy are sometimes ob-

508 PRINCIPLES OF PHYSICS.

tained from induction coils. If the secondary coil has several
miles of wire, a spark several inches in length jumps from one
terminal, x, to the other, y. Fig. 471, every time the circuit of
the primary coil, B, is closed or opened. When used in this
way, the galvanoscope must be removed, or the induced current
will pass through that. A bell in the battery circuit acts well
as a circuit breaker.

585. Transformers or Converters. — Large and expensive cop-
per wires must be used to send large currents of low voltage
over long distances. To save expense in copper, alternating cur-
rents of 1000 to 30,000 volts are transmitted by comparatively
small conductors over distances up to fifty miles. Such high
voltages are unsafe to handle and would often burn through
and destroy the insulation of motors. These high voltage cur-
rents are transformed by induction coils into currents of less
volts but a greater number of amperes. Coil B, Fig. 471,
through which the high voltage currents pass, has many turns
of wire; coil A, a few turns. Induction coils used for this
purpose are called transformers or converters,

686. Electrochemical Series. — Zinc is generally used in pri-
mary batteries, because it is cheap, and gives a higher voltage
than other cheap metals, such as iron. But any two metals
can form a cell. The direction of current from simple cells
made of any two of the following may be tested : silver (coin),
platinum, magnesium, zinc, iron, copper, tin, antimony, alumi-
num, carbon, lead, nickel. Determine as in Exercise 74, page
487, by which wire the current enters the galvanoscope when
the marked end of the needle moves to the right.

Place any two of the above-named substances in a tumbler
of sulphuric acid (one part) and water (one hundred parts),
The galvanoscope is to be permanently connected with the
battery stand. Fig. 376, page 405, and the different strips
placed in turn in the acid and clamped to the connectors.

TBE INDUCTION COIL. 609

For each combination, make a diagram like Fig. 472. Note

the direction of movement of the needle and the direction of

the current. Put the name of the substance

on each strip (oj, y), and by arrows show the

direction of the current. Eemember that the

current leaves the cell by the pole that is not

consumed.

Make a table, arranging the metals in such pig. 472.

order that if a cell is made of any two, the
current will leave the cell by the metal that is higher up in
the column. For instance, the current leaves a cell of gold
and platinum by the wire attached to the gold. The table
therefore begins : Gold

Platinum

The farther apart two substances are in the table, the higher
the voltage given by the cell. Carbon and potassium produce
a current of high voltage, but potassium is expensive and
wastes rapidly by uniting with moisture.

Exercise 80.

THEBMO-ELECTBICITT.

Apparatus : Sensitive galvanoscope ; coils of German silver, iron, copper, and
aluminum wire.

Insert the coil of lowest resistance in the galvanoscope. As in
Exercise 74, page 487, find by which wire the current enters the
galvanoscope when the pointer moves toward your right. Twist
together the ends of the German silver and
copper wires with a pair of pliers. Make
connection with the galvanoscope by the ends,
A and B, Fig. 473. Heat one junction, /, by
a candle or Bunsen burner, and let the other
junction, K, remain cool. Next, heat K and
'*' cool /. What is the direction of the current

generated ? Draw Fig. 473 ; mark the hot junction, and by arrows
show the direction of the current.

Repeat the experiment, using a junction of iron and copper. In

510 PBIXCIPLES or PHT8IC8.

all czaes, before twudng the wires, which should be of abont the
same diameter, scrape them clean. Notice that in the case of a
coi^r-iron junction, as the temperature is raised, the corrent goes
first in one direction, and then, at a temperature a little below a
red heat, the direction of the current rererses. On cooling, the
of^iosite phenomenon takes place.

587. Ttaenno-electrical Comhiiiatioiis. — Various combinations
of the metals mentioned, and zinc, lead, and magnesium may
be tried. In general, the higher the difference of temperature
between the two junctions, K and J, the greater the voltage
produced. When one junction of two different metals is
heated higher than the other junction, a current of electricity
is always generated, except in the case of a few combinations,
like copper and iron, when there is a certain difference of tem-
perature between the hot and the cold junction. For common
metals, the greatest voltage for a difference of temperature of
one degree Centigrade between the hot and cold junction is
given by bismuth and antimony, and is about one ten-thou-
sandth of a volt These metals are brittle and are difficult to
solder together permanently. As the electromotive force of
one pair is small, a large number are connected in series.

588. Thermopile, or Thermogenerator. — S, Fig. 474, shows
a number of pairs having the terminals soldered so that they

g are connected in series. In the figure,

XAAAAAAi^ ^^^ heavy lines represent Grerman silver;

V V V y V V V the lighter lines, copper. The free ends,

Fig. -474. ji and B, are joined to wires leading to

a motor through which the current is to pass.

A more convenient form is shown in Fig.

475. Heat is applied at C, and the outer

terminals are cooled. This instrument is

called a thermopile, or thermogenerator. It is

convenient as a generator of small currents,

but rapidly deteriorates. As an instnmient Pig. 475.

THE INDUCTION COO, 511

for detecting slight differences in temperature, the th»in<^ile
is many times mare soisitiTe tiun any mercoiy thermom^er.
Even one junction of coffer and iron shows cm a galTanosoope,
especially if the deflections are indicated by a reflected spot of
light (section 592, page 514), and if the instrument is made
more sraisitiTe by a magnet to neutralise the earth^s field.
The warmth of the hand on one junction produces a noticeable
deflection.

CHAPTER XXXIV.

siaNALLiNa THBonan ooean gables.

589. Lines of Force in a Galvanometer. — A current passing
through a coil of wire (Fig. 476) sets up lines of force, some of
which, as shown by arrows, are parallel with the axis of the
coil. The direction of the lines depends op the direction of

current in the coil (see section 495,
page 429). A magnet, 3f, held
nearly in the position shown in the
figure, is forced to place itself paral-
lel with these lines of force, so that
Pi^ 475 they have a path straight through

the magnet. In the galvanoscope
(Fig. 416, page 459), if the coil runs north and south, the little
suspended magnet, or needle, as it is called, does not generally
set itself exactly in the axis of the coil, as Jf is shown in
Fig. 476, because the earth's lines of force pull the magnet in
a different direction. In all these cases the coil is fixed and
the magnet moves.

590. Floating Coil. — Wind a coil of fine wire. Fig. 477, in
twenty to forty turns large enough for a magnet to slip into.
Fasten the coil to a piece of wood or cork, and solder a copper
strip to one terminal and a zinc strip to the other. Float in
a jar of dilute sulphuric acid. Bring a magnet near. Set
the coil in various positions, and notice the effect of the
magnet on it.

The floating coil of wire acts like a magnet. In fact, it is
an electromagnet without the iron core. Replace the magnet

612

SIGNALLING THROUGH OCEAN CABLES. 513

by a lighter one, and float this on a cork. Set the magnet
parallel with the coil and keep the magnet from turning.
The coil turns till the magnet points through the centre of
the coil. Then replace as before,
and this time let both be free to
move. As might be expected,
both move. If a person in one
boat pushes another boat, both
boats move.

Galvanometers and galvano-
scopes, as generally constructed
to-day, belong to two classes, —
one in which the needle moves, ^'' ^^^'

the other in which the coil moves. The tangent galvanometer
and the galvanoscope described in section 460, page 406, and
section 531, page 459, have fixed coils. The magnet needles
are free to move.

591. The First Atlantic Cable, laid in 1859, consisted of a cop-
per core covered with a non-conductor of rubber. The current
passed through the copper core and returned through the earth
or water of the ocean. The cable acted like an immense Leyden
jar, or condenser of circular form. The copper inside the rubber
took the place of one tinfoil coating of the condenser, the water
surrounding the rubber acted as the other coating, and the rub-
ber took the place of the glass. When the circuit was closed,
the current at first was absorbed, just as any Leyden jar would
absorb it (section 611, page 526). Only after eight seconds
would the current be large enough to operate an electromagnet
sounder (section 558, page 483).

592. Instruments for receiving Cable Signals. — The mirror
galvanometer, invented by Lord Kelvin in 1859, made it possible
to send nearly twenty words a minute instead of one word in
ten minutes. This instrument consists of a sensitive galvano-

514 PRINCIPLES or PHYSICS.

scope of many thousand tunis of wire. The movement of the
needle is made evident by a spot of light reflected from a little
mirror attached to the needle or the needle support The gal-
vanoscope, Fig. 416, page 459, when a small mirror is fastened
to the needle support, becomes a mirror galvanometer. It then
is capable of detecting very slight currents and can be used
in the most delicate experiments. It could be used for cable
work if a coil of fine wire replaced the thick wire coil of the
instrument.

A few years later. Lord Kelvin invented a still more con-
venient form of galvanometer, which consists of a coil of wire,

C, Fig. 478, suspended between the

poles, N and 5, of a powerful

magnet, or set of magnets. The

current enters the coil by one of

the wires, A or J5, and leaves by the

other. For cable work, the coil is

often suspended by a silk thread

and the electrical connections are

made with spirals of fine wire. A

current on passing through the coil

pj ^^ J sets up lines of force ; that is, the

coil acts like an electromagnet (Fig.

451). This is attracted by the large magnets, and tries to set

itself in line with them, as in Fig. 479. On breaking the

current, C is no longer a magnet, and r— ■ i -.

the twist of the suspending wire turns ^ ' ^ *

the coil back into place, ready to be de- '*'

fleeted again when a current is sent through it. The coil turns

in the opposite direction as the current is reversed.

593. D^Arsonval Galvanometer. — The coil C, Fig. 478, while
showing the principle of the instrument, is too heavy for quick
working. Wind a coil of fine wire. Flatten it like O, Fig. 480.
Suspend it by a wire, A, several inches long, and, if possible, as

BlGNALLlllG TBROUOB OCEAN CABLES.

51£

riy 4NM

fine as Na 36. This is connected with one end of the coil. Then

other end of the coil is connected with another wire, B. I'lwn

a coirent through the coil, and hold a magnet

near it in different positions. Finally, arrange

two bar magnets, or a single horseshoe magnet,

as in Fig. 480. The form of coil shown, which

differs only in shape from that of Fig. 478, is

now used in cable instniments and also as a

galvanometer, called the jyArsonval Oalvanom-

eier. N and S are sometimes the poles of a

powerful horseshoe electromagnet. Either a

mirror or a pointer several inches long is attacluvi

to the npper part of the coil, to magnify it^

movement

In this later and more convenient form of in
strmnent for receiving cable signals, the Tfcortl
ing apparatos is a siphon, suspended by threailH and nMivml hy a
thread ^tened to it and to the coil. A, Fif<. 4HI, tn a dlult nt
fhin ink; £ is a fine glass tube. The ink \h Hpirttifl nui. n.1 /i.
on a strip of paf^er movctl hy ^'.hir.livvnrU.
The end, />, does not qiiit^^ r^nir.li r.hti [Hi\mv
The ink is ma/le f/* flow by janiuK l.h«
apparatus, and trsiuu-H a Htrai(/hn Uhh on
the paper as long as no sij/naU ai'h tuuit.
As the coil moves back and forth midnr
tiie inflnence of a current in one direction or the othitr, tli«
■i^on, B, swings to the right or to the l#:ft, thus traitinj?
a wavy line.

The siphon is made in the followincr way : Heat a Hmall i/Iiimm
tabc a few inches from one end : remove it from thit tiiutih, ;ind
quickly pull the hand.s rwo feet apart. .^eief:t a portion of the
smallest size. Take -rhis hy one ^nd. keepint^ it lionwmtal, or
at any angle, and hold a lighted matftii above the tube unnl it
aoftena and fails.

CHAPTER XXXV.
PEAOTIOAL APPU0ATI0N8 OF ELEOTEIOITY.

594. Heating by Resistance. — All metals and almost all
alloys have a high resistance at high temperatures. Com-
pounds have a low resistance at high temperatures. Striking
examples of this are glass, marble, and porcelain. At ordinary
temperatures they are of enormous resistance, and are practi-
cally insulators. At a red heat they become fair conductors.

The Nernst incandescent lamp is essentially a rod of glass
or porcelain, arranged like the wire A in Fig. 482, to which
conductors, B and O, are connected. By heating the rod its
resistance becomes reduced, and a moderate current of elec-
tricity keeps the rod at incandescence.

595. Electric Heating. — Connect a short piece of No. 30
platinum wire, A^ Fig. 482, with two pieces of No. 30 copper

wire, B and O. Join the copper wires with the
^ terminals of a battery. Slip the wires B and

"\T qT C nearer together, until A is heated red-hot.
\ /^ While the copper is warmed somewhat, the
tlil platinum wire is heated to a higher tempera-

Fig.482. t\xvQ, because it has more resistance than the

same length of copper wire.
A wire like A is sometimes used to explode powder for
blasting. The connecting-wires, B and (7, of large size, care-
fully insulated, are laid under water, and torpedoes are ex-
ploded when the circuit is completed, usually on land. The
wire A gets hot when the current flows, ignites some gun-
powder or other explosive, and the shock from this makes

616

PRACTICAL APPLICATIONS OF ELECTRICITY. 517

the mass of guncotton or dynamite explode. Guncotton and
dynamite are not exploded by setting fire to them.

Coils of iron, German silver, or other high resistance wire
are used for heating tools, for soldering-irons, and for warming
street cars. Though more expensive than heating by gas or
coal, this is usually more convenient ; no draft is needed for
an electric heater. But for purposes where the heat can be
confined easily — as, for instance, in an oven having non-
conducting sides — electric heating on a small scale is the
cheapest method.

596. Electric Welding. — In case current is obtainable from
a dynamo or storage battery, connect arc-light carbons with
the terminals, as in Fig. 483. Let the ends of «
the carbons touch lightly. Of course, one small
cell of a battery is insufficient. At E, the point
of contact between the carbons, considerable heat
is developed. Eeplace the carbons by pieces
of fuse wire or solder not more than an inch '''^ ^'
long. The points of contact can be so heated that the metal
softens and the two pieces fuse, or weld together.

In electric welding, in practice, large, powerful clamps, C
and K, Fig. 484, hold the rods, A and B,
firmly together. C and K are so large
that they are scarcely warmed by a cur-
rent that would melt A and B. The
heat, then, is principally developed in
the part of A and B between the clamps,
and espcially where A and B touch. As
Fig. 484. g^^^ ^ ^ welding heat is reached, the

ends of A and B soften and soon run together. The clamps
push the rods into one another and thicken the joint.

597. Current for Electric Welding. — For electric welding,
currents of many hundred amperes, at a pressure of a few volts,

518 PRINCIPLES OF PHYSICS.

are obtained from special induction coils, or transformers.
The primary winding, P, Fig. 485, consists of small wire of
many turns, according to the voltage supplied to the coil, AB.
The secondary winding, S, is a massive copper casting of one
turn. The pieces to be welded are care-
fully clamped to C and D. A bundle of
iron wires, or sheets, passes through the
centre of the coils, P and S, Other sheets
of iron (not shown in the figure) cover
the outside of the coils. The two coils,
with an iron core, form an induction coil, or transformer (see
Exercise 79, page 506). Let the primary winding, P, have 100
turns and be supplied with an alternating current of 500 volts.
A current of about 5 volts will tend to flow through the circuit, S.
Just how many amperes of current this pressure of 5 volts will
send through S will depend upon the resistance of S and the
work to be welded between C and D. For every ampere flow-
ing in the primary coil, P, there will be about 100 amperes in
the secondary coil, S,

598. The Electric Furnace, in its simplest form, consists of an
arc lamp surrounded by a substance that conducts heat poorly.
M and 3f, Fig. 486, are blocks of marble ; C and C are carbons,
which slide in grooves cut in the
marble. In the space. A, between - I ^ J

the carbons is
graphite crucible containing

substance to be heated ; or the Fig. 486.

substance, mixed with a little charcoal to make it a conductor
of electricity, is put directly into A. On passing a current,
either direct or alternating, heat is generated in the high resist-
ance at A, and, as this heat is confined by the non-conducting
walls of the furnace, the temperature becomes very high, metals
melt and boil away, charcoal is changed into graphite, and many
chemical compounds may be formed.

placed 'a small (jl) C U( C (jji)
3 containing the ^ I — ^^ I ^

PRACTICAL APPLICATIONS OF ELECTRICITY. 519

599. Chemical Compounds formed by the Electric Furnace. — A
mixture of charcoal, or coke, and lime produces calcium carbide
— a substance that on contact with water sets free acetylene
gas. From charcoal, or coke, and sand, a compound that has
been named carborundum is obtained. Surpassed in hardness
only by the diamond, it is used in making wheels for grinding.
Direct currents of electricity may be used in making calcium
carbide and carborundum, and must be used in processes where
a decomposing action is required. Aluminum is never found
in the earth as a metal. It is a part of many minerals, and
from some — emery, for instance — it is easily reduced by the
intense heat and decomposing action of the electric furnace ; a
direct current is used. Caustic soda and bleaching powder are
made in part by decomposing a solution of common salt.

600. Resistance of Connections. — A telegraph key (Fig. 487)
often fails to conduct a current across the points of contact at
A when the lever, or spring, L, is pressed

down. The figure shows the key open. ^ i^<^

Even if the spring is pressed hard down ^^ ~

Fig. 487.

by a weight and made to touch the head
of the screw, Ay the current from a bat-
tery sometimes does not flow across the contact. By pressing
much harder, or by scraping the surfaces, the resistance at the
point of contact is decreased, and a current can flow through
the key from C to D. Twisted joints and loosely made con-
nections often act in the same way. If, however, enough elec-
tromotive force is used and a momentary current, however
slight, is forced through the bad contacts, they at once stick
together, or cohere, and become and remain good conductors
until jarred or disturbed.

601. The Coherer. — Fig. 488 shows a glass tube, holding
chips, or filings, of some metal. Nickel, iron, silver, and many
others may be used. A and B are stout wires, which pass

620 PRINCIPLES OF PHYSICS.

through corks into the filings. The resistance, as measured
through the filings between A and B, may amount to several
^ . ^ thousand ohms. This resist-

) ^^z^py/f^lpii^m £f ance is reduced to a few ohms

lEE^ by sending a spark through

^'i-'*^^' the filings from A to B. Even

a very small spark from an induction coil, an electrical machine,
or from any other source, such as a fast-running belt, is suffi-
cient to make a line of filings between A and B stick together,
or cohere, and become a good conductor. The resistance is at
once increased by shaking or tapping the tube. The coherer,
as it is called. Fig. 488, invented by M. Branly, has rendered
possible the sending of signals over a long distance without
employing a wire connecting the sending and receiving in-
struments.

602. Wireless Telegraphy. — One or more cells of a battery,
E, Fig. 489, cannot send enough current through the tube of
filings, or (joherer, C, at first to make the bell,
S, ring. An extremely small spark made to
pass between A and B is sufficient to make the
filings cohere, and offer a good path for the
battery current ; the r^istance of C is lessened
and the battery easily operates a bell, telegraph
sounder, or galvanometer at S. Shake the
coherer, C, and the bell stops; why? If the p. ^gg

coherer, C, is within fifty or one hundred feet
of a sparking device, such as an induction coil or frictional
machine, at every discharge or flash the resistance of the
coherer, C, is lessened, and the battery rings the bell through
it, and the bell keeps ringing till the coherer is shaken up.

The transmitting instrument consists of a vertical wire sep-
arated by a small gap at T, Fig. 490, from another wire con-
nected through a sparking device — an induction coil, for
instance — with the ground, O. At every spark that jumps

PRACTICAL APPLICATIONS OF ELECTRICITY. 521

across the gap, T, electric waves pass out in all directions
from T, The strength of these waves is increased by run-
ning the wire, F, high into the air, and by making the gap
at T longer and by sending a powerful flash across it. The
electric waves travel in all directions
with the velocity of light, and, on reach-
ing the vertical wire, R, of the receiving
station, cause a minute current to pass
up and down the coherer, C. The resist-
ance of C is lessened, and the local
battery, E, causes the receiving instru-
ment, aS, to give a signal. Tapping on
C decoheres the filings and stops the
flow of current through S,

With sensitive instruments and verti-
cal wires one hundred or more feet
high, signals are sent more than fifty
miles. Although the electric waves
pass through brick walls and other
obstructions to the passage of light and air, yet for long-dis-
tance working the vertical wires are elevated above all obstruc-
tions. Any number of receiving instruments within range can
receive signals at the same time, and the signals from two
transmitting instruments become hopelessly confused unless
they are tuned to different rates (see section 409, page 366).
Some of the earlier systems of wireless telegraphy do not have
these defects, but they are more expensive, and have been
made to work only for a few miles.

The only difference between the spark at T that makes the
filings cohere and a lightning flash is one of amount. A dis-
charge of lightning may be many miles long, and the electric
waves sent out are powerful enough to cause more than a
minute spark at C. The vertical wire of the receiving station
acts as a lightning-rod. During a thunder storm, electric light
and telephone wires act the part of a receiving instrument.

Fig. 490.

622 PRINCIPLES OF PHYSICS.

They snap and spark every time there is a powerful lightning
discharge, even though it be several miles away. In this case
there is no need of a coherer. The generating or transmitting
apparatus is so powerful that the current set up in the receiv-
ing apparatus, Ry Fig. 490, no longer has to pass through a
coherer, but jumps from A to B with a loud report, and the
discharge between those points is often dangerous.

603. Model of Wireless Telegraph. — Signals can be sent
through a wall by using a small induction coil or frictional
machine, the terminals of which are connected with T and G,
Fig. 490. Run a wire as high as possible in the room. Connect
the lower end of V with one pole of an electrical machine or with
the secondary coil of an induction coil. With the other pole con-
nect a wire, O, leading to the floor. Make a coherer by filling
a glass tube i% of an inch in diameter and one inch long with
iron filings. Pare down pieces of cork to fit the ends of the
tube, and pass copper wires through the corks. Lay the
coherer on its side. Erect a vertical wire and connect it with one
of the coherer wires A, Fig. 490 ; connect the other copper wire
with the floor or ground, Oi. Connect A and B with a battery
in circuit with the galvanoscope,^^, made more sensitive, if neces-
sary, by using a compensating magnet (section 532, page 460).
When a spark is made to pass at T, a deflection of the galvano-
scope shows the reduction in resistance of the coherer, C Tap
the coherer, and the needle of the galvanoscope swings back.

604. Geissler Vacuum Tubes. — Air insulates better than a
partial vacuum. A and B, Fig. 491, are platinum wires fused

in a closed glass tube. The wire by

-^ ( ^ S which the current enters is called

^1 the anode; the other wire, by which

To pump ^Yie current leaves, is called the

'** kathode. As the air is gradually

exhausted through E, which is attached to a pump, a vacuum

is obtained, which contains one-fifth to one five-hundredth of

PRACTICAL APPLICATIONS OF ELECTRICITY. 523

the original air. This rarefied air is a much better conductor
than either air at ordinary atmospheric pressure or a perfect
vacuum. A small induction coil can send a discharge through
the rarefied gas. A f-inch spark in air under increased air
pressure, as in a mixture of compressed air and gas in a gas
engine, gives only a very short spark. The apparatus shown in
Fig. 491 is called a Geissler tvbe. It may be filled with any
gas, and this becomes luminous on the passage of a discharge
through the tube. Attempts have been made to use these
tubes for lighting. Crookes carried the exhaustion further.

605. Crookes Tubes and Rontgen Rays. — It was found that dark
spaces appeared and filled the whole tube, while some kinds of
minerals, if placed in the tube, became luminous. The rays,
if we may call them rays, that cause these phenomena appear
to come from the kathode, and are called kathode rays. If the
exhaustion be carried still further, using a mercury pump, as is
always necessary in producing a good vacuum, so that only
one or two millionths of the original air remain in the tube, the
resistance rises somewhat and a discharge then causes the glass
to have a golden fluorescence. Rays are now sent out from the
tube, which have the property of passing through substances
that light cannot traverse. Wood, paper, muscles, and flesh of
the human body are fairly transparent to these rays ; bone is
less so; and solids like iron and lead stop them almost entirely.
These rays, acting in a manner hitherto unknown, were called
X-rays by their discoverer, Rontgen, meaning unknown rays,
X being the letter often employed in algebra to represent an
unknown quantity. These rays affect photographic paper,
making shadow pictures in much the same way that a lamp
makes shadow pictures of iron filings (section 438, page 388).
As these X-rays pass readily through paper and cardboard, the
sensitive paper or plates on which the pictures are to be made
are kept wrapped in paper during exposure to the X-rays, to
keep them from being affected by ordinary light

624 PRINCIPLES OF PHYSICS.

606. Fluorescent Screens. — Some chemicals as long as the
X-rays fall upon them are made luminous. The best for this
purpose are calcium tungstate and platinocyanide of barium.
If the hand is held between a card coated with a sensitive
substance and a tube from which X-rays are coming, the
shadow outline of the hand will be seen, the bones appearing
darker than the flesh ; an embedded iron needle or lead bullet
will cast an absolutely black shadow. If a sensitive photo-
graphic plate be substituted for the chemically coated screen,
a shadow picture is formed, which may be seen by soaking the
plate afterward in a developer. In a Crookes tube (Fig. 491),
the terminals A and B are made in va'rious shapes, often
curved. While the exhaustion must be very high to enable
the rays to be produced, still, if carried too far, they are no
longer formed, since a nearly perfect vacuum is a poor con-
ductor of electricity.

607. Surface Electricity. — In Greece, several hundred years
B.C., and perhaps earlier, it was known that a piece of amber,
when rubbed, attracted bits of leaves or straw. The Greek name
for amber is electron, from which the word electricity was
formed. Almost any non-conducting substance, — sealing-
wax, glass, ebonite, etc., — if rubbed with flannel, silk, or
catskin, acts just as amber does. When one of these sub-
stances, sealing-wax, for example, is rubbed with flannel,
both the sealing-wax and the flannel have this power of attrac-
tion. Conductors of electricity, such as copper, iron, etc., do
not have this power of attraction unless they are held in an
insulating handle of some sort, such as rubber, sealing-wax, or
glass ; for when rubbed with silk or flannel, the electricity which
is produced on them escapes as fast as it is generated. This
will happen in the case of insulators, also, if the surface is not
clean and dry. In damp weather a film of moisture condenses
on the surface and acts as a conductor. Therefore experiments
in frictional or static electricity succeed best in dry weather,

PRACTICAL APPLICATIONS OF ELECTRICITY. 625

and are often difficult to perform. The subject of frictional
electricity has become relatively of less importance since
batteries, dynamos, motors, electromagnets, and their applica-
tions have, in the last one hundred years, completely changed
and improved our ways of living.

608. The Practical Applications of Frictional or Static Elec-
tricity, as we call the force that glass, when rubbed, has of
attracting paper, etc., are comparatively few. Stand under a
belt that is running quickly, and notice how silk, feathers, or
one's hair is attracted. Hold the hand near the belt. A charge
of electricity collects on the body till the voltage is high enough,
.30,000 to 40,000 volts, perhaps, and in escaping with a rush
causes a spark. This spark is caused, possibly, by heating the
air. The spark will set fire to gunpowder or coal gas. In cotton
mills, during the spinning, the cotton becomes electrified, the
fibres stand apart, and do not lie well together, and twist into a
thread. In England this difficulty is not met with so often ;
for there the air is uniformly moist and the charge of electricity
escapes. In some parts of the United States the air is so dry
that sufficient moisture is added by allowing steam to escape*

609. Voltage of Surface Electricity. — The charge of electricity
exists only on the surface. A hollow rod of glass or vulcanite
retains a charge exactly as if it were solid. The amount of
electricity is small, but its electromotive force is large ; whereas,
a galvanic cell gives a relatively large current of electricity at
a low electromotive force. In other words, frictional or surface
electricity has an enormous voltage, many thousand volts, but
the current it can furnish is small.

610. Kinds of Electric Charge. — There are apparently two
kinds of electric charge. Glass rubbed with silk repels another
piece of glass that has been rubbed with silk. Hang a silk
thread, S, Fig. 492, from a support. A stirrup of wire at the
lower end of the thread carries a rod of glass, R, that has

526 PRINCIPLES OF PHYSICS.

been electrified by rubbing with silk. Bring near R another
piece of glass that has been rubbed with silk.
\s Two pieces of sealing-wax or rubber rubbed

^ with flannel, repel each other. But the glass
attracts the wax or the rubber. The glass is
said to be charged with positive electricity, the

«==^4^

Fig. 493.

Fig. 492. gjiij ^^^jj negative. Like electricities repel;

unlike attract. Cut a piece of tissue paper nearly in two
(Fig. 493), and lay it on the table ;
rub it briskly. Hold it up by the ^
end A, The free ends repel one
another, and fly apart. It is im-
possible to produce electricity of one kind without at the
same time producing an equal amount of the opposite kind;
for example, when the glass receives a positive charge, the silk
used in rubbing the glass receives a negative charge.

The discharge that takes place when a well-rubbed ebonite
plate is lifted from the table is minute (it can be seen in a

darkened room), because only a small

/ amount of electricity can be condensed

I (^i^s8 I on its surface. If a plate of glass or

p. ^04 \3 vulcanite of large size be covered on

both sides with a conductor, tinfoil, for
instance, nearly to the edge (Fig. 494), it can be charged with
a larger amount of electricity. Positive electricity will be con-
densed on one coating, negative on the other. The condenser
may be discharged by connecting A and B, Fig. 494. A spark
may be seen leaping across the space before the wire completely
joins A and B,

611. Leyden Jar. — The older form of condenser consisted of
a bottle coated inside and outside halfway up with tinfoil. It
was called a Leyden jar, from the town in Holland where it was
discovered. The inner coating is connected with a wire that
passes out through the cover. When overcharged, a discharge

PRACTICAL APPLICATIONS OF ELECTRICITY. 627

takes place either from the wire to the outer coating, or directly
from the inner to the outer coating, piercing the glass. A
lightning stroke is a similar, but much more powerful, discharge.
The clouds or particles of moisture in the air act as the upper
layer of tinfoil in Fig. 494, the earth answers as the other
coating, and the fairly dry air below the clouds acts like the
glass. When a condenser, like any reservoir, is overfilled or
overcharged, the pressure increases till an escape or discharge
takes place. A lightning stroke is analogous to a discharge
through the glass.

The discharge of an electrified body, such as a belt, a piece
of vulcanite, a Leyden jar, or other form of condenser, if allowed
to pass through a coil of wire, permanently magnetizes a needle
placed in the coil. This current or discharge, however, differs
principally from the current of a galvanic cell in that it is very
small and lasts only for a very short time.

612. Electroscope. — The parts of the piece of paper in Fig.
493, when charged, tend to fly apart, each piece being charged
with the same kind of electricity, and so repelling one another.
A modification of this instrument, making it more
sensitive for detecting a charge of electricity, is
called an electroscope. It consists of two leaves
of gold or aluminum foil, S, Fig. 495, hanging
from a wire which passes through W, the cover
of a glass bottle or jar, BB, If the ball, N, be **

touched with a glass rod that has been rubbed with flannel or
catskin, a part of the positive electricity on the glass rod goes
to the leaves, and they repel one another and separate. If any
positive charge of electricity be brought near JV, the leaves go
wider apart ; a negative charge makes them fall together ; but,
if the leaves are uncharged, a negative charge will make them
separate. If, now, the copper terminals of a galvanic cell be
touched to N, the leaves separate, showing that the copper pole
of the cell gives off positive electricity. The zinc pole gives

528 PRINCIPLES OF PHYSICS.

off negative electricity, and would canse the leaves to come
together. Since several hundred volts are required to cause
an appreciable separation of the leaves, one way of trying the
experiment would be to use a battery of several hundred cells
joined in a series.

613. Artificial Lightning from a Battery. — All the experi-
ments hitherto performed with static machines or induction
coils have been repeated on a large scale, using the storage
battery of twenty thousand cells (section 548, page 474), which
gives in series an electromotive force of forty thousand volts.
The so-called frictional electricity exists only on the surface
of bodies ; it escapes at once from conducting materials, unless
they are insulated. The discharge of an electrified body is
usually a comparatively small amount of current for a mil-
lionth or less part of a second. Using the batteiy just
mentioned to charge condensers, and then connecting these
condensers in series, discharges of a million volts or more are
made to imitate lightning.

614. Electric Car Motors. — The armature of an electric
motor, in order to do much work, must turn round fast. In
this it may be compared with a light, active person who can carry
or move a small load only, but by the quickness with which he
works accomplishes a great deal. The number of revolutions
of the armature per minute is as high as two thousand for a
one horse power motor, and is often one thousand or two thou-
sand for a ten or fifteen horse power. Compared with this
speed, the number of revolutions per minute of the axle of an
electric car moving eight or ten miles an hour is small, being
between one hundred and two hundred per minute. The
motor, therefore, is belted down, or geared down, to the wheel.

A, Fig. 496, is the pulley on the armature of the motor.
The belt passes around A and a pulley on the wheel axle, C.
This pulley on C is somewhat smaller than the car wheel, in

PRACTICAL APPLICATIONS OF ELECTRICITY. 529

order that its rim may not strike the track or surface of the
road. Assume that the diameters of the pulleys are as one to
five. Then A makes five times as
many revolutions as C But the power
is multiplied five times, and the force
that turns C is five times as great as
if the motor were directly on the axle
of the car.

In the early days of the electric car,
belts were used, but were abandoned

for gears. Both A and C are toothed like the gears of a
wringer or eggbeater. A is then placed near C, so that the
teeth of A fit into the teeth of C In high speed cars the
diameter of C is about three times that of A,

Rail

Fig. 496.

615. Model of an Electric Car. — Most electric cars in use

to-day gear directly from the

^^^^^^ armature shaft to the main axle

of the car, as in Fig. 496. The
diagram shown in Fig. 497, of
which Fig. 498, page 530, is
the completed model, shows
the principle of a "double re-
duction " used in the earlier
form of electric cars, in which
the ratio of the gearing was
• such that the car wheel made
one revolution to twelve of the
motor. A block of wood, W, Fig. 497, is held by screws to
the body of the car. The motor is fastened to one side of W,
and the truck to the other. Wind soft white string once or
twice around the grooves in A and in the large groove of B,
Tie the knot firmly. Wind another string twice around the
small axle of B and the large groove in C.

Turn A with the fingers, trying to find how many turns are

Rail

Fig. 497. ^«»'

530

PRINCIPLES OF PHT8IC8.

needed to make B go round once. How many turns must B
make in order that C may revolve once ? Finally, how many

turns must be made
by A while C revolves
once ? What is the
loss in speed and the
gain in power ?

Connect a large bat-
tery or a hand dynamo
with the binding-posts,
X and y, of the mo-
tor directly by flexible
wires, or use the ar-
rangement of Fig. 497.
The wheels of the cars
on one side run on the
edge of a brass strip.
The current enters
from the overhead wire, runs down the trolley to y, passes
through the armature, and back to x. Then it goes around
the field magnet and enters the metal frame of the car, and
thence, as shown by the dotted lines, passes to the rail and
through that back to the generating station. This car runs
only in one direction, unless the current is reversed in either
the field or the armature, and not in both at the same time.

Fig 496.

616. Electric Power. — If a fan motor on a 110-volt circuit
uses .6 ampere of current, the electrical energy is said to be
110 X .6, or ^^ volt-amperes. This represents electrical work.
In honor of James Watt (section 277, page 252), volts x
amperes are called watts. If a battery of cells sends a current
of 3 amperes at 5 volts pressure through a lamp, then 5 x 3 = 15
watts are consumed in the lamp. To find the number of watts,
multiply volts by amperes.

APPENDIX.

Sines, — ABC (Fig. 499^ is a right-angled triangle, having a right
angle at C. A person standing in the cor-
ner A could touch the sides b and c,
but the side a would be in front of him,
or opposite. The longest side, c, which
is called the hypothenuse, is opposite the
angle C. AB might be called a slide, or
slant. Keeping c always of the same length,
to make the slide steeper, that is, to in-
crease the angle Aj the side a must be made
longer. If a is divided by c, we have the
sine of angle A. Written in shorter form,

sine^ = 2PP2sitejide.
hypothenuse

This is to be read as **sine of A equals the opposite side

divided by the hypothenuse.'' As the angle A grows larger

(Fig. 600), a is more nearly equal to c, and when A is 90°,

— ^-— a will equal c. Then, as a quantity divided by an equal

A o C quantity gives 1, sine 90 = 1. The

Fig. 500. abbreviation for sine is «in, though the

pronunciation is unchanged.

Let us find the sin 45°. Fold over the edge DE
(Fig. 601) of the comer of a sheet of paper, starting
the crease at the corner E, and
make DE fall on EF. Lay the
angle OEF on a sheet of paper,
and mark the angle of 45°. *^'«- ^°'-

Make the lower edge of a sheet of paper touch EF
(Fig. 502), and draw along the right-hand edge, making

a perpendicular from G to F. Sin

Fig. 502.

E (46°)= ^.
^ ^ EG

Measure GF and EG and divide, reducing to a decimal.
The result is the sine of 45°.

Sine of 30° and 60°. — Fold over the edge DE, making the crease EG
(Fig. 503). Let DE fold over EH, Fold over again, making EH the
crease. If the three folds are not of the same size,
make another trial. One fold gives 30° ; two folds, 60°.
Draw right triangles, one having 30° at A, and another
having 60° at A, and find the sines of 30° and 60°.

In the same way, since 22 i° is half of 45°, and 16°
is half of 30°, the sine of those angles may be easily
found by drawing. Compare the results with a table
of sines. The table is not made by drawing, but by
certain computations that give as exact results as are
desired.

631

Fig. 503.

632

PRINCIPLES OF PHYSICS.

Referring to Fig. 499 and the tables on p. 537, study the following
problems, which are solved by substituting in the formula sin ^ = - .

1. ^ = 30° ; a = 60 ; c = what ?

.600 = - c = -^ c = m
c .500

2. ^ = 70° ; c = 20 ; a = what ? 4. Z^ = 40°;a = 90;c= what ?

3. a = 30;c = 50;findangleA 5. Z^ = 80° ; o = 50 ; find c.

6. lu a right-angled triangle the hypothenuse squared equals the sum
of the squares of the other two sides, or c^ = a^ -\- b^.

If a = 3, 6 = 4 ; find c

c2 = 92 + 42 c2 = 25 c = 5

7. If a = 9, 6= 15, c = what ?

The tangent of an angle is the opposite side divided by the adjacent
a

side ; in Fig. 499, tan ^ =

8. Find by drawing the tangent of 30° ; 45°; 60° ; 22i° ; 15°.

9. Z^ = 40° ; a = 12 ; 6 = what ?

tan 40° = — . Look up tan 40° on p. 537. Substitute, and find b.
b

10. Z^ = 80°; 6 = 220; a = ?

11. a = 3 ; 6 = 4; tan A = ? ZA = ? How can the work be proved ?

Plotting — In geography, points on
the earth's surface are located, if
two measurements are known : 1st,
the distance east from a prime me-
ridian, which runs north and south ;
2d, the distance north or south from the
equator.

Draw lines to represent the meridian
and the equator (Fig. 504), and locate
the position of a ship, north latitude 4,
east longitude 2.

Measure four equal divisions up from
O, where the lines cross ; also measure
off two equal divisions to the right from
O. North latitude 4 means that the
ship is anywhere 4° north of the equator.

The ship may be anywhere on the line AB^ Fig. 505. East longitude 2

means that the ship is 2° east of the meridian, or

anywhere on the line CD, for any part of that line

is 2° east. However, since the ship is in north

latitude 4 and east longitude 2 at the same instant,

it must be on both AB and (7Z>, and so must be at

their intersection, E.

Ey Fig. 605, is the position of the ship. The

divisions measured on the meridian and on the

equator may be of any length, long or short ; but

all the divisions are usually of the same size. f\g sos.

West 1
North 1

Equator

East
North

. West I
Sov.th t

East
South

Fig 504.

APPENDIX.

583

1. Locate the position of : south latitude 2 and east longitude 3 ; north
lat. 20, west long. 4 ; south lat. 5, west long. 4.

2. Locate the position of a vessel : Monday, north lat. 1, east long. 2
Tuesday, north lat. 2, east long. 4 ; Wednesday, north lat. 2, east long. 6
Thursday, north lat. 3, east long. 6 ; Friday, north lat. 4, east long. 4
Saturday, north lat. 6, east long. 2. Connect by a line the points repre-
senting the position of the vessel for each day in the week. This line
represents roughly the path of the vessel.

In physics and mathematics the location of points and lines is done in
a manner similar to that used in surveying and navigation. It is more
convenient, in many cases, to call distance to the
right of the meridian, plus x distance, and dis-
tance to the left, minus x. For example, if we
say a; = 2, the position is anywhere on the dotted
line in Fig. 506, for the line is 2 to the right or
east of the meridian. This is exactly the same as
saying that a ship is in east longitude 2. If noth-
ing is known of its latitude, — its distance north
or south of the equator, — in order to find that
ship we must search the whole length of the dotted
line, for the ship may be located anywhere on it.
Suppose that in some problem in physics or mathe-
matics where x = 2, y = 4. Call distance to the

north plus y. Then the point is somewhere on
- the dotted line, Fig. 507 ; since at the same time
X = 2, the point is somewhere on the dotted
line, Fig. 506 ; put these two dotted lines on the
same diagram, which will look like Fig. 505, E
being the point where x = 2, and y = 4.

In locating, or " plotting," the position of points
in the following problems, if necessary, translate
Plus values for x into east longitude.
Minus values for x into west longitude,
Plus values for y into north latitude,
Minus values for y into south latitude,
and then locate the point as you would the position of a ship.
Locate the following points : —

1. x = 3; y = 2.

2. X = 1 ; y = 4.

Notice that when x = 0, the point has distance neither east nor west,
and must therefore be on the meridian line.

Fig. 506.

Fig. 507.

x = 2; y=-4.
x = -3; y=-2.

The Picture of an Equation. — Such expressions as x -f y =* 2, y' = x,
x^ — y* = 1, X -H 2y = 2, occur on almost every page of algebra. One of
the ways in which they can be pictured out is as follows : —

Take x + y = 2. This means that the sum of two quantities is always 2.
X may have any value, plus or minus, but the value that y has at the
same time must be such as to make the sum 2. For instance, suppose
X = 0, then y is large enough so that when added to zero, the sum equals 2.
Suppose X = 4. Substitute 4 for x in the equation x -f y = 2.

534

PRINCIPLES OF PHYSICS.

Putting 4 in place of x, we have,

Put 4 on the other side of the equation :

-1

-2

— i

-s

JLongitude

Latitude

Fig 508.

■I-"

4 + y = 2

y = 2~4
y = -2

Thus, when a;=4, y= —2. Add 4 and — 2 and see
if the sum is 2.

Find what values correspond to the following
values of a; : 1, 2, 3, 4, - 1, - 2, - 3, - 4. Ar-
range the corresponding values in lines, as in Fig.
608.

To get the ** picture," or graphical representa-
tion of this line, proceed
exactly as in locating the
course of a ship. Draw
two lines (Fig. 609) in the
note-hook at right angles.
Lay off equal distances,

of any convenient size. Rub out x and y at the -*-*

top of Fig. 608, and write longitude in place of «,

and latitude in place of y. A few of the points

are located in Fig. 609. Locate all the points

given in Fig. 608. They will fall in a straight

line. Any number of values for x may be used,

and Fig. 609 made longer. A few points, however. Fig. 509.

often show the general way the line picture of

the equation looks. A line drawn through the points is a picture of

the line represented by the equation.

Plot — that is, find the picture of — some equations like the following r —

1. x-y = 1. 3. X -I- 4 y = 4.

2. x-\-y = S, 4. 2x-y=-4.

The square of 3 is 9 ; the square of -3 is also 9. Keeping this in mind,
plot x^ = y. Substituting values for x, those values must be squared
before replacing x^. Let x = 2 ; then x^ = 4. Putting 4 in place of x*^,
4 = y. Therefore, when x = 2, y = 4.

Find the values for y, when x = 0; 1; 3; 4; J; -}; etc.; and plot the
curve, which is a parabola.

Plot: 1. x2=-y. 3. y^--x.

2. x2 = y -H 2. 4. xy = 1.

Boyle's Law is pressure x volume = a constant. Call this constant 1 ;
then pv = 1. To get the picture of this is to call p = x and v = y. There-
fore plot xy = 1.

5. x2 - y2 _ 1.

/ / F

Call F= 1, to simplify the work, and let/= x and/ = y. Then,

X y

This is the equation for conjugate foci.

In physics and mechanics, other letters than x and y are nearly always
used. In plotting the variations of pressure of steam (Exercise 26) due to

APPENDIX, 535

changes of temperature, the values for either temperature or pressure may
be called x values. The number of divisions represents 1 cm. of pressure
and 1° of temperature, which are often not the same. To make the curve
as rounded as possible, — that is, more like a part of a circle or a parabola
than like a straight line, — choose, if necessary, two or three or any number
of divisions on the vertical axis to represent 1 cm., while one division or
less on the horizontal axis represents 1° change of temperature. In the
experiment just mentioned, if observations are made from 20° C. to 106°,
a very useful curve is obtained by letting one division stand for 1 cm.
and 1°.

Photographic Prints of Magnetic Lines of Force.— "Blue paper*'
can be purchased, or may be prepared as follows : Put one ounce of red
prussiate of potash and six ounces of water in one bottle ; in another
bottle put one ounce of ammonio-citrate of iron and six ounces of water.
These solutions will keep. See that the substances have completely
dissolved. Mix equal quantities of the solutions in a rubber or porcelain
dish, and dip a piece of unsized white paper (a good quality of book
paper will do) into the mixture, or apply the mixture with a bit of cotton
wool or a brush, giving the paper a thorough coat. Pin the paper in a
box or closet, away from the light. The next day the paper may be used.

Lay the magnet (or magnets) on a large book or board. Place the
paper over it, and sprinkle on iron filings, shaking them through a piece
of cheese cloth. Then, without disturbing either the filings or the magnet,
set the whole in sunlight for three minutes. Pour off the filings, and
wash the paper in water. Where the light struck, the paper is blue, but
the shadows made by the filings will wash white. A few arrow-heads
drawn in ink will show the general direction of the lines of force.

Prints of lines of force can be obtained in a few minutes by the use of
Velox paper in a darkened room. Lay a sheet of the paper, with the
film side up, on the magnet. Put iron filings previously sifted on a piece
of cheese cloth. Gather up the ends, making a bag. Hold it a few inches
above the paper, and gently shake out a thin coating of filings. Tap the
paper slightly. The filings arrange themselves in the lines of force. Hold
a gas flame or incandescent lamp twelve inches above the paper for half a
minute to one and a half minutes. Turn out the light, dust off the filings,
and immerse the paper in a dish of developing solution. The picture
should develop in less than a minute, and is then kept from five to ten
minutes in a fixing solution of one pound hyposulphite of soda dissolved
in water. Then wash the print fifteen minutes in running water. The
developing and fixing solutions may be kept and used for a large number
of prints. These are really negatives, the outlines of the filings appearing
as white spots. If it is desired to print a number of positives, make the
negative translucent by applying to the back of it a Uttle oil or melted
paraffine wax.

Grinding or Roughening the Surface of Glass. — Put a little carbo-
rundum powder on the surface of the glass to be roughened. Moisten
with a drop of water. Lay on a fragment of a sheet of glass and rub,
moistening when necessary.

Wax for Fiber Suspensions. — Heat dry flake shellac by letting a
Bunsen flame play down on it. Roll it into a stick form.

536

PRINCIPLES OF PHYSICS.

Marking on Glass. — A cross pencil if moved slowly leaves a broad
mark on glass. By moistening the surface of the glass, a copying pencil
(red and blue are useful colors) makes a line mark. Ground glass sur-
faces need not be moistened. £. Faber^s Nos. 725 and 726 and the Sun 823
copying pencil are suitable.

Critical Angle. — In Exercise 40, Fig. 267, the
distances LM and JilF were measured. Make
a diagram like Fig. 510. LM=FS; mark the
value on FS. MF = LS. Mark the value on LS.
The tangent of an angle equals the opposite
side divided by the adjacent side. To find the
tangent of the angle LFS, divide the opposite
side LS by the adjacent side FS. Look in the
table of tangents and find the angle.

Galvanoscope Needle. — The galvanoscope, Fig. 416, has a coil of wire
in front of which is suspended a needle. In its
simplest form, the bar magnet, N, Fig. 611, is
removed.

The instrument is so placed that the coil is
north and south. The cross piece on the needle
support, Fig. 416, is a pointer, and serves to pre-
vent the needle from turning completely around
and twisting the fibre. The needle support
extends down into a well. If the instrument
is used as a mirror galvanometer, sperm oil may
be placed in the well to damp the vibrations.
The coils are removable without disturbing the
needle.

Figure 511 shows how a magnet is placed to
neutralize partly the earth's field and make the
galvanoscope more sensitive. Let the pupil record
the rate of swing before and after bringing the
bar magnet, Ny near. The instrument is very
sensitive if the needle takes 10 seconds for a
vibration.

Exercise.
EBRORS IN A SFBINO BALANCE.

Apparatus: 250-gram balance; set of weights.

Attach in turn weights of 50 g., 100 g., 150 g., etc. Record the weights
applied and the readings of the balance. Find the correction that must
be added to each reading of the balance to give the true reading. For
instance, if a balance having 200 g. attached reads 210 g., then — 10 must
be added to any reading near 200 g. Plot on coordinate paper, letting
distances to the right represent weights applied to the balance ; distances
above, plus corrections ; distances below, minus corrections. It should
be noticed that in a horizontal plane the weight of the hook does not pull
on the spring. Lay the balance horizontally with the hook hanging freely.
Tap the balance. Notice the reading of the pointer. This reading should
be added to all readings taken with the balance in a horizontal position.

Fig 511.

APPENDIX

537

Values of Sines and Tangents.

When the angle is more than 45°, look in the right-hand columns and
read from the bottom up.

Angle

8kne

Tttntjt^ijl

0°

0.000

1.000

90=*

0.017

57.20

1.000

0,035

0.035

28.04

0.090

0.052

10.08

0.999

0.070

14.30

0.998

0.087

IL43

0.9^16

0.105

0,106

9.514

0.996

0.122

0.123

8.144

0.993

0.139

0.141 '

7.115

0.i}90

0.15ti

0.168

6.314

0.988

10^

0.174

0.170

5.071

0.985

80^

0.191

0.104

5.146

0.982

0.20B

0.213

4.705

0.978

0.225

0JJ31

4.331

0.974

0^42

0.249

4,011

0.970

0.259

0.26S

3.732

0.960

0.276

0.287

3,487

0.901

0.293

OJiOO

3.271

0.950

0.309

0..325

3.078

0.951

0.320

0.344

2.904

0.940

20°

0.342

0.364

2.747

0.040

70"

0,358

0.384

2.005

0.034

0.375

0.404

2.475

0.927

0.391

0.424

2.360

0.921

0.407

0.445

2.246

0.914

0.423

0.400

2.145

0.900

0.438

0.488

2.050

0.890

0.454

0.610

hO*t3

0.891

0.4G9

0.6.32

1,881

0.88:1

0.485

0.554

1.804

0.876

30°

0.500

0.677

1J32

0.800

60»

0.515

0.001

1.604

0.867

0.530

0.025

hOOO

0.848

0,545

0.649

1.540

0.830

0.559

0.675

1.483

0.829

3fi

0.574

0.700 !

1.428

0.819

0.588

0.727

1.370

0.809

o.ao2

0.764

1.327

0.709

0.616

0.781

1.280

0.788

0.029

0.810

1.235

0.777

40''

0.043

0.839

1,192

0.760

50=*

0.6.00

0.809

1.150

0.766 ,

0.009

0.000

IJll

0,743

0.682

0.933

1.072

0.731

0.0D5

n.iMUJ

t.030

0-^^

*f\

4&°

0.707

1.000

Tftnppnt,

638

PRINCIPLES OF PHYSICS.

Densities of Substance.
in grams per cubic centimeters.

Alcohol .
Aluminum
Brass . .
Coal . .
Cork . .
Copper .
Diamond .
German Silver
Glass (Flint)
Glass (Crown)
Gold . . .
Ice ....
Iron . . .

0.8

2.6

8.4
1.4 to 1.8
.14 to .3

8.9

3.6

8.6

3.0 to 3.6

2.6 to 2.7

19.3

0.917
7.2 to 7.8

Lead ....
Marble . . .
Mercury . . .
Platinum Wire
Silver . . .
Tin ... .
Water, Sea . .
Wood —

Ebony . .

Lignum Vitse

Oak . . .

Pine . . .
Zinc ....

11.4

2.7

13.6

21.6

10.6

7.3

1.03

1.2
1.3

.6
7.1

Table of Equivalents.

1 centimeter = 0.3937 inch.
1 kilometer = 0.6214 mile.

= 0.1650 sq. in.

= 0.0610 cu. in.

= 2.20 lbs. avoir.

= 1.0567 qts. (liquid).

= 0.908 qts. (dry).

1 square cm
1 cubic cm.
1 kilogram

1 liter \

1 inch =
1 mile =
1 sq. in. =
1 cu. in. =
1 oz. avoir. =

2.64 centimeters.

1.609 kilometers.

6.462 sq. cm.
16.387 cu. cm.
28.36 grams.

1 lb. avoir. = 463.6 grams.

Approximate Equivalents.

1 meter = 1 yard 3 inches.
1 kilometer = | mile.
1 liter = 1 quart.

1 gram =16^ grains.
1 kilogi'am = 2J lbs. avoir.

1 mile =1} kilometers.
1 oz. avoir. = 28J grams.
1 lb. avoir. = J kilogram.

Rules for Computation.

Area of triangle = J base x altitude.

Circumference of circle = ttZ) or 2 ttB,

7rZ)2

Area of circle

Surface of sphere

Volume of sphere

Volume of prism
Volume of cylinder

or 7ri?2.
4
= irZ)2 or 4 vB^.
7rZ)3 ^^ 4 7r/?8

= -6-"'-T-

I = area of base x altitude.

IT = 3. 1416 or nearly 3f

APPENDIX.

539

Table pur Calculation op Dew-point.

T stands for deg^rees centlfn^e; M, for the number by which the difference in read-
inff of the dry bulb and wet bulb must be multiplied to find how much the dew-point is
below the dry-bulb reading.

-10°

8.8

3.3

+10°

2.1

+20°

1.8

-9

8.6

2.9

2.0

1.8

-8

8.2

2.6

2.0

1.7*

-7

7.9

2.6

2.0

1.7

-6

7.6

2.4

1.9

1.7

-5°

7.3

+6°

2.3

+15°

1.9

+25°

1.7

-4

6.8

2.2

1.9

1.7

-3

6.0

2.2

1.9

1.7

-2

6.0

2.1

1.8

1.7

-1

4.1

2.1

1.8

1.7

10°

2.1

+30°

1.6

Brown & Sharpb Wire Gauge.

Numbers

Diameters in
millimeters

Areas in square
millimeters

Numbers

Diameters* in
millimeters

Areas in square
millimeters

6.544

a3.63

.8118

.617 6

5.827

26.67

.722 9

.410 4

5.19

21.16

.643 8

.325 6

4.621

16.77

.673 3

.2681

4.115

13.3

.510 6

.204 7

3.666

10.65

.454 6

.162 3

3.263

8.3b^

.404 9

.128 8

2.906

6.633

.360 6

.102 1

2.588

6.26

.3211

.081

2.306

4.173

.285 9

.0612

2.052

3.307

.254 6

.050 9

1.828

2.626

.226 7

.040 4

1.628

2.082

.2019

.032

1.449

1.649

.179 8

.025 4

1.2^)1

1.309

.KiOl

.0201

1.16

1.039

.142 6

.016

1.024

.823 6

.127

012 7

.911 6

.652 7

Specific Resistance.

Copper

AlumiDum .

Platinum

Iron (wire) .

Mercury

Carbon (arc lights)

Resistance of a centimeter cube

s number in this column

divided by 1,000,000

1.67
2.89
8.98
16

94 34
about 4000

Relative
conductance

100

1.6

Linear Coefficients op Expansion between 0 and 100° C.

Aluminum . .000022 Lead 000028

Copper 000017 Platinum 000009

Glass 000009 Zinc . . .000024 to .000029

Iron (steel) . .000012 Brass 000019

640

PRINCIPLES OF PHYSICS.

Magnetic Constants for thb United States.
The + denotes westerly declination.

Declination

Annual
Changs of
Declination

Dip

Horizontal
Intensity

•

Dynes
.1729

+ 9.9

+ 8

+ 8.5

+ 8.8

72.2

.1907

+ 8.1

.1824

+ 8.4

70.6

.2055

- 8

+ 8.6

64.8

.2536

- 8.8

+ 8.6

.2816

+ 4.5

+ 3.1

71.2

.1998

- 5.9

+ 4.2

60.1

.2746

- 6

+ 8.8

70.9

.2006

- 8.4

+ 8.5

70.2

.2097

+ 11.6

+ :5.6

78.5

.1728

+ 16

+ 2.4

74.7

.1614

+ 12.5

+ 5

74.9

.1660

- 0.4

+ 8

64.1

.2548

+ 8.4

+ 2.5

69.7

.2081

- 4.1

+ 8.8

72.2

.1880

- 2

+ 8.8

70.1

.2075

- 7.5

+ 4

69.1

2175

- 0.6

+ 8.8

70.9

.1924

+ 12.1

+ 4.8

74.1

.1656

-14

+ 8.1

67.7

.2271

- 8

+ 4.5

71.7

.1969

-11

+ 8

74.6

.1724

- 6

+ 8.9

71.8

.1952

+ 10

+ 3.5

72.8

.1774

-19.6

+ 2(?)

72.8

.1855

- 6

+ 8.5

62.5

.2646

- 2

+ 3.5

61.6

.2716

- 9.4

+ 8.4

68.7

.2190

+ 2.4

+ 8.4

69.4

.2185

-10.6

+ 4.6

70.8

.2075

- 6.7

+ 8

64.8

.2491

-14.2

+ 1

.2712

- 2

+ 3.6

69.6

.2111

- 6

+ 4.8

78.3

.1800

- 4.2

+ 5.4

78.4

.1764

- 9

+ 8(?)

74.6

.1664

- 5.1

+ 8.8

.2594

- 4

+ 4.6

67.1

.2825

+ 10.8

+ 8.8

72.6

.1814

- 5.6

+ 4.2

.2861

+ 8.8

72.4

.1852*

+ 6 -^

^4.4

71.7

.1938

+ 7.8

+ 3.6

71.9

.1888

- 6.7

+ 8.9

70.3

.2075

+ 1

+ 8.2

67.9

.2806

-17

+ 2(?)

64.5

.2420

+ 6.7

+ 4.5

74.1

.1658

-20.6

+ 1

68.5

.2092

-16.7

+ 2.6

67.1

.2814

-16.7

-0.5

62.8

.2586

-22

(H?)

71.1

.1988

- 4

+ 8.6

63.2

.2650

+ 10.5

+ 8.3

78.4

.1761

- 6.2

+ 4.4

69.8

.2175

- 8.9

+ 8.6

70.8

.2075

-10.8

+ 4(?)

72.4

.1924

+ 6.9

+ 2.4

10.7

.2025

Albany, N.Y. . .

Allegheny, Pa. . .

Ann Arbor, Mich. .

Athens, Ohio . . .

Atlanta, Oa. . . .

Austin, Tex. . . .

Baltiniore, Md. . .

Baton Koiige, La. .

Bloomington, III. .

Blooiuington, Ind. .

Boston, Mass. . .

Brunswick, Maine .

Burlington, Vt. . .

Charleston, S.C. . .

Charlottesville, Va. .

Chicago, 111. . . .
Cincinnati, Ohio.

Columbia, Mo. . .

Columbus, Ohio . .

Concord, N.U. . .

Denver, Colorado .

Des Moines, Iowa .

Fargo, N.D. . . .

Galesburg, 111. . .

Hartford, Conn. . .

Helena, Mont. . .

Jackson, Miss. . .

Jacksonville, Fla. .

Lawrence, Kansas .

Lexington, Va. . .

Lincoln, Neb. . . .

Little Rock, Ark. .

Los Angeles, Cal. .

Louisville, Kv. . .

Madison, Wis. . .
Milwaukee, Wis.

Minneapolis, Minn. .

Mobile, Ala. . . .

Nashville, Tenn. . .

New Haven, Conn. .

New Orleans, La. .

New York, N.Y. .

Philadelphia, Pa. .

Princeton, N.J. . .

Quincy, III. . . .

Raleigh, N.C. . . .

Reno, Nev. . . .

Rochester, N.Y. . .

Salem, Oregon . .
Salt Lake City, Utah

San Francisco, Cal. .

Seattle, Wash. . .
Sehna, Ala. ...

Springfield, Mass. .

St. Louis, Mo. . .

Terre Haute, Ind. .

Vermilion, S.D. . .

Washington, D.C. .

Ex.

, 1.

Ex.

, 2.

Ex.

16.

Ex.

12.

APPENDIX. 541

APPARATUS.

An asterisk (*) denotes that the apparatus is not absolutely required in a preparatory
course in physics.

I. Each piece of apparatus in the following list is that required for one
pupil unless otherwise specified.

§ 3. Meter stick. For a short meter rule, either strips cut from a
'* twentieth century note-book " or the Penfield protractor may
be used. The straight edge of a piece of cardboard will serve
for a ruler.
250-gpram spring balance ; blocks as described.
Steam boiler of Ex. 24 or overflow can; bucket; weighted

block.
Irregular pieces of various substances ; jar.
_-. Cylindrical rod ; support to hold rod vertical.
7. Glass-stoppered bottle.

Glass tubing, 2 pieces 80 cm. long; metal 3-way connector;

tumbler ; rubber tubing.
Boyle* s law apparatus. One for every 4 or 6 pupils.
Three 2000-gram spring balances ; fish-line ; adjustable clamps
having cam moving in horizontal plane ; wooden frame, 40
inches diameter, of J inch stock, 3 inches wide, one for 3
pupils.
Ex. 13. Boards and boxes as described.

Ex. 14 (2d method). Square board as described, one for 3 pupils; mar-
bles or bicycle balls.
§ 114. Cars having grooved wheels.

§ 204. Tin cans, 120 cc. capacity ; thermometer, all glass, 0° to 110° C.
§ 210. Screws and nuts, millimeter thread.

Ex. 24. Steam boiler, extension top ; dipper ; linear expansion apparatus.
Ex. 26, b. Jacketed barometer, one to 4 pupils.
Ex. 29. Nickelled can, should be used only for this experiment.
Ex. 31. Copper and aluminum clippings cut from wire; pan or plat-
form balances, one for 4 pupils.
Ex. 34. *' Law of Charles " tube, designed by Dr. Waterman of Smith
College.
§ 299. Mirrors, IJ inch wide, 3i inches long; pins: rubber bands.
Ex. 39. Refraction of water apparatus.
Ex. 40. Sheet of zinc as in Fig. 256. Penfield Goniometer.
Ex. 41. Glass plate.
Ex. 46. Prisms, 60°, 24°.

Ex. 48. Apparatus of Fig. 284 ; lenses, 4 inch to 6J inch focus.
Ex. 60. Screen with vertical slot; netting.
Ex. 52. Half lens, or fragment of a lens.
Ex. 56. * Bunsen photometer.
§ 430. Magnets, J inch by J inch by 2 inches, numbered as in Ex. 60;

iron filings ; nails ; needles.
§ 433. Compass, f inch diameter.
§ 439. Iron washers ; curved iron strips ; magnets f inch by 5 inches,

numbered, one for 5 pupils.
§ 441. Watch spring.

542 PRINCIPLES OF PHYSICS.

Ex. 61. No. 00 tacks; No. 16 iron wire.

Ex. 62. * Apparatus as described.
§ 460. Battery stands; copper and zinc strips; salphoric acid; No. 24
copper wire for connections; galvanoscope (galvanometer).
I., Fig. 377, is of the simplest form, and is merely a coil of
wire held upright. In II. the compass box is large and the
needle is suspended by a tine silk fibre. The coil is removable
from the base by loosening the upper screws. A coil of 5 or
10 turns of coarse wire, and another coil of 100 to 200 turns of
fine wire are useful. The instrument is, of course, set up with
the coil north and south. To make it less sensitive, that is,
to reduce the deflection of the needle, place the compass box a
little way from the coil.

Ex. 63. No. 28 German silver or manganin wire.
§ 479. Porous cup.
§ 483. Electric light carbons ; No. 18 annunciator wire.

Ex. 66. Current reverser.

Ex. 67. No. 30 and No. 28 Qerman silver wire ; micrometer caliper.

Ex. 68. Slide wire bridge ; resistance coils, or resistance box ; wires
as mentioned. Three triple connectors, meter support of
Fig. 295, as shown in Fig. 422, with the addition of a contact
key, make a simple bridge that may be substituted for the
common form of Fig. 423.

Ex. 71. The galvanometer of II., Fig. 377, becomes an ammeter by using
a coarse wire coil. Make a voltmeter by attaching a coil of
many turns to another instrument.
§ 558. Telegraph sounder parts.

Ex. 72. Coils of wire 2.5 cm. wide, diameter outside 3.7 cm., inside diam-
eter 1.5 cm. of No. 27 wire. A few coils of No. 33 to 35 are
useful. These coils are also used in the galvanoscope, tele-
graph sounder, etc.

Ex. 73. Iron wire.
§ 586. Metals mentioned in text

II. The following apparatus is that required for those experiments in
the book that may be performed by the teacher on the lecture table.
In case they are used as laboratory exercises, one piece of the apparatus
will suffice for a whole class, unless otherwise specified.

§ 7. Wooden cylinder, hard and soft burned bricks.
Ex. 4. Loaded stick, 23 cm. by 1 cm. by 1 cm. ; 1, 2, and 5 g. weights.

§ 17. Graduated jar.
Ex. 7. Suspended pulley. Fig. 7.

§20-41. Bottle; tube of large diameter; bent ta be; eight-in-one appa-
ratus clamp; vacuum-tipped arrows; air-pump and plate
* rubber balloon and support; barometer tube: iron dish
mercury ; enclosed barometer ; glass tube and piston. Fig. 24
siphon, j inch diameter, and piston. Fig. 28 ; rubber tubing.
§ 43. Metal tube, with side connections. Fig. 23.
Ex. 10. Two-liter bottle fitted with rubber stopper and metal valve,
Fig. 40 ; rubber pressure tubing ; bottle fitted with 2-holed
stopper ; prescription balance, with sliding weight

APPENDIX. 543

Ex. 11. Lamp chimney and cork pressure gauge ; inner tube bicycle
tire.
§ 73. Combined air and compression pump ; rectangular iron frame.
§ 86. Celluloid 30*^ triangle, Fig. 79.
Ex. 16. Pivoted stick, Fig. 95.
§ 107. Balanced lever, Fig. 104.

§ 127. Clamp with lengthened handle, or bolt and nut, Fig. 122.
§ 144. Circular piece of board loaded on one side.
§ 148. * Wooden wheel and rubber cord, Fig. 143.
§ 156. 50-gram weight with hole ; rubber thread.
Ex. 19. * Two ivory balls, different sizes, meter support and stops.
Ex. 20. * Apparatus for elasticity. Fig. 162.
Ex. 21. Breaking strength apparatus.
Ex. 22. * Bending apparatus.
Ex. 23. * Torsion apparatus.
§ 205. Flask, with 1-hole rubber stopper.
§ 206. Hope's apparatus.

§ 221. Test-tubes, 1 inch diameter, 8 inches long.
Ex. 26 a. Apparatus, Fig. 192 ; two or three pieces are sufficient for a large

class.
Ex. 31. U-tube manometer ; used also in Fig. 229, p. 257.
§ 296. Fire syringe. The piston is not tight if it touches the bottom
when pushed down sharply. To tighten, turn nut at end,
thereby compressing the leather washers. Lubricate with
sperm oil. The tinder is ignited by giving the piston one quick
plunge toward the bottom and pulling it out at once.
Ex.36. ^^Sparklef apparatus.
§ 274. Bent glass tube, U-form, for pressure gauge. See Fig. 229.
§ 282, Model reversing gear. Most engines that have a reversing gear
are reversed by sliding the valve rod from one end of the link
to the other.
§ 286. Model slide valve steam engine of iron or brass ; aspirator.
§ 290. Revolution counter.
§ 292. Test-tube fitted with 2-hole rubber stopper ; displacement piston,

Fig. 231.
§ 293. Model hot-air engine. The horizontal form is satisfactory.
§ 296. Model gas engine.
§ 308. Folding model of a kaleidoscope.
§ 309. Apparatus of Fig. 248.

§ 319. Plate of glass, one edge only straight. Fig. 263.
§ 320. Rectangular bottle, same model as glass plate of Ex. 41.
§ 322. Right-angled prism.
§ 332. Polyprism.

§ 334. 6-inch and 15-inch focus lens, 3 to 4 inches in diameter.
§ 337. Set of lenses.
Ex. 49. Set metal templates, radius 4 to 6 inches.
§ 346. If the object, Fig. 298, is brought near the lens, the virtual focus
/ falls inside the principal focus.
Ex. 54. * Cylindrical mirror.
§ 355. « Spherical concave mirror.

§ 369. Water prism and glass prism, achromatic when combined.
§ 385. Short-focus lens.

544 PBINCTPLES OF PHYSICS.

§ 408. * Simple siren. A circular disk having rows of evenly and un-
evenly spaced holes. Rotating apparatus.
§ 409. * Two tuning-forks of same pitch.
Ex. 58. * Simple chronograph.
§413. * Sonometer.

I .2(3* I '^^o metal flageolets, one fitted with a piston.

§ 439. Horseshoe magnet.

§ 440. Knitting-needle, brass wire.

§ 455. Pendulum bobs.

§ 491. Coil, same as the one used in the galvanoscope, Fig. 416.

§ 498. Apparatus for decomposing water.

§501. U-tube.

§ 513. Tangent galvanometer having a ring 20 to 30 cm. in diameter,
and a suspended compass needle at the centre of the coil.

§ 525. Volt-ammeter, reading to 3 volts and 3 amperes.

§ 529. Use apparatus of § 43.

§ 533. Astatic needle.

§ 534. Ground board, Fig. 418.

§ 539. Black lead for ordinary pencil.
Ex. (J9. * Wire woiuid on insulating tube.

Ex. 74. Model Siemens dynamo, or Page rotating machine of Fig. 465.
Ex. 70. Model Gramme machine ; magnet having hole through centre
Fig. 409.

§ 500. Floating coil.

§ 5t).'). No. 30 platinum wire ; a one-third c. p. 4-volt incandescent
lamp operated by 4 Daniell cells in series.

§ 010. * Glass rod ; * ebonite ; * silk ; * support, Fig. 492.

§612. * Electroscope.

§ 015. Small motor.

* Hand-power dynamo.

III. General supplies.

Alcohol ; Ammonio-citrate of iron ; Arc light carbons ; Bichromate of
soda ; Brass screws ; Brass rod ; Candles ; Coordinate paper ; Carbon
bisulphide ; Dry shellac ; Emery cloth ; Floss silk ; Glass tubing ; Glycerine ;
Hacksaw ; Ilypo ; Iron clamps ; Kerosene ; Linen thread ; Linseed oil ;
Liquid glue ; Mercury ; Plaster of Paris ; Potassium nitrate ; Red prussiate
potash ; Rubber stoppers ; Rubber tubing ; Sal ammonia ; Salt ; Sand-
paper ; Shears for cutting metal ; Shellac varnish ; Sodium sulphate ;
Solio paper ; Sulphate of copper ; Sulphuric acid ; Velox developer ;
Velox paper ; Watch springs ; Wax ; Zinc chlorid.

IV. Tools.

Brace ; Carborundum wheel and grinder stand ; J-inch chisel ; Draw
knife ; Flat^nose pliers ; Gas pliers ; Iron smoothing plane ; Miter-box
saw ; Nippers ; Screw-cutting lathe and tools to accompany the same ;
Screw drivers ; Vise (machinist's) .

INDEX.

(Ex., exercise ; ch., chapter ; app., appendix ; p., page.)

Aberration, spherical, § 386.

Absolute scale, § 268.

Absolute zero, § 262.

Absorption, of colors, § 864: of heat, §§ 197,
242, 24S. See Liquids ; Oases.

Acceleration, § 166 ; of falling bodies, § 170.

Accommodation, § 389.

Achromatic lenses, § 366.

Achromatic prisms, § 868.

Achromatism, § 865.

Acids and alkalies in cells, § 501.

Action and reaction, Ex. 19.

Air: buoyant force of, § 69 : compressibility,
Ex. 9a, Ex. 96 , density, Ex. 10 ; dissolved
in water, § 288 ; exhaustion, by air-pumps,
§ 54; exhaustion, rate of, § 58; uses of
compressed, § 28t; cooling by expansion,
§ 265 ; coefficient of expansion, Ex. 84 ;
work done by expansion, § 287 ; saturated
with moisture, § 288 ; capacity for holding
moisture, § 284 ; velocity of sound in, § 411,
Ex. 68 ; weight, § 28 ; weight of 1 cc, Ex.
10 ; computation of weight of, § 51.

Air pressure, §§ 27-29, 69; measurement
of, § 82 ; on mercury column, § 38 ; water
lifted by, % 36.

Air-pumps, §§ 52, 54.

Air thermometer, § 264.

Alternating currents, §§ 569, 572.

Alternator, § 572.

Amalgamation, § 470.

Ammeter, § 525 ; measurement bv, §§ 524,
627 ; plotting current measured by, § 527 ;
testing, § 526.

Ampere, §§ 507, 509.

Ampere's rule, § 494 ; application of, § 496.

Ampere turns, § 562.

Angle, critical, § 312, Ex. 40, A pp. p. 536 ;
of declination of compass needle, § 447 ; of
incidence and refraction, § 817 ; of inclina>
tion, § 450 ; of internal reflection, § 826 ; of
minimum deviation, § 380, Ex. 47.

Angles, location of image in convex mirror
by, Ex. 55, p. 327.

Annealing steel, § 437.

Anode, §§ 508, 604.

Apparatus, list of, A pp. p. 641.

Arc lights, §§ 508, 596

Armature, of dynamo, §S 571, 574 ; Gramme
ring, § 580 ; Siemens, § 582 ; lines of force
in, Ex. 77.

Astatic combination, § 533.

Atmospheric encrine, § 276.

Atmospheric pressure, see Air Pressure.

Attoaciion, of gravitation, § 133 ; measure-
ment of earth^s, § 158 ; magnetic, § 480.

Attractire force of planets, § 161.

Axle and crank, § 112.

Axis of lens, § 340.

Balance, errors of spring, App. p. 686.

Balancing columns, Ex. 8.

Balancing point, §§ 145, 146.

Balance wheel, § 209.

Barometer, § 85.

Base, the, § 186.

Batteries, Gh. xxvii.; internal resistance of,

Ch. xxxii, Ex. 72; high E.M.F. ftom,

§ 548 ; storage, §§ 550, 551, Ex. 78. See

Cells.
Battery, dry, § 487 ; of cells in series, rules

for, § 549 ; open circuit, § 486 ; Trowbridge,

§ 548.

Beats, § 429.

Bells, electric, § 563.

Bending, §§191, 198; Ex. 22a, Ex. 226; for-
mula for, § 194.

Bichromate cell, § 484.

Bicycle *' gear.*' §§ 116, 117.

Binding-post, § 210.

Body, acceleration of fitlling, § 170 ; buoyed
up in a liquid, § 68 ; buoyed up in air, § 69 ;
momentum, § 179 ; inertia of, § 160 ; in
motion, §§ 157, 168.

Boiling, Ch. xv., §§ 224, 240; difference
between evaporation and boiling, § 244.

Boiling-point, of liquids, Ex. 265, Ex. 80;
on thermometer, Ex. 25 ; how to vary, §221.

Boyle's Law, Ex. 9a, Ex. 9&, §§ 31, 46, 49 ;
limitations of, § 50.

Breaking strength, Ex. 21, §§ 187, 189 ; ex-
periments on, § 1^.

Bridge, slide wire, § 586 ; Wheatstone, § 585.

Brightness of a reflection, § 804. See Image.

Bunsen's photometer. § 876.

Buoyancy, centre of, § 142.

Buoyant force, of air, § 69 ; of liquids, § 68.

Cable, flrst Atlantic, § 591 ; instrument for
receiving signals, § 592.

Calorie, § 246.

Camera, principle of, § 383; photographic,
§384.

Candle power, §§ 878, 381.

Capillarity, § 78.

Cartesian diver, § 88.

Cells, direction of current in, §§ 466, 496
E.M.F., § 514; effect of size on E.M.F.
§515; formed, § 550; high E.M.F. from
§ 548 ; grouping of, Ch. xxxii. ; internal re
sistance, Ex. 72, Ch. xxxii., § 516; meas
urement of internal resistance, § 546 ; open
circuit, § 485 ; poles of, §§ 465, 467 ; short-
circuitedf, §§ 468, 469 ; varieties of, § 488.

ivi/;

546

INDEX,

Bichromate, § 484.

Daniell, \ All ; advantages of, § 481 ;
chemical action, $482 ; porous cup form of,
§ 480 ; study of, Ex. 66.
Dry, § Ahl.
Electrolytic, § 499.
Galvanic, % 464.

Gravity, §§ 478, 479 ; chemical action in,
§ 482.
Leclanch^, § 485 ; polarization, § 486.
Primary and Secondary, § 484.
Simple, fS 460,471: study of, Ex. 65;
curve of polarization, § 475.
Smee, § 474.

Storage, Ch. xxxii. ; as regulator,
§555; charging, § 553; efficiency, § 552;
forming, § 550 ; kinds of, § 551 ; resistance,
c 554
Voitaic, §464.
Cells in parallel, § 540 ; effect of joining,
§ M7; E.M.F., §§ 544, 548; internal re-
sistance, § 548 ; compared with cells in
series, § M2.
Cells in series, § 541 ; E.M.F., § 545; com-
pared with cells in parallel, § 542 ; internal
resistance, $ 548.
Centigrade scale, §§ 21S-220.
Centre of buoyancy, § 142.
Centre of curvature, in lens, § 889 ; of mir-
rors, § 858 ; of convex mirrors, § 354.
Centre Of gravity, Ch. ix., Ex. 18, § 184;

raising, § 140 ; fall of, § 144.
Centre of mass, i\M.
Centrifugal force, § 159.
Charge, kinds of electric, | 610.

Charging storage cells, $ 558.
"■ rles, ' ' "

Charles, Law of, Ch. xvi., §§ 261, 268, Ex.

Chemical compounds formed by electric

furnace, § 5}!9.
Chemical method of measuring current,

§ 506.

Chronograph, § 412.

Circuit, open and closed, § 462 ; primary and

secondary, § h^i ; telegraph, § 561.
Coal, power obtained from, § 291.
Coefficient of expansion, § 207, Ex. 24; of

air, Kx. -84 ; of gases, Ex. 84 ; table for

linear, A pp. p. 589.
Coefficient of friction, Ex. 18a, Ex. 185,

§§ 89, 95; computation of, § 97; effect of

load on, § 90 ; effect of speed on, § 94 ; effect

of surface on, § 91 ; formula, § 89.
Coefficient of resistance, temperature, Ex.

71.
Coherer, § 601.
Coil, floating, §590; induction, Ch. xxxiii.,

§ 584, Ex. 79 ; lines offeree about magnetic,

§ 492 ; lines offeree in, Ex. 68.
Cold, greatest degree of, § 262.
Color, § 861 ; absorption of, § 864 ; mixture

of, § 862 ; mixing, § 868.
Colors of spectrum, §361.
Columns, balancing, Ex. 8.
Commutation of currents, § 570.
Commutator, § 570.
Compass, § 488 ; angle of declination, § 447;

as magnetic pendulum, § 455 ; direction

of needle, § 445; effect of electric cur-
rent on, § 489 ; effect of one on another,
§484.

Compass needle, § 445; vibration of, § 456.

Component, of forces, Ex. 12; of parallei
forces, § 100.

Composition, of forces, Ex. 12; of light,
§860.

Compressed air, § 287.

Computation, of areas, etc., rules for, App.
p. 588.

Condensation, exhausting by, § 59 ; of steam,
§ 274.

Condenser, model of water, § 243 ; of engines.

Condensing engine, § 285.

Conduction of heat, § 199.

Conductors, of electricity, resistance of, Ex.
69; of heat, «§ 200, 201.

Conjugate foci, formula, §844; interchange-
able, § 848 ; of a lens, § 842 ; real, Ex. 51 ;
relation between, Ex. 50a, Ex. 50d.

Connections, resistance of, § 600.

Constant, § 47.

Constants, table of magnetic, App. p. 540.

Convection of heat, § 202.

Converters, § 585.

Cooling, by expansion, §§ 265, 266 ; by evap-
oration, § 258.

Cottnter-electromotxYe force, § 478.

Couples, § 128, Ex. 17 ; balancing. § 181 ; cal-
culation of, § 182 ; moments of, § 180.

Crank and axle, § 112.

Critical angle, § 812 ; of glass, Ex. 42 ; of
water, Ex. 40, App. p. 686.

Crookes tubes, § 605.

Cross-section of wire, calculation of, Ex. 21,
p. 165.

Cubical expansion, §§ 212, 218.

Current, see Electric current.

Current reverser, § 488.

Currents, induced, Ch. xxxni., Ex. 74, Ex. 75.

Curvature of lens, measurement of, Ex. 49.

Curve of polarization, § 475.

Daniell cell, see CelU.

D'Arsonval galvanometer, § 598.

Declination of magnetic needle, § 447.

Decomposition of water, § 500.

De Laval turbine, § 288.

Demagnetizing a magnet, § 486.

Densities, table of, App. p. 588.

Density, Ch. i. : defined, § 6 ; experiments
on, § 7 ; formula for, § 8 ; rule for, § 8 ; of
air, Ex. 10 ; of a floating body, § 16 ; of liq-
uids, Ex. 7, Ex. 8, § 45 ; of a solid, Ex. 1 ;
of water, § 206.

Depth. § 64 ; relation of pressure to, § 68.

Deviation, § 829 ; angle of minimum, § 880,
Ex. 47.

Dew-point, §§ 282, 285, Ex. 29 ; table for cal-
culation of, App. p. 589.

DifTusion of light, §§ 878, 374.

Digesters, § 228.

Dipping needle, § 449.

Direct current, dynamo, § 572 ; motor, §681.

Direction, of compass needle, §446; of cur-
rent in cell, §§ 466, 496 ; of galvanosoope
needle, § 498.

INDEX.

547

Discord, § 415.

Dispersion of light, Ch. xxii. ; § 859 ; effect

on focus of lens, § 867.
Displacement, measurement of, § 17 ; and

loss of weight, § 18.
Displacement method, density of a liquid,

Distance, covered by moving body, § 162 ;
formula for, § 165; object and image,
§841.

DistilUtion, §§ 248, 245.

Dolland's experiment, § 869.

Doppler's principle, § 417.

Dynamos, Ch. xxxiii., § 574; and motors
§ 575; direct current and alternating,
§ 572 ; lines of force in armature of, £x. 77 ;
principle of, §566; series, § 576; shunt,
§ 578 ; study of Siemens, Ex. 76 ; putting
together the parts of, Ex. 76, Ex. 78.

Dyne, § 171 ; and gram, § 172.

Dynes, conversion to grams, § 174.

Earth's magnetism, §451, App. p. 540;
weakening, §582.

Eccentric, §281.

Edison storage cell, § 479.

Efficiency, of pistons, § 78 ; of storage cells,
§552.

Elastic collision, Ex. 19.

Elasticity, Ch. xii., § 80, Ex. 20, Ex. 22a,
Ex. 22^ Ex. 28.

Electrical furnace, §§598, 599.

Electrical pressure, see Pressure.

Electric bell, §568.

Electric car motors, § 614 ; model of, § 615.

Electric charge, kinds of, §610.

Electric currents, alternating, §569;
amounts required for commercial uses,
§508; calculation of, in ampdres, §509;
commutation of, §570; detecting small,
§581 ; direction in a cell, j§ 466, 496 ; effect
on a compass, § 489 ; effect of hydrogen
bubbles on, §478; for electric welding,
§597 ; flow of, § 462 ; generation of, § 461 ;
heat produced oy, § 497 ; magnetic action
of, Ch. xxviii., Ex. 67 ; multiplying effect
of, § 491 ; refinement of metals by, § 505 ;
strength of, § 562 ; study of, in a simple
cell. Ex. 65.

Induced, Ch. xxxiii. ; by bar magnet,
Ex. 74 ; by electromagnet, Ex. 75.

Measurement of, Ch. xxix. ; by am-
meter, § 524 ; by chemical method, § 506 ;
by magnetic method, §511.
See Lines of Force ; Resistance.

Electricity, Ch. xxvi. ; practical applica-
tions of, Ch. XXXV. ; iVictional, §608; posi-
tive and negative, § 610 ; static, 608 ; sur-
face, §§607-609.

Electric heating, §595.

Electric power, measurement of, § 616.

Electric signals, §563.

Electric welding, §596.

Electrochemicalseries, §586.

Electrolysis, §502.

Electrolytic cell, §499.

Electromagnets, §49S, Ch. xxxiii., §N%;
current induced by, Ex. 75 ; uses of, § 564.

Electromotive force, §§ 514, 517 ; high, fh)m

batteries, § 548 ; effect of size of cell on,
§515; of ceUs in naraUel, §§544, 547; of
cells in series, § 545.

Electroplating, § 508.

Electroscope, § 612.

Electrotjrpes, § 504.

Elevator pistons . § 74.

Energy, derived from heat, § 273 ; equivalent
in heat units, § 271 ; heat derived from,
§ 270 ; obtained from coal, 291. See Elec-
tromotive force.

Engine, atmospheric, § 276; compound,
§ 285 ; cylindric valves of, § 279 ; eccentric
of, § 284 ; condenser of, § 277 ; condensing,
§ 281 ; Ericsson, § 298; four-cycle, § 296;
gas, §§ 294, 296 ; governor of, § 288 ; hot-
air, §§ 292, 298 ; Newcomen's, §§275, 278 ;
non-condensing, § 286; reversing gear of,
§ 282 ; slide valves, § 280 ; two-cycle, § 295 ;
vacuum, § 276.

Equation, App. p. 688.

Equilibrant force, § 79.

Equilibrium, § 187 ; neutral, § 148 ; stable,
§§ 188, 141 ; unstable, § 189.

Equivalents, table of, App. p. 588; table of
approximate, App. p. 588.

Erg, § 177.

Ericsson engine, § 298.

Estimating, § 4.

Ether, the, § 814.

Evaporation, §225; by exhaustion of air,
§ 289 ; cooling by, § 258.

Evaporation and boiling, Ch. xv.; difference
between, § 244.

Exhaustion of air, by air-pump, § 54; by
condensation, § 59; degree of, § 55; rate
of, § 58.

Expansion, coefficient of, § 207, Ex. 24;
cubical, §§ 212, 218 ; linear, Ex. 24 ; cool-
ing by, §§ 265, 266 ; of air, § 287 ; of air,
coefficient of, Ex. 84 ; of gases, Ch. xvi.,
§ 260 ; of gases, coefficient of, Ex. 84 ; of
gases, work done by, § 266 ; of rails, § 211 ;
of steam in engine, § 284.

Experiment, defined, § 2.

Eye, the, § 388.

Fahrenheit scale, §§ 218-220.

Fall of electrical pressure, § 529 ; in a wire,
§530.

Far-sightedness, § 891.

Faure, § 550.

Fibre suspensions, wax for, App. p. 585.

Field, magnetic, § 441.

Field magnet, §574; connected in shunt,

Floating bodies, specific gravity of, Ex. 4.

Floating coil, § 590.

Fluorescent screens, § 606.

Focal length of lens, § 888.

Foci, use of lenses of different, § 887. See

Conjugate foci.
Foci, virtual, § 846, Ex. 52.
Focus, principal, § 834, Ex. 48 ; of lenses,

§ 888 ; of concave lenses, § 888 ; of concave

mirrors, Ex. 56; effect of dispersion on

focus of a lens, § 867.
Force, centrifugal, § 159; defined. § 20;

direction, §§ 84, 104 ; electromotive, §§ 514,

548

INDEX.

515; form aU for, $175; moments of, % 102,
Ex. 15; sum of the moments, $ 105; to
resolve a force, § 88; unbalanced, % 26;
value of moment of, § 108. See Lines of
force.

Force and distance, relation of, § 121 ; for-
mula for, § 123.

Forced pressure of liquids and gases, § 70.

Force-pumps, § 89.

Forces, Ch. iv. ; acting on magnetic needle,
% 512 ; at right Angles in one nlane. Ex. 17 ;
composition of, Ex. 12 ; equilibrant, § 79 ;
i>arallelogram of, § 79 ; resolution of, §§ 82,
88, 96; resultant of, Ex. 12. § 80 ; three or
more, § 81. See Parallel forces.

Freezing-point of water, effect of dissolved
substances on, Ex. 28.

Freezing-points, § 281.

Friction, Oh. v. ; advantages of, § 93 ; be-
tween solid bodies, Ex. 13a ? laws of, §§ 90,
91 ; efxceptions to laws of, § 92 ; variation
of laws of, § 98. See Coefficient of fric-
tion.

Frictional electricity, § 608.

Fulcrum. § 106.

Fundamental, Ex. 60.

Furnace, electric, §§ 598, 599.

Galvanic cell, § 464 ; single fluid, §§ 460-463 ;
two fluid, Ex. 66.

Galvanometer, §461; d'Arsonval, §593;
line^ of force in, § 589 ; mirror, § 592 ; tan-
gent, §5li; formula for tangent, §518.

Galvanoscope, § 461 ; direction of needle,
§493 ; study of, §510 ; sensitive, § 5:31.

Gas engines, §§ 294-296 ; h.p. of, 296.

Gases, Ch. m. ; coetiicient of expansion,
Ex. 34; expansion of, Ch. xvi., § 260 ; in-
crease of pressure at constant volume, Ex.
85; pressure of, §81 ; forced pressure of,
§ 70 ; volume of, § 31 ; weight of 1 cc., Ex.
86 ; weight and volume, Ex. 86 ; work
done by expansion of, §266 ; uses of com-
pressed, § 269.

Gear, reversing, §2S2.

Geissler mercury pump, §§ 57, 58.

Geissler tubes, § 604.

Girder, stiffnoss of, § 192.

Glass, critical angle, Ex. 42 ; effect of, upon
light, § 318 ; grinding the surface of, App. p.
535; comparison of refraction of a liquid
and glass, §320; index of refraction, Ex.
41 ; index of refraction by parallax, Ex. 44 ;
variation of index of refraction, §319;
marlcing on, App. p. 5536 ; shoaling effect
of, Kx. 44; total internal reflection, §321.

Glass plate, reflection from inner surfaces,
§324; with parallel sides, path of ray
through, Ex. 45.

Glass rod, internal reflection in, § 825.

Glass tube, magnifying power of, §845.

Governor, § 283.

Gramme ring, § 579 ; armature, § 580 ; ma-
chine, study of, Ex. 78.

Grams, conversion to dvnes, §174.

Gravitation, action of, § 183.

Gravity, see Centre of ffrarity ; Specijlc
(iranity.

Gravity cell, see Cell;

Grouping of cells, Ch. xxxii.

Ground glass, preparing, App. p 68S.

Hardening steel, § 487.

Harmony, §414.

Heat, Ch. xiii. ; absorption of, §§ 197, 242,
248 ; conduction of, § 199 ; conductors, §§
200, 201 ; convection, 8 202 ; defined, § 197 ;
derived from work, § 270; examples of,
derived from work, § 272 ; effect on a mag-
net, Ex. 62 ; effect on size of substances,
§ 205 ; effect of surface on radiation, § 204 ;
point of absolutely no heat, § 262; pro-
duced by electric current, § 497 ; radiation
of, § 208 ; sensible, § 286 ; specific, of a
solid, Ex. 81 a, Ex. 316, § 249 ; temperature
and quantity, § 198; unit of, §§ 246, 251 ;
work derived from, § 278. See Latent heat;
Heat units.

Heating, electric, § 595 ; by resistance, § 594.

Heat units, § 246 ; required to melt 1 g. of
ice, §§ 251, 258, Ex. 82; number produced
by 1 gram -centimeter of work, § 271.

Horse power, § 289 ; measurement of, § 290 ;
of gas engines, § 296.

Hydraulic press, § 75.

Hydrogen, § 460.

Hydrostatic bellows, § 72.

Ice, effect of pressure on, § 280 ; heat units
required to melt 1 g., §§ 251, 258, Ex. 82;
melting-point of, Ex. 25; refrigerating
[»lant, § 268.

Ice-boat, § 86.

Ice machine, § 267.

Image, by small opening, §§ 885, 886 ; appar-
ent position of, § 802 ; large, § 849 ; size of,
§ 848; relative size of object and image,
§ 847, Ex. 58 ; real, formed by lens, Ex. 54;
virtual, Ex. 52 ; virtual, formed by lens,
§851.

Location of, by parallax, §§ 801, 850 ; by
shadows, § 805 ; in plane mirrors, Ex. 87 ;
in plane mirrors, by parallax, § 800 ; in con-
vex mirrors, by parallax, Ex. 55; in con-
cave mirrors, § 856.
See Mirrors ; Lenses.

Image distance, § 841.

Incandescent lamp, Nemst, § 594.

Incidence and refraction, angle of, § 817.

Incident ray, § 303.

Inclination of magnetic needle, angle of,
§450.

Inclined plane, Ex. 16; mechanical advan-
tage in, § 122.

Index of refraction, of glass, Ex. 41 ; of
glass, variation of, § 819 ; of glass, by par-
allax. Ex. 44; of water, Ex. 89.

Induced currents, Ch. xxxiii., Ex. 74, Ex. 75.

Induction coil, Ch. xxxiii.,§5S4; principle
of, Ex. 79.

Inelastic collision, § 180.

Inertia, § 160.

Internal reflection, see R^eciion,

Internal resistance, see Resihtanate.

Interrupter. § 563.

Inverse squares, law of, § 874.

Iron filings, tracing lines of force by, § 488,
A r>p. p. 585.

Joule's Law, § 273.

INDEX.

549

Kaleidoscope, S 808.

Kathode, §§ 508, 604.

Keel, § 85.

Key. telegraph, § 560.

Lamps, c. p. of, §881.

Latent heat, of melting, % 252, Ex. 82 ; of
steam, § 256; of vaporization, § 256, Ex.
88 ; of water, Ex. 32 ; practical applications
of, § 255; solution of problems. § 254;
effects of latent heat of vaporization, § 259.

Law Of poles, § 484.

Law Of Charles, Ch. xvi., §§ 261, 268, Ex.
84.

Laws of electrical resistance, § 520.

Leclanch^ cell, § 485 ; polarization of, § 4S6.

Length, measurement of, § 4.

Lens, § 882; conjugate foci, Ex. 50; focus
of, § 888 ; focus of concave, § 888 ; principal
focus, §884, Ex. 48.

Lenses, Ch. xx. ; radius of curvature, § 889 ;
concave, §§ 888, 890; convex, § 891;
crown and flint glass, § 870; defects in
single, § 885; effect of dispersion on the
focus, § 867 ; focal length of combinations
of, § 888 ; image formed by, compared with
image made by small opening, § 886 ; large
image formed by, § 849 ; measurement of
curvature of, Ex. 49; photographic, §884;
real image formed by, Ex. 54 ; relation be-
tween conjugate foci, Ex. 50rt, Ex. 506 ;
spherical aberration, § 886; virtual image
formed by, § 851 ; uses of lenses of difterent
foci, §887.

Lever, § 106, Ex. 14, Ex. 18; balancing-point,
§ 145 ; weight and power, § 107 ; power and
speed, § 108.

Ley den jar, §611.

Lifting-pump, §37.

Light, composition of, §860; diffusion of,
§ 878 ; dispersion of, Ch. xxii., § 859 ; effect
of glass upon, §818 ; law of diffusion, § 374 ;
measurement of, § 878 ; nature of, § 297 ;
reflection of, Ch. xviii., §298; refraction
of, Ch. XIX. ; refraction by water, § 809 ;
why refracted, § 816; Rumford's method
of measuring, §380; standard of, §371 ;
transmission through a vacuum, § 314 ;
velocity through space, § 818 ; velocity in
dense substances, §315.

Lightning, §§ 502, 611 ; artificial, from bat-
tery, §618.

Lights, candle power of, § 881 ; use of for-
mula for Photoraetrv in testing, § 379.

Linear expansion, Ex. 24, § 208 ; table for
coefficients of, App. p. 589.

Line of direction, § 135.

Lines of force, about a magnetic coil, § 492 ;
about a wire carrying a current, § 490 ; in
armature of dynamo or motor, Ex. 77 ;
in coil of wire. Ex, 68 ; in galvanometer,
§589 ; of magnet, Ex.61 ; plotting, around
a magnet, §489; photographic prints of,
App. p. 585: tracing with iron filings,
§ 48S, A pp. p. 535.

Liquid conductors of heat. §201.

Liquids, boiling, § 240 ; boiling-points of, Ex.
80; bodv buoved up in, §68; densitv of,
Ex. 7, Ex. S, § 45 ; pressure in, § 60, Ex. 1 1 ;

forced pressure of, § 70 ; relation of press-
ure to depth. § 68 ; speciflc gravity of, Ex.
7, Ex. 8, §§ 43, 45 ; comparison of refraction
of ^\&&6 and a liquid, § 820.

Liquids and gases, Ch. iii.

Local action, §469.

Lodestone §444.

Lubricants, ^89.

Machines — Pulleys, Ch. vii. ; power and
speed, *5 108 ; fortniila for problems, § 109.

Magdeburg hemispheres, §27.

Magic Lantern, §§ 898, 899.

Magnet, action if left free, § 482 ; action of
needle over, § 448 ; arrangement of par-
ticles in, §442; bar, current induced by,
Ex. 74; demagnetizing a magnet, §486:
distribution of magnetism in, §458, Ex. 64 ;
effect of heat on, Ex. 62 : effect of strength
of, § 578 ; floating, § 484 ; hard steel, § 444 ;
lines of force in, Ex. 61, §441 ; law for test-
ing strength of, §457; permanent, §481 ;
poles of, §485; strength of, §§452, 454;
temporary, §481 ; weakening earth's mag-
netic force by, §532.

Magnetic action of electric current, Ch.
xxviii., Ex. 67; attraction, §430; cofl,
§ 492 ; field, § 441 ; method of measuring
current, §511; moment, §459; needle,
§512; pendulum, §455; poles, §446,
screen, §440. See Linen of Force.

Magnetism, of earth, § 451 ; weakening, of
earth, §532; distribution of, in a magnet,
§458, Ex. 64; horizontal intensity of
earth's, App. p. 540; theory of, §448.

Magneto-telephone, § 567.

Magnets, Ch. xxvi. ; comparison of two,
§458.

Mass, deflned, § 147 ; change in weight,
§149; comparison, §148; weight as a
measure of, § 150.

Mass and weight, § 152 ; Ch. x.

Melting, latent heat of, §252, Ex. 82.

Melting-point of ice, Ex. 25 ; effect of press-
ure on, §230.

Melting points, § 228.

Mercury, weight of, § 82 ; effect on zinc, § 468.

Mercury column, § 88 ; pressure on, §84.

Mercury pump. §§57, 58.

Metal rod, expansion, §207.

Metals, coefficient of expansion of, § 207,
Ex. 24 ; examples of expansion, § 209 ; linear
expansion of, § 208 ; refinement of, by elec-
tric current, §505.

Metric system, § 8.

Micrometer, §210.

Microscope, compound, §896; model of
compound. §897 ; simple, §892.

Mirror galvanometer, § 592.

Mirrors, at right angles, Ex. 88; concave,
§ 855; convex, § 852; curved, Ch. xxi. ;
image, in parallel, § 807 ; image, in plane,
Ex. 87; image, in convex, Ex. 55; image,
in cylindrical concave, § 856 ; principal
focus of concave, Ex. 56 ; parabola, § 857 ;
reflection in two, § 806.

Modulus, Young's, § 185.

Moisture, deposited, Ex. 29 ; air saturat«d
with, § 288.

550

INDEX.

Moment, magnetic, % 459.

Moment of a force, see Force.

Moments of couples, § 130.

Momentum, of a body, § 179 ; before and
after collision, Ex. 19 ; starting from zero,
§182.

Morse alphabet, % 5S9.

Motion, setting a body in, §§ 21, 157 ; resist-
ance to, § 158 ; Newton's second law of,
§178.

Motor, lines of force in armature of, Ex. 77 ;
electric car, §§ 614, 615; series, § 577;
shunt, § 578; study of Siemens, Ex. 76;
putting together the parts of, Ex. 76, Ex.
78.

Moving bodies, formulas for, §§ 167, 176;
elimination in formulas, §§ 168, 169.

Musical scale, § 416; sound, § 408.

Nearsightedness, § 390.

Needle, compass, § 445; dipping, § 449;
galvanoscope, § 493 ; forces acting on mag-
netic, § 512.

Negative electricity, § 610.

Nodes, in vibrating strings, § 404; in open
pipe, § 423.

Non-condensing engines, § 286.

Notes, reen forcing, § 422.

Object and image, relative size of, % 847,
Ex. 53.

Object and image distance, § 341.

Ocean cables, Ch. xxxiv.

Ohms, measurement of, § 516.

Ohm's law, Ch. xxx., § 517.

Optical instruments, Ch. xxiv.

Overtones, in strings, Ex. 60 ; in open pipes,
§ 425 ; in closed pipes, § 426.

Oxygen, § 500.

ParaboU, § 357.

Parallax, real conjugate foci by, Ex. 51 ;
shoaling effect by, § 827 ; index of refiraction
of glass by, Ex. 44. See Images^ Location
of.

Parallel forces, Ch. vi., Ex. 14a, § 103,
Ex. 146 ; components of, S 100 ; in oppo-
site directions, § 129 ; resultant of, § 100.

Parallel lines, drawin?, p. 68, footnote.

Parallelogram of forces, § 79, Ex. 12.

Pendulum, magnetic, § 455; simple, Ex. 63;
vibration of, § 155.

Photometer, principle of, § 375; Bunsen,
§§ 376, 377 ; liumford, § 880.

Photometry, Ch. xxiii., § 372, Ex. 57 ; for-
mula, § 377; use of formula in testing
lights, § 379.

Physics, defined, § 1.

Pipes, closed, § 420, open, §§ 420, 428;
stopped, § 424 ; overtones in, §§ 425, 426.

Piston, elevator, § 74; liquid, § 56; effi-
ciency of, § 78.

Pitch, variation of, § 417.

Plane, inclined, Ex. 16, § 122.

Plotting, A pp. p. 532.

Polarization, § 472 ; curve of, § 475 ; reduc-
ing, § 474 ; of storage batteries, Ex. 73.

Pole, north geographical, § 445; magnetic
and geographical, § 446.

Poles, law of, § 434 ; of a magnet, §§ 484,
435; of a battery, §§ 465, 467.

Positive electricity, § 610.

Power, electric, § 616; transmission bv
pulleys, § 118; amount obtained from coal,
§291.

Power and speed, §§ 108, 127.

Pressure, Ch. ii. ; atmospheric, %% 27-29 ; cal-
culation of, § 65 ; corrections for pressure in
testing thermometer, § 226 ; denned, § 20 ;
distribution of, § 71; downward, § 61;
effect on melting-point of ice, § 280; fall of
electrical, § 529 ; fall of electrical in a wire,
§ 530 ; formula for, § 48 ; forced, of liquids
and gases, § 70; in a liquid, § 60, Ex. 11 :
increase of pressure of gas at constant
volume, Ex. 85; measurement of air
pressure, § 31 ; of air, §§ 28, 29, 261 ; of
gases, § 81; of steam, § 222; of steam
bubbles, § 241 ; perpendicular to surfiice,
§ 84 ; points of equal electrical, § 584 ; rela-
tion to depth, § 63 ; rules for computing,
§ 48 ; sideways and upward, § 62 ; tem-
peratures, corresponding to pressure of
steam, Ex. 26a, Ex. 266 ; transmission of,
§24.

Pressure and depth, § 67.

Pressure and weight, § 66.

Pressures, greater than at atmosphere, Ex.
9r/, §49 ; less than an atmosphere, Ex. 9&.

Primary batteries, § 484.

Primary circuit, § 583.

Principal focus, see Focus.

Prisms, achromatic, § 868 ; combinations of,
§ 331 ; internal redection in, § 822 ; pas-
sage of light through, §§ 869, 870; path
of a ray through, Ex. 46 ; water and glass,
§ 369.

Projectiles, formulas for studying, §§ 167,
176.

Pulleys, Ch. vii. ; combination of, §§ 110,
115; fixed, § 114; movable, § 113; study
of. as machines, § 111.

Pulleys and belts, § 118.

Pumps, air, §§ 52, 53 ; force, § 89 ; Ufting,
§ 37 ; mercury, §§ 67, 68.

Pyrometer, § 264.

Radiation, of heat, § 208 ; effect of surfkce
upon, § 204.

Radius of curvature of lens, § 889.

Rain, formation of, § 287.

Rarefaction, § 407.

Rays, incident and reflected, § 808 ; tracing
the path of, § 828. See Prisms; Glass,

Reaction, § 178, Ex. 19 ; examples of, % 183.

Reading glasses. §§ 392, 898.

Real conjugate foci, Ex. 51.

Real image, Ex. 54 ; defined, Ex. 61.

Reaumur scale, § 220.

Receiver, telephone, §§ 568, 569.

Recoil, § 181.

Reference books, p. iv.

Refining metals, § 506.

Reflected ray, § 308.

Reflected sound, § 418.

Reflection, brightness of, § 804; total, Ex.

40 ; fhom inner surfoce of plate glass, § 824.

Internal, angle of, § 826; in a prism,

§ 822; in a rod, § 826; law of, Ex. 48;

total, § 821.

INDEX.

661

Minors, at rl^ht angles, Ex. 88 ; in two,
§ 806 ; in parallel, § 307 ; from a plane,
§828.

Refraction, by water, § 809 ; effect of, on
vision, § 810 ; of a liquid and of glass,
comparison, § 820. See Indeoo of Be frac-
tion.

Refrigerating plant, § 268.

Regulators, stoi-agu cells as, § 555.

Resistance, § 119 ; of a body to being set in
motion. § 15S ; surface, § 88.

Blectncal, Ch. xxx.; of connections, §
600 ; of conductors, Ex. 69 ; effect of temper-
ature, § 589; heating by, § 594; internal,
of batteries, Uh. xxxii., Ex. 72, §§ 540-
542; internal, of cells in parallel and in
series, § 543 ; internal, § 516, Ex. 72 ; laws
of, § 520; measurement of, Ch. xxxi.;
measurement by Wheatstone bridge, § 535,
Ex. 70 ; measurement of internal resistance
of cells, § 546 ; of storage cells, § 554 ; of
wires in parallel or multiple, § 519 ; of vari-
ous materials, comparison of, Ex. 70
specific, §538; specific, table for, App. p
589 ; substitution method, § 518, Ex. 69 .
temperature-coefficient of, Ex. 71 ; prac-
tice in measurement, § 537.

Resistances in parallel, § 522 ; formula for,
§523; in series, §521.

Resolution of forces, §§ 82, 88, 96.

Resonance, § 419.

Resultant of forces, Ex. 12, §§ 99, 100 ; di-
rection and amount of, § 80.

Ring armature, § 580.

Rod. expansion of, § 207, Ex. 24.

Rttntgen rays, § 605.

Rotation, § 101.

Safety, factor of, § 190.

Scale, absolute, § 263 ; centigrade, §§ 218-220 ;
Fahrenheit, §§ 218-220; musical, § 416;
thermometer, §§ 218-220.

Screw, the, § 125; power of, § 126; power
and speed, § 127.

Secondary battery, § 484.

Secondary circuito, § 583.

Series, cells joined in, § 541 ; electrochemical,
§ 586; E.M.F. of cells in, § 545; compari-
son of cells in parallel and series, § 542 ;
resistances in, § 521 ; rules for battery of
cells in, § 549.

Series djmamo, § 576.

Series motor, § 577.

Shadows, location of image by, § 805.

Shoaling effect, by parallax, § 827 ; of glass,
Ex.44.

Short-circuiting, § 468; by local action,
§469.

Shunt dynamo and motor, § 578.

Siemen's dynamo, Ex. 76 ; armature, § 582.

Sight lines, location of image by, Ex. 55 ;
location of point by, § 299.

Signalling through ocean cables, Ch.
xxxiv.

Signals, electric, § 563.

Sines, App. p. 581 ; table of, App. p. 587.

Siphon, §§ 40. 41 ; intermittent, \ 42.

Siphon recorder, § 598.

Siren, % 408. I

Size of object and image, relative, § 847,
Ex.53.

Size of substance, effect of heat on, § 205.

Soap bubbles, pressure of air inside, § 71.

Solenoid, § 565.

Solids, density, Ex. 1 ; linear expansion, Ex.
24 ; specific heat, Ex. 81a, 31^, § 249 ; vol-
ume of, § 10 ; weight of, § 9 ; that sink,
Ex. 2, Ex. 3.

Sonometer, § 418.

Sound, Ch. xxv. ; interference of, § 428;
musical, § 408 ; quality of, § 427 ; reflected,
§ 418 ; transmission of, § 407 ; velocity of,
§ 411, Ex. 58 ; waves of, §§ 420, 421.

Sounder, telegraph, § 557 ; model of, § 558.

Spark, electric, § 602.

Specific gravity. Ch. i. ; by immersion, Ex.
5, Ex. 6; bv tlotation, §§ 15, 16; calcula-
tion by the knglish system, § 13; capacity*
of a bottle, Ex. 7 ; defined, § 12 ; formula
for, § 14 ; of a body that fioats, Ex. 4 ;
of a body that sinks,* Ex. 8; of a liquid,
Ex. 7, Ex. 8, § 45.

Specific heat of solids, Ex. 81a, Ex. 81&,
§ '^49.

Specific resistance, § 588; table for, App.
p. 589.

Spectrum, § 358.

Speed, average, defined, § 161 ; by belts and
palleys, § 118.

Speed and power, §§ 108, 127.

Spherical aberration, § 886.

Spring balance, calibrating, App. p. 686.

Static electricity, § 608.

Steam, condensation of, § 274; latent heat
of, § 256 ; pressure of, § 222 ; pressure of
bubbles, § 241 ; temperatures correspond-
ing to pressure, Ex, 26a, Ex. 266.

Steam turbines, § 288.

Steel, annealing and hardening, § 487.

Stereoscope, § 400.

StiU, model of, § 248.

Storage batteries, forming, § 550; kinds
of, § 551 ; polarization, Ex. 78.

Storage cells, Ch. xxxii.; charging, § 558;
Edison, § 479 ; efficiency of, § 552 ; as regu-
lators, § 555 ; resistance of, § 554.

Strength, breaking, §187, Ex.21, §189; of
electric current, § 562 ; of magnets, § 452 ;
law for testing strength of magnet, §457;
effect of strength of magnet, § 578.

Stretching, Ex. 20, § 186 ; experiments on,
§184: measure of, §185.

Substitution method, resistance, % 518,
Ex. 69.

Suction, §25.

Surface electricity, §§ 607-609.
Surface films, of liquids, §76.
Surface resistance. § 88.
Tangent galvanometer, §§512, 518.
Tangents, table of, App. p. 587.
Telegraph, circuit, § 561 ; key, § 560 ;

pounder, § 557 ; model of wireless, § 603.
Telegraphy, wireless, §602.
Telephone, magneto-, §§ 567-569.
Telephone receiver, action of, § 569.
Telescope, §898; magnifying power, §895;

model, § 894.

562

tNDtJX.

Temperature, and heat. §198; at which
iiioidtiire is deposited, Ex. 29 ; calculation
of,' $25U; effect on resistance, § 589;
measurement of, § 214 ; sensible, $ 286.

Temperature-cotfficient of resisUnce, Ex.
71.

Temperatures, corresponding to pressure
of >tfam, Ex. 26a, Ex. 266 ; F. and C,
§§21s-220; sUndard, §216.

Templates, Ex. 49.

Thermoelectrical combinations, §587.

Thermo-electricity, Ex. 80.

Thermodynamics, Ch. xvii.

Thermogenerator. §5b8.

Thermometers, Ch. xiv. ; construction of,
§216; dry-bulb and wet-bulb, § 285 ; cor-
rections for pressure in testing, §226;
practical working of, §227 ; testing for iP
and lOiP C, Ex. 25; testing for points
between 0° and 10()O, Ex. 27 ; testing for
82.5°, 48.1°, and 78°, §229.

Thermopile, § 588.

Transformers, § 585.

Translation, §101.

Transmission, medium of, §407.

Transmitter, §567.

Tuning-forks, Ex. 59.

Turbines, steam, § 288.

Twisting, § 195, Ex. 28 ; laws of, § 196.

Vacuum, § 55 ; by condensation, § 59.

Vacuum engine, § 276.

Vacuum pans. § 228.

Vacuum tipped arrow, § 28.

Vacuum tubes, § 004.

Valves, cylinder, § 279 ; slide, § 280.

Vaporization, § 257 ; latent heat of, § 256,
Ex. 83 ; effect of lotent heat of, § 259.

Velocity, Ch. xi. ; average, § 16B ; formula,
§ 164 ; in terms of force and time, § 178 ;
of sound, § 411, Ex. 58; measurement of,
§ 154. See Light.

Vibration, § 401 ; rate of, § 402 ; of compass
needle, § 456 ; of pendulum, § 155 ; point
of no, § 404.

Vibration method, distribution of magnet-
ism in a magnet, Ex. 64.

Vibrations, forced, § 410; longitudinal,
I 405; of musical scale, § 416; of tuning-
fork, Ex. 59 ; sympathetic, § 409 ; torsional,
§ 406 ; transverse. § 408.

Virtual foci, § 846, Ex. 52.

Virtual image, Ex. 52, § 851.

Voltage, see Electromotive force.

Voltaic cell, § 464.

Voltameter, § 506.

Voltmeter, § 528.

Volts, see Electromotive force.

Volume, §5; experiments on, § 11 : formula,
§10; of gas, §81.

Volume and displacement, § 44.

Volume and loss of weight, § 18.

Water, apparent depth of, §811; boiling,
§ 240 ; boiling and evaporation, difference
between, § 244 ; critical angle, §812, Ex. 40,
App. p. 586 ; decomposition of, § 500 ; dis-
solved air in, §288; distillaUon, §248;
effect of dissolved substances on freezing-
point of, Ex. 28; evaporation, §225; index
of refraction, Ex. 89 ; lifting effect of, Ex. 2 ;
maximum density of, § 206; mixing water
of different temperatures, §24T; refraction,
§ 809 ; shoaling effect, § 827.

Water-hammer, § 240.

Water solutions, boiling-points of, Ex. 80.

Watt, § 289 ; as measure of electrical work,
§616.

Watt condenser, § 277.

Wave length, §§ 420, 421.

Wedge, the, § 124.

Weight, as a measure of mass, § 150 ; compu-
tation of weight of air, § 51 ; defined, § 22 ;
of nir, § 28 ; of masses, change in, § 149 ; of
a solid, formula, § 9 ; of 1 cc. of air, Ex. 10 ;
of 1 cc. of gas. Ex, 86; of unit volume of a
substance, Ex. 1.

Weight and volume of gases, Ex. 86.

Welding, electric, «> 596 ; current for, § 597.

Wheatstone's bridge, § 585.

Wind, why a boat sails into the, § 87.

Wire, breaking strength, Ex. 21, § 189 ; com-

f)arison of, § 188 ; fall of electric pressure
n, § 580 ; lines of force about a wire carry-
ing current, «> 490.

Wireless telegraph, model of, § 608.

Wire gauge, table for, App. p. 539.

Wires, in parallel or multiple, § 519. See
/ietiiHtayice,

Work, Ch. vin., §119; bv compressed air,
§ 287; by expanding gases, §266; by ex-
pansion of air, § 287; derived from heat,
S 278 ; electrical, § 616; heat derived from,
§ 270 ; heat units produced by 1 gram-centi-
meter, § 271 ; measurement by h.p., §§ 289.
290 ; obtained from steam in engine, § 284 ;
unit of, § 120.

X-rays, § (505.

Toung's modulus, § 185.

Zero, absolute, § 262.

Zero point on thermometer, § 217.

Zinc, effect of mercury on, § 468.

THB NBW YORK PUBUC UBRARY
RBFBRBNGB DBPARTMBNT

Tliis book U under no eironniifanoas to be
taken from the Bnildini

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